the two
radiating lines that frame them they form obtuse angles on one side and
acute angles on the other; and these angles remain constant in the same
sector, because the chords are parallel.

There is more than this: these same angles, the obtuse as well as the
acute, do not alter in value, from one sector to another, at any rate so
far as the conscientious eye can judge. Taken as a whole, therefore, the
rope-latticed edifice consists of a series of cross-bars intersecting the
several radiating lines obliquely at angles of equal value.

By this characteristic we recognize the 'logarithmic spiral.'
Geometricians give this name to the curve which intersects obliquely, at
angles of unvarying value, all the straight lines or 'radii vectores'
radiating from a centre called the 'Pole.' The Epeira's construction,
therefore, is a series of chords joining the intersections of a
logarithmic spiral with a series of radii. It would become merged in
this spiral if the number of radii were infinite, for this would reduce
the length of the rectilinear elements indefinitely and change this
polygonal line into a curve.

To suggest an explanation why this spiral has so greatly exercised the
meditations of science, let us confine ourselves for the present to a few
statements of which the reader will find the proof in any treatise on
higher geometry.

The logarithmic spiral describes an endless number of circuits around its
pole, to which it constantly draws nearer without ever being able to
reach it. This central point is indefinitely inaccessible at each
approaching turn. It is obvious that this property is beyond our sensory
scope. Even with the help of the best philosophical instruments, our
sight could not follow its interminable windings and would soon abandon
the attempt to divide the invisible. It is a volute to which the brain
conceives no limits. The trained mind, alone, more discerning than our
retina, sees clearly that which defies the perceptive faculties of the
eye.

The Epeira complies to the best of her ability with this law of the
endless volute. The spiral revolutions come closer together as they
approach the pole. At a given distance, they stop abruptly; but, at this
point, the auxiliary spiral, which is not destroyed in the central
region, takes up the thread; and we see it, not without some surprise,
draw nearer to the pole in ever-narrowing and scarcely perceptible
circles. There is not, of course,