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POPULAR ASTRONOMY. 
 
THE GREAT COMET OF 1858, KNOWN AS " DONATl'S COMET." 
 
POPULAR ASTRONOMY 
 
 OR, THE 
 
 SUN, PLANETS, SATELLITES, AND 
 COMETS 
 
 BY 
 
 O. M. MITCHELL, LL.D. 
 
 AUTHOR OF "THE ORBS OF HEAVEN" 
 REVISED BY THE 
 
 REV. L. TOMLINSON, M.A. 
 
 LONDON 
 
 GEORGE ROUTLEDGE AND SONS, LIMITED 
 BROADWAY, LUDGATE HILL 
 
 MANCHESTER AND NEW YORK 
 
; , -TV 
 
 BY THE SAME AUTHOR, 
 UNIFORM WITH THIS VOLUME, 
 
 IN SIZE AND PRICE, 
 
 THE ORBS OF HEAVEN ; 
 
 OR, THE 
 
 PLANETARY AND STELLAR WORLDS. 
 
 With Full-page Plates and numerous 
 Woodcuts. 
 
M 
 
 ASTRONOMY 
 LIBRARY 
 
 PREFACE. 
 
 THE author has no other apology to present for offering 
 to the public the following work on " Popular Astronomy " 
 than the marked favour with which his " Orbs of Heaven " 
 has been received, both in this country and in Europe. 
 
 The science of Astronomy is so rapidly progressive, that 
 to keep the public advised of its advances new works are 
 required almost every year. This may be offered as an 
 additional reason for the present publication. 
 
 In the preparation of the work I have availed myself of 
 so many sources of information that it would be quite impos- 
 sible for me to specify the authors or the volumes to which 
 I am indebted. The plan and the cast is all my own. I 
 have endeavoured to follow the path of real discovery, and 
 in every instance to present the facts and phenomena, so as 
 to afford to the reader and student an opportunity to exer- 
 cise his own genius in their discussion and resolution, before 
 offering the explanation reached by ancient or modern science. 
 It is hoped that this method of treating the subject, which 
 is new (so far as I know), may avail in exciting a greater 
 interest in the examination of those great problems of the 
 universe, whose successful solution constitutes the chief 
 honour of human genius. 
 
 In a few instances I have ventured to present the results 
 of my own observations, and have occupied a short "space in 
 exhibiting a sketch of new methods and new instruments, 
 which have been introduced into the observatories at 
 Cincinnati and at Albany. 
 
 DUDLEY OBSERVATORY, January, 1860. 
 
CONTENTS. 
 
 CHAPTER I. 
 
 THE SUN, THE CENTRAL ORB OF THE PLANETARY 
 SYSTEM. 
 
 DISCOVERIES OF THE ANCIENTS. The Source of Life and Light and 
 Heat. The Sun's Motion among the Stars. His Orbit circular. 
 Length of the Year. Inequality of the Sun's Motion. Explained 
 by Hipparchus. Solar Eclipses. Their First Prediction. 
 
 DISCOVERIES OF THE MODEE^S. The Sun's Distance. His Hori- 
 zontal Parallax. Importance of this Element. Measured by the 
 transit of Venus. The Sun's actual Diameter and real Magni- 
 tude. His Rotation. The Solar Spots. Their Periodicity. 
 Speculations as to the Physical Constitution of the Sun Page 
 
 CHAPTER II. 
 
 MERCURY, THE FIRST PLANET IN THE ORDER OF DISTANCE 
 FROM THE SUN. 
 
 Its Early Discovery. Difficult to be distinguished from the Stars. 
 Elongations. Motion Direct and Retrograde. Sometimes Sta- 
 tionary. Nature of the Orbit. Variation in the Elongation ex- 
 plained. The Nodes. Transit of Mercury. Inclination of 
 Mercury's Orbit. Mean Distance from the Sun. Conjunctions. 
 Phases. Diameter and Volume Page 26 
 
 CHAPTER HI. 
 
 VENUS, THE SECOND PLANET IN THE ORDER OF DISTANCE 
 FROM THE SUN. 
 
 The First Planet discovered. Mode of its Discovery. Her Elonga- 
 tions. Morning and Evening Star. A Satellite of the Sun. Her 
 Superior and Inferior Conjunctions. Her Stations. Direct and 
 
CONTENTS. 
 
 Retrograde Motions. These Phenomena indicate a Motion of the 
 Earth. Transits of Venus. Inclination of the Orbit of Venus to 
 the Ecliptic. Her Nodes. Intervals of her Transits. Knowledge 
 of the Ancients. Phases of Venus. Her Elongations unequal. No 
 Satellite yet discovered. Sun's Light and Heat at Venus. Her 
 Atmosphere Page 32 
 
 CHAPTER IV. 
 
 THE EARTH AND ITS SATELLITE : THE THIRD PLANET IN 
 THE ORDER OF DISTANCE FROM THE SUN. 
 
 The Earth the apparent Centre of Motion. To all the senses it is at 
 rest. The Centre of the Motions of the Sun and Moon. Explana- 
 tion of the Acceleration of the Orbitual Motion of the Sun and 
 Moon. Ptolemy's Epicycles. The Explanation of Copernicus. 
 The Sun the Centre of Planetary Motion. The Earth one of the 
 Planets. Objections to this Hypothesis. The Answer. System of 
 Jupiter discovered by the Telescope. The Old system superseded 
 by the New. The Figure and Magnitude of the Earth. How 
 determined. The Earth's Motions. Rotation and Revolution. A 
 Unit of Time furnished by the Earth's Period of Rotation. Earth's 
 Orbitual Motion. Vernal Equinox. Perihelion of Earth's Orbit. 
 Its Period of Revolution. Solar and Sidereal Time. 
 
 THE MOON. Revolution in her Orbit. Her Phases. Earth's Line. 
 Eccentricity of her Orbit. Revolution of her Apogee. Inclination 
 of her Orbit. Moon's Parallax and Distance. Her Physical Con- 
 stitution. Centre of Gravity and Centre of Figure Page 40 
 
 CHAPTER V. 
 
 MARS, THE FOURTH PLANET IN THE ORDER OF DISTANCE 
 FROM THE SUN. 
 
 Phenomena of Mars difficult to explain with the Earth as the Centre 
 of Motion. Copernican System applied. Epicycle of Mars. Better 
 instruments and more accurate observations. Tycho and Kepler. 
 Kepler's method of investigation. Circles and Epicycles exhausted. 
 The Ellipse. Its Properties. The Orbit of Mars an Ellipse. 
 Kepler's Laws. Elliptical Orbits of the Planets. The Elements of 
 the Planetary Orbits explained. How these Elements are obtained. 
 Kepler's third Law. Value of this Law. The Physical Aspect of 
 Mar. Snow-Zones. Rotation of the Planet. Diameter and 
 Volume. Speculation as to its Climate and Colour Page 74 
 
CONTENTS. 
 
 CHAPTER VI. 
 
 THE ASTEROIDS : A GROUP OF SMALL PLANETS, THE FIFTH 
 IN THE ORDER OF DISTANCE FROM THE SUN. 
 
 The Interplanetary Spaces. Kepler's Speculations. Great Interval 
 between Mars and Jupiter. Bode's Empirical Law. Conviction 
 that a Planet existed between Mars and Jupiter. Congress of 
 Astronomers. An Association organized to search for the Planet. 
 Discovery of Ceres. Lost in the solar beams. Rediscovered by 
 Gauss. The New Order disturbed by the Discovery of Pallas. 
 Oiler's Hypothesis. Discovery of Juno and Vesta. The search 
 ceases. Renewed in 1845. Many Asteroids discovered. Their 
 Magnitude, Size, and probable Number Page 94 
 
 CHAPTER VII. 
 
 JUPITER, ATTENDED BY FOUR MOONS, THE SIXTH PLANET 
 IN THE ORDER OF DISTANCE FROM THE SUN. 
 
 Arc of Retrogradation. Stationary Point. Distance of the Planet 
 determined. Periodic Time. Synodical Revolution gives the Side- 
 real. Surface of Jupiter as given by the Telescope. Period of 
 Rotation. Diameter. Volume. Mean Distance. Amount of 
 Light and Heat. Figure of Jupiter. Equatorial and Polar Diame- 
 ters. Discovery of the Four Moons by Galileo. Effect on the 
 Copernican Theory. Jupiter's Nocturnal Heavens. 
 
 THE SATELLITES OF JUPITER. How discovered. Their Magnitude. 
 Form of their Orbits. Period of Revolution. Eclipses. Transits. 
 Occupations. Velocity of Light discovered. Terrestrial Longi- 
 tude. Rotation of these Moons on an Axis Page 101 
 
 CHAPTER VIII. 
 
 SATURN, THE SEVENTH PLANET IN THE ORDER OF DIS- 
 TANCE FROM THE SUN, SURROUNDED BY CONCENTRIC 
 RINGS, AND ATTENDED BY EIGHT SATELLITES. 
 
 The most distant of the Old Planets. Its Light faint, but steady. 
 Synodical Revolution. The Sidereal Revolution. Advances in 
 Telescopic Discovery. Galileo announces Saturn to be Triple. 
 Huygens discovers the Ring. Division of the Ring into Two. 
 Cassini announces the Outer Ring the brighter. Multiple Division. 
 Shadow of the Planet on the Ring. Belts and Spots. Period of 
 Rotation of the Planet and Ring. Disappearance of the Ring 
 explained. The Dusky Ring. 
 
X CONTENTS. 
 
 SATELLITES OP SATURN. By whom discovered. Eight in number. 
 Their Distances and Periods. Saturn's Orbit the boundary of tha 
 Planetary System, as known to the Ancients Page lift 
 
 CHAPTER IX. 
 THE LAWS OF MOTION AND GEAVITATION. 
 
 The demands of Formal Astronomy. Those of Physical Astronomy. 
 Synopsis of the Discoveries already made. Questions remaining 
 to be answered. Inquiry into Causes. The Laws of Motion de- 
 manded. Rectilineal Motion. Falling Bodies. Law of Descent. 
 Motion of Projectiles. Curvilinear Motion. First Law of Motion. 
 Second Law of Motion. Momentum of Moving Bodies. Motion 
 on an Inclined Plane. The Centrifugal Force. Central Attraction. 
 Gravitation. Laws of Motion applied to the Planets. Questions 
 propounded in Physical Astronomy. Newton's Order of Investi- 
 gation. His Assumed Law of Gravitation. Outline of his Demon- 
 stration. Its Importance and Consequences. The Law of Gravita- 
 tion embraces all the Planets and their Satellites. Gravitation 
 resides in every particle of Matter Page 127 
 
 CHAPTER X. 
 
 THE LAWS OF MOTION AND GRAVITATION APPLIED TO 
 A SYSTEM OF THREE REVOLVING BODIES. 
 
 A. System of two Bodies. Quantities required in its Investigation. 
 Five in number. Sun and Earth. Sun, Earth, and Moon, as 
 Systems of Three Bodies. The Sun supposed Stationary. 
 Changed Figure of the Moon's Orbit. Sun Revolving changes 
 the Position of the Moon's Orbit. Solar Orbit Elliptical. Effects 
 resulting from the Inclination of the Moon's Orbit. Moon's Motion 
 above and below the Plane of the Ecliptic. Revolution of the Line 
 of Nodes. Sun, Earth, and Planet, as the Three Bodies. Per- 
 turbations destroy the Rigour of Kepler's Laws. Complexity thus 
 introduced. Infinitesimal Analysis. Difference between Geome- 
 trical and Analytical Reasoning Page 151 
 
 CHAPTER XI. 
 
 INSTRUMENTAL ASTRONOMY. 
 
 Blethod for obtaining the Mass of the Sun. For getting the Mass 
 of a Planet with a Satellite. For Weighing a Planet having no 
 Satellite. For Weighing the Satellites. Planetary Distances to be 
 
CONTENTS. XI 
 
 measured. Intervals between Primaries and their Satellites to be 
 obtained. Intensity and Direction of the Iihpulsive Forces to be 
 determined. These Problems all demand Instrumental Measures. 
 Differential Places. Absolute Places. The Transit-Instrument. 
 Adjustments. Instrumental Errors. Corrections due to various 
 Causes. American Method of Transits. Meridian-Circle. The 
 Declinometer Page 164 
 
 CHAPTER XII. 
 
 URANUS, THE EIGHTH PLANET IN THE OKDER OF 
 DISTANCE FROM THE SUN. 
 
 A.ccidentally discovered by Sir William Herschel. Announced as a 
 Comet. Its Orbit proved it to be a Superior Planet. The Ele- 
 ments of its Orbit obtained. Arc of Retrogradation. Period of 
 Revolution. Figure of the Planet. Inclination of its Orbit. Six 
 Satellites announced by the elder Her&chel. Four of these now 
 recognized. Their Orbital Planes and Directions of Revolution 
 Anomalous. Efforts made to Tabulate the Places of Uranus unsuc- 
 cessful. This leads to the Discovery of a New Exterior Planet Page 203 
 
 CHAPTER XIII. 
 
 NEPTUNE, THE NINTH AND LAST KNOWN PLANET IN THE 
 ORDER OF DISTANCE FROM THE SUN. 
 
 Uranus discovered by Accident. Ceres by Research with the Tele- 
 scope. Rediscovered by Mathematical Computation. The Per- 
 turbations of Uranus. Not due to any known Cause. Assumed to 
 arise from an Exterior Planet. Nature of the Examination to find 
 the Unknown Planet. Undertaken at the same time by two Com- 
 puters. Computation assigns a Place to the Unknown Planet. 
 Discovered by the Telescope. Discoveries resulting. A Satellite 
 detected. The Mass of Neptune thus determined. Neptune's Orbit 
 the Circumscribing Boundary of the Planetary System Page 211 
 
 CHAPTER XIV. 
 THE COMETS. 
 
 Objects of Drawl in the Early Ages. Comets obey the Law of Gravi- 
 tation and revolve in some one of the Conic Sections. Character- 
 istics of these Curves. Comet of 1680 studied by Newton. Comet 
 of 1682 named " Halley's Comet." Its History. Its Return 
 predicted. Perihelion Passage computed. Passes its Perihelion 
 
Xll CONTEXTS. 
 
 13th April, 1759. Elements of its Orbit. Physical Constitution. 
 Nucleus. Envelopes? Tail. Intense Heat suffered by some 
 Comets in Perihelio. Dissipation of the Cometic Matter. Encke's 
 Comet. A Kesisting Medium. Deductions from Observation. 
 Biela's Comet. Divided. Number of Comets Page 224 
 
 CHAPTER XV. 
 
 THE SUN AND PLANETS AS PONDEKABLE BODIES. 
 
 General circumstances of the System. The Sun. His Diameter and 
 Mass. Gravity at the Surface. Mercury. His Mass and Pertur- 
 bations. Venus as a Ponderable Body. Long Equation of Venus 
 and the Earth. The Earth and Moon as heavy bodies. Figure and 
 Mass of the Earth. Precession. Aberration. Nutation. Mars. 
 His Mass and Density. Gravity at his surface. The Asteroids. 
 Jupiter's System. Saturn. His Moons and Rings as Ponderable 
 Bodies. Uranus. Neptune. Stability of the whole System Page 240 
 
 CHAPTER XVI. 
 THE NEBULAR HYPOTHESIS. 
 
 The Arrangement of the Solar System. The Phenomena for which 
 Gravitation is responsible. The Phenomena remaining to be ac- 
 counted for. Nebulous Matter as found in Comets. Nebulous 
 Matter possibly in the Heavens. The Entire Solar System once a 
 Globe of Nebulous Matter. Motion of Rotation. Radiation of 
 Heat. Condensation and its Effects. Rings disengaged from the 
 Equator of the Revolving Mass. Formation of Planets and of 
 Satellites Page 280 
 
 APPENDIX Page 291 
 
 GLOSSABY , p ag t 303 
 
INTRODUCTION. 
 
 THE great dome of the heavens, filled with a countless 
 multitude of stars, is beyond a doubt the most amazing 
 spectacle revealed by the sense of sight. It has excited the 
 admiration and curiosity of mankind in all ages of the world. 
 The study of the stars is therefore coeval with our race, and 
 hence we find many discoveries in the heavens of whose 
 origin neither history nor tradition can give any account. 
 The science of Astronomy, embracing, as it does, all the 
 phenomena of the celestial orbs, has furnished in all ages 
 the grandest problems for the exercise of human genius. In 
 the primitive ages its advances were slow ; but by patient 
 watching, and by diligent and faithful records transmitted 
 to posterity from generation to generation, the mysteries 
 which fill the heavens were one by one mastered, until at 
 length, in our own age, there remains no phenomenon of 
 motion unexplained, while the distances, magnitudes, masses, 
 reciprocal influences, and physical constitution of the celes- 
 tial orbs have been approximately revealed. In a former 
 volume * an attempt was made to trace the career of dis- 
 covery among the stars, and to exhibit the successive steps 
 by which the genius of man finally reached the solution of 
 the great problem of the universe. 
 
 The performance of that task did not permit the special 
 study of any one object, except so far as it was required in 
 the march of the general investigation. It is our object now 
 to execute what was then promised, and to examine in 
 detail the various bodies which are allied to the sun, con- 
 stituting (as we shall find) a delicately-organized system of 
 
 *" The Orbs of Heaven." 
 
XIV INTRODUCTION. 
 
 revolving worlds, a complex mechanical structure, whose 
 stability has challenged the admiration of all thinking minds, 
 and whose organization has furnished the most profound 
 themes of human investigation. 
 
 The plan adopted will lead us to present clearly all the facts 
 and phenomena resulting from observation ; with these facts 
 the student may exercise his own genius in attempting to 
 account for the phenomena, before proceeding to accept the 
 explanation laid down in the text. 
 
 To aid the memory, and to present a systematic investiga- 
 tion, we shall adopt the simple order of distance from the 
 solar orb, commencing with that grand central luminary, 
 and proceeding outward from planet to planet, until we 
 shall develop all the phenomena employed in the discovery 
 of the great law of universal gravitation. With a know- 
 ledge of this law the worlds already examined cease to be 
 isolated, and arrange themselves, under the empire of gravi- 
 tation, into a complex system, the delicate relations of whose 
 parts leads to a new discovery and to the final perfection of 
 the system of solar satellites. 
 
 Having closed our investigation of the planets and their 
 tributary worlds, we shall render an account of those 
 anomalous bodies called comets, which, by the suddenness of 
 their appearance, their rapid and eccentric motions, and the 
 brilliant trains of light which sometimes attend them, have 
 excited universal interest, not unattended with alarm, in all 
 ages of the world. 
 
 Before passing to the execution of this plan, we must 
 examine, to some extent, the phenomena of the nocturnal 
 heavens, as the stars furnish the fixed points to which all 
 moving bodies are referred. 
 
 To the eye the heavens rise as a mighty dome, a vast 
 hollow hemisphere, on whose internal surface the glittering 
 stars remain for ever fixed. In case we watch through an 
 entire night, we find the groupings of stars slowly rising 
 from the east, gradually reaching their culmination, and 
 then gently sinking in the west. A more attentive exami- 
 
INTRODUCTION. XV 
 
 nation enables the eye to detect some of these groups of 
 stars towards the north which ever remain visible, rising, 
 culminating, and descending, but never sinking below the 
 horizon. Every star in this diurnal revolution, as it is 
 called, is found to describe a circle, precisely as if the con- 
 cave heavens were a hollow sphere to which the stars were 
 attached, and that this hollow globe were made to revolve 
 about a fixed axis, passing through its centre. Indeed, we 
 find by attentively watching, that this hypothesis of a 
 spherical heavens, accounts for all the phenomena already 
 presented. As the stars are situated nearer to the extremity 
 of the axis of revolution, the circles they describe grow 
 smaller and smaller, until, finally, we find one star which 
 remain s fixed ; and this one must be at the point where the 
 axis of the heavens pierces the celestial sphere. This is 
 called the north star; and the point in which the axis 
 pierces the heavens is called the north pole. The opposite 
 point is called the south pole. 
 
 Only one half of the celestial sphere is visible at one 
 time above the horizon ; but this spherical surface extends 
 beneath the horizon, and forms a complete sphere, encom- 
 passing us on all sides, while its centre seems to be occupied 
 by the earth. It is true that, in the daytime, the stars 
 fade from the sight in the solar blaze ; but they are not lost ; 
 they still fill the heavens, as we shall see hereafter, and the 
 starry sphere sweeps unbroken entirely round the earth. 
 
 These great truths, the diurnal revolution of the heavens, 
 its spherical form, the central position of the earth, the north 
 polar star, the axis of the heavens, the circles described by 
 the stars, were among the discoveries of primitive antiquity, 
 and are matters of the most simple observation. 
 
 The spherical form of the heavens was soon imitated, and 
 the artificial globe became one of the first astronomical in- 
 struments. On this artificial globe certain lines were drawn 
 to imitate those described in the heavens by the celestial 
 orbs ; and as these lines must henceforth form a part of our 
 language, we proceed to give the following Definitions : 
 
XVI INTRODUCTION. 
 
 A great circle is one whose plane passes through the 
 centre of the sphere. 
 
 A small circle is one whose plane does not pass through 
 the centre of the sphere. 
 
 The axis of the heavens is an imaginary line passing 
 through the centre of the earth, and about which the 
 heavens appear to revolve once in twenty-four hours. 
 
 A meridian is a great circle passing through the highest 
 point of the celestial sphere (called the zenith') and the axis 
 of the heavens. 
 
 The equator or equinoctial is a great circle, perpendicular 
 to the axis of the heavens, and half-way between the north 
 and south polar points. 
 
 These important lines have been employed from the 
 earliest ages in the study of the heavenly bodies ; and having 
 thoroughly mastered their meaning and position, we are 
 prepared to examine any changes of location which may be 
 discovered among the vast multitude of shining bodies which 
 go to fill up the concave of the celestial sphere. 
 
 We shall proceed, then, without further delay, to the 
 execution of the plan already laid down. 
 
POPULAR ASTRONOMY. 
 
 CHAPTER I. 
 
 THE StTN, THE CENTRAL ORB OF THE PLANETARY 
 SYSTEM. 
 
 DISCOVERIES or THE ANCIENTS. The Source of Life and Light and 
 Heat. The Sun's Motion among the Stars. His Orbit circular, 
 Length of the Year. Inequality of the Sun's Motion. Explained by 
 Hipparchus. Solar Eclipses. Their First Prediction. 
 
 DISCOVERIES OF THE MODERNS. The Sun's Distance. His Horizontal 
 Parallax. Importance of this Element. Measured by the transit of 
 Venus. The Sun's actual Diameter and real Magnitude. His Rota- 
 tion. The Solar Spots. Their Periodicity. Speculations as to the 
 Physical Constitution of the Sun. 
 
 THE Sun is beyond comparison the grandest of all the 
 celestial orbs of which we have any positive knowledge. 
 The inexhaustible source of the heat which warms and 
 vivifies the earth, and the origin of a perpetual flood of 
 light, which, flying with incredible velocity in all directions, 
 illumines the planets and their satellites, lights up the 
 eccentric comets, and penetrates even to the region of the 
 fixed stars, it is not surprising that in the early ages of the 
 world, this mighty orb should have been regarded as the 
 visible emblem of the Omnipotent, and as such should have 
 received divine honours. 
 
 On the approach of the sun to the horizon in the earlj 
 dawn, his coming is announced by the gray eastern twilight, 
 before whose gradual increase the brightest stars, and even 
 the planets, fade and disappear. The coming splendour grows 
 
2 POPULAR ASTKONOMY. 
 
 and expands, rising higher and yet higher, until, as the first 
 beam of sunlight darts on the world, not a star or planet 
 remains visible in the whole heavens, and even the moon, 
 under this flood of sunlight, shines only as a faint silver 
 cloud. 
 
 This magnificent spectacle of the sunrise, together with 
 the equally imposing scenes which sometimes accompany the 
 setting sun, must have excited the curiosity of the very first 
 inhabitants of the earth. This curiosity led to a more care- 
 ful examination of the phenomena attending the rising and 
 setting sun, when it was discovered that the point at 
 which this great orb made his appearance was iiobjLxed, but 
 was slowly shifting on the horizon, the change being easily 
 detected by the observation of a few days. Hence was dis- 
 covered, in the primitive ages, 
 
 THE SUN'S APPARENT MOTION. In case the sun is observed 
 attentively from month to month, it will be found that the 
 point of sunrise on the horizon moves slowly, for a certain 
 length of time, toward the south. While this motion con- 
 tinues, the sun, at noon, when culminating on the meridian, 
 reaches each day a point less elevated above the horizon, and 
 the diurnal arc or daily path described by the sun grows 
 shorter and shorter. At length a limit is reached ; the 
 point of sunrise ceases to advance toward the south, remain- 
 ing stationary a day or two, and then slowly commences its 
 return toward the north. This northern movement con- 
 tinues ; each day the sun mounts higher at his meridian 
 passage, the diurnal arc above the horizon grows longer and 
 longer, until, again, a northern limit is reached, beyond 
 which the sun never passes. Here he becomes stationary 
 for one or two days, and then commences his return toward 
 the south. Thus does the sun appear to vibrate backward 
 and forward between his southern and northern limits, 
 marking to man a period of the highest interest ; for within 
 its limits the spring, the summer, the autumn, and the winter. 
 have run their cycles, and by their union have wrought out 
 the changes of the year. 
 
THE SUN. 3 
 
 The length of this important period was, doubtless, first 
 determined by counting the days which elapsed from the time 
 when the sun rose behind some well-defined natural object 
 in the horizon until his return in the same direction to the 
 same point of rising. Of course, these changes in the sun's 
 place were studied with profound attention. They were 
 among the first celestial phenomena discovered, and among 
 the first demanding explanation. The stars were found 
 never to change their points of rising, culmination, and setting. 
 Their diurnal arc remained for ever the same, and the amount 
 of time they remained above the horizon, depended on their 
 distance from the north polar point. 
 
 Observation having thus revealed the fact that the sun 
 was undoubtedly moving alternately north and south, a more 
 critical research showed the equally important truth, that 
 this great luminary was slowly shifting its place among the 
 fixed stars. This was not so readily determined ; but, by 
 noting the brilliant stars which first appeared in the evening 
 twilight, after sunset, it was soon discovered that these stars 
 did not long remain visible. Indeed, the whole starry heavens 
 seemed, from night to night, to be plunging downward to 
 overtake the setting sun, or rather, that the sun himself was 
 mounting upward to meet the stars ; and thus was discovered 
 a solar motion in a direction opposed to the diurnal revolution 
 of the heavens. 
 
 From month to month the sun was seen to advance among 
 the stars, and at the end of an entire year, after all the for- 
 mer changes of northern and southern motion had been 
 accomplished, the sun was found to return to the same group 
 of fixed stars from whence he set out ; and thus it became 
 manifest that this revolution among the stars was identical 
 in period with the changes from north to south ; and 
 hence these phenomena had, in all probability, a common 
 origin. 
 
 Here was the first great problem offered for solution to 
 the old astronomers. The facts and phenomena were care- 
 fully studied, and the reader may now exercise bis own 
 
 B 2 
 
POPULAR ASTRONOMY 
 
 the plane of tlie equinoctial. 
 subjoined figure. 
 
 This is readily seen from the 
 
 Let AB represent the gnomon, A' the shadow of tbo 
 vertex at noon on the day of the summer solstice, and 
 A" the shadow at noon on the day of the winter solstice. 
 Then will the angle A'AA" measure the entire motion of 
 the sun from north to south ; and as one half of this motion 
 lies north and the other half south of the equinoctial, it 
 follows that half the angle, A'AA", measures the inclination 
 of the ecliptic to the equinoctial. 
 
 In the earliest ages it was assumed that the sun's orbit 
 was absolutely fixed among the stars, and that the points 
 in which this circle crossed the equinoctial were in like 
 manner invariable. These points of intersection are of the 
 highest importance. That one through which the sun passes 
 in going from south to north is called the Vernal JZquinox ; 
 while the opposite point, through which the solar orb 
 passes in going from north to south, is called the Autumnal 
 Equinox. On the day of the equinoxes, as the sun's centre 
 was then on the equinoctial, the diurnal arc described by 
 the sun would lie one half above, and the other half below 
 the horizon, making the length of day and night precisely 
 iqual. 
 
 Among the ancient nations the day of the vernal equinox 
 Vas an object of especial interest, as it heralded the coming 
 vf spring ; and its approach was marked by the rising of a 
 Mnrtain bright star in the early dawn of the morning. Now 
 
THE SUN. 7 
 
 iii case the vernal and autumnal equinoxes were invariable, 
 the same star, by its heliacal rising (as it was called), would 
 mark the crossing of the equinoctial by the sun in the spring, 
 and the equality of day and night. After the lapse of few 
 centuries it was discovered, by the length of the noon shadow 
 of the gnomon, that the sun had reached the equinoctial 
 point, and yet the sentinel star did not make its appearance. 
 Either the equinox or the star was in motion. It was soon 
 decided that the vernal and autumnal equinoxes are both 
 slowly moving backwards along the equinoctial, and thus 
 the sun crosses this celestial circle each year a little behind 
 the point of the preceding year. 
 
 The ancient nations all seem to have attained to a 
 knowledge of this great truth ; and some of them are said 
 to have fixed the period in which the vernal equinox retro- 
 grades around the entire heavens a period of nearly twenty- 
 six thousand years. As this is a matter of simple observation, 
 and as the rate of motion can be obtained by comparing 
 recorded observations, made at intervals of four hundred or 
 five hundred years, we may readily credit the statement that 
 this period became known even anterior to the commence- 
 ment of authentic history. 
 
 This discovery of the retrocession of the equinoxes led 
 to a more critical examination of the sun's apparent motion. 
 This motion had been assumed to be uniform, and in case 
 this hypothesis could be maintained, the solar orb ought to 
 occupy an equal amount of time in passing over the two 
 portions of its orbit north and south of the equinoctial ; that 
 is, the number of days from the vernal to the autumnal 
 equinox ought to be precisely equal to the number of days 
 from the autumnal to the vernal equinox. 
 
 The Greek astronomer Hipparchus * was the first to dis- 
 cover the important truth that an inequality existed in 
 these two periods. He found, from his own observations, 
 that the sun occupied eight days more in tracing the 
 
 * Hipparchus was called the " Father of Astronomy," and nourished 
 about 140 B.C. 
 
8 POPULAR ASTRONOMY. 
 
 northern than it did in traversing the southern portion oi 
 its orbit. This was a discovery of the highest importance, 
 as it seemed to involve the then incredible fact, that the 
 lord of the celestial sphere, the great source of life, and 
 light, and heat, travelled among the stars with a variable 
 velocity. 
 
 In case the solar orbit was indeed a circle, this inequality 
 of motion seemed to be impossible. The circular figure of 
 the orbit could not be abandoned, neither was it possible, on 
 philosophical principles, to give up the hypothesis of uniform 
 motion. Here, then, was presented a problem of the deepest 
 interest, to preserve the circular figure of the solar orbit and 
 the uniform motion of the sun, and at the same time render 
 a satisfactory account of the inequality discovered in the 
 periods during which the sun remained north and south of 
 the equinoctial. This problem was solved by Hipparchus ; 
 and before proceeding to. examine the reasoning of the old 
 Greek, let the student exercise his own genius in an attempt 
 to explain the ascertained facts. 
 
 Hitherto it had been assumed, not only that the sun's 
 orbit was circular, and that his motion was uniform, but also 
 that the earth occupied the exact centre of the circle in which 
 the sun travelled round the heavens. By profound study, 
 Hipparchus discovered that all the facts could be explained 
 by giving to the earth a position, not in the centre of the 
 sun's orbit, but somewhat nearer to that portion of the solai 
 orbit where his motion was most rapid. This will become 
 evident from the figure. Let the circle A B C D represent 
 the sun's circular orbit, in which the sun is supposed to move 
 uniformly. This motion will only appear uniform to a spec- 
 tator at the centre 0. If the observer be removed to O', 
 and the line E E' be drawn perpendicular to O O', the por- 
 tion E' A B E of the orbit will require a longer time for its 
 description than the portion E C D E' ; and hence, in the 
 former, the sun will appear to move slower than in the latter. 
 Indeed, it is manifest that the point V, on the line O O' 
 prolonged, is the place of swiftest motion, while the 
 
THE SUN. 
 
 9 
 
 opposite point V is that in which the sun will appear to 
 move slowest. 
 
 Hipparchus, not satisfied with thus rendering a general 
 explanation of the phenomenon, undertook to determine the 
 actual place of the earth inside the solar orbit, or the value 
 of the distance O', which is called the eccentricity. Here 
 is another problem for the examination of the student. It 
 may be solved by simply knowing how many days longer 
 
 E E 
 
 the sun remained north of the equinoctial than it did on the 
 south of this circle. This quantity we have already given. 
 By dividing the circle A B C D into as many equal parts as 
 there are days in the year, and by drawing F F' through the 
 centre O, and perpendicular to V V, we have only to lay 
 off from F to E half the excess in days, and draw E E' 
 parallel to F F', and it will give at O' the true place of the 
 earth, and O O' will be the eccentricity. An observer at O' 
 will see all phenomena actually detected in the sun's motion, 
 while the circular orbit and uniform velocity are rigorously 
 retained. 
 
 Having determined the earth's eccentricity, it was now 
 very easy to calculate the sun's place from day to day during 
 his entire revolution among the fixed stars. This was 
 actually done by the old astronomers ; and as the computed 
 places agreed with those observed within the limits of 
 
10 POPULAR ASTKONOMY. 
 
 observation, with the rude instruments then in use, no 
 further advance would be made in the solar motions. 
 
 ECLIPSES OF THE SUN. No one has ever beheld the total 
 disappearance of the sun in the daytime without a feeling 
 of awe creeping through his frame ; and, even now, when 
 modern science predicts the coming of these amazing pheno- 
 mena with unerring precision, a total eclipse of the sun 
 never fails to inspire a certain feeling of gloomy apprehension. 
 What, then, must have been the effect in the rude ages of 
 the world of the fading out of the sun in mid-course through 
 the heavens ? Human genius, of course, bent all its energies 
 to the resolution of the great problems involved in the 
 occurrence of an eclipse of the sun. The first effort was 
 directed to the discovery of the cause of these startling 
 phenomena; and, this once determined, the second great 
 effort was put forth to so master all the circumstances as 
 not only to explain the eclipse but to predict its coming. 
 
 CAUSE OF A SOLAR ECLIPSE, In searching for the cause 
 by which the sun might be hidden, it was at once evident 
 that there was but one object in the heavens sufficiently 
 large to hide the whole surface of the sun. This body was 
 the moon. Thus attention was directed to the lunar orb, 
 and it was soon noticed that, while the bright stars and 
 planets became visible in the darkness attending an eclipse 
 of the sun, yet the brightest object in the heavens after the 
 sun, was never visible during an eclipse. The moon was 
 found to move among the stars with a velocity far greater 
 than that of the sun. It was, moreover, seen that the 
 moon's path crossed that of the sun twice during every 
 revolution of the moon ; and examining still more closely, it 
 was discovered that no eclipse of the sun ever occurred 
 except at the new moon. Now this rapidly revolving globe 
 was evidently the nearest to the earth of all the heavenly 
 bodies. It was seen, when a silver crescent, sometimes to 
 pass over and hide the larger stars which fell in its path ; it 
 was also found that the moon, though invisible during a 
 solar eclipse, always appeared immediately after very near 
 
THE SUtf. 11 
 
 the sun and as a slender crescent of light. These facts all 
 combined to prove beyond a question that the sun waa 
 eclipsed by being covered by the dark "body of the moon. The 
 cause of the eclipse was thus reached, and it now remained 
 to rob the phenomenon of its terrors by predicting when it 
 might be expected. 
 
 To predict a solar eclipse with precision is a problem of 
 great difficulty, even with the present extended knowledge 
 of the laws and structure of the solar system. And yet we 
 are informed that the old Greek astronomers succeeded in 
 the resolution of this complex problem. This may have 
 been done by long and persevering care in the record of 
 these phenomena ; for in case all the eclipses visible at any 
 given place are recorded year after year for a period of 
 nineteen years, it will be found that for the next period of 
 nineteen years eclipses will happen on the same days and in 
 the same order ; so that an astronomer, whose diligence had 
 been rewarded by the discovery of this grand truth, might 
 acquire the highest renown among his countrymen and 
 throughout the world by his superior wisdom in predicting 
 the coming of an eclipse, though no special genius was put 
 forth in the resolution of this great problem. 
 
 "We are not quite certain, however, that the prediction of 
 the first announced solar eclipse may not have been accom- 
 plished by the application of powerful thought and perse- 
 vering observation. In case the effort were now made to 
 predict a solar eclipse ; as a starting-point we know that no 
 eclipse of the sun ever occurred except at the new moon. 
 But at the time of a total eclipse of the sun the moon is 
 interposed precisely between the eye of the observer and the 
 sun, and a line joining the centres of these two great 
 luminaries, produced to the earth, passes through the place 
 of the observer. Hence, on the day and at the hour of an 
 eclipse, the new moon must be in the act of passing from one 
 side of the sun's path to the other. To render an eclipse 
 possible, two conditions must be fulfilled at the same time ; 
 the moon must be new. and the moon's centre must be ID 
 
12 POPULAR ASTRONOMY. 
 
 the act of crossing the surfs orbit. If the sun's annual route 
 in the heavens were marked among the stars by a line of 
 golden light, and the moon's motion be attentively watched, 
 it will be found that at every one of her revolutions she 
 crosses this golden line twice. The point of her crossing 
 from south to north is called the moon's ascending node, 
 while the point of crossing from north to south is the 
 descending node. 
 
 These nodes do not remain fixed, but are in comparatively 
 rapid motion, and finally accomplish an entire revolution 
 around the heavens, on the ecliptic. If, then, we unite all 
 these facts, it will be seen that to produce to any observer an 
 eclipse of the sun, the moon, at the new, must be exactly in 
 one of her nodes, so that the centre of the moon, the node, 
 and the centre of the sun, form one and the same straight 
 line. Here, then, are the conditions precedent to a solar 
 eclipse. It now remains to so follow these revolving orbs as 
 to be able to anticipate the certain occurrence of these 
 determined conditions. We follow, then, from night to 
 night, the waning moon ; she slowly approaches the sun ; 
 her light becomes a delicate crescent, just visible in the gray 
 twilight of morning, before the rising of the sun ; at length 
 the moon becomes invisible, and when she reappears, it is on 
 the opposite side of the sun, and her silver crescent of light 
 is just above the setting sun. There was no eclipse because 
 this new moon did not fall on the sun's path. It is, however, 
 easy to mark the time of new moon, and equally easy to see 
 and note the time when the moon is in her node, or on the 
 ecliptic ; and by thus watching, from new moon to new moon, 
 we may see whether the interval from the passage of the 
 node up to new moon is growing shorter, and at what rate 
 it decreases, till, finally, we shall perceive that on the coming 
 of a certain new moon it must fall precisely at the node, 
 and on the day of this computed conjunction : to him who 
 has watched, and waited, and pondered, and computed, the 
 sun must fade away in total eclipse. Such is the train of 
 reasoning and observation which may have first led to the 
 
THE SUN. 13 
 
 resolution of this great problem ; but to whose genius we are 
 indebted for this grand discovery neither history nor tradi- 
 tion furnishes any information. 
 
 In consequence of the near equality in the apparent 
 diameters of the sun and moon, and a slight change in both, 
 due to a change of the actual distance from the earth (as 
 will be shown hereafter), it sometimes happens that the 
 moon's diameter is less than that of the sun. When this 
 obtains during a solar eclipse, there remains around the black 
 disc of the moon a brilliant ring of solar light, and the 
 eclipse is said to be annular. Whenever the moon's centre, 
 at the new, is not precisely at the node, but not so remote 
 from it as the sum of the semi-diameters of those two orbs, 
 there will be a partial obscuration of the sun. 
 
 We have presented these facts in this place, as known to 
 the early astronomers, and as admirable means of exercising 
 the power of thought on the part of those who may desire 
 to devote themselves to the real study of the great pheno- 
 mena of nature. We will recur to this subject again, when 
 we shall have mastered the laws of motion and of gravita- 
 tion. 
 
 Such is a rapid survey of the discoveries of the ancients 
 in the study of that great orb, which, from its splendour, 
 even if it be a mere phantom of light, justly commands our 
 admiration, and deserves our best efforts to master its myste- 
 rious movements and its sublime phenomena. 
 
 We now proceed to exhibit those discoveries which could 
 only be accomplished after man had armed himself with 
 instruments of great power and delicacy, and with a vision 
 increased a thousand fold beyond that with which he is 
 endowed by nature. 
 
 DISCOVERIES OF THE MODERNS. The rude instruments 
 employed by the early astronomers sufficed to fix the places 
 of the sun and the other heavenly bodies with sufficient 
 accuracy to give a general outline of the curves they de- 
 scribed ; and as these curves, as determined by observation, 
 approximated the circular form, it was concluded that the 
 
POPULAR ASTRONOMY. 
 
 deviations from that exact figure were only errors of obser- 
 vation. Knowing the period in which the sun revolves 
 round the heavens, and the distance of the observer from 
 the centre* of his assumed circular orbit, it was easy to 
 compute accurately the sun's place among the stars on any 
 day of the year. This computation being made, no instru- 
 ment then in use could detect any difference between the 
 computed place and that actually held by the sun. It was, 
 therefore, unphilosophical to doubt the absolute truth of an 
 hypothesis thus sustained by the best observations which 
 could then be made. It was not at all difficult to observe 
 roughly mere position, and any error of observation in fixing 
 the place of the sun would, in the long run, be eliminated 
 in its effects by taking into account a large number of revo- 
 lutions. The degree of accuracy required in thus fixing the 
 sun's place among the stars was widely different from that 
 demanded in the 
 
 MEASUREMENT OF THE SUN'S DISTANCE. The principles 
 involved in the solution of this great problem were well 
 understood by the old Greek astronomers, and were applied 
 by them successfully in measuring the distances of inacces- 
 sible objects on the surface of the earth. These principles 
 are so simple, that a knowledge of the very first rudiments 
 of geometry will suffice to render intelligible the methods 
 which are employed in obtaining the data for computing the 
 distances of the heavenly bodies. 
 
 Suppose it were required to learn the distance of the 
 object A from, the point C. From C send to A the visual 
 ray C A, then lay off any line from C perpendicular to 
 A C, and measure its length. From B draw the visual ray 
 B C, and measure the angle C B A. We have thus formed 
 a right-angled triangle, in which the angle at C is a right 
 angle, the base, C B, is known by measurement, and the 
 angle B A is known in the same way ; hence may be com- 
 
 * /. e. the eccentricty. See p. 9. 
 
THE SUN. 
 
 , by the simplest elements of trigonometry, the length 
 or the distance A, or the required quantity. 
 
 Any error committed in the measurement of the angle 
 C B A grows more powerful in its effect on C A, in pro- 
 
 portion to the number of times B must be taken to 
 measure C A. In our attempt to measure the sun's dis- 
 tance, we are limited to a base line equal in length to 
 the earth's diameter; and hence it becomes necessary to 
 employ every refinement of art to eliminate as far as pos- 
 sible the errors involved in the measurement of the angle 
 CBA, or its complement, the angle CAB, on which, in 
 the application of these principles to the problem in ques- 
 tion, depends the measurement of the sun's distance. This 
 quantity is the great key which unlocks all the mysteries 
 of the entire system. Upon it depend directly the mass, 
 volume, and density of the sun, the distances, weights, and 
 magnitude of all the planets, and even the masses and dis- 
 tances of the fixed stars. It is for this reason that modern 
 science has spared neither time nor money, neither skill nor 
 ingenuity, in the effort to reach an exact solution of this 
 grand problem. 
 
 THE SOLAR PARALLAX. In case an observer were located 
 at the sun's centre, and from his eye two visual rays were 
 drawn, one to the centre of the earth, the other tangent tc 
 4 .he spherical surface of the earth, these rays would form an 
 
16 POPULAK ASTRONOMY. 
 
 angle with each other at the eye of the observer, ana tb*k 
 angle is called the suris horizontal parallax. 
 
 Thus, S representing the sun's centre, C the centre of the 
 earth, C R a radius of the earth perpendicular to the visual 
 ray SO, and S R the visual ray drawn to the extremity R 
 of the radius, the angle R S C is the solar parallax ; and in 
 case it were possible to measure that angle, as the angle 
 SCR is a right angle, the remaining parts of the triangle 
 R S C become known by computation. Thus it appears that 
 the problem of measuring the sun's distance from the earth 
 resolves itself into obtaining the value of the surfs horizontal 
 parallax, or the angle under which the earth's radius would 
 be seen from the sun's centre. 
 
 No instruments have yet been constructed sufficiently 
 delicate to accomplish directly the measure of this im- 
 portant quantity with the requisite precision. But there is 
 an indirect method, which has been employed by modern 
 astronomers to accomplish the same object, which has been 
 rewarded with satisfactory success. This method we shall 
 now proceed to explain. 
 
 From the most remote antiquity it has been known that 
 there are two planets, Mercury and Venus, which appear to 
 revolve around the sun, never receding from that orb beyond 
 certain narrow and well-defined limits. The distances from 
 these planets to the sun are less than the earth's distance 
 from the same luminary j and hence they must at each of 
 their revolutions pass between the earth and sun. Modern 
 science has confirmed these ancient discoveries, and the 
 telescope has even shown that on certain rare occasions each 
 of these planets actually passes between the solar disc and 
 the eye of an observer on the earth, and appears as a round 
 black spot on the bright surface of 'he sun. These passage? 
 
THE SUN. 
 
 17 
 
 of the planets across the solar disc are called transits, and 
 it happens that the transits of Venus furnish an admirable 
 means of reducing the errors involved in the direct measure- 
 ment of the solar parallax, as we shall now proceed to 
 explain. 
 
 We will first present the principle involved, and then 
 make the application. 
 
 Let it be required to determine the distance of the point 
 A from any inaccessible surface, as C D, and that A A' is 
 the longest base line which can possibly be employed. In 
 case the distance of the point B' on the surface G D be 
 required, then the angles B'A'A and B'AA' must be 
 measured, and their sum, subtracted from 180, gives for 
 a remainder the angle A B' A', or the angle under which 
 
 the line A A' would be seen by a spectator at B'. Now 
 this angle, because of its minute value, may be difficult to 
 measure, and we desire to find some artifice by which this 
 difficulty may be at least diminished, if not entirely re- 
 moved. Suppose, then, a material point to be located at B, 
 much nearer to A A' than to C D, an observer at A would 
 see the point B projected on C D at B", while an observer 
 at A' would see the same point projected at B'. Now let 
 us suppose that the points B' and B" can be identified and 
 seen as round, black, permanent spots on the remote surface 
 C D ; in case B is further from C D than from A A', it 
 is clear that the visual angle subtended by B' B", as seen 
 from A, will be larger than the visual angle subtended by 
 
20 POPULAR ASTRONOMY. 
 
 having an apparent diameter of 32' 1", must have a real 
 diameter of no less than 882,000 miles in length, or more 
 than 111 times longer than the diameter of our earth, as we 
 shall hereafter see. This enables us to compare the bulk or 
 volume of these two globes, and we find that it would 
 require no less than 1,384,472 globes as large as the earth 
 to fill the vast interior of a hollow globe as large as the sun. 
 This is a comparison of bulk only j the relative weights of 
 the earth and sun must be considered hereafter. 
 
 If this wonderful globe excited our admiration by the 
 splendour of its surface, and its floods of light and heat, 
 how must this admiration be increased when we contem- 
 plate its great distance and its gigantic proportions ? 
 
 THE PHYSICAL CONSTITUTION OF THE SUN. But for the 
 aid derived from the telescope, man could never have passed 
 beyond mere conjecture as to what lies on the surface of the 
 sun. The telescope, however, magnifying a thousand times, 
 transports the observer over a vast proportion of the distance 
 separating him from the solar orb, and plants him in space 
 within 95,000 miles of the sun's surface, there to examine 
 the phenomena revealed to his sight by this magic tube. 
 We may, therefore, regard the sun's distance as reduced to 
 the thousandth part of its actual value ; and we should riot 
 be suprised to find upon a globe of such grand proportions 
 fluctuations and changes which, at this reduced distance, 
 may become distinctly visible. This anticipation has not 
 been disappointed. 
 
 THE SOLAR SPOTS. To the naked eye the sun's surface 
 presents a blaze of insufferable splendour, and even when 
 this intense light is reduced by the use of any translucent 
 medium, the entire disc appears evenly shaded, with a slight 
 diminution of light around the circumference, but without 
 visible spot or variation. When, however, the power of 
 vision is increased a hundred or a thousand fold by telescopic 
 aid, and when the intense heat of the sun and his equally 
 intense light are reduced by the interposition of deeply- 
 coloured glasses, the eye recognizes a surface of most 
 
THE SUN'S LIMB 
 
 SOLAR SPOTS 
 
THE SUN. 21 
 
 wonderful character. Instead of finding the sun everywhere 
 equally brilliant, the telescope shows sometimes on it* 
 surface Hack spots, of very irregular figure, jagged and 
 broken in outline, and surrounded by a penumbra conforming 
 in figure to the general outline of the central black spot 
 (called the nucleus), but of muph lighter shade. Even 
 where there are no spots, the surface of the sun is by no 
 means uniformly brilliant. The entire surface has a mottled 
 appearance, with delicate pores or points, no one of which 
 can be readily held by the eye, but a group of them may 
 sometimes be seized by the vision under favourable atmo- 
 spheric circumstances, and can be held long enough to demon* 
 strate that these minute pores do not change their relative 
 position, or disappear while under the eye. 
 
 Besides the mottling of the surface, the telescope detects 
 in the solar orb a variety of brighter streaks, called faculce, 
 whose appearance has been connected, as some believe, with 
 the breaking out of the black spots. 
 
 Watching from day to day a single spot, or a group of 
 spots on the sun's surface, they are found to advance toge- 
 ther in the same direction, slowly to approach the edge of 
 the sun, finally to disappear from the sight, and after a 
 certain number of days to re-appear on the opposite side of 
 the sun's disc, revealing the surprising fact that the sun is 
 elowly rotating on an axis whose position seems to be inva- 
 riable. In case these spots were absolutely fixed on the 
 sun's surface, they would reveal the exact period in which 
 bis rotation is performed ; but in consequence of their 
 change of figure, and change of position as well, we can 
 only reach an approximate value of the period of rotation* 
 This is now fixed, by the best authorities, at twenty-jm 
 days, eight hours and nine minutes. 
 
 During the past thirty years, M. Schwabe, of Dessau,* 
 has given special daily attention to counting the groups and 
 spots on the sun ; and by preserving a record, it has been 
 
 * In Hanalt, Germany. 
 
22 POPULAK ASTRONOMY. 
 
 discovered that the amount of solar surface covered by the 
 black spots is not only variable, but that periodicity marks 
 this variation. The entire change, from a maximum ol 
 spots counted in any year, to the minimum, occupies about 
 five and a half years, and the same time elapses from a 
 minimum to a maximum, making the period^from maximum 
 to maximum eleven years. This fact is one of the most sur- 
 prising revealed in the physical constitution of any of the 
 heavenly bodies, and thus far has baffled the power of human 
 investigation to explain it, while its mysterious character is 
 increased by the fact recently discovered, that this periodicity 
 in the solar spots is identical in duration with a certain 
 variation observed in the intensity of terrestrial magnetism. 
 Thus, it would seem, that a new bond of union is about to 
 be established between the earth we inhabit and that mighty 
 orb whence we receive our supplies of light and heat. 
 
 Some astronomers account for the solar spots by supposing 
 the sun to be a solid, dark, opaque globe, surrounded by two 
 atmospheres, the exterior one a highly luminous and gaseous 
 envelope, the interior more dense, and possessing great 
 reflecting power. The spots are supposed to result from 
 powerful internal convulsions, upheavals from within break- 
 ing through these two envelopes, and producing a more 
 extended chasm, in the external luminous atmosphere. I 
 have examined the surface of the sun and closely observed 
 the large solar spots with a refractor of admirable perform- 
 ance, and so far from presenting an appearance such as the 
 above hypothesis would warrant, the entire exhibition 
 resembled the openings often found by melting through a 
 thick stratum of solid ice from below the spiky and jagged 
 outline of the black nucleus being well represented by a 
 similar form in the opening through the ice, while the 
 penumbra was very faithfully represented by the thinner 
 portions of ice remaining around the opening. It is not to 
 b* inferred from this comparison that the author entertains 
 the opinion that the exterior of the sun is a solid crust, and 
 that these solar spots are produced from the melting of this 
 
THE SUN. 23 
 
 crust by the action of internal fires. The comparison is 
 made for the purpose of illustrating, as strongly as possible, 
 the absolute appearance of these inexplicable phenomena, 
 and to present as strong a contrast as the facts warrant to 
 the statement made by a distinguished astronomer, that the 
 sun's surface, when viewed by a powerful telescope, resembles 
 " the subsidence of some flocculent chemical precipitates in a 
 transparent fluid." So far from this being the case, the 
 sharp outline of the penumbra surrounding the dark spots 
 has often been seen to cut directly across the minute pores, 
 dividing them sharply and sometimes equally. 
 
 Recent observations seem to demonstrate that what has 
 generally been considered the solar surface is really the 
 exterior of a cloudy atmosphere beneath the luminous ocean 
 surrounding the sun. Mr. Dawes, by an eye-piece of his 
 own construction, bearing a metallic diaphragm, in which a 
 minute hole is pierced, coincident with the axis of the 
 telescope, has been enabled to make a very critical examina- 
 tion of the solar spots. He finds in the centre of the dark 
 spot a smaller opening, which is, as now seen, intensely black, 
 and this is at present regarded as the real surface of the solar 
 orb. The same distinguished observer has announced the 
 discovery of an actual rotation of the solar spots about a 
 central axis. This important fact has given rise to specula- 
 tion as to "the probable cause of these wonderful fluctuations 
 which occur in the solar atmospheres. 
 
 It is conjectured that these exhibitions may be produced 
 by tremendous storms or whirlwinds resembling those which 
 sometimes sweep over the surface of the earth, and whose 
 vortices, if seen from above, would present an appearance 
 no': unlike the spots on the sun. We understand how these 
 tornadoes are generated in the atmosphere of the earth, but 
 it is useless to attempt to conjecture the causes which can 
 produce such amazing effects in the solar atmosphere. 
 
 INTENSITY OP THE SOLAR HEAT. Admitting that the heat 
 of the sun falling on the earth is diminished in the ratio of 
 the square of the sun's distance, it is not dillicult to form 
 
24 POPULAR ASTRONOMY. 
 
 some approximate idea of the intensity of the solar heat at 
 the surface of the sun. By exposing a surface of ice to the 
 direct action of the sun's heat, when the sun was nearly 
 vertical, Sir John Herschel determined by experiment the 
 thickness of the ice melted in a given time. 
 
 From this and like experiments it is determined that it 
 would require the combustion of more than one hundred and 
 thirty thousand pounds of coal per hour on each square foot 
 of the sun's surface to produce a heat equal to that radiated 
 from the solar orb. 
 
 When an image of the sun is received on any surface, it is 
 found that the central point of the image is more heated 
 than the parts near the circumference, and that the tem- 
 perature diminishes from the equator toward the poles. 
 
 THE SUN'S ATMOSPHERE. These facts have been accounted 
 for by supposing the sun to be surrounded by a dense 
 atmosphere, and that the heated rays which pass through 
 the deepest part of this atmosphere, lose a portion of their 
 heat, and hence the regions around the disc of the sun 
 should be, to us, less heated than those near the centre of 
 the solar orb. There are some phenomena attending a total 
 eclipse of the sun which seem to sustain this hypothesis of 
 a solar atmosphere. At the moment the eclipse becomes 
 total, there is seen to burst from the jet-black disc of the 
 moon a sort of halo or glory, radiating on every side, and 
 presenting a spectacle of wonderful grandeur, so much so 
 that on the occasion of the eclipse of July, 1842, witnessed 
 at Pavia,* the entire populace burst into a shout of wonder 
 and admiration. 
 
 There also appeared, at the same time, Barnes ofjlre dart- 
 ing from behind the limb of the moon, resembling mountains 
 of rose-coloured light, rising to the height of forty or fifty 
 thousand miles above the surface of the sun. These flames 
 are known to assume the form of cloudy exhalations, which, 
 in some instances, seem to be drifted like smoke ascending 
 
 * In Lombardy. 
 
THE SUN. 25 
 
 in a calm atmosphere to a certain level, where it meets a 
 current and is borne off horizontally. 
 
 There is another phenomenon attending the rising and 
 setting of the sun at certain seasons of the year in the shape 
 of a vast beam of faint gauzy light, of lenticular form, rising 
 from the point of sunset in the evening, and stretching 
 upward in the direction of the sun's path sometimes 70 or 
 80. This is called the Zodiacal Light, and has long been 
 regarded as the evidence of uncondensed nebulosity, or a 
 material atmosphere surrounding the equatorial regions of 
 the sun. The central line, or axis, of this luminous beam 
 does not appear to be fixed in position ; and hence a difficulty 
 arises not readily removed by the hypothesis of a material 
 atmosphere. 
 
 Some have supposed this mysterious luminous zone to be 
 a nebulous ring surrounding our moon, while others have 
 regarded it as an immense ring of minute asteroids or 
 meteors, revolving round the sun, and slowly subsiding into 
 this grand luminary, and by the conversion of their velocity 
 into heat, as they fall in a perpetual shower on the sun, or 
 are burned up in the solar atmosphere, keeping up a supply 
 equal to the vast radiation shot forth from the sun at every 
 moment of time. While we are willing to admit that a 
 material globe, falling into the solar atmosphere, may gene- 
 rate immense heat, in proportion to its magnitude and 
 velocity, it seems quite impossible to adopt the hypothesis 
 that the zodiacal light is either a material solar atmosphere 
 or a ring of revolving meteors, as it extends to such a vast 
 distance from the sun, that if revolving with the sun, as does 
 our atmosphere with the earth, the particles would be 
 thrown beyond the control of the sun and would be dissi- 
 pated into space. 
 
 We are compelled to acknowledge that up to the present 
 time science has rendered no satisfactory account of the 
 origin of the solar light or heat. Whence comes the ex- 
 liaustless supply, scattered so lavishly into space in every 
 direction, we know not. Neither is it possible to give a 
 
26 POPULAR ASTRONOMY. 
 
 satisfactory solution of the solar spots, or of any of thu 
 strange phenomena attending their rotation or translation 
 on the sun's surface. The idea that tornadoes and tempests 
 rage in the deep, luminous ocean that surrounds the sun, 
 like those which sometimes agitate the atmosphere of the 
 earth, has no solid foundation. We know the exciting causes 
 of the tornadoes on earth, but why such storms should exist 
 in the solar photosphere it is in vain to conjecture at present. 
 Doubtless the time will come when these phenomena will be 
 explained. Persevering and well-directed observation will, 
 in the end, triumph; but these are matters which must be 
 consigned to the researches of posterity. 
 
 CHAPTER II. 
 
 MEKCURY, THE FIKST PLANET IN THE ORDER OF DISTANCE 
 FROM THE SUN. 
 
 Its Early Discovery. Difficult to be distinguished from the Stars. 
 Elongations. Motion Direct and Retrograde. Sometimes Stationary. 
 Nature of the Orbit. Variation in the Elongation explained. The 
 Nodes. Transit of Mercury. Inclination of Mercury's Orbit. Mean 
 Distance from the Sun. Conjunctions. Phases. Diameter and 
 Volume. 
 
 No discovery made by the ancients gives us a higher idea of 
 the care and scrutiny with which their astronomical obser- 
 vations were conducted than the fact that the minute planet 
 Mercury, so difficult to be seen, and so undistinguishable 
 from the fixed stars, was discovered in the very earliest ages 
 of the world. That the brighter planets, such as Yenus and 
 Jupiter, whose brilliancy exceeds that of any of the fixed stars, 
 should have been detected to be wandering bodies, even in 
 the remotest antiquity, is by no means surprising. For in 
 watching the sun rising and the sun setting, so as to note, 
 in the first instance, the stars nearest to the sun, which were 
 the last to fade away, and in the second, those stars which 
 
MERCURY. 27 
 
 were the first to become visible, the change of position of the 
 planets Venus and Jupiter could not fail to attract the 
 attention of the student of the heavens ; but the planet 
 Mercury is so small, and so rarely visible even to the keenest 
 eye, that it is said Copernicus himself, during his whole 
 life devoted to the study of the heavens, never once caught 
 sight of this almost invisible world. 
 
 Mercury, in his appearance to the naked eye, is not dis- 
 tinguishable from the fixed stars. His close proximity to 
 the sun, the fact that he is never visible except near the 
 horizon, and the intense brilliancy of his disc give to him 
 that twinkling appearance which distinguishes the fixed 
 stars. Notwithstanding all these difficulties, the oldest astro- 
 nomers managed to acquire a very complete knowledge of 
 the principal facts connected with the movement of this 
 planet. By a careful and continuous examination it was 
 found that Mercury never receded more than about twenty- 
 eight degrees from the sun's centre. The amount of recess, or 
 elongation as it is called, was soon discovered to be a vari- 
 able quantity, a fact which demonstrated that in case the 
 planet revolved in a circular orbit, inclosing the sun, the 
 sun could not occupy the centre of this circle. By watching 
 the elongations from revolution to revolution, it was found 
 that they varied from a minimum of 16 12', to a maximum 
 of 2 8 48'. Knowing the amount of this variation, and 
 watching carefully the progressive change, it became possible 
 to reach a tolerably accurate knowledge of the nature 
 of the orbit described by the planet in its revolution 
 around the sun. It was soon discovered that in some por- 
 tions of his orbit Mercury advanced with the sun in his 
 march among the fixed stars, while in other parts of hia 
 orbit his motion became retrograde, and in the change from 
 direct to retrograde, and the reverse, the planet apparently 
 ceased to move, and for a short time became stationary. 
 
 It will be seen that all these changes are readily 
 accounted for by supposing the planet to revolve about the 
 sun in a circular orbit, the sun being eccentrically placed 
 
28 POPULAR ASTRONOMY. 
 
 If we conceive two visual rays to be drawn from the eye 
 of the observer, and tangent to the orbit of Mercury on the 
 right and on the left, the planet, while traversing that arc 
 of its orbit intercepted between the points of contact and 
 nearest to the eye, will move direct ; in passing through the 
 point of contact after direct motion ceases, it will move off 
 in the direction of the visual ray, and hence will appear 
 stationary for a short time. In the larger portion of its 
 orbit (that remote from the eye) its motion must be opposite 
 to that of the sun, and hence retrograde. In coming up to 
 the second point of contact, the planet will move along the 
 visual ray toward the eye of the observer, and hence for a 
 short time will appear stationary. 
 
 To account for the variation in the elongations of 
 Mercury, we must either suppose the point of nearest 
 approach of the planet to the sun, called its perihelion, to be 
 in motion, or else we must suppose the spectator to be 
 himself moving, and thus to behold the planet, its perihelion 
 point, and the sun, under varying relations to each other. 
 As the early astronomers assumed the immobility of the 
 earth, they explained the variations in the elongations of 
 Mercury by giving to its perihelion point a motion of revo- 
 lution about the sun. 
 
 It is impossible to follow the planet with the naked eye 
 in its close approach to the solar orb, as its feeble reflected 
 light is necessarily overpowered by the brilliancy of the 
 sun, but by close observation, and by marking the positions 
 of the planet at its disappearance and reappearance, the old 
 astronomers are said to have reached to a knowledge of the 
 fact that this planet sometimes crosses the sun's disc, pro- 
 ducing what is called a transit of Mercwry, identical in its 
 phenomena with the transit of Yenus, already spoken of in 
 connection with the determination of the solar parallax. In 
 case the plane of the orbit of Mercury were exactly coin- 
 cident with the plane of the sun's apparent orbit, it is mani- 
 fest that every revolution of the planet would produce a 
 transit. As this, however, is not the case, and as no central 
 
MERCURY. 20 
 
 transit can occur, except when the planet crosses the 
 visual ray drawn from the eye of the observer to the sun's 
 centre, it is manifest that the planet Mercury, during a 
 central transit, must actually pass through the ecliptic from 
 one side of this plane to the other. This point of passage 
 through the plane of the sun's apparent orbit is called the 
 node of the planet's orbit. There are, of course, two such 
 points. The planet passes its descending node in moving 
 from the north to the south side of the ecliptic, and its 
 ascending node on its return from the south to the north side. 
 
 It is thus seen that in order to produce a transit of 
 Mercury there must be a conjunction of the planet, its 
 node, and the sun. Whenever this conjunction is abso- 
 lute, Mercury will pass across the sun's centre. When 
 it is only approximate, the planet will transit a small 
 portion of the sun's disc, or possibly pass without contact 
 at all. 
 
 An attentive examination of the places of the planet, 
 before and after a transit, led to a pretty accurate deter- 
 mination of the angle under which the plane of the planet's 
 orbit is inclined to the plane of the ecliptic. This angle was 
 approximately determined by the ancients, while modern 
 science fixed it at the commencement of the present century 
 at 7 00' 10". 
 
 The motion of Mercury in its orbit is more rapid than 
 that of any of the planets thus far discovered, travelling, as 
 it does, more than one hundred thousand miles an hour, 
 and performing its entire revolution about the sun in 
 about eighty-eight of our days. In case this world has the 
 same variety of seasons which mark the surface of our own 
 earth, these will follow each other in such rapid succession 
 that the longest of them will consist of only about three of 
 our weeks. It is not difficult to compute the intensity of 
 solar light and heat which falls upon the surface of the 
 planet Mercury, in case these be subjected to the same 
 modifying influences which exist upon the earth. But as 
 we remain in ignorance of the circumstances which surround 
 
30 POPULAR ASTRONOMY. 
 
 this distant planet, it is vain to speculate upon the phy- 
 sical constitution of a world whose close proximity to the 
 sun has thus far shut it out from the reach of telescopic 
 examination. 
 
