146 INSECT ARTIZANS AND THEIR WORK 



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 view by propounding this 

 problem to Konig, a noted geometrician : " What 

 should be the angles of a hexagonal cell with a 

 pyramidal bottom formed of three similar and 

 equal rhomboid plates, so that the least matter 

 possible might enter into its construction ? " M. 

 Konig, it should be explained, knew nothing of 

 Maraldi's measurements. Konig employed the in- 

 finitesimal calculus, and found that the great 

 angles of the rhombs should be 109° 26' and the 

 small angles 70° 34'. Here was a surprising agree- 

 ment between theory and practice ! 



There for a time the matter rested, and then 

 Maclaurin, the Scots mathematician, took a turn 

 at the problem propounded to Konig by Reaumur. 

 The result he arrived at agreed precisely with the 

 measurements of Maraldi ; and it was then endea- 

 voured to discover how Konig had made the mis- 

 take. It was found that the book of logarithms 

 he had used as the basis for his calculations con- 

 tained an error which accounted for that difference 

 of z' in his results. So the bees led to the cor- 

 rection of the book of logarithms, whose error 

 might have led in other directions to lamentable 

 results. 



The comb is not built upwards from the base 

 but downwards from the roof. A small quantity 

 of wax is deposited by one bee, to which others add 

 in succession until sufficient is amassed for the 



