Purpose of this article is to examine philosophical implication of the “qunatitative revolution”. The paper is divided into three sections. ; first, the philoso-methodological implications of “qunatitative revolution” are identified. ; second, the traditional dicho-tomism of nomothetic-idiographic approaches is rejected because of obsolescence of the uniqueness thesis ; third as a substitution of the dichotomy, the paired concepts, “universal, abstract individual, concrete”, which show the two different geographer's concerns are introduced, and the philosophical implications of “revolution” are examined in terms of each of those concerns.
Main points of arguments addressed in the paper are as follows;
1) The so-called “qunatitative revolution” provided us various useful mathematical-quantitative techniques, it aimed, however, essentially to reformulate our discipline with introduction of the so-called scientific method.
2) So that, the “qunatitative revolution” should be considered not only from the techni-cal viewpoint, but also from the methodological one.
3) The attempt of reformulation started from Schaefer (1953) who criticized the Het-tner-Hartshorne type of idiographic approach and completed by Harvey (1969) via Bunge (1962).
4) The “classical” geographers considered as Wrigley (1965) pointed it out, that the ultimate goal of the discipline was to find a set of laws which governed geographical phe-nomena, and they had conviction that there was no difference methodologically between what would now be called the social and the physical sciences. Thus, the recent attempt by Schaefer, Punge and Harvey can be considered a revival of the “classical” paradigm of the discipline.
5) The trend was often expressed as the change from the nomothetic to the idiographic approach, but the traditional dichotomy of “nomothetic idiographic” is not adequate for describing the present situation. Because those concepts are already obsolete by rejection of the so-called uniqueness thesis and are not suitable to express the alternative concerns of the present geographers.
6) Therefore, the paired concepts, “uiversal, abstract individual, concrete” would be suggested to adopt for describing the present geographer's concerns.
7) we should keep it in our mind that we can not make any reasonable statement on our experiences without generalization, and that we are always seeking some kind of the regularity in our experiences. In terms of generalization and seeking the regularity, there-fore, there is no difference between the universal, abstract and the individual, concrete approaches.
8) There is, however, a definite difference between the universal statement (it should be abstract) and the individual one (it should be concrete). The geographers who have interest in the former are necessarily oriented to build “theory” and those who are concer-ned with the latter become “facts” oriented. Orientations toward theory and facts, often sited as though, they are complimentary are essentially contradicted with each other as like as figure and background.
9) Harvey (1969) wrote that his book concerned with methodology rather than with philosophy, but in his arguments on the methodology of science, the author seems to impli-citly assume that geographers are solely concerning with the universal, abstract statements. But we can not neglect that good many geographers are actually concerning the individual and concrete cases at least under the present circumstance. In this sense, Harvey (1969) raised the important philosophical issues which involve the arguments on the purpose or aimes of the geography.

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A general course of numerical analysis of topographic or in a broader sense geographic data is discussed here, assuming to use a high speed computer.
As long as a topographic map is employed as a common source of data, it is the first step to pick up numerical values from the map, and this generally requires a great effort. Once the data are obtained in the form of punched cards or tapes, it is rather easy today to process them by means of computer. A spatial analysis is now of great importance to geomorphologists and geographers in general who wish to interpret spatial interrelation or arrangement of landforms and other phenomena.
As examples of data processing by computer, the cases of a double Fourier (harmonic) analysis and a trend surface analysis are presented here, and the results are drawn by the XY plotter attached to the FACOM 270-30. The trend surface analysis is applied to the the Asan Mountains, Northeastern Shikoku. It gives a result which shows quantitatively a distinct contrast between the opposing sides of questa ridges developed on massive sand-stones which are constituent beds of the Cretaceous Izumi Group. The double Fourier analysis of topography of the Kinki District reveals that a dominant wave-length of 20-30km is of tectonic origin.
Processing the spatial data by computer is easy. What really matters is how to sake the effort required to take up numerous data correctly from the map. For this reason, it is desirable, in conclusion, to print a Cartesian co-ordinate grid on the map, as is the case in European and American maps. It is hoped further that a common data file concerning the informations read from the topographic maps is made to be available in the future.

