TABLE OF CONTENTS. 



CHAPTEE I. 



INTRODUCTION. 



1. Introductory i-emarki9 ..... .... 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 OP NEPTUNE. 



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



7. Formulae 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. Develojjment 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. Pormulse for computing an ephemeris ...... 36 



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



19. Elements and formulae 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 Lalande 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 diiferences between the results of different obser- 



vatories .......... 53 



