1878 



GLEANINGS IN BEE CTLTURE. 



by fostering and encouniging any desire 

 trait or disposition, the bees may be molde<l 

 to our will. The egg that is laid by a (lueen 

 to-day may, by proper care, be made to pro- 

 duce a queen laying eggs of tlie same Ivind 

 herself, in the short time of only 25 days, as 

 I liave explained heretofore. Well, if we 

 should pick out a queen whose progeny 

 made the thinnest comb, and rear others 

 iVom her, doing the same thing for several 

 generations, we would probably get bees 

 Avhose combs Avould break down by the 

 ^veight of the lioney. In a state of nature, 

 this extreme would correct itself, as well as 

 the other ; but the point I wish yon to see is 

 right here ; geometrical accuracy in the shape 

 of the celh can never be over done, and can 

 only he reached by absolute 'perfection ; and this 

 Hl)solvte perfectimi, the bees have been constant- 

 ly aiming at through endless ages. Is it any- I 

 thing strange, my friends, that the bees \ 

 liave got the honey comb pretty near right : 

 by this timeV I will give yon a little story, 

 and one which has been very interesting to j 

 me, from page ISO, Vol. II, Ainerican Bee 



Journal. i 



I 



If a single cell be isolated, it will be seen that the 

 sifies rise from the outer edges of the three lozen- : 

 j;es above mentioned, so that there are of course j 

 six sides, the transverse section of which g'ives a j 

 perfect hexagon. Many years ago, Maraldi, being j 

 struck with the fact that the lozenge-shaped plates | 

 A 70'32' i 



109°28' 



;o^;33' 



109^28' 



70'33' 



always hnd the snme angles, took the trouble to 

 inea*ure them, and found that in each lozenge the 

 hnrge angles measured 108 '28', and the smaller 70-32', 

 the two together making 180', the equivalent of two 

 right angles. He also noted the fact that the apex 

 of the three sided cup was formed bv the union of 

 three of the grenter angles. The three united lozen- 

 g'es are seen in the ligure above. 



Some time afterward, Keainnur, tliinking that 

 this remarkalile uniformity of angle might have 

 some eoinioctioi) with the wonderful economy of 

 sipace which is obsi^rv-ed in the V)ee-comb, hit upon a 

 very ingenious plan. W^ithout mentioning his reas- 

 ons for the question, he asked Kn:'nig, the mathema- 

 tician, to mnke the following caicuiation : Given a 

 hexagonal vessel terminated by three lozenge-shap- 

 ed i)lates, whfit are the angles which would give the 

 greatest amount of space with the least amount of 

 material? 



Ka»nigmad8 his calculations, and found that the 

 angles were 12EP2'i' and 70 '34', almost precisely agree- 

 ing with the measurements of Maraldi. The reader 

 Is requested to remember these angles. 



Roaumin-, on receiving the answei', concluded 

 that the bf^e had very nearly solved the difficult 

 mathematic;!l problem, the diderenee between the 

 meiisurcmeiif and the calculation bring so small as 

 to be practically negative in the actual construction 

 of so small an object as the bee-cell. 



Mathematicians were naturally delighted with the 

 result of the investig-ation, for it showed how beau- 

 tifully iiractical science could be aided by theoreti- 

 al knowledge; and the construction of the bee-cell 

 became a fauiovis problem in the economy of na- 

 ture. In comparison with the honej' which the cell 

 is intended to contain, the wax is a rare and costly 

 substance, secreted in very small quantities, and 

 reciuiring much time and a large expenditure of 

 honey for its production. It is therefore essential 

 that the quantity of wax employed in making the 

 ; comb should be as little, and "that of the honey 

 ; which could be stored in it as great, as possible. 

 For a long time these statements remained un- 

 controverted. Anyone with the proper instruments 

 could measure the angles f(n- himself, and the cal- 

 culations of a mathematician like Krenig would 

 ' hai-dly be questioned. However, Maclaurin, the 

 well-known Scotch mathematician, was not satii-- 

 fied. The two results very nearly tallied with each 

 I other, but not quite, and he felt that in a mathe- 

 matical question precision was a necessity. So he 

 tried the whole question himself, and found Mural- 

 di's measurement correct— namely, 100 28 , and 70°32'. 

 He then set to work at the problem which was 

 I worked out by Kcenig, and fnund that the true th(- 

 I oretical angles were 109^28' and 80^"i2', precisely cor- 

 responding with the actual measurement of the 

 bee-cell. 



Another question now arose. How did this dis- 

 crepancy occur? On investigation, it Avas found 

 that no blame attacheil to Kcrnig, bijt that the error 

 lay in the book of Logarithms which he used. Thus 

 a mistake in a mathenialicul work was accidentally 

 discovered by measuring the angles of a l)ee-cell— 

 a niistnki: xiitlirii)!!!!! tinat to have causrd the lanK of a 

 xhip irl}i)sr raptoiii hnfjjiriied to HSC a ciijtil of thr mmr 

 Liiuarithmk tahlcKfor caleulatino 7ii.s hinijitmhs. 



DIFFEIiENT KINDS OF CELLS IN THE HON- 

 EY COMB. 



The bees build two distinct, regular sizes; 

 drone, and worker cells. The worker comb 

 measures v^vy nearly live cells to the inch, 

 on an average. Some specimens average a 

 little larger, and some a little smaller ; but 

 when the comb is at all irregular, it is quite 

 apt .to be a little larger. The best specimens 

 of true worker comb, generally contain .5 

 cells within the space of an inch, and there- 

 fore this measure has been adopted for the 

 comb foundation. If there are five cells to 

 the inch, a square inch would give, on an 

 average, about 2.5 cells, and 25 on the oppo- 

 site side would make 50 young bees that 

 would be hatched from every square inch of 

 solid brood. As the artificial comb, or fdn., 

 is so much more regular than the natural 

 comb, we get a great many more bees in a 

 given surface of comb, and here, at least, 

 we can fairly claim to have improved on na- 

 ture. 



The drone comb measures just about 4 

 cells to the inch, but the bees seem less par- 

 ticular about the size of it, than with the 

 worker. They very often seem to make the 

 cells of such size as to best fill out a given 

 si>ace ; and we, accordingly, find them of 

 all sizes, from worker size all the w^ay up to 

 considerably larger tlian i of an inch in 

 width. Drones are raised in these extra 

 large cells without trouble, and honey is al- 

 so stored in them, but where they are very 



