When a land has been newly elevated above the sea there is often—we may say, indeed, generally—a very great difference between the height of its head waters and the ocean level. In this condition of a country the rivers have what we may call a new aspect; their valleys are commonly narrow and rather steep, waterfalls are apt to abound, and the alluvial terraces are relatively small in extent. Stage by stage the torrents cut deeper; the waste which they make embarrasses the course of the lower waters, where no great amount of down-cutting is possible for the reason that the bed of the stream is near sea level. At the same time the alluvial materials, building out to sea, thus diminish the slope of the stream. In the extreme old age of the river system the mountains are eaten down so that the torrent section disappears, and the stream becomes of something like a uniform slope; the higher alluvial plains gradually waste away, until in the end the valley has no salient features. At this stage in the process, or even before it is attained, the valley is likely to be submerged beneath the sea, where it is buried beneath the deposits formed on the floor; or a further uplift of the land may occur with the result that the stream is rejuvenated; or once more endowed with the power to create torrents, build alluvial plains, and do the other interesting work of a normal river.

It rarely, if ever, happens that a river valley attains old age before it has sunk beneath the sea or been refreshed by further upliftings. In the unstable conditions of the continents, one or the other of these processes, sometimes in different places both together, is apt to be going on. Thus if we take the case of the Mississippi and its principal tributaries, the Ohio and Missouri, we find that for many geological ages the mountains about their sources have frequently, if not constantly, grown upward, so that their torrent sections, though they have worn down tens of thousands of feet, are still high above the sea level, perhaps on the average as high as they have ever been. At the same time the slight up-and-down swayings of the shore lands, amounting in general to less than five hundred feet, have greatly affected the channels of the main river and its tributaries in their lower parts. Not long ago the Mississippi between Cairo and the Gulf flowed in a rather steep-sided valley probably some hundreds of feet in depth, which had a width of many miles. Then at the close of the last Glacial period the region sank down so that the sea flooded the valley to a point above the present junction of the Ohio River with the main stream. Since then alluvial plains have filled this estuary to even beyond the original mouth. In many other of our Southern rivers, as along the shore from the Mississippi to the Hudson, the streams have not brought in enough detritus to fill their drowned valleys, which have now the name of bays, of which the Delaware and Chesapeake on the Atlantic coast, and Mobile Bay on the Gulf of Mexico, are good examples. The failure of Chesapeake and Delaware Bays to fill with débris in the measure exhibited by the more southern valleys is due to the fact that the streams which flow into them to a great extent drain from a region thickly covered with glacial waste, a mass which holds the flood waters, yielding the supply but slowly to the torrents, which there have but a slight cutting power.

In our sketch of river valleys no attention has been given to the phenomena of waterfalls, those accidents of the flow which, as we have noted, are particularly apt to characterize rivers which have not yet cut down to near the sea level. Where the normal uniform descent which is characteristic of a river's bed is interrupted by a sudden steep, the fact always indicates the occurrence of one of a number of geological actions. The commonest cause of waterfalls is due to a sudden change in the character of horizontal or at least nearly level beds over which the stream may flow. Where after coursing for a distance over a hard layer the stream comes to its edge and drops on a soft or easily eroded stratum, it will cut this latter bed away, and create a more or less characteristic waterfall. Tumbling down the face of the hard layer, the stream acquires velocity; the débris which it conveys is hurled against the bottom, and therefore cuts powerfully, while before, being only rubbed over the stone as it moved along, it cut but slightly. Masses of ice have the same effect as stones. Bits dropping from the ledge are often swept round and round by the eddies, so that they excavate an opening which prevents their chance escape. In these confined spaces they work like augers, boring a deep, well-like cavity. As the bits of stone wear out they are replaced by others, which fall in from above. Working in this way, the fragments often develop regular well-like depressions, the cavities of which work back under the cliffs, and by the undermining process deprive the face of the wall of its support, so that it tumbles in ruin to the base, there to supply more material for the potholing action.

Waterfalls of the type above described are by far the commonest of those which occur out of the torrent districts of a great river system. That of Niagara is an excellent specimen of the type, which, though rarely manifested in anything like the dignity of the great fall, is plentifully shown throughout the Mississippi Valley and the basin of the Great Lakes. Within a hundred miles of Niagara there are at least a hundred small waterfalls of the same type. Probably three quarters of all the larger accidents of this nature are due to the conditions of a hard bed overlying softer strata.

Falls are also produced in very many instances by dikes which cross the stream. So, too, though rarely, only one striking instance being known, an ancient coral reef which has become buried in strata may afford rock of such hardness that when the river comes to cross it it forms a cascade, as at the Falls of the Ohio, at Louisville, Ky. It is a characteristic of all other falls, except those first mentioned, that they rarely plunge with a clean downward leap over the face of a precipice which recedes at its base, but move downward over an irregular sloping surface.

