Spatial interaction models have been based upon analogies to physical laws of Newtonian physics. These models have questionable value in theoretical explanations of people's interaction in space. The purpose of this paper is to derive the "gravity law" of spatial interaction within the framework of utility theory, thereby providing a theoretical explanation for well-known empirical regularities. Section 1 of this paper provides a brief background in spatial interaction models, and Section 2 presents the economic derivation of the "gravity law". SPATIAL INTERACTION MODELSSpatial aspects of economic phenomena have been virtually excluded from the mainstream of orthodox economic theory. Writings of location theorists, such as Von Thunen [33], Weber [35], Losch 1201, Hoover [14], Dunn [ll] and Isard [17],have essentially remained separate from general price and distribution theory, which has abstracted from space.The interaction of persons and things in space has been studied by economists, demographers, geographers, sociologists, planners and others. Models used by these investigators were developed from the writings of location, land, and rent theorists, most of them originally through analogies to physical relationships and were called social physics.As used in the behavioral sciences, spatial interaction models describe social phenomena in space, such as population migration, flow of goods, money, and information, traffic movement and tourist travel. These models are used extensively in market area, transportation, tourism and demographic studies.Many factors affect the movement or interaction of persons and things in space. If social phenomena are conceived as occurring between geographic areas or points, each of these factors can be categorized as (1) an origin factor, (2) a destination factor, or (3) a linkage factor. Origin factors are characteristics of an origin that * The authors are grateful to Gerhard Tintner for his suggestions and comments.

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Since our original article (Niedercorn and Bechdolt [5]) was published in this journal in August, 1969, an interesting sequence of comments and replies has developed, and it may be of some value to briefly review the thrust of this dialogue. In our original article, we derived the so-called "gravity-law" of spatial interaction from the economic principle of utility maximization, thereby establishing a more theoretically relevant foundation for the study of spatial interaction than the previously used analogy to Newtonian physical principles that had up t o that time served as the basis for an approach to the study of human behavior called social physics. Our derivation was worked out for the punctiform single-origin/multipledestination case beginning with the utility of tripmaking function for a representative individual k at origin i who has to allocate his limited money or time among alternative combinations of numbers of trips to n destinations. The utility-mrtximizing number of trips by all individuals from origin i to each destination j was derived.Mathur [3] proposed that we use the consumption technology approach developed by Lancaster [l, 21 to analyze tripmaking behavior. His argument was presented in terms of an individual who is attempting to attain a utility-maximizing combination of two characteristics, C1 and CZ , that are common, but in different proportions, first, to two kinds of trips and, second, to three kinds of trips.In our reply to Mathur (Niedercorn and Bechdolt [6]), we (1) stated his comments in more detail using the notation used in our article, (2) pointed out that Mathur's analysis did not yield a unique solution to the chief problem posed in our model, namely, the utility-maximizing number of trips by all individuals from origin i to each destination j, (3) pointed out that, if the number of types of trips was greater than the number of characteristics, then there is an infinite number of combinations of the trip characteristics vectors that would yield any given feasible utility-maximizing characteristic vector, and (4) showed how our derivation could be reformulated to meet