by a swarm that is beginning to build, is a matter of very great
difficulty. All comes to pass in the blackest depths of the crowd,
whose agglomeration, growing denser and denser, produces the
temperature needful for this exudation, which is the privilege of
the youngest bees. Huber, who was the first to study these
phenomena, bringing incredible patience to bear and exposing himself
at times to very serious danger, devotes to them more than two
hundred and fifty pages; which, though of considerable interest, are
necessarily somewhat confused. But I am not treating this subject
technically; and while referring when necessary to Huber's admirable
studies, I shall confine myself generally to relating what is patent
to any one who may gather a swarm into a glass hive.
We have to admit, first of all, that we know not yet by what process
of alchemy the honey transforms itself into wax in the enigmatic
bodies of our suspended bees. We can only say that they will remain
thus suspended for a period extending from eighteen to twenty-four
hours, in a temperature so high that one might almost believe that a
fire was burning in the hollow of the hive; and then white and
transparent scales will appear at the opening of four little pockets
that every bee has underneath its abdomen.
When the bodies of most of those who form the inverted cone have
thus been adorned with ivory tablets, we shall see one of the bees,
as though suddenly inspired, abruptly detach herself from the mass,
and climb over the backs of the passive crowd till she reach the
inner pinnacle of the cupola. To this she will fix herself solidly,
dislodging, with repeated blows of her head, such of her neighbours
as may seem to hamper her movements. Then, with her mouth and claws,
she will seize one of the eight scales that hang from her abdomen,
and at once proceed to clip it and plane it, extend it, knead it
with her saliva, bend it and flatten it, roll it and straighten it,
with the skill of a carpenter handling a pliable panel. When at last
the substance, thus treated, appears to her to possess the required
dimensions and consistency, she will attach it to the highest point
of the dome, thus laying the first, or rather the keystone of the
new town; for we have here an inverted city, hanging down from the
sky, and not rising from the bosom of earth like a city of men.
To this keystone, depending in the void, she will add other
fragments of wax that she takes in succession from beneath her rings
of horn; and finally, with one last lick of the tongue, one last
wave of antennae, she will go as suddenly as she came, and disappear
in the crowd. Another will at once take her place, continue the work
at the point where the first one has left it, add on her own, change
and adjust whatever may seem to offend the ideal plan of the tribe,
then vanish in her turn, to be succeeded by a third, a fourth, and a
fifth, all appearing unexpectedly, suddenly, one after the other,
none completing the work, but each bringing her share to the task in
which all combine.
{52}
A small block of wax, formless as yet, hangs down from the top of
the vault. So soon as its thickness may be deemed sufficient, we
shall see another bee emerge from the mass, her physical appearance
differing appreciably from that of the foundresses who preceded her.
And her manner displays such settled conviction, her movements are
followed so eagerly by all the crowd, that we almost might fancy
that some illustrious engineer had been summoned to trace in the
void the site of the first cell of all, from which every other must
mathematically depend. This bee belongs to the sculptor or carver
class of workers; she produces no wax herself and is content to deal
with the materials others provide. She locates the first cell,
scoops into the block for an instant, lays the wax she has removed
from the cavity on the borders around it; and then, like the
foundresses, abruptly departs and abandons her model. Her place is
taken at once by an impatient worker, who continues the task that a
third will finish, while others close by are attacking the rest of
the surface and the opposite side of the wall; each one obeying the
general law of interrupted and successive labour, as though it were
an inherent principle of the hive that the pride of toil should be
distributed, and every achievement be anonymous and common to all,
that it might thereby become more fraternal.
{53}
The outline of the nascent comb may soon be divined. In form it will
still be lenticular, for the little prismatic tubes that compose it
are unequal in length, and diminish in proportion as they recede
from the centre to the extremities. In thickness and appearance at
present it more or less resembles a human tongue whose sides might
be formed of hexagonal cells, contiguous, and placed back to back.
