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<br /> <br />EPHE:\.iERAL STREAMS <br /> <br />19 <br /> <br /> <br />FlGCRE 14.-Fin;t-::lrder tributaries in basin of Arroyo Caliente. Theso show the most head ward extensions of the smallest tributary rllts in the area. <br /> <br />and figure 15 which pictures Arroyo de los Frijoles at <br />a place where its size is typical of an 8th order stream, <br />Channels of order 5 and order 10 can be seen in figures <br />2 and 3, respectively_ <br />Because maximum stream length is a function of <br /> <br /> <br />FIGURE l1i.-Arroyo de 108 Frijolos at place where it t~'pitles a stream of eighth order. <br /> <br />drainage-basin area, it is not unexpected that the rela- <br />tion of drainage area to stream order is also a straight <br />line on semilogarithmic paper, as can be seen in figure <br />16. The smallest unbranched tributaries, which are. <br />rills about 8 inches wide and 1 to 4 inches deep, drain <br />on the average about .00006 square miles or .04 acre. <br />In the 670-square-mile basin of Rio Galisteo there are <br />roughly 190,000 snch first-order tributaries, as esti- <br />mated from figure 13. <br /> <br />EQUATIONS RELATING TO HYDRAULIC AND PHYSI- <br />OGRAPHIC FACTORS <br /> <br />From the previous work of Horton or from our data <br />plotted in figures 13 and 16, it. is apparent that stream <br />order, 0, bears a relation to nUInber of streams, .LV, in <br />t.he. form <br /> <br />O=k log N or Oo::log N <br /> <br />(1) <br /> <br />and a similar relation to stre,am length, IJ slope, 8, and <br />drainage area, Ad, <br /> <br />Oo::log 1 <br /> <br />(2) <br />(3) <br /> <br />Oo::log s <br />Oo::log A, <br /> <br />(4) <br />