There have been almost no studies on the changes in population and industries or functional changes in economies within the metropolitan areas throughout Japan because of the absence of statistical data based on metropolitan areas. The purpose of this paper, reviewing the above point, is to find the changes in population and industries in the 1960s, and to try to clarify metropolitan dynamics, factors for the dynamics and its mechanism.
Criteria for a central city in a metropolitan area and the integration of peripheral areas to a central city are as follows :
Central city: a legal city (shi) having 300, 000 inhabitants or more; daytime popu-lation surpassing residential population (1965 census year).
Inner zone: shi, town (machi) and village (mura) in which 10 percent or more of the workers living there work in the central city throughout the 1960, 1965 and 1970 census years.
Outer zone: shi, machi and mura in which 10 percent or more of the workers living there work in the central city only in the 1970 census year, in other words, peripheral areas integrated recently to the central city. The term a metropolitan peripheral area or a metropolitan suburb mean a total area of both inner zone and outer zone.
According to the above criteria, the author delimited 18 metropolitan areas. Among the 18 metropolitan areas, anazawa M. A. and Wakayama M. A. had no outer zone. Objects of analysis are residential population, total employed persons, agriculture, manufacturing, wholesale and retail trade, finance, insurance and real estate, and services. Methods of analysis are (1) location quotient and (2) chaning patterns based on propor-tional changes (chiefly 1960_??_1970) of central cities, inner zones and outer zones to the total population of metropolitan areas and the number of employed persons (at place of work) of each industry. As a preliminary step to the analysis, a hypothetical trend in spatial patterns of population change within a metropolitan area is summurized in Fig. 1. The formula of location quotient (L. Q.) is:
_??_
Where Oi is the number of employed persons in industry i in a given area, Op is the number of inhabitants in a given area, Ni is the total number of employed persons in industry i in Japan, and Np is the number of population in Japan.
The following general trends became clear after analyzing L. Q. of central cities, inner zones and outer zones for metropolitan areas.
1) Central cities have strengthened the character of place of work, whereas peripheral areas has the character of residence (Table 2) . 2) L. Q. of agriculture in central cities and peripheral areas shows a consistent decrease as the sizes of the central cities become larger (Table 3) . 3) L. Q, of manufacturing in metropolitan areas becomes lower in the order of central city, inner zone and outer zone; and the intrametropolitan equa-lization of manufacturing specialization proceeds with lowering L. Q. for central cities and increasing L. Q. for peripheral areas (Table 4) . 4) In the case of wholesale and retail trades, differences in L. Q. between central cities and peripheral areas are charac-terized by gain in the former's L. Q. and loss in the latter's L. Q. (Table 5). 5) Differ-ences in L. Q. of finance, insurance and real estate between central cities and peripheral areas show the maximum amount among all indices. Despite the fact that the central cities have generally decreased in L. Q. numerically, the substantial function of each central city seems to have declined if a rapid increase in the employed persons within the periph-eral areas of the three super metropolitan areas (Tokyo M. A., Osaka M. A, and Nagoya M. A.) is taken into account (Table 6). 6) Differences in L. Q. for services between central cities and peripheral areas are generally of minimum among all indices (Table 7).

