VII] OF THE BEE'S CELL 525 



us to define. The colour-pattern of the bean will then be found 

 following the direction of the boundary-lines, and occupying areas 

 or patches corresponding to parts of the orthogonal system. The 

 lines are equipotential hnes, or akin thereto. If we varnish an 

 elastic bag, dry it and expand it, the varnish will tend to crack along 

 the same orthogonal boundaries*. 



The bee^s cell 



The most famous of all hexagonal conformations, and one of the 

 most beautiful, is the bee's cell. As in the basalt or the coral, we 

 have to deal with an assemblage of co-equal cylinders, of circular 

 section, compressed into regular hexagonal prisms; but in this case 

 we have two layers of such cyhnders or prisms, one facing one 

 way and one the other, and a new problem arises in connection 

 with their inner ends. We may suppose the original cyhnders 

 to have spherical endsf, which is their normal and symmetrical way 

 of terminating; then, for closest packing, it is obvious that the end 

 of any one cylinder in the one layer will touch, and fit in between, 

 the ends of three cylinders in the other. It is just as when we 

 pile round-shot in a heap; we begin with three, a fourth fits into 

 its nest iDetween the three others, and the four form a ''tetrad," 

 or regular tetragonal arrangement. 



Just as it was obvious, then, that by mutual pressure from the 

 sides of six adjacent cells any one cell would be squeezed into a 

 hexagonal prism, so is it also obvious that, by mutual pressure 

 against the ends of three opposite neighbours, the end of each and 

 every cell will be compressed into a trihedral pyramid. The three 

 sides of this pyramid are set, in. plane projection, at co-equal angles 

 of 120° to one another; but the three apical angles (as in the 

 analogous case already described of a system of soap-bubbles) are, 



* M. Hirata, Coloured patches in kidney-beans, Set. Papers, Inst. Chem. Researchy 

 Tokyo, XXVI, pp. 122-135, 1936. 



f In the combs of certain tropical bees the hexagona structure is imperfect and 

 the cells are not far removed from cylinders. They are set in tiers, not contiguous 

 but separated by little pillars of wax, and the base of each cell is a portion of 

 a sphere. They differ from the ordinary honeycomb in the same sort of way as 

 the fasciculate from the massive corals, of which we spoke on p. 512. Cf. Leonard 

 Martin, Sur les Melipones de Bresil, La Nature, 1930, pp. 97-100. 



