[JS:|S'9-S'J' Cornell University Library arV15562 ' Elementary lessons in astronomy 3 1924 031 321 965 olln,anx Cornell University Library The original of tiiis bool< is in tile Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031321965 ELEMENTARY LESSONS ASTRONOMY s- RADIATION AND ABSORPTION SPKCTRA. [/•iv ,/,'Siri/^IU'n, ice- Ihiik. DESCRIPTION OF FRONTISPIECE. Continuous Spectrum. ^ \ Spectrum of Hydrogen, Ordinary Pressure. Spectrum of Hydrogen, very Low Pressure. \ Radiation. Spectrum of Magnesium Vapour, showing the Long and t Short Lines. __ _ _ I 5. Spectrum of Sodium Vapour, Low Temperature. 6. Spectrum of Sodiun Vapour, Low Temperature. 7. Spectra of the Vapc irs surrounding xst Class Star, Sinus. 8. Spectra of the Vi >oiirs s^ounding 2nd Class Star, the , Sun. #^. ( 9. Spectra of the "* apours ^unrounding 3rd Class Sur, a Oiionis. -w. ) 10. Spectrum of Chrom Kphere* IX. Spectra of Nebula. , Absor^iioHf \ Radiaiioni ELEMENTARY LESSONS ASTRONOMY BY J.^KORMAN LOCKYER, F.R.S. CORRESPONDANT OF THE INSTITUTE OF FRANCE, FOREIGN MEMBER OF THE ACADEMY OF THE LYNCEI OF ROME, ETC. ETC. ETC. PROFESSOR OF ASTRONOMICAL PHYSICS IN THE NORMAL SCHOOL OF SCIENCE MACMILLAN AND CO. AND NEW YORK 1888 //corn ELL UN i/LRt^r' \jJBRARV^ RicHAKD Clay and Soks, LONDON AND BUNGAY- First Ediiioit printed {P&it %vo) 1868. Reprinted^ 1870, 1871, 1873, 1874, 1876 ; {Fcap. Zz'a} 1877, 1879, 1881, 18. 1285, January and March 1886. New Edition, 1888, D.^ The Right of Translaiidn and Repriductioil isResenied. PREFACE TO THE 3STH THOUSAND. The present reprint has been revised throughout, and in the earlier portions of the work references have been made to the conclusions, having reference to the constitution of the heavenly bodies, that I have recently communicated to the Royal Society. I have to express my obligations to Miss A. M. Gierke, and to Mr. A. Fowler assistant to the Solar Physics Committee, for their kind help in the revision and in the reading of proof sheets. J. Norman Lockyer. Science Schools, February 29, 1 888. PREFACE TO FIRST EDITION. These " Elementaiy Lessons in Astronomy " are in- tended, in the main, to serve as a text-book for use in Schools, but I beUeve they will be found useful to " children of a larger growth," who wish to make them- selves acquainted with the basis and teachings of one of the most fascinating of the Sciences. The arrangement adopted is new ; but it is the result of much thought. I have been especially anxious in the descriptive portion to show the Sun's real place in the Cosmos, and to separate the real from the apparent movements. I have therefore begun with the Stars, and have dealt with the apparent movements in a separate chapter. It may be urged that this treatment is objectionable, as it reduces the mental gymnastic to a minimum ; it is right, therefore, that I should state that my aim throughout the book has been to give a connected view of the whole subject rather than to discuss any particular parts of it ; and to supply facts, and ideas founded on the facts, to serve as a basis for subsequent study and discussion. A companion volume to the present or>e — I allude to the altogether admirable " Popular Astronomy " from the pen of the late Astronomer Royal — may, from this point of view, be looked upon as a sequel to two or three chapters in this book. PREFACE. It has been my especial endeavour to incorporate the most recent astronomical discoveries. Spectrum-analysis and its results are therefore fully dealt with ; and distances, masses, &c., are based upon the recent determination of the solar parallax. The use of the Globes and of the Telescope have both been touched upon. Now that our best opticians are employed in producing " Educational Telescopes," more than powerful enough for school purposes, at a low price, it is to be hoped that this aid to knowledge will soon find its place in every school, side by side with the black- board and much questioning. All the steel plates in the book, acknowledged chefs- d'ceuvres of astronomical drawing, have been placed at my disposal by my friend Mr. Warren De La Rue- I take this opportunity of expressing my thanks to him, and also to the Council of the Royal Astrono- mical Society, M. Guillemin, Mr. R. Bentley, the Rev. H. Godfray, Mr. Cooke, and Mr. Browning, who have kindly supplied me with many of the other illustrations. I am also under obligations to other friends, espe- cially to Mr. Balfour Stewart and Mr. J. M. Wilson, for valuable advice and criticism, while the work has been passing through the press. J. N. L. CONTENTS. INTRODUCTION. LESSON General Notions. — The Uses of Astronomy CHAPTER I. THE NATURE OF THE HEAVENLY BODIES. I. — Magnitudes and Distances of the Stars. Shape of our Stellar System ... ..... g II- — The Constellations. Movements of the Stars. Movements of Dur Sun 12 III.— Double and Multiple Stars, Variable Stars ... 17 IV. — Coloured Stars. Apparent Size. The Structure of the Stars. Clusters of Stars . . . . . 28 V. — Nebulse. Classification and Description . • • 35 VI. — Nebulse {continued). Their Faintness. Variable Nebulse. Distribution in Space. Their Structure. Nebular Hypo- thesis . . . . .... 40 CHAPTER II. THE SUN. VII. — Its relative Brightness, its Size, Distance, and Weight ... 43 VIII. — Telescopic Appearance of the Sunspots. Penumbra, Umbra, Nucleus, Faculse, Granules. Red Flames -49 IX. — Explanation of the Appearances on the Sun's Surface. The Sun's Light and Heat. Sun-force. The Past and Future of the Sun . , . , '55 CONTENTS. CHAPTER III. THE SOLAR SYSTEM. LESSON PAGE X.— General Description. Distances of the Planets from the Sun. Sizes of the Planets. The Satellites. Volume, Mass, and Density of the Planets . ... 63 XI.— The Earth. Its Shape. Poles. Equator. latitude and Longitude. Diameter 70 XII. — The Earth's Movements. Rotation. Movement round the Sun. Succession of Day and Night . 74 XIII. —The Seasons 80 XIV. — Structure of the Earth. The Earth's Crust. Interior Heat of the Earth. Cause of its Polar Compression. The Earth once a Star . 85 XV. — The Earth {continued). The Atmosphere. Belts of Winds and Calms. The Action of Solar and Terrestrial Radiation. Clouds. Chemistry of the Earth. The Earth's Past and Future . . . 90 XVI. — The Moon : its Size, Orbit, and Motions : its Physical Constitution . . 96 XVII. — Phases of the Moon. Eclipses : how Caused. Eclipses of the Moon 102 XVIII.— Eclipses {continued). Eclipses of the Sun. Total Eclipses and their Phenomena. Corona. Red-flames . 107 XIX. — The other Planets compared with the Earth. Physical Description of Mars . . iiz XX. — The other Planets compared with the Earth {continued). Jupiter: his Belts and Moons. Saturn: General Sketch of his System . . 120 XXI.— The other Planets compared with the Earth (continued). Dimensions of Saturn and his Rings. Probable Nature of the Rings. Effects produced by the Rings on the Planet. Uranus. Neptune : its Discovery 124 CONTENTS. LESSON PAGE XXII.— The Asteroids, or Minor Planets. Bode's Law. Size of the Minor Planets : their Orbits : how they are observed 128 XXIir,— Comets : their Orbits. Short-period Comets. Head, Tall, Coma, Nucleus, Jets, Envelopes. Their probable Num- ber and Physical Constitution 131 XXIV. — Luminous Meteors. Shooting Stars. November Showers. Radiant Points 140 XXV. — Luminous Meteors {continued^ Cause of the Phenomena of Meteors. Orbits of Shooting Stars. Detonating Meteors. Meteorites : their Classification. Falls. Chemical and Physical Constitution . 146 CHAPTER IV. APPARENT MOVEMENTS OF THE HE A VENLV BO VIES. XXVI, — The Earth a moving Observatory. The Celestial Sphere. Effects of the Earth's Rotation upon the apparent Move- ments of the Stars. Definitions. 152 XXVII. — Apparent Motions of the Heavens, as seen from different parts of the Earth. Parallel, Right, and Oblique Spheres. Circumpolar Stars. Equatorial Stars, and Stars invisible in the Latitude of London. Use of the Globes . 157 XXVIII. — Position of the Stars seen at Midnight. Depends upon the two Motions of the Earth. How to tell the Stars. Celestial Globe. Star-maps. The Equatorial Constel- lations. Method or Alignments . 165 XXIX. — Apparent Motion of the Sun. Difference in Length be- tween the Sidereal and Solar Day. Celestial Latitude and Longitude. The Signs of the Zodiac. Sun's apparent Path. How the Times of Sunrise and Sunset, and the Length of the Day and Night, may be determmed by means of the Celestial Globe . 174 XXX. — Apparent Motions of the Moon and Planets. Extreme Meridian Heights of the Moon : Angle of her Path with the Horizon at different Times. Harvest Moon. Varying Distances, and varying apparent Size of the Planets. Conjunction and Opposition . . . 179 CONTENTS. LESSON PAGE XXXI. — Apparent Motions of the Planets {continued). Elongations and Stationary Points. Synodic Period, and Periodic Time 184 XXXII. — Apparent Movements of the Planets {continiced). In- clinations and Nodes of the Orbits. Apparent Paths among the Stars. Effects on Physical Observations. Mars. Saturn's Rings 190 CHAPTER V. THE MEASUREMENT OF TIME. XXXIII. — Ancient Methods of Measurement. Clepsydrae. Sun- Dials. Clocks and Watches. Mean Sun. Equation of Time . 198 XXXIV. — Difference of Time. How determined on the Terrestrial Globe. Greenwich Mean Time. Length of the Various Days. Sidereal Time. Conversion of Time . . . zoS XXXV.— The Week. The Month. The Year. The Calendar. Old Style. New Style 212 CHAPTER VI. LIGHT.— THE TELESCOPE AND SPECTROSCOPE. XXXVI. — ^What Light Is ; its Velocity ; how determined. Aberra- tion of Light. Reflection and Refraction. Index of Refraction. Dispersion. Lenses ... . 217 XXXVII. — Achromatic Lenses. The Telescope. Illuminating Power. Magnifying Power .... , , 224 XXXVIII.— The Telescope {continued). Powers of Telescopes of different Apertures. Large Telescopes^ Methods of Mounting the Equatorial Telescope . 230 XXXIX.— The Solar Spectrum. The Spectroscope. Kirchhoff's Discovery. Physical Constitution of the Sun . ... 23d XL.^Importartce of this method of Research. Physical Consti- tution of the Stars, Nebulae, Comets, Moon, aild Planets. Construction of the Spectroscope. Celestial Photography 242 CONTENTS. CHAPTER VII. DETERMINATION OF THe' APPARENT PLACES OF THE HEAVENLY BODIES. LESSON PAGE XLI. — Geometrical Principles. Circle. Angles. Plane and Spherical Trigonometry. Sextant. Micrometer. The Altazimuth and its Adjustments 253 XLII.— The Transit Circle and its Adjustments. Principles of its Use. Methods of Taking Transits. The Chronograph. The Equatorial 262 XLIII. — Corrections applied to Observed Places. Instrumental and Clock Errors. Corrections for Refraction and Aberration. Corrections for Parallax. Corrections for Luni-solar Pre- cession. Change of Equatorial into Ecliptic Co-ordinates . 271 XLIV. — Summary of the Methods by which true Positions of the Heavenly Bodies are obtained. Use that is made of these Positions. Determination of Time : of Latitude : of Longitude . 280 CHAPTER VIII. DETERMINATION OF THE REAL DISTANCES AND DIMENSIONS OF THE HEAVENLY BODIES. XL v.— Measurement of a Base Line. Ordnance Survey. Deter- mination of the Length of a Degree. Figure and Size of the Earth. Measurement of the Moon's Distance . . 285 XLVL— I^etermination of the Distances of Venus and Mars : of the Sun. Transit of Venus. The Transit of 1883 . 292 XLVIL— Comparison of the Old and New Values of the Sun's Dis- tance. Distance of the Stars. Determination of Real Sizes .300 CONTENTS. CHAPTER IX. UNIVERSAL GRAVITATION. LESSON PAGE XLVIII. — Rest and Motion. Parallelogram of Forces. Law of Fall- ing Bodies. Curvilinear Motion. Newton's Discovery. Fall of the Moon to the Earth. Kepler's Laws . . . 307 XLIX. — Kepler's Second Law proved. Centrifugal Tendency. Centripstal Force. Kepler's Third Law proved. The Conic Sections. Movement in an Ellipse 315 L. — Attracting and Attracted Bodies considered separately. Centre of Gravity. Determination of the Weight of the Earth; of the Sun; of the Satellites . 321 LT. — General Effect of Attraction. Precession of the Equinoxes : how caused. Nutation. Motions of the Earth's Axis. The Tides. Semi-diurnal, Spring, and Neap Tides. Cause of the Tides. Their probable Effect on the Earth's Rotation . . . . . 328 Appendix 339 Index 351 ILLUSTRATIONS. PAGE Frontispiece : Spectra of the Sun. Stars, and Nebulae {to face Title). Plate 1. Star Clusters 31 ,, II, Nebulse 37 ,, III. The Sun . to face 43 ,, IV. Sun-spots 51 „ V. The Solar System to face 63 , , VI. The Lunar Crater, Co- pernicus . to/ace roi „ VIT. Eclipse of the Sun to face 109 PAGE Plate VIII. Mars in 1856. to face ii<^ p, IX. Mars in 1862 .... 117 ,, X. Jupiter and Saturn to face 120 „ XI. Radiant - point of Shooting Stars . . 143 „ XII. How the Equation of Time is derived from Two Components . 206 ,, XIII. Equatorial Telescope 233 ,, XIV. Spectroscope .... 239 ,, XV. Portable Altazimuth 25+ ., XVI. Transit Circle . 265 Fig. r. Orbit of a Double Star . 18 2. The Double-double Star € Lyrje 19 3. Light curve of Mira . 21 4. Ditto of /9 Lyrae . . . . 23 5. Ditto of T Coronse and Nova Cygni . . 24 6. Ditto of Algol 25 7. Plan and Section of the Orbit of the Companion of Algol 27 8. Position of the Sun's axis 45 9. Curve showing period of rotation of Photosphere 46 10. Sun-spot passing over the Sun's edge 47 11. Part of a Sun-spot, as seen in a powerful tele- scope (Lockyer) .... 53 12. Sun-spot showing details of the Penumbra ... 56 1 3. Section of the Plane of the Ecliptic 65 14. Mode of constructing an Ellipse . . , 75 15. The Seasons 77 16. Explanation of the differ- ent Altitudes of the Sun in Summer and Winter So of Fig. 17, 18, 19, 20. The Earth, as seen from the Sun : — At the Summer Solstice ,, Winter . . , „ Vernal Equinox , , Autumnal 21. Cause of the Earth's sphe^ roidal form . . . 22. Phases of the Moon 23. General Theory Eclipses . . 24. Corona of 1878 as seen behind a screen 25. General View of Jupiter and his Moons 26. General View of Saturn and his Moons 27. Ecliptic Chart 28. Donati'<; Comet, general view (Bond) 29. Ditto, showing Head and Envelopes (Bond) 30. Great Comet and Nucleus 31. Fire-ball, as seen in a telescope . . . 32. A Parallel Sphere (God' fray) 33. A Right Sphere (Godfray) 34. An Oblique Sphere (God fray) . ... 90 103 123 130 136 138 148 158 ib. XVI ILLUSTRATIONS. Fig. 35- 36. 37- 38. PAGE Southern Clrcumpolar Constellations (Guille- min) 162 Northern Clrcumpolar Constellations (Guille- min) 163 The Great Bear at inter- vals of six hours (Guil- lemin) . 164 Equatorial Constella- tions : — Orion (GuiUe- min) Cas- Bootes Perseus, siopeia . . Sidereal and Solar Days Harvest Moon . . . Retrogradations, Elonga- tions, and Stationary Points of Planets . . . 186 Path of Venus among the Stars in 1868 191 Path of Saturn among the Stars, 1862 — 5 (Proctor) 192 Orbits of Mars and the Earth. In this wood- cut some of the oppo- sitions are taken from Proctor 193 Varying appearances of Saturn's Rings (Guil- lemin) 195 Saturn when the Plane of the Ring Passes through the Earth . .196 Ditto, when the North Surface of the Rings is visible ib. Construction of the Sun- dial (Godfray) . 200 Aberration of Light . . . 218 Atmospheric Refraction .219 Action of a Prism on a 'beam of light 220 Actions of two Prisms placed base to base . . 222 Action of a Convex Lens 223 Ditto, showing how the Image is inverted ib. Concave Lens .... 225 Theory of the Astrono- mical Telescope . - , 227 Star Spectroscope .... 250 Direct-vision Spectro- scope . . . . 251 Fig. 61. 62. 63. 64. 65- 76- PAGE Triangles 255 Ditto, with unequal bases 256 Trigonometrical Ratios . 257 Effect of the Aberration of Light on a Star's ap- parent place 273 Mode of Correction for Aberration . 274 Parallax 275 Transformation of Equa- torial and Ecliptic Co- ordinates (Godfray) . . 279 Measurement of the dis- tance of the Moon . . 291 Ditto of Mars 29 ^ Transit of Venus (Airy) . 295 Ditto,' Sun's Disc, as seen from the Earth (Airy) . 297 Ditto, reversed (Airy) . . ib. Ditto, illuminated side of the Earth at ingress (Airy) 298 Ditto, ditto, at egress (Airy) 299 Comparison Stars em- ployed in determining the parallax of <> Cen- tauri 304 Results of observations of a Centauri 305 Parallelogram of Forces . 308 Action of Gravity on the Moon's Path ... . 312 Kepler's Second Law . 314 Proof of ditto . . . . 316 Circular Motion . -317 The Conic Sections . 319 Orbital Velocities .... 320 Centre- of Gravity, in the case of equal Masses . 322 Ditto, in the case of Un- equal Masses 323 Fall of Planets to the Sun (Airy) 324 The Cavendish Experi- ment (Airy) 325 Showing the effects of Precession on the posi- tion of the Earth's a.xis . . . . . 333 INutation 333 Apparent motion of the Pole of the Equator round the Pole of the Heavens, or Ecliptic (Godfray) . ib. INTRODUCTION. General Notions.— The Uses of Astronomy. I. At night, if the sky be cloudless, we sec it spangled with so many stars, that it seems impossible to count them ; and we see the same sight whether we are in Eng- land, or in any other part of the world. The earth on which we live is, in fact, surrounded by stars on all sides ; and this was so evident to even the first men who studied the stars that they pictured the earth standing in the centre of a hollow crystal sphere, in which the stars were fixed like golden nails. a. In the daytime the scene is changed : in place of thousands of stars, our eyes behold a glorious orb whose rays light up and warm the earth, and this body we call the sun. So bright are his beams that, in his presence, all the " lesser lights," the stars, are extinguished. But if we doubt their being still there we have only to take a candle from a dark room into the sunshine to understand how their feeble light, like that of a candle, is " put out " by the greater light of the sun. 3. There are, however, other bodies which attract our attention. The moon shines at night now as a crescent ffi E ASTRONOMY. and now as a full moon, sometimes rendering the stars invisible in the same way as the sun does, though in a less degree, and showing us by its changes that there is some difference between it and the sun : for while the sun always appears round, because we receive light from all parts of its surface turned towards us, the shape of the bright or lit-up portion of the moon varies from night to night, that part only being visible which is turned towards the sun. 4. Again, if we examine the heavens more closely still, we may see, after a few nights' watching, one, or perhaps two, of the brighter " stars " change their position with regard to the stars lying near them, or with regard to the sun if we watch that body closely at sunrise and sunset. These are the planets; the ancients called them "wandering stars." 5. But the planets are not the only bodies which move across the face of the sky. Sometimes a comet may by its sudden appearance and strange form awaken our interest and make us acquainted with another class of objects unlike any of those which we have previously mentioned. 6. Such are the celestial bodies ordinarily visible to us. Far away, and comparatively so dim that the naked eye can make little out of them, lie the nebulae, so called because in the telescope they often put on strange cloud-like forms ; tihey differ as much from stars in their appearance as comets do from planets. 7. There are other bodies, to which we shall refer by and by, But we will, in this place, content ourselves with stating generally what Astronomy teaches us concerning star and sun, moon and planet, comet and nebula. 8. To begin then with the stars. So far from being fixed, and being stuck as it were in a hollow glass globe, which state of things would cause all to be at pretty nearly equal distances from us, they are all in rapid motion and their distances vary enormously; although all of them are so very far away that they appear to us to be at rest, as a ship does when saihng along at a great distance INTRODUCTION. from us. In spite, however, of their great and varying dis- tances, science has been able toget a mental bird's-eye view of all the hosts of stars which the heavens reveal to our eyes, as they would appear to us if we could plant ourselves far on the other side of the most distant one. The telescope — an instrument which will be fully described further on — has,in fact, taught us that all the stars which we see, form, after all, but a cluster of islands as it were in an infinite ocean of space ; so that we may think of all the stars which we see as forming our visible universe, and when we have got that thought well into our minds we may think of parts of space beyond our ken containing other universes, as there are other towns besides London in England. 9. Further, we know that our sun is one of the stars which compose this star-cluster, and that the reason that it appears so much bigger and brighter than the other stars is simply because it is the nearest star to us. We all of us know how small a distant house looks or how feebly a distant gas-lamp or candle seems to shine ; but the distant house may be larger than the one we live in, or the distant light may really be brighter than the one which, being nearer to us, renders the other insig- nificant. It is precisely so with the stars. Not only would they appear to us as bright as the sun, if we were as near to them, but we know for a fact that some of them are larger and brighter. 10. Now, why do the stars and the sun shine? They shine, or give out light, because they are red or white hot. At the surfaces of some, vapours of metals are mingling together with a heat more fierce than anything we can imagine. In others we have meteorites in collision, and the light is produced from these and the surrounding vapours. 11. What, then, are the planets ? We may first state that they are comparatively small bodies travelling round our sun at various distances from him. Our earth is one of them. A moment's thought on what we have said about B 3 ASTRONOMY. the sun and stars will, however, show us another important difference between the planets and the sun. We have seen that the sun is a white-hot body ; our earth, we know, is, on the contrary, a cold one : all the heat we get is from the sun. Because the earth is cold it cannot give out light any . more than a cold poker can. Astronomers have learnt that all the other planets are like the earth in this respect. They are all dark bodies — having no light in themselves — and they all, like us, get their light and heat from the sun. When, therefore, we see a planet in the sky, we know that its light is sunshine second- hand ; that, as far as its light is concerned, it is but a looking-glass reflecting to us the light of the sun. We have now got thus far: planets are dark or obscure, or non-self-luminous bodies travelling round the sun, which is a bright body — bright because it is white hot ; and the sun is a star, one of the stars which together form our universe; the reason that it appears larger and brighter than the other stars being because we are nearer to it than we are to the others. It seems likely that the other stars have planets revolving round them, although astron- omers have as yet no positive knowledge on the matter, as they are so very far away that the telescopes we pos- sess at present are not powerful enough to show us their planets, if they have any. 12. We now come to the moon. What is it.? The moon goes round the earth in the same way as we have seen the planets revolving round the sun : it is in fact a planet of the earth ; it is to the earth what the earth is to the sun. Like the earth and planets, it is a dark body, and this is the reason it does not always appear round as the sun does. We only see that part of it that is lit up by the sun. In the moon we have a specimen of a third order of bodies called sateUites, or companions as they are the companions of the planets, accompany- ing them in their courses round the sun. INTRODUCTION. We have then to sum up again — (i) the sun, a star, (2) the planets revolving round the sun, and (3) satellites revolving round planets. 13. The nebulse represent an early stage in the history of all stars. All the bodies in the universe are undoubt- edly different aggregations of meteorites, and the differ- ences between them are due to the different states of condensation. The light of the self-luminous bodies is due to the heat produced by collisions due to gravity. Nebulae are the most sparse and scattered swarms of meteorites ; the collisions are few and their light is consequently feeble. By the gradual condensation of the swarms, collisions become more numerous, the tempera- ture is increased, and different orders of stars are formed. Comets are similar in constitution to the nebulae and some stars, and differ from them only in coming within the limits of our system. They rush for the most part from distant regions to our sun, and having gone round him they go back again, and we only see them for a small part of their journey. 14. Such, then, are some of the bodies with which the science of Astronomy has to deal ; but astronomers have not rested content with the appearances of these bodies : they have measured and weighed them in order to assign to them their true place. Thus they have found out that the sun is 1,305,000 times larger than the earth, and the earth 50 times larger than the moon. On the other hand, as we have seen, they have discovered that, while we travel round the sun, the moon travels round us, and at a distance which is quite insignificant in comparison. In other words, the moon travels round us at a distance of 238,000 miles, while we travel round the sun at a distance of 93,000,000 miles. 15. We thus see how it is that the greater size of the sun is balanced, so to speak, by its greater distance ; the result being that the large distant sun looks about the same size as the small near moon. ASTRONOMY. 16. We already see how enormous are the distances dealt with in astronomy, although they are measured in the same way as a land-surveyor measures the breadth of a river that he cannot cross. The numbers we obtain when we attempt to measure any distance beyond our own little planetary system convey no impression to the mind. Thus the nearest fixed star is more than 25,000,000,000,000 miles away, the more distant ones so far away that light, which travels at the rate of 186,300 miles in a second of time, requires thousands of years to dart from the stars to our eyes ! 17. In spite, however, of this immensity, the methods employed by astronomers are so sure that, in the case of the nearer bodies, their distances, sizes, weights, and motions are now well known. We can indeed predict the place that the moon — the most difficult one to deal with — will occupy ten years hence, with more accuracy than we can observe its position in the telescope. 18. Here we see the utility of the science, and how upon one branch of it, .Physical Astronomy, which deals with the laws of motion and the structure of the heavenly bodies, is founded another branch. Practical Astronomy, which teaches us how their movements may be made to help mankind. 19. Let us first see what it does for our sailors and travellers. A ship that leaves our shore for a voyage round the world takes with it a book called the " Nautical Almanac," prepared beforehand — three or four years in advance — by our Government astronomers. In this book the places the moon, sun, stars, and planets will occupy at certain stated hours for each day are given, and this information is all our sailors and travellers require to find their way across pathless seaB or unknown lands. 20. But we need not go on board ship or into new countries to find out the practical uses of Astronomy. It IS Astronomy which teaches us to measure the, flow of time, the length of the day, and the length of the ySar : INTRODUCTION. without Astronomy to regulate them, clocks and watches would be almost impossible, and quite useless. It is Astronomy which divides the year into seasons for us, and teaches us the times of the rising and setting of the moon, which lights up our night. It is to Astronomy that we must appeal when we would inquire into the early history of our planet, or when we wish to map its surface. 21. Such, then, is Astronomy — the science which, as its name, derived from two Greek words (da-rrip, " star," and vofLos, " law,") implies, unfolds to us the laws of the stars. CHAPTER I. THE STARS AND NEBULA. Lesson I. — Magnitudes and Distances of the Stars. Shape of our Universe. 22. The first thing which strikes us when we look at the stars is, that they vary very much in brightness. All of those visible to the naked eye are divided into six classes of brightness, called " magnitudes," so that we speak of a very briUiant one as "a star of the first magnitude:" of the feeblest visible as a star of the sixth magnitude, and so on. The number of stars of all magnitudes visible to the naked eye is about 6,000 ; so that the greatest number visible at any one time — as we can only see one half of the sky at once — is 3,000. If we employ a small telescope this number is largely increased, as that instrument enables us to see stars too feeble to be perceived by the eye alone. For this reason such stars are called telescopic stars. The stars thus revealed to us still vary in brightness, and the classification into magnitudes is continued down to the I2th, 14th, i6th, or even lower magnitudes, according to the power of the telescope ; in powerful telescopes at least 20,000,000 stars down to the 14th magnitude are visible. 23. A star of the sixth magnitude is, as we have seen, ASTRONOMY. [chap. i. the faintest visible to the naked eye. It has been estimated that the other stars are brighter than one of the sixth magnitude, by the number of times shown in the following table : — Times. A star of the Sth magnitude 2 4th „ 6 3d „ .... 12 2d „ 25 „ 1st „ 100 Sirius, the brightest of the \ ^^ 1st magnitude stars . ./ The Sun, the nearest star I . 2,400,000,000,000 to us I 't ' ' ' 24. Now it is evident that these stars, as they all shine out with such different lights, one star differing from another star in glory, are either of the same size at very different distances, the furthest away being of course the faintest ; or are of different sizes at the same distance, the biggest shining the brightest ; or are of different sizes at different distances. Where the actual distances of the stars are known we can be certain ; but from other con- siderations it is most probabletihat the difference in bril- liancy is due to difference of distance, and not to size. 25. The distances of the stars from us are so great that it scarcely conveys any impression on the mind to state them in miles ; some other method, therefore, must be used, and the velocity of light affords us a convenient one. Light travels at the rate of 1 86,300 miles in a second of time — that is to say, between the beats of the pendtrium of an ordinary clock, light travels a distance equal to eight times round the earth. 26. In spite, however, of this great remoteness, the distances of some of them are known with considerable accuracy.- Thus, leaving the- sun out of the question, we CHAP, i.] THE STARS AND NEBULA. find that the next nearest is situated at a distance which light requires four years and four months to traverse. 27. From the measurements already made, we may say that, on the average, light requires fifteen and a half years to reach us from a star of the first magnitude, twenty-eight years from a star of the second, forty-three years from a star of the third, and so on, until, for stars of the I2th magnitude, the time required is 3,500 years. 28. Winding among the stars, a beautiful belt of pale light spans the sky, and sometimes it is so situated, that we see that it divides the heavens into two nearly equal portions. This belt is the Milky way j and the smallest telescope shows that it is composed of stars so faint, and apparently so near together, that the eye can only per- ceive a dim continuous glimmer. 29. We find the largest stars scattered very irregularly, but if we look at the smaller ones, we find that they gradually increase in number as their position approaches the portion of the sky occupied by the Milky Way. In fact, of the 20,000,000 stars visible, as we have stated, in powerful telescopes, at least 18,000,000 lie in and near the Milky Way. This fact must be well borne in mind. 30. Adding this fact to what has been said about the distances of the stars, we can now determine the shape of our stellar system. It is clear that it is most extended where the faintest stars are visible, and where they appear nearest together ; because they appear faint in conse- quence of.their distance, and. because their close packing does not arise from Iheir actual nearness to each other, but results from their lying in that direction at constantly increasing distances. Indeed, the stars which give rise to the appearance of the Milky Way, because in that part of the heavens they lie behind each other to an almost infinite distance, are probably as far from each other as our sun is from the nearest star. 31. The MUky Way, then; indicates to us, and traces ASTRONOMY. [chap. I. for us, the direction in which the system has its largest dimensions; the absence of faint stars in the parts of the sky furthest from the Milky Way shows us that the limits of our system in that direction are much sooner reached than in the direction of the Milky Way itself. We gather, therefore, that its thickness is small compared with its length and breadth. This flat stratum of stars is split, as we might split a round piece of thick cardboard, in those regions where we see the Milky Way divided into two branches, and here its edge is double. Our sun is situated near the point at which the mass of stars begins to divide itself into two portions ; and, as there are more stars on the south side of the Milky Way than there are on the north, we gather that our earth occupies a position somewhat to the north of the middle of its thickness. 32. But although the Milky Way thus enables us to get a rough idea of the shape of our system as we might get a rough idea of the shape of a wood from some point within it by seeing in which direction the trees appeared densest and thickest together, and in which direction it was most easy to pierce its limits, still what the telescope teaches us shows that its boundaries are most probably very irregular. 33. The MageUanic Clouds, called the Nubecula Major and Nubecula Minor, visible in the southern hemisphere, are two cloudy oval masses of light, and are very like portions of the Milky Way, but they are apparently unconnected with its general structure. Lesson II. — The Constellations. Movements of the Stars, Movements of our Sun. 34. We have in the last lesson considered our star- system as a whole ; we have discussed its dimensions, and given an idea of its shape. Before we proceed with a CHAP. I.] THE STARS AND NEBULA. detailed examination of the stars of which it is composed, it will be convenient to state the groupings into which they have been arranged, and the way in which any particular star may be referred to. 35. The stars then, from the remotest antiquity, have been distributed into groups called constellations, each constellation being fancifully named after some object which the arrangement of the stars composing it was thought to suggest. 36. The first formal classification is due to Ptolemy of Alexandria, who about the year 1 50 A.D., arranged the 1,022 stars observed by Hipparchus, the father of astronomy, at Rhodes, about one century before our era. His catalogue contains 48 constellations ; two were added by Tycho Brahe, and to these 50 (called the ancient) constellations have been added, in more modern times, 59, carrying the number up to 109. . 37. The names of the ancient constellations and of the more important of the modern ones are as follows, begin- ning witla those through which the sun passes in his annual round ; these are called the zodiacal constellations (very carefully to be distinguished, as we shall see further on (Art. 361), from the signs of the zodiac bearing the same names). In English and in rhyme these are as under : " The Ram, the Bull, the Heavenly Twins, And next the Crab, the Lion shines, The Virgin and the Scales, The Scorpion, Archer, and He-goat, The Man that bears the watering-pot. And Fish with ghttering tails." And in Latin they run thus : " Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces." 38- The constellations visible above the zodiacal con- 14 ASTRONOMY. [chap. I. stellations, called the northern constellations, are as follows : Ursa Major. Ursa Minor. Draco. Cepheus. Bootes. Corona Borealis. Hercules. Lyra. Cygnus. Cassiopea. Perseus. Auriga. Serpentarius. Serpens. Sagitta. Aquila. Delphinus. Hquuleus. Pegasus. Andromeda. Triangulum. Camelopardalis. Canes Venatici. Vulpecula et Ans^r. Cor Caroli. The Great Bear (The Plough). The Little Bear. The Dragon. Cepheus. Bootes. The Northern Crown. Hercules. The Lyre. The Swan. Cassiopea (The Lady's Chair). Perseus. The Waggoner. The Serpent Bearer. The Serpent. The Arrow. . The Eagle. The Dolphin. The Little Horse. The Winged Horse. Andromeda. The Triangle. The Cameleopard. The Hunting Dogs. The Fox and the Goose. Charles' Heart. 39. The constellations visible below the zodiacal ones, called the southern constellations, are : Cetus. The Whale. Orion. Orion. Eridanus. The River Eridanus. Lepus. The Hare. Canis Major. The Great Dog. Canis Minor. The Little Dog. CHAt. I.] THE STARS AND NEBULA. 15 Argo Navis. The Ship Argo. Hydra. The Snake. Crater. The Cup. Corvus. The Crow. Centaurus. The Centaur. L7ipus. The Wolf. Ara. The Altar. Corona Australis. The Southern Crown. Piscis Australis. The Southern Fish. Monoceros. The Unicorn. Coluniba Noachi. Noah's Dove. Crux Australis. The Southern Cross. 40. The whole heavens, then, being portioned out into these constellations, the next thing to be done was to in- vent some method of referring to each particular star. The method finally adopted and now in use is to arrange all the stars in each constellation in the order of brightness, and to attach to them in that order the letters of the Greek alphabet, using after the letters the genitive of the Latin name of the constellation. Thus Alpha (a) Lyrce denotes the brightest star in the Lyre ; u UrscE Minoris, the brightest star in the Little Bear. Some of the brightest stars are still called by the Arabian or other names they were known by in former times, thus, a Lyra: is known also as Vega, a Bodtis as Arcturus, fi- Orionis as Rigel, a Ursa Minoris as Polaris (the Pole star), &c. 41. All the constellations, and the positions of the prin- cipal stars, have been accurately laid down in Star-Maps and on Celestial Globes. With one or other of these the reader should at once make himself familiar. In star- maps the stars are laid down as we actually see them in the heavens, looking at them from the earth ; but in globes their positions are reversed, as the earth, on which the spectator is placed, is supposed to occupy the centre of the globe, while we really look at the globe from the outside. Consequently the positions of the stars are i6 ASTRONOMY. [chap. i. reversed. So if we suppose two stars, the brighter one of them to the right in the heavens, the brighter one will be shown to the right of the other on a star-map, but to the left of it on a globe. 42. The twenty brightest stars in the heavens, or first magnitude stars, are as follows: they are given in the order of brightness and should be found on a map or globe. Sirius, in the constellation Canis Major. Canopus, ,, Argo. Alpha Centauri, „ Centaur. Arcturus, ,, Bootes. Rigel, Orion. Capelia. Auriga. Vega, Lyra. Procyon, ,, Canis Minor. Betelgeuse, ,, Orion. Achernar, , , Eridanus. Aldebaran, ,, Taurus. Beta Centau-i, ,, Centaur. Alpha Cnicis, „ Crux. An tares, ,, Scorpio. Atair, ,, Aquila. Spica, „ Virgo. Fomalhaut, ,, Piscis Australis. Beta Crucis, ,, Crux. Pollux, Gemini. Regulus, „ Leo. 43- Now, although the stars, and the various constel- lations, retain the same relative positions as they did in ancient times, all the stars are, nevertheless, in motion ; and in some of them nearest to us, this motion, called proper motion, is very apparent, and it has been measured. Thus Arcturus is travelling at the rate of at least fifty-four miles a second, or three times faster than our Earth travels round the sun, which is one thousand times faster than an ordinary railway train. 44.. Nor is our Sun, which be it remembered is a star, an exception ; it is approaching the constellation Hercules at the rate of four miles in a second, carrying its system of planets, including our Earth, with it. Here, then, we CHAP. 1.] THE STARS AND NEBULAE. have an additional cause for a gradual change in the positions of the stars, for a reason we shall readily under- stand, if, when we walk along a gas-lit street, we notice the distant lamps. We shall find that the lamps we leave behind close up, and those in front of us open out as we approach them : in fact, the stars which our system is approaching are, generally speaking, slowly opening out, while those we are quitting are closing up, as our distance from them is increasing. We say " generally speaking," for it is found that the opening out and closing of the stars is not near so regular as that of the gas-lights, because all the stars themselves are moving about in different directions ; but, by taking a large number of stars, their own motions counteract each other, and we can tell that we are moving just as well as if we were on a ship sailing amongst a number of others in motion in different directions. 4.5. The real motions of the stars, — called as we have seen, their proper motions, — and the one we have just pointed out, however, are to be gathered only from the most careful observation, made with the most accurate in- struments. There are apparent motions, which may be detected in half an hour by the most careless observer. 46. These apparent motions are caused, as we shall fully explain by and by (Chap. IV.), by the two real motions of the Earth, first lound its own axis, and secondly round the Sun. Lesson III. — Double and Multiple Stars. Variable Stars. 4-7. A careful examination of the stars with powerful telescopes, reveals to us the most startling and beautiful appearances. Some stars which appear single to the unassisted eye, appear double, triple, or quadruple ; and in some instances the number of stars revolving round c iS ASTRONOMY. [chap. i. a centre common to all is even greater. Because our Sun is an isolated star, and because the planets are now dark bodies, instead of shining, like the Sun, by their own light, as they once must have done, it is difficult, at first, to realize such phenomena, but they are among the most firmly established facts of modern astronomy. A beautiful star in the constellation of the Lyre will at once give an idea of such a system, and of the use of the telescope in these inquiries. The star in question is Epsilon (e) Lyrae, and to the naked eye appears as a faint single star. A small telescope, or opera-glass even, suffices to show it double, and a powerful instrument reveals the fact that each star com- posing this double is itself double ; hence it is known as "the Double-double." Here, then, we have a system of four suns, each pair, considered by Fig. i.-Orbit of a Double Star, itself, revolving round a point situated between them ; while the two pairs considered as two single stars, perform a much larger journey round a point situated between them. (See Fig. 2.) It may be stated roundly that the wider pair will com- plete a revolution in 2,000 years ; the closer one in half that time ; and possibly both double systems may revolve round the point lying between them in something less than a million of years.' 48. Nearly 12,000 double stars are now known, and in about 600 of these orbital motion has been ascertained the motion in some cases being very rapid. In some cases the brilliancy of the component stars is nearly equal but in others the light is very unequal. For instance a first magnitude star may have a companion of the four- teenth magnitude. Sirius has, at least, one very faint * Admiral Smyth. CHAP. I.] THE STARS AND NEBULA. 19 companion. Here is a list of some double stars, showing the time in which a complete revolution is effected : Years. Zeta (f) Herculis 35 Eta (ri) Corona Borealis 42 Sirius . .... 49^ Zeta (0 Cancri 62 Alpha (a) Centauri ... . . . S8i Gatnma (7) Corona Borealis 95 Ome^a {a) Leonis in Delta (d) Cygni 336 Gamma (y) Leonis 403 61 Cygni 783 49. Here, then, there can be no doubt that the stars are connected, and such pairs are caWeA physical couples, to distinguish them from the optical couples, in which the component stars are really distant from each other, and have no real con- nexion ; their apparent near- ness to each other being an appearance caused by their ,-,.■, \. • u.. Fig. 2.— The Double-double Star lymg m the same straight ;„ ^^e constellation Lyra. .. As line, as seen from the Earth, seen in an opera-glass. «. As seen so. Where the distance of !" ^ ^^i" telescope 3. As seen ... J T_ 1 .. • in a telescope of great power. a physical double star is known, we can determine the dimensions of the orbit of one star round the other, as we can determine the Earth's orbit round the sun. Thus we know that the distance between the two stars of 61 Cygni is 5,658,000,000 miles, and yet the two stars seem as one to the naked eye. 51. The stars are not only of different magnitudes (Art. 22), but the brilliancy of some particular stars changes ' c 2 ASTRONOMY. [chap. I. from time to time. If the variation in the light is, as it is generally, slow, regular, and within certain limits, stars in which this is noticed are called variable stars, or shortly, variables. In some cases, however, the increase and decrease have been sudden, and in others the limits of change have been unknown ; and hence we read of new stars, lost stars, and temporary stars, in addition to the more regular variables. In some cases of variability the effect is produced by increase of light accompanied by higher temperature, in others we have only obscuration. 52. The variation is, of course, measured by the different magnitudes of the stars at different times, and the amount of variability is measured by the extreme magnitudes. T\x& period of the variability is generally the time that elapses between two successive greatest brightnesses. 53. We give a table of a few variable stars, in order that the foregoing may be clearly understood : rj Argils . R Cephei . R Cassiopea . o Ceti . . . /3 Lyrtz S Cancri ^ Persei . . U Cephei . . .Change of Magnitude front to . I . • 5 ' . 6 . I or 2 ■ 3i . 8 . . 2i. • 7 • Period of Change . . 7i . about 70 years. . . II . . {lower than \ H J 10 . 4i. . 12 . 4 9 • 73 „ 425 days 333 „ 13 „ 9l ,, 2i „ St is a very interesting one. S4. The fourth star on our lis and a picture of its changes is given in Fig. 3. At its period of greatest brightness it sometimes nearly reaches the first magnitude, sometimes stops at the fifth, while at minima it falls below the ninth magnitude. Among the acknowledged variables however /3 Persei is perhaps the most interesting, as its period is so short, and, unlike CHAP. I 1 THE STARS AND NEBULA. o Ceti — (called also Mira, or the Marvellous) — it is never invisible to the naked eye. The star in question shines as a star of the second magnitude for two days, thir- teen hours and a half, and then suddenly loses its light and in three hours and a half falls to the fourth magnitude ; its brilhancy then increases again, and in another period ASTRONOMY. [chap. i. of three hours and a half it re-attains its greatest bright- ness — all the changes being accomplished in less than three days. 55. Among the new, or temporary stars, those ob- served in 1572, 1866, 1876, and 1885, are the most noticeable. The first appeared suddenly in the sky and was visible for seventeen months ; its light at first was equal to that of the planets at their greatest brilliancy ; so bright was it, indeed, that it was clearly visible at noonday. It was long admitted without inquiry, on the unsupported asser- tion of an old writer named Leowitz, that in the years 945 and 1264 something similar had been observed in the same region of the sky (in Cassiopeia) in which this star appeared. But if we explain all these phenomena by the presence of a long-period variable star which is very bright at its maximum and fades out of view at its mini- mum, a reappearance of the star about the year 1880 might have been expected. Since this did not occur, the two earlier outbursts may the more readily be supposed apocrj'phal. 56. Wenow come tothe««TO.f^a/'of i866,intheconstel- lation of Corona Borealis, T, which was observed with much minuteness and with powerful methods of research not employed before. This star had been recorded some years previously as one of the ninth magnitude. On the 12th of May, 1866, however, it suddenly flashed up as a star of the second magnitude. On the 14th it had descended to the third magnitude ; the decrease of brightness was for some time at the rate of about half a magnitude a day, but became less rapid towards the end of May. There is every reason to believe that this increased brilliancy was due to the sudden collision of one swarm of meteorites with another, a very high temperature and evolution of hydrogen being produced by the collisions. S6(a). A similar apparition took place in the constellation Cygnus on the 24th of November, 1 876. In this instance the CHAP. I.] THE STARS AND NEBUL/E. 23 existence of the star had never been recorded until an abrupt accession of light raised it to the third magnitude. It can now be discerned only by the most powerful telescopes. Stranger still was the outburst of a new star near the very heart of the great nebula in Andromeda. 