V-Valleys. Vigorous rivers well armed with waste make short work of cutting their beds to grade, and thus erode narrow, steep-sided gorges only wide enough at the base to accommodate the stream. The steepness of the valley slopes depends on the relative rates at which the bed is cut down by the stream and the sides are worn back by the weather. In resistant rock a swift, well-laden stream may saw out a gorge whose sides are nearly or even quite vertical, but as a rule young valleys whose streams have not yet reached grade are V-shaped; their sides flare at the top because here the rocks have longest been opened up to the action of the weather. Some of the deepest canyons may be found where a rising land mass, either mountain range or plateau, has long maintained by its continued uplift the rivers of the region above grade.

Fig. 53. Section of the Yellowstone Canyon
This canyon is 100 feet deep, 2500 feet wide at the top, and about 250 feet wide at the bottom. Neglecting any cutting of the river against the banks, estimate what part of the excavation of the canyon is due to the vertical erosion of its bed by the river and what to weathering and rain wash on the canyon sides

In the northern hemisphere the north sides of river valleys are sometimes of more gentle slope than the south sides. Can you suggest a reason?

The Grand Canyon of the Colorado River in Arizona. The Colorado River trenches the high plateau of northern Arizona with a colossal canyon two hundred and eighteen miles long and more than a mile in greatest depth ([Fig. 15]). The rocks in which the canyon is cut are for the most part flat-lying, massive beds of limestones and sandstones, with some shales, beneath which in places harder crystalline rocks are disclosed. Where the canyon is deepest its walls have been profoundly dissected. Lateral ravines have widened into immense amphitheaters, leaving between them long ridges of mountain height, buttressed and rebuttressed with flanking spurs and carved into majestic architectural forms. From the extremity of one of these promontories it is two miles or more across the gulf to the point of the one opposite, and the heads of the amphitheaters are thirteen miles apart.

The lower portion of the canyon is much narrower ([Fig. 54]) and its walls of dark crystalline rock sink steeply to the edge of the river, a swift, powerful stream a few hundred feet wide, turbid with reddish silt, by means of which it continually rasps its rocky bed as it hurries on. The Colorado is still deepening its gorge. In the Grand Canyon its gradient is seven and one half feet to the mile, but, as in all ungraded rivers, the descent is far from uniform. Graded reaches in soft rock alternate with steeper declivities in hard rock, forming rapids such as, for example, a stretch of ten miles where the fall averages twenty-one feet to the mile. Because of these dangerous rapids the few exploring parties who have traversed the Colorado canyon have done so at the hazard of their lives.