CHAPTER III.. The Work of Running Water.

THE WORK OF RUNNING WATER.

Familiar phenomena, both of land and sea, reveal the constant activity and importance of water as a geologic agent. Even when there is no precipitation the moisture in the air influences its activity in certain ways. Just as iron “rusts” more readily in moist air than in dry, so changes in other mineral substances are influenced by atmospheric humidity. Where precipitation takes place the results are more obvious. The passing shower works changes in the surface of the land, striking in proportion to the rate and amount of precipitation. The rains feed the streams, and every stream is modifying its bed, and with increasing rapidity as its current is swollen. Even the moisture which is precipitated as snow works its appropriate results. Before it melts it protects the surface against other agents of change; but if it accumulates in sufficient quantity in appropriate situations, it may give rise to avalanches and glaciers, which, like running water, degrade the surface over which they pass.

A part of the water which falls as rain, and a part of that which results from the melting of snow and ice, sinks into the soil and into the rock below, becoming ground water. It is this ground water which especially justifies the name hydrosphere, often applied to the waters of the earth, for it literally forms a spherical layer in the outer portion of the solid part of the earth. During the stay of the water beneath the surface it effects changes in the rocks through which it passes, dissolving mineral matter here and depositing it there, substituting one substance for another in this place, and effecting new chemical combinations in that. Slow as these processes are, they have worked wondrous changes in the course of the earth’s history.

When the waters are gathered together in ponds, lakes, and oceans, they are still active, and the results of their activity are seen along the shores, where winds and waves produce their chiefest effects. Even the ocean currents, far from land, and the processes of the deep sea, are not without their effect on the course of geological history.

The work of the surface waters, ground (underground) waters, standing waters, and ice will be considered in order.

RAIN AND RIVER EROSION.

Rain and river erosion began when the first rains fell on land surfaces. Neither the location nor the nature of the first land surface is known. There is little reason to believe that the ocean was ever universal, but there is reason to believe that most land areas have at some time or other been covered by the sea. The prevalent conception that land areas which were once submerged came into existence by being elevated above sea-level, should be supplemented by the alternative conception that submerged areas may have become land by the depression of the ocean basins, thus drawing off the water from the areas where it was shallow. Thus in Fig. 36 the sinking of the sea-bottom from a to b would lower the surface of the water from cc′, to dd′, and draw off the water from the surfaces cd and c′d′.

Without attempting to picture the character of the original land our study of subaërial erosion may begin with an area which has just been changed from sea bottom to land. What is the nature of such a land surface? Of what material is it composed, and what is the character of its topography? Concerning its constitution something may be inferred from the nature of the deposits now found at the bottom of the sea. Near the shore and in shallow water they often consist of gravel and sand, though other materials are not wanting. Far from shore and in deep water they consist for the most part of fine sediments, some of which were washed or blown from the land, some of which came from the shells and other secretions of marine animals, some from volcanoes, and some from various other sources. The topography of the newly emerged land may have had some likeness to the topography of the sea bottom. The numerous soundings which have been made over large areas of the sea have shown that its bottom is, as a rule, free from the numerous small irregularities which affect the surface of the land. They seem to show that a large part of the ocean bottom is so nearly flat that, if the water were removed, the eye would hardly detect irregularities in the surface. This statement does not lose sight of the fact that the ocean bottom is, in certain places, markedly irregular. Volcanic peaks and striking irregularities of other sorts abound in some places. Nevertheless if the bottom of the sea could be seen as the land is, its most striking feature, taken as a whole, would be its apparent flatness.

With the topography of the sea bottom the topography of the land is, in its details, in sharp contrast. In order to get at the history of the latter, we may study the sequence of events which would follow the emergence of a portion of the former.

Subaërial Erosion without Valleys.

For the sake of emphasizing the fundamental principles involved in the work of running water, a hypothetical case will first be studied in some detail, even at the risk of elaborating processes already understood. The principles themselves will find application later in relations which are much less simple.

Let it be assumed that the area of newly emerged land is a circular dome-shaped island. The simplest possible condition is represented by assuming its slope to be the same in all directions from the center, and its materials to be absolutely homogeneous. Such an island would be subject to all the forces ordinarily operating on land surfaces. The chief agency tending to modify land surfaces is atmospheric precipitation. It will be assumed that the rain falls on the surface of the island with absolute equality at all points, and that all other forces which affect it operate equally everywhere.

The rain falling on a land area disappears in various ways; part of it evaporates, part of it sinks, and part of it runs off over the surface. If the island be composed of fine and unconsolidated materials, such as clay, the water which runs off over the surface will carry sediment down to the sea. If the island be composed of solid rock instead, exposure to the air will cause it to decay, and the products of decay, such as sand and mud, will suffer a like fate.

For the sake of a clear understanding of the processes involved, two cases may be postulated; one in which the waters of the sea remove the sediment washed down from the hypothetical island as fast as it reaches the shore, and one in which they allow it to accumulate without let or hindrance. In both cases the wear of the waves will be neglected.

1. In the first case the water flowing off over the surface (the run-off) will descend equally in all directions. It will constitute a continuous sheet of surface-water, and both its volume and its velocity will be the same at all points equally distant from the summit. Erosion accomplished by sheets of running water, as distinct from streams, is sheet (or sheet-flood) erosion. Since the material of the surface is homogeneous, the wear effected by the water will be equal at all points where its velocity and volume are equal. For obvious reasons the depth of the run-off will increase from summit to base. The gradient (slope) also increases in the same direction, and the increase of volume and of gradient conspire to augment the velocity of the water, and therefore of the wear effected by it. If the thin sheet of water starting from the top of the island with relatively low velocity be able to wash off even a little fine material from the surface, the thicker sheet farther down the slope, moving with greater velocity, will be able to carry away more of the same sort of material, and the increase will be progressive from summit to base. It follows, therefore, that the surface will be worn equally at points equally distant from the summit, but unequally at points unequally distant from it. The first shower which falls on the island may be conceived to wash off from its surface a very thin sheet of material, but a sheet which increases in thickness from top to bottom. The run-off will not be stopped immediately on reaching the sea, but will displace the sea-water to some slight depth, and wear the surface some trivial distance below the normal level of the sea. The result of successive showers working in the same way through a long period of time will be to diminish the area of the island and to steepen its slopes. The results of a considerable period of erosion under these conditions are shown diagrammatically in Fig. 37, which illustrates both the diminution in area which the island has suffered, and the increase in the angle of its slopes. Immediately about it, at the stage represented by aa, Fig. 37, there is a narrow marginal platform, or submerged terrace, in place of the land area which has been worn away at or just below the level of the sea. Long successions of rains working in the same way will give the island steeper slopes, a smaller area, and a wider marginal terrace. Successive stages are shown by the lines bb and cc, Fig. 37.

If rain falls on such an island until it completes the work which it is possible for running water to do, the island will be reduced essentially to the level of the sea, and in its place there will be a plain, the area of which will be equal to that of the original island. Its central point will be at the level of the sea, and its borders a trifling distance below it (Fig. 38). The island is gone, and in its place there is a plain as low as running water can wear it. Other agencies might come in to defeat the result just outlined, but if the island did not rise or sink after its formation, rain falling upon it would, under the conditions specified, finally bring about the result which has been sketched. The plain (Fig. 38) which succeeds the island is a base-level of erosion, though this term is also used in other ways. Under these conditions the slope of the land would remain convex at all stages, but the convex erosion profile of the land would meet a nearly straight line just below sea-level. The relative lengths of these two elements of the profile, the curve above and the straight line below, vary as erosion progresses, the convex portion becoming shorter and the other longer, The two parts of the profile taken together are concave upward at the lower end all the time, and for a greater distance from its lower end in all the advanced stages of erosion (Fig. 37).

In the destruction of the land under these conditions neither valleys nor hills would be developed, nor would the topography of the land be fashioned to correspond with the surfaces with which we are familiar.

It is to be distinctly borne in mind that the foregoing is a hypothetical case; it is not probable that such an island ever existed, or ever will; but that does not diminish the value of the illustration, since the principles involved are operating on every land mass, though in less simple relations.

2. The second case differs from the first in that the sediment washed down from the land is deposited about its borders. This results in the building up of a marginal platform, as shown in Figs. 39–41. As erosion goes on more sediment is washed down and deposited, partly on the narrow marginal shelf which has already been developed, and partly on its outer slope, as shown in the figures. The marginal flat is thus extended beyond the original shores of the island on the one hand, and toward its center on the other. As it develops, its inner portion, and indeed all except its outer edge (ab, Figs. 40 and 41), will be gradually built up above the level of the water. This marginal lowland is developed at a level as low as running water, under the conditions then and there present, can reduce the land. Such a surface may be said to be at grade, since running water neither wears it down nor builds it up. Its angle of slope is a function of (1) the volume of the water running over it, and (2) of the load which the water carries.

Since the marginal plain of the above illustration extends beyond the original shore of the island, the area of land is increased, though both its average elevation and its mass (above water) are reduced. In case destructive processes did not operate on the marginal graded plain the spreading and lowering suggested by Figs. 39 and 40 would go on until the central mass of the island was brought down to a gradient in harmony with that of the gently sloping border, as shown in Fig. 41. When this had been accomplished there would be a relatively large land area with low slopes (Fig. 41) in place of the smaller area with steeper ones (compare Figs. 39 and 40). The basal part of the larger island from the center to the original margin would be made up of the original material in its original position (unshaded part of Fig. 41). Its surface would be covered, least deeply near its center and most deeply near the original margin, with débris gradually shifted from higher levels, as shown in Fig. 41.

Were such an island as that shown in Fig. 41 once formed, the rain falling on it, and flowing off over its surface, would carry off its surface soil and spread it about the shores. Though the surface of the marginal flat of Fig. 40 was as low as running water could bring it at the time it was developed, the conditions of erosion have changed by the time the land reaches the conditions shown in Fig. 41, and the same amount of rainfall may now be effective in erosion. In the first case (Fig. 40) the water descending from the higher part of the land brought down sediment and started across the flat with a load. Its energy was consumed in transporting what it had, not in getting new material. In the second case (Fig. 41) the water flowing over the gently sloping surface has no initial load, and its energy is therefore available for erosion. Under continued rainfall, the area of the land shown in Fig. 41 would be increased as before by successive marginal deposits (see Fig. 42), and at the same time its average height would be reduced. The lowering and enlarging of the island would continue until the whole surface was brought so nearly to the level of the sea that water would cease to run over it with sufficient velocity to carry away even the fine material of its surface. Such a surface, brought down as low as running water can degrade it, is also (see p. 57) a base-level. It will be seen from the foregoing illustrations that a graded surface may pass into a base-level, with no sharper line of demarkation than that which separates a mature man from an old one. In this case, as in the preceding, the island has been base-leveled, but still without the formation of valleys or hills.

Both the preceding hypothetical cases make it clear that, from the point of view of erosion, every drop of water which runs off over the surface of the land has for its mission the getting of the land into the sea. Under ordinary conditions surface drainage must fail to bring a land area altogether to sea-level, the absolute base-level of subaërial forces; but it is not simply the water which runs off over the surface which degrades the land. That which sinks beneath the surface contributes to the same end by slowly dissolving mineral matter below the surface, and finally carrying it to the sea. In this way the reduction of land areas to sea-level may be completed.

The rain-water which evaporates from the surface without sinking beneath it does not effect much wear; but the water thus evaporated is subject to reprecipitation, so that, in the long run, it may assist in the work which has been sketched. Thus it is not simply the waters which run off over the surface of the land, but all which fall upon it, which unite to compass its destruction.

The Development of Valleys.

=By the growth of gullies.=—Had the slopes of the hypothetical island not been absolutely uniform the processes of erosion would have been different. Let the departure from uniformity be supposed to consist of a single slight meridional depression near the base of the island (Fig. 43). As the rain falls it will no longer run off equally in all directions. A greater volume will flow through the depression than over other parts of the surface having the same altitude, and the greater volume of water along this line will give greater velocity, greater velocity will occasion greater erosion, and greater erosion will deepen the depression. The immediate result is a gully or wash (Fig. 44). So soon as the gully is started it tends still further to concentrate drainage in itself, and is thereby enlarged. The water which enters it from the sides widens it; that which enters at its head lengthens it by causing its upper end to recede; and all which flows through it, so long as its bottom is above base-level, deepens it. The enlarged gully will gather more water to itself, and, as before, increased volume means increased velocity, and increased velocity increased erosion. As the gully grows, therefore, its increased size becomes the occasion of still further enlargement.

Continued growth transforms the gully into a ravine, though between a gully and a ravine there is no distinct line of demarkation. But growth does not stop with ravine-hood. Water from every shower gathers in the ravine, and, flowing through it, increases its length, width, and depth, until it reaches such proportions that the term ravine is laid aside, as childhood names are, and the depression becomes a valley.

It was assumed in the preceding paragraphs that the single depression in the slope was meridional and low on the slope, but almost any sort of depression in almost any position would bring about a similar result, since it would lead to concentration of the run-off. Had the original surface been interrupted by ridges instead of depressions, the effect on valley development would have been much the same, for a ridge, like a depression, would, in almost any position, occasion the concentration of the run-off, and so the development of valleys. Under the conditions represented in Fig. 44 the lengthening of the drainage depression is effected chiefly at its upper end, the head of the valley working its way farther and farther back into the land. This method of elongation is known as head erosion. But the lengthening of the valley is not always wholly by head erosion. The gully normally begins where concentration of run-off begins, and if this were not at sea-level, the gully might be lengthening at both ends at the same time. This would have been the case, for example, had the original depression of Fig. 43 been half-way up the slope of the island.

If while the slopes of the island were absolutely uniform its surface material failed of homogeneity, the result would be much the same as if the slopes were unequal. If the material lying along a certain meridian of the island be slightly softer than that over the rest of the surface, the run-off, which would at the outset be equal on all sides, would effect more erosion along the line of the less resistant material than elsewhere. The result would be a depression along this line, and, once started, the depression would be a cause of its own growth. If the soft material were disposed in any way other than that indicated, the final result would be much the same, for it would quickly give origin to a depression which would lead to the concentration of the surface-waters, and this is the condition for the development of a gully, a ravine, and finally a valley.

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.

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.

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, 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.

Had there been several initial meridional depressions instead of one in the island, or had there been several meridional belts where the material of the surface was less resistant than elsewhere, several valleys would have been developed, converging toward the center (Fig. 47). If the conditions were such as to allow of the equal development of valleys on all sides of the island, each would be lengthened by head erosion until it reached the center of the island, where the permanent divide between their heads would be established. Each would be widened by all the processes which widen valleys, and their widening would narrow the intervening areas (Figs. 48 and 49). Under conditions of equal erosion the limits of width for each valley would be the centers of the ridges on either side, and here the divides between them would be permanently established. Though erosion would continue even after the crest of the ridge had been narrowed to a line, the permanence of the divide would follow from the fact that erosion would be equal on both sides of this line, and its effect would be to lower the divide, but not to shift it horizontally (Fig. 50). The limits in length and width are therefore not the same where there are several valleys as where there is but one. The limit in depth, however, remains the same, and the final result of erosion, proceeding along these lines, would be the base-leveling of the land, leaving a plain but slightly above sea-level. The plain would not be absolutely flat, though its relief would be very slight, and the higher parts would be along the lines of the divides between the streams (Fig. 51. Compare also Fig. 42). Many valleys would occasion more rapid degradation than few, and the period of base-leveling would be correspondingly shortened.

Had the initial depressions which gave origin to the valleys had positions other than meridional, the valleys would have had other and less regularly radial courses, but the final result of their development would have been the same.

It is not to be inferred that the method of valley development which has been sketched is the only one. The processes of valley development are complex, and the history of some valleys has run a different course; yet the processes outlined above are in operation in all cases, and they were probably the most important ones in the development of the first drainage system on any land surface. As will be seen in the sequel the history of valleys is subject to serious accidents, and they are often of such a nature as to mask the simplicity of the more normal processes.

The permanent stream.—From the foregoing discussion, it is seen that a valley may be developed by the run-off of successive showers. If supplied only from this source surface streams would cease to flow soon after the rain ceased to fall, and a valley might attain considerable size without possessing a permanent stream. How does the valley developed by the run-off of successive showers come to have a permanent stream? The answer to this question involves a brief consideration of that part of the rainfall which sinks beneath the surface.

If wells be sunk in a flat region of uniform structure and composition the water in them is generally found to stand at a nearly common level. The meaning of this fact is not far to seek. If a hole 60 feet deep fills with water up to a point 20 feet from the surface, it is because the material in which the well is sunk is full of water up to that level. When the well is dug the water leaks into it, filling the hole up to the level to which the rock (or subsoil) is itself full. This level, below which the rock and subsoil (down to unknown depths) are full of water, is known as the ground-water level, ground-water surface, or water-table.

The ground-water level fluctuates. In a wet season it rises, because more water has fallen and sunk beneath the soil; but several processes at once conspire to bring it down again. Where there is growing vegetation its roots draw up water from beneath, and evaporation also goes on independently of vegetation. The water is drawn out through wells and runs out through openings. It may also flow underground from one region to another where the ground-water surface is lower. All these processes depress the ground-water surface.

A well sunk to such a level as to be supplied with abundant water in a wet season may go dry during a period of drought because the ground-water level is depressed below its bottom. Thus either well shown in Fig. 52 will have water during a wet season when the water-level is at a; but well No. 1 will go dry when the water surface is depressed to b.

The principles applicable to wells are applicable to valleys. When a valley has been deepened until its bottom reaches below the ground-water level, water seeps or flows into it from the sides. The valley is then no longer dependent on the run-off of showers for a stream. It will be readily seen that at some stage in its development, the bottom of a valley may be below the ground-water level of a wet season without being below that of a dry one. Thus the valley represented in cross-section by the line 2–2, in Fig. 53, will have a stream when the ground-water level is at aa, but none when this level is depressed to bb. If the rainfall of the year were concentrated in a single wet season, the intermittent stream would flow not only during that season, but for so long a time afterward as the ground-water level remained well above the valley bottom. In regions subject to frequent and short periods of heavy precipitation, alternating with droughts, the periods of intermittent flow may be many and short. Since the precipitation of many regions varies greatly from year to year, it follows that a stream may flow continuously one year and be intermittent the next. Many valleys in various parts of the earth are now in the stage of development where their streams are intermittent.

As a valley containing an intermittent stream becomes deeper, the periods when it is dry become shorter, and when it has been sunk below the lowest ground-water level, it will have a permanent stream (3, Fig. 53). Since a valley normally develops headward, its lower and older portion is likely to acquire a permanent stream, while its upper and younger part has only an intermittent one (Fig. 47 and Fig. 1, Pl. III, near Anthony, Kan. The intermittent part of the stream is indicated by the dotted blue line). For the same reason the head of a stream is likely to be farther up the valley in wet weather than in dry. So soon as a valley gets a permanent stream, the process of enlargement goes on without the interruption to which it was subject when the supply of water was intermittent.

In general a permanent stream at one point in a valley means a continuous stream from that point to the sea or lake which the valley joins; but to this rule there are many exceptions. They are likely to arise where a stream heads in a region of abundant precipitation, and flows thence through an arid tract where the ground-water level is low, and evaporation great. In such cases, evaporation and absorption may dissipate the water gathered above, and the stream disappears (Fig. 2, Pl. III, near Paradise, Nev.).

Fig. 1. KANSAS. U. S. Geol. Surv.

Fig. 2. NEVADA. U. S. Geol. Surv.]

Fig. 1. ILLINOIS. U. S. Geol. Surv.

Fig. 2. NORTH DAKOTA. U. S. Geol. Surv.]

=Other modes of valley development.=—If as a new area of land emerges from the sea its surface has a depression without an outlet, and such an assumption is by no means improbable, the depression would be filled with sea-water. The inflowing water from the surrounding land might fill the basin to overflowing, and the outflow, finding exit at the lowest point in the rim of the basin, would flow thence toward the sea. Such a stream would develop a valley, the history of which would be somewhat different from that which has been sketched. Instead of developing headward from the sea, the valley would be in process of excavation all the way from the initial basin to the sea at the same time (Fig. 54). The upper end of the valley might ultimately be cut to the level of the bottom of the basin, when the lake would disappear. The head of the valley might then work back across the former site of the lake into the territory beyond. Valleys might have developed above the lake before it was drained, and after this event, such valleys would make connections with the valley below (Fig. 55). A valley developed in this manner is not simply a gully grown big by head erosion, and the valley would not precede the stream.

If a surface of land were notably irregular before valleys were developed in it, there might be many lakes, and the flow from a higher lake might pass to a lower. If the lakes were ultimately drained, the several sections of the valley would be joined to one another without intervening basins. In certain regions, especially those which have been affected by continental ice-sheets, this has been a common method of valley development in post-glacial time. In this case also the stream precedes its valley, and not the valley its stream. Many post-glacial valleys, on the other hand, antedated their permanent streams, as in the cases first described.

If the gradient of a slope on which valleys are to develop is notably unequal, though without basins, the development of valleys may follow somewhat different lines. If on emergence the seaward part of a new land area assumes the form of a plain, bordered landward by a steeper slope (Fig. 56), the most notable early growth of the valleys would be on the latter. The run-off would develop gullies on the steep slope, but on reaching the plain below the velocity of the water would be checked, and it would drop much of the detritus washed down from above. This deposition would build up (aggrade) the surface, and much or even all the water might sink into and seep through the débris thus deposited, and disappear altogether from the surface, as at b, Fig. 56. This would be most likely to occur where the débris is abundant and coarse, and the precipitation slight. If the water disappears at the base of the mountain (see Fig. 2, Pl. III), the early growth of the valley may be confined to the steep slope remote from the sea (ab, Fig. 56); but on the slope where the valley is growing there will be headward lengthening, as in the general case already considered. If the surface drainage does not disappear at the base of the steep slope, the run-off will find its way over the plain along the lowest accessible route to the sea (de, Fig. 56). In this case the valley may be growing throughout its length at the same time.

