The next matter then to settle is, the magnitude of the angles at which the sides of the hexagon should slope towards each other, so as to be the most advantageous. Réaumur put the problem in mathematical language before M. König, a skilful geometrician, thus:--"To determine by calculations what ought to be the angle of a hexagonal cell, with a pyramidal bottom, formed of three similar and equal rhomboid plates, so that the least matter possible might enter into its construction." The result of his investigations was that the angles of the rhombs must be 109° 26′ and 70° 34′. Cramer, professor of mathematics in the University of Geneva, also undertook the problem. His calculations, made on somewhat different principles from König's, gave for the angles 109° 28′ 16″, and 70° 31′ 44″. Maraldi, a third mathematician, assuming the equality of the angles of the trapezia forming the sides of the hexagon adjacent to the rhombs and those of the rhombs themselves, and that the solid angle at the apex of the pyramid, composed of equal obtuse angles, is precisely equal to each of the three angles at the base, also composed of three equal obtuse angles, came to the conclusion that the angles must be 109° 28′ and 70° 32′. These three sets of results, so remarkably accordant, when we consider the minuteness of the differences between them, in figures so small as the actual honey-comb cells, show the closest correspondence to the actual measurements of the work of the bees. Maraldi found the angles of the latter to be 110° and 70°, as nearly as could be ascertained. We have dwelt at some length upon this point, because it illustrates, in a most marvellous manner, the power of that inborn faculty we call instinct, which arrives, without training, at results so precisely agreeing with those of the highest efforts of our intellectual reasonings. To the devout mind, the conclusion is inevitable that Divine Wisdom is the inspiring force which energizes the mental operations of the bees in their cell-building. A further advantage of the actual shape of the honey-comb prisms is that, thereby, strength is combined with economy. No other form would so efficiently have carried the heavy weights constantly stored in the forms of honey, brood, and bee-bread.