This section is from the book "The Psychic Life Of Insects", by E. L. Bouvier. Also available from Amazon: The Psychic Life of Insects.
The experiment of Piéron (page 256) shows that the sensorial excitants are not the direct cause of the circling. Transported to a distance, the insect follows a path parallel to the first direction, and begins to circle at a point from which, if it had not been moved, it would have quite certainly reached its nest. It circled to seek a guiding point; and it had, then, an idea of the distance to be covered.
Piéron explains this phenomenon by attributing to the ants a "muscular memory, the memory of the different motions made to go from one point to another, a reverse memory, allowing return to the original place. " It is clear that this faculty plays no part in orientation, for, as Cornetz justly says, "a pedometer is not a compass." Moreover, if we observe that the explorer does not on the return follow the path of going, that it meets other obstacles and ordinarily returns with a burden, we cannot accept such an hypothesis as Piéron's. But we may happily modify this hypothesis by supposing with Santschi that the insect can to a certain degree estimate the sum of the effort made during the outward journey and estimate the time of the return by taking into account the additional effort required by the burden. "We must not forget, also, that this estimate of distance is only approximate.
here is also the estimate of the distance the ant must travel in returning compared with that in going, when that was an angled line. In the rare cases where the two routes are very close, it is possible that the guiding points indicate to the insect the apex of each angle. But, contrary to Santschi, we do not believe that this rule is general. It seems more reasonable to admit that the ants have a notion of the distance between the apices of each angle, and that the changes of direction, are perhaps due to memory of angles (usually nearly right angles) or a more or less distant guiding point. Here again we must note that these estimates are always approximate.
As we have seen, our ignorance of these phenomena is still very great, especially if we add the fact that we do not know why the circuits for search made in going do not enter into the estimate of the effort to be produced on the return journey (Figure 14).
In the course of experiments carried on with Formica rufa, Szymansky has noticed that if one places an obstacle transversely upon the scent which the ants follow, the insects join the route diagonally when they have reached the extremity of a long obstacle. Working in the same way with M essor, Santschi observed that the individuals behaved differently; some continued their march in the direction of the obstacle, others took a direction parallel to the scent, and certain others rejoined the line of march diagonally like Formica rufa. It seems that these insects were urged by two "force ideas,"-the one which led them to return to the scent, the other which preserved the original orientation, and that from the conflict of these two ideas came the behavior of each individual.
Whatever may be the value of this interpretation proposed by the Swiss biologist, it is established that our insects are capable of taking the diagonal, but they do not do this when they are following a scent, an ant road. If the explorers do not behave the same and take on return the reverse of the outward route, it is perhaps because such a method would defeat the end which they are pursuing. They return to the nest and are guided to it by their memory of distances, of angles, and the orientations of the journey. By taking the diagonal at each angle they profoundly upset their recollections, for the road which they are following is not a scent, and after they have followed a diagonal nothing allows them to recognize where and how they ought to change their direction.
 
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