-- 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.

-- 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 themselves almost countless. In a single extremity of a magnolia spray, the uppermost figure in Plate +42+, including only sixteen leaves, each leaf having some three to five distinct curves along its edge, the lines for separate study, including those of the stems, would be between sixty and eighty. In a single spring-shoot of laburnum, the lower figure in the same plate, I leave the reader to count them for himself; all these, observe, being seen at one view only, and every change of position bringing into sight another equally numerous set of curves. For instance, in Plate +43+ is a group of four withered leaves, in four positions, giving, each, a beautiful and well composed group of curves, variable gradually into the next group as the branch is turned.

-- 17. The following Plate (+44+), representing a young shoot of independent ivy, just beginning to think it would like to get something to cling to, shows the way in which Nature brings subtle curvature into forms that at first seem rigid. The stems of the young leaves look nearly straight, and the sides of the projecting points, or bastions, of the leaves themselves nearly so; but on examination it will be found that there is not a stem nor a leaf-edge but is a portion of one infinite curve, if not of two or three. The main line of the supporting stem is a very lovely one; and the little half-opened leaves, in their thirteenth-century segmental simplicity (compare Fig. 9, Plate 8 in Vol.

III.), singularly spirited and beautiful. It may, perhaps, interest the general reader to know that one of the infinite curves derives its name from its supposed resemblance to the climbing of ivy up a tree.

[Ill.u.s.tration: FIG. 97.]

-- 18. I spoke just now of "well-composed" curves,--I mean curves so arranged as to oppose and set each other off, and yet united by a common law; for as the beauty of every curve depends on the unity of its several component lines, so the beauty of each group of curves depends on their submission to some general law. In forms which quickly attract the eye, the law which unites the curves is distinctly manifest; but, in the richer compositions of Nature, cunningly concealed by delicate infractions of it;--wilfulnesses they seem, and forgetfulnesses, which, if once the law be perceived, only increase our delight in it by showing that it is one of equity, not of rigor, and allows, within certain limits, a kind of individual liberty. Thus the system of unison which regulates the magnolia shoot, in Plate +42+, is formally expressed in Fig. 97. Every line has its origin in the point p, and the curves generally diminish in intensity towards the extremities of the leaves, one or two, however, again increasing their sweep near the points. In vulgar ornamentation, entirely rigid laws of line are always observed; and the common Greek honeysuckle and other such formalisms are attractive to uneducated eyes, owing to their manifest compliance with the first conditions of unity and symmetry, being to really n.o.ble ornamentation what the sing-song of a bad reader of poetry, laying regular emphasis on every required syllable of every foot, is to the varied, irregular, unexpected, inimitable cadence of the voice of a person of sense and feeling reciting the same lines,--not incognisant of the rhythm, but delicately bending it to the expression of pa.s.sion, and the natural sequence of the thought.

-- 19. In mechanically drawn patterns of dress, Alhambra and common Moorish ornament, Greek mouldings, common flamboyant traceries, common Corinthian and Ionic capitals, and such other work, lines of this declared kind (generally to be cla.s.sed under the head of "doggerel ornamentation") may be seen in rich profusion; and they are necessarily the only kind of lines which can be felt or enjoyed by persons who have been educated without reference to natural forms; their instincts being blunt, and their eyes actually incapable of perceiving the inflexion of n.o.ble curves. But the moment the perceptions have been refined by reference to natural form, the eye requires perpetual variation and transgression of the formal law. Take the simplest possible condition of thirteenth-century scroll-work, Fig. 98. The law or cadence established is of a circling tendril, terminating in an ivy-leaf. In vulgar design, the curves of the circling tendril would have been similar to each other, and might have been drawn by a machine, or by some mathematical formula. But in good design all imitation by machinery is impossible. No curve is like another for an instant; no branch springs at an expected point. A cadence is observed, as in the returning clauses of a beautiful air in music; but every clause has its own change, its own surprises.

The enclosing form is here stiff and (nearly) straight-sided, in order to oppose the circular scroll-work; but on looking close it will be found that each of its sides is a portion of an infinite curve, almost too delicate to be traced; except the short lowest one, which is made quite straight, to oppose the rest.

