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 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.
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.
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) 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; 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) 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. 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.
Sec. 43. I do not, indeed, know if the examples I have given from natural scenes, though they are as characteristic as I could well choose, are enough to accustom the reader to the character of true mountain lines, and to enable him to recognize such lines in other instances; but if not, at all events they may serve to elucidate the main points, and guide to more complete examination of the subject, if it interests him, among the hills themselves. And if, after he has pursued the inquiry long enough to feel the certitude of the laws which I have been endeavoring to illustrate, he turns back again to art, I am well assured it will be with a strange recognition of unconceived excellence, and a newly quickened pleasure in the unforeseen fidelity, that he will trace the pencilling of Turner upon his hill drawings. I do not choose to spend, in this work, the labor and time which would be necessary to analyze, as I have done the drawing of the St. Gothard, any other of Turner's important mountain designs; for the reader must feel the disadvantage they are under in being either reduced in scale, or divided into fragments: and therefore these chapters are always to be considered merely as memoranda for reference before the pictures which the reader may have it in his power to examine. But this one drawing of the St. Gothard, as it has already elucidated for us Turner's knowledge of crest structure, will be found no less wonderful in the fulness with which it illustrates his perception of the lower aqueous and other curvatures. If the reader will look back to the etching of the entire subject, Plate 21, he will now discern, I believe, without the necessity of my lettering them for him, the lines of fall, rounded down from the crests until they plunge into the overhanging precipices; the lines of projection, where the fallen stones extend the long concave sweep from the couloir, pushing the torrent against the bank on the other side; in the opening of the ravine he will perceive the oblique and parallel inclination of its sides, following the cleavage of the beds in the diagonal line A B of the reference figure; and, finally, in the great slope and precipice on the right of it, he will recognize one of the grandest types of the peculiar mountain mass which Turner always chose by preference to illustrate, the "slope above wall" of d in Fig. 13, p. 148; compare also the last chapter, Sec.Sec. 26, 27. It will be seen, by reference to my sketch of the spot, Plate 20, that this conformation does actually exist there with great definiteness: Turner has only enlarged and thrown it into more numerous alternations of light and shade. As these could not be shown in the etching, I have given, in the frontispiece, this passage nearly of its real size: the exquisite greys and blues by which Turner has rounded and thrown it back are necessarily lost in the plate; but the grandeur of his simple cliff and soft curves of sloping bank above is in some degree rendered.
We must yet dwell for a moment on the detail of the rocks on the left in Plate 37, as they approach nearer the eye, turning at the same time from the light. It cost me trouble to etch this passage, and yet half its refinements are still missed; for Turner has put his whole strength into it, and wrought out the curving of the gneiss beds with a subtlety which could not be at all approached in the time I had to spare for this plate. Enough, however, is expressed to illustrate the points in question.
Sec. 44. We have first, observe, a rounded bank, broken, at its edges, into cleavages by inclined beds. I thought it would be well, lest the reader should think I dwelt too much on this particular scene, to give an instance of similar structure from another spot; and therefore I daguerreotyped the cleavages of a slope of gneiss just above the Cascade des Pelerins, Chamouni, corresponding in position to this bank of Turner's. Plate 48 (facing p. 303), copied by Mr. Armytage from the daguerreotype, represents, necessarily in a quite unprejudiced and impartial way, the structure at present in question; and the reader may form a sufficient idea, from this plate, of the complexity of descending curve and foliated rent, in even a small piece of mountain foreground, where the gneiss beds are tolerably continuous. But Turner had to add to such general complexity the expression of a more than ordinary undulation in the beds of the St. Gothard gneiss.
Sec. 45. If the reader will look back to Chapter II. Sec. 13, he will find it stated that this scene is approached out of the defile of Dazio Grande, of which the impression was still strong on Turner's mind, and where only he could see, close at hand, the nature of the rocks in a good section. It most luckily happens that De Saussure was interested by the rocks at the same spot, and has given the following account of them, Voyages, Sec.Sec. 1801, 1802:—
"A une lieue de Faido, l'on passe le Tesin pour le repasser bientot apres [see the old bridge in Turner's view, carried away in mine], et l'on trouve sur sa rive droite des couches d'une roche feuilletee, qui montent du Cote du Nord.
"On voit clairement que depuis que les granits veines ont ete remplaces par des pierres moins solides, tantot les rochers se sont eboules et ont ete recouverts par la terre vegetale, tantot leur situation primitive a subi des changements irreguliers.
"Sec. 1802. Mais bientot apres, on monte par un chemin en corniche au dessus du Tesin, qui se precipite entre des rochers avec la plus grande violence. Ces rochers sont la si serres, qu'il n'y a de place que pour la riviere et pour le chemin, et meme en quelques endroits, celui-ci est entierement pris sur le roc. Je fis a pied cette montee, pour examiner avec soin ces beaux rochers, dignes de toute l'attention d'un amateur.
