Abstract: By modifying the assumptions of Steindl's model as allometric relationships: dP(T)/dT=gP(T),df(T)/dT=-rf(T),where P(T) is the average size of cities of age T,f(T) is the number of cities of age T,parameters g and r represent respectively coefficients of growth of P(T) and f(T),we deduce a set of generalized Beckmann-Davis model of city hierarchies and city-size distribution,namely, δⁿ-law advanced by the authors,as follows: P_m=P₁λ^1-m,f_m=f₁δ^m-1,where λ=e^g,δ=e^r,P₁ is the size of the largest city(cities), f₁ is the number of the largest city(cities),and generally, f₁ =1, m is the ordinal of city class (m=1,2,…,N).From the generalized Beckmann-Davis model,a three-parameter Zipf model can be derived as P(r)=C(r-α) ^-dz ,where r is the rank of a city, P(r) is the size of the r^th city,as for parameters, C=P₁δ/(δ-1)〕^dz, α=1/(1-δ),dz= ln λ/ln δ=g/r.Based on general geometrical measure relationship, P_m^1/Dp∝f_m^-1/Df,an equation of fractal dimension is constructed as dz=g/r=D_p/D_f,where D_p is the generalized dimension of P_m,and D_f,the dimension of f_m.In reality, D_p→D _f,g→r,so dz→1,and when dz=1,we have what is called 2ⁿ-law presented by K.Davis(1978).