We know that the Three-horned Osmia prefers to haunt the habitations of the Bees who nidify in populous colonies, such as the Mason-bee of the Sheds and the Hairy-footed Anthophora, in whose nests I have noted similar facts.

Thus the sex of the egg is optional. The choice rests with the mother, who is guided by considerations of space and, according to the accommodation at her disposal, which is frequently fortuitous and incapable of modification, places a female in this cell and a male in that, so that both may have a dwelling of a size suited to their unequal development. This is the unimpeachable evidence of the numerous and varied facts which I have set forth. People unfamiliar with insect anatomy--the public for whom I write--would probably give the following explanation of this marvellous prerogative of the Bee: the mother has at her disposal a certain number of eggs, some of which are irrevocably female and the others irrevocably male: she is able to pick out of either group the one which she wants at the actual moment; and her choice is decided by the holding capacity of the cell that has to be stocked. Everything would then be limited to a judicious selection from the heap of eggs.

Should this idea occur to him, the reader must hasten to reject it. Nothing could be more false, as the most casual reference to anatomy will show. The female reproductive apparatus of the Hymenoptera consists generally of six ovarian tubes, something like glove-fingers, divided into bunches of three and ending in a common canal, the oviduct, which carries the eggs outside. Each of these glove-fingers is fairly wide at the base, but tapers sharply towards the tip, which is closed. It contains, arranged in a row, one after the other, like beads on a string, a certain number of eggs, five or six for instance, of which the lower ones are more or less developed, the middle ones halfway towards maturity, and the upper ones very rudimentary. Every stage of evolution is here represented, distributed regularly from bottom to top, from the verge of maturity to the vague outlines of the embryo. The sheath clasps its string of ovules so closely that any inversion of the order is impossible. Besides, an inversion would result in a gross absurdity: the replacing of a riper egg by another in an earlier stage of development.

Therefore, in each ovarian tube, in each glove-finger, the emergence of the eggs occurs according to the order governing their arrangement in the common sheath; and any other sequence is absolutely impossible. Moreover, at the nesting-period, the six ovarian sheaths, one by one and each in its turn, have at their base an egg which in a very short time swells enormously. Some hours or even a day before the laying, that egg by itself represents or even exceeds in bulk the whole of the ovigerous apparatus. This is the egg which is on the point of being laid. It is about to descend into the oviduct, in its proper order, at its proper time; and the mother has no power to make another take its place. It is this egg, necessarily this egg and no other, that will presently be laid upon the provisions, whether these be a mess of honey or a live prey; it alone is ripe, it alone lies at the entrance to the oviduct; none of the others, since they are farther back in the row and not at the right stage of development, can be substituted at this crisis. Its birth is inevitable.

What will it yield, a male or a female? No lodging has been prepared, no food collected for it; and yet both food and lodging have to be in keeping with the sex that will proceed from it. And here is a much more puzzling condition: the sex of that egg, whose advent is predestined, has to correspond with the space which the mother happens to have found for a cell. There is therefore no room for hesitation, strange though the statement may appear: the egg, as it descends from its ovarian tube, has no determined sex. It is perhaps during the few hours of its rapid development at the base of its ovarian sheath, it is perhaps on its passage through the oviduct that it receives, at the mother's pleasure, the final impress that will produce, to match the cradle which it has to fill, either a female or a male.

PERMUTATIONS OF SEX.

Thereupon the following question presents itself. Let us admit that, when the normal conditions remain, a laying would have yielded m females and n males. Then, if my conclusions are correct, it must be in the mother's power, when the conditions are different, to take from the m group and increase the n group to the same extent; it must be possible for her laying to be represented as m - 1, m - 2, m - 3, etc. females and by n + 1, n + 2, n + 3, etc. males, the sum of m + n remaining constant, but one of the sexes being partly permuted into the other. The ultimate conclusion even cannot be disregarded: we must admit a set of eggs represented by m - m, or zero, females and of n + m males, one of the sexes being completely replaced by the other. Conversely, it must be possible for the feminine series to be augmented from the masculine series to the extent of absorbing it entirely. It was to solve this question and some others connected with it that I undertook, for the second time, to rear the Three-horned Osmia in my study.

The problem on this occasion is a more delicate one; but I am also better-equipped. My apparatus consists of two small closed packing-cases, with the front side of each pierced with forty holes, in which I can insert my glass tubes and keep them in a horizontal position. I thus obtain for the Bees the darkness and mystery which suit their work and for myself the power of withdrawing from my hive, at any time, any tube that I wish, with the Osmia inside, so as to carry it to the light and follow, if need be with the aid of the lens, the operations of the busy worker. My investigations, however frequent and minute, in no way hinder the peaceable Bee, who remains absorbed in her maternal duties.

I mark a plentiful number of my guests with a variety of dots on the thorax, which enables me to follow any one Osmia from the beginning to the end of her laying. The tubes and their respective holes are numbered; a list, always lying open on my desk, enables me to note from day to day, sometimes from hour to hour, what happens in each tube and particularly the actions of the Osmiae whose backs bear distinguishing marks. As soon as one tube is filled, I replace it by another. Moreover, I have scattered in front of either hive a few handfuls of empty Snail-shells, specially chosen for the object which I have in view. Reasons which I will explain later led me to prefer the shells of Helix caespitum. Each of the shells, as and when stocked, received the date of the laying and the alphabetical sign corresponding with the Osmia to whom it belonged. In this way, I spent five or six weeks in continual observation. To succeed in an enquiry, the first and foremost condition is patience. This condition I fulfilled; and it was rewarded with the success which I was justified in expecting.

