Chapter XVII: Resulting Forms:--Fourthly, Banks (1)

Sec. 1. During all our past investigations of hill form, we have been obliged to refer continually to certain results produced by the action of descending streams or falling stones. The actual contours assumed by any mountain range towards its foot depend usually more upon this torrent sculpture than on the original conformation of the masses; the existing hill side is commonly an accumulation of debris; the existing glen commonly an excavated watercourse; and it is only here and there that portions of rock, retaining impress of their original form, jut from the bank, or shelve across the stream.

Sec. 2. Now this sculpture by streams, or by gradual weathering, is the finishing work by which Nature brings her mountain forms into the state in which she intends us generally to observe and love them. The violent convulsion or disruption by which she first raises and separates the masses may frequently be intended to produce impressions of terror rather than of beauty; but the laws which are in constant operation on all noble and enduring scenery must assuredly be intended to produce results grateful to men. Therefore, as in this final pencilling of Nature's we shall probably find her ideas of mountain beauty most definitely expressed, it may be well that, before entering on this part of our subject, we should recapitulate the laws respecting beauty of form which we arrived at in the abstract.

Sec. 3. Glancing back to the fourteenth and fifteenth paragraphs of the chapter on Infinity, in the second volume, and to the third and tenth of the chapters on Unity, the reader will find that abstract beauty of form is supposed to depend on continually varied curvatures of line and surface, associated so as to produce an effect of some unity among themselves, and opposed, in order to give them value, by more or less straight or rugged lines.

The reader will, perhaps, here ask why, if both the straight and curved lines are necessary, one should be considered more beautiful than the other. Exactly as we consider light beautiful and darkness ugly, in the abstract, though both are essential to all beauty. Darkness mingled with color gives the delight of its depth or power; even pure blackness, in spots or chequered patterns, is often exquisitely delightful; and yet we do not therefore consider, in the abstract, blackness to be beautiful.

Just in the same way straightness mingled with curvature, that is to say, the close approximation of part of any curve to a straight line, gives to such curve all its spring, power, and nobleness: and even perfect straightness, limiting curves, or opposing them, is often pleasurable: yet, in the abstract, straightness is always ugly, and curvature always beautiful.

Thus, in the figure at the side, the eye will instantly prefer the semicircle to the straight line; the trefoil (composed of three semicircles) to the triangle; and the cinqfoil to the pentagon. The mathematician may perhaps feel an opposite preference; but he must be conscious that he does so under the influence of feelings quite different from those with which he would admire (if he ever does admire) a picture or statue; and that if he could free himself from those associations, his judgment of the relative agreeableness of the forms would be altered. He may rest assured that, by the natural instinct of the eye and thought, the preference is given instantly, and always, to the curved form; and that no human being of unprejudiced perceptions would desire to substitute triangles for the ordinary shapes of clover leaves, or pentagons for those of potentillas.

Sec. 4. All curvature, however, is not equally agreeable; but the examination of the laws which render one curve more beautiful than another, would, if carried out to any completeness, alone require a volume. The following few examples will be enough to put the reader in the way of pursuing the subject for himself.

Take any number of lines, _a b_, _b c_, _c d_, &c., Fig. 91, bearing any fixed proportion to each other. In this figure, _b c_ is one third longer than _a b_, and _c d_ than _b c_; and so on. Arrange them in succession, keeping the inclination, or angle, which each makes with the preceding one always the same. Then a curve drawn through the extremities of the lines will be a beautiful curve; for it is governed by consistent laws; every part of it is connected by those laws with every other, yet every part is different from every other; and the mode of its construction implies the possibility of its continuance to infinity; it would never return upon itself though prolonged for ever. These characters must be possessed by every perfectly beautiful curve.

If we make the difference between the component or measuring lines less, as in Fig. 92, in which each line is longer than the preceding one only by a fifth, the curve will be more contracted and less beautiful. If we enlarge the difference, as in Fig. 93, in which each line is double the preceding one, the curve will suggest a more rapid proceeding into infinite space, and will be more beautiful. Of two curves, the same in other respects, that which suggests the quickest attainment of infinity is always the most beautiful.

