The law of phyllotaxis, like that of the elastic curve, is carried out
in time as well as in space. As the formula for the elastic curve is
the same as that for the pendulum, so the law by which the spaces of
the leaves are divided in scattering them round the stem, to give each
its opportunity for light and air, is the same as that by which the
times of the planets are proportioned to keep them scattered about the
sun, and prevent them from gathering on one side of their central orb.

The forms of plants and trees are dependent upon the arrangement of the
branches, and the arrangement of the branches depends upon that of the
buds or leaves. The leaves are arranged by this numerical law,--that
the angular distance about the stem between two successive leaves shall
be in such ratio to the whole circumference as may be expressed by a
continued fraction composed wholly of the figure 1. It is, then, true,
that all the beauty of the vegetable world which depends on the
arrangement of parts--the graceful symmetry or more graceful apparent
disregard of symmetry in the general form of plants, all the charm of
the varying forms of forest trees, which adds such loveliness to the
winter landscape, and such a refined source of pleasure to the
exhilaration of the winter morning walk--is the result of the simplest
variations in a simple numerical law; and is thus clearly brought under
our fundamental canon. It is the perception of this unity in diversity,
of this similarity of plan, for instance, in all tree-like forms,
however diverse,--the sprig of mignonette, the rose-bush, the fir, the
cedar, the fan-shaped elm, the oval rock-maple, the columnar hickory,
the dense and slender shaft of the poplar,--which charms the eye of
those who have never heard in what algebraic or arithmetical terms this
unity may be defined, in what geometrical or architectural figures this
diversity may be expressed.