§ 36. This bolder quaintness of the missals is very slightly modified in religious paintings of the period.Fig. 86, by Cima da Conegliano, a Venetian, No. 173 in the Louvre, compared with Fig. 3 of Plate10(Flemish), will show the kind of received tradition about rocks current throughout Europe. Claude takes up this tradition, and, merely making the rocks a little clumsier, and more weedy, produces such conditions asFig. 87(Liber Veritatis, No. 91, withFig. 84above); while the orthodox door or archway at the bottom is developed into the Homeric cave, shaded with laurels, and some ships are put underneath it, or seen through it, at impossible anchorages.
§ 37.Fig. 87is generally characteristic, not only of Claude, but of the other painters of the Renaissance period, because they were all equally fond of representing this overhanging of rocks with buildings on the top, and weeds drooping into the air over the edge, always thinking to get sublimity by exaggerating the projection, and never able to feel or understand the simplicity of real rock lines; not that they were in want of examples around them: on the contrary, though the main idea was traditional, the modifications of it are always traceable to the lowermasses of limestone and tufa which skirt the Alps and Apennines, and which have, in reality, long contracted habits of nodding over their bases; being, both by Virgil and Homer, spoken of always as "hanging" or "over-roofed" rocks. But then they have a way of doing it rather different from the Renaissance ideas of them. Here, for instance (Plate41), is a real hanging rock, with a castle on the top of it, and (κατηρεφής) laurel, all plain fact, from Arona, on the Lago Maggiore; and, I believe, the reader, though we have not as yet said anything about lines, will at once, on comparing it withFig. 87, recognize the difference between the true parabolic flow of the rock-lines and the humpbacked deformity of Claude; and, still more, the difference between the delicate overhanging of the natural cliff, cautiously diminished as it gets higher87, and the ideal danger of the Liber Veritatis.
§ 38. And the fact is, generally, that natural cliffs are very cautious how they overhang, and that the artist who represents them as doing so in any extravagant degree entirely destroys the sublimity which he hoped to increase, for the simple reason that he takes away the whole rock-nature, or at least that part of it which depends upon weight. The instinct of the observer refuses to believe that the rock is ponderous when it overhangs so far, and it has no more real effect upon him than the imagined rocks of a fairy tale.
Though, therefore, the subject sketched on this page is sufficiently trifling in itself, it is important as a perfect general type of the overhanging of that kind of precipices, and of the mode in which they are connected with the banks above.Fig. 88shows its abstract leading lines, consisting of one great parabolic linex yfalling to the brow, curved aqueous lines down the precipice face, and the springing lines of its vegetation, opposed by contrary curves on the farther cliff. Such an arrangement, with or without vegetation, may take place on a small or large scale; but a bolder projection than this, except by rare accident, and on a small scale, cannot. If the reader will glance back toPlate37, and observe the arrangement of the precipices on the right hand, he will now better understand what Turner means by them. But the whole question of the beauty of this form, or mode of its development, rests on the nature of the bank above the cliffs, and of the aqueous forces that carved it; and this discussion of the nature of banks, as it will take some time, had better be referred to next chapter. One or two more points are, however, to be stated here.
§ 39. For the reader has probably been already considering how it is that these overhanging cliffs are formed at all, and why they appear thus to be consumed away at the bottom. Sometimes if of soft material they actuallyareso consumed by the quicker trickling of streamlets at the base than at the summit, or by the general action of damp in decomposing the rock. But in the noblest instances, such cliffs are constructed as at c inFig. 73, above, and the inward retirement of the precipice is the result of their tendency to break at right angles to the beds, modified according to the power of the rock to support itself, and the aqueous action from above or below.
