PART III. REDUCTION AND DETERMINATION OF POSITIONS OF THE FIXED STARS CHAPTER X. REDUCTION OF MEAN PLACES OF THE FIXED STARS FROM ONE EPOCH TO ANOTHER. Section I. The Proper Motions of the Stars. II. Trigonometric Reduction for Precession. III. Development of the Coördinates in the Powers of the Time. NOTES AND REFERENCES. CHAPTER XI. REDUCTION TO APPARENT PLACE. Section I. Reduction to Terms of the First Order. II. Rigorous Reduction for Close Polar Stars. III. Practical Methods of Reduction. IV. Construction of Tables of the Apparent Places of Fundamental Stars. Notes and References. CHAPTER XII. METHOD OF DETERMINING THE POSITIONS OF STARS BY MERIDIAN OBSERVATIONS. Section I. Method of Determining Right Ascensions. II. The Determination of Declinations. CHAPTER XIII. METHODS OF DERIVING THE POSITIONS AND PROPER MOTIONS OF THE STARS FROM PUBLISHED RESULTS OF OBSERVATIONS. Section I. Historical Review. II. Reduction of Catalogue Positions of Stars to a Homogeneous System. III. Methods of Combining Star Catalogues. NOTES AND REFERENCES List of Independent Star Catalogues. Catalogues made at Northern Observatories. Catalogues made at Tropical and Southern Observatories. APPENDIX EXPLANATION OF THE TABLES OF THE APPENDIX.—I. Constants and Formulæ in Frequent Use. II. Tables Relating to Time and Arguments for Star Reductions. III. Centennial Rates of the Precessional Motions. IV. Tables and Formulæ for the Trigonometric Reduction of Mean Places of Stars. V. Reduction of the Struve-Peters Precessions to the Adopted Values. VI. Conversion of Longitude and Latitude into R. A. and Dec. VII. Refractions. VIII. Coefficients of Solar and Lunar Nutation. IX. Three-place Logarithms and Trigonometrical Functions. -------------- THE MACMILLAN COMPANY, 64-66 Fifth Avenue, New York Transcriber's Notes Ditto marks have been replaced by the text they represent. Some presumed printer's errors have been corrected, including normalizing punctuation. Further corrections are listed below: Printed text Corrected text Page MITGLIED DER MITGLIED DER ASTRONOMISCHE GESELLSCHAFT ASTRONOMISCHEN GESELLSCHAFT Title page terrrane terrane 108 seem seems 247 End of the Project Gutenberg EBook of Mars and its Canals, by Percival Lowell