_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.

[Illustration: +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.

[Illustration: +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.

[Illustration: +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.

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.

[Illustration: +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.]

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]

[Illustration: +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.

[Illustration: +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.]

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

[Illustration: +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.

[Illustration: +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.

[Illustration: +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.

[Illustration: 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.).

[Illustration: PLATE III.

Fig. 1. KANSAS.

U. S. Geol. Surv.

Fig. 2. NEVADA.

U. S. Geol. Surv.]

[Illustration: PLATE IV.

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.

[Illustration: +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.]

[Illustration: +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.

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.

[Illustration: +Fig.+ 56.—Diagram showing the phases of valley

development described in the text.]

[Illustration: +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).

[Illustration: +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.

[Illustration: +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_.

[Illustration: +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.

[Illustration: +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.).

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.

[Illustration: +Fig.+ 63.—Diagram showing three parallel valleys in a

land surface.]

[Illustration: +Fig.+ 64.—Diagram to illustrate the lowering of the

surface by valley erosion. The successive cross profiles of the

valleys are represented by the lines 1–1, 1–1′, 2–2, 2–2′, etc.]

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.

[Illustration: +Fig.+ 65.—Diagram showing the dissection of the upland

shown in Fig. 64 by tributary valleys.]

[Illustration: +Fig.+ 66.—Diagram showing tributaries of several orders

developed from the conditions sketched in the text.]

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.”[29] 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,[30] 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.

[Illustration: +Fig.+ 67.—A gully developed by a single shower.

(Blackwelder.)]

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.

[Illustration: +Fig.+ 68.—A gully somewhat older than that shown in

Fig. 67. (Alden.)]

[Illustration: +Fig.+ 69.—A young valley in a region of slight relief.]

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.

[Illustration: PLATE V.

Fig. 1. KENTUCKY.

U. S. Geol. Surv.

Fig. 2. VIRGINIA.

U. S. Geol. Surv.]

[Illustration: PLATE VI.

PARTS OF LOS ANGELES AND SAN BERNARDINO COUNTIES, CALIFORNIA.

U. S. Geol. Surv.]

[Illustration: +Fig.+ 70.—The valley (canyon) of the Yellowstone. A

young valley in an elevated region.]

[Illustration: +Fig.+ 71.—Mature erosion topography in a region of

slight relief, Iowa. (Calvin.)]

[Illustration: +Fig.+ 72.—Mature erosion in a mountain region. From

mouth of Gray Copper Gulch, Silverton, Colo., quadrangle. (Cross,

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.

[Illustration: +Fig.+ 73.—Mature erosion in a mountain region.

Silverton, Colo. (Cross, U. S. Geol. Surv.)]

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.

[Illustration: +Fig.+ 74.—A peneplained surface where the elevations

are small but steep-sided. Near Camp Douglas, Wis. (Atwood.)]

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.

[Illustration: PLATE VII.

Fig. 1. KANSAS.

U. S. Geol. Surv.

Fig. 2. KANSAS.

U. S. Geol. Surv.]

[Illustration: PLATE VIII.

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.

[Illustration: +Fig.+ 75.—Bad-land topography. North of Scott’s Bluff,

Neb. (Darton, U. S. Geol. Surv.)]

[Illustration: +Fig.+ 76.—Toadstool Park, Sioux Co., Neb. The peculiar

topography is the result of erosion working on jointed rocks of

unequal hardness in an arid region of considerable elevation where

rainfall is unequally distributed. (Darton, U. S. Geol. Surv.)]

=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.

[Illustration: +Fig.+ 77.—Detail of bad-land topography. Head of Indian

Draw, Washington Co., S. D. Protoceras sandstone on Oreodon clay.

(Darton, U. S. Geol. Surv.)]

[Illustration: +Fig.+ 78.—Detail of bad-land topography. Southwest foot

of Mesa Verde, Colo. (Matthes, U. S. Geol. Surv.)]

[Illustration: +Fig.+ 79.—Grand Canyon of the Colorado. (Peabody.)]

[Illustration: +Fig.+ 80.—Grand Canyon of the Colorado. (Peabody.)]

[Illustration: +Fig.+ 81.—Diagram showing the relations of depth and

width of a valley, the width of which is eight times the depth.]

While all canyons are valleys, most valleys are not canyons. The

distinction between a canyon and a valley which is not a canyon is not

sharp. The canyon depends for its distinctive character on the relation

of depth, width, and angle of slope to one another; but any definition

of the depth, width, and angle of slope necessary to constitute a

valley a canyon is arbitrary.[31] In popular usage the rule seems to

be that if a valley is sufficiently deep, narrow, and steep-sided to

be distinctly striking, it is called a canyon in regions where that

term is in use. Whether a valley is deep, narrow, and steep-sided

enough to be striking clearly depends on the observer. The Colorado

Canyon (Figs. 79 and 80) is the greatest canyon known, but it is rarely

more than a mile deep, and where its depth approaches this figure it

is often eight, ten, or even twelve miles wide from rim to rim. Its

width at bottom is little more than the width of the stream; that is,

a few hundred feet. Its cross-profile throughout much of its course

is therefore not in keeping with the conventional idea of a canyon.

