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

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Discusses geometry related to the structure of bees' cells. Encloses notes and diagrams dealing with intersections of spheres.

## Summary Add

## Transcription

diagram of your basin if I have understood it rightly, & marked the distances
on it. A section passing thro. AF would be an equilateral
▵ and a little bit higher an irregular hexagon

I dont think it is possible to draw the intersections of spheres in a simpler manner
than the diagrams I return, they are all flat on the paper & real
dimensions. If you have 3 spheres only intersecting
the central one you will have

If you take a potato and slice it off at latitude 45^{o}, you will have the
circle of intersection of 2 spheres ^{o}
Equator P

You have a deal of trouble before you with carriage & horses worse than Bees cells

E D

[Enclosure 1]}

^{in}^{s} of rhomb =
0^{in}

[Enclosure 2]

I have drawn you several intersections separately in order not to confuse the drawing
& you. I. Projection of ⊙ of intersection parallel to the
paper. By way of practise in projections consider your eye to be in the center of one
sphere looking at the center of other sphere, or rather looking along the line joining
the centers of spheres then the large ⊙ is the projection of both spheres
& the small ⊙, the projection of intersection half way. If the
intersection plane is perpendicular to the paper then the figure to the right represents
it. Or you may consider the circle of intersection to be a parallel of latitude
45^{o} ii. Two spheres intersecting Then if the 2 circles are
inclined to one another at 120^{o} (∠ of hexagon) the figure will be
the ⊙ EHF with part cut off by EF iii a row of spheres the centers all in the
same plane IV. Two intersections the same as at iii. If they are inclined at
120^{o} & a 3^{rd} sphere intersecting them Imagine V to
be so placed that A′ rests upon A, B′ upon B, C′ upon C,
then the figure of V will be the semicircle C′GB′ bounded by the
half rhomb C′A′B′. ^{s}, CAF, BAF &
C′A′B′ form an obtuse ∠ of Dodec, & ABH,
A′B′P, form 2 of the plane ∠^{s} of
the acute ∠ of Dodec the other 2 being formed by the adjacent
spheres. [DIAGRAM 1] 1 P A B K K Sphere Intersec 45^{o} [DIAGRAM
2] ii Sphere Intersect ⊙ G K K H F [DIAGRAM 3] iii Sphere ⊙ of
Intersection Qx = ^{inch}

ED

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- f1 2287.f1
Dated by the postmark on a cover associated with the letter in DAR 162.1: 51/9. - +
- f2 2287.f2
See the first enclosure. - +
- f3 2287.f3
See the second enclosure. - +
- f4 2287.f4
See letter to W. E. Darwin, [20 June 1858]. - +
- f5 2287.f5
The enclosure is in DAR 162.1: 48/3. - +
- f6 2287.f6
The enclosure is in DAR 162.1: 51/1–8. The diagram labelled ‘iii’ has other annotations by CD which have not been transcribed.