The date is that of the postmark on the accompanying cover. It is not clear, however, whether the cover belongs with the material now enclosed in it (see nn. 2 and 3, below).

The two enclosures transcribed here are in a cover with other items, all of which relate to the geometry of bees’ cells. One is a model for a bee’s cell based upon a rhombic dodecahedron, which may have been made by William Erasmus Darwin (see letter to W. E. Darwin, [23 May 1858]). No covering letter from Miller has been located.

The ‘card rhomb’ to which Miller refers is with these instructions in DAR 48 (ser. 2): 1. There is also another similar cardboard figure marked by Miller: ‘This is not very accurately drawn.’ Both figures represent the rhombic face of a dodecahedron and were labelled as such by Miller. The angles are also given.

These instructions were written on a large piece of tissue paper on which Miller had sketched a rough plan for constructing a model of a bee’s cell based on part of an elongated rhombic dodecahedron. Miller indicated the sections to be folded and glued together. Miller’s first attempts to represent a bee’s cell had been erroneous (see letter to W. E. Darwin, [3 May 1858]). CD had enlisted Miller’s assistance after realising that there were problems with the geometry of George Robert Waterhouse’s theory (see letter from G. R. Waterhouse, 13 February 1858 and letter to W. H. Miller, [15 April 1858]). In his notes on [Waterhouse] 1835 (DAR 48 (ser. 2): 66a), CD remarked: ‘W. did not get aid of mathematician, [as curious] & necessary advantage which I owe to kindness of Professor Miller of Cambridge.’ See Origin, p. 226, where CD expressed his indebtedness to Miller for calculations relating to bees’ cells.

Kopp 1849.