HYMENOPTERA. 



325 



of each cell, when one has studied their arrangement, geometr}'- seems 

 to have guided the design for the whole work, and to have presided 

 over its execution. One finds that all the advantages which could 

 have been desired are here combined. The bees seem to have had 

 to solve a problem containing conditions which would have made the 

 solution appear to be difficult to many geometricians. This problem 



Fig. 317.— Cells constructed by Bees. 



may be thus enunciated :— Given a quantity of matter, say of wax, it is 

 required to form cells which shall be equal and similar to each other, 

 of a determined capacity, but as large as possible in proportion to the 

 quantity of matter which is employed, and the cells to be so placed 

 ^that they may occupy the least possible space in the hive. To satisfy 

 this last condition, the cells should touch each other in such a manner 

 ithat there may remain no angular space between them, no gap to fill 

 up. The bees have satisfied these conditions, and at the same time 

 they have satisfied the first conditions of the problem in making cells 

 which are tubes having six equal sides, or in other words, hexagonal 

 tubes We see still further that the best thing the bees 



