264 
STRANGE DWELLINGS. 
Another question now arose. How did this discrepancy 
occur ? How could so excellent a mathematician as Koenig 
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 mathema- 
tical 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 x /2, and EF, FG, GB, and BE, will 
be equal to A / 3, as can be seen at a glance by anyone who 
has advanced as far as the 47th proposition of the first book of 
Euclid. 
We have not yet exhausted the wonders of the bee-comb. 
If we take a piece of comb from which all the cells have 
been removed, and hold it up to the light,, we shall see that the 
cells are not placed opposite each other, but that the three 
lozenges which form the base of one cell form part of the base 
of three other cells, as is seen in fig. 2. 
It would, of course, be easy to fill many pages with the 
account of the Hive Bee and its habits ; but as this work is 
restricted to the habitations of animals, we can only look 
upon the Bee as a maker of social habitations. It will, how- 
ever, be necessary to mention the material of which the comb 
is made. 
The other hymenoptera obtain their materials from external 
sources. The hornet and wasp have recourse to trees and 
branches, and bear home in their mouths, the bundles of woody 
