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A Treatise on Astronomy

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A Treatise on Astronomy r PUB^I,!BrARYJ . A?tO". LTJ'OX '!i * -. '.• n --:'. jation J — ~ __ .LLcu.vt^ /W TREATISE ON ASTEONOMY. BY ELIAS L OOMIS, LL.D., I F•l'.OFESSOB O NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE ; AUTHOR OF "AM I NTRODUCTION TO PRACTICAL ASTRONOMY," AND OF A SERIES OF M ATHEMATICS FOR SCHOOLS AND COLLEGES. NEW Y ORK: HARPER & BROTHERS, PUBLISHERS, 327ND A 835 PEABL STREET. 186. 6 «-"'■* ■ ■ — iilF. N liW YORK 'PUBLIC LISRAR7 P. - »«C ■ J Entered, a ccording to Act of Congress, in the year 18G5, by Harper & B rothers, In the Clerk's Office of the Southern District of New York. •- M PREFACE. The d esign of the following treatise is to furnish a text-book for the instruction of college classes in the first principles of As tronomy. My aim has accordingly been to limit the book to such dimensions that it might be read entire without omissions, and to make such a selection of topics as should embrace every thing most important to the student. I have aimed to express every truth in concise and simple language ; and when it was nec essary to introduce mathematical discussions, I have limited my self to the elementary principles of the science. The entire book is divided into short articles, and each article is preceded by a caption, which is designed to suggest the subject of the article. "Whenever it could be done to advantage, I have introduced sim ple mathematical problems, designed to test the student's famil iarity with the preceding principles. At the close of the book will be found a collection of miscellaneous problems, many of them extremely simple, which are to be used according to the dis cretion of the teacher. I h ave dwelt more fully than is customary in astronomical text-books upon various physical phenomena, such as the consti tution of the sun, the condition of the moon's surface, the phe nomena of total eclipses of the sun, the laws of the tides, and the constitution of comets. I have also given a few of the results of recent researches respecting binary stars. It is hoped that the discussion of these topics will enhance the interest of the subject with a class of students who might be repelled by a treatise ex clusively mathematical. My s pecial acknowledgments are due to Professor H. A. New ton, who has read all the proofs of the work, and to whom I am indebted for numerous important suggestions. CONTENTS. CHAPTER I . THE E ARTH — ITS FIGURE AND DIMENSIONS. — DENSITY. — ROTATION. P«g« The P henomena of the Dinrnal Motion 9 The F igure of the Earth — how determined 15 Dimensions o f the Earth — how determined T. 16 The C elestial and Terrestrial Spheres 18 Effectsf o Centrifugal Force upon the Form of the Earth 22 Measurement o f an Arc of the Meridian 25 The D ensity of the Earth— how determined 28 Direct P roof of the Earth's Rotation 32 Artificial G lobes— Problems on the Terrestrial Globe 35 CHAPTER I I. THE P RINCIPAL ASTRONOMICAL INSTRUMENTS. The A stronomical Clock— its Error and Rate 3S The T ransit Instrument— its Adjustments 30 The M ural Circle— Reading Microscope 43 The A ltitude and Azimuth Instrument 47 The S extant— its Adjustments and Use 49 CHAPTER I II. ATMOSPHERIC R EFRACTION. — TWILIGHT. The L aw of Atmospheric Refraction 52 Refraction d etermined by Observation 53 The C ause of Twilight— its Duration 56 CHAPTER I V. EARTH'S A NNUAL MOTION. — EQUATION OF TIKE. — CALENDAR. The S un's apparent Motion— the Equinoxes, Solstices, etc 58 The C hange of Seasons— its Cause 62 The F orm of the Earth's Orbit 64 Sidereal a nd Solar Time— Mean Time and Apparent Time 67 The E quation of Time explained 69 The C alendar— Julian and Gregorian 72 Problemsn o the Celestial Globe 74 VI C ONTENTS. CHAPTER V . PARALLAX. — A STRONOMICAL PROBLEMS. Pap Diurnal P arallax — Horizontal Parallax 76 Howo t determine the Parallax of the Moon 77 Astronomical P roblems— Latitude — Time, etc 80 To f ind the Time of the Sun's Rising or Setting 83 CHAPTER V I. THEUN S — ITS PHYSICAL CONSTITUTION. Distance a nd Diameter of the Sun 88 The P hysical Constitution of the Sun 90 Theory o f the Constitution of the Sun 94 The Z odiacal Light described 99 CHAPTER V II. PRECESSION O P THE EQUINOXES. — NUTATION. — ABERRATION. Precession o f the Equinoxes — its Cause 100 Nutation, S olar and Lunar 104 Aberration o f Light — its Cause 105 Linef o the Apsides of the Earth's orbit 107 CHAPTER V IH. THE M OON — ITS MOTION — PHASES — TELESCOPIC APPEARANCE. Distance, D iameter, etc., of the Moon 109 Phasesf o the Moon — Harvest Moon 113 Has t he Moon an Atmosphere ? 