24 ASTRONOMY. [chap. I. When first perceived, August 17, 1885, it was of ninth magnitude, but had brightened to the seventh by August ■ ■■■■BI BiMllil 30, after which it declined in a few months to apparent extinction. A close parallel to this phenomenon was found in a brief stellar blaze observed in a nebula in CHAP. I.] THE STARS AND NEBULAE. Scorpio (numbered 80 in Messier's Catalogue) on the 2 1 St of May, i860. A supposed "new star" seen near tiae star Chi (x) Orionis, December 13, 1885, proves to be a variable of the '' Mira " type, since it reached a second maximum after 364 days, December 12, 1886. In neither 26 ASTRONOMY. [chap. i. of these two most recent cases was there the same evidence of gaseous incandescence as in the stars of 1866 and 1876. 57. The question of variable stars is one of the most interesting in the whole domain of astronomy. Prof. Pickering divides them into five classes, viz. 1. Temporary stars. 2. Stars markedly variable in long periods, such as Mira and Chi (x) Cygni. 3. Stars exhibiting slight fluctuations according to laws not yet recognised. Alpha Orionis and Alpha Cassiopeise are among the better known examples, but in Dr. Gould's opinion, there are few stars which do not partake more or less of this character. 4. Stars continuously and regularly variable in periods of a few days. A good specimen of this class is Beta ((3) Lyrse, of which the " light-curve " is traced in Fig. 4. The period of this remarkable star is thirteen days, during which it descends to two unequal minima, and twice resumes its original brightness of nearly third magnitude. 5. Stars discontinuously variable in very short periods. That is to say, they shine quite steadily except during one regularly recurrent interval of a few hours, during which they rapidly lose, and as rapidly regain, a large proportion of their light. To this class belong eight known stars, of which (/3; Persei, or Algol, is the most conspicuous. 58. There are various different causes at work to pro- duce these various effects. Such outbursts as those of T Coronse and Nova Cygni are occasioned by the vivid incandescence not of a sunlike body, since such a body would take hot a few weeks or months, but some millions of years to cool down again to its primitive state of comparative obscurity, while the extreme rapidity of their observed decline will be seen by a glance at Fig. 5. Effects of this kind are produced by an encounter be- tween two meteor swarms. 59. Recent investigations have shown that most of the variable stars are uncondensed meteorite-swarms, although CHAP. I] THE STARS AND NEBULAE. 27 the swarms are not so sparse as in nebuls. In the variables of regular period the variations are due to cometic swarms of meteorites moving around a bright or Fig. 7.— Plan and section of the orbit of the companion of Algol. dark body, the maximum occurring at periaetron, that is, when the swarm is nearest to the centre of the uncon- 28 ASTRONOMY. [chap. i. densed or condensed mass. In that case, the velocity is greater and the collisions more violent, so that there is more light given out. As regards the Algol class of variables. Prof. Pickering's investigations strongly countenance the hypothesis of par- tial eclipses at each revolution by a large dark satellite. In Fig. 6 the changes observed in the light of Algol are gra- phically represented ; in Fig. 7 the orbit of the obscure companion the interposition of which produces those changes, first as seen from the earth, then projected in its own plane. In the case of another member of the same class, U Cephei (included in our list of variables), Pickering has shown that there must be a total eclipse by a partially luminous body, whereas the companion of Algol is alto- gether dark. This view is borne out by the reddening of the light of U Cephei at minima, as if by transmission through the absorbing atmosphere of another sunlike mass. Lesson W .-—Coloured Stars. Apparent Size. The Structure of the Stars. Clusters of Stars. 60. The stars shine out with variously coloured lights ; thus we have scarlet stars, red stars, blue and green stars, and indeed stars so diversified in hue that ob- servers attempt in vain to define them, so completely do they shade into one another. Among large stars, Aldebaran, Antares, and Betelgeuse are unmistakably tinged with red ; Sirius, Vega and Spica are of a bluish white ; Arcturus, Capella, Procyon, and Dubhe in the Great Bear, show a yellow hue like that of our Sun. 61. In double and multiple stars, however, we meet with the most striking colours and contrasts ; Iota (i) Cancri, and Gamma (y) Anciromedce, may be instanced. In Eta (rj) Cassiopeim we find a large white star with a rich ruddy purple companion. Some stars occur of a red colour, almost as deep as that of blood. What CHAP. I.] THE STARS AND NEBUL/E. 29 wondrous colouring must be met with in the planets lit up by these glorious suns, especially in those belonging to the compound systems, one sun setting, say in clearest green, another rising in purple or yellow or crimson ; at times two suns at Once mingling their variously coloured beams ! A remarkable group in the Southern Cross pro- duced on Sir John Herschel "the effect of a superb piece of fancy jewellery." It is composed of over 100 stars, seven of which only exceed the tenth magnitude ; among these, two are red, two green, three pale green, and one greenish blue. 62. The colours of the stars also change. The ancients called Sirius a red star, but then the habit was to observe it near the horizon. There are some striking differences between Sir William Herschel's observations on the colours of double stars and those of more recent observers. 63. In some variable stars the changes of colours observed are very striking. In the new star of 1572, Tycho Brahe observed changes from white to yellow, and then to rod ; and we may add that generally when the brightness decreases the star becomes redder. 64. The size or diameter of the stars cannot be deter- mined by our most powerful instruments ; but we know that, as seen from the Earth, they are, in consequence of their distance, mere points of light, so small as to be beyond all our most delicate measurements. The Moon, which travels very slowly across the sky, sometimes (as we shall see by and by) gets before, or ^f/z'/j^ j, ox occults, some of them ; but they vanish in a moment — which they would not do if they were not as small as we have stated. 65. We will now pass on to what is known of the physical constitution of the stars. Recent researches have led to the conclusion that stars, and all other self- luminous bodies in the universe, consist of swarms of meteorites in various stages of condensation. The luminosity is due to the heat produced by collisions. 30 ASTRONOMY. [chap. i. Some of the meteor-swarms are sparse, and consequently the number of collisions will be small, and very little light will be given out. As the swarm contracts the number of collisions will increase, and more light will be given out. After further contraction, the temperature of the swarm will be so high that the meteorites will become a mass of vapour, similar to that composing the sun. The highest stage of temperature is represented by such stars as Vega (a Lyrse). The subsequent cool- ing of such a mass of vapour will produce bodies of a different order — instead of meteorites scattered through a mass of vapour, there will be a densely gaseous, liquid, or solid nucleus, surrounded by an absorbing atmosphere, the composition of which will vary with the degree of cooling. There will be a considerable difference be- tween an uncondensed swarm, and a condensed one at an equal mean temperature. The temperature of the former will be increasing, whilst that of the latter will be decreasing. 66. The vapours in a swarm will depend upon the temperature. Thus, while magnesium and manganese are driven off at the temperature of the Bunsen burner, the iron is only driven off at a very high tempera- ture. While ice melts at o° C, iron only melts at 2000° C. : the heat required to produce iron-vapour is not known. 67. The temperatures of the various celestial bodies can only be estimated by careful consideration of their spectra, and even then, in many cases, we have to be con- tent with relative temperatures. While some of them are no hotter than a Bunsen burner, others are at tempera- tures far beyond our powers of measurement. The various orders of celestial bodies have been arranged in groups, such that the members of each group are at nearly equal temperatures and in similar states of condensation. (See Art. 504a). Plate I. Stae-Clusters. I. The Cluster of Hercules. ■^. The Crab Cluster. CHAP. I.] THE STARS AND NEBUL/C. 33 68. The colour of a celestial body will depend upon the state of condensation of the meteor-swarm of which it is composed. In the sparse swarms the colour is almost entirely dependent upon radiation. In closer swarms, absorption will affect the colour ; light from the meteorites will be absorbed by the vapours surrounding them. A green glass is green because it absorbs all other light but the green ; and so on with glasses, solids, vapours, or liquids of other colours. Our Sun at setting seems sometimes blood-red, in consequence of the ab- sorption of our atmosphere ; if the absorption were in his own atmosphere, he would be blood-red at noon- day. The white stars are the hottest, the yellow ones are cooler, and the red ones are not much hotter than a Bunsen burner. 69. The elements already recognised in celestial bodies are those which are known to exist in meteorites. Those seen in the coolest bodies are those constituents of meteorites which are volatilised at lowest temperatures. 70. Having now dealt with the peculiarities of indi- vidual stars, — that is to say, their distance, arrangement, colour, variability, and structure, — we next come to the various assemblages or companies of stars observed in various parts of the heavens. 71. In the double and multiple systems (Art. 47) we saw the first beginnings of the tendency of the stars to group themselves together. In some parts of our system this tendency is exhibited in a very remarkable manner, the beautiful group of the Pleiades affording a familiar instance. The six or seven stars visible to the naked eye become 60 or 70 when viewed with a telescope of moderate power, while no less than 1,421 have recently been photo- graphed. The Hyades, in the constellation Taurus, and the Preesepe, or " Beehive,'' in Cancer, may also be mentioned. In other cases the groups consist of an in- numerable number of suns apparently closely packed together. That in the constellation Perseus is among the D 34 ASTRONOMY. [chap r. most beautiful objects in the heavens ; but many others, scarcely less stupendous, though much fainter by reason of their greater distance, are revealed by the telescope. 72. Assemblages of stars are divided" into ; — 1. IrregTilar groups, generally more or less visible to the naked eye. 2. Star-clusters, invisible to the naked eye, but which, in the most powerful telescopes, are seen to consist of separate stars. These are subdivided into ordinary clusters and globular clusters. 73. Clusters and nebute are designated by their num- ber in the catalogues which have been inade of them by different astronomers. The most important of these catalogues have been made by Messier, Sir William Herschel, and Sir John Herschel. A catalogue published by the latter in 1864 contains 5,079 objects, and the num- ber was brought up to 6,251 by Dr. Dreyer in 1877. 74.. We have already given some examples of star groups. The magnificent star-clusters, in the constel- lations Hercules, Libra, and Aquarius, may be instanced as among those which are best seen in moderate telescopes ; but some of the clusters which lie out of our universe, and which we must regard as other universes, are at such immeasurable distances, and are therefore so faint, that in the most powerful telescopes the real shape and boun- dary are not seen, and there is a gradual fading away at the edge, the last traces of which apperr either as a luminous mist, or as cloud-like filaments, which become finer till they cease altogether to be seen. The Dumb- Bell cluster, in Vulpecula, and the Crab cluster, in iTaurus, both of which have been resolved into stars, are instances of this. CHAP. I.] THE STARS AND NEBUL/E. 35 75. In some of these star-clusters the increase of bright- ness from the edge to the centre is so rapid that it would appear that the stars are actually nearer together at the centre than they are near the edge of the cluster ; in fact, that there is a real condensation towards the centre. Lesson V .— Nebula. Classification attd Description. 76. We now come to the Nebnise. "Nebula" is a Latin word signifying a cloud, and for this reason the name has been given to everything which appeared cloud- like to the naked eye or in a telescope. The group in Perseus, for instance, appears like a nebula to the naked eye ; in the smallest telescope, however, it is separated into stars. 77. Every time a telescope larger than any formerly used has been made use of, however, numbers of wh.it were till then called nebute, and about which as nebute nothing was known, have been found to be nothing but * star-clusters, some of them of very remarkable forms, so distant that even in telescopes of great power they could not be resolved, — that is to say, could not be separated into distinct stars. 78. Now, this is what has happened ever since the dis- covery of telescopes. Hence it was thought by some that all the so-called nebulffi were, in reality, nothing but distant star-clusters. 79. One of the most important discoveries of modern times, however, has furnished evidence of a fact, — long ago conjectured by some astronomers, — namely, that some of the nebulae are something different from masses of stars, and that the cloud-like appearance is due to something else besides their distance and the still comparatively small optical means one can at present bring to bear upon them. ASTRONOMY. [chap. r. 80. This discovery, however, has not yet led to an exhaustive re-arrangement of nebulae according to their intrinsic nature. Thus their classification is still based upon telescopic appearance, real nebute being as yet imperfectly sorted out from those which, by reason of their great distance, appear like nebulae. 81. By nebute, then, we understand all objects formerly classed as such, which up to this time have not been resolved into stars. They may be divided into the following classes: — 1. — Irregular neliulse. 2. — Ring nebulae and Elliptical nebulae. 3. — Spiral, or Whirlpool nebulae. 4. — Planetary nebulae. 5. — Nebulae surrounding stars. 82. Some of the irregular nebulse — those in the constellations Orion and Andromeda, for example — are visible to the naked eye on a dark night. 83. The great nebula of Orion is situated in the part of the constellation occupied by the sword-handle and sur- rounding the multiple-star Theta iff). The nebulosity near the stars is flocculent, and of a greenish white tinge. There seems no doubt that the shape of this nebula and the position of its brightest portions are changing. One part of it appears, in a powerful telescope, startlingly like the head of a fish. On this account it has been termed the Fish-mouth nebula. 84. Two other fine irregular nebulae are visible in the Southern hemisphere : one is in the constellation Dorado, the other surrounds Eta (?;) Argus, The latter occupies a space equal to about five times the apparent area of the Moon. 85. We have classed the ring-nebulae and elliptical nebulas together because probably the latter are, in several instances, ring-nebute looked at sideways. The finest Plata /I. Nebula,. I. The Nebula in Orion. 2. Spiral Nebula in Canes Venaiici. CHAP. I.] THE STARS AND NEBULA. 39 ring nebula is the 57th in Messier's catalogue (written 57 M. for short). It is in the constellation Lyra. The finest elliptical nebula is the one in Andromeda to which we have before referred. This nebula, the 31st of Messier's catalogue (31 M.) when viewed in large instruments, shows several curious black streaks running in the direc- tion in which the nebula is longest. 86. The spiral or whirlpool nebulse are repre- sented by that in the constellation of Canes Venatici (51 M.). In an ordinary telescope this presents the ap- pearance of two globular clusters, one of them surrounded by a ring at a considerable distance, the ring varying in brightness, and being divided into two in a part of its length. But in a larger instrument the appearance is en- tirely changed. The ring turns into a spiral coil of nebulous matter, and the outlying mass is seen connected with the main mass by a curved band. 33 M. Pisciura, and 99 M. Virginis, are other examples of this strange phenomenon, which indicate to us the action of stupendous forces of a kind unknown in our own universe. 87. The fourth class, or planetary nebulae, were so named by Sir William Herschel, as they shine with a planetary and often bluish light, and are circular or slightly elliptical in form. 97 M. Ursse Majoris and 46 M. Argias may be taken as specimens. 88. We come lastly to the nebulas surrounding stars, or nebulous stars. The stars thus surrounded are apparently like all other stars, save in the fact of the presence of the appendage ; nor does the nebulosity give any signs of being resolvable with our present telescopes. Iota (i) Orionis, Epsilon (f) Orionis, 8 Canum Venati- corum, and 79 M. Ursse Majoris, belong to this class. 40 ASTRONOMY. [chap. i. Lesson VI. — Nebula (continued). Their Faintness. Variable Nebula. Distribution in Space. Their Structure. Nebular Hypothesis. 89. Having stated and described the several classes into which nebulae may be divided, their general features and structure have next to be considered. 90. Like the stars, they are of different brightnesses, but as yet they have not been divided into magnitudes. This, however, has been done in a manner by determining what is termed the space-penetrating power or light-grasping power of the telescope powerful enough to render them visible. Thus supposing nebute to con- sist of masses of stars, it has been estimated that Lord Rosse's great Reflector, the most powerful instrument as yet used in such inquiries, penetrates 500 times further into space than the naked eye can ; that is, can detect a nebula or cluster 500 times further off than a star of the sixth magnitude. 91. Now, if we suppose that a sixth magnitude star is 12 times further off than a star of the first magnitude- — and this is within the mark — and that, as we have seen in Art. 27, light requires 120 years to reach us from such a star, the telescope we have referred to penetrates so pro- foundly into space that no star can escape its scrutiny " unless at a remoteness that would occupy light in over spanning it sixty thousand years." 92. An idea of the extreme faintness of the more dis- tant nebulae may be gathered from the fact, that the light of some of those visible in a moderately-large instrument has been estimated to vary from fj'ga to ijoJoQ °f the light of a single sperm candle consuming 158 grains of material per hour, viewed at the distance of a quarter of a mile; that is, such a candle a quarter of CHAP. 1.] THE STARS AND NEBULA. 41 a mile off is 20,000 times more brilliant than the nebula ! ' 93. The phenomenon of variable, lost, new, and tempo- rary stars has its equivalent in the case of the nebulse, the lig-ht of which, it has been lately discovered, is in some cases subject to great variations. 94. In 1861 it was found that a small nebula, dis- covered in 1 852 in Taurus, near a star of the tenth magni- tude, had disappeared, the star also becoming dimmer. In the next year the nebula increased in brightness again ; but was completely invisible 1877 — 1880. There is, be- sides, strong evidence of the periodical variability of two nebulas — one situated in Cetus, the other in Virgo. 95. In Art. 30 the marked character of the distribution of the stars of our universe, giving rise to the appearance of the Milky Way, was pointed out. The distribution of the nebulse, however, is very different ; in general they lie out of the Milky Way, so that they are either less con- densed there, or the visible universe (as distinguished from our own stellar one) is less extended in that direction. They are most numerous in a zone which crosses the Milky Way at right angles, the constellation Virgo being so rich in them that a portion of it is termed the nebulous region of Virgo. In fact, not only is the Milky Way the poorest in nebulae, but the parts of the heavens furthest away from it are richest. 96. We now come to the question. What is a Nebula ? The answer is — A true nebula consists of a sparse swarm of meteorites, the luminosity of which is due to the heat produced by collisions. The interspaces are partly filled with hydrogen and magnesium and other vapours, which are volatilised out of the meteorites. Amongst true nebute, are the great nebula in Orion, that surrounding Eta (tj) Argus ; the ring nebula in Lyra, and all ' Huggins. 42 ASTRONOMY. [chap, i planetary nebulas. The Andrfimeda nebula, on the other hand, seems to be of a stellar nature. 97. When, therefore, we see, in what we loiowl to be a true nebula, closely associated points of lights we must not regard the appearance as an indication of resolvability into true stars. These luminous points, in some nebulae at least, must be looked upon as probably denser aggregations of the meteorites composing the nebulae. 98. The nebular bypothesis supposed that all the countless bodies which are distributed through space once existed in the condition of gaseous matter, but recent researches have shown that all of them have their origin in meteorites. According to this view, a nebula is to be regarded as a future star, for, by the gradual contraction of the mass which will be produced by gravitation, the collisions between the meteorites will become more numerous and violent, and the nebula will get hotter and brighter, first forming a star of Group II., then of Group III., and, if hot enough, of Group IV. During the subse- quent cooling, it will become a star of Group V., then of Group VI., and finally it will become a cold body like a planet. (See Arts. 65 and 504a.) It may take long years to prove, or disprove, this hypothesis ; but the tendency of recent observations assuredly is to show its correct- Flatcin CHAPTER II. THE SUN. Lesson VII. — Its relative Brightness, its Size, Distance, and Weight. 99. We will now consider the star nearest to us — the Sun, which dazzles the whole family of planets by its brightness, supports their inhabitants by its heat, and keeps them in bounds by its weight. 100. The relative brilliancy of the centre of our system, compared to that of the stars, is, as we saw in Art. 23, so great that it is difficult at first to look upon it as in any way related to those feeble twinklers. This difficulty, however, is soon dispelled when we consider how near it is to us. Thus, to give another instance, though we receive 20,000,000,000 times more light from the Sun than we do from Alpha (a) Lyrce, that star is more than a million times further from us. There is reason to believe, indeed, that our Sun is, after all, by no means a large star compared with others ; for if we assume that the light given out by Sirius, for instance, is no more brilliant than is our sunshine, that star would be equal in bulk to nearly 600 suns. 101. Astronomers now know the distance of the Sun from the Earth. It is about 93,000,000 miles : and it is easy, therefore, as we shall see by and by (Chap. VIII.), to determine its size : and here again, as in the case of the 44 ASTRONOMY. [chap. ii. distances of the stars, we arrive at figures which convey scarcely any ideas to the mind. The distance from one side of the Sun to the other, through its centre — or, in other words, the diameter of the Sun, — is 867,000 miles. Were there a railway round our earth, a train, going at the rate of 30 miles an hour, would accomplish the journey in a month : a railway journey round the Sun, going at the same rate, would require more than ten years. In this way we may also obtain the best idea of the Sun's distance from us — a distance travelled over by light in eight and a third minutes. A train going at the speed we have named, and starting on the 1st of January, 1887, would not arrive at the Sun till past the middle of the year 2,240 ! 102. Such then are the distance and size of the centre of our system. If we represent the Sun by a globe about two feet in diameter, a pea at the distance of 215 feet will represent the Earth ; and let us add, the nearest fixed star would be represented by a similar globe placed at the distance of 1 1 ,000 miles. 103. More than 1,300,000 Earths, as commonly stated, would be required to make one Sun. This is expressed by saying that the volomQ of the Sun is 1,300,000 times greater than that of the Earth : but the statement takes into account only the globe bounded by the photosphere. The atmosphere of the Sun, however, extends to fully half a million of miles from its surface ; and this space may well be included in our estimate of its volume. We find then on this view, that the Sun is more than thirteen million times as large as the Earth, while it only weighs 330,000 times as much. That is, bulk for bulk, thirteen million, but by mass or weight 330,000 Earths would go to make up the Sun. The matter composing the Sun and its immediate appendages is then, on the average, only ^ as dense as the matter composing the Earth, or less than one seventh as dense as water. So that we are fully justified in asserting the Sun to be a mainly gaseous body ; though the enormous compression must produce, below the photo- ciiAr. II.] THE SUN. 45 sphere, a consistence very different from what we ordinarily associate with a gas. 104. The Sun, hke the Earth or a top when spinning, turns round, or rotates, on an axis ; this rotation was discovered by observing the spots on its surface, about which we shall have much to say in the next Lesson. It is found that the spots always make their first appearance on the same side of the Sun ; that they travel across it in about fourteen days ; and that they then disappear on the other side. This is not all : if they be observed September. December. March. Fig. 8. — Position cf the Sun's axis, and apparent paths of the spots across the disc, as seen from the Earth at different times of the year. The arrows show the direction in wliich the Sun turns round. The inclination of the Sun's axis is exaggerated, so that the effect it produces may be more clearly seen. in June, they go straight across the sun's face or disc with a dip downwards ; if in September, they then cross in a curve ; while in December they go straight across again, with a dip upwards ; and in March their paths are again curved, this time with the curve in the opposite direction. 105. Now it is important that we make this perfectly clear. We know that the Earth goes round the Sun once a year. It has been found also that its path is so level — that is, to say, the Earth in its journey does not go up or down, but always straight on— that we might almost imagine the earth floating round the Sun on a boundless 46 ASTRONOMY. [chap. n. ocean, both Sun and Earth being half immersed in it. We shall see further on that this level— this plane— called the Fig. 9- — Curve showing the period of rotation of the photosphere in different latitudes north and south from Carrington's observations ; 851' of -solar longitude per diem = rate of rotation in lat. 15° N. The vertical lines represent differences of lo' of longitude ■+■ to the right. - to the left, of the line cutting the curve in lat. 15° N. plane of the Ecliptic — is used by Astronomers in precisely CHAP. 11.] THE SUK. 47 the same way as we commonly use the sea level. We say, for instance, that such a mountain is so high above the level of the sea. Astronomers say that such a star is so high above the plane of the ecliptic. 106. Well then, we have imagined the Earth and Sun to be floating in an ocean up to the middle — which is the ^ '- ''''^'^^^^^H^^^l '^^-'^^^^^^H "^t '^^'I^^^^^H ;:. 5D ^ FlG.io. — Copy of part of a photograph taken at Dehra Dun in 1884, showing a sun-spot passing over the Sun's edge. meaning of half immersed. Now, if the Sun were quite upright, the spots would always seem at the same distance above the level of our ocean. But this we have not found to be the case. From two opposite points of the Earth's path (the points it occupies in June and December) the spots are seen to describe straight lines across the disc, while midway between these points (September and March) their paths are observed to be sharply curved, in one case 48 ASTRONOMY. [chap. n. with the convex side downwards, in the other with the convex side upwards. A moment's thought will show that these appearances can only arise from a dipping down of the Sun's axis of rotation. Now this we find to be the case. The Sun's axis inclines towards the point occupied by the Earth in September. When we come to deal with the Earth and the other planets, we shall find that their axes also incline in different directions. 107. It has been found that the spots, besides having an apparent motion, caused by their being carried round by the Sun in its rotation, have a motion of their own. This proper motion, as distinguished from their apparent motion, has recently been investigated in the most com- plete manner by Mr. Carrington. What he has dis- covered shows that there need be no wonder that different observers have varied so greatly in the time they have assigned to the Sun's rotation. As we have already shown (Art. 104), this rotation has been deduced from the time taken by the spots to cross the disc ; but it now seems that all sun-spots have a movement of their own, and that the rapidity of this movement varies regularly with their distance from the solar equator, — that is, the region half-way between the two poles of rotation. In fact, the spots near the equator travel faster t han those away from it (Fig. 9), so that if we take an equatorial spot we shall say that the Sun rotates in about twenty-five days ; and if we take one situated half-way between the equator and the poles, in either hemisphere, we shall say that it rotates in twenty-seven and a half days. 108. We have now considered the distance and size of the Sun ; we have found that it, like our Earth, rotates on its axis, and we have determined the direction in which the axis points. We must next try to learn something of its appearance and of its nature, or, as it is called, its physical constitution. Here we confess at once that our knowledge on this subject is not yet complete. This, however, is little to be wondered at. We have done so CHAP. II.] THE SUN. 49 much, and gleaned so many facts, at distances the very statement of which is ahiiost meaningless to us, so stupen- dous are they, that we forget that our mighty Sun, in spite of its brilliant shining and fostering heat, is still some 93,000,000 miles removed ; — that its diameter is 100 times that of our Earth ; and that the chasm we call a sun-spot is yet large enough to swallow us up, and half a dozen of our sister planets besides ; while, if we employ the finest telescope, we can only observe the various phenomena as we should do with the naked eye at a distance of 180,000 miles. To look at the Sun through a telescope, without proper appliances, is a very dangerous affair. Several astro- nomers have lost their eyesight by so doing, and our readers should not use even the smallest telescope without proper guidance. Lesson VIII. — Telescopic Appearance of the Sim-spots. Penumbra., Umbra, Nucleus, FaculcE, Granules. Red Flames. 109. We have already said that the first things which strike us on the Sun's surface, when we look at it with a powerful telescope, are the spots. In Plate IV. we give drawings of a very fine one, visible on the Sun in 1865. We shall often refer to them in the following description. The spots are not scattered all over the Sun's disc, but are generally limited to those parts of it a little above and below the Sun's equator, which is represented by the middle lines in Fig. 8. The arrows show the direction in which the spots, carried round by the Sun's rotation, appear to travel across the disc. 110. The spots float, as it were, in what, as we have already seen in the case of the stars, is called the photo- sphere ; the half-shade shown in the spot is called the peuniubra (that is, half shade) ; inside the penumbra is a still darker shade, called the umbra, and inside this E 50 ASTRONOMY. [chaf. ii. again is the nucleus. Diagrams 3 and 4 of Plate IV. will render this perfectly clear. The white surface repre- sents the photosphere ; the half tones the penumbra ; the dark, irregular central portions the umbra ; and the blackest parts in the centre of these dark portions, the nucleus. 111. Sun-spots are cavities, or hollows, eaten into the photosphere, and these different shades represent different depths. Their occasional appear- ance as notches on the Sun's limb, or edge (as shown in Fig. 4), renders this absolutely certain. 112. Diligent observation of the umbra and penumbra, with powerful instruments, reveals to us the fact that change is going on incessantly in the region of the spots. Sometimes changes are noticed, after the lapse of an hour even : here a portion of the penumbra is seen setting sail across the umbra ; here a portion of the umbra is melting from sight ; here, again, an evident change of position and direction in masses which retain their form. The enormous changes, e.\tending ever tens of thousands of square miles of the Sun's surface, which took place in the great sun-spot of 1865, are shown in Plate IV. 113. Near the edge of the solar disc, and especially about spots approaching the edge, it is quite easy, even with a small telescope, to discern certain very bright streaks of diversified form, quite distinct in outline, and either entirely separate or uniting in various ways into ridges and network. These appearances, which have been termed faculse, are the most brilliant parts of the Sun. Where, near the edge, the spots become invisible, undu- lated shining ridges still indicate their place — being more remarkable thereabout than elsewhere, though everywhere traceable in good observing weather. Faculae may be of all magnitudes, from hardly visible, softly-gleaming, narrow tracts 1,000 miles long, to continuous compli- cated and heapy ridges 40,000 miles and more in length, and 1,000 to 4;COO miles broad. Ridges of this kind Plate IV. 1 ■^ '^felP^" &^ Sun-spots (the great Sun-spot of 1865). I Thespotentering the Sun's disk Oct. 7th (foreshortened view). 2. Oct. 10th. 3. Oct. 14th ; central view, showing the formation of a bridge, and the nucleus. 4. .Oct. i6th. E 2 CHAP. II.] THE SUN. 53 often surround a spot, and hence appear the more con- spicuous ; such a ridge is shown in Fig. I, Plate IV. ; but sometimes there appears a very broad white platform round the spot, and from this the white crumpled ridges pass in various directions. 114. So much for the more salient phenomena of the Sun's surface, which we can study with our telescopes. There is much more, however, to be inquired into ; and here we may remark that the Sun himself has bestowed a great boon upon observational Astronomy ; and, whether brightly shining or hid in dim echpse, now tells his own story, and prints his image in all parts of the world on a retina which never forgets, and is withal so sensitive as to receive, in a small fraction of a second, impressions of more exact detail than could be made out by hours of scrutiny with a powerful telescope. 115. We may begin by saying, that the whole surface of the Sun, except those portions occupied by the spots, is more or less finely mo iUed ; as, indeed, may be seen with no very large amount of optical power. The general arrangement of this mot- tling comes out very plainly in some photographs of the Sun lately taken by Dr. Janssen at the Meudon C b- servatory near Paris. They ^/ show blurred patches Cir- Fig. n— Part of a Sun-spit. ^,,^^r~^^:u^A u,^ „ u.,4- .........^ " Willow .leaves " detaching them- Cumscnbed by what seem selves from the penumbra. Avery like currents of fine, distinct faint one at F. granulation. This curious appearance is known as the " photospheric network." The luminous masses between the dusky marblings present an irregularly rounded form : they have been variously called "nodules," "floccules," "rice grains," "granules or granulations," and so on. lie. The word "willow-leaf" very well paints the 54 ASTRONOMY. [chap. n. appearance of the minute details sometimes observed in the penumbrse of spots, which occasionally are made up apparently of elongated masses of unequal brightness, so arranged that for the most part they point like so many arrows to the centre of the nucleus, giving to the penumbra a radiated appearance. At other times and occasionally in the same spot, the jagged edge of the penumbra pro- jecting over the nucleus has caused the interior edge of the penumbra to be likened to coarse thatching with straw. 117. There are darker or shaded portions between the granules, often pretty thickly covered with dark dots, like stippling with a soft lead-pencil ; these are what were called "pores," or "incipient openings," by Sir William Herschel. They are sometimes almost black, and are like excessively small spots. 118. When the Sun is totally eclipsed, — that is, as will be explained by and by, when the Moon comes exactly between the Earth and the Sun, — other appearances are unfolded to us, which the extreme brightness of the Sun prevents our observing under ordinary circumstances : the Sun' s atmosphere is seen to contain red masses of fan- tastic shapes, some of them quite disconnected from the Sun ; to these the names of "red-flames" and "promi- nences " have been given. These are the higher waves of the more vivid portions of a solar envelope, from 5,000 to 10,000 miles in height, called the Chromosphere, which overlies the photosphere, and is composed chiefly of hydrogen, and an unknown gas named "helium." Outside the chromosphere lies the coronal atmosphere of the Sun, extending to an undetermined, and perhaps variable distance. On these appearances we shall say a word or two further on when we come to deal with Eclipses. CHAP. II.] THE SUN. 55 Lesson IX. — Explanation of the Appearances on the Sun's Surface. The Sun's Light and Heat. Sun-force. The Past and Future of the Sun. 119. We are now familiar with the appearances presented to us on the Sun's surface in a powerful telescope. Let us see if we can account for them. As the spots break out and close up with great rapidity, as changes both on a large and small scale are always going on on the surface, we can only infer that the photosphere of the Sun, and therefore of the stars, is of a cloudy nature ; but while our clouds are made up of particles of water, the clouds on the Sun must be composed of particles of various metals and other substances in a state of intense heat —how hot we shall see by and by. The photosphere is surrounded by an atmosphere composed of the vapours of the bodies which are incandescent in the photosphere. It seems also, that not only is the visible surface of the Sun en- tirely of a cloudy nature, but that the atmosphere is a highly absorptive one. Moreover its absorption chiefly affects the blue, or more refrangible end of the spectrum, so that, if it were removed, sunlight would be very much bluer than it actually- is. 119 a. Faculae reach high up into this atmosphere, and consequently escape some of its absorption. This ac- counts for their brilliancy, and also for their increased conspicuousness (as shown in Plate IV.) near the edge of the Sun, where they are thrown into relief by a greater depth of atmosphere. Faculae really consist of the bright granules, or " domes " of the Sun's mottled surface, heaped up together, or arranged in certain directions. Though by no means confined to the vicinity of spots, they are closely associated with them. Their development, however, is always subsequent to that of spots, and they appear pre- dominantly on their left-hand borders. They exist on a 56 ASTRONOMY. [chap. ii. vast scale. It is quite common to see reaches of them tens of thousands of miles long, lasting for days or even weeks. The more minute features of the solar surface — the granules — are most probably the dome-like tops of the smaller masses of the clouds, bright for the same reason that the faculse are bright, but to a less degree ; and the i-A^ Fig. 12. — Sun-Fpot showing details of the penumbra. The dark portion in the centre is the umbra, the surrounding half-tone is the penumbra, a, a bridge, or tongue or facula being carried over the umbra • b, clouds forming at the end ; c, part of the penumbra being driven over the spot (the domes are drawn out) ; d, domes on photosphere ; f, " thaich " on penumbra. fact that these granules lengthen out as they approach a spot and descend the slope of the penumbra, may possibly be accounted for by supposing them to be elongated by the current which causes their downrush into a spot, as the cilAP. II.] THE SUN. 57 clouds in our own sky are lengthened out when they are drawn into a current. 120. Some spots cover millions of square miles, and last for months ; others are only visible in powerful instruments, and are of very short duration. There is a great difference in the number of spots visible from time to time; indeed, there is a minimum period, when none are seen for weeks together, and a maximum period, when more are seen than at any other time. The interval between two maximum periods, or two minimum periods, is about eleven years. 121. Now, as the Sun is more energetic when he is covered with spots than when there are none, we may look upon him as a variable star, with a period of eleven years. This period most probably depends upon changes in the circulation of the Sun's atmosphere, and Mr. Balfour Stewart has suggested that it may be in some way modified by the action of the planets. It is also known that the magnetic needle has a period of the same length, its greatest oscillations occurring when there are most sun-spots. Auroras, and the currents of electricity which traverse the Earth's surface, are affected by a similar period. 122. The detailed spectroscopic examination of the Sun's surface and of his spots has afforded evidence of their being due to the absorption of the Sun's light by atmospheric layers of greater pressures than are at work in the other regions, A spot, we know, is a saucer-like depression in the photosphere. It is dark, because the de- pression is filled with comparatively cool, dense vapours which powerfully absorb light. These vapours have fallen from the upper regions of the Sun's atmosphere, so that each spot is the seat of a downrush, the answering uprush to which we see in faculEe and a certain kind of flames or prominences. Each " pore," too, is the visible effect of a descending current on a smaller scale. 123. We have before seen (Art. 67) what substances 5S ASTRONOMY. [chap. ii. exist in a state of incandescence in some of the stars. In the case of the Sun we are acquainted with a greater number. Here are tables based on the researches of Kirchhoff, Angstrom, Thalfen, and Lockyer, of the different substances, which, so far, have been traced in the Sun's atmosphere by means of their spectral lines. Table A. — Elements present in the Sun according to Kirchhoff, Angstrom, and Thalhi. Kirchhoff. Angstrom and 1 halen. Sodium Sodium Iron Iron Calcium Calcium Magnesium IVIagnesium Nickel Nickel Barium — Copper — Zinc — Chromium Cobalt Hydrogen Manganese Titanium Table B gives the substances which were added to the preceding list by taking a special consideration into account. Some time after the first work on the chemical composition of the solar atmosphere was accomplished, a method was introduced by which it was easy to determine the existence of a small quantity of any particular vapour in a mixture of vapours, so that the substances indicated in the second table are those substances which possibly exist in the sun's atmosphere in a small quantity only. CHAP. II.] THE SUN. 59 Table B. — Elements the Longest Lines of which coincide with Fraunhofer Lines. Certainly coincident. Probably coincident. Aluminium Indium Strontium Lithium Lead Rubidium Cadmium Caesium Cerium Bismuth Uranium Tin Potassium Silver Vanadium Glucinum Palladium Lanthanum Molybdenum Yttrium or Erbium It is, however, by no means certain that these vapours exist in the Sun just as we know them in the laboratory. There is, on the contrary, very strong evidence that, at the level of the photosphere, the heat is so tremendous as to drive them asunder into finer constituent particles than we have any terrestrial experience of. In this fact of "dis- sociation " is not unlikely to be found the key to many of the riddles of the solar constitution. 124, Now let us inquire into some of the benign in- fluences spread broadcast by the Sun. We all know that our Earth is lit up by its beams, and that we are warmed by its heat ; but this by no means exhausts its benefits, which we share in common with the other planets which gather round its hearth. 125. And first, as to its light. We have already com- pared its light with that which we receive from the stars, but that is merely its relative brightness; we want now to know its actual, or, as it is otherwise called, its intrinsic brightness. Now it is clear, at once, that no number of candles can rival this brightness ; let us therefore compare it with one of the brightest lights that 6o ASTRONOMY. [chap. ii. we know of^the lime-light. The lime-light proceeds from a ball of lime made intensely hot by a flame composed of a mixture of hydrogen and oxygen playing on it. It is so bright that we caimot look on it any more than we can look oh the Sun ; but if we place it in front of the Sun, and look at both through a dark glass, the lime-light, though so intensely bright, looks like a black spot. In fact. Sir John Herschel has found that the Sun gives out as much light as 146 lime-lights would do if each ball of lime were as large as the Sun and gave out light from all parts of its surface. 126. Then, as to the Sun's heat. The heat thrown out from every square yard of the Sun's surface is as great as that which would be produced by burning six tons of coal on it each hour. Now, we may take the surface of the Sun roughly at 2,284,000,000,000 square miles, and there are 3,097,600 square yards in each square mile. How many tons of coal must be burnt, therefore, in an hour, to represent the Sun's heat .' 127. But the Sun sends out, or radiates, its light and heat in all directions ; it is clear, therefore, that as our Earth is so small compared with the Sun, and is so far away from it, the light and heat the Earth can intercept is but a very small portion of the whole amount ; in fact, we only grasp the jaTuJcmnj''^ P^''' of it. That is to say, if we suppose the Sun's light and heat to be divided into two hundred and twenty- seven million parts, we only receive one of them. 128. But this is not all. There is something else be- sides light and heat in the Sun's rays, and to this some- thing we owe the fact that the Earth is clad with verdure ; that in the tropics, where the Sun shines always in its might, vegetable life is most luxuriant, and that with us the spring time, when the Sun regains its power, is marked by a new birth of flowers. There comes from the Sun, besides CHAP. II.] THE SUN. 6i its light and heat, another force, chemical force, which separates carbon from oxygen, and turns the gas which, were it to accumulate, would kill all men and animals, into the life of plants. Thus, then, does the Sun build up the vegetable world. 