Still later stages of development are represented by the cross-sections 3–3 and 4–4. Not only has the valley become larger, but the stream has deposited detritus (not shown in the figure) in the bottom of its valley, developing an alluvial flat. On this flat the stream meanders, and the valley may be widened by the undercutting of the bluffs wherever the stream in its wanderings reaches them (Pl. VIII, near St. Louis). A valley might possess the characteristics shown by the cross-sections 3–3, 2–2, and 1–1, Fig. 64, in its lower, middle, and upper courses, respectively.

The preceding discussion, and the illustrations which accompany it, give some idea of the topography which characterizes an area in various stages of its erosion history. Whether the valleys are deep or shallow, and the intervening ridges high or low, depends on the original height of the land and its distance from the sea. The higher the land, and the nearer it is to the sea, the greater the relief developed by erosion. A plateau near the sea may become mountainous in the mature stage of its erosion history, while a plain in the same situation would only become hilly. A plateau in the heart of a continent would have less relief in its maturity than one of equal elevation near the sea, since the grade-plain in the former position is higher than in the latter. Plates IV and IX show youthful topography where the relief is relatively slight, and Plate X shows youthful topography where the relief is great. Similarly, Plates V and VI show mature topography where the relief is great, and Fig. 1, Plate III, shows mature topography where the relief is relatively slight.

Topographic youth, topographic maturity, and topographic old age are also indicated in other ways, and especially by the presence of features which rivers tend to destroy. If, for example, the surface of the land, well above the valley bottoms, is marked by numerous ponds and marshes, it is clear that drainage has not yet progressed beyond its early stages, for, unless the lakes be very deep, valleys working back into the land will find and drain them before topographic maturity has been reached. Their presence is evidence that the region where they occur has not yet been thoroughly dissected by erosion lines, and therefore has not reached maturity. Still other marks of topographic youth, such as rapids, falls, etc., as well as marks of topographic maturity and old age, will be mentioned in the following pages.

GENERAL CHARACTERISTICS OF TOPOGRAPHIES DEVELOPED BY RIVER EROSION.

With the characteristics of river valleys and the methods by which they grow clearly in mind it is easy to say whether rivers have been the chief agents in the development of a given topography. River valleys are distinguished from other depressions on land surfaces by their linear form and, leaving out of consideration the relatively insignificant inequalities in a stream’s channel, by the fact that any point in the bottom of a river valley is lower than any other point farther up the stream in the same valley, and higher than any point farther down the stream. The second point might be otherwise stated by saying that every valley excavated by erosion leads to a lower valley, or to the sea, or an inland basin. Streams which dry up, or otherwise disappear as they flow, constitute partial exceptions. If, therefore, the depressions on a land surface are linear, lead to other and deeper valleys, and finally to an inland basin, or the sea, and if the elevations between these valleys are such as might have been left by the excavation of the valleys, it is generally clear that rain and rivers have been the chief factors in the development of the topography. If, on the other hand, a surface is characterized by topographic features which streams cannot develop, such as enclosed depressions, or hills and ridges whose arrangement is independent of drainage lines, other agents besides rain and surface streams have been concerned in its development.

SPECIAL FEATURES RESULTING FROM SPECIAL CONDITIONS OF EROSION.

Many striking topographic and scenic features result from rain and river erosion. Some of them depend primarily on the conditions of erosion, such as climate, altitude, etc., while others depend largely on the structure and resistance of the rock. Between these two classes there is no sharp line of demarkation. Illustrations of two types, dependent largely but by no means wholly on conditions independent of the rock, are cited at this point. Others will be mentioned in other connections.

Bad-land topography.—To a type of topography developed in early maturity in certain high regions where the rock is but slightly, though unequally, resistant, a special name is sometimes given. Such regions are termed bad lands. Some idea of bad-land topography is gained from Figs. 75 to 78. Bad-land topography is found in various localities in the West, but especially in western Nebraska and Wyoming, and the western parts of the Dakotas. The formations here are often beds of sandstone or shale, alternating with unindurated beds of clay. Climatic factors are also concerned in the development of bad-land topography. A semi-arid climate, where the precipitation is much concentrated, seems to be most favorable for its development. The bad-land topography is most striking in early maturity.

