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I have said that my very fundamental idea is that Bees & wasps common tend to make spheres & cylinders in a flat layer, but that they are impelled by instinct to commence working at one certain definite distance from each other, & that in consequence their cells interfere, & intermediate planes are formed. This one distance, I am informed by Prof. Miller is .........: we will call it e. The following statement has been drawn up after consultation with this eminent mathe geometrician, & he has kindly read it over & the whole of the discussion & answers for the accuracy of the geometrical statements.

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So that From this statement it certainly follows from this that if we grant that the Bees tend to make equal spheres in two parallel planes at one given distance (e). from each other in the same layer & at same distance from an adjacent spheres in plane (& we have seen in Melipona same tendency in which the points all this done in an imperfect manner) then a all the marvellous angular structures, every angle, ridge & plane, of the Bee's comb would follow. with the simple additions of, increasing the length of the tubes; & with this addition is nothing surprising, for Humble-Bees do this with their spherical pots.—

Now let us see how Bees practically work; taking as our guide

It may be worth while to see look consider, taking our facts from to Hubers ? inimitable works, observations, given with such inimitable clearness.

(In * (Title). see Back & remark that doubt these from his describing for simplicity sake the progress of single cell. He adds repeatedly whilst this one was forming, the production of others were laid, this is chief point on which more precise information is wanted)

& see how the Bees actually proceed in their geometrical work As sketch can be here only given: & then & gaps in our Knowledge must be filled up; but this can be done [illeg] only imperfectly & in some degree hypothetically. We will at first pass over the cells of the first & attached range, which differs from the others, & present some special difficulties, & consider the construction of the comb, after the first few rows in both faces have been formed. A thin little wall of wax in, about as thick as the depth of the trihedral pyramid, is added to the edge of the comb by the wax-sentry Bees.

A succession of Sculptor-Bees, standing (where I have marked cell) between two sides of the preexisting cells, which two sides will form two of the hexagon which a Bee is going

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* at first I was infinitely perplexed by Huber describing the cells at each stage as completed almost separately but afterwards he repeatedly emphatically says we must understand "whilst this going on, others are being elavated &c — But more precise Information is wanted on these heads. —

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to make, begins excavating a hollow in the thin & just [illeg] formed wall of wax; as he excavates the leaf he piles up the particles on either side, making two straight sides away from the spine of the preexisting cells which gives 4 sides of the next heagon: but the outer side is at first always invariably made curved;

But as soon, as a new built wall of wax is added to the comb, this arched surface is modified into the 2 other sides of the hexagon. This latter fact is important, for we see until the Bees have a new wall added, on which they can stand, at fixed distance 2e for 2 point hexagons, & either mark or survey or perhaps only survey their work, from a proper point stand-point (many at distance or for the centre of [illeg] under hexagons). faintly mark a new niche, or mark a point of intersection of the such new niches, made then in progress.

they cannot complete the 2 remaining sides of hexagonal outline. with respect to the 2 sides (c. d.) which they do make, they have already made the walls of wax on each side, whence they could sweep their circles, & so judge of the lines of intersection. (a) (b)

The hexagonal outline of the new cell is completed bef while the its basis of the new comb is simply concave & the trihedral pyramid incomplete not even sketched out. But it is a highly remarkable fact that this hexagonal outline is not a simple line all in same level; but it justly stated by Huber to be the extra extensive or upper (if we are looking into the hive) edges of the basal trihedral pyramid: it is the line a. b. c. d. e. f. & [sketch] in the opened out cell; here shown in perspective. [sketch] : it is an hexigonal outline, intricately zig-zag.

(over (a)

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(b) The end two further sides of every new cell, being usually made at first arched & then being made angular as soon as a wall of wax is made beyond; or the two lateral sides being made at first strength, then being on each side of these a wall of wax with cells under made in process of portions all made the circumference of the cell strongly confirm the view that the Bees require a stand point whence to survey or mark the work in progress so as to discover the lines of intersection.

