226 INSTINCT. Chap. VII. 



which thus tend to intersect. Hence each cell consists 

 of an outer spherical portion and of two, three, or 

 more perfectly flat surfaces, according as the cell ad- 

 joins two, three, or more other cells. When one cell 

 comes into contact with three other cells, which, from 

 the spheres being nearly of the same size, is very 

 frequently and necessarily the case, the three flat sur- 

 faces are united into a pyramid; and this pyramid, as 

 Huber has remarked, is manifestly a gross imitation of 

 the three-sided pyramidal basis 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 adjoining cells. It is obvious that 

 the Melipona saves wax 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 probably 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 