Sec. 5. These three curves being all governed by the same general law, with a difference only in dimensions of lines, together with all the other curves so constructible, varied as they may be infinitely, either by changing the lengths of line, or the inclination of the lines to each other, are considered by mathematicians only as one curve, having this peculiar character about it, different from that of most other infinite lines, that any portion of it is a magnified repetition of the preceding portion; that is to say, the portion between _e_ and _g_ is precisely what that between _c_ and _e_ would look, if seen through a lens which magnified somewhat more than twice. There is therefore a peculiar equanimity and harmony about the look of lines of this kind, differing, I think, from the expression of any others except the circle. Beyond the point _a_ the curve may be imagined to continue to an infinite degree of smallness, always circling nearer and nearer to a point, which, however, it can never reach.

Sec. 6. Again: if, along the horizontal line, A B, Fig. 94, we measure any number of equal distances, A _b_, _b c_, &c., and raise perpendiculars from the points _b_, _c_, _d_, &c., of which each perpendicular shall be longer, by some given proportion (in this figure it is one third), than the preceding one, the curve _x y_, traced through their extremities, will continually change its direction, but will advance into space in the direction of _y_ as long as we continue to measure distances along the line A B, always inclining more and more to the nature of a straight line, yet never becoming one, even if continued to infinity. It would, in like manner, continue to infinity in the direction of _x_, always approaching the line A B, yet never touching it.

Sec. 7. An infinite number of different lines, more or less violent in curvature according to the measurements we adopt in designing them, are included, or defined, by each of the laws just explained. But the number of these laws themselves is also infinite. There is no limit to the multitude of conditions which may be invented, each producing a group of curves of a certain common nature. Some of these laws, indeed, produce single curves, which, like the circle, can vary only in size; but, for the most part, they vary also, like the lines we have just traced, in the rapidity of their curvature. Among these innumerable lines, however, there is one source of difference in character which divides them, infinite as they are in number, into two great classes. The first class consists of those which are limited in their course, either ending abruptly, or returning to some point from which they set out; the second class, of those lines whose nature is to proceed for ever into space. Any portion of a circle, for instance, is, by the law of its being, compelled, if it continue its course, to return to the point from which it set out; so also any portion of the oval curve (called an ellipse), produced by cutting a cylinder obliquely across. And if a single point be marked on the rim of a carriage wheel, this point, as the wheel rolls along the road, will trace a curve in the air from one part of the road to another, which is called a cycloid, and to which the law of its existence appoints that it shall always follow a similar course, and be terminated by the level line on which the wheel rolls. All such curves are of inferior beauty: and the curves which are incapable of being completely drawn, because, as in the two cases above given, the law of their being supposes them to proceed for ever into space, are of a higher beauty.

Sec. 8. Thus, in the very first elements of form, a lesson is given us as to the true source of the nobleness and chooseableness of all things. The two classes of curves thus sternly separated from each other, may most properly be distinguished as the "Mortal and Immortal Curves;" the one having an appointed term of existence, the other absolutely incomprehensible and endless, only to be seen or grasped during a certain moment of their course. And it is found universally that the class to which the human mind is attached for its chief enjoyment are the Endless or Immortal lines.

Sec. 9. "Nay," but the reader answers, "what right have you to say that one class is more beautiful than the other? Suppose I like the finite curves best, who shall say which of us is right?"

No one. It is simply a question of experience. You will not, I think, continue to like the finite curves best as you contemplate them carefully, and compare them with the others. And if you should do so, it then yet becomes a question to be decided by longer trial, or more widely canvassed opinion. And when we find on examination that every form which, by the consent of human kind, has been received as lovely, in vases, flowing ornaments, embroideries, and all other things dependent on abstract line, is composed of these infinite curves, and that Nature uses them for every important contour, small or large, which she desires to recommend to human observance, we shall not, I think, doubt that the preference of such lines is a sign of healthy taste, and true instinct.

