224 THE ORIGIN OF SPECIES 



layer: each cell, as is well known, is an hexagonal prism, with the 

 basal edges of its six sides bevelled so as to join an inverted pyra- 

 mid, of three rhombs. These rhombs have certain angles, and the 

 three which form the pyramidal base of a single cell on one side of 

 the comb enter into the composition of the bases of three adjoining 

 cells on the opposite side. In the series between the extreme per- 

 fection of the cells of the hive-bee and the simplicity of those of 

 the humble-bee we have the cells of the Mexican Melipona do- 

 mestica, carefully described and figured by Pierre Huber. The Mel- 

 ipona itself is intermediate in structure between the hive and hum- 

 ble-bee, but more nearly related to the latter; it forms a nearly 

 regular waxen comb of cylindrical cells, in which the young are 

 hatched, and, in addition, some large cells of wax for 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 inter- 

 sected or broken into each other if the spheres had been com- 

 pleted ; but this is never permitted, the bees building perfectly 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 fre- 

 quently and necessarily the case, the three flat surfaces are united 

 into a pyramid ; and this pyramid, as Huber has remarked, is man- 

 ifestly 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 necessarily enter into the con- 

 struction 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 between the adjoining cells are not 

 double, but are of the same thickness as the outer spherical por- 

 tions, 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 symmet- 

 rically in a double layer, the resulting structure would have been 

 as perfect 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 