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An analysis of trend-surface has been one of the major subjects in quantitative geography. The present study was attempted to provide two examples of the trend-surface application by polynomials for the population densities distribution both in the Kanto District and in the central part of Tokyo, and to scrutinize to what degree the trend-surface mapping can extract the spatial structures given beforehand for the purpose of numerical experiments.
The data of population by grid-cells are obtained from the statistics of population by co-ordinate system that the Census Bureau of Japan has published. The population den-sities are measured by 457 grid-cells (10km×10km) for the Kanto District, and 404 grid-cells (1 km×1km) for the central part of Tokyo.
Trend-surface application to the Kanto District, the first through the sixth degrees, shows that the spatial structure of population densities distribution is basically concentric around Tokyo (see Fig. 1). The goodness-of-fit of trend-surface is at the one percent level of statistical significance for the first through the sixth degrees, and the variance ratios between two succeeding degrees of trend-surface are significant at the five percent level (see Table 1-(1) and (2)). The confidence interval of τ-values on the trend-surface is however rather wide as compared with the range of Z-values, and the spatial distribution of residuals (Z-τ) is far from randomness. In addition to those results, a trend-surface profile for the popu-lation densities distribution in the Kanto District indicates an extremely large deviation of trend-surface from the actual values at the maximum, although the fit becomes better as the higher degrees are applied to the distribution (see Fig. 2). Those results suggest that the goodness-of-fit test of trend-surface by coefficient of determination does not always reflect the spatial correspondence between the data values (Z-values) and the computed values of trend-surface (τ-values), and that the trend-surface analysis by polynomials is not appro-priate for extracting the spatial structure existing within a distribution whose maximum value is extremely large.
Compared with the case of the Kanto District, the spatial structure of population den-sities distribution in the central part of Tokyo seems to be less simple. That is, the fitted trend-surface reveals at the sixth degree three maxma surrounding the core area of Tokyo (see Fig. 3) . Both the goodness-of-fit test and the variance analysis of the trend-surfaces for this region suggest a little better fit than the case of the Kanto District, although the con-fidence interval of τ-values is rather wide (see Table l-(3)). The spatial correspondence is good in distribution between the Z-values and the τ-values (see Fig. 4), and the spatial dis-tribution of the residuals is rather random pattern. Therefore, the residuals of τ-values from the Z-values might be used as a clue for finding the local factors exerting influences on the population densities distribution associated with those areas of large residuals.
A noticeable fact is found for the direction of inclination of trend-surface at the first degree as one compares the Kanto District with the central part of Tokyo ; the former shows SE-NW direction while the latter an opposite direction of inclination, NW-SE. It seems to the writers that a hierarchical system does exist among a series of spatial structures involved ; one may find some different spatial structure of an areal phenomenon when he applies the trend-surface analysis to a different scale of areal extent which involves the same area.
A sensitivity of trend-surface analysis has as yet been left to be scrutinized in terms of extracting some spatial structure existing within the areal extent of the phenomenon under study.

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The purpose of this paper is to deduce the optimal land-use type from the viewpoint of regional planning. The whole area of Aichi Prefecture was divided into 5, 142 standard meshes (grids), and for each mesh, 17 variables were examined to determine the types of land-use.
Adopted variables are as followings;
A. Physiographic factors: (1) elevation, (2) relief energy (land relief) (3) drainage density (density of valleys) (4) gradient of land, (5) practically utilizable amounts of ground water, (6) potential of ground water, (7) fertility of farm land, and (8) fertility of forest.
B. Distance factors: time-distace to, (1) Nagoya, (2) regional centers, (3) freight terminals, (4) railway stations, and (5) highway interchanges.
C. Social factors: (1) forest reservation, (2) improved faun land, (3) irrigated up-land fields, and (4) density of road networks.
Five types of land-use (residential, commercial, industrial, agricultural, and forestal) were predesigned by factorial analysis. These types were individually diiend by control-ling the difinite amounts of area coverage in a mesh. The satisfied meshes (grids) were named here “typical”. By this procedure, 1, 037 meshes were accounted for “typical” ones and their numbers corresponding to each type of land-use were shown in Table 1. The ratio of discriminant power is accounted for 87.7 percent. The discriminant functions were listed in Table 2. The largest discriminant scores for each mesh were culculated employing those functions and they were utilized for the computer mapping (Figure 1).

