_A_, an area in its infancy, Buena Vista County, Iowa; _B_, an area in its maturity, Ringgold County, Iowa] [Illustration: Fig. 51. Successive Longitudinal Profiles of a Stream _am_, initial profile, with waterfall at _w_, and basins at _l_ and _l´_, which at first are occupied by lakes and later are filled or drained; _b_, _c_, _d_, and _e_, profiles established in succession as the stream advances from infancy toward old age. Note that these profiles are concave toward the sky. This is the _erosion curve_. What contrasting form has the weather weather curve (p. 34)?] =The longitudinal profile of a stream.= This at first corresponds with the initial surface of the region on which the stream begins to flow, although its way may lead through basins and down steep descents. The successive profiles to which it reduces its bed are illustrated in Figure 51. As the gradient, or rate of descent of its bed, is lowered, the velocity of the river is decreased until its lessening energy is wholly consumed in carrying its load and it can no longer erode its bed. The river is now _at grade_, and its capacity is just equal to its load. If now its load is increased the stream deposits, and thus builds up, or _aggrades_, its bed. On the other hand, if its load is diminished it has energy to spare, and resuming its work of erosion, _degrades_ its bed. In either case the stream continues aggrading or degrading until a new gradient is found where the velocity is just sufficient to move the load, and here again it reaches grade. [Illustration: Fig. 52. A V-Valley,--the Canyon of the Yellowstone Note the steep sides. What processes are at work upon them? How wide is the valley at the base compared with the width of the stream? Do you see any river deposits along the banks? Is the stream flowing swiftly over a rock bed, or quietly over a bed which it has built up? Is it graded or ungraded? Note that the canyon walls project in interlocking spurs] =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. [Illustration: Fig. 53. Section of the Yellowstone Canyon