210 THE LORE OF THE HONEY-BEE 



these figures, was much impressed by them, and de- 

 termined to find out the reason why the bee made 

 such constant choice of this particular shape of 

 rhomb. He therefore conceived the idea of submitt- 

 ing the bee's judgment on this cell-base question 

 to an independent authority. Without disclosing 

 his object, he propounded the following problem 

 to one of the greatest mathematicians of the day. 



"Supposing," said he, in effect, "you were 

 required to close the end of an hexagonal vessel 

 by three rhombs or diamond-shaped plates, what 

 angles must be given to these rhombs so that the 

 greatest amount of space would be enclosed by 

 the least amount of material ?" 



It was a difficult problem, but the mathematician 

 worked it out at last, and his answer was " 109° 26' 

 and 70° 34'." 



Now, the difference between the calculation of 

 the man and the calculation of the bee was an 

 exceedingly small one. No one thought of calling 

 into question the work of the man, who was pre- 

 eminent in his world of figures. It was therefore 

 accepted as a fact that the bee had made a trifling 

 mistake — so trifling, however, that, in the matter 

 of comb-building, it was of no importance. Her 

 reputation was unimpaired : to all intents and pur- 

 poses the honey-cell was still a perfect example of 

 utmost capacity secured by least material. 



But another mathematician — a Scotsman this 

 time — went over the whole business again, and he 



