168 BEES AND THEIR CELLS [CH. VIII 



plane of contact. Each of these faces makes half a right angle 

 with the face of the cube, since the sum of two of them is sup- 

 plementary to the angle between two adjacent faces of the cube. 

 Hence, in the final position, we have the twelve points of con- 

 tact represented by the mid-points of the edges of a smaller 

 cube, and the intermediate portions heaped up into six square 

 pyramids on the faces of the cube, the faces of the pyramids 

 making an angle of 45° with those of the cube. Thus the form 

 generated is a rhombic dodecahedron. 



Ke versing the process, it follows that if a homogeneous solid 

 has equally efficient centres of excavation distributed uniformly 

 through it, and excavation goes on till the walls of the cells 

 produced are of uniform thickness, we shall finally arrive at a 

 system of rhombic dodecahedrons filling the space excavated. 



Applying this theory to the construction of the honey comb, 

 Mrs Bryant states the following hypothesis as to why the bees 

 construct their cells in the form they do. "We might," says 

 she, "reasonably expect that the bees, who are the cell-excavators, 

 "should by natural instinct distribute themselves as densely as 

 "possible, and with a considerable degree of regularity, and that 

 "their activities should be equal and symmetrical about the 

 "working parts of their bodies. The facts confirm this reason- 

 "able expectation. The bees distribute themselves, with 

 "apparent uniformity, at the two sides of a homogeneous cake 

 "of wax which has been previously deposited. In it they 

 "excavate cells, at doubtless uniform rates of work, and continue 

 "excavating till their work is as complete as possible, and the 

 "walls of the cells therefore of uniform thickness. Meanwhile, 

 "the excavated wax is used to build up higher the open cell 

 "walls. Hence, the cells ought to be elongated rhombic semi- 

 "dodecahedra; and this is just what they are, the axis of the 

 "cell corresponding to a diagonal of the primary cube, and the 

 "apex being one of the trihedral vertices of the dodecahedron. 

 "Each face at the apex fits exactly against one face of a cell in 

 "the opposite system. Each cell, therefore, is in contact with 

 "three cells of the opposite system." 



"It follows, from this last mentioned fact, that the bees must 



