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Census enumerations are usually packaged in irregularly shaped geographical regions. Interior values can be interpolated for such regions, without specification of "control points," by using an analogy to elliptical partial differential equations. A solution procedure is suggested, using finite difference methods with classical boundary conditions. In order to estimate densities, an additional nonnegativity condition is required. Smooth contour maps, which satisfy the volume preserving and nonnegativity constraints, illustrate the method using actual geographical data. It is suggested that the procedure may be used to convert observations from one bureaucratic partitioning of a geographical area to another.

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The mathematics of a push-pull model are shown to incorporate many of Ravenstein's laws of migration, to be equivalent to a quadratic transportation problem, and to be related to the mathematics of classical continuous-flow models. These results yield an improved class of linear spatial interaction models. Empirical results are presented for one country.T is now approximately one hundred years I since the geographer Ernst Ravenstein reported his "Laws of Migration" to the statisticians of London (Ravenstein 1876, 1885, 1889). We commemorate this by outlining an elementary mathematical model of migration that incorporates several of his "laws" as direct and simple consequences. Having studied the literature,' grown large since Ravenstein's time, we believe that we can formulate the migration process as the resultant of a "push" factor and a "pull" factor, but must discount this combination by a distance deterrence between the places. The push factors are those life situations that give one reason to be dissatisfied with one's present locale; the pull factors are those attributes of distant places that make them appear appealing. We will specify this old idea as a very elementary equation system, and will make estimates using empirical data, but not in a regression format; rather, we will study the model from a structural point of view. By including distance discounting we place the model in the venerable class of "gravity" models, and show that it has properties similar to other models in this class (