he former to the latter,
the insect veers round by describing the arc of a circle. When this
turn has been effected, the distance is completed in a straight line.

Let us consider the Sirex at his starting-point. His stiffness of
necessity compels him to turn gradually. Here the insect can do
nothing of its own initiative; everything is mechanically determined.
But, being free to pivot on its axis and to attack the wood on either
side of the sheath, it has the option of attempting this reversal in a
host of different ways, by a series of connected arcs, not in the same
plane. Nothing prevents it from describing winding curves by revolving
upon itself: spirals, loops constantly changing their direction, in
fact, the complicated route of a creature that has lost its way. It
might wander in a tortuous maze, making fresh attempts here, there and
everywhere, groping for ever so long without succeeding.

But it does not grope and it succeeds very well. Its gallery is still
contained within one plane, the first condition of the minimum of
labour. Moreover, of the different vertical planes that can pass
through the eccentric starting-point, one, the plane which passes
through the axis of the tree, corresponds on the one side with the
minimum of resistance to be overcome and on the other with the
maximum. Nothing prevents the Sirex from tracing his path in any one
of the multitude of planes on which the path would possess an
intermediate value between the shortest and the longest. The insect
refuses them all and constantly adopts the one which passes through
the axis, choosing, of course, the side that entails the shortest
path. In brief, the Sirex' gallery is contained in a plane pointing
towards the axis of the tree and the starting-point; and of the two
portions of this plane the channel passes through the less extensive.
Under the conditions, therefore, imposed upon him by his stiffness the
hermit of the poplar-tree releases himself with the minimum of
mechanical labour.

The miner guides himself by the compass in the unknown depths
underground, the sailor does the same in the unknown ocean solitudes.
How does the wood-eating insect guide itself in the thickness of a
tree-trunk? Has it a compass? One would almost say that it had, so
successfully does it keep to the quickest road. Its goal is the light.
To reach this goal, it suddenly chooses the economical plane
trajectory, after spending its larval leisure in roaming tor