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Migration was the main motor of the transformation of a modest town that counted 279,370 inhabitants in 1860 into the dominant metropolis of a centralized state, a metropolis that approached one million inhabitants in 1930. The capital of Spain alone attracted 21 to 23 percent of all permanent Spanish internal migrants (Silvestre 2005). Most of the newcomers were unskilled workers coming from the large surrounding Castilian Plateau, but also from the North of Spain. Although such mobilities have been extensively studied by historical demographers, migratory fields have rarely been studied in-depth. In this communication, we propose a discussion of the concept and its statistical estimation. The aim is first to identify areas that were specifically attracted by the Spanish capital but also those which were significatively under-attracted. Our second objective is to verify if the populations with a preferential link to Madrid have grouped together in specific neighborhoods within the city. Analyzing a migratory field is more than a mere description of the migrants' places of birth. The theoretical foundations were elaborated by Ravenstein in his famous 1885 and 1899 articles on "The laws of migration", and later considerably developed by Hagerstrand (1957). The basic idea stresses the effect of distance. The further away you are from your destination, the fewer migrants there are. This relationships between the intensity of migrations to a point and distance to this point is moreover logarithmic, with an exponential decline from the nearest to the farthest areas. This relationship, however, does hold only if the absolute numbers of migrants from a given place are weighted by the population size of their locality of origin. Significant deviations above the regression line imply a preferential link with Madrid or, on the contrary, repulsion. Once the over- and the under-attracted regions are identified, explanations should be researched in their social and economic history. The newcomers' settlement of those in Madrid highly depended of their socio-economic status. The modernization of the city-center and major public health investment deepened the gap between affluent neighborhoods and the "barrios negros" or "barrios bajos" located in south and north outskirts. The latter acted as refuges for those who escaped the center and its excessive rental prices, as well as for the poor immigrants. We test the hypothesis that migrants coming from over-attracted regions tended to be spatially concentrated in Madrid. All our analyses are based on the 1905 Madrid padron. We cover two contrasted districts, Hospital and Congreso, with over 150'000 individuals. Migrants were 57/58% of the population. INE provided a database with the population at each census and the spatial coordinates X and Y for each municipality. Using those data, the number of migrants from each place is weighted by its population and the distance to Madrid calculated.
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