The quantitative analysis of watershed geomorphology started with the study of Horton (1945) and thereafter many results have been reported. It was suggested that there is a definite relationship between stream lengths and drainage areas. Hack (1957) has found that relationship between mainstream lengths and drainage areas can be expressed by the equation L=cAr, where constants c and r are 1.4 and 0.6 respectively. This relationship is called Hack's law.
In this paper, the Strahler's and the link magnitude ordering systems are applied to measure the drainage basin. The link magnitude system is a new, simple and rational one advocated by Shreve (1967). The mainstream length is defined by this link magnitude system. The author attempted to examine the Hack's law, which is a relationship between mainstream lengths and drainage areas, for 19 stream networks in Hokkaido where the Norton's laws hold good (Table 1). The results are summarized as follows :
1. The Hack's law holds good to the investigated 155 drainage basins larger than 5th order basins (Fig. 4) and to each from the 1st to the 7th order basins respectively (Fig. 5, Table2). It is also applicable to each of 19 networks, that is, an individual network (Table 3). The exponent r exceeds 0.5 and approaches to about 0.6 in both cases, and this result agrees with Hack et al. but not with Sakaguchi and Mueller.
2. The exponent r can be derived from the Horton's laws (ratio of stream length and ratio of drainage area), but it becomes somewhat smaller when the stream length ratio by the Strahler's ordering system is used (Table 4).
3. The effect of the map scale used to Hack's law is not significant, but it affects the coefficient more than the exponent (Fig. 6). This is because the length is more affects by the map scale than the area is (Fig. 7). Accordingly, we must be careful to use maps of different scales.
4. The Hack's law between basin lengths and drainage areas holds good, too (Fig. 8). But, both the coefficient and the exponent become somewhat smaller than in the relationship between mainstream lengths and drainage areas.
5. The deviation of r from 0.5 depends upon both mainstream sinuosity and shape change of drainge basin. Among the roughly equal drainage areas, it is more affected by shape change than mainstream sinuosity (Fig. 9, Table 2). But, both effects become nearly equal in case of wider range of drainage area (Table 2). In case of relationship within an identical network both effects become nearly equal on average in 19 networks, but their effects are reflected in geomorphic characteristics of individual networks (Table 3).
6. The Hack's law also holds good for the simulated drainage networks by a random walk model. The effects of mainstream sinuosity and shape change of drainage basin, mentioned in 5, are also found for these simulated drainage networks (Table 6).
7. Relative contribution of the mainstream sinuosity to the shape change of a drain- age basin relates with the entropy calculated from probabilities deciding stream flow direc- tions. The shape change is large when the entropy is small, but the sinuosity is large when the entropy is large (Fig. 10). The relative contribution could be a new index to indicate geomorphic characteristics of a drainage basin.=

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A field investigation has been underway since April 1960 of the adequacy of supplies of irrigation water from the Manno Reservoir. Using daily water level for 15 years (June 1958 to May 1973) of the reservoir, a time series analysis of water storage variation was made.
A storage ratio p=Q/Q_U was introduced to show the variation in reservoir water storage with time, where Q is the initial water storage plus inflow minus irrigation usage for a 10-day period and Q_U is the total storage capacity of the reservoir for irrigation water use. Results were as follows :
1) Values of p for the reservoir ranged from 0.056 to 1.008 during the 15 years.
2) Values of p> 1.0 occurred during seventeen 10-day periods in the non-irrigation season. Out of the 15 years, 5 years had the p-value greater than 1.0 at the beginning of the irrigation season, or the first decade in June. Thus, it is evident that there was excess water which was discharged from the reservoir unused. From the standpoint of conserving water resources, a larger reservoir would be needed. However, this would require a larger dam and would involve considerable expense.
3) On the other hand, p was as low as 0.056 to 0.074 from the second decade in September to the second decade in November, in 2 out of the 15 years. Although the reservoir was nearly empty during these periods, there was no serious shortage of irrigation water, because it was at the end of the irrigation season.
4) The term p₃₅₅ was defined as the minimum water storage occurring during the 355 day in an irrigation year. It is apparent that the larger the p₃₅₅ value, the securer the water supplies for irrigation. The values of p₃₅₅ varied from 0.08 to 0.72, with an average of 0.15 for the 15 years.
5) when water storage in the reservoir decreases below 350.0 × 104m3, water is no longer distributed to all of the irrigated areas. Most of the reduced flow goes to a small irrigated area nearest to the reservoir. Water storage used in such a manner is called “Shomonsui”. A p-value of 0.23 corresponds to the upper limit of the Shomonsui. Values of p _??_ 0.23 occurred in twenty three 10-day periods from the second period in August to the first period in April for 5 out of the 15 years. However, during the June to September irrigation period, p_??_0.23 occurred in only two 10-day periods (the second and third decade in September) for 7 out of the 15 years. From these results it is concluded that the Shomonsui having 350.0 × 104m3 in water storage is an adequate capacity for the reservoir.

