c 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.

Does the trajectory imply the minimum of work? Yes, under the
conditions of the insect's existence. If the larva had taken the
precaution to place itself in a different direction when preparing for
the nymphosis, to turn its head towards the nearest point of the bark
instead of turning it lengthwise with the trunk, obviously the adult
would escape more easily: he would merely have to gnaw straight in
front of him in order to pass through the minimum thickness. But
reasons of convenience whereof the grub is the sole judge, reasons
dictated perhaps by weight, cause the vertical to precede the
horizontal position. In order to pass from t