I have before alluded (inp. 157) to this somewhat perilous arrangement permitted in the secondary strata. The danger, be it observed, is not of the fall of thebrowof the precipice, which never takes place on a large scale in rocks of this kind (compare § 3 of this chapter), but of the sliding of one bed completely away from another, and the whole mass coming down together. But even this, though it has several times occurred in Switzerland, is not a whit more likely to happen when the precipice is terrific than when it is insignificant. The danger results from the imperfect adhesion of the mountain beds; not at all from the external form of them. A cliff, which is in aspect absolutely awful, may hardly, in the part of it that overhangs, add one thousandth part to the gravitating power of the entire mass ofthe rocks above; and, for the comfort of nervous travellers, they may be assured that they are often in more danger under the gentle slopes of a pleasantly wooded hill, than under the most terrific cliffs of the Eiger or Jungfrau.
§ 40. The most interesting examples of these cliffs are usually to be seen impendent above strong torrents, which, if forced originally to run in a valley, such asainFig. 89, bearing the relation there shown to the inclination of beds on each side, will not, if the cleavage is across the beds, cut their channel straight down, but in an inclined direction, correspondent to the cleavage, as atb. If the operation be carried far, so as to undermine one side of the ravine too seriously, the undermined masses fall, partially choke the torrent, and give it a new direction of force, or diminish its sawing power by breaking it among the fallen masses, so that the cliff never becomes very high in such an impendent form; but the trench is hewn downwards in a direction irregularly vertical. Among the limestones on the north side of the Valles, they being just soft enough to yield easily to the water, and yet so hard as to maintain themselves in massy precipices, when once hewn to the shape, there are defiles of whose depth and proportions I am almost afraid to state what I believe to be the measurements, so much do they differ from any which I have seen assigned by scientific men as the limits of precipitous formation. I can only say that my deliberate impression of the great ravine cut by the torrent which descends from the Aletsch glacier, about half way between the glacier and Brieg, was, that its depth is between athousand and fifteen hundredfeet, by a breadth of betweenforty and a hundred.
But I could not get to the edge of its cliffs, for the tops rounded away into the chasm, and, of course, all actual measurement was impossible. There are other similar clefts between the Bietschhorn and the Gemmi; and the one before spoken of at Ardon, about five miles below Sion, though quite unimportant in comparison, presents some boldly overhanging precipices easily observed by the passing traveller, as they are close to the road. The glen through which the torrent of the Trient descends into the valley of the Rhone, near Martigny, though not above three or four hundred feet deep, is also notable for its narrowness, and for the magnificent hardness of the rock through which it is cut,—a gneiss twisted with quartz into undulations like those of a Damascus sabre, and as compact as its steel.
§ 41. It is not possible to get the complete expression of these ravines, any more than of the apse of a Gothic cathedral, into a picture, as their elevation cannot be drawn on a vertical plane in front of the eye, the head needing to be thrown back, in order to measure their height, or stooped to penetrate their depth. But the structure and expression of the entrance to one of them have been made by Turner the theme of his sublime mountain-study (Mill near the Grande Chartreuse) in the Liber Studiorum; nor does he seem ever to have been weary of recurring for various precipice-subject, to the ravines of the Via Mala and St. Gothard. I will not injure any of these—his noblest works—by giving imperfect copies of them; the reader has now data enough whereby to judge, when he meets with them, whether they are well done or ill; and, indeed, all that I am endeavoring to do here, as often aforesaid, is only to get some laws of the simplest kind understood and accepted, so as to enable people who care at all for justice to make a stand at once beside the modern mountain-drawing, as distinguished from Salvator's, or Claude's, or any other spurious work. Take, for instance, such a law as this of the general oblique inclination of a torrent's sides,Fig. 89, and compare the Turnerian gorge in the distance ofPlate21here, or of the Grande Chartreuse subject in the Liber Studiorum, and consider whether anywhere else in art you can find similar expressions of the law.
"Well; but you have come to no conclusions in this chapterrespecting the Beauty of Precipices; and that was your professed business with them."
I am not sure that the idea of beauty was meant in general to be very strictly connected with such mountain forms: one does not, instinctively, speak or think of a "Beautiful Precipice." They have, however, their beauty, and it is infinite; yet so dependent on help or change from other things, on the way the pines crest them, or the waterfalls color them, or the clouds isolate them, that I do not choose to dwell here on any of their perfect aspects, as they cannot be reasoned of by anticipating inquiries into other materials of landscape.
