We examine the gyroresonance condition to determine which electrons can resonate with a specific electromagnetic wave (given &ohgr; and k∥) and find that for each gyroresonance harmonic the resonant electrons lie on an ellipse in v⊥--v∥ space. The growth rate for a given wave due to a given distribution f of electrons involves an integral around the 'resonant ellipse.' Using a contour plot of f in v⊥--v∥ space and a set of drawn ellipses, one can identify which waves grow fastest and which electrons contribute to the growth. We find that for ∂f/∂v⊥>0 at small v⊥ there always exist rapidly growing waves with k2∥c2/ &ohgr;2=n2 cos2&thgr;≪1. These ideas are applied to the interpretation of the terrestrial kilometric radiation (TKR). The growth rate for x mode radiation is calculated by using observations (from the ESRO 4 spacecraft) of the electron distribution in 'inverted V' events. A positive growth rate is found, providing strong support for the cyclotron theory of TKR. The calculated growth rate is smaller than required, but this may be partly a selection effect. It is argued that the specific features in the electron distribution that generate TKR should disappear in much less than a second and hence should not be observable in particle data averaged over more than a second. An analytic calculation of the maximum growth rate compatible with the data is at least in order of magnitude larger than that required to account for TKR. The basic feature in the electron distribution that gives rise to TKR is a one-sided loss-cone anisotropy in which upward-moving electrons with small pitch angles are missing. We speculate that the particular features causing large growth rates might be due to the effects of the parallel electric field.