t
difficulty are those of Halley's and Encke's comets. The orbit of the
former is so elongated and so inclined to the general plane of the
planetary orbits that its secular variation must be very slow indeed.
But it does not pass near the orbit of any planet except Venus; and even
here the proximity is far from being sufficient to have produced an
appreciable change in the period. The orbit of Encke's comet is entirely
within the orbit of Jupiter, and it also cannot have passed near enough
to a planet for thousands of years to have had its orbit changed by the
action in question. It therefore seems difficult to regard these two
comets as other than permanent members of the solar system.

_Special Periodic Comets._--One of the most remarkable periodic comets
with which we are acquainted is that known to astronomers as Halley's.
Having perceived that the elements of the comet of 1682 were nearly the
same as those of two comets which had respectively appeared in 1531 and
1607, Edmund Halley concluded that all the three orbits belonged to the
same comet, of which the periodic time was about 76 years. After a rough
estimate of the perturbations it must sustain from the attraction of the
planets, he predicted its return for 1757,--a bold prediction at that
time, but justified by the event, for the comet again made its
appearance as was expected, though it did not pass through its
perihelion till the month of March 1759, the attraction of Jupiter and
Saturn having caused, as was computed by Clairault previously to its
return, a retardation of 618 days. This comet had been observed in 1066,
and the accounts which have been preserved represent it as having then
appeared to be four times the size of Venus, and to have shone with a
light equal to a fourth of that of the moon. History is silent
respecting it from that time till the year 1456, when it passed very
near to the earth: its tail then extended over 60 deg. of the heavens,
and had the form of a sabre. It returned to its perihelion in 1835, and
was well observed in almost every observatory. But its brightness was
far from comparing with the glorious accounts of its former apparitions.
That this should have been due to the process of dissipation does not
seem possible in so short a period; we must therefore consider either
that the earlier accounts are greatly exaggerated, or that the
brightness of the comet is subject to changes from some unknown cause.
Previous appearances