[B75-B76]

(a) If my theory is right. Theory of construction. Begin with: I believe it can be shown all wondrous angles which it is impossible to suppose it. Bees can measure or even recognise whether accurately made result from very simple principles & assumption of one simple principle that insects can judge of distances. Premise that theory my theory is a considerable modification of Waterhouse (Penny Encyclop. Art. Bee. Ld Brougham opposed p/30, 267) I shd certainly never come to it, without reading it, [illeg] from Mr W. & his showing me many specimens. (1) single cell never found either one insect as wasp forms part a little bit of one cell & then goes to another so that several start together, or several as Hive Bee, work at same time partly excavating a made mass of wax laid down, partly building up. (2) Insects as Xylocopaga (?) can certainly make cylindrical burrow, or cylindrical tube; we must suppose & this supported by observation of Mr W. on Osmia by working from one position as much as possible. (3) it is Known, that when insects making cylinders or spheres & begin so close that they wd intersect if completed, that insects make along median plane of intersection a plane wall – Melipona irregular cells in comb of Hive Bee Mud Polistes I think beginning cells of Icaria. (4) Now we come to assumptions, viz that Bees & Wasps can judge very accurately of distance; we shd not be surprised at insects making a set of cylinders or spheres just touching each other; this is done by in cylinders of Melipona & Bombus (?). Now let us assume that an insect just traces a circle & then removes to another spot, not at distance of diameter, but at a particular distance (viz side of triangle inscribed within side) & tends to make second inside; they will intersect, & it will make plane wall between the 2 cells. (5) Now for one more & not great assumption - viz that when it goes to make 3 circles or spheres, it stands directly between 2 prism circles, & at same distances as before & tries to sweep its circle, but making plane when it will intersect 2 other circles, & so let it go on till 6 are completed round first circle. A hexagon like wasps nest will be formed - give diagram. Before passing to more

[B76]

My theory

(b) complex case of Hive-Bee cells - consider case of Icaria, & give notes on nest of sub-genus Polistes with hexagonal comb & hexagon rows of eggs in different states.

Now to apply the same exact principles to Hive Bees but starting with sphere instead of cylinders instead of one (or several) insect making a set of cylinders on one flat plane, let us suppose, that they begin (instead of only on both sides of wax, as is really the case) to make a solid agglomeration of spheres round a central area but each including central one commencing at the distance before specified, joining plane of intersection by flat surface then all the spheres will be dodecahedrons with rhomboidal faces, inclined to each other at 120, with angles of rhomb - ie exactly the shape of base of Bees cell. But instead of agglomeration of spheres, let us suppose that they begin to make a double row of spheres, thus the base & sides of these will be rhomboidal dodecahedrons, but the outer surface instead of being dodecahedron, will be either spherical or shall be built up as hexagon. This latter view is in itself probable from Huber account of Bombus elongating isolated spheres. A Bee cell is in fact a rhomb. dod. complete at one pole & carved up into hexagonal tubes at other end.

The only difficulty in this theory is judging so accurately of distance, as I have remarked they can to certain extent judge of distances, & this has to be perfected & the incidental result of this accuracy is a minimum of wax used. It cannot be that they judge by length of body for as F. Smith remarked to me large wasps make small cells for neuter & latter larger cells for females. However great assumption may be, it solves I think whole problem.

What is shape of base of wasp-cell.

what shape of part row of attached cells of comb.