This paper analyzes city system dynamics, based on a theoretical framework relating interaction potentials to agglomeration economies and density externalities. It employs new historical time series data on population size of cities in Sweden over two centuries (1810-2010) and introduces two schematic growth factors: (i) the intra-city potential and (ii) the extra-city potential located in in rings encircling each city. The first factor is measured by each city's population size, while the second is a vector of distance-discounted population size for each of a city's urban rings. In this way, we can explain a city's growth as a function of its interaction potential inside the city, as well as inside the first, second hand third ring. A robust finding is that cities with large ring potentials follow different development paths than those with small ring potentials. We also find clear evidence of structural change between the two centuries 1810-1910 and 1910-2010. In the first period, city growth is positively impacted by the size of the intra-city potential, whereas the same potential dampens or reduces the growth in the second period. Moreover, the ring potentials outside the city tend to switch from having negative growth stimulation in the first period to having positive stimulation in the second period.