210. We have hitherto been concerned only with the binding of our
various objects into beautiful lines or processions. The next point we
have to consider is, how we may unite these lines or processions
themselves, so as to make groups of _them_.
[Illustration: FIG. 41.]
[Illustration: FIG. 42.]
Now, there are two kinds of harmonies of lines. One in which, moving
more or less side by side, they variously, but evidently with consent,
retire from or approach each other, intersect or oppose each other;
currents of melody in music, for different voices, thus approach and
cross, fall and rise, in harmony; so the waves of the sea, as they
approach the shore, flow into one another or cross, but with a great
unity through all; and so various lines of composition often flow
harmoniously through and across each other in a picture. But the most
simple and perfect connection of lines is by radiation; that is, by
their all springing from one point, or closing towards it; and this
harmony is often, in Nature almost always, united with the other; as the
boughs of trees, though they intersect and play amongst each other
irregularly, indicate by their general tendency their origin from one
root. An essential part of the beauty of all vegetable form is in this
radiation; it is seen most simply in a single flower or leaf, as in a
convolvulus bell, or chestnut leaf; but more beautifully in the
complicated arrangements of the large boughs and sprays. For a leaf is
only a flat piece of radiation; but the tree throws its branches on all
sides, and even in every profile view of it, which presents a radiation
more or less correspondent to that of its leaves, it is more beautiful,
because varied by the freedom of the separate branches. I believe it has
been ascertained that, in all trees, the angle at which, in their
leaves, the lateral ribs are set on their central rib is approximately
the same at which the branches leave the great stem; and thus each
section of the tree would present a kind of magnified view of its own
leaf, were it not for the interfering force of gravity on the masses of
foliage. This force in proportion to their age, and the lateral
leverage upon them, bears them downwards at the extremities, so that, as
before noticed, the lower the bough grows on the stem, the more it
droops (Fig. 17, p. 67); besides this, nearly all beautiful trees have a
tendency to divide into two or more principal masses, which give a
prettier and more complicated symmetry than if one stem ran all the way
up the center. Fig. 41 may thus be considered the simplest type of tree
radiation, as opposed to leaf radiation. In this figure, however, all
secondary ramification is unrepresented, for the sake of simplicity; but
if we take one half of such a tree, and merely give two secondary
branches to each main branch (as represented in the general branch
structure shown at _b_, Fig. 18, p. 68), we shall have the form Fig. 42.
This I consider the perfect general type of tree structure; and it is
curiously connected with certain forms of Greek, Byzantine, and Gothic
ornamentation, into the discussion of which, however, we must not enter
here. It will be observed, that both in Figs. 41 and 42 all the branches
so spring from the main stem as very nearly to suggest their united
radiation from the root R. This is by no means universally the case; but
if the branches do not bend towards a point in the root, they at least
converge to some point or other. In the examples in Fig. 43, the
mathematical center of curvature, _a_, is thus, in one case, on the
ground, at some distance from the root, and in the other, near the top
of the tree. Half, only, of each tree is given, for the sake of
clearness: Fig. 44 gives both sides of another example, in which the
origins of curvature are below the root. As the positions of such points
may be varied without end, and as the arrangement of the lines is also
farther complicated by the fact of the boughs springing for the most
part in a spiral order round the tree, and at proportionate distances,
the systems of curvature which regulate the form of vegetation are quite
infinite. Infinite is a word easily said, and easily written, and people
do not always mean it when they say it; in this case I _do_ mean it: the
number of systems is incalculable, and even to furnish anything like a
representative number of types, I should have to give several hundreds
of figures such as Fig. 44.[60]
[Illustration: FIG. 43.]
[Illustration: FIG. 44.]
[Illustration: FIG. 45.]
211. Thus far, however, we have only been speaking of the great
relations of stem and branches. The forms of the branches themselves are
regulated by still more subtle laws, for they occupy an intermediate
position between the form of the tree and of the leaf. The leaf has a
flat ramification; the tree a completely rounded one; the bough is
neither rounded nor flat, but has a structure exactly balanced between
the two, in a half-flattened, half-rounded flake, closely resembling in
shape one of the thick leaves of an artichoke or the flake of a fir
cone; by combination forming the solid mass of the tree, as the leaves
compose the artichoke head. I have before pointed out to you the general
resemblance of these branch flakes to an extended hand; but they may be
more accurately represented by the ribs of a boat. If you can imagine a
very broad-headed and flattened boat applied by its keel to the end of a
main branch,[61] as in Fig. 45, the lines which its ribs will take,
supposing them outside of its timbers instead of inside, and the general
contour of it, as seen in different directions, from above and below,
will give you the closest approximation to the perspectives and
foreshortenings of a well-grown branch-flake. Fig. 25 above, p. 89, is
an unharmed and unrestrained shoot of healthy young oak; and, if you
compare it with Fig. 45, you will understand at once the action of the
lines of leafage; the boat only failing as a type in that its ribs are
too nearly parallel to each other at the sides, while the bough sends
all its ramification well forwards, rounding to the head, that it may
accomplish its part in the outer form of the whole tree, yet always
securing the compliance with the great universal law that the branches
nearest the root bend most back; and, of course, throwing _some_ always
back as well as forwards; the appearance of reversed action being much
increased, and rendered more striking and beautiful, by perspective.