"Les veines de ce granit forment en plusieurs endroits des zigzags redoubles, precisement comme ces anciennes tapisseries, connues sous le nom de points d'Hongrie; et la, on ne peut pas prononcer, si les veines de la pierre, sont ou ne sont pas paralleles a ses couches. Cependant ces veines reprennent aussi dans quelques places, une direction constante, et cette direction est bien la meme que celle des couches. Il paroit meme qu'en divers endroits, ou ces veines ont la forme d'un sigma ou d'une M couchee M, ce sont les grandes jambes du sigma, qui ont la direction des couches. Enfin, j'observai plusieurs couches, qui dans le milieu de leur epaisseur paroissoient remplies de ces veines en zigzag, tandis qu'aupres de leurs bords, on les voyoit toutes en lignes droites."
Sec. 46. If the reader will now examine Turner's work at the point x in the reference figure, and again on the stones in the foreground, comparing it finally with the fragment of the rocks which happened fortunately to come into my foreground in Plate 20, rising towards the left, and of which I have etched the structure with some care, though at the time I had quite forgotten Saussure's notice of the peculiar M-shaped zigzags of the gneiss at the spot, I believe he will have enough evidence before him, taken all in all, to convince him of Turner's inevitable perception, and of the entire supremacy of his mountain drawing over all that had previously existed. And if he is able to refer, even to the engravings (though I desire always that what I state should be tested by the drawings only) of any others of his elaborate hill-subjects, and will examine their details with careful reference to the laws explained in this chapter, he will find that the Turnerian promontories and banks are always simply right, and that in all respects; that their gradated curvatures, and nodding cliffs, and redundant sequence of folded glen and feathery glade, are, in all their seemingly fanciful beauty, literally the most downright plain speaking that has as yet been uttered about hills; and differ from all antecedent work, not in being ideal, but in being, so to speak, pictorial casts of the ground. Such a drawing as that of the Yorkshire Richmond, looking down the river, in the England Series, is even better than a model of the ground, because it gives the aerial perspective, and is better than a photograph of the ground, because it exaggerates no shadows, while it unites the veracities both of model and photograph.
Sec. 47. Nor let it be thought that it was an easy or creditable thing to treat mountain ground with this faithfulness in the days when Turner executed those drawings. In the Encyclopaedia Britannica (Edinburgh, 1797), under article "Drawing," the following are the directions given for the production of a landscape:—
"If he is to draw a landscape from nature, let him take his station on a rising ground, where he will have a large horizon, and mark his tablet into three divisions, downwards from top to the bottom; and divide in his own mind the landscape he is to take into three divisions also. Then let him turn his face directly opposite to the midst of the horizon, keeping his body fixed, and draw what is directly before his eyes upon the middle division of the tablet: then turn his head, but not his body, to the left hand and delineate what he views there, joining it properly to what he had done before; and, lastly, do the same by what is to be seen upon his right hand, laying down everything exactly, both with respect to distance and proportion. One example is given in plate clxviii.
"The best artists of late, in drawing their landscapes, make them shoot away, one part lower than another. Those who make their landscapes mount up higher and higher, as if they stood at the bottom of a hill to take the prospect, commit a great error; the best way is to get upon a rising ground, make the nearest objects in the piece the highest, and those that are farther off to shoot away lower and lower till they come almost level with the line of the horizon, lessening everything proportionably to its distance, and observing also to make the objects fainter and less distinct the farther they are removed from the eye. He must make all his lights and shades fall one way, and let every thing have its proper motion: as trees shaken by the wind, the small boughs bending more and the large ones less; water agitated by the wind, and dashing against ships or boats, or falling from a precipice upon rocks and stones, and spirting up again into the air, and sprinkling all about; clouds also in the air now gathered with the winds; now violently condensed into hail, rain, and the like,—always remembering, that whatever motions are caused by the wind must be made all to move the same way, because the wind can blow but one way at once."
Such was the state of the public mind, and of public instruction, at the time when Claude, Poussin, and Salvator were in the zenith of their reputation; such were the precepts which, even to the close of the century, it was necessary for a young painter to comply with during the best part of the years he gave to study. Take up one of Turner's views of our Yorkshire dells, seen from about a hawk's height of pause above the sweep of its river, and with it in your hand, side by side with the old Encyclopaedia paragraph, consider what must have been the man's strength, who, on a sudden, passed from such precept to such practice.
