A set of questions CD prepared for his meeting with WHM to discuss the geometry of bees' cells.
– Bees can make apparently true cylinders & spheres. (2) They never
begin one cell at time always several (3) they can judge distance to certain extent,
& (4) those that make their spheres or cylinders so that if completed, would
intersect make an intermediate flat wall. Then assume perfect judge of
distance, I thought that all angles might follow, for I c
(1) Question ‘planes of intersection’ ‘all the points of intersection united into an intermedial plane.’
(2) Distance in mere circle or section of cylinder = 1 side of equi-lat [DIAGRAM HERE] in the circle—each circle or mathematical cylinder being after the first two drawn at that distance (called [DIAGRAM HERE]) from 2 others.— Can this not be applied to mathematical spheres, saying from 3 others, after three have been described.
(3) Must I say ‘rhombic dodecahedron’ of crystallography; must I say math-ematical or ideal spheres & cylinders.
(4) About the angle of 120
4 (bis) May I quote you as authority about the rhombs &c, produced by intersection of the spheres?
(5) Show my statement of spheres in two planes.—
(6) About the rhombic bases holding most. Minimum of Wax.
(7) About Hexagons being reduced in size & their first commencement against a plane surface.—
- f1 2255a.f1The recipient of the questions listed in this memorandum is identified by the reference in Origin to Miller as the authority for statements about the geometry of bees' cells (see also n. 10, below).
- f2 2255a.f2The date is inferred from CD's statement in his letter to J. D. Hooker, 10 April , that he was going to London on 15 April ‘to meet Miller to get wisdom on the geometry of Bees cells’. See also the letter to H. N. Shaw, 16 April , in which CD stated that he ‘was in London yesterday’.
- f3 2255a.f3‘My notion … it.’ appears to have been added at a later date, presumably after CD's meeting with Miller on 15 April. CD refers to the theory of the formation of bees' cells put forward by George Robert Waterhouse in [Waterhouse] 1835, which was criticised by Henry Peter Brougham in Brougham 1839. Brougham had pointed out flaws in Waterhouse's geometry (Brougham 1839,1: 270, 279). These pages of Brougham 1839 are among those marked in CD's copy (Darwin Library–CUL), which he recorded having read in 1840 (Correspondence vol. 4, Appendix IV,119: 7a). In his notes on Brougham's account of bees' cells, CD wrote: ‘It is curious as L
dB. shows that W. makes the [’he‘ del] bottoms of cylinders intersect, whereas the cylinders do not intersect.’ (DAR 48 (ser. 2): 13). The theory that CD later expounded was a modified version of Waterhouse's theory, but developed from a more accurate geometrical model (Origin, pp. 225–7). See letters from W. H. Miller, [14 May 1858], and from E. A. Darwin, [May–June 1858], [before 8 June 1858],[8 June 1858], and [after 8 June 1858].
- f4 2255a.f4The phrase ‘planes of intersection’ has been double underlined in pencil then ink; ‘all … plane.’ has been deleted in ink.
- f5 2255a.f5Before this paragraph, CD wrote ‘letter (2)’ in pencil. Presumably this refers to a letter Miller wrote to CD, which is now lost.
- f6 2255a.f6The passage ‘of crystallography’ was deleted in pencil, then in ink; above it CD wrote in pencil ‘Afterw dodecahedron’, and over this he wrote, in ink, ‘& afterwards only dodecahedron’.
- f7 2255a.f7CD deleted ‘mathematical’ in ink and double underlined ‘ideal’.
- f8 2255a.f8‘Yes’ has been added by CD.
- f9 2255a.f9‘Yes’ has been added by CD.
- f10 2255a.f10‘Send M.S. to him’ was added. For the passage to which CD refers, see Origin, pp. 226–7.
- f11 2255a.f11‘Yes.’ has been added.
- f12 2255a.f12CD wrote: ‘—Must be unequal’.