THE HIVE BEE. 35 
tallied with each other, but not quite, and he felt that in 
a mathematical question precision was a necessity. So 
he tried the whole question himself, and found Maraldi’s 
measurements correct, namely, 109° 28’ and 70° 32’. 
He then set to work at the problem which was worked 
out by Koenig, and found that the true theoretical angles 
were 109° 28’ and 70° 32’, precisely corresponding with 
the actual measurement of the Bee-cell. 
Another question now arose. How did this discrepancy | 
occur ? How could so excellent a mathematician as Keenig 
make so grave a mistake? On investigation, it was found 
that no blame attached to Koenig, but that the error lay in 
the book of logarithms which he used. Thus, a mistake in a 
mathematical work was accidentally discovered by measuring 
the angles of a Bee-cell—a mistake sufficiently great to have 
caused the loss of a ship whose captain happened to use a copy 
of the same logarithmic tables for calculating his longitude. 
Now, let us see how this beautiful lozenge is made. 
There is not the least difficulty in drawing it. Make any 
square, ABCD (fig. 3), and draw the diagonal AC. 
Produce BA towards F and AD, both ways to any 
distance. 
Make AE and AG equal to AC, and make AF equal to AB. 
Join the points EFGB, and you have the required figure. 
Now comes a beautiful point. If we take AB as 1, 
being one side of the square on which the lozenge is 
founded, AE and AG will be equal to ./2, and EF, FG, 
GB, and BE, will be equal to /3, as can be seen at a 
glance by any one who has advanced as far as the 47th 
proposition of the first book of Euclid. 
Perhaps some of my readers may say that all these 
figures may be very true, but that they do not show how 
the cell is formed. If the reader will refer to fig. 4, he 
will see how the theory may be reduced to practice. After 
