The purpose of the present paper is to clarify the successive changes in a day, i.e. the daily rhythm, of functional regions within the Tokyo special wards in terms of automobile traffic flows. For this purpose, after the study area being regionalized into 59 unit zones (see Fig. 1) and the fourteen hours from 6:00 to 20:00 being divided into seven time periods of two-hour intervals, the O-D matrix including 59×59 elements is prepared by each time period. An analysis is made, first, to examine the periodical characteristics of automobile traffic flows from the viewpoint of their purposes (Fig. 2) and the land use of their origins and destinations (Fig. 3); secondly, to delineate functional regions by employing factor analysis to the O-D matrix of each time period (Fig. 4); and thirdly, to estimate the Pearson's product-moment correlation coefficients of the factor scores and loadings in order to clarify the similarities between the functional regions of adjoining time periods (Fig. 5). As a result, the daily rhythm includes the following three different stages:
1. In the morning from 6:00 to 10:00 when most of the flows occur from homes to offices and schools, a number of small functional regions are formed as shown in Fig. 6-A. The distinct functional regions extracted are the Joto region (A₁ in Fig. 4) in the east, the Johoku region (A₂) in the north, the Jonan region (B₂) in the south, and the west Jonan region (B₃) in the southwest. The three functional regions except for the west Jonan region cover the industrial areas of the downtowns, respectively. Among the four regions, both of the Joto and Johoku regions are formed at the earlier time period. This is probably due to both of them being focussed upon transport facilities.
The small functional regions rapidly expand by fusing into each other as indicated by broken lines in Fig. 6-A. To be exact, larger functional regions enlarge further as their centers come to dominate the hinterlands of the other adjacent smaller ones. For example, the Joto region comes to absorb the Johoku region because the first factor interpreted as the Joto region at the time period of 8:00 to 10:00 has significant correlations not only in factor score and loading with the first factor indicating the Joto region at the time period of 6:00 to 8:00 but also in the factor loading with the second factor indicating the Johoku region at the same time period (see Fig. 5). In like manner, the Jonan region enlarges by including the west Jonan region. As mentioned above, the stage of the daily rhythm of functional regions in the morning can be comprehended not only by the formation of many small and transient functional regions but also by their expansion due to fusion.
2. Three large-scale functional regions are delineated in a triangular position during the daytime from 10:00 to 16:00 when the business flows conveying goods predominate among the facilities of offices and commerce (Fig. 6-B). In detail, these functional regions are the Joto, Jonan and Josai regions. The Josai region is indicated by the third factor at each time period in the daytime (see C₃, D₃ and E₃ in Fig. 4) and has no significant correlation with the other functional regions (see Fig. 5). The hinterlands of the three functional regions are more or less stable in the daytime but, on the other hand, their centers are temporally variable. For example, the Jonan region has its centers in the C.B.D. during the time period during of 10:00 to 12:00 (see C₁ in Fig. 4) but in the southern district during the next two time periods (see D₂ and E₁). In the case of the Joto region, the centers gradually move into and near the C.B.D. (see C₂, D₁ and E₂).