The conditions represented by ab, Fig. 56, may be no more than temporary. Sooner or later a valley developing headward across the plain (hi, Fig. 56) may provide a channel for the water descending from the higher land beyond. In this case the valley develops in sections, the one on the slope above, the other on the plain below, and their union (compare fghi, Fig. 56, with Fig. 57) results from their growth.

The principles here sketched have been in operation wherever land areas were so elevated as to give rise to unequal slopes, and this has perhaps been the rule rather than the exception. The results effected by the operation of these principles would of course be dependent on the varieties of slope, on the abruptness with which a slope of one gradient gave place to another, on the texture of the rock, the amount and distribution of precipitation, etc., etc.

In the preceding paragraphs the lengthening of a valley at its upper end by head erosion has been repeatedly referred to. If all valleys began their development at the sea and lengthened headward, it might seem that their seaward ends should be their oldest parts; but since the development of valleys is begun somewhat promptly after the land appears above the sea, and since the emergence is generally gradual, that part of a valley which is at the seashore at one time may be far inland a little later, because the land has been extended seaward. On an emerging land area therefore the normal growth of a valley involves its lengthening at its lower end as well as at its upper. The lengthening of a valley, or at least the lengthening of a stream, also takes place at its lower end if the land in which it lies is being extended seaward by deposition.

=Structural valleys.=—In mountain regions valleys are sometimes formed by the uplift of parallel mountain folds, leaving a depression between (Fig. 58). Drainage will appropriate such a valley so that it becomes in some sense a river valley. But it is not a river valley in the sense in which the term has been used in the preceding pages. It is rather a structural valley. In its bottom a river valley may be developed (a, Fig. 58).

The foregoing illustrations by no means exhaust the list of conditions under which valleys develop, but they suffice for the present.

Figures to show why the head of a gully (and therefore a valley) departs from a direct course.]

=The courses of valleys.=—River valleys are rarely straight. To understand why they are crooked it is only necessary to understand the methods by which they grow. In so far as a river valley is a gully grown big, that is, in so far as its length is the result of head erosion, its course was determined by the course of the antecedent gully. If in the case shown in Fig. 59 the slope of the surface above the head of the gully is uniform, its material homogeneous, and the rainfall everywhere equal, more water will come into the gully from the direction a than from any other. In this case there would be more wear in the direct line of its extension than elsewhere, and the head would advance in a straight line. But if there be inequalities of slope about the head of a gully at any stage of its development more water may come in from some direction other than that in the direct line of its extension. In Fig. 59, for example, more water may enter from the direction of b than from that of a. Since most wear is likely to be affected along the line of greatest inflow, the head of the gully will be turned in that direction (Fig. 60). Started in this course it will continue in the new direction so long as erosion in this line is greater than that elsewhere; but whenever the configuration of the surface causes more water to enter the head of the gully from some direction other than that in which it is headed, the line of axial growth is again changed, as toward c, Fig. 60. Since new land surfaces are probably more or less undulatory, crookedness should be the rule among valleys developed from gullies by head erosion. Streams and valleys the courses of which are determined by the original slope of the land are said to be consequent.

Inequalities of material, leading to unequal rates of erosion, effect the same result, in the absence of inequalities of slope. If at any stage of a valley’s development erosion were equal in two directions at its head, and at the same time greater than at points between, two gullies would result (Fig. 61) diverging from the point in question.

In the case of a valley developed by overflow from a lake its course is determined by the lowest line of flow to which the water has access. If this line be straight the valley will be straight; if it is crooked, as it generally is, the valley is crooked also.

=The development of tributaries.=—Thus far valleys leading immediately to the sea have been considered, and no account taken of tributaries. As a matter of fact most considerable valleys have numerous tributaries. It is now in order to inquire into their mode of development.

So soon as a gully is started, the water flowing into it from either side wears back the slopes. The least inequality of slope, or the least variation in the character of the material, is sufficient to make the lateral erosion unequal at different points, and unequal erosion in the slopes results in the development of tributary gullies. The oldest tributaries may be nearly as old as the main which they join, and from which they developed, for the possibilities of unequal side erosion exist as soon as a gully is opened. While the main gully is developing into a ravine, and the ravine into a valley, the tributary gullies are likewise developing into maturer stages. Tributary to a young valley, therefore, there may be gullies near its head, ravines in its middle course, and small valleys along its oldest portion. It is not to be understood, however, that the oldest tributaries are necessarily the largest, for because of more favorable conditions for growth the younger tributaries often outstrip the older.

The position of tributaries with reference to their mains is worthy of note. The water flowing down a slope follows the line of steepest descent. A gully is usually wider at its lower end, and narrower at its upper. Wherever this is true the line of steepest descent down its side is not a line perpendicular to its axis, but a line slightly oblique to it (ef, Fig. 62), and oblique in such a direction that it meets the axis with an obtuse angle below and an acute angle above. It is in the direction corresponding to this line that tributary gullies tend to develop. Thus at the inception of its history a tributary gully is likely to join its main with an angle slightly acute on the up-stream side. If the tributary did not begin until after its main was farther advanced this tendency would be less and less pronounced. Inequalities of material or slope would often counteract this tendency, which, at best, would cause the courses of tributaries to depart but little from perpendicularity to their mains.

After the head of a tributary has worked back from the immediate slope of its main every condition which determines the course of a gully is likely to affect it, and it is by no means certain that it will continue to lengthen in the direction in which it started. Since the general slope of the surface into which the tributary works is likely to be seaward, more water is likely to enter from the landward than from the seaward side of its head, so that, except where there are notable irregularities of slope, its tendency will be to turn more and more toward the direction of its main (efg, Fig. 62).

In depth the tributary is always limited by its main. The principles which determine the length and width of a main valley determine also the length and width of a tributary (see p. 67 et seq.).

A CYCLE OF EROSION. ITS STAGES.

From what has preceded it is clear that the topography of a region undergoing erosion will change greatly from time to time. The first effect of erosion is to roughen the surface by cutting out valleys, leaving ridges and hills. The final effect is to make it smooth again by cutting the ridges and hills down to the level of the valleys.

The base-level of erosion has already been defined; but the mode of its development may now be illustrated in the light of the preceding discussion. Suppose a land surface affected by a series of parallel young valleys without tributaries (Fig. 63). Between them there is a series of upland plateaus. The profile of the surface between two adjacent valleys is represented in section by the uppermost line in Fig. 64. As the valleys are widened from 1–1 and 1,′-1′, to 2–2 and 2′-2′, the intervening plateau is correspondingly narrowed. When the valleys have attained the form represented by 3–3 and 3′-3′, the intervening upland has been narrowed to a ridge, a, and the valley flats have become wide. With continued erosion the ridge will be lowered (to b and below), and in time the surface will approach a plain. In this condition it is known as a peneplain (an “almost-plain”). Finally, when running water has done its utmost, the ridges will be essentially obliterated and a base-leveled plain (e, e′, e″) results. The figure expresses the fact that the base-level develops laterally from the axis of the valley. It also develops headward from the seaward end of the valley. Similarly, taking into account all the valleys which affect it, the seaward margin of a base-leveled plain is developed first, and thence it extends itself inland.

Tributaries are tolerably sure to develop along each main valley. The heads of the tributaries work back across the uplands between the main valleys, dissecting them into secondary ridges (Fig. 65). Tributaries will develop on the tributaries, and these tertiary valleys dissect the secondary ridges into those of a lower order. This process of tributary development goes on until drainage lines of the fourth, fifth, sixth, and higher orders are formed (Fig. 66). Since the process of valley development under such circumstances is also the process of ridge dissection, a stage is presently reached where the ridges are cut into such short sections that they cease to be ridges, and become hills instead. Even then the processes of erosion do not stop, for the rain-water falling on the hills washes the loose material from their surfaces, and starts it on its seaward journey. Thus the “everlasting hills” themselves are lowered, and, given time enough, will be carried to the sea. Under these conditions, as under those already discussed, the final result of stream erosion is the reduction of the land to base-level. The base-leveled surface, as before, would not be absolutely flat. The area reduced by each stream will have a slight gradient down-stream, and from each lateral divide toward the axis of the valley. The crests of the scarcely perceptible elevations which remain will be in the position of the former divides, and these will be highest where most distant from the sea by the course which this part of the drainage took. Even the insensible divides between streams flowing in a common direction may disappear, for when valleys have reached their limits in depth, their streams do not cease to cut laterally. Meandering in their flat-bottomed valleys, they often reach and undercut the divides (Pl. VII), whether they be high or low. By lateral planation, therefore, the divides between streams may be entirely eaten away.

It has now been seen that by whatever method erosion by running water proceeds, whether there be many valleys, or few or none, the final result of subaërial erosion must be the production of a base-level. It has also been seen that the base-level is first developed at the lower ends of the main streams, and that it extends itself systematically up the main valleys and up all tributaries. The time involved in the reduction of a land area to base-level is a cycle of erosion.

It will have been evident from the preceding pages that the terms “grade,” “graded plain,” and “base-level” and “base-leveled plain,” are somewhat variously, and therefore somewhat confusingly, used. “Grade is a condition of essential balance between corrasion and deposition.” A graded valley is one in which deposition and corrasion are, in the vertical sense, balanced. Its angle of slope is most variable, and is dependent on the capacity of the stream for work, and on the work it has to do. A weak river must have a higher gradient than a strong one; a stream with much sediment must have a higher gradient than one with little, and a stream with a load of coarse material must have a higher gradient than one with a load of fine. Thus the graded valley of the lower Mississippi has an inappreciable angle of slope, but the graded valleys of many of its tributaries have slopes of hundreds of feet per mile. Since both the size of the stream and the amount and coarseness of its load at a given place vary from time to time, it is clear that the inclination of a graded valley must vary also, and further, that it must be in process of continual readjustment. With the changing conditions of advancing years the slope of a graded valley normally decreases. The same principles apply to graded surfaces outside of valleys.

In the continual readjustment of grades incident to a river’s normal history the land is brought nearer and nearer to sea-level without ceasing to be at grade. When the inclination of a graded surface becomes so low that it is sensibly flat, the surface may be said to be at base-level, although this does not mean that the surface can never be degraded further. If the term be used in this way, it is clear that there is no sharp line of distinction between a graded surface and a base-leveled surface, and as the terms are now commonly applied no such distinction exists.

If the term base-level were made synonymous with sea-level, as has been proposed, the term might as well be discarded, for sea-level could always be used in its stead. Furthermore, streams often erode below sea-level. The bottom of the channel of the Mississippi is below sea-level for some 400 miles above its debouchure, and locally (Fort Jackson) it is nearly 250 feet below. This deep channel is the result of the erosive activity of the stream, not of subsidence. Again, the sea-level is itself inconstant. The extent of its changes cannot now be measured, but they have probably been more considerable in the course of geological history than has been commonly recognized. It is true that they take place slowly, as far as known, but it is also true that the duration of an erosion cycle is sufficiently long for even very slow changes to reach great magnitude. The sea-level, therefore, can hardly be accepted as the absolute base-level, unless (1) the absolute base-level is a variable, and unless (2) the absolute base-level be a surface below which rivers may cut to the extent of at least 250 feet.

The ocean may be looked upon as a barrier which in a general way limits the down-cutting of running water; for only very large streams cut much below its level. Other barriers, such as lakes, and the outcrops of hard rock in a stream’s bed, have a comparable, though more temporary, effect on the development of valley plains above. Plains thus developed have been called temporary base-levels. They differ from other graded plains in being controlled primarily by a barrier below, rather than by conditions which exist above.

Since river valleys have a beginning and pass through various stages of development before the country they drain is base-leveled, it is important to recognize their various stages of advancement. Nor is this difficult. An old valley and a young one have different characteristics, and the one would no more be mistaken for the other by those who have learned to interpret them, than the face of an aged man would be mistaken for that of a child.

The cycle begins with the beginning of valley development, and at that stage drainage is in its infancy. The type of the infant valley is the gully or ravine (Figs. 67 and 68). It has steep slopes and a narrow bottom. Fig. 1 of Plate IV represents similar, or rather older, ravines in contour (shore of Lake Michigan, just north of Chicago). With age, the valley widens, lengthens, and deepens, and passes from infancy to youth. In this stage also the valleys are relatively narrow, and the divides between them broad. They may be deep or shallow, according to the height of the land in which they are cut, and the fall of the water flowing through them; but in any case the streams flowing through them have done but a small part of the work they are to do before the country they drain is base-leveled. Figs. 69 and 70, respectively, represent youthful valleys in regions of moderate and great relief. Fig. 2, Plate IV, shows a youthful valley in a region of slight relief (near Casselton, N. D., lat. 46° 40′, long. 97° 25′). The uppermost line in Fig. 64 likewise represents topographic youth, as shown in cross-profile.

Not only are narrow valleys said to be young, but the territory affected by them is said to be in its topographic youth, since but a small part of the time necessary to reduce it to base-level has elapsed. An area is in its topographic youth when considerable portions of it are still unaffected by valleys. Thus the areas (as a whole), as well as the valleys, represented on Plate IV, are in their topographic youth. It is often convenient to recognize various sub-stages, such as early, middle, and late, within the youthful stage of valleys or topographies. The different parts of the areas shown on Plate IV, for example, represent different stages of youth.

Youthful streams, as well as youthful topographies, have their distinctive characteristics. They are usually swift; their cutting is mainly at the bottom rather than at the sides, and their courses are often marked by rapids and falls.

As valleys approach base-level they develop flats. As the valleys and their flats widen, and as their tributaries increase in numbers and size, a stage of erosion is presently reached where but little of the original upland surface remains. The country is largely reduced to slopes. In this condition the drainage and the topography which it has determined are said to be mature. Mature topography is shown in contours in the figures of Plate V, and in the northern part of Plate VI, where slopes, rather than upland or valley flats, predominate. Fig. 1 of Plate V represents an area in southeastern Kentucky (lat. 37° 12′, long. 83° 10′); Fig. 2, an area in western Virginia. Plate VI represents an area in southern California, somewhat west of San Bernardino. The three areas are alike in representing mature drainage, though not of equal stages of advancement. The striking differences of topography of the three areas are the result of differences in rock structure and altitude, and will be considered later. Mature topography is also shown in Fig. 71, where the relief is moderate, and in Figs. 72 and 73, where it is great. Figs. 72 and 73 illustrate clearly the universal tendency of rivers in regions of notable relief to develop new flats well below the old surface of the region. At the same time that these low-lying flats are developing, tributary drainage is dissecting and roughening the upper surfaces. This process is well shown in Fig. 73. In both Figs. 72 and 73 the summits of the mountains on either side of the valleys appear to have had about the same elevation. The new flat is therefore developed at the expense of the old flat. As will be seen in the sequel, the first flat which a stream develops along its course is usually somewhat above base-level. It is a graded flat.

Fig. 1. KENTUCKY. U. S. Geol. Surv.

Fig. 2. VIRGINIA. U. S. Geol. Surv.]

PARTS OF LOS ANGELES AND SAN BERNARDINO COUNTIES, CALIFORNIA. U. S. Geol. Surv.]

The same processes which have made young valleys mature will in time work further changes. When the gradients of the valleys have become low and their bottoms wide, and when the intervening ridges and hills have become narrow and small, the drainage and the drainage topography have reached old age, and the streams are in a condition of senility. This is illustrated by Fig. 1, Plate VII (central Kansas), and in section by the third and lower lines in Fig. 64. Topographic old age sometimes has a different expression; this is shown in Fig. 74, where most of the surface has been brought low. The elevations which rise above the general plain are small in area, but have abrupt slopes. This phase of old-age topography is usually the result of the unequal resistance of the rock degraded. The effects of unequal rock-resistance will be considered later.

The marks of old streams are as characteristic as those of young ones. They have low gradients and are sluggish. Instead of lowering their channels steadily they cut them down in flood, and fill them up when their currents are not swollen. They meander widely in their flat-bottomed valleys (Fig. 1, Pl. VII, Central Kansas) and their erosion, except in time of flood, is largely lateral.

If the processes of degradation were to continue until the land surface was brought to sea-level, and this might be done by solution though not by mechanical erosion of running water, the rivers would no longer flow, and the drainage system would have reached the end of its history—death.

Not only do valleys normally pass from birth to youth, from youth to maturity, and from maturity to old age, but a single river system may show these various stages of development in its various parts. Thus in the area shown in Fig. 2, Plate VII (north central Kansas), there is a tract (extreme southwest) where the erosion history is scarcely begun. The zone of land a little farther northeast, and just reached by the heads of the valleys (same figure), is in its youth. The well-drained and uneven tract southwest of the flat of the Solomon River is in maturity, while the flat of the main valley has the general characteristics of old age.

The age of valleys in terms of erosion is also expressed more or less perfectly by their cross-sections. The line 1–1 (and 1′-1′) of Fig. 64 represents in cross-section a narrow V-shaped valley. Such a section is always indicative of youth. The stream which developed it cut chiefly at its bottom, not at its sides. It was therefore rapid, and rapid streams are young. The line 2–2, (2′-2′) (Fig. 64) shows the same valley at a later and maturer stage when downward cutting has nearly ceased. The widening of the valley by slope wash has become relatively more important than before, and the stream has so far lost velocity as the result of diminished gradient as to be unable to carry away all the detritus washed down from the sides. As a result of deposition at the bases of the side slopes, a concave curve has been developed. Up the valley from the point where such a section as is represented by 2–2 occurs, the valley may still have a section similar to that represented by 1–1.

Fig. 1. KANSAS. U. S. Geol. Surv.

Fig. 2. KANSAS. U. S. Geol. Surv.]

ABOUT 15 MILES SOUTHWEST OF ST. LOUIS, MISSOURI. U. S. Geol. Surv.]

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. 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.

NIAGARA FALLS. U. S. Geol. Surv.]

Fig. 1. YELLOWSTONE PARK. U. S. Geol. Surv.

Fig. 2. ARIZONA. U. S. Geol. Surv.]

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.

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.

PART OF THE CATSKILLS, NEW YORK. U. S. Geol. Surv.]

Fig. 1. NEW MEXICO. U. S. Geol. Surv.

Fig. 2. VIRGINIA, WEST VIRGINIA AND MARYLAND. U. S. Geol. Surv.]

ANALYSES OF AMERICAN RIVER-WATERS.

