GIFT OF AUVHOR o4 d HOW TO KNOW THE STARRY HEAVENS ^. . FIG. 1. SOLAK PROMINENCES, BY TROUVELOT, OF HARVARD OBSERVATORY The white circle represents the size of the Earth on the same scale. HOW TO KNOW THE STARRY HEAVENS AN INVITATION TO THE STUDY OF SUNS AND WORLDS BY EDWARD IRVING WITH CHARTS, COLOURED PLATES, DIAGRAMS, AND MANY ENGRAVINGS OF PHOTOGRAPHS NEW YORK FREDERICK A. STOKES COMPANY PUBLISHERS COPYRIGHT, 1904 BY FREDERICK A. STOKES COMPANY All rights reserved Published in November, 1904 THE UNIVERSITY PRESS, CAMBRIDGE, U. S. A. "Everybody should study astronomy. It is the most delightful of all the sciences. It is the most inspiring of all. It lifts and broadens the mind. It rouses the imagination, and the imagination is the most God-like of human faculties, because it is the most creative. Let no one be deterred by the superstition that it is necessary to be a mathematician in order to understand and enjoy astronomy. You can let the mathematics of the subject severely alone and yet Jind inexhaustible pleasure and advantage in astro- nomical study. It is because they were compelled to begin at the mathematical end of the subject that hundreds of thousands of graduates from schools and colleges have virtually no knowledge of astronomy. Mathematical gifts are rare, but they are not essential to the enjoyment of astronomy." GARRETT P. SERVISS. PREFACE THIS volume is not so much a text-book on Astronomy, as an invitation to read text-books on that subject. In other words, it is a careful selection of the most typical, interesting, and instructive facts and theories concerning the Universe around us. The author has endeavoured to describe and illus- trate these in such a way as to attract, interest, and inform the general reader. But, though intended primarily for beginners, every effort has been made to avoid offending those who are further advanced, by sensationalism or a want of proportion and accuracy. The comparisons and illustrations used are the re- sult of many years' study, and have been successfully used in lectures and classes. They may interest some who are well acquainted with the facts of astronomy, but have not looked at them from the same standpoint. Many interesting and important astronomical methods, prin- ciples, and facts have been left out of this volume, to avoid overcrowding and confusion. The main object of the work is not so much to describe individual worlds, as to enable the reader to realise, as far as possible, what the Universe itself is like. In other words, it is to give a bird's-eye view of the celestial forest from a general and philosophical standpoint, so that the individual trees may be afterwards examined more at leisure. Until such a bird's-eye view has been obtained, the learner is apt to be confused by the details. As the old saying has it, he " cannot see the wood for the trees." When such a general view has once been obtained, the details no longer confuse, and text-books that were formerly thrown down in disgust become luminous with the ever-growing interest that rightly belongs to the physical sciences. viii PREFACE The figures given in this work are mostly round numbers. They do not claim absolute accuracy, but at the same time every effort has been made to avoid serious errors. The distance of the nearest star has been given as about 9,000 times as great as that of Neptune. It is quite possible that further investigations may result in other figures being adopted. But even if it should be changed to 8,000 or 10,000, the comparisons used will still serve to illustrate the relative dimensions of the visible Universe. The author gratefully acknowledges the kindness of Professor K. G. Aitken and other members of the staff at the Lick Ob- servatory, in reading the manuscript and making suggestions which have materially helped to perfect the work. Thanks are due to many who have given advice, suggestions, corrections, and information; also to those who have granted the reproduction of valuable photographs and drawings. Among these are : The late Dr. E. Keeler, Director of Lick Observatory, California. Dr. W. W. Campbell, Director of Lick Observatory, California. Dr. A. 0. Leuschner, Director of Students' Observatory, Berkeley, Cal. E. L. Larkin, Director of Lowe Observatory, California. C. Burckhalter, Director of Chabot Observatory, Oakland, Cal. G. E. Hale, Director of Yerkes Observatory, Wisconsin. E. C. Pickering, Director of Harvard Observatory, Massa- chusetts. W. H. M. Christie, M.A., Astronomer Eoyal, Greenwich, England. E. Walter Maunder, F.K.A.S., Greenwich, England. Besides giving an account of well-known and indisputable astronomical facts, the author has touched upon certain specu- lative theories which cannot yet be proved by either experiment or observation. The most that can be said for them is that they give a reasonable explanation of a large number of ob- served phenomena, and must therefore contain a certain amount PREFACE ix of truth. They also help to give us a better idea of the Infinite and Eternal Drama in which our little Earth is playing its obscure and ephemeral part. The reader is not asked to accept these theories if he can explain the observed phenomena by more probable speculations of his own. But he must beware of adopting theories which conflict largely with ascertained facts. It only remains to be said that these speculations have everywhere been carefully distinguished from those facts which are so well proved as to be practically indisputable. This volume is intended to be the first of a series, by the same writer, dealing with the sciences of astronomy, geology, biology, and sociology. These four were grouped together by the late Herbert Spencer under the name of the Concrete Sciences. Though the vast importance of these subjects is now generally recognised, many otherwise educated people are lamentably deficient in them. This is very unfortunate for the individuals concerned, for, however learned a man may be in all other subjects, it is impossible for him to be truly broad- minded, philosophical, and cosmopolitan, without some knowl- edge of these Concrete Sciences. 1 A general lack of scientific knowledge injures, not only the individuals themselves, but also society at large. In spite of the great advances made in all directions during the last century, there are still many imperfections remaining in our systems of government, of administrative justice, of national education, and in our entire social and moral organisations. These imperfec- tions are largely due to the fact that many of our statesmen, lawyers, teachers, doctors, and preachers are deficient in the above-mentioned sciences. Let us hope that during the present 1 As the philosophical A. Zazel truly says : " Astronomy, geology, biology, and sociology together form an impregnable bulwark against the inroads of superstition. And where the seeds of that deadly mental disease have been already sown, these sciences form an infallible antidote and cure." x PREFACE century this ignorance may be removed, so that our upward progress may no longer be impeded by the erroneous ideas that have been dragged up with us from the flat world in which our ancestors imagined themselves to be living. The second volume will deal with the history of the Third Planet in our System, from its nebulous birth to the advent of Man. Its title will probably be How to Know the Earth's History. EDWARD IRVING. BERKELEY, CAL. (U. S.), October, 1904. CONTENTS CHAPTER P AGK I. APPARENT MOTIONS OF THE HEAVENLY BODIES AS SHOWN BY OBSERVATION 1 II. RIVAL THEORIES TO EXPLAIN THE APPARENT MOTIONS OF THE HEAVENLY BODIES 15 III. PRINCIPLES UTILISED FOR MEASURING THE UNIVERSE 26 IV. SOME PROBLEMS USED IN CELESTIAL MEASUREMENTS 39 V. THE CHARIOT OF IMAGINATION 53 VI. DIMENSIONS OF THE UNIVERSE ......... 68 VII. SOME MORE DIMENSIONS 77 VIII. THE PRINCIPLES AND APPLICATIONS OF THE SPECTRO- SCOPE 87 IX. A STAR-SPANGLED BANNER 102 X. CONSTRUCTION OF THE UNIVERSE 114 XL SOLAR ARCHITECTURE 125 XII. A REELING WORLD 136 XIII. KEPLER'S THREE LAWS 155 XIV. GALILEO'S LAWS OF MOTION 163 XV. NEWTON'S LAW OF GRAVITATION 167 XVI. ANCIENT COSMOGONIES, AND THE NEBULAR HYPOTHESIS 178 XVII. THEORIES AND DISCOVERIES MODIFYING THE NEBULAR HYPOTHESIS 190 XVIII. MODIFICATIONS OF THE NEBULAR THEORY .... 205 XIX. THE MESSENGERS OF HEAVEN 219 XX. LARGE AND SMALL WORLDS 233 x COiNTENTS CHAPTER PAGE XXI. IGNEOUS FORCES ON THE MOON AND ELSEWHERE . . 243 XXII. LUNAR GEOLOGY AND GEOGRAPHY 257 XXIII. INHABITED WORLDS 265 XXIV. SIZE, IMPORTANCE, SPEED, AND DURATION .... 283 XXV. CONCLUSION 290 APPENDIX A. FACTS AND FANCIES CONCERNING MATTER . . 295 APPENDIX B. THE GREEK ALPHABET 301 APPENDIX C. THE LUNAR CRATERS 302 INDEX . , 309 ILLUSTRATIONS FULL-PAGE ILLUSTRATIONS FIGURE 1. Solar Prominences, by Trouvelot, of Harvard Observatory frontispiece in colours FACING PAGK 7. Northern Star-Trails 14 8. The Dipper, or Great Bear, at Intervals of Six Hours ... 14 24. Sun, Showing Spots and Faculse 52 25. Group of Sunspots 58 26. Solar Flames and Corona, as Seen During Eclipse of May 28, 1900. (In colours) 56 27. Eruptive Prominences 58 28. Solar Corona. Eclipse of May 28, 1900 60 29. North Polar Streamers of the Corona. May 28, 1900 ... 60 30. Mercury, the First Planet 62 31. Venus, the Second Planet 62 33. Mars, the Fourth Planet 62 35. The Zone of Asteroids Between Mars and Jupiter .... 64 36. Jupiter, the Largest Planet 64 38. Saturn, the Ringed Planet 66 41. Lick Observatory on Mount Hamilton, California 70 42. Main Entrance and Great Dome, Lick Observatory .... 70 43. The Thirty-Six-Inch Refractor at Lick Observatory . . . 72 44. Eye-Piece of the Great Lick Telescope 74 45. Yerkes Observatory, Williams Bay, Wisconsin 80 46. The Forty-Inch Refractor of the Yerkes Observatory: tin- Largest in the World 80 47. Milky Way Surrounding Messier II 48. The Star-Cluster Messier II 84 53. Laboratory and Celestial Spectra. (In colours) 94 54. Tele-Spectroscope 55. The Mills Spectrograph at Lick Observatory 96 56. Chief Lines in the Solar Spectrum (Herschel) . 57. Part of the Spectra of Four Red Stars (Hale and Ellerinan) . 100 58. Star Spectra Showing Displacement of Lines Due to Star's Motion in Line of Sight xiv ILLUSTRATIONS FIOUBE FACING PAGE 59. Coloured Double Stars. (In colours) 108 60. Star-Cluster in Hercules 112 61. Part of the Milky Way in Sagittarius 114 62. A Rope-like Nebula in Cygnus 114 63. Spiral Nebula in Triangulum 116 64. The Great Nebula in Andromeda 118 65. A Spiral Nebula Seen Edgeways 120 66. The Ring Nebula in Lyra 120 67. The Trifid Nebula in Sagittarius -122 68. Great Nebula in Orion 124 69. A Typical Sunspot 128 70. Solar " Flames " or Prominences 132 75. The Solar Corona During the Eclipse of July 29, 1878 ... 134 76. Theoretical Section of Solar Photosphere 132 79. Equatorial Mounting of the Crossley Reflector, Lick Observatory 150 80. Meridian Circle 150 82. Drawing an Ellipse 158 84. Mount Lowe Observatory, in Southern California 168 85. Spiral Nebula in Ursa Major (M 81) 172 91. Dumb-Bell Nebula 192 92. Nova Persei, 1901. Showing Movement of Surrounding Nebu- losity. Lick Photographs " 196 93. Spectra of Nova Persei, Showing Changes 200 94. The Star- Cluster Omega Centauri 204 100. A Celestial Messenger Approaching a Star 222 101. Brook's Comet, 1893 222 102. Comet 1903 C 222 106. Donati's Comet, 1858 228 107. Comet Rordame, 1893 228 109. The California Meteor of July 27, 1894 232 113. Full Moon, Showing Radiating Streaks 244 114. The Moon, at First and Last Quarter 248 117. Clavius and Tycho 252 118. Theophilus, a Lunar Crater-With-Cone 254 122. Mare Crisium, a Lunar Plain 258 123. Lunar Apennines and Alps 258 124. Copernicus 260 125. Schickard and Wargentin 262 126. Ptolemy, Alphons, and Arzachel 264 127. Twelve Views of Mars . 268 128. Disc of the Sun, August 12, 1903 274 ILLUSTRATIONS xv CHARTS Chart A. The Northern Heavens | PACING PAGE Key to Chart A. (In colours) J 282 Chart B. The Equatorial Constellations. For Spring Evenings ] Key to Chart B. (In colours) . j -290 Chart C. The Equatorial Constellations. For Summer Evenings ) Key to Chart C. (In colours) . } 294 Chart D. The Equatorial Constellations. For Winter Evenings ) Key to Chart D. (In colours) } 30 Chart E. Eastern Half of Moon. (In colours) ) Chart F. Western Half of Moon. (In colours) \ 804 Chart G. The Constellation Figures 308 ILLUSTRATIONS IN THE TEXT FIGURE p AG s 2. Umbrella-Apparatus for Illustrating (Apparent) Star Move- ments 5 3. The Earth, Showing Relative Positions of Apparatus when Used at Equator, Poles, etc 7 4. Umbrella- Apparatus Modified for Illustrating Apparent Move- ments of Sun and Planets 8 5. Circles of the Celestial Sphere with World in the Centre . . 9 6. An Adjustable Equatorial, Suitable for any Part of the World 13 9. The Ptolemaic System 19 10. The Tychonic System 20 11. Copernican System 23 12. Relative Positions of Earth and Sun at the four Seasons ... 24 13. Orbits of Mercury, Venus, and Earth 28 14. Estimating Distances with the Eyes 31 15. Surveying from a Base-line 32 16. Daily Positions of Earth and Moon ....*.... 37 1 7. Arc of Circle 40 18. Chord of Arc . 41 19. Sine of Angle 42 20. Measuring Width of River 43 21. Measuring Distance of Moon 46 22. Arc of Circle 47 23. Sine of Angle 50 32. Terra, the Third Planet, and Its Satellite or Moon .... 63 34. Relative Sizes of Earth and Mars 64 37. Relative Sizes of Jupiter and Earth 65 xvi ILLUSTRATIONS FIGURE PAGE 39. Relative Sizes of Saturn and Earth 66 40. Relative Sizes of Neptune and Earth 67 49. A Prism and its Spectrum 90 50. A One-prism Spectroscope 91 51. Section of a One-prism Spectroscope 92 52. A Compound Spectroscope 93 71. A Solar " Cloud " of Glowing Hydrogen (Professor Young) . . 131 72. The Same Region 35 Minutes Later (Young) 132 73. The Same Region 35 Minutes Later (Young) 133 74. The Same, 15 Minutes Later (Young) 133 77. Diagram Illustrating Zodiac 137 78. Diagram Illustrating Precession of Equinoxes and Advance of Perihelion 143 81. Alt- Azimuth Mounting for Small Telescope 153 83. An Elliptical Orbit, Divided into Twelve Monthly Parts . . . 