At one end of a short series we have humble-bees, which use their old
cocoons to hold honey, sometimes adding to them short tubes of wax, and
likewise making separate and very irregular rounded cells of wax. At the
other end of the series we have the cells of the hive-bee, placed in a
double layer: each cell, as is well known, is an hexagonal prism, with the
basal edges of its six sides bevelled so as to join on to a pyramid, formed
of three rhombs. These rhombs have certain angles, and the three which
form the pyramidal base of a single cell on one side of the comb, enter
into the composition of the bases of three adjoining cells on the opposite
side. In the series between the extreme perfection of the cells of the
hive-bee and the simplicity of those of the humble-bee, we have the cells
of the Mexican Melipona domestica, carefully described and figured by
Pierre Huber. The Melipona itself is intermediate in structure between the
hive and humble bee, but more nearly related to the latter: it forms a
nearly regular waxen comb of cylindrical cells, in which the young are
hatched, and, in addition, some large cells of wax for holding honey.
These latter cells are nearly spherical and of nearly equal sizes, and are
aggregated into an irregular mass. But the important point to notice, is
that these cells are always made at that degree of nearness to each other,
that they would have 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 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 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
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.
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 make 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 in wood many insects can make, 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
accurately at what distance to stand from her fellow-labourers when several
distance, that she always describes her spheres so as to intersect largely;
and then she unites the points of intersection by perfectly flat surfaces.
We have further to suppose, but this is no difficulty, that after hexagonal
prisms have been formed by the intersection of adjoining spheres in the
same layer, she can prolong the hexagon to any length requisite to hold the
stock of honey; in the same way as the rude humble-bee adds cylinders of
wax to the circular mouths of her old cocoons. By such modifications of
instincts in themselves not very wonderful,--hardly more wonderful than
those which guide a bird to make its nest,--I believe that the hive-bee has
acquired, through natural selection, her inimitable architectural powers.
But this theory can be tested by experiment. Following the example of Mr.
Tegetmeier, I separated two combs, and put between them a long, thick,
square strip of wax: the bees instantly began to excavate minute circular
pits in it; and as they deepened these little pits, they made them wider
and wider until they were converted into shallow basins, appearing to the
eye perfectly true or parts of a sphere, and of about the diameter of a
cell. It was most interesting to me to observe that wherever several bees
had begun to excavate these basins near together, they had begun their work
at such a distance from each other, that by the time the basins had
acquired the above stated width (i.e. about the width of an ordinary cell),
and were in depth about one sixth of the diameter of the sphere of which
they formed a part, the rims of the basins intersected or broke into each
other. As soon as this occurred, the bees ceased to excavate, and began to
build up flat walls of wax on the lines of intersection between the basins,
so that each hexagonal prism was built upon the festooned edge of a smooth
basin, instead of on the straight edges of a three-sided pyramid as in the
case of ordinary cells.
I then put into the hive, instead of a thick, square piece of wax, a thin
and narrow, knife-edged ridge, coloured with vermilion. The bees instantly
began on both sides to excavate little basins near to each other, in the
same way as before; but the ridge of wax was so thin, that the bottoms of
the basins, if they had been excavated to the same depth as in the former
experiment, would have broken into each other from the opposite sides. The
bees, however, did not suffer this to happen, and they stopped their
ex
cavations in due time; so that the basins, as soon as they had been a
little deepened, came to have flat bottoms; and these flat bottoms, formed
by thin little plates of the vermilion wax having been left ungnawed, were
situated, as far as the eye could judge, exactly along the planes of
imaginary intersection between the basins on the opposite sides of the
ridge of wax. In parts, only little bits, in other parts, large portions
of a rhombic plate had been left between the opposed basins, but the work,
from the unnatural state of things, had not been neatly performed. The
bees must have worked at very nearly the same rate on the opposite sides of
the ridge of vermilion wax, as they circularly gnawed away and deepened the
basins on both sides, in order to have succeeded in thus leaving flat
plates between the basins, by stopping work along the intermediate planes
or planes of intersection.
