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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.
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.
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 cells; and when one cell rests on three others, as 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 rudely resembling the three-sided pyramidal base of the hive bee's cell, and necessarily enter, like the three rhombs of the latter, into the construction of three adjoining cells. Reflecting on these remarkable gradations, it occurred to Mr.
At the higher end of the series, he saw hive bees making double layers of cells, each cell an hexagonal prism with the basal ends of its six sides bevelled so as to fit on to a pyramid formed of three rhombs, and each of the three rhombs which compose the pyramidal base of a single cell on one side of the comb entering into the composition of one of the three adjoining cells on the opposite side.
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.
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.
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 fit on to a pyramid, formed of three rhombs.
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.
It has been remarked that a skilful workman, with fitting tools and measures, would find it very difficult to make cells of wax of the true form, though this is effected by a crowd of bees, working in a dark room. Each cell, as is well known, is a hexagonal prism, with the basal edges of its six sides, beveled so as to join an inverted pyramid of three rhombs.
"Mineralogically speaking, this is a meteor or a block of volcanic basalt," judged the Master. "It seems sprinkled with small crystals, with rhombs of tile-red feldspath on a dark background like velvet or charcoal, except for one reddish protuberance of an unknown substance.
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