HABITATIONS OF INSECTS. 487 



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 com- 

 posed 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 infinitely ; but by a very accurate admeasurement 

 Maraldi found, that the great angles were in general 

 109° 28', the smaller ones 70° 32'. 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 ignorant 

 of Maraldi's experiments, to determine by calculations 

 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 pro- 

 blem the geometrician 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/ \ 



d Reaura. v. 390. 