Considering how flexible thin wax is, I do not see that there is any
difficulty in the bees, whilst at work on the two sides of a strip of wax,
perceiving when they have gnawed the wax away to the proper thinness, and
then stopping their work. In ordinary combs it has appeared to me that the
bees do not always succeed in working at exactly the same rate from the
opposite sides; for I have noticed half-completed rhombs at the base of a
just-commenced cell, which were slightly concave on one side, where I
suppose that the bees had excavated too quickly, and convex on the opposed
side, where the bees had worked less quickly. In one well-marked instance,
I put the comb back into the hive, and allowed the bees to go on working
for a short time, and again examined the cell, and I found that the rhombic
plate had been completed, and had become perfectly flat: it was absolutely
impossible, from the extreme thinness of the little rhombic plate, that
they could have effected this by gnawing away the convex side; and I
suspect that the bees in such cases stand in the opposed cells and push and
its proper intermediate plane, and thus flatten it.
From the experiment of the ridge of vermilion wax, we can clearly see that
if the bees were to build for themselves a thin wall of wax, they could
make their cells of the proper shape, by standing at the proper distance
from each other, by excavating at the same rate, and by endeavouring to
make equal spherical hollows, but never allowing the spheres to break into
each other. Now bees, as may be clearly seen by examining the edge of a
growing comb, do make a rough, circumferential wall or rim all round the
comb; and they gnaw into this from the opposite sides, always working
circularly as they deepen each cell. They do not make the whole
three-sided pyramidal base of any one cell at the same time, but only the
one rhombic plate which stands on the extreme growing margin, or the two
plates, as the case may be; and they never complete the upper edges of the
rhombic plates, until the hexagonal walls are commenced. Some of these
statements differ from those made by the justly celebrated elder Huber, but
I am convinced of their accuracy; and if I had space, I could show that
they are conformable with my theory.
Huber's statement that the very first cell is excavated out of a little
parallel-sided wall of wax, is not, as far as I have seen, strictly
correct; the first commencement having always been a little hood of wax;
but I will not here enter on these details. We see how important a part
excavation plays in the construction of the cells; but it would be a great
error to suppose that the bees cannot build up a rough wall of wax in the
proper position--that is, along the plane of intersection between two
adjoining spheres. I have several specimens showing clearly that they can
do this. Even in the rude circumferential rim or wall of wax round a
growing comb, flexures may sometimes be observed, corresponding in position
to the planes of the rhombic basal plates of future cells. But the rough
wall of wax has in every case to be finished off, by being largely gnawed
away on both sides. The manner in which the bees build is curious; they
always make the first rough wall from ten to twenty times thicker than the
excessively thin finished wall of the cell, which will ultimately be left.
We shall understand how they work, by supposing masons first to pile up a
broad ridge of cement, and then to begin cutting it away equally on both
sides near the ground, till a smooth, very thin wall is left in the middle;
the masons always piling up the cut-away cement, and adding fresh cement,
on the summit of the ridge. We shall thus have a thin wall steadily
growing upward; but always crowned by a gigantic coping. From all the
cells, both those just commenced and those completed, being thus crowned by
a strong coping of wax, the bees can cluster and crawl over the comb
without injuring the delicate hexagonal walls, which are only about one
four-hundredth of an inch in thickness; the plates of the pyramidal basis
being about twice as thick. By this singular manner of building, strength
is continually given to the comb, with the utmost ultimate economy of wax.