Fig. 25 shows the perspective of such a bough as it is seen from below;
Fig. 46 gives rudely the look it would have from above.
[Illustration: FIG. 46.]
212. You may suppose, if you have not already discovered, what
subtleties of perspective and light and shade are involved in the
drawing of these branch-flakes, as you see them in different directions
and actions; now raised, now depressed: touched on the edges by the
wind, or lifted up and bent back so as to show all the white under
surfaces of the leaves shivering in light, as the bottom of a boat rises
white with spray at the surge-crest; or drooping in quietness towards
the dew of the grass beneath them in windless mornings, or bowed down
under oppressive grace of deep-charged snow. Snow time, by the way, is
one of the best for practice in the placing of tree masses; but you will
only be able to understand them thoroughly by beginning with a single
bough and a few leaves placed tolerably even, as in Fig. 38, p. 149.
First one with three leaves, a central and two lateral ones, as at _a_;
then with five, as at _b_, and so on; directing your whole attention to
the expression, both by contour and light and shade, of the boat-like
arrangements, which, in your earlier studies, will have been a good deal
confused, partly owing to your inexperience, and partly to the depth of
shade, or absolute blackness of mass required in those studies.
213. One thing more remains to be noted, and I will let you out of the
wood. You see that in every generally representative figure I have
surrounded the radiating branches with a dotted line: such lines do
indeed terminate every vegetable form; and you see that they are
themselves beautiful curves, which, according to their flow, and the
width or narrowness of the spaces they inclose, characterize the species
of tree or leaf, and express its free or formal action, its grace of
youth or weight of age. So that, throughout all the freedom of her
wildest foliage, Nature is resolved on expressing an encompassing limit;
and marking a unity in the whole tree, caused not only by the rising of
its branches from a common root, but by their joining in one work, and
being bound by a common law. And having ascertained this, let us turn
back for a moment to a point in leaf structure which, I doubt not, you
must already have observed in your earlier studies, but which it is well
to state here, as connected with the unity of the branches in the great
trees. You must have noticed, I should think, that whenever a leaf is
compound,--that is to say, divided into other leaflets which in any way
repeat or imitate the form of the whole leaf,--those leaflets are not
symmetrical, as the whole leaf is, but always smaller on the side
towards the point of the great leaf, so as to express their
subordination to it, and show, even when they are pulled off, that they
are not small independent leaves, but members of one large leaf.
214. Fig. 47, which is a block-plan of a leaf of columbine, without its
minor divisions on the edges, will illustrate the principle clearly. It
is composed of a central large mass, A, and two lateral ones, of which
the one on the right only is lettered, B. Each of these masses is again
composed of three others, a central and two lateral ones; but observe,
the minor one, _a_ of A, is balanced equally by its opposite; but the
minor _b_ 1 of B is larger than its opposite _b_ 2. Again, each of these
minor masses is divided into three; but while the central mass, A of A,
is symmetrically divided, the B of B is unsymmetrical, its largest
side-lobe being lowest. Again, in _b_ 2, the lobe _c_ 1 (its lowest lobe
in relation to B) is larger than _c_ 2; and so also in _b_ 1. So that
universally one lobe of a lateral leaf is always larger than the other,
and the smaller lobe is that which is nearer the central mass; the lower
leaf, as it were by courtesy, subduing some of its own dignity or power,
in the immediate presence of the greater or captain leaf, and always
expressing, therefore, its own subordination and secondary character.
This law is carried out even in single leaves. As far as I know, the
upper half, towards the point of the spray, is always the smaller; and a
slightly different curve, more convex at the springing, is used for the
lower side, giving an exquisite variety to the form of the whole leaf;
so that one of the chief elements in the beauty of every subordinate
leaf throughout the tree is made to depend on its confession of its own
lowliness and subjection.
[Illustration: FIG. 47.]
215. And now, if we bring together in one view the principles we have
ascertained in trees, we shall find they may be summed under four great
laws; and that all perfect[62] vegetable form is appointed to express
these four laws in noble balance of authority.