High energy forward and backward scatterings for $\pi N$ cases are understood by the Regge pole theory obtained from a S-matrix formalism. Foregoing methods of parametrizations for both scattering cases are introduced to give practical comparisons with experimental data. Self-consistent feactures of this phenomenological theory are shown by sum rules which are derived from dispersion relations. Especially, several $\pi N$ parametrizations are tested by the Igi``s sum rule and the FESR with the input of low energy data. Discussions for a dual property of scattering amplitudes in the strong interaction which is suggested from the FESR are contributed to this thesis.