'I'? ■^'if^^- otiences , -■ T ' Libraiy PREFACE. To prevent a possible misapprehension in scientific quar- ters, the author desires it understood that the present work is not designed either to instruct the professional investi- gator or to train the special student of astronomy. Its main object is to j^resent the general reading public with a con- densed view of the history, methods, and results of astro- nomical research, especially in those fields which are of most popular and philosophic interest at the jDresent day, couched in such language as to be intelligible without mathematical study. He hopes that the earlier chapters will, for the most part, be readily understood by any one having clear geomet- rical ideas, and that the later ones will be intelligible to all. To diminish the difficulty which the reader may encounter from the unavoidable occasional use of technical terms, a Glossary has been added, including, it is believed, all that are used in the present work, as well as a number of others which may be met with elsewhere. Respecting the general scope of the work, it may be said that the historic and philosophic sides of the subject have been treated with greater fulness than is usual in works of this character, while the purely technical side has been pro- portionately condensed. Of the four parts into Avhich it ia divided, the first two treat of the methods by which the mo- % vi PREFACE. tions and the mutual relations of the heavenly bodies have been investigated, and of tlie results of such investigation, while in the last two the individual peculiarities of those bodies are considered in greater detail. The subject of the general structure and probable development of the universe, which, in strictness, might be considered as belonging to the first part, is, of necessity, treated last of all, because it re- quires all the light that can be thrown upon it from every available source. Matter admitting of presentation in tabular form has, for the most part, been collected in the Appendix, where will be found a number of brief articles for the use of both the general reader and the amateur astronomer. The author has to acknowledge the honor done him by several eminent astronomers in making his work more com- plete and interesting by their contributions. Owing to the great interest which now attaches to the question of the con- stitution of the sun, and the rapidity with which our knowl- edge in tliis direction is advancing, it was deemed desirable to present the latest views of the most distinguished investi- gators of this subject from their own pens. Four of these gentlemen— Kev. Father Secchi, of Kome ; M. Faye, of Paris ; Professor Young, of Dartmouth College ; and Professor Lang- ley, of Allegheny Observatory — have, at the author's request, presented brief expositions of their theories, which will be found in their own language in the chapter on the sun. PREFACE TO THE SEVENTH EDITION. The favor with which this work has been received by the pnl)lic has led the author and publishers to give it a sixth re- vision, in order to inckide the latest results of astronomical research. The subjects which were added in preceding edi- tions comprised Dr. Draper's investigations on the existence of oxygen in the sun ; Janssen's new method of photographing the sun; the conclusions from recent total eclipses; the pre- liminary results of the British observations of the late transit of Venus, as well as of other methods of determining the solar parallax; the discovery of the satellites of Mars; t|ie transit of Venus of December 6th, 18S2 ; recent developments in cometary astronomy ; Professor Langley's researches on the light and heat radiated by the sun ; and the completion of several of the greatest telescopes ever made, including that of the Lick observatory in California. The subject of greatest interest now included for the first time is the determination of the motion of certain stars by Vogel, Pickering, and Chandler. The intention has been to bring the work up to date in all important points, and it is hoped that the general reader will find in it the fullest practicable explanation of every branch of the subject which can interest