between two points. If the points of suspension be
near each other, we have such curves as at D; and if, as in nine cases
out of ten will be the case, one point of suspension is lower than the
other, a still more varied and beautiful curve is formed, as at E. Such
curves constitute nearly the whole beauty of general contour in falling
drapery, tendrils and festoons of weeds over rocks, and such other
pendent objects.[89]

Sec. 13. Again. If any object be cast into the air, the force with which it
is cast dies gradually away, and its own weight brings it downwards; at
first slowly, then faster and faster every moment, in a curve which, as
the line of fall necessarily nears the perpendicular, is continually
approximating to a straight line. This curve--called the parabola--is
that of all projected or bounding objects.

Sec. 14. Again. If a rod or stick of any kind gradually becomes more
slender or more flexible, and is bent by any external force, the force
will not only increase in effect as the rod becomes weaker, but the rod
itself, once bent, will continually yield more willingly, and be more
easily bent farther in the same direction, and will thus show a
continual increase of curvature from its thickest or most rigid part to
its extremity. This kind of line is that assumed by boughs of trees
under wind.

Sec. 15. Again. Whenever any vital force is impressed on any organic
substance, so as to die gradually away as the substance extends, an
infinite curve is commonly produced by its outline. Thus, in the budding
of the leaf, already examined, the gradual dying away of the
exhilaration of the younger ribs produces an infinite curve in the
outline of the leaf, which sometimes fades imperceptibly into a right
line,--sometimes is terminated sharply, by meeting the opposite curve at
the point of the leaf.

Sec. 16. Nature, however, rarely condescends to use one curve only in any
of her finer forms. She almost always unites two infinite ones, so as to
form a reversed curve for each main line, and then modulates each of
them into myriads of minor ones. In a single elm leaf, such as Fig. 4,
Plate +8+, she uses three such--one for the stalk, and one for each of
the sides,--to regulate their _general_ flow; dividing afterwards each
of their broad lateral lines into some twenty less curves by the jags of
the leaf, and then again into minor waves. Thus, in any complicated
group of leaves whatever, the infinite curves are themse