Thus, I have much to say of the cliffs of Grindelwald and the Chartreuse, but all so dependent upon certain facts belonging to pine vegetation, that I am compelled to defer it to the next volume; nor do I much regret this; because it seems to me that, without any setting forth, or rather beyond all setting forth, the Alpine precipices have a fascination about them which is sufficiently felt by the spectator in general, and even by the artist; only they have not been properly drawn, because people do not usually attribute the magnificence of their effect to the trifling details which really are its elements; and, therefore, in common drawings of Swiss scenery we see all kinds of efforts at sublimity by exaggeration of the projection of the mass, or by obscurity, or blueness or aerial tint,—by everything, in fact, except the one needful thing,—plain drawing of the rock. Therefore in this chapter I have endeavored to direct the reader to a severe mathematical estimate of precipice outline, and to make him dwell, not on the immediately pathetic or impressive aspect of cliffs, which all men feel readily enough, but on their internal structure. For he may rest assured that, as the Matterhorn is built of mica flakes, so every great pictorial impression in scenery of this kind is to be reached by little and little; the cliff must be built in the picture as it was probably in reality—inch by inch; and the work will, in the end, have most power which was begun with most patience. No man is fit to paint Swiss scenery until he can place himself front to front with one of those mighty crags, in broad daylight, with no "effect" to aid him, and work it out, boss by boss, only with such conventionality as its infinitude renders unavoidable. Wehave seen that a literal facsimile is impossible, just as a literal facsimile of the carving of an entire cathedral front is impossible. But it is as vain to endeavor to give any conception of an Alpine cliff without minuteness of detail, and by mere breadth of effect, as it would be to give a conception of the façades of Rouen or Rheims, without indicating any statues or foliation. When the statues and foliation are once got, as much blue mist and thundercloud as you choose, but not before.
§ 43. I commend, therefore, in conclusion, the precipice to the artist'spatience; to which there is this farther and final encouragement, that, though one of the most difficult of subjects, it is one of the kindest of sitters. A group of trees changes the color of its leafage from week to week, and its position from day to day; it is sometimes languid with heat, and sometimes heavy with rain; the torrent swells or falls in shower or sun; the best leaves of the foreground may be dined upon by cattle, or trampled by unwelcome investigators of the chosen scene. But the cliff can neither be eaten nor trampled down; neither bowed by the shower nor withered by the heat: it is always ready for us when we are inclined to labor; will always wait for us when we would rest; and, what is best of all, will always talk to us when we are inclined to converse. With its own patient and victorious presence, cleaving daily through cloud after cloud, and reappearing still through the tempest drift, lofty and serene amidst the passing rents of blue, it seems partly to rebuke, andpartlyto guard, and partly to calm and chasten, the agitations of the feeble human soul that watches it; and that must be indeed a dark perplexity, or a grievous pain, which will not be in some degree enlightened or relieved by the vision of it, when the evening shadows are blue on its foundation, and the last rays of the sunset resting in the fair height of its golden Fortitude.
