Part 14

ARCHITECTURE OF THE HIVE-BEE CONTINUED--FORM OF THE CELLS.

The obstruction of which M. Huber complains only operated as a stimulus to his ingenuity in contriving how he might continue his interesting observations. From the time of Pappus to the present day, mathematicians have applied the principles of geometry to explain the construction of the cells of a bee-hive; but though their extraordinary regularity, and wonderfully-selected form, had so often been investigated by men of the greatest talent, and skilled in all the refinements of science, the process by which they are constructed, involving also the causes of their regularity of form, had not been traced till M. Huber devoted himself to the inquiry.

As the wax-workers secrete only a limited quantity of wax, it is indispensably requisite that as little as possible of it should be consumed, and that none of it should be wasted. Bees, therefore, as M. Réaumur well remarks, have to solve this difficult geometrical problem:--a quantity of wax being given, to form of it similar and equal cells of a determinate capacity, but of the largest size in proportion to the quantity of matter employed, and disposed in such a manner as to occupy the least possible space in the hive. This problem is solved by bees in all its conditions. The cylindrical form would seem to be best adapted to the shape of the insect; but had the cells been cylindrical, they could not have been applied to each other without leaving a vacant and superfluous space between every three contiguous cells. Had the cells, on the other hand, been square or triangular, they might have been constructed without unnecessary vacancies; but these forms would have both required more material, and have been very unsuitable to the shape of a bee's body. The six-sided form of the cells obviates every objection; and while it fulfils the conditions of the problem, it is equally adapted with a cylinder to the shape of the bee.

M. Réaumur further remarks, that the base of each cell, instead of forming a plane, is usually composed of three pieces in the shape of the diamonds on playing cards, and placed in such a manner as to form a hollow pyramid. This structure, it may be observed, imparts a greater degree of strength, and, still keeping the solution of the problem in view, gives a great capacity with the smallest expenditure of material. This has actually, indeed, been ascertained by mathematical measurement and calculation. Maraldi, the inventor of glass hives, determined, by minutely measuring these angles, that the greater were 109° 28', and the smaller 70° 32'; and M. Réaumur, being desirous to know why these particular angles are selected, requested M. Koenig, a skilful mathematician (without informing him of his design, or telling him of Maraldi's researches), to determine by calculation what ought to be the angle of a six-sided cell, with a concave pyramidal base, formed of three similar and equal rhomboid plates, so that the least possible matter should enter into its construction. By employing what geometricians denominate the infinitesimal calculus, M. Koenig found that the angles should be 109° 26' for the greater, and 70° 34' for the smaller, or about two-sixtieths of a degree, more or less, than the actual angles made choice of by bees. The equality of inclination in the angles has also been said to facilitate the construction of the cells.

M. Huber adds to these remarks, that the cells of the first row, by which the whole comb is attached to the roof of a hive, are not like the rest; for, instead of six sides, they have only five, of which the roof forms one. The base, also, is in these different, consisting of three pieces on the face of the comb, and on the other side of two: one of these only is diamond-shaped, while the other two are of an irregular four-sided figure. This arrangement, by bringing the greatest number of points in contact with the interior surface, insures the stability of the comb.

It may, however, be said not to be quite certain, that Réaumur and others have not ascribed to bees the merit of ingenious mathematical contrivance and selection, when the construction of the cells may more probably originate in the form of their mandibles and the other instruments employed in their operations. In the case of other insects, we have, both in the preceding and subsequent pages of this volume, repeatedly noticed, that they use their bodies, or parts thereof, as the standards of measurement and modelling; and it is not impossible that bees may proceed on a similar principle. M. Huber replies to this objection, that bees are not provided with instruments corresponding to the angles of their cells; for there is no more resemblance between these and the form of their mandibles, than between the chisel of the sculptor and the work which he produces. The head, he thinks, does not furnish any better explanation. He admits that the antennæ are very flexible, so as to enable the insects to follow the outline of every object; but concludes that neither their structure, nor that of the limbs and mandibles, are adequate to explain the form of the cells, though all these are employed in the operations of building,--the effect, according to him, depending entirely on the object which the insect proposes.

