In the presence of sufficient rainfall, either heterogeneity of slope or of material will therefore occasion the development of valleys. If the lack of uniformity appears at but a single point there will be but a single valley. If it appears at many points the number of valleys will be large. Since it is incredible that a land mass of perfectly homogeneous material and of absolutely uniform slopes ever existed, it is believed that every land mass, affected for any considerable length of time by rain, has had valleys developed in it. The degree of heterogeneity of material and slope is usually so great as to lead to the development of many valleys, even on areas which are not large; but for the sake of emphasizing the simpler elements of the complex processes of stream work, the hypothetical case of an island with but a single valley, and that without tributaries, may first be studied. Under these conditions two cases may be considered, the one where there is no deposition about the island, and the other where deposition takes place.
1. If all the material eroded from the surface of such an island, both in and out of the valley, were carried well beyond the borders of the land before being deposited, the edge of the island would recede from its original position toward the center, as illustrated by Figs. [37] and [45]; but the recession would be most rapid where the valley joins the sea ([Fig. 45]). At this point therefore a reëntrant would be developed (a, [Fig. 45]), and the island would lose its circular outline. Continued erosion would cause the shore-line to retreat on all sides, but fastest at the lower end of the valley, and the final result would be a base-level differing from that developed under the conditions specified on [p. 60], in that the last part to be brought low would not be the center of the original island.
Fig. 46.—Diagram showing the outline of an island as modified by sheet and stream erosion where eroded material is deposited at the shore. The dotted line represents the original outline; the full line, a later one. The excess of deposition at the end of the valley causes a projection of land into the sea.
Under the foregoing conditions the profile of that part of the valley which is above sea-level (cb) would be convex, following the analogy of sheet erosion on a hypothetical island of uniform slopes and homogeneous material with no marginal deposition. Its side slopes, likewise developed under the influence of running water augmented in volume from top to bottom, would also be convex.
2. If the sediment washed down from the land is deposited about its borders, both the outline of the island and the profile of the valley will be altered. Deposition at the debouchure of the valley follows the same principles as deposition elsewhere; but if all the sediment brought to the sea be deposited at the shore, the seaward extension of the land by deposition would be more rapid opposite the valley than elsewhere, and the island would lose its circular outline, and develop some such form as is shown in [Fig. 46]. In this case the profile of the upper end of the valley, and the upper parts of its side slopes, as well as the upper parts of the extra-valley slopes of the island, are convex (compare Figs. [39] and [40]); but the convexity above is exchanged for concavity below, the change beginning at the point where downward erosion of the descending waters is checked. As a valley lengthens, the larger part of its profile becomes concave (compare the profiles of Figs. [39] to [41]), but the extreme upper end still remains convex. Since the side slopes of a valley are much shorter than its lengthwise slope, a larger proportion remains convex. Under the conditions here discussed the change from convexity above to concavity below would begin at about the point where deposition begins.[27]
Fig. 47.—Diagram representing several meridional valleys developing in a circular island. The valleys are all young and narrow. All are making deposits at their debouchures.
The deposition at the debouchure of the valley, and later above the debouchure, will follow the same course as about the island under the conditions already discussed (pp. [61], [62]).
Limits of growth.—In all cases there are limits in depth, length, and width, beyond which a valley may not grow. In depth it may reach base-level. At the coast, base-level is sea-level,[28] but inland it rises by a gentle gradient. In length, the valley will grow as long as its head continues to work inland. In the case represented by Figs. [45] and [46] the head of the valley would not cease to advance when the center of the island was reached, though beyond that point head erosion would not be more rapid than lateral erosion on either side. If but a single valley affected a land area the limit toward which it would tend, and beyond which it could never pass, would be the length of the land area in the direction of the valley’s axis. In width, a valley is increased by the side cutting of the stream, by the wash of the rain which falls on its slopes, and by the action of gravity which tends to carry down to the bottom of the slope the material which is loosened above by any process whatsoever. If there be but one valley in a land area its limiting width is scarcely less than the width of the land itself.