precision unnecessary.

No one, I think, would affirm that the area of the fissures would be
one-hundredth the area of the land. For let us consider the strain
upon a single line drawn over the summit of the protuberance from a
point on its rim to a point opposite. Regarding the protuberance as a
spherical swelling, the length of the arc corresponding to a chord of
100 miles and a versed sine of 3 miles is 100.24 miles; consequently
the surface to reach its new position must stretch 0.24 of a mile, or
be broken. A fissure or a number of cracks with this total width
would relieve the strain; that is to say, the sum of the widths of all
the cracks over the length of 100 miles would be 420 yards. If,
instead of comparing the width of the fissures with the length of the
lines of tension, we compared their areas with the area of the
unfissured land, we should of course find the proportion much less.
These considerations will help the imagination to realise what a small
ratio the area of the open fissures must bear to the unfissured crust.
They enable us to say, for example, that to assume the area of the
fissures to be one-tenth of the area of the land would be quite
absurd, while that the area of the fissures could be one-half or more
than one-half that of the land would be in a proportionate degree
unthinkable. If we suppose the elevation to be due to the shrinking
or subsidence of the land all round our assumed circle, we arrive
equally at the conclusion that the area of the open fissures would be
altogether insignificant as compared with that of the unfissured
crust.

To those who have seen them from a commanding elevation, it is
needless to say that the Alps themselves bear no sort of resemblance
to the picture which this theory presents to us. Instead of deep
cracks with approximately vertical walls, we have ridges running into
peaks, and gradually sloping to form valleys. Instead of a fissured
crust, we have a state of things closely resembling the surface of the
ocean when agitated by a storm. The valleys, instead of being much
narrower than the ridges, occupy the greater space. A plaster cast of
the Alps turned upside down, so as to invert the elevations and
depressions, would exhibit blunter and broader mountains, with
narrower valleys between them, than the present ones. The valleys
that exist cannot, I think, with any correctness of language be called
fissures. It may be urged that they originated i