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Innovation diffusion in a centralized decision-making setting should be examined in terms of the dynamic facilities location problem (Brown, 1981). This paper is concerned with the spatial diffusion of a non-profit motivated innovation in the above setting, taking the example of radio stations in Japan before World War II. Especially the following point will be discussed here: whether radio stations spread hierarchically or not, when a certain optimal location strategy is implemented.
If people are evenly distributed, efficiency and equity may be congruent. In the real world, however, the discrepancy between efficiency and equity is caused by various conditions, so that the optimal location pattern under the efficiency strategy will differ from that under the equity strategy. This paper asks which strategy could produce a hierarchical diffusion of new facilities. If the objective of the optimizing model is to minimize the total travel distance, facilities are oriented to densely populated areas. In addition, high income areas tend to be chosen under the efficiency strategy (Morrill, 1974; Morrill and Symons, 1977). Consequently, facilities would be preferentially located in larger cities with high population densities and high income levels. This discussion results in a working hypothesis that new facilities may spread hierarchically under the efficiency strategy.
Experimental approach to the hierarchical diffusion of new facilities To investigate the above hypothesis theoretically, the following simulation was attempted by using Törnqvist's model. We shall consider a set of cities in a hypothetical region. They are arranged in a 9×9 mesh of 81 cells. With regard to city-size distribution, two types of distribution are considered: 1) rank-size distribution where the largest city with population of 9, 000, 000 is followed by the 2nd and lower ranking cities to fit such a rank-size curve as P_r=9, 000, 000/r; 2) hierarchical distribution where the largest city with population of 9, 000, 000 is followed by the 2nd to 9th ranking cities, the 10th to 27th ranking cities, and the 28th and lower ranking cities to fit such rank-size curves as P_r=5, 000, 000/r, P_r=3, 000, 000/r and P_r=1, 000, 000/r respectively. With regard to the spatial distribution of population, the largest city is always fixed at the center of a region, and other cities are randomly arranged in such a way that population distribution shows either significantly positive spatial autocorrelation or no spatial autocorrelation, regardless of city-size distribution.
After the four hypothetical regions are constructed by the combination of city-size distribution and spatial distribution of population, facilities are located in each region under the following rules: 1) the total of 9 new facilities are located during the 9 unit periods according to the efficiency strategy; 2) only one facility is located during each unit period; 3) the first facility is always given to the largest city, and then 8 facilities are sequentially located one by one.
For each region, 10 different spatial distributions of population are produced by random numbers, and the total of 40 simulation runs is repeated. Then the significant difference of means of correlation coefficients between the period of facility location and population was tested for each pair of the four regions. Results (Table 2) are summarized as follows: 1) though there are statistically significant differences of means of correlation coefficients between all the pairs of regions, hierarchical diffusion is not present in all the regions even under the efficiency strategy; 2) a hierarchical diffusion tendency often emerges in regions where populations are not spatially autocorrelated, which suggests that spatial distribution of population is more critical than city-size distribution.

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Studies in the historical geography of mountain villages in the Edo period are progressing. These studies mainly focus on upland field villages and forestry villages. But in Japan there were also terraced paddy fields as a type of land use on mountain slopes. These terraced fields are a result of long term reclamation. Furthermore, many small scale Shinden (newly reclaimed field) settlements were created by such reclamation. These Shinden Settlements are often branch rural settlements (Edagô). This paper deals with a mountain village in Kubiki-county of Echigo province.
The purpose of this paper is to investigate the process of reclamation and socio-economic rural structures during the Edo period.
The results are as follows:
1) During the end of the 17th century (early part of in the Edo period), the farm lands were distributed around the lower mountain slopes, according to analysis of the cadastral books (Kenchi cho). In this period, the farmers were mostly small landowners. Especially numerous were many peasants (dependent farmers).
2) Such peasants sought more independence for themselves. They reclaimed farm lands for the expansion of their landownership. The forms of reclamation were extansive swidden cultivation and expansion of the borders of farm lands to the common lands (Iriaichi). During the early 18th century, this expansion was accelerated for the waste lands in the border areas between neighbouring villages. The peasant classes enclosed these lands and migrated to them. As a result, new branch rural settlements were created.
3) At the end of 18th century, the shortage of green manure for fertilizer occurred due to excessive reclamation. Therefore, the farmers converted extensive farm lands into new intensive paddy fields. The process of improvement was calld Hatadanari. This improvement was made possible by old land-slide landforms.
Thus, the reclamation of farm lands in mountain villages advanced with the independence of peasants and good use of physical conditions. I think that such processes were a new form of organization in which the settlements solved the problems of population increase and the hardships of farmer's lives, while stabilizing the old rural structures. This is a characteristic of rural communities in underdeveloped mountain villages in the Edo period.

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The variation principle is a concept for investigating the spatial pattern of any path on a given curved surface. From this point of view, properties of the Mt. Fuji climbing route are discussed, based on morphometric data. The route goes straight towards the summit on the gentle slope at the foot of the mountain, and shows a zigzag pattern on the steep slope near the summit.
The variation principle maintains that the route can be a stationary one which minimizes some quantity. The straight portion of the route near the foot is the geodesic on a conical mountain, which gives the shortest distance to the summit. In order to explain the zigzag pattern near the summit, however, the amount of energy required to climb the mountain has to be taken into account. From this point of view, two types of models, namely, the excess energy model and the total energy model are possible, among which the latter seems better.
If the latter model is employed, it is reasonable to assume that the energy required is proportional to the reciprocal of the power function of cosine of the slope. The exponent of the power function here is approximately 12. The zigzag route in this case has been designed so that the route needs 1.6 times as much energy as on a flat surface. The portion of the climbing route higher than 3200m in elevation is less steep, and this may correspond to the lower oxygen content above this level.

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