[89] 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.
[90] 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.
[91] 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 Pélerins 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 déborder.' 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 logée 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 ça, le roc est percé;' 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 châlet, 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 châlet, and sat down before its door. I had not been there five minutes before the cascade fell, and rose no more."
[92] 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 débris 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.
[93] 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.
[94] 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.
[95] The white spots on the brow of the little cliff are lichens, only four or five inches broad.
[96] What a comfortable, as well as intelligent, operation, sketching from nature must have been in those days!
[97] 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. § 20.