him. Washington, March, 1893. CONTENTS. PART I. THE SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. PAGK Introduction 1 CHAPTER I. The Ancient Astronomy, or the Apparent Motions of the Heav- enly Bodies 7 §1. The Celestial Sphere 7 §2. The Diurnal Motion 9 §3. Motion of the Sun among the Stars 13 § 4. Precession of the Equinoxes. — The Solar Year 19 §5. The Moon's Motion 2i §6. Eclipses of the Sun and Moon 24 §7. Tlie Ptolemaic System 32 §8. The Calendar 44 CHAPTER 11. The Copernican System, or the True Motions of the Heavenly Bodies 51 § 1. Copernicus 51 § 2. Obliquity of the Ecliptic ; Seasons, etc. ; on the Copeniicaii Sys- tem Gl §3. Tycho Brahe 66 §4. Kepler. — His Laws of Planetary Motion 68 I §5. From Kepler to Newton 71 X COXTEXTS. CHAPTER III. PAOB Universal Gravitation 74 §1. Newton. — Discovery of Gravitation 74 § 2. Gravitation of Small Masses. — Density of the Earth 81 §3. Figure of the Earth 86 §4. Precession of the Equinoxes 88 §5. The Tides 90 § C. InequaUties in the Motions of the Phanets produced by their Mutual Attraction Uiy § 7. Relation of the Planets to the Stars i03 PAET II. PEACTICAL ASTBOXOMY. Introductory Remarks 105 Cn.\PTER I. The Telescope 108 § 1. The First Telescopes 108 §2. The Achromatic Telescope 116 §3. The Mounting of the Telescope 120 §4. The Reflecting Telescope 123 § 5. The Principal Great Reflecting Telescopes of Modem Times... 127 §6. Great Refracting Telescopes 137 § 7. The Magnifying Powers of the Two Classes of Telescopes 141 CHAPTER II. Application of the Telescope to Celestial Measurements 148 § 1. Circles of the Celestial Sphere, and their Relations to Positions on the Earth 148 §2. The Meridian Circle, and its Use 154 §3. Determination of Terrestrial Longitudes 159 § 4. Mean, or Clock, Time 164 CONTENTS. Xi CHAPTER III. P^OE Measuring Distances in the Heavens 167 §1. Parallax in General 167 § 2. Measures of the Distance of the Sun 173 §3. Solar Parallax from Transits of Venus 177 § 4. Other Methods of Determining the Sun's Distance, and their Results 192 § o. Stellar Parallax 199 CHAPTER IV. The Motion of Light 208 CHAPTER V. The Spectroscope 220 PART III. THE SOLAR SYSTEM. CHAPTER I. General Structure of the Solar System 231 CHAPTER II. The Sun 237 § 1. The Photosphere and Solar Radiation 237 §2. The Solar Spots and Rotation 248 §3. Periodicity of the Spots 254 §4. Law of Rotation of the Sun 255 §5. The Sun's Surroundings 257 §6. Physical Constitution of the Sun 264 § 7. Views of Distinguished Students of the Sun on the Subject of its Physical Constitution 271 Xll CONTENTS. CHAPTER III. ,A8E The IsnsEU Grottp of Placets. 289 §1. The Planet Mercury 289 §2. The Supposed Intra-Mercurial Planets 292 §3. The Planet Venus 295 §4. The Earth 304 §5. The Moon 312 §6. The Planet Mars 326 §7. The Small Planets 331 CHAPTER IV. The Octer Group of Plaxets 339 § 1. The Planet Jupiter 339 §2. The Satellites of Jupiter 34-t § 3. Satuiti and its System, Physical Aspect, Belts, Rotation 346 §4. The Rings of Satura 34H §5. Constitution of the Ring 357 §6. The Satellites of Satuni 359 §7. Uranns and its Satellites 361 §8. Neptune and its Satellite 366 CHAPTER V. Comets asd Meteors 373 §1. Aspects and Forms of Comets 373 § 2. Motions, Origin, and Number of Comets 377 §3. Remarkable Comets 382 §4. Encke's Comet, and the Resisting Medium 393 §5. Other Periodic Comets 396 §6. Meteors and Shooting-stars 397 §7. Relations of Comets and Meteoroids 404 §8. The Physical Constitution of Comets 411 §9. The Zodiacal Light 416 PART IV. THE STELLAR UNIVERSE. Introdcctory Remarks 418 CONTENTS. Xiii CHAPTER I. p^„ The Stars as they ark Seen 422 § 1. Number and Orders of Stars and Nebula; 422 §2. Description of the Principal Constellations 429 §3. New and Variable Stars 433 §4. Double Stars 448 §5. Clusters of Stars 453 § 6. Nebulae 450 §7. Proper Motions of the Stars 4G4 CHAPTER II. The Sfructure of the Universe 472 §1. Views of Astronomers before Ilerschel 473 § 2. Researches of Herschel and his Successors 477 §3. Probable Arrangement of the Visible Universe 490 §4. Do the Stars really form a System? 