(a) This cursive line with each of the six portions inclined vertically at one particular angle to each other at another a & horizontally as shown clearly by Huber for to excavate down from it so as to form the trihedral basal pyramid & up from it to form the hexagonal portion

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Now what an extraordinary difficult line this is (this is clearly shown by Huber to be the foundation of all future work ) for the Bees to sculpture out of a plain surface of wax. (a) But if we imagine the Bees to stand at a distance 2e from each other, & begin to excavate a certain height when the layer at the same height or distance from the under surface of the wall of wax, which has a thickness about equal to the depth of the two trihedral pyramids, & begin to excavate equal spheres, the point of intersection of the spheres near (past a little above & past a little below) near [illeg] after [illeg] the surface of the wax will infallibly give this line, as as follows from the geometrical proposition given on authority of Prof. Miller.

Whilst the Bees are thus at work on one face the side of the new wall of wax the very same process is going on on the opposite face; the centre of each of hexagonal outlines (vertically zigzag) being thus drawn. below is the interior between the centers of two those on the next face; & this, also, follows from our supposed instinct of each Bee working at distance 2e both from the adjoining ones in same layer & from the adjoining ones in the other & parallel layer.

Each of these hexagonal outlines along the edge of the comb is hollowed out in the middle, but is not yet made angular, or connected with trihedral pyramids. But if we join the hexagonal reticulations on the two sides of the comb bearing is round the relative portion which they occupy & the distance at which they stand alone &c by plane surface, the series of trihedral pyramids with rhombic face, with no result, as inevitably follows from our geometrical proposition. of the two layers of spheres before given on Prof. Miller's authority.— & as seen in this diagram, where the hexagon (the outline necessarily repeated on same plane instead of vertically zigzag) on the near surface is represented by dark lines, & the 3 on opposite faces by fainter lines. [sketch]

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(a) It is the more wonderful, & without any theory to guide us quite inexplicable, as soon as even the pyramid base is with its 3 rhombs is completed, the hexagonal outline is made level, & is then added to, always kept level, so as to form hexagonal prisms.

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Now, according to Huber this is what the Bees actually do, for though the space within an hexagonal polygon outline is at first made concave, it is here rendered angular, till the hexagonal outline, or part of one, is found on the opposite face; & then the base excavate down to other bases of the lines on the opposite face, & plane & smooth the surface from between these lines to on the opposite face & the hexagonal cells on their own face.

Hence it is not at all imaginary for the bees to work on both faces of any case of 4 sheets, or on all 3 sheets at same time [illeg]

He supposes that they can see these lines, on the opposite face, for so transparent is the wax, that he could possibly see them (with [illeg] eye) whilst watching the other continue; or, owing to darkness of hive he [illeg] the [illeg] they can feel with their antennae, which are incessantly feeling on surface, by the difference of elasticity of the wax, when these hexagonal holes vertically, are traced which are in part elevated above the hole of wax& partly excavated in it, only a difference in elasticity along them, that the lines in the opposite face found by the unison of 3 hexagonal outlines is to [illeg] for [illeg] the surfaces between them & variety the hexagonal outline on their own face, I think is indeed very probable, by observing an irregular comb or chamber in which part of 4 cells on one side with correspond with base of one in a side, & then the base of instead of being a trihedral pyramid, with crust of 4 faces of all sorts various & graduated dimensions. (a) Book

I have never said that the cells of the first or attached row are different from the others & present some special difficulties: they are pentagonal, the surface of attachment requiring 2 sides of the hexagon, by which & by an endogenous modification of the trihedral basis the attachment is rendered stronger from the beginning of attachment & 2 cells. The cells of the first row differ

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(a) after the pyramidal bases are made completed & made perfect, Huber shows that the hexagonal faces as already combined are built up. & when & often I may add subsequently added to when space for honey required. There seems little difficulty in this. But H. has shown where by extension, no pyramidal bases were made, yet hexagons were found, but these will follow from our geometrical problem, if bases of spheres are not made, only the sides, yet the planes of intersection will form a hexagon. —

