§ 9. This example of the common ideal of aiguilles is, however, useful in another respect. It shows the strong impression which these Chamouni mountains leave, of their being above all others sharp-peaked and splintery, dividing more or less into arrowy spires; and it marks the sense of another and very curious character in them, that these spires are apt to be somewhat bent or curved.

Both these impressions are partially true, and need to be insisted upon, and cleared of their indistinctness, or exaggeration.

First, then, this strong impression of their peakedness and spiry separateness is always produced with the least possible danger to the travelling and admiring public; for if in reality these granite mountains were ever separated into true spires or points, in the least resembling this popular ideal in [Plate 30], the Montanvert and Mer de Glace would be as inaccessible, except at the risk of life, as the trenches of a besieged city; and the continual fall of the splintering fragments would turn even the valley of Chamouni itself into a stony desolation.

§ 10. Perhaps in describing mountains with any effort to give some idea of their sublime forms, no expression comes oftener to the lips than the word "peak." And yet it is curious how rarely, even among the grandest ranges, an instance can be found of a mountain ascertainably peaked in the true sense of the word,—pointed at the top, and sloping steeply on all sides; perhaps not more than five summits in the chain of the Alps, the Finster-Aarhorn, Wetterhorn, Bietschhorn, Weisshorn, and Monte Viso presenting approximations to such a structure. Even in the case of not very steep pyramids, presenting themselves in the distance under some such outline as that at the top of [Fig. 30], it almost invariably happens, when we approach and examine them, that they do not slope equally on all their sides, but are nothing more than steep ends of ridges, supported by far-extended masses of comparatively level rock, which, seen in perspective, give the impression of a steep slope, though in reality disposed in a horizonal, or nearly horizontal, line.

§ 11. Supposing the central diagram in [Fig. 30] to be the apparent contour of a distant mountain, then its slopes may indeed, by singular chance, be as steep as they appear; but, in all probability, several of them are perspective descents of its retiring lines; and supposing it were formed as the gable roof of the old French house below, and seen under the same angle, it is evident that the part of the outline a b (in lettered reference line below) would be perfectly horizontal; b c an angle slope, in retiring perspective, much less steep than it appears; c d, perfectly, horizontal; d e, an advancing or foreshortened angle slope, less steep than it appears; and e f, perfectly horizontal.

Fig. 30.

But if the pyramid presents itself under a more formidable aspect, and with steeper sides than those of the central diagram, then it may be assumed (as far as I know mountains) for next to a certainty, that it is not a pointed obelisk, but the end of a ridge more or less prolonged, of which we see the narrow edge or section turned towards us.

Fig. 31.

Fig. 32.
Angles with the horizon x y.
Of the linea b 17°
"b c 20½
"d y(general slope, exclusive of inequalities)35¾
"a x(ditto, ditto, to point of cliff above x)23½

For instance, no mountain in the Alps produces a more vigorous impression of peakedness than the Matterhorn. In Professor Forbes's work on the Alps, it is spoken of as an "obelisk" of rock, and represented with little exaggeration in his seventh plate under the outline [Fig. 31]. Naturally, in glancing, whether at the plate or the mountain, we assume the mass to be a peak, and suppose the line a b to be the steep slope of its side. But that line is a perspective line. It is in reality perfectly horizontal, corresponding to e f in the penthouse roof, [Fig. 30].