The first cells having been built, the foundresses proceed to add a
second block of wax to the roof; and so in gradation a third and a
fourth. These blocks follow each other at regular intervals so
nicely calculated that when, at a much later period, the comb shall
be fully developed, there will be ample space for the bees to move
between its parallel walls.
Their plan must therefore embrace the final thickness of every comb,
which will be from eighty-eight to ninety-two hundredths of an inch,
and at the same time the width of the avenues between, which must be
about half an inch, or in other words twice the height of a bee,
since there must be room to pass back to back between the combs.
The bees, however, are not infallible, nor does their certainty
appear mechanical. They will commit grave errors at times, when
circumstances present unusual difficulty. They will often leave too
much space, or too little, between the combs. This they will remedy
as best they can, either by giving an oblique twist to the comb that
too nearly approaches the other, or by introducing an irregular comb
into the gap. "The bees sometimes make mistakes," Reaumur remarks on
this subject, "and herein we may find yet another fact which appears
to prove that they reason."
{54}
We know that the bees construct four kinds of cells. First of all,
the royal cells, which are exceptional, and contrived somewhat in
the shape of an acorn; then the large cells destined for the rearing
of males and storing of provisions when flowers super-abound; and
the small cells, serving as workers' cradles and ordinary
store-rooms, which occupy normally about four-fifths of the
built-over surface of the hive. And lastly, so as to connect in
orderly fashion the larger cells with the small, the bees will erect
a certain number of what are known as transition cells. These must
of necessity be irregular in form; but so unerringly accurate are
the dimensions of the second and third types that, at the time when
the decimal system was established, and a fixed measure sought in
nature to serve as a starting-point and an incontestable standard,
it was proposed by Reaumur to select for this purpose the cell of
the bee.*
*It was as well, perhaps, that this standard was not
adopted. For although the diameter of the cells is admirably
regular, it is, like all things produced by a living
organism, not _mathematically_ invariable in the same hive.
Further, as M. Maurice Girard has pointed out, the apothem
of the cell varies among different races of bees, so that
the standard would alter from hive to hive, according to the
species of bee that inhabited it.
Each of the cells is an hexagonal tube placed on a pyramidal base;
and two layers of these tubes form the comb, their bases being
opposed to each other in such fashion that each of the three rhombs
or lozenges which on one side constitute the pyramidal base of one
cell, composes at the same time the pyramidal base of three cells on
the other. It is in these prismatic tubes that the honey is stored;
and to prevent its escaping during the period of maturation,--which
would infallibly happen if the tubes were as strictly horizontal as
they appear to be,--the bees incline them slightly, to an angle of 4
deg or 5 deg.
"Besides the economy of wax," says Reaumur, when considering this
marvellous construction in its entirety, "besides the economy of wax
that results from the disposition of the cells, and the fact that
this arrangement allows the bees to fill the comb without leaving a
single spot vacant, there are other advantages also with respect to
the solidity of the work. The angle at the base of each cell, the
apex of the pyramidal cavity, is buttressed by the ridge formed by
two faces of the hexagon of another cell. The two triangles, or
extensions of the hexagon faces which fill one of the convergent
angles of the cavity enclosed by the three rhombs, form by their
junction a plane angle on the side they touch; each of these angles,
concave within the cell, supports, on its convex side, one of the
sheets employed to form the hexagon of another cell; the sheet,
pressing on this angle, resists the force which is tending to push
it outwards; and in this fashion the angles are strengthened. Every
advantage that could be desired with regard to the solidity of each
cell is procured by its own formation and its position with
reference to the others."
{55}
"There are only," says Dr. Reid, "three possible figures of the
cells which can make them all equal and similar, without any useless
interstices. These are the equilateral triangle, the square, and the
regular hexagon. Mathematicians know that there is not a fourth way
possible in which a plane shall be cut into little spaces that shall
be equal, similar, and regular, without useless spaces. Of the three
figures, the hexagon is the most proper for convenience and
strength. Bees, as if they knew this, make their cells regular
hexagons.
