From E. A. Darwin [8 June 1858]1
I find I cannot draw a ⊙ round your [DIAGRAM HERE] two points, as the difference is so small only about a 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 HERE] obtuse ∠
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.
Over the page I will draw another little diagram to fix the positions of the acute ∠s
P A W N S E P 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
No 1 A d a c f K b C D e B No 2 A a C f k b D e B 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 = ae or Ke
Kc = eb = side of rhomb The obtuse ∠ at c is in the plane of the paper [therefore sign] Kc = radius of ⊙ passing thro’ obtuse ∠s Kb = 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
Encloses projections and models relating to geometry of bees’ cells.
Please cite as
Darwin Correspondence Project, “Letter no. 2283,” accessed on 20 October 2016, http://www.darwinproject.ac.uk/DCP-LETT-2283