80Distinguished from acrestby being thefaceof a large contiguous bed of rock, not the end of a ridge.81The contour of the whole cliff, seen from near its foot as it rises above the shoulder of the Breven, is as atFig. 76opposite. The part measured isa d; but the precipice recedes to the summitb, on which a human figure is discernible to the naked eye merely as a point. The bank from which the cliff rises,c,recedesas it falls to the left; so that five hundred feet may perhaps be an under-estimate of the height below the summit. The straight sloping lines are cleavages, across the beds. Finally, Fig. 4,Plate 25, gives the look of the whole summit as seen from the village of Chamouni beneath it, at a distance of about two miles, and some four or five thousand feet above the spectator. It appears, then, like a not very formidable projection of crag overhanging the great slopes of the mountain's foundation.Fig. 76.Fig. 76.82At an angle of 79° with the horizon. See the Table of angles,p. 181. The linea einFig. 33, is too steep, as well as in the plate here; but the other slopes are approximately accurate. I would have made them quite so, but did not like to alter the sketch made on the spot.83Professor Forbes gives the bearing of the Cervin from the top of the Riffelhorn as 351°, orN. 9°W., supposing local attraction to have caused an error of 65° to the northward, which would make the true bearingN. 74°W. From the point just under the Riffelhorn summit,e, inFig. 78, at which my drawing was made, I found the Cervin bearN. 79°W. without any allowance for attraction; the disturbing influence would seem therefore confined, or nearly so, to the summita. I did not know at the time that there was any such influence traceable, and took no bearing from the summit. For the rest, I cannot vouch for bearings as I can for angles, as their accuracy was of no importance to my work, and I merely noted them with a common pocket compass and in the sailor's way (S. byW. and ½W. &C.), which involves the probability of error of from two to three degrees on either side of the true bearing. The other drawing inPlate38was made from a point only a degree or two to the westward of the village of Zermatt. I have no note of the bearing; but it must be aboutS. 60° or 65°W.84Independent travellers may perhaps be glad to know the way to the top of the Riffelhorn. I believe there is only one path; which ascends (from the ridge of the Riffel) on its eastern slope, until, near the summit, the low but perfectly smooth cliff, extending from side to side of the ridge, seems, as on the western slope, to bar all farther advance. This cliff may, however, by a good climber, be mastered even at the southern extremity; but it is dangerous there: at the opposite or northern side of it, just at its base, is a little cornice, about a foot broad, which does not look promising at first, but widens presently; and when once it is past, there is no more difficulty in reaching the summit.85I ought before to have mentioned Madame de Genlis as one of the few writers whose influence was always exerted to restore to truthful feelings, and persuade to simple enjoyments and pursuits, the persons accessible to reason in the frivolous world of her times.86Veillées du Château, vol. ii.87The actual extent of the projection remaining the same throughout, the angle of suspended slope, for that reason, diminishes as the cliff increases in height.
80Distinguished from acrestby being thefaceof a large contiguous bed of rock, not the end of a ridge.
81The contour of the whole cliff, seen from near its foot as it rises above the shoulder of the Breven, is as atFig. 76opposite. The part measured isa d; but the precipice recedes to the summitb, on which a human figure is discernible to the naked eye merely as a point. The bank from which the cliff rises,c,recedesas it falls to the left; so that five hundred feet may perhaps be an under-estimate of the height below the summit. The straight sloping lines are cleavages, across the beds. Finally, Fig. 4,Plate 25, gives the look of the whole summit as seen from the village of Chamouni beneath it, at a distance of about two miles, and some four or five thousand feet above the spectator. It appears, then, like a not very formidable projection of crag overhanging the great slopes of the mountain's foundation.
82At an angle of 79° with the horizon. See the Table of angles,p. 181. The linea einFig. 33, is too steep, as well as in the plate here; but the other slopes are approximately accurate. I would have made them quite so, but did not like to alter the sketch made on the spot.
83Professor Forbes gives the bearing of the Cervin from the top of the Riffelhorn as 351°, orN. 9°W., supposing local attraction to have caused an error of 65° to the northward, which would make the true bearingN. 74°W. From the point just under the Riffelhorn summit,e, inFig. 78, at which my drawing was made, I found the Cervin bearN. 79°W. without any allowance for attraction; the disturbing influence would seem therefore confined, or nearly so, to the summita. I did not know at the time that there was any such influence traceable, and took no bearing from the summit. For the rest, I cannot vouch for bearings as I can for angles, as their accuracy was of no importance to my work, and I merely noted them with a common pocket compass and in the sailor's way (S. byW. and ½W. &C.), which involves the probability of error of from two to three degrees on either side of the true bearing. The other drawing inPlate38was made from a point only a degree or two to the westward of the village of Zermatt. I have no note of the bearing; but it must be aboutS. 60° or 65°W.
