The bees, however, are not infallible, nor does their certainty appear mechanical.  They will commit grave errors at times, when circumstances present unusual difficulty.  They will often leave too much space, or too little, between the combs.  This they will remedy as best they can, either by giving an oblique twist to the comb that too nearly approaches the other, or by introducing an irregular comb into the gap.  “The bees sometimes make mistakes,” Reaumur remarks on this subject,” and herein we may find yet another fact which appears to prove that they reason.”

[54]

We know that the bees construct four kinds of cells.  First of all, the royal cells, which are exceptional, and contrived somewhat in the shape of an acorn; then the large cells destined for the rearing of males and storing of provisions when flowers super-abound; and the small cells, serving as workers’ cradles and ordinary store-rooms, which occupy normally about four-fifths of the built-over surface of the hive.  And lastly, so as to connect in orderly fashion the larger cells with the small, the bees will erect a certain number of what are known as transition cells.  These must of necessity be irregular in form; but so unerringly accurate are the dimensions of the second and third types that, at the time when the decimal system was established, and a fixed measure sought in nature to serve as a starting-point and an incontestable standard, it was proposed by Reaumur to select for this purpose the cell of the bee.*

It was as well, perhaps, that this standard was not adopted.  For although the diameter of the cells is admirably regular, it is, like all things produced by a living organism, not _mathematically_ invariable in the same hive.  Further, as M. Maurice Girard has pointed out, the apothem of the cell varies among different races of bees, so that the standard would alter from hive to hive, according to the species of bee that inhabited it.

Each of the cells is an hexagonal tube placed on a pyramidal base; and two layers of these tubes form the comb, their bases being opposed to each other in such fashion that each of the three rhombs or lozenges which on one side constitute the pyramidal base of one cell, composes at the same time the pyramidal base of three cells on the other.  It is in these prismatic tubes that the honey is stored; and to prevent its escaping during the period of maturation,—­which would infallibly happen if the tubes were as strictly horizontal as they appear to be,—­the bees incline them slightly, to an angle of 4 deg or 5 deg.