t _c_ cannot exist at all on the large scale, unless it is built of
good materials, and it will then frequently stay in its fixed frown for
ages.

Sec. 4. It occasionally happens that a precipice is formed among the higher
crests by the _sides_ of vertical beds of slaty crystallines. Such rocks
are rare, and never very high, but always beautiful in their smoothness
of surface and general trenchant and firm expression. One of the most
interesting I know is that of the summit of the Breven, on the north of
the valley of Chamouni. The mountain is formed by vertical sheets of
slaty crystallines, rather soft at the bottom, and getting harder and
harder towards the top, until at the very summit it is hard and compact
as the granite of Waterloo Bridge, though much finer in the grain, and
breaking into perpendicular faces of rock so perfectly cut as to feel
smooth to the hand. Fig. 4, p. 107, represents, of the real size, a bit
which I broke from the edge of the cliff, the shaded part underneath
being the surface which forms the precipice. The plumb-line from the
brow of this cliff hangs clear 124 English feet; it is then caught by a
ledge about three feet wide, from which another precipice falls to about
twice the height of the first; but I had not line enough to measure it
with from the top, and could not get down to the ledge. When I say the
line hangs _clear_, I mean when once it is off the actual brow of the
cliff, which is a little rounded for about fourteen or fifteen feet,
from _a_ to _b_, in the section, Fig. 75. Then the rock recedes in an
almost unbroken concave sweep, detaching itself from the plumb-line
about two feet at the point _c_ (the lateral dimensions are exaggerated
to show the curve), and approaching it again at the ledge _d_, which is
124 feet below _a_. The plumb-line, fortunately, can be seen throughout
its whole extent from a sharp bastion of the precipice farther on, for
the face of the cliff runs, in horizontal plan, very nearly to the
magnetic north and south, as shown in Fig. 74, the plumb-line swinging
at _a_, and seen from the advanced point P. It would give a similar
result at any other part of the cliff face, but may be most conveniently
cast from the point _a_, a little below, and to the north of the summit.

[Illustration: FIG. 74.]

[Illustration: FIG. 75.]

Sec. 5. But although the other divisions of this precipice, below the ledge
which stops the plummet, give it altogether a height of