Evans. "_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. "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 may be cut into little spaces, that shall be equal, similar, and regular, without having 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, Oeconomy of materials. There are no useless partitions in a honey-comb, each of the six lateral panels of one cell forms also one of the panels 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 the panels that are at the back of it. "Secondly, Oeconomy of room; no interstices being left between adjoining cells. "Thirdly, the greatest possible capacity or internal space, consistent with the two former desiderata. "Fourthly, Oeconomy of materials and economy of room produce economy 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.