6 4 



THE HONEY-BEE. 



A further difficulty would arise with regard to the 

 storage of the honey, which finds points of attachment 

 in the angles of a hexagon, and so is less liable to 

 run out of the cells. The next matter then to settle 

 is, the magnitude of the angles at which the sides of 

 the hexagon should slope towards each other, so as 

 to be the most advantageous. Reaumur put the 

 problem in mathematical language before M. Kb'nig, 



FIG. 16 ARRANGEMENT OF CELLS. 



a skilful geometrician, thus : " To determine by cal- 

 culations what ought to be the angle 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." The result 

 of his investigations was that the angles of the rhombs 

 must be 109 26' and 70 34'. Cramer, professor of 

 mathematics in the University of Geneva, also under- 

 took the problem. His calculations, made on some- 

 what different principles from Konig's, gave for the 

 angles 109 28' 16", and 70 31' 44". Maraldi, a third 



