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EPHEMERAl" STREAMS 29 relation of channel slope to channel width is generally in line with that of the larger ephemeral channels. The solid triangles apply to similar unbranched rills occurring in steeper t.ributaries in the same area which drained the unconsolidated gravels of a pediment remnant somewhat nearer the nlountains than the Arroyo Caliente, The difference in stream slope between Arroyo Caliente and Fifth of July Wash can probably be attributed to the difference in size of the gravel characterizing the two small basins. To determine whether tIlls relation between slope and width would be maintained even by the very smallest rills, measurements were made of the smallest natural rills which could be found in the area. The values of slope and width of these miniature features are repre- sented by the black circles in the far upper left part of figure 18. They fall in a position so nearly representing an extension of the line in the diagram that it may be inferred that the slope-width relation in the area studied applies as far upstream as the smallest observable rill. In the same area are many places where modern highways have required deep road cuts through the same material as that constituting the drainage basins under study. On the steep road cuts little or no vegeta- tion has become established, and numerous steep parallel rills of an average depth of 0.2 feet have devel- oped. The width and slope of these road-cut rills were measured. The slope had changed but little from that determined by the blade of the highway grader. The rills on road cuts are shown by open triangles on figure 18. These points are no more scattered from the mean line than any other data. It appears then, that if the degrees of freedom are reduced, in this instance by a prescribed slope, the width of the rill will be formed in accordance with the slope-width relations for natural streams having a larger number of degrees of freedom. This is interpreted as further evidence that channels cut by '\o~ater carrying sediment tend to maintain a quasi-equilibrium even as far upstream as the most remote ephemeral rills. THE DISCONTINUOUS GULLY Beginning late in the 19th century the alluvial valleys of the West experienced an epicycle of erosion characterized by the development of valley trenches or arroyos (see fig. 25). These arroyos range in size from insignificant rills to canyons 600 feet wide, 50 feet deep, and 150 miles long. The notorious Rio Puerco (del Oriente) in K ew Mexico has the latter dimensions. Some gullies are narrow enough to step across but are deep enough to lose a giraffe in, As Gregg (1844, p. 184) said more than a century ago, FIGl.'RE 2.S.-A 13,picallarge continuous arroyo trenching an alluvial valley in New Mexico: Rio Pueroo (del oeste) near Manuelito, looking downstream. The sides are usually perpendicular-indeed, often shelving at the base, and therefore utterly impassable. . . Though, to a stranger, the appearance would indicate the very head of a ravine, I would sometimes be compelled to follow its meandering course for miles without being a.ble to double its" breaks. tl It is characteristic of the large arroyos that depth remains quite uniform through very long reaches. This uniformity of depth means that the gradient of the channel bed had attained a slope almost parallel to the original valley floor, There is also. another distinctive type of gully that is characterized by a vertical head-cut, a rapidly decreasing depth down- stream, and a fan at the lower end, Such channels generally occur in groups arranged irregularly along the length of the drainageway, and because of this characteristic are called discontinuous gullies, Bryan (1928) has presented evidence that when the Rio Puerr.o 'vas first reached by the reconnaissance teams of the Army of the 'Vest in 1846, the valley floor was already being dissected by discontinuous gullies. Some of them were evidently large, for in August 1846, Lt. Simpson had to cut down the gully wall of the Rio Puerco in order to get his brass cannon across. Yet, at the same time, there were long reaches in the Puerco valley so smooth that the native grass was cut for hay, and water was diverted from the channel by felling a cottonwood tree to form a dam, Discontinuous gullies have long presented a problem to the erosion-control engineer, In the first place, the mechanics of gully formation is very poorly understood, Although it is generally presumed that discontinuous gullies, at least in places, can coalesce and form a continuous channel, it is not known whether the nature