166 BEES AND THEIR CELLS [CH. VIII 



the cells are of uniform thickness. There are however other 

 objections to the conjecture, since it deals only with cells of 

 a very special shape, and neglects all consideration of their use 

 for purposes other than the storage of honey. It is reasonable 

 to hold that the form of cell adopted is on the whole that which 

 best suits the bees, but saving of wax cannot be the chief reason 

 for it. 



Another vague but more plausible explanation of the form 

 of the cells is that their shape and size depend largely on the 

 manner in which the bees can best use the organs of their 

 bodies and senses. One of the most striking features of the 

 cells is the fact that the angle between every adjacent pair of 

 planes is 120°, and perhaps this is an essential characteristic. 

 Leslie Ellis * in an interesting essay suggested that the explana- 

 tion of this may be found in the fact that bees, besides their 

 composite eyes, " have three single eyes placed lower down, and 

 "probably serving for the vision of near objects. Assume that 

 "the axes of these eyes diverge so as to be respectively normal 

 "to three ideal planes forming a solid angle, each dihedral angle 

 "of which is of 120 degrees. Geometry shows that every solid 

 "angle of the bee's cell is precisely similar to this type, so that 

 "a bee looking at it with his three single eyes, might have 

 "direct vision with each eye of one of the three planes of the 

 "solid angle. This direct vision may correspond to a particular 

 "sensation, so that a bee is not satisfied till it is attained." 

 This is ingenious : it is too artificial to make me think it prob- 

 able, but it is worth mentioning, for Leslie Ellis was an acute 

 observer. 



Another proffered explanation of the form of the cells rests 

 on the assumption that, when forming the comb from a slab 

 of wax, the bees work in as dense and regular a formation 

 as is possible. It will be observed that the upper portion of 

 a typical cell is half a rhombic dodecahedron : a fact noted 

 by Leslie Ellis, who gave the following construction for making 

 a model of a typical cell. Take two equal cubes. Divide 

 one of them into six pyramids, the apex of each being at the 



* B. Leslie Ellis, Mathematical.. .Writings, Cambridge, 1863, pp. 353—357. 



