Four years later, in 1889, Ravenstein published another article in the Journal of Royal Statistical Society. This article was based on the experience of North America and Europe (the first article was based on the experience of UK ). In this article, he said that people travel long distances to occupy unsettled land. Nearly 100 years later, in 1940 Samuel A. Stouffer published an article in American Sociological Review. He showed that the number of migrants from place i to place j is inversely proportional to intervening opportunities. The model was confirmed by 1n 1975 by Wadycki who found it to be quite an accurate description of migration. Zipf (1946) developed and validated a gravity model to represent that volume of migration between two cities (M ij ) is directly proportion to populations of the cities (P i and P j ) and inversely proportional to distance separating the two cities (d ij ) He assumed that income and unemployment are uniformly distributed over the areas.

M ij = K (P i * P j )/D

where K is a constant to be found out from the empirical data. To some sociologists the model may look funny or absurd, but Zipf found that the model fitted very well for all modes of transportation.

After all, if the logic used in the model is sound that accurate data are available, why would mathematical equations not produce a good fit to empirical data?