gren have shown that all of the suspected cases either rest upon insufficient observations of the comets at the time of their appearance, so that the orbits are uncertain, or that the disturbing attractions of our planets have converted the orbits from the elliptic to the hyperbolic form after the comets have got well within our planetary system. Another fact is equally important. By virtue of our rapid travels toward the Lyra-Hercules region we should meet more comets coming from that direction than there are comets overtaking us from the opposite direction. To state this point differently: of the comets which swing around the Sun, a greater number should have come into our system from the Lyra-Hercules region than from any other region, and especially from the region of sky which we are leaving behind. The facts are otherwise: we can not say that the approaches of comets favor any particular direction.
The orbits of the great majority of comets are very close to the parabolic form. The nature of comets is such that they are under observation for a few weeks or a few months, and only an occasional one for a year or more. When but a small section of the orbit has been thus observed it is difficult to decide between the parabola and a very elongated ellipse. It happens, however, when these comets have been accurately observed through many months, and the disturbing attractions of our planets have been taken into account, that the orbits are found to be very long ellipses and not parabolas; some of the ellipses are so elongated that thousands, and occasionally hundreds of thousands of years, are required to complete one circuit of the Sun. Let us assume that a comet belonging to the solar system starts at rest, with reference to the solar system, from a point midway between α Centauri and our Sun, and travels around our Sun. It would be 60,000,000 years in reaching us, or 120,000,000 years in completing its circuit. It is evident that an immense amount of cometary material must exist in the outer regions of our Sun's gravitational field in order that a minute part of it may visit the Sun every three months, which is about the average interval of time between the coming of these bodies.
It should be noted that the planes of the very elongated comet orbits show no preference for small angles with the plane of the solar system: they intersect the solar system plane at all angles, and these comets come into our system from all directions indifferently.
We must hold, I think, that the comets are genuine members of our solar system: the great majority spend most of their time in the outer parts of our system, far beyond the orbits of Neptune, but they are moving through space as companions to our Sun as truly as the Earth and Jupiter are.
Aside from the comets which come from great distances, there are, of course, the so-called periodic comets which move in relatively short ellipses, revolving around the Sun in a few years, and reappearing at