129. Now, let us think a little. The enormous engines which do the heavy work of the world ; the locomotives which take us so smoothly and rapidly across a whole continent ; the mail-packets which take us so safely across the broad ocean ; owe all their power to steam, and steam is produced by heating water by coal. We all know that coal is the remains of an ancient vegetation ; we have just seen that vegetation is the direct effect of the Sun's action. Hence, without the Sun's action in former times we should have had no coal. The heavy work of the world, therefore, is indirectly done by the Sun. 130. Now for the light work. Let us take man. To work a man must eat. Does he eat beef.'' On what was the animal which supplied the beef fed ? On grass. Does he eat bread.' What is bread.? Corn. In both these, and in all cases, we come back to vegetation, which is, as we have already seen, the direct effect of the Sun's action. Here again, then, we must confess that to the Sun is due man's power of work. All the world's work, therefore, with one trifling exception (tide-work, of which more presently,) is done by the Sun, and man himself, prince or peasant, is but a little engine, which directs merely the energy supplied by the Sun. 131. Will the Sun, then, keep up for ever a supply of this force ? It cannot, if it be not replenished, any more than a fire can be kept in unless we put on fuel ; any more than a man can work without food. At present, philoso- phers are ignorant of any means by which it is replenished. As, probably, there was a time when the Sun existed as matter diffused through infinite space, the coming together of which matter has stored up its heat, so, probably, there will come a time when the Sun, with all 62 ASTRONOMY. [chap. u. its planets welded into its mass, will roll, a cold, black ball, through infinite space.* 132. Such, then, is our Sun — the nearest star. Although some of the stars appear not to contain those elements which on the earth are most abundant, still we see that, on the whole, the stars differ from each other, and from our Sun, only by the lower order of differences of special modification, and not by the more important differences of distinct plans of structure. There is, there- fore, a probability that they fulfil an analogous purpose ; and are, like our Sun, surrounded with planets, which by their attraction they uphold, and by their radiation illu- minate and energise. As has been previously pointed out, the elements most widely diffused through the host of stars are some of those most closely connected with the constitution of the living organisms of our globe, including hydrogen, sodium, magnesium, and iron. The probable past and future of the Sun are, therefore, the probable past and future of every star in the firmament of heaven. * Sir W. Thomson. The So ir System. CHAPTER III. THE SOLAR SYSTEM. Lesson X. — General Description. Distances of the Planets from the StcH . Sizes of the Planets. The Satellites. Volume, Mass, arzd Density of the Planets. 133. From tile Sun we now pass to the system of bodies which revolve round it : and here, as elsewhere in the heavens, we come upon the greatest variety. We find planets — of which the Earth is one — differing greatly in size, and situated at various distances from the Sun. We find again a ring of little planets clustering in one part of the system ; these are called asteroids, or minor planets. We next come to systems of bodies like the comets, and meteors, or shooting-stars, or bolides, which a recent discovery has estabhshed to be connected phenomena. These bodies travel round the sun in orbits of all degrees of eccentricity. The systems of meteors are met by the Earth in her annual round, while some of the comets break in from all parts of space ; and then, passing round our Sun, rush back again. Besides these there is, according to some, although the point is a doubtful one, another ring which is rendered visible to us by the appearance called the Zodiacal Light, others holding that this light is located in the Earth's atmosphere. 64 ASTRONOMY. [chap. hi. 134. The Solar System, then, consists of the follow- ing:— Eight large Planets, as follow, in the order of distance from the Sun :* — 1. Mercury. 5. Jupiter. 2. Venus. 6. Saturn. 3. Earth. 7. Uranus. 4. Mars. 8. Neptune. Two hundred and seventy-tnro small Planets revolving round the Sun between the orbits of Mars and Jupiter. Their names are given in the Appendix. Comets and Meteoric bodies, which at times approach near the Earth's orbit, the latter occasionally reaching the Earth's surface. The Zodiacal Iiight. A ring of apparently nebu- lous matter, the exact nature and position of which in the system are not yet determined. 135. Let us begin by getting some general notions of this system. In the first place, all the planets travel round the Sun in the same direction, and that direction, looking down upon the system from the northern side of it, is in the opposite direction to that in which the hands of a clock or a. watch move. Secondly, the forms of the paths of all the planets and of many of the comets are elliptical, but some are very much more elliptical than others. 136. Next let the reader turn back to Article 105, in which we have attempted to give an idea of the plane of the Ecliptic. Now, the larger planets keep very nearly to this level, which is represented in the following figure. * A ninth planet, named Vulcan, has been suspected to revolve within the orbit of Mercury, but proof of its existence is stiil wanting. CHAP. III.] THE SOLAR SYSTEM. 6S Ftg. 13. — Section, or side view, of the plane of the Ecliptic, showing that the orbits of the large planets are nearly in the plane ; that the orbit of Pallas has the greatest dip or inclination to it ; and that the orbits of the comets are inclined to it in all directions. The Straight line we suppose to represent the Earth's orbit looked at edgeways, as we can look at a hoop edgeways. The others represent the orbits of some of the planets and of some of the comets seen edgeways in the same manner. The orbits of Mars, Jupiter, Saturn, Uranus, and Neptune lie so nearly in the plane of the ecliptic, that in our figure, the scale of which is very small, they tnay be supposed to lie in that plane. With some of the smaller planets and comets we see the case is very different. The latter especially plunge as it were down into the surface of our ideal sea, or plane of the ecliptic, in all directions, instead of floating on, or revolving in it. 137. Again, as we thus find planets travelling round the Sun, so also do we find other bodies travelling round some of the planets. These bodies are called Moons, or Satellites. The Earth, we know, has one Moon ; Mars has two; Jupiter four, Saturn eight, Uranus four, and Neptune, according to our present knowledge, one. 138. As we have before stated, all the planets revolve round the Sun in one direction, i.e. from west to east. They rotate, or turn on their axes and their satel- lites revolve in the same direction, with two exceptions, F 66 ASTRONOMY. [chap. iii. occurring at the outskirts of the system. The satellites both of Uranus and Neptune move froin east to west, and in planes widely different from that of the ecliptic. 139. Let us next inquire into the various distances of the planets from the Sun, bearing in mind, that as the orbits are elliptical, the planets are sometimes nearer to the Sun than at other times. This will be explained by and by ; in the meantime we may say, that the average or mean distances are as follow ; the times of revo- lution are also given : — Perl:d of revolution rounJ Distance in Miles. the Sun. D. H. M. Mercury 35,987,000 87 23 IS Venus 67,245,000 224 16 48 Earth 92,965,000 365 6 9 Mars 141,650,000 686 23 31 Jupiter 483,678,000 ■ 4332 14 n Saturn . 886,779,000 . 10759 5 16 Uranus • 1,783,383,000 . 30688 7 12 Neptune . • 2,794,000,000 . 60180 20 38 140. Let us next see what are the sizes of the different planets. Their diameters are as follow : — Diameter in Miles. Mercury 2,992 Venus 7,660 Earth 7,9i6 Mars 4,211 Jupiter 86,000 Saturn 70,500 Uranus 31,700 Neptune . . . . 34,500 14-1. We have before attempted to give an idea of the comparative sizes of the Earth and Sun, and of the dis- tance between them ; let us now complete the picture. Still CHAr. III.] THE SOLAR SYSTEM. 67 taking a globe about two feet in diameter to represent the Sun, Mercury will be represented by a grain of mustard-seed, revolving in a circle 164 feet in diameter for its orbit ; Venus, a pea, on a circle of 284 feet in diameter ; the Earth, also a pea, on a circle of 430 feet ; Mars, a rather large pin's head, on a circle of 654 feet ; the asteriods, grains of sand, in orbits of from 1,000 to 1,200 feet ; Jupiter, a moderate-sized orange, on a circle nearly half a mile across ; Saturn, a small orange, on a circle of four-fifths of a mile ; Uranus, a full-sized cherry, or small plum, upon the circumference of a circle more than a mile and a half; and Neptune, a good- sized plum, on a circle about two miles and a half in diameter.** 142. As the planets revolve round the Sun at vastly different distances, so do the satellites revolve round their primaries. Our solitary Moon courses round the Earth at a distance of 238,000 miles, and its journey is performed in a, month. The first satellite of the planet Saturn is at only just half this distance, and its journey is performed in less than a day. The first satellite of Uranus is about equally near, and requires about two days and a half The first satellite of Jupiter is about the same distance from that planet as our Moon is from us, and its revolution is accomplished in one and three- quarters of our days. The only satellite which takes a longer time to revolve round its primary than our Moon, is Japetus, the eighth satellite of Saturn. On the other hand, the inner satellite of Mars finishes its circuit in seven hours and thirty-nine minutes, revolving at a distance less than one-fortieth that of our Moon. We have seen above (Art. 140), that the diameter of the smallest planet- leaving the asteroids out of the question— is 2,992 miles. We find that among the satellites we have three bodies— the third and fourth satellites of Jupiter, and the sixth moon of Saturn — of greater dimensions than one of the * Sir John Herschel. F 2 68 ASTRONOMY. [chap. hi. large planets, Mercury, and nearly as large as another, Mars. It is not necessary in this place to give more details concerning the distances and sizes of the planets and satellites. A complete statement of them will be found in Tables II. and III. of the Appendix. 143. The relative distances of the planets from the Sun were known long before their absolute dis- tances — in the same way as we might know that one place was twice or three times as far away as another without knowing the exact distance of either. When once the distance of the Earth from the Sun was known, astro- nomers could easily iind the distance of all the rest from the Sun, and therefore from the Earth. Their sizes were next determined, for we need only to know the distance of a body and its apparent size, or the angle under which we see it, to determine its real dimensions. 144. In the case of a planet accompanied by satellites we can at once determine its weight, or mass, for a reason we shall state by and by (Chap. IX.) ; and when we have got its weight, having already obtained its size or volume, we can compare the density of the materials of which the planet is composed with those we are familiar with here ; having first also obtained experimentally the density of our own Earth. 145. Let us see what this word density means. To do this, let us compare platinum, the heaviest metal, with hydrogen, the lightest gas. The gas is, to speak roughly, a quarter of a million times lighter than the metal ; the gas is therefore the same number of times less dense : and if we had two planets of exactly the same size, one composed of platinum and the other of hydrogen, the latter would be a quarter of a million times less dense than the former. Now, if it seems absurd to talk of a hydrogen planet, we must remember that if the materials of which our system, including the Sun, is composed, once existed as a great nebulous mass extending far be- CHAP. III.] THE SOLAR SYSTEM. 69 yond the orbit of Neptune, as there is reason to believe, the mass must have been more than 200,000,000 times less dense than hydrogen! 14-6. Philosophers have found that the mean density of the Earth is a little more than five and a half times that of vv'ater, that is to say, our Earth is five and a half times heavier than it would be if it were made up of water. If we now compare the density of the other planets with it, we find that they almost regularly increase in density as we approach the Sun ; Mercury being the most dense ; Venus, the Earth, and Mars, having densities nearly alike, but less than that of Mercury ; while Saturn and Neptune are the least dense. 147. Here is a Table showing the volumes, masses, and densities, of the planets ; those of the Earth being taken as 100 : — Volume. Mass. Density Mercury . 6 7 ■ 121 Venus 90 n ■ 85 Earth . . 100 100 . 100 Mars 15 II . 74 Jupiter • 129,945 • 31,187 ■ 24 Saturn • 71,795 • 9,333 • 13 Uranus . 6,287 . 1,446 . 23 Neptune . • 8,430 . 1,686 20 t.8. To sura u D, then, our i irst general surve y of Solar System, we find it composed of planets, satellites, comets, and several rings or masses of meteoric bodies ; the planets, both large and small, revolving round the Sun in the same direction, the satellites revolving in a similar manner round the planets. We have learned the mean distances of the planets from the Sun, and we have compared the distances and times of revolution of some of the satellites. We have also seen that the volumes, masses, and densities of the various planets have been determined. There is still much more to be learnt, both 70 ASTRONOMY. [chap. hi. about the system generally, and the planets particularly ; but it will be best, before we proceed with our general examination, to inquire somewhat minutely into the move- ments and structure of the Earth on which we dwell. Lesson XI. — The Earth. Its Shape. Poles. Equator. Latitude and Longitude. Diameter. 149. As we took the Sun as a specimen of the stars, because it was the nearest star to us, and we could there- fore study it best, so now let us take our Earth, with which we should be familiar, as a specimen of the planets. 150. In the first place, we have learned that it is round. Had we no proof, yie. might have guessed this, because both Sun and Moon, and the planets observable in our telescopes, are round. But we have proof. The Moon, when eclipsed, enters the shadow thrown by the Earth ; and it is easy to see on such occasions, when the edge of the shadow is thrown on the bright Moon, that the shadow is circular. 151. Moreover, if we watch the ships putting out to sea, we lose first the hull, then the lower sails, until at last the highest parts of the masts disappear. Similarly, the sailor, when he sights land, first catches the tops of mountains, or other high objects, before he sees the beach or port. If the surface of the Earth were an extended plain, this would not happen ; we should see the nearest things and the biggest things best : but as it is, every point of the Earth's surface is the top, as it were, of a flattened dome ; such a dome therefore is interposed between us and every dis'.ant object. The inequalities of the land render this fact much less obvious on terra Jirma than on the surface of the sea. 152. On all sides of us we see a circle of land, or sea, or both, on which the sky seems to rest : this is called the sensible borizou. If we observe it from a little boat on CHAP. III.] THE SOLAR SYSTEM. 71 the sea, or from a plain, this circle is small ; but if we look out from the top of a ship's mast or from a hill, we find it largely increased — in fact, the higher we go the more is the horizon extended, always however retaining its circular form. Now, the sphere is the only figure ■w'hich, looked at from any external point, is bounded by a circle ; and as the horizons of all places are circular, the Earth is a sphere, or at all events nearly so. 153. The Earth is not only round, but it rotates, or turns round on an axis, as a top does when it is spinning ; and the names of north pole and south pole are given to those points on the Earth where the axis would come to the surface if it were a great iron rod instead of a mathematical line. Half-way between these two poles, there is an imaginary line running round the Earth, called the equator or equinoctial line. The line through the Earth's centre from pole to pole is called the polar diameter j the line through the Earth's centre, from any point in the equator to the opposite point, is called the equatorial diameter, and one of these, as we shall see, is longer than the other. 154. We owe to the ingenuity of a French philosopher, M. L6on Foucault, two experiments which render the Earth's rotation visible to the eye. For although, as we shall presently see, it is made evident by the apparent motion of the heavenly bodies arid the consequent suc- cession of day and night, we must not forget that these effects might be, and for long ages were thought to be, produced by a real motion of the Sun and stars round the Earth. The first method consists in allowing a heavy weight, suspended by a fine wire, to swing backwards and forwards like the pendulum of a clock. Now, if we move the beam or other object to which such a pendulum is suspended, we shall not alter the direction in which the pendulum swings, as it is more easy for the thread or wire, which supports the weight, to twist than for the heavy weight itself to alter its course or swing when once 72 ASTRONOMY. [chap. iii. in motion in any particular direction. Therefore, in the experiment, if the Earth were at rest, the swing of the pendulum would always be in the same direction with regard to the support and the surrounding objects, but would vary if the earth were in motion. 155. M. Foucault's pendulum was suspended from the dome of the Panthdon in Paris, and a fine point at the bottom of the weight was made to leave a mark in sand at each swing. The marks successively made in the sand showed that the plane of oscillation varied with regard to the building. Here, then, was a proof that the building, and therefore the Earth, moved. 156. Such a pendulum swinging at either pole would make a complete revolution in 24 hours, and would serve the purpose of a clock were a dial placed below it with the hours marked. As the Earth rotates at the north pole from west to east, the dial would appear to a spectator, carried like it round by the Earth, to move under the pendulum from west to east, while at the south pole the Earth and dial would travel from east to west ; midway between the poles, that is, at the equator, this effect, of course, is not noticed, as there the two motions in opposite directions meet. 157. The second method is based upon the fact, that when a body turns on a perfectly true and symmetrical axis, and is left to itself in such a manner that gravity is not brought into play, the axis maintains an invariable position ; so that if it be made to point to a star, which is a thing outside the Earth and not supposed to move, it will continue to point to it. A gyroscope is an instrument so made that a heavy wheel set into very rapid motion shall be able to rotate for a long period, and that all disturbing influences, the action of gravity among -them, are prevented. 158. Now, if the Earth were at rest, there would be no apparent change in the position of the axis, however long the wheel might continue to turn ; but if the Earth moves CHAP, in.] THE SOLAR SYSTEM. 73 and the axis remains at rest, there should be some differ- ence. Experiment proves that there is a difference, and just such a difference as is accounted for by the Earth's rotation. In fact, if we so arrange the gyroscope that the axis of its rotation points to a star, it will remain at rest with regard to the star, while it varies with regard to the Earth. This is proof positive that it is the Earth which rotates on its axis, and not the stars which revolve round it ; for if this were the case the axis of the gyroscope would remain invariable with regard to the Earth, and change its direction with regard to the star. 159. If we look at a terrestrial globe, we find that the equator is not the only line marked upon it. There are other lines parallel to the equator, — that is, lines which are at the same distance from the equator all round, — and other lines passing through both poles, and dividing the equator into so many equal parts. These lines are for the purpose of determining the exact position of a place upon the globe, and they are based upon the fact, that all circles are divided into 360 degrees (marked °), each degree into 60 minutes ('), and each minute into 60 seconds ("). 160. We have first the equator midway between the poles, so that from any part of the equator to either pole is one quarter round the Earth, or 90 degrees. On either side of the equator there are circles parallel to it ; that is to say, at the same distance from it all round, dividing the distance to the poles into equal parts. Now, it is necessary to give this distance from the equator some name. The term latitude has been chosen; north latitude from the equator towards the north pole ; south latitude from the equator towards the south pole. 161. This, however, is not sufficient to define the exact position of a place, it only defines the distance from the equator. This difficulty has been got over by fixing upon Greenwich, our principal astronomical observatory, and supposing a circle passing through the two poles and that place, and then reckoning east and west from the circle 74 ASTRONOMY. [chap. hi. as we reckon north and south from the equator. To this east and west reckoning the term lon^tude has been applied. 162. On the terrestrial globe we find what are termed parallels of latitude, and meridians of longitude, at every 10° or 15°. Besides these, at 23^° on either side of the equator, are the Tropics: the north one the tropic of Cancer, the southern one the tropic of Capricorn ; and at the same distance from either pole, we find the arctic and Antarctic circles. These lines divide the Earth's surface into five zones — one torrid, two temperate, and two firigid zones. 163. The distance along the axis of rotation, from pole to pole, through the Earth's centre, is shorter than the distance through the Earth's centre, from any one point in the equator to the opposite one. In other words, the diameter from pole to pole (the polar diameter) is shorter than the one in the plane of the equator (the equatorial diameter), and their lengths are as follows : — Feet. Equatorial diameter . . . 41,852,404 Polar diameter 41,709,790 Now turn these feet into miles : the difference after all is small ; still it proves that the Earth is not a sphere, but what is called an oblate spberoid. Lesson 'Kll..— The Earth's Movements. Rotation. Movement round the Sun. Succession of Day and Night. 164. The Earth turns on its axis, or polar diameter, in 23h. 56m. In this time we get the succession of day and night, which succession is due therefore to the Earth's rotation. Before we discuss this further we must return to another of the Earth's movements. We know CHAP. III.] THE SOLAR SYSTEM. 75 also that it goes round the Sun, and the time in which that revolution is effected we call a year. 16S. Let us now inquire into this movement round the Sun. We stated (Art. 135) that the planets travelled round the centre of the system in ellipses. We will here state the meaning of this. If the orbits were circular, the planet Fig. 14. — Showing the difference between a circle and ellipses of different eccentricities, and how they are constructed. would always be at the same distance from the Sun, as all the diameters of a circle are equal ; but an ellipse is a kind of flattened circle, and some parts of it are nearer the centre than others. 166. In Fig. 14 the outermost ring is a circle, which can be easily constructed with a pair of compasses, or by 76 ASTRONOMY. [chap. hi. sticking a pin into paper, throwing a loop over it, keeping the loop tight by means of a pencil, and letting the pencil travel round. The two inner rings are ellipses. It is seen at once that one is very like the circle, and the other un- like it. The points D E and F G are called the foci of the two ellipses, and the shape of the ellipse depends upon the distance these points are apart. We can see this for ourselves if we stick two pins in a piece of paper, pass a loop of cotton over them, tighten the cotton by means of a pencil, and, still keeping the. cotton tight, let the pencil mark the paper, as in the case of the circle. The pencil will draw an ellipse, the shape of which we may vary at pleasure (using the same loop) by altering the distance between the /oci. 167. Now the Sun does not occupy the centre of the ellipse described by the Earth, but one of the foci. It results from this, that the Earth is nearer the Sun at one time than another. When these two bodies are nearest together, we say the Earth is in perihelion.''^ When they are furthest apart, we say it is in apbelion. f Let us now make a sketch of the orbit of the Earth as we should see it if we could get a bird's-eye view of it, and determine the points the Earth occupies at different times of the year, and how it is presented to the Sun. 168. Now refer back to Art. io6, in which we spoke of the position of the Sun's axis. We found that the Sun was not floating uprightly in our sea, the plane of the ecliptic ; it was dipped down in a particular direction. So it is with our Earth. The Earth's axis is inclined in the same manner, but to a much greater extent. The direction of the inclination, as in the case of the Sun, is, roughly speaking, always the same. 169. We have then two completely distinct motions — one round the axis of rotation, which, roughly speaking, remains parallel to itself, performed in a day; — one * Trepii at or near to ; %Klos, the Sun. t anriit from, and %KiOS. CHAP. HI.] THE SOLAR SYSTEM. 77 round the Sun, performed in a year. To the former motion we owe tlie succession of day and night j to the latter, combined with the inchnation of the Earth's axis, we owe the seasons. 170. In Fig. 15 is given a bird's-eye view of the system. It shows the orbit of tlie Earth, and how the axis of tlie Fig. 15, — The Earth's path round the Sun. Eartli is inclined — the direction of the dip being such that on the 2 1 st of June the axis is directed towards the Sun, the inchnation being 235'. Now, if we bear in mind that the Earth is spinning round once in twenty-four hours, we shall immediately see how it is we get day and night. The Sun can only light up that half of 78 ASTRONOMY. [chap. hi. the Earth turned towards it ; consequently, at any moment, one half of our planet is in sunshine, the other in shade ; the rotation of the Earth bringing each part in succession from sunshine to shade. 171. But it will be asked, " How is it that the days and nights are not always equal ? " For a simple reason. In the first place, the days and nights are equal all over the world on the 22nd of March and the 22nd of September, which dates are called the vernal and autumnal equinoxes for that very reason — equinox being the Latin for equal night. But to make this clearer let us look at the small circle we have marked on the Earth — it is the arctic circle. Now let us suppose ourselves living in Greenland, just within that circle. What will happen ? At the spring equinos (it will be most convenient to follow the order of the year) we find that circle half in light and half in shade. One half of the twenty-four hours (the time of one rotation), therefore, will be spent in sunshine, the other in shade ; in other words, the day and night will be equal, as we before stated. Gradually, however, as we approach the summer solstice (going from left to right), we find the circle coming more and more into the light, in consequence of the inclination of the axis, until, when we arrive at the solstice, in spite of the Earth's rotation, we cannot get out of the light. At this time we see the midnight sun due north ! The Sun, in fact, does not set The solstice passed, we approach the autumnal equinox, when again we shall find the day and night equal, as we did at the vernal equinox. But when we come to the winter solstice, we get no more midnight suns ; as shown in the figure, all the circle is situated in the shaded portion ; hence, again in spite of the Earth's rotation, we cannot get out of the darkness, and we do not see the Sun even at noonday. 172. Now, these facts must be well thought of. If this be done there will be no difficulty in understanding how it is that at the poles (both north and south) the years CHAP. III.] THE SOLAR SYSTEM. 79 consist of one day of six months' duration, and one night of equal length. To comprehend our long summer days and short nights in England, we have only to take a part about half-way between the arctic circle and the equator, as marked on the plate, and reason in the same way as we did for Greenland. At the equator we shall find the day and night always equal. 173. Here is a Table showing the length of the longest days in different latitudes, from the equator to the poles. We see that the Earth's surface on either side the equator may be divided into two zones, in one of which the days and nights are measured by hours, and in the other by months : — Hours. 12 13 H IS i6 17 i8 '9 20 21 174. What we have said about the northern hemisphere applies equally to the southern one, but the diagram will not hold good, as the northern winter is the southern summer, and so on ; and moreover, if we could look upon our Earth's orbit from the other side, the direction of the motions would be reversed. The reader should construct a diagram for the southern hemisphere for himself. o (Equator) i6 44 . . . . 3° 48 . . . 41 24 . . 49 2 , . 54 31 S8 27 . 6i 19 63 23 ,. . 64 so . . . " Hours 65 48. . ... 22 66 21 . ■ 23 65 32 . . . . 24 Months 67 23 . . . . , . I 69 SI . ... 2 73 40. . ■ • 3 78 II . . . • 4 84 s . . . ■ • 5 90 (Pole) . 6 ■ _ ._i 8o ASTKONOMY. [chap. III. Lesson Xlll.— The Seasons. 175. So much, then, for the succession of day and night. The seasons next demand our attention. Now, the changes to which we inhabitants of the temperate zones are accustomed, the heat of summer, the cold of winter, the medium temperatures of spring and autumn, depend simply upon the height to which the Sun attains at midday. The proof of this lies in the facts that on the equator the Sun is never far from the zenith, and we have perpetual summer : near the poles, — that is, in the frigid zones, — the Sun never gets very high, and we have per- petual winter. How, then, are the changing seasons in the temperate zones caused? Fig. i6. — Explanation of the apparent altitude of the Sun, as seen from London, in summer and winter. 176. In Fig. 15 we were supposed to be looking down upon our system. We will now take a section from solstice to solstice through the Sun, in order that we may have a side view of it. Here, then, in Fig. 16, we have the Earth in two positions, and the Sun in the middle. On the left we have the winter solstice, where the axis of rotation is inclined away from the Sun to the greatest possible extent. On the right we have the summer sol- CHAP. III.] THE SOLAR SYSTEM. 8i stice, when the axis of rotation is indined towards the Sun to the greatest possible extent. The line ab in both represents the parallel of latitude passing through London. The dotted line from the centre through b shows the direction of the zenith — the direction in which our body points when we stand upright. We see that this line forms a larger angle with the line leading to Fig. 17. — The Earth, as seen from the Sun at the S-ummer Solstice (noon at London). the Sun, or the two lines open out wider, at the winter solstice, than they do at the summer one. Hence we see the Sun in winter at noon, low down, far from the zenith, while in summer we are glad to seek protection from his beams nearly overhead. The reader should now make a similar diagram to represent the position of the Sun at 82 ASTRONOMY. [chap. III. the equinoxes ;^he will find that the axis is not then in- clined either to or from the Sun, but sideways, the result being that the Sun itself is seen at the same distance from the point overhead in spring and autumn, and hence the temperature is nearly the same, though Nature ap- parently works very differently at these two seasons ; in one we have the sowing-time, in the other the fall of the leaf. Fig. i8.- -The Earth, as seen from the Sun at the Winter Solstice (noon at London). 177. Perhaps the Sun's action on the Earth, in giving rise to the seasons, will be rendered more clear by in- quiring how the Earth is presented to the Sun at the four seasons — that is, how the Earth would be seen by an observer situated in the Sun. First, then, for summer and winter. Figs. 1 7 and 1 8 represent the Earth as it would be seen from the Sun at noon in London, at the summer CHAP. III.] THE SOLAR SYSTEM. 83 and winter solstices. In the former, England is seen well down towards the centre of the disk, where the Sun is vertical, or overhead ; its rays are therefore most felt, and we enjoy our summer. In the latter, England is so near the northern edge of the disk that it cannot be properly represented in the figure. It is therefore furthest from the region where the Sun is overhead ; the Sun's rays are consequently feeble, and we have winter. Fig. 19. — The E^th, as seen from the Sun at the Vernal Equinox (noon at London). 178. In Figs. 19 and 20, representing the Earth at the two equinoxes, we see that the position of England, with regard to the centre of the disk, is the same — the only difference being that in the two figures the Earth's axis is inclined in different directions. Hence there is no differ- ence in temperature at these periods. 179. These figures should be well studied in connexion G 2 84 ASTRONOMY. [chap. III. with Fig. 15, and also with Art. 170, in which the cause of the succession of day and night is explained. All these drawings represent London on the meridian which passes through the centre of the illuminated side of the Earth. It must therefore be noon at that place, as noon is half-way between sunrise and sunset. All the places represented on the western border have the Sun rising upon them j all the Fig. 2o. — The Earth, as seen from the Sun at the Autumnal Equino.x. (noon at London). places on the eastern border have the Sun setting. As, therefore, at the same moment of absolute time we have the Sun rising at some places, overhead at others, and setting at others, we cannot have the same time, as measured by the Sun, at all places alike. 180. In fact, as the Earth, whose circumference is divided into 360° (Art. 159), turns round once in twenty- CHAP. Jli.] THE SOLAR SYSTEM. 85 four hours, the Sun appears to travel 1 5° in one hour from east to west. One degree of longitude, therefore, makes a difference of four minutes of time, and vice versa. Lesson XIV. — Structure of the Earth. The Earth's Crust. Interior Heat of the Earth. Cause of its Polar Compression. The Earth once a Star. 181. Having said so much of the motions of our Earth — we shall return to them in a subsequent Lesson — let us now turn to its structure, or physical constitution. We all of us are acquainted with the present appearr ance of our globe, how that its surface is here land, there water ; and that the land is, for the most part, covered with soil which permits of vegetation, the vegeta- tion varying according to the climate ; while in some places meadows and wood-clad slopes give way to rugged mountains, which rear their bare or ice-clad peaks to heaven. 182. Taking the Earth as it is, then, the first question that arises is. Was it always as it is at present? The answer given by Geology and Physical Geography, two of the kindred sciences of Astronomy, is that the Earth was not always as we now see it, and that for millions of years changes have been going on, and are going on still. 183. It has been found, that what is called the Barth's crust — that is, the outside of the Earth, as the peel is the outside of an orange — is composed of various rocks of different kinds and of different ages, all of them, how- ever, belonging to two great classes : — Class I, Rocks that have been deposited by water these are called stratified or sedimentary rocks. Class 11. Rocks that once were molten: these are called igneous rocks. 85 ASTRONOMY. [chap. m. 184. Now, the sedimentary rocks have not always existed, for when we come to examine them closely it is found that they are piled one over the other in suc- cessive layers : the newer rocks reposing upon the older ones. The order in which these rocks have been deposited by the sea is as follows : — List of Stratified Rocks. !( Alluvium. Upper \ Drift. I Crag. Lower Eocene. { Upper Cretaceous. Mesozoic, or Secondary .\ ^ ( Oolite. * Lower { Lias. Trias. Palseozoic, or Primary . Permian. Upper .J Carboniferous. )evonian. {Pel Ca De { Silurian. Lower \ Cambrian. Archaean. 185. That these beds have been deposited by water, and principally by the sea, is proved by the facts— first, that in their formation they resemble the beds being deposited by water at the present time ; and, secondly, that they nearly all contain the remains of fishes, reptiles, and shell-fish in great abundance — indeed, some of the beds are composed almost entirely of the remains of animal life. 186. It must not be supposed that the stratified beds of which we have spoken are everywhere met with as they are shown in the table ; each bed could only have been CHAP. III.] THE SOLAR SYSTEM. 87 deposited on those parts of the Earth's crust which were under water at the time ; and since the earliest period of the Earth's history, earthqualces and changes of level have been at work, as they are at work now — but much more effectively, either because the changes were more decided and sudden, or because they were at work over immense periods of time. 187. It is found, indeed, that the sedimentary rocks have been upheaved and worn away again, bent, con- torted, or twisted to an enormous extent; instead of being horizontal, as they must have been when they were originally formed at the bottom of the sea. they are now seen in some cases upright, in others dome-shaped, over large areas. 188. Had this not been the case, the mineral riches of the Earth would for ever have been out of our reach, and the surface of the Earth would have been a monotonous plain. As it is, although it has been estimated that the thickness of the series of sedimentary rocks, if found complete in any one locality, would be 14 miles, each member of the series is found at the surface at some place or other. 189. The whole series of the sedimentary rocks, from the most ancient to the most modern, have been disturbed by eruptions of volcanic materials, similar to those thrown up by Vesuvius, and other volcanoes active in our own time, and by intrusions of rocks of igneous origin proceeding from below ; of which igneous rocks, granite, which in con- sequence of its great hardness is so largely used for paving and macadamizing our streets, may here be taken as one example out of many. These rocks are extremely easy to distinguish from the stratified ones, as they have no ap- pearance of stratification, contain no fossils, and their constituents are different, and are irregularly distributed throughout the mass. 190. If we strip the Earth, then, in imagination, of the sedimentary rocks, we come to a kernel of rock, the ASTRONOMY. [chap. in. constituents of which it is impossible to determine, but which may be imagined to be analogous to the older rocks of the granitic series, and to have been part of the original molten sphere, which must have been both hot and luminous, in the same way that molten iron is both hot and luminous. Doubtless there was a time when the surface of our earth was as hot and luminous as the surfaces of the sun and stars are still. 191. Now, suppose we have a red-hot cannon-ball ; what happens ? The ball gradually parts with, or radiates away, its heat, and gets cool, and as it cools it ceases to give out light ; but its centre remains hot long after the surface in contact with the air has cooled down. 192. So precisely has it been with our earth ; indeed, we have numerous proofs that the interior of the earth is at a high temperature at present, although its surface has cooled down. Our deepest mines are so hot that, without a perpetual current of cold fresh air, it would be impos- sible for the miners to live down them. There are hot springs coming from great depths, and the water which issues from them is, in some cases, at the boiling temper- ature — that is, 1 00° of the Centigrade thermometer. In the hot lava emitted from volcanoes we have evidence again of this interior heat, and how it is independent of that at the surface ; for among the most active volcanoes with which we are acP"ainted are Hecla in Iceland, and Mount Erebus in the midst of the icy deserts which surround the south pole. 193. It has been calculated that the temperature of the earth increases as we descend at the rate of 1° (Centigrade) in about thirty yards. We shall therefore have a temperature of— Centigrade. Miles. 100°, or the temperature of 1 . j ^, , ' , .,. ^^ > at a depth of . 2 boihng water ... J ^ CHAP. 111.] THE SOLAR SYSTEM. Centigrade. 400' .", or the temperature Of K^ a depth of . . . 7I red-hot iron ... J ^ } " 1,000°, or the temperature of melted glass . . . 1,500°, or the temperature at which everything with which we are acquainted would be in a state of fusion 18 28 194. If this be so, then the Earth's crust cannot exceed 28 miles in thickness — that is to say, the ^ j^th part of the radius (or of half the diameter), so that it is comparable to the shell of an egg. But this question is one on which there is much difference of opinion, some philosophers holding that the liquid matter is not continuous to the centre, but that, owing to the great pressure, the centre itself is solid. Evidence also has recently been brought forward to show that the Earth may be a solid or nearly solid globe from surface to centre. 195. The density of the Earth's crust is only about half of the mean density of the Earth taken as a whole. This has been accounted for by supposing that the mate- rials of which it is composed are made denser at great depths than at the surface, by the enormous pressure of the overlying mass ; but there are strong reasons for believing that the central portions are made up of much denser bodies, such as metals and their com- pounds, than are common at the surface. 196. It was prior to the solidification of its crust, and whUe the surface was in a soft or fluid condition, that the Earth put on its present flattened shape, the flattening being due to a bulging out at the equator, caused by the Earth's rotation. If we arrange a hoop, as shown in Fig. 21, and make it revolve very rapidly, we shall see go ASTRONOMY. [chap. III. that that part of the hoop furthest from the fixed points, and in which the motion is most rapid, bulges out as the Earth does at the equator. 197. The form of the Earth, moreover, is exactly that which any fluid mass would take under the same circum- stances. M. Plateau has proved this by placing a mass of oil in a transparent liquid exactly of the same density as the oil. As long as the oil was at rest it took .the form of a perfect sphere floating in the middle of the fluid, exactly as the Earth floats in space; but the momenta slow motion of rotation was given to the oil by means of Fig. zi. — Explanation of the spheroidal form of the Earth. a piece of wire forced through it, the spherical form was changed into a spheroidal one, like that of the Earth. 198. The tales told by geology, the still heated state of the Earth, and the shape of the Earth itself, all show that long ago the sphere was intensely heated, and fluid. Lesson XV.— The Earth {continued). The Atmosphere. Belts of Winds and Calms. The Action of Solar and Terrestrial Radiation. Clouds. Chemistry of the Earth. The Earth's Past and Future. 199. Having said so much of the Earth's crust, we must now, in order to fully consider our Earth as a planet, pass CHAP. III.] THE SOLAR SYSTEM. 91 on to the atmosphere, which may be Hkened to a great ocean, covering the Earth to a height which has not yet been exactly determined. This height is generally sup- posed to be 45 or 50 miles, but there is evidence to show that we have an atmosphere of some kind at a height of 400 or 500 miles. 200. The atmosphere, as we know, is the home of the winds and clouds, and it is with these especially that we have to do, in order to try to understand the appearances presented by the atmospheres of other planets. Although in any one place there seems no order in the production of winds and clouds, on the Earth treated as a whole we find the greatest regularity ; and we find, too, that the Sun's heat and the Earth's rotation are, in the main, the causes of all atmospheric disturbances. 201. If we examine a map showing the principal move- ments and conditions of the atmosphere, we shall find, belting the Earth along the equator, a belt of equatorial calms and rains- North of this we get a broad region, a belt of trade-winds, where the winds blow from the north-east ; to the south we find a similar belt, where the prevailing winds are south-east. Polewards from these belts to the north and south respectively lie the calms of Cancer and the calnxs of Capricorn. Still further towards the poles, we find the counter-trades, in regions where the winds blow from the equator to the poles : i.e. in the northern hemisphere they blow south and west, and in the southern hemisphere north and west ; and at the poles themselves we find a region of polar calms. 202. Now if the Earth did not rotate on its axis we should still get the trade-winds, but both systems would blow from the pole to the equator ; but as the Earth does rotate, the nearer the winds get to the equator the more rapidly is the Earth's surface whirled round underneath them ; the Earth, as it were, slips from under them in an easterly direction, and so the northern trade-winds appear to come from the north-east, and the southern ones 92 ASTRONOMY. [chap. in. from the south-east. Similarly, the counter-trades, which blow towards the poles, appear to come, the northern ones from the south-west and the southern ones from the north-west. The nearer they approach the poles the slower is the motion of the Earth under them, compared with the regions nearer the equator ; consequently, they are travelling to the eastward faster than the parallels at which they successively arrive, and they appear to come from the westward. 203. Now, how are these winds set in motion ? The tropics are the part of the Earth which is most heated, and, as a consequence, the air there has a tendency to ascend, and a surface-wind sets in towards the equator on both sides, to fill up the gap, as it were ; when it gets there it also is heated ; the two streams join and ascend, and flow as upper-currents towards either pole. Where the two streams meet in the region of equatorial calms some 4° or 5° broad, we have a cloud-belt, and daily rains. The counter-trades are the upper-currents referred to above, which in the regions beyond the calms of Cancer and Capricorn descend to the Earth's surface, and form surface-currents. 204. We see, therefore, that it is the Sun which sets all this atmospheric machinery in motion, by heating the equatorial regions of the Earth ; and as the Sun changes its position with regard to the equator, oscillating up and down in the course of the year, so do the calm-belts and trade-winds. The belt of equatorial calms follows the Sun northwards from January to July, when it reaches 25° N. lat. and then retreats, till at the next January it is in 25° S. lat. 205. So much for the Sun's direct action, and one of its effects on our rotating planet — the prevailing wind- currents, which are set in motion by the 22 70^000 P^-rt of the Sun's radiation into space, which represents an amount of heat that would daily raise 7,513 cubic miles of water from the freezing to the boiling point. CHAP. III.] THE SOLAR SYSTEM. 93 206. To the radiation from the Earth, combined with the existence of the vapour of water in the air, must be ascribed all the other atmospheric phenomena. Aqueous vapour is the great mother of clouds. When it is chilled by a cold wind or a mountain-top, it parts with its heat, is condensed, and forms a cloud ; and then mist, rain, snow, or hail, is formed : when it is heated by the direct action of the Sun, or by a current of warm air, it absorbs all the heat and expands, and the clouds disappear. 207. We now come to the materials of which our planet, including the Earth's crust and atmosphere, is composed. These are about 70 in number ; they are called the chemical elements,* and consist of : — Non-Metallic ( Nitrogen, o.xygen, chlorine, bromine, elements j J iodine, fluorine, silicon, boron, or I carbon, sulphur, selenium, tellurium, Metalloids. ( phosphorus, arsenic. Gaseous metal: — Hydrogen. Metals of the alkalies : — Potassium, sodium, cesium, rubidium, lithium. Metals of the alkaline earths : — Cal- cium, strontium, barium. Other metals : — Aluminium, zinc, iron, tin, tungsten, lead, silver, gold, &c. The elements which constitute the great mass of the Earth's crust are comparatively few — aluminium, calcium, carbon, chlorine, hydrogen, magnesium, oxygen, potas- sium, silicon, sodium, sulphur. Oxygen combines with many of these elements, and especially with the earthy and alkaline metals ; indeed, one-half of the ponderable matter of the exterior parts of the globe is composed of oxygen in a state of combination. Thus sandstone, the most common sedimentary rock, is composed of silica, which is a compound of silicon and oxygen, and is half * See Roscoe's "Elementary Chemistry," a volume in this series. Metallic elements 94 ASTRONOMY. [chap. hi. made up of the latter ; granite, a common igneous rock, composed of quartz, feldspar, and mica, is nearly half made up of oxygen in a state of combination in those substances. 