TABLE OF CONTENTS. 



urn 



INTRODUCTION ........ . . , 1 



CHAPTER I. 



METHOD OP DETERMINING! THF. PERTURBATIONS OF THE LONGITUDE, RADIUS VECTOR, AND 

 I.ATIT1 HE OP A PLANET BY DIRECT INTEGRATION. 



Notation and jrcnernl differential formula . . . , . . . 6 

 Formation of the required derivatives of the perturbative function . . . .10 



Correction of these derivatives for terms of the second order . .... 12 



Integration fonnnhc for perturbations of radius vector ..... 13 



lo|>ment of functions of reetanpular co-ordinates . . . . . .14 



ration of perturbations of radius vector ....... 17 



Kiinniilii 1 for perturbations of longitude to terms of the second order . ... . 22 



Motion of the orbital planes ......... 24 



Perturbations of the second order depending on the motion of the orbital planes . . 25 



Redaction of the longitude to the ecliptic . . . . . ... 27 



K \jiressions for the latitude ......... 29 



CHAPTER II. 



APPLICATION OP THE PRECEDING METHOD TO THE COMPUTATION OF THE PERTURBATIONS 



OP URANUS BY SATURN. 



Data of computation. . . . . . . . '- 31 



Numerical expressions for R and its derivatives ...... 34 



Perturbations of radius vector ........ 44 



IVrturhntions of longitude ......... 49 



Perturbations of latitude ......... 61 



CHAPTER III. 



PERTURBATIONS OP URANUS PRODUCED BY NEPTUNE AND JUPITER, 



Adopted elements of Neptuno ......... 53 



lopment of R and its derivatives for the action of Neptune . . . .54 



The term of lonjr period between Neptune and Uranus . . . . . 55 



Perturbations of the longitude produced by Neptune ...... 58 



Port urbnt ions of the rndins vector produced by Neptnne ..... 00 



Perturbations of the latitude produced by Neptune . . . . .01 



Perturbations produced by Jupiter ..... 63 



(v) 



