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 the case of Anthidium scapulare. The insects divided themselves into two equal batches, one going to the right, the other to the left.
Tripoxylon figulus left me undecided. This feeble insect is not capable of perforating my partitions; it nibbles at them a little;and I had to judge the direction from the marks of its mandibles.
These marks, which are not always very plain, do not yet allow me to pronounce an opinion. Solenius vagus, who is a skilful borer, behaved differently from the Osmia. In a column of ten, the whole exodus was made in one direction.