We shall now follow M. Huber in the experiments which he contrived, in order to observe the operations of the bees subsequent to their laying a foundation for the first cell; and we shall again quote from his own narrative:--

"It appeared to me," he says, "that the only method of isolating the architects, and bringing them individually into view, would be to induce them to change the direction of their operations and work upwards.

"I had a box made twelve inches square and nine deep, with a moveable glass lid. Combs, full of brood, honey, and pollen, were next selected from one of my leaf-hives, as containing what might interest the bees, and being cut into pieces a foot long, and four inches deep, they were arranged vertically at the bottom of the box, at the same intervals as the insects themselves usually leave between them. A small slip of wooden lath covered the upper edge of each. It was not probable that the bees would attempt to found new combs on the glass roof of the box, because its smoothness precluded the swarm from adhering to it; therefore, if disposed to build, they could do so over the slips resting on the combs, which left a vacuity five inches high above them. As we had foreseen, the swarm with which this box was peopled established itself among the combs below. We then observed the nurse-bees displaying their natural activity. They dispersed themselves throughout the hive, to feed the young grubs, to clear out their lodgment, and adapt it for their convenience. Certainly, the combs, which were roughly cut to fit the bottom of the box, and in some parts damaged, appeared to them shapeless and misplaced; for they speedily commenced their reparation. They beat down the old wax, kneaded it between their teeth, and thus formed binding materials to consolidate them. We were astonished beyond expression by such a multitude of workers employed at once in labours to which it did not appear they should have been called, at their coincidence, their zeal, and their prudence.

"But it was still more wonderful, that about half the numerous population took no part in the proceedings, remaining motionless, while the others fulfilled the functions required. The wax-workers, in a state of absolute repose, recalled our former observations. Gorged with the honey we had put within their reach, and continuing in this condition during twenty-four hours, wax was formed under their rings, and was now ready to be put in operation. To our great satisfaction, we soon saw a little foundation-wall rising on one of the slips that we had prepared to receive the superstructure. No obstacle was offered to the progress of our observations; and for the second time we beheld both the undertaking of the founder-bee, and the successive labours of several wax-workers, in forming the foundation-wall. Would that my readers could share the interest which the view of these architects inspired!

"This foundation, originally very small, was enlarged as the work required; while they excavated on one side a hollow, of about the width of a common cell, and on the opposite surface two others somewhat more elongated. The middle of the single cell corresponded exactly to the partition separating the latter: the arches of these excavations, projecting by the accumulation of wax, were converted into ridges in a straight line; whence the cells of the first row were composed of five sides, considering the slip as one side, and those of the second row, of six sides.

"The interior conformation of the cavities, apparently, was derived from the position of their respective outlines. It seemed that the bees, endowed with an admirable delicacy of feeling, directed their teeth principally to the place where the wax was thickest; that is, the parts where other workers on the opposite side had accumulated it; and this explains why the bottom of the cell is excavated in an angular direction behind the projection on the sides of which the sides of the corresponding cells are to rise. The largest of the excavations, which was opposite to three others, was divided into three parts, while the excavations of the first row on the other face, applied against this one, were composed of only two.

"In consequence of the manner in which the excavations were opposed to each other, those of the second row, and all subsequent, partially applied to three cavities, were composed of three equal diamond-shaped lozenges. I may here remark, that each part of the labour of bees appears the natural result of what has preceded it: therefore, chance has no share in these admirable combinations.

"A foundation-wall rose above the slip like a minute vertical partition, five or six lines long, two lines high, but only half a line in thickness; the edge circular, and the surface rough. Quitting the cluster among the combs, a nurse-bee mounted the slip, turned around the block, and visiting both sides, began to work actively in the middle. It removed as much wax with its teeth as might equal the diameter of a common cell; and after kneading and moistening the particles, deposited them on the edge of the excavation. This insect having laboured some seconds, retired, and was soon replaced by another; a third continued the work, raising the margin of the edges, now projecting from the cavity, and with assistance of its teeth and feet fixing the particles, so as to give these edges a straighter form. More than twenty bees successively participated in the same work; and when the cavity was little above a line and a half in height, though equalling a cell in width, a bee left the swarm, and after encircling the block, commenced its operations on the opposite face, where yet untouched. But its teeth acting only on one half of this side, the hollow which it formed was opposite to only one of the slight prominences bordering the first cavity. Nearly at the same time another worker began on the right of the face that had been untouched, wherein both were occupied in forming cavities which may be designed the second and third; and they also were replaced by substitutes. These two latter cavities were separated only by the common margin, framed of particles of wax withdrawn from them; which margin corresponded with the centre of the cavity on the opposite surface. The foundation-wall itself was still of insufficient dimensions to admit the full diameter of a cell: but while the excavations were deepened, wax-workers, extracting their scales of wax, applied them in enlarging its circumference; so that it rose nearly two lines further around the circular arch. The nurse-bees, which appeared more especially charged with sculpturing the cells, being then enabled to continue their outlines, prolonged the cavities, and heightened their margins on the new addition of wax.

