etc

If the reader had the patience to work out the few initial terms of this
series, which has no limit, because the series of natural numerals itself
has none, he would find:

e=2.7182818...

With this weird number are we now stationed within the strictly defined
realm of the imagination? Not at all: the catenary appears actually
every time that weight and flexibility act in concert. The name is given
to the curve formed by a chain suspended by two of its points which are
not placed on a vertical line. It is the shape taken by a flexible cord
when held at each end and relaxed; it is the line that governs the shape
of a sail bellying in the wind; it is the curve of the nanny-goat's milk-
bag when she returns from filling her trailing udder. And all this
answers to the number e.

What a quantity of abstruse science for a bit of string! Let us not be
surprised. A pellet of shot swinging at the end of a thread, a drop of
dew trickling down a straw, a splash of water rippling under the kisses
of the air, a mere trifle, after all, requires a titanic scaffolding when
we wish to examine it with the eye of calculation. We need the club of
Hercules to crush a fly.

Our methods of mathematical investigation are certainly ingenious; we
cannot too much admire the mighty brains that have invented them; but how
slow and laborious they appear when compared with the smallest
actualities! Will it never be given to us to probe reality in a simpler
fashion? Will our intelligence be able one day to dispense with the
heavy arsenal of formulae? Why not?

Here we have the abracadabric number _e_ reappearing, inscribed on a
Spider's thread. Let us examine, on a misty morning, the meshwork that
has been constructed during the night. Owing to their hygrometrical
nature, the sticky threads are laden with tiny drops, and, bending under
the burden, have become so many catenaries, so many chaplets of limpid
gems, graceful chaplets arranged in exquisite order and following the
curve of a swing. If the sun pierce the mist, the whole lights up with
iridescent fires and becomes a resplendent cluster of diamonds. The
number _e_ is in its glory.

Geometry, that is to say, the science of harmony in space, presides over
everything. We find it in the arrangement of the scales of a fir-cone,
as in the arrangement of an Epeira's limy web; we find it in the spiral
of a Snail-shell, in the chaplet of a Spider's thread, as in the orbit