It is
merely a temporary construction, whereof naught but the central part
survives when the Spider has set its limy meshes. The second spiral, the
essential part of the snare, proceeds, on the contrary, in serried coils
from the circumference to the centre and is composed entirely of viscous
cross-threads.

Here we have, following one after the other merely by a sudden alteration
of the machine, two volutes of an entirely different order as regards
direction, the number of whorls and intersection. Both of them are
logarithmic spirals. I see no mechanism of the legs, be they long or
short, that can account for this alteration.

Can it then be a premeditated design on the part of the Epeira? Can
there be calculation, measurement of angles, gauging of the parallel by
means of the eye or otherwise? I am inclined to think that there is none
of all this, or at least nothing but an innate propensity, whose effects
the animal is no more able to control than the flower is able to control
the arrangement of its verticils. The Epeira practises higher geometry
without knowing or caring. The thing works of itself and takes its
impetus from an instinct imposed upon creation from the start.

The stone thrown by the hand returns to earth describing a certain curve;
the dead leaf torn and wafted away by a breath of wind makes its journey
from the tree to the ground with a similar curve. On neither the one
side nor the other is there any action by the moving body to regulate the
fall; nevertheless, the descent takes place according to a scientific
trajectory, the 'parabola,' of which the section of a cone by a plane
furnished the prototype to the geometer's speculations. A figure, which
was at first but a tentative glimpse, becomes a reality by the fall of a
pebble out of the vertical.

The same speculations take up the parabola once more, imagine it rolling
on an indefinite straight line and ask what course does the focus of this
curve follow. The answer comes: The focus of the parabola describes a
'catenary,' a line very simple in shape, but endowed with an algebraic
symbol that has to resort to a kind of cabalistic number at variance with
any sort of numeration, so much so that the unit refuses to express it,
however much we subdivide the unit. It is called the number _e_. Its
value is represented by the following series carried out ad infinitum:

e = 1 + 1/1 + 1/(1*2) + 1/(1*2*3) + 1/(1*2*3*4) + 1/(1*2*3*4*5) +