It seems at first to add to the difficulty of understanding how the cells
are made, that a multitude of bees all work together; one bee after working
a short time at one cell going to another, so that, as Huber has stated, a
score of individuals work even at the commencement of the first cell. I
was able practically to show this fact, by covering the edges of the
hexagonal walls of a single cell, or the extreme margin of the
circumferential rim of a growing comb, with an extremely thin layer of
melted vermilion wax; and I invariably found that the colour was most
delicately diffused by the bees--as delicately as a painter could have done
with his brush--by atoms of the coloured wax having been taken from the
spot on which it had been placed, and worked into the growing edges of the
cells all round. The work of construction seems to be a sort of balance
struck between many bees, all instinctively standing at the same relative
distance from each other, all trying to sweep equal spheres, and then
building up, or leaving ungnawed, the planes of intersection between these
spheres. It was really curious to note in cases of difficulty, as when two
pieces of comb met at an angle, how often the bees would entirely pull down
and rebuild in different ways the same cell, sometimes recurring to a shape
which they had at first rejected.
When bees have a place on which they can stand in their proper positions
for working,--for instance, on a slip of wood, placed directly under the
middle of a comb growing downwards so that the comb has to be built over
one face of the slip--in this case the bees can lay the foundations of one
wall of a new hexagon, in its strictly proper place, projecting beyond the
other completed cells. It suffices that the bees should be enabled to
stand at their proper relative distances from each other and from the walls
of the last complet
ed cells, and then, by striking imaginary spheres, they
can build up a wall intermediate between two adjoining spheres; but, as far
as I have seen, they never gnaw away and finish off the angles of a cell
till a large part both of that cell and of the adjoining cells has been
built. This capacity in bees of laying down under certain circumstances a
rough wall in its proper place between two just-commenced cells, is
important, as it bears on a fact, which seems at first quite subversive of
the foregoing theory; namely, that the cells on the extreme margin of
wasp-combs are sometimes strictly hexagonal; but I have not space here to
enter on this subject. Nor does there seem to me any great difficulty in a
single insect (as in the case of a queen-wasp) making hexagonal cells, if
she work alternately on the inside and outside of two or three cells
commenced at the same time, always standing at the proper relative distance
from the parts of the cells just begun, sweeping spheres or cylinders, and
building up intermediate planes. It is even conceivable that an insect
might, by fixing on a point at which to commence a cell, and then moving
outside, first to one point, and then to five other points, at the proper
relative distances from the central point and from each other, strike the
planes of intersection, and so make an isolated hexagon: but I am not
aware that any such case has been observed; nor would any good be derived
from a single hexagon being built, as in its construction more materials
would be required than for a cylinder.
As natural selection acts only by the accumulation of slight modifications
of structure or instinct, each profitable to the individual under its
conditions of life, it may reasonably be asked, how a long and graduated
succession of modified architectural instincts, all tending towards the
present perfect plan of construction, could have profited the progenitors
of the hive-bee? I think the answer is not difficult: it is known that
bees are often hard pressed to get sufficient nectar; and I am informed by
Mr. Tegetmeier that it has been experimentally found that no less than from
twelve to fifteen pounds of dry sugar are consumed by a hive of bees for
the secretion of each pound of wax; so that a prodigious quantity of fluid
nectar must be collected and consumed by the bees in a hive for the
secretion of the wax necessary for the construction of their combs.
Moreover, many bees have to remain idle for many days during the process of
secretion. A large store of honey is indispensable to support a large
stock of bees during the winter; and the security of the hive is known
mainly to depend on a large number of bees being supported. Hence the
saving of wax by largely saving honey must be a most important element of
success in any family of bees. Of course the success of any species of bee
may be dependent on the number of its parasites or other enemies, or on
quite distinct causes, and so be altogether independent of the quantity of
honey which the bees could collect. But let us suppose that this latter
circumstance determined, as it probably often does determine, the numbers
of a humble-bee which could exist in a country; and let us further suppose
that the community lived throughout the winter, and consequently required a
store of honey: there can in this case be no doubt that it would be an
advantage to our humble-bee, if a slight modification of her instinct led
her to make her waxen cells near together, so as to intersect a little; for
a wall in common even to two adjoining cells, would save some little wax.
Hence it would continually be more and more advantageous to our humble-bee,
if she were to make her cells more and more regular, nearer together, and
aggregated into a mass, like the cells of the Melipona; for in this case a
large part of the bounding surface of each cell would serve to bound other