This study is concerned with the examination of changing patterns of residential differentiation over time in a nineteenth-century British industrial city. In contrast to previous research, the work concentrates on one part of the city, the central area of Glasgow between 1871 and 1891. Taking due account of the literature in urban sociology, geography and multivariate statistics (chapters 1 to 3), a new approach to social area study is outlined, involving the development of a dynamic factorial ecology, together with its quantitative application. Such an approach is set against the background of the economic development, urban growth and population expansion of the city of Glasgow over the latter part of the nineteenth-century. (Chapter 4), and the study area for its detailed application is defined and described (Chapter 5). Data for quantitative, analysis were obtained from two 5 per cent samples of householders' schedules contained in the manuscript enumerators' records of the Census of Scotland. Problems associated with the samples drawn, the aggregation of households into grid squares and the particular method of factor analysis employed are solved by the development of new techniques for sampling error correction, sample analysis and the estimation of factor scores (Chapters 6 and 7). Six dimensions of social area change in Central Glasgow between 1871 and 1891, reflecting urbanism, familism, socio-economic status and birthplace composition, were extracted by principal components analysis from a data matrix of 18 socio-economic change variables observed for a network of 78 grid-square based subdivisions of the study area (Chapter 8). The same data base was used to compute three indicators of population change over the same time period, measuring natural increase and decrease, net local migration and extra-city immigration of the 0-20 age group (Chapter 9). Additional information on slum clearances carried out over the study period was derived from property purchase registers. The techniques of simple correlation, multiple regression and canonic analysis were used in the testing of a number of hypotheses relating social area change to population dynamics (Chapters 10 to 12). The prediction of social area change for a set of population change circumstances is also attempted. The results of the various analyses undertaken indicated that, while confirmation is realised of relationships between population loss, age structure and household composition, and for the overcrowding and social decline of areas adjacent to slum, clearance zones, additional consideration must be given to the relevance of the housing situation, societal evolution and the position of the individual in the life cycle to any model of social area change in the inner city. Finally, the concept of urban scale is introduced as an integrating framework for the study of social area change and population dynamics in a city context and directions are offered for future work in the field of nineteenth-century urban social geography.