84Independent travellers may perhaps be glad to know the way to the top of the Riffelhorn. I believe there is only one path; which ascends (from the ridge of the Riffel) on its eastern slope, until, near the summit, the low but perfectly smooth cliff, extending from side to side of the ridge, seems, as on the western slope, to bar all farther advance. This cliff may, however, by a good climber, be mastered even at the southern extremity; but it is dangerous there: at the opposite or northern side of it, just at its base, is a little cornice, about a foot broad, which does not look promising at first, but widens presently; and when once it is past, there is no more difficulty in reaching the summit.
85I ought before to have mentioned Madame de Genlis as one of the few writers whose influence was always exerted to restore to truthful feelings, and persuade to simple enjoyments and pursuits, the persons accessible to reason in the frivolous world of her times.
86Veillées du Château, vol. ii.
87The actual extent of the projection remaining the same throughout, the angle of suspended slope, for that reason, diminishes as the cliff increases in height.
§ 1.Duringall 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 débris; 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.
§ 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.
§ 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.
§ 4. All curvature, however, is not equally agreeable; butthe 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 cis one third longer thana b, andc dthanb 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 inFig. 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 inFig. 93, in which each line is double the preceding one, the curve willsuggest 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.
§ 5. These three curves being all governed by the same general law, with a difference only in dimensions of lines, togetherwith 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 betweeneandgis precisely what that betweencandewould 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 pointathe 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.
§ 6. Again: if, along the horizontal line,A B,Fig. 94, we measure any number of equal distances,Ab,b c, &c., and raise perpendiculars from the pointsb,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 curvex y, traced through their extremities, will continually change its direction, but will advance into space in the direction ofyas long as we continue to measure distances along the lineA B, always inclining more and more to the nature of a straight line, yet never becoming one, even if continued to infinity. Itwould, in like manner, continue to infinity in the direction ofx, always approaching the lineA B, yet never touching it.
§ 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.
§ 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 oftheir 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.
§ 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.
§ 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. § 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.
§ 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 quantity88of curvature is the same in both, though differently distributed.
§ 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 pointsAandB,Fig. 95, the weight of chain sustained by any given link increases gradually from the central link atC, which has only its own weight to sustain, to the link atB, which sustains, besides its own, the weight of all the links between it andC. This increased weight is continually pulling the curve of the swinging chain more nearly straight as it ascends towardsB; and hence one of the most beautifully gradated natural curves—called the catenary—of course assumed not by chains only, butby all flexible and elongated substances, suspended between two points. If the points of suspension be near each other, we have such curves as atD; 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 atE. 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
§ 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.
§ 14. Again. If a rod or stick of any kind gradually becomes more slender or more flexible, and is bent by any externalforce, 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.
§ 15. Again. Whenever any vital force is impressed on any organic substance, so as to die gradually away as the substance extends, an infinite curve is commonly produced by its outline. Thus, in the budding of the leaf, already examined, the gradual dying away of the exhilaration of the younger ribs produces an infinite curve in the outline of the leaf, which sometimes fades imperceptibly into a right line,—sometimes is terminated sharply, by meeting the opposite curve at the point of the leaf.
§ 16. Nature, however, rarely condescends to use one curve only in any of her finer forms. She almost always unites two infinite ones, so as to form a reversed curve for each main line, and then modulates each of them into myriads of minor ones. In a single elm leaf, such as Fig. 4, Plate8, she uses three such—one for the stalk, and one for each of the sides,—to regulate theirgeneralflow; 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 inPlate42, 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, inPlate43is a group of four withered leaves, in four positions, giving, each, a beautiful and well composed group of curves, variable gradually into the next group as the branch is turned.
§ 17. The following Plate (44), representing a young shoot of independent ivy, just beginning to think it would like to getsomething 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.
§ 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 beautyof 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, inPlate42, is formally expressed inFig. 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.
§ 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 thecircling 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.
§ 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 inFig. 99were 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.
§ 21. Thus much may suffice for our immediate purposeThe four systems of mountain line.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 débris 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 débris from a given point over surfaces of varied shape.
