107 
bees, gave them an advantage in the struggle of life above other bees ? This 
improvement was transmitted to the next generation. Then another 
improvement was made in the same manner ; and so on, till, in process of 
time, as an accidentally exposed nerve became a perfect eye, a race of bees 
gradually improved an almost shapeless cell into the mathematical perfection 
of that of the hive-bee. But the incredibility of this hypothesis, tried by so 
crucial an instance, seems even to strike Mr. Darwin. He strives, therefore, 
to render it more credible, by detracting in some degree from the perfection 
of the hive-bee’s instinctive work, and to make the bee work its structure by 
what he conceives simpler principles than have been observed in the actual 
operations of that insect. But the perfection of the bee’s cell does not consist 
simply in the economy of material produced by uniting hexagonal cells 
together. The wasp, building its comb with paper cells, and having the 
material for the manufacture of this paper always in abundance, is content 
with this degree of economy. It builds each comb parallel to the other, but 
it does not in that comb introduce a double row of cells each hexagonal cell 
being terminated by a plane or flat surface. The hive-bee, on the other hand, 
making its wax out of a material requiring great industry in its collection, 
to be found only for a short time while flowers are in fall blossom, 
having to manufacture the raw honey so gathered, and secrete it like milk, 
after a digestion of it in its stomach, has to use more economy in the 
structure of its comb with wax than the wasp using paper. It makes 
each comb of two sets of cells placed back to back. Each cell is terminated 
by three flat lozenge-shaped planes, each plane being shaped like the diamond 
on playing-cards. The three planes terminating a cell on one side of the comb, 
are the bottoms of three different cells on the other side ; so that the hexagonal 
cells are not placed back to back. Indeed, the partition wall of the two 
sets of cells forms a series of lozenge-shaped cups on either side, and gives 
marvellous strength to the structure of the comb, on the same principle 
which causes the Gothic architect to support the weight of his roof by flying 
buttresses. A thousand, nay, a myriad of angles might be chosen for the 
rhomb-lozenge, any one of which would imitate the structure of the bee’s 
cell as to its general appearance. Rigid mathematical evidence shows, how- 
ever, that the bee chooses just that one angle of 109° 28' which gives the 
greatest economy of material with the greatest power of storage. Indeed, 
the mathematicians made a mistake in their problem, and took the angle 
109° 26' as the perfect angle. Then it was said that the bee was nearly 
right. But after all, the mathematicians were wrong ! A miscalculation in a 
table of logarithms was the cause of their blunder, and the bee was demon- 
strated to have chosen the proper angle, accurate to a minute of a degree. 
Now Mr. Darwin strives to simplify the bee’s problem by one of his own, 
which he takes to Professor Miller at Cambridge, as to the intersection of 
equal spheres. He gets that professor’s solution as to the distance of the 
intersecting radii ; and then, assuming that the bee has contrived to calcu- 
late the square root of two to five places of decimals, he supposes that the 
whole instinct producing this marvellous structure can be brought credibly 
