Abstract: By expressing the stream function in terms of the symmetric and the antisymmetric component with respect to the equator, the barotropic vorticity equation can be separated into two equations, one describing the behaviours of the atmospheric symmetric motion, and the other describing those of the atmospheric antisymmetric motion. From them, for the entire spherical surface, the conservation of several basic physical quantities, such as vorticities, angular momentums etc. in the symmetric case and in the antisymmetric case, are discussed. In addition, the energy budget equations and the energy conversion expressions for the two kinds of motion are given. It can be seen from them that there are not only the conversion between the zonal mean kinetic energy and the disturbed energy in the atmosphere, but also the conversion between the kinetic energy generated by the symmetric motion and the kinetic energy by the antisymmetric motion.In the case of including orography and horizontal diffusion into the vorticity equation, a mechanism of the generation of asymmetric behaviours of the atmosphere is proposed. The results show that the asymmetric distribution of orography and that of horizontal diffusion coefficients are likely to be the causes leading to the asymmetric motion. Finally, a theoretical comparison between the global prediction model and the hemispheric one from physical point of view is made.