INSTINCT 203 



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 adjoins 

 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 surfaces are 

 united into a pyramid ; and this pyramid, as Huber has 

 remarked, is manifestly a gross imitation of the three- 

 sided pyramidal bases 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 J 2, or 

 radius x ] «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 



