"The cells themselves, or prisms, which result from the reunion and meeting of the sides, are next constructed. These are engrafted on the borders of the cavities hollowed in the mass. The bees begin them by making the contour of the bottoms, which is at first unequal, of equal height. Thus all the margins of the cells offer an uniformly level surface from their first origin, and until they have acquired their proper length. The sides are heightened in an order analogous to that which the insects follow in finishing the bottom of the cells, and the length of these tubes is so perfectly proportioned that there is no observable inequality between them." * * * * * Thus writes the great Swiss observer of bees. Without quoting at greater length from his published observations, we may give some additional particulars relating to the geometrical characters of honey-comb. The cells of the first row laid down are pentagonal in shape. This gives them a stronger attachment to the hive than if they had had the hexagonal figure of the succeeding rows. But no form besides the six-sided prism would have answered all the conditions of the problem "how with the least expenditure of material to secure the greatest available space with the best arrangement for the purposes to be served." [Illustration: Fig. 14.--Diagram of Cells.] [Illustration: Fig. 15.--Supposed Circular Cells.] Approached from the purely theoretical side, the question has been investigated by mathematicians. It requires no great acumen to determine that a hexagon of some sort is the geometrical figure which must be adopted. An equilateral triangle would make a very unsuitable abode for an insect with a nearly round body. A square cell would hardly be more convenient. A series of circles would, of course, leave interstices between them, causing a useless expenditure of space, material, time and strength. A further difficulty would arise with regard to the storage of the honey, which finds points of attachment in the angles of a hexagon, and so is less liable to run out of the cells. [Illustration: Fig. 16.--Arrangement of Cells.]