Sec. 48. On a sudden it was; for, even yet a youth, and retaining profound respect for all older artist's ways of work, he followed his own will fearlessly in choice of scene; and already in the earliest of his coast drawings there are as daring and strange decisions touching the site of the spectator as in his latest works; lookings down and up into coves and clouds, as defiant of all former theories touching possible perspective, or graceful componence of subject, as, a few years later, his system of color was of the theory of the brown tree. Nor was the step remarkable merely for its magnitude,—for the amount of progress made in a few years. It was much more notable by its direction. The discovery of the true structure of hill banks had to be made by Turner, not merely in advance of the men of his day, but in contradiction to them. Examine the works of contemporary and preceding landscapists, and it will be found that the universal practice is to make the tops of all cliffs broken and rugged, their bases smooth and soft, or concealed with wood. No one had ever observed the contrary structure, the bank rounded at the top, and broken on the flank. And yet all the hills of any importance which are met with throughout Lowland Europe are, properly speaking, high banks, for the most part following the courses of rivers, and forming a step from the high ground, of which the country generally consists, to the river level. Thus almost the whole of France, though, on the face of it, flat, is raised from 300 to 500 feet above the level of the sea, and is traversed by valleys either formed by, or directing, the course of its great rivers. In these valleys lie all its principal towns, surrounded, almost without exception, by ranges of hills covered with wood or vineyard. Ascending these hills, we find ourselves at once in an elevated plain, covered with corn and lines of apple trees, extending to the next river side, where we come to the brow of another hill, and descend to the city and valley beneath it. Our own valleys in Northumberland, Yorkshire, Derbyshire, and Devonshire, are cut in the same manner through vast extents of elevated land; the scenery which interests the traveller chiefly, as he passes through even the most broken parts of those counties, being simply that of the high banks which rise from the shores of the Dart or the Derwent, the Wharfe or the Tees. In all cases, when these banks are surmounted, the sensation is one of disappointment, as the adventurer finds himself, the moment he has left the edge of the ravine, in a waste of softly undulating moor or arable land, hardly deserving the title of hill country. As we advance into the upper districts the fact remains still the same, although the banks to be climbed are higher, the ravines grander, and the intermediate land more broken. The majesty of an isolated peak is still comparatively rare, and nearly all the most interesting pieces of scenery are glens or passes, which, if seen from a height great enough to command them in all their relations, would be found in reality little more than trenches excavated through broad masses of elevated land, and expanding at intervals into the wide basins which are occupied by the glittering lake or smiling plain.
Sec. 49. All these facts had been entirely ignored by artists; nay, almost by geologists, before Turner's time. He saw them at once; fathomed them to the uttermost, and, partly owing to early association, partly, perhaps, to the natural pleasure of working a new mine discovered by himself, devoted his best powers to their illustration, passing by with somewhat less attention the conditions of broken-summited rock, which had previously been the only ones known. And if we now look back to his treatment of the crest of Mont Pilate, in the figure given at the close of the last chapter, we shall understand better the nature and strength of the instinct which compelled him to sacrifice the peaked summit, and to bring the whole mountain within a lower enclosing line. In that figure, however, the dotted peak interferes with the perception of the form finally determined upon, which therefore I repeat here (Fig. 106), as Turner gave it in color. The eye may not at first detect the law of ascent in the peaks, but if the height of any one of them were altered, the general form would instantly be perceived to be less agreeable. Fig. 107 shows that they are disposed within an infinite curve, A c, from which the last crag falls a little to conceal the law, while the terminal line at the other extremity, A b, is a minor echo of the whole contour.
Sec. 50. I must pause to make one exception to my general statement that this structure had been entirely ignored. The reader was, perhaps, surprised by the importance I attached to the fragment of mountain background by Masaccio, given in Plate 13 of the third volume. If he looks back to it now, his surprise will be less. It was a complete recognition of the laws of the lines of aqueous sculpture, asserted as Turner's was, in the boldest opposition to the principles of rock drawing of the time. It presents even smoother and broader masses than any which I have shown as types of hill form; but it must be remembered that Masaccio had seen only the softer contours of the Apennine limestone. I have no memorandum by me of the hill lines near Florence; but Plate 47 shows the development of limestone structure, at a spot which has, I think, the best right to be given as an example of the Italian hills, the head of the valley of Carrara. The white scar on the hill side is the principal quarry; and the peaks above deserve observation, not so much for anything in their forms, as for the singular barrenness which was noted in the fifteenth chapter of the last volume (Sec. 8) as too often occurring in the Apennines. Compare this plate with the previous one. The peak drawn in Plate 46 rises at least 7500 feet above the sea,—yet is wooded to its top; this Carrara crag not above 5000,—yet it is wholly barren.
Sec. 51. Masaccio, however, as we saw, was taken away by death before he could give any one of his thoughts complete expression. Turner was spared to do his work, in this respect at least, completely. It might be thought that, having had such adverse influence to struggle with, he would prevail against it but in part; and, though showing the way to much that was new, retain of necessity some old prejudices, and leave his successors to pursue in purer liberty, and with happier power, the path he had pointed out. But it was not so: he did the work so completely on the ground which he chose to illustrate, that nothing is left for future artists to accomplish in that kind. Some classes of scenery, as often pointed out in the preceding pages, he was unfamiliar with, or held in little affection, and out of that scenery, untouched by him, new motives may be obtained; but of such landscape as his favorite Yorkshire Wolds, and banks of Rhenish and French hill, and rocky mountains of Switzerland, like the St. Gothard, already so long dwelt upon, he has expressed the power in what I believe to be for ever a central and unmatchable way. I do not say this with positiveness, because it is not demonstrable. Turner may be beaten on his own ground—so may Tintoret, so may Shakespeare, Dante, or Homer: but my belief is that all these first-rate men are lonely men; that the particular work they did was by them done for ever in the best way; and that this work done by Turner among the hills, joining the most intense appreciation of all tenderness with delight in all magnitude, and memory for all detail, is never to be rivalled, or looked upon in similitude again.
