Chap. VIII.] CELL-MAKING INSTINCT. 221 



are hatched, and, in addition, some large cells of wax foi holding 

 honey. These latter cells are nearly spherical and of nearly equal 

 sizes, and are aggregated into an irregular mass. But the im- 

 portant point to notice is, that 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 fiat 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 fiat 

 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 neces- 

 sarily the case, the three fiat 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 

 any one cell necessarily enter into the construction of three adjoin- 

 ing 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 Melipona 

 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 per- 

 fect as the comb of the hive-bee. Accordingly 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 aJ 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 distance from the centres of the ad- 

 joining spheres in the other and parallel layer ; then, if planes of 

 intersection 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 every angle identically 

 the same with the best measurements which have been made of the 

 cells of the hive-bee. But I hear from Prof. Wyman, who has 

 made numerous careful measurements, that the accuracy of the 