With a depth of one mile and a width of eight, the slope, if uniform,

would have an angle of less than 15°. Such a valley is represented in

Fig. 81. As a matter of fact the slopes of a canyon are not commonly

uniform. The slopes represented in Fig. 82 correspond more nearly than

those of Fig. 81, to the actual slopes of the Colorado Canyon. The

inequalities of slope are occasioned by the inequalities of hardness.

It is perhaps needless to say that to an observer on the rim of the

canyon the slopes seem several times as steep as those shown in the

diagrams.

Like all valleys which are narrow relative to their depth, the Colorado

Canyon, great as it is, is a young valley; for it represents but a

small part of the work which the stream must do to bring its drainage

basin to base-level.

While aridity and altitude are conditions which favor the development

of canyons, as shown by the fact that most canyons are high and dry

regions, they are not indispensable. Niagara River has a canyon below

its falls (Pl. IX), and the surrounding region is neither high nor

arid. The narrow part of the valley has been developed by the recession

of the falls, and is so young that side erosion has not yet widened the

valley or lowered its angle of slope to such an extent as to destroy

its canyon character. This canyon is often called a _gorge_, a term

frequently applied to small valleys of the canyon type.

[Illustration: +Fig.+ 82.—Cross-section of the Colorado Canyon. (After

Gilbert and Brigham.)]

[Illustration: +Fig.+ 83.—Detail of erosion in the Grand Canyon.

The inequalities of slope are the result of unequal hardness. The

vertical planes which give the architectural effect are the result of

joints. (Holmes.)]

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.

[Illustration: +Fig.+ 84.—A surface illustrating the struggle for

existence among gullies. Most of the smaller gullies shown on the

slope can have but little growth before being absorbed by their

larger neighbors. A type of erosion surface common in the Bad Lands.

Scott’s Bluff, Neb. (Darton, U. S. Geol. Surv.)]

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.

[Illustration: PLATE IX.

NIAGARA FALLS.

U. S. Geol. Surv.]

[Illustration: PLATE X.

Fig. 1. YELLOWSTONE PARK.

U. S. Geol. Surv.

Fig. 2. ARIZONA.

U. S. Geol. Surv.]

[Illustration: +Fig.+ 85.—Diagram illustrating the absorption of one

gully by another by lateral erosion. The successive lines represent

successive cross-sections.]

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.

[Illustration: +Figs.+ 86–88.—Diagrams to illustrate successive stages

in the struggle for existence and dominion among streams.]

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.

[Illustration: +Figs.+ 89 and 90.—Diagrams to illustrate piracy.]

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.

[Illustration: +Fig.+ 91.—Diagram showing the shifting of a divide

after piracy.]

[Illustration: +Figs.+ 92 and 93.—Domestic piracy. The tributary, _a_

of Fig. 92, develops headward until it taps the main stream at _b_,

giving the result shown in Fig. 93.]

Piracy may occur where the material in which the valleys are cut is

homogeneous; but, as will be seen later, heterogeneity of material,

by determining unequal rates of erosion, stimulates the piratical

proclivities of streams.

An actual case of piracy is shown on Plate XI. North and South Lakes

formerly drained westward to the Schoharie Creek, the present head

of which is in the extreme northwest corner of the map. The head of

Kaaterskill Creek, which had a much higher gradient, worked back

and captured the head of the westward-flowing stream, diverting the

drainage from North and South Lakes to itself. Schoharie Creek was thus

beheaded.

Plaatekill Creek, near the south limit of the map, appears to have

beheaded the creek flowing west and northwest, similarly diverting its

head waters. The Dells, Wis., quadrangle (U. S. Geol. Surv.) affords an

illustration of domestic piracy.

RATE OF DEGRADATION.

The amount of mechanical sediment which the Mississippi River carries

to the Gulf of Mexico is estimated to represent a rate of degradation

for the Mississippi basin of about one foot in 5000 years. But the

mechanical sediment carried to the Gulf does not really represent the

total degradation of the basin, for the water which sinks beneath the

surface is dissolving more or less rock substance, especially lime

carbonate. This material is carried to the sea in solution, and does

not appear in the sediment on which the above estimate is based. Taking

into account the matter dissolved by the water and carried to the sea

in solution, the average rate of degradation for the Mississippi basin

is estimated at one foot in 3000 to 4000 years.

It is not to be inferred that this rate is uniform, or even that

erosion at any rate whatsoever is taking place in all parts of the

basin. Such is not the fact. On the whole the rate of erosion is

doubtless greatest toward the margins of the basins where the land

is in its topographic youth or early maturity. It is notably less in

the middle courses of the valleys, and erosion is locally exceeded by

deposition along the lower courses of the Mississippi and some of its

main tributaries.