"Again, it has been demonstrated that, by making the bottoms of the
cells to consist of three planes meeting in a point, there is a
saving of material and labour in no way inconsiderable. The bees, as
if acquainted with these principles of solid geometry, follow them
most accurately. It is a curious mathematical problem at what
precise angle the three planes which compose the bottom of a cell
ought to meet, in order to make the greatest possible saving, or the
least expense of material and labour.* This is one of the problems
which belong to the higher parts of mathematics. It has accordingly
been resolved by some mathematicians, particularly by the ingenious
Maclaurin, by a fluctionary calculation which is to be found in the
Transactions of the Royal Society of London. He has determined
precisely the angle required, and he found, by the most exact
mensuration the subject would admit, that it is the very angle in
which the three planes at the bottom of the cell of a honey comb do
actually meet."
*Reaumur suggested the following problem to the celebrated
mathematician Koenig: "Of all possible hexagonal cells with
pyramidal base composed of three equal and similar rhombs,
to find the one whose construction would need the least
material." Koenig's answer was, the cell that had for its
base three rhombs whose large angle was 109 deg 26', and the
small 70 deg 34'. Another savant, Maraldi, had measured as
exactly as possible the angles of the rhombs constructed by
the bees, and discovered the larger to be 109 deg 28', and
the other 70 deg 32'. Between the two solutions there was a
difference, therefore, of only 2'. It is probable that the
error, if error there be, should be attributed to Maraldi
rather than to the bees; for it is impossible for any
instrument to measure the angles of the cells, which are not
very clearly defined, with infallible precision.
The problem suggested to Koenig was put to another mathematician,
Cramer, whose solution came even closer to that of the bees, viz.,
109 deg 28 1/2' for the large angle, and 70 deg 31 1/2' for the
small.
{56}
I myself do not believe that the bees indulge in these abstruse
calculations; but, on the other hand, it seems equally impossible to
me that such astounding results can be due to chance alone, or to
the mere force of circumstance. The wasps, for instance, also build
combs with hexagonal cells, so that for them the problem was
identical, and they have solved it in a far less ingenious fashion.
Their combs have only one layer of cells, thus lacking the common
base that serves the bees for their two opposite layers. The wasps'
comb, therefore, is not only less regular, but also less
substantial; and so wastefully constructed that, besides loss of
material, they must sacrifice about a third of the available space
and a quarter of the energy they put forth. Again, we find that the
trigonae and meliponae, which are veritable and domesticated bees,
though of less advanced civilisation, erect only one row of
rearing-cells, and support their horizontal, superposed combs on
shapeless and costly columns of wax. Their provision-cells are
merely great pots, gathered together without any order; and, at the
point between the spheres where these might have intersected and
induced a profitable economy of space and material, the meliponae
clumsily insert a section of cells with flat walls. Indeed, to
compare one of their nests with the mathematical cities of our own
honey-flies, is like imagining a hamlet composed of primitive huts
side by side with a modern town; whose ruthless regularity is the
logical, though perhaps somewhat charmless, result of the genius of
man, that to-day, more fiercely than ever before, seeks to conquer
space, matter, and time.
{57}
There is a theory, originally propounded by Buffon and now revived,
which assumes that the bees have not the least intention of
constructing hexagons with a pyramidal base, but that their desire
is merely to contrive round cells in the wax; only, that as their
neighbours, and those at work on the opposite side of the comb, are
digging at the same moment and with the same intentions, the points
where the cells meet must of necessity become hexagonal. Besides, it
is said, this is precisely what happens to crystals, the scales of
certain kinds of fish, soap-bubbles, etc., as it happens in the
following experiment that Buffon suggested. "If," he said, "you fill
a dish with peas or any other cylindrical bean, pour as much water
into it as the space between the beans will allow, close it
carefully and then boil the water, you will find that all these
cylinders have become six-sided columns. And the reason is evident,
being indeed purely mechanical; each of the cylindrical beans tends,
as it swells, to occupy the utmost possible space within a given
space; wherefore it follows that the reciprocal compression compels
them all to become hexagonal. Similarly each bee seeks to occupy the
utmost possible space within a given space, with the necessary
result that, its body being cylindrical, the cells become hexagonal
for the same reason as before, viz., the working of reciprocal
obstacles."
