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 8 December 2016, http://www.darwinproject.ac.uk/DCP-LETT-2283