Expressions are developed for the average power radiated by a high‐energy electron moving in a circular orbit. The instantaneous electron energyE(t) is assumed to vary with the time in accordance withE(t)Emsin2(&pgr;t/2T). Spectral distributions are obtained corresponding to the radiation emitted over a partial or full acceleration interval. The numerical results predicted from the general relations are examined for a particular value of the peak energyEm=6.0 Bev and the orbital radiusR=86.14 ft. In the case of these parameters, the continuous spectrum attains a peak at 0.36 A. Other numerical calculations, related to the case where the radiation is collected only over the low‐energy portion of the acceleration interval, indicate that it is feasible to utilize the continuum as a source for measurements in problems of interest to astrophysics and solid state spectroscopy.