20a. The chemical composition, by weight, of loo parts of the atmosphere at present is as follows : — Nitrogen 77 parts. Oxygen 23 „ Besides these two main constituents, we have — Carbonic acid . quantity variable with the locality. Aqueous vapour . quantity variable with the tem- perature and humidity. Ammonia ... a trace. We said at present, because, when the Earth was molten, the atmosphere must have been very different. We had, let us imagine, close to the still glowing crust — composed perhaps of acid silicates — a dense vapour, made up of compounds of the materials of the crust which were volatile only at a high temperature ; the vapour of chloride of sodium, or common salt, would be in large quantity ; above this, a zone of carbonic acid gas ; above this again, a zone of aqueous vapour, in the form of steam ; and lastly, the nitrogen and oxygen.* As the cooling went on, the lowest zone, composed of the vapour of salt, and other chlorides, would be con- densed on the crust, covering it with a layer of these sub- stances in a sohd state. Then it would be the turn of the steam to condense too, and form water ; it would fall on the layer of salt, which it would dissolve, and in time the oceans and seas would be formed, which would conse- quently be salt from the first moment of their appearance. Then, in addition to the oxygen and nitrogen which still remain, we should have the carbonic acid, which, in the * David Forbes, in the Geological Magazine^ vol. iv. p. 429. CHAP, in.] THE SOLAR SYSTEM, 95 course of long ages, was used up by its carbon going toform the luxuriant vegetation, the pressed remains of which is the coal which warms us, and does nearly all our work. 209. Now it is the presence of vapour in our lower atmosphere which renders life possible. When the surface of the Earth was hot enough to prevent the formation of the seas, as the water would be turned into steam again the instant it touched the surface, there could be no life. Again, if ever the surface of the Earth be cold enough to freeze all the water and all the gaseous vapour in the atmosphere, life — as we have it — would be equally im- possible. If this be true, all the Earth's history with which we are acquainted, from the dawn of life indicated in what geologists call the oldest rocks, down to our own time, and perhaps onwards for tens of thousands of years, is only the history of the Earth between the time at which its surface had got cold enough to allow steam to turn into ' water, and that at which its whole mass will be so cold that all the water on the surface, and all the vapour of water in the atmosphere, will be turned into ice. 210. The nebular hypothesis comes in here and shows us how, prior to the Earth being in a fluid state, it existed dissolved in a vast nebula, the parent of the Solar System ; how this nebula gradually contracted and condensed, throwing off the planets one by one ; and how the central portion of the nebula, condensed perhaps to the fluid state, exists at present as the glorious heat-giving Sun. Although, therefore, we know that stars give out light because they are white-hot bodies, and that planets are not self-luminous because they are comparatively cold bodies, we must not suppose that planets were always cold bodies, or that stars will always be white-hot bodies. Indeed, as we have shown, there is good reason for sup- posing that all the planets were once white-hot, and gave out light as the Sun does now. 96 ASTRONOMY. Tchap. m. Lesson XVI. — The Moon: its Size, Orbit, and Motions: its Physical Constitution. 211. Tlie Moon, as we have already seen, is one of the satellites, or secondary bodies ; and although it ap- pears to us at night to be so infinitely larger than the fixed stars and planets, it is a httle body of 2,160 miles in diameter ; so small is it, that 49 moons would be required to make one earth, 1,300,000 earths being required, as we have seen, to make one sun ! 212. Its apparent size, then, must be due to its near- ness. This we find to be the case. The Moon revolves round the Earth in an elliptic orbit, as the Earth revolves round the Sun, at an average distance of only 238,793 miles, which is equal to about 10 times round our planet. As the Moon's orbit is elliptical, she is sometimes nearer to us than at others. Her greatest and least distances are 251,947, and 225,719 miles : the difference is 26,228. When nearest us, of course she appears larger than at other times, and is said to be in perigee ( Trepi near, and yr\ the Earth) ; when most distant, she is said to be in apogee (lin-o'from, and 7^). 213. The Moon travels round the Earth in a period of 27d. 7h. 43m. I \\s. As we shall see presently, she requires more time to complete a revolution with respect to the Sun, which is called a lunar month, lunation, or synodic period. 214. The Moon, like the planets and the Sun, rotates on an axis ; but there is this peculiarity in the case of the Moon, namely, that her rotation and her revolution round the Earth are performed in equal times, that is, in 27d. 7h. 43m. Hence we only see one side of our satellite. But as the Moon's axis is inclined l" 32' to the plane of its orbit, we sometimes see the region round one pole, and sometimes the region round the other. This CHAP, in.] THE SOLAR SYSTEM. 97 is termed the libration in latitude. There are also a libration in longitude, arising from the fact, that though its rotation is uniform, its rate of motion round the Earth varies, so that we sometimes see more of the western edge and sometimes more of the eastern one ; and a daily libration, due to the Earth's rotation carrying the observer to the right and left of a line joining the centres of the Earth and Moon. When on the right of this Une, we see more of the right edge of the Moon ; when on the left, we see more of the left edge. 215. The plane in which the Moon performs her journey round the Earth is inclined 5° to the plane of the ecliptic, or the plane in which the Earth performs her journey round the Sun (Art. 105). The two points in which the Moon's orbit, or the orbit of any other celestial body, intersects the Earth's orbit, are called the nodes. The line joining these two points is called the line of nodes. The node at which the body passes to the north of the ecliptic is called the ascending node, the other the descending node. 216. The motions of the Moon, as we shall see by and by, are very complicated. We may get an idea of its path round the Sun if we imagine a wheel going along a road to have a pencil fixed to one of its spokes, so as to leave a trace on a wall : such a trace would consist of a series of curves with their concave sides downwards, and such is the Moon's path with regard to the Sun. 217. Besides the bright portion lit up by the Sun, we sometimes see, in the phases which immediately prece'de and follow the New Moon, that the obscure part is faintly visible. This appearance is called the "-Earth shine " {Luniett incinerosuyn, Lat. ; Licmiire cendrie, Fr.), and is due to that portion of the Moon reflecting to us the light it receives from the Earth. When this faint light is visible— when the "Old Moon" is seen in the " New Moon's arms " — the portion lit up by the Sun seems to belong to a larger moon than the other. This is an effect H 98 ASTRONOMY. [chap. in. of what is called irradiation, and is explained by the fact that a bright object makes a stronger impression on the eye than a dim one, and appears larger the brighter it is. 218. The average of four estimations gives the Moon's light as sjt'ji-j of that of the Sun, so we should want 547,513 full moons to give as much light as the Sun does ; and as there would not be room to place such a large number in the one-half of the sky which is visible to us, since the Moon covers ^tbWtt °^ ^^> ■' follows that the light from a sky full of moons would not be so bright as sunshine. 219. At rising or setting, the Moon sometimes appears to be larger than it does when high up in the sky. This is a delusion, and the reverse of the fact ; for, as the Earth is a sphere, we are really nearer the Moon by half the Earth's diameter when the part of the Earth on which we stand is underneath it ; as at moonrise or moonset we are situated, as it were, on the side of the Earth, half-way between the two points nearest to and most distant from the Moon. Let the reader draw a diagram, and reason this out. 220. Now a powerful telescope will magnify an object 1,000 times ; that is to say, it will enable us to see it as if it were a thousand times nearer than it is : if the Moon were 1,000 times nearer, it would be 240 miles off, con- sequently astronomers can see the Moon as if it were situated at a little less than that distance, since it is measured from centre to centre, and we look from surface to surface. In consequence of this comparative nearness, the whole of ^the surface of our satellite turned towards us has been studied and mapped with considerable accuracy. 221. With the naked eye we see that some parts of the Moon are much brighter than others ; there are dark patches, which, before large telescopes were in use, were thought to be, and were named. Oceans, Gulfs, and so on. The telescope shows us that these dark markings are smooth plains, and that the bright ones are ranges of mountains and hill country broken up in the most tremen- CHAP, III.] THE SOLAR SYSTEM. 99 dous manner by volcanoes of all sizes. A further study convinces us that the smooth plains are nothing but old sea-bottoms. In fact, once upon a time the surface of the Moon, like our Earth, was partly covered with water, and the land was broken up into hills and fertile valleys ; as on the Earth we have volcanoes, so did it once happen in the Moon, with the difiference that there the size of the volcanoes and the number and activity of them were far beyond anything we can imagine : Etna, the largest volcanic mountain in Europe, is a mere dwarf compared with many on the Moon. 222. The best way of seeing how the surface of our satellite is broken up in this manner, is to observe the terminator — the name given to the boundary between the lit-up and shaded portions : along this line the moun- tain peaks are lit up, while the depressions are in shade, and the shadows of the mountains are thrown the greatest distance on the illuminated portion. The heights of the mountains and depths of the craters have been measured by observing the shadows in this manner. 223. Besides the mountain-ranges and crater-moun- tains, there are also nailed plains, isolated peaks, and curious markings, called riUes. The principal ranges, craters, and walled plains have been named after distin- guished philosophers, astronomers, and travellers. 224. The diameter of the walled plain Schickard, near the south-east limb or edge of the Moon, is 133 miles. Clavius and Grimaldi have diameters of 142 and 138 miles respectively. Here is a table of the height of some of the peaks, with that of some of our terrestrial ones, for comparison : Feet. Dorfel . 26,691 Ramparts of f measured from the V 0-, Newton (. floor of the crater J ' ' ^' ^^ Eratosthenes (central cone) iS;7So Mont Blanc 15,870 Snowdon . 3,SOO H 2 ASTRONOMY. . [cHAr. ni. Beer and Madler have measured thirty-nine mountains higher than Mont Blanc. It must be recollected also ihat as the Moon is so much smaller than the Earth, the proportion of the height of a mountain to the diameter is much greater in the former. 225. As far as we know, with one or two very doubtful exceptions, the volcanoes are now all extinct ; the oceans have disappeared ; the valleys are no longer fertile ; nay, the very atmosphere has apparently left our satellite, and that little celestial body which probably was once the scene of various forms of life now no longer supports them. This may be accounted for by supposing (see Art. 191) that, on account of the small mass of the Moori, its original heat has all been radiated into space (as a bullet will take less time to get cold than a cannon-ball). 226. The rilles, of which nearly 1,000 are now known, are trenches with raised sides more or less steep. Besides the rilles, at full Moon, bright rays are seen, which seem to start from the more prominent mountains. Some of these rays are visible under all illuminations ; one, which, emanating from Tycho, crosses a crater on the north- east of Fracastorius, is not only distinctly visible when the terminator grazes the west edge of Fracastorius, but is even brighter as the terminator approaches it. Those emanating from Tycho are different in their character from those emanating from Copernicus, while those from Proclus form a third class. Mr. Nasmyth has been able to produce somewhat similar appearances on a glass globe by filling it with cold water, closing it up, and plunging it into warm water. This causes the inclosed cold water to expand very slowly, and the globe eventually bursts, its weakest point giving way, forming a centre of radiating cracks in a similar manner to the fissures, if they be fissures, in the Moon. 227. We say that the Moon has apparently no atmo-_ sphere : (i) because we never see any clouds there, and (2) because, when the Moon's motion causes it to travel LUNAR CRATERS COPERNICUS Plated. "" / r J '^ "ll^'Ul/i: '■■■■ vV^t W^." ^ , 3,0 5 O lO 20 3p «) CHAP, III.] THE SOLAR SYSTEM. loi over a star, or to occult it, as it is called, the star disap- pears at once, and does not seem to linger on the edge, as it would do if there were an atmosphere. 228. As the Moon rotates on her axis, as we do, only more slowly, the changes of day and night occur there as here ; but instead of being accomplished in 24 hours, the Moon's day is 29J of our days long, so that each portion of the surface is in turn exposed to, and shielded from, the Sun for a fortnight. Now it has been pointed out that if the Moon be absolutely devoid of atmosphere, its surface, undefended from the intense cold of space, could never, even under a vertical sun, rise above — 50° Fahrenheit ; in other words, would be always below the freezing-point of mercury. Some recent experiments, however, of a very delicate nature, seem to show that the temperature of the illuminated side of the Moon is not so excessively low, leading to the inference that a very thin lunar atmosphere does really exist. In Plate VI. we give a view of the crater Copernicus, one of the most prominent objects in the Moon. The details of the crater itself, and of its immediate neighbour- hood, represented in the drawing, reveal to us unmis- takable evidences of volcanic action. The floor of the crater is seen to be strewn over with rugged masses, while outside the crater-wall (which on the left-hand side casts a shadow on the floor, as the drawing was taken soon after sunrise at Copernicus, and the Sun is to the left) many smaller craters, those near the edge forming a regular line, are distinctly visible. Enormous unclosed cracks and chasms are also distinguishable. The depth of the crater floor, from the top of the wall, is 11,300 feet ; and the height of the wall above the general surface of the Moon is 2,650 feet. The irregularities in the top of the wall are well shown in the shadow. The scale of miles attached to the drawing shows the enormous proportions of the crater. ASTRONOMY. [chap. in. Lesson XVII. — Phases of the Moon. Eclipses: how Caused. Eclipses of the Moon. 229. Let us now explain what are called the pheises of the Moon, — that is, the different shapes the Moon puts on. We stated very early in this little book (Art. 1 2) that the Moon, like the Earth, got all her light from the Sun. Now, in the first place, it is clear that the Sun can only light up that half of the Moon which is turned towards it ; it is clear also that, if we could get on the same side of the Moon as the Sun is, we should see the lit-up half ; if we got on the other side, we should see just nothing at all of the Moon. But this is exactly what happens, and to explain this let us suppose the plane of the Moon's motion to be in the plane of the ecliptic. In Fig. 22, we suppose the Sun to lie to the right ; the Earth and its orbit are shown, the half turned towards the Sun being of course lit up. We also represent the Moon's orbit. Let us first take the Moon at A. We represent it with the side turned to the Sun lit up. Now it is clear that, as we are on the side opposite to the Sun, we cannot see the lit-up portion — this is the position occupied by the New Moon — and practically we do not see the New Moon. Now let us take the Moon at B ; it is equally clear that at this point we face the lit-up portion and see all of it. Now this occurs at Pull Moon, when the Moon arrives at such a position in her orbit that the Sun, Earth, and herself are in the same line, the Moon lying outside, and not in the middle as at New Moon. 230. At C and D our satellite is represented midway between these two positions. Again, it is evident that at C we shall see one-half of the lit-up Moon — that half lying to the right, as seen from the Earth ; at D we shall see the ht-up portion lying to the left, looking from the Earth. These positions are those occupied by the Moon at the First Quarter and Last Quarter respectively. CHAP. III. J THE SOLAR SYSTEM. 103 When the Moon is at E and F we shall see but a smalL part of the lit-iip portion, and we shall get a crescent Moon, the crescent in both cases being turned to the Sun. At G and H the Moon will be gibbous. Fig. 22. — Phases of the Moon. 231. So that the history of the phases is as follows : — New Moon. The Moon is invisible to us, because the Sun is lighting up one side and we are on the other. Crescent Moon. We just begin to see a little of the illumi- nated portion, but the Moon is still so nearly in a line with the Sun, that we only catch, as it were, a glimpse of the side turned towards the Sun, and see the Moon herself for a short time after sunset. I04 ASTRONOMY. [chap. hi. First Quarter. As seen from the Moon, the Earth and , Sun are at right angles to each other. When the Sun sets in the west, the Moon is south. Hence, as the illumination is sideways, the right-hand side of the Moon is ht up. Gibbous Moon. The Moon is now more than half lighted up on the right-hand side. Full Moon. The Earth is now between the Sun and Moon, and therefore the- entire half of the Moon which is illuminated is visible. 232. From Full Moon we return through the Second Quarter and other similar phases to the New Moon, when the cycle recommences. So that, from New Moon the illuminated portion of our satellite waxes, or increases in size, till Full Moon, and then wanes, or diminishes, to the next New Moon ; the illuminated portion, except at Full Moon, being separated from the dark one by a semi-ellipse, called, as we have seen (Art. 222), the terminator. 233. In Fig. 22 we supposed that the Moon's motion was performed in the plane of the ecliptic. Our readers now know (Art 215) that this is not the case : if it were so, every New Moon would put out the Sun ; and as the Earth, and every body through which light cannot pass, both on the Earth and off it, casts a shadow, every Full Moon would be hidden in that shadow. These appear- ances are called eclipses, and they do happen sometimes. Let us see if we can show under what circumstances they do happen. One-half of the Moon's journey is performed above the plane of the echptic, one-half below it ; hence at certain times— twice in each revolution — the Moon is in that plane, at those parts of it called the nodes. Now, if the Moon at that time happens to be new or full — that is, in line with the Earth and Sun — in one case we shall have an eclipse of the Sun, in the other we shall have an CHAF. ni.] THE SOLAR SYSTEM. eclipse of the Moon. This will be rendered clear by the accompanying figure. We have the Sun at bottom, the Earth at top, and the Moon in two positions marked A and B, the level of the page representing the level, or plane, of the ecliptic. We suppose therefore in both cases that the Moon is at a node, — that is, on that level, neither above nor be- low it. 234. At A, therefore, the Moon stops the Sun's light, its shadow falls on a part of the Earth ; and the people, therefore, who live on that particular part of it where the shadow falls cannot see the Sun, because the Moon is in the way. Hence we shall have what is called an eclipse of the Sun. 235. At B the Moon is in the shadow of the Earth cast by the Sun ; therefore the Moon cannot receive any light from the Sun, because the Earth is in the way. Hence we shall have what is called an eclipse of the Moon. 236. It will easily be seen from the figure, that whereas the eclipse of the Moon by the shadow of the much larger Earth will be more or less visible to the whole side of the Earth turned away from the Sun, the shadow cast by the small Moon in a solar eclipse is, on the contrary, so limited, fig. 23 —Eclipses of the that the eclipse is only seen over a Sim and Moon, small area. 237. In the figure two kinds of shadows are shown, one much darker than the other ; the former is called the I: lo6 ASTRONOMY. [chap. hi. umbra, the latter the penumbra. If the Sun were a point of light merely, the shadow would be all umbra-; but it is s6 large, that round the umbra, where no part of the Sun is visible, there is a belt where a portion of it can be seen ; hence we get a partial shadow, which is the meaning of penumbra. This will be made quite clear if we get two candles to represent any two opposite edges of the Sun, place them rather near together, at equal distances from a wall, and observe the shadow they cast on the wall from any object ; on either side the shadow thrown by both candles will be a shadow thrown only by one. 238. In a total eclipse of the Moon, as the Moon travels from west to east, we first see the eastern side of the Moon slightly dim as she enters the penumbra ; this is the first contact with the penumbra, spoken of in almanacs. At length, when the real umbra is reached, the eastern edge becomes almost invisible ; we have the first contact with the dark shadow; the circular shape of the Earth's shadow is distinctly seen, and at last she enters it entirely. When the Moon passes, how- ever, into the shadow of the Earth, it is scarcely ever quite obscured ; the Sun's light is bent by the Earth's atmo- sphere towards the Moon, and sometimes tinges it with a ruddy colour. The eclipses, however, which occurred in 1642, 1761, 1816, and on the .4th of October, 1884, were remarkable for the total disappearance of the Moon. A total eclipse of the Moon may last about i| hours. When the Moon again leaves the umbra we have the last contact with the dark shadow ; and after the last contact with the penumbra, the ecUpse is over. 239. If the Moon is not exactly at a node, we shall only get a partial eclipse of the Moon, the degree of eclipse depending upon the distance from the node. For instance, if the Moon is to the north of the node, the lower limb may enter the upper edge of the penumbra or of the umbra ; if to the south of the node, the upper portion will be obscured. CHAP. III.] THE SOLAR SYSTEM. 107 Lesson XVIU.— Eclipses {continued). Eclipes of the Sun. Total Eclipses and their Phenomena. Corona. Red-flames. 240. In a total eclipse of the Sun, the diameter of the shadow which falls on the Earth is never large, averaging about 150 miles ; the Moon, which obscures the Sun, revolves from west to east in a month, and the Earth's surface, on which the shadow falls, also rotates from west to east in a day, and the shadow sweeps across it from west to east with great rapidity. The longest time an eclipse of the Sun can be total at any place is seven minutes, and of course it is only visible at those places swept by the shadow. Hence, in any one place, total eclipses of the Sun are of very rare occurrence ; in London, for instance, there has been no total eclipse of the Sun since 1715. 241. In eclipses of the Sun there are no visible effects of umbra and penumbra seen on the Sun itself ; we have the real (though invisible) Moon eating into the real and visible Sun, the western edge of the Suh in the case of total eclipses being first obscured. The obscuration in- creases until the Moon covers all the Sun, and soon afterwards the western edge of the Sun reappears. 242. As in the case of the Moon, there are other eclipses besides total ones. To explain this we must give a few figures. As both Sun and Moon are round, or nearly so, the shadow from the latter is round ; and as the Sun is larger than the Moon, the shadow ends in a point. The shape of the shadow is, in fact, that of a cone — hence the term "cone of shadow." Now, the length of this cone varies with the Moon's distance from the Sun : when nearest, the Moon will of course throw the shortest shadow. The lengths are about as follow : — Miles. When the Moon and Sun are nearest together . 230,000 „ „ „ furthest apart . . 238,000 io8 ASTRONOMY. [chap. hi. But in Art. 212 we saw that the distance between the Earth and Moon varied as follows : — Miles. When the Moon and Earth are nearest together 225,7 19 „ „ „ furthest apart , 251,947 Hence, when the. Moon is furthest from the Earth, or in apogee, the shadow thrown by the Moon is not long enough to reach the Earth ; at such times the Moon looks smaller than the Sun ; and if she be at a node, we shall have an anntaar eclipse — that is, there will be a ring (annulus, Lat. ring) of the Sun visible round the Moon when the eclipse would otherwise have been total. 243. There may be partial eclipses of the Suu, for the same reason as we have partial eclipses of the Moon ; only as the Moon is not exactly at the node, in one case, she does not get totally eclipsed, because she does not pass quite into the shadow of the Earth ; an9 in the other, the Sun does not get totally eplipsed, because the Moon does not pass exactly between us and the Sun. 244. The nodes of the Moon are not stationary, but move backwards upon the Moon's orbit, a complete revo- lution taking place with regard to the Moon in 18 years 219 days, nearly. The Moon in her orbit, therefore, meets the same node again before she arrives at the same place with regard to the Sun again, one period being 27d. Jh. 6m., called the nodical revolution of tbe Moon; and the other, 29d. I2h. 44m., called the synodlcal revolution of tlie Moon, in which, it regains the same position with regard to the Sun. The node is in the same position with regard to the Sun after an interval of 346d. r4h. 52m. This is called a synodic revolution of the node. Now it so hap- pens that nineteen synodic revolutions of the node, after which period the Sun and node, would be alike situated, are equal to 223 synodic revolutions of the Moon, after which period the Sun and Moon would be alike situated ; so that, if we have an eclipse at the beginning of the period, we shall have one at the end of it, the Sun, Moon, lis B sa-a S -^ -P a^T-T^tnc p^ ^ ^^ jjj EhctogrKphedly "Warren De LaaueTJiS. CHAP. III.] THE SOLAR SYSTEM. 109 and node having got back to their original positions. This period of 18 years 10 days is a cycle of the Moon, known to the ancient Chaldeans and Greeks under the name of Saros, and by its means eclipses were roughly predicted before astronomy had made much progress. 24.5. A total eclipse of the Sun is at once one of the most awe-inspiring and grandest sights it is possible for man to witness. As the eclipse advances, but before the totality is complete, the sky grows of a dusky livid, or< purple, or yellowish crimson colour, which gradually gets darker and darker, and the colour appears to run over large portions of the sky, irrespective of the clouds. The sea turns lurid red. This singular colouring and darken- ing of the landscape is quite unlike the approach of night, and gives rise to strange feelings of sadness. The Moon's shadow is seen to sweep across the surface of the Earth, and is even seen in the air ; the rapidity of its motion and its intenseness produce a feeling that something material is sweeping over the Earth at a speed perfectly frightful. All sense of distance is lost, the faces of men assume a livid hue, fowls hasten to roost, flowers close, cocks crow, and the whole animal world seems frightened out of its usual propriety. 246. A few seconds before the commencement of the totality the stars burst out ; and surrounding the dark Moon on all sides is seen a glorious halo, generally of a silver-white light ; this is called the corona. It reveals to us for the most part the exterior portion of the Sun's atmosphere, which is not seen when the Sun itself is visible, owing to the overpowering light of the latter. It is slightly radiated in structure, and extends sometimes beyond the Moon to a distance equal to our satellite's diameter. Besides this, rays of light, called aigrettes, diverge from the Moon's edge, and appear to be shining through the light of the corona. In some eclipses some parts of the corona have reached to a much greater distance from the Moon's edge than in others. ASTRONOMY. [chap. III. 247. During the total eclipse observed in America on July 29, 1878, equatorial streamers were seen proceeding from the Sun to a distance of fully 10,000,000 miles, and F:g. 24. — Corona of 1S78, as seen behind a screen. something of the same extraordinary appearance had also been noticed in 1867. Now, it is remarkable that both these years were epochs of sun-spot minimum, so that the shape of the corona has been assumed to be in some way CHAP, in.] THE SOLAR SYSTEM. iii connected with the phases of the Sun's activity. The view has, however, lately been put forward that these apparent coronal extensions may really indicate a permanent solar appendage in a ring of cooled material revolving partly within the limits of the solar atmosphere. The fall of matter from this ring upon the Sun's surface, resulting from inevitable disturbances, would produce spots and prominences, and account for many of the best-marked features of the sun-spot period. It would also explain the acceleration of spots near the equator. 247a. The spectroscope tells us that the corona is in part made up of two kinds of gas — hydrogen, and an unknown gas emitting green light exclusively ; in part of solid or liquid particles reflecting sunlight. 248- When totality has commenced, apparently close to the edge of the Moon, and therefore within the corona, are observed fantastically-shaped masses, full lake-red, fading into rose-pink, variously called red flames and red prominences. Two of the most remarkable of these hitherto noticed were observed in the eclipse of 1 85 1. They have thus been described by the Rev. W. R. Dawes : — " A bluntly triangular pink body [was seen] suspended, as it were, in the corona. This was separated from the Moon's edge when first seen, and the separation increased as the Moon advanced. It had the appearance of a large conical protuberance, whose base was hidden by some intervening soft and ill-defined substance. . . To the north of this appeared the most wonderful phenomenon of the whole : a red protuberance, of vivid brightness and very deep tint, arose to a height of perhaps ij' when first seen, and increased in length to 2' or more, as the Moon's progress revealed it more completely. In shape it some- what resembled a Turkish cimeter, the northern edge being convex, and the southern concave. Towards the apex it bent suddenly to the south, or upwards, as seen in the telescope. ... To my great astonishment, this marvellous object continued visible for about five seconds, ASTRONOMY. [chap. hi. as nearly as I could judge, after the Sun began to reappear." 249. It has been definitely established that these pro- minences belong to the Sun, as those at first visible on the eastern side are gradually obscured by the Moon, while those on the western are becoming more visible, owing to the Moon's motion from west to east over the Sun. The height of some of them above the Sun's surface is upwards of 90,000 miles, and occasional uprushes have been watched, to elevations of more than 200,000 miles. 250. These red prominences are composed of incan- descent hydrogen gas and metallic vapours lying outside the photosphere ; and their spectroscopic examination indicates that the pressure in the high prominences is small. It indicates also that the matter composing them is in exceedingly rapid motion, upward movements up to 250 miles a second, having been detected by this means. (See Art. 504*.) Lesson XIX. — The other Planets compared with the Earth. Physical Description of Mars. 251. We are now in a position to examine the other planets of our system, and to bring the facts taught us by our own to bear upon them. In the case of all the planets we have been able to ascertain the facts necessary to determine the elements of their revolution round the Sun ; that is to say, the time in which the complete circuit round the common luminary is accomplished, and the shape and position of their orbits with regard to our own. Now, the shape of the orbit depends upon the degree of its ellipticity — for all are elliptical — and its position upon the distance of the planet from the Sun, and the degree in which the plane of each orbit departs from that of our own. When we have, in addition to these particulars, the position of the CHAP. III.] THE SOLAR SYSTEM. 113 nodes — the points in which the orbit intersects the plane of our orbit — and the position of the perihehon points, we have all the materials necessary for calculation or for making a diagram of the planet's path. 252. Still, however satisfactory our examination of the planets has been with regard to their revolution round the Sun, we are compelled to state that when we wish to in- quire into their rotations on their axes, the length of their days, their seasons, and their physical constitutions, the knowledge as yet acquired by means of the telescope is far from complete. Thus, of the planets Mercury and Venus we have nothing quite certain to tell on these matters ; they are both so lost in the Sun's rays, and so refulgent in consequence of their nearness to that body, that our observation of them, of Mercury especially, has been to a great extent baffled. Nevertheless, the ob- servations made in the beginning of this century by a German astronomer named Schroter have been so far confirmed in recent years, that we may pretty safely admit a period of about 25 hours for Mercury's rota- tion on his axis. That is, his day is an hour or so longer than ours. And the period assigned to Venus of 23h. 2lm. is probably still more nearly exact. This has been confirmed by the measurement of photographs taken during the transit of Venus in 1882. which show that the figure of the planet is nearly identical with that of the Earth. It is bulged ivi%t to the same extent (see Art. 196) ; consequently it rotates at just about the same rate. a52a. The same class of facts in the case of Uranus and Neptune are equally hard to get at, but for a different reason. At our nearest approach to Uranus we are nearly 1,700,000,000 miles away from that planet ; at our nearest approach to Neptune we are about 2,700,000,000 miles away, and we cannot be surprised that our telescopes almost fail us in delicate observations at such distances. Still, on the small disk of Uranus some delicate cloud- markings have lately been detected, evidently connected 114 ASTRONOMY. [chap. hi. with his rotation ; and the reappearances of a bright spot seem to. give for that rotation a period of about lo hours. 253. With regard however to Mars, Jupiter, and Saturn, the planets whose orbits are nearest to our Own, our information is comparatively full and complete. For instance, we can for these planets give- the following information in addition to that stated in Arts. 139 and 140, and Table II. of the. Appendix : — Length of Day. H. M. s. Inclination of Axis. Mars . . . 24 37 22 . . . 24° 52' 0" Jupiter . • 9 SS 21 . , 340 Saturn .10 14 23 . . . . 28 10 The first column requires no explanation. We see, however, at once that the day in Mars is nearly equal to our own, while in the large planets, Jupiter and Saturn, it is not half so long. Now the revolutions of these planets round the Sun are accomplished as follows : — Mars in 686 of our days. Jupiter in 4,333 „ Saturn in 10,759 » We can therefore easily find the number of days ac- cording to the period of rotation of each planet, which go to make each planetary year : thus in Saturn's year there are 24,584 Saturnian days, or 67 times more days than in our own. 254. In the second column the inclination of the planets' axes of rotation is given. It will be recol- lected that the inclination of our own is 23^°, and that it is on this inclination that our seasons depend. It will be seen at once therefore that Mars and Saturn are much like the Earth in this respect, and that Jupiter is a planet almost without seasons, for the inclination of its axis is only 3°, while that of Venus is 53°. The axis of rotation MaceMI V6rraiI)eLaEue,3el S RusselSculp CHAP. III.] THE SOLAR SYSTEM. 115 of Uranus is, so far as can be judged, tilted by about the same amount. 255. As in the case of the Earth, we find in many in- stances the axis of rotation, or polar diameter, of the other planets shorter than the equatorial diameter. The amount of polar compression, — that is, the amount of flattening, by which the polar diameter is less than the, equatorial one, — measured in fractions of the latter, is as follows : — Mercury . -^ \'enus Earth \'enus . 3I3 2 a 'J Mars . . ? Jupiter . Jy Saturn . 1 Uranus . ? Neptune ? From this table we learn that if the equatorial diameter of Mercury be taken as 29, the polar one is only 28 : in the cases of Jupiter and Saturn, the diameters are as 17 to 16 and 9 to 8, respectively. In these two last the rotation is very rapid (Art. 253) ; and this great flattening is what we should expect from the reasoning in Art. 196. 256. We now come to what we can glean of the physical structure of the planets as seen in the telescope when they are nearest the Earth. Let us begin with Mars. We give in Plate IX. two sketches, taken in the year 1862. Here at once we see that we have something singularly like the Earth. The shaded portions represent water, the lighter ones land, and the bright spot at the top of the drawings is probably snow lying round the south pole of the planet, which was then visible. 257. The two drawings represent the planet as seen in an astronomical telescope, which inverts objects so that the south pole of the planet is shown at top. The upper drawing was made on the 25th of September, the lower one on the 23rd. In the upper one a sea is seen on the left, stretching down northwards ; while, joined on to it, as the Mediterranean is joined on to the Atlantic, is a long narrow sea, which widens at its termination. I 2 ii6 ASTRONOMY. [chap. hi. In the lower drawing this narrow sea is represented on the left. The coast-line on the right strangely reminds one of the Scandinavian peninsula, and the included Baltic Sea. 258. It will now be easy to understand how we have been able to determine the length of the day and tlie inclination of the axis. We have only to watch how long it takes one of the spots near the equator of each planet to pass from one side to the other, and the direction it takes, to get at both these facts. 259. Mars not only has land and water and snow like us, but it has clouds and mists, and these have been watched at different times. The land is generally reddish when the planet's atmosphere is clear ; this is due to the absorption of the atmosphere, as is the colour of the setting Sun with us. The water appears of a greenish tinge. 259a. A very curious feature of the surface of Mars was detected in 1877, when the planet made one of its nearest approaches to the Earth. The so-called " con- tinents "were then seen to be divided into innumerable islands by a net- work of "canals," or long and narrow arms of the seas, sometimes running almost in a straight line for 3,000 or 4,000 miles. It was on the same occasion that the moons of Mars were discovered by Professor Hall at Washington. These two little bodies are quite the smallest of known satellites. They have been called Drimos and Photos, from a passage in the Iliad, in which Pain and Fear are represented as the attendants of Mars. 260. Now, if we are right in supposing that the bright portion surrounding the pole is ice and snow, we ought to see it rapidly decrease in the planet's summer. This is actually found to be the case, and the rate at which the thaw takes place is one of the most interesting facts to be gathered from a close study of the planet. In 1862 this decrease was very visible. The summer solstice of Mars Maks in iSjz. CHAP. III.] THE SOLAR SYSTEM. 119 occurred on the 30th of August, and the snow-zone was observed to be smallest on the nth of October, or forty- two of our days after the highest position of the Sun. This very rapid melting may be ascribed to the inclination of the axis, which is greater than with us ; to the greater eccentricity of the planet's orbit ; and to the fact that the summer-time of the southern hemisphere occurs when the planet is near perihelion. 261. For a reason that will be easily understood when we come to deal with the effect of the Earth's revolution round the Sun on the apparent positions and aspects of the planets, we sometimes see the north pole, and some- times the south pole of Mars, and sometimes both : when either pole only is visible, the features, which appear to pass across the planet's disk in about 12 hours — that is, half the period of the planet's rotation — describe curves with the concave side towards the visible pole. When both poles are visible they describe straight lines, exactly as in the case of the Sun (Art. 106). These changes enable all the surface to be seen at different times, and maps of Mars have been constructed, the exact position of the features of the planet being determined by their latitude and longitude, as in the case of the Earth. 262. But although we see in Mars so many things that remind us of our planet, and show us that the extreme temperatures of the two planets are not far from equal, a distinction must be drawn between them. In conse- quence of the great eccentricity of the orbit of Mars, the lengths of the various seasons are not so equal as with us, and, owing to the longer year, they are of much greater extent. In the northern hemisphere of the planet they are as under: — Spring lasts Summer ,, Days. 181 Autumn „ Winter „ 149 ■ 147 ASTRONOMY. [chap. hi. As we must reverse the seasons for the southern hemi- sphere, spring and summer, taken together, are 76 days longer in the northern hemisphere than in the southern. Lesson XX. — The other Planets compared with the Earth {continued). Jupiter : his Belts and Moons. Saturn : General Sketch of his System.* 263. Let us now pass on to Jupiter, by far the largest planet in the system, and bright enough sometimes, in spite of its great distance, to cast a shadow like Venus. The first glance at the drawing :(Plate X. Fig. i) will show us that we have here something very unlike Mars ; and such is the fact. The planet Jupiter is surrounded by an atmosphere so densely laden with clouds, that of the actual planet itself we know nothing. What are generally known as the belts of Jupiter are dusky streaks which cross a brighter background in direc- tions generally parallel to the planet's equator. And for the most part, the largest belts are situated on either side of it, in exactly the same way as the two belts of Trade- Winds on the Earth lie on either side of the belt of Equa- torial Calms and rains. Outside these, again, we get representatives of the Calms of Cancer and Capricorn, although these are not so regularly seen, the portion of the planet's surface polewards of the two belts being hable to great changes of appearance, sometimes in a very short tirne. The portions of the atmosphere representing the terrestrial calm-belts sometimes exhibit a beautiful rosy tint, the equatorial one especially. 264. The variations of this cloudy atmosphere lend great variety to the appearance of the planet at different times ; the belts are sometimes seen in large numbers, and extend almost to the poles. Besides the belts, some- * Proctor's "Saturn and his System," from which some of the statements concerning Saturn are taken, may be consulted by the teacher. CHAP, in.] THE SOLAR SYSTEM. times bright spots, sometimes dark ones, are seen, which have enabled us to determine the period of the planet's rotation, which, as we have seen, is very rapid — so rapid that on the equator an observer would be carried round at the rate of 467 miles a minute, instead of 17 as on the Earth. It is remarkable that spots near the equator travel faster than those remote from it, just as they do on the Sun, differences of as much as 7J minutes having been observed in the periods of rotation derived from differently situated spots. An enormous red spot, for instance, 30,000 miles long by nearly 7,000 wide, which appeared in 1878, and is still faintly visible, took about 5j minutes longer to complete a rotation than a brilliant white spot conspipuous at the same time. This sun-like mode of rotation, and other facts, favour the opinion that the internal temperature of Jupiter is still very high ; and the same conclusion probably holds good for Saturn, Uranus, and Neptune. 265. Although all astronomers do not agree that the surface of the planet is never seen, there are many strong reasons why it should not be seen. In the first place. Mars and the Earth, whose atmospheres are nearly alike, have nearly the same densities (Art. 145), while in the case of Jupiter and' Saturn — the belts of which latter planet, as far as we can observe them, resemble Jupiter's — the density, as calculated on the idea that what we see is all planet, is only about one-fifth that of the Earth ; and as the density of the Earth is 5J times that of water, it follows that the densities of the two planets in question are not far off that of water. 266. Now, if we suppose that the apparent volume of Jupiter (and similarly of Saturn) is made up of a large shell of cloudy atmosphere and a kernel of planet, there is no reason why the density of the real Jupiter (and of the real Saturn) should vary very much from that of the Earth or Mars, and this would save us from the water- planet hypothesis. Moreover, a large shell of cloudy ASTRONOMY. [chap. hi. atmosphere is precisely what our own planet was most probably enveloped in, in one of the early stages of its history (Art. 208). 267. In addition to the changing features of Jupiter itself, the telescope reveals to us four moons, which as they course along rapidly in their orbits, and as these orbits lie nearly in the plane of the planet's orbit, lend a great additional interest to the picture. In the various positions in their orbits the satelUtes sometimes appear at a great distance from the primary ; sometimes they come between us and the j^. ,, planet, appearing now as !< IG. 25. — Jupirer and his JVioons f . , t^ ". , (general view;. bright and now as dark spots on its surface. At other times they pass between the planet and the Sun, throwing their shadows on the planet's disk, and causing, in fact, eclipses of the Sun. They also enter into the shadow cast by the planet, and are therefore eclipsed themselves ; and sometimes they pass behind the planet and are said to be occulted. Of these appearances we shall have more to say by and by (Lesson XXXVI.). 268. Referring to the sizes of these moons and their distances from the planet, in Table III. of the Appendix, it may be here added that, like our Moon, they rotate on their axes in the same time as they revolve round Jupiter. This has been inferred from the fact that their hght varies, and that they are always brightest and dullest in the same positions with regard to Jupiter and the Sun. 269. In Plate X. the black spot is the shadow of a satel- lite, and the satellite itself is seen to the left ; the passage of either a satellite or shadow is called a transit. In a solar eclipse, could we observe it from Venus, we should see a similar spot sweeping over the Earth's surface. 270. We now come to Satnm j and here again, as in CHAP. III.] THE SOLAR SYSTEM. Fig. 26. — Saturn and his Moons (general view). llie case of Jupiter, we come upon another departure from Mars and the Earth. The planet itself, which is belted like Jupiter, is surrounded not only by eight moons, but by a series of rings, one of which, the inner one, is trans- parent ! The belts have been before referred to (Art. 265), they need not, therefore, de- tain us here ; and we may dismiss the satellites — as their distances from Sa- turn, &c., are given in Table III. of the Appendix — with the remark, that as the equator of Saturn, unlike that of Jupiter, is greatly inclined to the ecliptic, transits, e3lipses, and oc- cultations of the satellites, the orbits of which for the most part lie in the plane of Saturn's equator, happen but rarely. 