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." [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 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. [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.