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The results of a numerical experiment on water interchange among 21 sections of Setonaikai, or the Seto Inland Sea, are reported in this paper.
The numerical model in this experiment is based on the following assumptioms;
The first assumption is that the spatial distribution of chlorinity in Setonaikai is given as constant by the annual mean of chlorinity and water mass.
Thus, the solution of simultaneous equations with two unknown quantities of inflow and outflow gives the inflow and outflow ratios as shown in Fig. 6.
Next, the staying periods of fresh water are obtained by solving a matrix with corn-non en is of inflow and outflow ratios. They are shown in Table 1.

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Interaction data between nodes are usually presented as an interaction matrix to facilitate understanding and analysis of interaction. Temporal changes of an element or a part of an interaction matrix may be easily discerned, but overall changes of the matrix are often difficult to grasp. Such a difficulty is commonly encountered in investigation of a regional system, which is constructed on the basis of interaction data. In this paper, Medvedkov's method of settlememt pattern analysis (1967) is adapted to measure randomness of linkages and organizing potential for nodal regions associated with the randomness in the 1959 and 1965 United States air networks, whosee nodes consist of the 100 largest cities in terms of air passenger generation.
Medvedkov developed a method incorporating Shannon's entropic measure H_s in the method to separate the random and uniform components in an actual lattice of settlements. It is supposed that the actual lattice consists of two lattices, the random and uniform ones. In his method, H_s is calculated first, and the value is used to estimate the random component. In the present paper the same method was applied to the air connection matrices to sepa-rate the random and uniform components. The actual connection matrix is assumed to be composed of the random and uniform matrices. When the air network consists of only the uniform component, the network is undifferentiated and it does not have organizing potential for nodal regions at all. Hence, the regionalization potential of the netwrok can be attributed only to the other component of the actual matrix, the random matrix. When the air network is defined as an open system, the change of the total connection value B (Table 3) can be considered as arising from the external causes, which are multifactorial and rather complex. For this reason, it is more useful to compare the random and uniform components by their ratios within the system. The greater the random ratio, the greater the regionalization potential. As the random ratio declines in the connection matrix, the regionalization potential decreases, and the network division becomes more difficult.
From 1959 to 1965, the total connection value increased from 11, 536 to 16, 422 (Table 3). With the increase of B the random component also increased, but the ratio of the random component decreased 1.5% from 13% to 11.5% because the uniform component increased more rapidly than the random one. From the viewpoint of the entropic measure presented in this paper, the intensification of nodal fields associated with the increase of linkages in the air network resulted in the relative decline of regionalization potential in the system.
The adaptation of Medvedkov's method in this paper is more specialized than the use of H_s or relative entropy (H_s/H_max) alone as a means of analyzing regionalization potential from the geographer's viewpoint. The association of the random component of the connec-tion matrix with the regionalization potential of the matrix is conceptually interesting. This somewhat specialized use of entropy, however, is not without cost, since the method cannot be applied to matrices with the average values per cell of 1.0 or less, at least, with its present equation (3) for the approximation of the random component. Despite this short-coming of specialization, incorporation of other geographic variables such as distance and node size into the entropic model seems desirable.

