BEES AND V7ASPS — ARCHITECTUKE. 
173 
the most astonishing products of instinct that are pre- 
sented in the animal kingdom. A great deal has been 
written on the practical exhibition of high mathematical 
principles which bees display in constructing their combs 
in the form that secures the utmost capacity for storage 
of honey with the smallest expenditure of building 
material. The shortest and clearest statement of the 
subject that I have met with is the following, which has 
been given by Dr. Keid : — 
There are only three possible figures of the cells which can 
make them all equal and similar, without any useless interstices. 
These are the equilateral triangle, the square, and the regular 
hexagon. Mathematicians know that there is not a fourth way 
possible in which a plane may be cut into little spaces that 
shall be equal, similar, and regular, without useless spaces. Of 
the three figures, the hexagon is the most proper for convenience 
and strength. Bees, as if they knew this, make their cells 
regular hexagons. 
Again, it has been demonstrated that, by making the bottoms 
of the cells to consist of three plants meeting in a point, there 
is a saving of material and labour in no way inconsiderable. 
The bees, as if acquainted with these principles of solid 
geometry, follow them most accurately. It is a curious mathe- 
matical problem, at what precise angle the three planes which 
compose the bottom of a cell ought to meet, in order to make 
the greatest possible saving, or the least expense of material and 
labour. This is one of the problems which belong to the higher 
parts of mathematics. It has accordingly been resolved by 
some math ematicians, particularly by the ingenious Maclaurin, 
by a fluctionary calculation, which is to be found in the Transac- 
tions of the Boyal Society of London. He has determined 
precisely the angle required, and he found, by the most exact 
mensuration the subject would admit, that it is the very angle 
in which the three planes in the bottom of the cell of a honey- 
comb do actually meet. 1 
Marvellous as these facts undoubtedly are, they may 
now be regarded as having been satisfactorily explained. 
Long ago Buffon sought to account for the hexagonal 
form of the cells by an hypothesis of mutual pressure. 
Supposing the bees to have a tendency to build tubular 
Handcock on Instinct* p, 18* 
