526 THE FORMS OF TISSUES [ch. 



by the geometry of the case*, co-equal angles of 109° and so many 

 minutes and seconds. 



If we experiment, not with cyHnders but with spheres, if for 

 instance we pile bread-pills together and then submit the whole to 

 a uniform pressure, as we shall presently find that Buffon did : each 

 ball (hke the seeds in a pomegranate, as Kepler said) will be in contact 

 with twelve others — six in its own plane, three below and three above, 

 and under compression it will develop twelve plane surfaces. 

 It will repeat, above and below, the conditions to which the bee's 

 cell is subject at one end only; and, since the sphere is symmetrically 

 situated towards its neighbours on all sides, it follows that the 

 twelve plane sides to which its surface has been reduced will be all 

 similar, equal and similarly situated. Moreover, since we have 

 produced this result by squeezing our original spheres close together, it 

 is evident that the bodies so formed completely fill space. The regular 

 solid which fulfils all these conditions is the rhombic dodecahedron. 

 The bee's cell is this figure incompletely formed; it represents, so 

 to speak, one-half of that figure, with its apex and the six 

 adjacent corners proper to the rhombic dodecahedron, but six sides 

 continued, as a hexagonal prism, to an open or unfinished endf. 



The bee's comb is vertical and the cells nearly horizontal, but 

 sloping slightly downwards from mouth to floor; in each prismatic 

 cell two sides stand vertically, and two corners lie above and below. 

 Thus for every honeycomb or "section" of honey, there is one and 

 only one "right way up"; and the work of the hive is so far con- 

 trolled by gravity. Wasps build the other way, with the cells upright 

 and the combs horizontal; in a hornet's nest, or in that of Polistes, 

 the cells stand upright like the wasp's, but their mouths look down- 

 wards in the hornet's nest arid upwards in the wasp's. 



What Jeremy Taylor called "the discipline of bees and the rare 

 fabric of honeycombs " must have attracted the attention and excited 

 the admiration of mathematicians from time immemorial. "Ma 

 maison est construite," says the bee in the Arabian Nights, "selon 



* The dihedral angle of 120° is, physically speaking, the essential thing; the 

 Maraldi angle, of 109°, etc., is a geometrical consequence. Cf. G. Cesaro, Sur la 

 forme de Falveole de I'abeille, Bull. Acad. R. Belgique (Sci.), 1920, p. 100. 



t See especially Haiiy, the crystallographer; Sur le rapport des figures qui 

 existe entre Falveole des abeilles et le grenat dodecaedre, Journ. d'hist. naturelle, 

 n, p. 47, 1792. 



