The lower wall of the Antarctic earth-ionosphere waveguide is composed of rock covered by an ice sheet, the depth of which can be an appreciable fraction of a wavelength at very low frequencies. The complex permittivity of the ice cap is therefore an important parameter in connection with the prediction of propagation velocities and attenuation in the guide over long paths on the Antarctic continent. This paper describes an experiment conducted near Byrd Station during November, 1971, in which the properties of the surface magnetic field between 5 and 20 kHz were measured in the immediate vicinity of a buried 34-km dipole antenna just under the surface of the snow. The related analytical problem and data reduction process are described briefly to clarify the means for converting the data into bulk average values of the complex permittivity parameter of the ice over the frequency range of interest. The resulting dielectric and loss parameters are new and have not been determined before in connection with the Antarctic ice sheet.