IL OF REGIONAL SCIENCE 男,1891 WAVES OF SPATIAL DIFFUSION RECONSIDERED Herbert G. Kariel and Michael J. va Two stimulating and innovative papers by Morrill were concerned with waves of spatial diffusion.(Morrill,[1, 2 )The purpose of the first was to propose some insights and interpretations which can be obtained by characteriz ive-like phend Morrill scopic and theoretical implications of such a conceptualization. He was concerned with both time and distance, and noted that in earlier conceptualizations more emphasis had been placed on de ecay re elated to time than on that related to distance. He therefore hypothesized that the number of innovations would de- crease not only over time but also with distance from the original source; that is in areas farther from the source the final proportion of adopters would be smaller than in areas closer to it. This notion seemed to him compatible with wave henomena in general, where the size and force of the wave decrease over both time and space as it moves outward from the source Using standard wave equations, he showed by means of a diagram the relationship between adoption and distance. (Figure 1. )1 He also proposes that space and time are symmetrical in that they can be substituted for each other in the model In order to test this model, in the second paper he analyzed the actual diffusion of three phenomena He concluded that for these data space and time were not good substitutes for each other, because at the source of the innovation the peak of acceptance came well after the beginning of the diffusion proces, whereas according to the model it should have come at the beginning. He therefore suggested two modifications of the original equation, one for distance(Figure 2)and one for time(Figure 3) e propose to show that by extending the x-axis so as to include a zero oint, Morrill's original formulation is more accurate than he had realized. We also have expanded the model so as to incorporate the notion of energy which can be considered to exist in a system where spatial diffusion is occurring We first observed that in Morrill's original model the origin was not at the zero point, (Figure 1)whereas by convention a wave starts with an amplitude of zero. When he tested it, however, the origin was at the zero point(Figures 4 and Associate Professor and Student, Department of Geography, University of Calgary All figures are from Morrill, [1, 2] Figure 1= Figure 10 in [ u] Figure 2= Figure 10 in [2], Figure 3= Figure l1 in [2] Figure 4= Figur res 6,7, and 8 in [2]