18 THE HIVE AND THE HONEY-BEE; 



for in constructing the cells, would naturally be, economy of ma- 

 terials, of room, of labor, and the greatest possible quantity of 

 internal space. M. De Reaumur employed the celebrated mathe- 

 matician, Koenig, pupil of the no less celebrated Bernouilli, to 

 ascertain what the measurement of the angles composing these 

 prisms should be, in order to obtain the above requisites ; and 

 the result of his calculations showed the exquisite nicety with 

 which instinct enabled the bees to work. I shall explain in the 

 words of Dr. Bevan : — 



" The partition which separates the two opposing rows of cells, 

 and which occupies, of course, the middle distance between their 

 two surfaces, is not a plane, but a collection of rhombs, there 

 being three at the bottom of each cell ; the three together form 

 in shape a flattened pyramid, the basis of which is turned towards 

 the mouth of the cell ; each cell is in form, therefore, a hexagonal 

 prism, terminated by a flattened trihedral pyramid, the three sides 

 of which pyramid are rhombs, that meet at the apex by their 

 obtuse angles. 



" The union of the lozenges in one point, in addition to the 

 support which it is the means of afibrding to the three partitions 

 between opposing cells, is also admirably adapted to receive the 

 little egg, and to concentrate the heat necessary for its incubation. 

 Each obtuse angle of the lozenge or rhombs forms an angle of 

 110 degrees, and each acute one an angle of about 70 degrees. 

 M. Maraldi found, by mensuration, that the angles of these rhombs, 

 which compose the base of a cell, amounted to 109 degrees and 

 28 seconds, and 70 degrees and 32 seconds ; and the famous 

 mathematician, Koenig, pupil of the celebrated Bernouilli, having 

 been employed for that purpose by M. Reaumur, has clearly 

 shown, by the method of infinitesimals, that the quantity of these 

 angles, using the least possible wax, in the cell of the same ca- 

 pacity, should contain 109 degrees 26 seconds, and 10 degrees 

 and 24 seconds. This was confirmed by the celebrated Mr. Mac 

 Lauren, who very justly observes, that bees do truly construct 

 their cells of the best figure, and with the utmost mathematical 

 exactness." It will be seen, then, that, in their architecture, the 

 bees obtain the requisites wliich I above enumerated. 



Perhaps the following is the most wonderful of Huber's dis- 

 coveries : The design of every comb is sketched out, and the rudi- 

 ments laid by one single bee, who forms a block from a rough mass 

 of wax, from materials furnished him by hosts of indusiriom 



