Glacier troughs.  The channel worn to accommodate the big and clumsy glacier differs markedly from the river valley cut as with a saw by the narrow and flexible stream and widened by the weather and the wash of rains.  The valley glacier may easily be from one thousand to three thousand feet deep and from one to three miles wide.  Such a ponderous bulk of slowly moving ice does not readily adapt itself to sharp turns and a narrow bed.  By scouring and plucking all resisting edges it develops a fitting channel with a wide, flat floor, and steep, smooth sides, above which are seen the weathered slopes of stream-worn mountain valleys.  Since the trunk glacier requires a deeper channel than do its branches, the bed of a branch glacier enters the main trough at some distance above the floor of the latter, although the surface of the two ice streams may be accordant.  Glacier troughs can be studied best where large glaciers have recently melted completely away, as is the case in many valleys of the mountains of the western United States and of central and northern Europe (Fig. 114).  The typical glacier trough, as shown in such examples, is U-shaped, with a broad, flat floor, and high, steep walls.  Its walls are little broken by projecting spurs and lateral ravines.  It is as if a V-valley cut by a river had afterwards been gouged deeper with a gigantic chisel, widening the floor to the width of the chisel blade, cutting back the spurs, and smoothing and steepening the sides.  A river valley could only be as wide-floored as this after it had long been worn down to grade.

The floor of a glacier trough may not be graded; it is often interrupted by irregular steps perhaps hundreds and even a thousand feet in height, over which the stream that now drains the valley tumbles in waterfalls.  Reaches between the steps are often basined.  Lakelets may occupy hollows excavated in solid rock, and other lakes may be held behind terminal moraines left as dams across the valley at pauses in the retreat of the glacier.

Fjords are glacier troughs now occupied in part or wholly by the sea, either because they were excavated by a tide glacier to their present depth below sea level, or because of a submergence of the land.  Their characteristic form is that of a long, deep, narrow bay with steep rock walls and basined floor.  Fjords are found only in regions which have suffered glaciation, such as Norway and Alaska.

Hanging valleys.  These are lateral valleys which open on their main valley some distance above its floor.  They are conspicuous features of glacier troughs from which the ice has vanished; for the trunk glacier in widening and deepening its channel cut its bed below the bottoms of the lateral valleys.

Since the mouths of hanging valleys are suspended on the walls of the glacier trough, their streams are compelled to plunge down its steep, high sides in waterfalls.  Some of the loftiest and most beautiful waterfalls of the world leap from hanging valleys,—­ among them the celebrated Staubbach of the Lauterbrunnen valley of Switzerland, and those of the fjords of Norway and Alaska.