It remains to decide what form of polygon will serve as the base of these prisms. First of all, it is evident that this polygon will be regular, because the capacity of the cells has to be constant. Once the condition obtains that the grouping must be effected without gaps, figures that were not regular would be subject to variation and would give different capacities in one cell and another. Now of the indefinite number of regular polygons only three can be constructed continuously, without leaving unoccupied spaces. These three are the equilateral triangle, the square, and the hexagon. Which are we to choose? The one that will approximate most closely to the circumference of a circle and hence be best adapted to the cylindrical form of the larva; the one that, with a containing wall of the same extent, will yield the greatest capacity, a condition essential to the free growth of the grubs. Of the three regular figures that can be assembled without vacant intervals, our geometry suggests the hexagon; and it is the hexagon and none other that is chosen by the geometry of the Wasps. The cells are hexagonal prisms. Every high and harmonious achievement finds supersubtle minds that strive to degrade it. What has not been said on the subject of hexagonal cells, above all on the subject of the Bee’s, which are arranged in a double layer and united at the base? Reasons of economy of both wax and space demand that this base shall be a pyramid formed of three rhombs with angles of fixed value. Scientific calculations tell us the value of these angles in degrees, minutes and seconds. The goniometer subjects the work of the Bee to examination and finds that the value is precisely calculated to degrees, minutes and seconds. The insect’s work is in perfect agreement with the nicest speculations of our own geometry. There is no room for the glorious problem of the Bee-hive in these elementary essays. Let us confine ourselves to the Wasps. It has been said: “Fill a bottle with dried peas and add a little water. The peas, in swelling, will become polyhedrons by mutual pressure. Even so with the Wasps’ cells. The builders work in a crowd. Each builds at her own will, placing her work in juxtaposition to her neighbours’; and the reciprocal thrusts produce the hexagon.”