THE HIVE BEE . 
263 
comb, hit upon a very ingenious plaiv Without mentioning his 
reasons for the question, he asked Koenig, the mathematician, 
to make the following calculation. Given a hexagonal vessel 
terminated by three lozenge-shaped plates ; what are the angles 
which would give the greatest amount of space with the least 
amount of material ? 
Koenig made his calculations, and found that the angles were 
109° 26' and yo° 34', almost precisely agreeing with the measure- 
ments of Maraldi. The reader is requested to remember these 
angles. Reaumur, on receiving the answer, concluded that the 
Bee had very nearly solved the difficult mathematical problem, 
the difference between the measurement and the calculation 
being so small as to be practically negatived in the actual con- 
struction of so small an object as the bee-cell. 
Mathematicians were naturally delighted with the result of 
the investigation, for it showed how beautifully practical 
science could be aided by theoretical knowledge, and the con- 
struction of the bee-cell became a famous problem in the 
economy of nature. In comparison with the honey which the 
cell is intended to contain, the wax is a rare and costly sub- 
stance, secreted in very small quantities, and requiring much 
time for its production ; it is therefore essential that the quan- 
tity of wax employed in making the comb should be as little, 
and that of the honey contained in it as great, as possible. 
For a long time these statements remained uncontroverted. 
Anyone with the proper instruments could measure the angles 
for himself, and the calculations of a mathematician like Koenig 
would hardly be questioned. However, Maclaurin, the well- 
known Scotch mathematician, was not satisfied. The two 
results very nearly tallied with each other, but not quite, and 
he felt that in a mathematical question precision was a neces- 
sity. So he tried the whole question himself, and found 
Maraldi’s measurements correct, namely, 109° 28', and yo° 32'. 
He then set to work at the problem which was worked out 
by Koenig, and found that the true theoretical angles were 
1 69° 28', and yo q 32', precisely corresponding with the actual 
measurement of the bee-cell. 
