VII] OF THE BEE'S CELL 329 



conclusion that the bees were endowed with reason: "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, suspecting indeed that it could hold more honey than 

 either of the other two." Erasmus Barthohnus was apparently 

 the first to suggest that this hypothesis was not warranted, and 

 that the hexagonal form 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, and came later, than that of its sides. In general terms 

 this arrangement was doubtless often studied and described: as 

 for instance, in the Garden of Cyrus ' " And the Combes them- 

 selves so regularly contrived that their mutual intersections 

 make three Lozenges at the bottom of every Cell ; which severally 

 regarded make three Rows of neat Bhomboidall Figures, connected 

 at the angles, and so continue three several chains throughout the 

 whole comb." But Maraldi* (Cassini's nephew) was the first to 

 measure the terminal solid angle or determine the form of the 

 rhombs in the pyramidal ending of the cell. He tells us that the 

 angles of the rhomb are 110° and 70°: "Chaque base d'alveole 

 est formee par trois rhombes presque toujours egaux et semblables, 

 qui, suivant les mesures que nous avons prises, ont les deux angles 

 obtus chacun de 110 degres, et par consequent les deux aigus 

 chacun de 70°." He also stated that the angles of the trapeziums 

 which form the sides of the body of the cell were identical angles, 

 of 110° and 70° ; but in the same paper he speaks of the angles as 

 being, respectively, 109° 28' and 70° 32'. Here a singular con- 

 fusion at once arose, and has been perpetuated in the books f- 

 "Unfortunately Reaumur chose to look upon this second deter- 

 mination of Maraldi's as being, as well as the first, a direct result 

 of measurement, whereas it is in reality theoretical. He speaks of 

 it as Maraldi's more precise measurement, and this error has been 

 repeated in spite of its absurdity to the present day ; nobody 



* Observations sur les Abeilles, Mem. Acad. Sc. Paris, 1712, p. 209. 



t As explained by Leslie EUis, in his essay "On the Form of Bees' Cells," 

 in Mathematical and other Writings, 1853, p. 353; cf. 0. Terquem, Nouv. Ann. 

 Math. 1856, p. 178. 



