226 
INSTINCT. 
Chap. VII. 
intersected or broken into each other, if the spheres had 
been completed; 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 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 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 V 2, or 
radius X 1-41421 (or at some lesser distance), from the 
centres of the six surrounding spheres in the same 
