Using the RICE (Radio Ice Cherenkov Experiment) detector at the South Pole, we have estimated the variation in the index of refraction (n) of the firn, as a function of elevation (z) measured from the surface down to z =-150 m. Measurements were made by lowering a dipole transmitter into a dry (5 in (127 mm) caliber) borehole, originally drilled for the RICE experiment in 1998, and determining signal arrival times, as a function of transmitter depth, in the englacial RICE receiver array. We clearly confirm the expected correlation of n
(z) with ice density. Our measurements are in fair agreement with previous laboratory characterizations of the dielectric properties of ice cores. These are the first such in situ measurements to be performed at the South Pole.