[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.)]