The dispersion relation for the Bernstein mode in a two-component electron plasma of the type which often exists in the magnetosphere is shown to have solutions corresponding to the upper hybrid resonance, calculated two different ways. At long wavelengths the resonance corresponds to the total electron density. At intermediate wavelengths the resonance corresponds to the electron density of the cold component alone. At short wavelengths the frequency tends to a cyclotron harmonic. Using the upper hybrid resonance to measure the total electron density requires great care to insure that the received signals have quite long wavelengths. There is the possibility of detecting waves of intermediate wavelengths, which give a measurement of the cold electron density rather than the total electron density.