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

Dear Charles.

To make sure that I now understand look at my diagram.^{2} The two : A, F in the hexagon the section of the Dodec.

Call CB radius of sphere (r) & CF radius of ⊙ in which the hexagon is inscribed r′, then

diag

r′ : r :: .8165 : 1 in the bees hexagon r′ = 0^{inch} 125 or ⅛ ^{inch} [therefore sign] r = r′.8165 = .125.8165

= 0^{inch} 153 r−r′ = 0^{inch} 028

distance sought.

The distance from center to obtuse ∠ = r

.866 = 0^{in} 153 .866 = 0^{in} 1325 distance to ob: ∠ of Dodec = 0.1325 r′ = distance to ∠ of Heg = 0.1250

Difference = 0.0075 or ¾ of $\frac{1}{\mathrm{100}}$ inch.

ramme

Make no scruple of asking any number of explanations, as it is very little trouble to me, & saves you bother.^{3}

Yours E D

[Enclosure]^{4}

CB=R=1 CC’=R[SQUARE ROOT]2=1.414 EF=$\frac{1}{2}$FG=side of hexagon EF=EC [TIMES] tang 30^{o}=EC [TIMES] $\frac{1}{3}$ EF=EC=$\frac{2}{2}$ 2EF=FG=$\frac{2}{3}$= .8165 [DIAGRAMS HERE]

## CD annotations

*crossed pencil*; ‘Unimportant’

*added pencil*

*Bottom of first page*: ‘0.028 0.056 0.25 0.306 = diameter of sphere’; ‘sphere rather more than $\frac{1}{\mathrm{20}}$ inch larger than hexagon’

*pencil*.

*Enclosure*: ‘or one side of hexagon = radius’; ‘One side of Hexagon in circle equals radius of circle.’

*pencil*\note

^{5}

## Footnotes

*Correspondence*vol. 3, letter from E. A. Darwin, [May 1844 – 1 October 1846]).

## Letter details

- Letter no.
- DCP-LETT-2278
- From
- Darwin, E. A.
- To
- Darwin, C. R.
- Sent from
- unstated
- Physical description
- 2pp †,

## Summary

Gives calculations on the structure of bees’ cells.

## Please cite as

Darwin Correspondence Project, “Letter no. 2278,” accessed on 13 February 2016, http://www.darwinproject.ac.uk/DCP-LETT-2278