 The distance of. the planet Mercury from the sun may be 
 readily determined, in certain portions of its orbit, in case 
 we know first the earth's distance from the same orb. For 
 example, conceive a visual ray to be drawn from the earth, 
 tangent to the orbit of Mercury (supposed, for the prefcent, 
 to be circular) ; place the planet at the point of contact, and 
 join the centre of the planet with the centre of the sun ; 
 also join the centres of the earth and sun the triangle thus 
 formed, having the earth, Mercury, and the sun as the 
 vertices of its three angles, is right-angled at Mercury, 
 while the angle at the earth is readily measured, and is 
 nothing more, indeed, than the elongation, for the time 
 being, of that planet. Hence, in the right-angled triangle, 
 we know the angles and the longest side, extending from 
 the earth to the sun, and by the simplest principles of 
 trigonometry, we can compute the remaining parts namely, 
 the distance of Mercury from the sun and from the earth. 
 By this, and by other methods more accurate, it is found 
 that Mercury revolves in an orbit around the sun, and at 
 a mean distance of about thirty-six millions of miles. 
 
 As the entire orbit of this planet lies within the 
 limits already assigned, it follows that the planet can never 
 be seen in a quarter of the heavens opposite to the sun, 
 or can never be in opposition. When nearest the earth, 
 and on the right line joining the sun and earth, Mercury 
 is said to be in inferior conjunction. When 180 distant 
 from this place, it is on the other side of the sun, with 
 respect to the earth, and is then in its superior conjunction. 
 
 The telescope has demonstrated that this planet passes 
 through changes like those presented by the moon. When 
 in superior conjunction, the planet will be seen nearly 
 round, as in that position nearly the whole of the illu- 
 minated surface is turned toward the eye of the observer 
 
MERCURY. 31 
 
 on the earth. As the planet comes round to its inferior 
 conjunction,- the light gradually wanes, until at inferior 
 conjunction a slender crescent of great delicacy and beauty 
 is revealed to the eye, provided the planet does not lose 
 its light entirely in the passage across the sun's disc. 
 These phases of Mercury prove, beyond question, the fact 
 that the planet does not shine by its own light, but that its 
 brilliancy is derived from reflecting the light of the solar orb. 
 
 The degree of precision reached in .predicting the trans- 
 its of Mercury indicates, with wonderful force, the progress 
 of modern astronomy. The first predicted transit which 
 was actually observed, occurred in 1631, when the limits 
 of possible error were fixed by the computer at fowr days ; 
 and hence the watch commenced two entire days before the 
 predicted time. 
 
 If the transit had taken place in the night-time, the 
 opportunity for verification would have been lost. Fortu- 
 nately this was not the case, and the toil and zeal of 
 Gassendi were rewarded with the first view of Mercury 
 projected on the solar disc ever witnessed by mortal man. 
 Nearly two hundred years later, at the beginning of the 
 nineteenth century, the French astronomers ventured to 
 assert that their predictions could not be in error more 
 than forty minutes. The transit which occurred on the 
 8th November, 1802, verified this assertion very nearly. 
 By a more careful study of the causes affecting the place 
 of the planet, forty-three years later, the discrepancy be- 
 tween computation and observation was reduced to only 
 sixteen seconds of time, a quantity very minute, when we 
 take into account the variety of causes affecting the reso- 
 lution of the problem. The transits of Mercury recur at 
 certain regular intervals, repeating themselves after a cycle 
 of 217 years, falling for the present in the months of May 
 and November. 
 
 Having learned the distance of Mercury from the earth, 
 and having measured the angle subtended by its diameter, 
 we find its actual magnitude to be much smaller than that 
 
dS POPULAR ASTRONOMT. 
 
 of the earth. Its diameter is Vut 3,140 miles, and its vo- 
 lume is but 0-063, the earth's volume being counted as unity, 
 In comparison with the vast proportions of the sun, this 
 little planet sinks into absolute insignificance ; for if the sun 
 be divided into a million equal parts, Mercury would not 
 weigh as much as the half of one of these parts. 
 
 CHAPTER III. 
 
 VENUS, THE SECOND PLANET IN THE ORDER OF DISTANCE 
 FROM THE SUN. 
 
 The First Planet discovered. Mode of its Discovery. Her Elongations. 
 Morning and Evening Star. A Satellite of the Sun. Her Superior and 
 Inferior Conjunctions. Her Stations. Direct and Retrograde Motions. 
 These Phenomena indicate a Motion of the Earth. Transits of Venus. 
 Inclination of the Orbit of Venus to the Ecliptic. Her Nodes. Inter- 
 vals of her Transits. Knowledge of the Ancients. Phases of Venus. 
 Her Elongations unequal. No Satellite yet discovered. Sun's Light and 
 Heat at Venus. Her Atmosphere. 
 
 THIS planet is the second in order of distance from the sun, 
 and as it is the most brilliant of all the orbs, with the excep- 
 tion of the sun and moon, it was undoubtedly the first dis- 
 covered of all the planets. The movements of the sun and 
 moon among the fixed stars must have claimed the attention 
 of the observers of celestial phenomena in the earliest ages 
 of the world. In marking the rising and setting sun, and 
 in noting the stars which were the last to fade out in the 
 morning twilight and the first to appear in the evening after 
 the setting of the sun, the brilliancy of Venus could not fail 
 to have attracted the attention of the very first observer 
 of celestial phenomena. A star of unusual brightness was 
 noticed in comparative proximity to the sun in the early 
 evening. The sun's place, with reference to this object, 
 having been carefully marked, for a few consecutive nights, 
 it was found that the distance between them was rapidly 
 diminishing. It was readily seen that this diminution of 
 distance was due to the fact that the bright star was 
 
VENUS. 33 
 
 approaching the sun, for by comparing its place among 
 the fixed stars with what it was a few nights previous, 
 this star was found to have changed its position among 
 the group in which it happened to be located, and was 
 evidently advancing rapidly toward the sun. 
 
 We are thus presented with the exact facts which must 
 have marked the discovery of the first planet or wandering 
 star ever revealed to the eye of man. We know not the 
 name of the discoverer, nor the age or nation to which he 
 belonged, but we are satisfied that the facts as above stated 
 did undoubtedly occur ; and we find not only profane 
 authors, but one of the Hebrew prophets,* referring to 
 this planet more than two thousand five hundred years 
 ago. The student who desires may easily re-discover the 
 planet Venus. She will be readily recognized as the largest 
 and brightest of all the stars, and will be found never to 
 recede from the sun more than about 47. From this dis- 
 tance, which she reaches at her greatest elongation, the 
 planet will be found, at first slowly, but afterwards more 
 rapidly, to approach the solar orb. She will finally be lost 
 in the superior effulgence of the sun ; and when the unaided 
 eye ceases to follow her in her approach to the sun, tele- 
 scopic power will enable the observer to continue his observa- 
 tions, until, finally, the sun's direct beams mingling with 
 those of the planet, she ceases to be visible, and is now lost 
 for a greater or less period, until she emerges from the solar 
 rays, appearing just before the sun in the gray morning twi- 
 light. She now recedes from her central orb, finally reaches 
 her greatest elongation upon the opposite side, stops in her 
 career, returns again, and thus oscillates backward and for- 
 ward, never passing certain prescribed limits. 
 
 As already stated, the fact that Venus was a planet or 
 wandering star must have become known among the very 
 first of astronomical discoveries j but it required, doMbt- 
 less, a long series of observations to determine the truth 
 
 * Isaiah xiv. 12. 
 
34 POPULAR ASTRONOMY. 
 
 that the bright star which for some months had accom- 
 panied the setting sun, and which was at length lost in 
 the solar beams, was the same object which, at a later 
 period, became visible in the morning dawn, having passed 
 by or across the solar disc. This discovery, however, is 
 said to have been made by the Egyptian priests, and was 
 by them communicated to the Greek astronomer Pytha- 
 goras,* who taught this truth to his countrymen. 
 
 It is obvious, from the above facts, that the planet 
 Venus, like Mercury, is, beyond doubt, a true satellite 
 of the sun, even to the inhabitants of the earth ; and it 
 is equally manifest that, whatever be the true relations 
 between the earth and the sun, and whichever one of these 
 two bodies may be at rest, one thing is certain, the planets 
 Mercury and Yenus cannot by any possibility have the 
 earth for their centre of motion. No matter in what re- 
 gion of the heavens the sun may be found at any season 
 of the year, these two interior planets ever accompany him. 
 As Venus recedes to a greater distance from the sun than 
 Mercury, it follows that her orbit of revolution around the 
 sun must be the larger of the two. We are thus enabled, 
 by the simplest train of reason and observation, to fix the 
 following facts : The sun is a central orb, about which re- 
 volve, in regular order, two planets, the nearer of which is 
 Mercury, and next to Mercury, Venus, with periods of revo- 
 lution, readily determined by the spectator on the earth's 
 surface. These facts are exceedingly important as the pri- 
 mary ones which lead to the discovery of the true system of 
 the universe. 
 
 When Venus passes between the eye of the observer and 
 the sun, she is said to be in her inferior conjunction ; when 
 she is directly beyond the sun, with reference to the specta- 
 tor, she is in her superior conjunction. From her inferior to 
 her superior conjunction she occupies a position west of the 
 sun, rises in the early morning, before the sun, and is known 
 
 * Pythagoras flourished about 350 B.C. 
 
VENUS. 2| 
 
 as Phosphorus, or Lucifer, or the morning star. From her 
 superior to her inferior conjunction she follows the setting 
 sun ; she becomes our evening star, under the name of 
 Hesperus. 
 
 In examining the phenomena inrolved in the motions of 
 Venus, and watching her carefully in her approach to and 
 in her recess from the sun, it is found that her movements are 
 almost identical with those of Mercury her motions for a 
 certain portion of her revolution being direct, or like those of 
 the sun ; she then becomes stationary, then moves backward 
 or retrograde among the fixed stars, becomes stationary again, 
 and then commences her direct movement. All these facts 
 are readily accounted for by admitting that Venus revolves 
 about the sun in an orbit nearly circular, and that she is 
 viewed by a spectator situated exterior to her orbit, and 
 moving around the sun and Venus in a circle, whose plane 
 makes a small angle with the plane on which the orbit of 
 Venus lies. If a visual ray be drawn from the eye of the 
 observer, tangent to the orbit of Venus, should the planet 
 happen to fill the point of contact, she will appear to move 
 in the direction of this ray, and, for the time being, will be 
 directly advancing to, or receding from, the eye of the 
 observer, and thus will appear stationary. That the observer 
 is in motion, is manifest from the fact that the direct move- 
 ment of Venus does not bear that relation to the retrograde 
 movement which is required by such an hypothesis. Indeed, 
 if two visual rays were drawn from the eye of a stationary 
 observer, tangent to the orbit of Venus, she would appear 
 to move from one point of contact to the other, on the 
 hither side of her orbit, with a direct motion, while on the 
 further side of her orbit, between the points of contact, her 
 motion would appear retrograde. These facts, however, are 
 not presented in nature, and would be subverted, of course, 
 by supposing the spectator to be in motion. In case the 
 spectator were to occupy the line passing from the sun's 
 centre through Venus, and to revolve about the sun in the 
 same period occupied by the planet, then would the planet 
 
 D 2 
 
36 POPULAR ASTRONOMY. 
 
 always be seen in inferior conjunction with the sun. Aa 
 this is not the fact in observation, it is manifest that the 
 angular velocity of the spectator is not so great as that of 
 the planet Venus, as she finally emerges from the sun's rays, 
 after her inferior conjunction, beyond the line joining the 
 sun's centre and the eye of the beholder. Here, then, is 
 another important fact, which must be taken into account 
 when we shall inquire into the true system of nature, as 
 presented in the organization of the planetary worlds. 
 
 In case the eye of the observer were located in the same 
 plane in which the orbit of Venus lies, this plane, passing, as 
 it does, through the sun's centre, it is clear that at every 
 inferior conjunction of the planet there might be seen 
 a transit of Venus, while at every superior conjunction the 
 planet would be occulted, or hidden, by passing actually 
 behind the disc of the sun. It happens, however, that the 
 plane of the orbit of Venus does not coincide with the 
 plane of the ecliptic, or earth's orbit. These planes are 
 inclined to each other, under an angle of 3 23' 28" '5, 
 one half of the orbit of Venus lying above, or north of the 
 ecliptic, the other half lying below, or south of the ecliptic. 
 The point in which Venus passes from the north to the south 
 side of the ecliptic is called the descending node. She returns 
 from the south to the north of this plane through the ascend- 
 ing node; and the line joining these two points is called the 
 line of nodes. 
 
 The transits of Venus, unfortunately for astronomical 
 science, are of very rare occurrence, and are separated by 
 intervals of time which are very unequal. The periods from 
 transit to transit are 8,122, 8,105, 8,122, &c. years, for a 
 long period falling in the months of June and December. 
 As already stated, no transit can occur except when the 
 planet is in the act of passing her node at her inferior con- 
 junction, while, at the same time, the earth is crossing the 
 line of nodes of the planet prolonged. This line of nodes, 
 though not fixed, moves very slowly, and at this time crosses 
 the earth's orbit in those regions passed over by the earth 
 
VENUS." 37 
 
 in the months of June and December. After a transit* 
 the relative motion of Venus, the earth, and the node of the 
 orbit of Yenus, is such as to render it certain that within 
 eight years another transit will occur, as within this period 
 Venus does not, at her inferior conjunction, recede too 
 far from the plane of the ecliptic to render her transit 
 impossible. 
 
 In our account of the determination of the solar parallax 
 (chap. I. p. 15) we have stated that the distance of Venus 
 is readily determined by the measure of her horizontal 
 parallax. Her distance may also be determined, after "we 
 have learned the distance of the sun, by the same method 
 used in measuring the distance of Mercury (chap. II. p. 30). 
 
 By these and other methods the mean distance of this 
 planet from the sun is found to be about 68,000,000 of miles ; 
 and from the measure of her apparent diameter we conclude 
 her actual diameter to be 7,700 miles, or a little less than 
 the diameter of the earth, as we shall see hereafter. 
 
 The period of rotation of Venus has not been well deter- 
 mined ; but from an examination of indistinct spots, some- 
 times visible on her face, it is conjectured that she rotates 
 on her axis in about twenty-four hours, or in the same 
 period occupied by the earth. 
 
 The changes in the brilliancy of the planet Venus are 
 accounted for in a twofold way. In case the observer is 
 really exterior to her orbit, as the planet's distance from the 
 sun is on the average 68,000,000 of miles, then, when the 
 planet occupies that point in her orbit nearest the observer 
 she will be closer to the eye than when in the opposite point 
 of her orbit by an amount equal to no less than double her 
 mean distance from the sun, or 136,000,000 of miles. We 
 readily perceive that this vast increase of distance must 
 diminish in direct proportion the apparent diameter of the 
 planet, and thus her brightness must decline, as she recedes 
 from. her nearest to her greatest distance from the observer. 
 To this cause, however, of a change of brilliancy, is to be 
 added another of still greater importance. "We have already 
 
38 POPULAR ASTROXOMY. 
 
 stated that t*te planet Venus, when seen projected upon the 
 sun's disc during her transit, appears as a round black spot 
 on the brilliant surface of the sun. This fact demonstrates, 
 beyond a doubt, that the planet Venus is a dark, opaque 
 globe, destitute of light, and only visible by reflecting the 
 light which it receives from the sun. If further evidence 
 of this statement were wanting, it is found in the fact that 
 after the planet passes her inferior conjunction and becomes 
 visible in emerging from the sun's beams, she is first seen 
 by the telescope as a slender and delicate crescent of silver 
 light. As she recedes from the sun, this phase gradually 
 changes; more and more of her illuminated hemisphere 
 becomes visible, until, finally, at her superior conjunction, 
 her disc becomes round and well-defined. The same facts 
 are true of the planet Mercury ; and thus is added another 
 powerful evidence that these two planets are satellites of the 
 sun, revolving about this luminary in orbits nearly circular, 
 and deriving their light from this great central body. 
 
 When we come to measure accurately the greatest elonga- 
 tions of Venus, we find them unequal. In case the spectator 
 were stationary, and admitting the circular form of the orbit 
 of Venus, these inequalities could not occur. We thus are 
 led to believe, either that the orbit of the planet is not 
 circular, or, if it be circular, that the sun is eccentrically 
 situated, or that the observer himself is in motion. 
 
 It is possible that any two, or even all of these causes, 
 may combine to produce the phenomena presented in the 
 movements of Venus. We shall recur to these matters 
 when we come to consider the great problem of the true 
 system of the universe. 
 
 The extreme brightness of this planet makes it a very 
 beautiful but difficult object for telescopic observation. 
 Although spots have been seen upon the surface of Venus, 
 and by their close examination her period of rotation upon 
 her axis has been approximately determined, I have never 
 been able, at any time, with the powerful refractor of the 
 
PHASES OF VENUS 
 
VENUS. 39 
 
 Cincinnati Observatory, to mark any well-defined differences 
 in the illumination of her surface. If we are to trust to the 
 observations of others, the inequalities which diversify the 
 planet Venus far exceed in grandeur those found upon our 
 earth. It is stated by Mr. Schroter that, from his own 
 observations, the mountains of Yenus reach an altitude five 
 or six times greater than the loftiest mountains of our own 
 globe. 
 
 It has been affirmed by several distinguished astronomers 
 that this planet is accompanied by a minute satellite but 
 by the application of the most powerful telescopes, during 
 the present century, and after the most rigid examination, 
 this statement has not been confirmed. It was supposed 
 that during the transit which occurred in 1769 the disputed 
 question as to the existence of a moon of Yenus would be 
 positively settled. While the planet was distinctly seen as 
 a dark spot upon the surface of the sun, no telescopic power 
 could detect any dark object which might be a satellite. 
 Although we cannot absolutely affirm that Yenus has no 
 satellite, we may safely say, that if there be one, it yet 
 remains to be discovered. 
 
 The amount of light and heat which the earth would 
 receive from the sun, if revolving in the orbit of Yenus, 
 would be nearly twice as great as that now received ; but 
 this does not justify us in concluding that the planet Yenus 
 has a mean temperature nearly double that of the earth. 
 We know that a powerful influence is exerted by the earth's 
 atmosphere to modify the solar heat. There may exist an 
 atmosphere surrounding Yenus such that the temperature 
 at her surface may be no greater than our own. It is 
 useless, however, as we have already remarked, for us to 
 speculate about matters concerning which we positively 
 know nothing. There are some indications in the telescopic 
 appearance of Yenus that she is surrounded by an extended 
 atmosphere. When presenting the form of a crescent of 
 light, the slender horns are found sometimes to extend 
 
40 POPULAR ASTRONOMY. 
 
 beyond the limits of a semi-circumference a fact only to ba 
 accounted for, so far as we know, by admiting atmospheric 
 refraction. 
 
 CHAPTER IV. 
 
 THE EAETH AND ITS SATELLITE : THE THIRD PLANET IN 
 THE ORDER OF DISTANCE FROM THE SUN. 
 
 The Earth the apparent Centre of Motion. To all the senses it is at 
 rest. The Centre of the Motions of the Sun and Moon. Explanation 
 of the Acceleration of the Orbitual Motion of the Sun and Moon. 
 Ptolemy's Epicycles. The Explanation of Copernicus. The Sun the 
 Centre of Planetary Motion. The Earth One of the Planets. Objections 
 to this Hypothesis. The Answer. System of Jupiter discovered by the 
 Telescope. The Old system superseded by the New. The Figure and 
 Magnitude of the Earth. How determined. The Earth's Motions. 
 Rotation and Revolution. A Unit of Time furnished by the Earth's 
 Period of Rotation. Earth's Orbitual Motion. Vernal Equinox. 
 Perihelion of Earth's Orbit. Its Period of Revolution. Solar and 
 Sidereal Time. 
 
 THE MOON. Revolution in her Orbit. Her Phases. Earth's Line. Ec- 
 centricity of her Orbit. Revolution of her Apogee. Inclination of her 
 Orbit. Moon's Parallax and Distance. Her Physical Constitution. 
 Centre of Gravity and Centre of Figure. 
 
 THE ancients did not reckon the earth as one of the pla- 
 netary orbs. There seemed to be no analogy between the 
 world which we inhabit, with its dark, opaque, and diversi- 
 fied surface, and those brilliant planets which pursued their 
 mysterious journey among the stars. Sunk, as they were, 
 so deep in space, it was very difficult to reach any correct 
 knowledge of their absolute magnitude. The earth seemed, 
 to the senses of man, vastly larger than any or all of these 
 revolving worlds. About the earth, as a fixed centre, the 
 whole concave of the heavens, with all its starry constella- 
 tions, appeared to revolve, producing the alternations of 
 lay and night. It was not unnatural, therefore, knowing 
 the central position of the earth with reference to the fixed 
 
THE EARTH. 41 
 
 stars, to assume its central position with reference to the 
 sun, and moon, and planetary worlds. 
 
 There is no problem perhaps so difficult as that presented 
 in the attempt to discriminate between real and apparent 
 motion. To all the senses the earth appeared to be abso- 
 lutely at rest. It could not be affirmed that any one had 
 ever seen it move, or felt it move, or heard it move, while 
 the sense of sight bore the most positive testimony to the 
 motion of the surrounding orbs. It must be remembered 
 that, in the primitive ages, the great objects of observation 
 and study were the sun and moon. Five planets were, 
 indeed, discovered at a period so remote, that no historic 
 record of the facts of their discovery now exists. They seem 
 to have been known to all the nations of antiquity, and a 
 knowledge of their existence appears to have been derived 
 from a common origin, as we shall have occasion to notice 
 more particularly hereafter. A few of the more obvious 
 phenomena presented in the planetary movements were 
 known and studied by the old astronomers j but when these 
 motions became to them inexplicable, they frankly confessed 
 that these matters must be left for the study and develop- 
 ment of posterity. 
 
 If, then, we confine our attention principally to aL 
 examination of the solar and lunar motions, and to the 
 general revolution of the sphere of the fixed stars, in our 
 efforts to determine the true position and condition of the 
 earth, we shall find ourselves compelled, as were the cele- 
 brated Greek astronomers, Hipparchus an Ptolemy, tc 
 admit not only the earth's central position, but also its 
 absolute immobility. It is undoubtedly central to the 
 moon's motions, and it is equally central to the sun's move- 
 ment j that is to say, all the phenomena of the solar motions 
 are as well accounted for by supposing the earth to be the 
 centre about which the sun revolves, as by supposing the 
 converse hypothesis, that the sun is the centre about which 
 the earth revolves. 
 
 So far, then, as these two great luminaries are concerned. 
 
42 POPULAR ASTRONOMY. 
 
 the hypothesis of the earth's central position is well sustained, 
 and almost indisputable. It is only when we extend our 
 investigations to the inferior and superior planets, and gather 
 together a multitude of facts and phenomena demanding 
 explanation, that we find ourselves necessarily driven into 
 so great complexity by retaining the central position of the 
 earth, that at last we begin to doubt. We have already 
 noticed the remarkable movements of the two planets Yenus 
 and Mercury. We shall find hereafter that phenomena of 
 a like character were presented in the movements of Mars, 
 Jupiter, and Saturn, each of which planets was distinguished 
 by its stations, retrogradations, and advances among the fixed 
 stars. The ancients not only adopted the hypothesis of the 
 earth's central position and immobility, but, for evident 
 reasons, likewise adopted the hypothesis that all motion was 
 performed in circular orbits, and with uniform velocity. 
 We have already seen, in our examination of the solar 
 motions, that this orb did not move to the eye with uniform 
 velocity ; but this apparent deviation from uniformity was 
 readily accounted for by supposing the earth to be placed a 
 little eccentric with reference to the sun's circular orbit. The 
 same facts becoming known with reference to the moon's 
 motion, a like hypothesis was adopted, and the earth was 
 placed eccentrically within the lunar orbit. In marking the 
 planetary movements, they were found, however, to differ 
 radically in some particulars from the movements of the sun 
 and moon. While these great luminaries always advanced 
 in their revolution among the fixed stars, the planets were 
 found, in making their revolution, not only to stop, but for 
 a time actually to turn back, then stop again, and finally to 
 resume their onward movement. No eccentric position of 
 the earth could account for these stations and retrogradations ; 
 but a very simple expedient was devised, which rendered a 
 satisfactory account, in the primitive astronomical ages, of 
 these curious phenomena. Retaining the central position of 
 the earth and the circular figure of the planetary orbits, each 
 planet was supposed to revolve on the circumference of a 
 
THE EAETH. 43 
 
 small circle, whose centre was carried uniformly around OK 
 the circumference of the great circle constituting the orbit 
 of the planet. By such machinery it will be seen that it 
 became possible to render a satisfactory account of the 
 stations and retrogradations of the planets ; for while the 
 planet was describing that portion of the small circle in 
 which it revolved, nearest to the eye of the spectator, it 
 would seem to move backward in the order of the fixed 
 stars. Again, in coming directly toward the eye of the 
 spectator, or in moving in the opposite direction along two 
 visual rays, drawn tangent to its small circle, the planet 
 would appear stationary. Such was the general exposition 
 of the Greek astronomer Hipparchus, whose theory was 
 enlarged and extended by his successor Ptolemy, whose 
 theory of astronomy, based upon the central position of the 
 earth, known as the Ptolemaic System, endured for more 
 than fifteen hundred years. It was only after a long lapse 
 of time, and by the discovery of a large number of irregu- 
 larities in the solar, lunar, and planetary motions, making it 
 necessary (to render a just account of them) to increase the 
 number of these small circles, which were called epicycles, 
 that the whole scheme finally became so cumbrous and com- 
 plicated, that, after long and laborious study, extending 
 through more than thirty years of diligent observation, the 
 great Polish astronomer Copernicus* found himself com- 
 pelled to abandon the old hypothesis of the central position 
 of the earth, and to attempt a new solution of the great 
 problem of the universe. 
 
 In giving up the earth as the centre about which the 
 worlds were revolving, there was little difficulty in selecting 
 the object which, in greatest probability, occupied the true 
 centre. All the movements of the sun could, without the 
 slightest difficulty, be transferred to the earth, and thus the 
 sun could become central to the earth, revolving as one 
 among the planets. This hypothesis did not require any 
 
 * Copernicus, born at Thorn, in Polish Prussia, A.D. 1473. 
 
44 POPULAR ASTRONOMY. 
 
 change whatever in the computation of those tables which 
 gave from day to day the sun's apparent place among the 
 fixed stars. Again, as we have already seen, the planets 
 Mercury and Venus were undoubtedly satellites of the sun, 
 whether the sun be at rest or in motion ; and with these 
 suggestions the vigorous mind of Copernicus, transferring 
 himself, in imagination, to the sun, and thence looking out 
 upon the planetary revolutions, found that a large number of 
 those complexities and irregularities which had so confounded 
 him when viewed from the earth's surface, were swept away 
 for ever. When seen from the sun, as the centre of motion, 
 all the stations and retrogradations in the planetary revolu- 
 tions disappeared. The complications in the movements of 
 Mercury and Venus were reduced to perfect order and sim- 
 plicity when seen from the sun. The earth itself assumed 
 its proper rank among the planetary worlds, dignified by the 
 attendance of its satellite the moon, and beyond the earth 
 the planets Mars, Jupiter, and Saturn, performed their 
 orderly revolution in orbits nearly circular. Such is the true 
 scheme of nature in its grand outlines, as given to the world 
 by Copernicus. It will be seen that one of the remarkable 
 features of the old system, namely, the uniform circular 
 movement of the planets, was retained by the Polish astro- 
 nomer. By the use of eccentrics and epicycles, Copernicus 
 found it possible to render a satisfactory account of all the 
 phenomena of the solar system known during his age. We 
 can readily comprehend that a system involving the startling 
 doctrine of the swift rotation of the earth upon its axis, and 
 the rapid flight of its entire mass, with all its continents, 
 and oceans, and mountains, through space, must have been 
 received by the human mind with the greatest distrust. 
 Indeed, there seemed to be to the eye positive proof that 
 this bold theory was absolutely false. It was urged by the 
 anti-Copernicans, that, in case the earth did revolve about 
 the sun, in an orbit of nearly two hundred millions of miles 
 in diameter, the point where the axis of rotation, prolonged 
 to the sphere of the fixed stars, pierced the heavens, must 
 
THE EARTH. 45 
 
 by necessity travel around and describe a curve among the 
 stars identical with that described by the earth in revolving 
 about the sun. Now, as no such motion of the north polar 
 point was visible to the eye, but as the axis of the heavens 
 remained for ever fixed among the stars, it proved beyond 
 dispute the absolute impossibility of the earth's revolution 
 about the sun. This train of reasoning was undeniably true, 
 and the only response which the Copernicans could make 
 was this : " The earth does revolve about the sun ; the 
 earth's axis prolonged does pierce the celestial concave in 
 successive points, describing a curve precisely like the earth's 
 orbit, and whose diameter is indeed nearly 200,000,000 
 of miles ; but that the distance of the fixed stars is so great, 
 that an object having this immense diameter actually shrinks 
 into an invisible point, on account of the almost infinite 
 distance to which it is removed from the eye of the beholder." 
 And with this answer the world was compelled to rest 
 satisfied for more than two hundred years. 
 
 The doctrines of Copernicus gained a great accession of 
 strength by the invention of the telescope. By the use of 
 this extraordinary instrument, not only were the phases of 
 Mercury and Yenus detected, but also the greater discovery 
 of the satellites of Jupiter, presenting, in this central orb, 
 with his four revolving moons, a sort of miniature likeness 
 of the grander system, having the sun for its centre. The 
 simplicity of the hypothesis presented in the Copernican 
 system, the numerous complications which it removed from 
 the heavens, and the satisfactory account which it yielded 
 of the discoveries made by the telescope, caused it to be 
 adopted and defended by some of the best minds of the age 
 immediately following that of Copernicus, among whom none 
 is more distinguished than the great Florentine astronomer 
 and philosopher, Galileo Galillei. It is hardly necessary to 
 mention the historical fact, that the old system of astronomy, 
 which had held its sway over the human mind for more than 
 2,000 years, did not fall without a severe struggle. The 
 astronomy of Ptolemy and the philosophy of Aristotle had 
 
46 POPULAR ASTRONOMY. 
 
 taken so deep a hold of mankind, and were so firmly inter- 
 woven with all the systems of education and of science, that 
 we must behold with astonishment the downfall of systems 
 venerable from their antiquity, and whose ruin could only be 
 accomplished by the desertion of their adherents. 
 
 THE FIGURE AND MAGNITUDE OF THE EARTH. A know- 
 ledge of the globular figure of the earth seems to have been 
 reached at an early period in the history of astronomy. 
 Indeed, the concave heavens, presenting to the eye a hemi- 
 sphere above the horizon, and, undoubtedly, extending be- 
 neath the earth,^gso as to complete the grand hollow sphere, 
 suggested at once that the inclosed earth, minute in its 
 dimensions when compared with the celestial globe by which 
 it was encompassed, might also have the globular form. The 
 curvature of the earth's surface becomes at once visible to 
 the eye in marking the gradual approach of a ship at sea. 
 At first only the top of the mast can be discovered, even 
 with a glass, all the remaining parts of the vessel being 
 hidden by the outline of the interposed water. As the 
 distance diminishes, more and more of the ship lifts itself 
 above the horizon, until, finally, the water-line comes into 
 sight. The same evidence of the rotundity of the earth is 
 furnished by the circular form of the horizon, which always 
 sweeps round a beholder who ascends to the summit of a 
 lofty mountain. Thus, we are disposed to adopt the sphe- 
 rical form of the earth in consequence of its simplicity, even 
 before we have any conclusive demonstration as to its real 
 form. 
 
 The Greek astronomers comprehended the simple process, 
 whereby not only the true figure of the earth might be 
 obtained; but, in case it were spherical, whereby its real 
 diameter and absolute magnitude might be determined. 
 
 This process is remarkably simple. Suppose an observer 
 to be provided with the means of directing a telescope 
 precisely to the zenith of any given station, and that in the 
 zenith-point he marks a star, which from its magnitude and 
 position he can readily find again. Now, leaving this first 
 
THE EARTH. 
 
 '47 
 
 station, and moving due north, measuring the distance over 
 which he passes, he will find that, as he progresses toward 
 the north, the star under examination will leave the zenith 
 and slowly decline toward the south. Suppose the observer 
 to halt, set up his instrument, and find that his star his 
 declined one degree from the zenith toward the south. 
 
 This demonstrates that he has travelled from the firs' 
 station to the second, over one degree of a great circle of 
 the earth, or one part in 360 of the entire circumference 
 of the earth. It follows that, in case the earth is really 
 globular in form, the distance between the stations, multi- 
 plied by 360, will give the length of the entire circumference, 
 and this quantity, divided by 3'14159 (the ratio between 
 the circumference of a circle and its diameter), will give the 
 value of the earth's diameter. 
 
 It is by methods analogous to the above that the true 
 figure and actual magnitude of the earth have been deter- 
 mined. Yery numerous and delicate measures, performed 
 in many parts of the earth's surface, have revealed the 
 surprising fact that the true figure of the earth is not that 
 of a sphere, but of a spheroid, being more flattened at the 
 poles and more protuberant at the equator than a true 
 sphere. We shall hereafter exhibit the cause of this re- 
 markable fact, and present some very curious and surprising 
 results and phenomena which flow from it. By the most 
 reliable measure we find the polar diameter of the earth to 
 be 7,898 miles, while the diameter of the equator reaches to 
 7,924, being an excess of no less than twenty-six miles j which 
 excess would have to be trimmed off to reduce the earth 
 to a globular form. 
 
 THE EARTH'S MOTION. We have already noticed the fact 
 that the sun, as well as the planets thus far described, have 
 a motion of rotation about a fixed axis, while the planets 
 have also a motion of revolution in their orbits. Since we 
 are compelled to recognize the earth as one of the planets, 
 we naturally conclude that it will be distinguished by the 
 game motions which mark the movements of the other 
 
43 POPULAR ASTRONOMY. 
 
 planets. We shall find, indeed, that the earth has if tret 
 motions : a motion of rotation about an axis, accomplished 
 in a period of twenty-four hours, and producing an apparent 
 revolution of the sphere of the fixed stars in the same 
 period. A motion of revolution in an orbit whereby the 
 earth is carried entirely round the sun, effecting all those 
 changes which mark upon the earth's surface the seasons of 
 the year, and producing at the same time an apparent 
 revolution of the sun in a circular orbit among the fixed 
 stars. The earth has a third motion (which we will examine 
 more fully hereafter), occasioned by the fact that its axis of 
 rotation does not remain constantly parallel to itself. 
 
 THE EARTH'S ROTATION. Let us return to the consider- 
 ation of the diurnal revolution, to the inhabitants of the 
 earth, as well as to the student of astronomy, by far the 
 most important motion which has been revealed by human 
 investigation. It is, perhaps, impossible for the mind of 
 man to form any just notion of what we call time, except as 
 its flow is measured by some absolutely uniform succession 
 of events. This perfect measure of time is found in the 
 uniform rotation of the earth upon its axis, whereby the 
 fixed stars appear to the eye to perform revolutions in 
 circles of greater or less diameter, all in the same identical 
 period, and with a motion which, so far as we know, is 
 absolutely uniform. Thus the duration of one rotation of 
 the earth upon its axis, whereby any given fixed star re- 
 volves from the meridian of any place entirely round to the 
 same meridian again, furnishes to man a unit of time, which, 
 by its subdivisions and multiplications, renders it possible 
 to take account of historic and other events, and to mark 
 their relations to each other, not only in the order of time, 
 but also in the interval of time. Thus, a day is subdivided 
 into hours, minutes, and seconds, and the fractions of a 
 second, and by successive additions gives us larger portions 
 of time, as weeks, months, years, and centuries. To serve 
 this very important purpose, and to become a true unit of 
 measure of time, it is absolutely indispensable that the 
 
THE EARTH. 49 
 
 motion of rotation of the earth upon its axis shall be 
 rigorously uniform and invariable. 
 
 We have, at present, in all the active observatories in 
 the world, a constantly accumulating power of evidence that 
 the earth now revolves with uniform velocity. Not a star 
 passes the meridian-wire of a fixed telescope, true to the 
 predicted moment of transit, without testifying to the 
 absolute uniformity of the earth's rotation. So far, then, as 
 it is possible, by human observation and human means, to 
 determine any truth whatever, we are able to affirm the 
 absolute uniformity of the rotation of the earth upon its 
 axis. This truth is affirmed as of to-day ; and so far as we 
 can go back in the history of accurate astronomical observa- 
 tion, the same truth is affirmed of the past ; and La Place 
 informs us that, from a rigorous investigation of the whole 
 subject, he discovers that the period of rotation of the earth 
 upon its axis has not changed by the hundredth part of one 
 second of time in a period of more than 2,000 years. We 
 will explain hereafter the train of reasoning by which thi, 
 conclusion has been reached. We shall, for the present, 
 accept the statement as a fact. 
 
 THE KEVOLUTION OF THE EARTH IN ITS ORBIT. In the 
 examination already made of the sun's apparent revolution 
 among the fixed stars, we have found that the revolution 
 was performed in the same plane, cutting out of the sphere 
 of the fixed stars an exact great circle. All that was 
 then affirmed, with reference to the sun's apparent motion, 
 must now be affirmed as belonging to the earth's real 
 motion. 
 
 The earth, then, revolves around the sun in the plane of 
 the ecliptic, at a mean distance of about ninety-Jive millions 
 of miles, and in a period of about three hundred and sixty-Jive 
 days and a quarter. It, of course, always occupies a position 
 distant from the sun's place one half a circumference, or one 
 hundred and eighty degrees. The changes of the sun's 
 position at noon in the course of the year, which we have 
 already examined, are now readily accounted for by the fact 
 
 E 
 
50 POPULAR ASTRONOMY. 
 
 that the earth's axis of rotation neither coincides with the 
 plane of the ecliptic nor is perpendicular to it, but is inclined 
 under an angle, which is readily measured, and which is 
 found to undergo a very slow change from century to 
 century. In case the earth's axis were perpendicular to the 
 plane of the ecliptic, then the illuminated hemisphere of the 
 earth would always be bounded by a meridian-circle, and 
 every inhabitant of the earth would find his days and nights 
 precisely equal, no matter what his location upon the earth'* 
 surface. If, on the contrary, the axis of the earth lay on 
 the plane of the orbit, and remained ever parallel to itself, 
 then the illuminated hemisphere would be bounded by a 
 great circle, whose diameter would always be perpendicular 
 to the earth's axis, and an equality of day and night would 
 only occur when the earth held such a position that its axis 
 would be perpendicular to the line joining the earth's centre 
 with the sun. Neither of these cases exists in nature, and, 
 as we have already seen, the annual sweep of the sun from 
 north to south, and from south to north, measures the double 
 inclination of the earth's equator to the plane of the ecliptic, 
 while the length of the day, as compared with the night, 
 combined with the inclination of the solar beams, produces 
 the alternation and changes of the seasons. 
 
 To an inhabitant of the earth's equator, the poles of the 
 heavens will ever appear to lie in the horizon ; and while 
 the sun sweeps, during the year, from south to north, and 
 returns, yet the days and nights are ever equal, and a 
 perpetual summer reigns around the equatorial region, and 
 a belt of extraordinary heat encircles the earth. Could an 
 observer reach either pole of the earth, then the pole of the 
 heavens would occupy his zenith, all diurnal circles would 
 be parallel to the horizon, which would now coincide with 
 the equator, and so long as the sun was south of the equator 
 (the observer being at the north pole of the earth), just so 
 long would the sun be below the horizon, and every part of 
 its diurnal circle would be invisible. On the day of the 
 ernal equinox the sun would just reach the equator (now 
 
THE EARTH. 51 
 
 the horizon), and during the entire revolution would be seen 
 sweeping round the horizon, slowly rising above it. This 
 increase of elevation must now progress up to the summer 
 solstice, and then decline to the autumnal equinox ; the 
 daylight thus continuing for six entire months, and the 
 darkness for an equal length of time. These theoretic 
 statements are abundantly verified by the facts, as re- 
 ported by those who have visited high northern or southern 
 latitudes. 
 
 Our climates are, then, undoubtedly, determined by the 
 inclination of the earth's axis to the ecliptic, or, what amounts 
 to the same thing, by the inclination of the earth's equator 
 to the ecliptic, the one angle being the complement of the 
 other, or what it wants of ninety degrees. 
 
 The process employed by the ancients in measuring the 
 inclination of the equator and ecliptic we have explained 
 (chap. I.) ; and the same, with certain refinements, is still 
 used by the moderns. At the beginning of the present 
 century, this angle, called the obliquity of the ecliptic, 
 amounted to 23 27' 56"-5. Two hundred and thirty years 
 before Christ, the same angle, measured 'by the Greek 
 astronomer Eratosthenes, was 23 51' 20". After a lapse of 
 370 years, Ptolemy found the inclination to be 23 48' 45". 
 In the year 880 of our era, it was 23 35' 00". In 1690, 
 Flamsteed found the same angle to be 23 29' 00"; and thus 
 from century to century the change progresses, reaching, 
 however, a limit beyond which it cannot pass (as we shall 
 presently show), when it will commence a reverse motion; 
 and thus the one plane slowly rocks to and fro upon the 
 other in a calculable, but (so far as I know) not yet calcu- 
 lated period. 
 
 The time elapsing from the moment the earth is nearest 
 the sun, until it returns again to the same point, is called an 
 cmomalistic year. The time from vernal, equinox to the 
 same again, is called a tropical year ; while the time occupied 
 by the earth in passing from any one point of its orbit, 
 regarded as fixed, to the same point again, is called a sidereal 
 
 2 
 
52 POPULAR ASTRONOMY, 
 
 year. These different periods, at the commencement of the 
 current century, had the following values : 
 
 Mean Anomalistic Year, in solar days 365-2595981 
 
 Mean Tropical Year, in solar days 365-2422414 
 
 Mean Sidereal Year, in solar days 365-2563612 
 
 These figures, being different, demonstrate the great and 
 important fact, that, whatever be the precise figure of the 
 curve of the earth's orbit, the point of nearest approach to 
 the sun, called the perihelion, is itself in motion. The same 
 is true of the vernal equinox, the first evidently advancing, 
 the second as evidently retrograding ; and thus, while the 
 advance of the perihelion increases the length of the anoma- 
 listic year over the sidereal, the retrogression of the equinox 
 decreases the length of the tropical, as compared with the 
 sidereal year. 
 
 These figures are presented as the result of the best deter- 
 minations which have been reached in modern times ; but 
 it must not be understood that the existence of these three 
 different kinds of year is the discovery of our own times. 
 The discovery of the motion of the vernal equinox, as we 
 have seen, seems to reach back to the highest antiquity, and 
 was known to all the ancient nations. The rate of motion 
 was more exactly determined by the Greek astronomers, 
 and hence the discovery has been attributed to that nation. 
 Modern observations have confirmed this ancient discovery ; 
 while modern physical science has rendered a satisfactory 
 account of this remarkable phenomenon, and has determined 
 that the equinoctial point completes the entire circuit of the 
 heavens in 25,868 years. 
 
 To ascertain the condition of the perihelion-point as to 
 rest or motion, it is only necessary to determine the sun's 
 place among the fixed stars at the time of any perihelion, 
 and to transmit the same to posterity. Any change of the 
 sun's place among the stars at perihelion, which may become 
 known in future ages, will demonstrate the fact that the 
 perihelion is not only in motion, but will exhibit also the 
 direction of the motion, and the rate of advance or recess. 
 
THE EARTH. 53 
 
 By a comparison of ancient . observations with modern, the 
 perihelion-point of the earth's orbit is found to be slowly 
 advancing ; while, as we have stated before, the vernal 
 equinox is slowly retrograding, at such rates that these two 
 points pass each other once in 20,984 years. The perihelion 
 coincided with the vernal equinox, as we are able to compute 
 from their relative motions, 4,089 years before the Christian 
 era. Sweeping onward to meet the summer solstice, the 
 perihelion passed that point in the year 1250 of our 
 era, and will meet the autumnal equinox about the year 
 6483. 
 
 From the uniform rotation of the earth on its axis, we 
 obtain, as already stated, our unit of time. But this rotation 
 is not sensible to man except by its effect on the position of 
 objects external to the earth ; and hence we determine the 
 absolute period of rotation from marking the moment when 
 axed object, such as a star, passes the meridian of any 
 given place. The time elapsing from this moment up to the 
 next passage of the same object across the meridian, 
 supposing the earth to be immovable as to its central point, 
 would be the exact measure of the period of rotation of the 
 earth on its axis. Now the earth's centre, in the space of 
 one day and night, or during one rotation, actually passes 
 over nearly 2,000,000 of miles ; and it would seem as though 
 this change of position would sensibly affect the return of our 
 star to the meridian ; but such is the vast distance of the 
 fixed stars, that visual rays sent to the same star, from the 
 extremities of a base line of 2,000,000 miles in length, are 
 absolutely parallel under the most searching instrumental 
 scrutiny that man has been able to make. A sidereal day 
 the time which elapses between the consecutive returns of 
 the same fixed star to any given meridian is an invariable 
 unit of time, and, as such, is extensively used in practical 
 astronomy ; but in civil life, inasmuch as all the duties of 
 life are regulated by the return of the sun to the meridian, 
 wlar, and not sidereal time, has become the great standard 
 in the record of all historic and chronologic events. In case 
 
54 POPULAR ASTRONOMY. 
 
 the earth did not revolve upon .its axis, and had no motion 
 except that of revolution in its orbit around the sun, it ia 
 manifest that in the course of one revolution the earth's 
 axis, remaining parallel to itself, the circle dividing the 
 illuminated from the dark hemisphere of earth would take 
 up successively every possible position consistent with its 
 always remaining perpendicular to the line joining the centres 
 of the earth and sun. It is manifest, therefore, that by this 
 revolution around the sun, this luminary would be caused to 
 rise above the horizon of any and every place upon the 
 earth's surface successively, slowly to sweep across the 
 heavens, and at the end of six months again to sink beneath 
 the horizon. If, then, we define a solar day to be the time 
 which elapses from the passage of the sun's centre across any 
 given meridian until it returns to the same meridian again, 
 one such day would evidently be produced by the revolution 
 of the earth in its orbit ; hence we find a solar day to JDO 
 longer than a sidereal day, because of the fact that the sun's 
 centre is brought to the meridian later, in consequence of its 
 own apparent motion. Indeed, when we come to examine 
 carefully the length of the solar day, we find it to be in a 
 state of comparatively rapid change, a fact which we could 
 readily have anticipated, as we know the apparent movement 
 of the sun in its orbit, or rather the real motion of the earth, 
 is changing from day to day. When the earth is in peri- 
 helion, or nearest the sun, it then travels with its greatest 
 velocity, and passes over an arc of 1 01' 9"'9, in a mean 
 solar day ; whereas, when the earth is in aphelion, or furthest 
 from the sun, it sweeps over an arc, in the same time, of 
 only 57' 11 "'5. We thus perceive that the length of a true 
 solar day must vary throughout the year, and for the purpose 
 of obtaining a standard of time, the world has adopted what 
 is called a mean solar day, or a day having the average 
 length of all the true solar days in the year. All the time- 
 keepers employed in civil life, such as clocks and chrono- 
 meters, are regulated to keep mean solar time, while, for the 
 purposes of an observatory, sidereal time is in general use. 
 
THE MOON. 55 
 
 This, however, is slightly different from the sidereal time 
 already defined. The sidereal clock of the observatory, if 
 perfectly true, would mark Oh. 00m. OOs. at the moment the 
 vernal equinox is on the meridian of the observatory. It 
 would mark the same at the next return ; and hence this 
 sidereal day is really a vernal equinox day. Now, as the 
 sun's centre appears to sweep round the whole heavens in 
 the space of one year, and by virtue of this motion passes 
 across the meridian of any place and returns to the same 
 again, so, as we have seen, the vernal equinox sweeps around 
 the heavens in a period of 25,868 years, and thus passes 
 from one meridian to the same by virtue of this motion. 
 Thus, a vernal equinox day is shorter than a sidereal day by 
 an amount equal to one day in 25,868 years, a quantity very 
 minute indeed, but still insisted upon, as we desire to 
 impress upon the mind of the reader the differences between 
 these various measures of time. 
 
 THE MOON A SATELLITE OF THE EARTH. In prose- 
 cuting our plan of investigation, we must now give some 
 account of the moon, as she forms, astronomically speaking, 
 a part of the planet which we call the earth ; and we shall 
 find hereafter that when we speak of the orbit in which the 
 earth revolves about the sun, the real point tracing that 
 orbit is not the centre of the earth, but a point determined 
 by taking into consideration the fact that the earth and 
 moon must be combined, as forming a sort of compound 
 planet, revolving about the sun. Of all the celestial orbs 
 furnishing objects of investigation to man, no one of them 
 can rival the moon in the antiquity of its researches, or in 
 the importance and complexity of its revolutions. 
 
 If it were possible to trace the history of astronomical 
 discovery, it would be found, beyond a doubt, that the first 
 positive fact ever revealed to the student of the skies was the 
 motion of the moon among the fixed stars. This fact is so 
 obvious, that any one who chooses to mark the moon's place 
 by the stars which surround her to-night, and compare it 
 
56 POPULAR ASTRONOMY. 
 
 with her place to-morrow night, will make for himself th 
 great discovery that the moon is sweeping around the 
 heavens in a direction contrary to that of the diurnal 
 revolution of the celestial sphere. Thus, if we mark the 
 place of the new moon, in the evening twilight, when she 
 appears as a silver crescent, emerging from the sun's beams, 
 and just visible above the western horizon, we shall find that 
 on the next evening, at the same hour, her distance from 
 the horizon will have been greatly increased ; and this 
 increase of distance progresses from night to night, until we 
 find the moon actually rising in the east at the time the sun 
 is setting in the west. On the following night, at sunset, 
 the moon will not have risen ; but we shall be compelled to 
 wait nearly an hour after sunset, before she becomes visible 
 above the eastern horizon ; and thus she advances in her 
 orderly march among the fixed stars, until she circles en- 
 tirely around the heavens, passes through the solar beams, and 
 re-appears in the west above the sun, as a slender crescent. 
 
 THE MOON'S REVOLUTION IN HER ORBIT. We have 
 already stated that, in case it were possible for the sun's 
 centre to trace out in its revolution among the fixed stars a 
 line of golden light, visible to the eye of man, this line 
 would be a regular circle, perfected at the close of one revo- 
 lution, and ever after repeated along the same identical 
 track. Such, however, is not the case with our satellite. 
 Could the moon's course be traced by leaving behind her among 
 the stars a silver thread of light, at the completion of one 
 revolution, this thread would not join on the point of begin- 
 ning, but would be more or less remote, and the track 
 described in the second and successive revolutions would 
 not coincide with that first described ; and thus we should 
 find a multiplicity of silver lines sweeping round the circuit 
 of the heavens, crossing each other, and interlacing in the 
 most complicated manner, and thus making a girdle or zone 
 of definite width, beyond whose limits the moon could 
 never pass. The time occupied in completing one of these 
 revolutions from a given star, until it returns to the great 
 
THE MOON. 57 
 
 circle of the heavens, passing through the axis, and this star 
 again, is soon found to be variable within certain narrow 
 limits. This is called a sidereal revolution, and its mean 
 value at the beginning of the present century is fixed at 
 27d. 7h. 43m. ll'5s. The most obvious lunar period, how- 
 ever, and that doubtless first discovered, is that called a 
 synodical revolution, and is the period elapsing from the oc- 
 currence of full moon to full moon again, or from new moon 
 to new moon again. The average length of this period, 
 which is also called a mean lunation, amounted at the epoch 
 above mentioned to 29d. 12h. 44m. 2'87s. It is within the 
 limits of this period that the moon passes through all those 
 appearances which we call 
 
 THE MOON'S PHASES. These extraordinary changes in 
 the physical aspect of the moon must have perplexed the 
 early astronomers. While the sun ever remained round 
 and full-orbed in all his positions among the fixed stars, and 
 while all the planets and bright stars shone with a nearly 
 invariable light, the moon passed from a state of actual 
 invisibility to a condition in which her disc was as round as 
 that of the sun, and thence gradually losing her light, finally 
 faded from the eye as she approached the solar orb. It was 
 soon discovered that these changes were in some way 
 dependent strictly upon the sun, and not upon the moon's 
 place among the fixed stars. Any one who chooses may 
 verify this discovery ; for by marking the moon's place 
 among the fixed stars at the full, and waiting her return to 
 the same place again, it will be found that she has not yet 
 reached her figure of a complete circle. Indeed, more than 
 two days are required, after passing the position occupied 
 when last full, before she gains the point that shall present 
 us with a completely illumined disc. The discovery of this 
 truth aided undoubtedly in solving the mystery of the 
 moon's phases. It was clearly manifest that the moon was 
 revolving about the earth in an orbit nearly circular. This 
 was evident from the fact that the moon's apparent diameter 
 did not change, by any sensible amount, during an entire 
 
58 POPULAR ASTRONOMY. 
 
 revolution, which would have been impossible, in case her 
 approach to, or recess from, the earth, had been very great 
 in any part of her orbit. 
 
 Another phenomenon of startling interest aided greatly 
 in reaching a true solution of the changes of the moon. I 
 refer, of course, to solar and lunar eclipses. We have 
 already referred to solar eclipses, as being undoubtedly pro- 
 duced by the interposition of the dark body of the moon 
 between the eye of the spectator and the sun's disc. This 
 demonstrated the fact that the moon in her revolution 
 round the earth did sometimes cross the line joining the 
 earth's centre with the sun ; thus producing a central solar 
 eclipse. It was thus manifestly possible for the moon's 
 centre to cross the same line at a point lying beyond the 
 earth, with reference to the sun. When in this position, a 
 straight line drawn through the centre of the sun, and 
 through the centre of the earth, and produced onward, 
 would pass through the moon's centre ; and a person there 
 situated, and looking at the sun, would find the solar surface 
 covered by the round disc of the earth ; thus producing to 
 the lunarian a solar eclipse. When the moon was thus 
 situated, it was found to be shorn of a very large proportion 
 of its light, not entirely fading from the eye, as did the sun 
 when in total eclipse, but remaining indistinctly visible, 
 with a dull reddish colour. Now, as common observation 
 teaches us that every opaque object casts a shadow in a 
 direction opposite to the source of light, it follows that the 
 earth must cast a shadow in a direction opposite to the 
 sun ; and in case this shadow reached as far as the moon's 
 orbit, the moon, in taking up her successive positions, would 
 sometimes pass into the earth's shadow. If self-luminous, 
 the passage across the earth's shadow would occasion but a 
 trifling change in her appearance. If, however, her light 
 was either wholly or in greater part derived from the su/i, 
 then in passing into the earth's shadow, the stream of light 
 from the sun being intercepted by the earth, the moon would 
 lose her brilliancy, and could only be visible with an obscured 
 
THE MOOIt. 59 
 
 lustre. All the phejiomena presented in a solar as well as 
 a lunar eclipse, combine to demonstrate that the light of 
 the moon is not inherent, or that this orb is not a self- 
 luminous body ; and all these phenomena were perfectly 
 accounted for by admitting the hypothesis that the moon 
 shines by reflecting the light of the sun.* Thus, during a 
 total solar eclipse, when the illuminated hemisphere of the 
 moon was turned from the earth, her hither side appeared 
 absolutely black, while no lunar eclipse ever occurred, except 
 at a time when the moon's illuminated hemisphere was 
 wholly visible, or at the full moon. In passing from new 
 moon to full, it is evident, from the slightest reflection, that 
 as the moon slowly recedes from the sun, in her movement 
 round the earth, she will turn more and more of her illumi- 
 nated hemisphere towards the earth, the whole of which 
 will become visible when she is precisely opposite the sun, 
 while the light must decrease in a reverse order in passing 
 from the full moon to the new. Thus, all the facts and 
 phenomena of ancient as well as of modern discovery, com- 
 bine to demonstrate the truth that the earth's satellite, like 
 the planets already treated of, is only visible by reflecting 
 the light of the sun. 
 
 "We are ready by analogy to extend this reasoning to 
 embrace the earth, and to believe that our own earth shines 
 to the inhabitants of other planets (if such there be), by 
 reflecting the light of the sun. We are not left, however, 
 to mere analogy to demonstrate this truth, as we have the 
 most positive evidence in the phases of the moon that the 
 earth does reflect the solar light. No one can have failed 
 to notice the fact that when the moon appears as a slender 
 crescent, her entire disc may be traced, faintly visible even 
 to the naked eye ; but when the telescope is applied, we 
 readily distinguish in this darkened part all the outlines 
 and prominent features which become visible to the unaided 
 eye when the moon is entirely full. This faint luminosity 
 
 * This had been asserted by the Greek astronomer Thales, about 
 600 B.C. 
 
60 POPULAR ASTRONOMY. 
 
 is beyond all doubt occasioned by the reflection back to the 
 earth of that light which the earth reflects upon the moon ; 
 for if we consider the relative positions of the sun, moon, 
 and earth, we shall see that at the new moon the whole 
 illuminated hemisphere of the earth is turned full upon her 
 satellite, and at that time the largest amount of light from 
 the earth falls upon the surface of the moon. The relative 
 positions of the bodies now slowly change, and as the moon 
 increases in light, by like degrees the earth loses in light ; 
 and when the moon becomes entirely full, the earth will be 
 to the lunarian entirely dark, as her non-luminous hemi- 
 sphere is then turned directly to the moon. 
 
 We have already stated that, during a lunar eclipse, the 
 moon remains dimly visible. This is not due to the reflected 
 light of the sun, thrown upon the moon by the earth, but 
 arises from the fact that the solar rays are so much bent out 
 of their course in passing through the earth's atmosphere, 
 that many of them are still able to reach the moon's surface, 
 and thus in some degree to light up her disc, even during a 
 central eclipse. 
 
 Amid all the variations and changes which mark the 
 luminosity of the moon, one thing remains almost absolutely 
 invariable. No eye on earth has yet seen more than one 
 half of the lunar sphere. The hemisphere now visible to 
 man has (so far as we know) ever been visible, and, except 
 by the intrusion of some foreign body, will ever remain 
 turned toward the earth. There are slight deviations from 
 the positiveness of this statement to which we shall have 
 occasion to allude hereafter ; but the grand truth remains, 
 that the same hemisphere of the moon is ever turned toward 
 the earth. 
 
 To account for this remarkable fact, we are compelled to 
 acknowledge a rotation of the moon on her axis, in the exact 
 period employed by her in her revolution in her orbit. If 
 the moon had no motion of rotation about an axis, then in 
 the course of her orbital revolution every portion of her 
 surface would come into view successively. 
 
THE MOON. 61 
 
 This explanation, which it would seem ougnt to be per- 
 fectly satisfactory, has, in some strange way, been not only 
 misunderstood, but denied ; and yet, should the person most 
 sceptical undertake to walk round a central object, always 
 turning his face to the centre, without as well turning his 
 shoulders and person, he would receive a positive conviction 
 of the truth of our explanation, and that too of a most prac- 
 tical character. 
 
 The physical cause of this remarkable fact in the moon's 
 history will be duly considered hereafter. 
 
 The same kind of observation and reasoning which enabled 
 Hipparchus to determine the eccentricity of the sun's ap- 
 parent orbit (the earth's real oibit) sufficed to enable this 
 philosopher to determine the eccentricity of the moon's 
 orbit, and the epicyclical theory gave a tolerably fair account 
 of the most striking irregularities in the moon's motion. In 
 one respect, however, we find a remarkable difference between 
 the lunar and solar motions. The position of the perihelion 
 of the earth's orbit moves so slowly, that for a period of even 
 a hundred years this motion may be neglected without any 
 great error, while the moon's perigee, or least distance from 
 the earth, was found to be sweeping round the heavens with 
 a comparatively rapid motion, following the moon in her 
 course among the stars ; so that, while in a period of 6,585^ 
 days the moon performed 241 complete revolutions with 
 reference to the stars, she made but 239 revolutions with 
 regard to her perigee. Hipparchus succeeded in represent- 
 ing this motion by means of eccentrics and epicycles, and 
 finally was able to tabulate the moon's places with such 
 accuracy as to represent her positions, especially at the 
 new and the full, so as to predict roughly solar and lunar 
 eclipses. 
 
 Ptolemy discovered, 500 years later, a new irregularity in 
 the moon's motion, which reached its maximum value in what 
 are called the octants, that is, the points half-way between 
 the new moon and her first quarter, and so on a quarter of 
 a circumference in advance round the orbit. New attempts 
 
62 POPULAR ASTRONOMY. 
 
 were made to explain these irregularities by a combination of 
 circles and eccentrics. It was, finally, approximately accom- 
 plished ; but all these facts thus accumulating were preparing 
 the way for the abandonment of an hypothesis which could 
 only be maintained -by the imperfection of astronomical 
 observation. 
 
 The excursions made by the moon, north and south of the 
 ecliptic, or plane of the earth's orbit, were obviously to be 
 accounted for by the fact that this satellite revolved in a 
 plane, inclined under a certain angle, to the ecliptic. This 
 angle was readily measured by the ancients, and, though 
 slightly variable, was fixed at the beginning of our century 
 at 5 8' 47"-9. 
 
 THE LUNAR PARALLAX AND DISTANCE. The rude instru- 
 ments employed by the early observers in their astronomical 
 obervations were insufficient for any delicate work, and hence 
 we find them quite ignorant of the absolute value of even 
 the moon's parallax, a quantity which far exceeds any other 
 parallactic angle of the solar system. We have already 
 shown (chap. I.) how the distance of an inaccessible object 
 may be obtained by measuring the angles formed at the 
 extremities of a given base line, by visual rays drawn to the 
 object. In case the base line be very short in proportion 
 to the distance to be measured, the sum of the two angles 
 thus measured will approach in value 180, and the angle at 
 the distant object formed by the visual rays becomes smaller 
 in proportion to its distance. In our attempts to' measure 
 the solar parallax, using the earth's diameter as a base, it 
 was found that the delicacy of modern instruments was not 
 adequate to so difficult a task. This, however, is not the 
 case when we come to apply them in the determination of 
 the lunar parallax. Indeed, the moon is found to be so 
 near the earth that visual rays, drawn from spectators at 
 different parts of the earth, not very remote from each 
 other, to the moon's centre, form with each other sensible 
 angles ; and thus the moon, viewed from different stations, 
 is projected among different stars. When the moon's centre 
 
THE MOOW. 63 
 
 ?j? in the absolute horizon (that is, in a plane passing through 
 the centre of the earth and perpendicular to the earth's 
 radius drawn to the place of the spectator), lines drawn 
 from the centre of the earth and from the eye of the 
 observer unite at the moon's centre, under an angle called 
 the moon's horizontal parallax. In case the moon's distance 
 from the earth were constant, this angle would also be in- 
 variable. This, however, is not the case, and we find the 
 horizontal parallax reaches a maximum value equal to 
 1 l' 24", when the moon is nearest the earth, and a 
 minimum value of 53' 48" when most remote ; the 
 average value being 57' 00"'9. These angles give for 
 the moon's mean distance from the earth 237,000 miles. 
 
 As all the computed places of the planetary orbs assume 
 the spectator to occupy the earth's centre, we readily per- 
 ceive .that, in the case of the moon, the computed and 
 observed places would never agree, except in one instance, 
 namely, that in which a line joining the centre of the earth 
 with the moon's centre passes through the place of the 
 observer, or when the moon's centre is exactly in the zenith. 
 The effect of parallax on the apparent place of the moon is 
 to sink it below the position it would have held in case it 
 were seen from the earth's centre. 
 
 Knowing the actual distance of the moon, her real 
 diameter is readily determined, and is found to be about 
 2,160 miles; hence her volume is about one forty-ninth 
 part of that of the earth. "We shall have occasion here- 
 after to resume our examination of the moon's motions 
 when we come to discuss the physical causes by whose 
 power the planetary orbs are held in dynamical equili- 
 brium, and are retained in their orbits. We now proceed 
 to examine the physical constitution of 
 
 THE MOON, AS REVEALED BY -THE TELESCOPE. The 
 splendid instruments which modern skill and science have 
 furnished for the examination of the distant worlds, so far 
 increase the power and! reach of human vision, in the case of 
 the moon, as to bring thi? satellite of the earth compare- 
 
64 POPULAR ASTRONOMY. 
 
 tively within our reach. A telescope which bears a map^ 
 nifying power of one thousand times, applied to the 
 examination of the moon's surface, enables the observer to 
 approach to within 237 miles of this extraordinary world ; 
 and even this distance, under the most favourable circum- 
 stances, may be reduced by one half. This, perhaps, is the 
 nearest approach ever made to the moon ; and it is at a 
 distance of about 150 miles that we are permitted to stand 
 and examine at our leisure the features which diversify the 
 surface of our satellite. No subject has excited so deep an 
 interest from mere curiosity as that involved in the actual 
 condition of the moon's surface. Every one desires to know 
 if the other worlds are like our own. Have they oceans 
 and seas, lakes, rivers, islands, and continents ? Does their 
 soil resemble our own 1 Does vegetable life there manifest 
 itself in every variety of grass and flowers, and shrub and 
 tree 1 Are there extended forests and spicy groves, filled 
 with multitudinous animals, in these far-off worlds ? And, 
 above all, are these bright orbs inhabited by rational intelligent 
 beings like man ? The earnest desire to obtain responses to 
 these and like questions, caused to be received, many years 
 since, with the most wonderful delight and credulity, a 
 statement put forth in America, giving professedly the 
 details of lunar discoveries said to have been made by Sir 
 John Herschel at the Cape of Good Hope, in which all 
 these questions were most satisfactorily answered. We need 
 hardly say how great was the disappointment when these 
 pretended discoveries proved to be but fanciful inventions. 
 When we call to mind that with a telescope magnifying 
 2,000 times we are still separated from the moon 120 miles, 
 we readily perceive the utter impossibility of solving at 
 present, directly by vision, the problem of the moon's 
 habitability. We know not what may be accomplished by 
 human genius and human invention ; and after the pro- 
 duction of so marvellous an instrument as a telescope 
 capable of transporting the beholder to within 120 miles 
 of the surface of a body actually removed 237,000 miles, 
 
LUNAR SURFACE 
 
 GASSENDIUS, DUDLEY OBSERVATORY, JAN. 1860 
 
THE MOON. 65 
 
 we will not presume to set any specific limits to future 
 effort. We can only say that the telescope must become 
 vastly improved in its powers of definition and development 
 before we can hope to satisfy ourselves, from actual inspec- 
 tion, that our satellite is or is not inhabited by a race with 
 any of the faculties which distinguish man. 
 
