310 HABITATIONS OF INSECTS. 



the least matter possible might enter into its construction. For the solu- 

 tion of this problem the geometrician had recourse to the infinitesimal 

 calculus, and found that the great angles of the rhombs should be 109° 

 26', and of the small angles 70° 34'.^ What a surprising agreement be- 

 tween the solution of the problem and the actual admeasurement !^ 



Besides the saving of wax effected by the form of the cells, the bees 

 adopt another economical plan suited to the same end. They compose 

 the bottoms and sides of wax of very great tenuity, not thicker than a 

 sheet of writing-paper. But as walls of this thinness at the entrance 

 would be perpetually injured by the ingress and egress of the workers, 

 they prudently make the margin at the opening of each cell three or four 

 times thicker than the walls. Dr. Barclay discovered that, though of such 

 excessive tenuity, the sides and bottom of each cell are actually double, 

 or, in other words, that each cell is a distinct, separate, and in some mea- 

 sure an independent structure, agglutinated only to the neighboring cells, 

 and that when the agglutinating substance is destroyed, each cell may be 

 entirely separated from the rest.^ 



You must not imagine that all the cells of a hive are of precisely similar 

 dimensions. As the society consists of three orders of insects differing 

 in size, the cells which are to contain the larvae of each proportionally 

 differ, those built for the males being considerably larger than those which 

 are intended for the workers. The abode of the larvse of the queen bee 

 differs still more. It is not only much larger than any of the rest, but of 

 a quite different form, being shaped like a pear or Florence flask, and 

 composed of a material much coarser than common wax, of which above 

 one hundred times as much is used in its construction as of pure wax in 

 that of a common cell. The situation, too, of these cells (for there are 

 generally three or four, and sometimes many more, even up to thirty or 

 forty, in each hive) is very different from that of the common cells. 

 Instead of being in a horizontal they are placed in a vertical direction, 

 with the mouth downwards, and are usually fixed to the lower edge of the 

 combs, from which they irregularly project like stalactites from the roof of 

 a cavern. The cells destined for the reception of honey and pollen differ 

 from those which the larvae of the males and workers inhabit only by 

 being deeper, and thus more capacious ; in fact, the very same cells are 



' Reaum. v. 390. ~~~ ~ 



2 Father Boscovich observes, that all the angles that form the planes which compose the 

 cell are equal, i. e. 120"^ ; and he supposes that this equality of inclination facilitates much 

 the consiraction of the cell, which may be a motive for preferring it, as well as economy. 

 He shows that the bees do not economize the wax necessary for a flat bottom in the con- 

 structionof every cell, near so much as MM. Konig and Reaumur thought. 



MacLaurin says, that the difference of a cell with a pyramidal from one with a flat bot- 

 tom, in which is comprised the economy of the bees, is equal to the fourth part of six tri- 

 angles, which it would be necessary to add to the trapeziums, the faces of the cell, in order 

 to make them right angles. 



M. L'Hullier, professor of Geneva, values the economy of the bees at one fifty-one parts 

 of the whole expense ; and he shows that it might have been one fifth if the bees had no 

 other circumstances to attend to ; but he concludes, that if it is not very sensible in every 

 cell, it may be considerable in the whole of a comb, on account of the mutual seUingof the 

 two opposite orders of cells. Huber, Nouvelles Observations, dec. ii. 34. 



3 Memoirs of the Wernerian Society, ii. 259. This, however, has been denied by Mr. 

 Waterhouse, and seems inconsistent with the account given by Huber hereafter detailed ; 

 but Mr. G. Newport asserts that even the virgin cells are lined with a delicate membrane. 

 (Westwood, Mod. Class, of Ins. ii. 284.) 



