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Darwin Correspondence Project

DCP-LETT-2278

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 1100 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=12FG=side of hexagon EF=EC [TIMES] tang 30o=EC [TIMES] 13 EF=EC=22 2EF=FG=23= .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 120 inch larger than hexagon’ pencil . Enclosure: ‘or one side of hexagon = radius’; ‘One side of Hexagon in circle equals radius of circle.’ pencil \note5
Erasmus says Dodecahedron diameter is radius 2. In Wasps nest, hexagon = radius of sphere (on hexagonal theory) & saucer up to lower part of festoon will equal half radius.— from angle to angle of hexagon of course = twice radius. [therefore sign] saucer 14 of diameter of hexagon.—

Footnotes

1
Dated by the relationship to the following letter.
2
See enclosure.
3
CD was eager to revise his calculations relating to the construction of bees’ cells (see letter to W. E. Darwin, [26 May 1858]). Erasmus Alvey Darwin had helped him in the past with geometrical problems (see letter from E. A. Darwin, [May–June 1858], and Correspondence vol. 3, letter from E. A. Darwin, [May 1844 – 1 October 1846]).
4
The enclosure is in DAR 48 (ser. 2): 46 in association with CD’s notes on bees’ cells.
5
The note is in DAR 162: 48/2.

Summary

Gives calculations on the structure of bees’ cells.

Letter details

Letter no.
DCP-LETT-2278
From
Darwin, E. A.
To
Darwin, C. R.
Sent from
unstated
Source of text
DAR 162: 48b
Physical description
2pp †, CD note

Please cite as

Darwin Correspondence Project, “Letter no. 2278,” accessed on 25 August 2016, http://www.darwinproject.ac.uk/DCP-LETT-2278

letter