The average elevation of North America is not accurately known, but it

is probably not far from 2000 feet. If the present rate of degradation,

say one foot in 3500 years, were to continue, it would take something

like 7,000,000 years to bring the continent to sea-level. But this rate

of degradation could not continue to the end, for as the continent

became lower streams would become sluggish and erosion less rapid.

Long before the continent reached base-level the rate of degradation,

so far as dependent on mechanical erosion, would become so slow that

the time necessary to bring the continent to sea-level would be almost

inconceivably prolonged. Furthermore, it is quite possible that

the land is suffering, or is liable to suffer, uplift, relative or

absolute. If the rate of rise were equal to the rate of degradation the

average height of the continent would of course not be affected.

The amount of sediment carried by streams in suspension varies

notably according to the stage of the water. During a year when

the stream was under careful study the Mississippi at Carrollton

(Miss.) was found to carry ¹⁄₆₈₁ of its weight of sediment during

the high-water stage of June, and ¹⁄₆₃₈₃ during the low-water of

October, the average for the year being ¹⁄₁₈₀₈. The average of a

greater number of records gives about ¹⁄₁₅₀₀ as the average ratio

between the weight of the sediment and the weight of the water.

This corresponds to about ¹⁄₂₉₀₀ by volume, the average specific

gravity being about 1.9. The amount of material carried in the

upper part of the water was notably less than that carried at

greater depths, but that carried midway between top and bottom was

about the same as that carried at the bottom.[32]

The discharge of the Mississippi River is about 19,500,000,000,000

cubic feet of water per year, and the sediment it carries in

suspension is estimated to weigh about 812,500,000,000 pounds. This

is equivalent to about 6,714,694,400 cubic feet. It is estimated

that about 750,000,000 cubic feet of sediment is rolled along the

bottom, giving a total of 7,468,694,400 cubic feet as the aggregate

annual load carried to the Gulf by the river. This would be

adequate to cover an area one square mile in extent to the depth of

268 feet per year.

[Illustration: PLATE XI.

PART OF THE CATSKILLS, NEW YORK.

U. S. Geol. Surv.]

[Illustration: PLATE XII.

Fig. 1. NEW MEXICO.

U. S. Geol. Surv.

Fig. 2. VIRGINIA, WEST VIRGINIA AND MARYLAND.

U. S. Geol. Surv.]

ANALYSES OF AMERICAN RIVER-WATERS.[33]

[+Reduced to Parts per 1000 by Dr. H. J. Van Hoesen.+]

+----------------------------------+------------------+----------------+

|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 | [2].00298 |

| | | |

|Potassium, K | ...... | .00154 |

| | | |

|Calcium, Ca | .0432 | .00905 |

| | | |

|Magnesium, Mg | .0125 | .00336 |

| | | |

|Chlorine, Cl | .0049 | .00213 |

| | | |

|Carbonic acid, CO₂, | [3].0982 |[34].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 |

| | | | | |

[3].1544 | [3].0287 | [35].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[36] 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:[37]

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[38] showing the amount of

mineral matter in average river water:

_MATERIAL IN SOLUTION IN ONE CUBIC MILE OF AVERAGE RIVER WATER._[39]

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[40] 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[41] (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:[42]

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.[43] 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.[44]

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.[45] 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.

[Illustration: +Fig.+ 94.—Talus accumulation at the base of a steep

bluff. Weber Canyon, Uinta Mountains, Utah. The talus has accumulated

since the last glaciation of the valley and is therefore of very

recent origin. (Church.)]

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.

[Illustration: +Fig.+ 95.—Shows the downward creep of soil and slaty

rock under the influence of gravity.]

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.

[Illustration: +Fig.+ 96.—Diagram of a valley the top of which is ten

times the width of the stream.]

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.

[Illustration: +Figs.+ 97–99.—Diagrammatic representation of the effect

of increased velocity on transporting power.]

=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?

[Illustration: +Fig.+ 100.—Diagram to illustrate the relative strength

of the two forces acting on a particle in suspension. The arrows

represent the relative strength of the two forces when the stream’s

velocity is 5 miles per hour. No account is taken in the diagram of

the viscosity of the water, or of the acceleration of velocity of

fall.]

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.

[Illustration: +Fig.+ 101.—Diagram to illustrate the effect of

bowlders, _a_ and _b_, in a stream’s bed on the currents of water

impinging against them.]

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.[46]

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.[47] 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.

[Illustration: +Fig.+ 102.—Some of the tools with which a stream works.

The cobbles and bowlders have been shifted by the stream in its flow.

Other stones and bowlders now in transit cause the ripples in the

stream. The Chelan River, Wash., just above its junction with the

Columbia. (Willis, U. S. Geol. Surv.)]

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.

[Illustration: +Figs.+ 103 and 104.—Diagrams to illustrate the fact

that a stream crosses many more cleavage-planes when the beds of rock

are inclined than when they are horizontal.]

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.