 Quantity of curvature is as measurable as quantity of anything else; only observe that it depends on the nature of the line, not on its magnitude; thus, in simple circular curvature, a b, Fig. 96, being the fourth of a large circle, and b c the half of a smaller one, the quantity of the element of circular curvature in the entire line a c is three fourths of that in any circle,—the the same as the quantity in the line e f.
 The catenary is not properly a curve capable of infinity, if its direction does not alter with its length; but it is capable of infinity, implying such alteration by the infinite removal of the points of suspension. It entirely corresponds in its effect on the eye and mind to the infinite curves. I do not know the exact nature of the apparent curves of suspension formed by a high and weighty waterfall; they are dependent on the gain in rapidity of descent by the central current, where its greater body is less arrested by the air; and I apprehend, are catenary in character, though not in cause.
 I am afraid of becoming tiresome by going too far into the intricacies of this most difficult subject; but I say "towards the bottom of the hill," because, when a certain degree of verticality is reached, a counter protective influence begins to establish itself, the stones and waterfalls bounding away from the brow of the precipice into the air, and wearing it at the top only. Also it is evident that when the curvature falls into a vertical cliff, as often happens, the maximum of curvature must be somewhere above the brow of the cliff, as in the cliff itself it has again died into a straight line.
 The following extract from my private diary, giving an account of the destruction of the beauty of this waterfall in the year 1849, which I happened to witness, may be interesting to those travellers who remember it before that period. The house spoken of as "Joseph's," is that of the guide Joseph Coutet, in a village about a mile below the cascade, between it and the Arve: that noticed as of the "old avalanche" is a hollow in the forest, cleft by a great avalanche which fell from the Aiguille du Midi in the spring of 1844. It struck down about a thousand full-grown pines, and left an open track in the midst of the wood, from the cascade nearly down to the village.
"Evening, Thursday, June 28th. I set out for the Cascade des Pelerins as usual; when we reached Joseph's house, we heard a sound from the torrent like low thunder, or like that of a more distant and heavier fall. A peasant said something to Joseph, who stopped to listen, then nodded, and said to me, 'La cascade vient de se deborder.' Thinking there would be time enough afterwards to ask for explanations, I pushed up the hill almost without asking a question. When we reached the place of the old avalanche, Joseph called to me to stop and see the torrent increase. There was at this time a dark cloud on the Aiguille du Midi, down to its base; the upper part of the torrent was brown, the lower white, not larger than usual. The brown part came down, I thought, with exceeding slowness, reaching the cascade gradually; as it did so, the fall rose to about once and a half its usual height, and in the five minutes' time that I paused (it could not be more) turned to the color of slate. I then pushed on as hard as I could. When I reached the last ascent I was obliged to stop for breath, but got up before the fall could sensibly have diminished in body of water. It was then nearly twice as far cast out from the rock as last night, and the water nearly black in color; and it had the appearance, as it broke and separated at the outer part of the fall, of a shower of fragments of flat slate. The reason of this appearance I could not comprehend, unless the water was so mixed with mud that it drew out flat and unctuously when it broke; but so it was: instead of spray it looked like a shower of dirty flat bits of slate—only with a lustre, as if they had been wet first. This, however, was the least of it, for the torrent carried with it nearly as much weight of stone as water; the stones varying in size, the average being, I suppose, about that of a hen's egg; but I do not suppose that at any instant the arch of water was without four or five as large as a man's fist, and often came larger ones,—all vomited forth with the explosive power of a small volcano, and falling in a continual shower as thick, constant, and, had it not been mixed with the crash of the fall, as loud as a heavy fire of infantry; they bounded and leaped in the basin of the fall like hailstones in a thunder-shower. As we watched the fall it seemed convulsively to diminish, and suddenly showed, as it shortened, the rock underneath it, which I could hardly see yesterday: as I cried out to Joseph it rose again, higher than ever, and continued to rise, till it all but reached the snow on the rock opposite. It then became very fantastic and variable, increasing and diminishing in the space of two or three seconds, and partially changing its direction. After watching it for half an hour or so, I determined to try and make some memoranda. Coutet brought me up a jug of water: I stooped to dip my brush, when Coutet caught my arm, saying, 'Tenez;' at the same instant I heard a blow, like the going off of a heavy gun, two or three miles away; I looked up, and as I did, the cascade sank before my eyes, and fell back to the rock. Neither of us spoke for an instant or two; then Coutet said, 'C'est une pierre, qui est logee dans le creux,' or words to that effect: in fact, he had seen the stone come down as he called to me. I thought also that nothing more had happened, and watched the destroyed fall only with interest, until, as suddenly as it had fallen, it rose again, though not to its former height; and Coutet, stooping down, exclaimed, 'Ce n'est pas ca, le roc est perce;' in effect, a hole was now distinctly visible in the cup which turned the stream, through which the water whizzed as from a burst pipe. The cascade, however, continued to increase, until this new channel was concealed, and I was maintaining to Coutet that he must have been mistaken (and that the water only struck on the outer rock, having changed its mode of fall above), when again it fell; and the two girls, who had come up from the chalet, expressed their opinion at once, that the 'cascade est finie.' This time all was plain; the water gushed in a violent jet d'eau through the new aperture, hardly any of it escaping above. It rose again gradually, as the hole was choked with stones, and again fell; but presently sprang out almost to its first elevation (the water being by this time in much less body), and retained very nearly the form it had yesterday, until I got tired of looking at it, and went down to the little chalet, and sat down before its door. I had not been there five minutes before the cascade fell, and rose no more."
