372 THE ORIGIN OF SPECIES 



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. 



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 perfect as 

 the comb of the hive-bee. Accordingly, I wrote to Pro- 

 fessor 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 |/ 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 adjoining 

 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 workmanship of the bee has 

 been greatly exaggerated; so much so, that whatever the 

 typical form of the cell may be, it is rarely, if ever, 

 realized. 



