The studies in urban population density and their analytical methods have been remarkably developed since C. CLARK's study in 1951. Much has been written especially to lead to general understandings of density gradients and central densities, while some geographers analysed the urban population density by using the power series trend surface model. The purpose of this paper is to analyse and to clarify the characteristics of the spatial distribution and changing pattern of urban population density in Hiroshima city by using these quantitative methods. The main results are summarized as follows : 1) Density crater appeared first in 1975 in the analysis of the spatial distribution in 1965, 1970 and 1975 by NEWLING's quadratic exponential model. Of course, we should not regard it as the first appearance of density crater in the city but as the first good flitting of the model for such a phenomenon (Fig. 4). By using CLARK's linear exponential model, on the other hand, density gradients have gradually flattened, while central densities declined in the first five years (1965-70) and then became stagnant in the second period (1970-75) as shown in Fig. 3. Therefore, the structural change of urban population density can be expected between both periods. 2) The coefficients of determination (R2) have gradually declined between 1965 and 1975 in CLARK's as well as NEWLING's models as shown in Table. 1. It seems to be based on the development of spatial segregetion due to the urban growth as already pointed out in some works. 3) When the writer tried stepwise multiple regression analysis to see by what factors the spatial variations of the urban population density and of the urban growth can be explained, he found out that while the former is related to only the distance from the urban centre, the coefficient of determination for the latter can be raised by the addition of such factors as population density, percentage of population under 14 years of age, percentage of the new corners in 1965-70 to that factor (Table. 4). 4) It seems that the cubic trend surface may be that most suitable for the analyses of this paper. The spatial pattern of the cubic trend surface in comparison with Figs. 6 and 7 forms almost circular in 1965 as well as in 1975 and the highest point of urban population density appears about 1.5 km south of the city centre. Because of residential growth in the urban fringe, however, most of isopleths of the trend surface moved outwards in 1975 as compared with those in 1965. The distribution of residuals from the trend surface in 1975 (Fig. 8), shows the over-estimation in the urban centre and in the areas which contained non-residentials such as fabrics, schools and slope lands. On the other hand, the comparison of the two trend surface maps of percentage-change in population in the periods of 1965-70 and 1970-75 (Figs. 9 and 10), shows the spatial disturbance in the period 1970-75 as compared with the circular pattern in 1965-70 ; the areas of decreasing population have expanded in the overall existing built-up areas. The distribution of residentials from the cubic trend surface demonstrates spatial anomalies such as the under-estimation of urban renewal area and urbanized area located directly near the built-up areas and the over-estimation of the urban centre and an old fishing village in the suburbs (Fig. 11). 5) The critical density called by NEWLING has gradually declined and its location has moved outwards from the urban centre from 1965 to 1975 as shown in Tab. 3. Thus, the location of density crest tends to move outward as it declines. Under the present technological and economic conditions and the physical terrain sea in the south and mountains in all other directions…which prevents free expansion of the built-up area, the writer infers, however, that the outward movement of density crest will be stopped in due time.
In Bolivia the Cretaceous System is distribution widely in the Altiplano, Andes Oriental, Subandes, and eastern hill regions. It is underlain unconfermably by the Palaeozoic formations, lacking most of the Triassic and Jurassic sequence. The System is characterized by the predominance of reddish or brownish red rock facies, and is named by STEINMANN (1904) as the Puca Group. The name was derived from “puca” which means red in Quechus. The whole section of the System is distributed in the Altiplano and Andes Oriental regions, and the upper part of the System is in the Subandes and eastern hill regions. 1) In the Andes Oriental region the System forms a large syncline named the Huarachani-Mocomoco syncline. The System is divided into the Huayrapata, Ococoya, Suches, Moho and Huancané Formations in decending order. The Huancané and Moho Formations are well exposed along the northeast coast of Titicaca Lake, but the Suches, Ococoya, and Huayrapata Formations are typically seen in the area upper course of the Suches River which flows from northeast into Titicaca Lake. The Moho Formation is a marine deposits, consisting of fine-to medium-grained sandstone, brownish red or black shale and dark grey massive limestone. There are thin fossil beds in several horizons. These fossils are mostly of echinoids and brachiopods which consist poor number of species. The Huayrapata Formation yields Viviparus, Melanoides and others. Judging from these fossils the formation is considered to be a non-marine deposit. 2) The system in the Titicaca basin, consisting of the Muñane, Vilquechico, Cotacucho, Moho, and Huancané Formations, forms a large synclinorium with axes trending from NW to SE. 3) In the Miraflores district, southern Bolivia, the System can be classified stratigraphically into six formations, as follows : El Molino, Chaunaca, Aroifilla, Miraflores, Tarapay, and La Puerta Formations in descending order. The Miraflores Formation consist chiefly of black or dark grey massive limestone, and contains pelecypods, brachiopods and ammonites. Based on these fossils the formation corresponds to the Moho Formation in Altiplano and Andes Oriental regions. It has been considered as Cenomanian in age. The formation is stratigraphically important in central Bolivia, because it is the most pronounced marine beds in the Cretaceous and can be used as the horizon marker. The El Molino Formation is another shallow marine deposits, yielding brachiopods, pelecypods and vertebrates. The formation is late Cretaceous in age. 4) In the Altiplano region near Titicaca Lake, Subandes and eastern hill regions, the uppermost Cretaceous sediments are continous to the lower Tertiary formations which are composed of the remarkable reddish facies quite similar to the Cretaceous red beds. It is very difficult to define the boundary between the uppermost Cretaceous and the lower Tertiary sediments.