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Combinatorial analysis showed that the average number _mμ_l of streams of order l merging into streams of varoius orders higher than l in a subnetwork of order m which is a portion of infinite topologically random channel networks is (Tokunaga, 1974)**:
_??_(1)
This equation provides two prerequisite conceptions for understanding some laws of drainage composition of an idealized basin. One of them is the conception of an “ideal drainage basin”. It means a supposed drainage basin in which the law of stream numbers given by Eq. (1) holds for every subbasins as well as itself and which can be finally divided into infinitesimal basins and interbasin areas. The other is the conception of a “unit drainage basin”. It means the basin regarded as a basic basin in considering the laws of drainage composition and its order is determined arbitrarily. Consequently orders of basins have only relative meanig in the ideal drainage basin, and may be determined depending upon a scale of topographic maps or aerial photos in actual drainage basins. Thus both the order 1 of the unit drainage basin and the order m of given drainage basin are treated as variables in this paper.
According to the above mentioned rules, some equations to describe the laws of drain-age composition of the ideal drainage basin can be deduced from Eq. (1) after algebraic procedures.
1) The law of basin areas is derived from Eq. (1), on a reasonable assumption that the interbasin area which is formed among basins of given orders and a stream of order higher than them is in any case smaller than the basins. It is written by Eq. (2).
am=4^m-lα, (2)
where am is the average area of basins of order m and al is the average area of the unit drainage basins.
2) It is easily deduced from Eq. (1) that the number of streams of order l and orders higher than l which merge directly into a stream of order m is
N_{i, m, l}=2^m-l+ 1, and the number of interbasin areas contacting with a stream of order m is equal to that number. Conse-quently the number Ni, m, l of such interbasin areas is
N_{i, m}, l=2^m-l+1. (3)
Then Eq. (3) is named a “law of numbers of interbasin areas” in this paper. 3) A “law of interbasin areas” is derived from Eq. (1), (2) and (3). The average area βm, l of interbasin areas contacting with a stream of order m is written by Eq. (4)
β_{m, l} _??_ (4)
4) Assume the next relation between the average length L2 of streams of order A and average area a2 of basins of order A,
_??_
where e is constant independent from orders of basins and streams, and substitute the above relation into Eq. (2). Then the law of s tram lengths is given by Eq. (5).
Lm=2m-1L1, (5)
where Lm is the average length of streams of order m and Ll is the average length of streams of order L.
5) Combining Eq. (1), (2) and (5) leads to the equation, which expresses the drainage density Dm, 1, after some algebraic procedures.
_??_
Introduction of a parameter msa which is the average number of streams of order A entering into a stream of order m from sides and assumptions that ε1=λελ-1 and K=mελ-1/mελ take same values respectively for various values of A in a basin provide the laws of drainage composition of the basin in a mathematically generalized form. Corresponding equations to Eq. (2), (3), (4), (5) and (6) are written by Eq. (7), (S), (9), (10) and (11) respectively.
6) The law of basin areas.
_??_
where _??_.
7) The law of numbers of interbasin areas.
_??_
8) The law of interbasin areas.
_??_
9) The law of stream lengths.
_??_
10) The drainage density.
_??_
Hack's law is checked in the basin given in the mathematically generalized form as well as the ideal drainage basin.

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Cotton was cultivated at various places in Japan in the Edo era. The cotton cultiva-tion in Japan started in the Yamato and Yamashiro basins, and was extended to the out-skirts of Osaka and then to most parts of Japan with the progress of the exploitation of 'shinden'. Commercialization of cotton cultivation influenced the rural economy con-siderably. In consequence, the old type upper class farmers were gradually decreased in number, but on the other hand the middle class ones and zaigo-shonin (merchants living in the country) who played a major role in the development of cotton cultivation upgraded their economic position. But the development of cotton cultivation later reached a limit and after that the cotton cultivation began to decline. At the beginning of the Meiji era the middle class farmers and zaigo-shonin lost their importance in the rural economy. In place of them, the large scale landowner system was established by the merchants of the cities.
In this context this paper deals with the cotton cultivation and the development of the rural economy by the cotton industry in the Yamato basin. The cotton cultivation there has peculiar circumstances. Namely, cotton was cultivated on the rice fields alternatively with rice every other year. Free extention of the fields for cotton cultivation was restricted because of the irrigation system controlled by the rural communities.
Major results of the research are as follows
(1) According to the documents at the beginning of the Meiji era, the cotton cultiva-tion in the Yamato basin declined, resulting in 1 /2 or even 1 /3 of the flourishing period in area. The declining rate was even all over the basin in general. In some places, however, the cotton cultivation did not suffer from a sharp decline. It seems to be a character of the cotton cultivation in the Yamato basin that the landowner system was not developed very extensively.
(2) i) Minami-Katsuragi (the southernmost part of the Yamato basin), the cotton cultivation was very prosperous at the middle to Edo era. It was not because of the shortage in water that cotton was grown, for the fields for cotton cultivation were restricted only to the fields which were suited best for rice cultivation which needs water. In Nagara-mura, cultivated fields were divided into 4 districts in accodance with the irrigation system and the fields of each peasant were usually dispersed in the 4 districts. This was another reason for the fact that free extention of the fields for cotton cultivation reached a limit. Cotton cultivation there declined after the time of Bunka-Bunsei (1804_??_1830).
ii) Development of the trade (cotton) and industry (spinning and weaving) was quite conspicuous in Nagara-mura. This advantage was well taken by the zaigo-shonin and their economic status was further upgraded in the late Edo era.

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