To analyze the characteristics of geometric properties of small drainage basins and also to obtain the relationships between the above two, the writer conducted an investigation in landform in Tanabe and Sanda hill areas which are slightly different in geological and topographical features. Four drainage basins (Ta-d) located in Tanabe hills which are composed of Osaka group (Plio-Pleistocene) and five drainage basins (Sa-e) in Sanda hills which are composed of Kobe group (Miocene) were studied by the author. These stream networks were determined from topographic maps (1 : 5000) with more details based on field studies. Air photographs were also used for checking stream networks and stream heads. In this paper stream networks are classified in order after the Strahler's method. The results may safely be summerized as follows: 1) The bifurcation ratio of the first-order to the second-order streams ranges from 3.4 to 6.3 and that of the third-order to the fourth-order ranges from 2.0 to 4.0. Therefore, the number of stream segments of each order does not exactly form an inverse geometric series with order. 2) Frequency-distribution histograms of stream lengths of the first-and second-order show marked right-skewnesses, which appears to be corrected by plotting log values on the abscissa (Fig. 4a, b). The distribution of stream lengths of the first-order shows two peaks and that of the second-order ranges more widely than that of the first-order. 3) The histograms of drainage area of the first- and second-order show the log-normal distributions (Fig. 6a, b). 4) The stream lengths of each order do not form a geometric series with order. The scattered data of nine basins are markly around a reggression line fitted by the method of the least squares. However, the stream length which is obtained by the quasi-Horton's ordering system ([numerical formula]) is fitted with the reggression line (Fig. 3). In the least square method the plottings of drainage areas of different orders form a straight line with slight dispersions. 5) Fig. 7a and Fig. 7b show a high correlation of drainage area (A) with mainstream length (L) in two hill areas. This relation was expressed with the equation L =aA^r by Hack (1957). The exponents(r) of this regressional equations are 0.594 and 0.597, respectively. These values agree quite well with that 'obtained by Hack and Gray. Kayane (1972) proposed that the exponent (r) in Hack's relation may be expressed by r≒D/H (the length ratio e^D, the drainage area ratio e^H). Instead of length ratio e^D, the values e^K of which are obtained by the quasi-Horton's stream ordering system has been adopted by the author. Using e^K and e^H for two groups of basins, values of r are 0.600 and 0.597, respectively. These values agree remarkably with one obtained by the correlation with drainage area and mainstream length. . These results may support that Hack's relation is a difinite one. The stream length obtained by the quasi-Horton's relation may be useful index for the geometric analysis. 6) The reason why the value of r is about O. 6 may be pointed that the form of the drainage basin is prolonged with increasing of drainage area and/or the sinuosity of length is increased with that. In Tanabe hills the basin length (Lb) increases in accordance with increasing of drainage area. On the other hand, in Sanda hills the basin length scarcely in accordance with the increasing of drainage area, so that sinuosity may be enlarged.
