"From all these operations was produced a block of a rugged surface, hanging down from the arch, without any perceptible angle, or any traces of cells. It was a simple wall, or ridge, running in a straight line, and without the least inflection, two-thirds of an inch in length, above two-thirds of a cell, or two lines, high, and declining towards the extremities. We have seen other foundation walls from an inch to an inch and a half long, the form being always the same; but none ever of greater height.
"The vacuity in the centre of the cluster had permitted us to discover the first manoeuvres of the bees, and the art with which they laid the foundations of their edifices. However, it was filled up too soon for our satisfaction; for workers collecting on both faces of the wall obstructed our view of their further operations."[AP]
ARCHITECTURE OF THE HIVE-BEE CONTINUED--FORM OF THE CELLS.
The obstruction of which M. Huber complains only operated as a stimulus to his ingenuity in contriving how he might continue his interesting observations. From the time of Pappus to the present day, mathematicians have applied the principles of geometry to explain the construction of the cells of a bee-hive; but though their extraordinary regularity, and wonderfully-selected form, had so often been investigated by men of the greatest talent, and skilled in all the refinements of science, the process by which they are constructed, involving also the causes of their regularity of form, had not been traced till M. Huber devoted himself to the inquiry.
As the wax-workers secrete only a limited quantity of wax, it is indispensably requisite that as little as possible of it should be consumed, and that none of it should be wasted. Bees, therefore, as M. Réaumur well remarks,[AQ] have to solve this difficult geometrical problem:--a quantity of wax being given, to form of it similar and equal cells of a determinate capacity, but of the largest size in proportion to the quantity of matter employed, and disposed in such a manner as to occupy the least possible space in the hive. This problem is solved by bees in all its conditions. The cylindrical form would seem to be best adapted to the shape of the insect; but had the cells been cylindrical, they could not have been applied to each other without leaving a vacant and superfluous space between every three contiguous cells. Had the cells, on the other hand, been square or triangular, they might have been constructed without unnecessary vacancies; but these forms would have both required more material, and have been very unsuitable to the shape of a bee's body. The six-sided form of the cells obviates every objection; and while it fulfils the conditions of the problem, it is equally adapted with a cylinder to the shape of the bee.