+----------------------------------+------------------+----------------+ |Name of river | Bear | Croton | | | | | |Collected at | Evanston, Wy. | Reservoir, New | | | | York City | | | | | |Date | Dec., 1873 | 1881 | | | | | |Analyst | F. W. Clarke | E. Waller | | | | | |Reference |Bulletin No. 9, U.| Water supply of| | | S. Geol. Surv., | New York City,| | | p. 30 | 1881 | +----------------------------------+------------------+----------------+ |Sodium, Na | .0082 | .00298 | | | | | |Potassium, K | ...... | .00154 | | | | | |Calcium, Ca | .0432 | .00905 | | | | | |Magnesium, Mg | .0125 | .00336 | | | | | |Chlorine, Cl | .0049 | .00213 | | | | | |Carbonic acid, CO₂, | .0982 |.02248 | | | | | |Sulphuric acid, SO₃ | .0105 | .00441 | | | | | |Phosphoric acid, H₃PO | | | | | | | |Nitric acid, HNO₃ | ...... | ...... | | | | | |Silica, SiO₂ | .0070 | .03360 | | | | | |Alumina, Al₂O₃ | | | | | | | |Sesquioxide of iron, Fe₂O₃ | | ...... | | | | | |Sesquioxides of iron and alumina, | | | | Fe₂O₃ and Al₂O₃ | | .00078 | | | | | | „ „ iron and manganese,| | | | Fe₂O₃ and Mn₂O₃ | | | | | | | |Carbonates of iron and manganese, | | | | FeCO₃ and MnCO₃ | | | | | | | |Oxide of iron, FeO | | | | | | | | „ „ manganese, MnO | | | | | | | |Hydrogen in bicarbonates, H | | | | | | | |Chloride and sulphate of sodium, | | | | NaCl, and Na₂SO₄ | | | | | | | |Ammonia, NH₄ | | ...... | | | | | |Organic matter | | .00400 | | | | | |Carbonates and sulphates of | | | | Na, K, and Mg | ...... | ...... | | |------------------+----------------+ | | .1845 | .08433 | +----------------------------------+------------------+----------------+

--------------+--------------+---------------+----------------+-------------+--------------+ Cumberland | Delaware | Hudson, N. Y. | James | Los Angeles | Maumee, O. | | | | | | | Reservoir at | Reservoir at | | Richmond Water | Hydrant at | | Nashville, | Trenton, | | Works, Va. | Los Angeles,| | Tenn. | N. J. | | | Cal. | | --------------+--------------+---------------+----------------+-------------+--------------+ | | | Oct. 24. 1876, |Sept. 8, 1878| | | | |after light rain| | | | | | | | | N. T. Lupton | H. Wurtz | C. F. Chandler| W. H. Taylor | W. J. Jones |C. F. Chandler| | | | | | | Am. Chemist, |Geol. of N.J.,| Public Health | Ann. Rept. | Rept. Cal. | Report of | July 16, 1876,| 1868, p. 702 |Papers, Vol. I,|Board of Health,| State Board | Toledo Water | p. 16 | | Am. Pub. | Richmond, Va., | of Health, | Works, 1881 | | | Health Ass. |1876 | 1878 | | --------------+--------------+---------------+----------------+-------------+--------------+ | | | | | | .01032 | .00072 | .00244 | .00234 | .02968 | .00162 | | | | | | | .00050 | .00178 | .00058 | .00251 | ...... | .00309 | | | | | | | .02987 | .01104 | .02220 | .01284 | .01750 | .02645 | | | | | | | .00280 | .00435 | .00465 | .00377 | .02097 | .00443 | | | | | | | .00299 | .00121 | .00581 | .00105 | .01044 | .00250 | | | | | | | .05727 | .02552 | .07278 | .02954 | .05635 | .04438 | | | | | | | .00563 | .00175 | .01257 | .00363 | .05724 | .01401 | | | | | | | ...... | .00172 | | Trace | .02638 | | | | | | | | .00511 | ...... | ...... | .00231 | ...... | ...... | | | | | | | Trace | .00852 | .00698 | .01024 | .02005 | .00724 | | | | | | | | } { | | .00041 | .00171 | ...... | | } .00047 { | | | | | ...... | } { | ...... | | | .00100 | | | | | | | .00671 | | .00120 | ...... | | | | | | | | | | | | .00072 | ...... | | | | | | | | | ...... | | | .00443 | | | | | | | | | Trace | ...... | | | | | | | | | | | | .00121 | | | | | | | ...... | | | | | | | | | ...... | } { | ...... | .00001 | | ...... | | } .01087 { | | | | | .01666 | } { | .01197 | .00299 | | .00499 | | | | | | | ...... | ...... | ...... | ...... | ...... | ...... | | | | | | | --------------+--------------+---------------+----------------+-------------+--------------+ .13786. | .06795 | .14238 | .07246 | .24475 | .10971 | --------------+--------------+---------------+----------------+-------------+--------------+

----------------+----------------+---------------+--------------+------------+--------------+ Mississippi | Ottawa | Passaic | Rio Grande | Sacramento | St. Lawrence | | | | del Norte | | | Hydrant, City | St. Ann’s Lock,| 4 miles above | Fort Craig, | Hydrant, | South side | Water Works, | Montreal, Can. | Newark, N. J. | New Mexico | Sacramento,| Point des | New Orleans, La.| | | | Cal. | Cascades | | Mar. 9, 1854 | 1851 | 1873 |Sept., 1878 | Mar. 30, 1863| | | | | | | W. J. Jones | T. S. Hunt |E. N. Horsford | O. Loew | W. J. Jones| T. S. Hunt | | | | | | | Rept. La. State |Geol. of Canada,|Geol. of N. J.,| U. S. Geog. | Rept. Cal. | Geol. of | Board of Health,| 1863, p. 567 | 1868, p. 708 |Surv. west of |State Board | Canada, | 1882, p. 370 | | |100th M., Vol.| of Health, | 1863, p. 567 | | | | | III. p. 576| 1878 | | | | | | | ----------------+----------------+---------------+--------------+------------+--------------+ .0310 | .00239 | .02357 | .03220 | .00200 | .00513 | | | | | | | ...... | .00139 | .00163 | .00063 | ...... | .00115 | | | | | | | .0372 | .00992 | .01459 | .01633 | .01279 | .03233 | | | | | | | ...... | .00161 | .00404 | .00123 | .00121 | .00585 | | | | | | | .0480 | .00076 | .03192 | .03604 | .00242 | | | | | | | | .0383 | .02255 | .02634 | .01025 | .00887 | .06836 | | | | | | | | .00194 | .01716 | .04700 | .00397 | .00831 | | | | | | | | Trace | | Faint trace | .01794 | Trace | | | | | | | | ...... | Trace | | | | | | | | | | | .02060 |} {| Trace | .03167 | .03700 | | |} {| | | | | Trace |} .01342 {| Trace | .00120 | Trace | | |} {| | | | | |} {| | | | | | | | | | | | | | ...... | | | | | | | | | ...... | | ...... | .01088 | ...... | | | | | | | | Trace | | Trace | | Trace | | | | | | | | Trace | | | | Trace | | | | | | | | | | | ...... | | | | | | | | | | | | .02431 | | | | | | | | | | | Trace | | | | | | | | | ...... | | | .01392 | | | | | | | | | .0154 | ...... | ...... | ...... | ...... | ...... | ----------------+----------------+---------------+--------------+------------+--------------+ .1699 | .06116 | .13267 | .15760 | .11484 | .16055 | ----------------+----------------+---------------+--------------+------------+--------------+

------------------+------------------+------------------+----------------+--------------+----------------+ Humboldt | Truckee | Walker | Jordan | Mohawk | Genesee | | | | | | | Battle Mt., Nev. | Lake Tahoe, Nev. | Mason Valley, | Utah Lake | Utica, N. Y. |Rochester, N. Y.| | | Nev. | | | | | | | | | | Dec., 1872 | Oct., 1872 | Oct., 1872 | Nov., 1873 | | | | | | | | | T. M. Chatard | F. W. Clarke | F. W. Clarke | F. W. Clarke |C. F. Chandler| C. F. Chandler | | | | | | | U. S. Geol. Surv.,|U. S. Geol. Surv.,|U. S. Geol. Surv.,| Bulletin No. 9,| Johnson’s | Johnson’s | Monograph XI, | Monograph XI, | Monograph XI, | U. S. Geol. | Cyclopedia, | Cyclopedia, | p. 41 | p. 42 | p. 40 | Surv., p. 29 | Vol. IV | Vol. IV | ------------------+------------------+------------------+----------------+--------------+----------------+ | | | | | | .0467 | .0073 | .0318 | .0178 | .0036 | .0044 | | | | | | | .0100 | .0033 | Trace | ...... | .0009 | .0023 | | | | | | | .0489 | .0093 | .0228 | .0558 | .0318 | .0417 | | | | | | | .0124 | .0030 | .0038 | .0186 | .0069 | .00896 | | | | | | | .0075 | .0023 | .0131 | .0124 | .0023 | .0024 | | | | | | | .1544 | .0287 | .0576 | .0608 | .0569 | .0646 | | | | | | | .0477 | .0054 | .0284 | .1306 | .0187 | .0431 | | | | | | | | | | | ...... | | | | | | | | ...... | | ...... | ...... | ...... | ...... | | | | | | | .0326 | .0137 | .0225 | .0100 | .0067 | .0014 | | | | | | | .0013 | | | | | | | | | | | | | | | | | | | | | | ...... | ...... | | | | | | | | | | | .0013 | .0014 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ...... | | | | | | | | | | ...... | ...... | ...... | | | | | | | | | | ...... | ...... | ...... | | | | | | | | | | ...... | ...... | ...... | | | | | | | | | ...... | ...... | .0234 | .0250 | | | | | | | ...... | ...... | ...... | ...... | ...... | ...... | ------------------+------------------+------------------+----------------+--------------+----------------+ .3615 | .0730 | .1800 | .3060 | .1525 | .19526 | ------------------+------------------+------------------+----------------+--------------+----------------+

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

| | | | |Height |Thickness | | Mean | | |in Feet |of Sediment | | Annual | | |of Column |in Inches | Drainage |Discharge | | Ratio of |of Sediment |if Spread | Areas in |(in Cubic | |Sediment to |with a Base | over | Square |Feet.) per| Total Tons | Water by | of One |Drainage River. | Miles. | Second. | Annually. | Weight. |Square Mile.| Area. -----------+-----------+----------+-------------+------------+------------+-------- Potomac | 11,043 | 20,160 | 5,557,250 | 1 : 3,575 | 4.0 | .00433 Mississippi| 1,244,000 | 610,000 | 406,250,000 | 1 : 1,500 | 241.4 | .00223 Rio Grande | 30,000 | 1,700 | 3,830,000 | 1 : 291 | 2.8 | .00116 Uruguay | 150,000 | 150,000 | 14,782,500 | 1 : 10,000 | 10.6 | .00085 Rhone | 34,800 | 65,850 | 36,000,000 | 1 : 1,775 | 31.1 | .01075 Po | 27,100 | 62,200 | 67,000,000 | 1 : 900 | 59.0 | .01139 Danube | 320,300 | 315,200 | 108,000,000 | 1 : 2,880 | 93.2 | .00354 Nile | 1,100,000 | 113,000 | 54,000,000 | 1 : 2,050 | 38.8 | .00042 Irrawaddy | 125,000 | 475,000 | 291,430,000 | 1 : 1,610 | 209.0 | .02005 Mean | 334,693 | 201,468 | 109,649,972 | 1 : 2,731 | 76.65 | .00614 -----------+-----------+----------+-------------+------------+------------+--------

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

Organic carbon .99 part in 1,000,000 of water. Organic nitrogen .22 „ „ „ „ „ Ammonia .50 „ „ „ „ „ Nitrogen as nitrates and nitrites .07 „ „ „ „ „ Chlorine 6.30 parts in „ „ „ Total solids 39.50 „ „ „ „ „

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 showing the amount of mineral matter in average river water:

MATERIAL IN SOLUTION IN ONE CUBIC MILE OF AVERAGE RIVER WATER.

Constituents. Tons in a Cubic Mile. Calcium carbonate (CaCO₃) 326,710 Magnesium carbonate (MgCO₃) 112,870 Calcium phosphate (Ca₃P₂O₈) 2,913 Calcium sulphate (CaSO₄) 34,361 Sodium sulphate (Na₂SO₄) 31,805 Potassium sulphate (K₂SO₄) 20,358 Sodium nitrate (NaNO₃) 26,800 Sodium chloride (NaCl) 16,657 Lithium chloride (LiCl) 2,462 Ammonium chloride (NH₄Cl) 1,030 Silica (SiO₂) 74,577 Ferric oxide (Fe₂O₃) 13,006 Alumina (Al₂O₃) 14,315 Manganese oxide (Mn₂O₃) 5,703 Organic matter 79,020 ------- Total dissolved matter 762,587

Murray also estimates that the aggregate amount of water flowing into the sea annually is about 6528 cubic miles, which, on the above basis, would carry about 4,975,000,000 tons of mineral matter in solution.

A large number of analyses of waters of rivers from the United States and Canada give an average of about .15,044 part in a thousand of mineral matter in solution, more than one-third being CaCO₃. The average amount of mineral matter in solution in 48 European streams cited by Bischoff is .2127 part in a thousand, of which CaCO₃ is rather more than half. The average mineral matter in solution in 36 rivers cited by Roth (including some of those tabulated by Bischoff) is .2033 part in a thousand, of which CaCO₃ is slightly less than one-half.

An average for American and European rivers, so far as determinable from data at hand, is about .1888 part in a thousand in solution, of which CaCO₃ is slightly less than one-half. These last figures are probably not very far from an average for river water in general.

The following table shows the total amount of solids carried in solution by the rivers indicated:

Rhine 5,816,805 tons per year. Rhone 8,290,464 „ „ „ Danube 22,521,434 „ „ „ Thames 613,930 „ „ „ Nile 16,950,000 „ „ „ Croton 66,795 „ „ „ Hudson 438,000 „ „ „ Mississippi 112,832,171 „ „ „

ECONOMIC CONSIDERATIONS.

Certain considerations of human interest in connection with river erosion are worthy of note. When a drainage system has reached its mature stage its basin has the roughest topography which it will have at any time during that cycle of erosion. At that stage, therefore, road construction is relatively difficult. If the relief be great, roads must follow the valleys, or the crests of the ridges between them, if they would avoid heavy grades. In such regions roads are usually few and crooked.

The stage of development of valleys has an influence on the navigability of their streams. Streams well advanced in life are much more readily navigable than young ones, because their grades are lower and their volumes of water greater. Old streams, on the other hand, are sometimes depositing sand or silt along their lower courses to such an extent as to interfere with navigation.

At certain stages of their development the power of streams is more easily utilized than at others. Young streams, depending as they do for their supply on the rainfall of a limited area, are likely to be fitful in their flow, and therefore unreliable as a source of power. This is especially true where the precipitation is unequally distributed, and where the slopes are steep and free from forests. Because of their great volume, old and large streams, though sluggish, have great power, but it is less easily controlled. Where streams are large enough to be navigable industrial considerations often prevent the utilization of their power, the streams being more serviceable as highways than as sources of power. Other things being equal, it follows that streams are most available for water-power when they are large enough to have a moderately steady flow, and not so large as to be beyond ready control, or to be valuable for purposes of navigation.

Streams are subject to more disastrous floods in some stages of their development than in others. Floods resulting from heavy rains are likely to be greatest where the slopes above the drainage lines are on the whole greatest, for this is the condition under which the water is most quickly gathered into the drainage channels. The most disastrous floods, humanly speaking, are those which affect wide-bottomed valleys, where the flats are settled. In such cases a relatively slight rise may flood very extensive areas. In such valleys the most disastrous floods are generally in the spring, when the waters from the melting snows of the preceding winter are being discharged. Many other considerations enter into the problem of floods. The presence of forests and other forms of vegetation on the slopes retards the flow of water into the valleys, and so tends to prevent floods, or at any rate to make them less severe. Porous soil and subsoil, or in their absence porous rock, absorb the rainfall, and prevent its prompt descent into the valleys and so tends to prevent or diminish floods.

The acreage of arable land within a given area stands in some relation to its drainage development. At an early stage in its erosion history, before an upland has been dissected by valleys, nearly all of it may be arable. Later, when drainage is at its maturity, and when hillsides and ridge slopes constitute a large part of the area, there is probably the least acreage of arable land. This is especially true if the slopes are so steep as to allow the soil to be readily washed away. At a still later stage, when the valley bottoms have become wide and the slopes of the ridges and hills so reduced as to be available, the area of cultivable land is again increased.

Marshes, ponds, and lakes have some bearing on the resources and industries of a region, and they stand in a more or less definite relation to the stage of erosion in which a region finds itself. In its youth ponds and lakes may occupy much of the surface; in its maturity they will have been largely drained.

These suggestions are sufficient to show that the topography of a region, even in so far as shaped by erosion, touches human interests at many points.

ANALYSIS OF EROSION.

Erosion is the term applied to all the processes by which earthy matter or rock is loosened and removed from one place to another. It consists of three sub-processes, namely, weathering, transportation, and corrasion.

Weathering.

The term weathering is applied to nearly all those natural processes which tend to loosen or change the exposed surfaces of rock. The lettering of inscriptions on exposed marble becomes fainter and fainter as time goes by, and finally disappears, because the rock in which the letters were cut has weathered away. Some of it has crumbled off as the result of the expansion and contraction induced by changes of temperature, and some of it has been dissolved by the rain which has fallen upon it. In this case the weathering is effected partly by the atmosphere and partly by water. These are the chief, but not the only agents concerned in the general processes of weathering. Those phases of weathering which are the result of the activities of the atmosphere, whether physical or chemical, have been discussed in connection with the atmosphere (pp. 42 and 54).

The rain which falls upon the surface of exposed rock, and that which sinks through the soil to the solid rock below, dissolves, even if slowly, some of the rock constituents. Each constituent of a rock composed of several minerals may be looked upon as a binding material for the others. When one is dissolved the rock crumbles, much as mortar does when the lime which cements the sand is dissolved.

The solution of mineral matter by ground water, as well as the other chemical changes it effects, is greatly augmented by the impurities, especially carbonic and other organic gases, dissolved by the water from the atmosphere and the soil. The commonest chemical changes effected by the joint action of water and air, oxidation and carbonation, have been referred to in Chapter II. Hydration is more exclusively the work of water, and is one of the commonest processes of rock change, and often of rock disintegration. Numerous other less simple chemical changes resulting from the activities of ground water are constantly in progress, and in so far as they lead to the disintegration of rock are processes of weathering. Many chemical changes involve notable changes in volume of the mineral matter concerned. Merrill has calculated that in the conversion of the granitic rock of the vicinity of Washington, D. C., into soil, its volume has been increased 88 percent., largely as the result of hydration. Even when the chemical changes do not themselves directly involve the disintegration of the rock, the accompanying increase of volume is sometimes sufficient to cause its physical disruption. This also may be regarded as a phase of weathering.

The weathering accomplished by water, or under its influence, proceeds at rates which vary with the composition of the rock, the amount and composition of the water, the temperature, and certain other factors less susceptible of brief statement. The weathering effected by ground water has a wider range both in area and depth than that due to changes of temperature, for while the latter is effective only where temperature changes are considerable, and where coherent material lies at the surface (p. 45), the former is operative to all depths to which water sinks.

There are other processes of weathering not due directly either to the atmosphere or to water. The roots of trees and smaller plants frequently grow into cracks of rocks, and, increasing in size, act much like freezing water (p. 45) in similar situations. This wedge-work of roots is a phase of weathering.

From the faces of steep cliffs masses of rock frequently fall. However dislodged, their descent is effected by gravity. The quantities of débris at the bases of many cliffs, forming slopes of talus (Fig. 94), testify to the importance of the action of gravity in getting material from higher to lower levels. Another phase of gravity-work is shown in Fig. 95. Here, under the influence of gravity and expansion and contraction, due to freezing and thawing and wetting and drying, the surface material is creeping down slope. In the process the rock is being broken. The process illustrated by the figure involves weathering as well as other factors.

The foregoing are among the commoner processes of weathering, although they do not exhaust the list. The more active and tangible processes by which surface rocks are broken up, such as wave wear, river wear and glacier wear, are processes of corrasion. The mechanical wear effected by wind-driven sand might be considered either as corrasion or as weathering. It is more likely to be regarded as corrasion if the amount of wear is considerable enough to be obvious. Rock is sometimes decomposed by the chemical action of hot vapors, gases, and waters rising to the surface from considerable depths. This is often seen in volcanic regions. A conspicuous illustration is seen in the canyon of the Yellowstone in the National Park. Decay of this sort is perhaps not properly weathering, but is not always readily distinguished from it.

The importance of weathering in the general processes of erosion is shown in many ways. In regions where the mantle rock is the product of the decay of the solid rock beneath, and such regions constitute a large portion of the earth’s surface, the soil and subsoil represent the excess of weathering over transportation. Since most of the earth’s surface is covered with soil to a greater or less depth, it is clear that, on the whole, weathering keeps ahead of transportation. Again, it is clear that the loosening of rock by weathering greatly increases the erosion which a given amount of moving water can accomplish. Not only this, but weathering plays a much more important rôle in the development of valleys than is commonly realized. This is best illustrated by the valleys of young swift streams. The valley which is not at its top ten times as wide as its stream is rare. The stream which has such a canyon has been cutting chiefly at its bottom. Ignoring its lateral corrasion, which is slight, the valley which it would cut would have a width equal to its own. This is illustrated by Fig. 96. Weathering in its broadest sense is largely responsible for the width of such a valley, in so far as it exceeds the width of the stream. The work of weathering, slope wash, etc., has been to get the material which originally lay between a, b, and c down to the stream. The stream has then carried it away. The above illustration would not apply to old and sluggish streams, for they, by their meandering, widen their valleys independently of weathering.

Weathering is a part of erosion, but only a part. In so far as it is effected by solution the process involves the transportation of that which is dissolved to some other point. Transportation is also involved to some extent in the other processes of weathering, but the central idea of the processes embraced under this term is the loosening and disrupting of rock by which it is prepared for transportation.

Transportation.

The second element of erosion is transportation. The transportation of mechanical sediment is to be distinguished from the transportation of materials in solution. In so far as mineral matter is dissolved it becomes, so far as flowage is concerned, a part of the stream. If the quantity dissolved were large it might influence the mobility of the water, but the amount is usually too slight to influence the flow sensibly.

The sediment transported by a stream is either rolled along its bottom or carried in suspension at some higher level. The coarser materials (gravel and sand) are carried chiefly in the former position, and the finer (silt and mud) largely in the latter.

=Transporting power and velocity.=—The transporting power of running water depends on its velocity. The formula expressing the relations between them is as follows: Transporting power, t, varies as the sixth power of velocity, v, (tαv⁶); that is, doubling the velocity of the stream increases its transporting power 64-fold. Strictly speaking, this means that if a stream of given velocity is just able to move a stone of a given size, a stream with double that velocity will be just able to move a stone of the same shape 64 times as large as the first. This may be graphically illustrated as follows: Let a current be supposed just able to move the cube a (Fig. 97). If the current be doubled, twice as much water will strike the same surface with twice the force in the same time; that is, the force exerted on the cube a will be quadrupled. It will, therefore, be able not only to move the one cube, but it will be able to move three other cubes (b, c, and d) besides (Fig. 98). The same current against any other equal surface would also be able to move four small cubes, and there are sixteen such surfaces on the face of the large cube (Fig. 99). It follows that the dimension of the cube which the stream with the doubled velocity can move is four times as great as that of the cube which the original current could move, and the cubical contents of such a cube is 64 times as great as that of the first (64 = 2⁶) (Fig. 99). Swift streams, therefore, have enormously greater power of transportation than sluggish ones. It does not necessarily follow that transportation keeps pace with transporting power; that depends on the accessibility of materials suitable for transportation. A stream of great transporting power, like the Niagara at its rapids, may carry little sediment, because there is little to be had.