Sec. 10. I am not sure, however, how far the delightfulness of such line, is owing, not merely to their expression of infinity, but also to that of restraint or moderation. Compare Stones of Venice, vol. iii. chap. i. Sec. 9, where the subject is entered into at some length. Certainly the beauty of such curvature is owing, in a considerable degree, to both expressions; but when the line is sharply terminated, perhaps more to that of moderation than of infinity. For the most part, gentle or subdued sounds, and gentle or subdued colors, are more pleasing than either in their utmost force; nevertheless, in all the noblest compositions, this utmost power is permitted, but only for a short time, or over a small space. Music must rise to its utmost loudness, and fall from it; color must be gradated to its extreme brightness, and descend from it; and I believe that absolutely perfect treatment would, in either case, permit the intensest sound and purest color only for a point or for a moment.

Curvature is regulated by precisely the same laws. For the most part, delicate or slight curvature is more agreeable than violent or rapid curvature; nevertheless, in the best compositions, violent curvature is permitted, but permitted only over small spaces in the curve.

Sec. 11. The right line is to the curve what monotony is to melody, and what unvaried color is to gradated color. And as often the sweetest music is so low and continuous as to approach a monotone; and as often the sweetest gradations so delicate and subdued as to approach to flatness, so the finest curves are apt to hover about the right line, nearly coinciding with it for a long space of their curve; never absolutely losing their own curvilinear character, but apparently every moment on the point of merging into the right line. When this is the case, the line generally returns into vigorous curvature at some part of its course, otherwise it is apt to be weak, or slightly rigid; multitudes of other curves, not approaching the right line so nearly, remain less vigorously bent in the rest of their course; so that the quantity[88] of curvature is the same in both, though differently distributed.

Sec. 12. The modes in which Nature produces variable curves on a large scale are very numerous, but may generally be resolved into the gradual increase or diminution of some given force. Thus, if a chain hangs between two points A and B, Fig. 95, the weight of chain sustained by any given link increases gradually from the central link at C, which has only its own weight to sustain, to the link at B, which sustains, besides its own, the weight of all the links between it and C. This increased weight is continually pulling the curve of the swinging chain more nearly straight as it ascends towards B; and hence one of the most beautifully gradated natural curves--called the catenary--of course assumed not by chains only, but by all flexible and elongated substances, suspended 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 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.

Sec. 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.

Sec. 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 noble 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 passion, and the natural sequence of the thought.

Sec. 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 classed 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 noble 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.

I give one more example from another leaf of the same manuscript, 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.

Sec. 20. The quantity 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.

The four systems of mountain line.

Sec. 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 mass by the fall of water or of stones.

2. Lines of Projection. Those which are produced in debris by the bounding of the masses, 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 assumed 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.

Whenever a mass of mountain is worn gradually away by forces descending from its top, it _necessarily_ assumes, 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]

Sec. 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.

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.

Sec. 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.

Sec. 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 mass.

Sec. 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.

Sec. 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 analyze 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 masses remaining undisturbed at the bottom, while the smaller are gradually carried farther and farther by surface streams.

3. Lines of Escape.

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

Sec. 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.

Sec. 28. It may easily be imagined that when the operation takes place on a large scale, the mass 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 passes 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 circumstances, 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 passion, 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 lassitude it is brought back to its central course, and compelled to forego for a few weeks or months the luxury of deviation.

Sec. 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 quantity, 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 passes 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.

Sec. 30. I have etched above, Plate +35+, a portion of the flank of the valley of Chamouni, which presents nearly every class 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 multitude 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 shore. 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.

