The purpose of this paper is to explore the potential applicability of Multi-Dimensional Scaling (MDS) to a spatial analysis of diffusion problem. Especially it aims at presenting an approach to analyze the diffusion of household innovation by using INdividual Difference SCALing (INDSCAL). As shown in the fact that there exists a spatial covariation between the opportunity to get innovation and the accessibility to information (Hanham and Brown, 1976), some of structural elements constituting a diffusion process of innovation would be spatially correlated. Factor analysis has usually been applied to such a spatial covariation problem, but it is not so much concerned with extracting the spatial structure itself. Accordingly, it is not necessarily a suitable method for the spatial diffusion study wherein both the functional and spatial perspectives are required (Semple and Brown, 1976). Moreover, existing methods devised to analyze the diffusion of household innovation, for example, the spatiotemporal logistic model or the space-time autoregression model, lay their emphases on the spatial perspective too much to meet this requirement. Now, assuming that there exists a space common to structural elements correlated spatially one another, INDSCAL seems to present an alternative method to cover both the perspectives. Its framework consists of the following procedures:
(1) To prepare the data for structural elements, which are considered as (dis)-similarity data.
(2) To recover a two-dimensional common space from these data by using INDS-CAL.
(3) To apply four-variable trend surface analysis incorporating the common space and time coordinate system to the cross-sectional data for the rate of diffusion.
Based on the analytical framework outlined above, this paper investigates the diffusion process of radio subscription in the Tokai district, mainly focusing its attention on the aspects of the spatial interaction and the occupation structure of cities. The study period is from 1929 to 1933, which corresponds to the primary stage of the diffusion. Forty-four cities are studied with more than ten thousand population and with more than two thousand households in Aichi, Gifu and Mie Prefectures as of 1930 (Fig. 2). Among those cities the radio station of Nagoya had started its service in the year of 1925. First, in order to recover a two-dimensional interaction space, the matrix of spatial interaction of cmmuting workers and students was multidimensionally scaled by using M-D-SCAL. In spite of high stress of 36%, which is not good, the configuration shows four significant city groups reflecting the sub-areal divi-sion of the three prefectures (Fig. 3). That is, the cities of the Mino area of Gifu Prefecture, the Mikawa area of Aichi Prefecture, the Ise area of Mie Prefecture and the Owari area of Aichi Prefecture form four clusters clockwise from the top right-hand quadrant in Fig. 3. Second, to get input data for M-D-SCAL to recover the occupation structure space, a dissimilarity index suggested by Johnston (1979) was calculated from the percentages by eight groups of occupational population; agriculture, fishery, mining, manufacturing industry, commerce, transportation, service and others. Fig. 4 shows a two-dimensional solution of the occupation structure space, whose stress is as good as 4%. An application of non-metric hierarchical cluster analysis revealed that the first dimension was interpreted as representing the contrast of occupation structure such as agriculture versus non-agriculture, and the second dimension as representing the dominance of manufacturing industry among non-agricultural occupation. The two-dimensional space can thus be identified as arranging the cities according to the difference of occupation structure.
Then the set of matrices of inter-city distances in two-dimensional Euclidean spaces for both was used as input for INDSCAL.

