HABITATIONS OF INSECTS. 309 



upper part and sides, arranged vertically at a small distance from each 

 other, so that the cells composing them are placed in a horizontal position, 

 and have their openings in opposite directions — not the best position one 

 would have thought for retaining a fluid like honey, yet the bees find no 

 inconvenience on this score. The distance of the combs from each other 

 is about half an inch, that is, sufficient to allow two bees busied upon the 

 opposite cells to pass each other with facility. Besides these vacancies, 

 which form the high roads of their community, the combs are here and 

 there pierced with holes which serve as posterns for easy communication 

 from one to the other without losing time by going round. 



The arrangement of the combs is well adapted for its purpose, but it is 

 the construction of the cells which is most admirable and astonishing. As 

 these are formed of wax, a substance secreted by the bees in no great 

 abundance, it is important that as little as possible of such a precious ma- 

 terial should be consumed. Bees, therefore, in the formation of their cells 

 have to solve a problem which would puzzle some geometers, namely, a 

 quantity of wax being given, to form of it similar and equal cells of a 

 determinate capacity, but of the largest size in proportion to the quantity 

 of matter employed, and disposed in such a manner as to occupy in the 

 hive the least possible space. Every part of this problem is practically 

 solved by bees. If their cells had been cylindrical, which form seems 

 best adapted to the shape of a bee, they could not have been applied to 

 each other without leaving numberless superfluous vacuities. If the cells 

 were made square or triangular, this last objection, indeed, would be 

 removed ; but besides that a greater quantity of wax would have been 

 required, the shape would have been inconvenient to a cylindrical-bodied 

 animal. All these difficulties are obviated by the adoption of hexagonal 

 cells, which are admirably fitted to the form of the insect, at the same time 

 that their sides apply to each other without the smallest vacant intervals. 

 Another important saving in materials is gained by making a common base 

 serve for two strata of cells. Much more wax as well as room would have 

 been required, had the combs consisted of a single stratum only. But this 

 is not all. The base of each cell is not an exact plane, but is usually 

 composed of three rhomboidal or lozenge-shaped pieces, placed so as to form 

 a pyramidal concavity. From this form it follows that the base of a cell on 

 one side or stratum of the comb is composed of portions of the bases of 

 three cells on the other. You will inquire, Where is the advantage of this 

 arrangement ? First, a greater degree of strength ; and secondly, precisely 

 the same as results from the hexagonal sides — a greater capacity with less 

 expenditure of wax. Not only has this been indisputably ascertained, but 

 that the angles of the base of the cell are exactly those which require the 

 smallest quantity of wax. It is obvious that these angles might vary infi- 

 nitely ; 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 geo- 

 metrician, who was ignorant of Maraldi's experiments, to determine by 

 calculations what ought to be the angle of a hexagonal cell, with a pyra- 

 midal bottom formed of three similar and equal rhomboid plates, so that 



