388 PACIFIC ISLANDS. 
mere edge; and as a second, its partial or entire removal, so that the 
two valleys may become separated by a low wall, or terminate in a 
common head,—a wide amphitheatre enclosed by lofty mountain walls. 
In one case the ridge between two valleys begins at the shores of 
the island with rather a broad back, and high up, in the regions of 
mists and frequent rains, becomes a narrow wall, and thus connects 
with the central summit. In the second, the ridge finally terminates 
quite abruptly, leaving a deep valley separating it from the main 
mountain. 
The following sketch may assist the mind in conceiving of the 
action upon the Pacific mountains. It represents one of the valleys 
of Tahiti from the centre to the shore, excepting its irregularities of 
direction and descent, and the uneven character of its walls, arising 
from lateral valleys and minor denudations. The height of Tahiti is 
about eight thousand feet; its radius ¢s is ten geographical miles. 
The head of the valley at a is three thousand feet below the summit 
peak, p. The descent, from a@ to s, averages five hundred feet to the 
mile. If @ be four thousand feet below the summit, (the exact depth 
was not ascertained,) it would still give four hundred feet to the mile. 
This subject is beautifully illustrated in some of the tufa cones of 
Oahu, where, on a smaller scale, we have the same kind of gorges and 
valleys, (see figure, page 240;) and there is no doubt that denuda- 
tion was the cause by which they were produced. The valleys have 
the direction of the slope, and are similar in form and winding cha- 
racter to those of the mountains. ‘The intervening ridges are also 
similar: many of them become very thin at summit as they rise 
towards the crest of the volcanic cone, and others have this upper 
part adjoining the crest wanting, owing to the extent of the degrada- 
tion, so that two valleys have a common head against the vertical 
bluff. A better model of the mountain gorges could hardly be made, 
and it stands near by convenient for comparison. 
We need add little, in this place, on the capabilities of running 
water, after the statement, based on mathematics, that the transporting 
force varies as the sixth power of the velocity. If we remember that 
these mountain streams at times increase their violence a million fold 