 Leo us see what has actually been accomplished by tele* 
 scopic investigation j and although it falls far short of satis- 
 fying the curiosity of our nature, we shall find much to 
 interest and astonish. We can affirm, then, that the surface 
 of our satellite is diversified with hill and dale, with lofty 
 mountains and mighty cavities, with extensive plains and 
 isolated mountain-peaks, not very unlike the same features 
 presented by our earth. The hemisphere of the moon, visible 
 to man, has been studied and mapped with the greatest 
 care. Indeed, its elevations and depressions have been 
 accurately modelled, the mountain -elevations have been 
 measured, and the depths of the mighty cavities which dis- 
 tinguish her surface have all been carefully determined. 
 These measures all depend on the fact that the moon 
 receives its light from the sun, and presents its surface to 
 that orb under every angle in the course of its revolution. 
 The mountains of the moon, like those of the earth, have 
 their summits first lighted by the rays of the rising sun, 
 while all the plain beneath, and the rough and rugged sides 
 of the mountains, are in the deepest darkness. Thsse 
 summits, when so illuminated, glow and sparkle with a 
 dazzling beauty unsurpassed. As the sun rises, we perceive 
 distinctly the black shadow of the mountain falling to a 
 great distance on the plain below. These shadows slowly 
 decrease in length, and their outlines gradually creep up the 
 mountain-side as the sun reaches the moon's meridian. 
 When the sun begins to decline, the shadows fall in the 
 opposite direction, slowly extend their black masses over the 
 distant plains, and darkness finally gathers round the moun- 
 tain-sides, till again the summit is alone illumined by the 
 rays of a setting sun. It is by means of those shadows, 
 
 F 
 
66 POPULAR ASTRONOMY. 
 
 whose lengths are readily determined by micrometrical 
 measures, that we are enabled to estimate the heights of the 
 lunar mountains, and the depths of the lunar cavities. This 
 process is not more difficult than to determine the elevation 
 of a church-steeple or other lofty object by the length of its 
 shadow cast upon an horizontal plane below. The altitude 
 of the sun above the horizon at noon will give the direction 
 of the visual ray passing from the summit of the object to 
 the extremity of its shadow. Knowing the value of this 
 angle, and the measured length oi the shadow cast, we have 
 at once the means of determining the elevation of the object 
 under examination. These simple principles are readily 
 transferred to the determination of the heights and depths 
 of the lunar surface, while the figure of the shadow cast by 
 the summits of a mountain-range on an extended plain 
 below, gives to us almost as perfect a knowledge of the 
 actual forms of the lunar mountains as though it were 
 possible actually to tread their lofty summits. 
 
 "We find upon the moon's surface a range of mountains 
 lifting themselves above a level country and extending 
 nearly 200 miles, which have received the name of the 
 Apennines. This mountain-range comes into the sunlight 
 just after the moon has passed its first quarter, and is then 
 one of the finest objects that the telescope reveals to the 
 eye of man. The brilliancy of the illuminated heights and 
 ridges, the absolute blackness of the deep, rocky chasms, the 
 lofty peaks, the rugged precipices, and the deep shadows, all 
 combine to increase the natural grandeur of this extensive 
 mountain-range. Let it not be imagined that details in 
 such a scene, such as actual individual rocks, of definite form 
 and outline, are to be seen ; but as lights and shades pro- 
 duce the forms of every surface, so these lights and shadows 
 on the moon bring out the absolute forms in the most dis- 
 tinct and perfect manner. The contrasts between the dark 
 and illuminated parts of the moon are far deeper and 
 stronger than on the earth. This arises from the fact that 
 che sunlight on the moon is not reflected or refracted by an 
 
THE MOON. 67 
 
 atmosphere such as surrounds the earth. The twilight 
 which attends the setting sun and the dawn, which so beau- 
 tifully announces the coming of day, does not exist for the 
 lunarians. If any eye beholds the rising of the mighty orb 
 of day from those lofty lunar summits which are first illu- 
 mined by his horizontal beams, no gentle flashings, or rosy 
 tints, or purple hues, are gradually diffused; but from 
 intense darkness there is an instantaneous burst of brilliant 
 sunlight. The beauty of our dawns and twilights is due to 
 the atmosphere which surrounds the earth ; and while we 
 cannot affirm that no such atmosphere surrounds our satel- 
 lite, we are certain that whatever gaseous envelope may 
 encompass the moon on its hither side, its density cannot 
 compare with that of the terrestrial atmosphere. Under 
 very favourable circumstances, with the great refractor of 
 the Cincinnati Observatory, the author has either seen, or 
 fancied he saw, a faint penumbra edging the dark mountain- 
 shadows, and clinging to the black outline, as it slowly crept 
 up the mountain-side, as the sun rose higher and higher. 
 We shall return to this subject when we come to treat oi 
 certain peculiarities attending the eclipse of the sun, and 
 the occultation of stars by the moon. 
 
 Some of the mountains of the moon reach an elevation of 
 8,000 to 10,000 feet above the general level. Here and 
 there we find insulated peaks rising abruptly from extended 
 plains to a height of 6,000 or 7,000 feet, and in the early 
 lunar morning flinging their long, sharp, black shadows to a 
 vast distance. 
 
 But the most remarkable feature presented in the lunar 
 surface is the tremendou depths of some of the cavities, and 
 their immense magnitude^ Some of them extend beneath 
 the general level of the country to a depth of 10,000 to 
 17,000 feet, and their rough, misshapen, precipitous sides 
 exhibit scenes of rugged sublimity to which earth presents 
 no parallel. Of these cup-shaped cavities, especially in the 
 southern portion of the lunar hemisphere, the number is 
 beyond credibility ; and, in case we admit them to be the 
 
6\S POPULAR ASTRONOMY. 
 
 extinct craters of once active volcanoes, we are forced to the , 
 conclusion that convulsions, such as the earth is a stranger 
 to, have shaken the outer crust of our satellite into a 
 hideousness of form unknown in any region of our planet. 
 Some of these deep cavities are nearly circular in figure, and 
 with diameters of all magnitudes up to twenty miles. Very 
 often the interior will exhibit a uniformly shaded surface, and 
 in the centre a conical mountain will lift itself far above this 
 level plain. That these convulsions are of different ages is 
 clearly manifest from the fact that their outlines very often 
 overlap one another, and the oldest and the newest forma- 
 tions are thus distinctly traced by the eye of man. So sharp 
 and positive is the outline of these extraordinary objects, 
 that one cannot but feel that some sudden bursting forth 
 might even occur while under telescopic examination. Once 
 indeed, while closely inspecting these seemingly volcanic 
 mountains and craters of the moon, I was startled by a 
 spectacle which, for a moment, produced upon the mind a 
 most strange sensation. A mighty bird, huge in outline 
 and vast in its proportions, suddenly lifted itself a^ove the 
 moon's horizon, and slowly ascended in its flight towards 
 the moon's centre. It was no lunar bird, however, but one 
 of earth, high up in the heavens, winging its solitary flight 
 in the dead of night, and by chance crossing the field of 
 vision and the lunar disc. 
 
 Before the power of the telescope had reached its present 
 condition of perfection, the darker spots of the moon were 
 assumed to be seas and oceans ; but the power now applied 
 to the moon demonstrates that there cannot exist at this 
 time any considerable body of water on the hemisphere 
 visible from the earth. And yet we find objects such, that 
 in case we were gazing upon the earth from the moon, 
 possessing our actual knowledge of the earth's lakes and 
 rivers, we should pronounce them, without hesitation, lakes 
 and rivers. There is one such object which I will describe 
 as often seen through the Cincinnati refractor. The outline 
 is nearly circular, with a lofty range of hills on the western 
 
NORTH-WESTERN BOUNDARY. OF MARE SERENITATIS, FEB. 
 27, i860, 8 H. P.M., ALBANY TIME, DUDLEY OBSERVATORY 
 
THE MOON. 69 
 
 south-western sides. This range gradually sinks in the 
 east, and a beautiful sloping beach seems to extend down to 
 the level surface of the inclosed lake (as we shall call it, for 
 want of other language). With the highest telescopic 
 power, under the most favourable circumstances, I never 
 could detect the slightest irregularity in the shading of the 
 surface of the lake. Had the cavity been filled with quick- 
 silver, and suddenly congealed or covered with solid ice, 
 with a covering of pure snow, the shading could not be more 
 regular than it is. To add, however, to the terrene likeness, 
 into this seeming lake there flows what looks exactly as a 
 river should at such a distance. That there is an indenta- 
 tion in the surface, exactly like the bed of a river, extending 
 into the country (with numerous islands), for more than a 
 hundred miles, and then forking and separating into two 
 distinct branches, each of which pursues a serpentine course 
 for from thirty to fifty miles beyond the fork, all this is 
 distinctly visible. I may say, indeed, that, just before en- 
 tering the lunar lake, this lunar river is found to disappear 
 from sight, and seems to pass beneath the range of hills 
 which border the lake. The region of country which lies 
 between the forks or branches of this seeming river is evi- 
 dently higher, and to the eye appears just as it should do, so 
 as to shed its water into the stream which appears to flow 
 in the valley below. The question may be asked, Why is 
 this not a lake and a river ? There is no lunar atmosphere 
 on the visible hemisphere of the moon, such as surrounds 
 the earth ; and if there were water like ours on the moon, 
 it would be soon evaporated, and would produce a kind of 
 vaporous atmosphere, which ought to be shown in some of 
 the many phenomena involving the moon, but which has 
 not yet been detected. What, then, shall we call the objects 
 described ? I can only answer that this phenomenon, with 
 many other, presented by the lunar surface, has thus far 
 baffled the most diligent and persevering efforts to explain. 
 In some of these cavities, where the tinting of the level 
 surface is perfect with an ordinary telescope, when examined 
 
70 POPULAR ASTRONOMY. 
 
 with instruments of the highest power, we detect small 
 depressions in this very surface, cup-shaped, and in all 
 respects resembling the form and features of the principal 
 cavity. These hollow places are clearly marked by the 
 shadows cast on the interior of the edges, which change as 
 the sun changes, and seem to demonstrate that these level 
 surfaces do not belong to a fluid but to a solid substance. 
 
 Among what are called the volcanic mountains of the 
 moon, are found objects of special interest. One of them, 
 named Copernicus, and situated not far from the moon's 
 equator, is so distinctly shown by the telescope, that the 
 external surface of the surrounding mountains presents the 
 very appearance we should expect to find in mountains 
 formed by the ejecting from the crater of immense quanti- 
 ties of lava and melted matter, solidifying as it poured down 
 the mountain-side, and marking the entire external surface 
 with short ridges and deep gullies, all radiating from a 
 common centre. Can these be, indeed, the overflowing of 
 once active volcanoes 1 Sir William Herschel once enter- 
 tained the opinion that they were ; and, with his"" great 
 reflecting telescope, at one time discovered what he believed 
 to be the flames of an active volcano on the dark part of the 
 new moon. More powerful instruments have not confirmed 
 this discovery j and although a like appearance of a sort of 
 luminous or brilliant spot has been seen by more than one 
 person, it is almost impossible to assert the luminosity to be 
 due to a volcano in a state of irruption j but it is more com- 
 monly supposed to be some highly reflective surface of short 
 extent, and for a time favourably situated to throw back to 
 us the earth-shine of our own planet. 
 
 From some of these seeming volcanoes there are streaky 
 radiations or bright lines, running from a common centre, 
 and extending sometimes to great distances. These have by 
 some been considered to be hardened lava-streams of great 
 reflective power ; but, unfortunately for this hypothesis, 
 they hold their way unbroken across deep valleys and 
 abrupt depressions, whi$h no molten matter flowing as lava 
 
THE MOON. 71 
 
 does, could possibly do. To me they more resemble immense 
 upheavals, forming elevated ridges of a reflecting power 
 greater than that of the surrounding country. 
 
 We find on the level surfaces a few very direct cuts, as 
 they may be called, not unlike those made on our planet 
 for railway-tracks, only on a gigantic scale, being more than 
 a thousand yards in width, and extending in some instances 
 over a hundred miles in length. What these may be it is 
 useless to conjecture. We cannot regard them as the work 
 of sentient beings, and must rather consider them as abrupt 
 depressions or faults in the lunar geography. 
 
 THE MOON'S CENTRE OF FIGURE. The wonderful phe- 
 nomena presented to the eye on the visible hemisphere of 
 the moon have been rendered in some degree explicable by 
 a remarkable discovery recently made, that the centre of 
 gravity of the moon does not coincide with the centre of 
 figure. This is not the place to explain how this fact has 
 been ascertained. It is now introduced to present its effect 
 on the hither portion of the lunar orb. 
 
 If the material composing the moon was lighter in one 
 hemisphere than in the other, it is manifest that the centre 
 of gravity would fall in the heavier half of the globe. For 
 instance, a globe composed partly of lead and gartly of wood 
 could not have the centre of gravity coincident with the 
 centre of the globe ; but it would lie somewhere in the 
 leaden hemisphere. So it now appears that the centre of 
 gravity of the moon is more than thirty-three miles from the 
 centre of figure, and that this centre of gravity falls in the 
 remote hemisphere, which can never be seen by mortal eye. 
 
 Now, the centre of gravity is the centre to which all 
 heavy bodies gravitate. About it as a centre the lunar 
 ocean and the lunar atmosphere, in case such exist, would 
 arrange themselves, and the lighter hemisphere would rist 
 above the general level, as referred to the centre of gravity 
 to an extreme height of thirty-three miles. Admitting this 
 to be true, and as we shall see hereafter the fact appears to 
 be well established, we can readily perceive that no water, 
 
72 POPULAR ASTRONOMY. 
 
 river, lake, or sea, should exist on the hither side of th 
 moon, and no perceptible atmosphere can exist at so great 
 an elevation. Even vegetable life itself could not be main- 
 tained on a mountain towering up to the enormous height of 
 thirty-three miles ; and hence we ought to expect the hither 
 side of our satellite to present exactly such an appearance 
 rs is revealed by telescopic inspection. 
 
 If the centres of gravity and figure ever coincided in the 
 moon, and the change of form has been produced by some 
 great convulsion, which has principally expended its force in 
 an upheaval of the hither side of the globe, then we can 
 account for the rough, broken, and shattered condition of the 
 visible surface. Lakes and rivers may once have existed, 
 active volcanoes might once have poured forth their lava- 
 streams, while now the dry and desolate beds and the 
 extinct craters are only to be seen. 
 
 The consequences which flow from this singular discovery, 
 as to the figure of our satellite, are certainly very remark- 
 able, and will doubtless be traced with deep interest in 
 future examinations. 
 
 OCCULTATIONS. As the moon is very near the earth, and 
 her disc covers a very considerable surface in the heavens 
 in her sweep among the fixed stars, she must of course cross 
 over a multitude of stars in her revolutions. A star thus 
 hidden by the moon is said to be occulted, and these occulta- 
 tions are phenomena of special interest on many accounts. 
 As a general thing, r. star even of the first magnitude, in 
 passing under the dark limb of the moon, vanishes from the 
 sight instantaneously, as though it were suddenly stricken 
 from existence, and at its re- appearance its full brilliancy 
 bursts at once on the eye. This demonstrates the fact that 
 the stars can be nothing more than luminous points to 
 our senses, even when grasped by the greatest telescopic 
 power. 
 
 A strange appearance sometimes attends the occultation 
 of stars by the moon. The star comes up to the moon's 
 limb, entirely vanishes for a momer.t, then re-appears, glides 
 
THE MOOJS. 73 
 
 on the bright limb of the moon for a second or more, and 
 then suddenly fades from the sight. 
 
 This phenomenon, as also another of most startling 
 character attending sometimes the total eclipse of the sun, 
 when blood-red streaks in radiations are found to shoot sud- 
 denly from behind the moon's limb, are supposed by some to 
 demonstrate the existence of a lunar atmosphere. Much 
 attention has been bestowed on the total eclipses of the sun 
 during the past twenty years, for the express purpose of 
 solving, if possible, these mysterious radiations of red light. 
 Some entertain the opinion that they are due to the coloured 
 glasses used to soften the intense solar light, as seen through 
 the telescope. We can only say that these phenomena 
 remain without satisfactory explanation, and that the 
 physical condition of the moon is yet a problem of the 
 deepest interest. We can assert the irregularities of her 
 surface, her deep cavities and lofty elevations, her extended 
 plains and abrupt mountain-peaks, but beyond this, our 
 positive knowledge does not extend. 
 
 We shall resume the consideration of our satellite 
 when we come to discuss the great theory of universal gra- 
 vitation. 
 
POPULAR ASTRONOMY. 
 
 CHAPTER V. 
 
 MARS. THE FOURTH PLANET IN THE ORDER OF DISTANCE 
 FROM THE SUN. 
 
 Phenomena of Mars difficult to explain with the Earth as the Centre of 
 Motion. Copernican System applied. Epicycle of Mars. Better instru- 
 ments and more accurate observations. Tycho and Kepler. Kepler's 
 method of investigation. Circles and Epicycles exhausted. The Ellipse, 
 Its Properties. The Orbit of Mars an Ellipse. Kepler's Laws. 
 Elliptical Orbits of the Planets. The Elements of the Planetary Orbits 
 explained. How these Elements are obtained. Kepler's third Law. 
 Value of this Law. The Physical Aspoct of Mars. Snow-zones. 
 Rotation of the Planet. Diameter and Volume. Speculation as to its 
 Climate and Colour. 
 
 THIS planet is distinguished to the naked eye by its brilliant 
 red light, and is one of the planets discovered by the an- 
 cients. To the old astronomers Mars presented an object 
 of special difficulty. Revolving as it does in an orbit of 
 great eccentricity, sometimes receding from the earth to a 
 vast distance, then approaching so near as to rival in bril- 
 liancy the large planets Jupiter and Venus, on the old 
 hypothesis of the central position of the earth, and the 
 uniform circular motion of the planets, Mars presented 
 anomalies in his revolution most difficult of explanation. 
 
 These complications were partially removed by the great 
 discovery of Copernicus, which released the earth from its 
 false position, and gave to Mars its true centre, the sun ; 
 but even with this extraordinary advance in the direction 
 towards a full solution of the mysterious movements of 
 this planet, there remained many anomalies of motion of a 
 most curious and incomprehensible character. It will be 
 remembered that Copernicus, in adopting the sun as the 
 centre of the planetary orbits, was compelled to retain the 
 epicycle of the old Greek theorists, to account for the facts 
 which still distinguished the planetary t evolutions. As in 
 
MARS. 75 
 
 ihe revolution of the earth about the sun there was an 
 approach to, and recess from, this central orb, so in the 
 revolution of Mars it was manifest that there was a vast 
 difference between the aphelion and perihelion distances of 
 
 the planet. The epicycle was then retained to account for 
 this anomaly in the motion of Mars ; and it will be readily 
 seen from the figure above how this hypothesis rendered a 
 general explanation of the facts presented for examination. 
 
 The large circle, having the sun for its centre, represents 
 the orbit of Mars ; that is, a circle whose radius is equal to 
 the average or mean distance of the planet. The small 
 circles represent the epicycle, in the circumference of which 
 the planet revolves with an equable motion, while its 
 centre moves uniformly round on the circumference of the 
 large circle. When the planet is at A, it is in perihelion, 
 or nearest the sun. While the centre of the epicycle per- 
 forms a quarter-revolution, the planet also performs in its 
 epicycle a quarter of a revolution, and reaches the posi- 
 tion B. A half-revolution brings it to aphelion in C, and 
 three quarters of a revolution in the epicycle locates the 
 planet at D, and an entire revolution brings it again to A, 
 the point of departure. Thus it will be seen that the planet 
 
76 POPULAR ASTRONOMY. 
 
 must describe an oval curve, traced in the figure A B C D 
 and for general purposes this exposition of the phenomena 
 seemed entirely satisfactory. It is true that it only ac- 
 counted for the movement from east to west, or in longitude, 
 while the motion north and south of the earth's orbit, or in 
 latitude, was accounted for by supposing the plane of the 
 epicycle to vibrate or rock up and down, or right and left 
 of the plane of the ecliptic, while its centre moved uni- 
 formly round in the great circle constituting the orbit of 
 the planet. 
 
 So long as observation was so defective as to yield but 
 rough places of the heavenly bodies, the deviations from the 
 path marked out by the theory of epicycles escaped detec- 
 tion. The erection of the great observatory of Uraniberg, 
 by the celebrated astronomer Tycho Brahe, and the fur- 
 nishing it with instruments of superior delicacy, introduced 
 a new era in the history of astronomical observation. The 
 instruments employed by Copernicus were incapable of 
 giving the place of a star or planet with a precision such as 
 to avoid errors amounting to even the half of one degree, 
 or an amount of space equal to the sun's apparent diameter. 
 The instruments employed by Tycho reduced the errors of 
 observation from fractions of degrees to fractions of min- 
 utes of arc ; and when thus critically examined, the planets, 
 as well as the sun and moon, presented anomalies of motion, 
 requiring to account for them a large accumulation of com- 
 plexity in the celestial machinery. Such was the condition 
 of theoretic and practical astronomy at the era inaugurated 
 by 'the appearance of the celebrated Kepler. This dis- 
 tinguished astronomer early became a devoted advocate of 
 the Copernican system of the universe, adopting not only 
 the central position of the sun, but also the ancient doctrine 
 of uniform circular motion, and the theory of epicycles. 
 The investigations of Kepler on the motions of the planet 
 Mars commenced after joining Tycho at Uraniberg, in 1603, 
 and, based upon the accurate observations of this later astro- 
 
MARS. 77 
 
 nomer, finally led to .the overthrow of tlie old theory of 
 epicycles and circular motion, by introducing the true figure 
 of the planetary orbits ; and with the elliptical theory of 
 planetary motion, commenced the dawn of that brighter day 
 of modern science, which in our age sheds its light upon the 
 world. 
 
 The history of the great discoveries of Kepler presents 
 one of the most extraordinary chapters in 'the science of 
 astronomy. It must be remembered that the doctrine of 
 circular motion, at once so beautiful and simple, had held 
 its sway over the human mind for more than two thousand 
 years. Such, indeed, was its power of fascination, that even 
 the bold and independent mind of Copernicus could not 
 break away from its sway. When Kepler commenced bis 
 examination of the movements of Ma,rs, it was under the 
 full and firm conviction that the theory of circles and epi- 
 cycles was unquestionably true. ,His task, then, was simply 
 to frame a combination such as would account for the new 
 anomalies in the motions of Mars discovered by the refined 
 observations of Tycho. The amount of industry, perse- 
 verance, sagacity, and inventive genius displayed by Kepler in 
 this great effort, is unparalleled in the history of astronomical 
 discovery. His plan of operation was admirably laid, and 
 if fully and faithfully carried out, could not fail, in the end, 
 to exhaust the subject, and to prove at least the great nega- 
 tive truth, that no combination of circles and epicycles could 
 by any possibility truly represent the exact movements of 
 this flying world. It is useless to enumerate the different 
 hypotheses employed by Kepler. They were no less than 
 nineteen in number, each of which was examined with the 
 most laborious care, and each of which, in succession, he was 
 compelled to reject. Having adopted an hypothesis, he 
 computed what ought to be the visible positions of the planet 
 Mars, as seen from the earth, throughout its entire revolu- 
 tion. He compared these computed places or positions with 
 the observed places, or those actually occupied by the planet, 
 
78 POPULAR ASTRONOMY. 
 
 and finding a discrepancy between the two, his hypothesis 
 was thus shown to be false and defective, and must necessarily 
 be rejected. 
 
 It is curious to note the limits of accuracy in the observed 
 places of the planet, upon which Kepler relied with so much 
 confidence in this bold investigation. Many of the various 
 hypotheses which he worked up and applied with so much 
 diligence, enabled him to follow the planet in its entire 
 revolution around the sun, with discrepancies between ob- 
 servalion and computation not exceeding the tenth part of 
 the moon's diameter. Indeed, the whole error in the com- 
 puted place of Mars, when compared with its observed 
 place, when Kepler commenced the problem, did not exceed 
 eight minutes of arc, or about one-fourth of the moon's 
 apparent diameter ; and yet upon this slender basis this 
 wonderful man declared that he would reconstruct the entire 
 science of the heavens. 
 
 Having thus framed one hypothesis after another, each of 
 which was in its turn rigorously computed, applied, and 
 rejected, this exhaustive process finally brought Kepler to 
 the conclusion that no combination of circles, with circular 
 motion, could render a satisfactory account of the anomalies 
 presented in the revolution of Mars ; and he thus rose 
 to the grand truth, that the circle, with all its beauty, 
 simplicity, and fascination, must be banished from the 
 heavens. 
 
 The demonstration of this great negative truth was a 
 necessary preliminary to the discovery of the true orbit in 
 which Mars performed his revolution around the sun. Com- 
 plexity having been exhausted in the combination of circles 
 without success, Kepler determined to return to primitive 
 simplicity, and endeavour to find some one curve which might 
 prove to be that described by the planet. In tracing up the 
 movement of Mars, as we have seen, the figure of the true 
 orbit was evidently an oval, and among ovals there is a curve 
 known to geometricians by the name of the ellipse. This 
 
MARS. < y 
 
 curve is symmetrical in form, and enjoys some peculiar pro- 
 perties which we will exhibit to the eye. 
 
 The line A B is called the major axis, and is the longest 
 line which can be drawn inside the curve. It passes from 
 one vertex A to the other vertex at B, and the semi-ellipse 
 A D B is such that, if turned round the axis A B, it would 
 fall on, and exactly coincide with the semi-ellipse A C B. 
 The line C D is called the minor axis, and is the shortest line 
 which can be drawn in the ellipse. This line divides the 
 figure into two equal portions, exactly symmetrical. 
 
 The point L is called the centre of the ellipse, and divides 
 all the lines drawn through it and terminating in the curve 
 into two equal parts. But there are two points O and (X, 
 called the foci, which enjoy very peculiar properties. If 
 from C as a centre, and with a radius equal to A L, the 
 semi-major axis, we describe an arc, it will cut the major 
 axis in and 0', the two foci. Now, in case we assume any 
 point on the curve as P, and join it with O and O', the 
 sum of these lines, O P and O' P, will be equal to the major 
 axis, A B. 
 
 Such are the distinguishing properties of the curve, which 
 holds the next rank in order of beauty, simplicity, and 
 regularity, after the circle. While the circle has one central 
 point, from which all lines drawn to the curve are equal, the 
 ellipse has two foci, from which lines drawn to the same 
 
80 POPULAR ASTRONOMY. 
 
 point on the curve, are, when added together, equal in length 
 to the major axis. When the major axis of the ellipse 18 
 assumed as the diameter of a circle, the circumference will 
 wholly inclose the ellipse. When the minor axis is assumed 
 as the diameter, the circumference will lie wholly within the 
 ellipse. When the foci, O and 0', are very near the centre, 
 then these circles, and the ellipse lying between them, are 
 very close to each other. 
 
 When Kepler was compelled to abandon the circle and 
 circular motion as a means of representing the planetary 
 revolutions, he adopted the ellipse as the probable form of 
 the orbits of these revolving worlds, and made an especial 
 effort to apply this new figure to a solution of the mysteries 
 which still enveloped the motions of Mars. But here a new 
 difficulty presented itself. In the circular orbits and epi- 
 cycles a uniform motion was always accepted j but in the 
 ellipse, every point of which is at unequal distances from the 
 focus, some law of velocity had to be discovered to render it 
 possible to compute the planet's place, even after the axis 
 of the ellipse had been determined. Here again was opened 
 up to the mind of the laborious philosopher a wide field of 
 investigation. Many were the hypotheses which he framed, 
 computed, applied, and rejected ; but, finally fixing the sun 
 in the focus of the assumed elliptic orbit, and assuming that 
 the line drawn from the sun's centre to the planet would 
 sweep over equal amounts of area in equal times, he com- 
 puted the places of Mars through an entire revolution. 
 These newly- computed places were now compared with those 
 actually filled by the revolving world ; and Kepler found, to 
 his infinite delight, that the planet swept over the precise 
 track which his hypothesis had enabled him to predict ; and 
 with an exultation of victorious triumph to which the his- 
 tory of pure thought furnishes few parallels, Kepler announced 
 to the world his first two laws of planetary motion, which may 
 be given as follows : 
 
 1. Every planet revolves in cm elliptical orbit about the 
 sun, which occupies the focus. 
 
MARS. 81 
 
 2. The velocity of the planet on every point of its orbit is 
 such that the line drawn from the sun to the planet will 
 sweep over equal areas in equal times. 
 
 At the time Kepler lived, human genius could not have 
 won a grander triumph ; for it was not only a triumph over 
 nature, which compelled her to render up her inscrutable 
 secrets, but a triumph which for ever freed the mind from the 
 iron sway of the schools, and from the prejudices which had 
 become venerable with the lapse of more than twenty cen- 
 turies of unyielding power. No grander emotions ever swelled 
 the human heart than those which Kepler experienced when, 
 tracing this fiery world through his sweep among the fixed 
 stars, he found he had truly and firmly bound his now captive 
 planet in chains of adamant, from which in all future ages it 
 could never escape, having fixed for all time the figure of the 
 orbit and the law of its orbital velocity. This extended notice 
 is due to the well-merited fame of Kepler, as well as to the 
 grandeur of the laws discovered. 
 
 The elliptical theory, now successfully applied to the 
 planet Mars, was extended rapidly to Mercury, to the 
 moon, and in order to all the known planets. We shall 
 hereafter, in our treatment of the planets, adopt the ellip- 
 tical theory ; and to render our language entirely intelligible, 
 will proceed to explain what is meant by the elements of the 
 orbit of a planet. 
 
 To determine the magnitude of any ellipse, we must know 
 the longer and shorter axis, or the longer axis and the 
 distance from the centre to the focus, called the eccentricity. 
 
 To determine the position of the plane of an ellipse, we 
 must know the position of the line of its intersection with a 
 given plane (usually the ecliptic) called the line of nodes, and 
 also the angle of inclination with this fixed plane. 
 
 To determine the position of the elliptical orbit in its 
 own plane, we must know the position of the vertex, or 
 extremity of the major axis, called the perihelion. 
 
 And finally, to trace the planet after all these matters 
 shall be known as to its orbit, we must know its place <w 
 
 a 
 
82 POPULAR ASTRONOMY, 
 
 position in its orbit at a given moment of time, and ita 
 period of revolution. 
 
 Now, every plane of every planetary orbit passes through 
 the sun's centre. 
 
 Every longer axis of every planetary orbit passes through 
 the sun's centre, and every line of nodes of all the planetary 
 orbits passes through the sun's centre. Thus we have one 
 point of every axis, line of nodes, and plane of every orbit of 
 the primary planets. 
 
 To obtain the longer axis we have only to measure the 
 planet's distance from the sun when in aphelion and in 
 perihelion. These distances added together make the longer 
 axis of the orbit. The perihelion distance being known, we 
 readily obtain the eccentricity, hence the shorter axis, and 
 from these the entire ellipse in magnitude. The point at 
 which a planet passes from north to south of the ecliptic is 
 one point in its line of nodes, the sun's centre is another, 
 and these determine the direction of the line of nodes. The 
 inclination of the plane of the planet's orbit to the ecliptic 
 is measured by the angle formed between a line drawn from 
 the sun's centre perpendicular to the line of nodes in the 
 plane of the ecliptic, and one perpendicular to the same line 
 at the same point, but lying in the plane of the planet's 
 orbit. The elevation, therefore, of the planet above the 
 ecliptic, when 90 from the node, will be the angle of in- 
 clination. Having the line of nodes and inclination, we can 
 draw the plane. Having the perihelion-point, longer axis, 
 and eccentricity, we can construct and locate the elliptic 
 orbit ; and having the moment of perihelion-passage, we can 
 trace the planet in its future movements. 
 
 The elliptical theory being adopted and extended to all 
 the known planets successfully, it became manifest to the 
 searching genius of Kepler that there existed too many 
 common points of resemblance between these revolving orbs 
 not to involve some common bond which united them into 
 a scheme of mutual dependence. They all revolved in 
 el??.pt5.cal orbits. These orbits had one common focus, the 
 
MARS, AUG. 30, 8 H. 55 M. 1845 
 
 MARS, CINCINNATI OBSERVATORY, AUG. 5, 1845 
 
MARS. 33 
 
 sun. The lines of nodes and principal axes intersected in 
 the sun. They all obeyed the same law in their revolution 
 in their orbits ; and Kepler now undertook the task, almost 
 hopeless in its character, of discovering some bond of union 
 which might reduce a multitude of now isolated worlds to 
 an orderly and dependent system. 
 
 This problem occupied the mind of Kepler for no less 
 than ninet^n years. He examined carefully all the elements 
 of the planetary orbits, and finally selected the mean dis- 
 tances and periodic times as the objects of his special inves- 
 tigation. He found that the periods of revolution increased 
 as the planet was more remote from the sun, but certainly 
 \ot in the exact ratio of the distance. Thus 
 
 The mean distance of the earth is 95,000,000 of miles. 
 
 Its period of revolution 365| days. 
 
 Mean distance of Mars 142,000,000 of miles. 
 
 Period of revolution 687 days. 
 
 In case the distances and periodic times were exactly 
 proportional, we should have VV = ffi- But W = l'^ 
 nearly, while -|f-^=l'9 nearly. Finding that no simple pro- 
 portion existed between these quantities, Kepler broke away 
 from the ratios of geometry, which up to his own era had 
 almost exclusively been employed in all astronomical in- 
 vestigations, and conceived the idea that the hidden secret 
 might be found in proportions existing between some powers 
 of the quantities under consideration. He first tried the 
 squares, or simple products of the quantities by themselves. 
 Here he was again unsuccessful. He now rose yet higher, 
 and examined the relations of the cubes of the periods and 
 distances. But no proportion was found to exist among 
 these third powers. At length he was led by some influence, 
 he knew uot what, as he says, to try the relation between 
 the squares of the periods and the cubes of the distances, 
 .bus, ffi-xfli, and yj x VY x VV J and here lay ^the 
 grand secret ; for, if any one will perform the operations 
 above indicated, and square the periods of revolution, and 
 cube the mean distances, he will find the above quantities 
 
 a 2 
 
84 POPULAR ASTRONOMY. 
 
 to be equal to each other, or, in other language, he will find 
 the squares of the periodic times exactly proportional to the 
 cubes of the mean distances. 
 
 This is called the third law of Kepler, and is perhaps the 
 grandest and most important of all his wonderful discoveries. 
 Through its power the worlds are all linked together. The 
 satellites of the planets revolve in obedience to its sway, 
 and even those extraordinary objects, the revoking double 
 stars, are subjected to the same controlling law. It resolves 
 at once the most difficult problems involved in the solar 
 system, affording a simple method of determining the mean 
 distances of all the planets, by measuring the mean distance 
 of any one planet, and by observing the periods of revo- 
 lution. 
 
 As we have already seen, the periodic times are readily 
 determined from noting the days and fractions of days 
 which elapse from the planet's passage through its node 
 until it returns to the same node again. This, in case the 
 line of nodes remained absolutely fixed, would give the 
 time of revolution precisely ; and a slight correction suffices 
 to correct the error due to the movement of the nodes. 
 The determination of the mean distance of the earth, then, 
 becomes the key to a knowledge of all the planetary 
 distances, from which flow the absolute magnitudes of the 
 planets and their densities. 
 
 It is not, then, surprising that Kepler, seeing the grandeur 
 of the consequences flowing from the great discovery, should 
 have given utterance to his feelings in language of the most 
 lofty enthusiasm. 
 
 With the knowledge of the three laws discovered by 
 Kepler, modern astronomy commenced a career of won- 
 derful success. We shall find, hereafter, that even these 
 great laws of Kepler are but corollaries to a higher law yet 
 remaining to be developed ; but we prefer to follow out the 
 order of examination and development already commenced. 
 
 We resume our discussion of the planet under examina- 
 tion. The changes in the apparent diameter of Mars must, 
 
MARS. 85 
 
 of course, be very great. When in opposition to the sun, 
 or on a line joining the sun and earth, Mars is only 
 47,000,000 of miles from our planet, while, on reaching his 
 conjunction with the sun, this distance is increased by the 
 entire diameter of the earth's orbit, or 190,000,000 of miles. 
 When in opposition, Mars shines with great splendour, 
 presenting to the eye, as shown by the telescope, a large 
 and well-defined disc, with a surface distinctly marked with 
 permanent outlines of what have been conjectured to be 
 continents and oceans. The polar regions are distinguished 
 by zones of brilliant white light, which, in consequence of 
 their disappearance under the heat of summer, and their 
 reappearance as the winter comes on, have been considered 
 as due to snow and ice. I have examined these snow zones 
 with the great refractor of the Cincinnati Observatory, 
 under peculiarly favourable circumstances. To illustrate 
 the mode of observation employed in the determination of 
 the period of rotation of Mars on its axis, and the power of 
 the telescope in the revelation of the physical constitution 
 of this planet, I append some account of Maedler's observa- 
 tions, made in 1830, and also of those made at the Cincin- 
 nati Observatory in 1845 : 
 
 The last opposition of Mars, which occurred on the 20th 
 August, 1845, furnished a fine opportunity for the inspection 
 of the irregularities of its surface. When in opposition, the 
 planet rises as the sun sets, and the earth and planet are in 
 a straight line, which, by being prolonged, passes through 
 the sun. As the orbit of Mars incloses that of the earth, it 
 will be seen from a little reflection that when Mars is in 
 opposition it is nearer to the earth than at any other time ; 
 nearer than when in conjunction by the entire diameter of 
 the earth's orbit, or 190,000,000 of miles. In case the orbits 
 of Mars and the earth were exact circles, the distance betweec 
 the two planets at every opposition would be the same, but 
 the elliptic figure of the orbits occasions a considerable 
 variation in this distance, and the least distance possible 
 between the earth and Mars will be when an opposition 
 
86 POPULAR ASTRONOMY. 
 
 occurs at the time that the earth is furthest from the sun 
 and Mars nearest to the sun. Such were approximately the 
 relative positions of the planets in 1845, and their distance 
 was then less than it can be again for nearly fifteen years. 
 During the opposition which occurred in 1830, the earth 
 and Mars held nearly the same relative positions. The 
 planet was observed by Dr. Maedler, the present distin- 
 guished Director of the Imperial Observatory at Dorpat, 
 Russia, assisted by Mr. Beer. I have translated the following 
 notices from Schumacher's journal : 
 
 " The opposition of Mars which occurred in the month of 
 September of this year (1830), and at which time this planet 
 approached nearer the earth than it will again for fifteen 
 years, induced us to observe the planet as often as the clouds 
 would permit, in order to determine the position and figure 
 of its spots ; their possible physical changes, and especially 
 the time of revolution on its axis. The telescope employed 
 was a Frauenhofer Refractor, 4^ feet focus. 
 
 "The opposition occurred on the 19th September, and 
 the nearest approach to the earth (0'384) on ijie 14th of the 
 same month. In all succeeding oppositions up to 1845, this 
 distance amounts to 0'5, and even up to 0'65 (the unit being 
 the mean distance of the earth from the sun). On account 
 of the accurate definition of the instrument, we were able to 
 employ a power of 300 generally, and never less than 185. 
 With low magnifying powers, the greatest diameter was 
 determined to be a little less than 22". Our observations 
 extended from the 20th September to the 20th October, 
 during which time seventeen nights, more or less favourable, 
 occurred, and all sides of Mars came into view. Thirty-five 
 drawings were executed. It was not thought advisable to 
 apply a micrometer, as the thickness of the lines would have 
 produced greater errors in such minute measures than those 
 arising from a careful estimation by the eye. The drawings 
 were invariably made with the aid of the telescope. Com- 
 monly a little delay was had, till the undetermined figure ot 
 
MARS. 87 
 
 the spots visible at the first glance separated themselves (to 
 the eye) into distinct portions. 
 
 ******* 
 
 " On the 10th September a spot was seen so sharp and 
 well defined, and so near the centre of the planet, that it 
 was selected to determine the period of rotation. On the 
 14th September it retrograded from the eastern hemisphere, 
 through the centre to the western hemisphere, in the course 
 of three hours. Its figure unaltered during four days, and 
 its regularity as to rotation, left no doubt of its identity and 
 permanence. 
 
 " In the course of 2J hours Mars exhibited an entirely 
 different appearance. The spot (already alluded to) was 
 near the western disc of the planet. On the 16th it was 
 again observed, and the period of revolution deduced. It 
 was invisible up to the middle of October, appearing only in 
 the daytime on the side of the planet next to the earth. It 
 was first observed again on the 19th October, and the disc 
 of Mars showed itself with uncommon sharpness. On the 
 southern border of the principal spot, two red spots were 
 seen, resembling a ruddy sky on the earth. They appeared 
 fainter an hour after, and although they again seemed 
 brighter, they were never again seen red. We also observed 
 a faint spot near the principal one, which was never after 
 
 visible. 
 
 ******* 
 
 " The observations from the 26th September to the 5th 
 October showed to us some very dark spots, which in zone- 
 formed extensions showed a strong contrast to the brightly 
 illuminated surfaces free from spots. A fragment of one of 
 these spots was at the north end distinct and broad, while at 
 the south end it was so small as to be seen with difficulty. 
 Between the pole and the principal spot, there was seen a 
 broad stripe, of less shade, while the northern hemisphere 
 was almost entirely free from spots. Bad weather inter- 
 rupted the observations from the 5th to the 12th October. 
 
88 POPULAR ASTRONOMY. 
 
 'On the 13th, a spot appeared for the first time agaia 
 but so near the western disc that we recognized its return 
 only on the 14th. 
 
 "More accurate observations were had on the 19th and 
 20th October, when this spot passed the middle of Mars, 
 which movement was observed with all accuracy, and hence 
 a new determination of the period of revolution. Compu- 
 tation gave, the magnitude of the invisible parts of Mars on 
 the 13th October=0-06, on the 20th, 0-08, of the radius of 
 Mara. 
 
 " From the beginning of the observations there was seen 
 at the south pole, always with great distinctness, a white, 
 glittering, well-defined spot, which has long been observed, 
 and is called the ' snow zone.'' During the observations it 
 continually diminished up to the 5th of October. Here an 
 increase commenced, yet very slow. On the 10th September 
 we estimated it = -110 ; 5th Oct. = '110, and 20th Oct. = 
 115 of the diameter of Mars. 
 
 " In case we adopt Herschel's determination of inclination 
 and position of the axis of Mars, with reference to its orbit, 
 the south pole of Mars, on the 14th of April, 1830, must 
 have had its equinox, and on the 8th September, its summer 
 solstice. The smallest diameter of the ' snow zone ' occurred 
 on the twenty-seventh day after the summer solstice, a time 
 which corresponds to the last half of July on the northern 
 hemisphere of the earth, at which time it is well known 
 we have the greatest heat. 
 
 " Preceding observers in oppositions, where the pole was 
 further from the maximum temperature, have seen the 
 * snow zone * much larger, although nearly all regard it as 
 changeable in size. These facts seem to sustain the hypo- 
 thesis of a covering of snow." 
 
 As a further confirmation of this hypothesis, we subjoin 
 the following computations, by the same persons. The pre- 
 vious determinations of the elder Herschel are taken as the 
 basis of the calculations. This white polar region is now 
 distinctly visible, and seems to be accounted for in no other 
 
MARS. 89 
 
 way. Comparing the various seasons in Mars, Maedler finds 
 .as follows : 
 
 Duration of Spring, N. hemisphere 191 Mars' days. 
 
 Duration of Summer, 180 
 
 Duration of Autumn, 149 
 
 Duration of Winter, 147 
 
 " Adding spring and summer together, and fall and 
 winter, we have 
 
 Duration of Summer in N. H. to S. H. as 19 to 15 
 
 Intensity of sun's light in N. H. to S. H as 20 to 29 
 
 " Uniting these two proportions, and assuming that heat 
 and light are received in equal ratios, it will follow that the 
 south pole, by the greater intensity of solar heat, is more 
 than compensated for the shortness of its summer. But 
 since for the winter the proportion of twenty to twenty- 
 nine is reversed, so will the winter of the south pole, not 
 only on account of longer duration of cold, but also from 
 its greater intensity, be far more severe than in the north 
 pole. 
 
 " Herewith agree the facts, that preceding observers have 
 not lost sight of the ' snow zone ' of the south pole, even when 
 the pole became invisible ; whence it follows that it must 
 extend from the pole 45 and even further, while we, under 
 like circumstances, could not discover any such appearance 
 on the north side of Mars. On the contrary, the brightness 
 of this portion was exactly like that of the other parts of 
 the disc." 
 
 The conclusions reached by the German astronomers, a 
 above, were confirmed in the fullest manner by the observa- 
 tions made at the Cincinnati Observatory during the oppo- 
 sition of 1845. I will here record some singular pheno- 
 mena connected with the " snow zone," which, so far as I 
 know, have not been noticed elsewhere. 
 
 On the night of July 12th, 1845, this bright polar spot 
 presented an appearance never exhibited at any preceding 
 or succeeding observation. In the very centre of the white 
 surface was a dark spot, which retained its position during 
 
90 POPULAR ASTRONOMY. 
 
 several hours, and was distinctly seen by two friends, who 
 passed the night with me in the observatory. It was much 
 darker and better defined than any spot previously or sub- 
 sequently observed here, and, indeed, after an examination 
 of more than eighty drawings of the surface of this planet 
 by other observers at previous oppositions, I find no notice 
 of a dark spot ever having been seen in the bright snow 
 zone. On the following evening no trace of a dark spot was 
 to be seen, and it has never after been visible. 
 
 Again, on the evening of August 29th, 1845, the snow 
 zone, which for several weeks had presented a regular out- 
 line, nearly circular in appearance, was found to be some- 
 what flattened at the under part, and extended east and 
 west, so as to show a figure like a rectangle, with its corners 
 rounded. On the evening of the 30th August I observed, 
 for the first time, a small bright spot, nearly or quite round, 
 projecting out of the lower side of the polar spot. In the 
 early part of the evening the small bright spot seemed to be 
 partly buried in the large one, and was in this position at 
 8h. 55m. when the drawing, No. 1, was made. After the 
 lapse of an hour or more, my attention was again directed 
 to the planet, when I was astonished to find a manifest 
 change in the position of this small bright spot. It had 
 apparently separated from the large spot, and the edges of 
 the two were now in contact, whereas when first seen they 
 overlapped by an amount quite equal to one-third the 
 diameter of the small spot. On the following evening I 
 found a recurrence of the same phenomena. In the course 
 of a few days the small spot gradually faded from the sight 
 and was not seen at any subsequent observation. Should 
 Herschel's hypothesis be admitted, that the bright zone is 
 produced by snow and ice near the pole of the planet analo- 
 gous to what is known to exist at the poles of the earth, 
 these last changes may be accounted for, by supposing the 
 small bright spot to have been gradually dissipated by the 
 heat of the sun's rays. 
 
 Its apparent projection over the boundary of the large 
 
MARS. 91 
 
 snow zone may have been merely optical, and the separa- 
 tion may have been occasioned by seeing the two objects in 
 such a position as to prevent the one from being projected 
 on the other. Such change may have been produced by 
 the rotation of Mars on its axis in the space of a few hours. 
 
 To determine the exact period of rotation of Mars, Sir 
 William Herschel instituted a series of observations in 1777, 
 which were followed by others during the opposition of 
 1779. From the first series an approximate period of 
 rotation was obtained, and by uniting the observations of 
 1777 and those of 1779, and using 24h. 39m. as the approxi- 
 mate period of rotation, Herschel made a further correction, 
 and fixed the rotation at 24h. 39m. 21 -6s. 
 
 Maedler's determination, in 1830, gave, for a final result, 
 24h. 37m. 10s., which, in 1832, was corrected and fixed at 
 24h. 37m. 23-7s. 
 
 In 1839 Maedler reviewed Herschel's observations, from 
 whence his first results were deduced, and discovered that, 
 after introducing the necessary reduction, the discrepancy 
 of two minutes might be reduced to two seconds, by giving 
 to Mars one more rotation on its axis, between the observa- 
 tions of 1777 and 1779, than Herschel had employed. 
 
 In 1845, when Mars again occupied the same relative 
 position that it had done in 1830, it was too far south for 
 observation at Dorpat. 
 
 By combining Maedler's observation, made at Berlin, 
 1830, September 14, 12h. 30m., with one made at the Cin- 
 cinnati Observatory, 1845, August 30, 8h. 55m., making 
 the corrections due to geocentric longitude, phase, and aber- 
 ration, I find the period of rotation to be 24h. 37m. 20'6s. 
 differing by only two seconds from Maedler's period as last 
 corrected. 
 
 It is generally believed that Mars is surrounded by an 
 atmosphere which in many respects resembles our own. In 
 case this be true, we may anticipate the existence of belts of 
 clouds, and occasional cloudy regions, which would modify the 
 outline of the great tracts of sea and land, and would account 
 
92 POPULAR ASTRONOMY. 
 
 for the rapid changes which are sometimes noticed in the 
 surface of the planet. 
 
 The axis of the planet is inclined to its orbit (as may 
 readily be deduced from the rotation of the spots) under a?n 
 angle of a little more than 30 ; hence the variations of 
 climate and the changes of season in Mars will not be very 
 unlike those which mark the condition of our own planet. 
 Indeed, there are many strong points of resemblance in the 
 planetary features of the earth and this neighbouring world. 
 The planes of their orbits are but little inclined to each 
 other, a little less than 2. Their years are not widely 
 different, when we take into account the vast periods which 
 distinguish some of the more distant planets. 
 
 The seasons ought to be nearly alike, and the length of 
 day and night, as determined by the periods of rotation of 
 the two worlds, is nearly the same. In case the great 
 geographical outlines are alike, and seas and continents 
 really diversify the surface of Mars with an atmosphere and 
 clouds, the two worlds bear a strong resemblance to each 
 other. 
 
 The actual diameter of Mars is -only 4,100 miles, or a 
 little more than half the diameter of our earth, while its 
 volume is not much greater than one-tenth part of the 
 volume of our planet. 
 
 To the inhabitants of Mars (if such there be) the earth 
 and moon will present a very beautiful pair of indissolubly 
 united planets, showing all the phases which are presented 
 by Mercury and Yenus to our eyes, the two worlds never 
 parting company, and always remaining at a distance of 
 about a quarter of a degree, or about half the moon's appa- 
 rent diameter. 
 
 The amount of heat and light received from the sun by 
 Mars is about one-half of that which falls on the earth ; 
 and in case the planet were placed under the identical 
 circumstances which obtain on earth, the equatorial oceans 
 even would be solid ice. This, we have every reason to 
 believe, is not the case ; and hence we are induced to con- 
 
MAKS. 93 
 
 elude, as in other cases, that the light and heat of the sun 
 are subjected to special modifications, by atmospheric and 
 other causes, at the surfaces of each of the worlds dependent 
 on this great central orb. 
 
 The reddish tint which marks the light of Mars has been 
 attributed by Sir John Herschel to the prevailing colour of 
 its soil, while he considers the greenish hue of certain tracts 
 to distinguish them as covered with water. This is all pure 
 conjecture, based upon analogy and derived from our know- 
 ledge of what exists in our own planet. If we did not 
 know of the existence of seas on the earth, we could never 
 conjecture or surmise their existence in any neighbouring 
 world. Under what modification of circumstances sentient 
 beings may be placed, who inhabit the neighbouring worlds, 
 it is vain for us to imagine. 
 
 It would be most incredible to assert, as some have done, 
 that our planet, so small and insignificant in its proportions 
 when compared with other planets with which it is allied 
 is the only world in the whole universe filled with sentient, 
 rational, and intelligent beings capable of comprehending 
 the grand mysteries of the physical universe. 
 
94 POPULAR ASTRONOMY. 
 
 CHAPTER VI. 
 
 THE ASTEROIDS : A GROUP OF SMALL PLANETS, THE FIFTH 
 IN THE ORDER OF DISTANCE FROM THE SUN. 
 
 The Interplanetary Spaces. Kepler's Speculations. Great Interval 
 between Mars and Jupiter. Bode's Empirical Law. Conviction that 
 a Planet existed between Mars and Jupiter. Congress of Astronomers. 
 An Association organized to search for the Planet. Discovery of 
 Ceres. Lost in the solar beams. Rediscovered by Gauss. The New 
 Order disturbed by the Discovery of Pallas. Oiler's Hypothesis. 
 Discovery of Juno and Vesta. The search ceases. Renewed in 1845. 
 Many Asteroids discovered. Their Magnitude, Size, and probable 
 Number. 
 
 THE worlds thus far examined in our progress outward 
 from the sun have been known from the earliest ages. 
 Those constituting the group under consideration, called 
 asteroids, have all been discovered since the commence- 
 ment of the present century. 
 
 The circumstances attending the discovery of 
 CERES (1), OP THE ASTEROIDS, are replete with interest, 
 and demonstrate the power of the conviction in the human 
 mind, that, in the organization of the physical universe. 
 Borne systematic plan will be found to prevail. In draw- 
 ing to a scale the solar scheme of planetary orbits, it was 
 readily observed that the distances of the planets from the 
 sun increased in a sort of regular order up to the orbit of 
 Mars. Here, between Mars and Jupiter, there was found a 
 mighty interval, after which the order was restored as to the 
 planets beyond the orbit of Jupiter. 
 
 As early as the beginning of the seventeenth century, 
 Kepler, whose singular genius was captivated by mystical 
 numbers and curious analogies, conjectured the existence 
 of an undiscovered planet in this great space wliich inter- 
 vened between Mars and Jupiter. The thought thus thrown 
 out required no less than two hundred years to take root and 
 
THE ASTEROIDS. 95 
 
 yield its legitimate fruit. The discovery of a planet beyond 
 the orbit of Saturn, by Sir William Herschel, in 1781, greatly 
 strengthened the opinions based on the orderly arrangement 
 of the interplanetary spaces ; and the German astronomer 
 Bode, by the discovery of a curious relation, which seemed 
 to control the distances of the planets, gave additional force 
 and power to the conjecture of Kepler. This law is a very 
 remarkable one ; and, although no explanation could be 
 given of it, was verified in so many instances as almost to 
 force one to the conclusion that it must be a law of nature. 
 We present the law in a simple form. Write the series 
 
 0, 3, 6, 12, 24, 48, 96, &c. 
 
 add 4 4 4 4 4 4 4, &c. 
 
 Bum 4 7 10 16 28 52 100, &c. 
 
 Now, if ten be taken to represent the distance of the earth 
 from the sun, the other terms of the series will represent with 
 considerable truth the distances of the other planets, as we 
 may readily perceive; thus : 
 Mercury. Venus. Earth, Mars. Jupiter. Saturn. Uranus. 
 
 4 7 10 16 28 52 100 196 
 The true distances are roughly as under : 
 
 3-8 7-2 10 15-2 52 95-3 191-8 
 
 It is thus seen that the actual distances of the planets 
 agree in a most remarkable manner with those obtained by 
 the application of Bodds law ; and as no planet was yet 
 known to fill the distance (28) between Mars and Jupiter? 
 it required very little devotion to the analogies of nature 
 to create in any mind a firm belief in the existence of an 
 unknown planet. 
 
 The German astronomers, at the close of the last century, 
 took up the matter with earnest enthusiasm, and in the year 
 1800 a congress or convention of astronomers was assembled 
 .at Lilienthal, of which M. Shroeter was elected president 
 and Baron De Zach perpetual secretary. It was agreed to 
 commence a systematic search for the unknown planet, by 
 
96 POPULAR ASTRONOMY. 
 
 dividing the belt of the heavens near the sun's path, called 
 the zodiac (and within whose limits all the planetary 
 orbits are confined), among twenty-four astronomers, who 
 with their telescopes should search for the object in 
 question. 
 
 It was manifest that the unknown planet must be very 
 small too small to be visible to the naked eye, otherwise 
 its discovery must have been long since accomplished. It 
 might, however, prove to be large enough to exhibit a 
 planetary disc in the telescope, in which event a simple 
 search was all that was required. If, however, it should be 
 too diminutive to show a well-defined disc in the telescope, 
 then another method of examination would be required. 
 The planet could only be detected by its motion among the 
 fixed stars. This, indeed, is the way in which all the old 
 planets had been discovered ; but while the naked eye takes 
 in at the same time a large portion of the celestial sphere, 
 the telescope is extremely limited in its field of view, render- 
 ing the search laborious and difficult. Were it possible, how- 
 ever, to make an exact chart of all the stars in a given region 
 of the heavens to-night, if an examination on to-morrow 
 night of the same region should show a strange star among 
 those already charted, this stranger might with some pro- 
 bability be assumed to be a planet. 
 
 A few hours of patient watching would show whether it 
 was in motion ; and a few nights of observation would 
 reveal its rate of motion. 
 
 Such was the mode of research adopted by the society of 
 planet-hunters. The system thus adopted had been pursued 
 but a few months, when a most signal success crowned the 
 effort. On the night of the 1st January, 1801, Piazzi, of 
 Palermo, in Sicily, observed a star in the constellation 
 Taurus, which he suspected to be a stranger. On the 
 following night (having fixed its position anew with refer- 
 ence to the surrounding stars), he found it had changed 
 its place by an amount so large that its real motion could 
 not be doubted. The star was found to be retrograding, 
 
THE ASTEROIDS. 97 
 
 or moving backward, and this continued up to the 12th 
 January, when it became stationary. It was soon after lost 
 in the rays of the sun ; thus becoming invisible, before any 
 considerable portion of its orbit had been observed, and 
 before Piazzi could communicate his discovery to any mem- 
 ber of the society. 
 
 Piazzi, not considering it possible that a planet which had 
 remained hidden from mortal vision from its creation, could 
 be discovered with so little effort as had thus far been put 
 forth, conceived that the moving body which he had dis- 
 covered was a comet ; but the intelligence having been 
 communicated to the society, Bode promptly pronounced 
 this to be the long-sought planet, an opinion in which he 
 was sustained by Holbers and Buckhardt, Baron de Zach, 
 and Gauss, and I know not by how many other members of 
 the society. 
 
 It now became a matter of the deepest interest to 
 re-discover this stranger after its emergence from the sun's 
 rays, a task of no little difficulty, as we may see by the 
 slightest reflection. The star had been followed through 
 only about 4 of its orbit, and on this slender basis it seemed 
 almost impossible to erect a superstructure such as miglit 
 conduct the astronomer to the point occupied at any given 
 time by this almost invisible world. We shall see hereafter 
 that this most astonishing feat was successfully accomplished 
 by the German mathematician and astronomer Gauss, then 
 quite a young man, and who, in this early effort, gave evidence 
 of that high ability for which he became afterwards so greatly 
 distinguished. 
 
 Ceres being re-discovered, and closely observed, the data 
 were soon obtained for the exact computation of the elements 
 of its orbit, when it was found to occupy, in the planetary 
 system, the precise position which had been assigned to it 
 fifteen years before by Baron de Zach, in accordance with the 
 indications of the curious empirical rule, already presented, 
 known as Bodes law. 
 
 The harmony of the system was thus fully established, 
 
 H 
 
98 POPULAR ASTRONOMY. 
 
 the missing term in the series was now filled. The vast 
 interplanetary space between Mars and Jupiter was the 
 real locality of a discovered world, whose existence had 
 been conjectured by Kepler two hundred years before, and 
 whose discovery, by combined systematic and scientific 
 examination, constituted the crowning glory of the age. 
 True, the new planet was exceedingly small when compared 
 with any of the old planets, yet it acknowledged obedience 
 to the great laws established by Kepler, revolving in an 
 elliptical orbit of very considerable eccentricity, and sweep- 
 ing round the sun in a period of about four years and nine 
 months, and at a mean distance of about 263 millions of 
 
 The telescope yielded but little information as to the 
 absolute magnitude and condition of Ceres. Its diameter 
 has been measured by various astronomers, but the results 
 are so discordant that but little confidence is to be placed 
 in them. It cannot, probably, exceed 1,000 miles, and may 
 be much less. It is supposed to be surrounded by an 
 extensive atmosphere, but the evidence of this is not very 
 reliable. Under favourable circumstances, and with a power- 
 ful telescope, a disc can sometimes be seen, but for the 
 most part Ceres presents the appearance of a star of about 
 the eighth magnitude. 
 
 Such was the condition of astronomy, affording to those 
 interested cause for high gratification in the now known 
 orderly distribution of the planetary orbs, when an announce- 
 ment was made which was received with profound astonish- 
 ment, as it at once introduced confusion precisely at the 
 point in which order had been so lately restored. This 
 was the discovery of another small planet, by Olbers of 
 Bremen, revolving in an orbit nearly equal to that occupied 
 by Ceres. Computation and observation united in fixing, 
 beyond doubt, this most extraordinary discovery, and the 
 new and anomalous body received the name of Pallas. The 
 exact elements of the orbit of Pallas having been deter- 
 mined, it was found that a very near approximation to 
 
THE ASTEROIDS. 99 
 
 equality existed between the mean distances and periods of 
 Ceres and Pallas, as we find below : 
 
 Ceres' period of revolution 1,682-125 day*. 
 
 Pallas' 1,686-510 
 
 Ceres' mean distance 262,960,000 miles. 
 
 Pallas' 263,435,000 
 
 Here we find the mean distances and periods so nearly 
 equal, that, in case the planes of the orbits of the two 
 planets had chanced to coincide, these two worlds might 
 travel side by side for a long while, and at a distance from 
 each other only about double the distance separating the 
 earth from her satellite. The distance between Mars and 
 Ceres is no less than 120,000,000 of miles. The distance 
 from Ceres' orbit to that of Jupiter is more than 280,000,000 
 of miles ; and yet, here are two planets which may approach 
 each other to within a distance less than half a million of 
 miles. 
 
 It is true, the eccentricities of the orbits differ greatly, and 
 the inclinations of their orbital planes are also very great ; 
 so that Pallas, by this inclination, is carried far beyond the 
 limits within which the planetary excursions north and south 
 of the ecliptic had been previously confined ; yet a time 
 would come in the countless revolutions of these remark- 
 able worlds, when each would fill, at the same time, points 
 of the common line of intersection of their orbital planes ; 
 and these two points, owing to the revolutions of the peri- 
 helion, might, possibly, at some future period, come to 
 coincide. 
 
 In case these speculations were within the limits of the 
 probable, and if it were permitted to anticipate in the future 
 the possible collision or union of these minute planets, a like 
 train of reasoning, running back into the past, would lead to 
 the conclusion that in case their revolution had been in 
 progress for unnumbered ages, there was a time in the past 
 when these two independent worlds might have occupied 
 the same point in space ; and hence the thought that possibly 
 they were fragments of some great planet, which, by the 
 
 ii 2 
 
100 POPULAR ASTRONOMY. 
 
 power of some tremendous internal convulsion, had been 
 burst into many separate fragments. This strange hypo- 
 thesis was first propounded by Dr. Olbers, and has met with 
 more or less favour from succeeding astronomers, even up to 
 the present day, as we shall see hereafter. 
 
 True or false, it soon produced very positive results, for it 
 occasioned a renewal of the research which had been dis- 
 continued after the discovery of Ceres, and in a few years 
 two more planets were added to the list of asteroids. The 
 search was long continued, and it was not until the end of 
 fifteen years that Olbers and his associates became satisfied 
 that no more discoveries could be expected to reward their 
 diligence. Thus it became a received doctrine, that, in case 
 a large planet had been rent asunder by some internal explo- 
 sive power, it had been burst into four pieces, and that no 
 other fragments existed sufficiently large to be detected 
 even by telescopic power. 
 
 This opinion prevailed up to December, 1845, when the 
 astronomical world was somewhat startled by the announce- 
 ment of a new asteroid, discovered by Hencke, of Dresden. 
 This event awakened attention to this subject, and a new 
 generation of observers entered the field of research, whose 
 efforts have resulted in revealing a large group of small 
 planets, of which no less than fifty-five have already been 
 discovered, and their orbits computed.* 
 
 The theory of the disruption of one great planet as the 
 origin of the asteroids has been revived and extensively 
 discussed, but thus far no satisfactory conclusion has been 
 reached. So strangely are the orbits of these bodies related 
 to each other, that, in case they all lay on th'e same plane, 
 they would in some instances intersect each other, exhibiting 
 relations nowhere else found in the solar system. None of 
 the asteroids are visible to the naked eye, nor are they dis- 
 tinguishable from the stars with the telescope except under 
 the most favourable circumstances. When carefully watched, 
 
 * Three more of these Asteroids have been lately discovered ; making a 
 total of fifty-eight. 
 
