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The advent of precision microwave radiometry has placed a stringent requirement on the accuracy with which the dielectric constant of sea water must be known. To this end, measurements of the dielectric constant have been conducted at -band and -band with a quoted uncertainty of tenths of a percent. These and earlier results are critically examined, and expressions are developed which will yield computations of brightness temperature having an error of no more than 0.3 K for an undisturbed sea at frequencies lower than -band. At the higher microwave and millimeter wave frequencies, the accuracy is in question because of uncertainties in the relaxation time and the dielectric constant at infinite frequency.