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XX 71. On the Mathematics of Bees' Cells, 

 By Prof. J. D. Everett; F.R.S.'^ 



EOR the literature of this subject reference may be made 

 to a critical summary by Dr. Glaisher in the Philo- 

 sophical Magazine for August 1873, which contains an 

 exposure of seyeral popular errors. Later results of obser- 

 vation will be found in Darwin's ' Origin of Species/ 

 pp. 221-227. 



A bees'' comb consists of cells combined in double layers. 

 Each cell has the form of a regular hexagonal prism with 3 

 of the 6 corners at one end sliced off so as to give a pointed 

 apex. The 3 faces which meet at the apex are rhom])Uses 

 symmetrically arranged, and 3 corners of each rhombus lie 

 upon edges of the hexagonal prism. Three alternate edges 

 of the prism are accordingly longer than the other three, and 

 we shall denote this difference of length by h. Then h will 

 also denote the distance of the apex from the plane of the 

 ends of the 3 longer edges. The length of a side of the 

 regular hexagon which is the cross-section of the prism will 

 be denoted by ^\ 



Any number of equal and similar sharpened prisms, con- 

 structed according to this specification, can be fitted accu- 

 rately together, in two layers, in such a way that the apex of 

 a member of one layer is inserted between three apexes 

 belonging to the opposite layer. The axis of each prism will 

 then be in line, not with an axis, but with the common edge, 

 of 3 prisms belonging to the other layer. 



The annexed diagram is specialh' designed to set forth the 

 relations of the parts in the clearest manner by projecting 

 them on a plane perpendicular to the axes of the prisms. 



The ends of the longer edges of both sets of prisms lie in 

 the same plane, which is the plane of the paper. The two 

 * Communicated by the Physical Society : read ^Nlay 8. 1903. 



