This paper deals with the theory for rotational motion of a two-layer Earth model (an inelastic mantle and liquid core) including the dissipation in the mantle-core boundary(CMB) along with tidal effects produced by Moon and Sun. An analytical solution being derived using Hori's perturbation technique at a second order Hamiltonian. Numerical nutation series will be deduced from the theory.

The frequency distribution of HII regions radii in our galaxy has been investigated. The correlation between the number of these regions and their radii has been re-determined, and could be represented by an exponential function. The size distribution of the HII regions in 10 spiral galaxies has been derived and combined with that of our galaxy to derive the distances of these galaxies. It has been found that the distances derived are in a good agreement with the published ones. The interstellar extinction in the galaxies has no influence on the distance estimate when using this geometrical method.