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Letter 2278

Darwin, E. A. to Darwin, C. R.

[before 8 June 1858]

    Summary Add

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    Gives calculations on the structure of bees' cells.

Transcription

Dear Charles.

To make sure that I now understand look at my diagram. 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′ = 0inch125 or ⅛ inch [therefore sign] r = r′.8165 = .125.8165

= 0inch153 r−r′ = 0inch028

distance sought.

The distance from center to obtuse ∠ = r

.866 = 0in153 .866 = 0in1325 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.

Yours E D

[Enclosure]

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]

    Footnotes Add

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    f1 2278.f1
    Dated by the relationship to the following letter.
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    f2 2278.f2
    See enclosure.
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    f3 2278.f3
    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]).
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    f4 2278.f4
    The enclosure is in DAR 48 (ser. 2): 46 in association with CD's notes on bees' cells.
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    f5 2278.f5
    The note is in DAR 162: 48/2.
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