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 captaifi happened to use a copy of the same 

 logarithinic 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 i, 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 v/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 