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For an appropriate explanation of geomorphological features, it is necessary to study both the characters of materials which constitute the features and the transformation of the features.
Model experiments dealt in this paper offer one effective method to analyze the latter i. e., to examine the laws on the transformation of the features and their fundamental equations.
If the experiment is to be considered from the point of view of investigating the fundamen-tal equations, numerical experiments operated by computor today have the similar meaning with model experiments.
In either case the features in the prototype should be reproduced in the experiment. Numerical experiments are often useful when proper controlling factors and the laws of their working mechanism are well known. On the other hand, model experiments are sometimes operated in cases where their laws are not well known, because they can be operated with some knowledge on controlling factors in the trial and error steps.
As to geomorphological phenomena, generally it is difficult to obtain proper equations for them, and then model experiments may be used to estimate the basic relations among them.
The first problem in carrying out the model experiments on geomorphological pheno-mena is that the appropriate dynamic similarity conditions should be observed.
The fundamental conditions for satisfying the similarity laws are
P₁/m₁=P₂/m₂=……=P_n/m_n (1)
or
P_i/P_j=m_i/m_j (i, j=1, 2, …, n) (2)
Setting Pi/Pj=πp, m_i/m_j=πm
we obtain π_p=π_m (3)
where p is a physical factor in the prototype, and m that in the model.
Eq. (3) indicates that pr-numbers in the prototype must be equal to those in the model for the phenomenon to reappear in the model.
But it is seldom possible that all π-numbers in the model are in conformity with those in the prototype. This is the limitation of the model experiment. In some cases, however, it is possible to operate the experiment by easing the similarity law i. e., dividing a pheno-menon into some local regions in space and time.
In the model experiment on gully morphology, the eroding force by surface runoff was assumed to be a dominant factor. The fundamental equation of surface erosion is given by Horton (1945), which may be written as follows
d_mp/d_tp=k_epA_pτ_ep (4)
with m: eroded mass, t: time, k_e: erosion proportionality factor, A:area, τ_e: eroding force per unit area, and suffix p: prototype.
The scaling relations are developed simply by postulating that the fundamental equation be valid in the prototype as well as in the model.
Hence Eq. (4) becomes
dm_m/dt_m=kemA_mτ_em (5)
in the model. Here the suffix m indicates the model.
As the physical factors in the model and those corresponding in the prototype are related by scaling ratios, the ratio of Eq. (4) to Eq. (5) may be written as follows
dm_p/dm_m d_tm/d_tp=k_ep/k_em A_p/A_m τ_ep/τ_em (6)
Using m ∝ ρ₈l³, A ∝ l² and τe ∝ ρ_wV², Eq. (6)become s
ρ_wp/ρ_sp k_evp=ρ_wm/ρ_sm k_emV_m (7)
with ρ_s: the density of soil, l: length, ρ_w: the density of water, and v: velocity. Here, all variables are expressed by representative quantity.

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Remote sensing has been recognized as one of the most power full tools in the collection of geographical data. However, the application of remote sensing technology is rather underdeveloped compared with that of hardwares such as LANDSAT (ERTS) or scanners which show rapid progress in recent years. Therefore, the major objective of the research work done by present author is to develop the operational analitytical systems for fast image interpretation.
This paper deals with digital remote sensed image processing in land use and vege-tation. An analysis was made on discriminant analysis of land use classification using ERTS multi-spectral data. As the result, in 13 class discrimination, the rate of correct correspondence to the ground truth was about 40%. In 5 class discrimination, the rate was increased up to 69%. The main causes of errors are caused by 1) the scale affection of the size of picture cell, 2) lack in appropriateness in land use classification, and 3) noises in images.
Another analysis was made on classification of vegetation using digitalized multi-spectral photographs cdata. Interactive image processing system with color display unit was develo-ped for the analysis. This digital color system with mini-computer can be used not only for additive color display but also for the display of numerically processed images or for the pattern extraction by multidimensional threshold method. Using this system, vegetation was classified into the categories, and each categoriy is displayed in different colors.
As for the future prospects, further geographical applications are strongly recommended for the purpose of accumulating basic knowledge. The technological development, such as the introduction of pattern recognition methods in spatial context, is also indispen-sable for the future analysis.

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