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1) Recent studies agree that the Egyptian agriculture must have originated at Marimdah and Faiyum in Lower Egypt, under the influence of the Middle and Near East, about 2000±500 years later, and then extended to Upper Egypt and Nubia.
The northern hemisphere in the Post-Glacial Period had passed through several climatic fluctuations. These fluctuations not only put severe restrictions on the ecological distribution of plants and animals but also gave a remarkable effect on the pattern of life and migration of the food gathering-hunting and nomadic peoples, and therefore greatly decided the formation of Egyptian history in the Nile valley.
2) The southern Sahara and its circumferences, Nubia, hilly areas of the eastern Upper Egypt, must have held various and plentiful fauna, judging from such numerous relics as the rock-drawings remaining in those districts. As for the domestication of wild animals, we may presume that it extended from the southern Sahara and its environment to Nubia and Upper Egypt, contrary to the advance in the development of Egyptian agriculture. The principal promoters were gatheringhunting tribes of Sahara and the eastern Hamites who were half cattle-breeding nomads.
3) A little moist “Sub-Pluvial Period” fluctuated at the middle of the fourth millenium B.C., When the climatic conditions of the northern Africa began to get greater degree of aridity. Then the first fauna-break occured unquestionably in those areas of Sahara and its circumferencs, Sudan, Nubia, Upper Egypt.
Devastation started from the Nile valley and Upper Egypt, diminishing the particular savanna landscapes in the environment, and elephants, rhinoceroses, giraffes began to disappear first, and then various sorts of gazelles and other savanna fauna also decreased.
4) The transition to“Sub-Pluvial Period” played a role of a trigger to the “Neolithic Revolution”, viz. the commencement of the agriculture and domestication of wild animals. The end of “Sub-Pluvial Period” and the following climate of aridity brought about the second agricultural revolution, viz. building an open road to the history of Egyptian Old Kingdom (Pyramid Age) through the new productive mode of agriculture using the basin system of irrigation and drainage together with cattle-breeding.

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The purpose of this paper is to consider the characteristics of functional distance derived from Markov chain model. So far functional distance has been used as one of the tools for regionalization, but its properties as a distance have not been discussed enough. The author uses inter-prefectual migration data in Japan to obtain the distance referring to existing literatures. Before proceeding the analysis, we review the mathematical premises of Markov model and their implications for geographical study. These are 1) consideration of both direct and indirect flows, 2) relative amount of such flows and 3) non-reflectivity. Under such constraints, we should apply functional distance approach.
As a result, Japanese inter-prectual functional distance is revealed to have following features. First, each prefecture's functional distance, as compared each other regarding origin or row, has quite similar pattern, which implies that Japan as a whole consists of only one system and has no subsystems. Secondly, east-and west-Japan information regions are identified. The two regions are situated on opposite poles on common dimension in terms of principal component.

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This paper proposes to reconsider the significance of the cities arround metropolises, above all that of the concept of satellite city in the study of metropolitan areas.
First of all, the characteristics of 412 units are examined in the factor analysis. These units consist of wards, cities, towns, and villages in Osaka, Kyoto, Hyogo, Nara, and Wakayama prefectures, and the eastern part of Okayama and Tottori prefectures. 44 variables are selected for the factor analysis. After the analysis has been completed, 4 factors are created as the results. Using the scores of these 4 factors, the units are classified in the next place. Fig. 1 shows the results that are got from these analyses.
There are, however, some units which we cannot yet include to or exclude from Keihanshin Metropolitan Area. Then the flows of commuters and students are analyzed (Fig. 2). This analysis elucidates a part of the functional region structures of the metropolitan area. After these analyses, the extent and structure of Keihanshin Metropolitan Area are judged as Fig. 3. As the cores of it, there are Higashi ward of Osaka, Ikuta ward of Kobe and so on. Arround these cores, there exist the units classified into suburb and transitional zone to suburb. In them there are some cities recognized as the industrial centers. Besides they are central places in the metropolitan area. Himeji, Wakayama, and Nara, locating at the edge of the metropolitan area, belong to the model type. Sakai, Higashiosaka and Amagsaki, surrounding Osaka indicate higher score in the suburb, so these three cities also have the characteristics like industrial center.
Untill now, cities arround the metropolis have been studied in the sense of expansion of residental area in Japan. Accordingly satllite city have also meant domitory city in which commuters to metropolis live. In America, however, satellite city means industrial suburb in the original sense. Then on the base of the satellite city concept by R.E. Murphy, I want to think about the above mentioned cities in Keihanshin Metropolitan Area according to the concept that satellite city is a industrial center and a central place. In the Keihanshin Metropolitan Area, the cities of this type are Himeji, Wakayaula and Nara. Sakai, Higashiosaka and Amagasaki are the near type to them. It is these cities that are very important as base points of urbanization and central places in the metropolitan area. Without the study of these cities, the synthesis between the study of urbanization and that of functional region in the metropolitan area would not be accomplished.

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