[Ill.u.s.tration: FIG. 98.]

I give one more example from another leaf of the same ma.n.u.script, Fig.

99, merely to show the variety introduced by the old designers between page and page. And, in general, the reader may take it for a settled law that, whatever can be done by machinery, or imitated by formula, is not worth doing or imitating at all.

-- 20. The quant.i.ty of admissible transgression of law varies with the degree in which the ornamentation involves or admits imitation of nature. Thus, if these ivy leaves in Fig. 99 were completely drawn in light and shade, they would not be properly connected with the more or less regular sequences of the scroll; and in every subordinate ornament, something like complete symmetry may be admitted, as in bead mouldings, chequerings, &c. Also, the ways in which the transgression may be granted vary infinitely; in the finest compositions it is perpetual, and yet so balanced and atoned for as always to bring about more beauty than if there had been no transgression. In a truly fine mountain or organic line, if it is looked at in detail, no one would believe in its being a continuous curve, or being subjected to any fixed law. It seems broken, and bending a thousand ways; perfectly free and wild, and yielding to every impulse. But, after following with the eye three or four of its impulses, we shall begin to trace some strange order among them; every added movement will make the ruling intent clearer; and when the whole life of the line is revealed at last, it will be found to have been, throughout, as obedient to the true law of its course as the stars in their orbits.

[Ill.u.s.tration: FIG. 99.]

The four systems of mountain line.

-- 21. Thus much may suffice for our immediate purpose respecting beautiful lines in general. We have now to consider the particular groups of them belonging to mountains.

The lines which are produced by course of time upon hill contours are mainly divisible into four systems.

1. Lines of Fall. Those which are wrought out on the solid ma.s.s by the fall of water or of stones.

2. Lines of Projection. Those which are produced in debris by the bounding of the ma.s.ses, under the influence of their falling force.

3. Lines of Escape. Those which are produced by the spreading of debris from a given point over surfaces of varied shape.

4. Lines of Rest. Those which are a.s.sumed by debris when in a state of comparative permanence and stability.

1. Lines of Fall.

1. Lines of Fall. Produced by falling bodies upon hill-surfaces.

However little the reader may be acquainted with hills, I believe that, almost instinctively, he will perceive that the form supposed to belong to a wooded promontory at _a_, Fig. 100, is an impossible one; and that the form at _b_ is not only a possible but probable one. The lines are equally formal in both. But in _a_, the curve is a portion of a circle, meeting a level line: in _b_ it is an infinite line, getting less and less steep as it ascends.

[Ill.u.s.tration: FIG. 100.]

Whenever a ma.s.s of mountain is worn gradually away by forces descending from its top, it _necessarily_ a.s.sumes, more or less perfectly, according to the time for which it has been exposed, and the tenderness of its substance, such contours as those at _b_, for the simple reason that every stream and every falling grain of sand gains in velocity and erosive power as it descends. Hence, cutting away the ground gradually faster and faster, they produce the most rapid curvature (provided the rock be hard enough) towards the bottom of the hill.[90]

-- 22. But farther: in _b_ it will be noticed that the lines always get steeper as they fall more and more to the right; and I should think the reader must feel that they look more natural, so drawn, than, as at _a_, in unvarying curves.

[Ill.u.s.tration: FIG. 101.]

This is no less easily accounted for. The simplest typical form under which a hill can occur is that of a cone. Let A C B, Fig. 101, have been its original contour. Then the aqueous forces will cut away the shaded portions, reducing it to the outline _d_ C _e_. Farther, in doing so, the water will certainly have formed for itself gullies or channels from top to bottom. These, supposing them at equal distances round the cone, will appear, in perspective, in the lines _g h i_. It does not, of course, matter whether we consider the lines in this figure to represent the bottom of the ravines, or the ridges between, both being formed on similar curves; but the rounded lines in Fig. 100 would be those of forests seen on the edges of each detached ridge.

