Using the available observations in 1699, 1865-1866, and 1965, an orbi
t has been recomputed for periodic comet 55P/Tempel-Tuttle, the parent
body of the Leonid meteors. The comet's motion was numerically integr
ated back in time for two millennia and ephemerides were computed for
each perihelion return. Chinese observations of the comet in 1366 are
well represented, and possible (but not definite) observations of the
comet in October 1234 and January 1035 have been identified. The Leoni
d meteors have been observed since AD 902. Prior to the eighth century
, no Leonid meteors should have been visible because the comet's orbit
passed too far outside that of the Earth. By using previously recorde
d accounts of the Leonid meteor showers and storms as a guide, predict
ions for the forthcoming Leonid displays in November of 1996-1999 are
provided. The 1998 and 1999 events hold the most promise for an impres
sive Leonid meteor display, although there seems little likelihood tha
t the great storms of 1833 and 1966 will be repeated at this apparitio
n. (C) 1996 Academic Press, Inc.