Special forms of valleys; canyons.—Various conditions influence the size and shape of valleys, especially in the early stage of their development. If the altitude of the land be great, the gradient of the streams at this stage will be high. A high gradient means a swift stream, and a swift stream erodes chiefly at its bottom. High altitudes therefore favor the development of deep valleys. Such valleys will be narrow if the conditions which determine widening are absent or unfavorable. Since slope wash is one of the main factors in the widening of valleys, an arid climate favors the development of narrow valleys, if there be sufficient water to maintain a vigorous stream. Narrowness and steepness of slopes will also be favored if the valley is cut in rock which is capable of standing with steep faces. Thus a stream may develop a narrow valley in indurated rock where it would not do so in loose gravel, and, other things being equal, it will develop a narrower valley in rock which is horizontally bedded than in rock the beds of which are inclined. Aridity, high altitude, and the proper sort of rock structure therefore favor the development of canyons, and many of the young valleys in the western part of the United States where these conditions prevail, belong to this class.

While all canyons are valleys, most valleys are not canyons. The distinction between a canyon and a valley which is not a canyon is not sharp. The canyon depends for its distinctive character on the relation of depth, width, and angle of slope to one another; but any definition of the depth, width, and angle of slope necessary to constitute a valley a canyon is arbitrary.[31] In popular usage the rule seems to be that if a valley is sufficiently deep, narrow, and steep-sided to be distinctly striking, it is called a canyon in regions where that term is in use. Whether a valley is deep, narrow, and steep-sided enough to be striking clearly depends on the observer. The Colorado Canyon (Figs. 79 and 80) is the greatest canyon known, but it is rarely more than a mile deep, and where its depth approaches this figure it is often eight, ten, or even twelve miles wide from rim to rim. Its width at bottom is little more than the width of the stream; that is, a few hundred feet. Its cross-profile throughout much of its course is therefore not in keeping with the conventional idea of a canyon. With a depth of one mile and a width of eight, the slope, if uniform, would have an angle of less than 15°. Such a valley is represented in Fig. 81. As a matter of fact the slopes of a canyon are not commonly uniform. The slopes represented in Fig. 82 correspond more nearly than those of Fig. 81, to the actual slopes of the Colorado Canyon. The inequalities of slope are occasioned by the inequalities of hardness. It is perhaps needless to say that to an observer on the rim of the canyon the slopes seem several times as steep as those shown in the diagrams.

Like all valleys which are narrow relative to their depth, the Colorado Canyon, great as it is, is a young valley; for it represents but a small part of the work which the stream must do to bring its drainage basin to base-level.

While aridity and altitude are conditions which favor the development of canyons, as shown by the fact that most canyons are high and dry regions, they are not indispensable. Niagara River has a canyon below its falls (Pl. IX), and the surrounding region is neither high nor arid. The narrow part of the valley has been developed by the recession of the falls, and is so young that side erosion has not yet widened the valley or lowered its angle of slope to such an extent as to destroy its canyon character. This canyon is often called a gorge, a term frequently applied to small valleys of the canyon type.

Plate X shows portions of the canyons of the Yellowstone and the Colorado rivers respectively. In the first the contour interval is 100 feet, and in the second, 250 feet. The horizontal scale is ¹⁄₁₂₅₀₀₀ (about 2 miles to the inch) in the first, and ¹⁄₂₅₀₀₀₀ in the second. These scales should be borne in mind in interpreting the map.

Falls, rapids, narrows, and other peculiar features, due primarily to inequalities in the hardness of the rock affected by erosion, will be considered later.

THE STRUGGLE FOR EXISTENCE AMONG VALLEYS AND STREAMS.

It is not to be inferred that every gully becomes a valley, nor that every small valley becomes a large one. Among valleys, as among living things, there is a struggle for existence, and fitness determines growth and survival. At an early stage of its erosion history the number of small valleys in a given area is often great, while at a later stage the number is less and the size of the survivors greater.