159 86. Original Nebula, after its Rotation has Produced a Disc-like Form 184 87. Nebula with Outer Ring, left behind by Contraction and Conse- quent Quickening of Rotation 185 88. Central Condensation Surrounded by Rings 186 89. Rings Collapsing into Planets, and Central Condensation Turn- ing to a Luminous Sun 187 90. Solar System as it is now 188 95. Earth-tides, if the Day and Month Were Equal 213 96. Acceleration of Moon by Forward Pull of Earth-tide . . . . 214 97. Loop in Apparent Path of Mars 215 98. Diagram Showing Cause of Loop in Apparent Path of Mars . 216 99. A Celestial Messenger on a Journey 221 103. Parabolic Orbit of a Free Comet 227 104. Elliptical Orbits of Captive Comets 228 105. Tail of a Comet near Perihelion 229 108. A Meteor Bursting in the Atmosphere 230 110. Relative Sizes of Planets 234 111. Relative Sizes of Sun, Jupiter, and Earth 235 112. Relative Sizes of the First Four Asteroids and the Earth's Satel- lite 236 115. Section of Earthly Volcanoes 251 116. Section of Lunar Volcano in full Activity 252 119. Section of Mountain of Exudation 254 1 20. Section of Mountain of Elevation 254 121. Section of Lunar Crater with Cone 255 HOW TO KNOW THE STARRY HEAVENS CHAPTER- APPARENT MOTIONS OF THE HEAVENLY BODIES AS SHOWN BY OBSERVATION " Appearances are deceptive." Old Saying. "Ne jugez pas selon 1'apparence, raais jugez selon la justice." Fourth Gospel, vii, 24 (Segond). " Things are not what they seem." Longfellow. SUPERFICIAL APPEARANCES BEFORE describing the Universe as it is, I wish to say a few words about the Universe as it seems. We shall then be better able to judge as to the reasonableness, or otherwise, of the various theories which have from time to time been brought forward to explain the celestial phenomena which are going on around us. It may be well also, before dealing with the dimensions of the Universe, to give a very brief account of the methods used by astronomers to enable them to ascer- tain the distances and dimensions of those celestial bodies which are within a measurable distance of our World. The conclusions at which modern astronomy has arrived are not those which would naturally occur to the first observers of the heavenly bodies. The conditions, indeed, are such that superficial observations always lead to wrong conclusions. To- day, in most of our so-called civilised countries, the people in general take it for granted that the Earth is a planet going around the Sun. Many of them have also heard that the stars are far-off suns, floating in practically empty space. Yet not one person l 2 HOW TO KNOW THE STARRY HEAVENS in a thousand truly realises what these statements mean. They are merely hearsay, accepted in childlike faith, as some of the ancients accepted the statement that the Earth is supported by a number of elephants standing on the back of a big turtle whose legs reach all the way down ! Bu.t in those Countries where the secular schools have not familiarised the people' with the accepted teachings of modern astra'nc!ray,.a man who asserts to-day that the Earth goes around the Sun is regarded as either a wag or a lunatic. If people condescend to argue the point with him, they can overwhelm him with apparently good reasons for their incredulity. They can not only give plausible arguments from their own surround- ings and experiences, but can also prove their case by wholesale quotations from the writings of the " inspired " priests and prophets of former times. If he suggests that their surround- ings and experiences are wrongly interpreted, they laugh him to scorn. If he insists that the ancient writers were ignorant and mistaken, they abuse him as an infidel. If, to avoid their resentment, he tells them that the writers of their sacred books did not intend that their statements should be understood literally, they truly and philosophically reply that he is wrest- ing the Scriptures to his own destruction. ONLY FACTS WANTED Seekers after truth should not be satisfied with mere hear- say. Those who expect to get facts by faith alone generally accumulate fables instead of facts. Where faith is relied on, it is a mere matter of where we are born as to what we believe. Faith may possibly do no harm as regards immaterial or child- ish beliefs, but it is very hurtful when used for material or important matters, which require intelligent scepticism to enable us to sort out the true from the false. Even if by accident we should get the Truth by faith alone, it would do us no good. One of the founders of Christianity told his followers to "prove all things" and " hold fast that which is good " (I Thess. v, 21). A better precept was never APPARENT MOTIONS OF HEAVENLY BODIES 3 given, though many who profess to walk in his footsteps do not seem very enthusiastic about following his counsel. Those who are looking for actual facts concerning the Uni- verse should therefore leave faith to those who are satisfied with pleasant fables and flattering delusions. They should endeavour, by all the means at their command, to ascertain for themselves whether these things are truly as represented, and they should also try to realise what the facts of the case really involve. THE MUSIC OF THE SPHERES As regards the shape of our Earth, it is not now necessary to prove that it is a sphere. Many of us have travelled enough to satisfy ourselves by actual experience as to its general size and shape. Even those who have lived all their lives in one locality have now plenty of positive evidence that the old theory of its being flat is untenable. As regards the rest of the Universe, however, we still have to rely on observation and abstract reasoning. In order to ascertain whether the sky is a hollow rotating sphere surrounding the Earth, or whether it is, as now claimed, a boundless ocean swarming with suns and worlds, let us examine it and the various objects which appear to be " fixed " to it, or to be wandering around on it. The most noticeable of the permanent objects in the sky are known as the Sun and Moon. The most numerous and steadfast are called the "fixed " stars. They were so named because they do not appear to change places relatively to one another. A few objects which very much resemble the stars in appear- ance are distinguishable from them by several peculiarities. For example, they do not twinkle like the stars, but shine with a steady unflinching light. At some periods they shine very much more brilliantly than at other times. And they slowly change their places among the "fixed" stars. For this latter reason they are known as planets, or " wanderers." The best 4 HOW TO KNOW THE STARRY HEAVENS known of them go by the names of Latin deities who were formerly identified with them. They are called Saturn, Jupiter, Mars, Venus, and Mercury. Oft-repeated observations of the heavenly bodies, from differ- ent parts of our globe, long since proved that they all appear to have certain definite and well-defined motions which have been repeated over and over again for hundreds and thousands of years. There are, to be sure, certain irregularities in some of these motions, but close and long-continued observations show that even these irregularities are themselves regular and cyclic in their action. STELLAR MUSIC The most obvious of these motions may be imitated by tak- ing two twelve-ribbed umbrellas (real or imaginary), opening them both, and tying their handles together, so that the arrange- ment forms a kind of globe (see Figure 2). On the Equator. If the observer lives on the Equator, in that hot circle of the Earth which lies between the Tropics, he can represent the apparent motion of the star-strewn " sphere " by keeping the handles of his umbrellas horizontal in a north- and-south direction, and slowly spinning the whole thing around on its handles, so that the rims of the umbrellas rise in the east and descend in the west. The names of the various groups of stars can be chalked on the inside of the umbrellas, and the observer must imagine himself standing (in the centre of the apparatus) on a flat table which prevents him from seeing anything below his own level. The chalk-marks which are near the rims of the um- brellas will then seem to rise in the east, pass overhead, and sink in the west. Those farther north and south will pass more slowly over the handles or " poles " of the apparatus, which lie flat on the central table and do not change their posi- tion at all. So long as the observer stays on the Equator there will be no change in the position of the starry sphere, which appears APPARENT MOTIONS OF HEAVENLY BODIES 5 to turn completely over in about four minutes less than twenty- four hours. 1 It is obvious that, if we turn our apparatus so as to keep up with the stars, a fresh rib will pass the Zenith, or point over- head, every two hours (nearly), and that at the same instant AS USED ON THE EQUATOR . *F FIG. 2. UMBRELLA-APPARATUS FOR ILLUSTRATING (APPARENT) STAR MOVEMENTS Face the west when using this diagram. By reversing the points of the compass as here given, and facing the east, it will represent the Earth's real motion. the opposite rib will pass the Nadir, or point below. Also that one rib will rise above the eastern horizon at the same time, while another will descend below the western horizon. 1 If it were not for these four minutes' difference we should see the same stars, in the same part of the sky, at the same time of the night, the whole year through, 6 HOW TO KNOW THE STARRY HEAVENS At the North Pole. But if the observer travels to the north, the apparatus will not follow the motions of the stars unless he tips it up by raising the northern umbrella. By the time he reaches the frozen regions near the North Pole, he will have to tip up the apparatus so much that the handles will be per- pendicular. The southern umbrella will then be below, out of sight, and the chalk -marks on the northern umbrella will turn around the point overhead. If the observer now holds his watch overhead, with the face down, he will find that the chalk-marks are going the opposite way to the hands of the watch. At the South Pole. If the observer returns to the Equator, he will have to turn the northern umbrella down again, and when he sails into the southern seas the southern umbrella will have to be tipped up, to represent the motions of the stars. By the time he reaches the frozen regions around the South Pole, the southern umbrella will be uppermost. A fresh set of chalk- marks will then turn around the point over his head, and they will be found to turn the same way that the hands of the watch revolve when looked at from below. During these supposed journeys from the Equator to the Poles, the axis of the apparatus will not really le typed up either way, for the northern stick will point to the North Pole-Star all the time, and the southern stick will be directed toward the same part of the southern skies all the time. The apparent tipping up and down is due to the fact that the surface of the Earth is not flat, but round, and therefore dips toward the Poles. The annexed diagram will show this clearly, the large circle representing the Earth, and the five small objects representing our umbrellas in different parts of the world (see Figure 3). SOLAR MUSIC On the Equator. Let us suppose that the observer is again on the Equator with his apparatus, and that he wishes to follow the motions of the Sun. It will be necessary to put a hoop over the umbrellas where the twelve pairs of ribs come together. APPARENT MOTIONS OF HEAVENLY BODIES 7 This hoop will represent the Celestial Equator. The ribs of the umbrellas should be numbered from 1 to 12. Spring " Passover." If it is about the 20th of March, the Sun's position can be represented by hanging a small electric light where the equatorial hoop crosses the first pair of ribs. On turning the apparatus as before, the electric light will rise in the east, pass overhead, and set in the west. While it is FIG. 3. THE EARTH, SHOWING RELATIVE POSITIONS OF APPARATUS WHEM USED AT EQUATOR, POLES, ETC. above the level of the imaginary observer in the centre of the apparatus, the chalk-marks representing the stars must be supposed to be out of sight, on account of the greater brilliancy of the electric light. When it sets in the west, the chalk- marks above the horizon must be supposed to come into view again. Autumnal Equinox. Six months later about Septem- ber 22 the arrangement will be the same, except that the 8 HOW TO KNOW THE STARRY HEAVENS light will have to be shifted to where the equatorial hoop crosses the opposite or seventh pair of ribs. That is to say, if the light was where the first pair of ribs come together in March, it will be where the opposite or seventh pair of ribs come together in September. FIG. 4. UMBRELLA-APPARATUS MODIFIED FOR ILLUSTRATING APPARENT MOVEMENTS OF SUN AND PLANETS Face the west when using this diagram. If used north of the Equator, raise (N) till it points to the North Pole, and vice versa. The feathered arrows indicate the diurnal mo- tion; the plain arrows indicate the annual motion. Midsummer Solstice. About June 21 the light will be on the fourth rib, but will be some distance north of the equatorial belt. Yuletide Solstice. About December 21 it will be on the tenth rib, but some distance south of the equatorial belt. APPARENT MOTIONS OF HEAVENLY BODIES 9 If a second hoop be passed over the umbrellas, so that it will pass over these four places, it will represent the Ecliptic, or annual path of the Sun among the stars (see Figure 4). It will be seen that the light representing the Sun does not go its daily round exactly the same as the chalk-marks repre- senting the stars. It moves slowly backward on the second SUN JUNE. FIG. 5. CIRCLES OF THE CELESTIAL SPHERE WITH WORLD IN THE CENTRE Only the upper half of the diagram is supposed to be above the horizon of the observer. Face the west when using the diagram. Those living north of the Equator should raise (* until the axis (SN) points to the North Pole-Star, and vice versa. hoop, so that the average interval between one " mid-day " and the next is nearly four minutes longer than the " southing " of one of the chalk-marks on two successive " nights." The re- sult is that in the course of 366J revolutions of the umbrellas, which represent the star-sphere, there are only 365J revolutions 10 HOW TO KNOW THE STARRY HEAVENS of the light which represents the Sun. In other words, the Sun, whose motions we are trying to represent, creeps slowly back along the Ecliptic, so that in exactly one year it has lost one revolution, having gone completely around the " star-sphere " to the place where it was twelve months before. As the Sun's path is not on a line with the Equator, but crosses it obliquely, the Sun not only loses one complete revolution in a year, but also drifts to the north and south of the equatorial belt, which it " passes over " twice in each year, at the spring and autumn " Passover " or Equinox (see Figure 5). "THE BURNING ROW" In the apparatus just used, the hoop along which the light slowly travels represents the Celestial Ecliptic, or path of the Sun. This hoop lies over twelve sets of chalk-marks repre- senting twelve different constellations of stars. Each set of stars has a name by which it has been known for several thou- sands of years. The twelve form what are collectively known as the Signs of the Zodiac. They are also known as the Twelve Houses (or Mansions) of the Sun. The Book of Job (xxxviii, 32) mentions them under the name of the Mazzaroth. It takes the Sun a solar month (a little longer than a lunar month) to travel through each " house " or constellation. In March the Sun enters the constellation known by the Latin name for Fishes (Pisces) ; in June it gets to the group known as the Twins (Gemini) ; in September it reaches the Virgin ( Virgo) ; in December it is with the Archer (Sagittarius); and the following March it enters once more the constellation of Pisces. 