Sec. 31. I found it a matter of the greatest difficulty to investigate the picturesque characters of these lines of projection and escape, because, as presented to the eye, they are always modified by perspective; and it is almost a physical impossibility to get a true profile of any of the slopes, they round and melt so constantly into one another. Many of them, roughly measured, are nearly circular in tendency;[92] but I believe they are all portions of infinite curves either modified by the concealment or destruction of the lower lips of debris, or by their junction with straight lines of slope above, throwing the longest limb of the curve upwards. Fig. 1, in Plate +45+ opposite, is a simple but complete example from Chamouni; the various overlapping and concave lines at the bottom being the limits of the mass at various periods, more or less broken afterwards by the peasants, either by removing stones for building, or throwing them back at the edges here and there, out of the way of the plough; but even with all these breaks, their natural unity is so sweet and perfect, that, if the reader will turn the plate upside down, he will see I have no difficulty (merely adding a quill or two) in turning them into a bird's wing (Fig. 2), a little ruffled indeed, but still graceful, and not of such a form as one would have supposed likely to be designed and drawn, as indeed it was, by the rage of a torrent.

But we saw in Chap. VII. Sec. 10 that this very rage was, in fact, a beneficent power,--creative, not destructive; and as all its apparent cruelty is overruled by the law of love, so all its apparent disorder is overruled by the law of loveliness: the hand of God, leading the wrath of the torrent to minister to the life of mankind, guides also its grim surges by the laws of their delight; and bridles the bounding rocks, and appeases the flying foam, till they lie down in the same lines that lead forth the fibres of the down on a cygnet's breast.

Sec. 32. The straight slopes with which these curves unite themselves below, in Plate +33+ (_f g_ in reference figure), are those spoken of in the outset as lines of rest. But I defer to the next chapter the examination of these, which are a separate family of lines (not curves at all), in order to reassemble the conclusions we have now obtained respecting _curvature_ in mountains, and apply them to questions of art.

And, first, it is of course not to be supposed that these symmetrical laws are so manifest in their operation as to force themselves on the observance of men in general. They are interrupted, necessarily, by every fantastic accident in the original conformation of the hills, which, according to the hardness of their rocks, more or less accept or refuse the authority of general law. Still, the farther we extend our observance of hills, the more we shall be struck by the continual roundness and softness which it seems the object of nature to give to every form; so that, when crags look sharp and distorted, it is not so much that they are unrounded, as that the various curves are more subtly accommodated to the angles, and that, instead of being worn into one sweeping and smooth descent, like the surface of a knoll or down, the rock is wrought into innumerable minor undulations, its own fine anatomy showing through all.

Sec. 33. Perhaps the mountain which I have drawn on the opposite page (Plate +46+[93]) is, in its original sternness of mass, and in the complexity of lines into which it has been chiselled, as characteristic an instance as could be given by way of general type. It is one of no name or popular interest, but of singular importance in the geography of Switzerland, being the angle buttress of the great northern chain of the Alps (the chain of the Jungfrau and Gemmi), and forming the promontory round which the Rhone turns to the north-west, at Martigny. It is composed of an intensely hard gneiss (slaty crystalline), in which the plates of mica are set for the most part against the angle, running nearly north and south, as in Fig. 105, and giving the point, therefore, the utmost possible strength, which, however, cannot prevent it from being rent gradually by enormous curved fissures, and separated into huge vertical flakes and chasms, just at the lower promontory, as seen in Plate +46+, and (in plan) in Fig. 105. The whole of the upper surface of the promontory is wrought by the old glaciers into furrows and striae more notable than any I ever saw in the Alps.

Sec. 34. Now observe, we have here a piece of Nature's work which she has assuredly been long in executing, and which is in peculiarly firm and stable material. It is in her best rock (slaty crystalline), at a point important for all her geographical purposes, and at the degree of mountain elevation especially adapted to the observation of mankind. We shall therefore probably ascertain as much of Nature's mind about these things in this piece of work as she usually allows us to see all at once.

Sec. 35. If the reader will take a pencil, and, laying tracing paper over the plate, follow a few of its lines, he will (unless before accustomed to accurate mountain-drawing) be soon amazed by the complexity, endlessness, and harmony of the curvatures. He will find that there is not one line in all that rock which is not an infinite curve, and united in some intricate way with others, and suggesting others unseen; and if it were the reality, instead of my drawing, which he had to deal with, he would find the infinity, in a little while, altogether overwhelm him. But even in this imperfect sketch, as he traces the multitudinous involution of flowing line, passing from swift to slight curvature, or slight to swift, at every instant, he will, I think, find enough to convince him of the truth of what has been advanced respecting the natural appointment of curvature as the first element of all loveliness in form.

