Dispersion relations in which subtraction is transferred to points located at infinity are derived on basis of the Pomeranchuk assumptions regarding the asymptotic behaviour of the scattering amplitude. In this form the dispersion relations are most convenient for estimating the asymptotic behaviour of the amplitude on basis of the experimental data on π^± p-scattering. A preliminary numerical estimation of the asymptotic behaviour of the π^± p-scattering amplitude is presented. The question whether validity of the dispersion equation at high energies is consistent with the statistical theory is considered.