Do all comets belong to tile solar system?–Orbits -which are clearly hyperbolic– Opinion of Laplace with regard to the rarity of hyperbolic comets–Are there any comets which really describe parabolas?–First glance at the origin of comets.

Do all the comets which have been observed up to the present time belong to the solar system? Or, as we have already suggested, are there comets which visit the sun but once, and which before penetrating to the sphere of his activity and submitting to the influence of his attraction were altogether strangers to our system?

Theoretically speaking the reply is not doubtful. A celestial body, describing under the influence of gravitation an orbit of which the sun is the focus, may move in a parabola, an ellipse, or an hyperbola. All depends upon its velocity at any one given point of its course, that is, upon the relation existing between the velocity and the intensity of gravitation at that point. The better to explain this let us take a point whose distance from the sun is equal to the mean distance of the earth, and let us suppose the body to have arrived at this point.