The Glow-Worm and Other Beetles

by Jean-Henri Fabre

I am enraptured by this magnificent specimen. The curves, of which I uncover a layer at every stroke of the plane, far exceed my requirements; they are strikingly regular; they afford the compasses the full space needed for accurate measurement.

Before calling in geometry, let us, if possible, name the creator of these beautiful curves. The inhabitants of the poplar have disappeared, perhaps long ago, as is proved by the mycelium of the agaric; the insect would not gnaw and bore its way through timber all permeated with the felt-like growth of the cryptogam. A few weaklings, however, have died without being able to escape. I find their remains swathed in mycelium. The agaric has preserved them from destruction by wrapping them in tight cerements. Under these mummy-bandages, I recognise a Saw-fly, Sirex augur, KLUG., in the state of the perfect insect. And—this is an important detail—all these adult remains, without a single exception, occupy spots which have no means of communication with the outside. I find them sometimes in a partly-constructed curved passage, beyond which the wood remains intact, sometimes at the end of the straight central gallery, choked with sawdust, which is not continued in front. These remains, with no thoroughfare before them, tell us plainly that the Sirex adopts for its exit methods not employed by the Buprestes and the Longicorns.

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.

Let us return to the Sirex, reduced by abstraction to its axis. The metamorphosis is effected not far from the centre of the trunk. The insect lies lengthwise in the tree with its head up, very rarely with its head down. It must reach the outside as quickly as possible. The section of an inflexible straight line that represents it nibbles away a little wood in front of it and obtains a shallow cavity wide enough to allow of a very slight turn towards the outside. An infinitesimal advance is made; a second follows, the result of a similar cavity and a similar turn in the same direction. In short, each change of position is accompanied by the tiny deviation permitted by the slight excess of width of the hole; and this deviation invariably points the same way. Imagine a magnetic needle swung out of its position and tending to return to it while moving with a uniform speed through a resisting medium in which a sheath of a diameter slightly greater than the needle's opens bit by bit. The Sirex behaves more or less in the same fashion. His magnetic pole is the light outside. He makes for that direction by imperceptible deviations as his tooth digs.

The problem of the Sirex is now solved. The trajectory is composed of equal elements, with an invariable angle between them; it is the curve whose tangents, divided by infinitely small distances, retain the same inclination between each one and the next; the curve, in a word, with a constant angle of contingence. This characteristic betrays the circumference of the circle.

It remains to discover whether the facts confirm the logical argument. I take accurate tracings of a score of galleries, selecting those whose length best lends itself to the test of the compasses. Well, logic agrees with reality: over lengths which sometimes exceed four inches, the track of the compasses is identical with that of the insect. The most pronounced deviations do not exceed the small variations which we must reasonably expect in a problem of a physical nature, a problem incompatible with the absolute accuracy of abstract truths.

The Sirex' exit-gallery then is a wide arc of a circle whose lower extremity is connected with the corridor of the larva and whose upper extremity is prolonged in a straight line which ends at the surface with a perpendicular or slightly oblique incidence. The wide connecting arc enables the insect to tack about. When, starting from a position parallel with the axis of the tree, the Sirex has passed gradually to a transversal position, he completes his course in a straight line, which is the shortest road.