271. It is to the rings that most of the interest of this planet attaches. We may well imagine how sorely puzzled the earlier observers, with their very imperfect telescopes, were, by these strange appendages. The planet at first was supposed to resemble a vase ; hence the name Ansc?, or handles, given to the rings in certain positions of the planet. It was ne.xt supposed to consist of three bodies, the largest one in the middle. The true nature of the rings was discovered by Huyghens in 1655, who announced it in this curious form : — " aaaaaaa ccccc d eeeee g h iiiiiii 1111 mm nnnnnnnnn 0000 pp q rr s ttttt uuuuu," which letters, transposed, read : — " annulo cingitur, tenui piano, nusguam cohaerente. ad eclipticam mclinato." 124 ASTRONOMY. [chap, hi. There is nothing more encouraging in the history of astronomy than the way in which eye and mind have bridged over the tremendous gap which separates us from this planet. By degrees the fact that the appearance was due to a ring was determined ; then a separation was noticed dividing the ring into two ; further observations suggested to the French astronomers Du S^jour and Lalande that the number of rings should be multiplied many-fold; the extreme thinness of the ring came out next, when Sir William Herschel observed the satellites " like pearls strung on a silver thread." The making out of the transparent ring by Dawes and Bond followed in 1850; then the transparent ring was discovered to be divided as the whole system had once been thought to be ; last of all comes evidence that the smaller divisions in the various rings are subject to change, and that the ring- system itself is probably increasing in breadth, and approaching the planet. Lesson XXI. — The other Planets compared with the Earth {continued). Dimensions of Saturn and his Rings. Probable Nature of the Rings. Effects pro- duced by the Rings on the Planet. Uranus. Neptune : its Discovery. The lower iigure of Plate X. will give an idea of the appearance presented by the planet and its strange and beautiful appendage. It will be shown in the sequel (Chap, IV.) how we see, sometimes one surface, and some- times another, of the ring, and how at other times the edge of it is alone visible. 272. The ring-system is situated in the plane of the planet's equator, and its dimensions are as follow : — CHAP. III.] THE SOLAR SYSTEM. 125 Miles. 166,920 147,670 i,6So 144,310 109,100 91,780 9,760 72,250 Outside diameter of outer ring Inside „ „ Distance from outer to inner ring Outside diameter of inner ring . Inside „ „ Inside „ darlc ring Distance from dark ring to planet Equatorial diameter of planet so that the breadths of the three principal rings, and of the entire system, are as follow ; — Miles. Outer bright ring . .... 9,625 Inner bright ring . . . 17,605 Dark ring 8,660 Entire system . .... 37,570 and the distance between the two bright rings is 1,680 miles. In spite of this enormous breadth, the thickness of the rings is not supposed to exceed 100 miles. 273. Of what, then, are these rings composed ? There is great reason for believing that they are neither solid nor liquid ; and the idea now generally accepted is that they are composed of myriads of satellites, or little bodies, moving independently, each in its own orbit, round the planet ; giving rise to the appearance of a bright ring when they are closely packed together, and a very dim one when they are most scattered. In this way we may account for the varying brightness of the different parts, and for the haziness on both sides of the ring near the planet (shown in Fig. 26), which is supposed to be due to the bodies being drawn out of the ring by the attraction of the planet. 274. Although Saturn appears to resemble Jupiter in its atmospheric conditions, unlike that planet, and like our own Earth, its year, owing to the great inclination of its ASTRONOMY. [chap. hi. axis, is sharply divided into seasons, which however are here indicated by something else than a change of tem- perature ; we refer to the effects produced by the presence of the strange ring appendage. To understand these effects, its appearance from the body of the planet must first be considered. As the plane of the ring lies in the plane of the planet's equator, an observer at the equator will only see its thickness, and the ring therefore will put on the appearance of a band of light passing through the east and west points and the zenith. As the observer, however, increases his latitude either north or south, the surface of the ring-system will begin to be seen, and it will gradually widen, as in fact the observer will be able to look down upon it ; but as it increases in width it will also increase its distance from the zenith, until in lat. 63° it is lost below the horizon, and between this latitude and the poles it is altogether invisible. 275. Now the plane of the ring always remains parallel to itself, and twice in Saturn's year — that is, in two opposite points of the planet's orbit — it passes through the Sun. It follows, therefore, that during one half of the revolution of the planet one surface of the rings is lit up, and during the remaining period the other surface. At night, there- fore, in one case, the ring-system will be seen as an illumin- ated arch, with the shadow of the planet passing over it, like the hour-hand over a dial ; and in the other, if it be not lit up by the light reflected from the planet, its posi- tion will only be indicated by the entire absence of stars. 276. But if the rings eclipse the stars at night, they can also eclipse the Sun lay day. In latitude 40° there occur in Saturn morning and evening eclipses for more than a year, gradually extending until the Sun is eclipsed during the whole day — that is, when its apparent path lies entirely in the region covered by the ring ; and these total eclipses continue for nearly seven years : eclipses of one kind or another taking place for 8 years 292 days. This will give us an idea how largely the apparent phenomena of the CHAP. III.] THE SOLAR SYSTEM. 127 heavens, and the actual conditions as to climates and seasons, are influenced by the presence of the ring. As the year of Saturn is as long as thirty of ours, it follows that each surface of the rings is in turn deprived of the light of the Sun for fifteen years. 277. We have now finished with the planets known to the ancients ; the remaining ones, Uranus and Neptune, have been discovered in modern times — the former in 1 78 1, by Sir Wm. Herschel, and the latter in 1846, inde- pendently, by Professor Adams and M. Leverrier. 278. Both these planets are situated at such enormous distances from the Sun, and therefore from us, that Uranus is scarcely, and Neptune not at all, visible to the naked eye. Owing to this remoteness, nothing is known of their physical peculiarities. We have already stated, however, that the motion of the satellites of Uranus, as well as of the solitary moon of Neptune, is in the opposite direction to that of all the other planetary members of the system. 279. The discovery of the planet Neptune is one of the most astonishing facts in the history of Astronomy. As we shall see in the sequel, every body in our system affects the motions of every other body ; and after Uranus had been discovered some time, it was found, that, on taking all the known causes into account, there was still something affecting its motion ; it was suggested that this something was another planet, more distant from the Sun than Uranus itself. And the question was, where was this planet, if it existed ? When we come to consider the problem in all its grandeur, we need not be surprised that two minds, who felt themselves competent to solve it, should have inde- pendently undertaken it. As far back as July 1841, we find Mr. Adams determined to investigate the irregularities of Uranus : early in September 1846, the new planet had fairly been grappled. We find Sir John Herschel remarking, " We see it as Columbus saw America from 128 ASTRONOMY. [chap. hi. the shores of Spain. Its movements have been felt trembling along the far-reaching line of our analysis with a certainty hardly inferior to ocular demonstration." On the 29th July, 1846, the large telescope of the Cam- bridge Observatory was first employed to search for the planet in the place assigned to it by Professor Adams's calculations. M. Leverrier, in September, wrote to the Berlin observers, stating the place where his calcula- tion led him to believe it would be found : his theoretical place and Professor Adams's being not a degree apart. At Berlin, thanks to their star-maps, which had not yet been published, Dr. Galle found the planet the same evening, very near the position assigned to it by both Astronomers. Lesson XXII. — The Asteroids, or Minor Planets. JBode's Law. Size of the Minor Planets : their Orbits : how they are observed. 280. If we write down — o 3 6 12 24 48 96 and add 4 to each, we get 4 7 10 16 28 52 100 and this series of numbers represents very nearly the distances of the ancient planets from the Sun, as fol- lows : — Mercury, Venus, Earth, Mars, — , Jupiter, Saturn. This singular connexion was discovered by Titius, and is known by the name of Bode's liaw. We see that the fifth term has apparently no representative among the planets. Although ignorant of the existence of any such relation between the distances of the planets, Kepler boldly attempted to bridge the gap between Mars and CHAP. III.] THE SOLAR SYSTEM. 129 Jupiter by inventing an unknown body to revolvfe there. Up to the time of the discovery of Uranus the undetected planet did not reveal itself: when it was found, however, that the actual position of Uranus was very well repre- sented by the next term of the series, 196, it was deter- mined to make an organized search for it, and for this purpose a society of astronomers was formed ; the zodiac was divided into 24 zones, each zone being confided to a member of the society. On the first 'day of the present century a planet was discovered and named Ceres, which, curiously enough, filled up the gap. But the discovery of a second, third, and fourth, named respectively Pallas, Juno, and Vesta, soon followed, and up to the present time (February 1888) no less than 271 of these little bodies have been detected. A list of them, with their symbols, \ \ ''s_ Mt- - \ --''' \ M.y /^ / ia I M — \ 3 »■ / / \ liili- \ '^> / 3 ^ w^ m/?J ''•-,. 7 / .t« J \ y No h /• •Q 1 ^,'' ?r/ \ IT" ; „.X ■^'' \ '•^ — Diagram showing how the equation of time is derived from two components. Ordinates above the datum lines are positive (+), those below are negative( - ). The curve a b c D represents the differences between the mean and true Suns at different times of the year, due to the irregularity of the earth's motion round the feun, and the curve 1234 represents the differences due to the obliquity of the ecliptic. The equation of time curve E e'e"e"', is derived by takmg the algebraical sum of the ordinates of the other two. Sometimes the ordinates of the two components act against each other, but at other times they act together. Thus, on April 15 the + due to curve a bcd is exact y neutralised by the — due to i 2 3 4, and the equation of time is wz7. but on Feb, J I they act together and the resulting equation of time is + ^^\ minu.es. CHAP, v.] MEASUREMENT OF TIME. 207 sun is before the true sun, the dock will get behind the dial, and we must add the equation of time to the time shown by the true sun. 416. When the earth is in perihelion, or — what comes to the same thing^when the sun is in perigee, the real sun moves fastest, and therefore will gain on the mean sun, and the dial will be before the clock. When the sun is in apogee, the mean sun will move fastest, and the clock will be before the dial. The equation of time will therefore be additive or subtractive, or, as it is expressed, + or — with regard to the time shown by the true sun, or to apparent time. 417. So, to refer back to Art. 415, in November we must deduct l6Jm. from the apparent time, and in February we must add i4^m. to apparent time, to get clock time. In November, therefore, the true sun sets i6m. earlier than it would do if it occupied the position of the mean sun, by which our clocks are regulated. In February it sets 15m. later, and this is why the evenings begin to lengthen after Christmas more rapidly than they would otherwise do. 418. We cannot obtain mean time at once from obser- vation ; but, from an observation of the true sun with the aid of the equation of time, which is the angular distance in time between the mean and the true sun, we may readily deduce it. Suppose the true sun to be observed on the meridian of Greenwich, Jan. i, 1887 : it would then be apparent noon at that meridian ; the equation of time at this instant is 3m. 46'69s. as given in the almanacs, and is to be added to apparent time; hence the corre- sponding mean time is Jan. i, oh. 3m. 46'69 ; that is to say the mean sun had passed the meridian previously to the true sun, and at the instant of observation the mean time clock ought to indicate this time. In Plate XII. we have a graphic representation of the equation of time. Above and below the datum lines are scales of minutes. The curve A B c D represents the portion of the equation of time due to the inequality of the real 2o8 ASTRONOMY. [chap. v. sun's motion, and the curve 1234 represents the in- equality due to the obliquity of the ecliptic. The curve E E' E" e"' is the algebraical sum of these, and represents the differences between mean time and true time all the year round. Lesson XXXIV. — Difference of Tinte. How determined on the Terrestrial Globe. Greenwich Mean Time. Length of the Various Days. Sidereal Time. Con- version of Time. 4-19, Having said so much of solar days, both apparent and mean, we must next consider the start-points of these reckonings. We have — I. the apparent solar day, "reckoned from the instant the true sun crosses the meridian through about 24 hours, till it crosses it again; II. the mean solar day, reckoned by the mean sun in the same manner. Both these days are used by astronomers. III. The civil day commences from the preceding mid- night, is reckoned through 12 mean hours only to noon, and then recommences, and is reckoned through another 12 hours to the next midnight. The civil reckoning is therefore always 12 hours in advance of the astronomical reckoning ; hence the well known rule for determining the latter from the former, viz, : — For P.M. civil times, make no change ; but for a^m. ones, diminish the day of the month by I and add 12 to the hours. Thus: Jan. 2, 7h. 49m. P.M. civil time, is Jan. 2, 7h. 491T1. astronomical time ; but January 2, yh. 49m. A.M. civil time is January I, igh. 49m. astronomical time. The distinction, however, be- tween civil and astronomical reckoning is about to dis- appear, Greenwich civil time, counting from midnight to "midnight, and from o to 24 hours will be adopted in the " Nautical Almanac " for 1891. 420. Now the position of the sun, as referred to the centre of the earth, is independent of meridians, and is the same for all places at the same absolute instant ; but the CHAP, v.] MEASUREMENT OF TIME. 209 time at which it transits the meridian of Greenwich, and any other meridian, will be different. In a mean solar day, or 24 mean solar hours, the earth, by its rotation from west to east, has caused every meridian in succession from east to west to pass the mean sun ; and since the motion is uniform, all the meridians distant from each other 1 5° will have passed the mean sun, at intervals of one mean hour ; the meridian to the eastward passing first, or being, as compared with the sun, always one mean hour in advance of the westerly meridian. When it is 6 hours after mean noon at a place 15° west of Greenwich, it is therefore 7 hours after mean noon at Greenwich. When it is noon at Greenwich, it is past noon at Paris, because the svin has apparently passed over the meridian of Paris before it reached the meridian of Greenwich. Similarly, it is not yet noon at Bristol, for the sun has not yet reached the meridian of Bristol. 421. In civilized countries, at the present moment, not only is the use of mean time universal, but the mean time of the principal city or observatory is alone used. In England, for instance, Greenwich mean time (written G.M.T. for short) is used ; in France, Paris mean time 5 in Switzerland, Berne mean time^ and so on. This has become necessary owing, among other things, to the introduction of railways, so that with us Greenwich mean time is often called railway time. For- merly, before local time was quite given up, the churches in the West of England had two minute-hands, one show- ing local time, the other Greenwich time. 422. On the Continent, railway stations near the frontier of two states have their time regulated by their principal observatories. At Geneva, for instance, we see two clocks, one showing Paris time, and the other Berne time ; and it is very necessary to know whether the time at which any particular train we may wish to travel in starts, is regulated by Paris or Berne time, as there is a considerable difference between them. p ASTRONOMY. [chap. v. 423. Expressed in mean time, the length of the day is as follows : — Apparent solar day (Art. 419) . . . variable. h. m. 5. Mean solar day (Art. 419) . . . . 24 o o Sidereal day (Art. 538) . . . . 23 56 409 Mean lunar day 24 54 o 424. It will be explained further on (Chap. VII.) that sidereal time is reckoned from the first point of Aries, and that when the mean sun occupies the first point of Aries, which it does at the vernal equinox, the indications of the mean-time clock and the sidereal clock will be the same ; but this happens at no other time, as the sidereal day is but 23h. 56m. 4s. (mean time) long, so that the sidereal clock loses about four minutes a day, or one day a year (of course the coincidence is established again at the next vernal equinox), as compared with the mean time one. 425. A sidereal clock represents the rotation of the earth on its axis, as referred to the stars, its hour-hand performing a complete revolution through the 24 sidereal hours between the departure of any meridian from a star and its next return to it ; at the moment that the vernal equinox, or a star whose right ascension is oh. om. OS. is on the meridian of Greenwich, the sidereal clock ought to show oh. cm. os., and at the succeeding return of the star, or the equinox, to the same meridian, the clock ought to indicate the same time. 426. Sidereal time at mean noon, therefore, is the angular distance of the first point of Aries, or the true vernal equinox, from the meridian, at the instant of mean noon: it is therefore the right ascension of the mean sun, or the time which ought to be shown by a sidereal clock at Greenwich, when the mean-time clock indicates oh. om. OS. 427. The sidereal time at mean noon for each day is given in the " Nautical Almanac." Its importance will be easily seen from the following rules : — CHAP, v.] MEASUREMENT OF TIME. 2H Rule I. — To convert mean solar into sidereal time: — To the sidereal time at the preceding mean noon add the sidereal interval corresponding to the given mean time : the sum will be the sidereal time required. Rule II. — To convert sidereal into mean solar time : — To the time at the preceding sidereal noon, add the mean interval corresponding to the given sidereal time ; the sum will be the mean solar time required. 428, Tables of intervals are given in the Appendix, showing the value of seconds, minutes, &c., of sidereal time in mean time, and vice versd. 429, Suppose, for instance, we wish, under Rule I., to convert 2h. 22m. 25'62s. mean time at Greenwich, Jan. 7, 1887, into sidereal time, we proceed as follows : — h. m. s Sidereal time at the ^r^i:^(/z'«^ mean noon "I c ./■.. i.e. Jan. 7, from " Nautical Almanac" J '9 o SO 42 h. m. s, „ r2 o o ) We get in the f 2 o 197 13 !■ or mean I ^3 o ( table, equiva- ) 22 3-614 time mter-<^ 25 pent sidereal) 25-069 ^^ V. 0-623 intervals. (. 0-622 The sum is the sidereal time required . . 21 29 45-44 430, Suppose we wish, under Rule II., to convert 2ih. 28m. Il-36s. sidereal time at Greenwich, Jan. 7, 1887, into mean time, we proceed as follows : — h. m. s Mean time at the preceding sidereaH g 11-4.8 noon, i.e. Jan. 6 / ^^ For side- real in- tervals. ° 1 1 The table 1 f 20 56 33-579 1 1 gives the ) 27 55-413 " 1 1 equivalent ~\ 10-970 0-36 J ' mean intervals. 1 ' o'359 The sum is the mean time required, Jan. 7 . 2 20 51-80 ASTRONOMY. [chap. v. 431. If the place of observation be not on the meridian of Greenwich, the sidereal time must be corrected by the addition of 9'8s65s. for each hour (and proportional parts for the minutes and seconds) of longitude, if the place be to the west of Greenwich : but by its subtraction, if to the east. Thus in gh. lom. 6s. west longitude, the sidereal time at mean noon, Jan. 7, 1887, instead of being, as in the foregoing examples, igh. 6m. 56-425. must be corrected by adding im. 30-375., thus giving igh. 8m. 26-795. for the time to be used, instead of that set down in the column. Lesson XXXV.— 7%^ Week. The Month. The Year. The Calendar. Old Style. New Style. 4.32. Although the week, unlike the day, month, and year, is not connected with the movements of any heavenly body, the names of the seven days of which it is composed were derived by the Babylonians from the seven celestial bodies then known. The order of succes- sion established by them was continued by the Romans, their names being as follow : — Dies Saturni Dies Solis Dies LuncB . Dies Martis . Dies Merctirii Dies Jovis . Dies Veneris Saturn's day Sun's day . . Moon's day . Mars' day . Mercury's day Jupiter's day Venus's day . Saturday. Sunday. Monday. Tuesday. Wednesday. Thursday. Friday. 433. We see at once the origin of our English names for the first three days ; the remaining four are named from Tiu, Woden, Thor, and Friga, Northern deities equivalent to Mars, Mercury, Jupiter, and Venus in the classic mythology. 434. We next come to the month. This is a period of CHAP, v.] MEASUREMENT OF TIME. 213 time entirely regulated by the moon's motion round the earth (see Lesson XVI.). The lunar month is the same as the lunation or synodic month, and is the time which elapses between consecutive new or full moons, or in which the moon returns to the same position relatively to the earth and sun. The tropical month is the revolution of the moon with respect to the moveable equinox. The sidereal month is the interval between two succes- sive conjunctions of the moon with the same fixed star. The anomalistic month is the time in which the moon returns to the same point (for example, the perigee or apogee) of her moveable elliptic orbit. The nodical month is the time in which the moon accomphshes a revolution with respect to her nodes, the line of which is also moveable. The calendar month is the month recognised in the almanacs, and consists of different numbers of days, such as January, February, &c. 435. The lengths of these various months are as follow : — Lunar, or Synodic month Tropical month .... Sidereal „ . . Anomalistic month . . . Nodical „ Mean Time. d. h m s. 29 12 44 2-84 27 7 43 471 27 7 43 "•54 27 13 18 37-40 27 5 5 3560 436. We next come to the year. This is a term applied to the duration of the earth's movement round the sun, as the term " day " is applied to the duration of the earth's movement round its own axis ; and there are various sorts of years, as there are various sorts of days. Thus, we may take the time that elapses between two successive conjunctions of the sun, as seen from the earth, with a fixed star. This is called the sidereal year. 437. Again, we may take the period that elapses be- 214 ASTRONOMY. [chap. v. tween two successive passages through the vernal equinox. This is called the solar, or tropical year, and its length is shorter than that of the sidereal one, because, owing to the precession of the equinoxes, the vernal equinox in its recession meets the sun, which therefore passes through it sooner than it would otherwise do. 438. Again, we may take the time that elapses between two successive passages of the earth through the peri- helion or aphelion point ; and as these have a motion forward in the heavens, it follows that this year, called the anomalistic one, wiU be longer than the sidereal one. 439. The exact lengths of these years are as follow : — Mean Time, d. fa. m. s. Mean sidereal year .... 365 6 9 96 Mean solar, or tropical year . 365 5 48 46054440 Mean anomalistic year . . , 365 6 13 493 440. It is seen from this table that the solar year does not contain an exact niunber of solar days, but that in each yearthere is nearly aquarter of a day over. It is said that the inhabitants of ancient Thebes were the first to discover this. The calendar had got in such a state of confusion in the time of Julius Caesar, that he called in the aid of the Egyptian astronomer Sosigenes to reform it. He recommended that one day, every four years, should be added by reckoning the sixth day before the kalends of March twice ; hence the term bissextile. 441. With us, in every fourth year one additional day is given to February. Now this arrangement was a very admirable one, but it is clear that the year was over- corrected. Too much was added, and the matter was again looked into in the sixteenth century, by which time the over- correction had amounted to more than ten days, the vernal equinox faUing on March 11, instead of March 21. Pope Gregory, therefore, undertook to continue the good work begun by Julius Csesar, and made the following rule for CHAP, v.] MEASUREMENT OF TIME. 215 the future : — Every year divisible by 4 to be a bissextile, or leap-year, containing 366 days ; every year not so divisible to consist of only 365 days ; every secular year (1800, 1900, &c.) divisible by 400 to be a bissextile, or leap-year, containing 366 days ; every secular year not so divisible to consist of 365 days. 442. The period by which the addition of one day in four years exceeds the proper correction amounts to nearly three days in 400 years ; by the new arrangement there are only 97 intercalations in 400 years, instead of 100. This brings matters within 22'38s. in that period, which amounts to i day in 3866 years. 443. The Julian calendar was introduced in the year 44 B.C. ; the reformed Gregorian one in 1582. It was not introduced into this country till 1752, in consequence of religious prejudices. With us the correction was made by caUing the day after Sept. 3, 1752, Sept. 14. This was called the new style (N.S.), as opposed to the old style (o.S.). In Russia the old style is still retained, although it is customary to give both dates, thus : 1887 p^,^ ^^' 444. It is impossible to overrate the importance of these various improvements devised for a better knowledge of the length of the tropical or solar year : if the calendar were not exactly adjusted to it, the seasons would not commence on the same day of the same month as they do now, but would in course of time make the com- plete circuit of all the days in the year ; January, or any other month, might fall either in spring, summer, autumn, or winter. 445. At present, owing to a change of form in the Earth's orbit (Chap. IX.), the tropical year diminishes in length at the rate of y^ths of a second in a century, and it is shorter now than it was in the time of Hipparchus by about 12 seconds.* 446. If the tropical and the anomalistic year were of ♦ Hind. 2i6 ASTRONOMY. [chap. v. equal lengths, it would follow that, as the seasons are regulated by the former, they would always occur in the same part of the Earth's orbit. As it is, however, the line joining the aphelion and perihelion points, termed the line of apsides, slowly changes its direction at such a rate that in a period of 21,000 years it makes a complete revolution. We have seen before (Art 167) that at present we are nearest to the sun about Christmas time. In A.D. 6485 the perihelion point will correspond to the vernal equinox. 447. As the length of the seasons, compared with each other, depends upon the elliptical shape of the Earth's orbit, it follows that variations in the relative lengths will arise from the variation in the position of its largest diameter. CHAPTER VI. LIGHT.— THE TELESCOPE AND SPECTROSCOPE.* Lesson XXXVL— /^%a/ Light is; its Velocity; how determined. Aberration of Light. Reflection and Refraction. Index of Refraction. Dispersion. Lenses. 448. Modern science teaches us that light consists of undulations or waves of a medium called ether, which pervades all space. These undulations — these waves of light — are to the eye what sound-waves are to the ear, and they are set in motion by bodies at a high tempera- ture — the Sun, for instance — much in the same manner as the air is thrown into motion by our voice, or the surface of water by throwing in a stone ; but though a wave motion results from all these causes, the way in which the wave travels varies in each case. 449. As we have seen, light, although to us it seems instantaneous, requires time to travel from an illuminatz«^ to an illuminat^(^ body, although it travels very quickly. What has already been said about the planet Jupiter and his moons will enable us readily to understand how the velocity of light was determined by Roemer. He found that the eclipses of the moons (which he had calculated * Sir John Herschel's work on "The Telescope." and Sir Henry Roscoe's or Schellen's work on " Spectrum Analysis," should here be consulted by the teacher. 2l8 ASTRONOMY. [chap. VI. beforehand) happened l6m. 36s. later when Jupiter was in conjunction with the Sun than when he was in opposition. Now we know (Art. 377) that Jupiter is further from us in the former case than in the latter, by exactly the dia- meter of the Earth's orbit. He soon convinced himself that the difference of time was due to the light having so much further to travel. Now the additional distance, i.e. the diameter of the Earth's orbit, being 186,000,000 miles, it follows by a rule-of-three sum that light travels about 186,300 miles a second. This fact has been abundantly proved since Roemer's time, and what astronomers call the aberration of light is one of the proofs. Fig. 51. — Shawing how a tube in movement from C to B most be inclined so that the drop a may fall to b without wetting the sides. 450. We may get an idea of the aberration of light by observing the way in which, when caught in a shower, we hold the umbrella inclined in the direction in which we are hastening, instead of over head, as we should do were we standing still. Let us make this a little clearer. Suppose I wish to let a drop of water fall through a tube CHAP. VI.] LIGHT. 279 without wetting the sides : if the tube is at rest there is no difficulty, it has onlytobeheld upright in the direction A B ; but if we must move the tube the matter is not so easy. The diagram shows that the tube must be inclined, or else the drop in the centre of the tube at a will no longer be in the centre of the tube at b ; and the faster the tube is moved the more must it be inclined. Now we may liken the drop to rays of light, and the tube to the telescope, and we find that to see a star we must incline our telescopes in this way. By virtue of this, each star really seems to describe a small circle in the heavens, representing on a small scale the Earth's orbit ; the Fig. 52. — Showing how a ray coming from a star in the direction A B changes its direction, in consequence of the refraction of the atmosphere. extent of this apparent circularmotion of the star depend- ing upon the relative velocity of light, and of the Earth in its orbit, as in Fig. 51 the slope of the tube depends, upon the relative rapidity of the motion of the tube and of the drop ; and we learn from the actual dimensions of the circle that light travels about 10,000 times faster than the Earth does — that is, about 186,000 miles a second. This velocity has been experimentally proved by M. Foucault and more recently by Professor Newcomb, by means of a turning mirror. ASTRONOMY. [chap. vi. 451. Now a ray of light is reflected hy bodies which lie in its path, and is refracted, or bent out of its course, when it passes obliquely from a transparent medium of a certain density, such for instance as air, into another of a different density, such as water. 452. By an effect of refraction the stars appear to be higher above the horizon than they really are. In Fig. 52, A B represents a pencil of light coming from a star. In its passage through our atmosphere, as each layer gets denser as the surface of the Earth is approached, the ray is gradually refracted until it reaches the surface at C, so that from C the star seems to lie in the direc- tion C B. 453. The refraction of light can be best studied by means of a piece of glass with three rectangular faces. Fig. 53. — A Prism, showing its actioa on a beam of light. called a prism. If we take such a prism into a dark room, and admit a beam of sunlight through a hole in the shutter, and let it fall obliquely on one of the surfaces of the prism, we shall see at once that the direction of the ray is entirely changed. In other words, the angle at which the light falls on the first surface of the prism is different from the angle at which it leaves it. The difference between the angles, however, is known to depend upon a law which is expressed as follows: The sines of the angles of incidence and refraction have a con- stant proportion or ratio to one another. This CHAP. VI.] LIGHT. ratio, called the index of refraction, varies in different substances. For instance, it is — 2'9 for chromate of lead. 2"o for flint glass. I '5 for crown glass. I '3 for water. 454. If we receive a beam after its passage through the prism on a piece of smooth white paper, we shall see that this is not all. Not only has the ray been bent out of its original course bodily, so to speak, but instead of a spot of white light the size of the hole which admitted the beam, we have a lengthened figure of various colours, called a spectrum. 455. This spectrum will be of the same breadth as the spot which would have been formed by the admitted light, had it not been intercepted by the prism. The lengthened figure shows us, therefore, that the beam of light in its passage through the prism must have been opened out, the various rays of which it is composed having undergone different degrees of deviation, which are exhibited to us by various colours — from a fiery brownish red where the re- fraction is least, to a faint reddish violet at the point of greatest divergence. This is called dispersion. 456. If we pass the light through prisms of different materials, we shall find that although the colours always maintain the same order, they will vary in breadth or in degree. Thus, if we employ a hollow prism, filled with oil of cassia, we shall obtain a spectrum two or three times longer than if we used one made of common glass. This fact is expressed by saying that different media have different dispersive powers — that is, disperse or open out the light to a greater or less extent. 457. Every species of light preserves its own relative place in the general scale of the spectrum, whatever be the media between which the light passes, but only in ASTRONOMY. [chap. VI. order, not in degree ; that is, not only do the different media vary as to their general dispersive effect on the different kinds of light, but they affect them in different proportions. If, for instance, the green, in one case, holds a certain definite position between the red and the violet, in another case, using a different medium, this position will be altered. This is what is termed by opticians the irrationality of the dispersions of the different media — or shortly, the irrationality of the spectrum. 458. What has been stated will enable us to understand the action of a common magnifying-glass or lens. Thus as a prism acts upon a ray of light as shown in the above F'g- S3) tw° prisms arranged as in Fig. 54 would cause two Fig. 54. — Action of two Prisms placed base to base. beams coming from points at a and b to converge to one point at c. A lens, we know, is a round piece of glass, generally thickest in the middle, and we may look upon it as composed of an infinite number of prisms. Fig. 55 shows a section of such a lens, which section, of course, may be taken in any direction through its centre, and a little thought will show that the light which falls on CHAP. VI.] LIGHT. 223 its whole surface will be bent to c, which point is called the focus. If we hold a common burning-glass up to the sun, and let the light fall on a piece of paper, we shall find that when held at a certain distance from the lens a hole will be burned through it ; this distance marks the focal KiG. 55. — Action of a Convex Lens upon a beam of parallel rays. distance of the lens. If we place an arrow, a b (Fig. 56), in front of the lens mn,v!e shall have an image of an arrow be- hind at a' b', every point of the arrow sending a ray to every point in the surface of the lens ; each point of the arrow, Fig. 56. — Showing how a Convex Lens, 7n ft, with an arrow, a b, in front of it, throws an inverted image, a' J^ , behind it. in fact, is the apex of a cone of rays resting on the lens, and a similar cone of rays, after refraction, paints every point of the image. At a, for instance, we have the apex of a cone of rays, man, which rays are refracted so as to form the cone of rays, m a' n, painting the point a! in 224 ASTRONOMY. [chap. vi. the image. So with b, and so with every other point. We see that the action of a lens, like the one in the figure, thickest in the middle, called a convex lens, is to invert the image- The line x y \^ called the axis of the lens. 459. Such, then, is a, lens, and such a lens we have in our eye ; and behind it, where the image is cast, as in the diagram, we have a membrane which receives the image as the photographer's ground glass or prepared paper does ; and when the image falls on this membrane, which is called the retina, the optic nerves telegraph as it were an account of the impression to the brain, and we see. Lesson XXXVII. — Achromatic Lenses. The Telescope. Illuminating Power. Magnifying Power. 460. Now in order that we see, it is essential that the rays should enter the eye parallel or nearly so, and the nearer anything is to us the larger it looks ; but if we attempt to see anything quite close to the eye, we fail, because the rays are no longer parallel — they are divergent. Here the common magnifying-glass comes into use ; we place the glass close to the eye, and place the object to be magnified in its focus, — that is, at c in Fig. 55 : the rays which diverge from the object are i-endered parallel by the lens, and we are enabled to see the object, which appears large because it is so close to us. 461. Similarly if we place a shilling twenty feet off, and employ a convex lens, the focal length of which is five feet, half way between our eye and the shilling, we shall have formed in front of the eye an image of the shilling, which being within six inches of the eye, while the real shilling is twenty feet off, will appear forty times larger, although in this case the image is of exactly the same CHAP. VI.] LIGHT. size as the shilling. So much for the action of a single convex lens. 462. Now, if instead of arranging the prisms as shown in Fig. 54, with their bases together, we place them point to point, it is evident that the rays falling upon them will no longer converge, or come together to a point. They will in fact separate, or diverge. We may therefore sup- pose a lens formed of an infinite number of prisms, joined together in this way ; such a lens is called a concave lens, and the shape of any section of such a lens and its action are shown in Fig. 57. 463. In some lenses one surface is flat, the other being either concave or convex ; so besides the bi-convex and Fig. 57.- -Showing the action of a Ri-Concave Lens on a beam of parallel rays. bi-concave, already described, we have plano-convex and plano-concave lenses. 464. Now we have already seen (Art. 458) that a lens is but a combination of prisms ; we may therefore expect that the image thrown by a lens will be coloured. This is the case ; and unless we could get rid of such effects, it would be impossible to make a large telescope worth using. It has been found possible however to get rid of them, by using two lenses of different shapes, and made of different kinds of glass, and combining them together, so making a combination called an acliroinatic, or colourless, lens. Q ASTKOSOMT. fcaae. tj. 465. TUs is residesEd pn^aife liif t&e laij i sg dbyu- sme piwti ia j ^Axi. 4g5) rf^fieBEglt bodies, ffwes^aelwn fTTji-riy gjmiibr |Bia M h ima^ of gbe gg™** i mM i iM i itJ ^ aaj |fecE (Hse om lis ^de arad dae oAer bdiod it «raemeof itsaii^e%dielieaataf^^«iBliecBaiec3ed: z'sefn^i viD esacEhf inido &e sok done lif die odaes^ ^id te c^ viSl neafiaa' be xe&adfed zif}^ tlif^i»^-sed; b^ if we Sake a.«^ die ^apimiad ptisai and iqlace M: lin- ems i^ide of a smbsiance bzrii^ a b^ber d^esaie pomec, ~«e ^al of cfjsacse. be ayetooado tbe di^eBive msk dose bv' ^le fiis£ frisBi vidi a smallfT riwrtiaFsg^ of ibe secarafl. Bat dns ^irawlllfr dmciae^ vill sot ^ads a3 lie isfiac- tive voA. of die fiist |— ■'^■» Thetefine die beam win lease tbe seaaoAfo^ coaamr- lessy bat itf M rted; and diis is *'■-** '^ -vmr siRnted ; tbe ekiwj tac akerratioB is cooeclEd, Imt (fte cnrat- poQnd pnsm can stiu icDsct, o^ tip»wi ^]£ lullii ( wnit aA» indie sans V2f as an admniatic prism. Tbe dispeiate pLn»'t±i= cf Sht and cnsnm ^ass are as "lo^z to 1033. Tbe font or coaxes lens is made of crovn ^bss. Tbe dovaaatic afeoiafiaK of diis is collected bf anodier bt-concasel^K |dacedbeimid it of ffint gjass. Tbe secondlexisisnatsocia^czieasSiie fiist is coorex, so die action of tbe fiist I^b is pcedomi- nant as &r as tefiaction goes; but as tbe second lais ads mote eaexgeticaUy as legards disgiosian, a Miu i gh it can- not malce tbe lajr poralld to its ordinal d ii a ii un, it can make it coknnless, or neaify so. If socb an acbramatic lens be tniljr made, and its cartes iHoped^ legahtBd, it is said to have its spberical aberration corrected as v^ as its dbromatic one, and tbe image of a star will fiinn a nearly coloudess point at its focus. 407. A little examination into the constmctian of tbe telescope will sbow us tbat the principle of its constiactian is identical with the constniction of the eye, bnt the pro- cess carried on by the eye is ertended : that is to s^,in CHAP. VI.] LIGHT. 227 the eye nearly parallel rays fall on a lens, and this throws an image j in the telescope nearly parallel fall on a lens, this lens throms an image, and then another lens enables the eye to form an image of the image by rendering the rays again parallel. These parallel rays then enter the eye just as the rays do in ordinary vision. A telescope, then, is a com- bination of lenses. 4.68. In the figure, for in- stance, let A represent the first or front lens, called the objeot- glass, because it is the lens nearest to the object viewed ; and let C represent the other, called the eye-lens, because it is nearest the eye ; and let B repre- sent the image of a distant arrow, the beam of rays from which is seen falling on the object-glass from the left. This beam is refracted, and we get an inverted image at the focus of the object-glass, which is also the focus of the eye-lens. Now, the rays leave the eye-piece adapted for vision as they fall on the object-glass, so the eye can use them as it could have used them if no telescope had been there. 469. What then has the tele- scope done ? What is its power ? This question we will soon Q 2 lens rays 228 ASTRONOMY. [chap, vi answer ; and, first, as to what is called its illnminatlng power. The aperture of the object-glass, that is to say, its diameter, being larger than that of the pupil of our eye, its surface can collect more rays than our pupil ; if this surface be a thousand times gfreater than that of our pupil, for instance, it collects a thousand times more light, and consequently the image of a star formed at its focus has a thousand times more light than the image thrown by the lens of our eye on our retina. But this is not quite true, because light is lost by re- flexion from the object-glass and by its passage through it. If, then, we have two object-glasses of the same size, one highly polished and the other less so, the illuminating power of the former will be the greater. 470. The magnifying power depends upon two things. First, it depends upon the focal length of the object-glass ; because if we suppose the focus to lie in the circumference of a circle having its centre in the centre of the lens, the image will always bear the same proportion to the circle. Suppose it covers i° ; it is e\'ident that it will be larger in a circle of 12 feet radius than in one of 12 inches. That is, it ^vill be larger in the case of a lens with 12 feet focal length than in one of 12 inches focal length. 471. Having this image at the focus, the magnifying power of the eye-piece comes into play. This varies with the eye-piece employed, the ratio of the focal length of the object-glass to that of the eye-piece giving its exact amount ; that is to say, if the focus of the object-glass is 100 inches, and that of the eye-piece one inch, the tele- scope will magnify 100 times. Bearing in mind that what an astronomer wants is a good clear image of the object observed, we shall at once recognise that useful magnify- ing power depends upon the perfection of the image thrown by the object-glass and upon the illuminating power of which we have already spoken. If the object- glass does not perform its part properly, a slight magni- fication blurs the image, and the telescope is useless. CHAP. VI.] LIGHT. 229 Hence many large telescopes are inferior to much smaller ones in the matter of magnifying power, although their illuminating power is so much greater. 472. The eye-pieces used with the astronomical tele- scope vary in form. The telescope made by Galileo, similar in construction to the modern opera-glass, was furnished with a bi-concave eye-piece. As the action of the eye-piece is to render the rays parallel, this eye-piece is used between the object-glass and the focus, at a point where its divergent action (Art. 462) corrects the conver- gent action of the object-glass. A convex eye-piece for the same reason is placed outside the focus, as shown in Fig. 58. Such eye-pieces however colour the light coming from the image in the same way as the object-glass would colour the light going to form the image, if its chromatic aberration wei'e not corrected. 473. It was discovered by Huygens however that this defect might be obviated in the case of the eye-piece by employing two plano-convex lenses, the flat sides next the eye, a larger one nearest the image, called the field-lens, and a smaller one near the eye, called the eye-lens. This construction is generally used, except for micrometers (Art. S19); 3. name given to an eye-piece with spider-webs in the focus of the eye-piece for measuring the sizes of the different objects. In this case the flat sides are turned away from the eye. 474. The telescope-tube keeps the object-glass and the eye-piece in their proper positions, and the eye-piece is furnished with a draw-tube, which allows its distance from the object-glass to be varied. 230 ASTRONOMY. [chap. vi. Lesson XXXVIII. — The Telescope (continued). Powers of Telescopes of different Apertures. Large Telescopes. Methods of Mounting the Equatorial Telescope. 4.75. Very many of the phenomena of the heavens may be seen with a small telescope. In our climate a telescope with an object-glass of six inches aperture is probably the size which will be found the most constantly useful ; a larger aperture being frequently not only useless, but hurtful. Still, \\ or 3I inches are useful apertures, and if furnished with object-glasses made of course by the best makers, views of the sun, moon, planets, and double stars may be obtained sufficiently striking to set many seriously to work as amateur observers. Thus, in the matter of double stars, a telescope of two inches aperture, with powers varying from 60 to 100, will show the following Stars double : — Polaris. y Arietis. o Geminorum. u Piscium. f Herculis. y Leonis. /i Draconis. f Ursse Majoris. ^ Cassiopeiae. A 4-inch aperture, powers 80-120, reveals the duplicity of— /3 Orionis. a Lyras. 8 Geminolrum. e Hydras. | Ursas Majoris. n- Cassiopeise. £ Bootis. y Ceti. t Draconis. And a 6-inch, powers 240-300 — c Arietis. X Ophiuchi. f Equulei. 8 Cygni. 20 Draconis. f Herculis. 32 Orionis. K Geminorum. 