This is to study on the diffusion of supermarkets, an innovation in the Korean urban system. To clarify the process and the involved factors in their spreading, we examined their areal distribution. As their diffusion is closely related with the Korean urban system, it was compared with our previously verified dimensional characteristics of the Korean urban system (Sung, 1977) and with the hierarchical structure of the central place system (Sung, 1979b). Data were collected from 33 cities from 1968 to 1978, excluding such nonadoption cities as Kimcheon and Chungju. The main results are as follows: 1. The appearance and the diffusion of supermarkets imply a revolution of the retail system in Korean cities. The spatial distribution patterns of supermarkets can be classified into two types: the enterprises in the regional administrative centers and those in Seoul. To the former belong those whose head offices are in the regional administrative centers such as Daegu, Busan, Gwangju, and Daejon. They control all the cities under their influence. The latter are those whose head offices are in Seoul but whose branch offices are in the regional administrative centers of high population size and high centrality. They control all the cities within Korean urban system. The competition between the enterprises of Seoul and other regions are so severe that Seoul head offices meet with difficulties to set up their branches in the regional areas, and as a result the diffusion of Seoul branches are retarded. The correlation between adoption time (year) of supermarkets and the urban population size reveals γ=-0.774, which indicates that supermarkets tend to be adopted earlier in the larger urban centers (Tables 1-2 and Figs. 1-5).

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The hierarchical classification of central places, according to the analysis of multivariate data by a quantitative method, is a fundamental and important issue in a study of central place system. Therefore, the methodology based on the analysis of central establishments has been improved until now. Such methods as the location coefficient technique by Davies, factor analysis, principal component analysis, Beavon's method, cluster analysis, have been frequently used. However, each method has advantages and disadvantages so that we must examine its own characteristics. The main aim of this paper is to point out a feature in each method and search a more efficient method to measure the centrality (nodality) of central places. Prior to the concrete examination of methods, we begin to check the following points as the conditions for an efficient method: First, concerning the data, the matrix consisted of the numbers of central establishments is far more reliable than the incidence matrix just indicating the existence of a central function or not. The reason is that the incidence matrix causes not only a loss of the information but also depends on an unadaptable concept of 'threshold population' introduced by Berry and Garrison. Some of geographers indicate that the threshold population is really often neglected for the occurrence of each central function. Second, we decide to adopt the nodality (absolute centrality) rather than the centrality (relative centrality) in Christaller's sense, which is extremely difficult to measure and utilize. Third, it is more convenient to evaluate the nodality by a numerical value, concerning the analysis of recent changes in the nodality of each central place. For this reason, we avoid to adopt Beavon's method and a cluster analysis, which might have any advantage. From these points of view, we analyse the nodality of 87 central places in Okayama prefecture, which have 52 central functions, by using a rank order method and a metric MDS method, plus the methods above mentioned. The result is that we can get the most relevant hierarchical classification of central places, when we employ the coordinates of the first dimension for the metric MDS method and the first principal component scores for the principal component analysis which comes from the variance-covariance matrix and/or cross-product matrix instead of the correlation matrix. On the contrary, both the factor analysis and the principal component analysis in which the correlation matrix is adopted, can not produce a suitable result because the correlation coefficient can not measure the size difference between central places with similar central functions.

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This paper aims to clarify the land conditions under which debris flow and land slip are likely to occur due to heavy rainfall. Kure city which has been repeatedly damaged by debris flow is selected as a study area. The present writer used the Matrix Approach proposed by DeGraff and Romesburg (1980). In this method, the study area is divided into homogeneous units regions according to various combination among geology, slope inclination and slope direction. Then the relation between the occurrence of debris flows in 1967, and the homogenious units regions are examined. As a result, in Yasumiyama mountain, the region with high outbreakability lies in 1) area of coarse granite area in comparison with dike area, and 2) slope inclination between 20 and 40 degree. Homogeneous units regions with high occurrence rate is naturally considered to be dangerous regions against debris flow in future.

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