1 1 The Sun is commonly said to be at the "First Point of Aries" (the Ram) at the Spring Equinox. This is true only at certain long distant intervals, as will be explained in Chapter XII. The "point" has reference to the Earth's orbit, and not to the stars. It was named after the constellation which happened at the time to be beyond the Sun in March. APPARENT MOTIONS OF HEAVENLY BODIES 11 LUNAR MUSIC The positions and motions of the Moon are about the same as those of the Sun, only the Moon hangs back more and loses a revolution in a lunar " moonth," or month, instead of losing one in a year. In its backward drift it therefore catches up with the Sun nearly thirteen times in a solar year. Eclipses. The various phases of the Moon show that it is a dark body, like our Earth, lighted up on one side by the Sun. They also show that it is nearer to us than the Sun. Some- times, indeed, it passes exactly between us and the Sun, pro- ducing what is known as an Eclipse of the Sun. When it is opposite to the Sun, the shadow of the Earth sometimes falls on it, producing what is known as an Eclipse of the Moon. The reason why there is not an eclipse at every " conjunction " and " opposition " of the Sun and Moon is that the path of the lat- ter, although nearly on the same plane as that of the Sun, does not exactly coincide with it. The two paths, therefore, appear to cross or intersect, in the same way that the Ecliptic and the Equator cross each other. PLANETARY MUSIC The larger planets all keep on or near the Sun's path, but their apparent motions are more irregular, and each has a period of its own, varying from a few months to many generations. Those known as Mercury and Venus appear to drift back- ward and forward on each side of the Sun. They never go very far from it, and are therefore seen only shortly before sun- rise or soon after sunset. The other planets appear to drift eastward among the stars that lie along the path of the Sun and Moon. But when they get nearly opposite to the Sun (that is, when they pass the south about midnight) this eastward drift is reversed for a time, so that each planet appears to make a loop in the star-sphere. But they never go far away from the Ecliptic, or path of the Sun (see Figure 97). 12 HOW TO KNOW THE STARRY HEAVENS North and South of the Equator. If our observer takes his apparatus north or south of the Equator, and tips it up as before, when observing the stars, he will find that the positions and motions of Sun, Moon, and planets can all be approximately marked out on the hoop that represents the Ecliptic. This will be true for any and every part of the Earth's surface. The Moon and the large planets are never found in any other part of the sky than on (or close to) the Sun's path, or Ecliptic. The same apparatus will show why the days are long in June north of the Equator, and long in December to the south of that line. Going East and West. So far the observer has travelled only north and south. If he travels to the east or west, he will find that no change is needed in his apparatus so long as he does not change his latitude. On the Equator, for example, the motions of the heavenly bodies are the same whether the observer is in Africa, the East Indies, or in America. The only difference is in time. If he could telegraph from equatorial Africa at midnight, and get immediate answers from the East Indies and America, he would find that it was already sunrise in the East Indies, whilst it was only sunset in equatorial America. With this exception the phenomena observed are alike on all parts of the Earth lying under the Equator. The same is true of any other latitude. Although our apparatus represents very fairly the angular distances and apparent motions of the heavenly bodies, it does not directly throw any light on their actual distances or real motions. A PRIMITIVE EQUATORIAL It will be well for all who have not made a study of the above phenomena to observe for themselves as many of these apparent motions as can be seen from the part of the world they may happen to live in. All the apparatus that is really necessary is a straight stick set firmly in the ground (or other- wise supported) at such an angle that it will point to the Pole APPARENT MOTIONS OF HEAVENLY BODIES 13 Star, and a tube (or telescope) attached to it so that it can be moved in any direction. The tube or telescope can then be rotated so as to follow the diurnal motion of any of the heav- enly bodies. When the tube is at right angles to its support it is pointing to the celestial Equator (see Figure 6). Rude Fio. 6. AN ADJUSTABLE EQUATORIAL, SUITABLE FOR ANY PART OF THE WORLD The axis is clamped in such a position that its ends point to the poles of the heavens. as this method of observation may seem, it is capable of lead- ing intelligent observers to a correct solution of the main prob- lems of astronomy. A very interesting method of observing the daily motions of the stars is to point a camera to some part of the sky on a clear starlight night, and leave the plate exposed for an hour or so. On developing the print it will be found that each star has left a trail on the plate. Figure 7 is a photograph of the stars sur- 14 HOW TO KNOW THE STARRY HEAVENS rounding the North Pole. The further the star is from the centre of rotation, the longer and straighter is the trail it makes on the plate. Figure 8 shows the constellation of the Great Bear (or the Dipper, as it is often called), repeated four times, to show its position in the northern skies every six hours. It will be seen that the two " Pointers " are always in a straight line with the star which happens to be near the axis of rotation. This star is commonly known as (Stella) Polaris, or the Pole Star. FIG. 7. NORTHERN STAR-TRAILS Photographed by Barnard, with twelve hours' exposure. FIG. 8. THE DIPPKR, OR GREAT BEAR, AT INTERVALS OF Six HOURS It will be seen that the two "pointers" are always in a line with the Pole-star. \ CHAPTER II KIVAL THEORIES TO EXPLAIN THE APPARENT MOTIONS OF THE HEAVENLY BODIES (A) THE EARTH-CENTRED THEORIES OF THE UNIVERSE "Then the Evening (Erev) and the Morning ( Voker) brought to a close the Third Day ( Yom}. "And the Mighty Ones (Elohim) said : ' Let there be luminaries in the Ham- mered Plate (Rakia) of the sky, to separate the Day (Yom) from the Night (Lylah}; 1 let them be for signs and to mark the seasons, Days (Yamim), and years ; let them serve as luminaries, in the Hammered Plate of the sky, to give light upon the Earth.' And it was so. " And the Mighty Ones made two great luminaries, the larger one to preside over the Day ( Yom), and the smaller one over the Night (Lylah). [They made] the stars also. " The Mighty Ones placed them in the Hammered Plate of the sky, to give light upon the Earth, to preside over the Day (Yarn), and the Night (Lylah}, and to separate the light from the darkness. The Mighty Ones saw that it was good. "Then the Evening (Erev} and the Morning (Voker} brought to a close the Fourth Day (Yom}." Book of Origins, I, 13-19 (A. ZazeVs Translation). EARLY FLAT-WORLD SUPPOSITIONS IN trying to explain the observed motions real (or apparent) of the heavenly bodies the ancients were handicapped by their ignorance of the world itself. This appeared, from their local standpoint, to be a flat though uneven surface, the lower parts of which were filled with water. Their experiences on this Earth also prevented them from realising the possibility of anything solid and heavy remaining suspended in space without falling anywhere. Their entire ignorance as to the nature, dimensions, and distances of the celestial bodies led them to 1 Lylah was personified by the Israelites as Lilith, the first wife of Adam. Isaiah xxxiv, 14 (R. V. Margin). 16 HOW TO KNOW THE STARRY HEAVENS suppose that they were put in the heavens by somebody to throw light on the Earth, or to relieve the monotony of the sky. With them the Earth itself was the Universe, and even those who recognised the importance of some of the most prominent celes- tial objects made the natural mistake of supposing them to be Gods who ruled the Earth from their thrones on high. UNDERLYING FACTS Yet even three and four thousand years agone there were individuals who had discovered that " things are not what they seem." Some of the real facts relating to the Universe were known to a few learned men among the ancient Babylonians, Egyptians, Chinese, Greeks, and Hindus. But the world was not ready for their teachings, and during the Dark Ages that followed the establishment of Christianity the few truths that were known were trampled under foot, like pearls cast before swine. However, trampled pearls are apt to come to light again. Facts are stubborn things, and will not permanently down. So the lost facts have been rediscovered in modern times, and largely supplemented by fresh ones. Let us glance briefly at some of the primitive ideas held by the ancients with regard to the Universe, so that we may com- pare them with more modern explanations. We can then decide as to which best fit the observed phenomena, and are, on that account, the most deserving of credence. THE CANOPY THEORY The world we live in was at first supposed to be flat, or nearly so, with a massive firmament resting on the mountains at the edge and spanning the whole Earth. To the ancient Egyptians the sky was the bosom of Neit, a celestial ocean across which the divine Sun, Moon, and planets were carried in boats. In Greece it was supposed to be a solid canopy, across one part of which Helios, the Sun-God, daily RIVAL THEORIES 17 drove in a chariot of gold, while his sister Selene, the Moon- Goddess, followed him in a chariot of silver. Mount Olympus was supposed to reach up to the highest part of this canopy. On the summit of this holy mountain was the palace of Zeus, king of all the Gods. There the Greater Deities abode, ruling the world below to suit themselves, and dealing out a very pecu- liar kind of justice to the unfortunate mortals who lived thereon. Ancient books, as a rule, did not discuss or assert these things, any more than modern books discuss or assert the conclusions of modern astronomy. They merely alluded to them, taking them for granted as well-ascertained facts which were useful for illus- tration, but which it would be folly to argue about or assert. Thus one of the characters in the Hebrew drama of Job casu- ally mentioned that this firmament was " spread out " (Job ix, 8) "as strong as a molten mirror" (Job xxxvii, 18 R. V.). In the same way the Mohammedan Koran sought to show the fine workmanship of Allah by pointing out that he had stretched the firmament across the entire world without a crack in it. The Hebrew word for firmament (Ralda) really means a ham- mered plate of metal (Ex. xxxix, 3), and all its Greek and Latin equivalents have afirm or solid meaning. The modern idea that the writers meant an expanse is seen to be absurd when we notice that it was created (Gen. i, 1), or made (Gen. i, 7) ; that it was spread out over the Earth (Job ix, 8) ; and that it had windows in it (Gen. vii, 11) ; also that the Tower of Babel was intended to reach up to it (Gen. xi, 4) ; and that the top of Jacob's ladder rested against it (Gen. xxviii, 12). The mountains which were supposed to support this " hammered plate of heaven " were natu- rally spoken of as the pillars of heaven (Job xxvi, 11). When the writer of the Apocalypse was describing the ap- proaching end of the world he made an earthquake shake the stars out of this firmament on to the ground " as a fig-tree casteth her unripe figs when she is shaken of a great wind." He ended by letting the heavens roll together, as a scroll does when the ends are released (Rev. vi, 13-14 R. V.). The Venerable Bede, an eminent Christian writer of the 2 18 HOW TO KNOW THE STARRY HEAVENS seventh century, considered the Earth to be flat (or perhaps convex), with a star-spangled canopy over it. This canopy he supposed to be like an umbrella, with its centre at the Pole Star. The daily motion of the heavenly bodies he