476. Observations should always be commenced with the lowest power, or eye-piece, gradually increasing it until the limit of the aperture, or of the atmospheric condition CHAP. VI.] LIGHT. at the time, is reached : the former being taken as equal to the number of hundredths of inches which the diameter of the object-glass contains. Thus, a 3|-inch object-glass, if really good, should bear a power of 375 on double stars where light is no object ; the planets, the moon, &c., will be best observed with a much lower power. 477- In the case of stars, owing to their immense dis- tance, no increase in their size follows the application of higher magnifiers. With planets this is different, each increase of power increases the size of the image, and therefore decreases its brilliancy, as the light is spread over a larger area. Hence the magnifying power of a good telescope is always much higher for stars than for planets, although at the best it is always limited by the state of the air at the time of observation. 478. It is always more or less dangerous to look at the Sun directly with a telescope of any aperture above two inches, as the dark glasses, without which the observer would be at once blinded, are apt to melt and crack. A diagonal reflector, however, which reflects an ex- tremely small percentage of light to the eye, and by reason of its prismatic form refracts the rest away from the tele- scope, affords a very handy method of solar observation. Care should be taken that the object-glass is properly adjusted. This may be done by observing the image of a large star out of focus. If the light be not equally dis- tributed over the image, or the circles of light which are always seen in a good telescope are not perfectly circular, the telescope should be sent back to the optician for adjustment. 479. The testing of a good glass refers to two different quahties which it should possess. Its quality, as to material and the fineness of its polish, should be such that the maximum of light shall be transmitted. Its quality as to the curves should be such that the rays passing through every part of its area shall converge abso- lutely to the same point, with a chromatic aberration ASTRONOMY. [chap. vi. sufficient to sjuround objects with a faint dark blue light. 4-80. To give an idea of the great accuracy with which a fine object-glass re&acts the light transmitted, we will take for example an object-glass of 8 inches aperture and lo feet focal length, which, if a fine one, will separate the components of y^ AndromedJE, whose angular distance is about half a second — ^that is, it will depict at its focus two minute discs of light &irly separated, the distance of whose centres, as above stated, is half a second. To come ..: the value of this half-second, as measured on a scale of inches and parts of an inch, we must consider the centre of the object-g-lass to be the centre of a circle whose radius 15 the focal length of the object-glass. The focal value of a d^ree of such a circle is 2'o944, or nearly 2^\ inches ; of a minute, ^349 of an inch ; of a second, •0005818, or j^ij^ of an inch nearly : of half a second, "0002909 inch, which ;s liitle more than the fourth part of the one-thousandth of an inch. L-giit from a fixed star passing through four refracting surfaces, and half an inch or more in thickness of glass, and filling 50 square inches of surface, and travelling 1^3 inches down the tube, is so accurately concentrated at the focal point as all to pass through the smallest hole that could be made with the most delicate needle-point through a piece of fine paper. This requires a degree of accuracy in the figuring and polishing of the material of the lenses almost inconceivable^ 481. We have so far confined our attention to the principles of the ordinary astronomical telescope, and we have dealt n-ith it in its simplest form. There are other kinds ; the construction of some of which depends upon reflection ; that is to say, the light is reflected by a concave mirror instead of being refracted by a lens ; but we need not dwell upon them. Let us next inquire what the very largest telescope really can do. The largest re&aictor — as the refi^acting telescopes are called — in the world has recently been completed by Messrs. Alvan Clark Plate XIII. EiGHT-iNXH Equatorial Telescope, with the Cooke mounting. CHAP. VI.] LIGHT. 23s and Sons, American opticians of great eminence, for the Pulkowa Observatory, near St. Petersburg. The object- glass is 30 inches in diameter. Now, the pupil of our eye is one-fifth of an inch in diameter : this object-glass, there- fore, will grasp 22,500 times more light than the eye can : if used when the air is pure, it should easily bear a power of 3,000 on the Moon ; in other words, the Moon will appear as it would were it 3,000 times nearer to us, or at a distance of 78 miles, instead of, roughly, 234,000 ; measuring from the surfaces of the Earth and Moon, and not from their centres. The largest reflector in the world has been constructed by the late Earl of Rosse ; its mirror, or speculum, is six feet in diameter, and its illuminating power is such that it enables us to see, " as clearly as the heavens shine to us on a cloudless evening, the details of a starry uni- verse, stretching into space five hundred times further than those depths at which we are accustomed to gaze almost in oppressive silence." * 482. An astronomer wants telescopes for two kinds of work : he wants to watch the heavenly bodies, and study their physical constitution ; and he wants to note their actual places and relative positions ; so that he mounts or arranges his telescope in several different ways. 483. For the first requirement it is only essential that the instrument should be so arranged that it can command every portion of the sky. This may be accom- plished in various ways : the best method of accomplish- ing it is shown in Plate XIIL, which represents an 8-inch telescope, equatorially mounted — or, shortly, an equatorial — that is, an instrument so mounted that a heavenly body may be followed from rising to setting by one continuous motion of the telescope, which motion may be communicated by clockwork. 484. In this arrangement a strong iron pillar supports a head-piece, in which is fixed the polar axis of the instru- * Nichol. 236 ASTRONOMY. [chap. vi. ment parallel to the axis of the Earth, which polar axis is made to turn round once in twenty-four hours by the clock shown to the right of the pillar. 485. It is obvious that a telescope attached to such an axis will always move in a circle of declination, and that a clock, carrying the telescope in one direction as fast as the Earth is carrying the telescope from a heavenly body in the opposite one, will keep the telescope fixed on the object. It is inconvenient to attach the telescope directly to the polar axis, as the range is then limited : it is fixed, therefore, to a decimation axis, placed above the polar axis, and at right angles to it, as shown in the plate. 486. For the other kinds of work, telescopes, generally of small power except in important observatories, are mounted as altazimuths, transit-instruments, transit- circles, and zenith-sectors. These descriptions of mounting, and their uses, will be described in Chap. VII. Lesson XXXlX.— TAe Solar Spectrum. The Spectro- scope. KirchKoff's Discovery. Physical Constitution of the Sun. 437. A careful examination of the solar spectrum has told us the secret of the enormous importance of solar radiation (Art. 124). Not only may we liken the gloriously coloured bands which we call the spectrum to the key- board of an organ — each ray a note, each variation in colour a variation in pitch — but as there are sounds in nature which we cannot hear, so there are rays in the sunbeam which we cannot see. 488. What we do see is a band of colour stretching from red, through yellow, green, blue, violet, indigo, to lavender, but at either end the spectrum is continued. CHAP. VI.] LIGHT. 237 There are dark rays before we get to the red, and other dark rays after we leave the lavender — the former heat rays, the latter chemical rays ; and this accounts for the threefold action of the sunbeam : heating power, lighting power, and chemical power. 489. When a cool body, such as a poker, is heated in the fire, the rays it first emits are entirely invisible, or dark : if we looked at it through a prism, we should see nothing, although we can easily perceive by the hand that it is radiating heat. As it is more highly heated, the radiation from the poker gradually increases, until it becomes of a dull red colour, the first sign of incandes- cence ; in addition to the dark rays it had previously emitted, it now sends forth waves of red light, which a prism will show at the red end of the spectrum : if we still increase the heat and continue to look through the prism, we find, added to the red, orange, then yellow, then green, then blue, indigo, and violet, and when the poker is white- hot all the colours of the spectrum are present. If, after this point has been reached, the substance allows of still increased heating, it will give out with increasing in- tensity the rays beyond the violet, until the glowing body can rapidly act in breaking up chemical combinations, a p.ocess which requires rays of the highest refrangibility — the so-called chemical, actinic, or ultra-violet rays. 490. We owe the discovery of the prismatic spectrum to Sir Isaac Newton, but the colouring is but one part of it. Dr. Wollaston in the year 1802 discovered that there were dark lines crossing the spectrum of sunlight in dif- ferent places. These have been called Fraunhofer's lines, as an eminent German optician of that name after- wards mapped the plainest of them with great care : he also discovered that there were similar lines in the spectra of the stars. The explanation of these dark lines we owe to Stokes, and more particularly to Kirchhoff. The law which explains them was, however, first proved by Balfour Stewart. 238 ASTRONOMY. [chap. vi. 491. We shall observe the lines best if we make our sunbeam pass through an instrument called a spectro- scope, in which several prisms are mounted in a most careful manner. We find the spectrum crossed at right angles to its length by numerous dark lines — gaps — which we may compare to silent notes on an organ. Now if we light a match and observe its spectrum, we find that it is continuous — that is, from red through the whole gamut of colour to the visible limit of the violet : there are no gaps, no silent notes, no dark lines, breaking up the band. Another experiment. Let us burn something which does not burn white ; some of the metals will answer our purpose. We see at once by the brilliant colours that fall upon our eye from the vivid flame that we have here something different. The prism tells us that the spectrum, instead of being continuous as before, now consists of two or three lines of light in different parts of the spectrum, as if, on an organ, instead of pressing down all the keys, we but sounded one or two notes in the bass, tenor, or treble. Again, let us try still another experiment. Let us so arrange our prism, that while a sunbeam is decomposed by its upper portion, a beam proceeding from such a light- source as sodium, iron, nickel, copper, or zinc, may be decomposed by the lower one. We shall find in each case, that when the bright lines of which the spectrum of the metal consists flash before our eyes, they will occupy absolutely the same positions in the lower spectrum as some of the dark bands, the silent notes, do in the upper solar one. 492. Here, then, is the germ of KirchhofF's discovery, on which his hypothesis of the physical constitution of the Sun is based ; and here is the secret of the recent additions to our knowledge of the stars, for stars are suns. Vapours of metals, and gases, absorb those rays which the same vapours of metals and gases themselves emit. CHAP. VI.] LIGHT. 241 493. By experimenting in this manner, the following generalisations have been established : — I. — When solid or liquid or densely gaseous bodies are incandescent, they give out continuous spectra. II. —When a solid or liquid body reduced to a state of gas, or any gas itself, is rendered incandescent, the spectrum consists of bright lines only, and these lines are different for different substances. III. — When light from a solid or liquid passes through a gas, the gas absorbs those particular rays of light of which its own spectrum consists. This third law is the one established by Kirchhoff in i8S9- 494. We are now in a position to inquire what has become of those rays which the dark lines in the solar spectrum tell us are wanting — those rays which were arrested in their path, and prevented from bearing their message to us. Before they left the regions of our incan- descent Sun, they were arrested by those particular metallic vapours and gases in his atmosphere, with which they beat in unison; and the assertion, that this and that metal exists in a state of vapour in the Sun's atmosphere, is based upon their non-arrival ; for so various and constant are the positions of the bright bands in the spectra we can observe here, and so entirely do they correspond with certain dark bands of the spectrum of the Sun, that it has been affirmed, that the chances in favour of the hypothesis being right are something like 300,000,000 to I. 495. So much for the Sun. Fraunhofer was the first to apply this method to the stars ; and we have within the last score of years reaped a rich harvest of facts, in the actual mapping down of the spectra of several of the brightest stars, and the detailed examination of a very large number. In fact, a spectroscopic star catalogue to include all northern stars down to 7| magnitude, is now 242 ASTRONOMY. [chap. vi. in preparation, of which the first part, giving the spectra of 4,051 stars was published in 1883. The plan of struc- ture in all of them can be referred back to meteor-swarms. We find vapours sifting out the rays which come from the interior incandescent masses, which may consist of red- or white-hot mereorites, or of dense vapours produced by the volatilization of meteorites, according to the stage of condensation. (See Art 65.) 49Sa. Fraunhofer examined light coming from all parts of the Sun. In 1866 Lockyer proposed a detailed exam- ination of its surface and of the surrounding regions. In 1868 Janssen and Lockyer succeeded in rendering the red prominences visible by these means wherever the Sun shines, thereby opening a field of research which has proved of the highest importance. LESiOX XL. — Importarue of this method of Research. Physical Constitution of the Stars, Nebula, Moon, and Planets. Construction of tlie Spectroscope. Celes- tial Photography. 4-96. .\ few words will show the high significance of these facts from an astronomical point of view. They tell us, that as the spectrum of the Sun's light contains dark lines, the Ught is due to soUd or liquid particles in a state of great heat, or as it is called, incandescence, and that the light given out by these particles is sifted, so to speak, bv its atmosphere, which consists of the vapours of the substances incandescent in the photosphere. Further, as the lines in the reversed spectra occupy the same positions as the bright lines given out by the glowing particles would do, and as we can by experimenting on the different metals match many of the lines exactly, we can thus see which kind of light is thus abstracted, and what substance gives out this light: having done this, we know what sub- stances i^.Axt. 123) are present in the Sun. 497. Again, we learn by the same method that many of CHAP. VI.] LIGHT. 243 the stars are, more or less, like the Sun, for when they are analyzed in the same manner we find nearly the same appearances ; and here again in the same manner we can tell what substances are present in the stars Art. 67). 4-98. The spectra of the nebulas, instead of resembUng that of the Sun and stars, — that is, showing a band of colour with black lines across it, — -consist of a few bright lines merely. 499. On August 29, 1864, Dr. Huggins directed his telescope, armed with the spectrum apparatus, to the planetary nebula in Draco. At first he suspected that some derangement of the instrument had taken place, for no spectrum was seen, but only a short line of light, perpendicular to the direction of dispersion. He found that the light of this Nebula, unlike any other extra- terrestrial light which had yet been subjected to prismatic analysis, was not composed of light of different refrangi- bilities, as in the case of the Sun and stars, and it there- fore could not form a spectrum. A great part of the light from this Nebula is monochromatic, and was seen in the spectroscope as a bright line. A more careful exami- nation showed another line, narrower and much fainter, a little more refrangible than the brightest line, and sepa- rated from it by a dark interval. Beyond this again, at about three times the distance of the second line, a third exceedingly faint line was seen. 500. The strongest line was at first considered as due to nitrogen, but subsequent investigation has shown it to be due to magnesium vapour at a low temperature. The faintest of the lines of the Nebula coincides with the line of hydrogen, corresponding to the line F in the solar spectrum. The origin of the other bright line has not yet been determined, but it is seen in the spectra of some meteorites. 601. Here, then, we have three little lines for ever disposing of the notion that nebulas may be clusters of stars. How trumpet-tongued does such a fact speak 244 ASTRONOMY. [chap, vi. of the resources of modem science ! As we have already learned (Art. 96), nebulae are merely clouds of meteorites which are rendered luminous by the heat due to collisions. The spectra of some of them are almost perfectly con- tinuous, and this is because the meteorites composing them are only hot enough to be incandescent, and do not give off sufficient vapour to produce a spectrum of lines. When the temperature is increased by the condensation due to gravity, hydrogen and magnesium vapour fill the interspaces and give us a spectrum of bright lines. There are no absorption lines in the spectra of nebulas, because they are masked by the radiation from the greater volume of interspace. It is a comparatively simple matter to reproduce the spectra of nebute in the laboratory. A few pieces of a meteorite containing a fair percentage of magnesium, or a few pieces of olivine, are placed in a glass tube fitted with platinum points, so that an electric discharge can be made to pass along them. The tube having been exhausted by a Sprengel pump, and the meteorites heated, the spectrum of the glow is seen to contain the hydrogen lines which are seen in nebulae, and the chief nebula line, which has already been stated to be due to magnesium ; in some cases the middle line, between the hydrogen line F, and the magnesium line, is also seen, but this makes its appear- ance much more rarely than the principal line. The chief nebula line may also be observed by burning magnesium ribbon in front of the slit of a spectroscope. The brightest part of the spectrum seen is a fluting, the brightest edge of which coincides with the nebula line. In most of the nebulae, only a line is seen to correspond to this fluting, but on one occasion, at Greenwich, the spectrum of the nebula in Orion was observed to give a fluting in place of the ordinary line. We know that under certain conditions only the remnants of flutings are seen, so that they put on the appearance of lines. S02. In our own system, that moonshine is but sun- shine second-hand, and that the Moon has no sensible CHAP. VI.] LIGHT. 245 atmosphere, is proved by the fact, that in the spectroscope there is no difference, except in brilliancy, between the two ; and that the planets have atmospheres is shown in like manner, since in their light we find the same lines as in the solar spectrum, with the addition of other lines due to the absorption of their atmospheres. 503. In the frontispiece are given a representation of the solar spectrum, two maps of stellar spectra, and the spectrum of the nebula 37, H iv. The double line of sodium, showing the absorption as well as the radia- tion, is also given to explain the coincidences referred to in the next article, on which our knowledge of the sub- stances present in the atmospheres of the Sun and stars depends. The light given out by the vapour of sodium consists mainly of the double line shown in the plate. A black double line, in exactly the same position in the spectrum, is seen in the spectra of the Sun, Vega, and a Orionis. Similarly, the spectrum of the vapour of iron contains 400 or 500 bright lines matched by co-inci- dent lines in the spectrum of the Sun. The feebleness of the hght of the stars does not permit all these lines to be observed if they are present. It is seen in the plate that one of the bright lines in the spectrum of the nebula is coincident with one of the lines of hydrogen, while another (the least refrangible) agrees in position with the edge of the fluting in the spectrum of magnesium. The great Orion nebula and a few others show, in addition, a fourth bright line, found to be identical with the dark- blue ray of hydrogen. Photographed spectra of some of the nebulae show a low-temperature magnesium line in the ultra-violet. 504. The spectrum of a Orionis, which is a partially condensed meteor-swarm, consists of dark flutings and lines. The flutings are due to the vapours of magnesium, manganese, iron, lead, and barium, and some of the lines are due to sodium, magnesium, calcium, iron, and bis- muth. The absorption is brought about by the metallic 246 ASTRONOMY. [chap. vi. vapours surrounding the incandescent meteorites. This is one of the best examples of the bodies belonging to Group II. 504a. Stellar spectra were divided by Secchi into four classes, but having regard to the meteoric origin of the various orders of celestial bodies, it will be well to adopt the following classification. Group I. Radiation lines and flutings are predominant. This group includes nebulae and the so-called " stars " with bright-line spectra. /3 Lyras and y Cassiopeiae belong to this group. In the last species of the group, absorption begins. The radiation is chiefly that of hydrogen and magnesium. Group II. Mixed radiation and absorptidn predominant. The radiation is chiefly that of carbon vapour, which fills the interspaces, and the absorption is due to layers of vapours of magnesium, manganese, iron, lead, barium, &c., which surround the incandescent meteorites. The stars of this class are reddish and their spectra consist of dark flutings fading gradually towards the red, superposed upon the bright flutings of carbon, which fade towards the blue. Many variable stars belong to this group, notably " Mira " in the Whale, and the " new star" recently observed in Orion. There is a considerable variation in the spectra of this group, according to the proportion of meteorites to inter- space and carbon radiation to metallic absorption. In fact, it is convenient to subdivide this group into fifteen species, according to the number and intensities of the flutings present. Group III. Line absorption predominant, the tempera- ture also increasing. The various species will be marked by increasing simplicity of spectrum. The meteorites have all been volatilized. Group IV. Simplest line absorption predominant. The spectra are characterized by the strong absorption of hydrogen, while the metallic lines are thin and faint. CHAP. VI.] LIGHT. 247 The stars of this group are the hottest. Vega (a Lyrae) belongs to this group. (See Frontispiece.) Group V. Line absorption predominant with decreasing temperature. The various species will be marked by- decreasing complexity of spectrum. The mass of meteoric vapour is now cooling, and the phenomena will be very nearly the same as those of Group in. The Sun, Capella, and Pollux belong to this group. The lines are narrow and very numerous, the substances which they indicate being those known to exist in meteor- ites. The spectrum of the Sun can be almost perfectly reproduced by volatilizing a mixture of meteorites in the electric arc. Group VI. Carbon absorption predominant. The cen- tral portion of the mass of meteoric vapour has now become very densely gaseous or liquid, or solid, and is surrounded by an atmosphere consisting largely of carbon. None of the stars of this group are brighter than the fifth magni- tude, and are usually of a deep red tint. This classifi- cation is the one which the most recent researches in celestial physics has led to, and it will be seen that the basis of it is the differences brought about by differences of temperature. The substances present in all the bodies are the same, or, at least, there is no reason why there should be any differences in composition, and there is no necessity to assume any such differences in order to explain the various phenomena presented to us. We begin with sparse swarms of meteorites at low tempera- tures, pass through the various phenomena of increasing temperatures to stars like Vega, then through those of decreasing temperatures, finally ending with cold con- densed and consolidated masses. Further, it is possible that bodies of the latter kind may collide as individual meteorites do, and by such collisions become again re- solved into swarms of meteorites, and thus complete the celestial cycle. 248 ASTROXOilY. [chap. vi. 5041). The spectroscope not only gives us information as to the chemical constitution of the heavenly bodies, but teUs us also something of their movements. And, what i5 very fortunate, the kind of movements which can be determined spectroscopically are just those of which the eye takes no direct account, because they result in no \-isible displacement.- They are motions in the Une of sight, that 15, straight towards, or straight from the eye. Now the effect produced by very rapid motion of this kind upon light entering the eye from the moving object, is quite analogous to the rise and fall in the pitch of a steam- whistle when an express train dashes through a station. While the train is coming up, the shriUness of the whistle is increased because the vibrations of sound are crowded into the ear by the swiftness of its approach ; and the sound sinks as it retreats just for the opposite reason. In the same way, the \-ibrations of light are pushed together, or pulled asunder by the enormously more rapid move- ments of the stars. The whole gamut, so to speak, of the spectrum, is shifted a Uttle towards the blue or red accord- ing as the star, or other heavenly body, is advancing or retreating ; and the amount of this shifting can be measured by the comparison of the well-known bright or dark lines thus altered in position with the same lines as they ordinarily appear. It is in this way that the tre- mendous cyclone movements in the sun and atmosphere mentioned in Art. 250, have been ascertained ; and even the rate of the sun's rotation can be determined by the slighdy varied positions of the Fraunhofer lines in light taken from the right and left limbs, the effect of rotation being to bring the left limb continually forward while the right limb retreats from the eye with equal speed. Dr. Huggins in 1868 first succeeded in measuring the velocities of stars in the line of sight, and the work is now regularly carried on at Greenwich. Subjoined are some of the results : — CHAP. VI.] LIGHT. 249 Stars Approaching the Earth. Name of Star. Miles per second. Arcturus 42 Alpha Lyrse (Vega) 36 Alpha Cygni (Deneb) 37 Beta Geminorum (PoUu.x) . . 35 Alpha Ursae Majoris (Dubhe) . . .46 Alpha Andromedse 32 Delta Andromedse . 50 Beta Ceti 54 Alpha Pegasi (Markab) . . . . 32 Alpha Arietis .... . 10 Stars Receding from the Earth. Name of Star. Mile.s per second. Alpha Tauri (Aldebaraii) . . 45 Alpha Trianguli ... . . . 58 Beta Andromedae 45 Capella • . . . . 29 Alpha Orionis (Betelgeux) . . . . 16 Beta Orionis (Rigel) . . . .12 Sirius must at present be included amongst the stars approaching the earth, its rate of approach, as determined in 1886, being about thirty miles a second. But ten years previously, it was receding with about equal velocity, after which it gradually slackened, and in 1883, reversed its motion. Similar changes appear to have affected the movements of Procyon during the same interval. 505. The star spectroscope, Fig. 59, with which Dr. Muggins's earlier results were obtained, is attached to the eye end of an equatorial. As the spectrum of the point which the star forms at the focus is a line, the first thing done in the arrangement adopted is to turn this line into a band, in order that the lines or breaks in the light may be rentiered visible. The other parts of the arrangement are as follows : — A plano-convex cylindrical lens, of about fourteen inches 250 ASTRONOMY. [chap. VI. focal length, h placed with its axial direction at right angles to the direction of the slit, and at such a distance before the slit, within the converging pencils from the object-glass, as to give exactly the necessary breadth to CHAP. VI.] LIGHT. 251 the spectrum. Behind the slit, at a distance equal to its focal length, is an achromatic lens of 4^ inches focal length. The dispersing portion of the apparatus consists of two prisms of dense flint glass, each having a refracting angle of 60°. The spectrum is viewed through a small achromatic telescope, provided with proper adjustments, and carried about a centre suitably adjusted to the posi- tion of the prisms by a fine micrometer screw. This measures to about the -sir^oTth part of the interval between A and H of the solar spectrum. A small mirror attached to the instrument receives the light, which is to be com- pared directly with the star spectrum, and reflects it upon a small prism placed in front of one half of the slit. This light was usually obtained from the induction-spark taken between electrodes of different metals, raised to incan- descence by the passage of an induced electric current. 506. The spectroscope represented in Plate XIII. is a very powerful one, made by Mr. Browning for Mr. Gassiot, and was for some time employed at the Kew Observatory for mapping the solar spectrum. The light enters at a narrow slit in the left-hand collimator, which is furnished with an object-glass at the end next the prism, to render the rays parallel before they enter the prisms. In the passage through the prisms the cylindrical beam of light is made to describe a circular path, widening out as it goes, and in consequence enters the telescope on the right of the drawing. It is often convenient to employ what is termed a direct-vision spectroscope — that is, one in which the light Fig. 60. — Path of the ray in the Herschel-Browning spectroscope. enters and leaves the prisms in the sam.e straight line. How this is managed in the Herschel-Browning spectro- 252 ASTRONOMY. [chap. vi. scope, one of the best of its kind, may be gathered from Fig. 60. 507. In both telescopic and spectroscopic observations the visible rays of light are used. The presence of the chemical rays, however, enables photographs of the heavenly bodies to be taken, and celestial photography, in the hands of Mr. De la Rue and Mr. Rutherfurd, made its first rapid advance towards its present high state of perfection. The method adopted is to place a sensitive plate in the focus of a reflector or refractor properly cor- rected for the actinic rays, and then to enlarge this picture to the size required. Mr. De la Rue's pictures of the Moon, some I5 inches in diameter, are of such perfection that they bear subsequent enlargement to 3 feet. Prints of the Sun are now regularly taken at Greenwich and South Kensington ; and where the record is interrupted by clouds, it is filled in by pictures obtained on the same plan in the Mauritius and in India. The art promises to be one of the great engines of astronomical research in the future. Already a nebula has been discovered in the Pleiades by the camera, which had never previously been seen with the telescope, and stars down to the sixteenth magnitude can be photographed with such distinctness that the laborious process of charting small stars may be said to be superseded by the comparatively expeditious method of printing them, or rather, letting them print themselves. The absolute truthfulness of celestial photo- graphs gives them a special value as records. Mr. Com- mon's splendid picture of the Orion nebula may reveal to future astronomers changes of wonderful interest in that strange mass of glowing vapours. Tebbutt's comet was the first body of the kind successfully photographed, pre- vious attempts having failed through the extreme chemical feebleness of cometary light. Now, however, not only comets themselves, but their spectra, as well as the spectra of stars, nebute, sunspots, and even of the solar chromosphere across the blaze of daylight, stamp their im- pressions with the utmost delicacy on the sensitive plate. CHAPTER VII. DETERMINATION OF THE APPARENT PLACES OF THE HEAVENLY BODIES. Lesson XLI. — Geometrical Principles. Circle. Angles. Plane and Spherical Trigonometry. Sextant. Micro- meter. The Altazimuth and its Adjustments. 508. That portion of our subject which deals with apparent positions is based upon certain geometrical principles, among which the properties of the circle are the most important. 509. A circle is a figure bounded by a curved line, all the points in which are at the same distance from a point within the circle called the centre. The curved line itself is called the circumference ; a line from any part of the circumference to the centre is called a radius j and if we prolong this line to the opposite point of the circumference we get a diameter. Consequently, a diameter is equal to two radii. 510. The circumference of every circle, large or small, is divided into 360 parts, called degrees, which, as we have before stated (Art. 159), are divided into minutes and seconds, marked (') and ("), to distinguish them from minutes and seconds of time, marked (™) and ('). 254 ASTRONOMY. [chap. vii. 511. That part of the circumference intercepted by any lines drawn from it to the centre is called an arc, and the two lines which join at the centre inclose what is called an angle, the angle in each case being measured by the arc of the circumference of the circle intercepted. 512. The arc, and therefore the measured angle, will contain the same number of degrees, however large or small the circle may be — or, in other words, whatever be the diameter. Each degree will, of course, be larger in a large circle than in a small one, but the number of degrees in the whole circumference will always remain the same ; and therefore the angle at the centre will subtend the same number of degrees, whatever be the radius of the circle. 513. An angle of 90° is called a right angle, and there are therefore four such angles at the centre of a circle. The two lines which form a right angle are said to be at ^ right angles to each other. If we print a T, for instance, like this J_, we get two right angles, and the upright stroke is called a perpendicnlar. 514-. When the opening of an angle is expressed by the number of degrees of the arc of a circle it contains, it is called the angular measure of the angle. Another property of the circle is, that whatever be its size, the diameter, and therefore the radius, always bears the same proportion to the circumference. The circumference is a little more than three times the diameter — more exactly expressed in decimals, it is 3-14159 times the diameter ; in other words — diam. x 3i4i59=circumference ; and therefore circumference-=-3-i4i59 = 'lia™eter. For the sake of convenience, this number 3'i4iS9 is expressed by the Greek letter it. When either the radius, diameter, or circumference is known, we can easily find the others. CHAP, vii.] DETERMINATION OF POSITIONS. 255 515. We next come to the properties of triangles. A triangle is a figure which contains three angles, and it is therefore bounded by three sides. If all three sides are on the same plane, the triangle is called a plane triangle ; but if they lie on the surface of a sphere, it is called a spherical triangle, and the sides, as well as the angles, may be expressed in angular measure ; as the angular length of each side is the angle formed by its two ends at the centre of the sphere. For instance, if we on a ter- restrial globe draw lines connecting London, Dublin, and Edinburgh, we shall have a spherical triangle, as the Earth is a sphere ; and we can express the opening of each angle and the length of each side in degrees. We may treat three stars on the celestial sphere in the same manner. Each angle of a plane triangle is determined as we have already seen ; and it is one of the properties of a triangle that the three interior angles taken together are equal to two right angles — that is, 180°. It is clear, therefore, that if we know two of the angles, the third is found by subtracting their sum from 180°. Fig. 61. — Two Triangles. Here are two triangles, and they look very unlike ; but there is one thing in which we have just seen they exactly resemble each other. The angles abcm both are together equal to two right angles. Now one is a right-angled triangle, i.e. the angle b is 3. right angle, or an angle that contains 90° ; consequently, we know that the other angles, a and c, are together equal to 90° ; and therefore, 256 ASTRONOMY. [chap. vn. if we know how many degrees the angle a ox c contains, we know how many the other must contain. Why are we so anxious to know about these angles ? Let us see. Here are three more triangles — B Fig. 62. — Triangles with two equal sides and unequal bases. apparently very unlike ; but still we have made the sides ac, ad, ae, af, ag, ak, all equal. Now look at the upper angles a, and look at their bases B B B" : where the angle is widest, the base is longest ; where narrowest, the base is shortest. There is an obvious connexion between the angle and the side opposite to it, not only in the three triangles, but in each one taken separately ; and in fact, in any triangle, the sides are respectively proportional, not actually to the opposite angles them- selves, but to a certain ratio called the sine (Art. 516) of these angles. Moreover, we can express any side of a triangle in terms of the other sides and adjacent angles, or of the other sides and the angle between them. In short, that branch of mathematics called trigonometry teaches us to investigate the properties of triangles so closely that when in any triangle we have two angles, and the length of one side, or one angle and the length of two sides, whether the triangle lie before us on a piece of paper, or have at one of the angles a tower which we cannot reach, or the Sun, or a star, we can find out all about it. 516. Angles are studied by means of certain quantities called trigonometrical ratios, which we give here, in CHAP. VII.] DETERMINATION OF POSITIONS. 257 ofder that some terms which will be necessarily used in the sequel may be understood. Fig. 63. — Trigonometrical ratios. BACmay represent any angle, and PM is perpendicular to AB. Then, for the angle .4, PM . perpendicular T is called the sine of A AP, ' ■^' hypothenuse, J (written ««. A). AM . base 1 is called the cosine of A AP, ^ '^' hypothenuse, / (written cos. A). PM . perpendicular \ is called the tangent of A AM, *"^* '^' tese; J (written tan. A). AM . base 1 is called the co-tangent of PM, *^^* '^' perpendicular, J" A (written cot. A). AP . hypothenuse "lis called the secant oi A 'AM, *^' '^' base, / (written sec. A). AP . hypothenuse ) is called the co-secant of A PM, *^' '^' perpendicular, \ (written cosec. A). 517. We shall return to the use of plane triangles in astronomical methods in the next chapter. It may here be remarked that the apparent places of the heavenly bodies are referred to the celestial sphere by means of spherical triangles, which are investigated by trigonometrical ratios, in the same manner as plane triangles, and hence this part of our subject is called Spherical Astronomy. SIS. In all the instruments about to be described, s 258 ASTRONOMY. [chap, vii, angles are measured by means of graduated arcs, or circles attached to telescopes, the graduation being car- ried sometimes to the hundredth part of a second of arc by verniers or microscopes. It is of the last importance, not only that the circle should be correctly graduated, but that it should be correctly centred,— that is, that the centre of movement should be also the centre of graduation. To afford greater precision, spider webs, or fine wires, are fixed in the focus of the telescope to point out the exact centre of the field of view. An instrument with the cross wires perfectly adjusted is said to ba correctly collimated. 519. In addition to the fixed wires, moveable ones are sometimes employed, by which small angles may be measured. An eye-piece so arranged is called a micro- meter, or a micrometer eye-piece. The moveable wire is fixed in a frame, set in motion by a screw, and the dis- tance of this wire from the fixed central one is measured by the number of revolutions and parts of a revolution of this screw, each revolution being divided into a thou- sand parts by a small circle outside the body of the micrometer, which indicates C when the moveable and central wires are coincident, and at each complete revo lution on either side of the latter. The angular value of each revolution is determined by allowing an equa- torial star to traverse the distance between the wires, and turning the time taken into angular measurement. Attached to the micrometer, or to the eye-piece which carries it, is also a position-circle, divided into 360° ; by this the angle made by the line joining two stars, for instance, with the direction of movement across the field of view, is determined. The use of the position-circle in double-star measurements is very important, and it is in this way that their orbftal motion has been determined. The micrometer wires, or the field of view, are illuminated at night by means of a small lamp outside, and a reflector inside, the telescope (see Plate XIV.). Plate XV. Portable Altazimuth Instrument. CHAP.vn.J DETERMINATION OF POSITIONS. 261 520. If we require to measure simply the angular distance of one celestial body from another, we employ a sextant j but generally speaking, what is to be deter- mined is not merely the angular distance between two bodies, but their apparent position either on the sphere of observation or on the celestial sphere itself 521. In the former case, — that is, when we wish to determine positions on the visible portion of the sky, — we employ what is termed an altitude and azimttth instru- ment, or, shortly, an altazimuth; and if we know the sidereal time, or, in other words, if we know the exact part of the celestial sphere then on the meridian, we can by calculation find out the right ascension and dechnation (Art. 328), referred to the celestial sphere, of the body whose altitude and azimuth on the sphere of observation we had instrumentally determined. 522. An altazimuth is an instrument with a vertical central pillar supporling a horizontal axis. There are two circles, one horizontal, in which is fitted a smaller (ungraduated) circle with attached verniers fixed to the central pillar, and revolving with it ; another, vertical, at one end of the horizontal axis, and free to move in all vertical planes. To this latter the telescope is fixed. When the telescope is directed to the south point, the reading of the horizontal circle is 0° ; and when the tele- scope is directed to the zenith, the reading of the vertical circle is 0°. Consequently, if we direct the telescope to any particular star, one circle gives the zenith distance of the star (or its altitude) ; the other gives its azimuth. If we fix or damp the telescope to the vertical circle, we can turn the axis which carries both round, and observe all stars having the same altitude, and the hoi izontal circle will show their azimuths ; if we clamp the axis to the horizontal circle, we can move the telescope so as to make it travel along a vertical circle, and the circle attached to the telescope will give us the zenith distances of the stars (or their altitudes), which, in this case, will lie in 262 ASTRONOMY. [CHAP. vii. two azimuths i8o° apart A portable altazimuth is repre- sented in Plate XV., the various parts of which will be easily recognised from the foregoing description. 523. To make an observation with the altazimuth, we must first assure ourselves that the instrument itself is in perfect adjustment — that is, that the circles are truly graduated and centred (Art. 518), and that there is no error of coUimation in the telescope. This done, it must be perfectly levelled, so that the vertical circle is in all positions truly vertical, and the horizontal circle truly horizontal. Next, we must know the exact readings of the verniers of the azimuth circle when the telescope is in the meridian, and the exact readings of the verniers of the vertical circle when the telescope points to the zenith. This done, we may point the telescope to the body to be observed, bring it to the cross wires visible in the field of view, and note the exact time. The verniers on the two circles are then read, and from the mean of them the in- strumental altitude and azimuth are determined. The observation should then be repeated with the telescope on the opposite side of the central pillar, as by this means some of the instrumental errors are got rid of. Lessox XLII. — The Transit Circle and its Adjust- ments. Principks of its Use. Methods of Taking Transits. The Chronograph. The Equatorial. 524-. '\\Tien we wish to determine directly the position of a celestial body on the celestial sphere itself, a transit circle is almost exclusively used. This instrument consists of a telescope moveable in the plane of the meridian, being supported on two pillars, east and west, by means of a horizontal axis. The ends of the horizontal axis are of exactly equal size, and move in pieces, which, from their shape, are called Ys. When the instrument is in perfect adjustment, the line of coUimation of the telescope CHAP. VII.] DETERMINATION OF POSITIONS. 263 is at right angles to the horizontal axis, the axis is exactly horizontal, and its ends are due east and west. Under these conditions, the telescope describes a great circle of the heavens passing through the north and south points and the celestial pole ; in other words, the telescope in all positions points to some part of the meridian of the place. On one side of the telescope is fixed a circle, which is read by microscopes fixed to one of the supporting pillars. The cross wires in the eye-piece of the telescope enable us to determine the exact moment of sidereal time at which the meridian is crossed : this time is, in fact, the right ascension of the object. The circle attached shows us its distance from the celestial equator : this is its declination. So by one observation, if the clock be right, the instrument perfectly adjusted, and the circle correctly divided, we get both co-ordinates. In Plate XVI. is given a perspective view of the great transit circle at Greenwich Observatory, designed by the late Astronomer-Royal, Sir George Airy. It consists of two massive stone pillars, supporting the ends of the horizontal axis of the telescope, which rests on Ys, as shown in the case of one of the pivots in the drawing. Attached to the cube of the telescope (to which the two side-pieces, the eye -piece end and object-glass end, are screwed) are two circles. The one to the right is graduated, and is read by microscopes pierced through the right-hand pillar ; the eye-pieces of these microscopes are visible to the right of the drawing. The other circle is used to fix the telescope, or to give it a slow motion, by means of a long handle, which the observer holds in his hand. The eye-piece is armed with a micrometer, with nine equidistant vertical wires and two horizontal ones. The wheels and counterpoises at the top of the view are to facilitate the raising of the telescope when the collimators, both of which are on a level with the centre of the telescope — one to the north and one to the south — are examined. 264 ASTRONOMY. [chap. vii. 525. As we have already seen (Art. 329) a celestial meridian is nothing but the extension of a terrestrial one ; and as the latter passes through the poles of the Earth, the former will pass through the poles of the celestial sphere: consequently, in England the northern celestial pole will lie somewhere in the plane of the meridian. If the position of the pole were exactly marked by the pole- star, that star would remain immoveable in the meridian ; and when a celestial body, the position of which we wished to determine, was also in the meridian, if we adjusted the circle so that it read 0° when the telescope pointed to the pole, all we should have to do to determine the north polar distance of the body would be to point the telescope to it, and see the angnlar distance shown by the circle. 