The velocity of a stream depends chiefly on three elements—its gradient, its volume, and its load, (i.e., the sediment it is moving). The higher the gradient the greater the volume, and the less the load the greater the velocity. The relation between gradient and velocity is evident; that between volume and velocity is illustrated by every stream in time of flood, when its rate of flow is greatly increased. The relation between velocity and load is less obvious, but none the less definite. Every particle of sediment carried by a stream makes a draught on its energy, and energy expended in this way reduces the velocity. The draught on a stream’s energy of a particle carried in suspension is measured by its mass into the distance it would fall in a unit of time in still water. It follows that a large particle makes a stronger draught on a stream’s energy than the same amount of material in smaller pieces. It follows also that the comminution of sediment facilitates transportation in much more than a simple ratio, for not only can a given amount of energy carry more fine material than coarse, but a larger proportion of a stream’s energy can be utilized in the transportation of the fine.

=How sediment is carried.=—Coarse materials, such as gravel stones, are rolled along the bottoms of the swift streams which carry them. Their movement is effected by the impact of water. The same is true to a large extent of sand grains, especially if they be coarse. So far as concerns the material rolled along the bottom it is to be noted that a stream’s transporting power is dependent on the velocity of the water at its bottom. This is much less than the surface, or even the average velocity. The particles of fine sediments, such as silt and mud, are frequently carried by streams quite above their bottoms, as shown by the roiliness of many streams. A particle of mud is usually a small bit of mineral matter, the specific gravity of which is two or three times that of water. Why does it not sink through the water and come to rest at the bottom of the stream, or suffer transportation as the gravel does?

A particle of sediment in running water is obviously subject to two forces, that of the current which tends to move it nearly horizontally down-stream, and that of gravity which tends to carry it to the bed of the stream. In Fig. 100, the arrows ab and ac represent respectively the relative force of gravity and a current of 5 miles per hour. As a result of these two forces the particle would tend to descend in the general direction of ad, a line which represents the resultant of these forces, though not the exact path which a particle acted on by them would take in water. If a river were the simple straightforward current which it is popularly thought to be, a particle in suspension would reach its bottom in the time it would take to sink through an equal depth of still water, for the descent would be none the less certain and none the less prompt because of the forward movement of the water. The current would simply be a factor in determining the position of the particle when it reached the bottom, not the time of reaching it. Very fine particles, like those of clay, though having the same specific gravity as grains of sand, would sink less readily than coarser ones, because they expose larger surfaces, relative to their mass, to the water through which they sink. But even such particles, unless of extraordinary fineness, would presently reach the bottom if acted on only by a horizontal current and gravity. Since even sediment which is not of exceeding fineness is kept in suspension it is clear that some other factor is involved. This is found, in part at least, in the subordinate upward currents in a stream.

Where a bowlder occurs in the bed of a stream (Fig. 101) the water which strikes it is in part forced up over it. If there be many bowlders the process is frequently repeated, and the number of upward currents is great. Any roughness will serve the same purpose, and every stream’s bed is rough to a greater or less extent. Where there are roughnesses at the sides of a channel, currents are started which flow from them toward the center. The varying velocities of the different parts of a stream serve a similar purpose. The curves in a river tend to give the water a rotatory movement. A river is therefore to be looked upon not as a single straightforward current, but as a multitude of currents, some rising from the bottom toward the top, some descending from top to bottom, some diverging from the center toward the sides, and some converging from the sides toward the center. The existence of these subordinate currents is often evident from the boiling and eddying readily seen in many streams. It is, of course, true that the sum of the upward currents is always less than the sum of the downward, so that the aggregate motion of the water is down slope; but it is also true that minor upward currents are common. Sediment in suspension is held up chiefly by such currents, which, locally and temporarily, overcome the effect of gravity. The particles in suspension are constantly tending to fall, and frequently falling; but before they reach the bottom many of them are seized and carried upward by the subordinate currents, only to sink and be carried up again. Even if they reach the bottom, as they frequently do, they may be picked up again. It is probable that every particle of sediment of such size that it would sink readily in still water is dropped and picked up many times in the course of any long river journey, and its periods of rest often exceed its periods of movement.

Independently of the subordinate currents, the different velocities of the different parts of a stream tend to keep materials in suspension by exerting different pressures on the different sides of suspended particles.

River ice sometimes facilitates the transportation of débris which the water alone could not carry. The ice freezes to bowlders in the banks of the streams, to those which are partially submerged, and sometimes to those altogether submerged beneath slight depths of water. When the ice breaks up in the spring such bowlders, buoyed up by the ice, may be floated far down the stream. The influence of ice in this connection is most considerable in high latitudes, but it is of consequence as far south as Virginia, where the river deposits sometimes contain bowlders which the unaided streams could not have carried. Ground ice sometimes forms about bowlders in the bottoms of streams, especially in the quiet pools of turbulent rivers, and floats them to the surface before the surface itself is frozen. In the floods of spring rivers often spread their ice widely over their flood-plains. It is sometimes massed in constricted portions of valleys so as to form great dams, the breaking of which is attended with great destruction.

Corrasion.

=Abrasion.=—The wear effected by running water is corrasion. So long as the materials to be carried away are incoherent it is easy to see how running water picks them up and carries them forward. The water which gathers in the depressions on the slope of a cultivated field gathers earthy matter from the surface over which it passes, even before it is concentrated into rills, and the rills continue the process. Thus the loose materials of the surface are gathered at the very sources of the streams, and the amount of sediment in the water after a heavy shower, even at the head of the stream, may be great. The run-off from the slopes of any valley in any part of its course likewise brings sediment to the stream, which gathers more from its bed whereever it flows with sufficient velocity over incoherent material. Streams also undercut their banks, and receive new load from the fall of the overhanging material.

By far the larger part of the sediment acquired by a normal stream is made up of material loosened in advance by the processes of weathering. The stream, or the waters which get together to make the stream, find them ready-made; but rivers frequently wear rock which is not weathered, for the principal valleys of the earth’s surface are cut in solid rock, and many of them in rock of exceeding hardness. How does the stream wear the solid rock?

When a stream flows over a rock bed, the wear which it accomplishes depends chiefly on the character of the rock, the velocity of the stream, and the load it carries. If the rock be stratified and in thin layers, and if these thin layers be broken by numerous joints at high angles to the stratification planes, the impact of the water of a clear stream of even moderate strength may be effective in dislodging bits of the rock. This condition of things is often seen where streams run on beds of shale or slate. If the rock be hard and without bedding-planes and joints, or if its layers be thick and its joints few, clear water will be much less effective. If the surface of the rock be rough, the mechanical action of a swift stream of clear water might still produce some effect on it; but if massive hard rock presents a smooth surface to a clear stream, the mechanical effect of even a swift current is slight.

This general principle is illustrated by the Niagara River. Just above the falls the current is swift. When the river is essentially free from sediment, the surface of the limestone near the bank beneath it is sometimes distinctly green from the presence of the one-celled plants (fresh-water algæ) which grow upon it. The whole force of the mighty torrent is not able to sweep them from their moorings. Were the stream supplied with a tithe of the sand which it is capable of carrying, it would not take many hours, and perhaps not many minutes, to remove the last trace of vegetation. This illustration furnishes a clue to the method by which the erosion of solid rock in a stream’s bed is effected.

It has been seen that the ingathering waters which make a stream often have abundant sediment before they reach well-defined stream channels, and that the streams continue to gather sediment whereever their beds are composed of material which is readily detached. The sediments which the stream carries are the tools with which it works. Without them it is relatively impotent, so far as the abrasion of solid rock is concerned; with them, it may wear any rock over which it passes (Fig. 102).

We have next to inquire the methods by which running water uses its tools in the excavation of valleys. When gravel is rolled along in the channel of a stream there is friction between it and the bed over which it moves. If the pebbles be as hard as the bed over which they are rolled their movement must result in its wear, and even if they be softer more or less wear takes place. As the moving stones wear the rock of the stream’s bed they are themselves worn by impact with it and with one another. In all cases the softer material suffers the more rapid wear. The first effect of wear on materials in transportation is the reduction of their rugosities of surface. The projecting points and sharp angles are worn off, and the stones are reduced to rounded water-worn forms. The particles broken off make grains of sand, or, if very fine, particles of silt or mud. Even after a stone has been rounded it is subject to further wear and reduction, and in the course of time may be literally worn out.

The sediment carried in suspension, as well as that rolled along the bottom, may wear the rock bed of a stream. When a grain of sand in suspension escapes from an upward moving current it may not sink quietly. If it be caught by a downward current it may be made to strike a blow on the bed of the stream, and the effect of the blow is to wear the surface which receives it. The larger the grain and the stronger the current the greater the wear.

The ceaseless repetition of the blows struck by the material in suspension, or rolled on its bottom, hour after hour, day after day, and year after year, will accomplish sensible results. In the long course of the ages this process has excavated deep valleys. Concomitant processes are largely concerned in making valleys wide, but the depth of valleys cut in solid rock is chiefly the result of the impact and friction of the sediment in transportation.

The wear effected in this way is not proportional to the number of blows struck. Since every pebble and every grain of sand carried diminishes the velocity of a stream, and since with diminished velocity the force of the blows struck is diminished, it follows that the blows may become so weak, as the result of their multiplication, as to be ineffective. The larger the load, therefore, which the stream carries, the more the tools with which it has to work, but the less effectively can it use them; and the load may be so far increased as to destroy its corrasive power altogether. On the other hand, the smaller the load of the stream the greater its velocity and the more effectively will its tools be used; but their number may be so far reduced that their aggregate effect is slight. To accomplish the greatest results on a bed of solid rock a stream must have tools to work with, but must not be so heavily burdened as to interfere with its effective use of them.

Whatever the cause of their unequal velocities swift and slow streams corrade their valleys differently. The erosion of a swift stream is chiefly at the bottom of its channel. The sluggish stream lowers its channel less rapidly, while lateral erosion is relatively more important. The result is that slow streams increase the width of their valleys more than the depth, while swift streams increase the depth more than the width. It follows that slow streams develop flats, while swift ones do not. Not only is a slow stream more likely to have a flat, and therefore a better chance to meander, but it is more likely to take advantage of opportunities in this line, for a slow stream gets out of the way for such obstacles as it may encounter, while a swift stream is much more likely to get obstacles out of its way.

Special phases of corrasion are introduced where waterfalls and other peculiarities dependent on inequalities of rock resistance occur.

=Solution.=—In most cases the solution effected by a stream is much less important than its mechanical work. Only when conditions are unfavorable to the latter, is solution the chief factor in the excavation of a valley. This may be the case where a stream’s bed is over soluble rock, such as limestone, and where the stream is clear, or its gradient so low that its current is sluggish. The solvent power of water is not influenced by the presence of sediment, though the presence of sediment offers the water a greater surface on which to work.

CONDITIONS AFFECTING THE RATE OF EROSION.

In considering the rate of erosion, both the work of the stream in its valley and that of the general run-off are to be considered. The conditions which favor the most rapid erosion in a stream’s channel are not necessarily those which determine most rapid degradation in the basin outside of the valley.

The Influence of Declivity.

In general the greater the declivity the more rapid the rate of erosion, whether in the stream’s channel or on the slopes above it. The truth of this conclusion is illustrated by the great erosive power of swift streams as compared with slow ones.

It does not follow, however, that high declivity favors each element of erosion. The effect of declivity on weathering is far from simple. For example, great declivity, by allowing more of the rainfall to flow off over the surface, and by causing it to flow off more promptly, restricts the work of solution, and therefore of decomposition, both at the surface and beneath it. High declivity is also unfavorable to the growth of vegetation, and so to the wedge-work of roots. On the other hand, a given amount of wedge-work of roots and ice is more effective where the slope is steep than where it is gentle, for such materials as are loosened descend the slopes more readily. The prompt removal of weathered materials, by exposing fresh surfaces of rock, accelerates weathering. The total amount of weathering may therefore not be diminished by the increase of slope, even though certain of its processes are hindered.

The effect of high declivity on transportation, the second element of erosion, is too patent to need explanation.

Corrasion likewise is favored by high declivity, for the abrasive power of a stream increases as the square of its velocity. With corrasive power increased, corrasion will also be increased if the water has tools to work with. Since high declivity greatly increases both the transporting and the corrasive power of running water, and favors certain elements of weathering, it is clear that the aggregate effect of high declivity is to favor erosion, whether in the channel of the stream or on the general surface of its drainage basin.

The Influence of Rock.

The physical constitution, the chemical composition, and the stratigraphy of a rock formation, influence the rate at which it may be broken up and carried away. Clastic or fragmental rocks are usually stratified and made up of cemented pebbles (conglomerate), sand grains (sandstone), or particles of mud (shale). Igneous rocks, such as granite, are massive instead of stratified, and are usually made up of great numbers of interlocking crystals which bind one another together. Some crystalline rocks, such as schists, though not stratified, possess cleavage, which has much the effect of stratification, so far as erosion is concerned. All rocks are affected by systems of more or less nearly vertical cracks called joints. All these structures have their influence upon the rate of degradation.

=Physical constitution.=—Clastic rocks may be firmly cemented, or their constituents may be loosely bound together. The less the coherence the more ready the disintegration, and the finer the particles the more easily are they carried away. When the particles in transportation are angular they effect more wear on the bed over which they move, and on one another, than when they are round. The difference is great where the particles are large, and little where they are very small. If the materials carried be harder than the bed over which they pass, corrasion of the latter is favored.

=Chemical composition.=—Something also depends on the chemical composition of the rock, since this affects its solubility, and therefore its rate of decomposition. The more soluble the rock the larger the proportion of it which will be taken away in solution; but it does not follow that the most soluble rock will be most rapidly eroded, since the rate of erosion depends on abrasion as well as solution, and a rock which is readily soluble, as rocks go, may be less easily abraded than a rock which is made of discrete and insoluble particles bound together by a soluble cement. In such rocks, for example a sandstone in which the grains are cemented together by lime carbonate, the solution of the cement sets free a considerable quantity of sand, so that a small amount of solution prepares a large amount of sediment for removal. A stream might cut its valley much more rapidly in such a sandstone than in a compact limestone, though the latter is, as a whole, the more soluble. The constituent minerals of crystalline rocks resist solution and decay unequally, and when any one is dissolved or decomposed the rock crumbles and the less soluble constituents are ready for removal by mechanical means. So long as the material loosened by disintegration is removed, chemical heterogeneity favors erosion; but if the loosened débris is not removed erosion is not favored by chemical heterogeneity. In such a case erosion would be most rapid where the rock was most soluble.

=Structure.=—The structure of the rock has much to do with the rate of its erosion. Other things being equal, stratified rock is more readily eroded than massive rock, since stratification-planes are planes of cleavage, and therefore of weakness. Taking advantage of these planes the water has less breaking to perform to reduce the material to a transportable condition. For the same reason a thin-bedded formation is more easily eroded than a thick-bedded one.

The beds of stratified rock may be horizontal, vertical, or inclined, and inclined strata may stand at any angle between horizontality and verticality. In indurated formations the rate of erosion is influenced both by the position of the strata and by the relation of the direction of the flowing water to their dip and strike. On the whole the strata which are horizontal, or but slightly inclined, are probably less favorable for rapid erosion than those which are vertical or inclined at considerable angles. This is at least true where the layers are of uniform hardness and the joints infrequent.

Horizontal strata expose fewer cleavage planes to the water flowing over them than strata in any other position. In Fig. 103 the stream which has the profile ad crosses bedding-planes at b and c. In Fig. 104, where the beds dip up-stream, many more division-planes are crossed in the same distance. Since bedding-planes are planes of weakness, it follows that horizontal and nearly horizontal strata are not, under ordinary conditions of erosion, in a position favorable for most rapid wear. When strata are horizontal, it makes no difference which way the stream runs, for the current sustains the same relation to the cleavage-planes whatever its course.

In the case of incoherent material the position of the beds, or even their existence, has little influence on the rate of erosion. Such formations are weak in all directions, not simply along bedding-planes.

When the strata are vertical, three distinct cases may arise (Fig. 105). The stream may flow (1) with the strike (aa); (2) at right angles to the strike (bb); or (3) oblique to it (cc) at any angle whatsoever. It is perhaps not possible to say which of these positions is most favorable for erosion, for the character of the rock, the thickness of its layers, its ability to stand with steep slopes, and the strength of the currents concerned, would influence the result. A stream which flows at right angles to the strike (bb, Fig. 105) would cross more cleavage-planes in a given distance than a stream flowing in any other direction, and would strike the outcropping edges of layers at the angle of greatest advantage. A stream flowing along the strike (aa), on the other hand, has better opportunity to sink its channel on cleavage-planes, and the current oblique to the strike (cc), has some of the advantages of each of the others.

When the strata are inclined five cases may arise. (1) The stream may be parallel to the strike (aa, Fig. 106), when it makes no difference which way the current flows; it may be at right angles to the strike (bb′), and (2) flowing with the dip (toward b′), or (3) against it (toward b); it may be oblique to the strike, and flowing (4) in the general direction of dip (toward c′); or (5) in the opposite direction (toward c). As before, the stream flowing at right angles to the strike would cross the largest number of layers in a given distance, and so have an opportunity to take advantage of more cleavage-planes than a stream in any other position. But in the case of inclined strata a new element enters into the problem. When the stream flows parallel to the strike, the valley which is in process of deepening is not sunk vertically, but is shifted more or less in the direction of the dip (Fig. 107). This is called monoclinal shifting. The result is that there is a constant tendency to undermine (sap) the valley bluff on the down-dip side, and this process of sapping will, according to its rate, accelerate the growth of the valley, especially in width. Monoclinal shifting is favored by the presence of a hard layer (H), as shown in Fig. 107, if this stratum is the bed of the stream.

In the second and third cases mentioned above, the only difference is in the angle at which the current strikes the outcropping edges of layers and laminæ. The mechanical advantage is with the stream which flows with the dip. In the fourth and fifth cases something will depend on the angle which the stream’s course makes with the strike. In all these cases, as in those where the strata are vertical, much will depend on the thickness and resistance of the layers and on the strength of the currents concerned.

The Influence of Climate.

Climate has both a direct and an indirect effect on erosion. Its direct influence is through precipitation, evaporation, changes of temperature, and wind; its indirect, through vegetation. Like declivity and rock structure, climate does not affect all elements of erosion equally.

The chief elements of climate are temperature, moisture, and atmospheric movements; the principal factors which influence it are latitude, altitude, distance from the sea, direction of prevailing winds, and topographic relations.

The effects of variations in temperature on rock weathering have already been discussed (p. 43). They are chiefly mechanical, and are seen at their best where the daily range is great.

High temperature favors chemical action, and the weathering of rock by decomposition is at its best in the presence of abundant moisture in regions where the temperature is uniformly high. Furthermore, a warm moist climate favors the growth of vegetation, the decay of which supplies the water with organic acids which greatly increase its solvent power. The climatic conditions favoring mechanical weathering are therefore different from those favoring chemical weathering. High temperature and abundant moisture and vegetation are found in many tropical regions, and here the rock is often decomposed to greater depths, on the whole, than in high latitudes. How far this is the result of rapid weathering, and how far of slow removal, due in part to the protective influence of the plants, cannot be affirmed. If the weathered material is not removed, it will presently become a mantle thick enough to retard the processes which brought it into existence.

So long as the water of the surface and that in the soil remains unfrozen, temperature affects neither corrasion nor transportation. But in middle and high latitudes the surface is frozen for some part of each year. During this time corrasion is at a minimum, for although the streams continue to flow there is relatively little water running over the surface outside the drainage channels, and that little is relatively ineffective. Under some conditions, therefore, temperature affects both corrasion and transportation.

The humidity of the atmosphere has an influence even more important than that of temperature on the rate of erosion, and its influence is exerted on each of the elements of that complex process. A moist atmosphere favors oxidation, carbonation, hydration, and the growth of vegetation, all of which promote certain phases of rock weathering. On the other hand, humidity tends to prevent sudden and considerable variations in temperature, thus checking the weathering effected by this means. Precipitation, the most important single factor in determining the rate of erosion, is dependent on atmospheric humidity. Its amount, its kind (rain or snow), and its distribution in time, are the elements which determine its effectiveness in any given place.

Other things being equal the greater the amount of precipitation the more rapid the corrasion and transportation. Much, however, depends on its distribution in time. A given amount of rainfall may be distributed equally through the year, or it may fall during a wet season only. The maximum inequality of distribution would occur if all the rainfall of a given period were concentrated in a single shower. With such concentration the volume of water flowing off over the surface immediately after the down-pour would be greater than under any other conditions of precipitation, and since velocity is increased with volume, and erosive power with velocity, it follows that the erosive power of a given amount of water would be greater under these circumstances than under any other. Furthermore, a larger proportion of the precipitation would run off over the surface under these circumstances than under any other, for less of it would sink beneath the surface and less would be evaporated. If erosive power and rate of erosion were equal terms, this would therefore be the condition for greatest erosion; but erosive power and rate of erosion do not always correspond. If the water falling in this way could get hold of all the material it could carry, extreme concentration of precipitation would be the condition favorable for most rapid erosion. But if the amount of available material for transportation is slight, a large part of the force of the water could not be utilized in erosion. It follows that if there were a large amount of disintegrated material on the surface, erosion would be greater the greater the concentration of precipitation. If, on the other hand, there were but little disintegrated material on the surface, frequent showers, with intervening periods when conditions were favorable for weathering, that is, for preparing material for transportation, might be more favorable for rapid erosion. While the total energy of running water available for erosion under these conditions would be less than before, there might in the long run be more material for transport; for weathering in the presence of moisture, and all that goes with it, might be more effective in preparing material for transportation, than weathering during the long periods of drought which would occur if the precipitation were concentrated to its maximum. Temperature favoring, the uniform distribution of moisture through the year would allow the growth of vegetation, which, although favoring some processes of weathering, retards erosion in general. While therefore it is not possible to say what distribution of rainfall favors most rapid erosion without knowing the nature of the surface on which it is to fall, enough has been said to show that the problem is by no means a simple one. Some of the most striking phases of topography developed by erosion, such as those of the Bad Lands (Figs. 75 to 78, and 108), are developed where the rainfall is unequally distributed in time, and too slight or too infrequent to support abundant vegetation.

