TABLE OF CONTENTS. 



2V 



Chapter IV. Terms of the Second Order due to the Action of Saturn 

 Preliminary investigation of the orbit of Saturn 

 Perturbations of Saturn and Uranus .... 

 Formation of the expressions for the terms of the second order 

 Perturbations depending on the square of the mass of Saturn . 

 Perturbations depending on the product of the masses of Jupiter and 



Saturn .... ... 



Chapter V. Collection and Transformation of the preceding Perturba 



tions of Uranns. 

 Terms independent of the position of the disturbing planet 

 Secular variations ..... 



Auxiliary expressions on which the perturbations depend 

 Reduced expressions for the latitude of Uranus . 

 Positions of Uranus resulting from the preceding theory 

 Elements III of Uranus ..... 

 Chapter VI. Reduction of the Observations of Uranus, and their Com 



parison with the preceding Theory. 

 Reduction of the ancient observations 

 Their comparison with the provisional theory 

 Discussion of the modern observations . 

 Reduction of the Results to a uniform system 

 Adopted positions of fundamental stars . 

 Discussion of corrections to reduce the difl"erent observations to a homo 



geneous system ..... 



Table of these corrections .... 



Results of the observations from 1781 to 1830 . 

 Observations from 1.830 to 1872 .... 

 Table to convert errors of right ascension and declination of Uranus iuto 



errors of longitude and latitude 

 Tabular summary of results of observations, 1830 to 1872 

 Corrections to be applied to the positions of Uranus in the Berlin Jahr' 



buch and the Nautical Almanac to reduce them to positions from the 



provisional theory ....... 



Chapter VII. Formation and Solution of the Equations of Condition 

 Resulting from the preceding Comparisons. 



Expressions of the observed corrections to the longitudes of the provi- 

 sional theory in terms of the corrections to the heliocentric co-ordinates 



Expressions of the same quantities in terras of the corrections to the ele- 

 ments of Uranus and the mass of Neptune . . 



Table to express errors of heliocentric co-ordinates as errors of elements 



Discussions and solutions of the equations thus formed . 



Concluded corrections to the elements of longitude 



Corrections to the inclination and node of Uranus 



Chapter VIII. Cojnpletion and Arrangement of the Theory to fit it for 



Permanent Use. 

 Correction of the coefficients of the long inequality between Uranus and 



Neptune for the terms of the second order 

 Concluded elements, or elements IV of Uranus . 

 Long-period and secular perturbations of the elenicnis . 

 Table of these perturbations from A.D 1000 uniil A D 2200 

 Mean elements of Uranus .... 



Expressions for the concluded theory of Uranus . 



65 

 68 

 69 



76 



77 



79 

 80 

 81 

 93 

 98 

 99 



106 

 110 

 111 

 111 

 113 



115 



120 

 123 



126 



127 

 131 



151 



158 



ICl 

 162 

 165 

 173 

 173 



178 

 181 

 182 

 184 

 184 

 185 



