counsels of gravity, which tells it to dig upwards, and it will
infallibly reach the exit-door situated at the upper end. But, in my
apparatus, these same counsels betray it: it goes towards the top,
where there is no outlet. Thus misled by my artifices, the Osmiae
perish, heaped up on the higher floors and buried in the ruins.

It nevertheless happens that attempts are made to clear a road
downwards. But it is rare for the work to lead to anything in this
direction, especially in the case of the middle or upper cells. The
insect is little inclined for this progress, the opposite to that to
which it is accustomed; besides, a serious difficulty arises in the
course of this reversed boring. As the Bee flings the excavated
materials behind her, these fall back of their own weight under her
mandibles; the clearance has to be begun anew. Exhausted by her
Sisyphean task, distrustful of this new and unfamiliar method, the
Osmia resigns herself and expires in her cell. I am bound to add,
however, that the Osmiae in the lower storeys, those nearest the
exit--sometimes one, sometimes two or three--do succeed in escaping.
In that case, they unhesitatingly attack the partitions below them,
while their companions, who form the great majority, persist and
perish in the upper cells.

It was easy to repeat the experiment without changing anything in the
natural conditions, except the direction of the cocoons: all that I
had to do was to hang up some bramble-stumps as I found them,
vertically, but with the opening downwards. Out of two stalks thus
arranged and peopled with Osmiae, not one of the insects succeeded in
emerging. All the Bees died in the shaft, some turned upwards, others
downwards. On the other hand, three stems occupied by Anthidia
discharged their population safe and sound. The outgoing was effected
at the bottom, from first to last, without the least impediment. Must
we take it that the two sorts of Bees are not equally sensitive to
the influences of gravity? Can the Anthidium, built to pass through
the difficult obstacle of her cotton wallets, be better-adapted than
the Osmia to make her way through the wreckage that keeps falling
under the worker's feet; or, rather, may not this very cotton-waste
put a stop to these cataracts of rubbish which must naturally drive
the insect back? This is all quite possible; but I can say nothing
for certain.

Let us now experiment with vertical tubes open at both ends. The
arrangements, save for the upper orifice, are the same as before. The
cocoons, in some of the tubes, have their heads turned down; others,
up; in others again, their positions alternate. The result is similar
to what we have seen above. A few Osmiae, those nearest the bottom
orifice, take the lower road, whatever the direction first occupied
by the cocoon; the others, composing by far the larger number, take
the higher road, even when the cocoon is placed upside down. As both
doors are free, the outgoing is effected at either end with success.

What are we to conclude from all these experiments? First, that
gravity guides the insect towards the top, where the natural door is,
and makes it turn in its cell when the cocoon has been reversed.
Secondly, I seem to suspect an atmospheric influence and, in any
case, some second cause that sends the insect to the outlet. Let us
admit that this cause is the proximity of the outer air acting upon
the anchorite through the partitions.

The animal then is subject, on the one hand, to the promptings of
gravity, and this to an equal degree for all, whatever the storey
inhabited. Gravity is the common guide of the whole series from base
to top. But those in the lower boxes have a second guide, when the
bottom end is open. This is the stimulus of the adjacent air, a more
powerful stimulus than that of gravity. The access of the air from
without is very slight, because of the partitions; while it can be
felt in the nethermost cells, it must decrease rapidly as the storeys
ascend. Wherefore the bottom insects, very few in number, obeying the
preponderant influence, that of the atmosphere, make for the lower
outlet and reverse, if necessary, their original position; those
above, on the contrary, who form the great majority, being guided
only by gravity when the upper end is closed, make for that upper
end. It goes without saying that, if the upper end be open at the
same time as the other, the occupants of the top storeys will have a
double incentive to take the ascending path, though this will not
prevent the dwellers on the lower floors from obeying, by preference,
the call of the adjacent air and adopting the downward road.

I have one means left whereby to judge of the value of my
explanation, namely, to experiment with tubes open at both ends and
lying horizontally. The horizontal position has a twofold advantage.
In the first place, it removes the insect from the influence of
gravity, inasmuch as it leaves it indifferent to the direction to be
taken, the right or the left. In the second place, it does away with
the descent of the rubbish which, falling under the worker's feet
when the boring is done from below, sooner or later discourages her
and makes her abandon her enterprise.

There are a few precautions to be observed for the successful conduct
of the experiment; I recommend them to any one who might care to make
the attempt. It is even advisable to remember them in the case of the
tests which I have already described. The males, those puny
creatures, not built for work, are sorry labourers when confronted
with my stout disks. Most of them perish miserably in their glass
cells, without succeeding in piercing their partitions right through.
Moreover, instinct has been less generous to them than to the
females. Their corpses, interspersed here and there in the series of
the cells, are disturbing causes, which it is wise to eliminate. I
therefore choose the larger, more powerful-looking cocoons. These,
except for an occasional unavoidable error, belong to females. I pack
them in tubes, sometimes varying their position in every way,
sometimes giving them all a like arrangement. It does not matter
whether the whole series comes from one and the same bramble-stump or
from several: we are free to choose where we please; the result will
not be altered.