During its fall, and immediately after, rain is more effective than an equal amount of snow; but the snow may be accumulated through a considerable period of the year, and then melted rapidly, when it has an effect comparable to that which would be produced by the concentration of the rainfall into a limited period of the year. If the ground beneath be frozen when the snow melts (and this is often the case) the erosion accomplished by the resulting water will be diminished.

Except in dry regions, where wind-work sometimes exceeds water-work, the movements of the atmosphere are of less importance directly than precipitation in determining the rate of erosion. But even in regions which are not arid the winds have much to do with the rate of evaporation and the distribution of rainfall, so that their indirect effect is great. Even their direct effects in moist climates are not to be lost sight of, for even here the surface is sometimes dry enough to yield dust and sand, and the uprooting of trees so disturbs the surface as to make earthy débris more accessible to wind and water. Where trees gain precarious footholds on steep slopes, as they often do, they are likely to be overturned as soon as they are large enough to offer considerable resistance to the wind, and in the overturning, large quantities of rock are sometimes loosened and carried down the slope by gravity. This phase of destructive work is seen at its best on the walls of gorges, where trees often flourish until their tops project above the rim of the valley.

Through vegetation, climate influences erosion in ways which are easily defined qualitatively, but not quantitatively. Both by its growth (wedge-work of roots) and by its decay (supplying CO₂, etc., to descending waters) it favors certain phases of weathering; but, on the other hand, it retards corrasion and transportation both by wind and water. This is well shown along the banks of streams and on the faces of cliffs, in clay, sand, etc. Its aggregate effect is probably unfavorable to erosion by mechanical means, and favorable to that by chemical processes.

Erosion in high arid regions differs from that in regions of abundant rainfall in several ways. It is obvious that the valleys will develop more slowly in the former, that they will remain young longer, that the period necessary for the dissection of the surface is greater, that the watercourses will be less numerous, and that fewer of them will have permanent streams. There are certain other differences which are less obvious. If the arid region be high and composed of heterogeneous strata, the topography which erosion develops is more angular (Fig. 83) than that of the humid region. This is because there is less rock decay, and less vegetation to hold the products of decay. The more resistant beds of rock therefore come into greater prominence, especially on slopes, where they develop cliffs (Figs. 109 and 110). These general principles find abundant illustration in the plateaus of the western part of the United States, where the cliffs are by no means confined to the immediate valleys of the streams (Fig. 1, Pl. XII).

EFFECTS OF UNEQUAL HARDNESS.

In the preceding pages incidental reference has been made to the results of inequalities of rock resistance. This topic will now be considered more fully.

=Rapids and falls.=—Returning for a moment to the hypothetical island with which our study of erosion began, let a horizontal layer of hard rock be assumed to run through it (H, Fig. 111). As the rain falls on the land and runs off over it, wear will be less rapid where the hard layer comes to the surface than at the higher or lower levels. As a result, the slope will become steeper at and below the outcrop of the hard layer, and less steep immediately above it, as shown by ab in Fig. 111. Under these conditions the water passing over the hard ledge constitutes rapids. The increased erosion which accompanies the increased velocity makes the rapids more rapid. The process may continue until the water falls, rather than flows over the hard layer (cd, Fig. 111). With continued rainfall the edges of the hard layer, together with the slopes above and below, would continue to recede toward the center of the island. Under conditions of absolute homogeneity of material, save for the hard layer specified, no valley would be developed, and therefore no stream.

If the surface was so changed as to allow of the development of a valley (p. 63) the same principles would be applicable. As an active stream passes from a hard layer to one less resistant, the greater wear on the latter gives origin to rapids. At first the rapids would be slight (a, Fig. 112), but would become more considerable (b) as time and erosion go on. When the bed of the rapids becomes sufficiently steep, the rapids become falls (cd). When the water falls rather than flows over the rock surface below the hard layer, erosion assumes a new phase. The hard layer is then undermined, and the undermining causes the falls to recede. This phase of erosion is sometimes called sapping.

If the hard layer which occasions a fall dips up-stream (Fig. 112), its outcrop in the stream’s bed becomes lower as the fall recedes (e). When it has become so low that the water passing over it no longer reacts effectively against the less resistant material beneath (f), sapping ceases, and the point of greatest erosion may be shifted from the soft material beneath the fall to the hard layer itself. The actual rate of erosion at this point may be no greater than before, though the relative rate is. Under these circumstances the vertical edge of the hard layer will presently be converted into an incline (f), and as this takes place the fall becomes rapids. The conversion of the falls into the rapids begins about the time the lower edge of the hard stratum in the channel reaches grade. By continuation of the process which transformed the falls into rapids, the rapids become less rapid, and when the upper edge of the hard layer has been brought to grade, the rapids disappear (h, Fig. 112). The history of rapids which succeed falls is the reverse of that which preceded. The later rapids are steepest at the beginning of their history, the earlier at their end. Stated in other terms, rapids are steepest when nearest falls in time. Slight differences in hardness in successive layers often occasion successive falls or rapids (Fig. 114).

If the hard layer which occasions the falls be horizontal, instead of dipping up-stream, the general result would be the same; but, other things being equal, the duration of the falls developed under these conditions would be greater, since they must recede farther before becoming rapids.

If the layers of unequal hardness in a stream’s bed be vertical and the course of the stream at right angles to the strike, rapids, and perhaps falls, will develop (Fig. 115). The chances for falls are greater, the greater the difference in hardness. Falls developed under these conditions, as well as the rapids preceding and following, would remain constant in position until the resistant layer was brought to grade, but they would ultimately disappear as in the preceding cases. Falls are not likely to develop where the strata of the stream’s bed dip down-stream, though they may develop even under these conditions if the gradient of the stream is greater than the dip of the strata (Fig. 116).

The inequality of resistance in the rock which occasions a fall may be original or secondary. In the case of Niagara Falls (Fig. 113) relatively resistant limestone overlies relatively weak shale. At the Falls of St. Anthony (Minneapolis) limestone overlies friable sandstone. The falls of the Yellowstone and the Shoshone Falls of the Snake River (Idaho), are in igneous rock. In the former case the unequal resistance is occasioned by unequal decay of the rock, due perhaps to the rise of hot vapors which have decomposed the rock along the lines of their ascent; in the latter, a more resistant sort of igneous rock overlies a less resistant.

Structural features, such as jointing, sometimes give rise to falls, or determine their distinctive features (Fig. 117), even where the formations involved are of uniform hardness. A joint plane has the effect of a weak vertical or highly inclined bed. If an open joint is discovered in a stream’s bed, the water enters it. If it finds an outlet below, a channel is worn along the new line of flow, with rapids or falls where the water descends. Rock originally homogeneous may be much fractured in some parts, while it remains unbroken in others. Where a stream passes from the solid to the broken portion rapids, or even falls, may develop.

Falls may originate in still other ways. If for any reason a stream is forced out of its valley, it may in its flow find entrance to another valley, or to another part of its own valley, over a steep slope. If the structure of the slope favors, a fall may speedily develop. The Falls of St. Anthony are an example, the Mississippi having been turned out of its earlier course by deposits of glacial drift. Again, if an obstruction of any sort, such as a flow of lava, dams a stream, rapids or falls are developed where the water overflows the dam. When a main valley is notably deepened by glaciation the drainage from tributary valleys may fall into it, if the tributaries were not equally deepened. Falls which originated in this way are common in the western mountains of the United States, as well as in most mountain regions recently affected by local glaciers (Fig. 118).

One waterfall often breeds others. Thus where a fall recedes beyond the mouth of a tributary stream, the tributary falls. The Falls of Minnehaha, on a small tributary to the Mississippi, near Minneapolis, may serve as an illustration. In such cases the falls may not develop from rapids. Once in existence, the fall of a tributary follows the same history as that of a main stream.

Streams which have falls are relatively clear. If a stream favorably situated for the development of a fall carried a heavy load, deposition would take place below the rapids, and the tendency would be to aggrade the channel at that point and so to prevent the development of the fall. Falls occur only on streams which have relatively high gradients. This means that the streams which have falls are well above base-level, and streams well above base-level are young. Falls therefore are a mark of topographic youth.

The fall of the Niagara (Pl. IX) is one of the most remarkable known, both because of its large volume of water and its great descent, between 160 and 170 feet. The rate at which the fall is receding is a matter of interest not only in itself, but because, once determined, it may be made to serve as a unit of measurement for certain important events in geological history. It was formerly conjectured that this fall was receding at the rate of one to three feet per century, but it was not until recent years that its actual rate of recession was approximately fixed. By surveys executed in 1842 and 1890 it has been determined that its average rate of recession between those dates was something like 4½ feet per year, or about 150 times as great as the highest estimate stated above. It is to be noted that this is the average rate of recession, for all parts of the ledge over which the water falls are not receding at the same rate. The point of the “Horseshoe” has, during the same time, gone back at more than twice this rate.

Rapids and falls sometimes occasion the development of pot-holes (Fig. 119), a peculiar rather than important erosion feature. The holes are excavated in part by the falling and eddying of silt-charged water, but chiefly by stones which the eddies move. Pot-holes which are not now in immediate association with rapids or falls often point to the former existence of rapids or falls.

=Rock terraces.=—The tendency to sapping shown in many waterfalls is also shown in the weathering and erosion of the sides of a valley where a hard layer outcrops above the bottom, and the profile of the side slopes of the valley simulates that of the stream; that is, the slope becomes gentle just above the hard layer, and steep, or even vertical, at and below its outcrop. This is illustrated by Fig. 120, where the hard layer through which the stream has sunk its valley stands out as a rock terrace on either side of the valley. Such terraces are not rare and are popularly believed to be old “water-lines”; that is, to represent the height at which the water once stood. In one sense this interpretation is correct, since a river has stood at all levels between that of the surface in which its valley started, and its present channel, but the shelf of hard rock does not mean that the river, after attaining its present channel, was ever so large as to fill the valley to the level of the terrace. Rock terraces may also result from changes of level.

=Narrows.=—Inequalities in hardness occasion another peculiarity common to valleys. If a stream crosses vertical or highly inclined strata of unequal hardness, its valley is usually constricted at the crossing of the harder layers. If such a constriction be notable it is called a narrows, or sometimes a water-gap (Figs. 121, 159, and Fig. 2, Pl. XII). The Appalachian Mountains afford numerous examples. The constriction arises because the processes which widen the valley are less effective on the hard layer than on the less resistant ones on either hand. Though most narrows are due to the superior resistance of the rock where they occur, they are sometimes the result of other causes.

Narrows are much more conspicuous in certain stages of erosion than in others. While a valley is still so young as to be narrow at all points, no narrows will be conspicuous; but at a later stage in its history, when the valley is otherwise wide, narrows are more pronounced. At a still later stage, when the hard strata themselves approach base-level, the narrows again become inconspicuous.

From what has preceded it is clear that rapids or falls are likely to occur at narrows, especially in the early part of their history.

=Other effects on topography.=—Inequalities in the hardness of rock develop certain peculiarities of topography other than those of valleys. The less resistant portions of a land area more or less distant from streams are worn down more readily than those which are more resistant. If great areas of high land be capped with hard rock they are likely to remain as plateaus after surrounding areas of less resistance are brought low. If the hard capping affects a small area instead of a large one, the elevation is a butte, a hill, or a mountain, instead of a plateau (Fig. 110). Many buttes and small mesas are but remnants of former plateaus (Mesa Lauriano, N. M., Fig. 1, Pl. XII). A feature of buttes and mesas capped by hard rock is the steep slope or cliff corresponding to the edge of the hard bed (Figs. 78 and 109).

If the rock of a region be stratified and the layers tilted, the removal of the softer beds leaves the harder ones projecting above the general level in the form of ridges or “hog-backs” (Figs. 122 and 123). Dikes of igneous rock, harder than the beds which they intersect, likewise become ridges after the degradation of their surroundings. The plugs of old volcanic vents and other igneous intrusions of limited area often constitute conspicuous hills or mountains after erosion has removed their less resistant surroundings (Fig. 124). Inequalities of hardness are therefore responsible for many hills and ridges. In the isolation of the hills and ridges picturesque coves are developed, where the attitude and distribution of the weak and strong rocks are propitious. The bottoms of the coves are located on the weak rocks, and above them rise the precipitous slopes of the resistant ones. Round valley (Fig. 1, Pl. XVII, High Bridge, N. J., quadrangle, U. S. Geol. Surv.) and the coves about the head of Hiawassee River (Dahlonega, Ga., quadrangle) are examples.

Ridges and hills resulting from the unequal degradation of unequally resistant terranes are not equally prominent at all stages in an erosion cycle. In early youth the material surrounding the hard bodies of rock has not been removed; in early maturity considerable portions of their surroundings still remain about them; but in late maturity or early old age the outcropping masses of hard rock have been more perfectly isolated and are most conspicuous. Most of the even-crested ridges of the Appalachian system, as well as many others which might be mentioned, became ridges in this way. In the final stages of an erosion cycle the ridges of hard rock are themselves brought low. Isolated remnants of hard rock which remain distinctly above their surroundings in the late stages of an erosion cycle (Fig. 124) are known as Monadnocks, the name being derived from Mount Monadnock, N. H., an elevation of this sort developed in a cycle antedating the present.

=Adjustment of streams to rock structures.=—Valleys (gullies) locate themselves at the outset without immediate regard to the hardness and softness of their beds. It is primarily the slope about the head of a gully which determines its line of growth, though relative hardness often determines the details of slope, even in the early stages of an erosion cycle. Once established, streams tend to hold their courses, even if this involves the crossing of resistant layers.

While a region where more and less resistant layers of rock come to the surface is in a youthful stage of erosion, some of the valleys (and therefore the streams) are likely to be located on the less resistant rock, some on the more resistant, and some partly on the one and partly on the other. The streams on the weaker rock will deepen their valleys more rapidly than the others, and those which flow across stronger and weaker rocks alternately will deepen their valleys more rapidly than those which run on hard rock all the time. The former conclusion is self-evident. The latter appears from the fact that rapids will be likely to develop at the crossing of each hard layer, thus accelerating erosion at those points. Such a stream therefore not only has less hard rock to erode than one which flows on resistant rock all the time, but it erodes that which it does cross much faster.

Streams which do not cross hard layers therefore have an advantage over those which do, and the tributaries to such streams, since they join deeper mains, have an advantage over the tributaries to the others. The valleys of the former may lengthen until their heads reach the latter, and capture their streams. This sequence of events is illustrated in the accompanying diagrams (Figs. 125–27). Even where several streams cross the same resistant bed, piracy is likely to take place among them, for some are sure to deepen their valleys faster than others, because of inequalities of volume, load, or hardness. This is illustrated by Figs. 128–30. An actual case is shown in Figs. 131, 132. Though piracy may take place when streams do not flow over rock of unequal hardness (p. 103), it is much more common where unequal resistance of the rock puts one stream at a disadvantage as compared with another.

The changes in the courses of streams, by means of which they come to sustain definite and stable relations to the rock structure beneath, are known as processes of adjustment. Since streams and valleys adjust themselves to other conditions as well, this phase of adjustment may be called structural adjustment. Structural adjustment is not uncommon among rivers flowing over strata which are vertical or highly inclined, since in these positions the hard and soft strata are most likely to come to the surface in frequent alternation. The smaller streams suffer capture and adjustment first, since, as a rule, they have shallower valleys. It often happens that main streams, because of their deeper valleys, hold courses not in adjustment with structure (the Delaware, the Susquehanna, etc.), while tributary streams are captured, diverted, and adjusted. The capture of a tributary, however, leads both to the diminution of its main and to the increase of its captor, and the weakened stream may ultimately fall a prey to the one which is strengthened.

The processes of adjustment go on until the streams flow as much as possible on the weaker beds, and as little as possible on the stronger, when adjustment is complete. This amounts to the same thing as saying that the outcrops of the hard layers tend to become divides. In many cases an area is so situated that there is no escape for its drainage except across resistant rock. In this case its drainage is completely adjusted when as few streams as possible cross the resistant rock, and these by the shortest routes.

Adjustment has been carried to a high degree of perfection in most parts of the Appalachian system. Here, as in all other mountains of similar structure, strata of unequal hardness were folded into ridges. In this case, the folds have been truncated by erosion, exposing the more and the less resistant beds (H and S respectively) in alternate belts along the flanks of the truncated folds (ab and cd, Fig. 133). The streams, especially the lesser ones, now flow along the strike of the softer beds much more commonly than elsewhere, and where they cross the hard layers it is usually at right angles to the strike. This is shown in Fig. 134, where the arrows indicate the direction of strike. In the history of these rivers, however, a factor is involved which has not yet been considered, and these streams will be referred to later.

As base-level is approached, the outcrops of hard rock are brought low. When they have been reduced to the level of their surroundings, the streams may flow without regard to the resistance of the rock beneath, for downward cutting has ceased. As this stage of erosion is approached, a readjustment of the drainage may take place, and the waters which had taken long and circuitous courses to avoid hard rock, may change their courses to more direct ones (compare Figs. 130 and 135). Adjustment is, therefore, a relative term, and streams which are adjusted at one stage of erosion, are not necessarily adjusted at another.

It sometimes happens that rocks of unequal resistance are covered by beds of uniform hardness. A consequent stream developed on the latter may find itself out of structural adjustment when it has cut its channel down to the level of the heterogeneous beds below. Such a stream is said to be superimposed (Fig. 136) on the underlying structure. Structural adjustment is likely to follow.

INFLUENCE OF JOINTS AND FOLDS.

=Joints.=—Various structural features of rock other than hardness influence its erosion. Apart from the stratification planes, most rock formations are affected by joints or fissures. The joints are often, but not always, nearly vertical. Two sets are generally present, and sometimes more. If but two, they usually meet at a large angle; if more than two, two are likely to be nearly perpendicular to each other, while the third and fourth sets have such directions as to cut the others at large angles. These joints allow the ingress of water, roots, etc., which help to weather and disrupt rocks. Occasionally there is notable sag of the beds of rock along joint planes, but this effect is usually superficial only (Fig. 137). Where the jointage planes are frequent and open, the columns bounded by them sometimes topple over on cliff faces, either by undercutting, or by the wedge-work of roots or ice.

The effect of joints on erosion may often be seen along a stream which flows in a rock gorge. In such situations, the outlines of the banks are sometimes angular, and sometimes crenate (Fig. 138), the reëntrants being located at the joints. By working into and widening joints, running water sometimes isolates masses of rock as islands (Fig. 139). In a region free from mantle rock, or where the mantle rock is meagre, joints often determine the courses of valleys by directing the course of surface drainage. This is shown in many parts of the arid west. In regions where the rocks are notably faulted, the courses of the streams are sometimes controlled by the courses of the fault planes. This is the case, for example, in central Washington.

The jointing of rocks often shows itself distinctly in the weathered faces of cliffs (Figs. 140 and 141), especially in arid and semi-arid regions, or where the slope is too steep for the accumulation of soil and rock-waste on its surface.

If a stream flowing over jointed rock has falls, the conditions are sometimes afforded for the development of an exceptional and striking scenic feature. If above Niagara Falls, for example, there were an open joint in the bed of the stream (as at b, Fig. 142), some portion of the water would descend through it. After reaching a lower level it might find or make a passage through the rock to the river below the falls. If even a little water took such a course, the flow would enlarge its channel, making a passageway between the joint through which the water descended and the valley below the falls (bcde, Fig. 142). This passageway might become large enough to accommodate all the water of the river. In this case, the entire fall would be transferred from the position which it previously occupied (f) to the position of the enlarged joint (b). The fall would then recede. The underground channel between the old falls and the new would be bridged by rock (bf″ and f‴, Fig. 143), making a natural bridge. The natural bridge near Lexington, Va. (Fig. 144), almost 200 feet above the stream which flows beneath it, is believed to have been developed in this way. A similar bridge is now in process of development in Two Medicine River in northwestern Montana (Fig. 145). Once in existence, a natural bridge will slowly weather away.

It is not to be understood that all natural bridges have had this history. They are sometimes developed from underground caves when parts of their roofs are destroyed, as well as in various other ways.

=Folds.=—The erosion of folded strata (anticlines and synclines) leads to the development of distinctive topographic features. So soon as a fold begins to be lifted, it is, by reason of its position, subject to more rapid erosion than its surroundings. For the same reason the crest of the fold is likely to be degraded more rapidly than its lower slopes, and must suffer more degradation before it is brought to base-level. Folds are usually composed of beds of unequal resistance, and as the degradation of a fold proceeds, successive layers are worn from the top, and the alternating hard and soft layers composing it are exposed. So soon as this is accomplished, adjustment of the streams is likely to begin, and the watercourses, and later the valley plains, come to be located on the outcrops of the less resistant layers, while the outcrops of the harder beds become ridges.

If the axis of an eroded anticline were horizontal, a given hard layer, the arch of which has been cut off, would, after erosion, outcrop on both sides of the axis. When the topography was mature these outcrops would constitute parallel ridges, or parallel lines of hills; when the region had been base-leveled, the outcrops would be in parallel belts, though no longer ridges or hills. The lower the plane of truncation, the farther apart would the outcrops be in the anticline, and the nearer together in the syncline (compare ab and cd, Fig. 133).

