THE HIVE BEE. 263 



comb, hit upon a very ingenious plan. Without mentioning his 

 reasons for the question, he asked Koenig, the mathematician, 

 to make the following calculation. Given a hexagonal vessel 

 terminated by three lozenge-shaped plates ; what are the angles 

 which would give the greatest amount of space with the least 

 amount of material ? 



Koenig m^de his calculations, and found that the angles were 

 109° 26' and 70° 34', almost precisely agreeing with the measure- 

 ments of Maraldi. The reader is requested to remember these 

 angles. Reaumur, on receiving the answer, concluded that the 

 Bee had very nearly solved the difficult mathematical problem, 

 the difference between the measurement and the calculation 

 being so small as to be practically negatived in the actual con- 

 struction of so small an object as the bee-cell. 



Mathematicians were naturally delighted with the result of 

 the investigation, for it showed how beautifully practical 

 science could be aided by theoretical knowledge, and the con- 

 struction of the bee-cell became a famous problem in the 

 economy of nature. In comparison with the honey which the 

 cell is intended to contain, the wax is a rare and costly sub- 

 stance, secreted in very small quantities, and requiring much 

 time for its production ; it is therefore essential that the quan- 

 tity of wax employed in making the comb should be as little, 

 and that of the honey contained in it as great, as possible. 



For a long time these statements remained uncontroverted. 

 Anyone with the proper instruments could measure the angles 

 for himself, and the calculations of a mathematician like Koenig 

 would hardly be questioned. However, Maclaurin, the well- 

 known Scotch mathematician, was not satisfied. The two 

 results very nearly tallied with each other, but not quite, and 

 he felt that in a mathematical question precision was a neces- 

 sity. So he tried the whole question himself, and found 

 Maraldi's measurements correct, namely, 109° 28', and 70° 32'. 



He then set to work at the problem which was worked out 

 by Koenig, and found that the true theoretical angles were 

 109° 28', and 70° 32', precisely corresponding with the actual 

 measurement of the bee-celL 



