CELL-'MAKING INSTINCT. 361 



mass. But the important point to notice is, tbat these 

 cells are always made at that degree of nearness to each 

 other that they would have intersected or broken into each 

 other if the spheres had been completed; but this is never 

 permitted, the bees building perfectly flat walls of wax be- 

 tween 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 imi- 

 tation 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 anyone cell necessarily enter' into the 

 construction of three adjoining cells. It is obvious that 

 the Melipona saves wax, and what is more important, 

 labor, by this manner of building; for the flat walls be- 

 tween 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. 



Eeflecting 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 pei-fect as the comb of the 

 hive-bee. Accordingly I wrote to Professor Miller, of Cam- 

 bridge, and this geometer has kindly read over the follow- 

 ing statement, drawn up from his information, and tells 

 me that it is strictly correct : 



If a number of equal spheres be described with their 

 centers placed in two parallel layers; with the center of 

 each sphere at the distance of radius X V ^j °^' radius 

 X 1.41431 (or at some lesser distance), from the centers of 

 the six surrounding spheres in the same layer; and at the 

 same distance from the centers of the adjoining spheres in 

 the other and parallel layer; then, if planes of intersec- 

 tion between the several spheres in both layers be formed, 

 there will result 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 