495 CHAPTER III. The Cosmogony 503 § 1. The Modern Nebular Hypothesis 505 §2. Progressive Changes in our System 511 §3. The Sources of the Sun's Heat 517 §4. Secular Cooling of the Earth 523 §5. General Conclusions respecting the Nebular Hypothesis 526 §6. The Plurality of Worlds 528 APPENDIX. I. List of the Principal Great Telescopes of the World 533 II. List of the more Remarkable Double Stars 534 III. List of the more Interesting and Remarkable NEBtJL.a!: and Star Clusters 537 IV. Periodic Comets seen at more than One Return 539 xiv coNTi::sTs. TAGt V. Elements of tke Orbits of the Eight Major Planets for 18.")0. 540 Elements of the Satellites of Jdpitee 541 Elements of the Satellites of Saturn 541 Elements of the Satellites of Mars 541 Elements of the Satellites of Uranus 541 Elements of the Satellite of Neptune 541 VI. Elements of the Small Planets 542 VII. Determinations of Stellar Parallax 548 VIII. Synopsis of Papers on the Solar Parallax, 1854-77 551 IX. List of Astronomical Works, most of which have been con- sulted as Authorities in the Preparation of the Present Work 555 X. Glossary of Technical Terms of Frequent Occurrence in Astronomical Works 562 Index , 573 Explanation of the Star Maps ». 578 LIST OF ILLUSTRATIONS. FI«». PAQR Thk Great Telescope of the United States Naval Observato- ry, Washington Frontispiece 1. Section of the Imaginary Celestial Sphere 3 2. Map illustrating the Diurnal Motion round the Pole 10 3. The Celestial Sphere and Diurnal Motion 1'-' 4. Motion op the Sun past the Star Regulus 15 r>. Showing the Sun to be farther than the Moon 22 6. Annular Eclipsb of the Sun 2(5 7. Partial Eclipse of the Sun 2G 8. Eclipse of the Sun, the Shadow of the Moon falling on the Earth 20 9. Eclipse of the Moon, in the Shadow of the Earth 27 10. Showing the Apparent Orbit of a Planet 38 11. Apparent Orbits of Jupiter and Saturn 39 12. Arrangement of the Seven Planets in the Ptolemaic System... 41 13. The Eccentric 42 14. Shoaving the Astrological Division of the Seven Planets AMONG THE DaYS OF THE WeEK 46 15. Apparent Annual Motion of the Sun explained 55 16. Showing iioav the Apparent Epicyclic Motion of the Planets IS accounted for .50 17. Relation of the Terrestrial and Celestial Poles and Equators. G2 18. Causes of Changes of Seasons on the Copernican System G3 19. Enlarged View cf the Earth, showing Winter in the North- ern Hemisphere, and Summer in the Southern 65 20. Illustrating Kepler's First Two Laws of Planetary Motion... 69 21. Illustrating the Fall of the Moon towards the Earth 78 22. Baily's Apparatus for determining the Density of the Earth. 83 23. View of Baily's Apparatus 84 24. Diagram illustrating the Attraction of Mountains 85 25. Precession of the Equinoxes 88 Xvi LIST OF ILLUSTBATIOKS. ne. PAGE 26. Attractiox of the Moos tesdisg to produce Tides 91 27. Arjollabt Sphere as described bt Ptolemy 107 28. The Galilean Telescope 110 29. FoRJiATios of as Image bt a Less Ill 30. Great Telescope of the Sevesteesth Cestcrt 114 31. Refraction through a Compoxtsd Prism IIG 32. Section of an Achromatic Objective 117 33. Section of Eve-piece of a Telescope 120 34. Mode of Mounting a Telescope 121 35. Speculum Bringing Rays to a Single Focus bt Reflection 124 36. Herschelias Telescope 125 37. HoKizoxTAL Section of a Newtonian Telescope 125 38. Section of the Gregorian Telescope 126 39. Herschel's Great Telescope 129 40. Lord Rosse's Great Telescope 132 41. Mr. Lassell's Great Four-foot Reflector 134 42. The New Paris Reflector 136 43. The Great Melbourne Reflector 138 44. Circles of the Celestial Sphere 149 45. The Washington Transit Circle 155 4C. Spider Lines in Field of View of a Meridian Circle 156 47. Diagram illustrating Parallax 167 g 48. Diagram illustrating Parallax 168 49. Variation of Parallax with the Altitude 169 50. Apparent Paths of Venus across the Sun 178 51. Venus approaching Internal Contact on the Face of the Sun 180 52. Internal Contact of Limb of Vescs with that of the Sun 180 53. The Black Drop, or Ligament 181 54. Method of Photogr-^phing the Transit of Venus 188 55. Map of the World, showing the Regions in which the Tran- sit OF Ven-us will be visible on December Hth, 1882 193 56. Effect of Stellar Parallax 200 57. Aberration of Light 210 58. Revolting Wheel fob measuring the Velocity of Light 214 59. Illustratisg