CELL-MAKING iKSttNCf. 245 



#»e 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 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 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 rts 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 result- 

 ing 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 placed in two parallel layers ; with the centre of 

 each sphere at the distance of radius x V 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 to- 

 gether 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 Professor Wyman, who has made numerous care- 

 ful 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. 



Hence we may safely conclude that, if we could slightly 

 modify the instincts already possessed by the Melipona, and 

 in themselves not very wonderful, this bee would make 

 a structure as wonderfully perfect as that of the hive-bee. 

 We must suppose the Melipona to have the power of form- 



