TABLE OF CONTENTS. 



CHAPTER I. 



INTRODUCTION. 



SECT. PAGB 



1. Introductory remarks . . 1 



2. Account of Walker's theory ....... 1 



3. Account of Kowalski's theory ....... 3 



4. Form of Kowalski's equations of condition, and origin of the difficulties arising 



from it .......... 4 



5. Objects of the present investigation ...... 6 



CHAPTER II. 



PROVISIONAL THEORY OF NEPTUNE. 



6. Formulas for the perturbations of longitude and radius vector ... 8 



7. Formulas for the perturbations of latitude ..... 10 



8. Secular variations ......... 13 



9. Theory of the action of an inner on an outer planet through the Sun . 13 



10. Development of the preceding theory according to the powers of the ratio of the 



mean motions ......... 16 



11. Method of treating the long-period perturbations of the elements produced by 



Uranus .......... 19 



12. Adopted elements, masses, and constants of theory, for perturbations . 20 



13. Computation of the perturbations by Uranus, Saturn, and Jupiter . . 22 

 Action of Venus, the Earth, and Mars ...... 31 



14. Indirect perturbations by Saturn .... 31 



15. Collection of the long-period and secular perturbations of the elements . 32 



16. Collection of the perturbations of the co-ordinates Comparison with Peirce and 



Kowalski ...... 33 



17. Formulas for computing an ephemeris . . 36 



18. Elimination of the elliptic terms ...... 36 



19. Elements and formulas of the provisional theory . . . . .38 



20. Heliocentric and geocentric positions resulting from the provisional theory . 41 



CHAPTER III. 



DISCUSSIONS OF OBSERVATIONS OF NEPTUNE. 



21. Choice of observations, and method of discussing them . . 44 



22. Reduction of Lalande's observations, May 8-10, 1795 . 45 



23. Probable error and value of the Lalando positions . . .49 



24. Method of treating the modern observations . . . 49 



25. Mean corrections of ephemerides of Neptune, given by different observatories . 51 



26. Investigation of the systematic differences between the results of different obser- 



vatories . ..... 53 