One phase of the struggle for existence is often well illustrated on a freshly exposed slope of clay. The number of miniature gullies which develop on such a slope, even in a single shower, may be very large (Fig. 84); but the history of many of them is ephemeral. If two adjacent ones are of unequal depth the widening of the deeper narrows and finally eliminates the divide between them, and the two become one (Fig. 85).

Another phase of the struggle for existence is shown in other situations. Examination of a good map of the north shore of Lake Superior or the west shore of Lake Michigan shows a large number of small streams and gullies (Fig. 1, Pl. IV). The valleys are short and narrow, and between and beyond them are considerable areas untouched by erosion. The drainage near the lake is therefore young, and each of the small valleys is growing. This condition of things is perhaps typical of that which has been, is, or will be along the average coast at a certain stage in its erosion history. No equal stretch of coast-line where erosion is far advanced can boast of a number of large rivers comparable to that of the many small ones along the coasts mentioned. It therefore seems evident that of these many small streams a few only will attain considerable size.

Some of the methods by which the growth of the many is arrested are easily understood. Some of the young valleys on a given coast will work their heads back into the land faster than others because of inequalities of slope and material. This will be true of the tributaries no less than of their mains. If valleys develop in ways other than by head erosion (see p. 73) the chances are also against their equality of growth. If two streams, such as a and c, Fig. 86, develop faster than the intermediate stream b, it is clear that their tributaries may work back into the territory which at the outset drained into b, so as to cut off the supply of water from the latter stream (compare a′b′c′, Fig. 87). As a result, the growth of b will be checked, and ultimately stopped. Similarly other valleys, such as f, will get the better of their neighbors, and many of the competitors, as b, d, e, and g will soon drop out of the race. Between the stronger streams competition still goes on. If a′ and f′ develop faster than c′ its prospective drainage territory will be preëmpted by its rivals (compare Figs. 87 and 88). Thus as the result of the unequal rate at which valleys are lengthened, the larger number of those which come into existence are arrested in their development. As a result of growth in the manner indicated, the basins of even the large streams remain narrow at their lower ends while they expand above. This is the usual form of a drainage basin the development of which has been normal.

Did valleys grow in length only, competition would not destroy the small ones; it would simply limit them. But valleys widen as well as lengthen, and by widening, adjacent valleys may eliminate the divide between them and become one. The elimination of the intervening ridge may be by lateral planation (p. 82), or, if the valleys be of unequal depth, by slope wash (see Fig. 85). By these and other processes many young valleys are dwarfed, and many others are destroyed.

Piracy.—Streams do not always hold the courses which they establish for themselves at the outset. If the valley occupied by the stream a, Fig. 89, is deepened more rapidly than the valley occupied by b, a tributary from the former, c, may work back across the inter-stream area to e and steal the head waters of that stream (Fig. 90). The tributary which does the stealing is known as a pirate. Stream f (Fig. 90) is said to be beheaded, and its upper portion, de, diverted. The beheaded stream is diminished in volume; or if its total supply of water came in above the point of tapping it would disappear altogether.

The process may not end even here. If after the diversion of de the point in the channel to the left is lowered faster than the channel of the beheaded stream f, the divide between dg and the head of f (Fig. 90) will be shifted down the valley of the latter, as shown in Fig. 91. The shifting will go on until the divide reaches a position of stability, that is, until erosion on its opposite sides is equal.

The foregoing case may be called foreign piracy because the valleys of different systems are concerned. Domestic piracy may also take place, as illustrated in the accompanying diagrams (Figs. 92 and 93). Here a tributary to a crooked river may develop, working back until it taps the main at a higher point, thus straightening the course of the stream. The change takes place only when the highest point in the tributary valley is brought below the surface of the water in the main stream at the point where the tapping takes place. This would be likely to occur only after the main stream had attained a low gradient, for so long as it is deepening its channel notably, the small amount of water flowing through the tributary valley would not be likely to bring it down to the level of the main. In any case the flow of water from the main stream through the new valley would be likely to be started during flood, and at such time the erosion in the new channel would be great. The complete and final diversion of the stream through the new channel might be a slow process.

