The larva does not prepare the path of deliverance; it is left for the perfect insect to open itself a passage through the wood. What I have before my eyes tells me more or less plainly the sequence of events. The larva, whose presence is proved by galleries blocked with packed sawdust, do not leave the centre of the trunk, a quieter retreat, less subject to the vicissitudes of the climate. Metamorphosis is effected at the junction of the straight gallery and the curved passage which is not yet made. When strength comes, the perfect insect tunnels ahead for a distance of more than four inches and opens up the exit-passage, which I find choked, not with compact sawdust, but with loose powdery rubbish. The dead insects which I strip of their mycelium-shrouds are weaklings whose strength deserted them mid-way. The rest of the passage is lacking because the labourer died on the road. With this fact of the insect itself boring the exit passage, the problem assumes a more troublesome form. If the larva, rich in leisure and satisfied with its sojourn in the interior of the trunk, simplifies the coming emergence by shortening the road, what must not the adult do, who has so short a time to live and who is in so great a hurry to leave the hateful darkness? He above any other should be a judge of short cuts. To go from the murky heart of the tree to the sun-steeped bark, why does he not follow a straight line? It is the shortest way. Yes, for the compasses, but not perhaps for the sapper. The length traversed is not the only factor of the work accomplished, of the total activity expended. We must take into account the resistance overcome, a resistance which varies according to the depth of the more or less hard strata and according to the method of attacking the woody fibres, which are either broken across or divided lengthwise. Under these conditions, whose value remains to be determined, can there be a curve involving a minimum of mechanical labour in cutting through the wood? I was already trying to discover how the resistance may vary according to depth and direction; I was working out my differentials and my minimum integrals, when a very simple idea overturned my slippery scaffolding. The calculation of variations has nothing to do with the matter. The animal is not the moving body of the mathematicians, the particle of matter guided in its trajectory solely by the motive forces and the resistance of the medium traversed; it bears within itself conditions which control the others. The adult insect does not even enjoy the larva's privileges; it cannot bend freely in all directions. Under its harness it is almost a stiff cylinder. To simplify the explanation, we may liken the insect to a section of an inflexible straight line.