238 



Marvels of Insect Life. 



waste, and they have learned to make the maximum structure out of the minimum 

 of material. That is the reason for the six-sided shape of the cell. All the solitary 

 bees make their burrows cylindrical, based upon the form of their bodies, or at least 

 of the body revolved on its own axis, as they have to revolve in finishing off their 

 excavation. Now, though the hexagonal cell admirably fits the c\dindrical body 

 of the bee-grub, it cannot be modelled upon the bodv of the worker-bee. If the 

 individual cehs of the comb were fashioned separately as cylinders, and then a 

 number of them were brought together, under equal pressure they would form 

 hexagons ; but they arc not made separately but are built in a mass, and every 

 part of the walls of one cell forms part of the wall of a neighbouring cell. This is 

 even so with the base of the cell, which forms part of the base of three cells on the 

 other side of the comb. To human artificers the task would necessitate a resort 

 to mathematics, but the worker-bee issues from the chrysafis fully competent to 

 undertak<' the task without swallowing the books of Euclid, and without parental 



instruction even. Pure " rule of thumb " prac- 

 tice ; but even so, the mathematicians have failed 

 to find any flaw in its results ; indeed, there is 

 a well-known record of a mathematician's work 

 being corrected in a sense bv the bees. Maraldi, 

 a famous mathematician in the early part of the 

 eighteenth century, took an interest in bees, and 

 invented a glass hive in which he could observe 

 them at work. He found that the bottoms of the 

 cells formed an inverted pyramid, and that they 

 were hexagonal like the walls, but formed of three 

 lozenge-shaped plates. His mathematical mind 

 was curious to know if the bees were mathemati- 

 cians also, so accurate did their work appear to 

 the eye. So, with great care, he measured the 

 angles of these lozenges, and found that the 

 greater angles were 109° 28', and the lesser ones 

 70° 32'. Reaumur, who knew of IMaraldi's 

 calculations, and suspected that such prevision on the part of the bee 

 had relation to the desire for economy in the use of the precious wax, 

 thought to test the matter from that point of \'iew by propounding this 

 problem to Konig, a noted geometrician : " What sh(^uld be the angles of 

 a hexagonal cell with a pyramidal bottom formed of three similar and c(]ual 

 rhomboid plates, so that the least matter possible might enter into its con- 

 struction T' Konig, it should be explained, knew notliing of Maraldi's measure- 

 ments. Konig employed the infinitesimal calculus, and found that the great angles 

 of the rhombs should be 109'' 26', and the small angles 70° 34'. Here was a surprising 

 agreement between theory and i:)ractice ! There for a time the matter rested, 

 and then Maclaurin, a Scots mathematician, took a turn at the problem i)roi)ounded 

 to Konig by Reaumur. The results he arrived at agreed precisely with the measure- 

 ments of Maraldi ; and it was then endeavoured to discover how Kiuii-' had made 



Photo by J 'H. Baslin. 



Beginning of Comb Structure. 



.■\ miinbcr of wax-makers deposit their prodvicts in 

 a little heap, and a cell-maker then begins to 

 excavate in it the bases of cells from which the 

 cell-walls are built tip. 



