In cultivated regions, wells are of frequent occurrence. In a flat region of uniform structure, the depth at which well water may be obtained is essentially constant at all points. If holes (wells 1 and 2, Fig. [13]) be excavated below this level, water seeps into them, and in a series of wells the water stands at a nearly common level. This means that the sub-structure is full of water up to that level. These relations are illustrated by Fig. [13]. The diagram represents a vertical section through a flat region from the surface (s s) down below the bottom of wells. The water stands at the same level in the two cells (1 and 2), and the plane through them, at the surface of the water, is the ground water level. If in such a surface a valley were to be cut until its bottom was below the ground water level, the water would seep into it, as it does into the wells; and if the amount were sufficient, a permanent stream would be established. This is illustrated in Fig. [13]. The line A A represents the ground water level, and the level at which the water stands in the wells, under ordinary circumstances. The bottom of the valley is below the level of the ground water, and the water seeps into it from either side. Its tendency is to fill the valley to the level A A. But instead of accumulating in the open valley as it does in the enclosed wells, it flows away, and the ground water level on either hand is drawn down.

Fig. 13. -- Diagram illustrating the relations of ground water to streams.

The level of the ground water fluctuates. It is depressed when the season is dry (A' A'), and raised when precipitation is abundant (A'' A''). When it is raised, the water in the wells rises, and the stream in the valley is swollen. When it falls, the ground water surface is depressed, and the water in the wells becomes lower. If the water surface sinks below the bottom of the wells, the wells "go dry;" if below the bottom of the valley, the valley becomes for the time being, a "dry run." When a well is below the lowest ground-water level its supply of water never fails, and when the valley is sufficiently below the same level, its stream does not cease to flow, even in periods of drought. On account of the free evaporation in the open valley, the valley depression must be somewhat below the level necessary for a well, in order that the flow may be constant.

It will be seen that intermittent streams, that is, streams which flow in wet seasons and fail in dry, are intermediate between streams which flow after showers only, and those which flow without interruption. In the figure the stream would become dry if the ground water level sank to A' A'.

It is to be noted that a permanent stream does not normally precede its valley, but that the valley, developed through gully-hood and ravine-hood to valley-hood by means of the temporary streams supplied by the run-off of occasional showers, finds a stream, just as diggers of wells find water. The case is not altered if the stream be fed by springs, for the valley finds the spring, as truly as the well-digger finds a "vein" of water.

Limits of a valley.—So soon as a valley acquires a permanent stream, its development goes on without the interruption to which it was subject while the stream was intermittent. The permanent stream, like the temporary one which preceded it, tends to deepen and widen its valley, and, under certain conditions, to lengthen it as well. The means by which these enlargements are affected are the same as before. There are limits, however, in length, depth, and width, beyond which a valley may not go. No stream can cut below the level of the water into which it flows, and it can cut to that level only at its outlet. Up stream from that point, a gentle gradient will be established over which the water will flow without cutting. In this condition the stream is at grade. Its channel has reached baselevel, that is, the level to which the stream can wear its bed. This grade is, however, not necessarily permanent, for what was baselevel for a small stream in an early stage of its development, is not necessarily baselevel for the larger stream which succeeds it at a later time.

Weathering, wash, and lateral corrasion of the stream continue to widen the valley after it has reached baselevel. The bluffs of valleys are thus forced to recede, and the valley is widened at the expense of the upland. Two valleys widening on opposite sides of a divide, narrow the divide between them, and may ultimately wear it out. When this is accomplished, the two valleys become one. The limit to which a valley may widen on either side is therefore its neighboring valley, and since, after two valleys have become one by the elimination of the ridge between them, there are still valleys on either hand, the final result of the widening of all valleys must be to reduce all the area which they drain to baselevel. As this process goes forward, the upper flat into which the valleys were cut is being restricted in area, while the lower flats developed by the streams in the valley bottoms are being enlarged. Thus the lower flats grow at the expense of the higher.

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.