COMETS OF SHORT PERIOD. 185 



The last alternative appeared so much the more 

 probable one, that mathematicians began to examine 

 the path of the comet, to see whether it had approached 

 so near to any disturbing body as to have been driven 

 from its recently adopted orbit. The examination was 

 soon rewarded with success. If we consider the nature 

 of orbital motion, we shall at once see that, so long as 

 Lexell s comet was subjected to no new disturbing 

 attractions, it was compelled, once in every revolution, 

 to return to the scene of its former encounter with the 

 planet Jupiter. This return was fraught with danger 

 to the stability of the comet s motions. So long as 

 Jupiter was not near that particular part of his orbit 

 at which the encounter had taken place, the comet was 

 free to pass the point of danger, and return towards 

 the sun ; but if ever it should happen that Jupiter was 

 close at hand when the comet approached his orbit, 

 then the comet would be as liable to have its motions 

 disarranged as at the original encounter. It happened 

 that the period of the comet s motion in its new orbit 

 was almost exactly one-half of Jupiter s period. 

 This was unfortunate ; since it clearly follows that, 

 when the comet had revolved twice, Jupiter had re 

 volved onc,e round the sun. Thus the comet again 

 encountered the planet, with what exact result has 

 never become known ; but certainly with this general 

 result, that the comet s movements were completely 

 disarranged. It has never returned to the neighbour 

 hood of the earth. 



We may look upon Lexell s as the first discovered 



