106 INSECT ARCHITECTURE. 



striicted without unnecessary vacancies ; but these forms 

 would have both required more material and had been 

 very unsuitable to the shape of a bee's body. The six- 

 sided form of the cells obviates every objection; and 

 while it fulfils the conditions of the problem, it is. equally 

 adapted with a cylinder to the shape of the bee. 



M. Keaumur further remarks, that the base of each cell, 

 instead of forming a plane, is usually composed of three 

 pieces in the shape of the diamonds on playing cards, and 

 placed in such a manner as to form a hollow pyramid. 

 This structure, it may be observed, imparts a greater degree 

 of strength, and, still keeping the solution of the problem 

 in view, gives a great capacity with the smallest expendi- 

 ture of material. This has actually, indeed, been ascertained 

 b}^ mathematical measurement and calculation. Maraldi, 

 the inventor of glass hives, determined, by minutely 

 measuring these angles, that the greater were 109° 28', and 

 the smaller 70° 32' ; and M. Eeaumur, being -desirous to 

 know why these particular angles are selected, requested 

 M. Koenig, a skilful mathematician (^dthout informing him 

 of his design, or telling him of Maraldi's researches), to 

 determine by calculation what ought to be the angle of a 

 six-sided cell, with a concave pp-amidal base, formed of 

 three similar and equal rhomboid plates, so that the least 

 possible matter should enter into its construction. By em- 

 ploying what geometricians denominate the wfinitesimal 

 calculus, M. Koenig found that the angles should be 109^ 26' 

 for the greater, and 70^ 34' for the smaller, or about two- 

 sixtieths of a degree, more or less, than the actual angles 

 made choice of by bees. The equality of inclination in the 

 angles has al so been said to facilitate the construction of the 

 cells. 



M. Huber adds to these remarks, that the cells of the 

 first row, by which the whole comb is attached to the roof 

 of a hive, are not like the rest ; for, instead of six sides, 

 they have only five, of which the roof forms one. The 

 base, also, is in these diiferent, consisting of three pieces on 

 the face of the comb, and on the other side of two : one 

 of these only is diamond-shaped, while the other two are 