 It might be thought at first that the line to which such curves would approximate would be the cycloid, as the line of quickest descent. But in reality the contour is modified by perpetual sliding of the debris under the influence of rain; and by the bounding of detached fragments with continually increased momentum. I was quite unable to get at anything like the expression of a constant law among the examples I studied in the Alps, except only the great laws of delicacy and changefulness in all curves whatsoever.
 I owe Mr. Le Keux sincere thanks, and not a little admiration, for the care and skill with which he has followed, on a much reduced scale, the detail of this drawing.
 Allow ten feet square for average space to each pine; suppose the valley seen only for five miles of its length, and the pine district two miles broad on each side—a low estimate of breadth also: this would give five millions.
 The white spots on the brow of the little cliff are lichens, only four or five inches broad.
 What a comfortable, as well as intelligent, operation, sketching from nature must have been in those days!
 It is not one of the highest points of the Carrara chain. The chief summits are much more jagged, and very noble. See Chap. XX. Sec. 20.
RESULTING FORMS:—FIFTHLY, STONES.
Sec. 1. It is somewhat singular that the indistinctness of treatment which has been so often noticed as characteristic of our present art shows itself always most when there is least apparent reason for it. Modern artists, having some true sympathy with what is vague in nature, draw all that is uncertain and evasive without evasion, and render faithfully whatever can be discerned in faithless mist or mocking vapors; but having no sympathy with what is solid and serene, they seem to become uncertain themselves in proportion to the certainty of what they see; and while they render flakes of far-away cloud, or fringes of inextricable forest, with something like patience and fidelity, give nothing but the hastiest indication of the ground they can tread upon or touch. It is only in modern art that we find any complete representation of clouds, and only in ancient art that, generally speaking, we find any careful realization of Stones.
Sec. 2. This is all the more strange, because, as we saw some time back, the ruggedness of the stone is more pleasing to the modern than the mediaeval, and he rarely completes any picture satisfactorily to himself unless large spaces of it are filled with irregular masonry, rocky banks, or shingly shores: whereas the mediaeval could conceive no desirableness in the loose and unhewn masses; associated them generally in his mind with wicked men, and the Martyrdom of St. Stephen; and always threw them out of his road, or garden, to the best of his power.
Yet with all this difference in predilection, such was the honesty of the mediaeval, and so firm his acknowledgment of the necessity to paint completely whatever was to be painted at all, that there is hardly a strip of earth under the feet of a saint, in any finished work of the early painters, but more, and better painted, stones are to be found upon it than in an entire exhibition full of modern mountain scenery.
Sec. 3. Not better painted in every respect. In those interesting and popular treatises on the art of drawing, which tell the public that their colors should neither be too warm nor too cold, and that their touches should always be characteristic of the object they are intended to represent, the directions given for the manufacture of stones usually enforce "crispness of outline" and "roughness of texture." And, accordingly, in certain expressions of frangibility, irregular accumulation, and easy resting of one block upon another, together with some conditions of lichenous or mossy texture, modern stone-painting is far beyond the ancient; for these are just the characters which first strike the eye, and enable the foreground to maintain its picturesque influence, without inviting careful examination. The mediaeval painter, on the other hand, not caring for this picturesque general effect, nor being in anywise familiar with mountain scenery, perceived in stones, when he was forced to paint them, eminently the characters which they had in common with figures; that is to say, their curved outlines, rounded surfaces, and varieties of delicate color, and, accordingly, was somewhat too apt to lose their angular and fragmentary character in a series of muscular lines resembling those of an anatomical preparation; for, although in large rocks the cleavable or frangible nature was the thing that necessarily struck him most, the pebbles under his feet were apt to be oval or rounded in the localities of almost all the important schools of Italy. In Lombardy, the mass of the ground is composed of nothing but Alpine gravel, consisting of rolled oval pebbles, on the average about six inches long by four wide—awkward building materials, yet used in ingenious alternation with the bricks in all the lowland Italian fortresses. Besides this universal rotundity, the qualities of stones which rendered them valuable to the lapidary were forced on the painter's attention by the familiar arts of inlaying and mosaic. Hence, in looking at a pebble, his mind was divided between its roundness and its veins; and Leonardo covers the shelves of rock under the feet of St. Anne with variegated agates; while Mantegna often strews the small stones about his mountain caves in a polished profusion, as if some repentant martyr princess had been just scattering her caskets of pearls into the dust.
