# From E. A. Darwin [8 June 1858]^{1}

Dear Charles

I find I cannot draw a ⊙ round your [DIAGRAM HERE] two points, as the difference is so small only about a $\frac{1}{\mathrm{70\; or\; 80}}$ of an inch.

I send you 2 more projections as the more points of view you see it in the better^{2}

I also send you some rhombs cut out, with flaps to fasten over the edges, & I advise you to begin with the flap (A)^{3}

They are not the same size as Millers,^{4} & I do not know if you have any reason for that particular size.

Also a pyramid, with 2 circles on the base to be raised up & the circle on the short diameter will show you exactly how much the obtuse ∠’s are within the sphere

[DIAGRAM HERE] obtuse ∠

12 of these pyramids would make the Dodec.

You will be surprized how firm the model will feel when put together, but dont be in a hurry & let one flap dry before you paste another,

When you have got the model in your hand, & hold them in the same position as my diagrames, they will all become quite clear.

I think I have answered all your questions.

ED

Over the page I will draw another little diagram to fix the positions of the acute ∠^{s}

[DIAGRAM HERE]

P A W N S E P N E S W – equator S P N P’ – meridian W P E P’ – East & West circle 6 acute angles at the letters 8 obtuse angles (A) in the center of the quadrants

[Enclosure]^{5}

[DIAGRAMS HERE]

N^{o} 1 A d a c f K b C D e B N^{o} 2 A a C f k b D e B AB vertical axis passing thro’ acute ∠^{s} A & B CD horizontal axis passing thro’ centers of 2 Rhombs K axis perpendicular to CD & AB or the plane of the paper a b e f rhomb parallel to paper, natural size diameter bf = AC = side of square in ⊙ diameter ae = KA radius of ⊙ a b c d—rhomb oblique to the paper cb is parallel to ae and = $\frac{1}{2}$ ae or Ke

Kc = eb = side of rhomb The obtuse ∠ at c is in the plane of the paper [therefore sign] Kc = radius of ⊙ passing thro’ obtuse ∠^{s} Kb = $\frac{1}{2}$ distance of centers = distance from center of sphere to rhomb [N^{o} 2] The same as N^{o} 1 but turned round the axis AB 45^{o}. The 4 rhombs are all at ∠ 45^{o} with paper, but fAfB are the long diameter of the vertical plane, & fC, fD long diameters in the horizontal plane

## Footnotes

^{o}31.7’’ and ‘109

^{o}28.3’’. See

*Natural selection*, p. 513 and n. 1, where the angles of a rhombic face of a bee’s cell are discussed.

## Summary

Encloses projections and models relating to geometry of bees’ cells.

## Letter details

- Letter no.
- DCP-LETT-2283
- From
- Erasmus Alvey Darwin
- To
- Charles Robert Darwin
- Sent from
- unstated
- Source of text
- DAR 162: 48a, 50
- Physical description
- 4pp, encl 3pp

## Please cite as

Darwin Correspondence Project, “Letter no. 2283,” accessed on 26 April 2017, http://www.darwinproject.ac.uk/DCP-LETT-2283

Also published in *The Correspondence of Charles Darwin*, vol. 7