-- 23. Now although a mountain is rarely perfectly conical, and never divided by ravines at exactly equal distances, the law which is seen in entire simplicity in Fig. 101, applies with a sway more or less interrupted, but always manifest, to every convex and retiring mountain form. All banks that thus turn away from the spectator necessarily are thrown into perspectives like that of one side of this figure; and although not divided with equality, their irregular divisions crowd gradually together towards the distant edge, being then less steep, and separate themselves towards the body of the hill, being then more steep.

[Ill.u.s.tration: FIG. 102.]

-- 24. It follows, also, that not only the whole of the nearer curves, will be steeper, but, if seen from below, the steepest parts of them will be the more important. Supposing each, instead of a curve, divided into a sloping line and a precipitous one, the perspective of the precipice, raising its top continually, will give the whole cone the shape of _a_ or _b_ in Fig. 102, in which, observe, the precipice is of more importance, and the slope of less, precisely in proportion to the nearness of the ma.s.s.

-- 25. Fig. 102, therefore, will be the general type of the form of a convex retiring hill symmetrically constructed. The precipitous part of it may vary in height or in slope according to original conformation; but the heights being supposed equal along the whole flank, the contours will be as in that figure; the various rise and fall of real height altering the perspective appearance accordingly, as we shall see presently, after examining the other three kinds of line.

2. Lines of Projection.

2. Lines of Projection. Produced by fragments bounding or carried forward from the bases of hills.

-- 26. The fragments carried down by the torrents from the flanks of the hill are of course deposited at the base of it. But they are deposited in various ways, of which it is most difficult to a.n.a.lyze the laws; for they are thrown down under the influence partly of flowing water, partly of their own gravity, partly of projectile force caused by their fall from the higher summits of the hill; while the debris itself, after it has fallen, undergoes farther modification by surface streamlets. But in a general way debris descending from the hill side, _a b_, Fig. 103, will arrange itself in a form approximating to the concave line _d c_, the larger ma.s.ses remaining undisturbed at the bottom, while the smaller are gradually carried farther and farther by surface streams.

[Ill.u.s.tration: FIG. 103.]

3. Lines of Escape.

3. Lines of Escape. Produced by the lateral dissemination of the fragments.

-- 27. But this form is much modified by the special direction of the descending force as it escapes from confinement. For a stream coming down a ravine is kept by the steep sides of its channel in concentrated force: but it no sooner reaches the bottom, and escapes from its ravine, than it spreads in all directions, or at least tries to choose a new channel at every flood. Let _a b c_, Fig. 104, be three ridges of mountain. The two torrents coming down the ravine between them meet, at _d_ and _e_, with the heaps of ground formerly thrown down by their own agency. These heaps being more or less in the form of cones, the torrent has a tendency to divide upon their apex, like water poured on the top of a sugar-loaf, and branch into the radiating channels _e x_, _e y_, &c. The stronger it is, the more it is disposed to rush straightforward, or with little curvature, as in the line _e x_, with the impetus it has received in coming down the ravine; the weaker it is, the more readily it will lean to one side or the other, and fall away in the lines of escape, _e y_, or _e h_; but of course at times of highest flood it fills all its possible channels, and invents a few new ones, of which afterwards the straightest will be kept by the main stream, and the lateral curves occupied by smaller branches; the whole system corresponding precisely to the action of the ribs of the young leaf, as shown in Plate +8+ of Vol. III., especially in Fig. 6,--the main torrent, like the main rib, making the largest fortune, i. e. raising the highest heap of gravel and dust.

[Ill.u.s.tration: FIG. 104.]

-- 28. It may easily be imagined that when the operation takes place on a large scale, the ma.s.s of earth thus deposited in a gentle slope at the mountain's foot becomes available for agricultural purposes, and that then it is of the greatest importance to prevent the stream from branching into various channels at its will, and pouring fresh sand over the cultivated fields. Accordingly, at the mouth of every large ravine in the Alps, where the peasants know how to live and how to work, the stream is artificially embanked, and compelled as far as possible to follow the central line down the cone. Hence, when the traveller pa.s.ses along any great valley,--as that of the Rhone or Arve,--into which minor torrents are poured by lateral ravines, he will find himself every now and then ascending a hill of moderate slope, at the _top_ of which he will cross a torrent, or its bed, and descend by another gradual slope to the usual level of the valley. In every such case, his road has ascended a tongue of debris, and has crossed the embanked torrent carried by force along its centre.