116 Telescopic a ppearance of the Moon 118 Librations o f the Moon — Changes of the Moon's Orbit 124 CHAPTER I X. CENTRAL F ORCES. — GRAVITATION. — LUNAR IRREGULARITIES. Curvilinear M otion — Kepler's Laws 128 Theorems r especting Motion in an Orbit 129 Motionn i an Elliptic Orbit 132 The L aw of Gravitation — Motions of Projectiles 187 The P roblem of the Three Bodies 142 Sun's d isturbing Force computed 146 Evection, V ariation, Annual Equation, etc 148 Motion o f.the Moon's Nodes 150 CHAPTER X . PECLIPSES O TOE MOON. Dimensions, e tc., of the Earth's Shadow 153 Lunar E cliptic Limits— how determined 156 The E arth's Pennmbra— its Dimensions 157 The C omputation of Lunar Eclipses 158 Computation i llustrated by au Example 161 N \ CONTENTS. V U CHAPTER X I. ECLIPSESF O THE SUN. P «g» Dimensions, e tc., of the Moon's Shadow 16G Different K inds of Eclipses of the Sun .". 169 Phenomena a ttending Eclipses of the Sun 173 Corona — B aily'a Beads — Flame-like Protuberances 175 CHAPTER X II. METHODSF O FINDING THE LONGITUDE OF A PLACE. Methodf o Chronometers explained 179 Methody b Eclipses, Occultations, Lunar Distances, etc 181 Methody b the Electric Telegraph— Velocity of Electric Fluid 182 CHAPTER X III. THE T IDES. Definitions — C ause of the Tides 185 Cotidal L ines— Velocity of Tidal Wave 188 The T ides modified by Conformation of the Coast 192 The D iurnal Inequality in the Height of the Tides 194 Tidesf o the Pacific Ocean, Gulf of Mexico, etc 196 CHAPTER X IV. THE P LANETS — ELEMENTS OF THEIR ORBITS. Numberf o the Planets— The Satellites 198 Apparent M otions of the Planets explained 200 The E lements of the Orbit of a Planet 204 To d etermine the Distance of a Planet from the Sun 207 To d etermine the Position of the Nodes — Inclination of Orbit, etc 209 CHAPTER X V. THE I NFERIOR PLANETS. Greatest E longations — Phases 213 Mercury a nd Venus — their Periods, Distances, etc 214 Transitsf o Mercury and Venus across the Sun's Disc 217 Snn's P arallax — how determined 219 CHAPTER X VI. THE S UPERIOR PLANETS. Mars — D istance — Phases— Form, etc , 222 The M inor Planets — Discovery — Number, etc 224 Jupiter — D istance — Diameter — Belts, etc 227 Jupiter's S atellites— Distances — Eclipses — Occultations, etc 228 Velocity o f Light — how and by whom discovered ». 232 Saturn — D istance — Diameter — Rotation 233 His R ings — their Disappearance explained 234 Saturn's S atellites — their Number, Distance, etc 239 Uranus — D iscovery — Distance — Diameter, etc 240 Neptune— H istory of its Discovery— its Satellite 243 Vlll C ONTENTS. CHAPTER X VII. QUANTITYP O hatter in the sun and planets. — PLANETARY perturbations. Howo t determine the Moss of a Planet 247 The P erturbations of the Planets — how computed 250 The S ecular Inequalities of the Planets 253 The S tability of the Solar System 255 CHAPTER X VIII. COMETS. — C OMETABY ORBITS. — SHOOTIKG STARS. fNumber o Comets — the Coma — Nucleus — Tail, etc 257 Comets' T ails — Dimensions— Position 260 Cometary O rbits— how computed 265 Halley's C omet — its History and Peculiarities 269 Encke's C omet— Hypothesis of a resisting Medium 271 Biela's C omet — Faye's Comet— Brorsen's Comet, etc 272 Cometf o 1744— Comet of 1770— Comet of 1843, etc 276 Shooting S tars — Detonating Meteors — iErolites 279 CHAPTER X IX. THE F IXED STARS— THEIR LIGHT, DISTANCE, AND MOTIONS. Classification o f the Fixed Stars — their Brightness 284 The C onstellations — How Stars are Designated 287 Periodic S tars — Cause of this Periodicity — Temporary Stars 290 Distancef o the Fixed Stars — Parallaxes determined 292 Proper M otion of the Stars — Motion of the Solar System 295 CHAPTER X X. DOUBLE S TARS. — CLU8TERS. — NEBULE. Double S tars — Colored Stars — Stars optically Double 297 Binary S tars — Gamma Virginia — Alpha Centauri, etc 299 Mass o fa Binary Star computed — Triple Stars 303 Clustersf o Stars— Nebula 304 Planetary N ebula? — Variable Nebula; 308 The M ilky Way— its Constitution and Extent 310 The N ebular Hypothesis — how tested 314 Miscellaneous P roblems 316 Tables — E lements of the Planets, etc 321 Explanation o f the Tables 833 Explanation o f the Plates 837 • * ASTRONOMY. CHAPTEE I . GENERAL P HENOMENA OP THE HEAVENS. — FIGURE AND DIMEN SIONS OF THE EARTH. — DENSITY OF THE EARTH. — PROOF OF THE EARTH'S ROTATION. — ARTIFICIAL GLOBES. 1. A stronomy is the science which treats of the heavenly bodies. The heavenly bodies consist of the sun, the planets with their satel lites, the comets, and the fixed stars. Astronomy i s divided into Spherical and Physical.
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