Abstract
The theory of the polarization and propagation of an electromagnetic wave in a birefringent medium is briefly reviewed. Particular attention is given to those aspects of the theory which relate to the radio echo sounding of ice sheets. Methods of determining the polarization state of a radar wave are discussed, and it is shown that in certain circumstances this may be achieved by observing the variation of the signal strength in a pair of rotating receiving antennae. The results of experiments performed on the Greenland ice sheet are presented. The radio echo is shown to be elliptically polarized, confirming the suggestion that the ice sheet is birefringent at radio frequencies. A figure is obtained for the anisotropy of the dielectric constant of the ice sheet.

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