JUPITER. 101 
 
 some of them exhibit rapid changes in the intensity of theil 
 light, sometimes suddenly increasing in brightness, and 
 again as rapidly fading out. These changes have been ac- 
 counted for on the supposition that these worlds are indeed 
 angular fragments ; and that, rotating on an axis, they 
 sometimes present large reflective surfaces, and again angular 
 points, from whence but a small amount of light reaches the 
 earth. 
 
 As the stars of the smaller magnitudes are becoming more 
 extensively and accurately charted, their places being deter- 
 mined with great precision, we may anticipate a large 
 increase in the number of known asteroids during the 
 remainder of the current century, and so forward ; for, if so 
 great a multitude has already been revealed almost without 
 effort, and nearly by accident, what must be the result when 
 a systematic scheme of examination shall have been executed, 
 based on an accurate knowledge of the places of all the stars 
 down to the twelfth magnitude % We have just ground for 
 supposing that there are thousands of these little worlds 
 revolving in space. 
 
 CHAPTER VII. 
 
 JUPITER, ATTENDED BY FOUR MOONS, THE. SIXTH PLANET 
 IN THE ORDER OF DISTANCE FROM THE SUN. 
 
 Arc' of Retrogradation. Stationary Point. Distance of the Planet deter- 
 mined. Periodic Time. Synodical Revolution gives the Sidereal. 
 Surface of Jupiter as given by the Telescope. Period of Rotation. 
 Diameter. Volume. Mean Distance. Amount of Light and Heat. 
 Figure of Jupiter. Equatorial and Polar Diameters. Discovery of the 
 Four Moons by Galileo. Effect on the Copernican Theory. Jupiter's 
 Nocturnal Heavens. 
 
 THE SATELLITES OP JUPITER. How discovered. Their Magnitude. 
 Form of their Orbits. Period of Revolution. Eclipses. Transits. 
 Occultations. Velocity of Light discovered. Terrestrial Longitude. 
 Rotation of these Moons on an Axis. 
 
 IN passing from the diminutive asteroids to the magnitude 
 and splendour which distinguish the vast orb which holds 
 
102 POPULAR ASTRONOMY. 
 
 the next position in the planetary system, we are the more 
 disposed to adopt the theory that the exceeding disparity 
 now existing in the magnitude of these neighbouring worlds 
 is due to the fact that the asteroids are but a few of the 
 fragments of some object in which they were all once united. 
 We shall hereafter present a speculation on this subject, 
 which seems entitled to consideration. 
 
 The planet Jupiter is one of the five revolving worlds 
 discovered in the primitive ages. Its revolution among the 
 fixed stars is slow and majestic, comporting well with its 
 vast dimensions, and the dignity conferred by four tributary 
 worlds. 
 
 Like all the old planets, the ancients had determined 
 with considerable precision the period of revolution of 
 Jupiter, and his relative position among the planetary 
 worlds. The points in his orbit where he becomes sta- 
 tionary, the arc over which he retrogrades, and his period 
 of retrogradation, were all pretty well determined from the 
 early observations. 
 
 As we recede to greater distances from the sun, the arc 
 of retrogradation diminishes in extent, while the time em- 
 ployed in describing these arcs must by necessity increase. 
 This will become evident if we recall to mind the cause of 
 this apparent retrogradation. When the sun, earth, and 
 planet are all on the same straight line, the earth and planet 
 being on the same side of the sun, then the planet is exactly 
 in opposition. The earth and planet starting from this line, 
 as the earth moves the swifter in its orbit, at the end of, say 
 twenty-four hours, the line joining the earth and planet will 
 take a direction such, that it will meet the first line exterior 
 to the orbit of the planet, as seen below : 
 
JUPITER. 
 
 103 
 
 O E P is the line on which the three bodies are found on 
 the day of opposition. At the ei>d of, say twenty-four 
 hours, the earth arrives at E' in its orbit, the planet at P', 
 and then the planet is seen from the earth in the direction 
 E'P'S', whereas on the day previous it was seen in the 
 direction EPS. Thus it appears to have moved backwards 
 from S to S' among the fixed stars, while in reality it has 
 moved forward in its orbit from P to P'. Admitting the 
 orbits to be circles and the motions to be uniform, it is very 
 easy to locate the places of the earth and planet on suc- 
 cessive days after opposition, and joining those places by 
 straight lines, we should soon reach a position in which the 
 lines- thus drawn on consecutive days would be parallel. 
 There the planet would appear stationary among the fixed 
 stars, and there its advance would commence, as is manifest 
 from the figure below 
 
 in which S is the sun, E E' E" E'" the successive places of 
 the earth, P P' P" P'" the successive places of the planet. 
 The lines E P and E' P' meet on the side opposite the sun, 
 the lines E 7 P' and E" P" also meet on the same side ; but 
 E'" P'" and E" P" are parallels, and in P" the planet becomes 
 stationary; and after passing this point, the earth still 
 advancing, the lines joining the earth and planet meet on 
 the side next the earth, and henceforward the motion of the 
 planet, as seen from the earth, must continue to be direct, 
 until the earth comes round again to occupy the conjunction- 
 
104 POPULAR ASTRONOMY. 
 
 line, previous to which the stationary point will be passed, 
 and the retrogradation will be commenced. 
 
 The distance of any planet from the sun, in terms of the 
 earth's distance, may be obtained from a measurement of the 
 arc of retrogradation in a given time, say twenty -four hours, 
 provided we know the periodic time in which the earth and 
 planet revolve round the sun. This will become evident 
 from the figure below 
 
 in which S is the sun, E and P the places of the earth and 
 planet on the day of opposition, E' and P' their places at the 
 end of twenty-four hours. E E' and P P' may be regarded 
 as straight lines, as they are very short in comparison with 
 the entire circumference. As we are 'supposed to know the 
 periods of revolution of the earth and planet, the distances, 
 E' E and P P', are fractional parts of the whole circum- 
 ference, represented by one, divided by the number of days 
 in the periodic time. The fraction for the earth is -5-5-5-. 2-$, 
 and for Jupiter it is 433 1 2 .- rg -. 
 
 Tn the right-angled triangle E' E O, we know the value 
 of E' E, and the angle, E' O E, equal to S' O S", or the re- 
 tcogradation of the planet. Hence the other parts become 
 known either by construction or the simplest processes of 
 trigonometry. We thus determine the value of E O, 
 and adding S E, we have the value of S 0. Then in the 
 triangle S P' O, we have the side S 0, just determined, also 
 the angles P' S O and P' S. Hence we can construct the 
 
JUPITER. 105 
 
 triangle, or compute by trigonometry the other parts. Thus 
 S P', the planet's distance, becomes known. 
 
 In case the periodic times were accurately known, and 
 the orbits were exact circles, this mode of determining the 
 distance of a superior planet would be sufficiently exact ; but 
 by the third of Kepler's laws, which tells us that the squares 
 of the periodic times are proportional to the cubes of the 
 mean distances, we perceive that the entire problem of the 
 planetary distances resolves itself into fixing, with all pos- 
 sible precision, from observation, the periods of revolution, 
 and then in obtaining the exact distance of any one of 
 them. 
 
 We have already stated that the interval elapsing from 
 the passage of a planet from one side of the ecliptic to the 
 other, up to the same again, gives the period of revolution, 
 in case we correct for the various changes which may take 
 place from one node-passage to the next. This, however, in 
 the case of a planet like Jupiter, whose orbital plane nearly 
 coincides with the ecliptic, becomes difficult as a matter of 
 observation, and hence some better method must be employed. 
 This is best accomplished by observing tho exact time of 
 opposition, or the moment when the planet is 180 distant 
 from the sun. 
 
 The interval between two such oppositions is called a 
 synodical revolution, and in case the earth did not move, 
 would be the planet's period of revolution around the sun. 
 These synodical revolutions would be all precisely equal on 
 the hypothesis of circular orbits and equable motions. But 
 as the planetary orbits are elliptical, and hence the motions 
 variable, the synodical revolutions of any planet, as Jupiter, 
 will vary somewhat from each other in duration. If, how- 
 ever, a large number be counted, say as many as have occurred 
 in a thousand, or even two thousand years, then a mean 
 period is deduced of great accuracy. 
 
 This is possible, as we have the oppositions of the old 
 planets recorded by the ancients with sufficient precisioD 
 to be employed in such a discussion. 
 
106 POPULAR ASTRONOMY. 
 
 To derive the sidereal revolution from the synodical, w 
 have only to consider that the two bodies set out from the 
 same right line. The earth's velocity is known ; the time 
 required for the earth to overtake the planet is known (the 
 synodical revolution). The velocity or rate of the planet's 
 motion is required. This is readily found by simple pro- 
 portion. Take the following example : In a mean solar 
 day the earth travels in its orbit 0-9856. A mean syno- 
 dical revolution of Jupiter is observed to be equal to 398*867 
 solar days. But the earth performs its revolution, and comes 
 again to the starting-point in 365-256 days, and then must 
 travel for 398-867 365-256=33-611 days before overtaking 
 Jupiter. But in 33-611 days, at the rate of 0-9856 per 
 diem, the earth will travel about 33*128 ; and this is the 
 whole distance made by Jupiter in 398*867 days. Hence 
 his rate per diem is, ^^V=4'99=4'59''*2 ; and, at this 
 
 360 
 rate, to travel 360 will require ^/ 59 ,,. 9 =4*332d. 14h. 2m., 
 
 which is the time occupied by Jupiter in performing his 
 revolution around the sun. 
 
 These methods of investigation, which are perfectly simple, 
 were employed by the ancients, and used even by Copernicus, 
 Kepler, and others, and furnished the approximate values 
 of the periods and distances employed in the researches of 
 Kepler, whereby he discovered his celebrated laws. 
 
 PHYSICAL CONSTITUTION OF JUPITER. When examined 
 with powerful telescopes, the surface of Jupiter is found to 
 be diversified with shades of greater or less depth, forming 
 parallel bands or belts, especially about the equator of the 
 planet. 
 
 Upon these belts well-defined breaks, irregularities, and 
 spots are discerned, by means of which it is discovered that 
 the face of Jupiter, visible at any given time, is completely 
 hidden by rotation on an axis, a new face appearing at the 
 end of a little less than Jive hours. This gives a period of 
 axial rotation of 9h. 55m. 49*7s., as the result of investiga- 
 
JUPITER 
 
 ALLA VISTA, TENERIFFE, 1856 
 
JUPITER. 107 
 
 tions similar to those employed in determining the period of 
 rotation of Mars. 
 
 When the apparent diameter of Jupiter is accurately 
 measured, and his distance is taken into consideration, we 
 Snd his actual diameter to be nearly 90,000 miles, and his 
 volume to be equal to that of 1,281 globes such as our 
 earth. 
 
 The dark belts which encircle the equatorial regions of 
 the planet, and which revolve with the globe, show that the 
 axis of rotation is very nearly perpendicular to the plane of 
 the orbit. 
 
 Thus we have a planet twelve hundred and eighty-one 
 times larger than our earth, rotating on an axis but little 
 inclined to the plane of its orbit, in less than ten hours of 
 time, and sweeping round the sun in about twelve of our 
 years, at a mean distance of about 485,000,000 of miles. 
 
 The streaks and dark shades which distinguish the 
 equatorial region of Jupiter, are by many considered to be 
 belts of clouds floating in the atmosphere of the planet, thus 
 indicating the existence of all the great elements which dis- 
 tinguish the earth. In consequence of the fact that the axis 
 of Jupiter is very nearly perpendicular to the plane of the 
 orbit, the sun will always pour his rays vertically on the 
 equator of the planet, constituting one perpetual summer in 
 all parts of the globe. In case light and heat are governed 
 by the same laws which hold on the earth, 'the inhabitants 
 of Jupiter will receive from the sun only one twenty-seventh 
 part as much light and heat as falls on the earth. What 
 modifications of heat may be effected by the extensive 
 atmosphere which appears to surround Jupiter, if is im- 
 possible to conjecture. We may suppose, without reflection, 
 that a world would be only dimly illumined whose sun was 
 reduced to one twenty-seventh part of that which lights our 
 earth. This, however, is not the case, as any one will credit 
 who has ever witnessed the flood of light poured forth from 
 ihe smallest portion of the sun's disc in emerging from total 
 
108 POPULAR ASTRONOMY. 
 
 eclipse. The amount of light which falls on Jupiter far 
 exceeds that which is poured upon the earth on a moderately 
 cloudy day. 
 
 When we measure rigorously with the micrometer, the 
 figure of Jupiter's disc, we find a marked deviation from the 
 circular outline. This is analogous to the figures of the 
 earth and Mars, and indeed the same peculiarity (of which 
 a satisfactory account will be given hereafter) distinguishes 
 all the planets. In Jupiter the equatorial diameter exceeds 
 the polar by more than six thousand miles. 
 
 We are indebted to the telescope for the revelation of 
 the highly interesting fact that Jupiter is attended by no 
 less than four moons or satellites, nearly all of them larger 
 than our own moon. These satellites were discovered by 
 Galileo in 1610, soon after he had finished his second 
 telescope, which, as he tells us, cost him incredible pains, and 
 which bore a magnifying power of about thirty times. The 
 discovery of these moons of Jupiter may be regarded as 
 among the most important results of the application of the 
 telescope, if we take into account the then existing condition 
 of astronomical science. The scientific world was just in a 
 transition- state. The most honest, intelligent, and powerful 
 minds had already adopted the Copernican theory ; but in 
 the universities and other schools of science, as well as in 
 the church, the system of Ptolemy still reckoned among its 
 supporters a host of learned and dignified men. The beau- 
 tiful miniature of the solar system presented in Jupiter and 
 his moons, as given by Copernicus, could not fail to exert a 
 most powerful influence over all candid and unprejudiced 
 minds. Here was presented to the eye a central orb, and 
 about it a scheme of dependent worlds revolving in circular 
 orbits, and with such elegant simplicity as to shame the 
 cumbrous complexity which distinguished the epicyclical 
 theory of the old Greek school. Ifc is not at all surprising 
 that Galileo, the discoverer of this beautiful system, should 
 have become one of the most ardent supporters of the doc- 
 trines of Copernicus. 
 
JUPITER. 109 
 
 These satellites of Jupiter revolve in orbits whose planes 
 are nearly coincident with the equator of their primary. 
 The exterior, or most distant of the four, revolves in an 
 f>rbit somewhat inclined to the plane of J upiter's equator ; 
 out the three inner satellites, at every revolution, eclipse 
 the sun to the inhabitants of Jupiter, and are themselves 
 eclipsed in passing through the shadow of their primary. 
 The same phases which mark the revolution of our moon, 
 are also exhibited by Jupiter's moons ; and the periods of 
 revolution of three of the satellites are so adjusted that one 
 of them must be full when the other two are new. 
 
 The nocturnal heavens, as seen from this grand orb, must 
 be inexpressibly magnificent. Besides the same glittering 
 constellations which are seen from the earth, the sky of Jupiter 
 may be adorned with no less than four moons, with their 
 diverse phases, some waxing or waning, some just rising or 
 setting, some possibly just entering into or emerging from 
 eclipse. 
 
 The whole of this splendid celestial exhibition, sweeping 
 across the heavens, rising, culminating, and setting, in less 
 than five hours of our time ! Such are the scenes witnessed 
 by the inhabitants of Jupiter, if such there be. 
 
 THE SATELLITES OF JUPITER. As already stated, these 
 tributary worlds were discovered by Galileo in 1610. On 
 the evening of January the 8th, of that year, having com- 
 pleted his second telescope, capable of bearing a magnifying 
 power of thirty times, he went to his garden to test its 
 quality by an examination of Jupiter. Near the planet he 
 noticed three small stars, nearly in a straight line, passing 
 through the centre of Jupiter. He supposed them to be 
 fixed stars, but carefully noted their positions with reference 
 to Jupiter and to each other. On the following night he 
 remarked that there was a manifest change in the relative 
 places of these stars and the planet, which could hardly be 
 accounted for by the motion of Jupiter in his orbit. 
 
 Galileo began to suspect the true nature of the stars 
 which had attracted his attention, and seeing clearly the 
 
110 POPULAR ASTRONOMY. 
 
 immense importance of such a discovery, awaited with great 
 impatience the coming of the next evening to confirm his 
 conjectures. Clouds, however, coming up, disappointed his 
 hopes, and it was not until the evening of the 14th that he 
 was again permitted to direct his telescope to the planet, 
 when he found, to his great delight, not only the three stars 
 still in close proximity to the planet, but he also detected a 
 fourth one, whose appearance and position were such that 
 he announced at once the discovery of four moons resembling 
 our own, and revolving about the planet Jupiter as their 
 central orb. 
 
 This announcement created the greatest excitement in 
 the astronomical world. Its effect on the old theory ot 
 astronomy was at once perceived, and the disciples ot 
 Ptolemy determined that they would never believe in the 
 existence of any such pestilent worlds. Some of them 
 actually refused to do so much as look through the tube of 
 Galileo, declaring the whole was a deception, and unworthy 
 the attention of a true philosopher. 
 
 The discovery was not the less real because its truth was 
 denied, and to this important addition to the bodies which 
 constitute our system modern science is indebted for some 
 of its most elegant discoveries. 
 
 The great distance at which we are compelled to examine 
 these bodies has rendered it difficult to obtain, even with 
 our most delicate instruments, satisfactory measures of the 
 diameters of these satellites. Approximate measures have 
 been obtained, from which we learn that the nearest satellite 
 has a diameter of about 2,500 miles; the second, 2,068 ; the 
 third, 2,377 ; the fourth, 2,800 miles. We name them in 
 the order of their distances from the primary. 
 
 By careful measures of the elongations, or greatest distances 
 to which these bodies recede from their primary, the magni- 
 tude and form of their orbits have been well determined. 
 The first satellite is thus found to revolve round Jupiter in 
 an orbit nearly circular, whose diameter is 260,000 miles, in 
 A period of Id. 18h. 28m. The plane on which the orbit 
 
JUPITER. 1 1 1 
 
 lies is inclined to the plane of Jupiter's orbit, under an 
 angle of 3 05' 30", or less, by nearly one-half, than the 
 angle made by the moon's orbit with that of the earth. 
 The smallness of this angle, the nearness of the satellite to 
 its primary, the immense magnitude of the primary, and the 
 distance from the sun, combine to produce an eclipse of the 
 first satellite at every revolution ; while, in like manner, an 
 eclipse of the sun takes place quite as frequently, from the 
 fact that the shadow of the satellite falls on the planet at 
 every conjunction of the satellite with the sun. These 
 statements are not mere conjectures. They are verified by 
 the telescope j for these eclipses of the satellite and the 
 shadows cast on the primary are distinctly seen from the 
 earth, and furnish the data whereby the periods of revolu- 
 tion are determined with great precision. When Jupiter is 
 in opposition, it often occurs that the satellite when on the 
 hither side of the primary, is seen projected on the disc of 
 the planet as a round bright spot, while the shadow of the 
 same body may be seen in close proximity as a round black 
 spot. Any eye, situated within the limits of this shadow, 
 will witness an eclipse of the sun precisely such as is pro- 
 duced on earth by the shadow of the moon. The passage 
 of the satellite across the disc of Jupiter is called a transit. 
 From this position the moon of Jupiter revolves round half 
 its orbit, and then by necessity passes across the cone of 
 shadow cast by the primary in a direction opposite the sun. 
 Here we behold an eclipse of the secondary, as its light is 
 extinguished on entering the shadow, and is only regained 
 after passing beyond the limits of the shadow ; thus de- 
 monstrating beyond a doubt the fact that, like our moon, 
 these secondaries of Jupiter shine only by reflecting the 
 light of the sun. 
 
 In case Jupiter were at rest, it is evident that the obser- 
 vations of these eclipses would give the exact period of 
 revolution of the satellite, which would be precisely the 
 interval from one eclipse to the next. The fact that the 
 -earth is in motion would not affect the time of recurrence 
 
112 POPULAR ASTRONOMY. 
 
 of the eclipse ; for this would be entirely independent of 
 the place of the spectator, provided he sees the disappear- 
 ance of the satellite at the moment its light is extinguished. 
 It is manifest that the motion of Jupiter in his orbit will 
 change the position of the axis of the shadow, and as the 
 satellite revolves in the same direction in which the shadow 
 advances, it is clear that the time from one eclipse to the 
 next, is longer than the true period of revolution of the 
 satellite, by a quantity easily computed from the known 
 orbital velocity of the planet, as may be seen from the 
 figure below, where 
 
 S is the sun's place ; E, the earth; J, Jupiter in opposition ; 
 M, the satellite in eclipse. At the end of one exact revolu- 
 tion of the satellite, Jupiter has reached J', the satellite is 
 at M', but the axis of shadow is now J' M" ; and the centre 
 of the eclipse will not occur until the satellite reaches M", 
 passing over the angle M" J' M'. This angle is precisely 
 equal to the angular motion from eclipse to eclipse, a quan- 
 tity easily determined. The satellite will then revolve 360, 
 4- the angle JSJ', or M' J' M", in the interval from one 
 eclipse to the next ; hence the rate per hour becomes known, 
 and gives at once the period of revolution. 
 
 Galileo devoted himself for many years to a careful 
 observation of the eclipses of Jupiter's moons, and finally 
 constructed tables whereby these eclipses might be predicted 
 with tolerable precision. His successors devoted much time 
 to the same subject, for a reason we will give hereafter. 
 Long study of these phenomena revealed the curious fact 
 
JUPITER. 1 ] 3 
 
 that the interval from one eclipse to the next did not fulfil 
 the prediction based on the foregoing reasoning. The place 
 of the earth seemed in some mysterious way connected with 
 the time at which the eclipse occurred. This may to some 
 appear very reasonable j but, in fact, on the hypotheses that 
 at the moment of the extinction of a luminous object it 
 ceases to be visible, the place of the earth in its orbit, or 
 the position of the observer, could in no way affect the 
 moment of the satellite's disappearance by entering the 
 shadow of its primary. This will become manifest from a 
 very simple illustration. Suppose the persons in a large 
 circular hall to be gazing on the light of a taper, and the 
 taper is suddenly extinguished by being blown out, every 
 observer will certainly lose the light at the same absolute 
 moment, admitting the fact that the light dies at the instant 
 of extinction to every eye. Let us apply this illustration to 
 the eclipses of Jupiter's moons. They are only seen when 
 the sunlight falls on them. Cut off from them the sunlight 
 by entering the shadow of the primary, and admitting this 
 entrance to be instantaneous, every eye everywhere should 
 lose the light at the same moment of absolute time. 
 
 The earth's position in its orbit ought, therefore, to have 
 no effect on the time of the eclipse, and yet it became clearly 
 manifest that the earth's place was in some way connected 
 with certain irregularities in the intervals of these remote 
 eclipses. This matter will be best illustrated from the 
 figure below, in which S represents the sun, E E' E" E"' the 
 
 B' 
 
 earth's orbit, J Jupiter, and s the satellite. It was found 
 that when the earth was at E, or nearest to Jupiter, the 
 interval from eclipse to eclipse grew longer as the earth 
 receded from Jupiter. At E' the interval was at a maximum. 
 
 T 
 
114 POPULAR ASTRONOMY. 
 
 It now diminished by slow degrees, becoming nearly sta- 
 tionary at E", then growing shorter, reached a minimum at 
 E'", after which a slow increase was noticed up to E, and so 
 on in every revolution of the earth in its orbit. Due account, 
 of course, must be taken of the orbital movement of Jupiter, 
 f n case the student is ignorant of the explanation of these 
 variations in the synodical revolutions of the moons of 
 Jupiter, he may test his own powers of discovery by a closa 
 examination of the facts, as above presented. All the 
 satellites gave evidence of the same facts, and the irregu- 
 larities were found to follow in the same order, reaching 
 their maxima, minima, and stationary points at the same 
 time, or when the earth was at the same point of its orbit. 
 
 More than fifty years passed away without any satisfactory 
 explanation of the facts and phenomena above recorded 
 when, in 1675, Roemer was at length successful in solving 
 the mystery, and found it due to the progressive motion of 
 light, which up to this time had been considered by all 
 philosophers as instantaneous in its effects ; that is, if a 
 luminous body were created, all eyes, no matter how remotely 
 placed, would see the light at the same moment of time. 
 As the velocity of light, deduced from these investigations, 
 is so enormous, no less than 192,000 miles in one second, we 
 will enter into the explanation somewhat minutely. Suppose 
 a luminous body, as in the figure below, at S, suddenly to be 
 extinguished, the stream of light flowing from the body is 
 
 $& A B 
 
 S 
 
 at once cut off, and when the last particles or wave passes a 
 spectator at A, at that moment he will mark the ex- 
 tinction of the light, while to the spectator at B the really 
 extinct luminous body will remain visible until the last 
 particles of the stream of its light pass B, and then the body 
 vanishes to the spectator at B. Suppose the body to thus 
 disappear periodically, A and B will, while they remain 
 stationary, note the intervals from one disappearance to the 
 
JUPITER. 115 
 
 next to be precisely equal, and the interval, as observed by 
 A, though beginning at an earlier absolute moment of time, 
 will be equal to the interval, as observed at B. Let us now 
 suppose, that after a disappearance, and before the next, A 
 removes to B, it is manifest that the duration or period 
 whose beginning was observed at A, but whose ending was 
 noted at B, will be longer than it was before by an amount 
 of time required for the stream of light to pass from A to B. 
 The reverse would be true if B changed his position to A 
 
 These principles are precisely applicable to the case under 
 consideration. If the earth's orbit were a straight line, with 
 a length equal to A B, the conditions would be identical. 
 The nearly circular figure of the earth's orbit produces the 
 variations already noticed. When the earth is rapidly 
 receding from the source of light, the duration of the synod- 
 ical revolution of Jupiter's moon will be increased by the 
 time required for the light to pass over the space traversed 
 by the earth during the synodic revolution. This period 
 amounts to some seventeen days for the fourth satellite. 
 But the earth travels some 68,000 miles an hour, or in 
 seventeen days nearly thirty millions of miles ; so that the 
 synodical revolution, when longest, will exceed the same 
 period when shortest by an amount equal to the double 
 time required by light to travel 30,000,000 of miles. This 
 difference between the maximum and minimum synodic 
 periods, proved to be about five minutes, and hence it 
 became evident that light must fly at the rate of sixty 
 millions of miles in five minutes, or 12,000,000 miles in one 
 minute, or 192,000 miles per second. 
 
 Should this result appear incredible, we shall find hereafter 
 abundant confirmation of its truth by a train of reasoning 
 and phenomena entirely distinct from what have just been 
 given, 
 
 In case light travels with a finite velocity, we cannot fail 
 to perceive that this fact will introduce important modifica- 
 tions in all observations designed to fix the places of the 
 heavenly bodies at a given moment of time. Since the 
 
 i 2 
 
116 POPULAR ASTRONOMY. 
 
 earth is sweeping through space with great velocity, eveo 
 this fact will produce a certain displacement in the apparent 
 place of a fixed luminous body. When the body unde.' 
 observation is in motion, the velocity of light being finite, it 
 is clear that the light which falls on the eye of the spectator, 
 and which enables him to see the object, is not the light 
 emitted at the moment the object is seen. Thus, the planet 
 Jupiter is distant from the earth, say 480,000,000 of miles. 
 To travel this distance his light must occupy no less than 
 forty minutes, during which time Jupiter has advanced in 
 his orbit about one-third of his own diameter. During the 
 same time the earth has travelled in its orbit a certain 
 distance nearer to or further from Jupiter, which must be 
 taken into account in our effort to fix the absolute position 
 of the planet's centre at a given moment. This subject will 
 'be resumed when we come to consider the means and 
 instruments employed in astronomical observation. 
 
 The satellites of Jupiter have furnished, in their eclipses, 
 the earliest method of resolving the great problem of 
 
 TERRESTRIAL LONGITUDE. The position of any place on 
 the earth's surface is determined by fixing its distance 
 from the equator of the earth, north or south, called the 
 latitude, and also its distance east or west of any given 
 meridian line, called the longitude. The first of these 
 elements is very readily determined. In case a place is 
 situated on the equator, its latitude is zero, and to any 
 spectator at this place, as we have already shown, the poles 
 of the earth and heavens will lie on the horizon. Leaving 
 the equator and travelling due north along a meridian-line, 
 fore very degree we go north it is evident the pole of the 
 heavens will rise one degree above the horizon j and when 
 we reach the north pole of the earth, the north pole of the 
 heavens will be on the zenith, or ninety degrees above the 
 horizon. 
 
 Thus it appears that the latitude of any place is equal to 
 the elevation of the pole above the horizon of the place, and to 
 fix the latitude we have only to measure this angle of 
 
JUPITER. 117 
 
 elevation with a suitable instrument, and apply certain 
 corrections, to be hereafter explained. The problem of the 
 longitude does not admit of so easy a solution. To determine 
 accurately longitude at sea is a matter of the highest 
 importance to commerce and navigation, a problem for 
 whose solution maritime nations have in modern times 
 offered large rewards. The safety of a vessel, its crew and 
 cargo, depends on learning by some method its exact position 
 on the surface of the ocean, where there are no permanent 
 objects on our globe to mark its place ; and it is only from 
 the celestial sphere that it becomes possible to select fixed 
 objects which may reveal to the mariner the dangers by 
 which he is surrounded. 
 
 The latitude, as we have seen, is readily obtained \ not so 
 the longitude, which had, up to the time of Galileo,* been 
 regarded as almost an impossible problem at sea. The great 
 Florentine astronomer saw in the eclipses of the moons of 
 Jupiter the means of solving this highly-important problem ; 
 and to this end he devoted many years to most diligent and 
 careful observation of these eclipses, with a view to be able 
 to predict their coming, months or even years in advance. 
 We will now explain how these predicted eclipses of Jupiter's 
 satellites, conjoined with their actual observation, may be 
 employed in the determination of terrestrial longitude. 
 
 As the earth rotates on its axis with uniform velocity, 
 the 360 degrees of the earth's equator are fairly represented 
 by twenty-four hours of time. Thus an hour of time is 
 equal to 15 of longitude, a minute of time is equal to 4' oi 
 longitude, a second of time is equal to 4" of longitude. The 
 difference of longitude, then, of any two places on the earth's 
 surface is nothing more than the difference of local time ; for 
 a mean time solar clock marks Oh. 00m. OOs. when the centre 
 of an imaginary sun, moving with the mean or average 
 velocity of the true sun, reaches the meridian of the place 
 in question. A place west of the first one will have the 
 
 * Galileo flourished about 250 years ago, at Florence, in Tuscany. 
 
118 POPULAR ASTRONOMY. 
 
 centre of the mean sun on its meridian later by an amount 
 of time equal to the exact difference of longitude. It is 
 clear, then, that if any phenomenon, such as the sudden 
 extinction of a fixed star, could be noted by two observers 
 in different places, each will record the moment of disap- 
 pearance in his own local time, and an inter-comparison of 
 these records will give at once the difference of longitude 
 between the two stations. 
 
 Suppose it were possible to predict that the bright star 
 Yega, in the constellation of the Lyre, would suddenly dis- 
 appear on the first day of January, 1870, at Oh. 00m. OOs. 
 mean time at Greenwich, England, this fact being known 
 and published, vessels at sea, on long voyages, in all parts of 
 the globe, having the star above their horizon, by watching 
 for this phenomenon, and by noting the moment of disap- 
 pearance in their local time, would determine their longitude 
 from Greenwich, All observers recording the disappearance 
 before the predicted time would be in east longitude, while 
 those recording the same phenomenon later than the pre- 
 dicted time would be in west longitude, and as many hours, 
 minutes, and seconds west as was indicated by their local 
 time. 
 
 Now, at sea, very simple methods, as we shall show 
 hereafter, may be employed to obtain the local time ; and 
 thus, were it possible to predict a multitude of such phe- 
 nomena as above recorded occurring every day or two for 
 years in advance, seamen on long voyages, providing them- 
 selves with these predictions, would have the means of fixing 
 their longitude as often as any one of those predicted 
 phenomena could be observed. 
 
 The eclipses of the moons of Jupiter are precisely like the- 
 phenomenon of the sudden extinction of a star. As these- 
 moons shine only by reflected light, the moment they .enter 
 the shadow of their primary they vanish from the sight, or 
 are, to all intents and purposes, extinguished ; and as these 
 eclipses are constantly recurring at very short intervals, 
 Galileo saw at once the use to which they might be devoted 
 
SATURN. 119 
 
 in the resolution of this great problem of terrestrial 
 longitude. 
 
 Before they could be thus used, it became necessary to 
 master completely their laws, so that the moment of eclipse 
 might be accurately predicted years in advance. Though 
 the Tuscan philosopher did not live long enough to perfect 
 and apply his great discovery, his successors in modern 
 times have fully carried out and applied what was so 
 admirably conceived and so carefully commenced. 
 
 An attentive examination of the luminosity of Jupiter's 
 moons reveals the curious fact that it is variable, increasing 
 and decreasing at regular intervals, equal to the periods of 
 revolution in their orbits ; whence it has been inferred by Sir 
 William Herschel and others that each of these satellites 
 rotates (like our moon) upon an axis in the exact time in 
 which it revolves about the primary. 
 
 CHAPTER VIII. 
 
 SATURN, THE SEVENTH PLANET IN THE ORDER OF DIS- 
 TANCE FROM THE SUN, SURROUNDED BY CONCENTRIC 
 RINGS, AND ATTENDED BY EIGHT SATELLITES. 
 
 The most distant of the Old Planets. Its Light faint, but steady. 
 Synodical Revolution. The Sidereal Revolution. Advances in Tele- 
 scopic Discovery. Galileo announces Saturn to be Triple. Huygens 
 discovers the Ring. Division of the Ring into Two. Cassini announces 
 the Outer Ring the brighter. Multiple Division. Shadow of the Planet 
 on the Ring. Belts and Spots. Period of Rotation of the Planet and 
 Ring. Disappearance of the Ring explained. The Dusky Ring. 
 
 SATELLITES OF SATURN. By whom discovered. Eight in number. 
 Their Distances and Periods. Saturn's Orbit the boundary of the 
 Planetary System, as known to the Ancients. 
 
 WE now reach, in our outward journey from the sun, the 
 most distant world known to the ancients, revolving in an 
 orbit of vast magnitude, and in a period nearly thirty times 
 greater than that of our earth. Saturn, on account of his 
 
120 POPULAR ASTRONOMY. 
 
 immense distance, shines with a fainter light than either of 
 the old planets, though still a conspicuous object among the 
 fixed stars. Its light is remarkably steady, without the 
 scintillations which distinguish the stars, and the brilliant 
 glare which is shown by Yenus and Jupiter. There is a 
 yellowish or golden hue to this planet, which is not lost 
 when seen through the most powerful telescopes. 
 
 Such is the planet Saturn, as known to the old astrono- 
 mers, and as seen by the unaided vision. Its movement 
 among the fixed stars is distinguished by the same phe- 
 nomena which we have found to exist among all the planets. 
 Being the most remote of all the old satellites of the sun, its 
 stations are the best defined, its arc of retrogradation the 
 shortest, and the period employed in this retrograde move- 
 ment is longest. From observations made during opposition, 
 and by trains of reasoning identical with those laid down in 
 our examination of Jupiter, the periodic time and mean 
 distance of Saturn are concluded. 
 
 Owing to the very slow motion of this planet in its orbit, 
 the earth will pass between it and the sun, or bring it into 
 opposition, in a little over 378 days ; that is, Saturn and the 
 earth starting from the same straight line, passing through 
 the sun, the earth makes its revolution, comes up to the 
 starting-point, and then overtakes Saturn in about twelve 
 days and three-quarters. The earth's period must then be 
 to that of Saturn as twelve days and three-quarters is to 
 378, or as one to thirty, roughly. 
 
 This determination is a matter of such simplicity, that any 
 one, almost without instruments, may make the observations 
 which give the data for the computation. The opposition is 
 observed when Saturn is 180 from the sun; and we have 
 only to count the days from one opposition to the next to 
 obtain the synodical revolution. 
 
 Such were the few facts known to astronomy touching 
 this distant orb prior to the discovery of the telescope. The 
 immense multiplication and extension of human vision 
 effected by the invention and improvement of that instcu- 
 
SATURN. 121 
 
 ment, is in no case more signally displayed than in the 
 successive revelations which have been made in the physical 
 constitution of Saturn, and the extraordinary appendages 
 and scheme of dependent worlds now known to revolve 
 around him. 
 
 In 1610, the year in which Galileo first applied the 
 telescope to an examination of the celestial orbs the year 
 in which he announced the discovery of Jupiter's moons 
 an examination of Saturn resulted in the strange and 
 anomalous discovery that his disc was not circular, like all 
 the other planets, but elongated, as though two smaller 
 planets overlaid a larger central one extending somewhat to 
 the right and left of the centre. This remarkable figure 
 Galileo announced to his astronomical contemporaries under 
 the form of a puzzle produced by a transposition of the 
 Latin sentence, 
 
 " Altissimum planetam tergeminum observavi." 
 
 " I have observed the most distant of all the planets to be 
 triple." 
 
 This mode of presenting the discovery was adopted by the 
 Florentine astronomer to establish his priority, as many of 
 his great discoveries were claimed by some of his opponents, 
 while the truth of all was most obstinately "disputed by 
 others. It was urged, even in the case of Jupiter's moons, 
 that these were mere illusions, the offspring of the heated 
 imagination of the ambitious philosopher, and that other 
 eyes could never verify these pretended discoveries. We 
 can readily imagine what must have been the feelings of 
 Galileo when, not many months after the discovery of the 
 triple character of Saturn, he was compelled to acknowledge 
 that, even as seen through his most powerful telescope, the 
 planet was exactly circular, with an outline as sharp and 
 perfect as that of Jupiter. He exclaims, " Can it be possible 
 some demon has mocked me ! " He did not live to explain 
 this remarkable change ; but he saw the triple form restored, 
 and discovered these periodical transmutations of figure. 
 
 Fifty years later, in 1659, Huygens, with more powerful 
 
122 POPULAR ASTRONOMY. 
 
 telescopes, discovered the true figure of Saturn, and found 
 the triple form seen by Galileo to be produced by the fact 
 that the round planet was encircled by a broad flat ring of 
 .immense diameter, and so situated that the spectator on the 
 earth can never see it in a direction perpendicular to its 
 plane. Hence, although circular in form, the direction of 
 the visual ray gives it an oval or elliptical figure. Huygens 
 distinctly perceived the dark space intervening between the 
 body of the planet and the ring, right and left, which had 
 escaped the *eye of Galileo with a less perfect telescope. 
 Hence ; the Florentine astronomer only saw the planet 
 elongated, and pronounced it triple. Huygens explained 
 the mysterious change of figure which had so perplexed 
 Galileo, and found it due to the fact that the ring is 
 extremely thin so thin, indeed, that when the earth 
 chances to hold a place such that the plane of the ring 
 produced passes through the earth, and the ring comes to 
 be presented to the spectator edgewise, not even the tele- 
 scope of Huygens could discern the fibre of light presented 
 by the rim, or circumference of the ring, when thus located, 
 and to them the disappearance was complete, leaving the 
 planet round, clear, and well-defined. 
 
 In 1665, what had hitherto been regarded as one broad 
 flat ring, was observed to be divided into two portions by a 
 dark line, which, under favourable circumstances, was traced 
 entirely round the ring. This discovery was confirmed by 
 the elder Cassini, in 1675, who also discovered the unequal 
 brilliancy of the two rings, the outer one being the brighter. 
 He also was the first to announce the existence of a dark 
 stripe or belt surrounding the equator of the planet. Other 
 discoveries, such as additional belts, the shadow of the planet 
 on the ring, the shadow of the ring on the planet, were suc- 
 cessively made, as the powers of the telescope were improved. 
 During the present century many astronomers assert the 
 multiple division of the rings of Saturn, and the evidence 
 is so conclusive, that the existence of dark lines, concentric 
 with the rings (and like that which severs the two principal 
 
SATURN, CINCINNATI OBSERVATORY 
 
SATURN. 123 
 
 rings), cannot be denied ; though there is every reason to 
 believe that these lines are only to be seen occasionally. 
 With the full power of the refractor of the Cincinnati 
 Observatory, defining in the most beautiful manner all the 
 other delicate characteristics of Saturn and his rings, I have 
 never been able to perceive any trace of any other than the 
 principal division. 
 
 The bright and dark belts and certain spots, which mark 
 both the surface of the planet and the ring, have furnished 
 the means of fixing the period of rotation of the planet on 
 its axis at lOh. 29m. 16'8s., while the ring revolves on an axis 
 nearly coincident with that of the planet in lOh. 32m. 15s. 
 
 If we reflect on the structure and position of Saturn's 
 ring, the phenomena attending its disappearance and re- 
 appearance become readily explicable. The plane of the 
 ring produced indefinitely, intersects the plane of the earth's 
 orbit in a straight line. This is called the line of nodes of 
 the ring. This line of nodes, remaining nearly parallel to 
 itself, will manifestly move as the ring moves, carried with 
 the planet in its revolution round the sun. During one-half 
 of Saturn's revolution in its orbit the sun will illumine the 
 northern side of the ring ; during the other half it will 
 shine on the southern side. Thus the ring, carried by the 
 planet, will finally come into a position such that the sun- 
 light will fall on neither side, but on the edge of the ring 
 only, and when in this position it is manifest that the plane 
 of the ring passes through the sun. If, when in this posi- 
 tion, the earth comes between Saturn and the sun, a spectator 
 from the earth's surface will behold the edge of the ring, if 
 visible at all, as a delicate line of light extending beyond 
 the disc of the planet, and passing through its centre. 
 
 The earth, moving forward in its orbit from opposition of 
 the planet, will pass through the plane of the ring, and upon 
 the non-illuminated side. As Saturn moves very slowly in 
 comparison with the earth, while the plane of the ring is 
 sweeping from the one side of the sun to the other, the earth 
 may pass more than once through the plane of the ring, 
 
124 POPULAR ASTRONOMY. 
 
 repeating, in some sense, the phenomenon of disappearance. 
 As Saturn's period of revolution extends to nearly thirty of 
 our years, during one-half of this period the inhabitants of 
 the earth will behold one side of the ring, and during the 
 other half they will look upon its opposite surface. All the 
 changes from the greatest opening of the ring, when the 
 planet is seen like a magnificent golden ball, engirdled by 
 its ring of golden light, down to the total disappearance of 
 the ring, require about fifteen years. Then the reverse 
 changes occur, and all the phases and transmutations are 
 accomplished in about thirty years, when they are again 
 repeated in the same order. 
 
 The disappearance of the ring, which took place in 1848, 
 was watched by the author at the Cincinnati Observatory 
 with the powerful refractor of that institution. A minute 
 fibre of light remained clearly visible even when the edge of 
 the ring was turned directly to the eye of the spectator. The 
 delicacy of this line far exceeds anything ever before wit- 
 nessed, "When compared with the finest spider's web stretched 
 across the field of view, the latter appeared like a cable, so 
 greatly did it surpass in magnitude the filament of light pre- 
 sented in the edge of Saturn's ring. I had the pleasure of 
 witnessing the phenomena so beautifully described by Sir 
 William Herschel, the movement of the satellites along this 
 line of light, " like golden beads on a wire." This is a con- 
 sequence of the coincidence of the planes of the orbits of these 
 satellites with the plane of the ring ; hence, when the ring 
 is seen edgeways, these orbits will, in like manner, be seen 
 as straight lines, coincident with the line under which the 
 ring is seen. 
 
 To add to the extraordinary constitution of this wonderful 
 planet, another ring has recently been discovered by Bond, of 
 Cambridge (U.S.), and by Lassell, of Liverpool, more myste- 
 rious, if possible, than those previously known. This ring 
 lies between the planet and the bright ring, and is of a dusky 
 hue, and only discernible in powerful telescopes. Its outline 
 is the ame as that of the other rings, with the inner edge of 
 
SATURN. 125 
 
 the smaller of which it seems to unite. This extraordinary 
 appendage is so constituted as to reflect but little light, and 
 is sufficiently translucent to permit the body of the planet 
 to be seen through its substance. I have frequently ex- 
 amined this dusky ring with the Cincinnati refractor, and 
 have sometimes been confident that its breadth at the 
 extremities of its longer axis was much greater than that 
 which would be due to an elliptical figure concentric with 
 the bright rings. 
 
 Knowing, as we do, the distance of Saturn, it is easy, from 
 the measures of the diameter of his surrounding rings, to 
 compute their absolute dimensions. The exterior diameter 
 of the larger ring is no less than 176,418 miles, and its 
 breadth is 21,146 miles. The exterior diameter of the 
 second ring is 157,690 miles, leaving a chasm between the 
 bright rings of 1,791 miles across. The breadth of the 
 second ring is 34,351 miles, and the interval between the 
 planet and this ring is 19,090. The thickness of the rings 
 is a matter of conjecture, as it is too minute a quantity to 
 be obtained by any means of measurement at present within 
 our reach. Sir John Herschel does not believe it can exceed 
 250 miles. A single second of arc, at a distance equal to 
 Saturn, subtends nearly 5,000 miles ; so that a bright globe 
 5,000 miles in diameter, removed to Saturn's distance, would 
 be covered by the smallest spider's web stretched across the 
 field of view of the eye-piece of the telescope. In case we 
 admit the rings of Saturn to be 250 miles in thickness, then, 
 when seen edgeways, the filament of light seen reflected 
 from the outer circumference is only one-twentieth part the 
 diameter of the spider's web. 
 
 We pass now to an examination of the 
 
 SATELLITES OF SATURN. The largest of these satellites 
 was discovered by Huygens as early as 1665. Four others 
 were discovered some thirty years later by Cassini. Two 
 more were added by Sir William Herschel on the comple- 
 tion and application of his grand reflector in 1789, while an 
 eighth satellite was discovered by two observers, Bond and 
 
126 POPULAR ASTRONOMY. 
 
 Lassell, on the same night (Sept. 19th, 1848), the one ii 
 Cambridge, United States, the other in Liverpool, England. 
 We have thus, in addition to the anomalous rings which 
 surround Saturn, a scheme of no less than eight dependent 
 worlds, all of which revolve about the central orb in ellip- 
 tical curves, and in periods varying from twenty-two hours 
 to seventy-nine days. If the celestial scenery of Jupiter is 
 rendered magnificent by the splendour of his four moons, 
 what must be the amazing grandeur of the nocturnal sky 
 of Saturn, arched from horizon to horizon by his broad, 
 luminous girdle (on which the shadow of the planet, like the 
 dark hand of a mighty dial, will mark the hours of the 
 night) : the changes, phases, eclipses, the occupations of his 
 numerous moons, and the brilliant background of glittering 
 constellations which gem our nocturnal sky, must altogether 
 form a display of celestial splendour of which the human 
 mind can form but a faint conception. 
 
 In consequence of the vast distance at which the Satur- 
 nian system is removed, and the magnitude and power of 
 the telescope demanded for its examination, we are as yet 
 comparatively ignorant of many facts, which, in the case of 
 Jupiter's moons, have -been well determined. It will be 
 remembered that the moon's distance from the earth is 
 about 237,000 miles. Three of Saturn's moons fall far 
 within this limit, and the fourth is but 243.000 miles from 
 its primary. The fifth is 340,000 miles distant ; the sixth, 
 788,000 miles ; the seventh (latest discovered), is about 
 1,000,000 miles distant ; while the eighth is removed from 
 Saturn to a distance of nearly 2,300,000 miles. 
 
 The nearest of the moons, revolving at a distance of 
 120,000 miles, circulates round the primary in about twenty- 
 two hours and a half, presenting all the phases exhibited 
 by our moon, in less than a thirtieth part of the time. 
 Its disc, as seen from Saturn, will surpass the moon's disc 
 in the ratio of ten to one. Of the five earliest discovered 
 satellites, two are readily seen with any good telescope. 
 The five may now be seen by many refractors and reflectors 
 
MOTION AND GRAVITATION. 127 
 
 of modern construction, while the three smallest satellites 
 are only rendered visible by a few of the most powerful 
 instruments in the world. 
 
 We shall here close what we have to present of the 
 structure of the Saturnian system. We have thus termi- 
 nated the examination of all planetary bodies known to 
 the ancients, and have added to these the new objects re- 
 vealed by the telescope, and inclosed by the circumscribing 
 orbit of Saturn. Within these limits we find all the phe- 
 nomena known to the master minds to whom we are indebted 
 for the vast extension of the boundaries of human knowledge 
 in the solar system. 
 
 Before we pass these old limits, which for so many thou- 
 sand years were regarded as impassable, we must render an 
 account of the great discoveries, whereby it became possible 
 to achieve the crowning victories of human genius in the 
 planetary regions, and to extend these conquests far beyond 
 the limits of solar influence into regions of space and 
 among revolving orbs, of which the old philosophers had no 
 conception. 
 
 CHAPTER IX. 
 
 THE LAWS OF MOTION AND GRAVITATION. 
 
 The demands of Formal Astronomy. Those of Physical Astronomy. 
 Synopsis of the Discoveries already made. Questions remaining to be 
 answered. Inquiry into Causes. The Laws of Motion demanded. 
 Rectilineal Motion. Falling Bodies. Law of Descent. Motion of Pro- 
 jectiles. Curvilinear Motion. First Law of Motion. Second Law of 
 Motion. Momentum of Moving Bodies. Motion on an Inclined Plane. 
 The Centrifugal Force. Central Attraction. Gravitation. Laws of 
 Motion applied to the Planets. Questions propounded in Physical 
 Astronomy. Newton's Order of Investigation. His Assumed Law of 
 Gravitation. Outline of his Demonstration. Its Importance and Con- 
 sequences. The Law of Gravitation embraces all the Planets and their 
 Satellites. Gravitation resides in every particle of Matter. 
 
 discoveries thus far made among the revolving worlds 
 dependent on the sun have their origin in a rigorous com- 
 
128 POPULAR ASTRONOMY. 
 
 parison between the actual phenomena presented in nature 
 and the hypothetical facts derived from an assumed theory. 
 Hipparchus and Ptolemy surpassed their predecessors, because, 
 on careful examination, having discovered the motion of 
 the sun and moon and planets to be not uniform, as had been 
 asserted and believed, they explained this irregularity by 
 the hypothesis of an eccentric position in the central orb ; 
 thus enabling them to anticipate all the anomalous move- 
 ments known in the age in which they lived. Succeeding 
 discoveries, adding to the complexity of the theory of 
 eccentrics and epicyles, drove Copernicus to a new centre 
 of motion in the sun ; and this hypothesis, united to the old 
 theory of epicycles, was sufficient to harmonize the then 
 known facts of astronomy with the predictions of scientific 
 men. 
 
 Increased accuracy of observation, however, soon revealed 
 certain undoubted discrepancies between the absolute places 
 of the heavenly bodies, as given by instrumental observation, 
 and their places as obtained by computation ; and ' after 
 exhausting every possible expedient to restore harmony 
 between observation and computation, finding it impossible, 
 Kepler, as we have seen, was compelled to abandon the 
 circular theory, as Copernicus before him had been forced 
 to relinquish the geocentric hypothesis. 
 
 In all this long lapse of many thousands of years the human 
 mind has occupied itself exclusively with the great problem 
 of framing an hypothesis which would embrace all the 
 phenomena as presented in the heavens. It was a question 
 as to where was the centre of motion, not why it was there ; 
 what was the figure of the planetary orbits, not why this 
 particular figure existed ; how the planets deviated from a 
 uniform velocity in their revolution round the sun, not why 
 they were accelerated and retarded ; how the periods o* 
 revolution and the mean distances were related, not why 
 they were thus related. In short, the facts, and not the 
 causes, occupied the exclusive attention of the great astro- 
 aomers, until the science of facts, or formal astronomy, had 
 
MOTION AND GRAVITATION. f 129 
 
 reached its limit, and the mind, having exhausted this field 
 of investigation, was compelled to turn its attention to 
 causes, or to physical astronomy. 
 
 Let us review and condense the facts thus far developed 
 by formal astronomy. 
 
 The planets revolve about the sun as their common 
 centre of motion in orbits whose figure is nearly, ii not 
 quite, elliptical. 
 
 Their motion is not uniform, but grows swifter as they 
 approach the sun, and loses in velocity after passing their 
 perihelion or nearest point to the sun. 
 
 The dimensions of the planetary orbits are not absolutely 
 invariable. There are slight fluctuations not to be over- 
 looked in the periodic times and mean distances. 
 
 The positions of the orbits in their own plane are subject 
 to perpetual change, very slow in some of the planets, but 
 comparatively rapid in the moon and in the satellites of 
 other planets. 
 
 The inclinations of the planes of the planetary orbits to a 
 fixed plane are also in a state of fluctuation, some angles 
 increasing while others are diminishing. 
 
 The lines of nodes, in which the planes of the orbits ol 
 the planets intersect the plane of the earth's orbit, are not 
 fixed lines. They are found, on the whole, to retrograde, 
 but are sometimes found to advance in the order of planetary 
 revolution. 
 
 The moon exhibits anomalous movements, very marked 
 and well-defined, and which are evidently outside of her 
 elliptic motion, rising above and superior to the general law 
 of her revolution. 
 
 The most considerable of these lunar inequalities amounts 
 to 1 20' 30", by which quantity she is alternately in advance 
 and behind her elliptic place in her orbit. This motion was 
 known to the ancients, having been discovered by Ptolemy, 
 and was readily appreciable by the imperfect instruments 
 employed by the Greek astronomers. It is known as the 
 moon's evection. 
 
130 POPULAR ASTRONOMY. 
 
 A second inequality, amounting to 1 4', called the moon's 
 variation, was discovered by the Arabians, and by them 
 transmitted to posterity, showing the moon's motion accele- 
 rated in the quadrants of her orbit preceding her con- 
 junctions and oppositions, and retarded in the alternate 
 quadrants. 
 
 A third lunar inequality was called the annual equation, 
 a name adopted to express the fact that the moon's place in 
 her orbit is for half a year in advance of her elliptic place, 
 and for the other half-year behind it. 
 
 The line of apsides or longer axis of the lunar orbit 
 performs a complete revolution in the heavens in 3232 '57 
 days. 
 
 The line of nodes revolves round the heavens in 6793'39 
 days. 
 
 The vernal equinox is also in motion, sweeping round the 
 heavens in 25-868 years, while the north pole of the heavens 
 revolves round the pole of the ecliptic in the same exact 
 period. 
 
 Add to these facts, all discovered by observation and 
 reflection, the grand discovery of Kepler, that the squares of 
 the periods of revolution are precisely proportional to the 
 cubes of the mean distances of the planets ; and that this 
 and the other laws of Kepler govern the satellites ; and we 
 have a fair exhibition of the great truths of formal astronomy ; 
 and it is to answer why these phenomena exist, that physical 
 astronomy has been cultivated as a science. 
 
 "Why does a planet continue to revolve about the sun ? 
 In case it approach the sun at all, why not continue that 
 approach until it be precipitated on the surface of the solar 
 orb 1 Why do these revolving bodies describe elliptic orbits, 
 with the sun always in the focus of every orbit ? Why are 
 the deviations from elliptic motion what they are ? and how 
 comes it that the elliptic elements are in a state of perpetual 
 fluctuation ? Why do not the planets fall on the sun, or fly 
 off into space, or stop motionless in their orbits 1 What 
 Jiolds the earth to the sun, or the moon to the earth, so that 
 
MOTION AND GRAVITATION. 131 
 
 they never part company, and unitedly sweep harmoniously 
 round the sun 1 What bond unites all the satellites to their 
 primaries, and all these primaries to one central orb ? 
 
 Do all these interrogatories admit of a single answer, or 
 shall we find these phenomena to spring from diverse origins, 
 and due to a variety of causes 1 
 
 Before it was possible to consider any one of these grand 
 problems, it became necessary to reconstruct the old science 
 of mechanics, or mechanical philosophy, which was contem- 
 poraneous with the Greek astronomy of Ptolemy, and at the 
 time of Kepler and Galileo exerted quite as powerful an 
 influence over the human mind as did the doctrines of 
 Ptolemy and Hipparchus. The philosophy of Aristotle was 
 taught in all the schools, sustained by the immense influence 
 of professional organization, and received with a fulness oi 
 confidence and depth of submission which, so far from 
 tolerating doubt, actually prohibited inquiry. 
 
 As the planets and their satellites were bodies in motion, 
 no advance could be made in the inquiry concerning causes, 
 until the true nature of motion and the laws by which it 
 was governed could be determined. These laws could only 
 be revealed by accurate thought and observation, and would 
 naturally be independent of the cause producing the motion. 
 
 The most obvious example of motion is where a heavy 
 body is dropped vertically from any height, and falls toward 
 the earth. Observation teaches the rectilineal path of such 
 a falling body, as well as its direction, which is toward the 
 centre of the earth. It was a matter of experiment to 
 determine whether the velocity was uniform or accelerated, 
 and if accelerated, observation alone could determine the law 
 of acceleration. All this was quite independent of the cause 
 producing the original motion, the rectilineal direction, the 
 acceleration, and the direction toward the earth's centre 
 
 Aristotle had laid down the law of falling bodies, and 
 asserted that in case balls of unequal weight were dropped 
 at the same moment from equal elevations, the heavier ball 
 would move the swifter, and that the velocity of the two 
 
 K 2 
 
132 POPULAR ASTRONOMY. 
 
 balls would be directly proportional to their respective 
 weights. It was easy by experiment to prove or disprove 
 this statement, and Galileo is said to have given the first 
 powerful blow to the Greek philosophy, by showing ex- 
 perimentally (by dropping balls of unequal weights from the 
 summit of the leaning tower of Pisa), that the velocity of 
 the ball, or the time occupied in the fall, was entirely in- 
 dependent of the weight of the ball, the resistance of the 
 atmosphere being taken into account. 
 
 By measuring the space passed over by a falling body in 
 equal intervals of time, it became possible to determine the 
 law of descent, and it was thus found that every falling body 
 passes through, say, sixteen feet in the first second of its fall. 
 This is the velocity impressed in the first second of time ; 
 and were the body to move on with the velocity thus 
 acquired, it would pass uniformly over thirty-two feet in the 
 next second of time. But it is found that the velocity of 
 every falling body is increased in every second of time 
 by the same precise velocity acquired in the first second ; and 
 thus in case a cannon-ball were projected downward at the 
 rate of a thousand feet in one second, it would not only pass 
 over one thousand feet, but the sixteen additional feet 
 acquired by a body falling from a state of rest would be 
 added to the thousand feet due to the impulsive force of the 
 gunpowder. 
 
 Again, in projecting a body vertically upward, it was 
 discovered by experiment that at equal elevations in the 
 ascent and descent the velocities were identical j and thus, 
 whatever might be the cause retarding the ascending body, 
 or accelerating the descending one, that cause was found to 
 exert its force with a constant energy. 
 
 Galileo was the first fully to develop the facts above 
 stated, which facts manifestly began to couple motion and 
 velocity with some mysterious cause of acceleration and 
 retardation. 
 
 The rectilineal motion of falling bodies naturally led to 
 the inquiry as to the line in which a body, receiving a single 
 
MOTION AND GRAVITATION. 133 
 
 impulse, would move, if entirely free from the influence of 
 extraneous forces. A body shot from a gun horizontally, at 
 the commencement of its motion seemed to move in a right 
 line j but a more rigid examination showed that (the air as 
 a resisting medium out of consideration) the bullet com- 
 menced to fall at the moment of its flight, and actually did 
 fall in one second of time through a vertical height precisely 
 equal to the space it would have fallen through if dropped 
 from the muzzle of the gun. Here, then, was a deviation from 
 a rectilineal path accounted for by admitting a constant 
 deflecting force precisely equal to that force, wherever it 
 may be lodged, or whatever it may be, which produces and 
 accelerates the velocity of falling bodies. 
 
 As the right line is the most perfect of all lines, and 
 as uniform motion in a right line is the simplest of all 
 motions, Galileo conceived the idea that, in case a body 
 receive a single impulse giving a velocity of any rate per 
 second, the body thus set in motion will move off with 
 uniform velocity in a straight line, holding the direction in 
 which the impulse is applied, and will thus continue moving 
 for ever, unless some force or power be exerted to change 
 the direction or to destroy the velocity. 
 
 This conception or hypothesis could not be proved 
 directly from experiment. A ball perfectly hard, round, 
 and smooth, shot on a level surface like ice, would preserve 
 its rectilineal path and its initial velocity much longer than 
 if opposed by irregularities of surface and other resisting 
 causes ; and thus it became manifest that as the resistances 
 to motion were diminished, there was a nearer positive and 
 experimental approach to the verification of the principle 
 laid down by Galileo, till finally it became a settled princi- 
 ple, and was at length dignified as the first great law of 
 motion. 
 
 Previous to the discovery of this law, the mind had never 
 been able to conceive the idea that motion could continue 
 after the cause producing it had ceased to act; and yet 
 there is no motion produced by human contrivance, such as 
 
134: POPULAK ASTRONOMY. 
 
 the motion of a stone from a sling, or a ball from a cannon, 
 in which it is not manifest that the force producing the 
 motion ceases its action after the first impulse. The sling 
 cannot pursue the stone once liberated, nor the powder with 
 its expansive power follow the ball once released from the 
 gun ; and thus it is clear that' motion, once generated, 
 survives for a longer or shorter time the direct action of 
 the impulsive force. 
 
 So much for rectilineal motion. We are indebted to 
 Galileo again for the second law of motion, or the law by 
 which we pass from rectilineal to curvilinear motion. A 
 ball projected horizontally, as we have seen, soon began to 
 fall away from the straight line in which its motion com- 
 menced. Galileo proved that under the united effect of the 
 projectile force, and the force which caused it to fall toward 
 the earth, the ball would describe a regular curve, called a 
 parabola, which is nothing more than an ellipse, whose 
 major axis is infinitely long. This curve may be seen in 
 the form of the jet, when water or any other fluid spouts 
 from an orifice near the bottom of a cylindrical vessel. 
 
 The Florentine philosopher, in pursuing this subject, 
 finally came to generalize the principle involved, and dis- 
 covered that, if a body in motion at any given rate receive 
 an impulse, whose line of direction forms any angle with 
 the line of direction of the moving body, it will immediately 
 take up a new line of direction, according to a law which 
 may be thus announced : 
 
 If two sides of a square or rectangle represent the inten- 
 sities and directions of two impulsive forces acting at the 
 same instant, on a body at the angle formed by these sides, 
 then the body which, at the end of one second, would have been 
 found, under the impulse of either force, at the extremity of 
 the side representing the force, will neither follow the one side 
 of the rectangle nor the other, but will take the direction of the 
 diagonal, and at the end of one second will be found at the 
 extremity of that diagonal, as may be more readily compre 
 hended from the figures below. 
 
MOTION AND GRAVITATION. 135 
 
 Let F be any impulsive force, such, that acting on the 
 material point P, in the direction P B, would project it to 
 B in one second of time, and F' be an impulsive force which, 
 acting on the same material point P, in the direction P A, 
 would project it to A in one second ; then, in case the two 
 forces operate at the same moment on the material point P, 
 at the end of one second it will neither be found at B nor 
 at A, but will be found at C, the extremity of the diagonal 
 of the parallelogram. 
 
 This principle is known as the second law of motion, and 
 is also known as the parallelogram of forces. 
 
 In these investigations no account has been taken of the 
 weight or mass of the body moved. It was clearly perceived 
 that the force exerted by a body at rest pressing upon any 
 support was precisely proportioned to its weight, and hence 
 a ball weighing ten pounds would bend a spring through 
 ten times the space due to a ball weighing but one pound. 
 Aristotle, knowing this truth, and believing that this pressure 
 downward was the moving force, when a body fell freely, 
 asserted the principle that a body would fall with a velocity 
 proportioned to its weight, which, as we have said, was dis- 
 proved by Galileo in his celebrated experiment at the leaning 
 tower of Pisa. 
 
 It was manifest, however, that when two balls of unequal 
 weight fell from the same elevation, although they struck 
 the ground at the same moment, or fell with equal velocities, 
 the effect of the blow struck by the heavy body was very 
 different from that produced by the lighter body. Indeed, 
 it was easy, by experiment, to prove that the effect was 
 precisely proportioned to the weight of the falling body, and 
 
136 POPULAR ASTRONOMY. 
 
 that a body of ten pounds weight would strike a blow ten 
 times more powerful than a one-pound weight after falling 
 through equal heights. It was thus seen that to estimate 
 the effect of a blow struck by a moving body, we must take 
 into account not only the velocity, but also the weight or 
 mass of the body. The same body, with double velocity, 
 doubling its effect ; in short, the mass multiplied by the 
 velocity, now called the momentum, became the true repre- 
 sentative of the effect produced by the blow struck by a 
 moving body. 
 
 Having reached clear ideas and true laws on these im- 
 portant subjects, Galileo gave his attention to the circum- 
 stances of motion on an inclined plane. By experiment he 
 demonstrated that, if the same body roll down planes of the 
 same vertical height, but with different inclinations, the 
 velocity acquired on reaching the foot of any one of these 
 planes will be independent of the inclination, and will always 
 be equal to the velocity due to the vertical height of the 
 inclined plane. This discovery presented the principle of 
 the third and last law of motion, and, after much discussion, 
 came to be adopted as a fundamental truth in mechanical 
 science. These laws of motion were the result of clear 
 reasoning, based upon accurately conducted experiment, and 
 were quite independent of the actual causes producing 
 motion. 
 