The tubes employed are of two kinds. The first, which are cylindrical and of the same width throughout, will be of use for confirming the facts observed in the first year of my experiments in indoor rearing. The others, the majority, consist of two cylinders which are of very different diameters, set end to end. The front cylinder, the one which projects a little way outside the hive and forms the entrance-hole, varies in width between 8 and 12 millimetres. (Between .312 and .468 inch.--Translator's Note.) The second, the back one, contained entirely within my packing-case, is closed at its far end and is 5 to 6 millimetres in diameter. (.195 to .234 inch.--Translator's Note.) Each of the two parts of the double-galleried tunnel, one narrow and one wide, measures at most a decimetre in length. (3.9 inches.--Translator's Note.) I thought it advisable to have these short tubes, as the Osmia is thus compelled to select different lodgings, each of them being insufficient in itself to accommodate the total laying. In this way I shall obtain a greater variety in the distribution of the sexes. Lastly, at the mouth of each tube, which projects slightly outside the case, there is a little paper tongue, forming a sort of perch on which the Osmia alights on her arrival and giving easy access to the house. With these facilities, the swarm colonized fifty-two double-galleried tubes, thirty-seven cylindrical tubes, seventy-eight Snail-shells and a few old nests of the Mason-bee of the Shrubs. From this rich mine of material I will take what I want to prove my case.

Every series, even when incomplete, begins with females and ends with males. To this rule I have not yet found an exception, at least in galleries of normal diameter. In each new abode the mother busies herself first of all with the more important sex. Bearing this point in mind, would it be possible for me, by manoeuvring, to obtain an inversion of this order and make the laying begin with males? I think so, from the results already ascertained and the irresistible conclusions to be drawn from them. The double-galleried tubes are installed in order to put my conjectures to the proof.

The back gallery, 5 or 6 millimetres wide (.195 to .234 inch.--Translator's Note.), is too narrow to serve as a lodging for normally developed females. If, therefore, the Osmia, who is very economical of her space, wishes to occupy them, she will be obliged to establish males there. And her laying must necessarily begin here, because this corner is the rear-most part of the tube. The foremost gallery is wide, with an entrance-door on the front of the hive. Here, finding the conditions to which she is accustomed, the mother will go on with her laying in the order which she prefers.

Let us now see what has happened. Of the fifty-two double-galleried tubes, about a third did not have their narrow passage colonized. The Osmia closed its aperture communicating with the large passage; and the latter alone received the eggs. This waste of space was inevitable. The female Osmiae, though nearly always larger than the males, present marked differences among one another: some are bigger, some are smaller. I had to adjust the width of the narrow galleries to Bees of average dimensions. It may happen therefore that a gallery is too small to admit the large-sized mothers to whom chance allots it. When the Osmia is unable to enter the tube, obviously she will not colonize it. She then closes the entrance to this space which she cannot use and does her laying beyond it, in the wide tube. Had I tried to avoid these useless apparatus by choosing tubes of larger calibre, I should have encountered another drawback: the medium-sized mothers, finding themselves almost comfortable, would have decided to lodge females there. I had to be prepared for it: as each mother selected her house at will and as I was unable to interfere in her choice, a narrow tube would be colonized or not, according as the Osmia who owned it was or was not able to make her way inside.

There remain some forty pairs of tubes with both galleries colonized. In these there are two things to take into consideration. The narrow rear tubes of 5 or 5 1/2 millimetres (.195 to .214 inch.--Translator's Note.)--and these are the most numerous--contain males and males only, but in short series, between one and five. The mother is here so much hampered in her work that they are rarely occupied from end to end; the Osmia seems in a hurry to leave them and to go and colonize the front tube, whose ample space will leave her the liberty of movement necessary for her operations. The other rear tubes, the minority, whose diameter is about 6 millimetres (.234 inch.--Translator's Note.), contain sometimes only females and sometimes females at the back and males towards the opening. One can see that a tube a trifle wider and a mother slightly smaller would account for this difference in the results. Nevertheless, as the necessary space for a female is barely provided in this case, we see that the mother avoids as far as she can a two-sex arrangement beginning with males and that she adopts it only in the last extremity. Finally, whatever the contents of the small tube may be, those of the large one, following upon it, never vary and consist of females at the back and males in front.

Though incomplete, because of circumstances very difficult to control, the result of the experiment is none the less very remarkable. Twenty-five apparatus contain only males in their narrow gallery, in numbers varying from a minimum of one to a maximum of five. After these comes the colony of the large gallery, beginning with females and ending with males. And the layings in these apparatus do not always belong to late summer or even to the intermediate period: a few small tubes contain the earliest eggs of the entire swarm. A couple of Osmiae, more forward than the others, set to work on the 23rd of April. Both of them started their laying by placing males in the narrow tubes. The meagre supply of provisions was enough in itself to show the sex, which proved later to be in accordance with my anticipations. We see then that, by my artifices, the whole swarm starts with the converse of the normal order. This inversion is continued, at no matter what period, from the beginning to the end of the operations. The series which, according to rule, would begin with females now begins with males. Once the larger gallery is reached, the laying is pursued in the usual order.