Sec. 4. Some years ago, as I was talking of the curvilinear forms in a piece of rock to one of our academicians, he said to me, in a somewhat despondent accent, "If you look for curves, you will see curves; if you look for angles, you will see angles."
The saying appeared to me an infinitely sad one. It was the utterance of an experienced man; and in many ways true, for one of the most singular gifts, or, if abused, most singular weaknesses, of the human mind is its power of persuading itself to see whatever it chooses;—a great gift, if directed to the discernment of the things needful and pertinent to its own work and being; a great weakness, if directed to the discovery of things profitless or discouraging. In all things throughout the world, the men who look for the crooked will see the crooked, and the men who look for the straight will see the straight. But yet the saying was a notably sad one; for it came of the conviction in the speaker's mind that there was in reality no crooked and no straight; that all so called discernment was fancy, and that men might, with equal rectitude of judgment, and good-deserving of their fellow-men, perceive and paint whatever was convenient to them.
Sec. 5. Whereas things may always be seen truly by candid people, though never completely. No human capacity ever yet saw the whole of a thing; but we may see more and more of it the longer we look. Every individual temper will see something different in it: but supposing the tempers honest, all the differences are there. Every advance in our acuteness of perception will show us something new; but the old and first discerned thing will still be there, not falsified, only modified and enriched by the new perceptions, becoming continually more beautiful in its harmony with them and more approved as a part of the Infinite truth.
Sec. 6. There are no natural objects out of which more can be thus learned than out of stones. They seem to have been created especially to reward a patient observer. Nearly all other objects in nature can be seen, to some extent, without patience, and are pleasant even in being half seen. Trees, clouds, and rivers are enjoyable even by the careless; but the stone under his foot has for carelessness nothing in it but stumbling; no pleasure is languidly to be had out of it, nor food, nor good of any kind; nothing but symbolism of the hard heart and the unfatherly gift. And yet, do but give it some reverence and watchfulness, and there is bread of thought in it, more than in any other lowly feature of all the landscape.
Sec. 7. For a stone, when it is examined, will be found a mountain in miniature. The fineness of Nature's work is so great, that, into a single block, a foot or two in diameter, she can compress as many changes of form and structure, on a small scale, as she needs for her mountains on a large one; and, taking moss for forests, and grains of crystal for crags, the surface of a stone, in by far the plurality of instances, is more interesting than the surface of an ordinary hill; more fantastic in form and incomparably richer in color,—the last quality being, in fact, so noble in most stones of good birth (that is to say, fallen from the crystalline mountain-ranges), that I shall be less able to illustrate this part of my subject satisfactorily by means of engraving than perhaps any other, except the color of skies. I say, shall be less able, because the beauty of stone surface is in so great a degree dependent on the mosses and lichens which root themselves upon it, that I must place my richest examples in the section on vegetation. For instance, in the plate opposite, though the mass of rock is large and somewhat distant, the effect of it is as much owing to the white spots of silvery lichen in the centre and left, and to the flowing lines in which the darker mosses, growing in the cranny, have arranged themselves beyond, as to the character of the rock itself; nor could the beauty of the whole mass be explained, if we were to approach the least nearer, without more detailed drawing of this vegetation. For the present I shall only give a few examples of the drawing of stones roughly broken, or worn so as not to be materially affected by vegetation.
Sec. 8. We have already seen an example of Titian's treatment of mountain crests as compared with Turner's; here is a parallel instance, from Titian, of stones in the bed of a torrent (Fig. 108), in many ways good and right, and expressing in its writhed and variously broken lines far more of real stone structure than the common water-color dash of the moderns. Observe, especially, how Titian has understood that the fracture of the stone more or less depends on the undulating grain of its crystalline structure, following the cavity of the largest stone in the middle of the figure, with concentric lines; and compare in Plate 21 the top of Turner's largest stones on the left.
Sec. 9. If the reader sees nothing in this drawing (Fig. 108) that he can like,—although, indeed, I would have him prefer the work of Turner,—let him be assured that he does not yet understand on what Titian's reputation is founded. No painter's name is oftener in the mouth of the ordinary connoisseur, and no painter was ever less understood. His power of color is indeed perfect, but so is Bonifazio's. Titian's supremacy above all the other Venetians, except Tintoret and Veronese, consists in the firm truth of his portraiture, and more or less masterly understanding of the nature of stones, trees, men, or whatever else he took in hand to paint; so that, without some correlative understanding in the spectator, Titian's work, in its highest qualities, must be utterly dead and unappealing to him.
