The total space at her disposal would do for about a third of the laying.

Well, in the two large cells, she puts females; in the three small cells she puts males.
As we find the same sort of thing in all the old nests, we must needs admit that the mother knows the sex of the eggs which she is going to lay, because that egg is placed in a cell of the proper capacity.

We can go further, and admit that the mother alters the order of succession of the sexes at her pleasure, because her layings, between one old nest and another, are broken up into small groups of males and females according to the exigencies of space in the actual nest which she happens to be occupying.
Here then is the Chalicodoma, when mistress of an old nest of which she has not the power to alter the arrangement, breaking up her laying into sections comprising both sexes just as required by the conditions imposed upon her.

She therefore decides the sex of the egg at will, for, without this prerogative, she could not, in the chambers of the nest which she owes to chance, deposit unerringly the sex for which those chambers were originally built; and this happens however small the number of chambers to be filled.
When the mother herself founds the dwelling, when she lays the first rows of bricks, the females come first and the males at the finish.
But, when she is in the presence of an old nest, of which she is quite unable to alter the general arrangement, how is she to make use of a few vacant rooms, the large and small alike, if the sex of the egg be already irrevocably fixed?
She can only do so by abandoning the arrangement in two consecutive rows and accommodating her laying to the varied exigencies of the home.

Either she finds it impossible to make an economical use of the old nest, a theory refuted by the evidence, or else she determines at will the sex of the egg which she is about to lay.
The Osmiae themselves will furnish the most conclusive evidence on the latter point.