{58}
These reciprocal obstacles, it would seem, are capable of marvellous
achievement; on the same principle, doubtless, that the vices of man
produce a general virtue, whereby the human race, hateful often in
its individuals, ceases to be so in the mass. We might reply, first
of all, with Brougham, Kirby and Spence, and others, that
experiments with peas and soap-bubbles prove nothing; for the reason
that in both cases the pressure produces only irregular forms, and
in no wise explains the existence of the prismatic base of the
cells. But above all we might answer that there are more ways than
one of dealing with rigid necessity; that the wasp, the humble-bee,
the trigonae and meliponae of Mexico and Brazil achieve very
different and manifestly inferior results, although the
circumstances, and their own intentions, are absolutely identical
with those of the bees. It might further be urged that if the bee's
cell does indeed follow the law that governs crystals, snow,
soap-bubbles, as well as Buffon's boiled peas, it also, through its
general symmetry, disposition in opposite layers, and angle of
inclination, obeys many other laws that are not to be found in
matter. May we not say, too, of man that all his genius is comprised
in his fashion of handling kindred necessities? And if it appear to
us that his manner of treating these is the best there can possibly
be, the reason only can lie in the absence of a judge superior to
ourselves. But it is well that argument should make way for fact;
and indeed, to the objection based on an experiment, the best reply
of all must be a counter-experiment.
In order to satisfy myself that hexagonal architecture truly was
written in the spirit of the bee, I cut off and removed one day a
disc of the size of a five-franc piece from the centre of a comb, at
a spot where there were both brood-cells and cells full of honey. I
cut into the circumference of this disc, at the intersecting point
of the pyramidal cells; inserted a piece of tin on the base of one
of these sections, shaped exactly to its dimensions, and possessed
of resistance sufficient to prevent the bees from bending or
twisting it. Then I replaced the slice of comb, duly furnished with
its slab of tin, on the spot whence I had removed it; so that, while
one side of the comb presented no abnormal feature, the damage
having been repaired, the other displayed a sort of deep cavity,
covering the space of about thirty cells, with the piece of tin as
its base. The bees were disconcerted at first; they flocked in
numbers to inspect and examine this curious chasm; day after day
they wandered agitatedly to and fro, apparently unable to form a
decision. But, as I fed them copiously every evening, there came a
moment when they had no more cells available for the storage of
provisions. Thereupon they probably summoned their great engineers,
distinguished sculptors, and wax-workers, and invited them to turn
this useless cavity to profitable account.
The wax-makers having gathered around and formed themselves into a
dense festoon, so that the necessary heat might be maintained, other
bees descended into the hole and proceeded solidly to attach the
metal, and connect it with the walls of adjacent cells, by means of
little waxen hooks which they distributed regularly over its
surface. In the upper semicircle of the disc they then began to
construct three or four cells, uniting these to the hooks. Each of
these transition, or accommodation, cells was more or less deformed
at the top, to allow of its being soldered to the adjoining cell on
the comb; but its lower portion already designed on the tin three
very clear angles, whence there ran three little straight lines that
correctly indicated the first half of the following cell.