Foucaclts Method of measuring the Velocity OF Light 216 60. Course of Rats through a Spectroscope 222 61. Relative Size of Sun and Planets 232 C2. Orbits or the Planets from the Earth outward 235 LIST OF ILLUSTBATIOXS. Xvii no. PASt C3. Aspect of the Sux's Scetace as Photographed by Jassses at THE Obsertatoet OF 3Iect>os 240 G4, C4a. DisTEiBmos of the Heat SpECTErsi as detebkised os Mt. Whitxet 250, 251 65. Method of holding Telescope, to show Scs ox Screes 249 66. SoLAE Spot, after Secchi 250 67. Chasges is the Aspect of a Solar Spot as it ceosses the Sex's Disk 252 fiS. Total Eclipse of the Srs, as seen at Des Moises, Iowa, Ac- GrsT 7th, 1S69 259 69. Specimxss of Solar Prottberasces, as draws bt Secchi 262 70. The Scs, with its Chromosphere asd Red Flajies, os July 23d, 1S71 267 71. Illusteatisg Secchi's Theory of Solar Spots 275 72. Solar Spot, after L.*.sgley 287 73. Orbits of the Four Isser Plasets, iLLrsTRATiso the Ecces- TRICITY of those of ilERCURY ASD MaES 2S9 74. Phases of Vescs 297 75. Showisg the Thicksess of the Earth's Cbust 305 76. Distributios of Auroras 308 77. View of Aueoea. 309 ffS. SPECTErsf of Two of the Great Auroras of 1871 311 79. Relative Size of Eaeth asd Moos 312 80. View of Moos sear the Third Quarter 319 81. LusAR Crater " Copersicus "" 321 82. The Plaset Mars os Juke 23d, 1875 328 83. Map of Maes 328 84. Nobthers Hemisphere of Mars 329 85. Southers Hemisphere of JL^^rs 329 85a. Apparent Orbits of the Satellites of ^Iars is 1877, as ob- served ASD LAID DOWS BY PROFESSOR HaLL 331 86. Jupiter, as sees with the Great Washisgtos Telescope, March 21sT, 1876 339 87. View of Jupiter, as sees is Lord Rosse's Great Telescope, February 27th, 1861 341 88. View of Saturs ast> his Risgs 347 89. Specimess of Drawisgs of Saturs by Various Observers 351 90. Views of Escke's Comet is 1871 375 91. Head of Dosat^s Great Comet of 1858 376 92. Parabolic asd Elliptic Orbit of a Coscet 378 2 Xviii LIST OF ILLUSTBATION& no. faor 93. Orbit of Halley's Comet 385 94. Great Comet of 1858 388 95. Meteor Paths, illustrating the Radiant Point 403 96. Orbit of November Meteors and the Comet of 1861 407 97. Orbit of the Second Comet of 1862 408 98. Measure of Position Angle of Double Star 450 99. DisT.o<"CE OF Components of Double Star 450 100. Diagram to illustrate Position Angle 4.50 101. Telescopic View of the Pleiades 454 102. Cluster of 47 Toucani 456 103. Cluster u> Centauri 456 104. The Great Nebula of Orion 458 105. The Annular Nebula in Lyra 460 106. The Omega Nebula 462 107. Nebula Herschel 3722 463 108. The Looped Nebula; Herschel 2941 463 109. Herschel's View of the Form of the Universe 481 110. Illustrating Herschel's Orders of Distance of the Stars.... 483 111. Probable Arrangement of the Stars and Nebulje Visible WITH the Telescope 493 112. Diagram illustrating Elliptic Elements of a Plan^et 565 • STAR MAPS. Map I. — The Northern Constellations withis 60°' OF the Pole " II. — Southern Constellations Visible in Au- tujen and Winter " III. — Southern Constellations Visible in Win- ter AN"D Spring " IV. — Southern Constellations Visible in Spring AND Summer ( " V. — Southern Constellations Visible in Sum- mer AND Autumn J yAt End of Book. POPULAR ASTRONOMY. PART L — TBE SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. mTRODUCTIOK Astronomy is the most ancient of the physical sciences, be ing distinguished among them by its slow and progressive development from the earliest ages until the present time. In no other science has each generation which advanced it ' been so much indebted to its predecessoi-s for both the facts and the ideas necessary to make the advance. The conception of a globular and moving earth pursuing her course through the celestial spaces among her sister planets, which we see as stars, is one to the entire evolution of which no one mind and no one age can lay claim. It was the result of a gradual process of education, of which the subject was not an indi- vidual, but tlie human race. The great astronomers of all ages have built upon foundations laid by their predecessors ; and when we attempt to search out the first founder, we find ourselves lost in the mists of antiquity. The theory of uni- versal