medium such as Encke postulated (varying in density inversely as the
square of the distance from the sun), have been brought down, by its
first perihelion passage, to elliptic movement in a period of
twenty-four years, with such rapid diminution that its next return would
be in about ten. But such restricted observations as were available on
either occasion of its visibility gave no sign of such a rapid progress
towards engulfment.

Another form of the theory was advocated by Klinkerfues.[1287] He
supposed that four returns of the same body had been witnessed within
historical memory--the first in 371 b.c., the next in 1668, besides
those of 1843 and 1880; an original period of 2,039 years being
successively reduced by the withdrawal at each perihelion passage of
1/1320 of the velocity acquired by falling from the far extremity of its
orbit towards the sun, to 175 and 37 years. A continuance of the process
would bring the comet of 1880 back in 1897.

Unfortunately, the earliest of these apparitions cannot be identified
with the recent ones unless by doing violence to the plain meaning of
Aristotle's words in describing it. He states that the comet was first
seen "during the frosts and in the clear skies of winter," setting due
west nearly at the same time as the sun.[1288] This implies some
considerable north latitude. But the objects lately observed had
practically _no_ north latitude. They accomplished their entire course
_above_ the ecliptic in two hours and a quarter, during which space they
were barely separated a hand's-breadth (one might say) from the sun's
surface. For the purposes of the desired assimilation, Aristotle's comet
should have appeared in March. It is not credible, however, that even a
native of Thrace should have termed March "winter."

With the comet of 1668 the case seemed more dubious. The circumstances
of its appearance are barely reconcilable with the identity attributed
to it, although too vaguely known to render certainty one way or the
other attainable. It might however, be expected that recent observations
would at least decide the questions whether the comet of 1843 could have
returned in less than thirty-seven, and whether the comet of 1880 was to
be looked for at the end of 17-1/2 years. But the truth is that both
these objects were observed over so small an arc--8 deg. and 3 deg.
respectively--that their periods remained virtually undetermined. For
while the shape and position of the