430 HOMES WITHOUT HANDS. 



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 uncontioverted. 

 Any one 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 necessity. So 

 he tried the whole question himself, and found Maraldi's measure- 

 ments correct, namely, 109° 28', and 70° 32'. 



He then set to work at the problem which was worked out by 

 Kceuig, and found that the true theoretical angles were 10.9° 28', 

 and 70° 32', precisely corresponding with the actual measui-e- 

 nient of the bee-cell. 



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 Kceuig, 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 ivhose 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 he equal to v'2, and EF, FG, GB, and BE, wiU 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 wiU refer to fig. 4, he will see liow the 

 theory may be reduced to practice. After he has drawn the 



