Structure in the Uranian ring system as observed in recent occultations may contain indirect evidence for the existence of undiscovered satellites. Using the Alfven and Arrhenius (1975, 1976) scenario for the formation of planetary systems, the orbital radii of up to nine hypothetical satellites interior to Miranda are computed. These calculations should provide interesting comparisons when the results from the Voyager 2 encounter with Uranus are made public. 15 refs., 1 fig., 1 tab.