"The arch, formed by the edge of each of these cavities, was next divided as by two equal chords, in the line of which the bees formed stages or projecting borders, or margins meeting at an obtuse angle: the cavities now had four margins, two lateral and perpendicular to the supporting slip, and two oblique, which were shorter.

"Meantime, it became more difficult to follow the operations of the bees, from their frequently interposing their heads between the eye of the observer and the bottom of the cell; but the partition, whereon their teeth laboured, had become so transparent as to expose what passed on the other side.

"The cavities of which we speak formed the bottom of the first three cells; and while the bees engaged were advancing them to perfection, other workers commenced sketching a second row of cells above the first, and partly behind those in front--for, in general, their labour proceeds by combination. We cannot say, 'When bees have finished this cell, they will begin new ones;' but, 'while particular workers advance a certain portion, we are certain that others will carry on the adjacent cells.' Further, the work begun on one face of the comb is already the commencement of that which is to follow on the reverse. All this depends on a reciprocal relation, or a mutual connexion of the parts, rendering the whole subservient to each other. It is undoubted, therefore, that slight irregularities on the front will affect the form of the cells on the back of the comb."

When they have in this manner worked the bottoms of the first row of cells into the required forms, some of the nurse-bees finish them by imparting a sort of polish, while others proceed to cut out the rudiments of a second row from a fresh wall of wax which has been built in the meanwhile by the wax-workers, and also on the opposite side of this wall; for a comb of cells is always double, being arranged in two layers, placed end to end. The cells of this second row are engrafted on the borders of cavities hollowed out in the wall, being founded by the nurse-bees, bringing the contour of all the bottoms, which is at first unequal, to the same level; and this level is kept uniform in the margins of the cells till they are completed. At first sight nothing appears more simple than adding wax to the margins; but from the inequalities occasioned by the shape of the bottom, the bees must accumulate wax on the depressions, in order to bring them to a level. It follows accordingly that the surface of a new comb is not quite flat, there being a progressive slope produced as the work proceeds, and the comb being therefore in the form of a lens, the thickness decreasing towards the edge, and the last-formed cells being shallower or shorter than those preceding them. So long as there is room for the enlargement of the comb, this thinning of its edge may be remarked; but as soon as the space within the hive prevents its enlargement, the cells are made equal, and two flat and level surfaces are produced.

M. Huber observed, that while sketching the bottom of a cell, before there was any upright margin on the reverse, their pressure on the still soft and flexible wax gave rise to a projection, which sometimes caused a breach of the partition. This, however, was soon repaired, but a slight prominence always remained on the opposite surface, to the right and left of which they placed themselves to begin a new excavation; and they heaped up part of the materials between the two flutings formed by their labour. The ridge thus formed becomes a guide to the direction which the bees are to follow for their vertical furrow of the front cell.

