The orbit of the Perseid comet (1862 III P/Swift-Tuttle) is redetermined, and backward calculation of the perturbations indicates that the comet should previously have passed perihelion during 1746-1750. No defmite eighteenth-century candidate for the be identified, but if the revolution period were somewhat longer, Kegler's Comet 1737 1! is found to have been a rather promising one. As a by product of this investigation, an orbit is determined for Wargentin's Comet of 1750. The fact that there are no really convincing observations of P 1 Swift-Tuttle at its perIhelion passages during the fifteenth through eighteenth centuries is then used to narrow down the search region at the forthcoming return, and it is indicated that perihelion will most probably be during March-November 1980, April-June 1981, or May-December 1982-although searches should not be entirely confmed to these times and could begin as early as 1978. For this purpose, a perennial ephemeris is provided. The question of identity with comet 1737 11 is further examined, with consideration made of the effects of nongravitational forces; while the possibility of identity still seems to be rather small, it is suggested that, if the comet has not been recovered by late 1983, the search should be resumed in 1992.