 So soon as the knowledge of the second law of motion 
 was attained, whereby it became demonstrable that a body 
 set in motion by a single impulse, and then operated on by 
 a constant power, would describe a curve, it seems strange 
 to us, surrounded as we now are by the full illumination of 
 a true science, that this principle was not directly applied 
 to account for the motions of revolution of the celestial 
 orbs. 
 
 Kepler, . whose fertile genius, ever active and untiring, 
 sought the cause of planetary motion, being ignorant of the 
 laws of motion, felt that he must discover and reveal some 
 constantly active power operating in the direction of the 
 
MOTION AND GRAVITATION. 137 
 
 planetary motion so as to keep up the velocity, believing 
 that without some such ever-active force the planets must 
 of necessity stop. The successors of Kepler and of Galileo, 
 for fifty years, or during the first half of the seventeenth 
 century, felt strongly the necessity of a physical theory of 
 the planetary motions, without attaining to anything clear 
 or satisfactory. 
 
 That all heavy bodies were in some way attracted by the 
 earth, and that the centre of attraction was in the earth's 
 centre, was manifest from the fact that every body falling 
 freely, sought the earth's centre. But how a central force, 
 lodged in the earth or in the sun, could operate to keep up 
 a motion of revolution round that centre, in distant bodies, 
 was the inexplicable mystery. The ancients had already 
 remarked that when a stone in a sling is whirled rapidly 
 round the head of the slinger, a force is developed which 
 powerfully stretches the string by which the stone is held. 
 This force was called the centrifugal force, and it finally came 
 to be accepted that, *u all revolving bodies, this tendency to 
 fly from the centre must be generated ; and hence in the 
 planets and their satellite^ a like tendency must exist. 
 Reasoning, then, upon the two great facts, that all bodies 
 gravitate to the earth, and from analogy all bodies equally 
 gravitate to the sun, and that all revolving bodies, by the 
 action of the centrifugal force generated in their revolution, 
 are disposed to fly from the centre of motion, Borrelli, of 
 Florence, in 1666, seems to have been the first to conceive 
 the idea that in the planets and their satellites these two 
 forces might mutually destroy or counterbalance each other, 
 and leave the planet in a state of dynamical equilibrium to 
 pursue its journey round the sun. 
 
 Here we find the germ of the grand theory which at the 
 present day embraces within its grasp the entire physical 
 universe of God. It was, however, but the germ. Borrelli 
 did not pretend to demonstrate the truth of his suggestion. 
 To accomplish this, it became necessary to demonstrate the 
 law of thp centrifugal force and the law of gravitation, and 
 
138 POPULAR ASTRONOMY. 
 
 then to show that the first of these forces, as developed by 
 the velocity of revolution of any planet, was precisely equal 
 to the force of gravitation exerted by the sun at the distance 
 to which the planet was removed. 
 
 The law governing the development of the centrifugal 
 force could be investigated experimentally. A cord suf- 
 ficiently strong to hold a body suspended from a fixed point 
 was not strong enough to hold the same body when made to 
 revolve about the point, and, as the velocity of revolution 
 was increased, the strength of the cord had to be increased. 
 But it was soon found that, with double the velocity, a cord 
 twice as strong would not retain the revolving body. The 
 centrifugal force increased, therefore, in a higher ratio than 
 the simple velocity. By further experiment it was dis- 
 covered that when the velocity of the revolving body was 
 doubled, the cord holding it must be quadrupled, and when 
 the velocity was tripled, the cord must be made nine-fold 
 stronger ; and hence it became finally a fixed principle that 
 the centrifugal force in every revolving body increased with 
 the square of the velocity. It remained yet to ascertain in 
 what way this force was affected by the distance of the re- 
 volving body from the centre of motion. This was accom- 
 plished experimentally, and the complete law regulating the 
 development of the centrifugal force in all revolving bodies 
 having been determined, this force was found to increase as 
 the square of the velocity, and to decrease directly as the 
 distance from the centre of motion increased. 
 
 With the knowledge of this important law, we can return 
 to the consideration of the planetary revolutions. That 
 these bodies were urged directly from the sun by the action 
 of the centrifugal force generated by their velocity of revo- 
 lution, could not be doubted, and to counterbalance this 
 tendency to fly from the centre of motion some force 
 precisely equal and opposite must exist. This force was 
 called the gravitating force, or force of gravity, and the law 
 regulating its intensity remained to be discovered. 
 
 Kepler bad not failed to conjecture the existence of some 
 
MOTION AND GRAVITATION. 139 
 
 such central force lodged in the sun and in the earth. He 
 even went further, and conceived the same force of attraction 
 to exist in the moon ; and finding the tides of the ocean to 
 be swayed by that distant orb, he conceived that the same 
 energy which manifested itself in a heaving-up of the 
 ocean wave, must exert itself with equal power on the 
 solid mass of the earth. These, however, were mere spe- 
 culations with Kepler, and even, in case he had seriously 
 undertaken to prosecute the research, the ignorance of the 
 true laws of motion then existing would have rendered any 
 success impossible. From the days of Kepler to those of 
 Newton this great problem constantly occupied the thoughts 
 of the most eminent philosophers : Was the gravitating 
 force whereby bodies fell to the earth's surface a constant or 
 variable force ? Was this force operative in the distant 
 regions of space 1 Did its power extend to the moon ? and 
 was it there precisely what it should be in order to counter- 
 balance the energy of the centrifugal force ? Did this 
 same gravitating power dwell in the sun and other planets 
 as well as in the earth ? Did the sun's gravity extend to each 
 of the planets, and exert at these different distances an 
 energy equal and opposite to the existing centrifugal force 
 due to the planet's distance and velocity ? In short, was 
 there a force or energy dwelling in every particle of ponder- 
 able matter whereby every existing particle attracted to 
 itself every other existing particle, with an energy propor- 
 tioned in some way to their weights and to the distances 
 by which they were separated 1 Could such a force, lodged 
 centrally in the sun, and operating by any law, convert the 
 rectilinear motion of a body darted into space by a single 
 impulse into elliptical motion, and at the same time, at 
 every point in the elliptical orbit, precisely counterpoise the 
 centrifugal force due to the planet's distance and velocity ? 
 Could the same force, governed by the same laws and lodged 
 in the primary planets, control the movements of their 
 satellites ? These were the grand inq \iries which engrossed 
 the attention of the generation of philosophers which 
 
140 POPULAR ASTRONOMY. 
 
 flourished from the time of Kepler and Galileo up to the 
 era rendered immortal by the grand discovery of the law of 
 universal gravitation by Newton. 
 
 NEWTON'S DISCOVERY OP THE LAW OF GRAVITATION. We 
 are now prepared to consider the train of reasoning em- 
 ployed by the English philosopher in his researches for the 
 law of gravitation. Many astronomers before Newton had 
 conjectured that the force exerted by the sun on the planets, 
 and by the primaries on their satellites, decreased as the 
 square of the distance increased, or followed the law of the 
 inverse ratio of the square of the distance. This was in- 
 ferred from the consideration of fact, that this attractive 
 energy, called gravity, was lodged in the centre of the sun, 
 and issued from that centre in all possible directions, like 
 light emanating from a luminous point. As the distance 
 increased from the centre, the force would become less intense 
 and might follow the law of the decrease in the intensity 
 of light, which was well known by experiment to be the 
 inverse ratio of the square of the distance. It was one thing 
 to conjecture this to be the law regulating the force of 
 gravity, but quite a different thing to demonstrate the truth 
 of such a conjecture. 
 
 The investigation as pursued by Newton, and the disco- 
 veries made by that distinguished philosopher, followed 
 progressively in a series of distinct propositions, the demon- 
 strations of which were reached at different periods. 
 
 First, Newton demonstrated that, assuming the third law 
 of Kepler as a fact derived from observation, as a consequence 
 of this fact (combined with the law of the centrifugal 
 force), the gravitation of the planets to the sun must 
 diminish in the inverse ratio of the square of their respective 
 distances. This demonstration was accomplished by a train 
 of mathematical reasoning, of which we will not stop to 
 give any account at present. It was based, however, on the 
 assumption that the planetary orbits were circles, and hence 
 did not meet the case of nature. 
 
 The second step was to prove that, in case a planet revolved 
 
MOTION AND GRAVITATION. 141 
 
 in an elliptical orbit, at every point of its revolution the 
 force exerted on it by the BUD, or its gravitation to the solar 
 orb, was always in the inverse ratio of the square of its 
 distance. This was equivalent to proving that if a body in 
 space, free to move, received a single impulse, and at the 
 same moment was attracted to a fixed centre by a force 
 which diminished as the square of the distance at which it 
 operated increased, such a body, thus deflected from its rec- 
 tilineal path, would describe an ellipse, in whose focus the 
 centre of attraction would be located. 
 
 The third step in this extraordinary investigation was to 
 demonstrate that this gravitating power lodged in the sun, 
 and controlling the planetary movements, was identical with 
 that force exerted by the earth over every falling body, and 
 extending itself to the moon, decreasing in intensity in pro- 
 portion as the square of the distance increased, and thus 
 opposing itself as a precise equipoise at every moment to the 
 effect of the centrifugal force generated by the motion of 
 this revolving satellite. 
 
 The fourth step required the philosopher to demonstrate 
 that not only did the planets gravitate to the sun, and 
 the satellites to their primaries, but that each and every 
 one of these bodies, sun, planet and satellite, gravitated to 
 the other, and that each attracted the other by a force which 
 varied in the inverse ratio of the square of the distance. But 
 here it was found that another matter had to be taken into 
 account. The energy of gravitation did not depend alone on 
 distance. The power exerted by the sun on the planet 
 Jupiter was vastly greater than that exerted by Saturn 
 though Jupiter was nearly equidistant from these two 
 bodies when in conjunction with Saturn. Newton proved 
 that the power of gravitation, lodged in any body, depended 
 on the mass or weight of the body ; and hence, if the sun 
 weighed a thousand or ten thousand times as much as a 
 planet, its energy at equal distances would, by so much, 
 exceed that put forth by the smaller orb. 
 
 The fifth and final step in this sublime intellectual ascent 
 
142 PCPULAR ASTRONOMY. 
 
 to the grand law of the physical universe, required the philo- 
 sopher to prove that the force, power, or energy, now called 
 gravitation, lodged in the sun, planets, and satellites, per- 
 vaded equally every constituent particle of each of these 
 bodies, and did not dwell alone in the mathematical centre 
 of the sun or planet. In short, it was required to show that 
 every ponderable particle of matter in the whole universe 
 possessed and exerted this power of attraction in the direct 
 proportion of its mass, and in the inverse ratio of the square 
 of the distance at which its energy was manifested. 
 
 In case these propositions could be clearly and satis- 
 factorily demonstrated, an instant and absolute revolution 
 must commence in the whole science of astronomy, and the 
 business of future ages would be nothing but the verification 
 of this one grand controlling law, in its application to the 
 phenomena presented in the movements not only of the 
 sun's satellites and their attendants, but in those grander 
 schemes of allied orbs revealed by telescopic power in the 
 unfathomable regions of the sideral heavens. 
 
 We shall now exhibit an outline of the demonstration 
 accomplished by Newton to prove that the law of universal 
 gravitation, as above announced, was the exact law, accord- 
 ing to which the earth exerted its attractive power on the 
 moon, and held this globe steady in its orbit. 
 
 The intensity of any force, as we have seen, is measured 
 by the velocity it is capable of producing in a heavy particle 
 in any unit of time, as one second. The earth's gravity at 
 the surface is measured then by the space through which a 
 body falls in a second of time, which space (as experiment 
 demonstrates) is about sixteen feet. In case it were possible 
 to measure with absolute precision the space through which 
 a body falls at the level of the sea, and then at the summit 
 of a mountain (if there were any such) 4,000 miles high, it 
 would be easy to verify the truth of the assumed law by 
 actual experiment ; but no mountain exists on the earth's 
 surface whose height is comparable with the length of the 
 earth's radius, and as it is as absolutely impossible to ascend 
 
MOTION AND GRAVITATION. 
 
 143 
 
 vertically above the earth to any considerable height, 
 Newton soon saw that no means existed on the surface of 
 the earth whereby the truth or falsehood of his assumed 
 hypothesis might be ascertained. In this dilemma he con- 
 ceived the idea that the moon might be employed in the 
 experiment, not by arresting her motion and dropping her 
 literally to the earth, but by considering the earth's attrac- 
 tive power as the cause of her deflection from a rectilineal 
 movement. In one sense the moon is perpetually falling to 
 the earth, as may be readily comprehended from an ex- 
 amination of the figure below : 
 
 M'M" 
 \ 
 
 Let E represent the earth's centre, M a point of the 
 moon's orbit, in which she is at rest with no force whatever 
 operating on her. Now let an impulse be applied to the 
 moon, in the direction M M'", tangent to the orbit, or per- 
 pendicular to the line M E, and with such intensity that at 
 the end of one second of time the moon will be found at M'". 
 Return the moon to M, and conceiving her to drop toward 
 the earth, under the power of the earth's attraction, let us 
 suppose that she passes over the distance M M' in one 
 second. In case the moon be brought back again to M, and 
 the impulse be now applied, and at the instant the moon 
 darts off along the straight line M M"' she is seized by the 
 earth's attractive power, and, bending at once under these 
 conjoined influences, she commences her elliptical orbit, and 
 at the end of one second is found at M", passing over a sort 
 of curvilinear diagonal of the parallelogram formed on the 
 two sides M M'" and M M'. Now, it is manifest that the 
 
144 POPULAR ASTRONOMY. 
 
 line M'" M" is equal to M M ; , that is, that the amount bj 
 which the moon is deflected from a right line is precisely 
 the amount by which she falls to the earth in one second of 
 time. The problem then resolved itself into a computation 
 of the line M M', or the distance through which the moon 
 ought to fall in one second, in case the assumed law of 
 gravitation be true, and the exact measurement instru- 
 mentally of the distance M"' M", the space through which 
 the moon did fall in one second. An exact equality between 
 these two quantities would establish the law of the decrease 
 of the earth's power of attraction to be in the inverse ratio 
 of the square of tKe distance. 
 
 It will be seen that to compute how far a body would 
 fall in one second, when removed to the moon's distance, in 
 case the earth's gravity be diminished as the square of the 
 distance increases, is a matter involving no difficulty or 
 uncertainty whatever, in case we know what the moon's 
 distance is. In like manner, to obtain the space through 
 which the moon actually falls to the earth in one second or 
 minute of time, knowing her distance, admitting her orbit 
 to be circular, and assuming that we know her periodic time, 
 is a problem of easy solution. 
 
 The chief difficulty lay in accomplishing an accurate 
 determination of the moon's distance from the earth, a 
 matter which could not be determined without an accurate 
 knowledge of the earth's diameter or radius, as we have 
 already seen. 
 
 When Newton commenced his investigation, the measures 
 which had been executed of an arc on the meridian, whereby 
 the entire circumference of the earth might be obtained and 
 its diameter computed, were comparatively imperfect, 
 yielding only an approximate value of the earth's radius. 
 As this quantity was the unit employed in the measure of 
 the moon's distance, any error in its value would be re- 
 peated some sixty times in the value of the moon's distance ; 
 and as the gravity of the earth was assumed to decrease as 
 the square of the distance increased, we perceive that any 
 
MOTION AND GRAVITATION. 145 
 
 error in the radius of the earth would operate fatally on the 
 solution of this problem, involving the fate of the most 
 comprehensive and far-reaching hypothesis ever conceived 
 by the human mind. 
 
 Unfortunately for Newton, the value of the earth's 
 diameter, employed in his first computations, was in error ; 
 and in executing the computation the values of the space 
 through which the moon ought to fall, and the space through 
 which she did fall, were discrepant by an amount equal to 
 the sixth part of the entire quantity. So great a disagree- 
 ment was fatal to the theory in the truth-loving and exact 
 mind of Newton, and for many years he abandoned all hope 
 of demonstrating the truth of his favourite hypothesis. Still 
 his mind was in some way powerfully impressed with the 
 conviction that he had divined the true law of Nature, and 
 he returned again and again to his computations in the 
 hope of removing the discrepancy by detecting some nu- 
 merical error. It was impossible, however, to find an error 
 where none existed, and for a time the great philosopher 
 abandoned all hope of accomplishing this, the grandest of all 
 the efforts of his own sublime genius. Such was the con- 
 dition of this investigation, when a new determination of 
 the value of the earth's diameter was accomplished in 
 France, by the measurement of an arc of the terrestrial 
 meridian. Having obtained this new value of the earth's 
 diameter, Newton resumed once more the consideration of 
 the problem which had so long occupied his thoughts. The 
 new value was substituted for the old j the moon's distance 
 being now accurately known,*fche space through which a 
 body would fall in a unit of time, under the power ot 
 gravitation, when removed to this new distance, was rapidly 
 computed. In like manner the distance through which the 
 moon must actually fall was also obtained by using the new 
 value of the earth's diameter. 
 
 It would be impossible to form any just idea, of the 
 intense emotions which must have agitated the mind of 
 the English philosopher while engaged in bringing these 
 
146 POPULAR ASTRONOMY. 
 
 last computations to a close. Upon a comparison of th 
 results now reached, there hung consequences of incalculable 
 value. No less than nineteen years of earnest study, of 
 profound thought, and of the most laborious investigation, 
 had already been exhausted on this grand problem ; and 
 now within a few minutes the fate of the theory and the 
 fame of the astronomer were to be for ever fixed. No 
 wonder, then, that we are told that even the giant intellect 
 of Newton reeled and staggered under the tremendous 
 excitement of the moment ; and seeing that the figures 
 were so shaping themselves as inevitably to destroy the 
 discrepancy which had so long existed, overcome by his 
 emotions, Newton was compelled to ask the assistance of a 
 friend to finish the numerical computation, and when com- 
 pleted, it was found that the space through which the moon 
 did fall in a unit of time was identical with the space 
 through which she ought to fall, in case her movements 
 were controlled by a power lodged in the earth's centre, and 
 decreasing in energy as the square of the distance at which 
 it operated was increased. 
 
 Here was presented the first positive proof of the prevalence 
 of that universal law of mutual attraction which energizes 
 every particle of ponderable matter existing in the universe. 
 The earth's power of attraction was thus shown to exert 
 itself according to a fixed law, in deflecting the moon from 
 the rectilineal path it would otherwise have followed, con- 
 verting its motion into one of revolution, giving to its orbit 
 the elliptical form, and maintaining at every point of its 
 revolution the most exact anil perfect equilibrium. 
 
 It may, perhaps, seem extraordinary that so much con- 
 sequence should have been attached by Newton to the 
 successful demonstration of this particular problem. If he 
 had already shown that the sun's attraction upon the planets 
 followed the law of the inverse ratio of the square of the 
 distance, and that the same law prevailed in the attraction 
 of the sun upon any one planet at different points of its 
 orbit, why regard as'a natter of such high value the demon- 
 
MOTION AND GRAVITATION. 14) 
 
 Oration of the fact that the earth's attraction upon the 
 moon was governed by the same identical law ? The answer, 
 I think, may be readily given. 
 
 The great problem was this : Does one law reign supreme 
 over all the ponderable masses of the physical universe, or are 
 there many subordinate laws holding their sway in the diverse 
 systems and bodies which are revealed by sight ? Might it 
 not be that the sun would attract the planets according to 
 one law, while the planets might attract their satellites 
 according to a different law ? By demonstrating that the 
 earth controlled the moon by the same precise power 
 whereby the sun controlled the planets, it was demonstrated 
 that the ponderable matter of the earth was identical in 
 character with the ponderable matter of the sun, and from 
 this it followed that as the earth was one of the planets con- 
 trolled by the power of gravitation of the sun, so likewise 
 the other planets which were controlled by the same power 
 must be composed of ponderable matter, governed by the 
 same laws which reign in the sun and earth. 
 
 We perceive, then, that this demonstration, executed by 
 Newton, in which he proves that the earth's attraction 
 controlled the moon, deserves the high rank which he has 
 assigned it ; for it is nothing less, when conjoined with his 
 previous demonstrations, than proving that every globe which 
 shines in space planet, and satellite, and sun, are but parts 
 of one mighty system linked together by indissoluble bonds, 
 forming one grand scheme, in which each exerts its influence 
 upon the other, the whole controlled by one supreme and 
 all-pervading law. 
 
 It only remained now to extend by demonstration the 
 empire of the law of universal gravitation over each par- 
 ticle of matter composing the several worlds. This was a 
 problem of no ordinary difficulty; for Newton soon dis- 
 covered that, in case a mass of ponderable matter were 
 fashioned into the shape of a sphere, for all the purposes ot 
 computation it would be safe to consider the entire globe as 
 concentrated in one single point at the centre. Observation 
 
 L * 
 
148 POPULAR ASTRONOMY. 
 
 taught that all the planets, as well as their satellites, were 
 bodies of globular form ; and hence, in applying the law of 
 universal gravitation to the study and computation of their 
 movements, the same results would be obtained by admitting 
 the whole force of attraction belonging to these bodies to be 
 concentrated in their central points, or to be distributed 
 among the different particles composing the globe. To show, 
 then, that gravity resided in every particle composing a globe, 
 and not in its central point, was an impossible thing, so far 
 as the distant worlds were concerned. In the world which 
 we inhabit, however, and where we can study its individual 
 portions, and where we can penetrate to certain depths 
 toward its centre, it may not be impossible to learn whether 
 the power of gravitation dwells in every ponderable atom 
 which goes to make up the entire earth, or whether it is 
 concentrated in the central point alone. 
 
 There are several methods which may be employed to 
 ascertain whether there be any power of attraction in 
 separate portions of the earth or in the crust of the earth. 
 The effect of a high mountain on the direction of the plumb- 
 line (which at the level of the sea holds a direction perpen- 
 dicular to the surface), in causing it to deviate from this 
 direction, may be measured with sufficient accuracy to 
 demonstrate the power of attraction existing in the moun- 
 tain. Such an experiment, however, could not be employed 
 to demonstrate that the law of universal gravitation pre- 
 vailed among the particles composing the mountain ; it 
 would only show that there was a power of attraction 
 exerted by the mountain ; and in case we knew the exact 
 amount of deviation of the plumb-line from the vertical, 
 and the magnitude of the mountain, as well as the law 
 according to which its attractive power was exerted, we 
 could then obtain the quantity of matter contained in the 
 mountain mass. 
 
 A second method may be employed to ascertain whether 
 the whole power of gravitation is lodged in the centre of 
 the earth, or is distributed among all its constituent particles. 
 
MOTION AND GRAVITATION. 14* 
 
 If it were possible to penetrate toward the earth's centre, a 
 thousand miles below the surface, and there drop a heavy 
 body, and measure the space through which it falls in a unit 
 of time ; if this measured space should be identical with 
 that over which the body ought to fall, on the supposition 
 that its velocity depended simply on its distance from the 
 centre, such an experiment would demonstrate that the 
 earth's gravitating force resided in the central point alone : 
 this experiment cannot be performed in the exact manner 
 announced, but it can be, and has been substantially per- 
 formed, with very great delicacy, in the following manner : 
 It is found that a pendulum of given length will vibrate 
 seconds at the equator of the earth. If this pendulum be 
 removed nearer to the earth's centre by carrying it toward 
 the poles, the power of gravitation producing its vibration 
 thereby growing more intense, the pendulum will vibrate 
 more than sixty times in a minute j and thus the number ot 
 vibrations in a given time becomes a very exact means of 
 measuring the distance of any point on the earth's surface 
 from its centre. These experiments, however, are performed 
 upon the earth's surface. If, instead of removing the 
 pendulum from the equator toward the poles, and thereby 
 reducing its distance from the earth's centre, this distance 
 were reduced by the same amount by transporting the 
 pendulum vertically downward into a deep mine if distance 
 alone from the centre be the cause affecting the time of the 
 vibration of the pendulum, then the number of vibrations 
 in a unit of time will be the same in the mine as at a point 
 on the exterior equidistant from the earth's centre. When 
 this experiment comes to be performed, it is found that 
 there is a great difference between the number of vibrations 
 in the interior, when compared with the number of vibra- 
 tions at the exterior, at equal distances from the centre, in 
 any unit of time, say a mean solar day ; clearly demonstrat- 
 ing that the matter of the earth, lying above the pendulum 
 located in the mine, produces a very sensible and powerful 
 effect upon the number of its vibrations. 
 
[50 POPULAR ASTRONOMY. 
 
 Here, again, we find it impossible, from this experiment, 
 to determine the exact law which regulates the attractive 
 power of the individual particles composing the earth, but 
 we do demonstrate the fact that the earth's gravity is not 
 concentrated at its centre, but dwells, according to some 
 law, in all the atoms which compose its mass ; and this law, 
 we shall prove hereafter, is none other than the great law 
 of universal gravitation. 
 
 It is impossible to form a just idea of the vast importance 
 which attaches to the grand discovery of Newton. It 
 worked out, instantly and absolutely, a complete revolution 
 in the whole science of astronomy. Previous to the discovery 
 of the law of universal gravitation, all the observations upon 
 the stars and planets, which had been accumulating for so 
 many centuries, could only be regarded as so many isolated 
 facts, having no specific relation the one to the other. The 
 planets were independent orbs, moving through space in 
 orbits peculiar to themselves, and only united by the single 
 fact that the sun constituted the common centre of revolu- 
 tion. The discovery made by Newton converted this scheme 
 of isolated worlds into a grand mechanical system, wherein 
 each orb was dependent upon every other, each satellite 
 affecting every other, and the whole complex scheme gravi- 
 tating to the common centre, which exerted a predominant 
 power over each and every one of these revolving worlds. 
 
 Those eccentric bodies which we denominate comets, whose 
 abrupt appearance in the heavens with their glowing trains 
 of light, whose rapid movements and sudden disappearance 
 have excited such a deep interest in all ages of the world, 
 were found not to be exempt, as we shall hereafter show, from 
 the empire of gravitation. 
 
MOTION AND GRAVITATION. 
 
 CHAPTER X. 
 
 THE LAWS OF MOTION AND GEAVITATION APPLIED TO 
 A SYSTEM OF THKEE REVOLVING BODIES. 
 
 A. System of two Bodies. Quantities required in its Investigation. Five 
 in number. Sun and Earth. Sun, Earth, and Moon, as Systems of 
 Three Bodies. The Sun supposed Stationary. Changed Figure of the 
 Moon's Orbit. Sun Revolving changes the Position of the Moon's Orbit. 
 Solar Orbit Elliptical. Effects resulting from the Inclination of the 
 Moon's Orbit. Moon's Motion above and below the Plane of the 
 Ecliptic. Revolution of the Line of Nodes. Sun, Earth, and Planet, 
 as the Three Bodies. Perturbations destroy the Rigour of Kepler's 
 Laws. Complexity thus introduced. Infinitesimal Analysis. Differ- 
 ence between Geometrical and Analytical Reasoning. 
 
 WE shall now present, as clearly as we can, without the 
 aid of mathematical reasoning, the application of the laws 
 of motion and gravitation to the circumstances arising in a 
 system of three bodies mutually affecting each other. We 
 will commence even with a simpler case, and suppose a 
 solitary planet to exist, subjected to the attractive power of 
 one sun, and that these are the only bodies in the universe. 
 Let us consider what quantities are demanded to render it 
 possible for the mathematician to take account of the 
 circumstances of motion which will belong to this solitary 
 world. 
 
 First of all, it is evident that the quantity of matter 
 contained in the sun, or its exact weight, must be known ; 
 for the energy or power of the sun varies directly as its 
 mass ; and two suns, so related that the weight of one is 
 tenfold greater than that of the other, the heavier one will 
 exert a power of attraction tenfold greater than the lighter 
 one. 
 
 In the second place, we must know the distance of the 
 planet from the sun, for the power of the sun's attraction 
 decreases as the square of the distance at which it operates, 
 
152 POPULAR ASTRONOMY. 
 
 increases j so that, if at a distance of unity it exerts at 
 attractive force which we may call one, at a distance two this 
 force will be diminished to one-fourth ; at a distance three 
 to one-ninth ; at a distance four to one-sixteenth ; at a 
 distance ten to the one-hundredth part of its first value. 
 
 In the third place, the mass or weight of the planet must 
 be known ; for not only does the sun attract its planet, but 
 in turn the planet attracts the sun, and the intensity of this 
 attraction, which affects the motion of the planet as well as 
 that of the sun, depends exclusively upon the mass or weight 
 of the planet, 
 
 In the fourth place, we must know the intensity of the 
 impulsive force which is employed to start the planet in its 
 orbit ; for, upon the intensity of this force will the initial 
 velocity of the planet depend, and we see readily that the 
 form of the orbit as to curvature will depend upon the initial 
 velocity. The greater this velocity, the more nearly will the 
 curvature of the orbit coincide with the straight line in 
 which the planet would have moved, in case it had been 
 operated upon by the impulsive force alone. 
 
 In the fifth place, before we c'an completely master the 
 circumstances of motion to the planet, we must know the 
 direction in which the impulse is applied ; for upon this 
 direction it is manifest that the figure of the orbit will 
 depend. If the impulsive force be applied in a direction 
 passing through the sun's centre, and toward the sun, it is 
 clear that the planet will simply fall to the sun in a straight 
 line. If it met with no resistance it would pass through and 
 beyond the sun's centre, until its velocity would be entirely 
 overcome by the attraction of gravitation, when it would 
 stop, fall again to the sun, and thus vibrate for ever in a right 
 line. In case the direction of the impulse is oblique to the 
 line joining the planet and the sun (the angle falling within 
 certain limits of value), then the planet will describe an 
 elliptical figure in its revolution around the sun, and will 
 return precisely to the point of departure to repeat the same 
 identical curve, with the same velocities precisely at each of 
 
MOTION AND GRAVITATION. 153 
 
 the points of its orbit, in the same exact order for ever. In 
 examining the peculiarities which distinguish the movements 
 of this revolving body, we shall find as a necessary conse- 
 quence of the laws under which it moves, that its motion 
 must be slowest at that point of its orbit where it is farthest 
 from the sun. Leaving this point as it approaches the sun, 
 its velocity must rapidly increase, and will reach its maxi- 
 mum at the perihelion of its orbit, where, being nearest to 
 the sun, it will move with its swiftest velocity. Receding 
 now from the centre of attraction, it will lose its velocity by 
 the same degrees with which it was augmented, and will 
 again pass its aphelion with its slowest velocity. Thus we 
 perceive that the movements of a single planet revolving 
 about the only sun in existence are marked with great simpli- 
 city; and in case the mathematician knows precisely the five 
 quantities already named, viz. : the suris mass, the planet's 
 distance, the planet's mass, the intensity of the impulsive force, 
 and the direction of this force, it is not at all difficult to 
 determine all the circumstances of motion of the planet, and 
 to predict its place in its orbit with absolute precision at 
 the end of ten thousand revolutions. 
 
 We will not at present attempt to show how these five 
 quantities may be obtained. These determinations belong 
 to the department of instrumental astronomy, a subject 
 which will be treated after closing what we have to say on 
 the application of the law of gravitation to the movements 
 of a system of three bodies. 
 
 In case the planets had been formed of a material such as 
 to be attracted by the sun, but not to attract each other, 
 and if the satellites had been composed of a material such as 
 to be attracted by their primaries only ; then the elements 
 of the orbits of all these revolving bodies would have 
 remained for ever absolutely invariable. So soon, then, as 
 accurate observation should have furnished the five quan- 
 tities required in determining the circumstances of motion 
 in any revolving body, mathematical computation would 
 have fitted an invariable orbit to each one of these bodies, 
 
POPULAR ASTRONOMY. 
 
 and would have furnished by calculation the exact place of 
 each one of these bodies in all coming time. The whole 
 system would have been one of perfect equilibrium ; and, 
 although complexity would have presented itself apparently 
 in the interlacing revolutions of these revolving worlds, yet 
 absolute simplicity, combined with short periodical changes, 
 would have restored each one of these bodies to the exact 
 position occupied when first launched in its orbit. 
 
 This, however, is not the case of nature. The sun not 
 only attracts the planets, but also attracts their satellites. 
 The primary planets not only attract their satellites, but 
 attract each other ; and thus not a single body exists in the 
 whole universe, which is not dependent upon every other. 
 
 We have already seen that, in case the sun with one 
 planet were the only objects in existence, having traced the 
 planet in one single revolution round the sun, the variations 
 of motion thus developed would be repeated without the 
 slightest change in any succeeding revolution for all coming 
 time. 
 
 Suppose this solitary planet to be the earth ; and that 
 from a knowledge of the weight of the sun, the distance of 
 the earth from the sun, the weight of the earth, the intensity 
 of the impulsive force, and the direction in which that force 
 is applied to start the earth in its orbit, we determine the 
 elements of its orbit. The form of this orbit, its magnitude, 
 and position in space, will remain absolutely invariable ; and 
 the changes of motion in the first revolution will be repeated 
 exactly in all succeeding revolutions. Let us now add to 
 our system of two bodies a third body, as the moon. In 
 case the sun had no existence, or was removed to an infinite 
 distance, then the circumstances of motion in the moon, 
 once determined, would remain absolutely invariable ; but 
 the moment we unite the three bodies, the sun, earth, and 
 moon, into a system of three orbs, mutually dependent upon 
 each other, the perfection and simplicity which marks a 
 system of two bodies is for ever destroyed; and modifications 
 are at once introduced into the motion of the earth revolving 
 
MOTION AND GKAVITATION. 150 
 
 around the sun, and also into that of the moon revolving 
 around the earth, of an exceedingly complex and difficult 
 character, and requiring the highest developments of mathe- 
 matical analysis to grapple successfuly with this great 
 problem of the three bodies. 
 
 The solution of this problem has never been positively 
 accomplished, but approximations of wonderful delicacy have 
 been reached by the successors of Newton ; so that, for all 
 practical purposes in astronomy, this approximate solution 
 may be fairly regarded as absolute. 
 
 As the plan laid down in this work does not admit the 
 use of any but the simplest mathematical elements, we shall 
 only trace out, in general terms, the consequences which 
 must follow from the introduction of a third body into a 
 system of two revolving orbs ; and, for the purpose of fixing 
 our ideas, we will suppose the earth and moon to be our two 
 bodies. The moon's orbit in magnitude, and figure, and 
 position, is supposed to be known ; her period of revolution 
 and the circumstances of her motion in her orbit are also 
 supposed to be accurately determined. The earth being 
 fixed in position, and the moon performing her revolution 
 under the laws of motion and gravitation, let us now add to 
 this simple system a third body, the sun ; and to render our 
 investigation as simple as possible, we will adopt the hypo- 
 thesis that the earth continues at rest, but that a new 
 force, namely, the sun's attraction, now begins to exert its 
 influences upon the moon. In order still further to sim- 
 plify the case, let us suppose the sun's centre to be situated 
 in the prolongation of the longer axis of the moon's orbit ; 
 and that the moon, in passing through her aphelion, will 
 cross the line joining the centres of the earth and sun. 
 Under this configuration it is clearly manifest that the 
 figure of the moon's orbit will be changed ; because the 
 attractive power of the sun will certainly increase the dis- 
 tance to which the moon travels from the earth ; for the 
 velocity with which the moon moves away from her peri- 
 helion pq'nt will be reinforced by the attractive power of 
 
156 POPULAR ASTRONOMY. 
 
 the sun, and thus her aphelion distance will be increased. 
 By the same reasoning it will appear that her perihelion 
 distance will be somewhat diminished, and thus the longer 
 axis will be increased in length, and the period of revolution 
 of the moon will, in like manner, be increased. 
 
 These changes having been once accomplished, and the 
 moon having taken up her new orbit under the action of the 
 new forces, so long as these forces remain constant, that is, 
 so long as the sun remains fixed in position, the new orbit 
 will remain as invariable as did the old before the intro- 
 duction of the sun. All the changes accomplished by the 
 sun's power, whereby the new orbit is made to differ from 
 the old, are called, in astronomy, perturbations, and the sun 
 is called the disturbing body. 
 
 Let us now suppose the sun, retaining its distance from 
 the earth, to start from its position on the prolongation of 
 the longer axis of the moon's orbit, and to commence a 
 revolution around the earth in a circular orbit, lying in the 
 plane of the moon's orbit. A little reflection will show us 
 that the moment the disturbing body begins to move, the 
 direction of its attractive power upon the revolving moon 
 will begin to change ; a new set of disturbances will now 
 commence, not affecting the new figure of the moon's orbit, 
 but changing the position of the principal lines of the orbit 
 in its own plane ; for it is clearly manifest that the strongest 
 power will be exerted to draw the moon away from the 
 earth on the line joining the centres of the earth and sun ; 
 and hence the aphelion point of the moon's orbit will neces- 
 sarily tiy to follow this moving line. The subject will be 
 made plainer by an examination of the figure below, in 
 which E represents the earth in the focus of the moon's 
 orbit, S the place of the sun on the prolongation of P M the 
 longer axis, P the perigee, and M the apogee of the moon's 
 orbit. In case the sun be removed to S', and there remain 
 stationary, it is manifest that each time the moon crosses 
 the line ES' it will be subjected to the most powerful 
 
MOTION AND GRAVITATION. 
 
 influence to draw it away from the earth at E ; and in case 
 the sun remain stationary for a sufficiently long time at each 
 
 of the moon's revolutions, the point M will approach M', and 
 finally it will actually fall on M', where it will remain fixed, 
 so long as the sun is stationary. 
 
 In case, however, the sun again advances in the same 
 direction, the apogee of the moon will again advance ; and 
 should the sun, by successive steps, slowly perform an entire 
 revolution, pausing at each step sufficiently long for the 
 moon's apogee to come up to the line joining the centres of 
 the earth and sun ; when the revolution of the sun shall 
 have been completed, the revolution of the moon's apogee 
 will, in like manner, have been finished. 
 
 If, instead of supposing the sun to advance by successive 
 steps, we admit his uniform progress, it is clearly manifest 
 that in each revolution of the moon, the apogee of her orbit 
 must advance a certain amount in the direction of the sun's 
 motion, and, in the end, a complete revolution of the moon's 
 apogee will be accomplished under the disturbing influence 
 of the sun's attraction. 
 
 We have seen that, if the sun were stationary, his dis- 
 turbing power would only go to change the figure of the 
 moon's orbit, leaving the direction of the longer axis undis- 
 turbed. The revolution of the sun in a circular orbit by 
 slow degrees accomplishes an entire revolution of the apogee, 
 or of the line of apsides ; and thus, in case the line of 
 apsides should perform its revolution in a period which shall 
 
158 POPULAR ASTRONOMY. 
 
 be an exact multiple of the period of the sun's revolution, 
 then at the end of one such cycle the moon will have passed 
 through all the changes which can arise from the disturbing 
 influence of the sun. Tkese changes will therefore be 
 strictly periodical, and in the end the moon will return to 
 its first position, and will repeat the same identical changes 
 for ever. 
 
 "We will now consider the solar orbit to be elliptical. 
 This involves, by necessity, a perpetual change in the sun's 
 distance ; and as his disturbing power varies in intensity 
 inversely with the square of his distance, it is manifest that 
 this variation in the disturbing force will introduce a cor- 
 responding variation into the figure of the moon's orbit. If 
 the sun be supposed to advance toward the earth and the 
 moon, in the direction of the line of apsides, its disturbing 
 power would be exerted to draw the moon further from 
 the earth the nearer the sun approached ; in other language, 
 to increase the magnitude of the moon's orbit and the 
 period of her revolution. This action will be varied in case 
 the sun recede from the earth along the same line ; and if 
 this approach and recess were made by successive steps, at 
 intervals sufficiently long to allow the moon's orbit to assume 
 a fixed form, then one vibration of the sun advancing and 
 receding through equal space, would work out a series of 
 changes in the form of the moon's orbit identical with those 
 accomplished by each successive vibration, while in all these 
 changes the direction of the line of apsides would remain 
 fixed. 
 
 If now we suppose the advance and recess of the sun to 
 be effected by its revolution in an elliptic orbit, then we 
 shall find that the changes of figure in the moon's orbit, 
 just noticed, as due to the sun's change of distance, will be 
 combined *dth an advance and final complete revolution of 
 the line of apsides ; and admitting the figure of the sun's 
 orbit to remain unchanged, and the principal axis of its 
 orbit to remain fixed for ever in position, a time will come 
 when the sun will have been presented to the moon in every 
 
MOTION AND GRAVITATION. 159 
 
 possiMe position ; and all the changes in the figure of the 
 moon's orbit, and the revolution of the line of apsides of 
 the moon's orbit, due to the revolution of the sun in his 
 orbit, will have been accomplished. The moving bodies 
 return to their primitive points of departure, and a new 
 cycle of changes begins, to be repeated, in the same order 
 for ever. 
 
 Thus far we have supposed the line of apsides of the 
 sun's orbit to remain fixed in position and unchanged in 
 length. It is manifest that a revolution of the line of 
 apsides of the sun's orbit, definite in period and fluctuations, 
 in its length also periodical, would introduce additional 
 fluctuations in the moon's motion, and in the length and 
 position of the principal axis of her orbit. But while we 
 rise in complexity, and while the periods requisite for 
 effecting all these changes expand into ages, we still recog- 
 nize the great fact that periodicity remains, and that in the 
 end, at the termination of a vast cycle, the revolving bodies 
 must return again to their points of departure, to repeat 
 the same identical changes through endless ages. 
 
 In all our reasoning thus far, we have supposed that the 
 three bodies under consideration always lie in the same 
 plane ; in other language, that the planes of the orbits of 
 the moon and earth coincide. This, however, is not the 
 case of nature. As we have already seen, the moon's orbit 
 is inclined to the plane of the ecliptic under an angle of 
 about 5 ; the line of intersection of the two planes being 
 called the line of the moon's nodes, which line must, of 
 course, always pass through the earth's centre. 
 
 We shall now proceed to take this inclination into con- 
 sideration, and ascertain whether the sun's disturbing force 
 has any, and if any, what effect on the position of the line 
 of nodes, and on the inclination of the moon's orbit. For 
 this purpose, let us suppose the earth to be stationary, and 
 that the line of nodes of the moon's orbit holds a position 
 perpendicular to the line joining the centres of the earth 
 and sun, and that the moon starts from her ascending node 
 
160 POPULAR ASTRONOMY. 
 
 to describe that portion of her orbit lying above the plane 
 of the ecliptic. The power of attraction of the sun will 
 manifestly exert itself in such a manner, as to cause the 
 moon to deviate from its old orbit, and to describe a new 
 orbit, which will lie in all its points a little nearer to the 
 plane of the ecliptic. The moon will not, therefore, rise in 
 this superior part of her orbit as high above the plane of 
 the ecliptic as she did before her motion was disturbed by 
 the sun ; and in descending to pass through her node, she 
 will clearly reach the plane of the ecliptic quicker than she 
 did when undisturbed, and pass through her node at a point 
 nearer to herself than that occupied by the former node ; in 
 other language, the old node comes up to meet the advancing 
 moon, and thus takes up a retrograde motion. 
 
 Let us now examine the motion of the moon in that 
 portion of her orbit lying beneath the plane of the ecliptic, 
 and most remote from the sun. Here the sun's disturbing 
 influence will be diminished somewhat, in consequence of 
 the increased distance at which it operates j but its effect 
 will manifestly be to cause the moon to descend more rapidly, 
 and to reach a lower point beneath the ecliptic than when 
 undisturbed, increasing the inclination of the plane of the 
 orbit, and causing the moon to reach her ascending node at 
 a point earlier than when undisturbed, and thus producing 
 a retrocession or retrograde motion of the line of nodes. 
 Thus it appears that, in the long run, the sun's disturbing 
 influence will tend to change within certain limits the angle 
 of inclination of the moon's orbit ; and, indeed, if the earth 
 were fixed in position, would finally destroy this inclination 
 entirely, reducing the plane of the moon's orbit to absolute 
 coincidence with that of the earth; but, as the moon is 
 carried by the earth around the sun, and as the moon's orbit 
 in the course of an entire revolution of the earth is thus 
 presented to the sun at opposite points of the orbit under 
 reverse circumstances, there is a compensation accomplished, 
 so far as the angle of inclination is concerned, and also a 
 partial compensation in the retrogression of the line of 
 
MOTION AND GRAVITATION. 161 
 
 nodes of the moon's orbit, but not such as to prevent, in the 
 end, a complete revolution of the moon's nodes in a period 
 which we have already seen amounts to eighteen years and 
 two hundred and nineteen days. 
 
 We have thus attempted to present a general account of 
 the effect of a disturbing force. These same principles may 
 be extended yet further, and will give a general idea of the 
 effects produced by the planets and their satellites upon 
 each other. 
 
 If we return for a moment to the hypothesis that the 
 earth is the only planet revolving about the sun, the mag- 
 nitude of its orbit, as well as the length and position of the 
 line of apsides, will remain for ever fixed. If, however, we 
 introduce into our system a new planet revolving in an 
 orbit interior to that of the earth, whatever force is exerted 
 upon the earth by the attractive power of this new planet, 
 will go to reinforce the power exerted by the sun ; and 
 hence the disturbing influence of the planet will tend to 
 diminish the magnitude of the earth's orbit, and to decrease 
 its periodic time. If the disturbing planet revolve in the 
 same direction with the earth, by applying the reasoning 
 hitherto used, we shall find that its effect will be to cause 
 the perihelion point of the earth's orbit to advance and 
 retreat during the revolution of the disturbing body, always 
 leaving, however, a slight preponderance of the advancing 
 movement over the retrograde. 
 
 In case the disturbing body revolve in an orbit exterior 
 to that of the earth, then its effect will be to expand the 
 earth's orbit and to increase the periodic time, while the 
 influence exerted upon the position of the line of apsides 
 will, in the long run, produce an advance. 
 
 The reasoning hitherto employed with reference to the 
 inclination of the moon's orbit to the ecliptic is directly 
 applicable to the effect produced by any planet upon the 
 inclination of the orbit of any other planet, as referred to 
 a fixed plane. Take the earth for example, and let us con- 
 sider the effect of any planet, either interior or exterior, 
 
 M 
 
162 POPULAR ASTRONOMY. 
 
 upon the inclination of this plane to any fixed plane. So 
 long as the disturbing body is revolving in that part of it? 
 orbit lying below the plane of the ecliptic, the tendency of 
 the disturbing force will be to draw the earth from its 
 undisturbed path below the plane of a fixed ecliptic ; while 
 this effect will be reversed, whenever the disturbing planet 
 shall pass through the plane of the ecliptic, and commence 
 the description of that part of its orbit which lies above 
 this plane. 
 
 From the above reasoning it is clearly manifest that, as 
 not a solitary planet or satellite is moving undisturbed 
 under the attractive power of its primary body, not one 
 of the heavenly bodies describes rigorously an elliptic orbit ; 
 nor does the line joining the sun with any planet sweep 
 over precisely equal areas in equal times ; neither are the 
 squares of the periodic times of the planets exactly pro- 
 portioned to the cubes of their mean distances from the sun. 
 In short, every law of Kepler, whereby perfect harmony 
 seemed to be introduced among the heavenly bodies, is now 
 seen to fail, in consequence of the law of universal gravita- 
 tion, and we find ourselves surrounded by a problem of 
 wonderful grandeur, but of almost infinite complexity. 
 Before this problem can be fully solved, we must measure 
 the distance which separates every planet from the sun, and 
 which divides every satellite from its primary ; we must 
 weigh the sun and all his planets and every satellite ; we 
 must determine the exact periods of revolution of each of 
 these revolving worlds ; and, when all this is accomplished, 
 to trace out the reciprocal influences of each upon the other 
 demands powers of reasoning far transcending the abilities 
 of the most powerful genius, and hence the mind must 
 either forego the resolution of this problem, or prepare for 
 itself some mental machinery which shall give to thought 
 and reason the same mechanical advantages which are 
 obtained for the physical powers of the body by the inven- 
 tion and construction of the mighty engines of modern 
 mechanics. 
 
MOTION AND GRAVITATION. 163 
 
 This has actually been accomplished in the discovery and 
 gradual perfection of a branch of mathematics called the 
 infinitesimal analysis. Up to the time of Newton, the 
 mind employed alone the reasoning of geometry in the 
 examination and discussion of the problems presented in 
 the heavens. Even Newton himself was content to publish 
 to the world the results of the application of the law of 
 gravitation to the movement of the planets and their satel- 
 lites under a geometrical form, exhibiting, in the use of 
 these old methods, a sort of gigantic power which has ever 
 remained as a monument of his wonderful ability. 
 
 He was, however, fully conscious of the fact, that the 
 mind demanded for its use, in a full investigation of the 
 physical universe in the pursuit of these flying worlds, 
 journeying through space amid such a crowd of disturbing 
 influences a far more subtle, pliable, and powerful mental 
 machinery than that furnished in the cumbrous forms of 
 geometrical reasoning. Conscious of this want, the genius 
 of Newton supplied the deficiency, and gave to the world 
 the infinitesimal analysis, which, as improved and extended 
 by the successors of the great English philosopher, has 
 enabled man to accomplish results which seem to place him 
 almost among the gods. 
 
 The plan of our work does not permit any attempt to 
 explain the nature and powers of this new method of 
 reasoning. We can only illustrate imperfectly the difference 
 between the use of geometry and analysis. The demonstra- 
 tion of a problem by geometry demands that the mind shall 
 comprehend and hold the first step in the train of reasoning ; 
 then, while the first is held, the second must be compre- 
 hended j and while intently holding these two steps, the 
 third must be mastered and held, while the mind advances 
 to the fourth step : thus progressing with a constantly- 
 accumulating weight oppressing the attention, and tending 
 to crush and destroy further effort to advance ; till, finally, 
 the steps become so numerous and complex, that only those 
 possessed of a genius of surpassing vigour are able to reach 
 
 M 2 
 
164 POPULAB ASTRONOMY. 
 
 in safety the last step, and thus grasp the full demonstration 
 of the problem. Such is the reasoning of geometry. That 
 of analysis is entirely different. Here the great effort is put 
 forth to master fully and perfectly the conditions of the 
 problem, and then to fasten upon the problem thup mastered 
 the analytical machinery demanded in its resolution. This 
 once accomplished, the mind puts forth its energy and 
 accomplishes the first step, and may there stop and rest, in 
 the full confidence that what has been gained can never be 
 lost. Days, even months may pass, before the problem be 
 resumed ; but in this lapse of time there is no loss, and the 
 investigation may be taken up precisely where it was left 
 off j and so one step after another may be taken, each 
 dependent on the other, but each in some sense stereotyped 
 as the mind advances, and remaining fixed without the 
 putting forth of any mental effort to retain it. In short, 
 geometry demands a vigour of mind sufficient to grasp, and 
 hold at the same instant, every link in the longest and most 
 complex chain of reasoning, while analysis only requires a 
 power of genius sufficient to deal with individual links in 
 succession; thus, in the end, reaching the conclusion by 
 short and comparatively easy mental marches. 
 
 CHAPTER XI. 
 
 INSTRUMENTAL ASTRONOMY. 
 
 Method for obtaining the Mass of the Sun. For getting the Mass of a 
 Planet with a Satellite. For Weighing a Planet having no Satellite. 
 For Weighing the Satellites. Planetary Distances to be measured. 
 Intervals between Primaries and their Satellites to be obtained. 
 Intensity and Direction of the Impulsive Forces to be determined. 
 These Problems all demand Instrumental Measures. Differential Places. 
 Absolute Places. The Transit-Instrument. Adjustments. Instru- 
 mental Errors. Corrections due to various Causes. American Method 
 of Transits. Meridian-Circle. The Declinometer. 
 
 THE general reasoning presented in the preceding chapter 
 can only be reduced to exact application after having 
 
INSTRUMENTAL ASTRONOifY. 165 
 
 obtained the numerical values of the quantities demanded 
 in the investigation. The mathematician may assume these 
 quantities at his pleasure, and with the assumed weight of 
 his sun, and planets, and satellites, and with their assumed 
 distances, and with the assumed directions and intensities of 
 the impulsive forces, he may master, by analytical reasoning, 
 all the circumstances attending the revolutions of these sup- 
 posed worlds, and thus trace their imaginary history for ages, 
 either past or future. 
 
 This is the work of the pure mathematician. The physical 
 astronomer takes up the general mathematical reasoning thus 
 perfected ; and to employ it in writing out the history of 
 the real bodies constituting the solar system, he must mea- 
 sure the actual distances between the sun and the planets, 
 and the distances from each primary to its satellites ; he 
 must weigh exactly the sun and each of the planets and 
 satellites, and he must measure in some way the direction 
 and intensity of the impulsive forces by which the planets 
 and their satellites were projected in their respective 
 orbits. 
 
 We shall now proceed to show that the determination of 
 all these quantities depends on exact astronomical measure- 
 ments, which measurements demand the invention and con- 
 struction of instruments of the highest order of power, 
 delicacy, and perfection. 
 
 To WEIGH the SUN AND PLANETS. Let it be borne in 
 mind that the law of gravitation asserts that bodies attract 
 with a force or power directly in proportion to their mass 
 or weight. Hence a sun, weighing twice as much as the 
 central orb of the solar system, would (at the same distance; 
 attract with a double force. The same is true of the earth ; 
 and if it were possible to hollow out the interior of the 
 earth until its weight were reduced to one-half of what it ia 
 now, its power of attraction would be diminished in the 
 same exact proportion. 
 
 Thus, to know with what power the sun or any planet or 
 any satellite attracts a body at a_ given distance, we are com- 
 
166 POPULAR ASTRONOMY. 
 
 pelled to ascertain the exact weight of the sun, planet, or 
 satellite. 
 
 We shall show hereafter that it is possible to reach an 
 approximate value of the weight of the earth in pounds 
 avoirdupois ; but for our present purpose it will be sufficient 
 to state that the weight of the earth is well represented by 
 the intensity of its power of attraction at a unit's distance 
 from its centre. For this unit of length we will take the 
 earth's radius, and hence a body on the surface is attracted 
 by a force or power such as will measure the mass or weight 
 of the earth ; but the intensity of any force is measured by 
 the quantity of motion it is capable of generating in a given 
 time. Hence the intensity of the earth's attractive power 
 will be correctly measured by the velocity it impresses on a 
 body free to fall, in, say, one second of time. This is a matter 
 of the simplest experiment, by which it is found that the 
 earth's attractive power generates in one second a motion in 
 a falling body such as to carry it over a space equal to about 
 sixteen feet in one second. In case the earth were twice as 
 heavy, the space passed over by a falling body in one second 
 would be doubled, and so forward in like proportion for any 
 increase of weight. 
 
 Having thus found a measure of the weight of the earth 
 in the space passed over in a second of time by a falling 
 body, in case it were possible to transport this body to the 
 surface of the planet Yenus (assuming the diameter of 
 Venus and the earth to be equal), then permitting it to fall, 
 and measuring the space over which it passes in one second, 
 this space would hold the same proportion to sixteen feet as 
 the weight of Yenus does to that of the earth. If the 
 diameters of the planets are unequal, then we must take into 
 account the fact that the falling body is not at equal 
 distances from the centres of the planets, and that the force 
 of attraction is thus diminished inversely as the square of 
 the distance from the centre is increased. Let us attempt 
 to weigh two planets, whose diameters are in the proportion 
 of one to two. At the surface of the smaller planet suppose 
 
INSTRUMENTAL ASTEONOMY. 167 
 
 the body falls sixteen feet in one second, while at the surface 
 of the larger planet it passes over sixty-four feet in the same 
 time. In case the diameters were equal, this result would 
 show that one body was four times as heavy as the other ; 
 but the falling body is twice as far from the centre of the 
 large planet as it is from the centre of the small one ; and 
 hence the force or power of attraction of the large planet is 
 only one-fourth part what it would have been in case the 
 falling body had been brought to within one unit of its 
 centre. If, then, with an energy reduced at a distance of 
 two units to one quarter, it causes a fall of sixty-four feet in 
 one second, the entire energy would, at a unit's distance, 
 cause a fall through four times sixty-four feet, or through 
 256 feet ; and hence the weights of the planets under 
 examination are in the proportion of 16 to 256 or 1 to 16. 
 
 The train of reasoning here presented may be extended 
 to embrace any given case ; and if it were possible to make 
 the experiment of the falling body, as above described, at 
 the surfaces of the sun, planets, and satellites (admitting 
 that we know the diameters of all these bodies), then would 
 it be possible to ascertain their masses, as compared with 
 that of the earth, taken as a unit. 
 
 But it is impossible to pass to the sun and planets for such 
 experimentation, and hence we must devise some substitute 
 which may fall within the limits of practicability. To obtain , 
 the relative weights of the sun and earth, we have only to 
 call to mind the fact that the moon, under the power of the 
 earth's attraction, is ever falling away from the rectilineal 
 path in which it would fly but for this very power of attra- 
 tion ; while in like manner the earth is ever falling away 
 from the right line in which it would move but for the 
 attractive energy of the sun. Here, then, are two bodies 
 the earth falling to the sun, the moon falling to the earth ; 
 and in case we could measure the precise distance which 
 each of these bodies falls, under the respective powers of 
 attraction exerted on them, taking into account the effect 
 produced on the two forces by the inequality of the distances 
 
168 POPULAR ASTRONOMY. 
 
 at which they operate, we should reach the exact relative 
 weights of the sun and earth. Thus, admitting that the 
 distance at which the sun operates on the earth is 400 times 
 greater than the distance at which the earth operates on the 
 moon, in case the effects were equal, the sun would be 
 160,000 times heavier than the earth, since its power of 
 attraction is reduced by the distance in this exact ratio. 
 But again, admitting that we find, even with this high 
 reduction, the sun's power on the earth is still two and a 
 half times greater than the earth's power on the moon (as is 
 shown in their respective deflections from a right line in one 
 second of time), then will the sun be 2^x160,000 times 
 heavier than the earth ; and this, indeed, as we shall find 
 hereafter, is about the relative weights of these two globes. 
 
 To resolve this great problem, then, of weighing the sun 
 against the earth, we must first measure the sun's distance 
 and the moon's distance, and the exact amounts by which 
 the earth and moon are caused to fall away from a rectilineal 
 orbit in one second of time, which measurements demand 
 instruments of the highest order. 
 
 To WEIGH AGAINST THE EARTH, A PLANET ATTENDED BY 
 
 A SATELLITE. In case any planet be attended by a satellite, 
 if we can measure the precise distance separating these two 
 bodies, and determine the period of revolution of the satellite, 
 we can thence derive the weight of the planet as compared 
 with that of the earth. To fix our ideas, let us suppose 
 Jupiter's nearest satellite to be as far from Jupiter as our 
 moon is from the earth, and to perform its orbital revolution 
 in the same exact time occupied by the moon. This would 
 prove Jupiter to be just as heavy as the earth. But suppose 
 now that at equal distances Jupiter's moon revolves ten 
 times as rapidly as the earth's moon, this fact proves that 
 Jupiter must be one hundred times as heavy as the earth. 
 This is evident from what we have already said, that the 
 centrifugal force in any revolving body increases as the 
 squwre of the velocity ; and, as the moon of Jupiter is now 
 supposed to revolve ten times as fast as our moon, its centri- 
 
INSTRUMENTAL ASTRONOMY. 169 
 
 .gal force will be one hundred times as great as that of the 
 earth's moon ; and hence Jupiter's attraction, to counter- 
 balance this tendency to fly from the centre, must be one 
 hundred-fold greater than that of the earth. This is on the 
 hypothesis of equal distances. But if Jupiter's moon be 
 supposed to be twice as remote from its primary, and to 
 revolve ten times as rapid as our moon, then will it be 
 demonstrated that Jupiter is one hundred times heavier, on 
 account of the square of the velocity of the revolving moon ; 
 but this weight must be multiplied by the square of two on 
 account of the double distance at which it acts. Hence, 
 under these circumstances, Jupiter would be 400 times as 
 heavy as the earth. 
 
 Thus, to determine the weight of a planet in terms of the 
 earth's weight as unity, we must learn the exact distance 
 and periodic time of our moon, and also the interval by 
 which the planet" and its moon are separated, as well as the 
 period of revolution of the satellite, all of which again 
 demand the use of instruments of a high order of accuracy 
 and delicacy. 
 
 To WEIGH A PLANET HAVING NO SATELLITE. Three of 
 the planets, viz., Mercury, Venus, and Mars, so far as 
 known, are not accompanied by a moon. The preceding 
 method of obtaining the mass or weight will not apply to 
 either of these planets. It is only after acquiring a very 
 exact knowledge of the movements of the planets whose 
 masses may be derived from their satellites, that it becomes 
 possible to determine the weights of the remaining planets. 
 Let us suppose that the earth alone revolved around the 
 sun, and that its orbit was perfectly determined. In an 
 exterior orbit of known dimensions let us place the planet 
 Mars. This will at once modify the former orbit of the 
 earth, and the change will depend, in quantity, upon the 
 mass of the new planet ; and in case it became possible to 
 measure these changes, their values will give the weight of 
 the body producing them. 
 
 The same hypothesis remaining with reference to the 
 
170 POPULAR ASTRONOMY. 
 
 earth's orbit, we may imagine the new planet to revolve in 
 the orbit of Venus, interior to that of the earth, and th 
 same kind of investigation will lead to the determination oi 
 the mass of this interior planet. 
 
 We shall see hereafter that certain periodical comefeSj 
 favourably located, furnish the means of corroborating the 
 results reached by the above train of reasoning, by the data 
 their perturbations furnish for reaching the mass of the 
 planet producing these effects. 
 
 To WEIGH THE SATELLITES. The effect produced by the 
 moon on the earth in causing the figure of its orbit to sway 
 to and fro under the moon's attractive power furnishes again 
 the data whereby the moon's mass may be determined. In 
 the case of many satellites to the same planet, their effects 
 on each other being carefully determined, furnish the means 
 of computing their masses. This, however, is a difficult 
 problem, and one in which a solution has been effected only 
 in the system of Jupiter. The masses of the satellites of 
 the other superior planets have as yet not been obtained 
 with any reliable certainty. 
 
 We have thus presented methods by which the masses of 
 the sun, planets, and satellites may be obtained, provided 
 certain measurements can be made, which measurements 
 demand the aid of powerful and accurate instruments. 
 
 The distances separating the sun and planets, and separa- 
 ting the primaries and their satellites, must be obtain eu 
 before we can trace the history of any one of these revolving 
 worlds. We have already explained the processes by which 
 the earth's distance from the sun may be obtained, by the 
 use of the phenomena attending the transit of Venus. This 
 problem again demanded instrumental measurement. Ad- 
 mitting the earth's distance from the sun to be known, 
 Kepler's third law will give the distances of all the planets 
 of our system, provided we have obtained their periods of 
 revolution around the sun. The method of obtaining the 
 periodic times has also been explained, and in this process 
 instrumental measurements are demanded. 
 
INSTRUMENTAL ASTRONOMY. 171 
 
 In like manner, to reach the periods and distances of thfe 
 satellites, their elongations, occupations, and eclipses, must 
 be carefully measured and noted, demanding instruments of 
 a high order. 
 
 To trace a planet or satellite, in addition to the quantities 
 already pointed out, we have seen that we must know the 
 intensity of the impulsive force by which it was projected in 
 its orbit. But we have seen that the intensity of any 
 impulse is measured by the velocity it is capable of producing 
 in a unit of time. Admitting, then, that we know the 
 distance of a planet from the sun, and its period of revolu- 
 tion, we know the velocity with which it moves, in case its 
 orbit be circular. The earth, for example, in 365J days 
 accomplishes a journey round the sun in a circle whose 
 diameter is 190,000,000, and whose circumference is equal 
 to this quantity taken 3 '141 56 times. Hence, by dividing 
 the number of miles travelled in the entire circuit by the 
 number of days occupied in the journey, we have the rate 
 per diem, or velocity. Dividing the space passed over in one 
 day by 24, we have the rate per hour, and finally may obtain 
 the rate per second. If the orbit be not circular, we can 
 always find a circle which, for a very short distance, will 
 coincide with an elliptic or other curve ; and on this circle 
 we may suppose the planet to move for a very short time, 
 as one second, with uniform velocity, and the space passed 
 over in this unit will again measure the intensity of the 
 impulsive force at this part of the orbit. Here again we 
 have presupposed a knowledge of the magnitude and figure 
 of the elliptic orbit before the intensity of the impulsive 
 force can be reached, and to determine these quantities 
 instrumental measurement is demanded, requiring instru- 
 ments of great perfection. 
 
 The last quantity demanded by the mathematician in 
 writing out the history of a planet moving in space, is the 
 direction of the impulsive force projecting it in its orbit. 
 This is readily obtained, when we shall have learned the 
 exact direction of a line tangent to any point of the planetary 
 
172 POPULAR ASTRONOMY. 
 
 orbit; for the direction of the impulse must always be 
 tangent to the curve described by the body set in motion. 
 If we join the planet with the sun by a right line, this line 
 will form an angle with the tangent to the planetary orbit; 
 and we shall find hereafter that the nature of the orbit will 
 depend upon the value of this angle, or in other language, on 
 the direction in which the impulse is applied. 
 
 Thus we find that not a single quantity of the five required 
 to determine the circumstances of motion of a body revolving 
 under the laws of motion and gravitation, can be reached 
 without instrumental measurement ; so that our entire know- 
 ledge of the physical universe hangs at last on the accuracy 
 and perfection of the instruments which have been invented 
 and constructed for making these measures, a fact which 
 elevates instrumental astronomy to a position of the highest 
 dignity and importance. 
 
