HABITATIONS OF INSECTS. 487 



of each ceil is not an exact plane, but is usually com- 

 posed of three rhoraboidal or lozenge-shaped pieces, 

 placed so as to form a pyramidal concavity. From tliis 

 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 infinitely ; but by a very accurate admeasurement 

 Maraldi found, that the great angles were in general 

 109° 2S', the smaller ones 70° 3'2'. Reaumur ingeni- 

 ously suspecting that the object of choosing these an- 

 gles from amongst so many was to spare wax, proposed 

 to M. Koenig, a skilful geometrician, who was igno- 

 rant of Maraldi's experiments, to determine by calcu- 

 lations wiiat ought to be the angle of a hexagonal 

 ceil, 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 so- 

 lution of this problem the geometrician had recourse 

 to the infinitesimal calculus, and found tlmt 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 

 measure''! 



' Reaum. v. 390. 



'^ Father Boscovich observes, that al! the angles that form the planes 