526. But as the pole-star does not exactly mark the position, we have to adopt some other method. We observe the zenith distance (Art. 329) of a circumpolar star when it passes over the meridian above the pole, and also when it passes below it, and it is evident that if the observations are perfectly made, half the sum of these zenith distances will give the zenith distance of the celes- tial pole itself. When we have found the position of the celestial pole, we can determine the position of the celestial equator, which we know is exactly 90" away from it. As we already know the zenith distance of the celestial pole, the difference between this distance and go" gives us the zenith distance of the equator. Here, then, we have three points from which with our transit circle we can measure angular distances : — I. From the zenith, II. From the celestial pole, III. From the celestial equator, and we may add, IV. From the horizon, as the horizon is 90° from the zenith. Any of these distances can be easily turned into any other. Plate XVI, Perspective View of the Transit Circle at Greenwich. 26S ASTRONOMY. [chap. vii. will be determined. That is to say, the Earth itself, by its rotation, performs the most difficult part of the task for us, and every star will in turn be brought into the meridian of our place of observation ; all we have to do is to note its angular distance either from the zenith or from the celestial equator, and note the sidereal time : one enables us to determine, or actually gives us, its declination ; the other gives us its right ascension. 529. Of course, the method which is good for deter- mining the exact place of a single heavenly body is good for mapping the whole heavens, and in this manner the position of each body has been determined, until the whole celestial sphere has been mapped out, the right ascension and declination of every object having been determined. The most important of the catalogues in which these positions are contained is due to the German astronomer Argelander. This catalogue contains the positions of up- wards of 324,000 stars, from N. Decl. 90° to S. Decl. 2°, and Schonfeld's extension of it to S. Decl. 23° gives 1 33)6S° more. Bessel also published a catalogue of up- wards of 50,000 stars. The late Astronomer-Royal and the British Association have published similar lists, and a great number of southern stars have been lately deter- mined with equal care. There are besides catalogues dealing with double stars, variable stars, and red stars exclusively. 530. In order that the angular distance from the zenith, and the time of meridian passage, may be cor- rectly determined, observations of the utmost delicacy are required. 531. The circle of the Greenwich transit, for instance, is read in six different parts of the limb at each observa- tion by microscopes, the eye-pieces of which are shown in Plate XV., and the recorded zenith distance is the mean of these readings. The other co-ordinate, — that is, the right ascension,— CHAP. VII.] DETERMINATION OF POSITIONS. 269 is obtained with equal care. The transit of the star is watched over nine equidistant wires, in the micrometer eye-piece (called in this case a transit eye-piece), the middle one being exactly in the axis of the telescope. The following table of some objects observed at Green- wich on Aug. 7, 1856, will show how the observation made at this central wire is controlled and corrected by the observations made at the other wires on either side of it. NAME OF OBJECT. Seconds of Transit over th e Wires. Concluded Transit over ihe Centre Wire. I. II. III. IV. V. VI. VII. VIII. IX 11 Lyras. . 1; Cygni . . x^ Sagittarii B.A.c.eree cl Cygni . . r- Cygni Neptune s 407 49 3 599 55 •= 578 4S"3 52-4 3' I 59 '4 2'I -S. 3-0 498 55'S 6-2 3'7 6-4 s. 6 '8 54-6 58-4 9-2 7-8 10 -8 14-3 35 4-4 I5'6 le-s 194 n5 s. 22 'o 12-8 10*6 21-8 25-2 27-9 25 '3 s. =5 9 I7'S 13-8 24-9 29-7 32 3 39 'o s. 297 22'0 167 28 34-0 36-6 s. 33'S 267 197 31 'I 38-2 40-9 h. m. s. 18 50 14'34 19 13 3'58 19 16 4-48 19 2o 15"48 19 37 ie'57 19 37 19'28 23 23 ii'sa 532. There are two methods of observing the time of transit over a wire, one called the eye and ear method, the other the electrical method. In the former, the ob- server, taking his time from the sidereal clock, which is always close to the transit circle, listens to the beats and estimates at what interval between each beat the star passes behind each wire. An experienced observer in this manner mentally divides a second of time into ten equal parts with no great effort. 533. In the second method a barrel covered with paper is made to revolve at a uniform rate. By means 270 ASTRONOMY. [chap. vii. of an electric current, a pricker attached to the keeper of an electro-magnet is made at each beat of the sidereal clock to make a puncture on the revolving barrel. The pricker is carried along the barrel, so that the line of punctures forms a spiral, the pricks being about half an inch apart. Here then we have the flow of time fairly recorded on the barrel. At the beginning of each minute the clock fails to send the current, so that there is no confusion. What the clock does regularly at each beat the observer does when a star crosses the wires of his transit eye-piece. He presses a spring, and an additional current at once makes a puncture on the barrel. The time at which the transit of each wire has been effected is estimated from the position the additional puncture occupies between the punctures made by the clock at each second. 534. By this method, which is also termed the chrono- graphic method, the apparatus used being called a chro- nograph, the observer is enabled to confine his attention to the star, and after observing with the telescope can at leisure make the necessary notes on the punctured paper, which when filled, is taken off the barrel and bound up as a permanent record. 535. With the transit circle the position of a body on the celestial sphere can only be determined when it is on the meridian. The equatorial enables this to be done, on the other hand, in every part of the sky, though not with such extreme precision. The object is brought to the cross wires of the micrometer eye-piece, and the declination circle at once shows the declination of the object. The right ascension is determined as follows:— At the lower end of the polar axis is a circle divided into the 24 hours of right ascension. This circle is not fixed. Flush with the graduation are two verniers ; the upper one fixed to the stand, the lower one move- able with the telescope. The fixed vernier shows the position occupied by the telescope, and therefore by the CHAP, vn.] DETERMINATION OF POSITIONS. 271 moveable vernier, when the telescope is exactly in the meridian. Prior to the observation, therefore, the circle is adjusted so that the local sidereal time, or, in other words, the right ascension of the part of the celestial sphere in the meridian, is brought to the fixed vernier. The circle is then carried by the clockwork of the instru- ment, and when the cross wires of the telescope are adjusted on the object, the moveable vernier shows its right ascension on the same circle. Lesson KLlU.—Cofrec/ions applied to Observed Places. Instrumental and Clock Errors. Corrections for Re- fraction and Aberration. Corrections for Parallax. Corrections for Liini-solar Precession. Change of Equatorial into Ecliptic Co-ordinates. 536. After the astronomer has made his observations of a heavenly body — and has freed them from instru- mental and clock errors, if his telescope is not perfectly levelled or collimated, or his circle is not perfectly centred, or if the clock is either fast or slow — he has obtained what is termed the observed or apparent place. This, however, is worth very little : he must, in order to obtain its true place, as seen from his place of observation, apply other corrections rendered necessary by certain properties of light. These properties have been before referred to in Arts. 450 and 451, and are termed the refraction and aberration of light. Refraction causes a heavenly body to appear proportionately higher the nearer it is to the horizon ; in the zenith its action is nil; near the horizon it is very decided, so decided that at sunset, for instance, the sun appears above the horizon after it has actually sunk below it. It will be seen, therefore, that refraction depends only upon the altitude. of the body on the sphere of obser- vation. 272 ASTRONOMY. [chap. VII. S37. The correction for refraction is applied, therefore, by means of some such table as the following : — Table of Refractions. Apparent .Altitude. Mean Refraction. Apparent Altitude. Mean Refraction. o r » ' / • o o 34 54 II 4 49 o 20 30 52 j 12 4 25 40 27 23 13 4 5 I 24 25 14 3 47 I 30 20 51 15 3 32 2 18 9 20 2 37 2 30 16 I 25 2 3 3 14 IS 30 I 40 3 30 12 48 35 I 22 4 II 39 40 I 9 5 9 47 45 58 i 6 8 23 50 48 7 7 20 60 33 8 6 30 70 21 9 5 49 80 10 10 5 16 90 538. This table will give a rough idea of the correction applied ; in practice, the corrections are in turn corrected according to the densities of the air at the time of obser- vation. In the case of the transit circle, or altazimuth, the correction for refraction is applied by merely reducing CHAP, vii.] DETERMINATION OF POSITIONS. 273 the observed zenith distance by the amount shown in the refraction table. 539. The aberration results from the fact that the observer's telescope carried by the Earth's annual mo- tion round the Sun must always be pointed a little in advance of the star (Art. 451), in order, as it were, to catch the ray of light. Hence the star's aberration ^lace will be different from its real place, and as the Earth travels round the Sun, and the telescope is carried round with it always Fig. 64. — Annual change of a Star's position, due to Aberration ; « ^trrf, the Earth, in different parts of its orbit : afb'c'd', the corresponding Aberration places of the Star, varying from the true place in the direction of the Earth's motion at the time. pointed ahead of the star's place, the aberration place re- volves round the real place exactly as the Earth (if its orbit be supposed circular) would be seen to revolve round the Sun, as seen from the star : the aberration places of all stars, in fact, describe circles parallel to the plane of the Earth's orbit— if the star lie at the pole of the ecliptic the circle will appear as one : the aberration place of a star in the ecliptic, since we are in the plane of the circle will oscillate backwards and forwards ; that of one in a middle celestial latitude will appear to describe an ellipse. The diameter of the circle, the major axis of the elUpse, and the amount of oscillation, will in all cases be equal ; but the minor axes of the ellipses described by the stars in middle latitudes will increase from the equator to the pole. The invariable quantity is 2o"492, and is termed the constaut of aberration. It expresses, as we have seen, the relative velocities of light and of the Earth in her orbit. It is determined by the following proportion, bearing in mind 274 ASTRONOMY. [chap. vir. that the 360° of the Earth's orbit are passed over in 365^ days, and that light takes 8m. 19s. to come from the Sun : Days. m. s. ° " 365! : 8 19 :: 360 : 20.492 The mode in which the correction for aberration is applied may be gathered from Fig. 67. Fig. 65. — J, the Star's true place ; s't the Aheiration place. 540. The direction of the Earth's motion in its orbit, called the Earth's Way, is always 90° behind the Sun's position in the ecliptic at the time ; therefore the aber- ration place of the star will lie on the great circle passing through the star and the spot in the ecliptic lying 90° behind the Sun. 541. Observations of the celestial bodies near the Earth, such as the Moon and some of the planets, when made at different places on the Earth's surface, and cor- rected as we have indicated, do not give the same result, as their position on the celestial sphere appears different to observers on different points of the Earth's surface. This effect will be readily understood by changing our CHAP. VII.] DETERMINATION OF POSITIONS. 275 position with regard to any near object, and observing it projected on different backgrounds in the landscape ; the nearer we are to the object the more will its position appear to change. 542. To get rid of these discordances, the observa- tions are further reduced and corrected to what they would have been had they been made at the centre of the Earth. This is called applying the correction for parallax. Fig. 66. — Parallax of a heavenly body. Parallax is the angle under which a line drawn from the observer to the centre of the Earth would appear at the body of which observations are being made. When the body is in the zenith of an observer, therefore, its parallax is nil; it is greatest when the body is on the horizon. This is termed the borizontal parallax. The line is always equal to the radius of the Earth, but being seen more or less obliquely, the parallax varies accordingly. 276 ASTRONOMY. [chap. vii. 543. The value of the correction for parallax is found as follows : — In Fig. 65, let j be a star, z the zenith, o an observer, c the centre of the Earth, and h the horizon. The angle o s c'vs, the parallax of the star s. It is one of the properties of triangles that the sides are proportional to the sines of the opposite angles : in the triangle o s c, for instance, we have Sin. o s c : sin. c o s : : o c : c s. 544. The angle o s cis the parallax of the star ; let us therefore call it p. The angle c o s = 180° — the zenith distance, which we will write shortly, 180° — z j o c is the Earth's radius, which may be called r, and c s the star's distance, which we will call D; so the equation takes this form : — Sin. p : sin. (180° — z)::r:D. Or (since the sine of 180° — z is equal to the sine of 2), Sin./ = n^'°- ^ (')• It is seen that in the case of horizontal parallax sin. z becomes equal to i, so that Sin./ = ^ (2). As will be seen in the next chapter, this formula en- ables us to find the distances of all the heavenly bodies that are near enough to have any sensible parallax. 545. From what has been said it will be seen that on the celestial sphere the positions of the heavenly bodies are determined by means of either of two fundamental planes — one of them the plane of the ecliptic, the other the plane of the Earth's equator ; and that a point in the line of intersection of these two planes, — that, namely, occupied by the Sun at the vernal equinox, called the first CHAP. VII.] DETERMINATION OF POSITIONS. 277 point of Aries, written shortly, T,— is the start-point of one of the co-ordinates. Thus : Declination is reclioned N. or S. of the plane of the earth's equator. Celestial latitude is reckoned N. or S. of the plane of the ecliptic. Right ascensioii and celestial longitude are both reckoned from the great circle which passes through the first point of Aries, in the intersection of the two fundamental planes. 54.6. Now one plane marks the plane of the Earth's yearly motion round the Sun, the other marks the plane of the Earth's daily rotation. If therefore these are change- less, a position once determined will be determined once for all ; but if either the plane of the Earth's yearly motion or the direction of the inclination of the Earth's axis change, then the line of intersection will vary, and corrections will be necessary. 547. We stated in Art. 168 that, roughly speaking, the Earth's axis was always pointed in the same direction, or remained parallel to itself; but strictly speaking this is not the case. It is now known that the pole of the Earth is constantly changing its position, and revolves round the pole of the ecliptic in about 25,810 years, so that the pole- star of to-day will not be the pole-star 3,000 years hence. 548. Now a very important fact follows from this ; as the Earth's axis changes, the plane of the equator changes with it ; and so that each succeeding vernal equinox hap- pens a little earlier than it otherwise would do. This is called the precession of the equinoxes (because the equinox seems to move backwards, or from left to right, as seen in the heavens from the northern hemisphere of the Earth,so as to meet the Sun earlier) ,or luni-solar precession. The result of this is, that could we see the stars behind the Sun, we should see different ones at each successive 278 ASTRONOMY. chap. vii. equinox. In the time of Hipparchus — 2,000 years ago — the Sun at the vernal equinox was in the constellation Aries j now-a-days it is in the constellation Pisces (Art. 361). 649. The plane of the ecliptic is also subject to variation. This is termed the secular variation of the obliquity of tbe ecliptic. 550. Of these changes, the luni-solar precession is the most important ; it causes the intersection of the two fundamental planes to recede So"37572 annually, the general precession amounting to 5o"2ii29. To this is due the difference in length between the sidereal and tropical years (Art. 439). 551. The cause of these changes, as will be seen in Chap. IX., is the attraction exercised by the Sun, Moon, and planets upon the protuberant equatorial portions of our Earth. The effect is to render both latitudes and longitudes, and right ascensions and declinations variable. Hence the observed position of a heavenly body to-day will not be the position occupied last year, or to be occupied next year, and apparent positions have to be corrected, to bring them to some common epoch — such as 1800, 1850, 1880, &c., so that they may be strictly comparable. 552. As was pointed out in Lesson XXIX., astronomers not only deal with positions on the celestial sphere de- termined by right ascension and declination, but they require to look at it, as it were, from the ecliptic point of view, and to know the distances of bodies from that plane, still using the same first point of Aries, as in RA. These co-ordinates are termed celestial latitude and longitude; they are not determined from observation, but are calcu- lated from the true RA. and Decl. by means of spherical trigonometry. 553. The first thing to be done is to determine what is called the obliquity of the ecliptic (written . H J3 d Annual ^n 6 rt « Name of Star. Observer. t proper mottf'n Parallax. tanc mbe froir the m in arc. s dis or nu light each Star units, which r p a. Centauri ... G. and E. I 3-67 75 4-36 I4'4 Sirius G. and E. I I 24 0-38 8-6 9-6 Lacaille 9352 G. 7* 6'95 0-2S 1 1-6 6 Indi G. and E. Si 4-68 0"22 15 63 02 Eridani ... G. 4« 4'io 0-17 19 69 e Eridani ... E. 4* 3 '03 014 23 64 f 'I ucause ... E. 2-05 o'o6 54 lOI Canopus E. I o'oo Insensible. — ^ Centaun... G. I ' Insensible. — 304 ASTRONOMY. [chap. viii. The same principle was adopted in a series of researches lately carried out with great exactness by Drs. Gill and Elkin at the Cape of Good Hope. Fig. 75 shows on an enormously magnified scale the parallactic ellipse de- scribed by a Centauri, and the stars by comparison with which it was measured. Fig. 76 shows the annual fluctua- FiG. 75. — Showing comparison stars emplojfed in determining the parallax of a Centauri. tions of apparent distance between a Centauri and the comparison stars. 596. So much for the measurement of distances. When the distance of a body is known, and also its angular measurement, its size is determined by a simple propor- tion, for the distance is, in fact, the radius of the circle on which the angle is measured. There are 1,296,000 seconds in an entire circum- , , 1296000 , . , ference : there are therefore . ^ seconds m that part al " S « WON d *" 9 K, « ^ 1-. S C a> nj rt d S 2 w.^« 0) f3 jj G **- o o S i c ^■2 bfl C S5 K o « u ■S— M . 3 )j = 9 X i6t\ = 1 44 A }} 4 ') = 16 X i6^ = 257A J) S ;; = 25 X I6IV = 4021^ 612. The Moon's curved path is an exact representa- tion of what the path of our cannon-ball (Art. 604) would be at the Moon's distance from the Earth ; in fact, the Moon's path MM', in Fig. 78, is compounded of an ori- ginal impulse in the direction at right angles to EM, and Of Fig. 78. — Acticn cf Gravity on the Moon's path. therefore in the direction MB, and a constant pulltoviaxAs the Earth — the amount of pull being represented for any arc by the line MA (Fig. 78). To find the value oi MA, let us take the arc described by the Moon in one minute, the length of which is found by the following propor- tion : — ■ 27d. 7h. 43m. ; im. : : 360° : 33" nearly = MM'. From this value of the arc, the length of the line MA is found to be 16]^ feet when ME = 240,000 miles. That CHAP. IX.] UNIVERSAL GRAVITATION. 313 -is, a body at the moon's distance falls as far in one minute as it would do on the Earth's surface in one second — that is, it falls a distance 60 times less. A body on the Earth's surface is 4,000 miles from the Earth's centre, whereas the Moon lies at a distance of 240,000 from that centre — that is, exactly (or exactly enough for our present purpose) 60 times more distant. 613. It is found, therefore, that the deflection pro- duced in the Moon's orbit from the tangent to its path in one second is precisely of zsm a foot. Here we see that, as the Moon is sixty times further from the Earth's centre than a stone at the Earth's surface, it is attracted to the Earth 60 X 60, or 3600 times less. In fact, the force is seen experimentally to vary inversely as the square of the distance ai the falling body from the surface. It was this calculation that revealed to Newton the law of universal gravitation. 614. Long before Newton's discovery, Kepler, from observations of the planets merely, had detected certain laws of their motion, which bear his name. They are as follows : — I. Each planet describes round the Sun an orbit of eUiptic form, and the centre of the Sun occupies one of the foci. II. The areas described by the radius-vector of a planet are proportional to the time taken in de- scribing them. III. If the squares of the times of revolution of the planets round the Sun be divided by the cubes of their mean distances, the quotient will be the same for all the planets. 615. We have already in many places referred to the first law : II. and III. require special explanation, which we will give in this place. We stated in Art. 293 that the 314 ASTRONOMY. [chap. i.x. planets moved faster as they approached the Sun ; 11. tells how much faster. The radms-vector of a planet is the line joining the planet and the Sun. If the planet were always at the same distance from the Sun, the radius-vector would not vary in length ; but in elliptic orbits its length varies ; and the shorter it becomes, the more rapidly does the planet progress. This law gives the exact measure of the increase or decrease of the rapidity. 616. In Fig. 79 are given the orbit of a planet and the Sun situated in one of the foci, the cUipticity of the Fig. 79. — Explanation of Kepler's second law. planet's orbit being exaggerated to make the explanation clearer. The areas of the three shaded portions are equal to each other. It is readily seen that where the radius- vector is longest, the path of the planet intercepted is shortest, and vice versd. This, of course, is necessary to produce the equal areas. In the figure, the arcs P P^, P^ P3, and PiP^, are those described at mean distances perihelion and aphelion respectively, in equal times ; there- fore, as a greater distance has to be got over at perihelion CHAP. IX.] UNIVERSAL GRAVITATION. 31S and a less one at aphelion than when the planet is situated at its mean distance, the motion in the former case must be more rapid, and in the latter case slower, than in other parts of the orbit. 617. The third law shows that the periodic time of a planet and its distance from the Sun are in some way bound together, so that if we represent the Earth's dis- tance and periodic time by i, we can at once determine the distance of, say, Jupiter from the Sun, by a simple proportion ; thus — Square of \ Earth's I period \ Square of Jupiter's period. Cube of Earth's distance Cube of Jupiter's distance I X I ) { ii'86 X 11-86; V I X I X I ( i4o'559. That is, whatever the distance of the Earth from the Sun may be, the distance of Jupiter is ^'4° times greater. 618. The following table shows the truth of the law we are considering : — Mean distance. Time squared. Periodic Time. Eaith = 1. Distance cubed. Mercury . 87-97 • 0-3871 . 133,421 Venus . 22770 . • 0-7233 . 133,413 Earth • 365-25 • . I -0000 . 133,408 Mars . . . 68698 1-5237 133,410 Jupiter ■ 4332-58 . . 5-2028 . 133,29+ Saturn 10759.22 . 9-5388 . 133,401 Uranus . . 30688-30 . 19-1834 133,404 Neptune . . 6oi8o'86 . 30-0544 . 133,411 Lesson XLIX. — Kepler's Second Law proved. Centri- fugal Tendency. Centripetal Force. Kepler's Third Law proved. The Conic Sections. Movement in an Ellipse. 619. As these laws were given to the world by Kepler, they simply represented facts ; for, owing to the backward 3i6 ASTRONOMY. [chap. ix. state of the mechanical and mathematical sciences in his time, he was unable to see their hidden meaning. This was reserved for the genius of Sir Isaac Newton, after Kepler's time. 620. Newton showed that all these laws established the truth of the law of gravitation, and flowed naturally from it. In Fig. 80, let ^ represent the centre of the Sun, and P a planet, at a given moment. During a very short time this planet will describe a part of its orbit PP\ and its radius-vector will have swept over the area PSF. If no new force intervene, in another similar interval the planet will have reached P", the area P'SF' being equal to SC Fig. 80. — Proof of Kepler's second law. PSP' according to Kepler's second law. But the planet will really describe the arc PB, and the area P'SB will be equal to PSP" ; as the triangles are equal, and on the same base, the hne P"B will be parallel to FS ; and completing the parallelogram P'F'BC, we see that the planet at P' was acted upon by two forces, measured by P'P" and P'C — that is, by its initial velocity and a. force directed to the Sun. Hence Kepler's second law shows that this force is directed towards the Sun. 621. A good idea of the tendency of bodies to keep in the direction of their original motion may be gained by attaching a small bucket, nearly filled with water, to a rope, and by swinging it round gently ; the ten- dency of the water to fly off will prevent its falling out of the bucket ; and it will be found that the more rapidly CHAP. IX.] UNIVERSAL GRAVITATION. 317 the bucket is whirled round, the greater will be this tendency, and therefore the tighter will be the rope. 622. The circular movement of the bucket is repre- sented in Fig. Si. A represents the bucket, OA the rope; let us suppose that the bucket receives an impulse which in the absence of the rope, would have sent it in the direc- tion AB with an uniform motion. In a very short time, being held by the rope, it will arrive at c, and A d Fig. 81.— Circular Motion; measures the force applied by the rope. Call this force/, we have Ad=\ff ... . (I). Further, the distance traversed— that is, A c — is deter- mined by the velocity (v) of the bucket, and the time taken (/), so we have Ac = vt; and the arc A c being taken equal to its chord, we have, representing the radius by -ff, Ac^=2RxAd (2;. But Ac = v(, and Ad = \ffl ; therefore, v'fi ='2Ry.\ff (3). and/=^, (4)' 3i8 ASTRONOMY. [chap. ix. This gives the acceleration in feet independently of the mass m of the bucket ; if the force is sought in pounds, m must be introduced, and the equation becomes This measures, in the instance we have quoted, the amoimt of pull on the rope, the rope holding the bucket by a force ^=- equal in amount and opposite. The first is called the centrifugal tendency ; the second the centripetal force. As the entire circumference 2 tt 7? (where vn- 3' 141 6 and R = radius) is traversed at the velocity v in the time i, we have 2TrR = vi, IttR .,. that is, V — — — (6). Substituting this in equation 4, we get f = -72- or = 47r2 ^ . . . (7). 623. Now if for a moment the orbits of the planets be treated as circles, this formula gives the acceleration of their motion — that is, the force of attraction on a unit of mass at the planet's distance, as attraction does exactly for the planet what the rope does for the bucket. Let it next be supposed that several planets at differ-, ent distances from the Sun represented hy RR' R" .... are revolving round him in different times, TT'V .... we shall have in each case f = 4^'^^ /' = 4'r' j^ f" = 4'>-^ ^T-2 But, by Kepler's third law, in each case the squares of the times of revolution T'^ T'^ T"^ are proportional to the CHAP. IX.] UNIVERSAL GRAVITATION. 3«9 cubes of the distance from the Sun R, R', &c. Calling this law L, we have in each case L = R'^ L = R"^ Dividing the former equations by these, we get ■^ — 2^2 /=w A'2 /' = 4T^ 2i'i f" =4T^ IF'^' that is, in each case/, or the attraction on the unit of Fig. 82. The Conic Sections : A B the circle ; C D the eclipse ; E F the hyperbola ; G H the parabola. mass, varies in the inverse ratio of the square of the distances. 624. Newton also showed, in a similar manner, that the attraction is proportional to the product of the masses of the bodies ; and that if we take two bodies, the Sun 320 ASTRONOMY. [chap. ix. aijd our Earth, for instance, we may imagine all the gravitating energies of each to be concentrated at their centres, and that if the smaller one receives an impulse neither exactly towards nor from the larger one, it will describe an orbit round the larger one, the orbit being one of the conic sections — that is, either a circle, ellipse, hyperbola, or parabola. Which of these it will be de- pends in each case upon the direction and force of the original impulse, which, as the movements of the heavenly bodies are not arrested as bodies in movement on the Earth's surface are, is still at work, and suffices for their present movements. Were the attraction of the Fig, B3. — XiLagram showing how the varying veloci:ies of a body revolving in an orbit are caused and controlled. central body to cease, the revolving body, obeying its original impulse, would leave its orbit, in consequence of the centrifugal tendency it acquired at its original start : were the centrifugal tendency to cease, the centripetal force would be uncontrolled, and the body would fall upon the attracting mass. 625. Next let us inquire how it is that equal areas are swept over in equal times. This is easily understood in a circle, and may be explained as follows in the ellipse : — In a circle the motion is always at a right angle ^o the line joining the two bodies ; this condition of things occurs only at two points in an ellipse, ix. at the apses, or extremities of the major axis — the aphelion and perihelion points. CHAP. IX.] UNIVERSAL GRAVITATION. 321 626. In Fig. 83 the planet P is moving in the direction PT, the tangent to the ellipse at the place it occupies, and this direction is far from being at right angles to the Sun, so that the attractive force of the Sun helps the planet along. At P' it is equally evident that the attrac- tive force is pulling the planet back. At P" the attractive force is strong, but the planet is enabled to overcome it by the increased velocity it has acquired from being acted upon at P j while at P" the attractive force is weaV, but the planet is not able to overcome it, on account of its velocity having been enfeebled from being acted upon as at /". Lesson L. — Attracli7ig and Attracted Bodies considered separately. Centre of Gravity. Determination of the Weight of the Earth j of the Sun; of the Satellites. 627. As every particle of matter attracts every other particle, the smaller bodies attract the larger ones ; so that, to speak of the Sun and Earth as examples, the Earth attracts the Sun as well as the Sun the Earth. 628. Now, it must here be remarked that, at the same distance, the attraction of one body on another is quite independent of the mass of the attracted body. If we take the Earth as the attracting body, for instance, and the Sun and Jupiter when equally distant from the Earth as the attracted bodies, leaving for the present mutual attractions out of the question, the Earth's attractive power over both is equal, and is the same as it would be on a pea or on a mass larger even than the Sun, at the same distance. That is, if we had the Sun, Jupiter, a pea, and a mass larger than the Sun, at the same distance from the Earth, the Earth's attraction would pull them Y 322 ASTRONOMY. [chap. ix. through the same number of feet and inches in one second of time. 629. Secondly, still dealing with attracted bodies at the same distance from the attracting body, not only will the attraction be the same for all, but it will depend upon, and vary with, the mass of the attracting body. 630. Thirdly, if the attracted bodies be at different distances, the power of the attracting body over them ^■aries inversely as the square of its distance from them. 631. If we consider the mutual attractions, then the attraction of a body with, say, one unit of mass will be i,ooo times less than that of a body with i,ooO' units of mass — this proportion being, of course, kept up at all distances. If in the case of two bodies, such as the Earth and Sun, all the attraction were contained, say, in the Fig. 84. — Centre of Gravity and Motion in the case of cgital rr.asses. A and B^ two equal masses ; c, tlie centre of gravity and motion. Sun, then the Earth would revolve round the Sun, the Sun's centre being the centre of motion ; but as the Earth pulls the Sun, as well as the Sun the Earth, a conse- quence of this is, that both Earth and Sun revolve round a point in a Hne joining the two, called the centre of gravity. The centre of gravity would be found if we could join the two bodies by a bar, and find out the point of the bar by which they could be suspended, scale fashion. It is clear that if the two bodies were of the same mass, such a point of suspension would be half-way between the two ; if one be heavier than the other, the point of sus- pension will approach the heavier body in the ratio of its greater weight. In the case of the Sun and Earth, for CHAr. IX.]- UNIVERSAL GRAVITATION. 323 instance, the centre of gravity of the two lies within the Sun's surface. 632. It follows from what has been stated, that the masses of the Sun, and of those planets which have satel- lites, can be determined, if the mass of our own Earth and the various distances of the attracted bodies from their centres of motion are known : for, knowing the mass of our Earth, we can compare all attracting bodies with it, as their attractions are independent of the masses of the attracted bodies (Art. 628), and the law that attrac- tion varies inversely as the square of the distance is FrG. 85. — Centre of Gravity and Motion in the case of tmeqnal masses. A and B, two unequal masses ; c, the centre of gravity and mot.on. established (Art. 606) ; so that we can exactly weigh them against the Earth. Thus we can weigh the Sun, because the planets revolve round him ; and from the curvature of their paths we can determine his pull, and contrast it with the Earth's pull. We can similarly weigh Jupiter, Saturn, Uranus, Neptune, and the double stars whose distances and orbits are known. 633. Further, attraction is not only a controlling force keeping each planet and satellite in its orbit with regard to the central body, but it is a disturbing or pertur bating' force, seeing that every body attracts every other body : hence its effects are of the most complicated kind, as will be seen presently. By carefully watching the per- turbating effects of our Moon on the Earth ; and of those planets which have no satellites, and of the satellites of Jupiter, Saturn, Uranus, and Neptune upon each other ; Y 2 324 ASTRONOMY. [chap. IX. their masses, in terms of the Earth's mass, have also been determined. Let us see how this has been done. 634. It is not sufficient to determine the Earth's bulk or volume, because it might be light, like a gas, or heavy, like lead. The mean density, or specific gravity, of its Fig. 86. — Showing the differences in the curvature of the orbits of Jupiter and the Earth. / K and E F, the fall towards the Sun. materials — that is, how much the materials weigh, bulk for bulk, compared with some well-known substance such as water — must be determined. 635. The following methods have been used to deter- mine the density of the Earth : — I. By comparing the attractive force of a large ball of metal with that of the Earth. CHAr. IX.] UNIVERSAL GRAVITATION. 325 II. By determining the degree by which a large moun- tain will deflect, or pull out of the upright towards it, a plumb-line. III. By determining the rate of vibration of the same pendulum — (a) on the top and at the bottom of a mountain. {6) at the bottom of a mine, and at the Earth's surface. 636. It will be sufficient here to describe the first mentioned method, which was adopted by Cavendish in Fig. 87. — T/ie Cavendish Experitnent. A B, the small leaden balls on the rod C. D E, the suspending wire. FG. the large leaden balls on one side of the small ones. // /f, the large leaden balls in a positijn on the other side. 1 798, and called the Caveiidish experiment. The weight of anything is a measure of the Earth's attraction. Caven- dish, therefore, took two small leaden balls of known weight, and fixed them at the two ends of a slender wooden rod six feet long, the rod being suspended by a fine wire. When the rod was perfectly at rest, he brought two large leaden balls, one on either side of the small 326 ASTRONOMY. [chap. ix. ones. If the large balls exerted any appreciable attrac- tive influence on the smaller ones, the wire would twist, allowing each small ball to approach the large one near it ; and a telescope was arranged to mark the deviation. 637. Cavendish found there was a deviation. This enabled hini to calculate how large it would have been had each large ball been as large as the Earth. He then had the attraction of the Earth, measured by the weight of the small balls, and the attraction of a mass of lead as large as the Earth, as the result of his experiment. The density of the Earth then was to the density of lead as the attraction of the Earth to the attractive force of a leaden ball as large as the earth. This proportion gave a density for the Earth of 5-45 (corrected later to S'SS) as compared with water, the density of lead being 11 '35 compared with water. With this density, the weight or mass of the whole Earth can readily be determined ; it amounts in round numbers to 6,000,000,000,000,000,000,000 tons : but this number is not needed in Astronomy ; the relative masses indicated in Art. 147 are sufficient. 638. Then as to the mass of the Sun. The question is, how many times is the mass of the Sun greater than the mass of the Earth ? We shall evidently get an answer if we can compare the action of the Earth and Sun upon the same body. Now, on the Earth's surface, i.e., at 4,000 miles from its centre, a body falls le^ij feet in a second. Can we determine how far it would fall at 4,000 miles from the centre of the Sun? This is easy since we can determine as in the case of the Moon (Art. 612) how far the Earth falls to the Sun in a second : it is found to be -0099 feet. But this is at a distance of 92,965,000 miles from the Sun's centre. We must bring this to 4,000 miles from the Sun's centre, or 23,241 times nearer. Now as attraction varies inversely as the square of th^ CHAP. IX.] UNIVERSAL GRAVITATION. 327 distance, we must multiply the square of 23,241 by "0099 to represent the fall of the body in one second at 4,000 miles from the Sun's surface. The result is 5,337,427 feet. Then ft. ft. i6i\ : 5,337,427 : : I : 331,8^7 The mass of the Sun therefore is roughly 331,867 times greater than that of the Earth. The correct mass is stated in Table IV. of the Appendix. 639. Similarly from the orbit of any one of the satel- lites we determine its rate of fall at 4,000 miles from the centre of any of the planets, and then compare it with the lejij feet fall on the Earth's surface. 640. Or we may determine the Sun's mass from equation 7 (Art. 622) in this way : — The centrifugal tendency of the Earth in her orbit = 47r^— .g. and this equally measures the Sun's attrac- tion, which is proportional to his mass, and inversely as the square of the distance ; so that we have Sun's mass „ R , . A^- =4"V^ ^') Or Sun's mass = A-'^ —^ . . . (2) Again, we may take 477° -^ to represent the Earth's attraction on the Moon ; so that Earth's mass 477" —, (3). Dividing the Sun's mass by the Earth's mass (that is, dividing equation 2 by equation 3), we get — Sun's mass _j^' ii /.n Earth's mass 2' r' ' ' ' 32^ ASTRONOMY. [chap. ix. We next substitute values : — Ji2= the Sun's distance! _ t- ^i. j- .. " ^ , , }= 11,744 Earth diameters, from the earth f "^^ T = the Earth's year . = 365'265 days. r = the Eartli's distance) o t- »t i- , , ,, M- = 29 982 Earth diameters, from the Moon .3 / = the Moon's peiiod. . = 27'32i days. So equation 4 becomes : Sun's mass 11,744" x 27'32i^ . Earth's mass~ 365'265'' X 29'982' This should be worked out. In the same way we may determine the mass of Jupiter, Saturn, Uranus, or Neptune. 641. The force of gravity on the surface of the Sun or a planet, compared to that on our Earth, may be deter- mined in the following manner : Let us take the case of the Sun. If we take the Earth's radius, mass, and gravity, each as i, then the gravity on the Sun's surface compared to that on the Earth's will be — Sun's mass _ 3^o'ooo Square of distance ~ io9'3-' ~ ' ' Lesson LI.— General Effect of Attraction. Precession of the Equinoxes ; how caused. Nutation. Motions of the Earth's Axis. The Tides. Semi-diurnal, Spring, and Neap Tides. Cause of the Tides. Their pro- bable Effect on the Earth's Rotation. 642. What has gone before will show that it is the attraction of gravitation which causes the planets and satellites to pursue their paths round the central body ; that their motion is similar to that of a projectile fired on CHAP. IX.] UNIVERSAL GRAVITATION. 329 the Earth's surface, if we leave out of consideration the resistance of the air ; and tliat Newton's law enables us to determine the masses of the Sun and of the other bodies from their motions, when the mass of the Earth itself is known. 643. Moreover, the orbit which each body would de- scribe round the Sun or round its primary, if itself and the Sun or primary were the only bodies in the system, is liable to variations in consequence of the existence of the other planets and satellites, since these attract the body as the Sun or primary attracts it, the attractions varying according to the constantly changing distances between the bodies. These irregular attractions, so to speak, are called perturbations, and the resulting changes in the motions of the bodies are called inequalities if the dis- turbances are large, and secular inequalities if they are of such a nature that they require a long period of time to render them sensible. 644. These perturbations, and their results on the orbits of the various bodies, are among the most difficult sub- jects in the whole domain of astronomy, and a sufficient statement and explanation of them would carry us beyond the limits of this little book. Vfe will conclude this chapter, therefore, with a reference to two additional effects of attraction of a somewhat different kind, and of the utmost importance, on the Earth itself. One results from the attractions of the Sun and Moon on the equa- torial protuberance, and is called the precession of the equinoxes ; the other is due to the attractions of the Sun and Moon on the water on the Earth's surface, whence result the tides. 645. Let the equatorial protuberance of the Earth be represented by a ring, supported by two points at the extremities of a diameter on a horizontal concentric ring, and inclined to its support as the Earth's equator is inclined to the ecliptic. Let a long string be attached to the highest portion of the ring, and let the string be pulled 33° ASTRONOMY. [chap. ix. horizontally, at right angles to the two points of suspension, and away from the centre of the ring. This pull will represent the Sun's attraction on the protuberance. The effect on the ring will be that it will at once take up a horizontal position ; the highest part of the ring will fall as if it were pulled from below, the lowest part will rise as if pulled from above. 646. The Sun's attraction on the equatorial protuber- ance in certain parts of the orbit is exactly similar to the action of the string on the ring, but the problem is com- plicated by the two motions of the Earth. In the first place — in virtue of the yearly motion round the Sun — the protuberance is presented to the Sun differently at different times, so that twice a year (at the solstices) the action is greatest, and twice a year (at the equinoxes) the action is nil ; and, in the second place, the Earth' s rotation is constantly varying that part of the equator subjected to the attraction. 647. If the Earth were at rest, the equatorial protuber- ance would soon settle down into the plane of the ecliptic ; in consequence, however, of its two motions, this result is prevented, and the attraction of the Sun on a particle situated in it is limited to causing that particle to meet the plane of the ecliptic earlier than it otherwise would do if the Sun had not this special action on the protuber- ance. If we take the presentation of the Earth to the Sun at the winter solstice (Fig. l8), and bear in mind that the Earth's rotation is from left to right in the diagram, it will be clear, that while the particle is mounting the equator, the Sun's attraction is pulling it down ; so that the path of the particle is really less steep than the equator is represented in the diagram : towards the east the particle descends from this less height more rapidly than it would otherwise do, as the Sun's attraction is still ex- ercised : the final compound result therefore is, that it meets the plane of the ecliptic sooner than it otherwise would have done. CHAP. IX.] UNIVERSAL GRAVITATION. 331 648. What happens with one particle in the protuber- ance happens with all ; one half of it, therefore, tends to fall, the other half tends to rise, and the whole Earth meets the strain by rolling on its axis ; the inclination of the protuberance to the plane of the ecliptic is not altered, but, in consequence of the rolling motion, the places in which it crosses that plane precede those at which the equator would cross it were the Earth a perfect sphere : hence the term precession. 649. In what has gone before the sphere inclosed in the equatorial protuberance has been neglected, as the action of the Sun on the spherical portion is constant : it plays an important part, however, in averaging the pre- cessional motion of the entire planet during the year, acting as a break at the solstices, when the Sun's action on the equatorial protuberance is most powerful, and continuing the motion at the equinoxes, when, as before stated, the Sun's action is nil. 650. Also, for the sake of greater clearness, we have omitted to consider the Moon, although our satellite plays the greatest part in precession, for the following reason : The action referred to does not depend upon the actual attractions of the Sun and Moon upon the Earth as a whole, which are in the proportion of 120 to I, but upon the difference of the attraction of each upon the various portions of the Earth. As the Sun's distance is so great compared with the diameter of the Earth, the differential effect of the Sun's action is small ; but as the Moon is so near, the differential effect is so considerable that her precessional action is three times that of the Sun. 651. An important result of the motion of the protu- berance has now to be considered. The change in the position of the equator, which follows from the rolling motion, is necessarily connected with a change in the Earth's axis. 65B. In Fig. 88, let a 3 represent the plane of the ecliptic, C Q z. line perpendicular to it, hfe the position of the 332 ASTRONOMY. [chap. IX. equator at any time at which it intersects the plane of the ecliptic in e. The position of the Earth's axis is in the direction C p. When, by virtue of the precessional move- ments, the equator has taken up the position Ikg, crossing the plane of the ecliptic in g, the Earth's axis will occupy the position C p'. 653. The lines Cp and Cp' have both the same inclina- tion to CQ. It follows, therefore, that the motion of the Fig. 88. — Showing the effects of Precession on the posilijn of the Earth's axis. Earth's axis due to precession consists in a slow revolution round the axis of the celestial sphere, perpendicular to the plane of the ecliptic. 654. Superadded to the general effect of the Sun and Moon in causing the precession of the equinoxes, or luni- solar precession, is an additional one due to the Moon alone, termed nutation. CHAP. IX.] UNIVERSAL GRAVITATION. -333 655. The Moon's nodes perform a complete revolution in nineteen years (Art. 244) ; consequently for half this period the Moon's orbit is inclined to the ecliptic in the same way as the Earth's equator is, though in a less Fig. 89. — Explanation of Nutation. degree(?««, Fig. 89, misrepresenting the mean inclination). During the other half the orbit is inclined so that its divergence from the plane of the Earth's equator, E Q, is very considerable {pq). 