A theoretical examination is made of the scattering cross section of an obstacle plunged into plane incident waves, concerning their limiting wave lengths. The scattering cross section, which is proportional to the imaginary part of amplitude of the scattered wave in the forward direction, is formulated in a form that is stationary with respect to small variations of the surface fields. These fields are dominated by amplitude functions both at the high and the low frequency ranges. The Rayleigh's scattering law for long wavelength is set forth as well, as twice the geometrical cross section, in the limit of short wavelength.
