The form of the French urban hierarchy can easily be
described by using a rank-size representation. On the whole, the form
of the urban hierarchy has persisted over the studied period (figure
1.
). It is characterized by the maintenance of the Parisian primacy with a ratio of 1 to 7 between the population of the agglomeration of Paris and that of the second city. The largest cities maintain during the studied period their size inequality but we can observe for middle-sized cities (size between 10000 and 60000 in 1831, and between about 40000 and 450000 inhabitants in 1982) a change in the shape of the curves. In 1831, their sizes are less important than previewed by the Pareto's law and the rank-size distribution shows an upward concavity. Progressively, this class of cities becomes more and more important and the shape of the curve shows an increasing downward concavity. Before examining this particular behaviour, we have computed in a classical way the value of the straight rank-size slope fitting the rank-size distribution by using Lotka's formulation:
For this, we have used all the urban units, ie. of more than 2000
inhabitants.
The continuous augmentation of the absolute value of the Pareto-exponent
in the figure 2
expresses an increase of the inequality of the city-size within the urban system. This tendency slowed down between 1926 and 1954, and then shows a clear upturn since 1975.