ORIGIN OF COMETS AND METEORS. 57 



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 to- 

 gether 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 per- 

 turbing 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 cer- 

 tainties, but it would introduce this tremendous difficulty : the num- 

 ber 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 



