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<br />8 <br /> <br />Law of Stream Numbers. When the number of stream segments in a basin <br />is plotted against stream order number on semi-logarithmic paper the values <br />tend to follow a straight line (Figure 4) forming an inverse geometric <br />sequence. In every case the number of segments of an order decreases with <br />successively higher order numbers. Therefore the Law clf Stream Numbers has <br />been stated as fClllows: The numbers of strE',am seg;;;;.;tS:-of successiv;Iy <br />lower orders in a given basin tend to form a geometric series, beginning <br />with a single segment of the highest order and increasiE& according to a <br />constant bifurcation ratio. For example, if the bifurcation ratio is 3, <br />and the main stem (trunk) is of the sixth order, the numbers of segments <br />will be 1 (sixth order), 3, 9, 27, 81, and 243 (first order). <br /> <br />J <br /> <br />~ <br /> <br />j~ <br /> <br />figure <br /> <br />Figure 4. <br /> <br />8 <br /> <br /> 10 -,- <br /> c 1 <br /> , I <br />4 <br />E <br />i . <br />gal <br />I <br /> A' '] <br /> . <br />ao" <br /> -L~j <br /> 1 1. J 4. <br /> 5treo'non:lef" <br /> <br />61N:t.ts&ra"cl'lol:J(1.,eGIUlKills <br /> <br />.. <br /> <br />10 <br /> <br />" <br /> <br /> <br />, <br /> <br />. <br />~ <br />E <br />" <br />J <br /> <br />, <br /> <br />o. <br /> <br />2 J ~ I 1. J " <br />Stream order <br /> <br />01 <br /> <br />Watts Branch' Hf1rton analysiJ (>1 drQi"(I~,. ""Ii'Qrh. II. <br />R~/4rjon of o,'UtI!(# h'''~lh (I"d rmmhrr of J/rranu In ,r",.OI>I <br />ordlt'. C. R,./mjofl 01 Jrr,.arll ordrr 10 d,,'i"a~,. Q'to. <br /> <br />(tom Leopold et al. 1964. fluviAl ~roresses in <br />Geofllorpholopov. Freeman, San Franc:1sco. <br /> <br />Law of Streaa Length. Even a curs!>ry examination of a map designating <br />stream order.DUIIlben will reveal that first order segaents are shortest and <br />that the length progressively increases with each increa,se in order :number <br />(Table 2). Measurement of large numbers of stream segments with a <br />planimeter indicates that the mean length of stream segm1ents, in IIliles, <br />increases by a ratio of approximately three, with each increase in stream <br />order. Thi. ,consistent proportion of length :increase is known as th.~ <br />le9ltb\,ratfo and tends to be approximately COlnstant for .. given drainage <br />basin. ~D1fferences are generally ascribed to chance varIations in <br />