Remarks on Bees. [From Proceedings of the American Academy of Arts and Sciences 4 (8 May 1860): 432-433.] ⁹

Mr. C. Wright made some remarks on the architecture of bees, in reference to previous discussions upon the instinct of the honey-bee.

Mathematicians have regarded the economical characteristics of the honey-cell too exclusively, to the neglect of those symmetries which Maraldi pointed out.

The more prominent of these symmetries are the regularity of all the solid angles of the cell, and the consequent equality of all the angles made by the sides and rhombs with each other to 120°, or to 4/3 of a right angle. Another important symmetry which follows from these is seen in the position of that point in the axis of the cell which is directly over the middle points of the rhombs; for this point is at the same distance from all the nine planes of the cell, and just opposite similar points in the nine contiguous cells; so that little spheres which would just fit the honey-cells would, if pressed to the bases of the cells on both sides of the comb, touch the rhombs in their middle points, and the sides in their middle lines, by points in the spheres themselves, at which they would touch each other but for the thickness of the intervening walls.

While the common mode of considering the form of the honey-cell regards it as the effect of rational economy, these symmetries show how the cell might be the natural result of simple or sensible economy, as applied to the building of simple nests, the common type of which is a cylindrical cavity with a hemispherical base. The construction of a series of such nests side by side, and with the bases of two opposite series in closest contact, would, by the simple removal of the interstitial material, result in two series of cells like the normal ones of the honeycomb, both in the forms and the arrangement of the sides and bases. Hence, as the bee builds the two series of cells from their common bases, making the incipient depressions on one side form the interstitial elevations

around the cavities of the other side, and as it builds by continual trimming and saving, we may infer that the form of the honey-cell does not require, in the bee’s instinct, any reference to supersensible properties of form, but only a reference to sensible economy and facility of construction; especially as no one would contend that the utility, to innumerable nest-building animals, of spherical and cylindrical surfaces, depends upon their economy (which is still greater than that of the honey-cell), rather than upon their far more obvious symmetries and facilities for construction. It appears, therefore, that the instinct of the bee does not differ in kind from instincts in general.