3. THE LAW OF CONTINUITY.

Another important and pleasurable way of expressing unity is by giving some orderly succession to a number of objects more or less similar. And this succession is most interesting when it is connected with some gradual change in the aspect or character of the objects. Thus the succession of the pillars of a cathedral aisle is most interesting when they retire in perspective, becoming more and more obscure in distance; so the succession of mountain promontories one behind another, on the flanks of a valley; so the succession of clouds, fading farther and farther towards the horizon; each promontory and each cloud being of different shape, yet all evidently following in a calm and appointed order. If there be no change at all in the shape or size of the objects, there is no continuity; there is only repet.i.tion--monotony. It is the change in shape which suggests the idea of their being individually free, and able to escape, if they liked, from the law that rules them, and yet submitting to it. I will leave our chosen ill.u.s.trative composition for a moment to take up another, still more expressive of this law. It is one of Turner's most tender studies, a sketch on Calais Sands at sunset; so delicate in the expression of wave and cloud, that it is of no use for me to try to reach it with any kind of outline in a woodcut; but the rough sketch, Fig. 33., is enough to give an idea of its arrangement. The aim of the painter has been to give the intensest expression of repose, together with the enchanted lulling, monotonous motion of cloud and wave. All the clouds are moving in innumerable ranks after the sun, meeting towards the point in the horizon where he has set; and the tidal waves gain in winding currents upon the sand, with that stealthy haste in which they cross each other so quietly, at their edges: just folding one over another as they meet, like a little piece of ruffled silk, and leaping up a little as two children kiss and clap their hands, and then going on again, each in its silent hurry, drawing pointed arches on the sand as their thin edges intersect in parting; but all this would not have been enough expressed without the line of the old pier-timbers, black with weeds, strained and bent by the storm waves, and now seeming to stoop in following one another, like dark ghosts escaping slowly from the cruelty of the pursuing sea.

I need not, I hope, point out to the reader the ill.u.s.tration of this law of continuance in the subject chosen for our general ill.u.s.tration. It was simply that gradual succession of the retiring arches of the bridge which induced Turner to paint the subject at all; and it was this same principle which led him always to seize on subjects including long bridges where-ever he could find them; but especially, observe, unequal bridges, having the highest arch at one side rather than at the centre.

There is a reason for this, irrespective of general laws of composition, and connected with the nature of rivers, which I may as well stop a minute to tell you about, and let you rest from the study of composition.

[Ill.u.s.tration: FIG. 33.]

All rivers, small or large, agree in one character, they like to lean a little on one side: they cannot bear to have their channels deepest in the middle, but will always, if they can, have one bank to sun themselves upon, and another to get cool under; one shingly sh.o.r.e to play over, where they may be shallow, and foolish, and childlike, and another steep sh.o.r.e, under which they can pause, and purify themselves, and get their strength of waves fully together for due occasion. Rivers in this way are just like wise men, who keep one side of their life for play, and another for work; and can be brilliant, and chattering, and transparent, when they are at ease, and yet take deep counsel on the other side when they set themselves to their main purpose. And rivers are just in this divided, also, like wicked and good men: the good rivers have serviceable deep places all along their banks, that ships can sail in; but the wicked rivers go scoopingly irregularly under their banks until they get full of strangling eddies, which no boat can row over without being twisted against the rocks; and pools like wells, which no one can get out of but the water-kelpie that lives at the bottom;--but, wicked or good, the rivers all agree in having two kinds of sides. Now the natural way in which a village stonemason therefore throws a bridge over a strong stream is, of course, to build a great door to let the cat through, and little doors to let the kittens through; a great arch for the great current, to give it room in flood time, and little arches for the little currents along the shallow sh.o.r.e.

This, even without any prudential respect for the floods of the great current, he would do in simple economy of work and stone; for the smaller your arches are, the less material you want on their flanks. Two arches over the same span of river, supposing the butments are at the same depth, are cheaper than one, and that by a great deal; so that, where the current is shallow, the village mason makes his arches many and low; as the water gets deeper, and it becomes troublesome to build his piers up from the bottom, he throws his arches wider; at last he comes to the deep stream, and, as he cannot build at the bottom of that, he throws his largest arch over it with a leap, and with another little one or so gains the opposite sh.o.r.e. Of course as arches are wider they must be higher, or they will not stand; so the roadway must rise as the arches widen. And thus we have the general type of bridge, with its highest and widest arch towards one side, and a train of minor arches running over the flat sh.o.r.e on the other; usually a steep bank at the river-side next the large arch; always, of course, a flat sh.o.r.e on the side of the small ones; and the bend of the river a.s.suredly concave towards this flat, cutting round, with a sweep into the steep bank; or, if there is no steep bank, still a.s.suredly cutting into the sh.o.r.e at the steep end of the bridge.

