t, labour, 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 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 sqrt(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 Professor 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,
realised.

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
forming her cells truly spherical, and of equal sizes; and this would
not be very surprising, seeing that she already does so to a certain
extent, and seeing what perfectly cylindrical burrows many insects make
in wood, apparently by turning round on a fixed point. We must suppose
the Melipona to arrange her cells in level layers, as she already does
her cylindrical cells; and we must further suppose, and this is the
greatest difficulty, that she can somehow judge accur