Abstract: An allometric equation of urban systems and its Beckmann’s form were deduced from the equations of general urban dynamic systems,and the Pareto′s formula of city-size distribution can be obtained out of the mathematical transformation,based on which the theoretical foundations can be laid for Zipf′s Law of urban geography.The fractal nature of rank-size rule of cities and its degenerational form were discussed,Davis′ double law (2n-law) was proved equivalent to Zipf′s formula with three parameters,and Cur...