CELL-MAKING INSTINCT 281 



completed; but this is never permitted, the bees building per- 

 fectly flat walls of wax between the spheres which thus 

 tend to intersect. Hence, each cell consists of an outer 

 spherical portion, and of two, three, or more flat surfaces, 

 according as the cell adjoins two, three, or more other cells. 

 When one cell rests on three other cells, which, from the 

 spheres being nearly of the same size, is very frequently 

 and necessarily the case, the three flat surfaces are united 

 into a pyramid; and this pyramid, as Huber has remarked, 

 is manifestly a gross imitation of the three-sided pyramidal 

 base of the cell of the hive-bee. As in the cells of the hive- 

 bee, so here, the three plane surfaces in any one cell neces- 

 sarily enter into the construction of three adjoining cells. 

 It is obvious that the Melipona saves wax, and what is more 

 important, labour, by this manner of building; for the flat 

 walls between the adjoining cells are not double, but are 

 of the same thickness as the outer spherical portions, and 

 yet each flat portion forms a part of two cells. 



Reflecting on this case, it occurred to me that if the Meli- 

 pona had made its spheres at some given distance from each 

 other, and had made them of equal sizes and had arranged 

 them symmetrically in a double layer, the resulting structure 

 would have been as perfect as the comb of the hive-bee. Ac- 

 cordingly I wrote to Professor Miller of Cambridge, and 

 this geometer has kindly read over the following statement, 

 drawn up from his information, and tells me that it is 

 strictly correct : — 



If a number of equal spheres be described with their 

 centres placed in two parallel layers ; with the centre of each 

 sphere at the distance of radius X y 2, or radius X 1.41421 

 (or at some lesser distance), from the centres of the six 

 surrounding spheres in the same layer; and at the same dis- 

 tance from the centres of the adjoining spheres in the other 

 and parallel layer; then, if planes of intersection between 

 the several spheres in both layers be formed, there will re- 

 sult a double layer of hexagonal prisms united together by 

 pyramidal bases formed of three rhombs; and the rhombs 

 and the sides of the hexagonal prisms will have every angle 

 identically the same with the best measurements which have 

 been made of the cells of the hive-bee. But I hear from 



