Abstract: This paper is an extension of the autherks words (1),(2),(3).Simple anisotropic distribution of horizontal kinetic energy is assumed,i.e.,the zonal kinetic energy is twice that of the meridional kinetic energy.The large scale atmospheric motion is considered as consisted of quasi-horizontal eddies and regular flow.The techniques of quasi-eddy,quasi-steady,quasi-geostrophic and quasi-adiabatic approximations are used in order to get the analytical solutions of the system of equations governing the variation of the zonal mean characteristics.The results show that the zonal mean characteristics of the atmospheric motion are a combination of different periods ranged fron a few days to a few weeks depending on the components of the Tschebyscheff polynomials of tke sine of the latitude.When more general anisotropy of horizontal kinetic energy is assumed,Gegenbauer polynomials appear instead of Chebyshev polynomials.When the distribution of horizontal hintic energy is isotropic,the polynomials retrograde to Legendre polynomials.