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Recent comparisons of computed and measured backscattering cross sections of cylindrical bodies revealed unexpectedly large discrepancies which were apparently due to the finite range used in the measurements. This led to a reexamination of the farfield criterion for a variety of two-dimensional scatterers and one three-dimensional object. It was found that large errors can be incurred in measurements at the standard far-field distance, especially of bodies characterized by strong edge scattering. Errors as great as 6 dB can occur and it may be necessary to exceed the usual farfield distance by a factor of 5 or more in order to reduce the error to 1 dB.