We have already seen that the first cell determines the place of all that succeed it, and two of these are never, in ordinary circumstances, begun in different parts of the hive at the same time, as is alleged by some early writers. When some rows of cells, however, have been completed in the first comb, two other foundation-walls are begun, one on each side of it, at the exact distance of one-third of an inch, which is sufficient to allow two bees employed on the opposite cells to pass each other without jostling. These new walls are also parallel to the former; and two more are afterwards begun exterior to the second, and at the same parallel distance. The combs are uniformly enlarged, and lengthened in a progression proportioned to the priority of their origin; the middle comb being always advanced beyond the two adjoining ones by several rows of cells, and these again beyond the ones exterior to them. Did the bees lay the foundations of all their combs at the same time, they would not find it easy to preserve parallelism and an equality in their distances. It may be remarked further, that beside the vacancies of half an inch between the cells, which form what we call the highways of the community, the combs are pierced in several places with holes which serve as postern-gates for easy communication from one to another, to prevent loss of time in going round. The equal distance between the combs is of more importance to the welfare of the hive than might at first appear; for were they too distant, the bees would be so scattered and dispersed, that they could not reciprocally communicate the heat indispensable for hatching the eggs and rearing the young. If the combs, on the other hand, were closer, the bees could not traverse the intervals with the freedom necessary to facilitate the work of the hive. On the approach of winter, they sometimes elongate the cells which contain honey, and thus contract the intervals between the combs. But this expedient is in preparation for a season when it is important to have copious magazines, and when, their activity being relaxed, it is unnecessary for their communications to be so spacious and free. On the return of spring, the bees hasten to contract the elongated cells, that they may become fit for receiving the eggs which the queen is about to deposit, and in this manner they re-establish the regular distance.

We are indebted to the late Dr. Barclay of Edinburgh, well known as an excellent anatomist, for the discovery that each cell in a honeycomb is not simply composed of one wall, but consists of two. We shall give the account of his discovery in his own words:--

"Having inquired of several naturalists whether or not they knew any author who had mentioned that the partitions between the cells of the honeycomb were double, and whether or not they had ever remarked such a structure themselves, and they having answered in the negative, I now take the liberty of presenting to the Society pieces of honeycomb, in which the young bees had been reared, upon breaking which, it will be clearly seen that the partitions between different cells, at the sides and the base, are all double; or, in other words, that each cell is a distinct, separate, and in some measure an independent structure, agglutinated only to the neighbouring cells; and that when the agglutinating substance is destroyed, each cell may be entirely separated from the rest.

"I have also some specimens of the cells formed by wasps, which show that the partitions between them are also double, and that the agglutinating substance between them is more easily destroyed than that between the cells of the bee."

Irregularities in their Workmanship.

Though bees, however, work with great uniformity when circumstances favour their operations, they may be compelled to vary their proceedings. M. Huber made several ingenious experiments of this kind. The following, mentioned by Dr. Bevan, was accidental, and occurred to his friend Mr. Walond. "Inspecting his bee-boxes at the end of October, 1817, he perceived that a centre comb, burthened with honey, had separated from its attachments, and was leaning against another comb so as to prevent the passage of the bees between them. This accident excited great activity in the colony; but its nature could not be ascertained at the time. At the end of a week, the weather being cold, and the bees clustered together Mr. Walond observed, through the window of the box, that they had constructed two horizontal pillars betwixt the combs alluded to, and had removed so much of the honey and wax from the top of each as to allow the passage of a bee: in about ten days more there was an uninterrupted thoroughfare; the detached comb at its upper part had been secured by a strong barrier, and fastened to the window with the spare wax. This being accomplished, the bees removed the horizontal pillars first constructed, as being of no further use."

A similar anecdote is told by M. Huber. "During the winter," says he, "a comb in one of my bell-glass hives, having been originally insecure, fell down, but preserved its position parallel to the rest. The bees were unable to fill up the vacuity left above it, because they do not build combs of old wax, and none new could be then obtained. At a more favourable season they would have engrafted a new comb on the old one; but now their provision of honey could not be spared for the elaboration of this substance, which induced them to insure the stability of the comb by another process.

"Crowds of bees taking wax from the lower part of other combs, and even gnawing it from the surface of the orifices of the deepest cells, they constructed so many irregular pillars, joists, or buttresses, between the sides of the fallen comb, and others on the glass of the hive. All these were artificially adapted to localities. Neither did they confine themselves to repairing the accidents which their works had sustained. They seemed to profit by the warning to guard against a similar casualty.

"The remaining combs were not displaced; therefore, while solidly adhering by the base, we were greatly surprised to see the bees strengthen their principal fixtures with old wax. They rendered them much thicker than before, and fabricated a number of new connections, to unite them more firmly to each other and to the sides of their dwelling. All this passed in the middle of January, a time that these insects commonly keep in the upper part of their hive, and when work is no longer seasonable."