If, on the other hand, the axis of the anticline or syncline to be eroded was not horizontal, that is, if it plunged, the topographic result would be somewhat different. Suppose a plunging anticline to be truncated at base-level. If either end of the fold plunged below the plane of truncation, the outcrops of a given layer on opposite sides of the axis would converge in the direction of plunge, and come together at the end. At a stage of erosion antedating planation (say late maturity) there would have been a ridge, or a succession of hills, in the position corresponding to the outcrop of a hard layer, with a canoe-shaped valley within. If two hard layers were involved, instead of one, there would be two encircling ridges, with a curved valley between them, and a canoe-shaped valley within the innermost (Fig. 146). If the anticline plunged both ways, the valley enclosed by the hard-layer ridge would be canoe-shaped at both ends (Fig. 147). In such a case there would be likely to be a low gap (water-gap) in the rim of the valley through which the drainage which degraded the surface escaped, but there would be likely to be but one, for if two or more streams had drained the area of the valley at an early stage of erosion, one would be likely to have captured the others (see p. 138) before late maturity. A succession of doubly-plunging anticlines and synclines might give rise to a very complex series of ridges and valleys. Illustrations of the above phenomena are found at various points in the Appalachian Mountains, especially in eastern Pennsylvania.

In the structural adjustment which goes with the erosion of folds, it often happens that the valleys come to be located on the anticlines, while the outcrops of the hard layers on the flanks of the anticlines, or even in the original synclines, become the mountains. The adjustments by which valleys come to be located on anticlines are somewhat as follows: Fig. 148 represents two doubly-plunging anticlines with a syncline between, the relative elevations being shown by contour lines. At the outset, the drainage of such a region must have followed the structural valley, and its initial course, consequent on the slope, must have been down the axial trough. Drainage from the anticlines into the synclines would have promptly developed valleys, and the valleys would soon have acquired streams.

The anticlines and synclines under consideration are assumed to have a thick hard layer at the surface, and softer beds below. This is shown in the cross-section introduced in the figure, the upper hard stratum (m) being indicated by the dots, while the softer one (n) is white. The line oo represents base-level, which is below the hard layer both in the syncline and anticline, but much farther below in the latter position than in the former. Because of their higher gradients, and because of the greater fracturing to which the region they drain was presumably subject at the time of folding, the tributary streams might cut through the hard layer sooner than the main stream which they join. This done, they would enlarge their valleys rapidly in the softer rock beneath, and secondary tributaries would be developed (Fig. 149). When the condition of things represented in Fig. 149 is reached, the streams c and d, tributary to the synclinal stream, come into competition. The former has the advantage over the latter, because it joins the main stream at a lower level. Stream c will therefore be likely to capture d. The incipient stages of the capture are stealthy, and the later bold. At first the divide between their head waters is shifted northward inch by inch, because the gradient toward g is higher than that toward e. The capture of the head waters of e is as slow as the migration of the divide, until the divide reaches the point where e joins f. The stream f is then diverted promptly into the valley of g, and is at once led away to c (see Fig. 150). Strengthened by its increased volume, the stream c (Fig. 150) lowers its valley across the hard layer more rapidly than before, and so holds the advantage it has gained. Not only this, but the beheaded stream d (Fig. 150), because of its diminished volume, sinks its valley into the hard layer less rapidly than before, and its decrease in power also works to the advantage of the stream leading to c. The result is that the divide between fg and d does not remain constant, but is driven back step by step toward a.

Similarly a tributary to the main stream at b (Fig. 150), may by means of its tributary h, capture the waters of fg, and lead them to the synclinal valley at b (compare Figs. 150 and 151). Deprived of its main source of supply (at c) the synclinal stream is greatly diminished above b, and cuts more and more slowly, while the stream fgh (Fig. 151), having greater volume and working mainly in softer rock, sinks its channel faster than the stream in the synclinal axis. Under these circumstances, the stream at f may cut its valley below the valley in the synclinal axis a (Fig. 150). In this event, the divide between f and a (Fig. 150) may be pushed back until the synclinal stream is beheaded at a and carried out of the syncline and over into the anticlinal valley (Fig. 151). Thus, the old anticlinal axis comes to be the course of the main stream. Similarly the stream entering the syncline at b (Fig. 151) might later be captured by i, thus lengthening its anticlinal course.

It is not to be understood that this sequence of events will take place in the degradation of every anticline, but the principles here set forth will always be operative. The result specified will be accomplished wherever hard and soft layers have the relations indicated in the diagrams; that is, where the stream in the syncline finds itself on a resistant layer as it approaches base-level, while at the same time the (original) tributary streams are working in softer beds. It is not to be understood, therefore, that streams migrate from synclines to anticlines for the sake of getting out of the former positions into the latter. If they shift their courses it is to find easier ones.

That these changes are not fanciful is shown by the fact that the adjustment described corresponds with that shown in many parts of the Appalachian Mountains, and in other mountains of similar structure.

If in a later stage of its history, the new main stream, fh, were to cut its bed down to a lower hard layer, while the original stream, ab, reached a softer bed beneath the hard one above, the latter would again have an advantage, and a new series of adjustments would be inaugurated which might result in re-establishing the main stream in its original synclinal position.

EFFECT OF CHANGES OF LEVEL.

=Rise.=—If after being base-leveled, or notably reduced by erosion, a region is uplifted so as to increase the gradients and therefore the velocities of the streams which drain it, the streams are said to be rejuvenated, and a new cycle of erosion is begun. If the rise of the area were equal everywhere, while the coast line remained constant in position, there would be an immediate increase in velocity only at the debouchures of the streams flowing directly into the sea. At the debouchures of such streams there would be rapids or falls. Each rapids or falls would promptly recede, and with the recession, the acceleration of velocity resulting from the uplift would be felt farther and farther up-stream, and ultimately to its source. The rejuvenated streams would cut new valleys in the bottoms of their old ones (Figs. 152 and 153). The new valleys would begin where the increase in velocity was first felt, and they would be lengthened by head erosion just as valleys of the first cycle were lengthened.

When the head of the new part of a valley of a rejuvenated stream recedes past the mouth of a tributary adjusted to the gradient of the main stream before rejuvenation, the velocity of the tributary is accelerated at its debouchure, and it begins to excavate a new valley in the bottom of its old one. The new valley commences at the lower end of the old one, and develops headward (a and b, Fig. 153). Good illustrations are furnished by the streams in the west central part of New Jersey. The Delaware has here a sharply defined valley, and its tributaries are essentially as deep as their main at the point of junction. Above this point they have high gradients for a short distance (three to six miles), beyond which they wind sluggishly in wide valleys with low gradients across a relatively high plateau. Their profiles are illustrated by Fig. 154. The flat, though high, surface in which their upper courses lie, appears to have been nearly base-leveled in an earlier cycle, and then to have been elevated. The date of the elevation is fixed, in terms of erosion, by the time necessary for the excavation of the Delaware gorge, and the narrow gorges along the lower courses of its tributaries. It was so recent that the effects of rejuvenation, proceeding from the debouchures of the tributaries toward their heads, have not yet advanced far from the Delaware. Similar relations are found elsewhere (Fig. 1, Pl. XIII, s. c. Col.). Another peculiarity of rejuvenated drainage is shown in Fig. 2, Plate XIII (s. Kan.). Here Elm Creek flows at a level 200 feet below that of Sand Creek, 4 miles distant. The valley of the former appears to have entered upon a new cycle as the result of uplift, while that of the latter, in the area shown on the map, is still unrejuvenated. Farther down-stream, the valley of Sand Creek shows signs of rejuvenation. It may be noted that a tributary of Amber Creek has good opportunity to capture Sand Creek, for the latter flows about 25 miles before reaching the level of Amber Creek at its junction with Elm Creek.

Fig. 1. COLORADO. U. S. Geol. Surv.

Fig. 2. KANSAS. U. S. Geol. Surv.]

Fig. 1. PENNSYLVANIA. U. S. Geol. Surv.

Fig. 2. CALIFORNIA. U. S. Geol. Surv.]

Should the lower end of a tributary valley fail to be degraded as fast as the valley of the main at the point of junction, the tributary is out of topographic adjustment with its main. Falls or rapids may result. When the lower end of a tributary valley is distinctly above the level of its main, the former is called a hanging valley. Hanging valleys developed by stream erosion alone are not common except just after the recession of a falls past the mouth of a tributary. Hanging valleys, as well as the characters and relations illustrated by Figs. 152–154 are criteria of rejuvenation, but they must be applied with discretion. Such profiles, for example, as that shown in Fig. 154 may be developed when the rock of a stream’s bed is unequally resistant, and hanging valleys are generally a result of glaciation (see Chapter V).

Rejuvenated streams sometimes inherit certain peculiarities from their aged ancestors. Thus a rejuvenated stream may intrench the meanders possessed by the old stream which preceded (see Fig. 1, Pl. XIV, near Harrisburg, Pa.), and intrenched meanders are one of the marks of rejuvenated streams. They are not uncommon in the Appalachian Mountain regions, and are known in other parts of the world. The Seine and the Moselle furnish further illustrations.

The history of the new cycle of erosion inaugurated by the uplift would differ from that of the preceding cycle in that the new one would begin with a drainage system already developed. Other things being equal, therefore, the reduction of the land would proceed more rapidly in a subsequent cycle than in the first.

The recognition of different cycles of erosion, separated by uplifts, is often easy. The principles involved are illustrated by Fig. 155 which represents an ideal profile of considerable length (say 50 miles). The points a, a′, and a″ reach a common level. Below them there are areas b, b′, and b″ which have a nearly common elevation, below which are the sharp valleys d, d′, and d″. The points a, a′, and a″ represent the cross-sections of ridges formed by the outcrops of layers of hard rock. If the crests of the ridges are level, the points a, a′, and a″ must represent remnants of an old base-level, since at no time after a ridge of hard rock becomes deeply notched does it acquire an even crest, until it is base-leveled. At all earlier stages its crest is uneven. After the cycle represented by the remnants a, a′, and a″ was completed, the region suffered uplift. A new cycle represented by the plain b, b′, and b″ was well advanced, though not completed, when the region was again elevated, and the rejuvenated streams began to cut their valleys d, d′, and d″ in the plain of the previous incomplete cycle. The elevations, c and c′ (intermediate in elevation between a, a′, and a″, and b, b′, and b″) may represent either remnants of the first base-level plain which were lowered, but not obliterated, while the plane b, b′, b″ was developing; or they may represent a cycle intermediate between that during which a, a′, a″ and b, b′, b″ were developed. If the intermediate elevations (c, c′) have a common height and level crests, the presumption would be in favor of the latter interpretation. If they be numerous and of varying heights, as is possible, they may in the field obscure the planes (a, a′, a″ and b, b′, b″) developed in the different cycles, which, in the figure, are distinct.

If the strata involved be horizontal the determination of cycles is sometimes less easy. Thus in Fig. 156, it is not possible to say whether a and a′ represent remnants of an old base-level, or whether they represent the original surface from which degradation started. So, too, the various benches below a, such as b, b′, and b″ may readily be the result of the superior hardness of the beds at this level. For the determination of successive uplifts in the field it is necessary to consider areas of considerable size, and to eliminate the topographic effects of inequalities of hardness, and of certain other factors to be mentioned presently.

The inequalities in the depths of the young valleys in Figs. 155 and 156 may be explained on the supposition that the deeper ones belong to main streams, and the shallower ones to tributaries. Such a valley as that shown at e, Fig. 155, suggests rejuvenation at this point; but farther up the stream which occupies this valley, rejuvenation might not be apparent. In this case, the main streams might be flowing in new valleys, d, d′, etc., while the heads of their tributaries are still flowing in the older valleys of the preceding cycle (compare Fig. 154 and Fig. 1, Pl. XIII).

It is by the application of the preceding principles that it is known that the Appalachian Mountains, after being folded, were reduced to a peneplain (p. 76), throughout their whole extent from the Hudson River to Alabama. The peneplain level is indicated by the level crests of the Appalachian ridges, shown in cross profile by the high points of Fig. 157. The system was then uplifted, and in the cycle of erosion which followed, broad plains were developed at a new and lower level, corresponding in a general way to the plains b, b′, and b″ of Fig. 155. The plains were located, for the most part, where the less resistant strata come to the surface. Above them rose even-crested ridges, the outcrops of the resistant layers, which had been isolated by the degradation of the softer beds between. They constitute the present mountain ridges (the high points of Fig. 157). The evenness of their crests, testifying to the completeness of the first peneplanation, is shown in Fig. 158, which represents, diagrammatically, a longitudinal profile of an Appalachian Mountain ridge. The evenness of the crest is interrupted by (1) notches (b, c, etc., Fig. 158) cut by the streams in later cycles, and (2) by occasional elevations above the common level (monadnocks, a, a′, Fig. 158). The monadnocks are generally rather inconspicuous, but there is a notable group of them in North Carolina and Tennessee. Mount Mitchell and Roane Mountain are examples. When long distances are considered, the ridge crests depart somewhat from horizontality. This is believed to be due, in part at least, to deformations of the old peneplain during the uplift which inaugurated the second cycle of erosion.

The extent to which the second cycle of erosion recorded in the present topography had proceeded before its interruption by uplift, is indicated by the extent of the valley plains (Fig. 157) below the mountain ridges. While these plains were being developed on the weak rocks, narrow valleys only (Fig. 158) were cut in the resistant rocks which now stood out as ridges. In Fig. 158 some of these valleys are shallow (c, c′, c″, etc.), and but one of them deep. The former may be either (1) the valleys of streams which crossed the hard layer at the beginning of the cycle, and which were diverted before their valleys became deep; or (2) they may represent the heads of valleys now working back into the ridges. The deep valley (b) represents the work of a stream which has held its course across the hard layer while the latter was being isolated as a mountain ridge (compare Figs. 131 and 132). Deep narrows of this sort are often called water-gaps. Similar valleys, whether shallow or deep, from which drainage has been diverted, are sometimes called wind-gaps. The second cycle of erosion, while still far from complete, was interrupted by uplift (relative or absolute), and a new cycle inaugurated. This event was so recent that the new (third) cycle has not yet advanced far.

Recently it has been urged that another cycle, intermediate between the first and second, is to be recognized.

Some of the features just described are illustrated by Fig. 159. The even mountain crest in the background is the Kittatinny Mountain of New Jersey and its continuation in Pennsylvania. In common with other corresponding crests it represents the oldest recorded base-level (or peneplain) of the region. The great gap in the mountain is the Delaware Water-Gap. Below the mountain crest there is another plain, developed in a subsequent cycle of erosion, while the valley plain in the foreground represents the work of a still later cycle.

The oldest erosion plain of the Appalachian Mountains, the results of which are seen in the even-crested ridges so characteristic of the system, is sometimes called the Kittatinny base-level. It was completed early in the Cretaceous period, and hence is sometimes known as the Cretaceous base-level. The next lower plain, imperfectly developed, has been called the Shenandoah Plain, from the Shenandoah Valley where it is well seen (Fig. 132 and Fig. 2, Pl. XII). It is to be noted that the terms base-level and peneplain have both been used in connection with these old plains. Graded plain is equally applicable. The truth is that the topographic types represented by these three terms grade into one another. It may be questioned whether definitions should be insisted on which differentiate these types more sharply than Nature has.

Many of the peculiarities of the drainage of the Appalachian Mountain system are intimately connected with the history just outlined. Thus three great rivers, the Delaware, the Susquehanna, and the Potomac, have their sources west of the Appalachians proper, cross the system in apparent disregard of the structure, and flow into the Atlantic. The James and Roanoke head far to the west, although not beyond the mountain system, and flow eastward, while the New River (leading to the Kanawha) farther south, heads east of the mountain-folds, and flows northwestward across the alternating hard and soft beds of the whole Appalachian system, to the Ohio (Fig. 160). The French Broad, a tributary to the Tennessee, has a similar course. Such streams are clearly not in structural adjustment, and afford good opportunities for piracy. Their courses were apparently assumed during the time of the Kittatinny base-level, when the streams had so low a gradient as not to be affected by the structure (p. 150). Elevation rejuvenated them, and they have held their courses in succeeding cycles across beds of unequal resistance, though smaller streams have become somewhat thoroughly adjusted. Crustal deformations have also helped them to hold their courses, for the Cretaceous peneplain seems to have been tilted to the southeast at its northern end, and to the southwest at its southern, when the succeeding cycle began.

Streams which hold their early courses in spite of changes which have taken place since their courses were assumed are said to be antecedent. They antedate the crustal movements which, but for pre-existent streams, would have given origin to a different arrangement of river courses. As a result of crustal movements, therefore, a consequent stream may become antecedent. Master streams are more likely to hold their courses, and therefore to become antecedent, than subordinate ones.

The uplift of base-leveled beds, especially if the beds are tilted so as to bring layers of unequal resistance to the surface at frequent intervals, affords conditions favorable for extensive adjustment. The numerous wind-gaps in the mountain ridges, representing the abandoned courses of minor streams, and the less numerous water-gaps, which indicate the resistance of large streams to structural adjustment, are instructive witnesses of the extent to which adjustment has gone. So extensive has been the adjustment among the streams of the Appalachian Mountains that there is probably no considerable stream in the whole system which has not gained or lost through its own or its neighbors’ piracy. The history of the rivers of the Appalachian Mountains has been further complicated by a considerable amount of warping during the periods of uplift.

=Sinking.=—The land on which a river system is developed may be depressed relative to sea-level. In this case the sea would occupy the lower ends of valleys, converting them into bays and estuaries. A stream in this condition is said to be drowned. Of drowned rivers there are many examples along the Atlantic coast. Thus the St. Lawrence River is drowned up to Montreal, and the Hudson up to Albany. If the drowned portion of the latter valley were not so narrow, it would be a bay. Delaware and Chesapeake Bays, as well as many smaller ones, both north and south, are likewise the drowned ends of river valleys (see figures, Chapter VI). If all parts of a drainage basin sank equally, the velocities of the streams above the limit of drowning would not be changed, for the gradients would remain the same as before. The fact that a river’s channel is below sea-level is not to be taken as proof that the valley is drowned. Thus the bottom of the channel of the Mississippi is as much as 100 feet below the level of the Gulf, some 20 miles above New Orleans.

=Differential movement. Warping.=—Where a land surface on which a river system is established suffers warping, some parts going up and others down, the opposite movements being either absolute or relative, various phenomena would result. This may be illustrated by the accompanying diagrams (Figs. 161 and 162), where the profiles of the streams are represented as warped from the positions represented by the dotted lines, to the positions shown by the full lines. The velocity will be accelerated below the points of differential elevation (between a and b, Fig. 161, and between a and b, and c and d, Fig. 162), but checked above (above a, and between b and c, Fig. 162). Above an elevation which notably checks its flow, a stream is ponded. If the ponding is slight, a marsh may develop above the obstruction; if more considerable, a lake is formed. Lakes of this class are likely to be short-lived, since the ponded waters are likely to soon overflow and lower their outlet so as to drain the lake. The elevation which ponds the stream may be great enough and rapid enough so that the resulting lake finds an outlet by some course other than that originally followed by the stream. Where a stream holds its course across an uplift athwart its valley, either with or without ponding, it becomes an antecedent stream (see p. 169), since it has a course assumed before the latest deformation of the crust and in apparent disregard of present surface configuration. Thus the Columbia River holds its antecedent course across areas which have been uplifted (differentially) hundreds and even thousands of feet. Some of the striking scenic features of this noble valley are the result of these changes in the country through which it flows. A lesser stream would have been diverted, as many of its tributaries have been. Even its course across the Cascade ranges is believed to be antecedent.

Another peculiarity of valleys and streams resulting from changes of level is illustrated in Fig. 2, Pl. XIV (southern California). The main valleys of this part of the coast were developed when the land stood considerably higher than now. Later the subsidence of the coast converted the lower ends of the valleys into bays or fiords. The bays were then transformed into lagoons by deposition. Subsequent rise of the land or depression of the sea allowed the drainage from the old lagoons to cut across the deposits which had converted the bays into lagoons. The result is an old, wide valley above, suggested by a young one below.

If the warpings were considerable, much more decisive changes in drainage would result. Suppose the drainage of a given region to be represented by the streams in Fig. 163. If there is uplift along the axis 1–2, that part of ac above the axis of uplift would be ponded, or at least have its velocity checked, while the flow of some of the tributaries of d would be accelerated, and might work back and capture the other stream (Fig. 164).

Crustal warping was one of the conditions under which the Tennessee achieved its present anomalous course, and its history is illustrative of the complex changes which drainage suffers when warping affects the area where the rock structures are of unequal resistance. At the close of the Cretaceous cycle of erosion, when the Appalachian Mountains had been reduced to a peneplain, the waters falling in the area now drained by the upper course of the Tennessee flowed south-south-west to the Gulf in a stream (the Appalachian River, a, Fig. 165) the lower part of which had the general position of the Coosa and the Alabama.

To the west of the Appalachian River, shorter streams flowed west and southwest into the Mississippi embayment (Fig. 165) by courses which are not now definitely known. The succeeding cycle of erosion was inaugurated by uplift and deformation of the peneplain. The axis of greatest elevation (AB, Fig. 166) was nearly parallel to the Appalachian River, and the effect of the differential uplift was to impose a greater task on this river (a, Fig. 166), which flowed along the axis of uplift, than upon the rivers which flowed westward and southwestward to the Mississippi embayment. The result was that the strongest of the southwesterly flowing streams worked its head back into the drainage basin of the Appalachian River, and captured, one by one, the head-waters of its westerly tributaries, establishing some such drainage relations as are shown in Fig. 166. Still later, after the land area of the region had been considerably extended by the withdrawal of the sea, the Appalachian River itself was reached by the invading stream, and its waters carried away to the Mississippi Bay by a course the lower part of which is thought to have corresponded approximately with the course of the present Black River (b, Fig. 167).

