CHAPTER I. 



I. COMETARY ORBITS : 1. Prescience of the astronomer. 2. Strikingly 

 illustrated by cometary discovery. 3. Motion of comets explained by 

 gravitation. 4. Conditions imposed on the orbits of bodies which 

 are subject to the attraction of gravitation. 5. Elliptic orbit. 6. 

 Parabolic orbits. 7. Hyperbolic orbits. 8. Planets observe in their 

 motions order not exacted by the law of gravitation. 9. Comets 

 observe no such order in their motions. 10. They move in conic 

 sections, with the sun for the focus. 11. Difficulty of ascertaining in 

 what species of conic section a comet moves. 12. Hyperbolic and 

 parabolic comets not periodic. 13. Elliptic comets periodic like the 

 planets. 14. Difficulties attending the analysis of cometary motions. 

 15. Periodicity alone proves the elliptic character. 16. Periodicity 



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