eometric measurements, I find that the spiral groove
intersects this generating line at an angle of unvarying value.

The consequence of this result is easily deduced. If projected on a
plane perpendicular to the axis of the shell, the generating lines of the
cone would become radii; and the groove which winds upwards from the base
to the apex would be converted into a plane curve which, meeting those
radii at an unvarying angle, would be neither more nor less than a
logarithmic spiral. Conversely, the groove of the shell may be
considered as the projection of this spiral on a conic surface.

Better still. Let us imagine a plane perpendicular to the aids of the
shell and passing through its summit. Let us imagine, moreover, a thread
wound along the spiral groove. Let us unroll the thread, holding it taut
as we do so. Its extremity will not leave the plane and will describe a
logarithmic spiral within it. It is, in a more complicated degree, a
variant of Bernouilli's '_Eadem mutata resurgo_:' the logarithmic conic
curve becomes a logarithmic plane curve.

A similar geometry is found in the other shells with elongated cones,
Turritellae, Spindle-shells, Cerithia, as well as in the shells with
flattened cones, Trochidae, Turbines. The spherical shells, those
whirled into a volute, are no exception to this rule. All, down to the
common Snail-shell, are constructed according to logarithmic laws. The
famous spiral of the geometers is the general plan followed by the
Mollusc rolling its stone sheath.

Where do these glairy creatures pick up this science? We are told that
the Mollusc derives from the Worm. One day, the Worm, rendered frisky by
the sun, emancipated itself, brandished its tail and twisted it into a
corkscrew for sheer glee. There and then the plan of the future spiral
shell was discovered.

This is what is taught quite seriously, in these days, as the very last
word in scientific progress. It remains to be seen up to what point the
explanation is acceptable. The Spider, for her part, will have none of
it. Unrelated to the appendix-lacking, corkscrew-twirling Worm, she is
nevertheless familiar with the logarithmic spiral. From the celebrated
curve she obtains merely a sort of framework; but, elementary though this
framework be, it clearly marks the ideal edifice. The Epeira works on
the same principles as the Mollusc of the convoluted shell.

The Mollusc has years wherein to construct its sp