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Darwin Correspondence Project

From E. A. Darwin   [8 June 1858]1

Dear Charles

I find I cannot draw a ⊙ round your diagram two points, as the difference is so small only about a 170 or 80 of an inch.

I send you 2 more projections as the more points of view you see it in the better2

I also send you some rhombs cut out, with flaps to fasten over the edges, & I advise you to begin with the flap (A)3

They are not the same size as Millers,4 & I do not know if you have any reason for that particular size.

Also a pyramid, with 2 circles on the base to be raised up & the circle on the short diameter will show you exactly how much the obtuse ∠’s are within the sphere diagram

12 of these pyramids would make the Dodec.

You will be surprized how firm the model will feel when put together, but dont be in a hurry & let one flap dry before you paste another,

When you have got the model in your hand, & hold them in the same position as my diagrames, they will all become quite clear.

I think I have answered all your questions.

ED

Over the page I will draw another little diagram to fix the positions of the acute ∠s

diagram
N E S W equator
S P N P’ meridian
W P E P’ East & West circle
6 acute angles at the letters
8 obtuse angles (A) in the center of the quadrants

[Enclosure]5

diagram
[No 1]
AB vertical axis passing thro’ acute ∠s A & B
CD horizontal axis passing thro’ centers of 2 Rhombs
K axis perpendicular to CD & AB or the plane of the paper
a b e f } rhomb parallel to paper, natural size
diameter bf = AC = side of square in ⊙
diameter ae = KA radius of ⊙
a b c d— rhomb oblique to the paper
cb is parallel to ae and = 12 ae or Ke
.:. Kc = eb = side of rhomb

The obtuse ∠ at c is in the plane of the paper

.:. Kc = radius of ⊙ passing thro’ obtuse ∠s

Kb = 12 distance of centers = distance from center of sphere to rhomb
[No 2]
The same as No 1 but turned round the axis AB 45o.
The 4 rhombs are all at ∠ 45o with paper, but fAfB are the long diameter of the vertical plane, & fC, fD long diameters in the horizontal plane

Footnotes

Dated by the postmark on a cover associated with the letter (DAR 162: 50).
See enclosure.
The figures have not been found.
See letter from W. H. Miller, [14 May 1858] and n. 2. Associated with William Hallowes Miller’s letter are two pasteboard figures labelled ‘Rhombic face of dodecahedron’ (DAR 48 (ser. 2): 1). The angles of the rhombs are marked ‘70o 31.7’’ and ‘109o 28.3’’. See Natural selection, p. 513 and n. 1, where the angles of a rhombic face of a bee’s cell are discussed.
The diagrams are in DAR 162: 48/5 and 48/6.

Bibliography

Natural selection: Charles Darwin’s Natural selection: being the second part of his big species book written from 1856 to 1858. Edited by R. C. Stauffer. Cambridge: Cambridge University Press. 1975.

Summary

Encloses projections and models relating to geometry of bees’ cells.

Letter details

Letter no.
DCP-LETT-2283
From
Erasmus Alvey Darwin
To
Charles Robert Darwin
Sent from
unstated
Source of text
DAR 162: 48a, 50
Physical description
ALS 4pp, encl 3pp

Please cite as

Darwin Correspondence Project, “Letter no. 2283,” accessed on 23 April 2024, https://www.darwinproject.ac.uk/letter/?docId=letters/DCP-LETT-2283.xml

Also published in The Correspondence of Charles Darwin, vol. 7

letter