w in towards the sun; in fact, it must make
periodic circuits of its orbit, as the planets are found to do. But in
the case of the true parabola the body can never return; to do so it
would have to double the distant focus, and as that is infinitely
remote, it could not be reached except in the lapse of infinite time.

The characteristic feature of the movement in a parabola may be thus
described. The body draws in gradually towards the focus from an
indefinitely remote distance on one side, and after passing round the
focus gradually recedes to an indefinitely remote distance on the other
side, never again to return. When Newton had perceived that parabolic
motion of this type could arise from the law of gravitation, it at once
occurred to him (independently of Doerfel's discovery, of which he was
not aware) that by its means the movements of a comet might be
explained. He knew that comets must be attracted by the sun; he saw that
the usual course of a comet was to appear suddenly, to sweep around the
sun and then retreat, never again to return. Was this really a case of
parabolic motion? Fortunately, the materials for the trial of this
important suggestion were ready to his hand. He was able to avail
himself of the known movements of the comet of 1680, and of observations
of several other bodies of the same nature which had been collected by
the diligence of astronomers. With his usual sagacity, Newton devised a
method by which, from the known facts, the path which the comet pursues
could be determined. He found that it was a parabola, and that the
velocity of the comet was governed by the law that the straight line
from the sun to the comet swept over equal areas in equal times. Here
was another confirmation of the law of universal gravitation. In this
case, indeed, the theory may be said to have been actually in advance of
calculation. Kepler had determined from observation that the paths of
the planets were ellipses, and Newton had shown how this fact was a
consequence of the law of gravitation. But in the case of the comets
their highly erratic orbits had never been reduced to geometrical form
until the theory of Newton showed him that they were parabolic, and then
he invoked observation to verify the anticipations of his theory.

[Illustration: PLATE XII.

COGGIA'S COMET.

(AS SEEN ON JUNE 10TH AND JULY 9TH, 1874.)]

The great majority of comets move in orbits which cannot be sensibly
discriminated from para