BEES AND WASPS ARCHITECTURE. 171 



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 planes 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 mathematicians, particularly by the ingenious Maclaurin, 

 by a fluctionary calculation, which is to be found in the Transac- 

 tions of the Royal 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 



1 Handcock on Instinct, p. 18. 



