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′ = 0inch.125 or ⅛ inch [therefore sign] r = r′.8165 = .125.8165
= 0inch.153 r−r′ = 0inch.028
distance sought.
The distance from center to obtuse ∠ = r
.866 = 0in.153 .866 = 0in.1325 distance to ob: ∠ of Dodec = 0.1325 r′ = distance to ∠ of Heg = 0.1250
Difference = 0.0075 or ¾ of 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=FG=side of hexagon EF=EC [TIMES] tang 30o=EC [TIMES] EF=EC= 2EF=FG== .8165 [DIAGRAMS HERE]
CD annotations
Footnotes
Bibliography
Correspondence: The correspondence of Charles Darwin. Edited by Frederick Burkhardt et al. 28 vols to date. Cambridge: Cambridge University Press. 1985–.
Summary
Gives calculations on the structure of bees’ cells.
Letter details
- Letter no.
- DCP-LETT-2278
- From
- Erasmus Alvey Darwin
- To
- Charles Robert Darwin
- Sent from
- unstated
- Source of text
- DAR 162: 48b
- Physical description
- ALS 2pp †, CD note
Please cite as
Darwin Correspondence Project, “Letter no. 2278,” accessed on 22 May 2022, https://www.darwinproject.ac.uk/letter/?docId=letters/DCP-LETT-2278.xml
Also published in The Correspondence of Charles Darwin, vol. 7