 The measures demanded in instrumental astronomy are 
 divided into two great classes. In the first class all the 
 measures of position are absolute ; that is, a star or planet 
 whose place is thus determined is located on the celestial 
 sphere, and fixed for the moment in position by a measure 
 of its distance, say, from the north pole of the heavens along 
 the arc of a great circle, and also its distance measured on 
 the equinoctial from the vernal equinox, or from some cither 
 fixed points which may have been selected. In the second 
 class all the measures are relative or differential ; that is, an 
 interval between two points in close proximity is determined. 
 To this class belong the measures of the diameters of the 
 sun and moon and planets ; the elongations of the satellites 
 from their primaries ; the measures of the transits of Venus 
 and Mercury across the disc of the sun ; the measures of the 
 solar and lunar spots ; the distances between the doublo and 
 multiple stars ; in short, all those measures involviiig mere 
 differences of position. 
 
 Each of these classes of measures demands its own peculiar 
 and appropriate instruments, each of them involving the 
 
INSTRUMENTAL ASTRONOMY. 173 
 
 data required in the solution of the sublimest problems oi 
 celestial science. 
 
 We shall now proceed to exhibit an outline of the structure 
 of a few of the most important instruments belonging to 
 these two classes, only for the purpose of presenting the ex- 
 traordinary difficulties which must be met and conquered in 
 the seemingly simple mechanical problem of fixing the place 
 of a star in the celestial sphere. 
 
 For the purpose of giving position to the heavenly bodies, 
 astronomers refer them to the surface of a celestial sphere, 
 whose poles are the points in which the earth's axis prolonged 
 pierces the sphere of the fixed stars. To determine a point 
 on the surface of any sphere, we must fix its distance >n the 
 arc of a great circle from the north pole, and we must also 
 know the distance of the meridian- line on which it is located, 
 from a fixed meridian. 
 
 Astronomers have chosen for their prime meridian that 
 one which passes through the vernal equinox ; and as the 
 celestial sphere revolves to our senses with uniform velocity 
 once in twenty-four hours, the vernal equinox will come at 
 the end of this period to the meridian of the place from 
 whence it started. Any object, therefore, which crosses the 
 meridian of a given place an hour later than the vernal 
 equinox, has its place fixed somewhere on the circumference 
 of a known meridian, or hour-circle. If at the same time 
 its distance from the north pole can be determined, its posi- 
 tion on the celestial sphere will be positively defined by these 
 two elements. As we have already seen, the vernal equinox 
 is the point in which the great circle of the heavens, cut out 
 by the indefinite extension of the plane of the earth's orbit, 
 intersects the equinoctial circle, or that circle cut from the 
 celestial sphere by the indefinite extension of the plane of 
 the earth's equator. If the vernal equinox were absolutely 
 fixed, and if in that point a star were located, this star 
 would revolve with all the other stars of the heavens once 
 in twenty-four sidereal hours. To mark the movement of 
 
174 POPULAR ASTRONOMY". 
 
 this vernal equinox astronomers employ the sidereal clock, 
 whose dial is divided into twenty-four hours, and which, 
 when perfectly adjusted, will mark Oh. Om. Os. at the moment 
 the vernal equinox is on the meridian of the place where the 
 clock is located. All points on the celestial sphere will pass 
 the meridian necessarily at intervals of time marking the 
 position of the hour-circle in which they are located, relative 
 to the prime meridian passing through the vernal equinox. 
 These intervals of time which elapse between the passage of 
 the vernal equinox across the meridian of a given place, and 
 the passage of any heavenly body across the same meridian, 
 are called right ascensions. Thus a star which follows the 
 vernal equinox, after an interval of 2h. 10m. 20s., as 
 marked by a perfect sidereal clock, has a right ascension 
 of 2h. 10m. 20s. 
 
 Thus, to fix the place of any heavenly body on the celestial 
 sphere, two instruments have been devised, the one having 
 for its object to measure north polar distances, while the 
 other is employed in the measurement of right ascensions ; 
 the first of these is denominated a mural circle, while the 
 second is called a transit-instrument. 
 
 We shall first consider the principles involved in the con- 
 struction of the transit-instrument. This instrument consists 
 of a telescope mounted upon an axis perpendicular to the 
 axis of the tube of the telescope. This perpendicular axis 
 terminates at each extremity in two pivots of equal size and 
 perfectly cylindrical in form. To give support to this instru- 
 ment a solid pier of masonry is built, resting upon a 
 firm foundation, and isolated from the surrounding building. 
 On the upper surface of this stone pier tw. stone columns 
 are placed, whose centres are separated by a distance equal 
 to the length of the axis of the transit ; on the tops of 
 these columns metallic plates are fastened, to which metal 
 pieces are attached, cut into the shape of the letter Y. If in 
 these Y's the pivots of the transit be laid, in case the axis 
 be precisely level, and lying due east and west, then the axis 
 of the telescope, or visual ray, being carried around the 
 
INSTRUMENTAL ASTRONOMY. 175 
 
 heavens, by revolving the instrument in its Y's, will describe 
 a meridian-line which will pass through the north pole of the 
 heavens. If this meridian-line could be rendered visible, it 
 would be possible to note the passage of any star or other 
 heavenly body across this visible meridian. This cannot be 
 accomplished directly, but the same end is reached by 
 stretching a delicate filament of spider's web across the 
 Centre of a metallic ring, and placing it in the focus of the 
 eye-piece of the telescope ; when this spider's web is lighted 
 up by a lamp, through a suitable orifice, it is seen as a 
 delicate golden line of light stretching across the field of 
 view, and resting on the dark background of the heavens. 
 Revolving the ring which bears the spider's web, we may 
 bring this web to coincide, throughout its entire length, with 
 a true meridian-line, and thus, in reality, we procure for our- 
 selves a visible meridian quite as perfect for our purposes as 
 though it were an actual line of light, sweeping from north 
 to south across the celestial sphere. To render visible the 
 axis of the telescope, or to direct the visual ray, another 
 spider's web is stretched across the field of view, in direction 
 perpendicular to the first, and precisely in the centre of the 
 field, so that by their intersection these spiders' webs form 
 a point of almost mathematical minuteness. 
 
 Let us now examine what is demanded in the construction 
 of the transit to render it an instrument perfect in perform- 
 ance. The object-glass and the eye-piece, forming the optical 
 portion of the telescope, should be perfect in their figure and 
 adjustments ; the tube in which they are placed should be 
 perfectly rigid and inflexible ; the optical axis or line of 
 collimation should be exactly perpendicular to the horizontal 
 axis on which the instument revolves ; the pivots should be 
 exactly equal to each other, and precisely cylindrical in form ; 
 the horizontal aods should lie in a direction exactly east and 
 west, and should be absolutely level. In connection with the 
 transit we require a perfect time-keeper. The clock, when 
 properly adjusted, will mark Oh. 00m. OOs. at the moment 
 the vernal equinox is seen to pass the visible spider's 
 
176 POPULAR ASTRONOMY. 
 
 line meridian of the telescope ; it must then move uniformly 
 during the entire revolution of the heavens, and mark the 
 zero of time again when the vernal equinox returns to the 
 meridian-line. Such are the mechanical demands required in 
 the construction and use of the transit and clock : but, to 
 obtain a perfect result, the observer is required to perform 
 his part in the operation ; he must note the exact instant at 
 which the vernal equinox passes the visible meridian, so as 
 to set his sidereal clock ; this being accomplished, to obtain 
 the right ascension of any heavenly body he must seize the 
 precise moment, as marked by his clock, at which the centre 
 of the object under observation passes the meridian. 
 
 To obtain, then, the element of right ascension required 
 to fix the place of a heavenly body at a given moment, we 
 require a perfect transit, perfectly adjusted, a perfect clock, 
 perfectly rated, and a perfect observer, with a perfect method 
 of subdividing time into minute fractions. Not one single 
 one of these demands can ever be met. Even admitting the 
 possible construction of a perfect instrument, every change 
 of temperature will effect certain changes in the material of 
 which it is composed. No two pivots can possibly be made 
 exactly equal, nor precisely cylindrical in form ; and should 
 the observer succeed in placing the axis of his transit so as 
 to lie east and west, as well as horizontal, it will not remain 
 in this position for even a single hour of time. If the clock 
 be adjusted so as to mark the exact zero of time, and to move 
 off with a uniform rate, this rate will soon sensibly change, 
 and must be carefully watched even from hour to hour. The 
 observer himself is but an imperfect and variable machine, 
 utterly incapable of marking the exact moments required, 
 his work being subject to errors, whose values fluctuate from 
 day to day ; and to add to all these difficulties, the atmo- 
 sphere which surrounds the earth not only possesses the 
 power of diverting the rays of light from their rectilineal 
 path, but because of its constant fluctuations and changes 
 produces a tremulous or dancing motion in the stars under 
 observation which, to a certain extent, renders it impossible 
 
INSTRUMENTAL ASTRONOMY. 177 
 
 to do exact work, even with perfect instruments and perfect 
 observers, could such be found. 
 
 We will now examine the instrumental means required to 
 determine the second element, the north polar distance, which 
 is demanded in fixing the place of a heavenly body. For this 
 purpose let us suppose a metallic circle to be permanently 
 fastened to the horizontal axis of the transit, having its 
 centre in the central line of the axis, and its plane perpen- 
 dicular to this line. Let us suppose the rim of this circle to 
 be divided into degrees, minutes, and seconds of arc, and this 
 division to have been perfectly accomplished. Let us direct 
 the transit-telescope precisely to the north pole of the heavens, 
 and when thus directed let us fix upon the stone pier a per- 
 manent mark or pointer, directed to the zero point on the 
 divided circle. As we turn the transit away from the north 
 pole toward the south the zero point on the circle will in 
 like manner leave the fixed pointer, and thus the distance 
 from the north pole to any object to which the telescope 
 may be directed will be read on the divided circle from the 
 zero round to the division to which the pointer directs. 
 Such an instrument is called a meridian- circle. Here again 
 new mechanical difficulties present themselves. The cen- 
 tring of the circle, the perfection of the divisions upon its 
 circumference, are matters which cannot be accomplished 
 with absolute accuracy ; and even if this were possible, they 
 are liable to changes to which all material is subjected at 
 every moment. The same is true of the stability of the 
 pointer, any change in whose position must involve an error 
 in the measured north polar distance. 
 
 Thus far we have supposed that in our celestial sphere 
 we have two fixed points of reference, namely, the vernal 
 equinox and the north polar point. Unfortunately for the 
 observer, and to increase the difficulties by which he is 
 surrounded, neither of these points remains absolutely fixed, 
 and even their rate of movement is not uniform ; and thus 
 one difficulty rises above another, culminating in the fact 
 that even the light whereby objects become visible does not 
 
 y 
 
178 POPULAR ASTRONOMY. 
 
 dart through space with infinite velocity, but wings its flight 
 with a measurable speed, which, when conjoined with the 
 Bpeed of the earth's revolution in its orbit, sensibly changes 
 the apparent place of every object under examination. Add 
 to this long catalogue of difficulties the fact that the earth's 
 rotation on its axis is rapidly revolving the observer, his 
 instruments and observatory, at a possible rate of a thousand 
 miles an hour, and some idea may be formed of the embar- 
 rassments under which astronomers are compelled to work 
 out the resolution of the great problem of the heavens. 
 
 Having presented this array of difficulties, we shall not 
 undertake to show in every instance by what precise means 
 they are overcome. So far as regards the movement of the 
 vernal equinox and the north pole, the most extended and 
 elaborate observations have been made through a long 
 series of years by the best instruments and the most skilful 
 observers, and these have been reduced and discussed by the 
 most able mathematicians, until by different methods astro- 
 nomers have reached to so perfect a knowledge of the values 
 of the errors due to these two causes, that it seems as though 
 no greater approximation to accuracy can be made by the 
 same methods. That correction due to the movement of 
 the vernal equinox is called precession; that due to the 
 movement of the north pole is called nutation; of which 
 we shall give a more accurate account hereafter. The error 
 arising from the velocity of light, combined with the orbital 
 and rotary motion of the earth, is called aberration. This 
 subject will also be treated hereafter. Of the three prin- 
 cipal instrumental errors, that arising from want of exact 
 perpendicularity in the position of the axis of the telescope 
 to the horizontal axis of the transit is called the collimation 
 error, and may be detected and measured by mechanical 
 means ; its effect is to cause the visual ray to pierce the 
 heavens east or west of the true meridian, and in the revo- 
 lution of the transit this point of piercing will describe 
 a small circle of the sphere, instead of the great meridian- 
 circle, which it ought to describe. The error arising from a 
 
INSTEUMENTAL ASTRONOMY. 179 
 
 failure to place the transit axis in a truly horizontal position 
 is called the level error ; its effect is to cause the visual ray 
 to pierce the heavens east or west of the true meridian, and 
 the point of piercing, by the revolution of the transit on its 
 axis, will describe a great circle of a sphere inclined to the 
 true meridian, under an angle equal to that which the axis 
 of the transit makes with the horizon, or equal to the level 
 error. The failure to place the axis of the transit precisely 
 east and west gives rise to what is called the azimuthal error. 
 This causes the visual ray or line of collimation of the tele- 
 scope to pierce the heavens on the true meridian only when 
 directed to the zenith. This point of piercing, by revolving 
 the transit on its axis, describes a great circle, which departs 
 from the true meridian at the zenith, under an angle pre- 
 cisely equal to the azimuthal error. Methods have been 
 devised for measuring these various errors, and for com- 
 puting their effect upon the apparent places of the heavenly 
 bodies. 
 
 The rays of light by which every object is rendered 
 visible, as we have already stated, on entering the earth's 
 atmosphere, are bent from their rectilineal path, giving 
 rise to a source of error called refraction. The laws govern- 
 ing the direction of the light, as affected by the atmosphere, 
 have been carefully studied ; so that at present ifc is possible 
 to compute with great exactitude the change of place of any 
 object under observation due to the effects of refraction. 
 The flexure of the tube of the telescope, under the various 
 circumstances by which it may be surrounded, have been 
 thoroughly investigated, while the exact figure of the pivots* 
 of the axis has been subjected to the most rigorous me- 
 chanical tests; in short, all the mechanical deficiencies in. 
 the instrument have occupied the attention of many of the 
 best minds for the past two hundred years, and thus slow 
 but steady advances in accuracy have been accomplished. 
 
 To remedy the errors arising from the perturbations of 
 the atmosphere, as well as those arising from personal error 
 in the observer, in seizing the moment of transit across the 
 
 N 2 
 
180 POPULAR ASTRONOMY. 
 
 visible meridian-line, several spider's lines, commonly called 
 wires, parallel to each other, have been introduced into the 
 focus of the eye-piece of the transit ; and thus the instant 
 at which the star passes, each one of these wires being noted 
 as accurately as possible, the average of all gives a better 
 result than could have been obtained from any one wire. 
 
 To remedy the defects arising from the imperfect divisions, 
 from imperfect centring, and from changes of figure in the 
 circle from whence the north polar distances are read, it is 
 usual to have four pointers, and even sometimes six, by 
 means of which the north polar distance is read in as many 
 places on the divided circle, the average of all giving a better 
 result than any one reading. These pointers, as we have 
 named them, are in reality powerful microscopes, perma- 
 nently fixed in the heavy stone pier on which the instru- 
 ment rests, and having their visual ray fixed by the 
 intersection of spiders' webs, as in the principal telescope. 
 
 From these instrumental imperfections we pass to those 
 which belong to the clock, and here again we are compelled 
 to work with an imperfect machine. No clock has ever 
 been made which can keep perfect time j and the great 
 object of the observer is to learn the peculiarities of his 
 clock, to determine its deviations from absolute accuracy, 
 and to be able to mark these deviations, if possible, from 
 minute to minute. 
 
 The observer, having mastered all the sources of error 
 above described, next comes to the consideration of his own 
 personal deviations from accuracy in attempting to mark 
 the moment at which a star crosses his visible meridian. 
 To observe the transit of a star across the meridian, he 
 places himself at the transit-instrument, enters in his note- 
 book the hour and minute from the face of the clock, then 
 fixing his eye through the telescope upon the star, and 
 counting the beats of the pendulum, he follows the star as it 
 slowly advances t<* the meridian-wire. Between some two 
 beats thus counted the star crosses the wire. The observer 
 holds in his mind, as well as he can, the star's position at 
 
INSTRUMENTAL ASTRONOMY. 181 
 
 the close of the beat before the passage, and at the close of 
 the next beat after the passage, and mentally subdividing 
 this space passed over in one second into ten equal parts, 
 he estimates how many of these parts precede the passage of 
 the star across the meridian, and these parts are the fractions 
 or tenths of a second, which mark the time of transit, 
 Thus he adds to the entry in his note-book already made 
 the number of beats of the pendulum and also the fractions 
 of a second above obtained, and thus the time of transit is 
 obtained, approximately to the tenth part of one second of 
 time. 
 
 In the method of observing transits just explained, so 
 many things are demanded of the observer, that his atten- 
 tion cannot be given exclusively to the determination of the 
 moment of transit ; he must keep up the count of the clock- 
 beat ; he must hold in his mind the interval passed over by 
 the star from one beat to the next during the transit ; he 
 must divide this space by estimation into tenths ; he must 
 assign the number of tenths which precede the transit ; he 
 must enter the seconds and tenths in his note-book, keeping 
 up the count of the beats of the pendulum, and thus pass 
 from one wire to the next successively through all the 
 system of wires, so that in this multiform effort his powers 
 of attention are taxed beyond what they are able to bear, 
 and it is only by long practice that any valuable results are 
 ever reached. The observer also finds that his modes of 
 observation often lead him into false habits. He may mark 
 the time from his own mental count of the beat, rather than 
 from the sound of the beat itself, or he may find himself 
 running into the habit of fixing his tenths of seconds pre- 
 dominantly in one or two portions of the scale of tenths. 
 It is manifest that in a thousand observations the tenth of a 
 second on which the transit falls ought to be uniformly 
 divided among the whole number. Thus there should be 
 a hundred observations in which the time of transit should 
 fall on the first tenth of a second, a hundred observations in 
 which the time should fall on the second tenth, and so on 
 
182 POPULAR ASTRONOMY. 
 
 Tor each of the tenths. But an observer may find, when 
 he comes to examine a thousand of his observations, that 
 two or three hundred are entered as falling on the third 
 tenth, and three or four hundred as falling on the seventh 
 tenth. This only demonstrates that he has fallen into 
 habitual error, due to the fact that he is compelled to 
 estimate. In attempting to escape from this particular 
 error, and finding himself too much attached to one portion 
 of his scale of tenths, he is very likely to fall into the other 
 extreme, and thus he finds himself a variable instrument, 
 always imperfect, even in these legitimate sources of error. 
 
 By studying his own peculiarities more rigorously, and 
 comparing himself with others, it will be found that in case 
 the two persons compared could at the same time look through 
 the same telescope at the same star coming up to cross the 
 same meridian-wire, each attempting to note the moment of 
 passage, by listening to the beat of the same clock, the re- 
 corded times would differ, one of the observers being uni- 
 formly in advance of the other. Should this experiment be 
 repeated, at the end of a month, with every possible pre- 
 caution, the difference between the two observers will in 
 general be. found to change ; demonstrating that one or the 
 other or both have varied in this particular, and that an 
 inter-comparison of their observations now made by the 
 former difference would produce inaccurate results. This 
 difference is what is denominated technically personal equa- 
 tion, and is supposed to arise from the fact that time is really 
 an element in the operation of the senses : that two persons 
 listening to the same sound, as the sharp crack of a pistol, 
 the sense of hearing of the one may perform its office of 
 conveying this sound to the brain more rapidly than the 
 other, and that the same may be asserted of the sense of 
 sight. 
 
 For the purpose of comparing the observations of different 
 Astronomers, it becomes necessary to determine the pecu- 
 liarities ot each, and it would be a matter of great import- 
 ance if it were possible to fix some absolute standard to which 
 
INSTRUMENTAL ASTRONOMY. 183 
 
 all observations might be reduced. This is accomplished, so 
 far as the three instrumental errors and the clock error are 
 concerned, by actually applying a correction which reduces 
 each observation to what it would have been in case none of 
 these errors had existed. The same may be said of the cor- 
 rection applied for refraction and for aberration. As to 
 precession, the position of the equinoctial point, supposing it 
 to move with its mean or average velocity, is always given 
 for the epoch to which the observation is referred. The 
 observations are also reduced for parallax, whenever this 
 element becomes sensible, and are thus recorded as though 
 the observer were located at the centre of the earth. To 
 accomplish the inter-comparison of observations made at 
 different observatories, there yet remains the reduction due 
 to difference of longitude, and that depending upon the per- 
 sonal peculiarities of the observers. 
 
 The high demand for accuracy in instrumental observation 
 can only be fully appreciated by those actually engaged in 
 the computation of the places of the heavenly bodies. Obser- 
 vations are valuable in the ratio of the squares of their 
 probable errors : that is, if one set of observations can be 
 produced in which the probable errors remain among the 
 tenths of seconds of time, while in another set of observations 
 the errors are driven into the hundredths of seconds, or are 
 but one-tenth part as large as the former, then the second 
 set will be a hundred fold more valuable that the first. This 
 principle applies to all observations ; but there are some 
 distances so great and some motions so slow that even the 
 best and most delicate methods of observation hitherto 
 applied fail altogether to measure the one or to appreciate 
 the other. This remark is especially true when applied to 
 the distance and movements which are found in the region 
 of the fixed stars. Among these remote objects, while in 
 some instances the motion is sufficiently rapid to be detected 
 and approximately measured, even in a single year, in other 
 instances, and by far the larger number, these motions are 
 so slow that they must accumulate for hundreds of years 
 
184 POPULAR ASTRONOMY. 
 
 to become appreciable and measurable by the most re- 
 fined and perfect instruments hitherto prepared by human 
 skill. 
 
 In the three great departments of astronomy there is but 
 one in which there is much hope for increased facility and 
 accuracy. The great laws of motion and gravitation are no 
 doubt perfectly determined. The mathematical formulae 
 whereby these laws are applied to the circumstances of 
 motion of the planets and their satellites are now brought to 
 great simplicity and perfection ; and if it were possible to 
 give to the physical astronomer perfect data, he would be able 
 to obtain perfect results. We know by geometry that the 
 area of a rectangle is the product of its base by its altitude.. 
 This rule or formula is absolutely accurate ; and whenever 
 we wish to apply it to determine the area of any particular 
 rectangle, we must first accomplish the mechanical measure- 
 ment of the length of the base and altitude. To do this 
 perfectly is impossible; but approximate results may be 
 reached of greater or less precision, in proportion to the 
 accuracy of the instruments employed, and the time and 
 pains expended upon the work. Thus one measure may 
 reduce the probable errors to one-hundredth of an inch, 
 while in another the error may only reach one-thousandth of 
 the same unit. 
 
 In like manner the theory and formulae of physical astro- 
 nomy are nearly, if not quite perfect ; while, however, the 
 observations whence we derive the data to be used in com- 
 putation are, as we have seen, comparatively imperfect. 
 The author of this work has attempted to contribute some- 
 thing to the accuracy and facility of astronomical observation. 
 
 The following is a brief account of the circumstances 
 attending the invention of this new mode of observation, 
 now known as 
 
 THE AMERICAN METHOD OP TRANSITS. In the autumn 
 of the year 1848, the late Professor S. C. Walker, then of 
 the United States Coast Survey, was engaged with me at the 
 Cincinnati Observatory in a series of observations, having for 
 
INSTRUMENTAL ASTRONOMY. 185 
 
 their object the determination of the difference of longitude 
 between the observatories of Philadelphia and Cincinnati. 
 In comparing our clocks or chronometers with those of 
 Philadelphia, an observer at Philadelphia listening to the 
 clock-beat touched the magnetic key of the telegraph-wire 
 at every beat, and we received at Cincinnati an audible tick 
 every second of time, which was carefully noted, and thus 
 our clocks were compared. There were two sources of error 
 in this method of comparison, arising from an imperfect 
 imitation of the clock-beat by the Philadelphia operator, 
 also from our noting the arrival of that beat in Cincinnati. 
 On the 26th of October, 1848, Professor Walker, while 
 conversing on this subject, first presented to me the mecha- 
 nical problem of causing the clock to send its own beats by 
 telegraph from one station to the other, or what amounted 
 to the same thing, the problem of converting time into space, 
 as already explained ; for in case the clock could send its own 
 beats by telegraph, and these beats could be received on a 
 uniformly flowing time scale, the star transit could be also 
 r.ent by telegraph, and received on the same scale ; and thus 
 a new method of transits would at once spring from the 
 resolution of the first mechanical problem. I was informed 
 by Professor Walker that the problem had already been 
 presented to others, but so far as he knew had never been 
 solved. The full value of the idea was at once appreciated ; 
 and on the same evening a common brass clock, the only one 
 then in the observatory, was made to record its own beats 
 by the use of the electro-magnet on a Morse fillet. 
 
 The problem once solved, nothing more remained than to 
 elaborate such machinery as would render it possible to 
 apply this new discovery or invention to the delicate and 
 positive demands of astronomical observations. 
 
 It is well known that signals are transmitted along a line 
 of telegraphic wire by closing or by breaking the wire 
 circuit over which the electricity passes from pole to pole of 
 the battery. The finger of the telegraphic operator, by 
 touching a magnetic key, " breaks or makes" the circuit, and 
 
186 POPULAR ASTRONOMY. 
 
 thus either interrupts or starts the flow of electricity. The 
 problem of causing a clock to record its beats telegraphically 
 was then nothing more than to contrive some method 
 whereby the clock might be made (by the use of some 
 portion of its own machinery) to take the place of the finger 
 of the living, intelligent operator, and " make" or " break" 
 the electric circuit. The grand difficulty did not lie in 
 causing the clock to play the part of an automaton in this 
 precise particular ; but it did lie in causing the clock to act 
 automatically, and at the same time perform perfectly its 
 great function of a time-keeper. This became a matter of 
 great difficulty and delicacy ; for tQ tax any portion of the 
 clock machinery with a duty beyond the ordinary and 
 contemplated demands of the maker, seemed at once to 
 involve the machine in imperfect and irregular, action. 
 After due reflection it was decided to apply to the pendulum 
 for a minute amount of power, whereby the making or 
 breaking the electric circuit might be accomplished with the 
 greatest chance of escaping any injurious effect on the going of 
 the clock. The principle which guided in this selection was, 
 that we ought to go to the prime mover (which in this case 
 was the clock-weights, and which could not be employed), 
 and failing to reach the prime mover, we should select the 
 nearest piece of mechanism to it, which in the clock is the 
 pendulum. A second point early determined by experiment 
 and reflection was this : that the making or breaking of the 
 circuit must be accomplished by the use of mercury, and not 
 by a solid metallic connection. The method evolved and 
 based on these two principles is the one which has been in 
 use now for more than ten years in the Cincinnati Obser- 
 vatory. 
 
 The simplest possible method of causing the pendulum to 
 "make" the circuit may be described as follows : 
 
 Attach to the under surface of the clock pendulum with 
 
 gum shell-lac a small bit of wire bent thus, , ^ ; then 
 
 right and left of the point over which the pendulum vibrates 
 when lowest, place two small globules of mercury, into each 
 
INSTRUMENTAL ASTRONOMY. 187 
 
 of which there shall dip a wire from the poles of the battery. 
 Now, as the pendulum swings over the globules of mercury, 
 the two points of the attached wire will finally come, for one 
 moment, to dip in the mercury cups, and thus make a 
 momentary bridge, over which the current of electricity may 
 pass from pole TO pole. This method, among others, having 
 been tried, was soon abandoned as uncertain and irregular in 
 its results ; and the following plan was adopted : 
 
 A small cross of delicate wire was mounted on a short 
 axis of the same material, passing through the point of 
 union of the four arms constituting the cross. This axis was 
 then placed horizontal on a metallic support, in Y's, where 
 it might vibrate, provided the top stem of the cros? could be 
 in some way attached to the pendulum of the clock, aLJ/the 
 " cross" should thus rise and fall at its outer stem as the 
 pendulum swings backward and forward. The metallic 
 frame bearing the " cross " also bore a small glass tube bent 
 at right angles. This was filled with mercury, and into 
 one extremity one wire from the pole of the battery was 
 made to dip ; the other wire was made fast by a binding 
 screw to the metallic stand bearing the " cross," and thus 
 every time the " cross " dipped into the mercury in the bent 
 tube the electricity passed through the metallic frame, up 
 the vertical standards bearing the axis of the cross, along 
 the axis to the stem, and down the stem into the mercury, 
 and finally through the mercury to the other pole of the 
 battery. Thus at every swing of the pendulum the circuit 
 was made, and a suitable apparatus might, by the electro- 
 magnet, record each alternate second of time. 
 
 The amount of power required of the pendulum to give 
 motion to the delicate wire-cross was almost insensible, as 
 the stems nearly counterpoised each other in every position. 
 Here, however, there was great difficulty in procuring a 
 fibre sufficiently minute and elastic to constitute the physical 
 union between the top stem of the cross and the clock 
 pendulum. Various materials were tried, among others a 
 delicate human hair, the very finest that could be obtained, 
 
188 POPULAR ASTRONOMY. 
 
 but this was too coarse and stiff. Its want of pliancy and 
 elasticity gave to the minute "wire-cross" an irregular 
 motion, and caused it to rebound from the globule of 
 mercury into which it should have plunged. After many 
 fruitless efforts, an appeal was made to an artisan of wonder- 
 ful dexterity ; the assistance of the spider was invoked ; his 
 web, perfectly elastic and perfectly pliable, was furnished, 
 and this material connection between the wire-cross and the 
 clock pendulum proved to be exactly the thing required. 
 In proof of this remark I need only state the fact that one 
 single spider's web has fulfilled the delicate duty of moving 
 the wire-cross, lifting it, and again permitting it to dip into 
 the mercury every second of time for a period of more than 
 three years ! How much longer it might have faithfully 
 performed the same service I know not, as it then became 
 necessary to break this admirable bond, to make some 
 changes in the clock. Here it will be seen, the same web 
 was expanded and contracted each second during this whole 
 period, and yet never, so far as could be observed, lost any 
 portion of its elasticity. The clock was thus made to close 
 the electric circuit in the most perfect manner ; and inas- 
 much as the resistance opposed to the pendulum by the 
 " wire-cross" was .a constant quantity and very minute, thus 
 acting precisely as does the resistance of the atmosphere, the 
 clock, once regulated with the " cross " as a portion of its 
 machinery, moved with its wonted steadiness and uniformity. 
 Thus one grand point was gained. The clock was now 
 ready to record its own beats automatically and with 
 absolute certainty, without in any way affecting the regu- 
 larity of its movement. It was early objected to the 
 mercurial connection just described, that in a short time the 
 surface of the mercury would become oxidized, and thus 
 refuse to transmit the current of electricity ; but experiment 
 demonstrated that the explosion produced by the electric 
 discharge at every dip into the mercury threw off the oxide 
 formed, and left the polished surface of the globule of 
 
INSTRUMENTAL ASTRONOMY. 189 
 
 mercury in a perfect state to receive the next passage of the 
 electricity. 
 
 So far as known, all other methods are now abandoned, 
 and the mercurial connection is the only one in use. 
 
 THE TIME-SCALE. The clock being now prepared tc 
 record its beats, accurately and uniformly, the next im- 
 portant step was to obtain, if possible, a uniformly-moving 
 time-scale, which should be applicable to the practical 
 demands of the astronomer. 
 
 In case the fillet of paper used in the Morse telegraph 
 could have been made to flow at a uniform rate upon its 
 surface, the clock could now record its beats, appearing as 
 dots separated from each other by equal intervals. But it 
 was soon seen that the paper could not be made to flow uni- 
 formly ; and even had this been possible, a single night's 
 work would demand for its record such a vast amount of 
 paper, that this method was inapplicable to practice. After 
 careful deliberation, the " revolving disc " was selected as the 
 best possible surface on which the record of time and ob- 
 servation could be made. The preference was given to the 
 disc over the cylinder for the following reasons : The 
 uniform revolution of the disc could be more readily reached. 
 The record on the disc was always under the eye in every 
 part of it at the same time, while on the revolving cylinder 
 a portion of the work was always invisible. One disc could 
 be substituted for another with greater ease, and in a shorter 
 time ; and the measure of the fractions of seconds could be 
 more rapidly and accurately performed on the disc than on 
 the cylinder. 
 
 After much thought and experiment it was decided to 
 adopt " a make circuit " and " a dotted scale " rather than 
 a "break circuit" and a " linear scale ;" and I think it will 
 be seen hereafter that in this selection the choice has been 
 fully justified in practice. These points being settled, the 
 mechanical problems now presented for solution were the 
 following : First, to invent some machinery which could 
 
190 POPULAR ASTRONOMY. 
 
 give to a disc of, say, twenty inches diameter, mounted OR 
 a vertical axis, a motion such that it should revolve uni- 
 formly once in each minute of time ; and, second, to connect 
 with this disc the machinery which should enable the clock 
 to record on the disc each alternate second of time, in the 
 shape of a delicate round dot. Third, the apparatus which 
 should enable the observer to record on the same disc the 
 exact moment of the transit of a star across the meridian, or 
 the occurrence of any other phenomenon. 
 
 The first of these problems was by far the most difficult j 
 and, indeed, its perfect solution remains yet to be accom- 
 pli shed, though, for any practical astronomical purpose, the 
 problem has been solved in more than one way. 
 
 The plan adopted in the Cincinnati observatory may be 
 described as follows : The clock-work machinery employed 
 to give to the great equatorial telescope a uniform motion 
 equal to that of the earth's rotation, on its axis, offered to 
 me the first obvious approximate solution of the problem 
 under consideration. This machinery was accordingly applied 
 to the motion of the disc, or rather to regulate the motion 
 of revolution, this motion being produced by a descending 
 weight, after the fashion of an ordinary clock. It was soon 
 discovered that the " Frauenhofer clock," as this machine is 
 called, was not competent to produce a motion of such uni- 
 formity as was now required. Several modifications were 
 made with a positive gain ; but, after long study, it was 
 finally discovered that, when the machinery was brought 
 into perfect adjustment, the dynamical equilibrium obtained 
 was an equilibrium of instability ; that is, if from a motion 
 such as produced a revolution in one exact minute, it began 
 to lose, this loss or decrement in velocity went on increasing, 
 or if it began to gain, the increment went on increasing at 
 each revolution of the disc. Now, all these delicate changes 
 could be watched with the most perfect certainty; as, in 
 case the disc revolved uniformly once a minute, then the 
 seconds' dots would fall in such a manner (as we shall see 
 directly), that the dots of the same recorded seconds would 
 
INSTRUMENTAL ASTRONOMY. 191 
 
 radiate from the centre of the disc in a straight line. Any 
 deviation from this line would be marked with the utmost 
 delicacy down to the thousandth of a second. By long and 
 careful study it was at length discovered that, to make any 
 change in the velocity of the disc, to increase or decrease 
 quickly its motion, in short, to restore the dynamical equili- 
 brium, the winding-key of the " Frauenhofer clock " was the 
 point of the machinery where the extra helping force sjiould 
 be applied ; and it was found that a person of ordinary in- 
 telligence, stationed at the disc, and with his fingers on this 
 key, could, whenever he noticed a slight deviation from 
 uniformity, at once, by slight assistance, restore the equili- 
 brium, when the machine would perhaps continue its 
 performance perfectly for several minutes, when again some 
 slight acceleration or retardation might be required from 
 the sentinel posted as an auxiliary. 
 
 The mechanical problem now demanding solution was 
 very clearly announced. It was this : Required to construct 
 an automaton which should take the place of the intelligent 
 sentinel, watch the going of the disc, and instantly correct 
 any acceleration or retardation. This, in fact, is the great 
 problem in all efforts to secure uniform motion of rotation. 
 This problem was resolved theoretically in many ways, 
 several of which methods were executed mechanically 
 without success, as it was found that the machine stationed 
 as a sentinel to regulate the going of the disc was too weak, 
 and was itself carried off by its too powerful antagonist. 
 The following method was, however, in the end, entirely 
 successful. Upon the axis of the winding- key, already men- 
 tioned, a toothed wheel was attached, the gearing being so 
 adjusted that one revolution of this wheel should produce 
 a whole number of revolutions of the disc. The circum- 
 ference of this wheel was cut into a certain number of 
 notches, so that, as it revolved, one of these notches would 
 reach the highest point once in two seconds of time. By 
 means of an electro-magnet a small cylinder or roller, at the 
 extremity of a lever-arm, was made to fall into the highest 
 
192 POPULAR ASTRONOMY. 
 
 notch of the toothed wheel at the end of every two seconds. 
 In case the disc was revolving exactly once a minute, the 
 roller, driven by the sidereal clock by means of an electro- 
 magnet, fell to the bottom of the notch, and performed no 
 service whatever ; but in case the disc began to slacken its 
 velocity, then the roller fell on the retreating inclined face 
 of the notch, and thus urged forward, by a minute amount, 
 the laggard disc ; while, on the contrary, should the variation 
 from a uniform velocity present itself in an acceleration, then 
 the roller struck on the advancing face of the notch, and thus 
 tended slowly to restore the equilibrium. Let it be remem- 
 bered that this delicate regulator has but a minute amount 
 of service to perform. It is ever on guard, and detecting, as 
 it does instantly, any disposition to change, at once applies 
 its restoring power, and thus preserves an exceedingly near 
 approach to exact uniformity of revolution. This regulator 
 operates through all the wheel-work, and thus accomplishes 
 a restoration by minute increments or decrements spread 
 over many minutes of time. 
 
 With a uniformly revolving disc, stationary in position, 
 we should accomplish exactly, and very perfectly, the record 
 of one minute of time, presenting on the recording surface 
 thirty dots at equal angular intervals on the circumference 
 of a circle. To receive the time-dots of the next minute on 
 a circle of larger diameter, required either that the recording 
 pen should change position, or that at the end of each revo- 
 lution the disc itself should move away from the pen by a 
 small amount. We chose to remove the disc. To accomplish 
 accurately the change of position of the disc, at the end of 
 each revolution, the entire machine was mounted on wheels 
 on a small railway-track, and by a very delicate mecha- 
 nical arrangement accomplished its own change of posi- 
 tion between the fifty-ninth and sixtieth second of every 
 minute. 
 
 THE RECORDING PENS. It now remains only to describe 
 the simple machinery by which the clock records its beats, 
 and the observer makes the record of his observation. These 
 
INSTRUMENTAL ASTRONOMY. 193 
 
 instruments are called the recording pens. That belonging 
 to the clock is called the time pen ; the one used by the 
 observer the observing pen. They are constructed and 
 operate in the following raarmor : A metallic arm is con- 
 structed with a short axis, perpendicular to its length. The 
 extremities of this axis are pivots working in the jaws of a 
 metallic frame, which supports the axis of the pen in a hori- 
 zontal position. The longer arm of the pen reaches over 
 into the centre of the disc, and is armed at its extremity 
 with a steel point or stylus. Upon the long arm of the pen 
 and near the axis is located a piece of soft iron denominated 
 an armature, and beneath this armature an electro-magnet 
 is firmly fixed. This magnet is placed on the circuit closed 
 by the wire-cross vibrating with the clock pendulum, and 
 thus, at every dip of the cross into the mercury cup, the 
 armature of the pen is suddenly drawn down on the head of 
 the magnet, and the moment the circuit is broken a spring 
 acting on the short arm of the pen lifts it from the head of 
 the magnet. It is readily seen that in this way the stylus is 
 brought down by a sudden shock or blow on the material 
 placed on the revolving disc to receive the record. The pen 
 is so adjusted that in case the armature be simply placed 
 and held by hand on the head of the magnet, the steel point 
 of the stylus does not quite touch the recording surface on 
 the disc. The elasticity of the long arm of the pen is, 
 therefore, a matter of the greatest moment, for this elasticity 
 causes the pen to make a simple dot, by a sudden blow and 
 recoil; whereas were the pen non-elastic, there would be a 
 drag for the time during which the magnet holds the pen, 
 which would at once destroy the uniformity in the going of 
 the disc. 
 
 A pen constructed in precisely the same way, and placed 
 at right angles to the former, so that the points of the two 
 pens fall in close proximity on the disc, is operated by a 
 magnet made by a circuit closed at will by the finger of the 
 observer ; and thus he is enabled to throw down upon the 
 time-scale a dot, which, falling between some two-second dots 
 
 
 
194 POPULAR ASTRONOMY. 
 
 on the disc, records the exact instant of any phenomenon 
 under observation. 
 
 When the disc is filled, we have only to lift it from its 
 socket and replace it with a new disc. To read the time- 
 scale it is only necessary to mark on the disc from the 
 clock-face the time denoted by any one dot ; for example, 
 12h. 15m. OOs. The circle next outside will be 12h. 16m., 
 the next circle 12h. 17m., &c. ; while the first or marked 
 radius of dots will be the second of all the minutes, the 
 next in order will be the second, the next the fourth, 
 and so on to the 58th and second again. Thus we read 
 the scale as rapidly as we read a clock-face, for the hour, 
 minute, and second; and it only remains to construct a 
 machine for measuring the fractions of seconds. 
 
 THE ANGULAR TIME-MICROMETER. This instrument is 
 very simple. Take a common carpenter's two-foot rule; cut 
 away the inner portion of one of the legs for two-thirds of 
 its length, and insert a piece of plane glass; draw from the 
 centre of the joint with a diamond point, on the under surface 
 of this glass, a delicate straight line, and blacken by rubbing 
 in black-lead pencil. The arms of this micrometer are a 
 little longer than the radius of the disc. To the left hand 
 arm, at its outer extremity, attach a small brass arc, divided 
 into seconds and tenths, and make it, say, 2^ seconds in 
 length. "When the two legs are closed, the black line on the 
 glass will read on this scale of seconds. At the joint drill 
 a small hole, and at the centre of the disc to be measured 
 erect a small vertical pin to fit this hole. Lay the instru- 
 ment on the disc, the pin being inserted in the hole, and 
 thus the fractions of seconds may be measured with any 
 degree of precision. 
 
 Such is an outline of the machinery now in use in the 
 Dudley Observatory at Albany, and at the Cincinnati Ob- 
 servatory. 
 
 As we have seen, in the old method of transits the atten- 
 tion of the observer was divided among many objects. He 
 was compelled to keep up the counting of the clock-beat ; to 
 
INSTRUMENTAL ASTRONOMY. 195 
 
 estimate the space passed over by the star under observation 
 in a second of time; to subdivide this space by estimation 
 into tenths; to write down in his note-book the observed 
 moment of transit across each of the wires, and all this 
 while his eye continued to follow the movement of the 
 object under observation. To give the observer time to 
 make his record, the spider's lines or wires were necessarily 
 separated by such an interval from each other that several 
 seconds would be required by the star to pass from one to 
 the other, and thus but few wires could be employed in 
 transit- observations. 
 
 In the new method the observer is released from all 
 responsibility with reference to time, counting of clock- beat, 
 estimation of spaces, or entries in note-book. The clock 
 records its own beat, and the observer has nothing to do but 
 touch a magnetic key at the exact moment in which his star 
 is bisected by the meridian-wire. This touch records the 
 moment of observed transit, and as this record is accom- 
 plished almost instantaneously, the observer is ready to 
 record the transit across the next wire, and thus the interval 
 between the wires may be greatly reduced, and their number 
 extended almost indefinitely. While in the old method long 
 practice was required to make an accomplished observer (the 
 best of whom could not record more than the transits on 
 seven wires), in the new method a few nights of practice 
 gives all desirable experience, and the observer may record 
 the transits across as many as fifty wires, should so large a 
 number ever be desirable under any circumstances. It is 
 found in the use of this method that erroneous habits of 
 observation may either be entirely avoided or detected, and 
 thus corrected. It furnishes the means of measuring with 
 great accuracy the value of personal equation, and has demon- 
 strated, indeed, that the large differences existing between 
 observers, amounting in some instances to a whole second of 
 time, are not due to physiological constitution, but almost 
 entirely to false habits of observation. It has furnished the 
 means of measuring the amount of time which elapses 
 
 o 2 
 
196 POPULAR ASTRONOMY. 
 
 between the occurrence of any phenomenon falling within 
 the grasp of the senses of sight and hearing, and the possi- 
 ble record by the touch of a magnetic key. In this opera- 
 tion there are three distinct processes : the sense of sight, for 
 example, conveys to the brain information of the occurrence 
 of the external phenomenon ; the mind thus perceives, and 
 the will issues an order to the nerves to record ; the nerves 
 execute this order. Thus far it has been impossible to 
 ascertain the amount of time occupied in each of these 
 processes; but the sum of the times, or that elapsing between 
 the moment of occurrence of a phenomenon and its record, 
 has been measured both for the sense of sight and the sense 
 of hearing, in a large number of persons of both sexes and 
 of all ages. From these experiments it has been ascertained 
 that while different individuals present prominent and 
 marked differences, these differences are only found to exist 
 in the hundredths of a second of time, and not, as has been 
 imagined, in whole seconds. In conducting these experi- 
 ments, it was ascertained that all observers, without a single 
 exception, in attempting to mark the moment at which a 
 star crossed a wire, anticipated the moment of transit, and 
 the recorded time was thus in advance of the true time. 
 Having learned this fact, the observer is placed upon his 
 guard, and is furnished with the means of correcting this 
 false habit, and of bringing himself up to a standard of 
 positive accuracy. Another advantage derived from this 
 mode of observation arises from the fact that it imposes but 
 a slight tax upon the nervous system, and hence an observer 
 is able to continue his work without exhaustion for a much 
 longer period of time. 
 
 We have mentioned that one of the most hidden sources of 
 rror lies in the uncertainty of the rate of going of the clock. 
 The old methods furnish the means of ascertaining with 
 comparative accuracy how much the clock has lost or gained 
 in twenty-four hours ; and if this quantity should amount 
 only to a fraction of a second, it is almost impossible to 
 assert that this loss or gain may not have occurred even a 
 
INSTRUMENTAL ASTRONOMY. 191 
 
 hundred times, or possibly a thousand times during the 
 twenty- four hours. By causing two or more clocks to record 
 their beats upon the same time-scale, the new method fur- 
 nishes the means of inter-comparison between these clocks, 
 even from second to second, if required, and thus from a 
 record of this kind may be obtained a positive standard of 
 time. 
 
 The electro-magnetic method of observation, in connection 
 with the system of telegraphic wires now extending over 
 nearly all the civilized world, furnishes a very rapid and 
 exact method of determining the difference of longitude 
 between any two points. This difference of longitude is 
 nothing more than the time which elapses from the transit 
 of a star across the meridian of one place until it crosses the 
 meridian of the other place. In case the two observatories 
 whose difference of longitude is required are connected by 
 telegraph, and are furnished with the electro-magnetic 
 apparatus, the observer in the eastern observatory may send 
 to his correspondent by telegraph the moment of transit of 
 the star across his own meridian. He will receive in return 
 by telegraph the moment the same star crosses the meridian 
 of the western observatory, and in case the observations are 
 perfectly made, transmitted with infinite velocity along the 
 wires, and recorded with perfect accuracy, the result will be 
 absolutely perfect. The common errors of observation are 
 readily eliminated, the errors of recording, in like manner, 
 are easily detected and measured, and the only matter of 
 difficulty which remains is to ascertain whether the message 
 sent along the wire travels at a finite rate, and if so, to 
 determine what this rate may be. The conversion of time 
 into space, and the delicacy of the machinery now employed 
 in recording and subdividing time, has furnished the means 
 of measuring the velocity with which signals are transmitted 
 along the wires of the telegraph. No doubt this velocity is 
 modified by a variety of circumstances, and may depend 
 upon the direction in which the telegraphic wire is laid, the 
 eeason of the year, the temperature of the earth and atmo- 
 
198 POPULAR ASTRONOMY. 
 
 sphere ; but none of these causes can interfere to mar the 
 accuracy of the work employed for longitude purposes ; for 
 there is no difficulty in determining the exact velocity with 
 which the signals are transmitted by the wires at the time 
 of observation. These are a few among many advantages 
 which have been gained by the conversion of time into space, 
 and the application of this principle to the observation of 
 astronomical transits. 
 
 The author has attempted to add something to the facility 
 and accuracy of the determination of north polar distances 7 
 the second great element employed in fixing the place of a 
 heavenly body. As already explained, this element i& 
 reached by the division of a circle attached to the axis of 
 the transit, and the accuracy of the work depends upon the 
 perfection of these divisions, the permanence of the figure of 
 the circle, the permanence in the place of the reading micro- 
 scopes, and the precision attainable in reading the sub- 
 divisions of the circle. As the errors which arise from these 
 different sources are found to be comparatively large, for the 
 measurement of small differences of north polar distances, 
 or small arcs of space, resort has been had to other and 
 more delicate mechanical contrivances ; hence the invention 
 and construction of the various micrometers now in use, all 
 of which depend for their accuracy upon the performance of 
 a micrometer-screw. Very extended experiments with these 
 instruments first created a doubt in my own mind as to the 
 accuracy with which the micrometer-screw would repeat its- 
 own measures. This doubt, added to the fact that the mea- 
 surements by the micrometer were very slow and tedious, 
 gave rise to the effort which has resulted in the construc- 
 tion of a new system whereby differences of north polar 
 distance may be determined with great rapidity and pre- 
 cision, which principle can readily be extended to the deter- 
 mination of absolute north polar distances. A description 
 of the machinery employed for this purpose may be found 
 elsewhere. We are only concerned here to notice some of 
 the possible advantages of this new method of north polar 
 
INSTRUMENTAL ASTRONOMY. 199 
 
 distances. I will only state that the machinery employed 
 in all its joints and connections is of the simplest kind, and 
 everywhere visible to the eye. There is no concealed por- 
 tion, as in the screw-micrometer, no joints to grow imperfect 
 by wearing, and no strong resistance to change the figure of 
 any part of the machinery. If the tube of the telescope, 
 loaded as it is with the weight of the object-glass and eye- 
 piece, and its own weight, can be depended upon to retain 
 its figure without a counterpoise, it is absolutely certain that 
 the declination-arm, which in the new method is attached to 
 the axis of the transit, if perfectly counterpoised and bearing 
 no weight whatever, can be relied upon to retain its figure. 
 The lower extremity of this arm, moving as it does in 
 north polar distance, with the line of collimation of the 
 telescope, by a connecting bar, gives motion to the axis of 
 the reading-microscope, which, being directed to a distant 
 scale, magnifies in a very high ratio by mechanical means 
 the arc through which the transit revolves in the plane of 
 the meridian. Thus it will be seen that this new method 
 is nothing more than the use of a mechanical magnifier, and 
 the only question is, can the scale be so- divided as to read 
 seconds of arc, and can it be made of invariable length ? 
 There is little difficulty in accomplishing both of these 
 objects, for scales have already been divided with such pre- 
 cision that no error amounting to the hundredth part of a 
 single second of arc could possibly exist ; and in order to 
 retain an invariable length in the scale, all that is necessary 
 is to grade it upon a surface constituting one face of a 
 rectangular tube ; fill this tube with water and broken ice, 
 and thus a permanent temperature of 32 may be had for 
 any length of time. To measure the exact value of the 
 divisions on the scale, we have only to employ these divi- 
 sions in measuring round the entire circumference of the 
 circle attached to the axis of the transit. Suppose the 
 length of the scale to be sixty minutes approximately, then, 
 if this length is contained 360 times in the whole circum- 
 ference, its approximate value becomes its absolute value, 
 
200 ' POPULAR ASTRONOMY. 
 
 and at all events this experiment furnishes the means of 
 determining the absolute value. Thus, while the circle fur- 
 nishes the means of measuring the scale, the scale furnishes 
 in rtf-urn the means of measuring the subdivisions of the 
 circle. These amount only to 3 GO, and may be reduced even 
 to the fifth part of this number, t should practice prove this 
 reduction desirable. This small number of divisions can 
 "^pidly be read up with a scale of invariable length, and by 
 performing this reading at temperatures widely different, a 
 correction for temperature may be determined with great 
 exactness. In the old circle, as there are no less than 
 10,000 divisions, and as there exists no permanent scale for 
 the reading of these divisions, it becomes almost impossible 
 to learn their actual values and to tabulate their errors ; 
 hence astronomers have been compelled to rely to a great 
 extent upon the assumed accuracy of the subdivisions of 
 their circles, as received from the hands of the manufacturer. 
 
 By a combination of the electro-magnetic method with 
 the new method of measuring north polar distances, a very 
 simple, convenient, and accurate instrument is obtained for 
 recording the places of the stars or other heavenly bodies 
 with great rapidity and exactitude, rendering it possible to 
 construct, in a comparatively short time, a very extended 
 and exact catalogue of the places of all the fixed stars, clearly 
 visible, with any optical power. 
 
 We have thus presented a rapid sketch of the old and 
 new methods of fixing the elements for the determination 
 of the heavenly bodies : it only remains in this connection 
 to speak of the optical power of the telescope. 
 
 These instruments are divided into two great classes, 
 called reflecting and refracting telescopes. In the reflecting 
 telescopes the rays of light from the external object, passing 
 down the tube of the telescope, fall upon a metallic mirror 
 or speculum, whose surface, perfectly polished, has the figure 
 of a paraboloid of revolution. Being reflected by this surface, 
 the rays of light are concentrated at a certain point, called 
 the focus, where an intensely luminous image of the object 
 
INSTRUMENTAL ASTRONOMY. 201 
 
 is formed. This image is then examined by a magnifying 
 glass or eye-piece, and its dimensions expanded to any re- 
 quired degree. 
 
 In the refracting telescope the light falls upon what is 
 called the object glass, a powerful lens, which concentrates, 
 by refraction, the rays of light which pass through it, thus 
 forming an image of the object at the focal point. This 
 image is then examined, as in the reflecting telescope, by 
 eye-pieces having different magnifying powers. Hitherto it 
 has been found impracticable to construct object glasses of 
 any very considerable diameter, the largest of these glasses 
 in use not exceeding sixteen to twenty inches in diameter. 
 These narrow limits do not exist, however, in the construc- 
 tion of the metallic specula which belong to the reflecting 
 telescope ; and hence we find gigantic instruments have been 
 constructed by different observers, one of which, now in use 
 by Lord Ross, has a speculum of no less than six feet in 
 diameter, with a focal length of fifty-two feet. Such immense 
 instruments, requiring ponderous machinery for their manage- 
 ment, are not well adapted for that kind of observation 
 which has for its object to determine the places of the 
 heavenly bodies. Their use has been rather confined to 
 examinations of the planets, double stars, clusters, and 
 nebulae, demanding a large amount of light rather than a 
 perfect definition or exactitude in measurement. It is true, 
 that in the hands of Lassell, of Liverpool, we find the 
 reflecting telescope performing admirably in the routine 
 work of an observatory. But these instruments are com- 
 paratively small, their dimensions not much exceeding those 
 of the largest refractors. 
 
 There are two qualities which distinguish the telescope, 
 the space-penetrating power and the power of definition. The 
 first of these depends exclusively upon the amount of light 
 received and refracted, or reflected to the focus, and thus 
 forming the image. In case all the light falling upon the 
 object-glass or speculum could b& concentrated in the forma- 
 tion of the image, then the space-penetrating power of 
 
202 POPULAR ASTRONOMY. 
 
 telescopes would be exactly proportioned to the diameters 
 of their apertures ; and we can compare then, readily, the 
 space-penetrating power of different instruments, not only 
 among themselves, but directly with the space-penetrating 
 power of the human eye. The diameter of the pupil of 
 the eye determines the amount of light which can enter and 
 form the image, just as the diameter of an object-glass in 
 a telescope determines the amount of light which in that 
 instrument forms the focal image : hence, if we desire to 
 know how many times deeper a telescope can penetrate 
 space than the eye, we have only to learn how many times 
 the area of the object-glass exceeds that of the pupil of the 
 eye. We shall have occasion hereafter to employ this 
 principle when we come to examine the relative distances to 
 which the nebulae and clusters are sunk in space. 
 
 We have only spoken of the mounting of the transit, with 
 its attached circle, for reading north polar distances. This 
 instrument revolves only, as we have seen, in the plane of 
 the meridian, and of course no object can be seen with the 
 transit except when in the act of passing the meridian-line. 
 
 A telescope mounted in such a manner that it can be 
 directed to any point of the heavens, is called an extra- 
 meridional instrument, and of these the equatorial is the 
 most used, and is the best adapted for all observations off 
 the meridian. The tube of the telescope is carried by a 
 heavy metallic casting, very firm and strong, which is made 
 fast to a metallic cylinder, through which passes a steel axis, 
 called the equatorial axis. The metallic cylinder is also 
 screw-bolted to the extremity of a heavy steel axis, so placed 
 on its supports as to lie parallel to the earth's axis. These 
 supports rest on heavy metallic plates, bolted to a massive 
 stone pier, called the " foot of the instrument," which, in 
 turn, is placed on the top of a heavy pier of masonry, resting 
 on a rock-foundation, or something equally solid, and entirely 
 disconnected from the building. 
 
 The instrument is so counterpoised in all its many parts 
 as to be readily moved either on its polar or equatorial axis. 
 
URANUS. 203 
 
 and may thus be directed to any point of the celestial sphere. 
 To enable the observer to follow the object under examina- 
 tion, these telescopes are usually furnished with a species of 
 clock-work, which causes the instrument to revolve round its 
 polar axis with a velocity equal to that of the earth's rota- 
 tion, causing it to follow a heavenly body, and to hold it 
 steady in the field of view for any required period of time. 
 
 Without extending further our notice of the instruments 
 employed in reaching the data required in astronomical 
 investigation, we will now return to our examination of the 
 bodies which compose the sun's retinue, and shall proceed 
 in our plan, preserving the order of distance from the sun. 
 
 The interruption which was made after closing the dis- 
 cussion of the system of Saturn, to introduce to the student 
 the laws of motion and gravitation, and the instruments 
 employed in astronomical measures, was necessary to a full 
 comprehension of the extraordinary investigations which are 
 now to follow. We are hereafter to treat the planets and 
 their satellites as ponderable bodies, mutually affecting eacb 
 other, and all subjected to the dominion of the laws of 
 motion and gravitation. 
 
 CHAPTER XII. 
 
 URANUS, THE EIGHTH PLANET IN THE OEDER OP 
 DISTANCE FROM THE SUN. 
 
 Accidentally discovered by Sir William Herschel. Announced as a Comet. 
 Its Orbit proved it to be a Superior Planet. The Elements of its 
 Orbit obtained. Arc of Retrogradation. Period of Revolution. Figure 
 of the Planet. Inclination of its Orbit. Six Satellites announced by 
 the elder Herschel. Four of these now recognized. Their Orbital 
 Planes and Directions of Revolution Anomalous. Efforts made to 
 Tabulate the Places of Uranus unsuccessful. This leads to the Discovery 
 of a New Exterior Planet. 
 
 IT was remarked at the close of our investigation of the 
 Saturnian system, that this planet inclosed by its orbit aK 
 
204 POPULAR ASTRONOMY. 
 
 t-he objects belonging to the solar system which were known 
 to the ancients, and whose phenomena, as observed and re- 
 corded in all time, furnished the data for the discovery of 
 Kepler's laws and the law of universal gravitation, as finally 
 revealed by Newton. While many of the modern astro- 
 nomers, from an examination of the inter- planetary spaces, 
 had ventured to suggest the probable existence of a large 
 planet revolving in an orbit intermediate between those of 
 Mars and Jupiter, no one had ventured to predict the possible 
 discovery of planets lying exterior to the mighty orbit of 
 Saturn. From the very dawn of astronomy this planet had 
 held the position of sentinel on the outposts of the planetary 
 system, and many strong minds had long entertained the 
 opinion that no other bodies existed exterior to the orbit of 
 Saturn, forming a part of the scheme of worlds revolving 
 around the sun. Such, indeed, was the prevalence of this 
 opinion, that when, in 1781, Sir William Herschel, in a 
 course of systematic exploration of the heavens, discovered 
 an object having a well-defined planetary disc, and whose 
 movement among the fixed stars became measurable, even 
 at the end of a few hours, he did not even suspect this new 
 object to be a planet, but announced to the world that he 
 had discovered a most extraordinary comet, without any of 
 the usual haziness which attends these bodies, but presenting 
 a clear and well-defined planetary disc. 
 
 This newly-discovered object soon attracted universal 
 attention. It was observed at the royal observatory at 
 Greenwich, and the then astronomer royal, Dr. Maskelyne, 
 was the first to suspect its planetary character. Efforts 
 were made by several computers to give to the new comet, 
 as it was called, a parabolic orbit ; this, however, was found 
 to be impossible ; and it was very soon found that the newly- 
 discovered object was revolving around the sun in an orbit 
 nearly circular in form, lying in a plane, nearly coincident 
 with the ecliptic, and completing its mighty revolution in a 
 period of no less than eighty-two years. It must be remem- 
 bered that these extraordinary discoveries and announce- 
 
URANUS. 205 
 
 merits were made at the end of a very short examination, 
 while the periods of revolution of all the old planets had been 
 obtained from actual observation, through long centuries of 
 patient watching. The periodic time of this last-discovered 
 of all the planets, which, by the old method of watching its 
 return to the same fixed star, could not have been determined 
 in less than eighty -two years, and even then only approx- 
 imately, was, by the new method, based upon the law of 
 universal gravitation, guided by the results of a few nights 
 of accurate observation, and worked out by the powerful 
 formulae of analytic reasoning, given to the world with 
 accuracy after only a few months of investigation. This is 
 the first illustration of the change wrought in the whole 
 movement of astronomical science by the great discoveries 
 of Newton, and by the almost equally extraordinary step 
 accomplished by Descartes, in fastening the powers of analysis 
 upon geometry. All the circumstances of motion of this 
 planet were rapidly investigated ; the eccentricity of its 
 orbit ; the position of its perihelion ; the inclination of its 
 orbit to the plane of the ecliptic ; the position of its line of 
 nodes j the measure of its actual diameter ; the determination 
 of its various distances from the sun ; all these and many 
 other peculiarities were accurately determined from actual 
 observation and computation. These facts strike us with 
 the more astonishment when we reflect that the planet 
 TJranus is removed to a distance of eighteen hundred millions 
 of miles from the sun and that, although its actual diameter 
 is thirty-Jive thousand miles, it is absolutely invisible to the 
 naked eye, and, when seen through the most powerful 
 telescope, presents a disc of only the Jive-hundredth part of 
 the apparent diameter of the sun. At such an immense 
 distance it has been impossible thus far to determine any- 
 thing with reference to the precise figure of Uranus. The 
 discoverer of the planet thought that he saw a flattening at 
 the poles, but subsequent observation has not confirmed this 
 announcement. We have only, therefore, analogy to induce 
 us to believe that this planet, like all the others, rotates upon 
 
206 POPULAR ASTRONOMY. 
 
 an axis, and that, consequently, its figure is that of the 
 ellipsoid and not of the sphere. The immense magniti.de 
 of the orbit of Uranus, when compared with that of th? 
 earth, causes this planet to retrograde over an arc of only 
 3 36' ; but the duration of the retrograde motion extends 
 over a period of no less than one hundred and fifty-one days. 
 No telescope has yet been able to discern, upon the surface 
 of Uranus, any spot or belt, or any well-defined point, dis- 
 tinguished from the entire surface ; so that we have no means, 
 thus far, of fixing the period of rotation upon its axis. The 
 amount of light and heat received by Uranus, admitting the 
 law of diminution, which seems to govern these elements, 
 could only be the quarter part of that received by the planet 
 Saturn ; while the apparent diameter of the sun, as seen 
 from Uranus, would be less than the tr rtieth part of his 
 diameter, as seen from the earth. 
 
 This planet is surrounded by at least four satellites. Two 
 others were announced by Sir Win. Herschel, who not only 
 gave their distances, but their periods of revolution, yet no 
 telescope has since been able to detect these minute point? 
 of light, and their very existence is now doubted by many 
 of the best observers. Four of the satellites had been studied, 
 with much care, and their periods of revolution and their 
 mean distances had been well determined. Of these, the 
 second and fourth are most readily seen, and different 
 astronomers have obtained results which agree with each 
 other within comparatively small limits of error. Thus the 
 elder Herschel fixed the period of revolution of the second 
 satellite, in the order of distance, at 8d. 16h. 56m. 5s. 
 Sir John Herschel made the same period twenty-six seconds 
 longer. Dr. Lamont, of Munich, obtained, for this same 
 period, a value of 8d. 16h. 56m. 28s.5. The period of revolu- 
 tion of the fourth satellite in the order of distance, as de- 
 termined by Lamonfc, amounts to 13d. llh. 07m. 06s.3. The 
 period of revolution of the nearest satellite is about five 
 days and twenty-one hours, while the third satellite in order 
 of distance performs its revolution in a period of about eleven 
 
URANUS. 2f>7 
 
 days. These are among the most difficult of all the objects 
 revealed to the eye by telescopic power. After Sir William 
 Herschelj no one for many years was able to see any of these 
 satellites, the forty-foot reflector of Herschel having gone 
 into- disuse. In 1828, Sir John Herschel, after many un- 
 successful attempts, by confining himself in a dark room for 
 many minutes previous to observation, and thus giving to 
 the eye great acuteness, succeeded in detecting two of these 
 satellites. In 1837, Lamont, with the powerful refractor 
 of the royal observatory of Munich, managed to follow, with 
 tolerable certainty, the two larger satellites, and occasionally 
 obtained glimpses of two others. 
 
 At this time there are four or five telescopes in the world 
 capable of showing these four satellites, under favourable 
 circumstances. I have frequently seen two of them with 
 the Cincinnati refractor, but they are certainly objects of 
 great difficulty, and only to be discerned under the most 
 favourable circumstances in the observer, and under the 
 best possible conditions of atmosphere. 
 