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on the two faces, but both are pentagonal. According to Huber a succession of Bees first make on what he calls the anterior face of a little wall of wax a single pentagonal cell, of which A b c d e is a section & which is higher than but no greater is larger than an ordinary cell; & which at first, as in all other cases is only arched over, its summit b c d. & not made angular like the Bees can start above. I hypothetical suppose that lines b b', d d' are formed in usual manner by Bees standing on the two out sides of this first cell & judging of distance so as to get their intermediate lines of intersection; & that they are then produced to the surface of attachment e a. The hexagon is not attached, as shown by completed on [illeg] attached surface, as shown by the dotted lines are as Bees could not possibly stand to sweep their spheres e a being a solid surface of attachment.

Before even the upper edge, in its arched condition, of this first cell is completed, the Bees commence making on the posterior face of comb two on the opposite face new cells, one on each side of central line of the primordial cell on the anterior face. Huber asserts that he has seen a mark on the posterior face made to guide the Bees from this position of the cells on the posterior face; but as the very thin wall of built wax is at this point so low not so high enough of first cell to be completed, I can hardly think that the Bees clustering round the edge could have difficulty in placing centering the cells on the opposite face. (a)  Before these 2 cells on posterior face ie the second & third cells) are completed a fourth is made above these 2, see fig 2, in which this 4th cell is seen to be in the stage have arched upper surfaces, prefatorily to being

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(a)
Indeed it may be suspected that one notion for the bees making such slight successive increments to the built walls of wax, is that they may perceive how the work goes on on both faces, though this is not the opinion of Huber.

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cemented into a hexagon. now these two lower attached cells of the first row on the posterior face, are pentagonal like the primordial one on the anterior face, but they differ from it in a very remarkable manner insisted on by Huber, but they have a much less diameter, as seen in section fig. 2.

Now by our theory as the Bees have 3 cells on the posterior face & one on anterior, in order to follow their supposed instinct of making centres of all at distance 2e from each other; it is indisputable that the 2 lower cells sh^d be commenced, or perhaps rather be modified during completion, so as to stand so much lower, that the upper 4^th cell of posterior face sh^d stand at this distance from the anterior & primordial cell. —

Upon the whole this theory of Bees instinctly working at a certain definite distance, & where these spheres would intersect making by excavation & building up intermediate planes, explains I think pretty satisfactory all the pertinent facts. therefore combs have hexagonal prisms only on one side & the same. How Bees judge of distance I know not, but we have seen that they other insects can do so to a certain extent & we have only to perfect this instinctive faculty. I do not think that as I first thought that there was much difficulty in judging from opposite side of comb, seeing how they work on a very knife edge. — It cant be by lengths of

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their own bodies, that they measure this distance or the diameter of cells, for both before & after Bees make true cells; larger also as in a bent conmb, they control or increase diameter of the same cells. As F. Smith remarked to me lastly Queen Wasp makes small cell for worker & worker larger cell for Queen. — However when Bees comb [illeg] injuries by any accident or in making Drone cells, they must gradually & invariably construct them hexagons, i.e. as I believe tend to make less & less spheres, & it is beautiful to see, how gradually this is done, as shown by the lessening & final disappearance of a 4th rhombic plate, which form part of base, when one cell on one face comes up composite from cells on the opposite face.

In Wasps & Hornets &c. nest, the combs gradually form single layer of Hexagons: this presents a difficulty on one [Theory] we have only to suppose cylinders; & one of Family does make cylinders & their intention will make hexagonal prism terminated by flat on concave basis. But we have one remarkable case Icaria. F. Smith. Ent. Proc. woodcut. —

Lastly final cause, only instant of judging distance tending to make quite equal sphere or cylinder in simple or double layer in the same wax. — [illeg] have shown this - many workers do nothing but secrete wax most consume food from [it] be kept, if less wax needed. —