nd were further so to
dispose them as that the centre of each should be at the distance of
radius x [mathematical symbol 'square root']2 or radius x 1.41421 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 on both layers were formed, there would 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 would have
every angle identically the same with the best measurements that have
been made of the cells of the hive bee.' Then, submitting this view to
Professor Miller of Cambridge, he had the gratification of being assured
by that distinguished geometer that it was strictly correct. Certainly a
very happy example of an ingenious conjecture verified by a species of
demonstration hardly inferior to the experimental. Certainly a very
valuable testimony to the soundness of all the main and really essential
principles of Darwinism. Good cause, certainly, is hereby shown for
believing that the cell-making faculty of the hive bee may be nothing
more than the aggregate of many minute and successive improvements upon
that of the melipona, and this, again, than a similar aggregate of
improvements on that of the humble bee; and for believing further that
hive bee and melipona may both be either descendants from the humble
bee, or joint-descendants with it from some still earlier common
progenitor. In order to believe this it suffices to believe that a bee
which at one period made, like the humble bee, cells very unequally
sized and irregularly rounded, came gradually, in the course of time, to
make them as nearly equal in size and as nearly spherical as those of
the melipona; and subsequently, during a further lapse of time, came to
arrange them at the same distances from each other, and in double
layers like those of the humble bee. To assume thus much requires no
inordinate stretch of faith; and thus much being assumed, it is seen at
once that the hive bee, requiring for its cells only about half as much
wax as the humble bee does, and consequently only about half as much
honey for the secretion of the requisite wax, would, in a struggle for
existence, leave the humble bee so little chance that in all probability
the two species would nowhere coexist, were it no