si? TABLE OF CONTENTS. 



PAOK 



Order Siphophycea; . . . . . . .174 



Family Hydrogastreae . . . . . .175 



Family Vaucheriaceae . . . . . .176 



Family Ulvaceae / . . . . . .182 



Family Confervaceae . . . . . .186 



Family (Edogoniaceae . . . . . .188 



Family Chroolepideae ...... 203 



Family CliEetophoracese ...... 205 



Class Rhodophyeese . . . . . . .213 



Family Porphyracese . . . . . .214 



Family Chantransiacese . . . . . .215 



Family Batrachospermacese . . . . ,217 



Family Lemaneaceae ...... 221 



Supplement ........ 225 



Geographical List of Species ...... 229 



Bibliography . . . . . . . . 235 



Index ......... 249 



Explanation of the Plates ...... 253 



ARTICLE IV. (No. 262.) AN INVESTIGATION OF THE ORBIT or URANUS, WITH GENERAL 

 TABLES OF ITS MOTION. By SIMON NEWCOMB, Professor of Mathematics, 

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

 INTRODUCTION ........ 1 



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



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

 Notation and general 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 formulae for perturbations of radius vector . . .13 



Development of functions of rectangular co-ordinates . . .14 



Integration of perturbations of radius vector . . . .17 



Formulae 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 



Reduction of the longitude to the ecliptic . . . .27 



Expressions for the latitude ...... 9 



CHAPTER II. Application of the Preceding Method to the Computation 



of the Perturbations of Uranus by Saturn. 

 Data of computation . . . . . . .31 



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



Perturbations of radius vector ...... 44 



Perturbations of longitude ...... 49 



Perturbations of latitude . . . . . .51 



CHAPTER III. Perturbations of Uranus produced by Neptune and Jupiter 

 Adopted elements of Neptune ...... 53 



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



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



Perturbations of the longitude produced by Neptune . . .58 



Perturbations of the radius vector produced by Neptune . . 60 



Perturbations of the latitude produced by Neptune . . .61 



Perturbations produced by Jupiter ..... 62 



