┌───────────────────────────────────────────────────────────────────┐ │ PLATE 20. │ │ │ │ [Illustration: Map of the surface modeled by mountain glaciers in │ │ the Sierra Nevadas of California (after I. C. Russell).] │ └───────────────────────────────────────────────────────────────────┘ When the backward grades upon the valley floor are especially steep, the rock step becomes a _rock bar_, or _Riegel_, of which nearly every Alpine valley has its examples. In a walk from the Grimsel to Meiringen many such bars are passed. Carrying in suspension the sharp rock sand from the glacier deposits along its bed, the stream which succeeds to the glacier as it vacates its valley saws its way through these obstructions with a rapidity that is amazing, thus producing narrow defiles, of which the Gorge of the Aar near Meiringen and that of the Gorner near Zermatt are such well-known examples (Fig. 403). [Illustration: FIG. 402.—Map of an area near the continental divide in Colorado, showing an unglaciated surface to the west of the divide, where the westerly winds have cleared the ground of snow, and the glacier-carved country to the eastward. Note the regular forms of the youthful cirque, the glacier stairway, and the rock basin lakes (U. S. G. S.).] [Illustration: FIG. 403.—Gorge of the Albula River near Berkum in the Engadine, cut through a rock bar by the river which has succeeded to the earlier glacier.] [Illustration: FIG. 404.—Idealistic sketch showing both glaciated and nonglaciated side valleys tributary to a glaciated main valley (after Davis).] It is characteristic of rivers that the tributaries cut their valleys more rapidly than does the main stream within the neighboring section, though they cannot cut lower than their outlets—the side streams enter _accordantly_. This is easily explained because the grades of the tributary streams are the steeper, and, as we well know, the corrosion of a valley is augmented at a most amazing rate for each increase of its grade. No such law controls the processes of plucking and abrasion by which the glacier lowers its floor, for these processes appear to depend for their efficiency upon the depth of the ice, and the supply of cutting tools, quite as much as upon the grade of the bed. To apply a homely illustration, the hollowing of flagstones upon our walks is dependent more upon the number of persons that pass over them, and upon their size and the number of protruding nails in their boot heels, than upon the grades upon which they are placed. At all events we find that the main glacier valleys are cut deeper than the side valleys, so that the latter become _hanging valleys_—they enter the main valley, not upon its bed, but some distance above it (Fig. 404).