Now this kind of bridge, sympathising, as it does, with the spirit of the river, and marking the nature of the thing it has to deal with and conquer, is the ideal of a bridge; and all endeavours to do the thing in a grand engineer's manner, with a level roadway and equal arches, are barbarous; not only because all monotonous forms are ugly in themselves, but because the mind perceives at once that there has been cost uselessly thrown away for the sake of formality.[248]

Well, to return to our continuity. We see that the Turnerian bridge in Fig. 32. is of the absolutely perfect type, and is still farther interesting by having its main arch crowned by a watch-tower. But as I want you to note especially what perhaps was not the case in the real bridge, but is entirely Turner's doing, you will find that though the arches diminish gradually, not one is _regularly_ diminished--they are all of different shapes and sizes: you cannot see this clearly in 32., but in the larger diagram, Fig. 34., opposite, you will with ease. This is indeed also part of the ideal of a bridge, because the lateral currents near the sh.o.r.e are of course irregular in size, and a simple builder would naturally vary his arches accordingly; and also, if the bottom was rocky, build his piers where the rocks came. But it is not as a part of bridge ideal, but as a necessity of all n.o.ble composition, that this irregularity is introduced by Turner. It at once raises the object thus treated from the lower or vulgar unity of rigid law to the greater unity of clouds, and waves, and trees, and human souls, each different, each obedient, and each in harmonious service.

4. THE LAW OF CURVATURE.

There is, however, another point to be noticed in this bridge of Turner's. Not only does it slope away unequally at its sides, but it slopes in a gradual though very subtle curve. And if you subst.i.tute a straight line for this curve (drawing one with a rule from the base of the tower on each side to the ends of the bridge, in Fig. 34., and effacing the curve), you will instantly see that the design has suffered grievously. You may ascertain, by experiment, that all beautiful objects whatsoever are thus terminated by delicately curved lines, except where the straight line is indispensable to their use or stability: and that when a complete system of straight lines, throughout the form, is necessary to that stability, as in crystals, the beauty, if any exists, is in colour and transparency, not in form. Cut out the shape of any crystal you like, in white wax or wood, and put it beside a white lily, and you will feel the force of the curvature in its purity, irrespective of added colour, or other interfering elements of beauty.

[Ill.u.s.tration: FIG. 34.]

Well, as curves are more beautiful than straight lines, it is necessary to a good composition that its continuities of object, ma.s.s, or colour should be, if possible, in curves, rather than straight lines or angular ones. Perhaps one of the simplest and prettiest examples of a graceful continuity of this kind is in the line traced at any moment by the corks of a net as it is being drawn: nearly every person is more or less attracted by the beauty of the dotted line. Now it is almost always possible, not only to secure such a continuity in the arrangement or boundaries of objects which, like these bridge arches or the corks of the net, are actually connected with each other, but--and this is a still more n.o.ble and interesting kind of continuity--among features which appear at first entirely separate. Thus the towers of Ehrenbreitstein, on the left, in Fig. 32., appear at first independent of each other; but when I give their profile, on a larger scale, Fig.

35., the reader may easily perceive that there is a subtle cadence and harmony among them. The reason of this is, that they are all bounded by one grand curve, traced by the dotted line; out of the seven towers, four precisely touch this curve, the others only falling back from it here and there to keep the eye from discovering it too easily.

[Ill.u.s.tration: FIG. 35.]

And it is not only always _possible_ to obtain continuities of this kind: it is, in drawing large forest or mountain forms essential to truth. The towers of Ehrenbreitstein might or might not in reality fall into such a curve, but a.s.suredly the basalt rock on which they stand did; for all mountain forms not cloven into absolute precipice, nor covered by straight slopes of shales, are more or less governed by these great curves, it being one of the aims of Nature in all her work to produce them. The reader must already know this, if he has been able to sketch at all among the mountains; if not, let him merely draw for himself, carefully, the outlines of any low hills accessible to him, where they are tolerably steep, or of the woods which grow on them. The steeper sh.o.r.e of the Thames at Maidenhead, or any of the downs at Brighton or Dover, or, even nearer, about Croydon (as Addington Hills), are easily accessible to a Londoner; and he will soon find not only how constant, but how graceful the curvature is. Graceful curvature is distinguished from ungraceful by two characters: first, its moderation, that is to say, its close approach to straightness in some parts of its course;[249] and, secondly, by its variation, that is to say, its never remaining equal in degree at different parts of its course.

This variation is itself twofold in all good curves.

[Ill.u.s.tration: FIG. 36.]

A. There is, first, a steady change through the whole line from less to more curvature, or more to less, so that _no_ part of the line is a segment of a circle, or can be drawn by compa.s.ses in any way whatever.

Thus, in Fig. 36., _a_ is a bad curve, because it is part of a circle, and is therefore monotonous throughout; but _b_ is a good curve, because it continually changes its direction as it proceeds.

[Ill.u.s.tration: FIG. 37.]

The _first_ difference between good and bad drawing of tree boughs consists in observance of this fact. Thus, when I put leaves on the line _b_, as in Fig. 37., you can immediately feel the springiness of character dependent on the changefulness of the curve. You may put leaves on the other line for yourself, but you will find you cannot make a right tree spray of it. For _all_ tree boughs, large or small, as well as all n.o.ble natural lines whatsoever, agree in this character; and it is a point of primal necessity that your eye should always seize and your hand trace it. Here are two more portions of good curves, with leaves put on them at the extremities instead of the flanks, Fig. 38.; and two showing the arrangement of ma.s.ses of foliage seen a little farther off, Fig. 39., which you may in like manner amuse yourself by turning into segments of circles--you will see with what result. I hope, however, you have beside you by this time, many good studies of tree boughs carefully made, in which you may study variations of curvature in their most complicated and lovely forms.[250]

[Ill.u.s.tration: FIG. 38.]

