ho Brahe believed
that comets moved in circular orbits, and Kepler imagined that they
travelled in straight lines outwards from the Sun. Newton, however, was
able to demonstrate that any conic section can be described about the
Sun consistent with the law of gravitation, and that the orbits of
comets correspond with three of the four sections into which a cone can
be divided. Consequently, they obey the laws of planetary motion. Comets
which move in ellipses of known eccentricity and return with periodical
regularity may be regarded as belonging to the solar system. Twenty of
these are known, and eleven of them have more than once passed their
perihelion. Those most familiarly known complete their periods in years
as follows:--Encke's 3.3; Swift's, 5.5; Winnecke's, 5.6; Tempel's, 6;
Brorsen's, 5.5; Faye's, 7.4; Tuttle's, 13.8, and Halley's, 76. Comets
with parabolic and hyperbolic orbits may be regarded as stray objects
which visit our system once, and depart never to return again. Besides
those already mentioned there are many comets with orbits of such marked
eccentricity that their ellipses when near perihelion cannot be
distinguished from parabolae. The great comets of 1780, 1811, 1843, 1858,
1861, and 1882 traverse orbits approaching this form, and some of them
require hundreds and thousands of years to accomplish a circuit of their
paths.

Numerous instances of the appearance of remarkable comets have been
recorded in the annals of ancient nations. The earliest records of
comets are by the Chinese, who were careful observers of celestial
phenomena. A comet is said to have appeared at the time of the birth of
Mithridates (134 B.C.), which had a disc as large as that of the Sun; a
great comet also became visible in the heavens about the time of the
death of Julius Caesar (44 B.C.), and another was seen in the reign of
Justinian (531 A.D.). A remarkable comet was observed in 1106, and in
1456, the year in which the Turks obtained possession of Constantinople
and threatened to overrun Europe, a great comet appeared, which was
regarded by Christendom with ominous forebodings. The celebrated
astronomer Halley was the first to predict the return of a comet.
Having become acquainted with Newton's investigations, which showed that
the forms of the orbits of comets were either parabolae or extremely
elongated ellipses, he subjected the next great comet, which appeared in
1682, to a series of observations, calculated its orb