Geology, Vol. 1 [of 3]

by Thomas C. Chamberlin; Rollin D. Salisbury

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′.

Fig. 36.—Diagram to illustrate the origin of lands by the lowering of the sea-level due to depression of the sea bottom. If the bottom is depressed from a to b the surface will be drawn down from cc′ to dd′, and the surfaces cd and c′d′ will become land.

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.[26] 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].

Fig. 37.—Diagram to illustrate the effect of rain erosion on an island where there is no deposition or wave erosion about its borders. The uppermost curve represents the original surface, while aa, bb, and cc represent successive surfaces developed by sheet erosion, on the supposition that no material is deposited along the shores.

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]).

Fig. 38.—Diagram to illustrate the final effect of rain erosion under the conditions specified in the text. The diagram expresses the final result of the processes suggested by [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.

Fig. 39–41.—Diagrams to illustrate the effect of rain erosion on an island when all the eroded material is deposited about the shore. The black portions represent deposition. The dotted lines represent the original surface. The several diagrams represent successive stages in the process.

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.

Fig. 42.—Diagram to illustrate the result of the continuation of the processes shown in Figs. 39–41.

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.

Fig. 43.—Diagram showing a slight meridional depression in the surface of an otherwise even-sloped island.

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.

Fig. 44.—Diagram illustrating the development of a gully, starting from the condition shown in [Fig. 43].

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.

Fig. 45.—Diagram to illustrate the effect of sheet and stream erosion on the outline of an island when no deposition takes place about its borders. The dotted line represents the original outline of the island, the full line its border at a later time. The stream develops a reëntrant (bay) in the outline.

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.

Fig. 46.—Diagram showing the outline of an island as modified by sheet and stream erosion where eroded material is deposited at the shore. The dotted line represents the original outline; the full line, a later one. The excess of deposition at the end of the valley causes a projection of land into the sea.

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.[27]

Fig. 47.—Diagram representing several meridional valleys developing in a circular island. The valleys are all young and narrow. All are making deposits at their debouchures.

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,[28] 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.

Fig. 48.—Same as [Fig. 47], with the valleys more developed. The dotted line represents the original outline of the island. Its area is being extended by deposition everywhere, but most at the debouchures of the streams.

Fig. 49.—A later stage of the island shown in [Fig. 48].

Fig. 50.—Diagram to illustrate the lowering of a divide without shifting it. The crest of the divide is at a, b, and c successively. If erosion were unequal on the two sides, the divide would be shifted.

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.

Fig. 51.—Diagram illustrating the further development of [Fig. 49]. The land here has been reduced greatly, though not yet to base-level.

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.

Fig. 52.—Diagram illustrating the fluctuation of a ground-water surface. a = wet-weather ground-water level; b = ground-water level during drought. Well No. 1 will contain water during the wet season, but will go dry in times of drought. Well No. 2 will be permanent.

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.

Fig. 53.—Diagram to illustrate the intermittency of streams due to fluctuations of the ground-water level. The water level aa would be depressed next the valley 2–2 by the flow of the water into the valley. The profile of the ground-water surface would therefore be aca rather than aa.

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.).

PLATE III.

U. S. Geol. Surv.

Scale, 2+ mile per inch.

Fig. 1. KANSAS.

U. S. Geol. Surv.

Scale, 4+ mile per inch.

Fig. 2. NEVADA.

PLATE IV.

U. S. Geol. Surv.

Scale, 1+ mile per inch.

Fig. 1. ILLINOIS.

U. S. Geol. Surv.

Scale, 2+ mile per inch.

Fig. 2. NORTH DAKOTA.

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.

Fig. 54.—Diagram to show how a valley may be developing all the way from a water-filled basin (lake) to the sea at the same time. Small valleys leading to the lake are also developing. The black area = the sea.

Fig. 55.—The stream leading out from the lake ([Fig. 54]) has drained the lake, and the valleys above and below the site of the former lake have united.

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.

Fig. 56.—Diagram showing the phases of valley development described in the text.

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.

Fig. 57.—Diagram representing the further development of the valleys fg and hi in [Fig. 56]. The head of the latter ([Fig. 56]) has worked back until it has reached the lower end of the former.

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]).

Fig. 58.—Structural valley with a river valley developing its bottom.

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

Fig. 59. Fig. 60.
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.

Fig. 61.—Diagram illustrating the development of two equal gullies from the head of one.

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.

Fig. 62.—Diagram to illustrate the oblique position of a tributary gully at its inception, and its later normal change of direction.

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.).