Sec. 10. I give one more example from the lower part of the same print (Fig. 109), in which a stone, with an eddy round it, is nearly as well drawn as it can be in the simple method of the early wood-engraving. Perhaps the reader will feel its truth better by contrast with a fragment or two of modern Idealism. Here, for instance (Fig. 110), is a group of stones, highly entertaining in their variety of form, out of the subject of "Christian vanquishing Apollyon," in the outlines to the Pilgrim's Progress, published by the Art-Union, the idealism being here wrought to a pitch of extraordinary brilliancy by the exciting nature of the subject. Next (Fig. 111) is another poetical conception, one of Flaxman's, representing the eddies and stones of the Pool of Envy (Flaxman's Dante), which may be conveniently compared with the Titianesque stones and streams. And, finally, Fig. 112 represents, also on Flaxman's authority, those stones of an "Alpine" character, of which Dante says that he
"Climbed with heart of proof the adverse steep."
It seems at first curious that every one of the forms that Flaxman has chanced upon should be an impossible one—a form which a stone never could assume: but this is the Nemesis of false idealism, and the inevitable one.
Sec. 11. The chief incapacity in the modern work is not, however, so much in its outline, though that is wrong enough, as in the total absence of any effort to mark the surface roundings. It is not the outline of a stone, however true, that will make it solid or heavy; it is the interior markings, and thoroughly understood perspectives of its sides. In the opposite plate the upper two subjects are by Turner, foregrounds out of the Liber Studiorum (Source of Arveron, and Ben Arthur); the lower by Claude, Liber Veritatis, No. 5. I think the reader cannot but feel that the blocks in the upper two subjects are massy and ponderous; in the lower, wholly without weight. If he examine their several treatment, he will find that Turner has perfect imaginative conception of every recess and projection over the whole surface, and feels the stone as he works over it; every touch, moreover, being full of tender gradation. But Claude, as he is obliged to hold to his outline in hills, so also clings to it in the stones,—cannot round them in the least, leaves their light surfaces wholly blank, and puts a few patches of dark here and there about their edges, as chance will have it.
Sec. 12. Turner's way of wedging the stones of the glacier moraine together in strength of disorder, in the upper subject, and his indication of the springing of the wild stems and leafage out of the rents in the boulders of the lower one, will hardly be appreciated unless the reader is fondly acquainted with the kind of scenery in question; and I cannot calculate on this being often the case, for few persons ever look at any near detail closely, and perhaps least of all at the heaps of debris which so often seem to encumber and disfigure mountain ground. But for the various reasons just stated (Sec. 7), Turner found more material for his power, and more excitement to his invention, among the fallen stones than in the highest summits of mountains; and his early designs, among their thousand excellences and singularities, as opposed to all that had preceded them, count for not one of the least the elaborate care given to the drawing of torrent beds, shaly slopes, and other conditions of stony ground which all canons of art at the period pronounced inconsistent with dignity of composition; a convenient principle, since, of all foregrounds, one of loose stones is beyond comparison the most difficult to draw with any approach to realization. The Turnerian subjects, "Junction of the Greta and Tees" (Yorkshire Series, and illustrations to Scott); "Wycliffe, near Rokeby" (Yorkshire); "Hardraw Fall" (Yorkshire); "Ben Arthur" (Liber Studiorum); "Ulleswater" and the magnificent drawing of the "Upper Fall of the Tees" (England Series), are sufficiently illustrative of what I mean.
Sec. 13. It is not, however, only, in their separate condition, as materials of foreground, that we have to examine the effect of stones; they form a curiously important element of distant landscape in their aggregation on a large scale.
It will be remembered that in the course of the last chapter we wholly left out of our account of mountain lines that group which was called "Lines of Rest." One reason for doing so was that, as these lines are produced by debris in a state of temporary repose, their beauty, or deformity, or whatever character they may possess, is properly to be considered as belonging to stones rather than to rocks.
Sec. 14. Whenever heaps of loose stones or sand are increased by the continual fall of fresh fragments from above, or diminished by their removal from below, yet not in such mass or with such momentum as entirely to disturb those already accumulated, the materials on the surface arrange themselves in an equable slope, producing a straight line of profile in the bank or cone.
The heap formed by the sand falling in an hour-glass presents, in its straight sides, the simplest result of such a condition; and any heap of sand thrown up by the spade will show the slopes here and there, interrupted only by knotty portions, held together by moisture, or agglutinated by pressure,—interruptions which cannot occur to the same extent on a large scale, unless the soil is really hardened nearly to the nature of rock. As long as it remains incoherent, every removal of substance at the bottom of the heap, or addition of it at the top, occasions a sliding disturbance of the whole slope, which smooths it into rectitude of line; and there is hardly any great mountain mass among the Alps which does not show towards its foundation perfectly regular descents of this nature, often two or three miles long without a break. Several of considerable extent are seen on the left of Plate 46.
