appreciation of all tenderness with delight in all magnitude, and memory for all detail, is never to be rivalled, or looked upon in similitude again. FOOTNOTES [88] _Quantity_ of curvature is as measurable as quantity of anything else; only observe that it depends on the nature of the line, not on its magnitude; thus, in simple circular curvature, _a b_, Fig. 96, being the fourth of a large circle, and _b c_ the half of a smaller one, the quantity of the element of circular curvature in the entire line _a c_ is three fourths of that in _any_ circle,--the the same as the quantity in the line _e f_. [Illustration: FIG 96.] [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.