Sec. 36. "Nay, but there are hard and straight lines mingled with those curves continually." True, as we have said so often, just as shade is mixed with light. Angles and undulations may rise and flow continually, one through or over the other; but the opposition is in quantity nearly always the same, if the mass is to be pleasant to the eye. In the example previously given (Plate +40+), the limestone bank above Villeneuve, it is managed in a different way, but is equal in degree; the lower portion of the hill is of soft rock in thin laminae; the upper mass is a solid and firm bed, yet not so hard as to stand all weathers. The lower portion, therefore, is rounded into almost unbroken softness of bank; the upper surmounts it as a rugged wall, and the opposition of the curve and angle is just as complete as in the first example, in which one was continually mingled with the other.

Sec. 37. Next, note the _quantity_ in these hills. It is an element on which I shall have to insist more in speaking of vegetation; but I must not pass it by, here, since, in fact, it constitutes one of the essential differences between hills of first-rate magnificence, and inferior ones. Not that there is want of quantity even in the lower ranges, but it is a quantity of inferior things, and therefore more easily represented or suggested. On a Highland hill side are multitudinous clusters of fern and heather; on an Alpine one, multitudinous groves of chestnut and pine. The number of the things may be the same, but the sense of infinity is in the latter case far greater, because the number is of nobler things. Indeed, so far as mere magnitude of space occupied on the field of the horizon is the measure of objects, a bank of earth ten feet high may, if we stoop to the foot of it, be made to occupy just as much of the sky as that bank of mountain at Villeneuve; nay, in many respects its little ravines and escarpments, watched with some help of imagination, may become very sufficiently representative to us of those of the great mountain; and in classing all water-worn mountain-ground under the general and humble term of Banks, I mean to imply this relationship of structure between the smallest eminences and the highest. But in this matter of superimposed _quantity_ the distinctions of rank are at once fixed. The heap of earth bears its few tufts of moss or knots of grass; the Highland or Cumberland mountain its honeyed heathers or scented ferns; but the mass of the bank at Martigny or Villeneuve has a vineyard in every cranny of its rocks, and a chestnut grove on every crest of them.

Sec. 38. This is no poetical exaggeration. Look close into that plate (+46+). Every little circular stroke in it among the rocks means, not a clump of copse nor wreath of fern, but a walnut tree, or a Spanish chestnut, fifty or sixty feet high. Nor are the little curves, thus significative of trees, laid on at random. They are not indeed counted, tree by tree, but they are most carefully distributed in the true proportion and quantity; or if I have erred at all, it was, from mere fatigue, on the side of sparingness. The minute mounds and furrows scattered up the side of that great promontory, when they are actually approached, after three or four hours' climbing, turn into independent hills with true _parks_ of lovely pasture land enclosed among them, and avenue after avenue of chestnuts, walnuts, and pines bending round their bases; while in the deeper dingles, unseen in the drawing, nestle populous villages, literally bound down to the rock by enormous trunks of vine, which, first trained lightly over the loose stone roofs, have in process of years cast their fruitful net over the whole village, and fastened it to the ground under their purple weight and wayward coils, as securely as ever human heart was fastened to earth by the net of the Flatterer.