[Ill.u.s.tration: FIG. 39.]

B. Not only does every good curve vary in general tendency, but it is modulated, as it proceeds, by myriads of subordinate curves. Thus the outlines of a tree trunk are never as at _a_, Fig. 40, but as at _b_. So also in waves, clouds, and all other n.o.bly formed ma.s.ses. Thus another essential difference between good and bad drawing, or good and bad sculpture, depends on the quant.i.ty and refinement of minor curvatures carried, by good work, into the great lines. Strictly speaking, however, this is not variation in large curves, but composition of large curves out of small ones; it is an increase in the quant.i.ty of the beautiful element, _but not a change in its nature_.

5. THE LAW OF RADIATION.

[Ill.u.s.tration: FIG. 40.]

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_.

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 sh.o.r.e, 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 connexion 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 ma.s.ses 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.

295.); besides this, nearly all beautiful trees have a tendency to divide into two or more princ.i.p.al ma.s.ses, which give a prettier and more complicated symmetry than if one stem ran all the way up the centre.

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. 296), 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 centre 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 any thing like a representative number of types, I should have to give several hundreds of figures such as Fig. 44.[251]

[Ill.u.s.tration: FIG. 41.]

[Ill.u.s.tration: FIG. 42.]

[Ill.u.s.tration: FIG. 43.]

[Ill.u.s.tration: FIG. 44.]

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 ma.s.s 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,[252] as in Fig. 45., the lines which its ribs will take, and the general contour of it, as seen in different directions, from above and below; and from one side and another, will give you the closest approximation to the perspectives and foreshortenings of a well-grown branch-flake. Fig. 25. above, page 316., 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 leaf.a.ge; 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. Figure 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.

[Ill.u.s.tration: FIG. 45.]

[Ill.u.s.tration: FIG. 46.]

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 gra.s.s 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 ma.s.ses; 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. page 372. 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 ma.s.s required in those studies.

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 s.p.a.ces they enclose, 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 encompa.s.sing 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.

[Ill.u.s.tration: FIG. 47.]

Fig. 47., which is a block-plan of a leaf of columbine, without its minor divisions on the edges, will ill.u.s.trate the principle clearly. It is composed of a central large ma.s.s, A, and two lateral ones, of which the one on the right only is lettered, B. Each of these ma.s.ses 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 ma.s.ses is divided into three; but while the central ma.s.s, A of A, is symmetrically divided, the B of B is unsymmetrical, its largest side-lobe being lowest. Again _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 ma.s.s; 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.

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[253] vegetable form is appointed to express these four laws in n.o.ble balance of authority.

1. Support from one living root.

2. Radiation, or tendency of force from some one given point, either in the root, or in some stated connexion with it.

3. Liberty of each bough to seek its own livelihood and happiness according to its needs, by irregularities of action both in its play and its work, either stretching out to get its required nourishment from light and rain, by finding some sufficient breathing-place among the other branches, or knotting and gathering itself up to get strength for any load which its fruitful blossoms may lay upon it, and for any stress of its storm-tossed luxuriance of leaves; or playing hither and thither as the fitful sunshine may tempt its young shoots, in their undecided states of mind about their future life.

4. Imperative requirement of each bough to stop within certain limits, expressive of its kindly fellowship and fraternity with the boughs in its neighborhood; and to work with them according to its power, magnitude, and state of health, to bring out the general perfectness of the great curve, and circ.u.mferent stateliness of the whole tree.

I think I may leave you, unhelped, to work out the moral a.n.a.logies of these laws; you may, perhaps, however, be a little puzzled to see the meeting of the second one. It typically expresses that healthy human actions should spring radiantly (like rays) from some single heart motive; the most beautiful systems of action taking place when this motive lies at the root of the whole life, and the action is clearly seen to proceed from it; while also many beautiful secondary systems of action taking place from motives not so deep or central, but in some beautiful subordinate connexion with the central or life motive.

The other laws, if you think over them, you will find equally significative; and as you draw trees more and more in their various states of health and hardship, you will be every day more struck by the beauty of the types they present of the truths most essential for mankind to know;[254] and you will see what this vegetation of the earth, which is necessary to our life, first, as purifying the air for us and then as food, and just as necessary to our joy in all places of the earth,--what these trees and leaves, I say, are meant to teach us as we contemplate them, and read or hear their lovely language, written or spoken for us, not in frightful black letters, nor in dull sentences, but in fair green and shadowy shapes of waving words, and blossomed brightness of odoriferous wit, and sweet whispers of unintrusive wisdom, and playful morality.

Well, I am sorry myself to leave the wood, whatever my reader may be; but leave it we must, or we shall compose no more pictures to-day.