VII] OF THE BEE'S CELL 527 



lesloisd'une severe architecture; et Euclidos lui-meme s'instruirait 

 en admirant la geometrie de ses alveoles*." Ausonius speaks of 

 the geometrica forma favorum,, and Pliny tells of men who gave a 

 lifetime to its study. 



Pappus the Alexandrine has left us an account of its hexagonal 

 plan, and drew from it the conclusion that the bees were endowed 

 Vith "a certain geometrical forethought "f- "There being, then, 

 three figures which of themselves can fill up the space round a point, 

 viz. the triangle, the square and the hexagon, the bees have wisely 

 selected for their structure that which contains most angles, sus- 

 pecting indeed that it could hold more honev than either of the 



•Y^^v;v^<"r 



Fig. 204. Portion of a honeycomb. After WiJlem. 



Other two J." Erasmus Bartholin was apparently the first to 

 suggest that the hypothesis of '"economy" was not warranted, and 

 that the hexagonal cell was no more than the necessary result of 

 equal pressures, each bee striving to make its own little circle as 

 large as possible. 



The investigation of the ends of the cell was a more difficult 

 matter than that of its sides, and came later, in general terms the 

 arrangement was doubtless often studied and described: as for 



* Ed. Mardrus, xv, p. 173. 



t (pvaLK7]v ye(i}/j.eTpiKi]u Trpbvoiav. Pappus, Bk. V; cf. Heath, Hist, of Gk. Math, ii, 

 p. 589. St Basil discusses ttiv yewixerplav t^s cro<pu}Ta.TTj<> fxeXlaoTjs: Hexaem. vni, 

 p. 172 (Migne); Virgil speaks of the pars divinae mentis of the bee, and Kepler 

 found the bees anxmd praedifas et geomet. riae suo modo capaces. 



X This was according to the "theorem of Zenodorus." The use by Pappus of 

 "economy" as a guiding principle is remarkable. For it means that, like Hero 

 with his mirrors, he had a pretty clear adumbration of that principle of minima, 

 which culminated in the principle of least action, which guided eighteenth-century 

 physics, was generalised (after Fermat) by Lagrange, inspired Hamilton and 

 Maxwell, and reappears in the latest developments of wave-mechanics. 