 Enough, however, has been determined with reference to 
 these four satellites to warrant the assertion of a fact of 
 most extraordinary character, and nowhere else to be found 
 in the whole range of the solar system, namely, that their 
 orbits are nearly perpendicular to the plane of the ecliptic, and 
 that their motions are retrograde. We have seen that all 
 the planets revolve in orbits whose planes are nearly co- 
 incident with the plane of the ecliptic ; that they all re- 
 volve in the same direction round the sun j that the sun and 
 all the planets rotate on their axes in the same direction in 
 which they revolve in their orbits. We have found, in like 
 manner, that all the satellites of every planet revolve around 
 their primaries in the same direction, and in planes nearly 
 coincident with the planes of the equators of their primaries j 
 go that it became a settled opinion that there was but one 
 direction in which any rotation or revolution could be per- 
 formed by a member of the planetary system ; and thus 
 when the asteroids were discovered, although there were 
 
208 
 
 POPULAR ASTRONOMY. 
 
 considerable deviations in the angles of the inclination of 
 the planes of their orbits from those of the old planets, yet 
 in every instance their motions are found to be direct. 
 These satellites of Uranus present, then, the only example 
 of retrograde movement among the legitimate members of 
 the solar system. We shall see hereafter that among the 
 comets (which may be regarded as satellites of the sun) 
 there are a few which present tin's same anomaly of retrograde 
 movement j yet this is not nearly so surprising as to find 
 this anomalous motion among the satellites of a primary 
 planet. We shall return to the consideration of this subject 
 when we come to discuss the cosmogony of the universe. 
 
 If we recall to mind the relations which exist between 
 the distances and periodic times of Uranus and Saturn, we 
 shall find that these two planets, when nearest to each 
 other, or in conjunction, are separated by a distance of about 
 nine hundred millions of miles. When most remote from 
 each other, this distance of separation is increased by the 
 whole diameter of the orbit of Saturn, or by eighteen hundred 
 millions of miles, as will be readily seen from the figure, in 
 which S represents the sun, A and B the places of Saturn 
 and Uranus when in conjunction, while B' represents the 
 place of Uranus in the opposite part of its orbit, or when in 
 
 opposition to the sun. Thus the distance between the planets 
 when located at A and B is just equal to the interval be- 
 
URANUS. 209 
 
 tween their orbits j while this interval is increased as Uranus 
 recedes from B up to the time that it reaches B' ; and on 
 reaching this point, Saturn being supposed to occupy the 
 point A, the two plants will be separated by a distance of 
 about twenty-seven hundred millions of miles. Since Saturn 
 performs its revolution in about twenty-nine years and a 
 half, and Uranus performs its revolution in about eighty -two 
 years, the interval from o*ne conjunction to the next is 
 readily computed to be about forty years. 
 
 This extraordinary change of distance produces a cor- 
 responding change in the reciprocal influences exerted by 
 these planets upon each other. The same remark is ap- 
 plicable to the configurations of Jupiter and Uranus, and 
 may be extended indeed to all the planets. Thus we perceive 
 that the greatest possible effect to draw Uranus closer to the 
 sun will be produced when all the planets lie on the same 
 straight line, and on the same side of the snn. 
 
 The prevalence of the law of universal gravitation, where- 
 by every particle of matter in the universe feels the attrac- 
 tion of every other particle, unites all the planets and their 
 satellites into one grand scheme of revolving worlds, in 
 which each is subjected to the influence of all the others. 
 After the discovery of Uranus an effort was made to assign 
 to this planet a curve whose magnitude and position were 
 derived from observations embracing but a small portion of 
 its orbit. This, of course, was a matter of necessity ; for 
 even one revolution has not yet been completed by Uranus 
 since the date of its discovery in 1781. The orbit assigned 
 to the planet was sufficiently accurate to trace backward its 
 movement among the fixed stars. This was done in the 
 hope that the planet might have been seen and its place 
 recorded as a fixed star by some of the early astronomers. 
 If it should happen that the computed place of the planet 
 should coincide with the recorded place of a star of th 
 same magnitude as the planet, then a suspicion would arise 
 that this star and the planet were one and the same body. 
 If on directing the telescope to the point once occupied by 
 
210 POPULAR ASTRONOMY. 
 
 the star the place should be found vacant, this evidence 
 would be almost conclusive that the supposed star was 
 actually the planet. By an examination of this kind it was 
 found that the planet Uranus had been observed, and its 
 place carefully recorded by no less than three astronomers, 
 each of whom had seen it several times, without any sus- 
 picion of its planetary character. The astronomer Flamsteed 
 was the first who had mistaken this planet for a star nearly 
 ninety years before its discovery by Sir William Herschel. 
 It was subsequently observed by Bradley, by Mayer, and by 
 Le Monnier, who fixed its place no less than twelve times 
 during the period from 1750 to 1771. These ancient 
 observations furnished an opportunity to test the accuracy 
 of the computed elements of the orbit of the new planet, 
 and to correct these elements, in case they were found to be 
 sensibly in error. This work was executed in a most 
 faithful and exact manner by M. Bouvard, who also com- 
 puted tables predicting the places of Uranus for many years 
 in advance. It was supposed with reason that these tables 
 would point out the places of Uranus with the same cer- 
 tainty as those of Saturn and Jupiter computed by the 
 same astronomer gave the places of these planets. In this 
 the hopes of the astronomical world were disappointed, and 
 this extraordinary discrepancy between computation and 
 observation gave rise to the discovery of an exterior planet, 
 w we shall now relate. 
 
NEPTUNE. 211 
 
 CHAPTEK XIII. 
 
 NEPTUNE, THE NINTH AND LAST KNOWN PLANET IN THE 
 OKDEK OF DISTANCE FKOM THE SUN. 
 
 Uranus Discovered by Accident. Ceres by Kesearch with the Telescope. 
 Rediscovered by Mathematical Computation. The Perturbations of 
 Uranus. Not due to any known Cause. Assumed to arise from an 
 Exterior Planet. Nature of the Examination to find the Unknown 
 Planet. Undertaken at the same time by two Computers. Computa- 
 tion assigns a Place to the Unknown Planet. Discovered by the 
 Telescope. Discoveries resulting. A Satellite detected. The Mass 
 of Neptune thus determined. Neptune's Orbit the Circumscribing 
 Boundary of the Planetary System. 
 
 THE discovery of Neptune is undoubtedly the most remark- 
 able event in the history of astronomical science an event 
 without a parallel, and rising in grandeur pre-eminently 
 above all other efforts of human genius ever put forth in the 
 examination of the physical universe. 
 
 The planet Uranus was discovered by the aid of the 
 telescope, not exactly by accident, but still without any 
 expectation on the part of the discoverer that his examina- 
 tion of the fixed stars would result in the addition of a 
 primary planet to the system. Indeed, as we have seen, 
 so little did the astronomical world then anticipate the 
 discovery of a new planet, that the announcement by Sir 
 William Herschel that he had detected a most remarkable 
 comet was accepted on all hands, and it was only continued 
 observation that finally compelled astronomers to accept the 
 new object as a planet. In the case of the discovery of the 
 first asteroid we find a systematic organization of astrono- 
 mical effort to detect a body whose existence was conjectured, 
 on the single ground of the harmony of the universe, or 
 that the law of interplanetary spaces, interrupted between 
 Mars and Jupiter, would be restored by finding a planet 
 revolving within that .vast interval. Hence a search wa? 
 
 p 2 
 
212 POPULAR ASTRONOMY. 
 
 commenced which consisted in examining every star in the 
 region of the ecliptic, to ascertain whether its place was 
 already laid down on any known map or chart of the 
 heavens. Now, it is evident that if it were possible to 
 make a perfect daguerreotype of any region of the celestial 
 sphere, say to-night, and the same could be effected on the 
 following night, the comparison of these two pictures would 
 exhibit to the eye any change which may have occurred in 
 the interval from the one picture to the other ; and hence, 
 if a star were found on the second and not on the first 
 picture, this star might fairly be suspected to be a planet, 
 or the same suspicion would attach to a star found on the 
 first, but missing on the second picture. Now, a map of 
 the heavens, so far as it includes the correct places of the 
 stars, answers our purpose quite as well as the daguerreo- 
 type, and any star found in a region well charted, but not 
 laid down on the map, may be fairly suspected to be a planet. 
 A few hours of examination will show it to be at rest or in 
 motion. If in motion, then its planetary character is 
 decided. 
 
 This method of research has been employed in the dis- 
 covery of all the asteroids, and there is but one example in 
 which a more powerful and searching examination became 
 necessary. This was in the case of the asteroid Ceres, 
 which, as we have seen, was discovered by Piazzi, at a time 
 when but few observations could be made previous to its 
 being lost in the rays of the sun. For a long time it seemed 
 almost a hopeless task to undertake the rediscovery of the 
 planet, as the telescope would be compelled to grope its way 
 slowly roTind the heavens, in the region of the ecliptic, 
 comparing every star with its place in the chart. In this 
 dilemma mathematical analysis essayed to erect a structure 
 on the narrow basis of the few observations obtained by 
 Piazzi, whereon the instrumental astronomer might stand 
 and point his telescope to the precise point occupied by the 
 lost planet. The genius of Gauss succeeded in this herculean 
 task, and when the telescope was pointed to the heavens in 
 
NEPTUNE. 213 
 
 the exact place indicated by the daring computer, there, in 
 the field of view, shone the delicate and beautiful light oi 
 the long-lost planet. 
 
 This was certainly a most wonderful triumph of analytic 
 reasoning ; yet in this case the planet had been discovered, 
 was known to exist, and had been observed over 4 out oi 
 the 360 of its revolution round the sun. On this basis oi 
 4 it was possible to rise to a knowledge of the planet's 
 position at the end of a few months of time. 
 
 The case of the discovery of Neptune is entirely different. 
 Here no planet was known to exist ; no telescopic power, 
 however great, had ever seen it. For ages it had revolved 
 round the sun in its vast orbit, far beyond the utmost known 
 verge of the planetary system, unfathornably buried from 
 human gaze and from human knowledge. No sage of 
 antiquity had ever dreamed of its existence. The fertile 
 brain of even Kepler had failed to imagine its being, and 
 the powerful penetration of Newton's gigantic intellect had 
 failed to pierce to the far-off region inhabited by this 
 unknown and solitary planet. 
 
 Indeed, with the knowledge which existed prior to the 
 discovery of Uranus, no human genius, however mighty, 
 could have passed the tremendous interval which separates 
 the orbits of Saturn and Neptune from each other. The 
 discovery of an intermediate planet was requisite to furnish 
 a firm foothold to him who would adventure to pass a gulf 
 of not less than 2,000 millions of miles at its narrowest 
 place. 
 
 We shall now proceed to relate the circumstances which 
 led to the discovery of Neptune. As already stated, a 
 -careful and elaborate study of the orbit of Uranus had been 
 accomplished by M. Bouvard, and tables giving the computed 
 places of this planet had been prepared by the same astro- 
 nomer. It was not anticipated that these tables would be 
 absolutely perfect, even if based on perfect observations. 
 We must remember that each body of the solar system 
 effects every other, and hence no single set of observations 
 
214 POPULAR ASTRONOMY. 
 
 are sufficient to give a perfect orbit. In case all the other 
 worlds were blotted out of existence, and there remained 
 only the sun and Uranus, then three perfect observations of 
 the planet's place would suffice to determine positively all 
 the elements of its orbit, and fix for ever all the circum- 
 stances of its motion. We shall call the figure of the orbit 
 of Uranus, obtained under the above hypothesis, the normal 
 figure, and the ellipse which it would describe about the 
 sun, under the above circumstances, the normal ellipse. If 
 now we introduce another planet into our system, as, for 
 example, Saturn, it is possible, as we have already seen, to 
 compute the exact amount of power exerted by Saturn to 
 disturb the movements of Uranus, and to change the figure 
 of its orbit. In like manner, by adding successively all the 
 interior planets, it is possible to compute the perturbations 
 that each produces upon the orbit of any particular one, 
 until, finally, by using all the power of analytic reasoning, 
 the human mind may reach to a complete knowledge of all 
 possible derangements produced by the combined action of 
 all existing known causes of perturbation. 
 
 Supposing our knowledge in this way to become perfect 
 as to the movements and orbit of Uranus, we can then 
 predict its places in all coming time, and these predictions, 
 being arranged in tabular form, may be verified by com- 
 parison in after years with the observed places of the planet. 
 If now a new planet were added to the system, revolving in 
 an orbit exterior to that of Uranus, perturbation would 
 arise from the introduction of this disturbing body into our 
 system, which would at once cause the planet to deviate 
 from its predicted track, and the observed and computed 
 places would no longer agree. 
 
 "We can perceive at once, from this statement of the 
 problem, that these very discrepancies between the old 
 track and the new one, pursued by the planet, would give 
 us a clue whereby it might become possible to determine, in 
 space, the position of the disturbing body. 
 
NEPTUNE. 216 
 
 Difficult and incomprehensible as the above problem may 
 appear, it is far less difficult than the one actually presented 
 in nature. We have supposed the normal ellipse, described 
 by Uranus, to be known ; whereas, in reality, this very 
 ellipse had to be determined by a train of reasoning of the 
 most searching and powerful character, while the whole 
 problem was almost hopelessly embarrassed by the fact that 
 the movements of Uranus were actually being disturbed all 
 the time by the unknown body whose position in space was 
 required. As the normal orbit could only be determined by 
 a series of approximations, based upon the observed places 
 of the planet, it was impossible, in any one of these approxi- 
 mations, to free Uranus from the disturbing effects of the 
 unknown body. It was only, therefore, by comparing with 
 each other the results reached by these successive approxi- 
 mations to the orbit of Uranus, that it became manifest 
 that no increase of accuracy was being reached by these 
 successive efforts ; and after every known cause of disturb- 
 ance had been carefully taken into account, a grand conclu- 
 sion was finally reached, that no satisfactory account could 
 be rendered of the movements of Uranus by the combined 
 effects of all known disturbing causes. 
 
 To reach this conclusion required investigations of the 
 most profound and laborious character ; but before it was 
 possible to explain these anomalous movements of Uranus, 
 a problem of far greater difficulty remained to be solved, 
 involving nothing less than a determination of the weight 
 of the unknown planet, its distance from the sun, the 
 nature of its orbit, and its position in the heavens at a 
 particular time, indicating the region to which the tele- 
 scope must be pointed to render visible what had hitherto 
 remained for ages unseen by the eye of man. 
 
 To those who have given but little attention to the study 
 of these extraordinary problems, an attempt to resolve a 
 question like that just presented may seem to be even pre- 
 sumptuous j yet when we come to examine the circumstances, 
 
216 POPULAR ASTRONOMY. 
 
 we shall see dimly a way whereby we may leach a certain 
 approximate knowledge of the place of this unknown world. 
 
 The fact that the planes of the orbits of all the more 
 distant planets are nearly coincident with the ecliptic 
 reduced the examination to the great circle in the 
 heavens cut out by the indefinite extension of this plane. 
 This is a most important consideration ; and but for this 
 fortunate circumstance no powers of research could ever 
 have made even the most distant approximation to the 
 place of the unknown planet. 
 
 The empirical Jaw of Bode, whereby it seemed that the 
 order of distances of the planets was governed, assigned to 
 the hypothetical world a distance about double that of 
 Uranus, or say, 3,600 millions of miles from the sun. 
 Assuming this as the probable distance, the third of 
 Kepler's laws would determine the period of revolution 
 of the world whose position was sought. It remained now 
 to assign a mass and position to the planet such as would 
 fender a satisfactory account of the perturbations of Uranus, 
 which remained outstanding after the known causes of dis- 
 turbance were exhausted. To accomplish this, let us recall 
 to mind the fact that, in case the mean distance of the dis- 
 turbing body had been rightly selected, then the interval 
 between Uranus and the unknown, when in conjunction, 
 would be about 1,800 millions of miles. In this position 
 the disturbing force would exhibit its maximum power in a 
 twofold sense : first, to cause Uranus to recede to its greatest 
 distance from the sun ; and, second, to cause the same planet 
 to lag behind the place it would otherwise have reached. In 
 the above figure let U U' U" represent the computed orbit of 
 Uranus, as existing under the combined influence "of all known 
 causes, P the place of the unknown, when in conjunction with 
 Uranus at U'. It is manifest that the force exerted by P on 
 Uranus will tend to accelerate its velocity in coming up to 
 conjunction, and to cause the path described to lie outside the 
 computed path along the dotted line, the planet really reaching 
 the point U'", instead of U' in the undisturbed orbit. Leaving 
 
NEPTUNE. 217 
 
 this point, the force exerted by the unknown would reverse 
 its effect, and a retardation would commence, and by slow 
 
 degrees receding from the disturbing body, it would gradually 
 return to the undisturbed orbit, and there continue until the 
 period for the next conjunction might approach. 
 
 Such is a rough exhibition of the reasoning which was 
 employed to narrow the limits of research in the effort to 
 point the telescope to the unknown cause of the perturba- 
 tions of Uranus. No account, of course, can be given of 
 the mathematical treatment of the problem. It was under- 
 taken at about the same time by Adams, of England, and by 
 Le Terrier, of Paris. Each computer, unknown to the other, 
 reached a result almost identical. Le Verrier communicated 
 his solution to the Academy of Sciences on the 31st August, 
 1847, and on the evening of the 18th September, 1847, 
 M. Galle, of Berlin, directed the telescope to the point in 
 which the French geometer declared the unknown planet 
 would be found. A star of the eighth magnitude appeared 
 in the field of view, whose place was not laid down on any 
 known chart. Suspicion was at once aroused that this 
 might possibly be the planet of computation ; and yet it 
 seemed incredible that a problem far surpassing in difficulty 
 any which had ever been attempted by human genius 
 should thus at the first effort have been solved with such 
 marvellous precision. 
 
 The suspected star was examined with the deepest interest 
 
218 POPULAR ASTRONOMY. 
 
 in the hope that it might exhibit a planetary disc. In this, 
 however, the astronomer was unsuccessful ; and there re- 
 mained but one method by which its planetary character 
 might be determined, that of watching sufficiently long to 
 detect its motion. This process, however, must have tried 
 very sorely the patience of the observer, as the motion of the 
 planet at so great a distance as three thousand six hundred 
 millions of miles, was so slow as to require three entire months 
 to pass over a space equal to the apparent diameter of the 
 moon. The position of the suspected star having been accu- 
 rately determined on the first night of observation, it became 
 evident on the next night that the star had moved by an 
 amount such as was fairly due to the slow motion of so vast 
 an orbit. It could be none other than the unknown planet ! 
 A success almost infinitely beyond the expectations of the 
 most sanguine computer had crowned this mighty effort, and 
 the amazing intelligence that the planet was found startled 
 the astronomical world. 
 
 The planet was soon recognized by the astronomers in every 
 part of the world. The elements assigned by Le Terrier and 
 Adams by computation were accepted everywhere with most 
 unhesitating faith in their accuracy, and it was believed that 
 it only remained for the telescope to verify the computations 
 of these most wonderful mathematicians. In this the astro- 
 nomical world were destined to meet a most remarkable dis- 
 appointment. The new planet proved, indeed, adequate to 
 account for all the anomalous movements of Uranus, while 
 in all its elements it differed so widely from those of the 
 computed hypothetical planet that the computed and real 
 planet could not in any way be regarded as the same body. The 
 first restriction proved to be correct, for the orbit of the 
 new planet (afterwards named Neptune) did coincide almost 
 exactly with the plane of the ecliptic. The second restric- 
 tion, based on the extension of Bode's law of interplanetary 
 spaces, was falsified in the event ; for here the law of Bode 
 failed, and the distance of the true planet was about 732 
 millions of miles less than that of the computed one. 
 
NEPTUNE. 219 
 
 The third restriction due to the application of Kepler's 
 fchird law is verified in the real planet ; but as the distance 
 of the unknown was assumed greatly too large, of course 
 the periodic time depending on this distance was also too 
 large. This by necessity involved an error in the mass 
 assumed for the unknown, whose erroneous distance de- 
 manded, of course, an erroneous mass greater than that of 
 the true planet ; and yet, notwithstanding the magnitude 
 of the errors of these elements, the computers succeeded in 
 pointing the telescope within less than one degree of the 
 actual place of the body which had caused the anomalous 
 movements of Uranus ! 
 
 We will endeavour to render a brief account of this most 
 astonishing fact. It is evident that the disturbing effects of 
 Neptune will become most powerful when the disturbing 
 planet is nearest the disturbed one, or what amounts to the 
 same thing, the maximum disturbance will occur when the 
 planets are in conjunction. We know that the periodic time of 
 Uranus is 82 years, the periodic time of Neptune is 164 years, 
 and hence it is easy to compute the interval from one con- 
 junction to the next, which is no less than 171 years. The 
 two planets passed their conjunction in 1822, and therefore 
 the previous conjunction must have occurred 171 years 
 before, or in 1651 ; but the earliest recorded observation of 
 Uranus was not made till 1690, or nearly 40 years after the 
 conjunction, and at a time when the disturbing force of 
 Neptune was so much diminished as to be nearly, if not 
 quite insensible for a long while. The minute disturbing 
 power of Neptune still existing in 1690, would go on de- 
 creasing until, in 1732, the planets would be in opposition, 
 and would be separated by a maximum interval. After this 
 date the distance between the planets would slowly de- 
 crease as they approached their conjunction, and in 1781, 
 when Uranus was discovered, a small disturbing effect would 
 begin to be appreciable, which would go on increasing up to 
 the time of conjunction in 1822. Thus we perceive that 
 mathematicians found the planet Uranus in such conditioo 
 
220 POPULAR ASTRONOMY. 
 
 that the perturbing effects of Neptune were increasing ih 
 intensity from year to year ; and hence no set of elements 
 could correctly represent the places of Uranus, because the 
 observations did not extend back far enough to embrace the 
 disturbed places of the planet at the former conjunction 
 in 1651. No correct solution was then possible until the 
 perturbations should reach their maximum value, which 
 occurred in 1822, when the planets were in conjunction, and 
 subsequently to which period the planet Uranus would slowly 
 return to its computed orbit as it receded further and still 
 further from the influence of the disturbing body, as may be 
 more clearly seen from the figure below, in which the 
 smaller circle may represent the orbit of Uranus, the larger 
 one the orbit of Neptune. For a long while prior to con- 
 
 junction in 1822, Uranus would be slowly overtaking 
 Neptune, during which time the direction of the disturbing 
 force would be such as to accelerate the orbital motion of 
 Uranus, and to increase its distance from the sun. The 
 acceleration would cease at conjunction, and would there be 
 changed into equal and opposite retardation, as is manifest 
 from the figure, while the increase of the distance of Uranus 
 must continue to increase even after conjunction, but the 
 disturbing force must rapidly decline in power as the interval 
 
NEPTUNE. 221 
 
 between the planets increases. Thus the great problem 
 demanded the position of a disturbing planet at a given 
 time, which could account for the known perturbations, all 
 of which were crowded into a few years, say 25, before and 
 after the conjunction in 1822. While this narrowing of the 
 limits of sensible perturbation increased the chances of 
 directing the telescope to the unknown disturber, it seems 
 to have really increased the difficulty of assigning to this 
 disturber his exact orbit. Indeed, even with circular orbits, 
 several might have been chosen, such that by varying the 
 mass of the unknown, the perturbations might have been 
 tolerably well represented j but, in case elliptical orbits are: 
 chosen, then our limits are much extended, and the mean 
 distance may be made to vary within very broad limits, 
 provided the eccentricity may be chosen at pleasure. Thus 
 the ellipse shown in the figure coincides between N and N f 
 very nearly with the circular orbit, and in case a planet 
 revolving in the circle could account for the anomalies of 
 Uranus, the same would be tolerably well represented by the 
 effects of a planet with a very different period and mean 
 distance revolving in the elliptic orbit. Now, this was 
 exactly the case as developed in the final history of this 
 grand discovery. The great geometers chose an elliptic orbit 
 of such eccentricity, and having its major axis in such posi- 
 tion, that the. computed and true orbits agreed with each 
 other in a most remarkable manner during the twenty 
 years before and after conjunction. Their efforts were thus 
 crowned with the success which they so eminently deserved ; 
 and although the computed orbit came finally to differ 
 greatly from the true one, yet, for the time when the com- 
 puted orbit was required to represent the places of the 
 unknown, and to point the telescope to its actual location, 
 the computed orbit responded nearly as perfectly as the true 
 one could have done, even had it been then known- 
 
 It has been already stated that after the discovery of 
 Uranus, when the elements of its orbit had been obtained 
 with sufficient accuracy to render it possible to trace the 
 
222 POPULAR ASTRONOMY. 
 
 planet backwards among the fixed stars, it was ascertained 
 that it had been observed and its place recorded as early as 
 1690, and had been seen many times subsequently and prior 
 to its discovery, being always mistaken for a fixed star ; so 
 we find in the case of Neptune, a like examination by Pro- 
 fessor Walker led to the discovery that the new planet had 
 been twice recorded in position by La Lande, in May, 1795. 
 These two observations were found to be outside the path 
 which had been assigned the planet by the theory of both 
 Le Verrier and Adams ; and such was the deep confidence 
 in the accuracy of the elements assigned by these two 
 geometers, that it was with great difficulty that some of the 
 ablest astronomers could be induced to believe that the 
 missing star twice observed by La Lande could be the new 
 planet. The identity was, however, soon demonstrated, and 
 hence arose the discussion which led to the declaration by 
 an eminent mathematician, that the discovery of Neptune 
 was the result of a happy accident ; but we have seen that 
 the grand problem propounded by both the French and the 
 English astronomer, and which each resolved with such 
 astonishing precision, was to point the telescope in the direc- 
 tion of the unknown, which had produced the late excessive 
 perturbations of Uranus. It remains, so far as I know, yet 
 to be decided whether the data in possession of Adams and 
 Le Yerrier can be so treated by analysis, as to give an orbit 
 to the unknown more nearly agreeing with that of the known 
 planet. 
 
 NEPTUNE'S SATELLITE. The vast distance to which 
 Neptune is buried in space will perhaps render it impossible 
 to learn how many satellites revolve about this remote pri- 
 mary. The great refractors have certainly discovered the 
 existence of one satellite, and another is suspected. The 
 discovery of this one satellite of Neptune becomes, under all 
 the circumstances, a matter of deep interest, as it enables us 
 to determine the mass or weight of the primary a matter 
 of the first moment in computing the effects of the planet as 
 a disturbing body. The satellite is found to perform its 
 
NEPTUNE. 23i> 
 
 revolution about the primary in a period of about five days 
 and twenty-one hours, and at a mean distance of 232,000 
 miles, or nearly equal to the distance of our moon from the 
 earth. In case these distances are assumed to be exactly 
 equal, then, as at the same distance the centrifugal force 
 increases as the square of the velocity ; and as the velocity 
 of Neptune's moon is about four and a half times greater 
 than that of our moon, its centrifugal force in its orbit must 
 be 4-5 x 4-5, equal to about twenty times the centrifugal 
 force of the moon. Now, the attractive force of Neptune is 
 exactly proportioned to its weight or mass ; and hence, to 
 counterbalance this centrifugal force in his satellite, which 
 is twenty times as great as that of the moon, the mass of 
 Neptune must be twenty times as great as that of the earth. 
 Thus has been revealed, not one world, but two the one 
 containing a mass of matter sufficient to form no less than 
 twenty worlds as heavy as our earth the other a satellite, 
 indeed, of the first, yet sufficiently large to send back to us, 
 at a distance of 3,000,000,000 of miles, the light of the sun, 
 enfeebled by its dispersion over this vast distance to the one- 
 thousandth part of the intensity it pours on our earth. We 
 have reached the known boundary of that mighty confedera- 
 tion of revolving orbs which, whilst they acknowledge in the 
 most specific manner a mutual dependence, are all controlled 
 by the predominating influence of the sun, which occupies 
 the common focus of all their orbits, and around which they 
 all roll and shine in obedience to the grand law of universal 
 gravitation. 
 
 We shall now retrace our steps toward the sun, and 
 consider a remarkable class of bodies, which for ages were 
 regarded as evanescent meteors, suddenly blazing athwart 
 the sky, and as suddenly fading from the vision, never more 
 to reappear. Modern science has given to these bodies 
 determinate orbits, and in some instances, as we shall see, 
 has assigned them a permanent place among the satellites of 
 the HUH. 
 
224 POPULAR ASTRONOMY. 
 
 CHAPTER XIV. 
 
 THE COMETS. 
 
 Objects of Dread in the Early Ages. Comets obey the Law of Gravitation 
 and revolve in some one of the Conic Sections. Characteristics of these 
 Curves. Comet of 1680 studied by Newton. Comet of 1682 named 
 " Halley's Comet." Its History. Its Eeturn Predicted. Perihelion 
 Passage computed. Passes its Perihelion 13th April, 1759. Elements 
 of its Orbit. Physical Constitution. Nucleus. Envelopes. Tail. 
 Intense Heat suffered by some Comets in Perihelio. Dissipation of the 
 Cometic Matter. Encke's Comet. A Resisting Medium. Deductions 
 from Observation. Biela's Comet. Divided. Number of Comets. 
 
 IN all ages of the world these anomalous objects have 
 excited the deepest interest, not only among philosophers, 
 but among all classes of men. The suddenness with which 
 they sometimes blaze in the sky, the vast dimensions of their 
 fiery trains, the exceeding swiftness with which they pursue 
 their journey among the stars, the rapid disappearance of 
 even the grandest of these seeming chaotic worlds, have all 
 combined to invest these bodies with a power to excite a 
 kind of superstitious terror which even the exact revelations 
 of science cannot wholly dispel. History records the appear- 
 ance of these phenomena ; and in general they were regarded 
 as omens of some terrible scourge to mankind, the precursors 
 of war or pestilence or famine, or at the very least announcing 
 the death of some prince or potentate. Some of the ancients, 
 of course, rose above these superstitious ideas, and the 
 Roman philosopher Seneca even entertained the opinion 
 that these erratic bodies would some day fall within the 
 domain of human knowledge, that their paths among the 
 stars would eventually be traced, and that they would be 
 found in the end to be permanent members of the solar 
 system. How remarkably this prediction has been veri- 
 fied will appear in the concise sketch we are about tc 
 present. 
 
THE COMETS, 225 
 
 The discovery of the law of universal gravitation was 
 followed by a mathematical demonstration, also accomplished 
 by the great English philosopher, which was the reverse of 
 the problem he had just solved, and may be announced as 
 follows : Given, the intensity of a fixed central force, decreasing 
 in power as the squares of the distances increase, and the 
 direction and intensity of an impulsive force operating to set 
 in motion a body subject to the central power : Required, the 
 nature and figure of the path described by the revolving 
 body? 
 
 Previous to the resolution of this problem Newton 
 naturally expected to find the curve sought to be an ellipse. 
 The sun was the source of a fixed central force which 
 obeyed the above law. The planets were retained in their 
 orbits by this central force. These described ellipses in their 
 revolution around the sun, and it was natural to conclude 
 that the solution of the inverse problem would lead to the 
 elliptic orbit. On completing the solution and reaching the 
 mathematical expression representing the orbit, it was found 
 not to be the usual expression for the ellipse ; and after 
 careful examination proved to be the general expression, 
 embracing within its grasp no less than four curves, the 
 circle, the ellipse, the parabola, and the hyperbola. These 
 curves are allied in a most remarkable manner, having cer- 
 tain properties in common, and having in one sense a common 
 origin. They may all be obtained by cutting the surface of 
 a cone by a plane passing in different directions, as may be 
 seen from the figure in next page. Let A be the vertex, and 
 C D E L the circular base of a cone seen obliquely. Any 
 plane passed parallel to the base, or perpendicular to the 
 axis A B, will cut from the surface a circle, as F E G. A 
 plane passed obliquely to the axis will cut from the surface 
 an ellipse, as M O O'. Any plane passed parallel to the 
 side of the cone A C will cut the curve T W X, called a 
 parabola ; and any plane passed parallel to the axis of the 
 cone A B will cut out from the surface the curve K I L, 
 called a hyperbola. These curves are thus all derived from the 
 
 Q 
 
POPULAR ASTRONOMY. 
 
 conic surface by intersecting it with a plane, and are hence 
 called conic sections. Now, a little examination will show 
 
 us that, while the circle and ellipse are re-entering curves of 
 limited extent, this is not the case with the parabola and 
 hyperbola. If the conic surface were indefinitely extended 
 below the base, it is evident that the cutting plane X W T, 
 being parallel to the side A C, could never cut that par- 
 ticular line ; and hence the parabola, departing from the 
 point W, and passing through T and X, would extend inde- 
 finitely on the surface of the cone without ever coming 
 together, though the curves would approach each other for 
 ever. Thus the parabola is the limit of all possible ellipses ; 
 for it is manifest that, as the cutting plane becomes more and 
 more nearly parallel to the side A C, the axis of the ellipse 
 cut out grows longer and longer; and just at the point where 
 parallelism is reached the parabola is formed, and it is only 
 nn ellipse with an infinitely elongated axis. 
 
 While it is seen that the branches of the parabola approach 
 
THE COMETS. 5?27 
 
 each other, and may be said to come together at an infinite 
 distance from the vertex at W, this is riot the case with he 
 branches of the hyperbola. Departing from the vertex!, 
 and passing the points K and L, the branches of the hyper- 
 bola recede from each other for ever, losing by slow degrees 
 their curvature, until at an infinite distance the curves 
 degenerate into straight lines, and thus continue to recede 
 for ever. Such are some of the general characteristics of 
 these remarkable curves. They all, like the ellipse, have a 
 major axis, on each side of which they are symmetrical. 
 They all have at least one focus, possessing special properties. 
 They all have a vertex lying at the extremity of the major 
 axis and the nearest point of the curve to the focus ; and, 
 strange as it may seem, in either one of these curves mathe- 
 matical analysis demonstrated that a satellite of the sun 
 might revolve under the law of universal gravitation. The 
 elliptic orbits of the planets and the circular orbits of some 
 of the satellites of Jupiter presented examples in the 
 heavens of two of these curves ; and it occurred to the 
 sagacious mind of Newton that the hitherto unexplained 
 eccentricity of the cometary revolutions might be accounted 
 for by finding that they revolved around the sun in ellipses 
 of great eccentricity, or possibly in parabolic, or even in 
 hyperbolic orbits. The English astronomer had the opportu- 
 nity of putting to the test this grand idea by the appearance 
 of a great comet in 1 680, which displayed a train of light of 
 wonderful dimensions, and seemed to plunge nearly vertically 
 downwards from the pole of the ecliptic, made its perihelion - 
 passage with almost incredible velocity, and, with a speed 
 always diminishing as it receded from the sun, again swept 
 out into the unfathomable depths of space. To this comet 
 Newton first attempted to apply the law of gravitation, and 
 to assign it an orbit among the conic sections. This could be 
 done in the same manner from observation as in the case of 
 a planet. Having obtained as many places of the comet as 
 possible among the fixed stars, it remained to see whether 
 any elliptic orbit or any parabolic orbit could be assigned f,o 
 
 Q2 
 
228 POPULAR ASTRONOMY. 
 
 the comet, which would at the same time pass through all 
 these observed places. If this could be done, then it would 
 become possible from this known orbit to predict the places 
 of a comet as of a planet ; and in the event of the orbit 
 proving elliptic, then the return of the comet to its perihe- 
 lion might be computed and announced. 
 
 The comet of 1680 was carefully studied by Newton, and 
 its orbit was found to be an extremely elongated ellipse, 
 approaching very nearly to the form of a parabola; but 
 while its physical features and its near approach to the sun 
 made it an object of extraordinary interest, the exceeding 
 velocity with which it swept around the sun rendered it 
 difficult to execute exact observations ; and hence this comet 
 was not well adapted to demonstrate the truth of the 
 rigorous application of the law of gravitation to the orbital 
 movements of these eccentric bodies. Another great comet 
 appeared two years later, in 1682, to whose history there 
 attaches a special interest, on account of the fact that it was 
 the first of these bodies shown to have a permanent orbit in 
 connection with the solar system, and the first whose 
 periodic time was sufficiently well computed to render it 
 possible to predict its return. This comet bears the name 
 of the great English astronomer Halley, to whom we are 
 indebted for the computation of the elements of its orbit 
 a problem, at the time it was executed, far more difficult 
 than any belonging to the whole range of physical astronomy. 
 
 The elements of the orbit of a comet are nearly identical 
 with those which fix- the magnitude and position of a 
 planetary orbit. To obtain the magnitude of the cometary 
 ellipse we must have two elements, the length of the major 
 axis and the perihelion-distance. To obtain the direction of 
 the longer axis we must have the position of the perihelion- 
 point ; this point , being joined to the sun's centre, gives the 
 direction of the major axis. To obtain the position of the 
 plane of the orbit we must have the place of the ascending 
 or descending node, and also the inclination of the plane of 
 the cometary orbit to that of the ecliptic. If, in addition to 
 
THE COMETS. 229 
 
 these elements, we have the time of perihelion passage, then 
 it becomes possible to follow the cornet in its erratic move^ 
 ments with a certainty almost as great as that with which 
 the orderly movements of the planets are pursued. 
 
 On the appearance of the great comet of 1682, Halley 
 undertook the laborious and hitherto unaccomplished task 
 of computing rigorously the elements of its orbit, which task 
 he accomplished after incredible labour in the most masterly 
 manner. It then occurred to him to gather up all historic 
 details with reference to the appearance of comets, as well as 
 all astronomical observations, so that by examination and 
 inter-comparison he might learn whether any recorded comet 
 had ever pursued the same track in the heavens which had 
 just been passed over by the comet of 1682. In the course 
 of this historical investigation he found that comets, some- 
 what resembling in physical appearance, and traversing 
 nearly the same regions of space passed over by his own 
 comet, had appeared in the years 1531 and 1607, and now 
 again in 1682. These epochs are separated by an interval 
 of between seventy-five and seventy-six years ; and Halley, 
 after long and laborious computation, announced that in 
 1759, three quarters of a century from the date of the 
 prediction, this same comet would again return to our 
 system ! We can readily sympathize with the feelings of 
 this great astronomer when we find him appealing to pos- 
 terity to remember, in the event of his prediction being 
 verified, that such an occurrence as the return of a comet 
 was first announced by an Englishman. As the year 1759 
 approached, the prophetic declaration of Halley excited an 
 unusual interest throughout the astronomical world. To 
 predict the exact point in the heavens to which the telescope 
 must be directed to catch the first faint glimpse of the 
 returning stranger, and to give the date of its perihelion- 
 passage, required investigations of so high an order, that in 
 case they had been demanded of Halley, seventy-six yeara 
 before, the then existing condition of mathematical and 
 physical science would not have furnished the means for 
 
230 POPULAR ASTRONOMY. 
 
 their accomplishment. The whole subject of planetary 
 perturbations had by this time been tolerably well-developed, 
 and the laborious task of computing the disturbing influence 
 of Jupiter and Saturn was undertaken by Clairaut, assisted 
 by La Lande and by a lady, Madame Lepaute, whose name 
 stands in honourable union with the two profound mathe- 
 maticians. After many months of indefatigable labour the 
 computors announced that for want of time they had been 
 compelled to omit several matters which might make a differ- 
 ence of thirty days, one way or the other, in the return of 
 the comet, but that within these limits this long-lost celestial 
 wanderer would pass his perihelion on the 13th April, 1759. 
 The limits of error were justly chosen, for the comet actually 
 returned and passed its perihelion on the 12th March, just 
 a month ahead of the predicted time. 
 
 This successful computation settled for ever the doctrine 
 of the cometary orbits, and demonstrated beyond doubt their 
 subjection to the attractive power of the sun, and that this 
 orb extended its influence into the profound depths of space, 
 to which the comet descended during its journey of seventy- 
 six years. It was further established that Halley's comet 
 was a permanent member of the solar system, performing its 
 orbital revolution around the sun in an exceedingly elongated 
 ellipse, but with a regularity equal to that of the planets. 
 It was further determined that the entire mass of the comet 
 was very inconsiderable, as no account of this mass was 
 made in the computations for perturbation, while the masses 
 of Jupiter and Saturn required to be known with precision. 
 This comet has returned a second time since its discovery by 
 Halley, when its elements were more accurately obtained by 
 many modern astronomers, and perhaps best of all by 
 Hermann WestpJialen, who predicted its perihelion-passage, 
 after an absence of seventy-six years, to within jive days ! 
 This appearance took place at the close of 1835. We shall 
 have occasion to recur to this comet, when we come to speak 
 of the physical constitution of comets. 
 
THE COMETS. 231 
 
 Westphalen furnishes the following as the actual dimen- 
 sions of Halley's comet : 
 
 Perihelion distance 55,900,000 miles. 
 
 Aphelion 3,370,300,000 
 
 Length of the major axis 3,426,200,000 
 
 Breadth of the orbit 826,900,000 
 
 It is thus seen that in its journey from the sun this comet 
 crosses the orbits of all the known planets, and passes the 
 boundary of Neptune more than three hundred millions ot 
 miles. 
 
 Having thus demonstrated the subordination of these 
 extraordinary bodies to the law of universal gravitation and 
 to the received laws of motion, we will proceed to examine 
 their 
 
 PHYSICAL CONSTITUTION. The solid earth we inhabit, the 
 moon her satellite, the sun, and all the planets, are compact 
 masses of matter of differing densities, but of firm, compact 
 materials. The comets, on the contrary, as a class, seem to 
 be vaporous masses, far more unsubstantial than the lightest 
 summer-cloud, and in general transparent, or at least trans- 
 lucent, even in their most condensed portions. This is evi- 
 dent from the fact, that the minute stars are still visible with 
 undiminished light when seen sometimes through a depth 
 of cometary matter millions of miles in extent. Comets in 
 general consist of a nucleus or head, the centre of force and 
 the most condensed portion of their matter. Around this 
 head there is seen usually a vaporous envelope or atmosphere 
 of greater or less extent, sometimes evidently divided into 
 concentric layers of nearly globular form. Many comets, on 
 approaching the sun, undergo extraordinary physical changes 
 in the head or nucleus, which experiences an excessive 
 agitation, flinging out jets or streams of fiery light in a 
 direction towards the sun, which assume many and strange 
 forms, sometimes spreading out into a fan-shaped figure, and 
 rapidly fading in intensity, as they recede from the nucleus. 
 This phenomenon is almost invariably attended or followed 
 
232 POPULAR ASTRONOMY. 
 
 by another even more remarkable the throwing-off of a 
 train of luminous matter, called the tail, in a direction 
 opposite the sun, and sometimes extending to a prodigious 
 distance. Thus the tail of the great comet of 1680, already 
 mentioned, according to the computations of Sir Isaac 
 Newton, reached to a distance of more than 140,000,000 of 
 miles, while only two days were occupied in projecting this 
 inscrutable and mysterious appendage to this enormous 
 distance. The form of the tail is usually that of a hollow 
 paraboloid, the nucleus occupying the focus, and thus the 
 tail, as it recedes from the head, seems to diverge into two 
 streams of light, while the axis or central line is compara- 
 tively dark. Sometimes, as in the great comet of 1858, the 
 region immediately behind the nucleus on the axis is jet 
 black the intensity of this blackness growing less and less 
 along the axis until it finally fades out in the general lu- 
 minosity of the tail. 
 
 The nucleus is sometimes tolerably well defined, and 
 presents a planetary disk of greater or less magnitude. It 
 is not intended to assert that there are no comets which are 
 solid bodies, at least in some portion of their central masses. 
 Indeed, if we are to credit the records, some have been seen 
 in the act of crossing the disk of the sun, when they have 
 appeared as round, well-defined, circular black spots, exactly 
 like the planets Yenus and Mercury, when seen in the same 
 condition on the bright surface of the sun. For the most 
 part, however, we know that these, bodies do not present 
 any evidence of solidity. Their heads or nuclei are ill- 
 defined when examined by powerful telescopes, and their 
 gaseous condition is demonstrated by the fact that they 
 expand and contract their dimensions with great rapidity, 
 according to circumstances. 
 
 This contraction generally takes place as the comet ap- 
 proaches its perihelion-passage, which is certainly a very 
 curious fact, and quite contrary to what we would expect, 
 as the excessive heat to which a comet must be subjected 
 in perihelio ought (as would seem) to greatly expand its 
 
THE COMETS. 233 
 
 dimensions. It is doubtless owing to the fact, that this 
 enormous heat extends its influence so far that the vaporous 
 mass is expanded and rarified to such a degree as to become 
 absolutely transparent and invisible, and it is only when 
 released from this intense heat by recess from the sun that 
 a condensation takes place, and thus the seeming dimensions 
 of the comet increase. It is difficult to comprehend how 
 some of these bodies, in their nearest approach to the sun, 
 are not absolutely burned up and dissipated for ever. The 
 great comet of 1680, when in perihelio, was only about 
 147,000 miles distant from the sun's surface ; and admitting 
 that the heat of the sun diminishes as the square of the 
 distance increases, Newton computed that the comet was 
 subjected to a heat 2,000 times more intense than that of 
 red-hot iron. The great comet of 1843 is computed to have 
 approached the sun's surface to within half the above dis- 
 tance, and Sir John Herschel computes that the intensity 
 of the heat then experienced by this comet was 47,000 
 times greater than the heat of the sun as received at the 
 earth, or more than twenty-eight times greater than the 
 heat concentrated at the focus of a lens of thirty-two inches 
 diameter, which melted agate and rock crystal, and dissi- 
 pated these refractory solids into an invisible gas ! 
 
 After passing under the influence of such intense heat, it 
 seems almost impossible that any well-defined form should 
 ever be recovered ; and yet the comet of 1680 and that of 
 1843 finally receded from the sun, the nucleus in some 
 mysterious way slowly gathering up its dispersed particles 
 and sweeping away into the depths of space, a well-defined 
 luminous object, not in any sensible degree injured in its 
 form or magnitude by this fiery ordeal. 
 
 The envelopes of comets and their tails are by far the 
 most inscrutable problems of nature. Of these phenomena 
 no satisfactory account has yet been rendered. The en- 
 velopes of the comet of 1858 were beautiful in form, with a 
 well-defined circular outline, in whose centre the nucleus 
 blazed with its fiery light. The diameter of this seemingly- 
 
234 POPULAR ASTRONOMY. 
 
 globular roass changed from night to night. Its texture 
 varied ; sometimes evenly and beautifully shaded and gauze- 
 like in its surface, and sometimes this gauzy surface broken 
 by dark and irregular patches. A second concentric sphere 
 became visible, fainter in its outline than the interior one, 
 and finally a third circle dimly presented its outline, very 
 faint, and only to be seen in powerful telescopes, under 
 favourable circumstances. 
 
 The beautiful forms exhibited in these envelopes and 
 retained by them seem to demonstrate the existence of some 
 central repulsive force located in the nucleus, and capable of 
 holding these gaseous particles in equilibrium. What this 
 force may be it is vain to conjecture. If the envelope of 
 the nucleus is a phenomenon surpassing the reach of human 
 thought, what shall we say of the still more mysterious and 
 incomprehensible phenomena presented in the tails of 
 comets 1 
 
 We have already said that these tails are thrown off in 
 a direction opposite the sun, as the comet approaches its 
 perihelion~passage. As the comet sweeps around the sun 
 with almost inconceivable velocity, the tail retains its direc- 
 tion, just as though its axis were a solid bar of iron, passing 
 through the nucleus to the sun and hanging on the centre 
 of the solar orb. This bar, extending out to the furthest 
 extremity of the tail, sometimes 120 millions of miles beyond 
 the nucleus, sweeps round angularly with equal rapidity at 
 every point, so that its rectilinear figure is preserved in this 
 tremendous sweep. In case the tail were composed of pon- 
 derable particles, obedient to the laws of gravitation and 
 motion, this would be impossible ; for if we consider each 
 particle an independent body, describing an elliptic or 
 parabolic orbit about the sun, the laws of their motion, 
 would compel the more distant particles to lag behind the 
 nearer ones in angular velocity. 
 
 If no comet ever exhibited any other than this peculiar 
 form of tail, straight and directed from the sun, we might 
 frame an hypothesis which could account for the facts ; but 
 
THE COMETS. 235 
 
 in some instances there are many tails to the one nucleus, 
 and these not straight, but curved like a scimitar. In other 
 cases there are two tails, the one, as usual, directed from the 
 sun, the other pointing towards the source of light. Some- 
 times the principal tail is straight, and in the direction from 
 the sun, while a lateral ray shooting from the nucleus may 
 form with the axis of the tail an angle of thirty or even 
 sixty degrees. 
 
 We have already said that the tail swings around the 
 sun in the perihelion-passage, preserving its form and direc- 
 tion ; and hence, when the comet is receding from the sun, 
 the tail, in all its vast dimensions, is driven before the head 
 of the comet, preceding the nucleus as it sweeps outward 
 into space. 
 
 In some instances coruscations have been noticed to take 
 place in these grand but mysterious appendages, darting 
 with incredible velocity from the very nucleus to the ex- 
 tremity of the tail, and thus flashing backwards and forwards 
 like a magnificent auroral display. 
 
 The question arises, What are these luminous displays? 
 Are the tails of comets composed of ponderable matter 1 If 
 so, do they yield obedience to the known laws of motion and 
 gravitation ? Is there any matter in the universe which 
 may ever become luminous, but is imponderable ? Can 
 these tails be a mere effect produced on the waves of light 
 emitted by the sun in passing through the mass of cometary 
 matter ? These and many other questions equally difficult 
 present themselves in this connection. The re-absorption 
 of the tail into the head would seem to demonstrate that 
 the matter composing the tail was ponderable ; while the 
 facts already stated as to the rigid form preserved by the 
 tail in sweeping around the sun positively contradicts this 
 hypothesis. 
 
 One thing we know : cometary matter is ponderable 
 matter, and obeys the laws of motion and gravitation, is 
 swayed by the sun and by the planets, and in all particulars 
 complies with the laws governing other ponderable matter. 
 
236 POPULAR ASTRONOMY. 
 
 This we know, because, as we have seen, it is possible to 
 predict the return of a comet revolving even in so great a 
 period as seventy-five years, and such predictions have been 
 rigorously verified. In case any portion of this ponderable 
 matter were absorbed in the sun, or dissipated by the intense 
 heat which it suffers in the perihelion-passage, then would 
 the mass of the comet grow less at each return, and the 
 periodic time would slowly diminish. There is one comet, 
 named after its illustrious discoverer, Encke, whose history 
 for the past thirty years has been followed with high interest, 
 because it is now a fixed truth that at each return its 
 perihelion-passage is accelerated by about two and a half 
 hours. It revolves in an elliptical orbit of small dimensions 
 comparatively, and performs its revolution around the sun 
 in a period of only 1,205 days, or about three and a third 
 years. By assuming the existence of a rare resisting medium, 
 Professor Encke has succeeded in accounting for the accelera- 
 tion in the motion of these comets, and this hypothesis has 
 been generally received. In case its truth becomes esta- 
 blished, it involves remote consequences from which the 
 mind naturally revolts ; for if there be a medium capable of 
 destroying any portion of the velocity of Encke's comet, the 
 same resistance must in like manner destroy a part of the 
 orbital velocity of every planet and satellite, and sooner or 
 later each in its turn must by slow degrees approach the sun, 
 and in the end this grand central orb must become the grave 
 of every planet and satellite and comet ! Such an hypo- 
 thesis is combated, possibly disproved, by the fact that its 
 influence has not yet been discovered, on any one of the 
 planets, or on any satellite. It may be argued that on these 
 solid substantial bodies it would require ages to produce 
 sensible effect, while on the vaporous ethereal mass of 
 Encke's comet even an almost evanescent medium might 
 produce a sensible effect, even in a single revolution of 
 1,205 days. May it not be possible to account for the 
 decrease of the periodic time of Encke's comet without 
 having resort to an hypothecs involving the destruction of 
 
THE COMETS. 237 
 
 the entire universe ? In case we admit that it loses a 
 portion of its ponderable matter at each perihelion-passage, 
 then there must result an effect like the one observed, the 
 comet slowly approaching the sun, to be dissipated entirely,, 
 however, before absolutely falling on the surface of the 
 central orb. 
 
 However, it is useless to speculate. The facts now in our 
 possession are not sufficient to enable us to render a satis- 
 factory account of the various phenomena in the physical 
 constitution of these bodies which have been enumerated, 
 and we can only hope that the diligence and pertinacity 
 with which this branch of astronomy is now pursued may 
 before long eventuate in removing from the science this only 
 source of doubt and uncertainty. 
 
 In the meanwhile the conclusions reached by Sir John 
 Herschel, from an extended and careful observation of 'all 
 the phenomena presented by Halley's comet in 1835-6, have 
 been strengthened by the facts recorded both in Europe and 
 America of the great comet of 1848. All the observations 
 go to demonstrate 
 
 1. That the surface of the nucleus nearest the sun 
 becomes powerfully agitated, and finally bursts forth into 
 luminous jets of gaseous matter. 
 
 2. That this matter, with an initial velocity driving it 
 towards the sun, is, by some unknown repelling force, driven 
 backwards from the sun, and drifted outward from the sun 
 to vast distances, forming the tail. 
 
 3. That a portion of this vaporized material is not subject 
 to this repulsive force, but remains under the influence of 
 some equally inscrutable central power lodged in the centre 
 of the nucleus, and forming the corona or envelope, and 
 assuming forms of great delicacy and beauty. 
 
 4. That the force which ejects the tail cannot be gravita- 
 tion, as it a^ts with a power and in a direction opposed to 
 this central power. 
 
 5. That the power lodged in the nucleus, and by whose 
 energy the particles composing the tail are again re-absorbed 
 
238 POPULAR ASTRONOMY. 
 
 into the head, cannot be gravitation, as the minute mass of 
 the comet could not by its gravitating power bring back the 
 particles flung off to such enormous distances. 
 
 In this catalogue of inscrutable phenomena we must place 
 the remarkable fact of the splitting-up of a comet into two 
 distinct portions. A comet of short period, known as Biela's 
 comet, revolving in about six and three quarter years, was 
 recognized as early as 1826, as a permanent member of the 
 solar system. 
 
 This comet, at its appearance in 1832, excited a profound 
 sensation, in consequence of the prediction that it would 
 cross the earth's path, thereby creating the greatest alarm 
 among the ignorant, lest this crossing might occasion a col- 
 lision between the comet and the earth. The prediction 
 was verified ; but while the comet was in the act of crossing 
 the earth's track or orbit, the earth was many millions of 
 miles removed from this special point of intersection. 
 
 The appearance in 1846 was again rendered memorable 
 by the strange phenomenon already mentioned the actual 
 severation of the comet into two bodies, distinct and sepa- 
 rate, each cometary in its appearance, and each alternately 
 preponderating in apparent magnitude and brilliancy. These 
 two comets possessed all the characteristics which mark these 
 anomalous bodies. Each had its nucleus, its envelope, and its 
 tail. The first indication of a separation occurred as early as 
 the 19th December, 1845. By the middle of January, 1846, 
 the separation was complete, and was well observed in Europe 
 and America. By the beginning of March the interval had 
 increased to a maximum, when it was about one-third as great 
 as the apparent diameter of the moon. From this time the 
 companion-comet began to fade, remaining faintly visible up 
 to the 15th March. After this the old comet remained single, 
 and finally disappeared. 
 
 Here we have phenomena of the most extraordinary 
 character ? What convulsion could have split this nebulous 
 mass into two distinct fragments ? What wonderful power 
 
THE COMETS. 239 
 
 iculd have occasioned the alternations in the intensity of 
 their light ? What mysterious bond could have united 
 these severed and separated bodies, and caused them to 
 vibrate about their common centre of gravity ? Have 
 these bodies been permanently re-united 1 or will they 
 ever appear as individual and independent objects ? These 
 questions it is now impossible to answer. 
 
 THE NUMBER OF COMETS far exceeds that of the planets 
 and their satellites ; and, indeed, judging from the list of 
 recorded comets, and taking into account the fact that mul- 
 titudes of these bodies must escape notice entirely by their 
 remaining above the horizon in the day-time, we are forced 
 to the conclusion that they are not to be numbered by hun- 
 dreds or thousands, but probably by millions ! They seem 
 to obey no law as to the inclination of their orbits or the 
 direction of their motions. Some appear to plunge verti- 
 cally downwards from the very pole of the ecliptic, while 
 others rise upward from below this plane in a direction 
 diametrically opposite. Their planes are inclined under all 
 angles, and their perihelion points are at all distances from 
 the sun. Some revolve in orbits of moderate eccentricity, 
 while others sweep away into space in parabolic or even in 
 hyperbolic orbits, never again to visit our system unless 
 arrested and diverted from their path by some disturbing 
 power. The mighty depths to which some of these bodies 
 penetrate into space, sweeping, as they must, vastly beyond 
 the boundary of the planetary system, would excite a doubt 
 in the mind as to whether there might be room enough in 
 space for the undisturbed revolution of these wonderful 
 objects. We shall see hereafter that profound investiga- 
 tions have answered this inquiry and dispelled every doubt 
 as to the grandeur of the scale on which the universe is 
 built. 
 
 In the Appendix will be found the elements of the orbits 
 of such comets as are regarded permanent members of the 
 solar system. 
 
240 POPULAR ASTRONOMY. 
 
 We here close our examination of the various classes of 
 attendants on the solar orb. We find this mighty system of 
 revolving worlds composed of bodies which are diverse in 
 their physical constitution, some more dense and solid than 
 the earth on which we dwell, some far more rare and unsub- 
 stantial than the atmosphere we breathe all obedient to the 
 grand controlling power of the central orb, while no one is 
 relieved from the disturbing influence of every other a 
 vast complicated display of celestial mechanism, whose 
 equilibrium and stability present the grandest problem for 
 human investigation to be found in the whole universe of 
 matter. 
 
 CHAPTER XV. 
 
 THE SUN AND PLANETS AS PONDERABLE BODIES. 
 
 General circumstances of the System. The Sun. His Diameter and 
 Mass. Gravity at the Surface. Mercury. His Mass and Perturbations. 
 Venus as a Ponderable Body. Long Equation of Venus and the 
 Earth. The Earth and Moon as heavy bodies. Figure and Mass of the 
 Earth. Precession. Aberration. Nutation. Mars. His Mass and 
 Density. Gravity at his surface. The Asteroids. Jupiter's System. 
 Saturn. His Moons and Rings as Ponderable Bodies. Uranus. 
 Neptune. Stability of the whole System. 
 
 HAVING now completed a rapid survey of the bodies which 
 owe allegiance to the sun, and having reached to a know- 
 ledge of those laws which extend their empire over all these 
 revolving planets, we come to the consideration of the modi- 
 fications which are introduced into the circumstances of 
 motion of each of these worlds, by the fact that it is sub- 
 jected to the influence of all the others. As, under the 
 great law of universal gravitation, every particle of matter 
 in the universe attracts every other particle of matter with 
 a force which varies inversely as the square of the distance 
 and directly as the mass, it follows that each planet- and 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. ii41 
 
 comet and satellite of the entire system of the sun is, to a 
 greater or less degree, affected by the attraction of every 
 other. 
 
 We have already considered generally the great problem 
 of the " three bodies " a central, a disturbing, and a dis- 
 turbed body. The train of reasoning there presented is now 
 to be carried out and extended in succession to the planets 
 and their satellites. Before proceeding to examine the 
 changes wrought in the orbits of the planets and theif 
 satellites by the action of all the disturbing forces, we will 
 make a more general examination of the various elements 
 of the planetary orbits, to learn, if possible, whether any of 
 these elements are subjected to changes which are merely 
 periodic in their character, returning after intervals, longer 
 or shorter, to their normal condition, to repeat the same 
 changes in the same order for ever. "We desire also to 
 inquire whether any of the elements are subjected to per- 
 turbations which always progress in the same direction; 
 and if so, whether these changes in any way involve the 
 destruction of the system as such. 
 
 This is undoubtedly the grandest problem ever pro- 
 pounded to the human mind ; for it is neither more nor less 
 than an inquiry into the perpetuity of the great scheme of 
 worlds dependent on the sun. It demands a vision which 
 shall penetrate the future ages, to predict the mutations and 
 their effects at the end of these ages. It will not be ex- 
 pected that in such a treatise as this we are to enter into 
 *,n exhaustive discussion of this great subject. "We can do 
 little more than announce the results reached by the pro- 
 found investigations of the great mathematical successors of 
 Newton. 
 
 We shall commence, then, by an inquiry touching those 
 elements of an orbit which involve the well-being of a 
 planet, or its fitness to sustain the animal and vegetable life 
 which exists on its surface. 
 
 The figure and magnitude of an orbit are determined by 
 
242 POPULAR ASTRONOMY. 
 
 the length of the major axis and by the eccentricity ; and ii\ 
 case but one planet existed, these are the only elements 
 whose value could in any way affect the physical condition 
 of the planet, so far as its supply of light and heat received 
 from the sun are concerned. In this case the position of 
 the orbit in its own plane (determined by the place of the 
 perihelion-point) and also the position of the plane of the 
 orbit, as referred to any fixed plane (determined by the 
 angle of inclination and line of nodes), and also the epoch (or 
 place of the planet in its orbit at a given moment of time), 
 all those quantities would not in any degree affect the actual 
 condition of the planet ; but as no planet is isolated, and as 
 each is subjected to the influence of every other, it becomes 
 a matter of grave importance to ascertain whether there be 
 any fluctuations in the values of all these elements, whether 
 these fluctuations are confined within any specific limits, 
 and whether, if thus confined, any injurious effect can result 
 to those elements which involve the well-being of any 
 planet ; and finally, whether there be any guarantee for the 
 perpetuity of the planetary system in the condition now 
 existent. 
 
 In case the planes of the orbits of all the planets were 
 coincident, then the investigations would be confined to the 
 fluctuation in the values of the major axes, eccentricities, 
 and perihelia ; but from the reasoning already presented in 
 the problem of " the three bodies," we have seen that, if we 
 consider the relation of two planets whose orbits are inclined 
 under any angle, in their reciprocal influence, if we assume 
 the plane of the orbit of one of these planets, for example, 
 the earth, as fixed in position, and the plane of the other 
 planet's orbit (as Mars) as inclined to this, under a given 
 angle, it is clearly manifest that the disturbing influence of 
 the earth on Mars will be reversed when Mars passes through 
 the plane of the earth's orbit. Suppose we could place our 
 eye in the prolongation of the line of intersection of the two 
 orbits, then we should see them as two straight lines, in- 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 243 
 
 clined to each other, as in the figure below, in which S repre- 
 sents the place of the sun, E E' places of the earth, and M 
 
 and M' places of Mars. Now, when Mars and the earth are 
 on the same side of the sun, or the line of nodes, Mars 
 ascending towards M', above the plane of the earth's orbit, 
 the force exerted by the earth on the ascending planet tends 
 to draw it downward to the ecliptic ; and hence it will not 
 quite reach the elevation M' ; and thus all this while the 
 plane of the orbit of Mars will be forming a less and less 
 angle with the ecliptic. The moment, however, the planet 
 reaches its highest elevation and begins to descend towards 
 the ecliptic to pass its descending node, then the earth, 
 remaining stationary, will pull the planet towards its own 
 plane, and hence the descent will be made steeper, and the 
 angle of inclination of the orbit of Mars will, while the 
 planet thus descends, be always increasing. Following 
 Mars below the plane of the ecliptic, the earth remaining 
 as before, we see that here the tendency is to pull Mars 
 up to the earth's orbit ; and hence it will not quite reach 
 the point M, or the inclination in this descent below the 
 ecliptic will diminish. From this point, as Mars begins to 
 ascend, the earth's attractive energy will cause it to ascend 
 more rapidly, and will make it pass its ascending node 
 earlier than if undisturbed ; and as it comes up faster, it must 
 ascend a steeper grade, or the inclination will increase. Thus 
 we see that Mars, in ascending or descending to pass eithei 
 
 a 2 
 
244 POPULAR ASTRONOMY. 
 
 node, will both ascend and descend by a steeper grade 
 because of the earth's attraction ; while, in passing from 
 either node to the highest and lowest points of its orbit, the 
 same force will op-erate to make the planet reach points less 
 remote from the ecliptic than if undisturbed, and hence to 
 ascend and descend with a smaller angle of inclination. 
 Now, a careful inspection will show that the effects pro- 
 duced by the earth on Mars, while situated at E', will be 
 greater in the half of the orbit of Mars which lies above the 
 ecliptic ; and at the end of one revolution an exact com- 
 pensation may not be effected; so that the increase of the 
 angle of inclination may not be exactly equal to the decrease. 
 But as the earth is revolving, a time will come when this 
 body will occupy the point E, and then the most powerful 
 effect will be produced when Mars is below the ecliptic, and 
 in case the orbits are circular, an exact symmetry existing, 
 at the end of a certain cycle the inclinations will be exactly 
 restored. 
 
 The fact that the orbits of the planets are elliptical in 
 figure cannot in any way lessen the force of the reasoning 
 we have employed ; it can only postpone to a more remote 
 period the final restoration of the inclinations of the 
 planetary orbits. Under the powerful and masterly analysis 
 of Lagrange this subject was completely exhausted, and a 
 result reached which in the following proposition guarantees 
 the stability of the inclinations through all ages : 
 
 " If the mass or weight of every planet be multiplied by 
 the square root of its major axis, and this product be mul- 
 tiplied by the tangent of the angle of inclination of the 
 plane of the planetary orbit to a fixed plane, and these 
 products be added together, their sum will be constantly the 
 same." 
 
 Now, we will show hereafter that the major axes remain 
 nearly invariable ; the masses of the planets are absolutely 
 so ; and hence the third factor of the product, the tangent of 
 the inclination, can only vary within narrow limits, return- 
 ing at the end of a vast cycle to the primitive value- 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 245 
 
 We shall see hereafter how important the stability of the 
 inclination of the earth's orbit is to the well-being of the 
 living and sentient beings now on the earth's surface. 
 