Still later there was further deformation which caused additional changes in the drainage. The whole region was uplifted, relatively if not absolutely, but the uplift was differential, being greatest along the axis represented by AB, Fig. 167. The effect of the deformation was to stimulate the tributaries of the Ohio flowing north from this axis. Their growth was further accelerated by the weakness of the strata over which they ran. At the same time, the uplift to the south led the southwesterly flowing stream (b, Fig. 167) to discover relatively hard beds of rock in its lower course, and these beds retarded its down-cutting. The result was that a tributary of the Ohio (a, Fig. 167) finally tapped the main stream flowing to the southwest (b, Fig. 167) and carried its upper part over to the Ohio (Fig. 168). This was the beginning of the present Tennessee.

THE AGGRADATIONAL WORK OF RUNNING WATER.

=Principles involved.=—Since deposition results from the failure of transportation, the factors which control transportation also influence deposition. Transportation by streams is determined largely by velocity, and the most important factors influencing velocity are slope, volume, and load (p. 115). Of these the first two are usually of greater importance than the third.

A stream is said to be loaded when it has all the sediment it can carry; it is loaded with fine material when it has all the fine material it can carry, and with coarse material when it has all the coarse it can transport. A stream loaded with coarse material flows more swiftly than one loaded with fine, for a larger percentage of a stream’s energy can be utilized in carrying fine material than coarse, and hence a larger percentage of the energy of a stream which carries a load of the latter will express itself in velocity.

Deposition takes place whenever a stream finds itself with more load than it can carry, and is an expression of the stream’s refusal to remain overloaded. A stream may become overloaded in various ways. It might at first seem unnecessary to inquire whether a stream may be overloaded at its source, but the question is not necessarily to be answered in the negative. The source of a stream is not always a definite point. In a general way it may be said that the source of the normal stream is at that point in its valley where the bottom is as low as the ground-water level of the region. But since the ground-water level is not constant (p. 71) the source of a stream is likely to be farther up its valley in a wet season than in a dry one (p. 72). After a heavy shower, the run-off descends to the axis of the valley from the slopes on all sides, and temporarily the stream begins above the point which marks even its wet-season source. If under such circumstances the slopes about the head of the valley are notably steeper than the slope of the valley itself, as they frequently are, the water flowing down them may gather an amount of material which it cannot carry after it reaches the bottom of the valley. This may be the case at, or even above, the point which marks the source of the permanent stream. It is, therefore, possible for a stream to be overloaded at its source, if we take the source to be the point whence the water permanently flows. Deposition may, therefore, be taking place in a valley at the head of its permanent stream, or temporarily even in the valley above it.

Streams issuing from glaciers sometimes have more load than they can carry after they escape from the ice. If the stream be regarded as beginning at the point where it issues from beneath the ice it may be overloaded at its source.

Under certain circumstances, a stream may overload itself. Thus if a stream loaded with coarse detritus reaches a portion of its valley where fine material is accessible in abundance, some of the velocity which is helping to carry the coarse may be used in picking up and carrying the fine. This reduces the velocity, and since the stream already had all the coarse material it could carry, reduction of velocity must result in deposition. It follows that when a stream fully loaded with coarse material picks up fine, it becomes overloaded, so far as the coarse material is concerned.

Again, tributaries may overload their mains. While tributaries are usually smaller than their mains, they frequently have higher gradients, and the smaller stream of higher gradient may bring to the larger stream of lower gradient more material than the latter can carry away. Thus deposition may take place at the point of junction of tributaries with their mains. This may go so far as to pond the latter enough to cause its expansion into a river-lake. Lake Pepin, in the Mississippi River at the mouth of the Chippewa (in Wis.), is an example.

Streams may become overloaded by losing velocity or volume, or both. Decrease in velocity is brought about either by decrease in declivity or in volume. In general, streams have lower gradients and greater volumes in their lower courses than in their upper, and these two elements affect velocity in different ways. If the increase in volume be not enough to counterbalance the decrease in declivity, as is often the case, a stream which is loaded in its upper course will deposit in its lower. The decrease of velocity at the debouchure of a stream almost always leads to deposition.

Decrease in velocity as the result of decrease in volume is less common. When decrease in volume occurs, it may be the result of (1) evaporation, (2) the absorption of water into the bed of the stream, or (3) branching—the giving off of distributaries. While evaporation is going on everywhere, the diminution of a stream by this means is usually more than balanced by the increase from tributaries, rainfall, and springs; but in arid regions a very different condition of things sometimes exists. If mountains in an arid region be capped with snow, its melting supplies the streams during the melting season. As the streams flow out from the mountains through dry regions, they receive little or no increment from rainfall, tributaries, or springs, and evaporation reduces the volume of water, or even dissipates it altogether. Absorption of water into the bed of the stream often accompanies evaporation. Reduction of volume by evaporation and by absorption is especially common in arid regions. Wherever loaded streams are reduced in volume, whether by evaporation or absorption, deposition takes place.

The third way by which velocity is decreased as the result of decreasing volume is illustrated at the debouchures of many streams. Near the Gulf, for example, the Mississippi branches repeatedly (see Fig. 190). The same phenomena are often seen where one stream joins another (Fig. 169). Individually the distributaries are much smaller than the main stream before they separated from it, and because they are smaller their combined surfaces are greater, and the amount of energy consumed in the friction of flow is increased. The velocity of the water and its carrying power are, therefore, reduced. Thus the branching of streams gives rise to deposition, and where deposition takes place the gradient of the stream is reduced, and this occasions still further deposition. The sediment which fills up the channel and checks the flow finally compels the stream, or some part of it, to transgress its banks. Deposition, therefore, favors the development of distributaries, and the development of distributaries in turn favors deposition.

The foregoing statements make it clear that a stream may be eroding in one part of its valley while it is depositing in another, and that erosion may alternate with deposition in the same place, on account of fluctuations in volume, and, therefore, in velocity of the stream. It will be seen in the sequel that erosion and deposition may be taking place at the same time in the same part of the valley. The activities of a river are so nicely balanced that slight disturbance at one point causes disturbance at all points below.

The deposits.

=Types.=—Turning from the principles which underlie river deposition to the deposits themselves, they are found to occur in various situations. Running water usually descends from steeper slopes above to gentler slopes below, and ends at the sea, or in a lake or inland basin. Wherever there is a sudden decrease in its gradient, as at the base of a hill, ridge, or mountain, running water is likely to leave a large part of its load, building an alluvial fan or cone (Figs. 67, 68, and Pl. VI). Even where there is no sudden decrease in the gradient of a stream, there is likely to be a gradual one, and in spite of the fact that the increased volume of a stream in its lower course tends to overcome the effect of diminished gradient on velocity, deposition is likely to take place as the gradient is reduced. Deposits occasioned by the gradual reduction of a stream’s velocity often have great extent in the direction of a stream’s flow. They cover the flood plains of streams, making them alluvial plains (Fig. 73). When a stream reaches the sea or a lake its current is destroyed and its load dropped, unless taken in charge by the waves and currents of the standing water. Sediment accumulated in quantity at the debouchures of streams gives rise to deltas (Figs. 169, 187). Alluvial cones and fans, alluvial plains, and deltas, are the principal types of river deposits. Apart from these well-defined types there are bars in the channels of depositing streams, and much ill-defined alluvium which does not allow of ready classification.

=Alluvial fans and cones.=—The only distinction between the alluvial fan and the alluvial cone is one of slope, the cones (they are but half-cones at best) being steeper than the fans. Alluvial fans and cones have their most striking development where temporary torrents, occasioned by showers or the rapid melting of snow, issue from mountain ravines. Such streams usually carry heavy loads of detritus, the coarser part of which is likely to be deposited at the base of the mountain slope. Cones and fans built by such streams have a periodic rather than a steady growth.

At the beginning of its development the material of the alluvial cone is deposited much as in a talus cone (compare Fig. 170 with Figs. 67 and 68). Its deposition chokes the channel of the stream, and some of the water then seeks new courses to right and left of the apex of the deposit. This expands the area of deposition to right and left, while the water which flows over it lengthens it in the direction of flow.

The course and behavior of the water after reaching an alluvial cone is instructive. As its velocity is checked, deposition often takes place in the channel, diminishing its capacity. As the channel is filled up, the water tends to overflow on either side. The overflowing water, being shallow, has so little velocity that much of its load is dropped on either margin of the channel, building up levees. The water ever and anon breaks through the levees, giving rise to distributary streams, each of which aggrades its channel and builds its own miniature levees (Fig. 171). Not rarely this process of channel-filling and levee-building goes on until the channels of the little rivulets are above the general level of the cone on which they rest. The rivulet then runs in a groove on the crest of a little ridge. The channels on the surfaces of fans and cones are fewest and deepest at their heads, and more numerous and shallower below. In some cases the surface-water disappears altogether before the outer border of the fan is reached, by sinking into the débris.

Alluvial fans and cones have various forms, and often attain considerable dimensions. Their angles of slope depend on the amount of reduction of velocity which the depositing water suffers, and the amount and kind of load which it carries. The maximum slope of the cone is the angle at which the loose material involved will lie. The minimum slope of the fan, on the other hand, approaches horizontality. If many alluvial fans develop in proximity to one another, as at the base of a mountain range, they may expand laterally until they merge. A long succession of them may thus give rise to an extensive alluvial piedmont plain, or a compound alluvial fan. The lower edge of such a fan is often somewhat lobate. Such plains exist along the bases of many mountain ranges (Pl. VI), and may be seen in miniature even along low ridges.

A permanent stream, as well as a temporary one, may develop an alluvial fan at the base of a mountain slope; but since the mountain course of the former is likely to be less steep than that of the latter, its waters suffer a correspondingly less reduction of velocity at any one point. The fan of the permanent stream is therefore likely to be relatively flat, and to stretch far down the valley. Such fans grade into valley plains. From the general principles already discussed, it is clear that well-developed fans go with relatively youthful stages of erosion, and belong normally to the upper parts of drainage lines.

=Ill-defined alluvium.=—There is a widespread mantle of alluvial material deposited by running water which was not organized into distinct streams. The water which runs down smooth slopes in sheets during showers carries fine earthy matter, as well as some that is coarser. These materials are largely deposited at the bases of the slopes, forming basal accumulations of greater or less extent, comparable in origin to alluvial fans. A relatively small amount of the slope wash is carried far out from the base of the declivities. It is not easy to realize the extent to which this process is taking place. There is hardly a slope without loose material, and there is hardly an acre of low land below a slope on which running water has not deposited sediment washed down from above. When it is remembered that this is as true of gentle slopes and their surroundings as of steep slopes, though perhaps not to the same extent, and that a very large part of the earth’s surface is made up of sensible slopes, or of flats at their bases, some idea of the aggregate effect may be gained.

There is another way of looking at the same question. Earthy matter is being continually transferred from land to sea, and chiefly from high land. Rarely does it start from any point distant from the shore and move uninterruptedly to it. It is transported a short distance and lodged, to be again picked up, carried forward another step in its journey, and lodged again. For a very large part of the earth’s surface it would be true to say that its mantle rock is material in transit from higher land to the sea.

=Alluvial plains.=—Most streams, whether heading in mountains or not, have gentler gradients in their lower courses than in their upper, and in spite of increasing volume are usually unable to carry to their debouchures all the material gathered above. The excess of load is dropped chiefly on the flood-plains of the streams and constitutes them alluvial plains.

The making of an alluvial plain usually involves both erosion and deposition. When a stream has cut its channel to grade, downward erosion ceases, or more exactly, downward cutting is, on the average, counterbalanced by deposition. So long as a stream is cutting downward rapidly, it carries away whatever débris descends the side slopes. When it approaches grade, the débris which descends the side slopes tends to accumulate at their bases, and the V-shaped cross-section of the valley becomes U-shaped (see Fig. 172). At about the same time the stream begins to meander, for, having lost something of its former velocity, it is more easily turned from side to side. As it begins to meander, it widens the bottom of its valley. This is the initial stage in the development of the valley flat (2 and 3, Fig. 172). In its meandering the stream encroaches on the talus accumulations at the bases of its valley’s slopes. The side-cutting may remove all the loose débris and even undercut the bluff as at a, Fig. 173. The stream’s meanders shift their positions from time to time so that the valley flat is successively widened at different points. By lateral planation, therefore, a stream tends to develop a flat as soon as it reaches grade. This is the initial part of erosion in the making of a river flat, but a flat developed by erosion alone is not an alluvial plain.

So soon as the flat developed by a stream exceeds the width of its channel, the water (except in times of flood) does not cover it all at the same time. On any part which it temporarily abandons, some débris (alluvium) is likely to be left. This deposit of alluvium constitutes the valley flat an alluvial plain (Fig. 174). It will be seen that the valley flat is commonly an alluvial plain from the beginning.

Once the valley flat and alluvial plain are begun, their further development is easily followed. The stream in flood overflows the banks of its channel. The velocity of the overflowing water is reduced, and if it has much load a part of it will be dropped and the plain aggraded. Meantime meandering and lateral planation continue. Thus the flood-plain is widened by erosion, and aggraded by alluviation, the two processes going on simultaneously.

Flood-plains, chiefly the result of planation, but partly of aggradation, are a normal feature of river valleys, after a certain stage of development has been reached. This stage is that at which downward erosion becomes slight in comparison with lateral erosion. It follows that an alluvial plain normally begins its development where the valley is first brought to grade, that is, in its lower course. As the development of the valley goes on, the head of the flood-plain advances up-stream, and at the same time its older parts become wider.

=Flood-plains due to alluviation only.=—Exceptionally, an alluvial plain is developed by deposition only. Thus if a stream becomes overloaded while its valley is still narrow, as sometimes happens, deposition follows, and, as aggradation proceeds, the narrow valley acquires a progressively wider bottom (Fig. 175). Wide valley plains are sometimes developed in this way. Flood plains developed wholly by alluviation are sometimes formed under conditions which are independent of the stage of a valley’s development. Thus if a stream suddenly acquires an exceptional supply of detritus in its upper course, the development of an alluvial plain begins immediately below the point of overloading.

The overload might be acquired in various ways. (1) If a stream taps another (piracy) which carries a large quantity of sediment, carrying off both water and sediment to a channel with a lower gradient, deposition may take place where, under the earlier conditions, there was none. (2) Again, when a stream cuts through a barrier near its head waters, its velocity, and, therefore, its eroding power, may be so increased in its upper course that sediment enough is acquired to occasion deposition below, where none took place before. (3) In working back through formations of varying degrees of resistance, a stream’s head may presently reach a formation or a region which yields abundant sediment, even though there was no especial barrier below. (4) If an advancing glacier should reach the head waters of a stream, its discharge to the stream would greatly increase the load of the latter, and, although its volume would be augmented at the same time, deposition might result. As a matter of fact, streams carrying glacial drainage are usually aggrading streams. In general, anything which greatly increases the load of a stream near its head is likely to cause deposition, and so the development of a flood plain, at some point farther down the valley.

Streams which are actively aggrading their valleys are likely to anastomose (Figs. 176, 177). This results from the filling of the channels until they are too small to accommodate all the water. The latter then breaks out of the channel at few or many points. The new channels thus established suffer the same fate.

=Flood-plains due to obstructions.=—Again, any obstacle in a stream’s course is likely to cause deposition above. Thus dams built across rivers entail the deposition of sediment above. Where a stream flows over the outcropping edges of strata of different strength, the more resistant serve, in some sense, as dams. Above them the stream cuts its bed to a low gradient, and, becoming sluggish, drops more or less of the detritus brought down from above. Obstacles of any sort across a stream’s channel, therefore, favor the development of alluvial plains.

=Levees.=—As the stream in flood escapes its channel and overspreads its plain, its immediate banks are the site of active deposition, for it is here that the velocity of the overflowing water is first notably checked. On the banks of the channel, therefore, low alluvial ridges, called natural levees, are built up (Fig. 178, and Pl. XV). They may be narrow, or hundreds of feet in width, and are often several feet above the plains behind them, giving the latter a slope away from the channel of the stream. They are sometimes high enough to control the courses of tributary streams, as shown by numerous tributaries to the Mississippi below the Ohio. The Yazoo, for example, flows some 200 miles on the flood-plain of the Mississippi before it joins that river near Vicksburg. The levees even become divides, directing drainage away from the streams they guard (Pl. XV). Streams sometimes build levees faster than their tributaries aggrade their channels. The latter are then ponded, giving rise to lakes. The lakes on the lower courses of the tributaries to the Red River of Louisiana are examples. They are sometimes built up above their natural level and kept in repair by human agency so as to confine the streams in time of flood. This is a source of danger unless they be steadily maintained, for the breaking of such levees often occasions great destruction. A case in point is the breaking of the levees of the Mississippi near New Orleans in 1890. The water broke through the levees at the Nita and Martinez crevasses (Fig. 187) and flowed eastward (from the former) with a current of 15 miles per hour, spreading destruction in its path. The water flowed eastward through Lakes Pontchartrain and Borgne, and entered Mobile Bay with such volume, velocity, and load of mud, as to destroy for a time the oyster and fish industries of that locality.

NEAR HAHNVILLE, LOUISIANA. U. S. Geol. Surv.]

Fig. 1. MISSOURI. U. S. Geol. Surv.

Fig. 2. MISSOURI. U. S. Geol. Surv.

Fig. 3. MISSOURI. U. S. Geol. Surv.]

=Flood-plain meanders. Cut-and-fill.=—A stream with an alluvial plain is likely to meander widely (Pl. XVI). In general terms this may be said to be the result of low velocity, which allows it to be easily turned aside. Were the course of such a stream made straight, it would soon become crooked again. The manner of change is illustrated by Figs. 180 and 181. If the banks be less resistant at some points than at others, as is always the case, the stream will cut in at those points. If the configuration of the channel is such as to direct a current against a given point, a (Fig. 180), the result is the same, even without inequality of material. Once a curve in the bank is started, it is increased by the current which is directed into it. Furthermore, as the current issues from the curve, it impinges against the opposite bank and develops a curve at that point. The water issuing from this curve develops another, and so on.

Once started, the curves or meanders tend to become more and more pronounced (compare Figs. 180 and 181). In the case represented by Fig. 1, Plate XVI (Missouri River near Brunswick, Mo.) the narrow neck of land between curves is almost cut through. When this is accomplished, the stream will abandon its wide curve. A later stage in the process is shown in Fig. 2, Plate XVI (the Osage River near Schell, Mo.).

The straightening of the channel is often accomplished in another way. Even before the meanders reach the stage represented by Fig. 1, Plate XVI, the position of the channel becomes unstable. In time of flood, the whole flat is covered with flowing water. The greater depth of water in the channel tends to give it a velocity greater than that of the water on the flat outside. But the distance from a to c via b (Fig. 181) is much greater than that in a direct line. It follows that the slope from a to c direct is greater than that by way of b. If the current between a and c in time of flood be strong enough to erode, it may deepen its bed, and thereby increase the volume of water following this course. The increased volume gives increased velocity, and the result may be the opening of a channel between a and c direct. The channel may be worn so deep that when the flood subsides, the stream will follow it. So long as the abandoned channel-curve remains unfilled with sediment, it is often called a cut-off. If it contains standing water and has the proper form, it is called an ox-bow lake (Fig. 182), or sometimes a bayou. The water-filled portions are not always bows (Fig. 183, Osage River, near Butler, Mo.). Cut-offs, with or without standing water, are of common occurrence along most rivers with wide plains. Meandering is not confined to streams which are near sea-level. Even small creeks at high altitudes may meander, if so situated as to have slight velocity. Trout Creek in the Yellowstone Park (Fig. 184) is an example.

There seems to be some relation between the width of the belt within which a stream meanders, and the width of the stream itself. Recently it has been estimated that the ratio between them is 18 : 1.

During the development of the meanders it is to be noted that lateral planation on the one side of a stream is accompanied by deposition on the other. This is cut-and-fill. The sediment eroded from the curve which is concave toward the stream is shifted down-stream, while that deposited in the curve which is convex toward the stream is brought down from above. Thus even in the development of meanders, the material which is dislodged is shifted down-stream. Since the current directed against the down-stream side of a growing meander is on the average stronger than that directed against the opposite side, the meander itself has a tendency to migrate down-stream (Fig. 182).

In their evolution, the curves of a stream’s channel often reach and undermine the valley bluff (Pl. VII). Since the meanders are, on the average, shifted down-stream individually, and since meanders are frequently developed in new places, it follows that a meandering stream tends to widen its valley throughout. Widening is also effected in other ways, for a stream with a flood-plain sometimes abandons its channel altogether for miles at a stretch, and the new course chosen may be against one of the bluffs of the valley. Such changes are most likely to take place where deposition along channel and levees has brought the part of the flood-plain (though not necessarily the bottom of the channel) adjacent to the stream above the level of that farther from it (Fig. 178). The change is likely to be effected in time of flood.

Flood-plains often attain great size. That of the Mississippi below the Ohio (Fig. 179) has a width ranging from rather more than 20 miles at Helena (Ark.), to something like 80 miles in the latitude of Greenville (Miss.). Below the Ohio its area is something like 30,000 square miles, and its entire area has been estimated at about 50,000 square miles.

Theoretically, the rotation of the earth should affect the erosion of streams, increasing it on the one bank (the right in the northern hemisphere and the left in the southern) and decreasing it on the other. The streams doubtless accommodate themselves to the rotation of the earth in the original development of their gradation-plains and flood-plains, and the later effects of rotation are usually inconspicuous.

