THE AMERICAN BEE JOURNAL AND GAZETTE. 



151 



wTiose captain Jiappened to use a copy of the 

 same Lo garithmic tables for calculaiiny Ms longi- 

 tudes. 



Now let us see how this heautiful lozenge is 

 made. There is not the least difhculty iu 

 drawing it. Make any square, A B C D, (Fig. 

 2,) and draw the diogoual A C. 



Fig. 2. 



Produce B A toward F and A D both ways 

 to any distance. 



Make A E and A G equal to A C, and make 

 A F equal to A B. Join the points E F G B, 

 and you have the required figure. 



Mow comes the beautiful point. If we take 

 A B as 1, being one side of tlie square on which 

 the lozenge is founded, A E and A G will be 

 equal to the square of 2, and E F, F G, and B E 

 will be equal to the square of 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 

 will refer to Fig. 3, he will see how the theory 



Fig. 3. 



may be reduced to practice. After he has 

 drawn the lozeuge-shaped figure which has just 

 been described, let him draw upon a curd-board 

 nine of them, as is shown iu the illustration, 

 Fig 4. Then let him cut out the figure, and 



draw his pen-knife half through the card-board 

 at all the lines of junction. He will then find 

 that the card-l)oard will fold into an exact model 

 of a bee-cell, the three lozenges which project 

 from the sides forming the base, and the others 

 the sides. This cell will of course have very 

 short sides; but by the simple expedient of 

 widening the lozenges whicli form tlic sides, 

 without altering the angles, the imitation cell 

 can be made of any desired length. 



Fig. 4. 



The best way of showing this beautiful struc- 

 ture is to make two models, one to lie flat or be 

 folded and opened at discretion, and the other 

 formed into a cell, and the angles written on 

 the card-board. A little gummed paper will 

 hold the sides together, so that the model can 

 be handled without breaking. A very amusing 

 puzzle may be formed by cutting out the nine 

 lozenge-shaped pieces of card-board, and re- 

 questing that they may be so put together as to 

 form the model of a bee-cell. 



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 thai the cells are not placed 

 opposite to each other, but that the three lozen- 

 ges which form the base of one cell form part of 

 the base of three other cells, as is seen iu Fig. 8. 

 Thus a still further economy of material is at- 

 tained, while the strength is enormously in- 

 creased, each of the edges formed by the junction 

 of two lozenges making a buttress which per- 

 forms precisely, the same oflice as the buttresses 

 of architecture do. 



The same principle is observable throughout 



