which
returns into itself by a route that is drawn out considerably in one
direction; and the _hyperbolic_ curve, that never returns into itself
at all, but has, on the other hand, a course which sets outwards each
way for ever. The _parabolic_ curve, as it is called, is a line
partaking of the closeness of the ellipse on the one hand, and the
openness of the hyperbola on the other. A parabola is an ellipse
passing into a hyperbola; or, in other words, it is a part of an
ellipse whose length, compared with its breadth, is too great to be
estimated, and is consequently deemed to be endless for all practical
purposes.

In most instances, comets move in space, about the sun, in ellipses so
very lengthened, that their paths seem to be parabolas as long as the
cloudy bodies are visible in the sky. Two of them, Ollier's Comet and
Halley's, are known to return into sight after intervals of
seventy-four and seventy-six years, during which they have visited
portions of space a few hundred millions of miles further than the
orbit of Neptune. Six comets travel in elliptical orbits that are
never so far from the sun as the planet Neptune, and return into
visibility in short periods that never exceed seven or eight years.
These interior comets of short period seem to be regular members of
our world-system in the strictest sense. Their paths, although more
eccentric, are all contained in planes that nearly correspond with the
planes of the planetary orbits, and they travel in these paths in the
same general direction with their planetary brethren in every case.
The planetoid comets of short period are--Encke's, De Vico's,
Brorsen's, D'Arrest's, Biela's, and Fage's. The comet of 1843 is half
suspected to belong to the group, and to be also a periodic body,
revisiting our regions punctually at intervals of twenty-one years.

The comet's motions strikingly illustrate the almost absolute voidness
of space. If the thin vapour experienced any resistance while moving,
its free passage would be checked, although that resistance was many
thousand times less than the one the hand feels when waved in the air.
It is found, however, that Encke's Comet does indicate the presence of
some such resistance. It goes slower and slower with each return, and
contracts the dimensions of its elliptical journey progressively. But
it must be remembered, that this is one of the close comets that never
gets well out of the solar domain in which our neighbouri