=River valleys.= In their courses to the sea, rivers follow valleys of various forms, some shallow and some deep, some narrow and some wide. Since rivers are known to erode their beds and banks, it is a fair presumption that, aided by the weather, they have excavated the valleys in which they flow. Moreover, a bird's-eye view or a map of a region shows the significant fact that the valleys of a system unite with one another in a branch work, as twigs meet their stems and the branches of a tree its trunk. Each valley, from that of the smallest rivulet to that of the master stream, is proportionate to the size of the stream which occupies it. With a few explainable exceptions the valleys of tributaries join that of the trunk stream at a level; there is no sudden descent or break in the bed at the point of juncture. These are the natural consequences which must follow if the land has long been worked upon by streams, and no other process has ever been suggested which is competent to produce them. We must conclude that valley systems have been formed by the river systems which drain them, aided by the work of the weather; they are not gaping fissures in the earth's crust, as early observers imagined, but are the furrows which running water has drawn upon the land. As valleys are made by the slow wear of streams and the action of the weather, they pass in their development through successive stages, each of which has its own characteristic features. We may therefore classify rivers and valleys according to the stage which they have reached in their life history from infancy to old age. Young River Valleys =Infancy.= The Red River of the North. A region in northwestern Minnesota and the adjacent portions of North Dakota and Manitoba was so recently covered by the waters of an extinct lake, known as Lake Agassiz, that the surface remains much as it was left when the lake was drained away. The flat floor, spread smooth with lake-laid silts, is still a plain, to the eye as level as the sea. Across it the Red River of the North and its branches run in narrow, ditch-like channels, steep-sided and shallow, not exceeding sixty feet in depth, their gradients differing little from the general slopes of the region. The trunk streams have but few tributaries; the river system, like a sapling with few limbs, is still undeveloped. Along the banks of the trunk streams short gullies are slowly lengthening headwards, like growing twigs which are sometime to become large branches. [Illustration: Fig. 44. A Young Lacustrine Plain; the Red River of the North Scale 5 inches = about 11 miles. Contour interval, 20 feet] The flat interstream areas are as yet but little scored by drainage lines, and in wet weather water lingers in ponds in any initial depressions on the plain. [Illustration: Fig. 45. A Young River, Iowa Note that it has hardly begun to cut in the plain of glacial drift on which it flows]