I04 THE LIFE OF THE BEE 



S7 



" There are only," says Dr. Reid, " 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 shall 

 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 

 mathematical problem at what precise angle the three planes 

 which compose the bottom of a cell ought to meet, in order 



* Reaumur suggested the following problem to the celebrated mathematician Koenig : 

 " Of all possible hexagonal cells with pyramidal base composed of three equal and 

 similar rhombs, to find the one whose construction would need the least material ? " 

 Koenig's answer was, the cell that had for its base three rhombs whose large angle was 

 109° 26", and the small 70° 34". Another savant, Maraldi, had measured as exactly as 

 possible the angles of the rhombs constructed by the bees, and discovered the larger 

 to be 109° 28", and the other 70° 32". Between the two solutions there was a difference 

 therefore of only 2". It is probable that the error, if error there be, should be 

 attributed to Maraldi rather than to the bees ; for it is impossible for any instrument 

 to measure the angles of the cells, which are not very clearly defined, with infallible 

 precision. 



The problem suggested to Koenig was put to another mathematician, Cramer, whose 

 solution came even closer to that of the bees, viz. 109° 28^" for the large angle and 70° 

 3ii"for the small. Maclaurin, correcting Koenig, gives 70° 32' and 109° 28'; M. Leon 

 Lalanne, 109° 28' 16" and 70° 81' 44". As regards this point, cf. Maclaurin, Philos. 

 Trans, of London, 1743 ; Brougham, Rech. anat. et exper. sur Its alv. des ab. ; 

 L. Lalanne, JVoie sur farc/t. des abeilles, Sf'c. 



