Professor G. T. Trewartha delivered the presidential address on “A Case for Population Geography” before the Association of American Geographers on the occation of its 49th annual meeting held in Cleveland, Ohio, March 20 _??_ April 2, 1953.
He, then, suggested that in geography the central theme is human life and fundamentally geography is to be anthropocentric, and emphasized the necessity of the research of population geography.
After the Second World War, the research works on population geography have increased so much in comparison to the Pre-War days, and it owes to a greater degree of spatial mobility than ever before, in almost all countries containing the developing and developed countries due to the results of stability of political conditions. The mobility has taken many forms; some have been in response to the general evolution of national societies and economies, others have acted as stimuli for fundamental social, economic, and political changes in the nations. In Japan, too, spatial mobility after the War has been equally intense as European countries. About eight millions or seven percents of the national population changed their residences in every year and such spatial mobility has changed the regional conditions in the country.
Spatial mobility in Japan after the War has taken three types as follows: (1) rural-to-urban migration, especially in the first stage, (2) residential mobility in and around the great cities as the results of population concentration, (3) inter-urban migration mainly since the oil shock in 1973.
As to the regional factors of the rural-urban migration, it has been, hitherto, insisted on that the economic motivation, that is, the lower level of income in the farm areas is the most important regional factor for the rural-to-urban migration. But it is not necessarily the most important. There are many other social factors which push out people to urban areas from rural farm, especially the breakdown of human relations in rural areas.
As to the residential mobility and inter-urban migration, we are also forced to explain the factors from human values, want, needs, and choice of the inhabitants, in addition to the economic motivation.

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A new diffusion model was introduced to simulate the profile evolution of the river consisting of gravelly bed materials and receiving no water from tributaries. In this model, diffusion coefficient a (x) is expressed as an exponential function of position x;
a(x)=k exp (rx)
where k and r are constants. Sediment flux J per unit width is proposed to be proportional to the gradient u_x of river bed;
J=- a(x)u_x Therefore, change of river bed height with time is expressed by the following equation;ut=-J_x=∂/∂x{a(x)u_x=}
This equation is wellposed if the upper boundary condition is given by the flux and grain size of sediment supplied at the top of alluvial fan, and the lower one by the sea level as a free boundary problem concerning the passively moving river mouth and the material excha-nge ratio to the sea.
The steady solution of the differential quation shows an exponential curve:u=(Je/kr)exp(-rx)+C
for the longitudinal profile of the graded river, where J_e is equilibrium flux of sediment and C is an integral constant that will be determined by the sea level.
The author examined the model as a Markov process. Sternberg's abrasion law was newly interpreted on a basis of stochastic concept as follows: the stay-time of grains at a given position of river bed is randomly changed after progressive decreasing of grain weight/diameter, and the exponential diffusion coefficient is derived from this random time-change for the basic diffusion process (Wiener process) and Shulits's empirical equation;ux∝p (or d)
where p (d) is weight (diameter) of grains.
In conclusion, a clear explanation of the empirical equation for the graded rivers;u=C₁exp(-rx)+C₂(C₁, C₂; const.)
was given under the above-mentioned theoretical basis.

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Two kinds of indices, the warmth index (WI) and the coldness index (CI) were proposed by Lira (1945, 1948) to correlate the geographical distribution of vegetation zones with the thermal condition. This Lira's concept is considered to be useful for the reconstruction of past vegetation during the last 20, 000 years. The distribution maps of WI and CI are made on the basis of the mean monthly temperature for the period from 1921 A. D, to 1950 at 860 weather stations distributed over Japan (Figs. 1 and 2). In this paper, five distribution maps are presented as the representative temperature conditions during the past 20, 000 years. These maps show the thermal limitation of the vegetation zones for five periods when the mean annual tempetature are -7°C, -5°C, -3°C, -1°C and +2°C at different from the present temperature, respectively.
The distribution map of WI and CI at the time when the mean annual temperature is 7°C lower than the present (Fig. 3) roughly represents the thermal limitation of the forest types at the maximum glacial period (about 20, 000_??_18, 000 years B. P.). Based on this map, Hokkaido should be covered with the tundra and subalpine conifer forests. The subalpine conifer forest also covers the Tohoku and Chubu districts. While, most of southwest Japan should be covered with the cool-temperate deciduous forest. Evergreen oak-laurel forests are only found in the lowland in southern Kyushu, Tanegashima and Yakushima islands.
The second map for the case of 5°C lower than the present (Fig. 4) approximately shows the thermal limitation at the late glacial period (about 13, 000_??_10, 000 years B. P.). This map indicates that subalpine conifer forests spread in Hokkaido. While mountainous regions in the Tohoku and Chubu districts are still under the subalpine conifer forest, the forest in the lowlands should be changed into the cool-temperate deciduous one. Evergreen oak-laurel forests invade into the southern coastal area of the Kii Peninsula. It is notable that warm-temperate deciduous forests should appear in western Kyushu, Setouchi and Osaka Bay areas.
The third map for the case of 3°C lower than the present (Fig. 5) is roughly correlated with the condition at the early Holocene period. The thermal limitation of the cool-temperate deciduous forest appears in the Ishikari Plain, Hokkaido. The the main part of Tohoku and Chubu districts are covered with cool-temperate deciduous forests. Warm-temperate deciduous forests extend a wide area in northern Kanto Plain, marginal part of Nobi Plain, and coastal lowlands along the western part of the Japan Sea. The northern limit of the evergreen oak-laurel forest should attain to the southern Kanto Plain in the Pacific Ocean side, while it is located at Matsue City in Shimane Prefecture in the Japan Sea side.
The fourth map for the case of 2°C higher than the present (Fig. 6) approximately shows the thermal limitation at the Hypsithermal time (about 7, 000_??_6, 500 years B. P.). Forests in Hokkaido should be changed into the cool-temperate deciduous one. Inland basins of the Tohoku and Chubu district are covered by the warm-temperate deciduous forest. Evergreen oak-laurel forests spread over the central and southern part of Japan. The northern limit of this forest is located at Kuji City, Iwate Prefecture in the Pacific Ocean side and at the Lake of Jusan, Aomori Prefecture in the Japan Sea side.
The fifth map for the case of 1°C lower than the present (Fig. 7) roughly represents the condition at the latest Jomon and early Yayoi periods (about 3, 000_??_2, 000 years B. P.) . This map is similar to the present potential natural vegetation maps which were made by Honda (1912), Horikawa (1968), Yoshioka (1973) and, Miyawaki et at. (1975), although there are some differences between two types of the maps.

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