With my pan-pipe apparatus displayed on the walls of my enclosure and with old hurdle-reeds left lying flat out of doors, I obtained the Horned Osmia in fair quantities. I persuaded Latreille's Osmia to build her nest in reeds, which she did with a zeal which I was far from expecting. All that I had to do was to lay some reed-stumps horizontally within her reach, in the immediate neighbourhood of her usual haunts, namely, the nests of the Mason-bee of the Sheds. Lastly, I succeeded without difficulty in making her build her nests in the privacy of my study, with glass tubes for a house. The result surpassed my hopes. With both these Osmiae, the division of the gallery is the same as with the Three-horned Osmia. At the back are large cells with plentiful provisions and widely-spaced partitions; in front, small cells, with scanty provisions and partitions close together. Also, the larger cells supplied me with big cocoons and females; the smaller cells gave me little cocoons and males. The conclusion therefore is exactly the same in the case of all three Osmiae. Before dismissing the Osmiae, let 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.