gravitation was founded by Newton upon the laws of Kepler, the observations and measurements of his French con- temporaries, and the geometry of Apollonius. Kepler used as his material the observations of Tycho Brahe, and built upon the theory of Copernicus. When we seek the origin of the instruments used by Tycho, we soon find ourselves among 2 SYSTEM OF TEE WORLD HISTORICALLY DEVELOPED. the mediaeval Arabs. The discovery of the true system of the world by Copernicus was only possible by a careful study of the laws of apparent motion of the planets as expressed in the epicycles of Ptolemy and Hipparchus. Indeed, the more carefully one studies the great work of Copernicus, the more surprised he will be to find how completely Ptolemy furnished him both ideas and material. If we seek the teachers and predecessors of Hipparchus, we find only the shadowy forms of Egyptian and Babylonian priests, whose names and writings are all entirely lost. In the earliest historic ages, men knew that tlie earth was round ; tliat the sun appeared to make an annual revolution among the stars; and that eclipses were caused by the moon entering the shadow of the earth, or the earth that of the moon. Indeed, each of the great civilizations of the ancient world seems to have had its own system of astronomy strongly marked by the peculiar character of the people among whom it was found. Several events recorded in the annals of China show that the movements of the sun and the laws of eclipses were studied in that country at a very early age. Some of these events nii.st be entirely mythical ; as, for instance, the despatch of astronomers to the four points of the compass for the purpose of determining the equinoxes and solstices. But there is another event which, even if we place it in the same category, must be regarded as indicating a considerable amount of astronomical knowledge among the ancient Chinese. We refer to the tragic fate of Hi and Ho, astronomers royal to one of the ancient emperors of that people. It was part of the duty of these men to carefully study the heavenly movements, and give timely warning of the approach of an eclipse or other remarkable phenomenon. But, neglecting this duty, they gave themselves up to drunkenness and riotous living. In conse- quence, an eclipse of the sun occurred without any notice being given ; the religious rites due in such a case were not performed, and China was exposed to the anger of the gods. To appease their wrath, the unworthy astronomers were seized and sum- marily executed by royal command. Some historians have INTBODVCIION. 3 gone so far as to fix the date of this occurrence, which is vari- ously placed at from 2128 to 2159 yeai-s before the Christian era. If this is correct, it is the earliest of which profane his- tory has left us any record. In the Hindoo astronomy we see the peculiarities of the contemplative Hindoo mind strongly reflected. Here the imagination revels in periods of time which, by comparison, dwarf even the measures of the celestial spaces made by mod- ern astronomers. In this, and in perhaps other ancient sys- tems, we find references to a supposed conjunction of all the planets 3102 years before the Christian era. Although we have every reason for believing that this conjunction was learned, not from any actual record of it, but by calculating back the position of the planets, yet the very fact that they were able to make this calculation shows that tlie motions of the planets must have been observed and recorded during many generations, either by the Hindoos themselves, or some other people from whom they acquired their knowledge. As a matter of fact, we now know from our modern tables that this conjunction was very far from being exact; but its error could not be certainly detected by the rude observations of the times in question. Among a people so prone as the ancient Greeks to speculate upon the origin and nature of things, while neglecting the ob- servation of natural phenomena, we cannot expect to find a.r\y- thing that can be considered a system of astronomy. But there are some ideas attributed to Pythagoras which are so frequent- ly alluded to, and so closely connected with the