There are also limits in length which a valley may not exceed. The head of any valley may recede until some other valley is reached. The recession may not stop even there, for if, on opposite sides of a divide, erosion is unequal, as between 1A and 1B, Fig. 14, the divide will be moved toward the side of less rapid erosion, and it will cease to recede only when erosion on the two sides becomes equal (4A and 4B). In homogeneous material this will be when the slopes on the two sides are equal. [Illustration: Fig. 14.--Diagram showing the shifting of a divide. The slopes 1A and 1B are unequal. The steeper slope is worn more rapidly and the divide is shifted from 1 to 4, where the two slopes become equal and the migration of the divide ceases.] It should be noted that the lengthening of a valley headward is not normally the work of the permanent stream, for the permanent stream begins some distance below the head of the valley. At the head, therefore, erosion goes on as at the beginning, even after a permanent stream is acquired. Under certain circumstances, the valley may be lengthened at its debouchure. If the detritus carried by it is deposited at its mouth, or if the sea bottom beyond that point rise, the land may be extended seaward, and over this extension the stream will find its way. Thus at their lower, as well as at their upper ends, both the stream and its valley may be lengthened. _A cycle of erosion._--If, along the borders of a new-born land mass, a series of valleys were developed, essentially parallel to one another, they would constitute depressions separated by elevations, representing the original surface not yet notably affected by erosion (see Plate XIV, Fig. 1). These inter-valley areas might at first be wide or narrow, but in process of time they would necessarily become narrow, for, once, a valley is started, all the water which enters it from either side helps to wear back its slopes, and the wearing back of the slopes means the widening of the valleys on the one hand and the narrowing of the inter-valley ridges on the other. Not only would the water running over the slopes of a valley wear back its walls, but many other processes conspire to the same end. The wetting and drying, the freezing and the thawing, the roots of plants and the borings of animals, all tend to loosen the material on the slopes or walls of the valleys, and gravity helps the loosened material to descend. Once in the valley bottom, the running water is likely to carry it off, landing it finally in the sea. Thus the growth of the valley is not the result of running water alone, though this is the most important single factor in the process. [Illustration: WISCONSIN GEOL. AND NAT. HIST. SURVEY. BULLETIN NO. V., PL. XIV. FIG. 1. The same valleys as shown in Plate XIII, Fig. 3, in a later stage of development. Illustration: FIG. 2. Same valleys as shown in Fig. 1, in a still later stage of development.]