From E. A. Darwin [before 8 June 1858]1
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
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
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.
Make no scruple of asking any number of explanations, as it is very little trouble to me, & saves you bother.3
Yours E D
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]
Gives calculations on the structure of bees’ cells.
Please cite as
Darwin Correspondence Project, “Letter no. 2278,” accessed on 27 May 2016, http://www.darwinproject.ac.uk/DCP-LETT-2278