TABLE OF CONTENTS. 



Introduction 



PACIE 

 1 



CHAPTER I. 



METHOD OF DETERMIXINWTnE rERTTRBATIONS OF TnE LONGITTTIE, RADIUS VECTOR, AND 

 LATITUDE OF A PLANET BY DIRECT INTEGRATION. 



Notation and general differential formulae ..... 



Formation of the required derivatives of the pcrturliative function 



Correction of these derivatives for terms of the second order . 



Integration formulae for perturbations of radius vector 



Development of function;? of rectangular co-ordinates .... 



Integration of perturbations of radius vector ..... 



Formulas for perturbations of longitude to terras of the second order 

 Motion of the orbital planes ....... 



Perturbations of the second order depending on the motion of the orbital planes 

 Reduction of the longitude to the ecliptic ..... 



Expressions for the latitude ....... 



6 

 10 

 12 

 13 

 14 



n 



22 

 24 

 25 

 27 



29 



CHAPTER II. 



APPLICATION OF THE PRECEDING METHOD TO THE COMPUTATION OF THE PERTURB-iTIONS 



OF URANUS BY SATURN. 



Data of computation 



Kumerical expressions for 77 and its derivatives 



Perturbations of radius vector 



Perturbations of longitude 



Perturbations of latitude 



31 

 34 



44 

 49 



51 



CHAPTER III. 



PERTURBATIONS OF URANUS PRODUCED BY NEPTUNE AND JUPITER. 



Adopted elements of Neptune ..... 

 Development of R and its derivatives for the action of Nciitune 

 The term of long period between Neptune and Uranus 

 Perturbations of the longitude produced by Neptune . 

 Perturbations of the radius vector produced by Neptune 

 Perturbations of the latitude produced by Neptune 

 Perturbations produced by Jupiter 



53 



54 



55 

 58 

 GO 

 fil 

 G2 



(V) 