656. It follows, from what we have already seen in the case of the Sun, that in the former position, mn, the precessional effect will be small, while in the latter posi- tion, p q, it will be great. 657. Hence the circular movement of the axis which causes the precession of the equinoxes is not the only Fig. 90. -Apparent motion cf the Pole of the Equator, /*, round the Pule of the heavens (or Ecliptic), n. one ; there is another due to the nutation. Were the pole at rest, we should have from this latter cause a small ellipse described every nineteen years ; but since it is in motion, as we have seen in Art 653, the two motions are 334 ASTRONOMY. [chap. ix. compounded so that the motion of the pole of the equator round the pole of the ecliptic, instead of being circular, is waved. 658. The effect of these motions of the Earth's axis on the apparent position of the heavenly bodies, and the corrections which are thereby rendered necessary, have already been referred to at length in Lesson XLIII. We next come to the tides. 659. The waters of the ocean rise and fall at intervals of 12 hours and 25 minutes — that is, they rise and fall twice in a lunar day (Art. 423). When the tide is highest, we have bigli water, or flood ; after this the tide ebbs, or goes down, till we have low water, or ebb : and after this the water flows, or increases again to the next high water, and so on. 660. We not only have two tides in a lunar day, but twice in the lunar month — about three days after new and full Moon — the tides are higher than usual : these are the spring tides. Twice also, three days after the Moon is in her quadratures, they are lower than usual : these are the neap tides. It will be gathered from the foregoing that the tides have something to do with the Moon ; in fact; these phenomena are due to the attraction of the Sun and Moon on the fluid envelope of the Earth, and, as in the case of luni-solar precession, not only is it to the differential action of these bodies, and not to their abso- lute action, that the effect is due, but the two periods correspond with the lunar day and the lunar month, because the Moon' s differential attraction is far greater than that of the Sun. 661. If we take the Sun's distance as 23,482 terrestrial radii, and its mass as 330,000 times that of the Earth, the Earth's action on a particle of water at its surface being 33o>°oo 1 330,000 .,, represented by i, then g--^ and — -^-^ will represent 23,4812 23,4832 ^ the Sun's attraction on a particle on the sides of the Earth adjacent to it and turned away from it respectively. CHAP. IX.] UNIVERSAL GRAVITATION. 335 'OI 2 'i In the case of the Moon we shall have, similarly, ;r 592 and -^--2 . it is readily seen that the differential attrac- tion, therefore, in the case of the Moon is much' greater than in the case of the Smi. 662. It may be stated generally, that the semi-diurnal tides are caused by the Moon (although there is really a smaller daily tide caused by the Sun), that the semi- monthly variation in their amount is due to the Sun's tide being added to that of the Moon when she is new and full — that is, when the Sun and Moon are pulling together ; and subtracted from it when at the first and last quarters they are pulling crosswise, or at right angles to each other. 663. The double daily tide arises from the action of the Moon on both the water and the Earth itself. On the side under the Moon the water is pulled from the Earth, piled up under the Moon, as the Moon's action on the surface water is greater than its action on the Earth's centre ; but, for the same reason, the Moon's attraction on the Earth's centre is greater than its attraction on the water on the opposite side of the Earth, so that in this case, as the solid earth must move with its centre, the Earth is pulled from the water. There are, therefore, always two tides on the Earth's surface ; and it is to the motion of rotation of the Earth under this double tide — which is a state of the water merely without progressive motion — nearly at rest under the Moon, and under which the Earth (as it were) slips round — that the occurrence of two tides a day instead of one is due. There is, in fact, an ellipsoid of water inclosing the Earth, which always remains with its longer axis pointing to the Moon. 664. The existence of a state of high water under, or nearly under, the Moon, does not depend merely upon the direct attraction of our satellite upon the particles imme- diately underneath it, but upon its action upon all the 336 ASTRONOMY. [chap. ix. particles of water on the side of the Earth turned to it, all of which tend to close up under the Moon. The force acting upon these particles is called the tangential com- ponent of the attraction ; and this is by far the most powerful cause of the tides, as it acts at right angles to the Earth's gravity, whereas the direct attraction of the Moon acts in opposition to it. 665. The spring and neap tides, which, as we have seen, depend upon the combined or opposed action of the Sun and Moon in longitude, are also influenced by the difference of latitude between the two bodies. Of course, that spring tide will be highest which occurs when the Moon is nearest her node, or in the ecliptic. The apex of the semi-diurnal tide also follows the Moon throughout her various declinations. 666. The phenomena of the tides are greatly compli- cated by the irregular distribution of land. The time of high water at any one place occurs at the same interval from the Moon's passage over the meridian ; this period is different for different places. The interval at new or full Moon between the times of the Moon's meridian passage and high water is termed the establishment of the port. 667. Although in the open ocean the velocity of the tidal undulation may be 500 or even 900 miles an hour, in shallow waters the undulation is retarded to even seven miles at the same time that its height is increased. The average height of the tide round the islands in the Atlantic and Pacific Oceans is but 34 feet ; whereas at the head of the Bay of Fundy it is 70 feet. As the tidal undulation does not move so rapidly as the Earth does, since it is re- gulated by the Moon, it appears to move westward while the Earth is moving eastward ; and it has been suggested that this apparent backward movement acts as a break on the Earth's rotation, and that, owing to the effects of tidal action, the diurnal rotation is, and has been, constantly decreasing in velocity to an extremely minute extent. At CHAP. IX.] UNIVERSAL GRAVITATION. 337 . all events, if the sidereal day be assumed to be invariable, it is impossible to represent the Moon's true place at intervals 2,000 years apart by the theory of gravitation. On this assumption the Moon, looked upon as a time- piece, is too fast by 6" or 12s. (nearly) at the end of each century. This may be due to the fact that our standard of measurement of the sidereal day is too slow j and it has been calculated that this part of the apparent acceleration of the Moon's mean motion maybe accounted for by sup- posing that the sidereal day is shortening, in consequence of tidal action, at the rate of j^^th part of a second in 2,500 years. APPENDIX. Table I. Astronomical Symbols and Abbreviations. n. Elements of the Planets. III. „ Satellites. IV. „ Sun, V. ,, Moon. VI. Time. VII. Conversion of Intervals of Sidereal Time into Mean Time. VIII. ,, ,, Mean Time into Sidereal Time. APPENDIX, Table I. EXPLANATION OF ASTRONOMICAL SYMBOLS AND ABBREVIATIONS. Signs of the Zodiac. o. I. II. III. IV. V. r Aries . . . tj Taurus . n Gemini sd Cancer . . &, Leo . m Virgo . . The Sic7t. © g Mercury. ? Venus. B or S The Earth. i Mars. A Comet. (J Conjunction. Quadrature. Opposition. Ascending Node. Descending Node. Sextile. Hours. Minutes of Time. Seconds of Time. p 3° 60 90 120 ISO VI. ^ Libra ... 180 VII. 115 Scorpio . . 210 VIII, : Sagittarius:. 240 IX. ic? Capricornus 270 X. ^ Aquarius XI. )i Pisces. . T/te Moon. 300 330 Major Planets. % Jupiter. Tz Saturn. 9 Uranus. f Neptune. A Star. * ° Degrees. ' Minutes of Arc. " Seconds of Arc. R.A, or M. or a., Right Ascension. Decl. or D. or 5., Declina- tion. N.P.D., North Polar Distance. © ® Ceres. Pallas. Juno. Vesta. Minor Planets. © Astrjea. © Hebe. © Iris. © Flora. ® Metis. © Hygeia. © Parthenope. © Victoria. 342 APPENDIX. Minor Planets — continued. © Egeria. ® Hestia. (g) Eurynome. Irene. © Aglaia. @ Sappho. © Eunomia, @ Doris. © Terpsichore. @ Psyche. © Pales. @ Alcmene $Z) Thetis. © Virginia. @ Beatrix. @ Melpomene. @ Nemausa. © Clio. © Fortuna. @ Europa. © lo. © Massalia. @ Calypso. @ Semele. ® Luletia. @ Alexandra. © Sylvia. © Calliope. % Pandora. ® Thisbe. @ Thalia. @ Melete. © Julia. © Themis. @ Mnemosyne. @ Antiope. © Phocaea. @ Concordia. © .(Egina. @ Proserpine. @ Olympia. © Undina. © Euterpe. © Echo. @ Minerva. @ Bellona. © Danae. © Aurora. © Amphitrite. © Erato. @ Arethusa. © Urania. @ Ausonia. ® ^gle. © Euphrosyne. @ Angelina. © Clotho. ® Pomona. © Maximiliana. ® lanthe. ® Polyhymnia. ® Maia. ® Dike. ® Circe. (g) Asia. @ Hecate. @ Leucothea. @ Leto. @ Helena. @ Atalanta. © Hesperia. @ Miriam. @ Fides. © Panopsea. © Hera. ® Leda. © Niobe. @ Clymene. © Laetitia. © Feronia. @ Artemis. ® Harmonia. © Clytie. @ Dione. @ Daphne. @ Galatea. @ Camilla. © Isis. © Eurydice. @ Hecuba. @ Ariadne. @ Freia. @ Felicitas. @ Nysa. © Frigga. © Lydia. © Eugenia. @ Diana. @ Ate. APPENDIX. 343 Minor Planets — continued. © Iphigenia. @ Adeona. @ Belisana. @ Amalthea. ^ Lucina. @ Clytemnestra. @ Cassandra. @ Protogeneia. @ Garumna. © Thyra. @ Gallia. ® Eucharis. ® Sirona. @ Medusa. @ Elsa. @ Lomia. @ Nuwa. @ I stria. @ Peitho. @ Abundantia. @ Deiopeia. ® Althaea. @ Atala. @ Eunike. @ Lachesis. @ Hilda. @ Celuta. @ Hermione. @ Bertha. @ Lamberta. @ Gerda. @ Scylla. @ Menippe. @ Brunhilda. @ Xantippe. @ Phthia. @ Alcestis. @ Dejanira. @ Ismene. © Liberatrix. ® Coronis. @ Colga. @ Velleda. @ ^Emilia. @ Nausicaa. © Johanna. @ Una. @ Ambrosia. © N emesis. @ Athor. @ Procne. @ Antigone. @ Laurentia. @ Eurycleia. © Electra. @ trigone. @ Philomela. ffl) Vala. @ Eva. @ Arete. @ ^thra. ® Loreley. @ Ampella. @ Cyrene. @ Rhodope. @ Byblis. @ Sophrosyne. @ Urda. (§) Dynamene. © Hertha. ® Sibylla. @ Penelope. @ Austria. @ Zelia. @ Chryseis. @ Melibaea. @ Maria. @ Pompeia. @ Tolosa. @ Ophelia. @ Callisto. @ Juewa. @ Baucis. @ Martha. @) Siwa. @ Ino. @ Hersilia. Lumen. @ Phasdra. @ Hedda. @ Polana. @ Andromache. @ Lachrymosa. Adria. @ Idunna. @ Dido. Vibilia. @ Irma. @ Isabella. 344 APPENDIX. Minor Planets — continued. % @ @ @) Isolda. Medea. Li'Isea; Aschera. CEnone. Cleopatra. Eudora. Bianca. Thusnelda. Stephania. Eos. Lucia. Rosa. Oceana. Henrietta. Weringia. Philosophia. Agathe. Adelinda. Athamantis Vindobona. @ Russia. @ Asterope. @ Barbara. @ Carolina. @) Honoria. @ Caelestina. @ Hypatia. . @ Ad^astea. @ Vanadis. @ Germania. @ Kriemhilda. .@ Ida. @ Sita. @ Vera. @ Asporina. @ Eukrate. @ Lameia. @ Use. @ Bettina. @ Sophia. @ Clementina. @ @ @ @ @ @ Mathilde. Augusta. Oppavia. Walpurga. Silesia. Tyche. Aletheia. Huberta. Prymus. Valda. Dresda. Libussa. Anna. Aline. Tirza. Adorea. (Palisa.) Anahita. Penthesilea. (Charlois.) APPENDIX. 345 'Hi .5 > SCO r. lU O C Q 00 pi • CTioo p -p ^ij- t^VD 'O O ,/ vD O m r^oo M "O C/1 ^ C>\ t^ (N pi _m _M roco C rt P^Viro '« Oioo O P O CO N ^O D3 m irioo oo XI l-< w rove "^ f^'D " •Jij ^ o o o >0m .vovO'0"lf^ I o a\ ' 0^ « ■^1- O « rr, -^ OD Th I- CO -^ ro m O^ in^O ■^ O fo\5 M M H Cf WCOr-'OOOOt--'-" (Ucooo O -^-^r-^Ooo ns in tN. -4- ■* ro M t-oo^ g 00 lo i-Tco" o" t^ o'co" uco o NVD "-co inc. 3 fO P^ m->o o ro O >- H l^ O^OO 00 V 00 'i-lO "A ^i tNiCO ( x>i>fe'<3i==fH2r';^^ «B nj Voi : 'no VfOM J in o lo m S H W 5?.°" . NOOOt^NMNM gS II HO<-OO.JOO qM '0:3 H p. 1 Oioo O IN O n lo M CQfa ^ mcsoooooooro O t^ Hco ro -^ca |l|ii H H ro ■Oo'Oi=^^£'K'^ p, OJ 40 346 APPENDIX. -: >C w V JS •S£ o ^ el K "."'£■? . 1 to u Kao M ^ ^3 X 1 ::^ <-*— ., *— — ^ A„^-S.; App ren Sta Mag s 2 t^ eN*o t^ \o torow " or^w V0«0 fO-*- ^ ii « M 0\ S!,g;^S* 8 8888 8 « O -d-O* 5o- loiriN mo- da rt s cT cT t*> cT H M cn M CO. i o o « m w O O o-o o o o hn ^ natio rbit t ne of iptic. IDIO -fWOtOO OOOOM-*0-d- ^ M H M CO -* £►5- in iza ■»*• o VOO CO CO CO 00 OO tN.00 03 l-H O ««C»(H««NM 1-S i OOO t^ - W t) t5 O w H m t^vo OMMW-^UlMCh w ■♦qo ro m p: «-. M t^ 14 n S8 CKI VO MP. !§§§!§§§ i§§§ i lO -^ tC inoo cT O ui iH "O foxo f^ --r COM «\£f o 3 \D W l-sO» M »och-»*-^o\0 w w r^oa t^ n .— u- •£ N ^^0^►^^ M H « t*l « ■52 II § II sS-sgS|g.g, mi : d 2 - M N M M cn"<- H N m "* in»o ^*o^ M M t*!-* - >^ *« ■"■ .11 -7 . ° U) « aJ'S 4} E ■s 1 i i'oi & In S £ a ^ ^Sll s APPENDIX. 347 Table IV.— THE SUN. Old Value. New Value. Equatorial horizontal parallax . . 8''5776 8"794 Mean distance from the Earth . 95,274,000 92,965,000 ^Variable with the latitude. The ro- Time of rotation . } *^'*°". '"^ ^^ hours of mean solar I time is expressed by the formula, I 865' ± 165' sin II. Diameter in miles 888,646 867,000 354,936 ZZOfioo 0"250 i,4iS>225 1,305,000 Mass Density . . . . ^ j-^^^y^ ^^ Volume . . . . ( _ Force of gravity at "" Equator ... J l^ 287 27-6 Inclination of Axis to plane of ecliptic 82° 45' ) , „ Longitude of Node 73 40 ) Apparent diameter as seen from the Earth — Maximum 32'36"'4i Minimum 31 32'o Table V. ADDITIONAL ELEMENTS OF THE MOON. Mean Horizontal Parallax .... = 57' 2"7o Mean Angular Telescopic Semi-diameter 15' 33'36 Ascending Node of Orbit .... 13° 53' 17" Mean Synodic Period 29-5305887 15 days Time of Rotation 27'32i66i4i8 „ Inclination of Equator to the EcUptic 1° 32' 9" Longitude of Pole ? Daily Geocentric Motion 13 1° 35 Mean Revolution of Nodes .... 67937 19 17-0465 19-0520 0-28 0-30 0-2808 0-3008 8 8 I 18-851 20 20 3-2855 20 20-0548 0-31 0-3108 9 9 I 28-708 21 21 3-4498 2[ 21-0575 0-34 0-3409 23 23 3-7783 23 23-0630 0-37 0*3710 lo 10 I 38-564 25 25 4-I069 25 25-0685 0-40 O-4OII II I 48-421 27 27 4-4354 27 27-0739 0-43 04312 29 29 4'7640 29 290794 046 0-4613 12 12 I 58-277 30 30 4-9282 30 30-0821 0-49 0-4913 13 13 2 8-134 31 31 S'o92S 31 31-0849 0-50 0-5014 33 33 5'42ii 33 33-0904 0-52 0-5214 14 14 2 17-990 35 35 5-7496 35 35-0958 0-55 0-5515 15 2 27-847 37 37 6-0782 37 37'ioi3 0-58 0-5816 15 39 39 6-4067 39 39-1068 0-61 0-6167 i6 16 2 37-703 40 40 6-5710 40 40-1095 0-64 0-6417 17 17 2 47-560 41 43 4" 67353 43 7 ■0638 41 43 41-11-23 43"ii77 0-67 0-70 0-6718 0-7019 i8 18 2 57-416 45 45 7"39=4 45 45-1232 0-73 0-7320 19 19 3 7-273 47 47 7"7209 47 47-1287 0-76 07631 49 49 8-0495 49 49"i342 0-79 0-7922 20 20 3 17-129 50 50 8-2137 50 50-1369 0-82 0-8223 21 3 26-985 51 51 8-3780 51 51-1396 o-Ss 0-8523 ~^ S3 53 8-7066 53 53"i45l 0-88 0-8824 22 22 3 36-842 55 55 90351 55 55-1506 0-90 0-9025 23 3 46-698 57 57 9*3637 57 57-1561 0-91 0-9125 *3 59 59 9^6922 59 59'i6i5 094 0-9426 24 24 3 5«'535 60 60 9-8565 60 60-1643 0-97 0-9737 INDEX. INDEX, INCLUDING AN ETYMOLOGICAL VOCABULARY OF ASTRONOMICAL TERMS. Abbreviations used in astronomy, see Appendix, 'J'able 1. Aberration of light iab, from, and errare-, to wander, as the apparent place is not the true one), 449 ; re- sults of, 539 ; how the aberration place of a star is corrected, 540; constant of, 539 ; spherical and chro- matic, of lenses, 466. Absorption of the atmospheres of stars, 68 ; of sun, 119. Acceleration^ Secular, of the moon's mean motion, an increase in the velocity of the moon's motion caused by a slow change in the eccentricity of the earth's orbit, see 667. Achromatisni of lenses, 464. Adams discovers Neptune, 277. Adjustments of altazimuth, 523 ; transit circle, 524 ; equatorial, 485. Aerolite {p.-f\9-, the air, and Ai'^os, a stone), a meteor which falls to the earth's surface, 314, Areosiderites (avjp and tn'fiepo?, iron), an iron which falls to the earth's surface, 314. Air, refraction of the, 450-53 ; table of refraction, 537. Almanac, Nautical, 557. Altazimutb (contraction ck, s;o, 555- Evection {evehere., to carry away). One of the lunar inequalities whicK increases or diminishes her mean longitude to the extent of i" 20'. Evenings star, 3S0. Eye-pieces of telescopes, 471 ; their various forms, 472-73 ; transit eye- piece, 531. Faculse (Lat. torches), the brightest parts of the solar photosphere, 119, IIQfZ. Field of view, the portion of the heavens visible in a telescope. Figure of the earth, see Earth. Fixed stars, see Stars. Focus (Lat. Jiearik), the point at which converging rays meet, 458. Foci of an ellipse, 166. Foucault proves the earth's rota- tion, 154 ; determines the velocity of IJght, 450- Fraunhofer's lines, 490. Galasy (yaXa/cro?, of milk), the Greek name for the MJky Way, or Via Lactea. Geocentric (yfj, the earth, and kcV- Tpoy, a centre), as viewed from the centre of the earth ; latitude and longitude, 360, Geography, physical, 182 et seq. Geology, 182. Gibbous (Lat. g-ihbns, bunched) moon, 231. Globes, use of the, 337 ; terrestrial. 159; celestial, 41 ; compass, 338 ; brazen meridian, 338 ; wooden hori- zon, 33^ ; rectifying the globe, 339, 349; globe, celestial, explains sun's da.Iy motion. 365 ei seq. Gnomon (yvu/xcof , an index), a sun dial, 398. Granulations on the solar surface, "5. Gravitation, Universal, 606 et seq. ; the moon's path, 6 12 ; Kepler'&laws, 614 : results of, 642 et seq. ; pertur- bations, 643 ; nutation, 654 ; preces- sion, 64s ; tides, 659. Gravity {gravis, heavy), 602 ; mea- sure of, on the earth, 603, 611 ; on the sun and planets, 641 ; centre of, 631. Gregorian calendar, style, 443. Gyroscope, 157. Harvest moon, 373.. XXead of comets, 291. Heavens^ how to observe the, 342. Heliacal^ rising or setting of a star is when it just becomes visible in morning or evening twilight. Heliocentric (y;A.to?, the sun, and KivTpov, a centre), as seen from, or referred to. the centre of the sun ; latitude and longitude, 360. Heliometer (ijAio? and |w,eVpoi/, a measure), a telescope with a divided object-glass designed to measure s nail angular distances with great ' accuracy. It is so called because it was first used to measure the sun. Hemispheres (^fit, half, and (r4>aipa, a sphere), half the surface of the celestial sphere. The sphere is divided into hemispheres by great circles such as the equator and ecliptic. Herschel, Sir W., discovers the inner satellites of Saturn, 271 ; dis- covers Uranu=;, 277. Horizon (opt'^w, I bound), true or rational, 329 ; sensible, 152. Horizontal parallax, see Parallax. Hour angle, the angular distance of a heavenly body from the meri- dian. Hour circle, the circle attached to the equatorial telescope, by which right ascensions are indicated, 535. Huggins, Mr., his spectroscopic observations, 499. Hyperbola, the, one of the conic sections, 624. Immersion Hmmergere, to plunge into), the disappearance of one heavenly body behind another, or in the shadow of another. Inclination of an orbit, the angle between the plane of the orbit and the plane of the ecliptic: of the sun, 106; of the earth, 16B; of the axes of planets, 253, 254. Inequalities, Secular ; perturba- tions of the celestial bodies so small that they only become important in a long period of time, 643. Inferior conjunction, see Conjunc- tion ; planet, see Planet. Instruments, astronomical, 518 et seq. Irradiation, 217. 358 INDEX. Jets in comets, 294. Jovicentric (jmns, of Jupiter, and KivTpov, a centre), as seen from, Of referred to, the centre of Jupiter. jTlllan period, calendar and style, 443- Jupiter^ distance from; the sun and period of revolution, 134, 139 ; diameter, 140 ; volume, mass, and density, 147; polar compression, 255 ; description of, 263 et seq. ; satellites, 267. Kepler's laws, 614 ; proofs of, 6ig et seq. Kirclilioff's, investigations on spec* tra, 492. Latitude ilatitudo, breadth), terres- trial, 160 ; how obtained, 560 ; celes- tial, 360 ; how obtained, 554; latitude of a place is equal to the altitude of the pole^ 336 ; Geocentric, Helio- centric, Jovicentric, Saturnicentric, latitude as reckoned from the centres of the planets named. liens, its action on a ray of Lght, 458 ; convex and concave 461, 462 ; bi-convex and bi-concave, &c. 463 ; axis of a, 458 ; achromatic lenses, 464; chromatic and spherical aberra- t.on of, 465. Iieverrier discovers Neptune, 277. XiibratioiL of the moon, 214. Iiig^htj what it is, 448 ; velocity of. 16, 449; aberration of, 449; refrac- tion and reflection, 450 et seq. ; dis- persion, 465 ; light curves of variable stars, 54, et seq. Iiimbj the edge of the disc of the moon, sun, or a planet. Iiine^of collimation, 518 ; of nodes, the imaginary line be ween the as- cending and descendmg node of an orbit. IiOngritude {Jongitudo, length), ter- restrial, 161 *, how determined, 554 ; celestial, 360.; how determined, 563 et seq. ; mean, the angular distance from the first point of Aries of a planet or comet, supposed to move with a mean rate of motion ; Geo- centric, Heli:'centric, Jovicentric, or Saturnicentric, longitude as reckcmed from the centres of the planets named. liUxni^re cendr^e, 217. Lunar distances^ used to deter- mine terres'.rial knguudep. 565. Lunation {Junatid)-, the period of the moon's journey round the earth, 434- Luni-SOlar precession, see Preces- sion, Magellanic clouds, 33. Magnitudes of stars, 22, 23. Major axis, see Axis. Maps of countries, how constructed^ 572- MarSy 134; distance from the sun and period of revolution, 139 : diameter, 140 ; volume, mass, and density, 147 ; polar compression. 255 ; description of, 256 ; moons of, 259^1; seasons, 262 ; how presented to the earth in different parts of its orbit, 393 ; how its distance from the earth is determined. 583. Mass. The mass of a heavenly body is the quantity of matter it contains : of sun, 103; of planets, 147; of comets, 295. Mean distance of a planet, &c. is half the sum of the aphelion and peri- helion distances. This is equal to the semi-axis major of an elliptic orbit, 139; mean anomaly, see Ano- maly ; mean obliquity is the obliquity unaffected by nutation ; mean time, see Time ; mean sun, 405. Medium, resisting, 295. Mercury^ 134 ; distance from sun and period of revolution, 139 ; dia- meter, 140; volume, mass, and den- sity, ■■147 ; polar compression, 255; elongation of, 380. Meridian {jneiidiesy midday), the great circle of the 'heavens passing through the zenith of any-place and the poles of the celestial sphere, 162. Metals and metalloids, list of, 207. Meteorites^ aerolites, aeroside- rites, and aerosiderolites, 314 ; spo- radic meteors, 315; rennarkable meteoric falls, 316 ; chemical con- stitution, 317 et seq. ; meteoric origin of nebulse, 96 ; of comets, 287 ; of all celestial to lies, 65, 504(1;. Meteors, luminous, their position in the system, 134, divisions of, 29S; numbers seen in a star-shower, ib.-. explanation cf star-showers, 301 et seq. ; the November ring, 308 ; radiant point, 305 ; cause of bril- liancy, 310 ; shape of orbits, 308, INDEX. 359 312 ; weight of, 311 ; velocity of 310 I detonating meteors, 313. Micrometer (ju.LKp6?, small, and H-irpov, measure), an instrument with fine moveable wires attached to eye- pieces to measure small angular dis- tances, 473, 519. Microscopes, 518. Midniglit Suiij 171. Milky W"ay , 28 ; stars increase in number as they approach, 29 ; ne- bulae do not, 95. nSinOr axis, see Axis. Minor planets, how discovered, 280, 284; sizes, 281 ; orbits and distances from the sun, 282 ; eccentricity of orbits, 283 ; brilliancy, 2S4 ; atmo- sphere-, 286. Month, the, 43J, Moon, why its shape changes, 12 ; dimension and distance of, 211-12; line of revolution, 213; libration,2i4; nodes, 215, 244; moon's path con- cave with respect to the earth, 216; earth-shine, 217; brightness of, 218 ; description of surface, 221 ei seg. ; rotation, 228; no atmosphere, 227; phases, 229 ; eclipses, 233 et seq. ; nodial and synodical revolution of, 244. ; apparent motions, 370 et seg. ; harvest moon, 373 ; how the distance of the moon is determined, 579 ; ele- ments of the moon, see Appendix, Table V. Morning star, 380, Motion, proper, of stars, 43; appa- rent, of planets, 374 et seq. ; direct, 381 ; retrograde, 381 ; laws of, 399 et seq. ; circular, 622 Mountains, lunar, heights of, 224. Nadir {natura, to correspond), 328 Neap tides, 660. Nebulae, why so called, 6, 76; are swarms of meteorites, 13, 96 ; classi- fication of, Bi ; light- of, 92 ; vari- ability of, 94 ; spectrum analysis of the, 498, 501 et seq. Nebular hypothesis, g8, 210, 504 a. Nebulous stars, see Stars. Neptune, distance from the sun and period of revolution, 134, 139; diameter, 140 ; volume, mass, an J density, 147 ; discovery of, 277 et seq. Node {nodus, a knot), the points at which a comet's or planet's orbit in- tersects the plane of the eclipuc ; one is termed the ascending, the other the descending node, 215. Longitude of the, one of the elements of an orbit. It is the angular distance of the node from the first point of Aries. Nubeculse, 33. Nucleus (Lat. kernel), of a comet, 291, 294; of sun-spots, no Nutation inutatio, a nodding), an oscillatory movement of the earth's axis due to the moon's attraction on the equatorial protuberance, 654 et seq. Object-glass of telescopes, c n- struction of, 466 ; aperture and illu- minating power of, 470 ; accuracy required in constructing, 480 ; largest object-glass, 481. Obliquity of the ecliptic, see Ecliptic, Occultation {occidtare, to hide), the eclipsing of a star or planet by the moon or another planet. Opposition. A superior plant is in opposition when the sun, earth, and the planet are on the same straight line and the earth in the middle, 378. Optical double stars, see Stars. Orbit iprhis, a circle), the path rf a planet or comet round the sun, or of a satellite round a primary, 282 Ordnance Survey of England, 570. Orion, 353, Parabola, a section of a cone parallel to one of its sides, 624, Parabolic orbits of comets, 288. Parallactic inequality, an irregu- larity in the moon's mtion, arising from the difference of the sun's attraction at aphelion and peri- heli.'in. Parallax (7ropaA\a^ts, a change), 542 ; corrections for, 543, 544 ; equa- torial horizontal, 542 ; of the moon, 580 ; of Mars, 583 ; of the sun, 585 et seq. ; old and new values of, 593 ; of the stars, 594. Parallels of latitude, 162; of de- clination, 328. Penumbra (^ene, almost, and umbra, a shadow), the half-shadow which surrounds the deeper shadow of the earth, 237 ; of sun-spots, 110. Perigee (Trcpt, near, and yij, the 36o INDEX. earth.) (i) The point in the rmcn's orbit nearest the earth, 212 ; (2) the position in which the sun or other body is nearest the earth. PeribeliOXi {irepi, near, and -IjAio?), the point in an orbit nearest the sun, 167 ; distance, the distance of a heavenly body from the sun at its nearest approach : longitude of, one of the elements of an orbit ; it is the angular distance of the peri- helion point from the first point of Aries : passage, the time at which a heavenly body makes its nearest approach to the sun, 3. Peri- Jove, Satumium , &c. , the nearest approach of a satellite to the primary named, Jupiter, Saturn, &c. Period (irepC, round, and oSos, a path), or periodic time, the time of a planet's, c -jmet's, or satellite's revoluiion ; synodic, the time in which a planet returns to the same position with regard to the sun and earth, 384. Perturbations {J>eriurhare, to in- terfere with), the effects of the attractions of the planets, comets, and satellites upon each other, con- sisting of variations in their motions and orbits described round the sun, 633. Phases ((/lao-i?, an apperance), the various appearances presented by the illuninated portions of them'-on, (229) and inferior, planets (377) in various parts of their orbit with regard 'o the earth and sun. Phobos, onecfthe satellites of Mar.;, 25;a. Photography^ solar, 114 ; celestial, 507- Photospheres of the stars, 65 ; ■sun, lie. Physical constituticn of the stars, f'5, t<^ \ of the sun. Tip et seq. Plane of the ecliptic, 105. 136, 300. Planet (TrXai/^-n)?, a wanderer), a cojI body revolving round a central incandescent one. Planets change their positions with regard to the stars, 4 ; what they ar^, ii.;_namesof, 134; travel round the sun in elliptical orbits, 135, 377 ; and in one direction, 138 ; 'distances of, from the sun, 139 ; periods of revolution, 139; real sizes of, 140; comparative sizes of, i<)i ; mass, volume, and density, 144-47 > com- pared with the earth, 251 et seq. ; apparent movements of, 374 et seq. ; varying distances from the earth. "^fd ; brilliancy and phases, 377 1 inferior and superior, 378; conjunc- tion and opposition, 378 ; elonga- tions, 380; direct and retrograde motion, 381 ; stationary points, 382 ; ■ synodic periods, 384 ; inclinations and nodes of orbits, 388; apparent paths among the stars, 391 et seq, \ elements of the, see Appendix, Table II. Planetary nebulae, see Nebulae. Plateau's experiment, 197. Pointers, the, 341. Polar axis of the earth, 153, 163 ; compre?sion {see Compression), 255; distance, 329. Polaris (Lat.), the pole-star, 341 ; is not always the same, 547. Poles (jToAew, I turn), the extremi- ties of the imaginary axis on which the celestial bodies rotate, 153, 261 ; the poles of the heavens, 328 ; are the extremities of the axis of the celestial sphere which is parallel to the earth's axis ; the poles of the ecliptic are the extremities of the axis at right angles to the plane of the ecliptic, 360 ; of the earth, 153- Position-circle (of micrometers), Precession (/n^f^rf^re, to precede) of the equinoxes, or luni-s.lar pre- cession, a slow retrograde motion of the equinoctial points upon the ecliptic, 361, 548; cause of, explained, 644 et seq. Prime, vertical, see Vertical. Prisms refract light, 453. Prominences, red, of the sun, 118, 248. Proper motion, see Moticn. Quadrant (qnadrans, a fourth part), the fourth part of the circumference of a circle or 90° ; of altitude, a flexible strip of brass gradual ed into go°, attached to the celestial globe for determining celestial latitudes, declinations being determined by the brass meridian. Quadrature. Two heavenly bodies are said to be in quadrature when INDEX. 361 there is a difference of longitude of 00° between them. Thus the moon 13 in quadrature with respect to the sun at the first and last quarters. Quarters of the moon, 231. Radiant point of shooting stars, 305; Radiation, solar 12.^ ei seg. Radius (Lat. a spoke of a wheel) vectorj an imaginary line joining the sun and a planet or comet in any point of its orbit, 615 Red prominences and flames, 118, 248. Reflecting telescope, or reflector, 481. Reflection, 451. Refracting telescope, or refractor, see Telescope. Refraction {refrangercy to bend), atmospheric, 450, 453, 5^7 ; cf light by prisms, 433 ; index of, 453. Resisting medium see Medium. Retro gradation, arc of. The arc apparently traversed by planets while their motion is retrograde, 381. Retrograde motion, see Motion. Revolution, the moti n of one body round an -ther, 12 ; time of, the period in which a heavenly bcdy returns to the same point of its orbit ; the revolution may either he anomalistic if measured from the aphelion orperiheli n points, sidereal with reference to a star, synodical M'ith reference to a node, or tr. pical w!th reference to an equinox or topic. Right ascension, see Accensi: n, Right. Rilles on the mron, 226. Rings of Saturn, see Saturn. Rocks, Kst of terrestrial, 183. Rotation, the motion of a body round a central axis : of sun, 104 ; of earth, T53 ; of moon, 214 ; possibly slackening, 667. Rutherford, Mr., his lunar photo- graph, 507. Saros, a term appKed by the Chal- deans to the cycle of eclipses, 244. Satellite isatelles, a comparJon), a term applied to the smaller bod.es revolving round planets and stars, 1^7, 142, 267; elements of the, see Appendix, Table III. Saturn^ distance from the sun and period of revolution, 134, 139, diameter, 140 ; volume, mass, and density, 147 ; polar compression, 255 ; the rings, 270 et seg. ; dimen- sion of, 272; of what c.mp-sed, 273 ; appearance of, 274 ; atmo- sphere, ib. ; solar eclipses due to the rings, 276 ; how presented to the earth in different parts of its orbit, 395- Sciutillation {scintilla., a spark), the "twinkling" of the stars. Seasons of the earth, 169, 175, et seg. ; of Mars, 254, 262 ; of Jupiter, Secular {seculuvz, an age) inequa- lities, see Inequalities ; accelerati )n cf tlie moon's mean motion, see Acceleration. Selenography (o-eA^'t/rj the mcon), the geography of the moon. Semi-diurnal arc, see Arc. SeKtant, an instrument consisting of the sixth part of a circle, finely graduated, by which, by means of reflecti jn, the angular distances of celestial bodies are measured, 520. Shooting stars, see Meteors, lumi- nous. Sidereal {sidus, a star), relating to the stars ; clock, see Clock ; day, 358 ; time, see Time. Signs of the zodiac, see Zodiac. Sncw on Mars, 260. Solar spectrum, see Spectrum. Solar system, 133, et seg. Solstices, or solstitial points {sol, the sun, and stare, to stand sti]l\ the pcints in the sun's path at which the extreme ncrth and south decli- nations are reached, and at which the motion is apparently arrested before the direction of motion is changed, 171. Solstitial colure, see Colure. Sorhys researches on meteorites, 320. Spectroscope, 491 ,- star spectro- scope, 505 ; the Kew spectroscope, 506 ; direct vision, 506. Spectrum, 454 ; irrationality of the, 458 ; the solar, 487 ; descriptu n < f, 48S ; dark lines and bright lines, 490, 491, 494; spectrum analysis, 489 et seg ; general laws of, 493 ; general reRults of, 496-8. Sphere (cr0aipa), celestial, the sphere 362 INDEX. of Stars which apparently incHses the earth, i, 326 ; of observation, 329. Spberical trigonometry, see Trigo- nometry. Spheroid^ the solid formed by the rotation of an eclipse on one of its axes : it is oblate if it rotates en ihe minor axis, and prolate if it rotates on the major axis. Spring: tides, 6£o. Star-shofvers, see Meteors. StarSj why invisible in daytime, 2 ; why they appear at rest, 8 ; why they shine, 10 ; distance of nearest, 16 ; their distance generally, 25-27 ; magnitudes of, 22, 23 ; telescopic, 22 ; comparative brightness of,23; divided into constellations, 35-41 ; brightest, 42 ; double and multiple, 47-50 ; vari- able and temporary, 51-59 ; the new star in Cygntis, $6 a ; the sun a vari- able star, 121 ; coloured, 60-63 : size of, 64 ; physical constitution of, 65-69 ; clusters of, 71, 75 ; apparent movements of, 326 ; positions of, on celestial sphere, 326 et seq. ; appa- rent daily movement, 331 et seq. ; apparent yearly movement, 344 et seq.; movement in line of sight, 504 i ; pole-star, 341 ; zone of, 335 ; how to observe the, 342, 349 ; those seen at midnight are opposite to the sun, 344 et seq. : constellations visible throughout the year, 352 et seq. ; circumpolar, 335 ; sidereal day, 358 ; how the elements in the stars are determined, 493, 495, 497 ; parallax cf the stars, 594-95 ; classificati n of stars according to their spectra, 504 a,. Stationary points, those points in a planet's orbit at which it appears to have no motion among the stars, 382. Stellar parallax, see Parallax. Stones^ meteoric, 313. Styles, old and new, 443; of sun- dials, 402. Sun^ is a star, g ; why it shines, 10 ; its relative brilliancy, 23, 100 ; dis- tance, loi ; diameter, 101 ; volume, 103 ; mass, 103 ; rotation, 1C4 ; posi- tion of axis, 106 ; sun-spots, proper motion of, 107 ; description cf, no; size of, 120; period of, 12c; tele- scopic appearance of, 109 et seq. ; photosphere, no, 119 ; atmosphere, 119, 123 ; faculse, 113 ; willow leaves and granules, 115, 116; red flames, 118; elements in the photosphere, 123 ; how determined by spectrum analysis, 494-96 ; amount, of light, 125 ; heat, 126 ; chemical force, 128 ; solar radiation, 205 ; eclipses of, 234 et seq. ; their phenomena, 2.^0 et seq.; apparent motions, 357 ; solar day, 358 ; motion in the ecliptic, 363 ; rising and setting and apparent daily path, 364 ; mean sun, motion of the, 405 ; how the sun's distance is determined, 585 et seq. ; old and new values of the solar parallax, 593 ; solar elements, see Appendix, Table IV. Sun-dial, the, 399, 400. Superior conjunction, see Con- junction. Superior planets, see Planets. Symbols (oy^jSoAov), the name given to certain signs, used as abbre- viations, see Appendix, Table I. Synodic period, see Period. Syzigies (pvv, with, and fuyor, a yoke), the points in the moon's orbit at which it is in a line with the earth and sun, or when it is in conjunction or opposition. Tails of comets, 291, 294, 295. Telescope (r^Xe, afar, and o-kottcw, I see), construction of, 467 ; illumi- nating or space-penetrating power, 90, 469 : magnifying power, 470 ; eye-pieces, 471-73 ; object-glass, 466, 470 ; tube, 474 ; powers of, 475 ; how to use the, 476-79 ; largest, 481 ; various mountings, 482 ; equatorial, 482 ; altazimuth, 486, 521 et seq. ; transit circle, 486, 524 et seq.; transit instrument, 486, 5^8, Temperature of the sun, 126 ; of the earth's crust, 193 ; relative temperatures of celestial bodies. Temporary star, see Star. Terminator, 222. Tides {tidan^ to happen, Saxon), 659 et seq. Time, how measured, 405 ; the mean sun, motion of, 408 ; equation of tine, 415 ; apparent and mean solar day, 419 ; Greenwich mean time, 421 ; rules for converting solar into sidereal time, and vice •versd, 427, ^.vApieniix, Tables VII. and VIII.; INDEX. 353 civil, 369 ; week, 432 ; month, 434 ; year, 436 ; bissextile, 440 ; Julian and Gregorian calendars (new style and old style), 443 ; time required by light to reach us from the stars, 27 ; from the nebulae, 91 ; hiw ob- tained, 558, see Appendix, Tables VI. VII. and VIII. Total eclipse, see Eclipses. Trade winds, zoi. Transit {trans, across, and ire, to gn), the passage (i) of a heavenly body across the meridian of a place (in the case of circumpolar stars there is an upper and a lower transit, the latter sometimes called the tran- sit sub f>olo) ; (2) of one heavenly body across the disc of another, e.g. the transit of Venus across the sun, 536 ; of a satellite of Jupiter across the planet's disc, 267, Transit circle^ 486; when used and general description of, 524 ; how used, 525 et seq. Transit instrument, 486, 558. Triangulation^ the application of trigonometry to the determination of distances, or, 570 et seq. Trigonometry, plane and spheri- cal, 515. Trigonometrical ratios, 516. Tropical revolution, see Revoluti'^n. Tropics (rpeVto, I change) of Can- cer and Capricorn respectively, the circles of declination which mark the most northerly and southerly points in the ecliptic, in which the sun occupies the signs named, 162. Ultra- zodiacal planets^ a name sometimes given to the minorplanets, because their orbits exceed the limits of the zodiac. Umbra (Lat. a skadoiv), the darkest central portion of the shadow cast by a heavenly body, such as the moon or earth, is so called : it is sur- rounded by the penumbra, _ ^37 ; umbra of sun-spots, no. Universe, our, one of many, 8 ; shape of, 30-32. Uranus, 134 ; distance from the sun and period of revolution, 139 ; diameter, 140 ; volume, mass, and density, 147 ; inclination of axis, 254 ; discovery of, 277. Vapour, aqueous, 200. Variable star, see Stars ; nebulse, see Nebulse. Variation of the moon, one of the lunar inequalities. Venus, 134; distance from the sun and period of revolution, 139 ; dia- meter, 140 ; volume, mass, and den- sity, 147 ; polar compression, 255 ; a morning and evening star by turns, 380 ; transits of, across the sun's disc, 582, 586 et seq,; the transit of 1882, 591. Vernier, 518. "VertiCBl (vertex, the top). A vertical line (329) is a line perpendicular to the surface of the earth at any place, and is directed therefore to the zenith ; a vertical circle is one that passes through the zenith and nadir of the celestial sphere, 329 ; the prime vertical (329) is the vertical circle passing through the east and west points of the horizon. Via Lactea, ^^^ Milky Way. Volume (voliiinen. b)ulk) is the cubi* cal contents of a celestial body ; of the sun, 103 ; of the planets, 147. "Week, names of the days of the, 432. ■Weight, what it is, 602. "Willowr leaves in the penumbra of sun-spots, 116. "Winds, 202. Wire micrometer, see Micrometer. Year, 164, 436 ; length of the planets' years, 253. Ziemth, the point of the celestial sphere over head, 328 ; distance, 329. Zodiac, the portion of the heavens extending 9° on either side of the ecliptic, in which the sun and major planets appear to perform their annual revolutions, 37, 361. It is divided into twelve parts, termed signs of the zod.ac. 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With Notes, Vocabulary, and Exercises, by the Rev. G. E. Jeans, M.A., Fellow of Hertford College, Oxford, and A. V. Jones, M.A. ; Assistant-Masters at Haileybury College. Eutropius. — Adapted for the Use of Beginners. With Notes, Vocabulary, and Exercises, by William Welch, M.A., and C. G. Duffield, M.A., Assistant-Masters at Surrey County School, Cranleigh. Homer.— ILIAD. BOOK I. Edited by Rev. John Bond, M.A., and A. S. Walpole, M.A. ELEMENTARY CLASSICS. S Homer.— ILIAD. BOOKXVIIL THE ARMS OF ACHILLES. Edited by S. R. JameS, M.A., Assistant-Master at Eton College. ODYSSEY. BOOK I. Edited by Rev. John Bond, M. A. and A. S. Walpole, M.A. Horace. — ODES. BOOKS L— IV. Edited by T. E. Page, M.A., late Fellow of St. John's College, Cambridge ; Assistant-Master at the Charterhouse. Each is. dd, Latin Accidence and Exercises Arranged for Be- GINNERS. By William Welch, M.A., and C. G. Duffield, M.A., Assistant Masters at Surrey County School, Cranleigh. Livy. — BOOK I. Edited by H. M. Stephenson, M.A., late Head Master of St. Peter's School, York. THE HANNIBALIAN WAR. Being part of the XXI. AND XXII. BOOKS OF LIVY, adapted for the use of beginners, by G. C. Macaulay, M.A., late Fellow of Trinity College, Cambridge. THE SIEGE OF SYRACUSE. Being part of the XXIV. and XXV. BOOKS OF LIVY, adapted for the use of beginners. With Notes, Vocabulary, and Exercises, by George Richards, M.A., and A. S. Walpole, M.A. LEGENDS OF EARLY ROME. Adapted for the use of begin- ners. With Notes, Exercises, and Vocabulary, by Herbert Wilkinson, M.A. \In preparation. Lucian. — EXTRACTS FROM LUCIAN. Edited, with Notes, Exercises, and Vocabulary, by Rev. John Bond, M.A., and A. S. Walpole, M.A. NepOS. — SELECTIONS ILLUSTRATIVE OF GREEK AND ROMAN HISTORY. Edited for the use of beginners with Notes, Vocabulary and Exercises, by G. S. Farnell, M.A. Ovid. — SELECTIONS. Edited by E. S. Shuckburgh, M.A. late Fellow and Assistant-Tutor of Emmanuel College, Cambridge. EASY SELECTIONS FROM OVID IN ELEGIAC VERSE. Arranged for the use of Beginners with Notes, Vocabulary, and Exercises, by Herbert Wilkinson, M.A. STORIES FROM THE METAMORPHOSES. Edited for the Use of Schools. With Notes, Exercises, and Vocabulary. By J. Bond, M.A., and A. S. Walpole, M.A. Phaedrus. — SELECT FABLES. Adapted for the Use of Be- ginners. With Notes, Exercises, and Vocabularies> by A. S. Walpole, M.A. Thucydides. — THE RISE OF THE ATHENIAN EMPIRE. BOOK I. cc. LXXXIX. — CXVII. and CXXVIII. — CXXXVIII. Edited with Notes, Vocabulary and Exercises, by F. H. COLSON, M.A., Senior Classical Master at Bradford Grammar School ; Fellow of St. John's College, Cambridge. Virgil. — ^NEID. BOOK I. Edited by A. S. Walpole, M.A. .^NEID. BOOK IV. Edited by Rev. H. M. Stephenson, ■""■ * [/» the press. 6 MACMILLAN'S EDUCATIONAL CATALOGUE. Virgil ^NEID. BOOK V. Edited by Rev. A. Calvert, M.A., late Fellow of St. John's College, Cambridge. ^NEID. BOOK VI. Edited by T. E. Page, M.A. .^NEID. BOOK IX. Edited by Rev. H. M. Stephenson, M.A. GEORGICS. BOOK L Edited by C. Bryans, M.A. [In proration. SELECTIONS. Edited by E. S. Shuckburgh, M.A. Xenophon. — ANABASIS. BOOK I. Edited by A. S. Walpole, M.A. ANABASIS. BOOKL Chaps. L—VIIL for the use of Beginners, with Titles to the Sections, Notes, Vocabulary, and Exercises, by E. A. Wells, M. A. , Assistant Master in Durham School. ANABASIS. BOOK II. Edited by A. S. Walpole, M.A. [/« the press, ANABASIS. BOOK IV. THE RETREAT OF THE TEN THOUSAND. Edited for the use of Beginners, with Notes, Vocabulary, and Exercises, by Rev. E. D. SxoNE, M.A., formerly Assistant-Master at Eton. \In preparaiion. SELECTIONS FROM THE CYROP^DIA. Edited, with Notes, Vocabulary, and Exercises, by A. H. CooKE, M. A., Fellow and Lecturer of King's College, Cambridge, The following more advanced Books, with Introductions and Notes, but no Vocabulary, are either ready, or in preparation : — Cicero. — select letters. Edited by Rev. G. E. Jeans, M.A., Fellow of Hertford College, Oxford, and Assistant-Master at Haileybury College. Euripides. — HECUBA. Edited by Rev. John Bond, M.A. and A. S. Walpole, M.A. Herodotus. — SELECTIONS FROM BOOKS VIL and VIII., THE EXPEDITION OF XERXES. Edited by A. H. Cooke, M.A., Fellow and Lecturer of King's College, Cambridge. Horace. — selections from the satires and EPISTLES. Edited by Rev. W. J. V. Bakek, M.A., FeUow of St. John's College, Cambridge. SELECT EPODES AND ARS POETICA. Edited by H. A. Dalton, M.A., formerly Senior Student of Christdiurch ; Assistant- Master in Winchester College. Plato. — EUTHYPHRO AND MENEXENUS. Edited by C. E. Graves, M.A., Classical Lecturer and late Fellow of St. John's College, Cambridge. Terence.— SCENES FROM THE ANDRIA. Edited by F. W. Cornish, M.A., Assistant-Master at Etoa College. CLASSICAL SERIES. 7 The Greek Elegiac Poets. — FROM CALLINUS TO CALLIMACHUS. Selected and Edited by Rev. Herbert Kynaston, D.D., Principal of Cheltenham College, and formerly Fellow of St. John's College, Cambridge. Thucydides. — BOOK IV. Chs. l— xll the capture OF SPHACTERIA. Editec" by C. E. Graves, M.A. Virgil. — GEORGICS. BOOKIL Edited by Rev. J. H. Skrine, M. A., late Fellow of Merton College, Oxford ; Warden of Trinity College, Glenalmond. *,* Other Volumes to follow. CLASSICAL SERIES FOR COLLEGES AND SCHOOLS. Fcap. 8vo. Being select portions of Greek and Latin authors, edited with Introductions and Notes, for the use of Middle and Upper forms of Schools, or of candidates for Public Examinations at the Universities and elsewhere. Attic Orators.— Selections from ANTIPHON, ANDOKIDES, LYSIAS, ISOKRATES, AND ISAEOS. Edited by R. C. Jebb, M.A., LL.D., Litt.D., Professor of Greek in the University of Glasgow. [New Edition in the press. .ffischines. — in CTESIPHONTEM. Edited by Rev. T. GWATKIN, M.A., late Fellow of St. John's College, Cambridge, [/» the^ress, .ffischylus. — PERS^. Edited by A. O. Prickard, M.A. Fellow and Tutor of New College, Oxford. With Map. y. dd. SEVEN AGAINST THEBES. Edited by A. W. Verrall, M.A. School Edition prepared by Rev. M. A. Bayfield, M.A. [/» the Jiress. Andocides. — DE MYSTERIIS. Edited by W. J. HicKiE, M.A., formerly Assistant-Master in Denstone College. 2s. 6d. Caesar. — the gallic war. Edited, after ICraner, by Rev. John Bond, M.A., and A. S. Walpole, M.A. With Maps. 6s. Catullus, — SELECT POEMS. Edited by F. P. Simpson, B.A,, late Scholar of Balliol College, Oxford. New and • Revised Edition, ^s. The Text of this Edition is carefully adapted to School use. Cicero., — the CATILINE orations. From the German of Karl Halm. Edited, with Additions, by A. S. Wilkins, M.A., LL.D., Professor of Latin at the Owens College, Manchester, Examiner of Classics to the University of London. New Edition. y. 6d. 8 MACMILLAN'S EDUCATIONAL CATALOGUE. Cicero. — pro lege MANILIA. Edited, after Halm, by Pro- fessor A. S. WiLKiNS, M. 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Wilkins, LL.D., and Herman Hager, Ph.D., of the Owens College, Manchester. [In preparation. Euripides — HIPPOLYTUS. Edited by J. P. Mahaffy, M. A., Fellow and Professor of Ancient History in Trinity College, Dub- lin, and J. B. Bury, Fellow of Trinity College, Dublin, jf. 6d. MEDEA. Edited by A. W. Verrall, M.A., Fellow and Lecturer of Trinity College, Cambridge. %s. 6d. IPHIGENIA IN TAURIS. Edited by E. B. England, M.A., Lecturer at the Owens College, Manchester. 4?. 6d. Herodotus.— BOOKS V. and VI. Edited by J. Strachan, M.A., Professor of Greek in the Owens College, Manchester. [In frcparation. BOOKS VII. AND VIIL Edited by Miss A. Ramsay. [/« the press. Hesiod. — the works and days. Edited by W. T. Lendrum, Assistant Master in Dulwich College. \In preparation. Homer. — ILIAD. BOOKS I., IX., XL, XVL— XXIV. THE STORY OF ACHILLES. Edited by the late J. H. Pratt, M.A., and Walter Leaf, M.A., Fellows of Trinity College, Cambridge, ds. ODYSSEY. BOOK IX. Edited by Pro£ John E. B. 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THE AGRTCOLA AND GERMANY, WITH THE DIALOGUE On oratory. Translated by A. J. Church, M.A., and W. J. Brodribb, M.A. With Notes and Maps. New and Revised Edition. Crown 8vo. 4^. 6d. INTRODUCTION TO THE STUDY OF TACITUS. By A. J. Church, M.A. and W. J. Brodribb, M.A. Fcap. 8vo. Is. 6d. (Classical Writers Series.) Theocritus, Bion, and Moschus. Rendered into English Prose, with Introductory Essay, by A. Lang, M.A. Crown 8vo. ds. Virgil. — THE WORKS OF VIRGIL RENDERED INTO ENGLISH PROSE, with Notes, Introductions, Running Analysis, arid an Index, by James Lonsdale, M.A., and Samuel Lee, M.A. New Edition. Globe 8vo. 3^. td. THE .(ENEID. Translated by J. W. Mackail, M.A., Fellow of Balliol College, Oxford. Crown 8vo. "js. 6d. Xenophon. — complete works. Translated, with Introduc- tion and Essays, by H. G Dakyns, M.A., Assistant-Master in Clifton College. Four Volumes. Crown Svo. [/» the press. GRAMMAR, COMPOSITION, & PHILOLOGY. 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