The first time that I prepared one of these horizontal tubes open at
both ends, I was greatly struck by what happened. The series
consisted of ten cocoons. It was divided into two equal batches. The
five on the left went out on the left, the five on the right went out
on the right, reversing, when necessary, their original direction in
the cell. It was very remarkable from the point of view of symmetry;
moreover, it was a very unlikely arrangement among the total number
of possible arrangements, as mathematics will show us.

Let us take n to represent the number of Osmiae. Each of them, once
gravity ceases to interfere and leaves the insect indifferent to
either end of the tube, is capable of two positions, according as she
chooses the exit on the right or on the left. With each of the two
positions of this first Osmia can be combined each of the two
positions of the second, giving us, in all, 2 x 2 = (2 squared)
arrangements. Each of these (2 squared) arrangements can be combined,
in its turn, with each of the two positions of the third Osmia. We
thus obtain 2 x 2 x 2 = (2 cubed) arrangements with three Osmiae; and
so on, each additional insect multiplying the previous result by the
factor 2. With n Osmiae, therefore, the total number of arrangements
is (2 to the power n.)

But note that these arrangements are symmetrical, two by two: a given
arrangement towards the right corresponds with a similar arrangement
towards the left; and this symmetry implies equality, for, in the
problem in hand, it is a matter of indifference whether a fixed
arrangement correspond with the right or left of the tube. The
previous number, therefore, must be divided by 2. Thus, n Osmiae,
according as each of them turns her head to the right or left in my
horizontal tube, are able to adopt (2 to the power n - 1)
arrangements. If n = 10, as in my first experiment, the number of
arrangements becomes (2 to the power 9) = 512.

Consequently, out of 512 ways which my ten insects can adopt for
their outgoing position, there resulted one of those in which the
symmetry was most striking. And observe that this was not an effect
obtained by repeated attempts, by haphazard experiments. Each Osmia
in the left half had bored to the left, without touching the
partition on the right; each Osmia in the right half had bored to the
right, without touching the partition on the left. The shape of the
orifices and the surface condition of the partition showed this, if
proof were necessary. There had been a spontaneous decision, one half
in favour of the left, one half in favour of the right.

The arrangement presents another merit, one superior to that of
symmetry: it has the merit of corresponding with the minimum
expenditure of force. To admit of the exit of the whole series, if
the string consists of n cells, there are originally n partitions to
be perforated. There might even be one more, owing to a complication
which I disregard. There are, I say, at least n partitions to be
perforated. Whether each Osmia pierces her own, or whether the same
Osmia pierces several, thus relieving her neighbours, does not matter
to us: the sum-total of the force expended by the string of Bees will
be in proportion to the number of those partitions, in whatever
manner the exit be effected.

But there is another task which we must take seriously into
consideration, because it is often more troublesome than the boring
of the partition: I mean the work of clearing a road through the
wreckage. Let us suppose the partitions pierced and the several
chambers blocked by the resulting rubbish and by that rubbish only,
since the horizontal position precludes any mixing of the contents of
different chambers. To open a passage for itself through these
rubbish-heaps, each insect will have the smallest effort to make if
it passes through the smallest possible number of cells, in short, if
it makes for the opening nearest to it. These smallest individual
efforts amount, in the aggregate, to the smallest total effort.
Therefore, by proceeding as they did in my experiment, the Osmiae
effect their exit with the least expenditure of energy. It is curious
to see an insect apply the 'principle of least action,' so often
postulated in mechanics.

An arrangement which satisfies this principle, which conforms to the
law of symmetry and which possesses but one chance in 512, is
certainly no fortuitous result. It is determined by a cause; and, as
this cause acts invariably, the same arrangement must be reproduced
if I renew the experiment. I renewed it, therefore, in the years that
followed, with as many appliances as I could find bramble-stumps;
and, at each new test, I saw once more what I had seen with such
interest on the first occasion. If the number be even--and my column
at that time consisted usually of ten--one half goes out on the
right, the other on the left. If the number be odd--eleven, for
instance--the Osmia in the middle goes out indiscriminately by the
right or left exit. As the number of cells to be traversed is the
same on both sides, her expenditure of energy does not vary with the
direction of the exit; and the principle of least action is still
observed.

It was important to discover if the Three-pronged Osmia shared her
capacity, in the first place, with the other bramble-dwellers and, in
the second, with Bees differently housed, but also destined
laboriously to cut a new road for themselves when the hour comes to
quit the nest. Well, apart from a few irregularities, due either to
cocoons whose larva perished in my tubes before developing, or to
those inexperienced workers, the males, the result was the same in