vx 



TABLE OF CONTENTS. 



CHAPTER IV. 



TERMS OF THE SECOND ORDER DUE TO THE ACTION OF SATURN. 



Preliminary investigation of tlie orbit of Satnni .... 



Perturbations of Saturn and Uranus ...... 



Formation of tlie expressions for tlic tonus of the second order 



Perturbations depending on (lie square of the mass of Saturn 



Perturbations depending ou the product of tlie masses of Jupiter and Saturn 



PAGE 



65 

 68 

 69 

 76 

 71 



CHAPTER- V. 



COLLECTION AND TRANSFORMATION OF TUE PRECEDING PERTURBATIONS OF URANUS. 



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 .... 



79 

 80 

 81 

 93 

 98 

 99 



CHAPTER VI. 



REDUCTIOS OF THE OBSERVATIONS OF URANUS, AND THEIR COMPARISON 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 different observations 



Table of these corrections .... 



Results of the observations from 1781 to 1830 



Observations from 1830 to 1872 



Table to convert errors of right ascension and declination of 



and latitude .... 



Tabular summary of results of observations, 1830 to 1872 

 Corrections to be applied to the positions of Uranns in the Berlin Jahrbuch and the Nautical 



Almanac to reduce them to positions from the provisional' theory 



to a homogeneous system 



Uranns into errors of longitude 



106 

 110 

 111 

 111 

 113 

 115 

 120 

 122 

 126 



127 

 181 



151 



CHAPTER. VII. 



FORMATION AND SOLUTION OF THE EQUATIONS OF CONDITION RESULTING FROM THE 



PRECEDING COMPARISONS. 



Expressions of the observed coirections to the longitudes of the prorision.il theory in terms 



of the corrections to the heliocentric co-ordinates ..... 158 



Expressions of the same quantities in terras of the corrections to the elements of Uranns and 



the mass of Neptune . . . . . . . . .161 



Table to express errors of heliocentric co-ordinates as errors of elements . . .162 



Discussions and solutions of the equations thus fornieil . . . . .165 



Concluded corrections to the elements of hmgitude . . , . . .173 



Corrections to the inclination and node of Uranus ...... 173 