astronomy of a subsequent age, tliat we may give them a passing mention. He is said to have taught that the heavenly bodies were set in a number of crystalline spheres, in the common centre of which the earth was placed. In the outer of these spiieres were set the thousands of fixed stars which stud the firma- ment, while each of the seven planets had its own sphere. The transparency of each cr3'stal sphere was perfect, so that the bodies set in each of the outer spheres were visible through all the inner ones. These spheres all rolled round on each 4 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. other ill a daily revolution, thus causing the rising and setting of the heavenly bodies. This rolling of tlie spheres on each other made a celestial music, the " music of the sj)lieres," which filled the firmament, but was of too elevated a char- acter to be heard by the ears of mortals. It must be admitted that the idea of the stars being set in a hollow sphere of crystal, forming the vault of the firmament, was a very natural one. They seemed to revolve around the earth every day, for generation after generation, without the slightest change in their relative positions. If there were no solid connection between them, it does not seem possible that a thousand bodies could move around their vast circuit for such long periods of time without a single one of them vary- ing its distance from one of the others. It is especially diffi- cult to conceive how they could all move around the same axis. But when they are all set in a solid sphere, eveiy one is made secure in its place. The planets could not be set in the same sphere, because they change their positions among the stars. This idea of the sphericity of the heavens held on to the minds of men with remarkable tenacity. The funda- mental proposition of the system, both of Ptolemy and Coper- nicus, was that the universe is spherical, the latter seeking to prove the naturalness of the spherical form by the analogy of a drop of water, although the theory served him no pur- pose whatever. Faint traces of the idea are seen here and there in Kepler, with whom it vanished from the mind of the race, as the image of Santa Clans disappears from the mind of the growing child. Pythagoras is also said to have taught in his esoteric lect- ures that the sun was the real centre of the celestial move- ments, and that the earth and planets moved around it, and it is this anticipation of the Copernican system which constitutes his greatest glor}^ But he never thought proper to make a public avowal of this doctrine, and even presented it to his disciples somewhat in the form of an hypothesis. It must also be admitted that the accounts of his system which have reached us are so vague and so filled with metaphysical specu- INTRODUCTION. 5 lation that it is questionable whether the frequent application of his name to the modern system is not more pedantic than justifiable. The Greek astronomers of a later age not only rejected the vague speculations of their ancestors, but proved themselves the most careful observers of their time, and first made astron- omy worthy tlie name of a science. From this Greek astrono- my the astronomy of our own time may be considered as com- ing by direct descent. Still, were it not for the absence of his- toric records, we could probably trace back both their theories and their system of observation to the plains of Chaldea. The zodiac was mapped out and the constellations named many centuries before they commenced their observations, and these works marked quite an advanced stage of development. This prehistoric knowledge is, however, to be treated by tlie histo- rian rather than the astronomer. If we confine ourselves to men whose names and whose labors have come down to us, we must concede to Tlipparchus the honor of being the father of astronomy. Not only do his observations of the heavenly bodies appear to have been far more accurate than those of any of his predecessors, but he also determined the laws of the apparent motions of the planets, and prepared tables by which these motions could be calculated. Probably he was the first propounder of the theory of epicyclic motions of the