4. Lines of Rest. Those which are assumed by débris when in a state of comparative permanence and stability.
1. Lines of Fall.
However little the reader may be acquainted with hills, I believe1. Lines of Fall. Produced by falling bodies upon hill-surfaces.that, almost instinctively, he will perceive that the form supposed to belong to a wooded promontory ata,Fig. 100, is an impossible one; and that the form atbis not only a possible but probable one. The lines are equally formal in both. But ina, the curve is a portion of a circle, meeting a level line: inbit 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, itnecessarilyassumes, more or less perfectly, according to the time for which it has been exposed, and the tenderness of its substance, such contours as those atb, for the simple reason that every stream and every falling grain of sand gains in velocity and erosive power as it descends. Hence, cutting away the ground gradually faster and faster, they produce the most rapid curvature (provided the rock be hard enough) towards the bottom of the hill.90
§ 22. But farther: inbit 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 ata, 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. LetA C B,Fig. 101, have been its original contour. Then the aqueous forces will cut away the shaded portions, reducing it to the outlinedCe. 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 linesg 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 onsimilar curves; but the rounded lines inFig. 100would be those of forests seen on the edges of each detached ridge.
§ 23. Now although a mountain is rarely perfectly conical, and never divided by ravines at exactly equal distances, the law which is seen in entire simplicity inFig. 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.
§ 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 ofaorbinFig. 102, in which, observe, the precipice is of more importance, and the slope of less, precisely in proportion to the nearness of the mass.
§ 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.
§ 26. The fragments carried down by the torrents from the2. Lines of Projection. Produced by fragments bounding or carried forward from the bases of hills.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 theirowngravity, partly of projectile force caused by their fall from the higher summits of the hill; while the débris itself, after it has fallen, undergoes farther modification by surface streamlets. But in a general way débris descending from the hill side,a b,Fig. 103, will arrange itself in a form approximating to the concave lined 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.
§ 27. But this form is much modified by the special direction3. Lines of Escape. Produced by the lateral dissemination of the fragments.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. Leta b c,Fig. 104, be three ridges of mountain. The two torrents coming down the ravine between them meet, atdande, with the heaps of ground formerly thrown down by their own agency. These heaps being more or less in the form of cones, the torrenthas a tendency to divide upon their apex, like water poured on the top of a sugar-loaf, and branch into the radiating channelse x,e y, &c. The stronger it is, the more it is disposed to rush straightforward, or with little curvature, as in the linee 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, ore 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 Plate8of 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.
§ 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,—intowhich minor torrents are poured by lateral ravines, he will find himself every now and then ascending a hill of moderate slope, at thetopof 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 débris, 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 débris; 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.
§ 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, alongwhich 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.
§ 30. I have etched above,Plate35, 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 Côte and Taconay, shown from base to summit, with the Glacier des Bossons and its moraine. The reference figure given atp. 212will 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 asb c,cB.
d e. First lines of projection. The débris 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 Pélerins91) descendsfrom behind the promontoryh: its natural or proper course would be to dash straight forward down the linef 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, ati. If it is stronger, the impetus from the hill above shoots it farther out, in the linek; if stronger still, atl; 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 débris.
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 débris, 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 débris has formerly stopped.
§ 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 modifiedby 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;92but I believe they are all portions of infinite curves either modified by the concealment or destruction of the lower lips of débris, or by their junction with straight lines of slope above, throwing the longest limb of the curve upwards. Fig. 1, inPlate45opposite, 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.§ 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.
§ 32. The straight slopes with which these curves unite themselves below, inPlate33(f gin reference figure), are thosespoken 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 respectingcurvaturein 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.
§ 33. Perhaps the mountain which I have drawn on the opposite page (Plate4693) 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 inFig. 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 inPlate46, and (in plan) inFig. 105. The whole of the upper surface of the promontory is wrought by the old glaciers into furrows and striæ more notable than any I ever saw in the Alps.
§ 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.