Under such circ.u.mstances, the entire tongue or heap of land ceases of course to increase, until the bed of the confined torrent is partially choked by its perpetual deposit. Then in some day of violent rain the waves burst their fetters, branch at their own will, cover the fields of some unfortunate farmer with stones and slime, according to the torrent's own idea of the new form which it has become time to give to the great tongue of land, carry away the road and the bridge together, and arrange everything to their own liking. But the road is again painfully traced among the newly fallen debris; the embankment and bridge again built for the stream, now satisfied with its outbreak; and the tongue of land submitted to new processes of cultivation for a certain series of years. When, however, the torrent is exceedingly savage, and generally of a republican temper, the outbreaks are too frequent and too violent to admit of any cultivation of the tongue of land. A few straggling alder or thorn bushes, their roots buried in shingle, and their lower branches fouled with slime, alone relieve with ragged spots of green the broad waste of stones and dust. The utmost that can be done is to keep the furious stream from choosing a new channel in every one of its fits of pa.s.sion, and remaining in it afterwards, thus extending its devastation in entirely unforeseen directions. The land which it has brought down must be left a perpetual sacrifice to its rage; but in the moment of its la.s.situde it is brought back to its central course, and compelled to forego for a few weeks or months the luxury of deviation.

-- 29. On the other hand, when, owing to the nature of the valley above, the stream is gentle, and the sediment which it brings down small in quant.i.ty, it may be retained for long years in its constant path, while the sides of the bank of earth it has borne down are clothed with pasture and forest, seen in the distance of the great valley as a promontory of sweet verdure, along which the central stream pa.s.ses with an influence of blessing, submitting itself to the will of the husbandman for irrigation, and of the mechanist for toil; now nourishing the pasture, and now grinding the corn, of the land which it has first formed, and now waters.

-- 30. I have etched above, Plate +35+, a portion of the flank of the valley of Chamouni, which presents nearly every cla.s.s of line under discussion, and will enable the reader to understand their relations at once. It represents, as was before stated, the crests of the Montagnes de la Cote and Taconay, shown from base to summit, with the Glacier des Bossons and its moraine. The reference figure given at p. 212 will enable the reader to distinguish its several orders of curves, as follows:

_h r_. Aqueous curves of fall, at the base of the Tapia; very characteristic. Similar curves are seen in mult.i.tude on the two crests beyond as _b c_, _c_ B.

_d e_. First lines of projection. The debris falling from the glacier and the heights above.

_k_, _l_, _n_.Three lines of escape. A considerable torrent (one of whose falls is the well-known Cascade des Pelerins[91]) descends from behind the promontory _h_: its natural or proper course would be to dash straight forward down the line _f g_, and part of it does so; but erratic branches of it slide away round the promontory, in the lines of escape, _k_, _l_, &c. Each row of trees marks, therefore, an old torrent bed, for the torrent always throws heaps of stones up along its banks, on which the pines, growing higher than on the neighboring ground, indicate its course by their supremacy. When the escaped stream is feeble, it steals quietly away down the steepest part of the slope; that is to say, close under the promontory, at _i_. If it is stronger, the impetus from the hill above shoots it farther out, in the line _k_; if stronger still, at _l_; in each case it curves gradually round as it loses its onward force, and falls more and more languidly to leeward, down the slope of the debris.

_r s_. A line which, perhaps, would be more properly termed of limitation than of escape, being that of the base or termination of the heap of torrent debris, which in shape corresponds exactly to the curved lip of a wave, after it has broken, as it slowly stops upon a shallow sh.o.r.e. Within this line the ground is entirely composed of heaps of stones, cemented by granite dust and cushioned with moss, while outside of it, all is smooth pasture. The pines enjoy the stony ground particularly, and hold large meetings upon it, but the alders are shy of it; and, when it has come to an end, form a triumphal procession all round its edge, following the concave line. The correspondent curves above are caused by similar lines in which the debris has formerly stopped.

[Ill.u.s.tration: 45. Debris Curvature.]