Animal Intelligence / The International Scientific Series, Vol. XLIV.

by George John Romanes

Besides theft and plunder, there are other causes of warfare among bees, which, however, are only apparent in their effects. Thus, for some undiscernible reason, duels are not infrequent, which generally end in the death of one or both combatants. At other times, equally without apparent reason, civil war breaks out in a hive, which is sometimes attended with much slaughter.

Architecture.—Coming now to the construction of the cells and combs, there is no doubt that here we meet with the most astonishing products of instinct that are presented in the animal kingdom. A great deal has been written on the practical exhibition of high mathematical principles which bees display in constructing their combs in the form that secures the utmost capacity for storage of honey with the smallest expenditure of building material. The shortest and clearest statement of the subject that I have met with is the following, which has been given by Dr. Reid:—

There are only three possible figures of the cells which can make them all equal and similar, without any useless interstices. These are the equilateral triangle, the square, and the regular hexagon. Mathematicians know 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 useless spaces. Of the three figures, the hexagon is the most proper for convenience and strength. Bees, as if they knew this, make their cells regular hexagons.

Again, it has been demonstrated that, by making the bottoms of the cells to consist of three planes meeting in a point, there is a saving of material and labour in no way inconsiderable. The bees, as if acquainted with these principles of solid geometry, follow them most accurately. It is a curious mathematical problem, at what precise angle the three planes which compose the bottom of a cell ought to meet, in order to make the greatest possible saving, or the least expense of material and labour. This is one of the problems which belong to the higher parts of mathematics. It has accordingly been resolved by some mathematicians, particularly by the ingenious Maclaurin, by a fluctionary calculation, which is to be found in the Transactions of the Royal Society of London. He has determined precisely the angle required, and he found, by the most exact mensuration the subject would admit, that it is the very angle in which the three planes in the bottom of the cell of a honeycomb do actually meet.[58]

Marvellous as these facts undoubtedly are, they may now be regarded as having been satisfactorily explained. Long ago Buffon sought to account for the hexagonal form of the cells by an hypothesis of mutual pressure. Supposing the bees to have a tendency to build tubular cells, if a greater number of bees were to build in a given space than could admit of all the parallel tubes being completed, tubes with flat sides and sharp angles might result, and if the mutual pressure were exactly equal in all directions, these sides and angles would assume the form of hexagons. This hypothesis of Buffon was sustained by such physical analogies as the blowing of a crowd of soap-bubbles in a cup, the swelling of moistened peas in a confined space, &c. The hypothesis, however, as thus presented was clearly inadequate; for no reason is assigned why the mutual pressure, even if conceded to exist, should always be so exactly equal in all directions as to convert all the cylinders into perfect hexagons—even the analogy of the soap-bubbles and the moistened peas failing, as pointed out by Brougham and others, to sustain it, seeing that as a matter of fact bubbles and peas under circumstances of mutual pressure do not assume the form of hexagons, but, on the contrary, forms which are conspicuously irregular. Moreover, the hypothesis fails to account for the particular prismatic shape presented by the cell base. Therefore it is not surprising that this hypothesis should have gained but small acceptance. Kirby and Spence dispose of it thus:—'He (Buffon) gravely tells us that the boasted hexagonal cells of the bee are produced by the reciprocal pressure of the cylindrical bodies of these insects against each other!!'[59] The double note of admiration here may be taken to express the feelings with which this hypothesis of Buffon was regarded by all the more sober-minded naturalists. Yet it turns out to have been not very wide of the mark. As is often the case with the gropings of a great mind, the idea contains the true principle of the explanation, although it fails as an explanation from not being in a position to take sufficient cognizance of all the facts. Safer it is for lesser minds to restrain their notes of exclamation while considering the theories of a greater; however crude or absurd the latter may appear, the place of their birth renders it not impossible that some day they may prove to have been prophetic of truth revealed by fuller knowledge. Usually in such cases the final explanation is eventually reached by the working of a yet greater mind, and in this case the undivided credit of solving the problem is to be assigned to the genius of Darwin.

Mr. Waterhouse pointed out 'that the form of the cell stands in close relation to the presence of adjoining cells.' Starting from this fact, Mr. Darwin says,—

Let us look to the great principle of gradation, and see whether Nature does not reveal to us her method of work. At one end of a short series we have humble-bees, which use their old cocoons to hold honey, sometimes adding to them short tubes of wax, and likewise making separate and very irregular rounded cells of wax. At the other end of the series we have the cells of the hive-bee, placed in a double layer. . . . . In the series between the extreme perfection of the cells of the hive-bee and the simplicity of those of the humble-bee we have the cells of the Mexican Melipona domestica, carefully described and figured by Pierre Huber. . . . . It forms a nearly regular waxen comb of cylindrical cells, in which the young are hatched, and, in addition, some large cells of wax for holding honey. These latter cells are nearly spherical and of nearly equal sizes, and are aggregated into an irregular mass. But the important thing to notice is, that these cells are always made at that degree of nearness to each other that they would have intersected or broken into each other if the spheres had been completed; but this is never permitted, the bees building perfectly flat cells of wax between the spheres which thus tend to intersect. Hence each cell consists of an outer spherical portion; and of two, three, or more flat surfaces, according as the cell adjoins two, three, or more other cells. When one cell rests on three other cells, which, from the spheres being nearly of the same size, is very frequently and necessarily the case, the three flat surfaces are united into a pyramid; and this pyramid, as Huber has remarked, is manifestly a gross imitation of the three-sided pyramidal base of the cell of the hive-bee. . . . .

Reflecting on this case, it occurred to me that if the Melipona had made its spheres at some given distance from each other, and had made them of equal sizes, and had arranged them symmetrically in a double layer, the resulting structure would have been as perfect as the comb of the hive-bee. Accordingly I wrote to Prof. Miller of Cambridge, and this geometer has kindly read over the following statement, drawn up from his information, and tells me that it is strictly correct.

This statement having fully borne out his theory, Mr. Darwin continues:—