Piracy may occur where the material in which the valleys are cut is homogeneous; but, as will be seen later, heterogeneity of material, by determining unequal rates of erosion, stimulates the piratical proclivities of streams.

An actual case of piracy is shown on Plate XI. North and South Lakes formerly drained westward to the Schoharie Creek, the present head of which is in the extreme northwest corner of the map. The head of Kaaterskill Creek, which had a much higher gradient, worked back and captured the head of the westward-flowing stream, diverting the drainage from North and South Lakes to itself. Schoharie Creek was thus beheaded.

Plaatekill Creek, near the south limit of the map, appears to have beheaded the creek flowing west and northwest, similarly diverting its head waters. The Dells, Wis., quadrangle (U. S. Geol. Surv.) affords an illustration of domestic piracy.

RATE OF DEGRADATION.

The amount of mechanical sediment which the Mississippi River carries to the Gulf of Mexico is estimated to represent a rate of degradation for the Mississippi basin of about one foot in 5000 years. But the mechanical sediment carried to the Gulf does not really represent the total degradation of the basin, for the water which sinks beneath the surface is dissolving more or less rock substance, especially lime carbonate. This material is carried to the sea in solution, and does not appear in the sediment on which the above estimate is based. Taking into account the matter dissolved by the water and carried to the sea in solution, the average rate of degradation for the Mississippi basin is estimated at one foot in 3000 to 4000 years.

It is not to be inferred that this rate is uniform, or even that erosion at any rate whatsoever is taking place in all parts of the basin. Such is not the fact. On the whole the rate of erosion is doubtless greatest toward the margins of the basins where the land is in its topographic youth or early maturity. It is notably less in the middle courses of the valleys, and erosion is locally exceeded by deposition along the lower courses of the Mississippi and some of its main tributaries.

The average elevation of North America is not accurately known, but it is probably not far from 2000 feet. If the present rate of degradation, say one foot in 3500 years, were to continue, it would take something like 7,000,000 years to bring the continent to sea-level. But this rate of degradation could not continue to the end, for as the continent became lower streams would become sluggish and erosion less rapid. Long before the continent reached base-level the rate of degradation, so far as dependent on mechanical erosion, would become so slow that the time necessary to bring the continent to sea-level would be almost inconceivably prolonged. Furthermore, it is quite possible that the land is suffering, or is liable to suffer, uplift, relative or absolute. If the rate of rise were equal to the rate of degradation the average height of the continent would of course not be affected.

The amount of sediment carried by streams in suspension varies notably according to the stage of the water. During a year when the stream was under careful study the Mississippi at Carrollton (Miss.) was found to carry ¹⁄₆₈₁ of its weight of sediment during the high-water stage of June, and ¹⁄₆₃₈₃ during the low-water of October, the average for the year being ¹⁄₁₈₀₈. The average of a greater number of records gives about ¹⁄₁₅₀₀ as the average ratio between the weight of the sediment and the weight of the water. This corresponds to about ¹⁄₂₉₀₀ by volume, the average specific gravity being about 1.9. The amount of material carried in the upper part of the water was notably less than that carried at greater depths, but that carried midway between top and bottom was about the same as that carried at the bottom.[32]

The discharge of the Mississippi River is about 19,500,000,000,000 cubic feet of water per year, and the sediment it carries in suspension is estimated to weigh about 812,500,000,000 pounds. This is equivalent to about 6,714,694,400 cubic feet. It is estimated that about 750,000,000 cubic feet of sediment is rolled along the bottom, giving a total of 7,468,694,400 cubic feet as the aggregate annual load carried to the Gulf by the river. This would be adequate to cover an area one square mile in extent to the depth of 268 feet per year.

The following table[36] gives the percentage of material carried in suspension by various rivers:

The composition of rain-water falling near London, as determined by analysis, was as follows:[37]

A comparison of the composition of rain-water with that of springs and rivers gives some idea of the solvent work of water. From a study of the water of nineteen of the principal rivers of the world Murray has compiled the following table[38] showing the amount of mineral matter in average river water: