HYMENOPTERA. - 325 
geometry seems to have guided the design for the whole work, 
and to have presided over its execution. One finds that all the 
advantages which could have been desired are here combined. 
The bees seem to have had to solve a problem containing con- 
ditions which would have made the solution appear to be difficult 
to many geometricians. This problem may be thus enunciated : 
given a quantity of matter, say of wax, it is required to form cells, 
which shall be equal and similar to each other, of a determined 
capacity, but as large as possible in proportion to the quantity of 
matter which is employed, and the cells to be so placed that they 
may occupy the least possible space in the hive. To satisfy this 
last condition, the cells should touch each other in such a manner 
that there may remain no angular space between them, no gap to 
fill up. The bees have satisfied these conditions, and at the same 
time they have satisfied the first conditions of the problem in 
making cells which are tubes having six equal sides, or in other 
words, hexagonal tubes... . . We see still further that the best 
thing the bees could do to economise their space and materials, 
was to compose their honeycombs of two rows of cells turned in 
opposite directions.” 
This arrangement, it will be seen, enables them to economise the 
‘half of the wax intended for making the bases of the cells. They 
economise it still more by making the bases and the sides of the 
tubes extremely thin ; the borders only of the comb being’ fortified 
by an excess of wax. These two-sided combs descend from the 
roof of the hive in parallel series, their thickness being about half 
aninch. They are fixed to the top by a sort of wax foot, and 
fastened to the sides by numerous bands. The bees pass between 
the rows, besides excavating circular openings, which serve as 
doors of communication. The form and the general arrangement 
of these buildings are otherwise very varied, according to circum- 
stances. ‘The bees always accommodate themselves to the nature 
of the hive. 
In all these operations they exhibit great judgment. It is im- 
possible, when one has once seen them at work, to look on them 
as mere organised machines, whose instinct is their spring of 
action ; we are forced to concede to them intelligence. 
The cells are of three dimensions: the small ones intended for 