Sec. 39. And it is this very richness of incident and detail which renders Switzerland so little attractive in its subjects to the ordinary artist. Observe, this study of mine in Plate +46+ does not profess to be a _picture_ at all. It is a mere sketch or catalogue of all that there is on the mountain side, faithfully written out, but no more than should be put down by any conscientious painter for mere guidance, before he begins his work, properly so called; and in finishing such a subject no trickery nor shorthand is of any avail whatsoever; there are a certain number of trees to be drawn; and drawn they must be, or the place will not bear its proper character. They are not misty wreaths of soft wood suggestible by a sweep or two of the brush; but arranged and lovely clusters of trees, clear in the mountain sunlight, each specially grouped and as little admitting any carelessness of treatment, though five miles distant, as if they were within a few yards of us; the whole meaning and power of the scene being involved in that one fact of quantity. It is not large merely by multitudes of tons of rock,--the number of tons is not measurable; it is not large by elevation of angle on the horizon,--a house-roof near us rises higher; it is not large by faintness of aerial perspective,--in a clear day it often looks as if we could touch the summit with the hand. But it is large by this one unescapable fact that, from the summit to the base of it, there are of timber trees so many countable thousands. The scene differs from subjects not Swiss by including hundreds of other scenes within itself, and is mighty, not by scale, but by aggregation.

Sec. 40. And this is more especially and humiliatingly true of pine forest. Nearly all other kinds of wood may be reduced, over large spaces, to undetailed masses; but there is nothing but patience for pines; and this has been one of the principal reasons why artists call Switzerland "unpicturesque." There may perhaps be, in the space of a Swiss valley which comes into a picture, from five to ten millions of well grown pines.[94] Every one of these pines must be drawn before the scene can be. And a pine cannot be represented by a round stroke, nor by an upright one, nor even by an angular one; no conventionalism will express a pine; it must be legitimately drawn, with a light side and a dark side, and a soft gradation from the top downwards, or it does not look like a pine at all. Most artists think it not desirable to choose a subject which involves the drawing of ten millions of trees; because, supposing they could even do four or five in a minute, and worked for ten hours a day, their picture would still take them ten years before they had finished its pine forests. For this, and other similar reasons, it is declared usually that Switzerland is ugly and unpicturesque; but that is not so; it is only that _we_ cannot paint it. If we could, it would be as interesting on the canvas as it is in reality; and a painter of fruit and flowers might just as well call a human figure unpicturesque, because it was to him unmanageable, as the ordinary landscape-effect painter speak in depreciation of the Alps.

Sec. 41. It is not probable that any subjects such as we have just been describing, involving a necessity of ten years' labor, will be executed by the modern landscape school,--at least, until its Pre-Raphaelitic tendencies become much more developed than they are yet; nor was it desirable that they should have been by Turner, whose fruitful invention would have been unwisely arrested for a length of time on any single subject, however beautiful. But with his usual certainty of perception, he fastened at once on this character of "quantity," as the thing to be expressed, in one way or another, in all grand mountain-drawing; and the subjects of his on which I have chiefly dwelt in the First Volume (chapter on the Inferior Mountains, Sec. 16, &c.) are distinguished from the work of other painters in nothing so much as in this redundance. Beautiful as they are in color, graceful in fancy, powerful in execution,--in none of these things do they stand so much alone as in plain, calculable quantity; he having always on the average twenty trees or rocks where other people have only one, and winning his victories not more by skill of generalship than by overwhelming numerical superiority.

Sec. 42. I say his works are distinguished in this more than in anything else, not because this is their highest quality, but because it is peculiar to them. Invention, color, grace of arrangement, we may find in Tintoret and Veronese in various manifestation; but the expression of the infinite redundance of natural landscape had never been attempted until Turner's time; and the treatment of the masses of mountain in the Daphne and Leucippus, Golden Bough, and Modern Italy, is wholly without precursorship in art.

Nor, observe, do I insist upon this quantity _merely_ as arithmetical, or as if it were producible by repetition of similar things. It would be easy to be redundant, if multiplication of the same idea constituted fulness; and since Turner first introduced these types of landscape, myriads of vulgar imitations of them have been produced, whose perpetrators have supposed themselves disciples or rivals of Turner, in covering their hills with white dots for forest, and their foregrounds with yellow sparklings for herbage. But the Turnerian redundance is never monotonous. Of the thousands of groups of touches which, with him, are necessary to constitute a single bank of hill, not one but has some special character, and is as much a separate invention as the whole plan of the picture. Perhaps this may be sufficiently understood by an attentive examination of the detail introduced by him in his St. Gothard subject, as shown in Plate +37+.