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 antic.i.p.ating 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 ma.s.s, 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 a.s.sured 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. We have 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 facades 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's _patience_; 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 leaf.a.ge 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 pa.s.sing rents of blue, it seems partly to rebuke, and partly to 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 Fort.i.tude.

FOOTNOTES

[80] Distinguished from a _crest_ by being the _face_ of a large contiguous bed of rock, not the end of a ridge.

[81] The contour of the whole cliff, seen from near its foot as it rises above the shoulder of the Breven, is as at Fig. 76 opposite.

The part measured is _a d_; but the precipice recedes to the summit _b_, on which a human figure is discernible to the naked eye merely as a point. The bank from which the cliff rises, _c_, _recedes_ as 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.

[Ill.u.s.tration: FIG. 76.]

[82] At an angle of 79 with the horizon. See the Table of angles, p. 181. The line _a e_ in Fig. 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.

[83] Professor Forbes gives the bearing of the Cervin from the top of the Riffelhorn as 351, or N. 9 W., supposing local attraction to have caused an error of 65 to the northward, which would make the true bearing N. 74 W. From the point just under the Riffelhorn summit, _e_, in Fig. 78, at which my drawing was made, I found the Cervin bear N. 79 W. without any allowance for attraction; the disturbing influence would seem therefore confined, or nearly so, to the summit _a_. 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 compa.s.s and in the sailor's way (S. by W. and W. & C.), which involves the probability of error of from two to three degrees on either side of the true bearing. The other drawing in Plate +38+ was 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 about S. 60 or 65 W.

[84] Independent 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.

[85] I 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.

[86] Veillees du Chateau, vol. ii.

[87] The actual extent of the projection remaining the same throughout, the angle of suspended slope, for that reason, diminishes as the cliff increases in height.

CHAPTER XVII.

RESULTING FORMS:--FOURTHLY, BANKS.

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

-- 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 ma.s.ses may frequently be intended to produce impressions of terror rather than of beauty; but the laws which are in constant operation on all n.o.ble and enduring scenery must a.s.suredly 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, a.s.sociated 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.

[Ill.u.s.tration: FIG. 90.]

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 n.o.bleness: 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 a.s.sociations, his judgment of the relative agreeableness of the forms would be altered. He may rest a.s.sured 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 subst.i.tute triangles for the ordinary shapes of clover leaves, or pentagons for those of potentillas.

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

[Ill.u.s.tration: FIG. 91.]

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

These characters must be possessed by every perfectly beautiful curve.

If we make the difference between the component or measuring lines less, as in Fig. 92, in which each line is longer than the preceding one only by a fifth, the curve will be more contracted and less beautiful. If we enlarge the difference, as in Fig. 93, in which each line is double the preceding one, the curve will suggest a more rapid proceeding into infinite s.p.a.ce, 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.

[Ill.u.s.tration: FIG. 92.]

[Ill.u.s.tration: FIG. 93.]

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

[Ill.u.s.tration: FIG. 94.]

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

-- 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 mult.i.tude 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 cla.s.ses. The first cla.s.s consists of those which are limited in their course, either ending abruptly, or returning to some point from which they set out; the second cla.s.s, of those lines whose nature is to proceed for ever into s.p.a.ce.

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 s.p.a.ce, 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 n.o.bleness and chooseableness of all things.

The two cla.s.ses 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 cla.s.s 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 cla.s.s 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 canva.s.sed 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 n.o.blest compositions, this utmost power is permitted, but only for a short time, or over a small s.p.a.ce. 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.

[Ill.u.s.tration: 42. Leaf Curvature. Magnolia and Laburnum.]

[Ill.u.s.tration: 43. Leaf Curvature. Dead Laurel.]

[Ill.u.s.tration: 44. Leaf Curvature. Young Ivy.]

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 s.p.a.ces 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 s.p.a.ce 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; mult.i.tudes of other curves, not approaching the right line so nearly, remain less vigorously bent in the rest of their course; so that the quant.i.ty[88] of curvature is the same in both, though differently distributed.

[Ill.u.s.tration: FIG. 95.]

-- 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 a.s.sumed 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 const.i.tute 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 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 a.s.sumed by boughs of trees under wind.