et us devote a moment to their cocoons, a
comparison of which, in the matter of bulk, will furnish us with fairly
accurate evidence as to the relative size of the two sexes, for the
thing contained, the perfect insect, is evidently proportionate to the
silken wrapper in which it is enclosed. These cocoons are oval-shaped
and may be regarded as ellipsoids formed by a revolution around the
major axis. The volume of one of these solids is expressed in the
following formula:

4 / 3 x pi x a x (b squared),

in which 2a is the major axis and 2b the minor axis.

Now, the average dimensions of the cocoons of the Three-horned Osmia are
as follows:

2a = 13 mm. (.507 inch.--Translator's Note.), 2b = 7 mm. (.273
inch.--Translator's Note.) in the females;

2a = 9 mm. (.351 inch.--Translator's Note.), 2b = 5 mm. (.195
inch.--Translator's Note.) in the males.

The ratio therefore between 13 x 7 x 7 = 637 and 9 x 5 x 5 = 225 will be
more or less the ratio between the sizes of the two sexes. This ratio
is somewhere between 2 to 1 and 3 to 1. The females therefore are two or
three times larger than the males, a proportion already suggested by a
comparison of the mass of provisions, estimated simply by the eye.

The Horned Osmia gives us the following average dimensions:

2a = 15 mm. (.585 inch.--Translator's Note.), 2b = 9 mm. (.351
inch.--Translator's Note.) in the females;

2a = 12 mm. (.468 inch.--Translator's Note.), 2b = 7 mm. (.273
inch.--Translator's Note.) in the males.

Once again, the ratio between 15 x 9 x 9 = 1215 and 12 x 7 x 7 = 588
lies between 2 to 1 and 3 to 1.

Besides the Bees who arrange their laying in a row, I have consulted
others whose cells are grouped in a way that makes it possible to
ascertain the relative order of the two sexes, though not quite so
precisely. One of these is the Mason-bee of the Walls. I need not
describe again her dome-shaped nest, built on a pebble, which is now so
well-known to us. (Cf. "The Mason-bees": chapter 1.--Translator's Note.)

Each mother chooses her stone and works on it in solitude. She is an
ungracious landowner and guards her site jealously, driving away any
Mason who even looks as though she might alight on it. The inhabitants
of the same nest are therefore always brothers and sisters; they are the
family of one mother.

Moreover, if the stone presents a large enough surface--a condition
easily fulfilled--the Mason-bee has no reason to leave the support
on