Evans.
The bees, as has been already observed, build their cells of an hexangular form, having six equal sides, with the exception of the first or uppermost row, the shape of which is an irregular pentagon, the roof of the hive forming one of the members of the pentagon, thus:
“There are only three possible figures of the cells,” says Dr. Reid, “which can make them all equal and similar, without any useless interstices. These are the equilateral triangle, the square and the regular hexagon. It is well known to mathematicians that there is not a fourth way possible, in which a plane maybe cut into little spaces that shall be equal, similar, and regular, without leaving any interstices.” Of these three geometrical figures, the hexagon most completely unites the prime requisites for insect architecture. The truth of this proposition was perceived by Pappus, an eminent Greek philosopher and mathematician, who lived at Alexandria in the reign of Theodosius the Great, and its adoption by bees in the construction of honey-comb was noticed by that ancient geometrician. These requisites are;
First, Œconomy of materials. There are no useless partitions in a honey-comb, each of the six lateral pannels of one cell forms also one of the pannels of an adjoining cell; and of the three rhombs which form the pyramidal base of a cell, each contributes one-third towards the formation of the bases of three opposing cells, the bottom or centre of every cell resting against the point of union of three pannels that are at the back of it.
Secondly, Œconomy of room; no interstices being left between adjoining cells.
Thirdly, The greatest possible capacity or internal space, consistent with the two former desiderata.
Fourthly, Œconomy of materials and œconomy of room produce œconomy of labour. And in addition to these advantages, the cells are constructed in the strongest manner possible, considering the quantity of materials employed. Both the sides and bases are so exquisitely thin, that three or four placed on each other are not thicker than a leaf of common writing-paper; each cell, separately weak, is strengthened by its coincidence with other cells, and the entrance is fortified with an additional ledge or border of wax, to prevent its bursting from the struggles of the bee-nymph, or from the ingress and egress of the labourers. This entrance border is at least three times as thick as the sides of the cell, and thicker at the angles than elsewhere, which prevents the mouth of the cell from being regularly hexagonal, though the interior is perfectly so.
“On books deep poring, ye pale sons of toil.
Who waste in studious trance the midnight oil,
Say, can ye emulate with all your rules.
Drawn or from Grecian or from Gothic schools.
This artless frame? Instinct her simple guide,
A heaven-taught Insect baffles all your pride.
Not all yon marshal’d orbs, that ride so high.
Proclaim more loud a present Deity,
Than the nice symmetry of these small cells,
Where on each angle genuine science dwells.
And joys to mark, through wide creation’s reign,
How close the lessening links of her continued chain.”
Evans.