=Scour-and-fill.=—It has already been shown that aggrading streams cut laterally at the same time that they build up their plains. It is now to be added that they periodically deepen their channels to a notable extent, and that the deepening of the channel takes place at the very time when the flood-plain is being aggraded. In other words, the stream in flood aggrades its plain, and degrades its channel. This follows from the fact that the current is sluggish in the former position, where the water is shallow, and rapid in the latter, where it is deep. When the flood subsides, the channel, deepened while the current was torrential, is filled again by the feebler current which follows. This alternate deepening and filling is known as scour-and-fill. It is well illustrated by the Missouri River. At Nebraska City, scour is believed to occasionally reach depths of 70 to 90 feet. At Blair, about 25 miles above Omaha, the same river is believed to cut to bed-rock (about 40 feet below the bottom of the channel in low water) twice a year, that is, during floods. Fig. 185 shows the changes recorded in the channel of the river at this point during the year 1883. It shows that the scour-and-fill during this year amounted to almost 40 feet. All streams similarly situated do a like work. The material thus eroded is shifted down-stream, some of it for short distances only, and some of it to the sea. Even an aggrading stream therefore is not without erosive activity; it is a stream whose fill exceeds its scour, not one which has ceased to erode.

=Materials of the flood-plain.=—As a result of its varying velocities in flood and low water, a stream may deposit coarse material at one time and fine at another. A similar sequence of deposits takes place in the flood-plain of a meandering stream, irrespective of floods. Flood-plain deposits are often therefore very heterogeneous, as shown in Fig. 186, which represents the constitution of the alluvium of the Missouri River at Omaha. The deposits of the streams range from the finest clay, through sand to gravel, and even bowlders. In general they become finer down-stream. In a given plain, they are usually coarser below and finer above.

=Topography of the flood-plain.=—The flood-plain is nearly, but not altogether, flat. It has a gentle slope down-stream, and often for a distance from the sides toward the center (Fig. 174). This latter slope is the result of deposition by waters descending to the plain from the sides. It is destroyed wherever a meandering stream reaches its bluffs. When levees are well developed, there is a slope from them toward the sides of the valley (Fig. 178), but it rarely continues to the limiting bluffs. Since a stream with a well-developed flat frequently shifts its course, old levees and abandoned channels lend variety to the topography of the flood-plain.

=The topographic adjustment of tributaries.=—The meandering and shifting of a main stream affects its tributaries. If a main stream swings against the bluff through which a tributary enters, the latter brings its channel into topographic adjustment by lowering its end to the level of the main. If now the main stream opposite the tributary swings to the other side of its valley, the tributary must make its way across the flat with a very low gradient. Not only this, but the flat of the main valley through which the tributary must flow is likely to be aggraded by the main in time of flood. The result is that the tributary stream becomes an aggrading stream at its debouchure, and topographic adjustment is not established until it has filled up the lower end of its valley to some notable extent. The filling of the lower end of the tributary likewise affects the lower ends of its lower tributaries.

If the main stream again swings over to the point where the tributary issues from its valley, the tributary stream and all its affected tributaries again become eroding streams. Thus scour-and-fill are not confined to the valley of the main stream.

=River-lakes.=—While rivers are in general hostile to lakes, they sometimes give origin to them. Oxbow lakes (Fig. 182 and Pl. XVI), due to the cut-offs of meandering streams, have already been referred to. Lakes formed in the same way have other forms (Pl. XVI and Fig. 183). Rivers also give rise to lakes through the deposits they make. If a main stream obstructs its tributaries by deposition at their debouchures, their lower courses are ponded and converted into lakes. The lakes along the tributaries to the Red River of Louisiana have already been cited as examples. If a tributary brings more load to its main than the latter can carry away, the detritus constitutes a partial dam, ponding the river and causing it to expand into a lake above. Such is the origin of Lake Pepin already referred to. In mountain regions, the alluvial cones of tributary valleys sometimes pond their mains.

Rivers may be dammed in other ways, as by lava flows, by landslides, by glacial drift, etc. In all such cases, lakes may come into existence, but they are not due primarily to the activity of the river itself.

=Deltas.=—Where a stream enters standing water, or a slower stream, a special form of plain, the delta, is sometimes built up (Figs. 169, 187, and 188). Deltas and alluvial fans have much in common, and their only notable differences are those imposed by the differences in the conditions of deposition. The current of the stream is checked, but not altogether stopped, at its immediate debouchure. If it carries abundant sediment, much of it will be promptly dropped where the decrease in velocity is first felt. Such flow as there is beyond the debouchure is not confined to a definite channel, and the deposits made are therefore spread more or less on either side of the line which represents the continuation of the stream’s course.

As the depth of the water into which the stream flows increases, the current diminishes. Out to the point where the depth of the standing water is less than the depth of the current, the latter affects the bottom, and the surface of the deposits made slopes gently seaward; but where the depth of the standing water is such that the projected stream current is ineffective at the bottom, all the load rolled along the bottom is dropped, and a depositional slope is established (Fig. 188), its upper edge being below sea-level by an amount corresponding roughly to the depth of the current which brings the detritus. The outer slope is relatively steep and well-defined where the detritus is coarse, and relatively gentle and ill-defined where it is fine. Thus the stream tends to construct a sort of platform in the water just beyond its debouchure. The successive deposits on the outer abrupt slope will dip conformably with its surface (Fig. 189). The finest sediment will be carried beyond the steep slope, and conform to the topography of the bottom beyond (c, Fig. 189).

At the beginning, the top of the delta platform is at the level of the bottom of the stream’s channel at the point of debouchure, but it is gradually aggraded as water continues to flow over it. Its landward margin is presently built up to sea-level and then above it, and as the delta grows the delta-land is extended seaward (compare Figs. 188 and 189). At the same time the channel of the stream above the original head of the delta is aggraded, for the current there is checked by the aggradation of the delta. Thus alluvial deposits continuous with the delta are extended landward.

The projection of the direction of the lower end of the stream may be said to be the axis of the extra-debouchure current. From this axis, where the flow is strongest, the movement diverges more or less to right and left. Since the velocity of the diverging water is reduced more rapidly than that of the water which follows the axis of flow, deposition is likely to take place faster on either side of the axis than along the axis itself. The result is that the extra-debouchure current tends to build up levee-like ridges on either side, making a sort of sluice-way for itself. This sluice-way is gradually extended seaward, and at the same time gradually filled. As its capacity is reduced, more and more of the water flows over its sides. Presently the escape of the water over the little side-levees will develop a break at some point, and a line of distinct flow then diverges from the main current. This distributary repeats the history of its main. Thus the processes of levee-building, channel-filling, and levee-breaking follow one another, until some such system of currents as shown in Fig. 190 is developed. The result is that a delta’s growth is not simply in the line of extension of the main stream, but in a more or less semicircular area, the center of the circle being a point slightly below the position of the debouchure of the stream when the delta began. At any stage in its development the margin of the delta is more or less crenate (Fig. 191), or characterized by delta fingers (Fig. 190), the projections corresponding to the positions of the debouchures of the latest streams flowing across it. The extreme ends of the delta lobes (Fig. 190), and of groups of the delta fingers, often have something of the shape of the Greek letter from which the name originated, but the resemblance in form between a well-developed delta and the Greek letter is not striking. Deltas are sometimes built in bays, and in such cases their forms are predetermined on all sides but one. The head of a delta is sometimes arbitrarily located at the point where the first distributaries are given off. Since this point shifts widely with time, the definition can hardly be accepted. On this basis the head of the Mississippi delta is about 200 miles above its lower end. In reality it is much farther north.

The structure of a delta, shown in Fig. 189, shows its history. At any stage in its growth the river discharges its sediment across that part of the platform already built. The sediment rolled at the bottom of the current is dumped on reaching the steep slope, and constitutes the inclined fore-set beds shown in Fig. 189. The material in suspension is carried farther, settles more gradually, and constitutes the bottom-set beds (c, Fig. 189). In time the bottom-set beds, originally deposited some distance beyond the debouchure, may come to be overlain by the fore-set beds, deposited at a later time. While the fore-set beds are being deposited on the steep slopes of the delta, and the bottom-set beds beyond, deposition is also taking place on the top of the delta. These top-set beds are laid down in a nearly horizontal position, and their seaward margin is gradually extended. Thus the delta comes to have the threefold structure shown in Fig. 189.

That part of the delta which is above the abrupt slope of its front corresponds in all essentials to an alluvial fan; but the delta as a whole differs from the fan in its abrupt and crenate or digitate margin.

It is to be noted that the delta is not wholly the product of a stream’s activity. The stream supplies the material, but the lake or sea renders at least passive assistance in its disposition. Not all rivers opening into the sea build deltas, and their failure is often the result of waves or shore currents which carry off the river sediment. Deltas are, however, sometimes formed in tidal seas, as at the debouchures of the Yukon; the Mackenzie, where the tidal range is three feet; the Niger, where the range is four feet; the Hoang-Ho, where the range is eight feet; and the Brahmaputra and Ganges, where the range is sixteen feet. Since lakes, bays, gulfs, and inland seas have weaker waves and currents than the open sea, they are more favorable than the latter for the growth of deltas. Hence occur such deltas as those of the Mississippi, the Nile, the Po, and the Danube.

Deltas are likely to be absent, or confined to the heads of bays, on coasts which have recently sunk. Their general absence on the Atlantic coast of the United States is a case in point.

The following figures give some idea of the extent of deltas, and of their importance in land building. The Mississippi delta is advancing into the Gulf at the rate of about 100 yards per year, or a mile in 16 or 17 years. Its length is more than 200 miles, its area more than 12,000 square miles, and its depth at New Orleans has been estimated at 700 to 1000 feet. This great depth is believed to be the result of subsidence, and so of the superposition of one delta on another. The delta of the Yukon has a sea margin of 70 miles, and extends more than 100 miles inland. The delta of the Rhône has also had a remarkable growth, considering the size and the history of the stream. Arles, near the debouchure of the stream, was 14 to 16 miles inland in the fourth century +B.C.+, and is now 30 miles inland. The Rhône has also built a great delta in Lake Geneva, and its lower delta is built of sediment gathered below the lake. The Po has built a delta 14 miles beyond Adria, the port which gave its name to the Adriatic Sea. The extension of this delta has been at the average rate of about 50 feet per year, but recently, on account of artificial embankments, the rate has been much more rapid. The Ganges and Brahmaputra together have made a delta of great size. Its area is sometimes estimated to be as high as 50,000 or 60,000 square miles, and its head is more than 200 miles from the sea. The head of the Nile delta is 90 miles from the sea, and it has a coastal border of 180 miles. The head of the delta of the Hoang-Ho is about 300 miles from the coast, and its seaward border has a length of about 400 miles, though with some highland interruptions.

After a delta has been built into a lake, the lake may disappear, leaving the delta out of water. Such “fossil” deltas, if so recently exposed that erosion has not destroyed their distinctive features, are readily recognized by their flat tops, their abrupt and lobate fronts, and their characteristic structure. They are often a means of determining the former existence of extinct lakes, or the former higher levels of lakes which still exist. Elevated deltas on seashores show either a rise of the land or a depression of the sea-level.

The material which is carried along the coasts or shores from the mouths of rivers may take on various and peculiar forms, according to the strength, direction, and relations of waves and currents. The consideration of these forms belongs more properly to the work of the sea than to that of rivers, since rivers are not concerned in their construction except in supplying material.

=Delta lakes.=—Delta-building streams sometimes help to form lakes by throwing their deposits around an area which fails to be aggraded to sea-level. Lake Pontchartrain, and other lakes in the delta of the Mississippi are examples (Fig. 187).

STREAM TERRACES.

Stream terraces are bench-like flats or narrow plains along the sides of valleys (Fig. 192). They are usually narrow, but sometimes have great length in the direction of the axis of the valley. They originate in various ways.

=Due to inequalities of hardness.=—Reference has already been made (p. 140) to the effect of hard horizontal layers in the development of terraces and terraciform projections on the sides of valleys (Fig. 120). Such terraces are the result of differential degradation, and the upper surface of the hard layer marks the lower limit of the terrace, which commonly has a distinct slope toward the stream. Except where interrupted by tributary valleys, such terraces are likely to be continuous in a valley so long as the structure remains the same and the stream sustains the same relation to it. Such terraces would first show themselves in the older part of the valley. The effect of inclination of the hard stratum on the development of such terraces will be readily inferred. Terraces and benches of this sort are not equally distinct at all stages of a valley’s history. For great distinctness, the hard layer should have been exposed long enough to allow the general processes of erosion to have effected considerable differential wear, but not long enough to allow the topographic effects of unequal resistance to be obliterated.

=Normal flood-plain terraces.=—It has been seen that deposition in a river valley stands in more or less definite relationship to the stage of its development, and that the deposition which leads to the development of an alluvial plain is likely to take place where the higher gradient of the upper course gives place to the gentler gradient of the lower. It has also been seen that as a stream’s history advances, the stretch where the gradient is high recedes up-stream, and that the point which marks the head of active deposition follows. It follows that a river flat or flood-plain normally begins in the lower part of a valley, and works progressively headward, its upper end following, at some considerable distance, the head of the valley itself.

The commoner river terraces are remnants of former flood-plains, below which the streams which made them have cut their channels. It has already been pointed out (p. 184) that processes of erosion and deposition work together in the development of flood-plains, and that some flood-plains have but little alluvium (Fig. 174), while others owe their origin wholly to stream deposits (Fig. 175). It follows that terraces developed from flood-plains may be of rock, of alluvium, or of rock covered with alluvium.

The amount which a river channel must be deepened in order to change the remnants of its flood-plain to terraces cannot be definitely stated. When a channel is so deep that the remnants of a former flood-plain are no longer flooded, they would be called terraces, especially if a lower flood-plain has been developed. Even though not above the reach of floods, they are often called terraces if they are notably above the channel and separated from it by a lower plain. Thus the flat at b, Fig. 193, would be called a terrace, even though covered by water in exceptional floods; but the flat at c, but slightly above the channel, would hardly be called a terrace.

The question now arises why a stream, having once developed a flood-plain, should sink its channel to a lower level, leaving parts of the old flood-plain as terraces. This may be brought about by the operation of various causes.

(1) In the first place, the head of the valley-plain where the first notable deposition takes place normally advances up-stream. After the advance has been considerable, the descending stream may, on reaching the head of its valley-plain, lose so much of its load as to be able to sink its channel into the flood-plain farther down the valley (Fig. 194).

(2) Ordinarily a stream does not drop all its load at the head of its plain, but only its excess; but it will always drop coarse sediment to take fine, if fine be available. For a relatively small amount of coarse material dropped, a relatively large amount of fine may be taken up (p. 179). Other things being equal, it follows that when a stream drops coarse material to take fine, its channel is degraded unless there is at the same time a great reduction in the stream’s energy. Such reduction is likely to go with the decreasing declivity down-stream; but this is partly, or sometimes wholly, counterbalanced by the increasing volume of water. By the exchange of load, therefore, a stream may ultimately sink its channel below the flood-plain which the earlier and perhaps smaller stream had developed.

(3) Again, so long as a stream is actively eroding at its head, there is likely to be some aggradation below. At a later stage in the stream’s history, when active erosion at the head has ceased because of the reduction of the surface, less material will be carried from the upper part of the valley, and the stream on the flood-plain below, formerly loaded with material from up the valley, is now free to take up and carry away material temporarily left on the flood-plain. The result is a deepening of the channel.

(4) Any stream which has reached the flood-plain stage is likely to meander. After the flood-plain has become wide, the width of the belt within which the stream meanders is less than the width of its plain. In the Lower Mississippi, for example, the meander belt is often no more than a third to a tenth of the width of the flood-plain. It has already been pointed out that the meanders migrate down the valley. In so doing they depress the meander belt, the tendency being to reduce it to the level of the channel, and, therefore, below the level of the flood-plain. As the meander belt widens, the depression which it develops becomes more and more capacious. Presently it may attain such dimensions as to hold the water of ordinary floods. At this stage, or even before, such parts of the earlier flood-plain as remain, are terraces.

These several tendencies conspire to partially destroy river flood-plains, and to transform such parts as remain into terraces in the normal course of a river’s history. They appear first in the lower part of the valley, and migrate headward, following the course of nearly every other phase of activity in a stream’s history. The heads of the terraces follow, at a respectful distance, the head of the flood-plain, just as the head of the flood-plain follows at a distance the head of the valley. The second and subsequent flood-plains and the terraces to which they give origin follow the same course.

Terraces developed by the normal activities of a stream are always low, and it is improbable that they would ordinarily be conspicuous. The vertical distance between the first (highest) and second is greater than that between the second and third. The principles developed on page 65 et seq., in connection with the erosion of the hypothetical island, are applicable here.

=Flood-plain terraces due to other causes.=—Certain other causes, accidental rather than normal to a stream, result in the development of terraces from flood-plains. (1) If there be uplift in a region where the rivers have flats, the streams are rejuvenated, and the remnants of their former flood-plains become terraces. (2) If an alluvial flood-plain has been built as the result of an excessive supply of sediment (p. 186), the exhaustion or withdrawal of the excessive supply would leave the stream again relatively clear, and free to erode where it had been depositing. It would forthwith set to work to carry away the material which it had temporarily unloaded on the plain. The plains built up in many valleys in the northern part of our continent during the glacial period, when the drainage from the ice coursed through them, have subsequently been partially destroyed by erosion, and their remnants have become terraces. A notable reduction in the amount of available sediment, even when the earlier supply was not excessive, produces a similar result. (3) A notable increase in the volume of a stream, without corresponding increase in load, as when one stream captures another, may occasion the development of terraces by allowing the stream to deepen its channel. (4) Above any barrier which dams a stream, a flood-plain is likely to be developed. When the barrier is removed the stream will cut more or less deeply into the plain above, leaving terraces. (5) The recession of a falls through a flood-plain converts such parts of it as remain, into terraces.

In conclusion, it may be stated that many river terraces, mostly very low, are normal features of valley development, coming into existence at definite stages in a valley’s history. They are generally composed, in large part, of river alluvium. Others result from more or less accidental causes, working singly or in conjunction, and to this class belong all of the more conspicuous terraces developed from flood-plains. The structure of a terrace often affords some clue to its origin (Fig. 196).

=Discontinuity of terraces.=—When a stream sinks its channel into its flood-plain, it does not follow that a terrace remains on each side. Where the stream’s deepened channel is in the middle of its flood-plain, there is, temporarily, a terrace on either side; but wherever the deepened channel is at one margin of its flood-plain, a terrace remains on the other side only. Even where continuous at the outset, terraces soon become discontinuous, for all processes of subaërial erosion conspire to destroy them. A stream is likely to meander on its second and later flood-plains, as on its first and highest one. Wherever the meanders on its second flood-plain reach the borders of the first flood-plain, the terrace at that point disappears, and since the meanders are continually migrating, terraces are continually disappearing. The same would be true of the second terrace, if a second were developed. The removal of portions of a terrace by the sweep of meanders is likely to leave the remnants cuspate toward the stream. Again, tributary streams, in bringing their channels into topographic adjustment with their mains, cut through the terraces of the latter. New gullies develop on the faces of the terraces and their heads work back across them, dissecting them still further. At the same time, sheet erosion and other phases of slope wash tend to drive the scarps of the terraces back toward the bluff beyond. By the time a second series of terraces is well developed, no more than meagre remnants of the first may remain.

From the foregoing considerations it is clear that the extent to which river terraces once developed, now remain, is dependent in part on the length of time which has elapsed since the river sank its channel below them. Other things being equal, the greater their age the more meagre their remnants.

Terraces developed from river plains formed chiefly by alluviation stand a better chance of long life than most other alluvial terraces. This is because of the configuration of the original valley, the aggradation of which gave origin to the plain. The principle involved is illustrated by Fig. 197. In developing the second flood-plain the river encounters the rock wall of the valley. This greatly retards lateral erosion, and the terrace above, defended by the rock, is likely to be long-lived.

Alluvial terraces, like rock shelves, are popularly thought to mark “old levels of the river.” In one sense this is true, but not in the sense in which the expression is commonly used. Every level, from the crest of the bounding bluffs to the bottom of a valley, is a level at which water ran for a longer or shorter time; but the terrace does not mean that the river was once so much larger than now as to fill the valley from its present channel to the level of the terraces.

=Termini of terraces.=—From the mode of development of terraces it will be seen that, traced up-stream, each terrace should theoretically grade into a flood-plain at its upper end (Fig. 194), and that the upper end of the second (from the top) terrace, where there are two, would not be so far up-stream as the upper end of the first (highest). This is represented diagrammatically in Fig. 198.

The down-stream termini of terraces are rarely distinct. This is partly because the notable meandering of the streams in their lower courses is antagonistic to the preservation of terraces. If all terraces once developed remained, and if delta-building proceeded without interruption from waves, the relations should be somewhat as follows: Traced down-stream, the cliff between the oldest (highest) terrace and the next younger becomes gradually lower until it finally disappears, and the continuation of the two is found in a common plain. The cliff between the second and third terraces should disappear in the same way, and below its disappearance the plain representing their continuation is continuous with that representing the continuation of the first and second. The cliff between the second and third terraces may or may not continue farther down-stream than that between the first and second. The plains below the terraces finally become continuous with the lowest flood-plain and with the delta. These relations can rarely be seen because of the destruction of the older terraces, and because of the erosion by waves along shore.

The topography of terraces is similar to that of flood-plains, except in so far as modified by erosion. While flat in general, the terrace may slope either toward or from the valley bluff, and its surface may be marked by all the minor irregularities which characterize a flood-plain.