explained by supposing the canopy to spin round, like the tent over the " merry-go-rounds " of our country fairs. His ideas on the sub- ject are a curious mixture of accurate observation and childlike speculation. He says : " The Creation was accomplished in six days. The Earth is its centre and its primary object. The Heaven is of a fiery and subtile nature, round and equidistant from every part, as a canopy from the centre of the Earth. It turns round every. day with ineffable rapidity, only moderated by the resistance of the seven planets, three above the Sun Saturn, Jupiter, Mars then the Sun ; three below Venus, Mercury, the Moon. The stars go round in their fixed courses, the northern perform the shortest circle. The Highest Heaven . . . contains the angelic virtues. . . . The Inferior Heaven is called the Firmament, because it separates the superincumbent waters from the waters below." THE CRYSTAL SPHERES Such were the primitive ideas of unenlightened men with regard to the Universe. Sometimes, however, the problem was investi- gated in a scientific spirit. It was then readily seen that the celestial phenomena could not be explained on the canopy theory. Observation, as well as theory, ultimately led to the overthrow of this primitive idea of a solid star-strewn firmament resting on the mountains. For many of these so-called "pillars of heaven " had been ascended, and no " hammered plate of heaven" had been found resting on them. So new theories arose, each of which came a little nearer the truth than the one before. It was suggested that the world was inside a crystal globe or sphere, to which the stars were attached. The nightly motions of the stars were explained by supposing that this crystal sphere rolled over every twenty-four hours. RIVAL THEORIES 19 This theory explained very well the motions of the stars, but did not fit in with the more varied movements of the Sun, Moon and five planets. Some explained their irregularities of motion by supposing that they were carried around with the stare, but that, instead of being fixed to the revolving sphere, like the stars, they were at liberty to crawl around on it very slowly, like so FIG. 9. THE PTOLEMAIC SYSTEM many insects. Others suggested that each of these seven wan- derers had a crystal sphere all to himself (see II Cor. xii, 2). The seven spheres were supposed to be one inside the other. Each was thought to share in the general daily rotation, but to lag behind or have a slight independent motion of its own (see Figure 9). Even this far-fetched notion did not fit in satisfactorily with the observed phenomena. So Tycho Brahe* suggested that the Earth was a globe, spinning round on its axis every twenty-four 20 HOW TO KNOW THE STARRY HEAVENS hours ; that the Sun and Moon went around the Earth in a year and in a month, respectively ; and that the five planets went around the circling Sun (see Figure 10). FIG. 10. THE TYCHONIC SYSTEM EPICYCLES As even this complex arrangement did not fit in with the observed motions, the planets were then supposed to move in a series of eccentrics around their ideal orbits, with the star- sphere outside of all. For a time this theory was thought to explain the observed motions. But it was such a complex, improbable, lumbering, incomprehensible, and absurd theory that Alphonso, king of Castile, ventured the remark that if he had been consulted by the Creator he could have considerably improved upon the plan. RIVAL THEORIES 21 FAUSTUS ON THE SPHERES These mediaeval speculations are well illustrated by the fol- lowing dialogue from Marlowe's " Faustus" written toward the close of the sixteenth century. " Faust. Tell me, are there many heavens above the Moon ? Are all celestial bodies but one globe, As is the substance of this centric Earth ? Mephistopheles. As are the elements, such are the spheres, Mutually folded in each other's orb. And, Faustus, All jointly move upon one axletree, Whose terminine is termed the World's wide pole : Nor are the names of Saturn, Mars, or Jupiter Feign'd, but are erring stars. Faust. But, tell me, have they all one motion, both situ et tempore ? MepJi. All jointly move from east to west in twenty-four hours upon the poles of the World, but differ in their motion upon the poles of the zodiac. Faust. Tush, these slender trifles Wagner can decide : Hath Mephistopheles no greater skill? Who knows not the double motion of the planets? The first is finished in a natural day; The second thus; as Saturn in thirty years, Jupiter in twelve; Mars in four ; the Sun, Venus, and Mercury in a year ; the Moon in twenty-eight days. Tush, these are fresh- men's suppositions. But, tell me, hath every sphere a dominion or intellitjencia ? Meph. Aye. Faust. How many heavens or spheres are there ? Meph. Nine ; the seven planets, the firmament, and the empyreal heaven. Faust. Well, resolve me in this question ; why have we not con- junctions, oppositions, aspects, eclipses, all at one time, but in some years we have more, in some less ? Meph. Per incequalem motum respectu totius. Faust. Well, I am answered." 22 HOW TO KNOW THE STARRY HEAVENS The writer of a recent magazine article l sums up these old ideas of the Universe very neatly. He says : " To the men of the Middle Ages the world was a little space shut tight within a wheelwork of revolving spheres. It was compendious,, complete, ingenious, like a toy in a crystal box. Beyond the outer shell nothing existed. The heavens were uncorruptible. No change could occur in the whole system, save in the Earth alone. The Uni- verse was created for the sole use of man. It was small and finite." THE ROUND WORLD While all these speculations were going on, people had been going to and fro on the Earth, and travelling up and down on it. In this way they had discovered for an actual fact that the world is not flat, but is a round ball, 8,000 miles thick, suspended in space, with the starry heavens on every side of it. This being the case, it follows that if the stars are fixed to a massive firmament, it is not a mere " dish-cover " or umbrella over a flat Earth, but is in the form of a hollow crystal sphere, rolling over (to the west) every twenty-four hours, with the round World in the centre, supporting itself on nothing. (B) THE SUN-CENTRED THEORY OF COPERNICUS. "The first formal assertion of the heliocentric theory was made in a timid manner, strikingly illustrative. of the expected opposition. It was by Copernicus, a Prussian, speaking of the revolutions of the heavenly bodies ; the year was about 1536. In his preface ... he complains of the imperfections of the existing system, states that he has sought among ancient writers for a better way, and so had learned the heliocentric theory. ... In their decree prohibiting [the work of Copernicus], ' De RevolutionilmsJ the Congregation of the Index, March 5, 1616, denounced the new system of the Universe as 'that false Pythagorean doctrine utterly contrary to the Holy Scriptures.' . . . The opinions thus defended by the Inquisition are now objects of derision to the whole civilized world." 2 1 Dr. E. S. Holden, in the " Popular Science Monthly," November, 1903. 2 Dr. J. W. Draper. RIVAL THEORIES 23 " People gave heed to an upstart astrologer who strove to show that the Earth revolves, not the heavens or the firmament, the Sun and Moon. . . . This fool wishes to reverse the entire science of astronomy." l The final outcome of all these speculations was that the whole of the Earth-centred theories were thrown overboard, and re- placed by an old Sun-centred theory originally brought from India by Pythagoras. According to this new yet ancient theory, the stars are practically immovable bodies suspended far off in space, and the Sun is the centre around which all the planets, including the Earth itself, revolve (see Figure 11). FIG. 11. COPERNICAN SYSTEM Including four of the most tilted orbits of Minor Planets. Neptune's orbit is here omitted. It has been found, however, that the Moon does actually go around the Earth, completing a revolution in about a month. The daily motion of all the heavenly bodies is not real, but only apparent. It is explained by the fact that the Earth itself rolls completely over (to the east) every twenty-four hours, at the same time that it travels around the Sun once every year. This daily rotation of the Earth causes all the heavenly bodies to appear to turn in the opposite direction. The peculiarities of the Sun's annual drift to the north and south, and the resulting seasons, are readily explained by the l Martin Luther. 24 HOW TO KNOW THE STARRY HEAVENS fact that the Earth has a. heavy " list " to one side, with reference to its path around the Sun (see Figure 12). The other planets are also drifting around the Sun, in the same general direction, but at different distances from it. This Indian system of cosmogony is now known as the Coper- nican Theory, because Copernicus first established its truth in modern Europe. It explains the motions of the heavenly bodies so well that there is no doubt about its being true as far as it FIG. 12. RELATIVE POSITIONS OF EARTH AND SUN AT THE FOUR SEASONS goes. In spite of the long-continued opposition of unprogres- sive theologians, it has now been adopted by all competent judges, and is accepted, on hearsay, even by those who do not realise the subordinate position to which it reduces our Earth, and by those who do not profess to be competent to judge as to its correctness. The adoption of this theory has led to the solution of a mul- titude of otherwise inexplicable phenomena. Without it, the planetary bodies appeared to be swinging around us in a labyrinth of perplexing knots and meaningless tangles. As a result of its adoption, the knots and tangles have all been unravelled, and the structure and dimensions of the Solar System have been RIVAL THEORIES 25 tolerably well ascertained. The telescope and other opitical in- struments have now greatly increased our knowledge of the heavenly bodies generally, and have revealed to us similar sys- tems moving in actual conformity with the Copernican Theory. This same theory has also enabled astronomers to apply them- selves, not entirely without success, to the task of ascertaining the structure, and measuring the distances and dimensions, of the more distant luminaries known to us by the misleading name of " fixed stars." Every observed peculiarity is explained by this theory, without any absurd and impossible suppositions like the " eccentrics " and " epicycles " of other theories. And many facts have been discovered by following it up to its logical conclusions. It is therefore the true explanation of the mechanism of the Universe. How and why these movements of the heavenly bodies are kept up will be briefly dealt with in subsequent chapters. CHAPTER III PRINCIPLES UTILISED FOR MEASURING THE UNIVERSE "And there was given me a reed like unto a rod, and the angel stood, saying, Rise and measure the temple of God." Rev. xi, 1. "And he that talked with me had a golden reed to measure the city, . . . and he measured the city with the reed, twelve thousand furlongs. The length and the breadth and the height of it are equal." Rev. xxi, 15, 16. "The measure of the Moon's distance involves no principle more abstruse than the measure of the distance of a tree on the opposite side of a river." Sir George Airy. HOW IT IS DONE I WILL now say a few words about the way in which as- tronomers have been enabled to find out the distances and dimensions of many of the objects which -compose the L T ni verse. It was very early recognised that the heavenly bodies are not all at the same distance from us. STARS ARE BEYOND PLANETS The stars, for example, have a far-away look and a fixity of position that would naturally lead one to think that they were beyond the larger, brighter, and more active luminaries which are found on or near the Ecliptic. This was proved beyond a doubt when observers at a distance from one another compared notes. For it was sometimes found that when an observer in the north saw a certain planet a little to the south of a particu- lar star, an observer in the south would see it north of the same star. The only possible explanation of this is that the planet is nearer to us than the stars. THE ORDER OF THE PLANETS Leaving the " fixed " stars out, there were seven celestial " wanderers " known to the ancients. Of these, two appear to PRINCIPLES FOR MEASURING THE UNIVERSE 27 be very much nearer to us than the other five. The Sun, for example, is evidently either very near or very large, bright, and hot. But the Moon is nearer to us than the Sun, for it some- times passes in front and shuts off its light and heat from us. As it also passes between us and every other celestial object that comes in its way, it is evidently the nearest of all the heavenly bodies. Now the Moon performs its circuit of the heavens in less time than any other wanderer. It seems natural, then, to suppose that the wanderers which take the most time to perform their circuit are the farthest away from their common centre of revolution. This reasoning led the early astronomers to regard slow-moving Saturn as the most distant planet. The stately Jupiter they put next, followed by fiery Mars. As regards the other three, there was some difference of opinion, due to the fact that, on the Earth-centre theory, their real motions were not distinguished from their apparent ones, due to perspective. But when once it was recognized that the Sun was the centre around which the planets turned, it became evident that our own populous Earth and pale-faced Moon were travelling in partner- ship, next to Mars ; that " Venus the beautiful " followed ; and that fast-flying Mercury kept nearest to the central Sun. COMPARATIVE DISTANCES The order of the planets being thus settled, the next thing was to ascertain their distances from the Sun. In the case of the inferior or inner planets, Mercury and Venus, their proportional distances from the Sun were easily found. All that had to be done was to point one leg of a pair of dividers, or compasses, at the setting or rising Sun, and the other leg at the planet Venus when at its greatest angular dis- tance from it, as an Evening or Morning Star. The dividers were then laid on a sheet of paper, and two lines drawn to indicate the V shape of the open dividers (see S E V in Figure 13). 