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EPHEMERAL STREA."\!S 1.58, with a median of 1.29. For perennial rivers, the average value of j lies between 1.5 and 2.0. As this exponent is greater than unity, load must increase faster than discharge, or in other words, suspended-load concentration increases with increasing discharge. CHANGES OF HYDRAULIC CHARACTERISTICS IN THE DOWNSTREAM DIRECTION The. graphs just presented show how width, depth, velocity, and suspended load vary with changing dis- charge at individual channel cross sections, Each discharge on these at-a.-station curves represents an occurrence of different frequency. The hydraulic vari- ables (width, depth, and others) at several cross sections along the length of a stream may appropriately bc compared only for some constant frequency of discharge. Thus, the change of a variable in the downstream dircction can be determined by drawing a line through those points on the at-a-station graphs which represent a discharge of equal frequency at all cross sections. This construction is' part of the hydraulic geometry. As the arroyos ,vere measured whenever and wherever an opportunity was afforded, it is not possible to esti- mate the frequency or recurrence interval of thc dis- charge recorded in the individual floods. We feel certain that none of the arroyo flo\vs gaged ,vere from unusually severe storms. Lacking other alternatives, we assume that the lines defined by plotting all measurements of each variable against discharge represent the downstream changes at some constant frequency of discharge, The plot of width against discharge (fig, 11) lends credence to this assumption. Previous work has shown that the most nearly constant relation among the hydraulic variables in natural stream channels is the rate of increase of width with discharge in the downstream dircction. This is the value of the exponent b, in w=aQ' The average value of b for rivers and regime canals is .5. In figure 11 the slope of the width-discharge relations for all our arroyo measurements is nearly)') regardless of exactly how one chooses to draw the line through the points, Because of the general agreement, in the value of this exponent, it is believed that the plots in figure 11 approximate the downstream rela- tions at a constant, though unknown, frequency of discharge. The values of j and m, respectively the downstream rate of increase of depth and of velocity, are .3 and ,2 for arroyos as compared with ,4 and .1 for perennial streams. No great reliance should be placed on the exact value of these exponents for arroyos, considering 355.397-56-3 13 the nature of the data and the limited number of observations. Indeed, the average values of the same exponents in river data need verification with additional data. Tentatively, however, we conclude that for arroyos the downstream increase of depth is less and velocity greater than had been found for river data. An explanation of these differences appears to be found in a consideration of the sediment load. Parallelism of the individual at--a-station graphs simplifies development of downstream relations for the sediment data. Regardless of the frequency chosen, any line representing the increase of suspended load with increasing discharge in the downstream direction would nearly coincide with the at-a-station lines already plotted on figure 10. Such a line has a slope of about 1.3, which is the median of the slopes of the individual at-a-station graphs. Although the scatter allows some latitude of choice, it is apparent that any line through the data plotted on figure 10 must have a slope greater than unity. This leads to a conclusion of considerable interest. From analyzing data for rivers, Leopold and :\!addock concluded t,hat in the downstream direction suspended- sediment load increased less fast than discharge. By a rather roundabout analysis, they found the mean value of j to be 0.8. Sediment stations are not ar- ranged along the length of any single river in sufficient number to analyze directly thc change of sediment load in the downstream direction. Whereas the j value of 0.8 also could be justified by deduction, the fact remains that those authors did not have so good a check on the downstream change of sediment load as is available in the present data. The arroyo data indicate that suspended-sediment load increases downstream morc rapidly than discharge and.. therefore, suspended-sediment concentration in- creases dO\vnstream. From analysis of data for peren- nial rivers the opposite conclusion was reached; namely.. that suspended-sediment concentration decreases in the downstream direction. A downstrearu increase in sediment concentrat,ion requires (1) that runoff entering the river at downstream points carry larger sediment concentrations than in the headwaters, or (2) that the water pick up progres- sively more and more sediment off the stream bed as it flows down the channel, or (3) that water be progres- sively lost by percolation into the channel. For an area of uniforrll rock and climate, slopes tend to be steeper near the headwaters than down- stream. Drainage density tends to decrcasc down- stream, and this means that the length of overland flow contributing to headwater rills is less than to minor channels "\vhich enter the main stream in down-