412 



HABITATIONS OF INSECTS. 



of the cell are exactly those which require the smallest quan- 

 tity of wax. It is obvious that these angles might vary infin- 

 itely ; but, by a very accurate admeasurement, Maraldi found 

 that the great angles were in general 109° 28', the smaller 

 ones 70° 32'. Reaumur, ingeniously suspecting that the object 

 of choosing these angles from amongst so many was to spare 

 wax, proposed to M. Konig, a skilful geometrician, who was 

 ignorant of Maraldi's experiments, to determine by calcula- 

 tions 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. For the solution of this problem the geo- 

 metrician 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 

 between the solution of the problem and the actual admeasure- 

 ment ! ^ 



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 pru- 

 dently 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 



1 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 in- 

 clination facilitates much the construction of the cell, which may be a motive for 

 preferring it, as well as economy. He shows that the bees do not economise 

 the wax necessary for a flat bottom in the construction of 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 bottom, in which is comprised the economy of the bees, is equal to the 

 fourth part of six triangles, 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 5^ 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 setting of the two opposite orders of cells. Huber, NouvelJes Ob- 

 servations, &c. ii. 34. 



