some way of representing the ratio of the circumference of a circle to the diameter as a fraction of some sort. The fact remains that this has been proved to be impossible; and it has equally been shown to be impossible that any flight of meteors could be captured (that is, brought into the solar domain for good) as such, by any planet, even by the giant Jupiter. Either the meteors must lie so very close together that their mutual attractions would make them practically one body, and keep them such after capture by the planet, which is not the case with any of the meteor-streams, or else the differences of perturbing action on the meteors would be so great that the flight must be entirely dispersed in the act of capture—not merely dispersed so as to form a stream or a larger flight, but so dispersed as no longer to form a meteor system at all.
But, extending our generalized theory to the case of the giant planets—as, be it observed, we are not only entitled but bound to do—we see that as there would be flights of meteors passing always near the earth's orbit because of their original derivation from the earth in her sun-like stage, so would there be flights of meteors passing always near the orbit of each one of the giant planets; unless, indeed, in the fullness of the vast periods of time which must have elapsed since their formation, processes such as seem to affect Encke's comet should have altered their orbits considerably. Even then they would exhibit an approach to the orbits of their parent planets such as to suggest the idea of some sort of physical association. And accordingly, we find this peculiarity so far manifested, that years before the idea ever occurred to me that any comets or meteor systems could have been expelled from the giant planets, I wrote an essay on what I called the "Comet Families of the Giant Planets," describing just such comets, though I was unable to find any interpretation at that time of the peculiarity in question.
It is worthy of notice that quite a number of difficulties, some of them very serious ones, disappear, even as these last two have done, so soon as we adopt this generalization of the special theory to which we found ourselves forced first by direct evidence.
For example, if the capture theory advanced by Schiaparelli were accepted, not only would it leave all our perplexities unexplained, not only would it involve our running directly against mathematical certainties, but it would introduce this tremendous difficulty: the number of meteor-flights traveling about in interstellar space must exceed many millions of times those which visit our solar system, and the number of such flights visiting our solar system must exceed millions of millions of times those which chanced, by a strange combination of accidents, to come within capturing distance of a planet. Again, if many of the meteor systems which cross our earth's orbit are not to be attributed to a terrestrial origin, then the number of meteor systems within the solar domain must exceed millions of millions of millions