In the torrent district of rivers waterfalls are commonly very numerous, and are generally due to the varying hardness in the rocks which the streams encounter. Here, where the cutting action is going on with great rapidity, slight differences in the resistance which the rocks make to the work will lead to great variations in the form of the bed over which they flow, while on the more gently sloping bottoms of the rivers, where the débris moves slowly, such variations would be unimportant in their effect. When the torrents escape into the main river valleys, in regions where the great streams have cut deep gorges, they often descend from a great vertical height, forming wonderful waterfalls, such as those which occur in the famous Lauterbrunnen Valley of Switzerland or in that of the Yosemite in California. This group of cascades is peculiar in that the steep of the fall is made not by the stream itself, but by the action of a greater river or of a glacier which may have some time taken its place.

Waterfalls have an economic as well as a picturesque interest in that they afford sources of power which may be a very great advantage to manufacturers. Thus along the Atlantic coast the streams which come from the Appalachian highlands, and which have hardly escaped from their torrent section before they attain the sea, afford numerous cataracts which have been developed so that they afford a vast amount of power. Between the James on the south and the Ste. Croix on the north more than a hundred of these Appalachian rivers have been turned to economic use. The industrial arts of this part of the country depend much upon them for the power which drives their machinery. The whole of the United States, because of the considerable size of its rivers and their relatively rapid fall, is richly endowed with this source of energy, which, originating in the sun's heat and conveyed through the rain, may be made to serve the needs of man. In view of the fact that recent inventions have made it possible to convert this energy of falling water into the form of electricity, which may be conveyed to great distances, it seems likely that our rivers will in the future be a great source of national wealth.

We must turn again to river valleys, there to trace certain actions less evident than those already noted, but of great importance in determining these features of the land. First, we have to note that in the valley or region drained by a river there is another degrading or down-wearing action than that which is accomplished by the direct work of the visible stream. All over such a valley the underground waters, soaking through the soil and penetrating through the underlying rock, are constantly removing a portion of the mineral matter which they take into solution and bear away to the sea. In this way, deprived of a part of their substance, the rocks are continually settling down by underwear throughout the whole basin, while they are locally being cut down by the action of the stream. Hence in part it comes about that in a river basin we find two contrasted features—the general and often slight slope of a country toward the main stream and its greater tributaries, and the sharp indentation of the gorge in which the streams flow, these latter caused by the immediate and recent action of the streams.

If now the reader will conceive himself standing at any point in a river basin, preferably beyond the realms of the torrents, he may with the guidance of the facts previously noted, with a little use of the imagination, behold the vast perceptive which the history of the river valley may unfold to him. He stands on the surface of the soil, that débris of the rocks which is just entering on its way to the ocean. In the same region ten thousand years ago he would have stood upon a surface from one to ten feet higher than the present soil covering. A million years ago his station would have been perhaps five hundred feet higher than the surface. Ten million years in the past, a period less than the lifetime of certain rivers, such as the French Broad River in North Carolina, the soil was probably five thousand feet or more above its present plane. There are, indeed, cases where river valleys appear to have worked down without interruption from the subsidence of the land beneath the sea to the depth of at least two miles. Looking upward through the space which the rocks once occupied, we can conceive the action of the forces in their harmonious co-operation which have brought the surface slowly downward. We can imagine the ceaseless corrosion due to the ground water, bringing about a constant though slow descent of the whole surface. Again and again the streams, swinging to and fro under the guidance of the underlying rock, or from the obstacles which the débris they carried imposed upon them, have crossed the surface. Now and then perhaps the wearing was intensified by glacial action, for an ice sheet often cuts with a speed many times as great as that which fluid water can accomplish. On the whole, this exercise of the constructive imagination in conceiving the history of a river valley is one of the most enlarging tasks which the geologist can undertake.

Where in a river valley there are many lateral streams, and especially where the process of solution carried on by the underground waters is most effective, as compared with erosive work done in the bed of the main river, we commonly find the valley sloping gently toward its centre, the rivers having but slight steeps near their banks. On the other hand, where, as occasionally happens, a considerable stream fed by the rain and snow fall in its torrent section courses for a great distance over high, arid plains, on which the ground water and the tributaries do but little work, the basin may slope with very slight declivity to the river margins, and there descend to great depths, forming very deep gorges, of which the Colorado Cañon is the most perfect type. As instances of these contrasted conditions, we may take, on the one hand, the upper Mississippi, where the grades toward the main stream are gentle and the valley gorge but slightly exhibited; on the other, the above-mentioned Colorado, which bears a great tide of waters drawn from the high and relatively rainy region of the Rocky Mountains across the vast plateau lying in an almost rainless country. In this section nearly all the down-wearing has been brought about in the direct path of the stream, which has worn the elevated plain into a deep gorge during the slow uprising of the table-land to its present height. In this way a defile nearly a mile in depth has been created in a prevailingly rather flat country. This gorge has embranchments where the few great tributaries have done like work, but, on the whole, this river flows in an almost unbroken channel, the excavation of which has been due to its swift, pebble-bearing waters.