484 HABITATIONS OF INSECTS. 



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 suspect- 

 ing that the object of choosing these angles from amongst 

 so many was to spare wax, proposed to M. Koenig, a 

 skilful fjeometrician, who was ignorant of Maraldi's ex- 

 periments, to determine by calculations what ought to 

 be the angle of a hexagonal cell, with a pyramidal bot- 

 tom formed of three similar and equal rhomboid plates, 

 so that the least matter possible might enter into its con- 

 struction. 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 pro- 

 blem and the actual admeasurement '' ! 



Besides the saving of wax effected by the form of the 



=■ Reaum. v. 390. 



•^ 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 construction 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 necessar}' for 

 a flat bottom in the construction of every cell, near so much as 

 MM. Koenig 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 