28 HOW TO KNOW THE STARRY HEAVENS The Earth was then supposed to be at E, where the two lines come together, and the Sun was supposed to be at the other end (S) of one of the lines. Venus would evidently be somewhere on the line E V. Taking it for granted that the planetary orbits were circular, a circle was then drawn through E from S as a centre. This represented the Earth's or- bit. Another and smaller circle was drawn from the same centre, just large enough to touch the other arm, E V. This circle evidently represented the orbit of the planet Venus. The same process was gone through with the planet Mercury, and the result transferred to the same figure (see S E M). On measuring the radii or semi-diameters of these three circles, representing the planetary orbits, it was found that their lengths varied in the ratio of 100, 72, and 38. These figures, therefore, represent the relative distances of the Earth, Venus, and Mercury. A comparison of the distances with the times of revolution then enabled the relative distances of the superior or outer planets to be computed by means of their times of revolution, taking it for granted that they all obeyed the same law, what- ever that law might be. The result was that the distances of the outer planets, when computed on the same scale as the inner ones (=100 to the Earth's distance), were found to be 152, 520, and 953. FIG. 13. ORBITS OF MERCURY, VENUS, AND EARTH PRINCIPLES FOR MEASURING THE UNIVERSE 29 PLANETS MOVE IN ELLIPSES It may be as well to state here, that while the above observa- tions were being made it was discovered that the orbits of the inner planets are not exactly circular, but slightly egg-shaped, or, rather, elliptical. It has since been found that the paths of all the planets share this peculiarity, the cause of which has also been ascertained. NEWLY DISCOVERED PLANETS Since the invention of the telescope two large planets have been discovered beyond the orbit of Saturn. They bear the names of Uranus and Neptune. On the same scale as that used above, their distances from the Sun are represented by the numbers 1,920 and 3,000. A great number of small planets have also been discovered in the interval between the orbits of Mars and Jupiter. Their numbers are so great, their sizes so small, and their orbits so peculiar, that astronomers formerly looked upon them as the scattered fragments of larger planets which had met with an accident. 1 ACTUAL DISTANCES The comparative distances of all the planets having been thus discovered, all that had to be done was to find the real distance of one of them in miles. All the other distances could then be readily computed in miles. It took many generations to solve this little problem, and even yet the answer is not as free from error as could be wished. It has, however, been solved, with a very fair amount of accuracy, by several independent methods. The distances usually meas- ured are those of the neighbouring planets when they are at their least distances from us or are otherwise favourably placed. 1 The orbits of four of these " Asteroids " are shown in Figure 11. It will be noticed that the four represented do not lie in the same general plane as those of the larger planets, but are more or less tilted up, some one way, and some another. These, however, are exceptions. The majority move in or near the general plane. 30 HOW TO KNOW THE STARRY HEAVENS There are many people who do not put much faith in celestial measures. They cannot see any possibility of obtaining them, seeing that we cannot stretch a tape-line from one flying world to another. There are, however, a number of ways in which in- accessible distances may be accurately measured. For example, if you wish to measure the height of a tree without ascending it, all you have to do, if the ground is level, is to put a stick upright in the sunshine, and measure the length of its shadow. If a three-foot upright makes a three-foot shadow, then a hun- dred-foot shadow indicates that the tree which casts it is a hundred feet high. And if the Sun is so low down that the three-foot stick makes a six-foot shadow, then a two-hundred- foot shadow will indicate that the tree which casts it is a hundred feet high. There are other methods which are just as simple, though most of them require more elaborate apparatus. A little study will show that celestial and other inaccessible measurements may be as accurate as any made with the help of a chain or tape-line. Let us see what are the principles involved and methods employed. ESTIMATING DISTANCES If you close one eye and keep your head still, you will find that with one eye alone you will be unable to judge as to the distance from you of the object you are looking at. The only exception to this is, that if you already know the size of the object you can estimate its distance by noticing whether it appears to be large or small. To be able to estimate your distance from any object, you must either move your head or open the other eye, so as to get another picture of it to compare with the image already ob- tained. Then you can estimate with a tolerable amount of accuracy how far the object is from you (see Figure 14). The two eyes form the extremity of a three-inch base-line, and if you draw an imaginary line from each eye to the point you are looking at, you will obtain a three-cornered or triangular PRINCIPLES FOR MEASURING THE UNIVERSE 31 figure of known dimensions. That is, you will know (approxi- mately) the length of all its three sides. LAND-SURVEYING The surveyor, when he wishes to find the width of a river without crossing to the other side, measures off a base-line on his own side of the stream. Then, by noting with his instru- ments the position of an object on the other side of the river, as his base-line, he river is. either calculate the result by means of FIG. 14. ESTIMATING DIS- TANCES WITH THE EYES seen from each end of can tell how wide the In this case he can distance, or get the a diagram on paper. If he wishes to do the latter, he draws a line to represent his base- line, and from each end of it sets off a line at the same inclination or angle to it as that used on his real base-line. The place where these two lines cross each other represents the position of the object observed on the other side of the river (see Figure 15). By measuring the sides of his triangle he gets the dis- tance required in terms of his base. For instance, if the sides of his triangle are 10 times as long as the base thereof, and the latter is 10 yards long, then the width of the river is 100 yards. 1 A whole continent can be surveyed in the same way, by measuring off three-cornered areas of land, and using every dis- tance obtained as a base to measure other distances with. In this way (with certain details and precautions which need not be here specified) the shape and size of the Earth can be obtained. 1 A right-angled triangle gives the best results. Those who wish for further details will find them in the next chapter, which is written for those who are not afraid of a little simplified trigonometry and diluted mathematics. HOW TO KNOW THE STARRY HEAVENS SKY-SURVEYING The astronomer then finds out the distance of the Moon in the same way, by using a measured base-line about 4,000 miles long. As he cannot see one end of his base-line from the other end of it, he gets his angles indirectly, by polar distances, or by observing how much the Moon is displaced among the stars when viewed from different parts of the world at the same time. The same principle, rather differently applied, enables him to tell the distance of the Sun. With a 4,000-mile base-line the Moon's distance is found to be about 60 times as long as the base-line. On multiplying 4,000 by 60 we get the Moon's distance, 240,000 miles. 1 With the same base-line of 4,000 miles the Sun's distance is found to be about 388 times greater than that of the Moon. It will be seen that the longest base-line we can get is very short when compared with the distance to be meas- ured ; but as it is the longest available, astronomers have to make up for its shortness by using different methods and taking advantage of every favourable opportunity to correct their measurements. Now 388 times 240,000 comes to about 93,000,000 miles, which is approximately the Earth's distance from the Sun. As we already know the comparative distances of the other planets from the Sun, their actual distances can now be obtained without difficulty. The following table gives in one column the relative distances of the planets, the Earth's distance being represented by 1.000. In another column it gives the real distances in miles. They are calculated according to the most recent estimates of the solar parallax, which will be explained in the next chapter. 1 These figures are not exact, but will serve to show the principles involved. FIG. 15. SURVEYING FROM A BASE-LINE PRINCIPLES FOR MEASURING THE UNIVERSE 33 PLANETARY DISTANCES (Solar Parallax, 8.81") RELATIVE ACTUAL (IN MILES) Mercury . . . . .387 . . 35,909,000 . . . .723 . . . 67,087,000 Earth . . . 1.000 . . . 1.523 . . 141,384,000 Asteroids ( 2.080 . '1 4.262 . . . 193,000,000 . . 395,470,000 Jupiter . .... 5.203 . . . 482,786,000 Saturn .... 9.538 . . 885,105,000 Uranus .... 19.183 . . . 1,779,990,000 Neptune .... 30.055 . . . 2,788,800,000 It will be seen by those who have followed the argument thus far that there is no guessing about the process. It is a mere matter of observation and calculation. In the first instance given, the width of the river can be found by stretching a cord across it, or the result can be tested in various other ways. In the case of the Sun, Moon, and planets, the results can also be tested in other ways, as well as by repeating the experiment under different conditions. As soon as the observations can be carried out without error, the distances can be obtained exactly. But not before. 1 STAR DISTANCES The stars are too far off for their distances to be measured by a 4,000-mile base-line. But as it is found that the Earth in Jan- uary is at an enormous distance from the place which it occupies in July, the positions of the stars are observed at both periods,, and compared together. 1 A few years ago it was discovered that one of the asteroids, or minor planets, which goes by the name of Eros, moves in an elongated orbit, one part of which is nearer to us than that of Mars. At certain periods this planet (which is only about twenty miles thick) comes within a distance of 14,000,000 miles from the Earth. By its means celestial distances will before long be much more accurately known than they are now, 8 34 HOW TO KNOW THE STARRY HEAVENS This gives a base-line of nearly 186,000,000 miles. But even with this gigantic base there are only a few of the nearest stars whose distances can be even approximately estimated. The distance of the nearest of them is about 135,000 times as great as the length of our enormous base-line. It is 9,000 times as far off as Neptune, the outside planet in our system. About sixty stars have measurable parallaxes, a few more have per- ceptible ones, but all the others are at present out of reach in the unsoundable depths of infinite space. If our eyes were as powerful and accurate as the instruments of the astronomer, we could look at a shining grain of sand thirty miles away, and estimate its distance from us by observ- ing how much the eyes had to be drawn together to focus on the object. The same principle of triangulation which enables a surveyor to plot off a township or measure the height of a mountain en- ables the astronomer to measure the world and ascertain the distances of the Sun, Moon, planets, and some of the stars. Enormous as many of the distances are, all these measure- ments depend on an ordinary yard-stick, they are all based on the common three-foot rule. "E PUR SI MUOVE" It should be observed that the above-described method of measuring the distances of the heavenly bodies will in some cases give the same results whether we suppose the Earth to stand still, with the Sun, Moon, planets, and stars swinging around it once every twenty-four hours, or whether we suppose that the diurnal changes are caused by the Earth revolving on its axis. But, having once found the distances, it is evident that the latter is the true explanation of the phenomena. For if the planet Neptune distant as it is really goes around the Earth in a day, it must go at the unthinkable speed of 190,000 miles in a second of time. And if the stars, whose distances are so much greater than that of Neptune, also go around the Earth PRINCIPLES FOR MEASURING THE UNIVERSE 35 every day, their speed must be thousands and millions of times faster still. On the other hand, if it is the Earth that revolves, the motion is nowhere greater than one mile in three seconds. The proba- bilities are evidently altogether in favour of the latter proposi- tion. The former one is impossible and absurd. There is only one way of getting over the difficulty. In spite of all who deny it, or fail to realise it, the fact still remains that " the Earth does move." MEASURING THE PLANETS While measuring the distances of the Sun and planets, astron- omers have been able, by measuring their apparent diameters (in degrees, minutes, and seconds of arc), to ascertain their real diameters in miles. The principle is a very simple one, and may be illustrated in this way. A two-inch ball is 8 times as large as a one-inch ball (2 x 2x2 = 8). But if a one-inch ball is viewed from a distance of ten feet, it will be just large enough to hide a two-inch ball twice as far away, or a four-inch ball four times as far away. Now, suppose that we have found the Moon to be 239,000 miles away. Let us get a ball 11 feet 5 inches in diameter, and place it in a conspicuous position on the top of a steep mountain. Having done so, let us measure off 1,262 feet (which is the one- millionth part of the Moon's distance), to a place where the ball will come between us and the rising or setting Moon. It will be found that the ball is just large enough, at that distance, to hide the Moon from us. Now, as the Moon is just a million times as far from us as the ball which hides it, it follows that its diameter is just a million times greater (11 feet 5 inches X 1,000,000 = 2,162 miles). So far, so good. It is interesting to note that, in an eclipse of the Sun, the Moon acts the part of the ball just used. It so happens that, while the Sun's average distance from us (92,790,000 miles) is about 388 times that of the Moon (239,000 miles), his diameter (864,000 miles) exceeds hers (2,162 miles) 36 HOW TO KNOW THE STARRY HEAVENS in about the same proportion. They therefore look as though they were about the same size, although the Sun's diameter is really almost 400 times as long, and his bulk is more than 60,000,000 times as great (400 x 400 x 400 = 64,000,000). Most of the planets have no measurable diameter when seen by the naked eye, but by means of the telescope their dimen- sions also have been ascertained. The stars cannot be measured in this way, as they are so far off that they have no perceptible size, even when seen through the most powerful telescopes. The amount of light we receive from them is almost the only guide we have to their size, and even this is of no avail unless we know something of their distances from us. WEIGHING THE PLANETS One of the most astonishing things that astronomers have been able to do is to weigh the Sun and planets, so as to ascer- tain their mass or weight. 