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. 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. [Illustration: +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.]