96 THE BUILDING OF BEES. 
without any useless spaces between them. These are the equi- 
lateral triangle, the square, and the regular hexagon. It is well 
known to mathematicians, that there is not a fourth way possible 
in which a plane may be cut into little spaces that shall be equal, 
similar, and regular, without leaving any interstices.” 
An equilateral triangle would have been impossible for 
an insect with a round body to build. A circle seems to be 
the best shape for the development of the larve ; but such 
a figure would have caused a needless sacrifice of space, 
materials, and strength. The body of the immature insect, 
as it undergoes its changes, is charged with a superabun- 
dance of moisture, which passes off through the reticulated 
cover of its cell; may not a hexagon, therefore, while ap- 
proaching so nearly to the shape of a circle, as not to 
incommode the young bee, furnish, in its six corners, the 
necessary vacancies for a more thorough ventilation? 
Is it credible that these little insects can unite so many 
requisites in the construction of their cells? 
213. The fact is that the hexagonal shape of the cells is 
naturally produced, and wihout any calculation, by the bee. 
She wants to build each cell round; but as every cell 
touches the next ones, and as she does not wish to leave any 
space between, each one of the cells flattens at the contact, 
as would soap bubbles if all of the same diameter. It is the 
same for the lozenges of the bottom. ‘The bee, wanting the 
bottom of the cell concave inside, makes it, naturally, con- 
vex outside. As this convexity projects on the opposite 
side of the median line, the bee who builds the opposite 
cells begins, naturally, on the tip of the convexity, the 
walls of cells just begun, since she wants also to make their 
bottom concave. The final result is that one-third of the 
bottom of each of three cells makes the bottom of the one 
cell opposite, and each one of the lozenges is flattened, so 
as not to encroach on the opposite cells. 
214. The cells are not horizontal, but inclined from the 