1 Yet the principle is as simple as that used in ascertaining their dimensions. Get a light straight stick, and make a 'sharp point at each end of it. Then stick a potato on each point, and hang the appa- ratus from the ceiling by a string. Shift the string on the stick till the potatoes balance one another. Now give it a twirl and release it. The two potatoes will swing around the common centre of gravity, where the string is fastened to the stick. If the two potatoes are of the same weight, the centre of gravity will be the same distance from each of them, and it will be found that each one swings around the other one in the same sized circle. But if one is heavier than the other, the centre of gravity will be nearer to the heavy one, and it will be found that the small one makes the largest circle. The appa- ratus, indeed, makes a primitive pair of scales with which the relative weight of each potato can be ascertained by noting the size of the circle it makes. 1 These terms are not absolutely identical. The word mass refers to the amount of matter contained in anything, while weight has reference also to the force of gravi- tation, which varies iu different worlds. The distinction is not important here. PRINCIPLES FOR MEASURING THE UNIVERSE 37 Now the Earth aud Moon form a similar weighing-machine. They are all the time swinging around their common centre of gravity, like our two potatoes, and their relative weights can be found by the same process. But at the same time that the Earth and Moon are swinging around their common centre of gravity, the Earth-Moon family on the one hand, and the Sun on the other, are also swinging FIG. 16. DAILY POSITIONS OF EARTH AND MOON It will be seen that the lunar path is always concave towards the Sun. around their common centre of gravity. In this case the Earth and Moon together are so small, in comparison with the Sun, that they are doing nearly all the swinging. Nevertheless the Sun is doing his part of the motion, even if it is too small to be easily perceived. All the members of our Solar System (including even the Sun) swing around their various centres of gravity and influence one another in the same way, the amount of their influence depending on their mass and distance. The Sun outweighs all the planets 745 times, so that his part of the swinging is very small. Still it exists, and although it is convenient to say that the Moon swings around the Earth, and that the Earth swings around the Sun, it would be more correct to say that the Earth and Moon swing around their common centre of gravity, and that the Earth-Moon family and Sun do the same. It will be seen that any family of worlds can be used as a weighing-machine, with which the relative weight of each indi- vidual can be ascertained by its influence over the other mem- bers of the family. Some of the stars, even, can be weighed against one another when they belong to one family. 38 HOW TO KNOW THE STARRY HEAVENS ACTUAL WEIGHT When we have found the relative masses or weights of the Sun and planets, we can, by finding the actual weight of one of them, in tons, find the actual weight of any, or all of them, in tons. The readiest way of doing this is to weigh the Earth and find out how many tons of material it contains. Of course this is a very easy thing to do. All that appears to be necessary is to get a very strong weighing-machine, turn it upside down, so that the Earth rests in the pan, and then adjust the scale and read off the weight. This last item must not be taken too seriously. The problem of weighing the Earth is really one of the most difficult tasks astronomers ever undertook. It has been solved, however, by several different methods, 1 and it is interesting to know that the Earth weighs about 6,600 millions of millions of millions of American tons (6,600,000,000,000,000,000,000). And the Sun contains 330,000 times that amount of material. 1 The best plan is one which employs a torsion -balance to measure the mutual attraction of lead balls at known distances from one another. This is then com- pared with the observed attraction of the Earth for the same lead balls, which are known to be at a distance of about 4,000 miles from the centre of attraction. The mutual attraction of the balls being known, the law of gravitation shows how dense the World must be in order to give the balls their observed weight. (See Chapter XV for the key to this problem. ) CHAPTER IV SOME PROBLEMS USED IN CELESTIAL MEASUREMENTS "The methods used for measuring astronomical distances are in some applica- tions absolutely the same as the methods of ordinary theodolite surveying, and are in other applications equivalent to them. . . . There is nothing in their principles which will present the smallest difficulty to a person who has attempted the common operation of plotting from angular measures." Sir George Airy. IN order that the beginner may better understand the prin- ciples upon which celestial measures depend, a few examples are given here, going further into details than in the preceding chapter. I do not undertake to say that everyone will be able to follow them all ; but I have simplified them and explained the terms as much as possible, so as to help a non-mathematician who is willing to try. DEGREES IN A CIRCLE In trigonometry, which deals with the properties of three-sided figures, we (after the Greeks) divide the circumference of a circle into 360 degrees of arc, denoted thus (360). These degrees are indicated by straight lines radiating from the centre of the circle, which is supposed to be the point of observation. Where two of these radiating lines enclose a square corner or right-angle, that angle evidently contains 90 of arc as measured off on the circumference. Each degree is, for convenience, divided into 60 minutes ('), and each minute into 60 seconds (") of arc. These minutes and seconds of arc have nothing whatever to do with minutes and seconds of time. It is a mere accident (and misfortune) that they are called by the same names. 40 HOW TO KNOW THE STARRY HEAVENS Each line going from the centre to the circumference (like a spoke in a wheel) is termed a radius (plural radii). RADII AND ARC OF CIRCLE It has been found that when two radii are so placed that the central corner or angle contains 57 17' 45" (= 206,265"), then the arc of circle cut off by the two radii is just equal in length to one radius. 1 Such an arc is termed a radian. FIG. 17. ARC OF CIRCLE It naturally follows from this that when the angle is half of that just given then the arc cut off is just half as long as each radius (see Figure 17). This is expressed as follows : Let A B represent arc of circle " Z " size of angle " Y " radius of circle " X angle of 57 17' 45" Then when Z = X, A B = Y When Z = JX, A B = j Y WhenZ = JX, A B = JY And so on. 1 That is, the part of the tire which is cut off would be, if straightened out, just as long as one of the spokes, PROBLEMS IN CELESTIAL MEASUREMENTS 41 The result is, that if we know the distance of an object in miles, we can tell its diameter in miles by measuring the angle enclosed by its opposite sides. For example, if an object 15 miles away is long enough to subtend an angle of 3 49' 11" (=y a ^ of X), then it must be about a mile long. On the other hand, if we know the diameter of an object in miles, we can tell its distance from us in miles. For example, if we know that a certain object is a mile long, and we find by FIG. 18. CHORD OF ARC our instruments that it subtends an angle of 3 49' 11" (= & of X), then it must be about 15 miles away. These two things can be ascertained; however, only when the distant object is near enough to have a measurable size when seen through a telescope. THE CHORD OF AN ARC For many purposes it is convenient to draw a straight line cpnnecting the outer ends of the two radii. This line is called a chord, and the three straight lines together form what is known as a triangle (see Figure 18). In such a triangle the two outside corners or angles, A and B, are equal to one another, and are each sharper or more acute than a right angle. This is true whether the centre angle Z be 42 HOW TO KNOW THE STARRY HEAVENS great or small. In fact the greater the central angle is, the more acute become the outer angles. It is useful to remember that if the number of degrees in all the three angles of a triangle be added together, they are always equal to the number contained FIG. 19. SINE OF ANGLE in two right angles. That is, they always contain exactly 180 of arc. The chord of an arc is of course shorter than the arc with which it begins and ends. The smaller the angle, the less differ- ence there is between the two, and in very small angles this difference can be neglected, it is so minute. The Greeks made great use of chords in their investigations. Ptolemy, the astronomer (/. 127-151 A. D.), constructed tables PROBLEMS IN CELESTIAL MEASUREMENTS 43 SHORE. giving the length of both arcs and chords for every half-degree up to two right angles. THE SINE OF AN ANGLE The Hindus, however, simplified their problems by taking the chord of double the angle, and then cutting it in two and discarding one half. The half-chord used (A B) is known as a sine of the angle (A Z B) it measures (see Figure 19). The advantage of a sine over a chord is this: In solving problems in trigo- nometry it is often conven- ient to have one of the outer angles a right angle, that is, one containing 90 of arc. Now, as the chord (A F) is cut in the middle by the bisecting radius (Z B), the two lines always cross at right angles (at B), and the resulting triangle (A B Z) is a right-angled one. The result of one of the angles being invariable is that part of the labour is saved, as the calculations are confined to the other two angles. All books on trigonometry have tables giving the length of sines, etc., for every degree and fraction of a degree. MEASURING INACCESSIBLE DISTANCES The advantage of a right-angled triangle is shown in the fol- lowing problem, which is something similar to one given in the preceding chapter : BASE YDS'. FIG. 20. MEASURING WIDTH OF RIVER 44 HOW TO KNOW THE STARRY HEAVENS A surveyor wishes to measure the width of a river without crossing to the other side (see Figure 20). First he measures off, on his own side of the river, a base-line (A B) 10 yards long. He stands at one end (B) of his base- line, and points his instrument at the other end of it (A). He then turns the instrument one quarter round (90 of arc), and selects an object (Z) on the opposite bank of the river. Having made a note of the number of degrees he has turned the instru- ment (90), he goes over to the other end (A) of the base-line and repeats the operations. He will find that he will not have to turn his instrument so far around to make it point to the object selected (Z). Let us suppose that he has to turn it only 89. The two angles at the base will then together equal 179. Now, as the three angles of a triangle, added together, always equal two right angles (180), it is obvious that the opposite angle (Z) must be just 1. The problem then stands as follows : As the sine of 1 (angle Z) Is to the sine of 89 (angle A), So is 10 yards (length of base A B) To the perpendicular Z B (or Y). After obtaining the length of the sines of 1 and 89 (which are given in all books on trigonometry), the problem is solved as follows : As 01745 is to 99985, so is 10 yards to the answer, 573 yards, which is the width of the river as exactly as it can be found with five-place logarithms. PARALLAX The angle (Z) opposite the base of such a triangle is called by surveyors and astronomers the parallax of the distant object. The further off the object is, the smaller becomes its parallax. PROBLEMS IN CELESTIAL MEASUREMENTS 45 The longer the base from which it is measured, the larger becomes the parallax. 