Sec. 15. I call these lines of rest, because, though the bulk of the mass may be continually increasing or diminishing, the line of the profile does not change, being fixed at a certain angle by the nature of the earth. It is usually stated carelessly as an angle of about 45 degrees, but it never really reaches such a slope. I measured carefully the angles of a very large number of slopes of mountain in various parts of the Mont Blanc district. The few examples given in the note below are enough to exhibit the general fact that loose debris lies at various angles up to about 30 deg. or 32 deg.; debris protected by grass or pines may reach 35 deg., and rocky slopes 40 deg. or 41 deg., but in continuous lines of rest I never found a steeper angle.
Sec. 16. I speak of some rocky slopes as lines of rest, because, whenever a mountain side is composed of soft stone which splits and decomposes fast, it has a tendency to choke itself up with the ruins, and gradually to get abraded or ground down towards the debris slope; so that vast masses of the sides of Alpine valleys are formed by ascents of nearly uniform inclination, partly loose, partly of jagged rocks, which break, but do not materially alter the general line of ground. In such cases the fragments usually have accumulated without disturbance at the foot of the slope, and the pine forests fasten the soil and prevent it from being carried down in large masses. But numerous instances occur in which the mountain is consumed away gradually by its own torrents, not having strength enough to form clefts or precipices, but falling on each side of the ravines into even banks, which slide down from above as they are wasted below.
Sec. 17. By all these various expedients, Nature secures, in the midst of her mountain curvatures, vast series of perfectly straight lines opposing and relieving them; lines, however, which artists have almost universally agreed to alter or ignore, partly disliking them intrinsically, on account of their formality, and partly because the mind instantly associates them with the idea of mountain decay. Turner, however, saw that this very decay having its use and nobleness, the contours which were significative of it ought no more to be omitted than, in the portrait of an aged man, the furrows on his hand or brow; besides, he liked the lines themselves, for their contrast with the mountain wildness, just as he liked the straightness of sunbeams penetrating the soft waywardness of clouds. He introduced them constantly into his noblest compositions; but in order to the full understanding of their employment in the instance I am about to give, one or two more points yet need to be noticed.
Sec. 18. Generally speaking, the curved lines of convex, fall belong to mountains of hard rock, over whose surfaces the fragments bound to the valley, and which are worn by wrath of avalanches and wildness of torrents, like that of the Cascade des Pelerins, described in the note above. Generally speaking, the straight lines of rest belong to softer mountains, or softer surfaces and places of mountains, which, exposed to no violent wearing from external force, nevertheless keep slipping and mouldering down spontaneously or receiving gradual accession of material from incoherent masses above them.
Sec. 19. It follows, rather, that where the gigantic wearing forces are in operation, the stones or fragments of rock brought down by the torrents and avalanches are likely, however hard, to be rounded on all their edges; but where the straight shaly slopes are found, the stones which glide or totter down their surfaces frequently retain all their angles, and form jagged and flaky heaps at the bottom.
And farther, it is to be supposed that the rocks which are habitually subjected to these colossal forces of destruction are in their own mass firm and secure, otherwise they would long ago have given way; but that where the gliding and crumbling surfaces are found without much external violence, it is very possible that the whole framework of the mountain may be full of flaws; and a danger exist of vast portions of its mass giving way, or slipping down in heaps, as the sand suddenly yields in an hour-glass after some moments of accumulation.
Sec. 20. Hence, generally, in the mind of any one familiar with mountains, the conditions will be associated, on the one hand, of the curved, convex, and overhanging bank or cliff, the roaring torrent, and the rounded boulder of massive stone; and, on the other, of the straight and even slope of bank, the comparatively quiet and peaceful lapse of streams, and the sharp-edged and unworn look of the fallen stones, together with a sense of danger greater, though more occult, than in the wilder scenery.
The drawing of the St. Gothard, which we have so laboriously analyzed, was designed, as before mentioned, from a sketch taken in the year 1843. But with it was made another drawing. Turner brought home in that year a series of sketches taken in the neighborhood of the pass; among others, one of the Valley of Goldau, covered as it is by the ruins of the Rossberg. Knowing his fondness for fallen stones, I chose this Goldau subject as a companion to the St. Gothard. The plate opposite will give some idea of the resultant drawing.
Sec. 21. Some idea only. It is a subject which, like the St. Gothard, is far too full of detail to admit of reduction; and I hope, therefore, soon to engrave it properly of its real size. It is, besides, more than usually difficult to translate this drawing into black and white, because much of the light on the clouds is distinguished merely by orange or purple color from the green greys, which, though not darker than the warm hues, have the effect of shade from their coldness, but cannot be marked as shade in the engraving without too great increase of depth. Enough, however, has been done to give some idea of the elements of Turner's design.