REV. n. E. PEEL— BEES AND BEE-KEEPING. 193 



to assume its hexagonal or six-sided form. Each, cell is perfect in 

 itself, and has six sides of its own, so that the side of one cell 

 does not form a party wall to the cell adjoining, as it seems to do 

 in this model which I hold in my hand, but each wall is spi'ead upon 

 the outside of the adjoining one. The cells have been separated 

 in order to prove this curious fact. Eveiy wall of each cell is 

 varnished over with a thin layer of propolis. This is a gummy 

 substance which the bees obtain from certain trees, more especially 

 from the horse-chestnut. Every one must be familiar with the 

 sticky substance that coats the buds of this tree, and guards them 

 from the weather. Had it not been for this varnish of propolis, 

 the separate walls would soon merge into one through the heat of 

 the hive. Most living creatures make their nests in a circular 

 form, most probably from their fixing themselves on their feet as 

 a pivot, and working round them in a circle with their jaws. If 

 the bees did not place so high a value on wax, their cells would 

 probably be cylincbical also, but their economy as regards this 

 precious substance leads them to scrape away as much as can be 

 spared at the junction of the cells. If a cylinder be surrounded 

 by other cylinders of equal diameter, six will exactly reach round 

 it, and if the points of junction of the central cylinder were 

 scooped away, the cylinder would become six-sided. The first 

 set of cells which a bee makes upon the frame on the top of the 

 skep are formed in this manner ; they are circular at the com- 

 mencement, and made hexagonal afterwards; but the bee, when 

 once it has a hexagonal model on which to work, does not trouble 

 itself to build cylinders and then cut away the angles, but fabricates 

 hexagonal cells at once, only the first set being made on the cylin- 

 drical principle. 



It will be interesting here, I think, to remind you of the wonder- 

 ful testimony to the accuracy of mathematical science which has 

 been borne by the work of the honey-bee. The base of each cell 

 consists of three lozenge- shaped plates of wax. Many years ago, 

 at the beginning of this century, Maraldi, the original inventor of 

 a glass hive, being struck with the fact that these lozenge- shaped 

 plates always had the same angles, took the trouble to measure 

 them, and found that in each lozenge the large angles measured 

 109° 28', and the smaller 70° 32', the two together making 180°, 

 the equivalent of two right angles. Some time afterwards, Reaumur, 

 thinking that this remarkable uniformity of angle must have some 

 connexion with that economy of space which is so striking a feature 

 in the construction of the honey-comb, hit upon a very ingenious 

 plan to ascertain whether his surmises were correct. Without 

 mentioning his reasons for the question, he asked Koenig, the 

 mathematician, to make the following calculation : — " Given an 

 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 calculation and 

 found that the Lirge angles ought to be 109° 26', and the smaller 

 TO"" 34', together 180°, being a difference of only two minutes less 