After forty-eight hours, and notwithstanding the fact that only
three bees at a time were able to work in the cavity, the entire
surface of the tin was covered with outlined cells. These were less
regular, certainly, than those of an ordinary comb; wherefore the
queen, having inspected them, wisely declined to lay any eggs there,
for the generation that would have arisen therefrom would
necessarily have been deformed. Each cell, however, was a perfect
hexagon; nor did it contain a single crooked line, a single curved
figure or angle. And yet the ordinary conditions had all been
changed; the cells had neither been scooped out of a block,
according to Huber's description, nor had they been designed within
a waxen hood, and, from being circular at first, been subsequently
converted into hexagons by the pressure of adjoining cells, as
explained by Darwin. Neither could there be question here of
reciprocal obstacles, the cells having been formed one by one, and
their first lines traced on what practically was a bare table. It
would seem incontestable, therefore, that the hexagon is not merely
the result of mechanical necessities, but that it has its true place
in the plans, the experience, the intellect and will of the bee. I
may relate here another curious instance of the workers' sagacity:
the cells they built on the tin had no other base than the metal
itself. The engineers of the corps had evidently decided that the
tin could adequately retain the honey; and had considered that, the
substance being impermeable, they need not waste the material they
value so highly by covering the metal with a layer of wax. But, a
short time after, some drops of honey having been placed in two of
these cells, the bees discovered, in tasting it, that the contact of
the metal had a deteriorating effect. Thereupon they reconsidered
the matter, and covered over with wax the entire surface of the tin.
{59}
Were it our desire to throw light upon all the secrets of this
geometric architecture, we should have more than one curious
question still to consider; as for instance the shape of the first
cells, which, being attached to the roof, are modified in such a
manner as to touch the roof at the greatest possible number of
points.
The design of the principal thoroughfares is determined by the
parallelism of the combs; but we must admire the ingenious
construction of alleys and gangways through and around the comb, so
skilfully contrived as to provide short cuts in every direction and
prevent congestion of traffic, while ensuring free circulation of
air. And finally we should have to study the construction of
transition cells, wherein we see a unanimous instinct at work that
impels the bees at a given moment to increase the size of their
dwellings. Three reasons may dictate this step: an extraordinary
harvest may call for larger receptacles, the workers may consider
the population to be sufficiently numerous, or it may have become
necessary that males should be born. Nor can we in such cases
refrain from wondering at the ingenious economy, the unerring,
harmonious conviction, with which the bees will pass from the small
to the large, from the large to the small; from perfect symmetry to,
where unavoidable, its very reverse, returning to ideal regularity
so soon as the laws of a live geometry will allow; and all the time
not losing a cell, not suffering a single one of their numerous
structures to be sacrificed, to be ridiculous, uncertain, or
barbarous, or any section thereof to become unfit for use. But I
fear that I have already wandered into many details that will have
but slender interest for the reader, whose eyes perhaps may never
have followed a flight of bees; or who may have regarded them only
with the passing interest with which we are all of us apt to regard
the flower, the bird or the precious stone, asking of these no more
than a slight superficial assurance, and forgetting that the most
trivial secret of the non-human object we behold in nature connects
more closely perhaps with the profound enigma of our origin and our
end, than the secret of those of our passions that we study the most
eagerly and the most passionately.
{60}
And I will pass over too--in my desire that this essay shall not
become too didactic--the remarkable instinct that induces the bees
at times to thin and demolish the extremity of their combs, when
these are to be enlarged or lengthened; though it must be admitted
that in this case the "blind building instinct" fails signally to
account for their demolishing in order that they may rebuild, or
undoing what has been done that it may be done afresh, and with more
regularity. I will content myself also with a mere reference to the
remarkable experiment that enables us, with the aid of a piece of
glass, to compel the bees to start their combs at a right angle;
when they most ingeniously contrive that the enlarged cells on the
convex side shall coincide with the reduced cells on the concave
side of the comb.
But before finally quitting this subject let us pause, though it be
but for an instant, and consider the mysterious fashion in which
they manage to act in concert and combine their labour, when
simultaneously carving two opposite sides of a comb, and unable
therefore to see each other. Take a finished comb to the light, fix
your eyes on the diaphanous wax; you will see, most clearly
designed, an entire network of sharply cut prisms, a whole system of
concordances so infallible that one might almost believe them to be
stamped on steel.