planets, commonly called after the name of his successor, Ptolemy, who lived three centuries later. Commencing with the time of Ilipparchus, the general theory of the structure of the universe, or "system of the world," as it is frequently called, exhibits three great stages of development, each stage being marked by a system quite dif- ferent from the other two in its fundamental principles. These are : 1. The so-called Ptolemaic system, which, however, really belongs to Ilipparchus, or some more ancient astronomer. In this system the motion of the earth is ignored, and the appar- ent motions of the stars and planets around it are all regarded as real. 6 SYSTEM OF THE WOBLD HISTORICALLY DEVELOPED. 2. The Copernican system, in which it is shown that the sun is really the centre of the planetary motions, and that the earth is itself a planet, both turning on its axis and revolving round the sun. 3. TheXewtonian system, in which all the celestial motions are explained by the one law of universal gravitation. This natural order of development shows the order in which a knowledge of the structure of the universe can be most clearly presented to the mind of the general reader. "VVe shall therefore explain this structure historically, devoting a separate chapter to each of the three stages of development which we have described. We commence with what is well known, or, at least, easily seen by every one who will look at the heavens with sufficient care. We imagine the observer out-of-doors on a starlit night, and show him how the heav- enly bodies seem to move from hour to hour. Then, we show him what changes he will see in their aspects if he contin- ues his watch through months and years. By combining the apparent motions thus learned, he forms for himself the an- cient, or Ptolemaic, system of the world. Having this system clearly in mind, the passage to that of Copernicus is but a step. It consists only in showing that certain singular oscilla- tions which the sun and planets seem to have in common are really due to a revolution of the earth around the sun, and that the apparent daily revolution of the celestial sphere arises from a rotation of the earth on its own axis. The laws of the true motions of the planets being perfected by Kepler, they are shown by Newton to be included in the one law of gravitation towards the sun. Such is the coui-se of thought tc wluch we first invite the reader. TEE CELESTIAL SPHERE. CHAPTER I. THE ANCIENT ASTKONOMY, OK THE APPARENT MOTIONS OF THE HEAVENLY BODIES. § 1. The Celestial Sphere. It is a fact with which we are familiar from infancy, that all the heavenly bodies — sun, moon, and stars — seem to be set in an azure vault, which, rising high over our heads, curves down to the horizon on every side. Here the earth, on which it seems to rest, prevents our tracing it farther. But if the earth were out of the way, or were perfectly transparent, we could trace the vault downwards on every side to the point beneath our feet, and could see sun, moon, and stars in every direction. The celestial vault above us, with the correspond- ing one below us, would then form a complete sphere, in the centre of which the observer would seem to be placed. This has been known in all ages as the celestial sphere. The direc- tions or apparent positions of the heavenly bodies, as well as their apparent motions, have always been defined by their sit- uation and motions on this sphere. The fact that it is purely imaginary does not diminish its value as enabling us to form distinct ideas of the directions of the heavenly bodies from us. It matters not how large we suppose this sphere, so long as we always suppose the observer to be in the centre of it, so that it shall surround him on all sides at an equal distance. But in the language and reasoning of exact astronomy it is always supposed to be infinite, as then the observer may con- ceive of himself as transported to any other point, even to one of the heavenly bodies themselves, and still be, for all practical purposes, in the centre of the sphere. In this case, however, the heavenly bodies are not considered as attached to the cir B 8 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. cumference