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The central management functions of cities and the related issues have drawn a consid-erable attention in the held of urban economics and urban geography and it has been more so because of the recent understanding that those functions have direct influence on the growth of cities. In the urban structural study of metropolitan areas, central manage-ment functions draw special attentions.
In this article, only the economic function, which is considered as an important part in the capitalistic economy of Japan, is researched and analyzed. Here, the head offices and branch offices are treated as economic central management functions. The present study covers the period from 1907 to 1970. The objectives are to recognize the changes of the economic management area in each city (Sapporo, Sendai, Tokyo, Nagoya, Kanazawa, Kyoto, Osaka, Hiroshima, Takamatsu, Fukuoka), and to understand the process of growth of Central Regional Cities Sapporo, Sendai, Hiroshima, Takamatsu, and Fukuoka in Japan by analyzing the changes of concentration of their economic central management functions.
The changes of the economic management area in each city are shown in tables 3_??_7 and figures 1_??_4, and results are summarized as follows. (1) Economic management areas of Tokyo and Osaka have become smaller. Till 1935, their management areas were very wide. For example, that of Tokyo included Hokkaido, Tohoku, Kanto and the eastern part of Chubu region, however in 1960, it was reduced into only Kanto and the eastern Chubu region. (2) Kyoto also had a great deal of concentration, but its area has always been small. (3) The rank of Kanazawa as a management city has gradually dropped out. Especially after world war II, its importance as a management city dro-pped out rapidly. And Kanazawa has become a sub-regional management city. (4) Conversely, Nagoya has enlarged its economic management area after world war II, including Hokuriku region of Toyama, Ishikawa, Fukui prefectures. (5) Eukuoka, Sen-dai continue to have considerably large concentration. (6) Although Hiroshima and Takamatsu seem to have become Regional Management Cities only recently, the origin of such a transformation can be traced in the period before world war II.
Generally speaking, in parallel with the fact that Regional Management Cities enrich their management functions and widen their management area, the central management cities like Tokyo and Osaka lose the importance and their management areas become smaller. This process seem to have started around 1935.
It has been said that the Central Regional cities emerged only after 1955. But by an-alizing the concentration of economic management centers and the economic management area of each city, we can conclude that the periods around 1935 are considered to be more critical one.
This article is hoped to answer to the comments made by Mr. Yoshida on my previous essay appeared on Geographical Review of Japan vol 47, no. 5, 1974.

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This paper deals with remains of the Joni system, the grid-pattern land development of the Ancient Ages, located in the vicinity of Ashikaga City of the northern Kanto District. The original layout of the Joni is recognized in the area covering three ancient villages, Tanaka, Sukedo and Kakabo, on the both sides of the Watarase River.
Tanaka is situated on an alluvial fan, and conserved the original land allotment of the Joni system until fifteen years ago. Changes of watercourse of the Watarase River in the latter half of the sixteenth century destroyed the Joni structure, especially in the northern part, and that portion was separated from the rest of the village land by the river. A new irrigation channel was constructed right after that. Sukedo and Kakabo lie on flood plain in hilly area, and the flat land is used for paddy field as at Tanaka. The paddy field is irrigated by several tributaries of the Watarase River.
Existence of land patterns derived from the Joni system was confirmed in the area by consulting with old cadastral maps and other documents, and the former state of the Joni was restored as one unit stretching on both sides of the river. Most of the remains of the Joni system dealt with in this paper has been destroyed these sixty years.

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The Yahagi River which flows through the eastern part of Aichi Prefecture has a length of 117km, and two big cities, Toyota and Okazaki. There are many gravel and silica sand pits in this river basin (Fig. 1). In recent years, water pollution of the river has worsened. A series of investigations of water quality of the river was carried out during the period from December 1971 to November 1972, and the findings were as follows.
As shown in Table 1 and Fig. 2, the water quality of the Yahagi River is characterized by higher concentration of suspended solids.
Outflows of suspended solids and COD are approximately constant without reference to the change of river discharge under about 90m³/sec. Outflows of other components increase as the discharge of river rises (Fig. 4).
A comparison between the water quality at the end of and before the New Year holidays shows that the former has a lower concentration of suspended solids (Fig. 5).
It may be said that the largest factor contributing to water pollution is waste water containing a large quantity of clay discharged from the gravel and silica sand pits.

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