1 In the problem just considered it is obvious that if the object Z is exactly west of the observer at B, it will no longer be ex- actly west of him when he goes to A. It will be a little to the south of west. It is also obvious that the amount of its displace- ment will depend on its distance from him. The farther off the object is, the less it is displaced when he goes from one end of the base to the other. In other words, as stated before, the more distant the object is, the smaller becomes its parallax. If it is a very long way off, it may appear to be exactly west from both ends of the base-line. In this case it will be necessary to greatly lengthen the base-line in order to measure the distance of the object. The word " parallax " is rather a hard one to remember. But astronomers can simplify matters when referring to the Sun's parallax by calling it the " mean equatorial long horizontal solar parallax." This is a useful thing to know. A few examples of how astronomers utilize these principles will conclude this chapter, which some may consider to be dryer than a California summer, and more uninteresting than a Baedeker's guide-book to one who never travels. MEASURING THE MOON'S DISTANCE We will of course start with the problem of finding the Moon's distance from the Earth. In Figure 21 the large circle represents a section of the Earth through the two poles of rotation. The small circle in the dis- tance represents the Moon. B and L are the two stations at the ends of the measured base-line B L. We will imagine that they are 4,000 miles apart, and that they are both on the same meri- dian and at the same distance from the equator, which lies between them. 1 " Parallax may be defined, generally, as the change produced in the apparent place of an object when it is viewed from a point other than that of reference." - ENCY. BRIT., Parallax. 46 HOW TO KNOW THE STARRY HEAVENS Let us suppose that, to the observer at L, the Moon's centre is exactly on the celestial equator, and is therefore exactly 90 from the south pole (as well as from the north pole). Then, to the observer at B, the Moon's centre will be found to be 57 minutes of arc (nearly 1) south of the equator. That is to say, it will be only 89 3' from the south pole, of which the position is known even when it is out of sight. In the triangle B L M, therefore, the angles B and L lack 57' of making two FIG. 21. MEASURING DISTANCE OF MOON right angles (180). This 57' is evidently the size of the other angle M. We have now a problem absolutely identical in principle with the preceding one, which dealt with the width of a river. It stands as follows: As the sine of 51' (the angle M) Is to the sine of 89 3' (the angle B), So is 4,000 miles (the length of base B L) To the perpendicular L M. The problem is easily solved with almost the same figures as in that dealing with the width of the river. As 01658 is to 99986, so is 4,000 miles to 240,000 miles, which is the approximate distance of the Moon at the time when the angles were measured. 1 1 The above problem has been simplified as much as possible, so that the prin- ciple may be readily grasped. As a matter of fact, the two ends of the base-line PROBLEMS IN CELESTIAL MEASUREMENTS 47 For convenience of comparison, all results are reduced to fit a right-angled triangle having a base-line equal to the radius, or semi-diameter, of the Earth at the equator. The parallax is then known as the horizontal equatorial parallax. The distances of Mars and Eros are measured in the same way as that of the Moon. But in the case of the Sun the results have to be obtained by taking advantage of a transit of Y FIG. 22. ARC OF CIRCLE Venus, or by some other indirect method. The principles and results are, however, the same. ARC PROBLEMS The five following problems are worked out by means of two radii and the enclosed arc (see Figure 22). The observer is supposed to be at Z. PROBLEM I. Given the angular diameter of Sun or Moon, 32' of arc (=1920" of arc), as seen from the Earth, find their distances from us in terms of their own diameter A B (= 1). are never exactly on the same meridian. Nor are they ever exactly the same dis- tance north and south of the equator. And the distance required is not from the Moon to the station L, but from the centre of the Moon to the centre of the Earth. Quite a number of corrections and precautions have to be taken to give trust- worthy results. But they need not be given here. It is sufficient if the principle of the problem is thoroughly understood. 48 HOW TO KNOW THE STARRY HEAVENS X 20fi 265" 2 A B = Y. Therefore l J 2(r A B = 107 A B. [NOTE. For meaning of letters see the table at page 40.] So that the distances of the Sun and Moon from the Earth are both alike in terms of their diameters ; that is to say, the dis- tance of each one of them is 107 times as great as its actual diameter, whatever that may be. This problem does not tell us how far they are from us or how large they are. It merely proves that if the Sun (or Moon) is a mile across, then it is 107 miles away from us ; while if it is 1,000,000 miles across, then it is 107,000,000 miles away. PROBLEM II. Given the real distance of the Sun, 92,790,000 miles, and its angular diameter, 32' of arc (=1,920"), find its real diameter in miles. MILE$ MILKS Z 1 920 ^ Y = A B. Therefore ^265 92 > 790 > 000 = 863,727 The following form of this problem may perhaps be better understood : As X is to Z, so is Y to A B. Worked out, this is as follows : MILKS MILES As 206,265" : 1,920" : : 92,790,000 : 863,727 PROBLEM III. Given the real distance of the Moon, 239,000 miles, and its angular diameter, 31' 6" (= 1,866"), find its real diameter in miles. This is a similar problem to the preceding one. MILES MILES rj 1 Q A A = Y = A B. Therefore 2^265 239 > 000 = 2 > 162 Or, by the " rule of three " : MILES MILES As 206,265" : 1,866" : : 239,000 : 2,162 PROBLEMS IN CELESTIAL MEASUREMENTS 49 PROBLEM IV. Given the real diameter of the Sun, 863,727 miles, and its angular diameter 32' ( 1,920"), find its real dis- tance in miles. It will be seen that this is the reverse of Problem II. MILES MILES X 206,265 ~ A B = Y. Therefore 863,727 = 92,790,000 Or, as before : MILES MILKS As 1,920" : 206,265" : : 863,727 : 92,790,000 PROBLEM V. Given the real diameter of the Moon, 2,162 miles, and its angular diameter, 31' 6" (= 1,866"), find its real distance in miles. It will be seen that this is the reverse of Problem III. It is worked the same as Problem IV. MILES MILES ^A B = Y. Therefore ^f|fjf 2,162 = 239,000 SINE PROBLEMS The following problems are worked out by means of a right- angled triangle constructed of two radii and the sine (or half- chord) of the enclosed angle (see Figure 23 ; lettering same as before). PROBLEM VI. Given the Sun's distance, 92,790,000 miles, and angular semi-diameter 16' (= 960"), find its real semi- diameter in miles. This is like Problem II, except that the semi-diameter is used instead of the diameter. MILKS MILES Z 960" Y Y = A B. Therefore 9nr 9r - 92,790,000 = 431,863 .A. ^UDj^OiJ PROBLEM VII. Given the Moon's distance, 239,000 miles, and its angular semi-diameter, 15' 33" (= 933"), find its real semi-diameter in miles. 4 50 HOW TO KNOW THE STARRY HEAVENS This is like Problem III, but uses the semi-diameter instead of the diameter. MILKS MILES Z 933" Y = A B. Therefore // 239,000 = 1,081 FIG. 23. SINE OF ANGLE In all the following problems the observers are supposed to be at A and B. Z is supposed to be the centre of the celestial body under observation. PROBLEM VIII. Given the Sun's parallax, 8.81", and the Earth's semi-diameter, 3,963 miles, find the Sun's distance in miles. PROBLEMS IN CELESTIAL MEASUREMENTS 51 All solar and planetary parallaxes are for convenience reduced to fit the semi-diameter of the Earth. This is here represented by A B, and the parallax by the opposite angle Z. MILES MILKS X 206 265" - A B = Y. Therefore 8 ' 8]// 3,963 = 92,790,000 PROBLEM IX. Given the Moon's parallax, 57' (= 3,420'% and the Earth's semi-diameter, 3,963 miles, find the Moon's dis- tance in miles. This is a similar problem to the preceding one. MILES MILES X 206,265" 2~ A B = Y. Therefore 3 ^ 2Q , 3,963 = 239,000 Here is the same problem worked by logarithms, which must be obtained from published tables of logarithms : As the sine of 57' (angle Z) 8.21958 Is to base 3,963 miles (A B) 3.59802 So is sine of 89 3' (angle A) 9.99994 13.59796 8.21958 To perpendicular (Z B) 5.37838 = 239,000 miles [NOTE. In small angles Z B = Y.] PROBLEM X. Given the Sun's distance, 92,790,000 miles, and the Earth's semi-diameter, 3,963 miles, find the Sun's parallax. This is the reverse of Problem VIII. 4j? X = Z. Therefore ^fg^O 206 > 265 " = 8 ' 81 PROBLEM XI. Given the Moon's distance, 239,000 miles, and the Earth's semi-diameter, 3,963 miles, find the Moon's parallax. This is the reverse of Problem IX, and similar to Problem X, 52 HOW TO KNOW THE STARRY HEAVENS A B 3,963 ~~ X = Z. Therefore 206 > 265 " = 57 ' [If it is not too late, I would here suggest that those who do not like Mathematics would do well to " skip " the foregoing chapter.] FIG. 24. SUN, SHOWING SPOTS AND FACUL^C Photographed at Greenwich Observatory, Feb. 13, 1892. V CHAPTER V THE CHARIOT OF IMAGINATION " Before their eyes in sudden view appear The secrets of the hoary deep ; a dark Illimitable ocean, without bound, Without dimension, where length, breadth, and height, And time, and place, are lost." Milton, " Paradise Lost," Book IL " Oh Deep, whose very silence stuns ! Where Light is powerless to illume, Lost in immensities of gloom, That dwarf to motes the flaring suns ! " G. Sterling, " The Testimony of the Suns." A LONG JOURNEY TO enable us to realise, to some extent, what position man holds with reference to the Universe, let us leave our Earth for a short time, and hasten away, in the Chariot of Im- agination, to a point in space half-way between our Sun and Alpha Centauri, the nearest of the other stars. We will take with us a specially constructed chronometer, made to indicate long periods of time ; a special cyclometer, made to fit the wheels of our chariot ; and a number of other scientific instruments which may prove useful in our celestial researches. In order that we may not get lost or have any corners to turn, we make our start from Cape Town, South Africa, in the night- time, when the Moon is above the horizon and Alpha Centauri is on the meridian. As this may be the first time some of us have travelled through space unaccompanied by Mother Earth, it will be well for us to travel slowly, so that we can get a good view of our surroundings, and at the same time avoid running into unnecessary danger. We will therefore keep a firm hand on the lines, from the start, 54 HOW TO KNOW THE STARRY HEAVENS so as to prevent our imaginary steeds from running away with us. On such a long journey the most satisfactory speed for us to keep up will perhaps be that at which light travels, about 186,000 miles per second. Everything being ready for our trip, the signal is given. " One, two, three. Away we go I " Before the words are fairly uttered, we find ourselves at the Moon's distance and in the bright sunshine. By a curious optical delusion we did not seem to move when the word was given, but the moonlit Earth suddenly dropped from beneath our feet. For a fraction of a second it appeared to swell, as dis- tant lands and moonlit seas sprang above the horizon. Then the Sun rose with a jerk, and the crescent Earth began to shrink in size as its distance increased. 1 At the end of one minute the Earth is still plainly visible in the bright sunlight, but the Moon is almost out of sight. In five minutes nothing is to be seen of either of them. For a time we are in the sunshine, but the light soon begins to wane as we recede from the Sun and approach the confines of the Solar System. In four hours we are at the distance of Neptune, and the Sun is not much more than a very brilliant star in the gathering twilight. Although the Sun continues to dwindle in size as we leave it behind, it shines continuously, there being no horizon to hide it from us. After we have been a month on our journey, as shown by our chronometer, it is practically nothing but a bright star among the multitude of stars by which we are entirely sur- rounded. By this time we have discovered that we have left behind many things which seemed very real and important while we remained on terra firma. There is now no north or south, no up or down. The star- 1 For the above effects to be produced, we should really have to travel slower than light, otherwise nothing would be visible in our rear. Every impossible illustration has its discrepancies, as Artemus Ward would say, THE CHARIOT OF IMAGINATION 55 sphere has ceased to turn on its axis, so that there are no pole stars. The wandering planets have long- since disappeared. There is no Sun or Moon. Day and night have ceased to roll. Seed-time and harvest come no more. Summer and winter are meaningless terms. Aside from our chronometer, months, years, and centuries have now no significance. Away from our Earth, geological periods trouble the mind no more. We keep on in a straight line, at the same speed, for two long years> as registered by our chronometer. The star which used to be our Sun is now directly behind us, but has long ceased to be conspicuous for either size or brilliancy. And now the special cyclometer which we brought along tells us that we are at last nearing our goal, the half-way house between the centre of our system and the nearest outside star. AMONG THE STARS Arrived at our lonely destination, let us check our imaginary horses, hitch them to an imaginary post, and take a survey of our actual surroundings. As we did not bring our Earth along with us, our view is not impeded in a downward direction. We can see clearly below and around, as well as above. What is there to be seen from our point of vantage ? One of the first things to attract our attention is that we do not appear to have any immediate surroundings. We are soli- tary in empty space. Instead of being surrounded by houses and trees lighted up by the dazzling glare of a hot Sun, or half-revealed by the soft glamour of a pale Moon, we find ourselves alone in the midst of perpetual starlight, which no Sun or Moon ever interferes with. There is no cloud or fog, for all is cold, clear, still, dark, and