  We study a potential genetic relationship of comets C/1846 O1 and C/1973 D1,
whose apparent orbital similarity was tested by Kresak (1982) only
statistically, using the Southworth-Hawkins (1963) criterion D. Our orbit
determination for C/1846 O1 shows its period was ~500 yr, ~30 times shorter
than that of C/1973 D1. Formerly unrecognized, this incongruity makes the
objects' common origin less likely. Long-term orbit integration suggests that,
if related, the two comets would have to have separated far away from the Sun
(probably ~700 AU) 21 millennia ago and, unlike C/1973 D1, C/1846 O1 would have
to have been subjected to a complex orbital evolution. Given the chance of
encountering Jupiter to ~0.6 AU some 400 days after perihelion, C/1846 O1 and
C/1973 D1 may have been perturbed, during their return in the 15th millennium
BCE, into orbits that were, respectively, smaller and larger than was the
parent's, with a net difference of more than 0.002 (AU)^{-1} in 1/a. Whereas
C/1973 D1 was on the way to its 1973 perihelion, C/1846 O1 should have been
subjected to recurring encounters with Jupiter, during which the orbital period
continued to shorten by integral multiples of the Jovian orbital period, a
process called high-order orbital-cascade resonance. While the integrated
perturbation effect of C/1846 O1 by Jupiter does not appear to reduce the
comet's orbital period to below ~1200 yr by the mid-19th century, we find that
orbital-cascade resonance offers an attractive mechanism for rapid inward
drifting of aphelion especially among dynamically new comets.