of the infinite spliere, but only as lying on tiie line of sight extending from the observer to some point of the sphere. Their relation to it may be easily understood by the observer conceiving himself to be luminous, and to throw out rays in every direction to tlie infinitely distant sphere. Then the apparent positions of the various heavenly bodies will be those in which their shadows strike the sphere. For instance, the observer standing on the earth and looking at the moon;, Pig. 1 Section of the imaginary celestial ephere. The observer at 0, looking: at the stars or other bodies, marked p, q, r, s, t, u, v, will imagine them situated at P, Q, Ft, S, T, O, V, on the surface of the sphere, where they will appear projected along th3 straight pP, qQ, etc. the shadow of the latter will strike the sphere at a point on a straight line drawn from the observer's eye through the centre of the moon, and continued till it meets the sphere. The point of meeting will i-epresent the position of the moon as seen by the observer. Now, suppose the latter transported to the moon. Then, looking back at the earth, he will see it projected on the sphere in a point diametrically opposite to that in Avhich he formerly saw the moon. To whatever planet he might trans- THE DIUBNAL MOTION. 9 port himself, he would see the earth and the other planets pro- jected on this imaginary sphere precisely as we always seem to see the heavenly bodies so projected. This is all that is left of the old crystalline spheres of Py- thagoras by modern astronomy. From being a solid which held all the stars, the sphere has become entirely immaterial, a mere conception of the mind, to enable it to define the di- rections in which the heavenly bodies are seen. By examin- ing the figure it will be clear that all bodies which lie in the same straight line from the observer will appear on the same point of the sphere. For instance, bodies at the three points marked t will all be seen as if they were at T. § 2. The Diurnal Motion. If we watch the heavenly bodies for a few hours we shall always find them in motion, those in tlie east rising upwards, those in the south moving towards the west, and those in the west sinking below the horizon. We know that this motion is only apparent, arising from the rotation of the earth on its axis ; but as we wisli, in this chapter, only to describe things as they appear, we may speak of the motion as real. A few days' watching will show that the whole celestial sphere seems to revolve, as on an axis, every day. It is to this revolution, carrying the sun alternately above and below the horizon, tliat the alternations of day and night are due. The nature and effects of this motion can best be studied by watching the ap- parent movement of the stars at night. We should soon learn from such a watch that there is one point in the heavens, or on the celestial sphere, which does not move at all. In our latitudes this point is situated in the north, between the zenith and the horizon, and is called the pole. Around this pole, as a fixed centre, all the heavenly bodies seem to revolve, each one moving in a circle, the size of which depends on the dis- tance of the body from the pole. There is no star situated exactly at the pole, but there is one which, being situated lit- tle more than a degree distant, describes so small a circle that the unaided eye cannot see any change of place without mak- 10 SYSTEM OF THE WORLD HISTOEICALLY DEVELOPED. ing some exact and careful observation. This is therefore called the pole star. The pole star can nearly always be very readily found by means of the pointers, two stai"s of the con- stellation Ursa Major, the Great Bear, or. as it is familiarly called, the Dipper. By referring to the fignre, the reader will readily find this constellation, by the dotted line from the pole and thence the pole star, which is near the centre of the map. Fis. 2. — Map of the principal stars of the northern sky, iC'-iwing the constellations which never set in latirnde 40=^, bnt revolve round the pwle star every day in the direction shown by the arrows. The two lower stars of UrM, Mayjr, on the left of the m^, point to the p