apparently void. But in the far distance there are plenty of objects to make up for an unoccupied " fore-space." The " back-space " of sky is all more or less crowded with stars. To the naked eye there are about 6,000 visible. These 56 HOW TO KNOW THE STARRY HEAVENS are distributed promiscuously in irregular clusters and hap- hazard groups, without any regard to pattern or symmetry. But besides these groups of stars there are, in some parts of the sky, great irregular streaks of nebulous haze. One set of these hazy streaks is so long-drawn-out that its snake-like folds and spirals almost form a girdle around us. The unaided eye cannot pierce this haze, and without further insight even the imagination itself is unable to invent a reason- able explanation of this " Milky Way." THE EYES OF SCIENCE Let us now imagine that our eyes improve in light-grasping power till they equal the most powerful telescopes in existence. What is there now to be seen from our point of vantage ? The result is something startling astounding overwhelm- ing. The scene is grand beyond the power of language to describe magnificent beyond the ability of the mind to conceive. The Earth we came from is still invisible lost in the depths of infinite space. The Sun that ruled our Solar System with such undisputed sway is visible still, but it rules no more. It was a SUN that reigned supreme among a thousand little twinkling stars. It is now but a star among a hundred million fellow-stars. But though we have lost our Earth and its Sun, we have gained more than we have lost. For we have revealed before us a goodly portion of the Universe itself. And though we see no more a panoramic succession of days and nights, seasons and years, we do not miss these earthly phenomena. For in their stead we see the stately evolutions of countless squadrons of heavenly orbs, circling through never-ending time in an ocean of limitless space. We have here no need of the Sun, neither of the Moon ; for the everlasting glory of the Great Cosmos enlightens us, and the iridescent mantle of Universal Nature enfolds us. FIG. 26. - SOLAH FLAMES AND COHONA, AS SEEN DUKIXG ECLIPSK OF MAY 28, 1900 By Burckhardt. (From Comstock's " Text-book of Astronomy,' 11 published by Messrs. D. Applelon & Co.) VTBRAT7 or THE UNIVERSITY or JzALirCi* THE CHARIOT OF IMAGINATION 57 On every side, above and below, we see stars by the million. They are strewn through endless space like the blinding snow- flakes of a Western blizzard. They are as thick as the leaves of an earthly forest. And we know that each and every star is a SUN, more or less like unto our Sun. Many, if not all of them, have subject worlds revolving around them like the planets which compose our own system. Gazing on such a picture, words are not equal to express our sense of littleness. As the poet says : This is a wondrous sight, And mocks all human grandeur." Contemplating the star-strewn heavens, the deist may well exclaim with one of old " When I contemplate the heavens, The work of thy hands, The Moon and the stars, That thou hast disposed, What is Man, That thou shouldst remember him, The Son of Man, That' thou shouldst watch over him ? " Ps. viii, 3 (Segond and Diodati). The poet Shelley has beautifully described such a scene. He says: " Below lay stretched the Universe. There, far as the remotest line That bounds imagination's flight Countless and unending orbs In mazy motion intermingled, Yet each fulfilled immutably Eternal Nature's law. Above, below, around, The circling systems formed A wilderness of harmony ; Each with undeviating aim, In eloquent silence, through the depths of space, Pursued its wondrous way." 58 HOW TO KNOW THE STARRY HEAVENS All around us is " the abyss of an immense concave, Radiant with million constellations, tinged With shades of infinite colour." A RUSH THROUGH SPACE After having gazed for a while at the wonderful scene around us? a scene so magnificent that even the words of a Saul among the poets fail to give any adequate conception of it, we un- hitch our imaginary horses from our imaginary post, turn our Chariot of Imagination toward one of the stars, and rapidly approach it. ONLY A STAR The star we selected for examination was a very ordinary- looking star. It was far smaller than many of its neigh- bours, and did [not shine anything like so brightly as some of them. But now that we have arrived in its vicinity it has grown in size and brilliancy till all the other stars have either gone out of sight or become faint dots of light, just perceptible in the growing daylight. It has, indeed, become so overwhelmingly radiant that we have to put on dark spectacles to enable us to use our eyes without being blinded. Let us stop and watch this star for a thousand years or so, and see what changes are going on around it as it drifts along in the ocean of space. The star itself is a round yellowish-white ball more than 800,000 miles in diameter. Its glowing surface, or photosphere, is one vast mass of shining cloud, which has the appearance of being dotted all over with still brighter specks, like rice-grains. This cloud-like photosphere is composed of calcium and other elements, kept in a white-hot state by an unimaginably intense heat rising from the gaseous interior of the star. The white photosphere radiates into outer space about four times as much FIG. 25. GROUP OF SUNSPOTS Photographed with the Greenwich 26-inch Refractor, on Sept. 11, 1898. The largest nucleus was about 24,000 miles long. FIG. 27. ERUPTIVE PROMINENCES Eclipse of May 28, 1900 (Barnard and Ritchey). The largest of these " hydrogen flames ' is 60,000 miles high. THE CHARIOT OF IMAGINATION 59 light and heat as an electric arc-light of the same size would do. 1 There are some peculiar features about this star as seen from a short distance. Physical and mechanical reactions of incon- ceivable violence are taking place beneath its surface. In some places they give rise to what look like volcanic eruptions on a vast and awe-inspiring scale. To an outside observer these centres of eruption appear like great irregular black blotches scattered about the white cloud-like photosphere. They are sur- rounded by plume-like shadows or penumbrae. By watching these black spots we soon find that the star is spinning slowly around on its axis, completing a revolution in about twenty-seven of our days. The light given out by this white photosphere is so dazzling that little more can be made out, even with dark glasses. We will therefore use special instruments to turn it aside, so as to enable us to see more clearly what other phenomena are going on in the neighbourhood. We can now see that the entire body of the star is buried under a shoreless ocean of transparent fire of a scarlet hue. This fiery ocean, or atmosphere, is everywhere from 4,000 to 5,000 miles deep, and appears to rest on the white cloud-like photo- sphere already described. The storm-tossed surface of this fiery ocean bristles at every point with huge ascending " flames " of the same scarlet colour. Those on our side of the star are not readily examined, on account of the brilliancy of the photosphere, but those around the edges are plainly visible with proper apparatus. Most of them are about 8,000 or 10,000 miles high, but here and there are larger ones, reaching up 60,000 miles or more. These huge ruddy flames assume a great variety of forms. They re- semble jets of steam, fireworks, fountains, ocean breakers, cy- clones, torpedo explosions, and volcanic eruptions, all on a scale of inconceivable magnitude.' 1 By the way, an electric arc-light the size of a pin's head cannot be examined without the aid of dark glasses, it is so overwhelmingly bright. And its tempera- ture is 6,300 F. But this star is nearly a million miles through and is very much brighter and hotter ! 60 HOW TO KNOW THE STARRY HEAVENS As we watch this stormy scene it reminds us of a wind-tossed prairie fire as seen by night through a telescope on our little Earth. The flames rise and dart forward, fall back and roll over ; bend, twist, and curl ; embrace, wrestle, and fling them- selves apart. Before our eyes they change into all imaginable shapes, so that we find it almost impossible to realise their over- whelming magnitudes and the terrific speed of their varied movements. Every once in a while we see great ruddy blasts of fiery gas rise from the surface with tremendous force and in- conceivable velocity. Some of these flaming jets shoot up at the rate of 250 miles in a second of time, and reach an altitude of 200,000 or 300,000 miles. They then branch out in tree-like clouds, and finally break up and scatter in a shower of solar fireworks. The very largest of these flames are long enough to be wrapped sixteen times around our Earth. These ruddy flames (though cooler than the white photosphere beneath them) are so inconceivably hot that they do not burn. In fact they would " unburn " any burnt substance which might fall into them, even if it should happen to be as large and heavy as our Earth. No chemical compound could exist for a second in such a terrific heat. No element, even, could remain there in a solid or liquid state. The flames are composed of incandescent hydrogen and helium, while the ruddy sea from which they rise contains also iron, magnesium, sodium, and other metals, all vaporised by the tremendous heat. This scarlet ocean of fiery gas is termed a sierra or chromo- sphere. The flames which rise from it are known as prom- inences. Outside of all these is a corona, consisting of great hazy radi- ating streaks of some light and apparently gaseous substance, extending a million miles or more into outer space. Owing to their distribution, and to the fact that the star is spinning around on its axis, these " repulsive " streaks are not straight, but slightly curved, and have a very peculiar plume-like appearance. FIG. 28. SOLAR CORONA. ECLIPSE OF MAY 28, 1900 Photographed by Chabot-Dolbeer Eclipse Expedition. FIG. 29. XOKTH POLAR STREAMERS OF THE CORONA. MAY 28, 1900 Crocker Eclipse Expedition. THE CHARIOT OF IMAGINATION 61 OFFSPRING OF A STAR As we watch the eruptive " freckles " which come and go every eleven years on the surface of the star, we notice a number of small balls sweeping around and around it, all going in the same general direction. These are all worlds, more or less like the one on which we used to live before we began our heavenly wanderings. Let us watch them as they eddy around the star, like moths circling around a lantern in the dark. THREE CLASSES OF WORLDS The most noticeable of them are four outer or superior planets. These are so much larger and more powerful than the rest that they form a kind of aristocracy, subject only to the reigning monarch in the centre. They do not appear to shine by their own light, yet they are still puffed up with heat. They have followers, or satellites, of their own, so that they are something like petty rulers subject to a higher power. Four very insignificant planets form an inner or inferior family of worlds. They give out neither light nor heat of their own, so they may be called terrestrial planets. They are much more under the control of the central ruler, but at the same time may be said to bask in the sunshine of his favour. They are, in fact, the bourgeoisie or well-to-do citizens of the monarchy. Between these two families of worlds there is a whole regiment of almost invisible planets, which may be called asteroids, from their small size and star-like appearance. They are the pro- letarians, the working-class of the monarchy, subject not only to the legitimate rule of the sovereign, but also to the overbearing authority of the aristocracy on the one hand, and to the petty bossing of the bourgeoisie on the other. They are in fact " be- tween the upper and the nether millstone." The result is shown by the steep, elongated, and apparently dangerous paths some of them are compelled to follow, with neither hope of relief nor promise of reward. 62 HOW TO KNOW THE STARRY HEAVENS Although the four outer planets appear to us to be very large, yet they are extremely small compared with the central star, which is 560 times as large and 745 times as heavy as all the planets put together. Let us now examine some of the individuals composing these three classes of worlds, beginning with the inner planets. THE INNER PLANETS The one which is nearest to the central star is small, and very little can be seen of it. The second is larger, with a dense atmos- phere which somewhat obscures the planet itself. Both of these little wgrlds move at a speed many times greater than that of a cannon-ball, yet it takes them several months to go once around the central star. PLANET NUMBER THREE Planet No. 3 is slightly larger than No. 2, its diameter being nearly 8,000 miles. It is, indeed, the largest of the inner family of worlds. It is more than 90,000,000 miles from the star around which it is sweeping. It takes just a year to complete a revolution, although it travels at the astounding rate of eighteen miles in a second of time. On looking more closely at this world, another and smaller planet is seen buzzing around and around it. This is a moon or satellite, which goes around its primary in the same direction as that is going around the central star. It is a little over 2,000 miles thick, so that the principal planet is about fifty times as large as its companion. A more attentive look at No. 3 reveals several peculiarities. It is spinning around like a top, turning in the same gen- eral direction as that in which it goes around the central star. The two points which form its poles of rotation are white, as though covered with ice and snow. Its surface is variegated, and is evidently composed of land and water. There are con- tinents, oceans, islands, seas, lakes, rivers, and mountains. The land appears to be more or less covered by vegetation of a green FIG. 30. MERCURY-, THE FIRST PLANET By Schiaparelli. (From Todd's " Stars and Telescopes," published by Messrs. Little, Brown,