Paper, 'Second note on the geometrical construction of the cell of the honey bee' by Henry Hennessy

Description

Hennessy writes: 'If from the intersections of the diagonals of the three lozenges forming the apex of the cell, perpendiculars be erected, these will meet at a point on the cell’s axis, and each of them is manifestly the radius of a sphere tangent to the three lozenges. A plane passing through a radius and the axis passes through the short diagonal, e, of the lozenge whose length is h√(3/2); using the notation and results of the paper above cited. The distance intercepted on the axis by a perpendicular let fall from the middle of the lozenge is equal to x = h/(2√2), and as this perpendicular is manifestly equal to √(¼e^2—x^2), and as we have evidently— r/√(¼e^2—x^2) = e/2x, we obtain r = ½h√3.' For Hennessy's earlier investigations into the geometrical construction of the cell of the honey bee, see PP/7/11 and PP/9/14.

Annotations in pencil and ink.

Subject: Mathematics / Geometry

Received 21 February 1887. Read 17 March 1887.

A version of this paper was published in volume 42 of the Proceedings of the Royal Society as 'Second note on the geometrical construction of the cell of the honey bee (‘Roy. Soc. Proc.,’ vol. 39, p. 253, and vol. 41, p. 442)'.

Reference number

PP/10/21

Earliest possible date

1887

Physical description

Ink and graphite pencil on paper

Page extent

2 pages

Format

Manuscript