Themis (hypothetical moon)
On April 28, 1905, William H. Pickering, who had seven years earlier discovered Phoebe, announced the discovery of a tenth satellite of Saturn, which he promptly named Themis. The photographic plates on which it supposedly appeared, thirteen in all, spanned a period between April 17 and July 8, 1904. However, no other astronomer has ever confirmed Pickering's claim.
Pickering attempted to compute an orbit, which showed a fairly high inclination (39.1° to the ecliptic), fairly large eccentricity (0.23) and a semi-major axis (1,457,000 kilometres (905,000 mi)) slightly less than that of Hyperion. The period was supposedly 20.85 days, with prograde motion.
Pickering estimated the diameter at 61 kilometres (38 mi), but since he also gave 68 kilometres (42 mi) as the diameter of Phoebe, he was clearly overestimating the albedo; using the modern figure for Phoebe gives Themis a diameter of 200 kilometres (120 mi).
Oddly, in April 1861, Hermann Goldschmidt had also believed that he had discovered a new satellite of Saturn between Titan and Hyperion, which he called Chiron. Chiron also does not exist (however, the name was used much later for the comet/asteroid 2060 Chiron).