SIT 



TABLE OF CONTENTS. 



Order Sipliophyceaj . 



Funiily Ilydrogastrca; 



Family Vaucheriacefc 



Family Ulvaccae 



Family Confcrvaeeic 



Family tEdogoniaceae 



Family Chroolepidese 



Family CliKtophoraeeaj 

 Class Khodopbycese 



Family Porphyracesc 



Family Chaiitransiaccse 



Family Batrachospermaceaj 



Family Lemaneaceae 

 Supplement 



Geographical List of Species 

 Bibliography 

 Index 

 Explanation of the Plates 



ARTICLE IV. (No. 262.) An Investigation of the Orbit op Uranus, with General 

 Tables of its Motion. By Simon Newcomb, Professor of Mathematics, 

 United States Navy. October, 1873. 4to. pp. 296. 

 Introduction ......■■ 



Chapter I. Method of Determining the Perturbations of the Longitude, 

 Radius Vector, and Latitude of a Planet by direct Integration. 

 Notation and general differential formulas 



Formation of the required derivatives of the perturbative function 

 Correction of these derivatives for terms of the second order 

 Integration formulae for perturbations of radius vector . 

 Development of functions of rectangular co-ordinates 

 Integration of perturbations of radius vector 



Formulae for perturbations of longitude to terms 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 

 E.\pressions for the latitude 



Chapter II. Application of the Preceding Method to the Computation 

 of the Perturbations of Uranus by Suturn. 

 Data of computation 



Numerical e.xpressions for E and its derivatives 

 Perturbations of radius vector 

 Perturbations of longitude 

 Perturbations of latitude 



Chapter IIL Perturbations of Uranus produced by Neptune and Jupiter 

 Adopted elements of Neptune ..... 

 Development of li and its derivatives for the action of Neptune 

 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 Jujiiter 



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