Recordings of the relative phase and amplitude of the signal from GBR, Rugby, U.K., have been made for several years at Byrd Station, Antarctica. Diurnal variations and the behavior of the signal received on a loop and a vertical antenna are consistent with the hypothesis that the dominant signal arrives at Byrd over the short great circle path when it is in maximum darkness and over the long great circle path when it is in maximum darkness. This is to be expected for a path of this length (short path, 16,248 km; long path, 23,759 km) because the attenuation of VLF signals is very much less for dark than for sunlit conditions. The short and long paths from GBR to Byrd contain portions of the Antarctic ice cap about 1250 and 725 km long, respectively. Using reasonable assumptions about the attenuation over the non-ice-cap portions of the path, calculations were made of the excess attenuation introduced by the ice cap on the two paths when the ice cap is completely dark or illuminated, assuming that the inconsistencies in the signal level over the two paths were due to the additional attenuation over the ice cap. The results indicate that the excess attenuation rate over the sunlit ice cap is between 17 and 31 db/1000 km, which corresponds to a range of conductivities between 0.01 and 0.05 mmho/m for 16 kHz. The nighttime data indicated an attenuation rate of 17 to 22 db/1000 km, which is outside the range of calculated attenuation rate versus conductivity.