 We proceed to examine the changes of the lines of nodes 
 due to perturbation. These changes are allied to those of 
 inclination, and are, indeed, a necessary consequence of these 
 changes, as may readily be shown. 
 
 E , 
 
 For this purpose we return to the figure already em- 
 ployed, using the same planets, Mars and the earth, regard- 
 ing the movements of Mars to be disturbed by the earth's 
 attraction. 
 
 We have already seen that in case Mars be at M, the 
 earth being at E, the planet, in descending its orbit to the 
 line of nodes seen as in S (the eye of the spectator being in 
 the prolongation of the line of nodes), during the entire 
 descent the planet will be drawn down to the plane of the 
 ecliptic E E' on a steeper grade than the normal one M S ; 
 and hence the planet will pass through the ecliptic earlier 
 than if undisturbed, or at a point which will be seen some- 
 where between S and E. Thus during this descent the node 
 will go backwards to meet the planet, or will retrograde. 
 Passing below the ecliptic, the planet, continuing to descend 
 will, as we have seen, be prevented by the disturbing body 
 from reaching a point so low as M' ; and hence if its path for 
 a moment were anywhere produced backwards, this line 
 would meet the ecliptic at some point always approaching E', 
 or here again the line of nodes retrogrades. The same 
 reasoning will show that, with the above configuration, the 
 retrogradation of the line of nodes must continue with 
 
246 POPULAR ASTRONOMY. 
 
 unequal velocity during the entire revolution of the planet. 
 In other configurations there is sometimes an advance of the 
 node ; but in the long run it is easily demonstrated that the 
 nodes of all the planetary orbits on any fixed plane will 
 retrograde and perform entire revolutions in periods of 
 greater or less duration. 
 
 This perpetual recess of the lines of nodes in one direction 
 does not in any way affect the physical condition of a planet, 
 but serves an admirable and necessary purpose in securing 
 final stability in the planetary system by presenting the 
 disturbed orbits to the disturbing bodies under all possible 
 configurations. 
 
 We shall not attempt to exhibit in full the reasoning by 
 which the variations of the remaining elements are shown to 
 be periodic, when periodicity is essential to stability; or 
 progressive, when progression does not involve destruction ; 
 but from a single figure deduce, if possible, the great prin- 
 ciples involved in this wonderful problem. 
 
 Let S represent the sun, E the earth, and P any planet 
 disturbed by the earth, and let us suppose that undisturbed 
 in any small portion of time it would reach P', but subjected 
 to the influence of the earth's attraction it reaches P" in the 
 same time. The question is, in what way does this change 
 the elements of P's orbit ? 
 
 We have already seen the effect on the inclination and 
 line of nodes. These elements do not affect the magnitude 
 of the orbit, nor the position of that orbit in its own plane. 
 The magnitude and position depend on the length of the 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 247 
 
 major axis, eccentricity, and perihelion-point. Let us 
 examine these in order, commencing with the length of the 
 major axis. 
 
 We suppose the planet P to be moving, when undisturbed, 
 with its normal elliptic velocity; and of course, on reaching 
 P', the longer axis of its orbit, and in fact all the elements, 
 remain unchanged in value ; but being disturbed, so as to 
 be prevented from reaching P', and being compelled to reach 
 P", will this compulsion merely change the position of the 
 planetary orbit, or will it increase or decrease the length of 
 the major axis 1 
 
 Kepler's third law tells us that the squares of the periodic 
 times are proportional to the cubes of the major axes ; and 
 from this relation it is manifest that any change in the 
 elliptic velocity of a planet must change the period of its 
 revolution, and this involves a change by necessity in the 
 major axis of the orbit. 
 
 The question of change in the major axis, then, resolves 
 itself into an inquiry as to whether the disturbance has pro- 
 duced any change in the elliptic velocity of the disturbed 
 planet. 
 
 At the first glance it may seem impossible to drag a planet 
 from its normal elliptic path without affecting its velocity. 
 This, however, is not the fact. If a body be moving in a 
 straight line, and a force be applied to it perpendicular to 
 the direction of its motion, this force will not in any degree 
 affect the velocity, but only the direction of the moving 
 body. Thus, a ball fired from a rifle on the deck of a fixed 
 or a moving boat, with the same initial force, will reach the 
 opposite shore in the same time ; but its direction of absolute 
 motion is changed, if fired from a moving boat, from what it 
 would be if shot from one at rest. So a flying planet may 
 be subjected to the action of a force always perpendicular to 
 the direction of its motion, which force may push it from its 
 normal path, but cannot affect its elliptical velocity. Such 
 a force, then, can have no influence on the length of the 
 major axis, or on the periodic time of the revolving body. 
 
248 
 
 POPULAR ASTRONOMY. 
 
 Now, every force is capable of being changed into three 
 other forces, whose combined action will produce the same 
 effect as the primitive force, as in the figure. 
 
 Let P P"" represent the direction and intensity of any 
 force ; on this line as a diagonal construct the solid figure, a 
 parallelepiped. Then the sides P F, P P" and P P'" will 
 represent the direction and intensity of three forces, which 
 would produce the same effect as the force P P"". 
 
 Precisely in this way the disturbing force exerted by the 
 earth on the planet P can be converted into three other 
 forces, whose combined effect shall be identical with the 
 original force. Two of these forces shall lie in the plane of 
 the planet's motion, the one tangent to the orbit, or in the 
 exact direction of the planet's motion, the second perpen- 
 dicular to the direction of motion, or normal to the orbit, 
 and the third perpendicular to the plane of the orbit of the 
 planet. 
 
 Now, from what we have said, it is clear that but one of 
 these new or substituted forces can in any way affect the 
 velocity of the planet, and that is the force tangent to the 
 orbit, or coincident with the direction in which it is moving. 
 The normal component (as it is called) pushes the planet 
 from its old orbit, and the perpendicular component pushes 
 the planet above or below its own plane of motion; but 
 neither of these affects the velocity of the moving planet, 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 249 
 
 and neither of them can in any degree affect the length of 
 the major axis. 
 
 The perpendicular component has already been considered 
 in its effects ; for it is this force which changes the inclina- 
 tion and gives motion to the line of nodes. We may, there- 
 fore, in our future examinations leave this force out of 
 consideration, or, which conies to the same thing, consider 
 the planes of the orbits of the disturbing and the disturbed 
 planet as the same. 
 
 Let us, then, represent by the two circles the orbits of 
 the planets in question, S being the place of the sun, E the 
 
 earth, and P the planet when in conjunction. In this con- 
 figuration the entire disturbing power of E is exerted along 
 the line E P, or perpendicular to the direction of the planet's 
 motion, or normal to its orbit ; and in this position the 
 tangential force being nothing, the major axis is undisturbed 
 by E. As P moves towards P' the direction of the force 
 exerted by E ceases to be normal to P's orbit, and may be 
 replaced by a normal and a tangential force. The tangential 
 force from P towards P' is manifestly in opposition to the 
 motion of P in its orbit, and therefore retards its motion, 
 and thus decreases its major axis j but there is a point P" 
 symmetrically placed with reference to P, where the tan- 
 gential force is in the opposite direction, and in an equal 
 .degree becomes an accelerating force, and whatever the 
 major axis might lose in- 1 length from the disturbing power 
 
250 POPULAR ASTRONOMY. 
 
 at P', it would gain from the same power when it comes to 
 occupy the point P". So that, if E should remain fixed 
 during an entire revolution of P, a compensation would be 
 effected, and the velocity of the planet on reaching its point 
 of departure would be identical with that with which it 
 started; and hence the major axis, though it would have 
 lost and gained, would in the end be restored to its primitive 
 value. 
 
 If the orbits were elliptical and their major axes were 
 coincident, the same reasoning from symmetry would still 
 hold good, and demonstrate the restoration of the major 
 axis; and as action and reaction are always equal, it is 
 manifest that by fixing P and causing E to revolve, the 
 changes wrought by E on P would now be wrought by P on 
 E, only in the reverse order that is, wherever P was ac- 
 celerated by E, E will be retarded by P, and vice versd. 
 
 Admitting the major axes to be inclined to each other 
 destroys the symmetry of the figure, and an exact restoration 
 is not effected in one revolution ; but, as the perihelia of the 
 planetary orbits are all in motion, the time will come when 
 a coincidence of the major axes will be effected ; and if 
 there be a certain amount of outstanding uncompensated 
 velocity, when the coincidence takes place, the action will 
 be reversed, and at the end of one grand revolution of the 
 major axes from coincidence to coincidence, the restoration 
 will be completed, and the axes will return to their primitive 
 value. 
 
 Here we are compelled to leave the problem, and simply 
 state the result which a complete solution has effected. We 
 are again indebted to Lagrange for the resolution of this 
 most important of all the problems involving the stability 
 of the solar system, who presents the final result as fol- 
 lows : 
 
 " If the mass of each planet be multiplied by the square 
 root of the major axis of its orbit, and this product by the 
 square of the tangent of the inclination of the orbit to a 
 fixed plane, and all these products be added together, their 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 251 
 
 sum will be constantly the same, 110 matter what variations 
 exist in the system." 
 
 The mass or weight of each planet is invariable, while the 
 loss or gain in the values of the major axes is always 
 counterpoised by the gain or loss in the inclination of the 
 orbits ; and thus in the long run, in cycles of vast periods, a 
 complete restoration of the major axes is fully accomplished, 
 and the system in this particular returns to its normal con- 
 dition. 
 
 We have thus far considered the effect of two out of the 
 three forces into which a disturbing force may be decom- 
 posed. The normal component remains to be examined. 
 This acts in a direction normal to the curve described by 
 the planet, or perpendicular to the tangent to the orbit at 
 the point occupied by the planet. We shall not enter into 
 any extended examination of this subject, and will only say 
 that this component of the disturbing force gives rise to a 
 movement in the perihelion-points of the planetary orbits 
 sometimes advancing these points, sometimes giving them 
 a retrograde motion, and in some instances producing 
 oscillations. 
 
 These effects are necessarily mixed up and combined with 
 those produced by the action of the tangential force, for, as 
 we have seen, the effect of this force goes to increase or 
 decrease the value of the major axis ; but no increase or 
 decrease of the major axis can take place without a corre- 
 sponding change in the eccentricity j so that these changes 
 thus modified, the one by the other, finally become exceed- 
 ingly complex, and can only be traced and computed by the 
 application of the highest powers of analytic reasoning. 
 
 The complexity is further increased from the fact that in 
 the consideration of the entire problem of perturbations the 
 varying distances of the disturbing and disturbed bodies 
 must be rigorously taken into account, and may modify and 
 even reverse the effects due simply to direction. With 
 difficulties so extraordinary and diversified, with complica- 
 tions and complexities mutually extending to each other, 
 
252 POPULAR ASTRONOMY. 
 
 involving movements so slow as to require ages for their 
 completion, it is a matter of amazement that the human 
 mind has achieved complete success in the resolution of this 
 grand problem, and can with confidence pronounce the 
 changes to fall within narrow and innocuous limits ; while 
 in the end, after a cycle of incalculable millions of years, the 
 entire system of planets and satellites shall return once more 
 to their primitive condition, to start again on their endless 
 cycles of configuration and change. 
 
 There remains one more source, whence arises an ac- 
 cumulation of disturbance, progressive in the same direction 
 through definite cycles of greater or lesser duration. I mean 
 the effects due to a near commensurability of the periods of 
 revolution of the disturbed and disturbing planets. The 
 nearer the approach to commensurability, the longer will be 
 the duration of the resulting inequality. 
 
 We shall have occasion to resume this subject in our 
 examination of the circumstances of disturbance belonging 
 to each individual planet, which we shall now proceed to 
 examine briefly, commencing at the sun, and proceeding 
 outwards. 
 
 THE SUN CONSIDERED AS A GRAVITATING BODY. We shall 
 now return to the great centre of the planetary worlds with 
 a full knowledge of the laws of motion and gravitation, and 
 provided with the instrumental means of securing those 
 delicate measures whereby the solar orb may be determined 
 in distance, volume, and weight. 
 
 We have already explained how these quantities may be 
 obtained, and we now present the results of exact measures 
 and accurate computation. The sun's mean distance from 
 the earth may be taken at ninety -five millions of miles. By 
 exact measures the mean diameter of the sun subtends an 
 
THE SUN AND PLANETS AS PONDERABLE BODIES 253 
 
 angle equal to 32'-01"'8, and an angle of this value indicates 
 a real diameter in the sun of 883,000 miles, as may be seen 
 from the figure above, in which it is evident that a line A B 
 subtends at A' B' a much smaller angle than when located 
 at A B, nearer the vertex. If, then, we have a given angle 
 A' E B', and a given distance E B', from the vertex, if we 
 erect the line B' A' it is evident the length of this line will 
 be determined by the value of the angle B' E A' and the 
 length of the line E B' ; so the sun's distance and angular 
 diameter determine his real diameter. This diameter of the- 
 sun (883,000 miles), in terms of the diameter of the earth, 
 amounts to 111-454 ; and as the volumes of two globes are 
 in the proportion of the cubes of their diameters, we shall 
 have the volume of the sun to the volume of the earth aa 
 (111-454) 3 is to (1)3 or as 1,384,472 to 1 ; or it would re- 
 quire no less than one million three hundred and eighty-four 
 thousand four hundred and seventy-two globes as large as 
 the earth to fill the vast interior of a hollow sphere as large 
 as the sun. By this we do not mean to assert that the sun 
 weighs as much as 1,384,472 earths. This is 'not the fact. 
 We have seen already the process by which the relative 
 weights of these globes may be reached, and we have found 
 that the force exerted on the earth by the sun, enfeebled 
 by the distance at which it acts, and thus reduced to the 
 160,000th part of its actual value at a distance equal to 
 that of the moon, still exceeds in a more than twofold 
 ratio the force exerted by the earth on the moon ; and when 
 the exact ratio is applied, we find the weight of the sun to 
 be equal to 354,936 earths, and this is what we call the 
 mass of the sun. 
 
 If we divide the mass by the volume, we obtain the 
 specific gravity of the sun, in terms of that of the earth, 
 equal to ^|^ 3 T - =0-2564 ; that is, the average weight of 
 one cubic foot of the sun is only one-fourth as great as the 
 average weight of one cubic foot of the earth. 
 
 It is the mass of the sun, and not its volume, which 
 determines the amount of force which this great central 
 
25 i POPULAR ASTRONOMY. 
 
 globe exerts. Its weight is such as vastly to exceed that of 
 any one of the planets, and indeed it rises so superior to 
 the combined masses of all the planets, that the centre of 
 gravity of the system falls even within the surface of the 
 sun. This may be shown by an examination of the weights 
 and respective distances of the planets. We will explain 
 the reasoning. If the sun and earth were equal in weight, 
 then the centre of gravity would lie in the middle of the 
 line joining their centres ; but the sun is equal in weight 
 to 354,936 earths, and hence, dividing the distance between 
 the centres (ninety-five millions of miles) into 354,936 equal 
 parts, the centre of gravity of the sun and earth will fall 
 on the first point of division nearest the sun's centre, that 
 is, at a distance of about 267 miles ; but from the centre of 
 the sun to his surface is a distance of 440,000 miles, and 
 thus the centre of gravity of the sun and earth falls far 
 within the limits of the solar surface. 
 
 The energy exerted by the sun on any one of his satellites 
 is in a constant state of fluctuation, growing out of the 
 variation in the distance of the planet. The sun's force 
 decreases as the square of the planet's distance increases. 
 If, then, we take the earth's distance as unity, and call 
 the force exerted on the earth by the sun one, the 
 force exerted on a planet twice as remote from the sun 
 as the earth, would be but one-fourth, at three times the 
 distance one-ninth, at ten times the distance it would be but 
 one hundredth part of that exerted on the earth. This 
 law of gravitation should be well understood, as we shall 
 have occasion to make frequent applications in our future 
 examinations. 
 
 POWER OF GRAVITATION ON THE SOLAR SURFACE. If it 
 were possible to transport a- body weighing at the earth's 
 equator one pound to the equator of the sun, as the weight 
 of the body is due to the power of the earth's attraction, 
 and as the sun is heavier than the earth in the high ratio of 
 354,936 to 1, we might suppose that the pound weight on 
 the earth removed to the sun would be increased in the same 
 
SUN AND PLANETS AS PONDERABLE BODIES. 255 
 
 ratio. This would be true in case the sun's diameter were 
 precisely equal to that of the earth. This, however, is not 
 the case. The radius of the sun is 111-454 times that of 
 the earth, and this distance will reduce the attractive power 
 of the sun in the ratio of (111-545) 2 to (I) 2 , or as 12442-28 
 to 1. If, therefore, we reduce 354,936 in the above ratio, 
 or, in other language, divide it by 12442 '2 8, we obtain for a 
 quotient 28, showing that a body weighing one pound at the 
 earth's equator, would weigh 28 pounds at the sun's surface. 
 This would be slightly reduced, from the uplifting action of 
 the centrifugal force due to the velocity of rotation of the 
 sun on its axis. This diminution may be readily computed. 
 We shall see hereafter that the centrifugal force at the earth's 
 equator is equal to ir T of the force of gravity. Now, if the 
 sun rotated in the same time as the earth, and their diameters 
 were equal, the centrifugal force on the equators of the two 
 orbs would be equal. But the sun's radius is about 111 times 
 that of the earth ; and, if the period or rotation were the 
 same, the centrifugal force at the sun's equator would be 
 greater than that at the earth's, in the ratio of (111) 2 to 1, or 
 more exactly in the ratio of 12442*28 to 1. But the sun 
 rotates on its axis much slower than the earth, requiring 
 more than 25 days for one revolution. This will reduce 
 the above in the ratio of 1 to (25) 2 , or 1 to 625 ; so 
 that we shall have the earth's equatorial centrifugal force 
 ^x 12442-28^625=M r %% 2 ^ff =0-07 nearly, for the sun's 
 equatorial centrifugal force. Hence the weight before ob- 
 tained, 28 pounds, must be reduced seven hundredths of its 
 whole value, and we thus obtain 28 0-196=27-804 pounds, 
 as the true weight of one pound transported from the earth's 
 equator to that of the sun. 
 
 These principles enable us to compute readily the gravi- 
 tating force exerted by the sun at any given distance ; and, 
 as we shall see hereafter, this mighty central orb is pre- 
 eminently the controlling body in the scheme of revolving 
 worlds, which move about him as their centre, in obedience 
 to the laws of motion and gravitation. 
 
256 POPULAR ASTRONOMY. 
 
 We close what we have to say of the sun by stating that 
 a. heavy body weighing, as it does, 27 '8 times as much at the 
 solar as at the terrestrial equator, if free to fall, will pass 
 over in one second a space equal to 27'8 x 16-1 = 447 '58 
 feet. 
 
 PERTURBATIONS OF MERCURY. In our discussion of the 
 planets already given, we were only prepared to present the 
 discoveries of formal astronomy. These involved the elements 
 of the elliptic orbits and the observed circumstances of the 
 planetary movements. We are now prepared to understand 
 how the system of solar satellites constitutes a grand as- 
 semblage of worlds in motion and yet in equilibrio, so that, 
 although there be fluctuations to and fro, which are really 
 perpetual, in the end the system is stable and in exact 
 dynamical counterpoise. The great law of universal gravi- 
 tation being known, as also the laws of motion, it becomes 
 possible to determine the exact conditions of this mighty 
 systematic equilibrium, and in a strict SCDSC to weigh each 
 of the worlds belonging to the system. Indeed, this weight 
 or mass of the planets must be first ascertained before it 
 becomes, possible to compute the influence exerted by one 
 body on another, even when their actual distances are 
 known. The distances being the same, two bodies attract 
 a third by a force which is in direct proportion to their 
 masses. Hence, if our moon could be conveyed successively 
 to each of the planets, and be located at the same distance 
 from each it now is from the earth, the period of revolution 
 of our satellite round any one of these worlds would show 
 us whether that world weighed more or less than ours. 
 Thus, in case the period of revolution of the moon around 
 a planet should be one-half its present period, then that 
 planet, holding, as it does, the moon with double the velocity 
 at the earth, it must be double the weight of the earth ; 
 and so for any other period. 
 
 It is in this way that we are enabled very exactly to 
 weigh the planets which are surrounded by satellites, as we 
 have already seen ; but those planets which have no satel- 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 257 
 
 lite, such as Mercury, "Venus, and Mars, can only be weighed 
 by the effect they produce on other bodies of the system, 
 and especially on those vaporous masses the comets, which 
 occasionally come sufficiently near these bodies to be sub- 
 jected to very powerful perturbations. 
 
 The mass of Mercury is, of course, subject to some un- 
 certainty ' } but, as now determined, in case the sun were 
 divided into one thousand millions of equal parts, it would 
 require 2,055 of these parts to be placed in one scale of a 
 balance to counterpoise Mercury in the opposite scale. 
 
 Knowing the mass of a planet and its volume, we can 
 easily deduce its specific gravity or density. For example, 
 the volume of Mercury is equal to 0-595, the earth being 
 unity ; but the mass of- the earth in the same parts of the 
 sun just employed, as we shall see, is 28,173. Hence, if 
 these planets were equally dense, their volumes would be to 
 each other as 28,173 to 2,055, or nearly as 13-7 to 1, or as 1 
 to 0-072 ; but Mercury's volume is but 0-595, the earth being 
 taken as unity ; and hence Mercury must be denser than 
 the earth in the ratio of 0'072 to 0-595, or as 1-2 to 1 
 nearly. 
 
 Thus are we made acquainted with the very structure or 
 material of the planets by the process of weighing them, 
 revealed by the laws of motion and gravitation ; and that 
 these results cannot be much in error, is manifest from the 
 fact that at the transit of Mercury across the sun's disc, which 
 occurred on the 8th May, 1845, and was observed at the 
 Cincinnati Observatory, the computed and observed contact 
 of the planet with the sun's limb differed by only sixteen 
 seconds of time I 
 
 This prediction also verifies the values of the secular 
 inequalities, or slow changes in the elements of Mercury's 
 orbit, due to the planetary perturbations, which were fixed 
 for the beginning of the present century as follows : The 
 perihelion makes an absolute advance each year of 5" -8 ; the 
 node recedes annually 7"-8. The eccentricity, in terms of 
 the serai-axis major, was 0-210551494-, and its decrease in 
 
 9 
 
258 POPULAR ASTRONOMY. 
 
 one hundred years amounts to 0'000003866, in terms of 
 the same unit. Let us admit these changes to be progressive 
 at the same rate, and then convert them into intelligible 
 terms, and examine the results. The perihelion-point ad- 
 vancing at the rate of 5"*8 a year, -will require to pass over 
 360, or 1,296,000 seconds, i-^f'Qoo = 223,449 years. 
 Such is the vast period required for one revolution of the 
 perihelion-point. In like manner we may see that the node 
 requires a period exceeding 100,000 years for its revolution. 
 
 The eccentricity is slowly wearing away, the orbit be- 
 coming more nearly circular ; and if this change progresses 
 uniformly, it will require no less than 5,446,200 years to 
 reduce the figure of Mercury's orbit to that of an exact 
 circle ! 
 
 The present eccentricity of the orbit of Mercury is such, 
 that the aphelion distance exceeds the perihelion distance 
 by more than 15,000,000 of miles. The energy exerted by 
 the sun on the planet at perihelion, as compared with that ex- 
 erted at aphelion, may be readily computed thus : Mercury's 
 greatest distance from the sun amounts to about 44,000,000 
 of miles. This is about ten times the solar radius ; and at 
 this distance the sun's power will be reduced to the one- 
 hundredth part of what it is at the sun's surface ; but the 
 planet when nearest the sun is distant about 29,000,000 of 
 miles, that is, less than seven times the solar radius, and 
 hence the power of gravitation is reduced to the one forty- 
 ninth part of what it is at the sun's surface ; or, what 
 comes to the same thing, Mercury at aphelion is attracted 
 with a force only one-half as great as that by which it is 
 affected when nearest the sun. 
 
 If a person were transported to the equator of Mercury, 
 his weight would be greatly reduced from that found on the 
 earth. The mass of Mercury, in terms of that of the earth 
 as unity, is but 0729, and if Mercury's diameter were equal 
 to that of the earth, then one pound on the earth would 
 weigh 0'7291b. when removed to Mercury ; but as the 
 radius of Mercury is only 1,544 miles, or twenty-six 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 259 
 
 huudredths of the earth's radius, this will increase the 
 weight in the ratio of (2'6) 2 to (I) 2 , or as 676 to 1. Hence, 
 by multiplying 0729 by 676, we have O4931b. as the 
 weight of a terrestrial pound removed to Mercury, that is, 
 the power of gravitation on the surface of this planet is 
 about one-half of what it is on the earth. 
 
 All the planets exterior to the orbit of Mercury exert 
 an amount of power on this nearest planet to the sun which 
 varies directly as the mass, and inversely as the square of 
 the distance of the disturbing body. Let us suppose the 
 earth and Yenus to be in conjunction with Mercury, and 
 that these planets are at their mean distances from the sun, 
 and let us compute in this configuration the relative power 
 of the sun, of Yenus, and of the Earth, over Mercury. 
 
 In the figure let S represent the sun, M Mercury, V 
 Yenus, and E the Earth. Taking the distance S E to be 1, 
 SM will be 0-387, and SY will be 0-723. Hence, M Y 
 will be equal to S Y S M=0-723 0-387 = 0-336, and Y E 
 will be equal to S E S Y= 1 -000 0723 = 0'277. As the 
 mass of Yenus is but the 390,000th part of the sun's mass, 
 her effect on Mercury at equal distances would be but one 
 part in three hundred and ninety thousand of the sun's 
 power. The fact that Yenus is nearer Mercury than the 
 sun, in the ratio of YM to SM, or of 0-336 to 0-387, will 
 increase her relative power in the ratio of the squares of 
 these quantities inversely, that is, as (0-336) 2 to (0-387) 2 , or 
 as 0-113 to 0-147, or as 1 to 1-3 that is, we must multiply 
 TFo.Voo" by 1 '3 to obtain the effect of Yenus on Mercury, as 
 compared with that of the sun j in other language, if the 
 sun's power over Mercury be divided into 390,000 equal 
 
 3 2 
 
260 POPULAR ASTRONOMY. 
 
 parts, the power of Venus over the same planet will amount 
 to just one and one-third of these parts. 
 
 Let us now compute the attraction of the earth as com- 
 pared with that of the sun. As the earth weighs 1, while 
 the sun weighs 354,936, at equal distances the powers of the 
 earth and sun would be as 1 to 354,936 ; but the distance S M 
 is 0-387, while the distance M Eis 1 -000 0-387=0-613. As 
 the sun is the nearer, his power will be increased in the ratio 
 of the square of distance inversely, or as (0-613) 2 to (0-387)*, 
 or as 0-376 to 0-147, or as 2'56 to 1 j that is, the earth's 
 power, which, on account of its mass, is but one part in 
 354,936 of that of the sun at equal distances, must further 
 be reduced on account of its distance to a fraction of this 
 quantity, represented by -^.^ ; that is, in case we divide the 
 sun's power of attraction upon Mercury into 787,340 parts, 
 the attractive power of the earth will be represented by one 
 of these parts. 
 
 We have seen above that the power of Yenus over 
 Mercury is equal to s-o-^-^o, the power of the sun being 
 1. The power of the earth is T^y,Vrff> or no * quite one-half 
 of the, former quantity. Hence the disturbing influence of 
 Venus is evidently the predominating one in the case of 
 Mercury. 
 
 It may be well to extend our investigation a little further, 
 and examine the influence of the massive planet Jupiter on 
 Mercury, to see whether Venus still predominates in its 
 power over that of the heaviest planet of the system. The 
 distance of Jupiter from the sun is 5-2, that of the earth 
 being 1. The distance of the earth from Mercury is 0*613. 
 The distance of Jupiter from Mercury is 5-2000-387 = 
 4-813. In case the earth and Jupiter were equal in mass, 
 then the power of Jupiter over Mercury would be to the 
 power of the earth as (0-613) 2 to (4-813) 2 , or as 0-376 to 
 23-164, or as 1 to 61*6 ; that is, Jupiter's effect is reduced 
 to the fraction -gi-g- of what it would be at a distance from 
 Mercury equal to that of the earth ; but this is supposing 
 the earth and Jupiter to be equal in mass, whereas Jupiter 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 261 
 
 really requires 338 earths to counterpoise bis weight. We 
 must, therefore, increase the fraction -^-.-^ 338 times, and we 
 have |~p|-=5'5 about. Hence Jupiter exerts a power over 
 Mercury when in conjunction 5 '5 times as great as that 
 exerted by the earth, or two and a half times greater than 
 the attraction of Venus. 
 
 These computations have been made to show how minute 
 a portion of the sun's power is that exerted by any planet, 
 to disturb the motions of another planet ; and also to show 
 that we cannot neglect any disturbing body because of the 
 great distance at which it may be placed. 
 
 It will be readily seen that when Mercury is in opposition 
 with respect to Venus, her power is greatly reduced on 
 account of the increased distance by whicb the planets will 
 be then separated. Indeed, the attractive force computed at 
 conjunction will be reduced to about one-tenth at opposition. 
 
 This is not true, however, of the attractive power of 
 Jupiter. The distance 4*813 in conjunction will only be 
 increased by the diameter of Mercury's orbit, or by 2(0*387) 
 =0-774 when in opposition, and the distances will stand 
 4-813 and 6 '587. Jupiter's power at the increased distance 
 will be reduced only in the ratio of the square of 4-813 to 
 that of 6-587, or about as 1 to 2. 
 
 As an exercise the student should compute the energy 
 exerted by the other planets over Mercury, and thus obtain 
 a familiarity with the application of the law of gravitation 
 to the problems of nature. 
 
 While we are writing, the intelligence has reached this 
 country that a new planet has actually been discovered, 
 revolving in an orbit between Mercury and the sun. M. Le 
 Verrier some time since announced that there were pertur- 
 bations in the elements of the orbit of Mercury not explained 
 by any of the known causes, and hence he drew the con- 
 clusion that possibly a ring of very small planets were 
 revolving within the limits of Mercury's orbit. One of 
 these minute planets is said to have been actually seen more 
 than once by an amateur astronomer, whose namo is M. Les 
 
262 POPULAR ASTRONOMY. 
 
 carbault. This planet is said to complete its revolution in 
 about three weeks, and hence its distance from the sun must 
 be about fourteen or fifteen millions of miles.* 
 
 YENUS CONSIDERED AS A PONDERABLE BODY. The angle 
 subtended by this planet at its mean distance from the earth 
 amounts to 17""55, showing an actual diameter nearly equal 
 to that of the earth. The weight or mass of Yenus is not so 
 well determined as that of the planets attended by satellites ; 
 yet we have reason to believe that the approximate value 
 does not differ by any very considerable amount from the 
 true one. As now determined by the best authorities, 
 Yenus weighs 0*900, the weight of the earth being assumed 
 as 1 -000. If an inhabitant of the earth were transported to 
 Yenus, his weight would be reduced in the ratio of 1 to 
 0'94, and a heavy body, free to fall, would pass over 15T 
 feet in the first second of time. Here we might repeat the 
 reasoning already employed in the case of the sun to reach 
 these results ; but as we shall have occasion hereafter to 
 apply the reasoning to the cases of the larger planets, we 
 shall merely refer to the demonstration already made. 
 
 All the elements of the orbit of Yenus are in a state of 
 constant fluctuation. The exact condition of these elements 
 will be given hereafter, as well as the measured amount of 
 the changes. We find in Yenus the first example of a re- 
 markable perturbation arising from a cause already adverted 
 to, viz. : an approximate commensurability between the 
 periods of revolution of Yenus and the earth. The planet 
 performs her revolution around the sun in 224-7 days, while 
 the earth occupies 365-25 days in accomplishing her revolu- 
 tion. If we multiply 224'7 by 13 we obtain 29211 ; mul- 
 
 * It was hoped and expected that the reported observations of M. Les- 
 carbault would have been verified by other astronomers in some parts of 
 the world: but such has not been the case, as far as we know. It had 
 been announced that a transit of the intra-Mercurial planet would pro- 
 bably occur, about April 2 and October 5, in every year ; when the earth 
 would be within the limiting distance of visibility from the line of nodes. 
 The earth would reach the planet's descending node about noon, April 2 ; 
 
 wid the opposite, or ascending node, soon after midnight, October 5; 
 
 tfhen the sun, planot, and earth would be in a line. The transit could not 
 
 occupy more than 4^ hours. 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 263 
 
 tiply 365-256 by 8, and we have 2922-048. Thus we perceive 
 that, in case Venus and the earth are in conjunction on any 
 given day, at the end of 2,921 days they will be nearly in 
 conjunction again at the same points of their orbits. What- 
 ever perturbation the one planet produces on the other will 
 be again repeated on the return of the same identical con- 
 figuration. But we have already seen that the synodical 
 revolution of Venus is accomplished in 583*9 days. This 
 quantity, multiplied by 5, produces 29 19 -6 ; that is, during 
 the time involved in the long cycle of 2,921 days there have 
 occurred five conjunctions of the earth and Venus distributed 
 equally around the orbits of the planets. If we examine the 
 figure below, and suppose S, V, and E to represent the places 
 of the sun, of Venus, and the earth, at the commencement 
 of a great cycle of 2,921 days, at the end of one synodic 
 
 revolution of Venus V and E' will be the places of the two 
 planets. At the end of the second synodic revolution the planets 
 will be in V" and E" ; and thus they will pass round the orbits, 
 making their conjunctions at intervals of 5 83 -9 days, and 
 separated by arcs equal to one-fifth part of 360. Let us 
 now carefully examine the reciprocal influence of V and E 
 Starting from the places V and E in the figure, Venus will 
 
264 
 
 POPULAR ASTRONOMY. 
 
 t.ake the lead, and will tend to drag forward the earth, whil 
 the earth will pull back the planet, and as the planets sweep 
 around the sun, Yenus overtakes the earth at V"" E"", and 
 as the earth is now in advance, it will accelerate Yenus, and 
 will in turn be retarded. Thus a partial compensation is 
 effected, and the motions of the planets return nearly to what 
 they were at the start. This same process is repeated at 
 every conjunction ; and in case the planets fall exactly on the 
 right line S Y E, at the end of five of these conjunctions a 
 complete restoration would be effected. But this is not 
 exactly true. The periods are not precisely equal, and the 
 fifth conjunction does not fall on S Y E, but on a dotted line 
 a little behind the position S Y E. There will, therefore, 
 remain a very small amount of outstanding perturbation at 
 the close of one great cycle, which will go on accumulating 
 so long as the dotted line falls in the same half of the 
 earth's orbit. But the difference between 2921*160 days 
 and 2922-048 is 0-852, and by this fraction of one day is 
 the earth later than Yenus in reaching the point of depar- 
 ture. Hence, the conjunction of the planets must have 
 taken place on a line behind that of the former conjunction, 
 whose position may be readily computed. The daily motion 
 of Yenus is 1-612, while that of the earth is 0'985, and 
 thus Venus gaina daily on the earth by an amount equal to 
 1-612 0-985=0-627. Let S Y E be the line of the first 
 
 conjunction. At the end of thirteen revolutions of Yenus 
 she returns to the point Y, while the earth is in the point E', 
 requiring yet 0'852 days to reach E. Venus must, therefore, 
 have passed the earth on some line as S V"E", such that Yenus 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 265 
 
 will have gained 0'852 days on the earth when she arrives 
 at V. But the daily 'motion of Venus is 1 0> 612, and in the 
 fraction of onedayO-852,shewillmovel-612 x 0'852 = l-373. 
 Hence, the new line of conjunction S. V"E" must fall behind 
 the old line by this amount in each great cycle of thirteen 
 revolutions of Venus and eight revolutions of the earth. 
 
 At the end of a great cycle, formed by dividing 360 by 
 l-373, and multiplying the quotient by 8, the line of con- 
 junction will return to its former position ; and in case the 
 orbits remain circular, all the perturbations of both the 
 planets resulting from this cause, as affecting the orbital 
 velocities and consequently the lengths of the major axes, 
 will have been completely obliterated. The orbits are, 
 however, not exact circles, neither are the elements invariable, 
 and hence the restoration will not be perfect even at the end 
 of this great cycle ; but, as the changes are all periodical, 
 and as the lines of apsides revolve entirely around, periodicity 
 again marks these minute perturbations, and at the end of a 
 grand cycle, composed of many subordinate ones, these com- 
 plexities and modifications will all be entirely swept away, 
 and the system return to its primitive condition. The sin- 
 gular equation (as it is called) above described in the mean 
 motions of Venus and the earth was first detected by the 
 present Astronomer Royal. The period is about 240 years, 
 and in the whole of this time the accumulated effect on the 
 longitude of Venus cannot exceed 2"-95, while its effect on 
 that of the earth only reaches 2" -06. This result of com- 
 putation yet remains to be verified by actual observation. 
 
 For other particulars of the characteristics of this planet 
 and of the elements of its orbit, we refer the reader to the 
 Appendix. 
 
 THE EARTH AND MOON AS PONDERABLE BODIES. We 
 have already determined the weight of the earth in terms 
 of that of the sun, and we have seen that it would require 
 354,936 earths like ours to balance the ponderous orb which 
 occupies the focal point of the solar system. It remains 
 now to determine the absolute weight of the earth in pounds 
 
266 POPULAR ASTRONOMY. 
 
 avoirdupois. "We shall assume water as the standard, and 
 admit that one cubic foot of water weighs 62 '321 libs. 
 From the known magnitude of the sphere of the earth, 
 assuming, say, the mean diameter to be 7941*12 miles, 
 we can obtain the solid contents in cubic miles, amount- 
 ing to no less than 259,373,000,000. The number of cubic 
 feet in a cubic mile is readily computed, being equal to 
 5,280 x 5,280 x 5,280. Thus, if we knew the weight of one 
 cubic foot of the earth, in terms of the weight of one cubic 
 foot of water, the total weight of the entire globe could be 
 readily obtained in pounds. 
 
 This weighing of the earth, absolutely, is a problem of 
 great difficulty, yet it has been executed ; and the final 
 results, though not precisely accurate, are, no doubt, close 
 approximations. We can only give a general outline of the 
 principle involved in the method employed. Suppose an 
 inflexible rod with a small leaden ball at each extremity 
 suspended in the middle by a delicate wire. When abso- 
 lutely at rest the wire will hang vertically without twisting 
 or torsion. Any force applied to either leaden ball to move 
 it horizontally will tend to twist the suspending Avire, and 
 this torsion will resist the action of the force, and this re- 
 sistance will finally be brought into equilibrium with the 
 force, and will thus in some sense become its measure. 
 Thus, in case a delicate weight is attached to one of the 
 leaden balls and suspended over a pulley, it will descend 
 until the torsion of the wire shall be such as to exactly 
 balance the small weight, and then the torsion and weight 
 will stand in equilibrio, and the value of the weight (friction 
 out of consideration) measures the force of resistance to 
 torsion. Suppose a divided scale placed beneath the leaden 
 ball, and a needle used as a pointer, then as the ball moves 
 over this scale, a microscope properly adjusted may read the 
 amount of motion with the greatest delicacy. 
 
 This machinery being arranged, suppose we bring a leaden 
 ball one foot in diameter to within, say six inches of the 
 small ball. Its power of attraction will move this ball over 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 26} 
 
 a space easily read off from the divided scale, and this will 
 measure the attractive force of the large leaden ball. 
 
 Having thus learned the power exerted by a leaden ball 
 one foot in diameter, on a material point located one foot 
 from its centre, it is easy, from the principles already laid 
 down, to compute what would be the attractive power of a 
 globe of lead as large as the earth ; and in case this power 
 of attraction thus computed should be precisely equal to 
 that exerted by the earth, then the earth must weigh 
 exactly as much as the leaden globe of equal size. This, 
 however, is found from many experiments, tried with the 
 most refined apparatus, not to be the case. The leaden 
 globe is much heavier than the earthen one, and, indeed, we 
 find that one cubic foot of earth of the mean density of the 
 whole globe is as heavy as about five and a half cubic feet 
 of water. Hence, every cubic foot of earth weighs on the 
 average 62-3211 x 5 -5 =3 42 -7 6 Ibs. ; and as there are in the 
 entire globe 259,373,000,000 of cubic feet, the whole globe 
 must weigh 34276x259,373,000,000 of pounds avoir- 
 dupois. 
 
 With this knowledge of the absolute weight of our earth 
 it is easy to obtain the weight of the sun and planets in 
 pounds, were it necessary. Multiply the number of pound* 
 in the weight of the earth by 354,936, and we obtain the 
 actual weight of the sun. 
 
 THE FIGURE OF THE EARTH. We have already seen 
 that the earth is not a sphere, but a spheroid, protuberant 
 at the equator and flattened at the poles. The exact 
 methods of astronomy employed in the measurement of arcs 
 of the earth's meridians, together with the vibrations of the 
 pendulum in different latitudes, have fixed with great 
 accuracy the relative values of the polar and equatorial 
 diameters of the earth. The mean of a large number of 
 measures results in giving the 
 
 Equatorial diameter 41,847,192 feet. 
 
 Polar diameter 41,707,324 
 
 This gives a compression of 139,768 
 
268 POPULAR ASTRONOMY. 
 
 Some very remarkable results flow from this peculiar 
 figure of the earth. Among these we shall consider first 
 the equilibrium of the ocean. If it be true, as just asserted, 
 that the equatorial diameter of our globe exceeds the polar 
 diameter by 139,768 feet, then, in case the earth were 
 reduced to the figure of an exact sphere, by turning off the 
 redundant matter, we should be compelled to turn down at 
 the equator, to a depth of no less than 69,884 feet (one-half 
 of the above quantity), and hence the equatorial region may 
 be considered as a vast mountain range, belting the whole 
 earth, and rising above the general level nearly 70,000 feet. 
 On the sides and over the summit of this mountain-range 
 the ocean sweeps its currents and its tides, and yet the moat 
 delicate and beautiful equilibrium is maintained. 
 
 This is due to the fact that the velocity of rotation of 
 the earth on its axis is absolutely uniform and invariable ; 
 and hence the centrifugal force, whose power precisely 
 counterbalances the gravity on the mountain-side on which 
 the ocean rests, is ever the same. This great principle is 
 beautifully exemplified by taking a glass vase, filling it with 
 a coloured liquid, and suspending it by a cord. So long as 
 the vase is at rest the fluid on its upper surface is precisely 
 level and plain. Now, give to the vase a motion of rotation 
 about a vertical axis (as by the untwisting of the suspending 
 cord), and at once the fluid commences to rise upon the 
 sides of the vase, and a disk-shaped cavity is formed. This 
 rising continues so long as the velocity of rotation increases. 
 Should the velocity become uniform, then the figure of the 
 fluid in the vase assumes a form of exact equilibrium, and 
 the delicate circle that marks the height to which the fluid 
 rises in the vase remains constant, and will so continue as 
 long as the velocity of rotation is unchanged. The stability 
 of the figure of the ocean depends on the same principle ; 
 and, were it possible to arrest the rotation of the earth, 
 instantly the equatorial ocean would rush towards the poles 
 and would there rise until the general level should become 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 269 
 
 Buch as is due to a spherical figure, which the ocean would 
 assume. 
 
 NUTATION AND PRECESSION. We have in these remark- 
 able phenomena another effect of the figure of the earth. 
 We have already mentioned the fact that the vernal equinox 
 (the point in which the sun's centre crosses the equinoctial 
 in the spring season) does not remain fixed in the heavens. 
 The discovery was made by the early astronomers, the fact 
 noted, and an approximate period of revolution, amounting 
 to some twenty-five or twenty-six thousand years. Modern 
 science has not only determined the exact period to be 
 25,868 years, but has traced the phenomenon to its origin, 
 and has revealed the cause to lie in the fact that the protube- 
 rant mass of matter surrounding the equator of the earth is 
 a sufficient purchase to enable the sun and moon to tilt the 
 entire earth, and consequently the plane of the earth's equa- 
 tor. Suppose the earth revolved on an axis perpendicular to 
 the ecliptic, or that the equator of the earth and the ecliptic 
 coincided. Then, so far as the sun is concerned, there could 
 arise no power to effect a change in the plane of the equator; 
 but as the moon revolves in an orbit inclined to the plane of 
 the ecliptic, the moon will be sometimes above and some- 
 times below the plane of the earth's equator, now supposed 
 to be coincident with the ecliptic. Whenever the moon is 
 above the equatorial ring of the earth, she will tend to lift 
 the nearest portion of that ring above the ecliptic, and to 
 sink the opposite part below the same plane ; and as the 
 moon revolves around the earth, she will cause the equatorial 
 ring to tilt towards her position, and thus the line of nodes 
 of the ring will revolve as do the lines of nodes of the pla- 
 netary orbits ; and this is precisely what we find to be true 
 of the line of equinoxes, or the line cut by the plane of this 
 equatorial ring from the plane of the ecliptic, producing, as 
 we have seen, a retrocession of the equinoctial point, and a 
 precession of the time of the equinox. 
 
 THE NUTATION OF THE EARTH'S Axis is a phenomenon 
 springing out of the same causes producing precession. If 
 
270 POPULAR ASTRONOMY. 
 
 we consider the axis of the earth as an inflexible bar, passing 
 through the earth's centre and perpendicular to the equator, 
 extending indefinitely in opposite directions, to the celestial 
 sphere, it is clear that any tilting of the earth's equatorial 
 ring will equally tilt the axis of the earth. This is actually 
 seen in the slow revolution of the pole of the earth's equator 
 around the pole of the ecliptic in a period precisely equal to 
 that employed in the revolution of the equinoxes. Nutation 
 is but a subordinate fluctuation whereby the pole of the 
 equator, instead of describing an exact circle around the pole 
 of the ecliptic, makes certain short excursions a little on the 
 inside and on the outside of this circle, in a period which 
 agrees exactly with that occupied by the revolution of the 
 nodes of the moon's orbit. This at once suggests the moon 
 to be the principal cause of this nodding of the earth's 
 axis ; and, indeed, modern analysis has pointed out the 
 origin of the movement, and has accurately computed its 
 value. 
 
 In all we have said -we have supposed the equator and 
 ecliptic to coincide. This, however, is not the case of nature. 
 These , planes are inclined to each other, and hence we find 
 the sun producing results (analogous to those already traced 
 to the moon) on the mass of protuberant matter surround- 
 ing the earth's equator. The exact values of these constants 
 of precession and nutation will be found in the Appendix. 
 The greatest pains have been bestowed- on their determina- 
 tion, as they are of the first importance in fixing the abso- 
 lute places of all the heavenly bodies. 
 
 FIGURE OF THE EARTH'S ORBIT. The ellipticity of the 
 earth's orbit is slowly wearing away, under the combined 
 influence of all the planets. The eccentricity at the com- 
 mencement of the present century amounted to 0-016783568, 
 the semi-major axis being considered as unity. The amount 
 by which this quantity is decreased in a hundred years is 
 0-00004163. Let us reduce these figures to intelligible 
 quantities. The eccentricity is the distance from the centre 
 of the ellipse to the focus, and in miles is equal to 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 271 
 
 0-016783568 x 95,000,000 = 1,594,100. This quantity de- 
 creases in one hundred years by 0*00004163 x 95,000,000 = 
 3954-85 miles. If, now, we divide 1,594,100 by 3954-85, 
 the quotient 405 + will be the number of centuries which 
 must elapse before the earth's orbit will become an exact 
 circle at the present rate of change. It is ascertained by a 
 rigorous analytical investigation of this great problem, that, 
 so soon as the circular figure is reached by the earth's orbit, 
 the same causes reverse their effects, and the circular figure 
 is lost, and the eccentricity of the elliptic figure slowly 
 increases, until finally, at the end of a vast period, the 
 original form of the orbit is regained, to be again lost ; and 
 thus an expansion and contraction marks the history of the 
 earth's orbit, vibrating through periods of time swelling 
 into millions of years. 
 
 ACCELERATION OF THE MOON'S MEAN MOTION. This 
 change in the figure of the earth's orbit produces a minute 
 change in the mean motion of the moon, which was, after 
 long years of the most laborious research, finally traced to 
 its true origin by La Place. The fact that the moon was 
 moving faster in modern than in ancient times, became 
 evident from a comparison of the modern and ancient eclipses. 
 These eclipses can only occur when the sun, earth, and moon 
 occupy the same right line nearly; and hence their record 
 gives a very precise knowledge of the relative position of 
 these three bodies. It thus became manifest that the 
 average speed with which the moon was moving in her orbit, 
 was slowly increasing from century to century. This follows 
 necessarily from the fact, that the loss of eccentricity by the 
 orbit removes the earth by a small amount (on the average) 
 further from the sun. This carries both the earth and her 
 satellite by so much away from the disturbing influence of 
 the sun, leaving to the earth a more exclusive control of the 
 moon. As the sun is outside the moon's orbit with refer- 
 ence to the earth, his attraction will increase the magnitude 
 of the moon's orbit, and, of course, her periodic time. Any 
 diminution of the sun's disturbing power will* therefore by 
 
272 POPULAR ASTRONOMY. 
 
 so much permit the moon to approach the earth, and to 
 increase her velocity of revolution ; and this is precisely 
 what observation has revealed with reference to our satellite 
 during the entire period that history has recorded the pro- 
 gress of astronomy. 
 
 This gradual acceleration must continue up to the time 
 when the earth's orbit shall become exactly circular in form. 
 This limit once attained, as this orbit slowly resumes its 
 elliptic form, the acceleration of the moon's mean motion is 
 converted into retardation ; and thus at the end of a mighty 
 period this change will be entirely destroyed, and the moon 
 and earth return to their primitive condition. This accele- 
 ration of the mean motion of the moon is so slow that from 
 the earliest record of eclipses by the Babylonians down to 
 the present time, some 2,500 years, the moon has got in 
 advance of her mean place by about three times her owr> 
 diameter. 
 
 The facts above related indicate with how much diligence 
 the moon's motions have been studied. Though she is our 
 nearest neighbour, and consequently more directly under the 
 eye of the astronomer than any other heavenly body, her 
 motions have been more complex and difficult of perfect 
 exposition than any object in the heavens. The recent 
 investigations of the European and American astronomers 
 and mathematicians seem to have finally conquered this 
 refractory satellite ; so that now it becomes possible to 
 unravel her involved and intricate march among the stars 
 with such precision, that we can fix her place with certainty 
 for even thousands of years. 
 
 MARS AS A PONDERABLE BODY. This planet revolves in 
 an orbit of such eccentricity as to present very marked 
 differences in the power of attraction of the sun on the 
 planet when at its greatest and least distances. Its mean 
 distance is 142,000,000 of miles, giving its semi-major axis 
 a length equal to 71,000,000 of miles. The eccentricity of 
 the orbit (the distance between the centre and focus of the 
 ellipse) amounts to nearly one-tenth of this quantity, or to 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 273 
 
 about 64 millions of miles. Hence, the perihelion distance 
 is 64-6 millions of miles, while the aphelion distance is 77*4 
 millions of miles. The attractive power exerted by the sun 
 in perihelion will be greater than that exerted in aphelion 
 in the ratio of (77'4) 2 to (64'6) 2 , or as 5,991 to 4,172, or 
 nearly as three to two. To resist this increased power of 
 attraction in perihelion the planet must there move with a 
 far higher velocity than when in its aphelion. All these 
 deductions from theory are verified by observation. 
 
 It was from an examination of the movements of Mars 
 that Kepler deduced his celebrated laws. These laws we 
 have had occasion to use constantly in our computations, 
 but in consequence of the mutual actions of the planets, not 
 one of these laws is rigorously true. The orbits of the 
 planets are not exact ellipses ; nor do they so revolve that 
 the lines joining them with the sun sweep over precisely 
 equal spaces in equal times ; nor are the squares of the 
 periods of revolution precisely proportional to the cubes of the 
 mean distances ; but the failure in these laws is due entirely 
 to mere perturbation ; and in case a single planet existed 
 revolving around the sun, they would all be scrupulously 
 fulfilled. 
 
 The planet Mars was, however, well situated for the 
 examination conducted by Kepler. This becomes manifest, 
 if we call to mind the great distance separating Mars and 
 Jupiter, and the comparatively small disturbance which the 
 earth can produce. To present this problem still clearer, 
 let us suppose the earth, Mars, and Jupiter to be in con- 
 junction, and situated as in the figure. Then the distance 
 
 from S to E is 95,000,000 of miles, from S to M 142,000,000, 
 from S to J 890,000,000 of miles. Hence, the distance 
 EM is 142 95=47 millions of miles, while the distance 
 
 T 
 
274 POPULAR ASTRONOMY. 
 
 M T is 890142 = 648 millions of miles. We will first 
 coupute the power of attraction of Jupiter on Mars, as 
 compared with the power of the sun. If the masses were 
 equal, the energy of Jupiter would, on account of the greater 
 distance, be reduced below that of the sun in the ratio of 
 (142) 2 to (648) 2 , or nearly as 1 to 21. But the masses are 
 not equal, for the sun weighs as much as 3,502 such globes 
 as Jupiter, and hence, by combining these causes of reduc- 
 tion, we find the force exerted by Jupiter to be less than 
 that exerted by the sun in the ratio of 1 to 3,502 x 21, or as 
 1 to 115,542. 
 
 Let us now see what force the earth exerts on Mars, when 
 compared with the sun's force. As the earth is nearer to 
 Mars than the sun, in case the sun and earth were of equal 
 weights their energy at Mars would be in the ratio of (142) 2 
 to (47) 2 , or as 20,164 to 2,209, or nearly in the ratio of 9 to 1. 
 But the sun weighs as much as 354,936 earths, and if we 
 divide 354,936 by 9, we obtain 39,437 as a quotient, and 
 hence the power of the sun on Mars is to the power of the 
 earth as 39,437 to 1. 
 
 It ,is thus seen that the earth is more powerful than 
 Jupiter to disturb Mars in the ratio of 115,542 to 39,437, 
 or in the ratio of about 3 to 1. To exhibit more clearly 
 the minute character of the effects of the earth and of Jupiter 
 on this planet, let us compute the space through which a 
 body would fall in one second, if as far removed from the 
 sun as Mars. We have already seen that gravity at the 
 solar surface is 2 8 '7 greater than at the surface of the earth. 
 At the earth gravity impresses such a velocity on a falling 
 body that it passes over a space of 16-1 feet in the first 
 second of time ; therefore, a body at the sun's surface would 
 fall through a space represented by 28'7 x 16'1 = 461 feet 
 in the first second of its fall. If we remove the falling 
 tody to double the distance from the sun's centre, the force 
 of the sun's gravity is reduced to one quarter, and hence the 
 apace passed over by the falling body at two units from the 
 centre of the sun will be A1= 115-25 feet. But Mars' dis- 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 275 
 
 tance from the sun is 142,000,000 of miles, while the solar 
 radius is 441,500 miles ; in other words, a falling body, 
 removed to the distance of Mars from the sun, is about 
 thirty-two times more remote from the sun's centre than 
 when on the sun's surface, and the energy of the sun's 
 gravity would be reduced at this distance in the ratio of 
 (I) 2 to (32) 2 , or as 1 to 1,024 ; so that a body would fall in 
 one second, if as far removed from the centre of the sun 
 as is the planet Mars, through a space represented by 
 ^VV= 0-4501 94 feet. To what extent will this quantity 
 be affected by the attraction of the earth ? The answer is 
 given in the result already reached, that the power of the 
 earth is only the thirty-nine thousand four hundred and 
 thirty-seventh part of that of the sun, and hence the falling 
 body will only pass over the additional space represented by the 
 minute fraction - 450194 = 0-000011, or about the one hun- 
 dred thousandth part of one foot. These quantities look to 
 be minute and quite unworthy of notice ; and yet from these 
 small disturbing effects, accumulating through ages, arise 
 all the amazing changes which are progressing among the 
 elements of the planetary orbits. 
 
 We will not extend these details, but refer for further 
 particulars to the Appendix. 
 
 THE ASTEROIDS AS PONDERABLE BODIES. As yet we 
 have no certain knowledge of the magnitude or masses of 
 these minute worlds. We are assured that they are 
 subjected to the laws of motion and gravitation, and that the 
 elements of their orbits are undergoing the same modifica- 
 tions to which the elements of the orbits of all the planets 
 are subjected. These planets are disturbed principally by 
 the action of Jupiter, as we may readily determine by an 
 examination of the masses and distances of the two nearest 
 planets, inside and outside the orbits of the asteroids. 
 
 The mean distance of the group from the sun is about 
 2 '5 times the earth's distance. The distance of Mars, in 
 terms of the same unit, is 1-5, and the distance of Jupiter 
 from the sun is 5-2. Hence, from the mean distance of the 
 
 T 2 
 
276 POPULAR ASTRONOMY. 
 
 asteroids to Jupiter is 5-2 2'5 = 2'7, and from the same to 
 Mars is 2 -5 1'5 = 1*0. Hence, if Mars and Jupiter were 
 equal in weight, the power of Mars over the central asteroid 
 would exceed the power of Jupiter in the ratio of (2-7) 2 to 
 (l-O) 2 , or in the ratio of 7'3 to 1. But Jupiter is 256 times 
 heavier than Mars, and hence his power will he increased in 
 like proportion, and the attraction of Mars will be to that of 
 Jupiter as 7 '3 to 256, or as 1 to 35 nearly. Hence we 
 perceive that Jupiter is the principal disturber in the move- 
 ments of the asteroids. For further particulars the reader 
 ivill consult the Appendix. 
 
 JUPITER AND HIS SATELLITES AS HEAVY BODIES. This 
 planet is not only heavier, but its volume is much greater 
 than that of any one of the planets. Being 5-2 further from 
 the sun than the earth, it will be attracted by a power 
 diminished in the ratio of the square of 5'2 to 1, or as 27 to 
 1 nearly. 
 
 The weight of Jupiter is to that of the earth as 338 to 1, 
 and in case his diameter were exactly equal to that of the 
 earth, a body weighing one pound at the terrestrial equator 
 would weigh at the equator of this planet 338 pounds. But 
 the diameter of Jupiter is 90,734 miles, and its radius 
 45,377 miles, or more than ten times the radius of the 
 earth. His attraction on a body upon the surface will 
 therefore be reduced on account of this tenfold distance to 
 the one-hundredth of 338 pounds, or to 3-38 pounds, or, if 
 the computation be made precisely, the result gives us 2-81 
 as the weight of one terrestrial pound at the equator of this 
 planet. The student can compute the reduction in the 
 gravity of the planet at the equator arising from the action 
 of the centrifugal force, the planet revolving on its axis in 
 9h. 55m. 27s. 
 
 The principal disturber of Jupiter is the planet Saturn. 
 From the sun to Jupiter is 5-2, the earth's distance being 1. 
 From Jupiter to Saturn the distance is 4 '3 in the same 
 terms. Hence, if Saturn weighed as much as the sun, his 
 power over Jupiter would be greater in the ratio of (5'2) 2 to 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 277 
 
 (4-3) 2 , or as 27-04 to 18-44, or as 147 to 1. But the sun 
 weighs as much as 3,502 Saturns, and hence his power over 
 Jupiter will exceed that of Saturn in the ratio of 3 -pf to 1, 
 or as 2,380 to 1. This, of course, is the ratio of the forces 
 when the planets are in conjunction. When in opposition, 
 the interval between them is increased by the diameter oi 
 the orbit of Jupiter, or by 10-4, and thus it becomes 14 7, 
 instead of 4'3 ; and in this position the disturbing power of 
 Saturn is reduced in the ratio of (14-7) 2 to (4-3) 2 , or as 
 216-09 to 18-44, or as 12 to 1. 
 
 We have already seen how we can ascertain the weight of 
 this planet by observing the period of revolution of his 
 satellites, and by measuring their distances. By taking 
 these quantities from the table in the Appendix, the student 
 may compute readily the mass of Jupiter as compared with 
 that of the earth. 
 
 The eccentricity of the orbit of this planet amounts to 
 0'0481, the semi-major axis being unity; or the distance 
 from the centre of the ellipse to the focus is equal to 
 {242,500,000) x 0-0481 = 1 1,664,250 miles. This quantity is 
 now slowly increasing, and gains every year in length 388 
 miles. This is due to the disturbing influence of the sur- 
 rounding planets, and after an immense period will reach a 
 limit beyond which it cannot pass. The increment will then 
 be converted into decrement, and a limit being again reached, 
 the orbit in its figure thus oscillates between these limits in 
 calculable, but (so far as I know) in periods not yet calculated. 
 
 The same fact is true of the inclination of the plane of 
 -Jupiter's orbit to that of the ecliptic. On the 1st January, 
 1840, this inclination amounted to 1 18' 42"-4. Its present 
 annual decrease is 0"-23, and should this continue, at the end 
 of about 200,000 years these planes would coincide. This 
 however, can never take place. The decrease finally comes 
 to be converted into increase, and thus the plane of the 
 orbit of Jupiter may be said to rock to and fro on the plane 
 of the ecliptic in periods reaching to even millions of years. 
 
 We have already noticed a source of perturbation in the 
 
278 POPULAR ASTKONOMY. 
 
 case of Venus and the earth, arising from the approximate 
 commensurability of the periods of revolution of these 
 planets. A like equation, as it is called, exists in the case of 
 Jupiter and Saturn. Five periods of Jupiter are 21,663, 
 and two of Saturn's periods are 21,519 days ; so that, in case 
 the planets start at any given time from a conjunction, at 
 the end of five revolutions of Jupiter and two of Saturn, the 
 planets will return to nearly the same points of their orbits 
 and to the same relative positions. But the synodical 
 period, or the time from conjunction to conjunction of these 
 planets, is 72534 days, and three times this quantity 
 amounts to 21760-2. Hence we perceive Jupiter in this 
 period will have performed five revolutions and 21,760 
 21,663 = 97 days over, while Saturn will describe two revo- 
 lutions and 240 days over, and during these excesses the 
 planets advance in their respective orbits 8 6'. Thus every 
 third conjunction will fall 8 6' in advance of the former one, 
 and the conjunction-line will be thus carried round the 
 entire orbit in about 44 times x 21,760 days, or in 2,648 
 years, at the end of which cycle the same exact condition 
 will be restored, and all the perturbations in the same time 
 completely obliterated, provided the figures of the orbits 
 remain unchanged. Indeed, a restoration is effected partially 
 and almost completely in consequence of the triple conjunc- 
 tion which takes place in the period of 21,760 days. These 
 conjunctions fall at points on the orbits 120 apart, and thus 
 tend to effect a restoration, which is only fully perfected, 
 however, at the end of the great cycle of 2,648 years. 
 
 Here we find again the cause which prevents the laws of 
 Kepler from being rigorously applicable to the planetary 
 movements. In case Jupiter existed alone, then the line 
 drawn from the planet to the sun would sweep over equal 
 areas in equal times, as it is carried by the planet around 
 the sun. But the association of the two- planets renders the 
 application of this law no longer possible. Jupiter is dragged 
 back by Saturn, and Saturn is dragged forward by Jupiter 
 when they start off" from their line of conjunction ; but here 
 
THE SUN AND PLANETS AS PONDERABLE BODIES. 279 
 
 comes in a most wonderful compensation in the fac* #iat, 
 whatever Jupiter's motion loses by the disturbing influence 
 of Saturn, Saturn's motion gains by the disturbing influence 
 of Jupiter; so that the sum of the areas swept over by the 
 lines joining the two planets with the sun will always be 
 equal in equal times. 
 
 We shall not extend further our notices of the results 
 arising from the action of gravitation on the planets and 
 their satellites having discussed to some extent the mutual 
 perturbations of Uranus and Neptune in a former chapter. 
 
 We will close by an extension of the principle laid down 
 in the case of Jupiter and Saturn to the entire planetary 
 system. If at any moment lines were drawn from the 
 centre of the sun to each of the planets in the entire system, 
 and from the centre of each of the planets to their respective 
 satellites, the areas swept over by all these lines thus drawn 
 will always be equal in equal times. Thus, while not a 
 solitary planet or satellite can follow this law of equal areas, 
 the combined scheme is bound by it in the most rigorous 
 manner; and if the amount of area described by the entire 
 system in one hour were determined to-day, and be sent 
 down to posterity, at the end of ten thousand years, a 
 like computation being made, the same identical result will 
 be reached, provided the system remain free from any dis- 
 turbing influence exterior to itself. 
 
 In case, therefore, the sun with all his planets and comets 
 is, indeed, drifting through space into other stellar regions, 
 the time may come when the fixed stars may so disturb the 
 sum of the areas as to point out clearly the fact, that our 
 system has positively changed its location in space. 
 
 We will close our discussion of the sun and his satellites 
 by the examination of an hypothesis, which has been pro- 
 pounded to account for the peculiar organization of this vast 
 scheme of revolving worlds. 
 
280 POPULAR ASTRONOMY. 
 
 CHAPTER XVI. 
 
 THE NEBULAR HYPOTHESIS. 
 
 The Arrangement of the Solar System. The Phenomena for which 
 Gravitation is responsible. The Phenomena remaining to be accounted 
 for. Nebulous Matter as found in Comets. Nebulous Matter possibly 
 in the Heavens. The Entire Solar System once a Globe of Nebulous 
 Matter. Motion of Rotation. Radiation of Heat. Condensation and 
 its Effects. Rings disengaged from the Equator of the Revolving Mass. 
 . Formation of Planets and of Satellites. 
 
 IN our examination of the scheme of worlds which revolve 
 around the sun, we have found that the orbits of the planets 
 are all nearly circular, that their planes are all nearly coin- 
 cident with the plane of the ecliptic, and that this plane is 
 nearly coincident with the plane of the sun's equator ; that 
 the planets all revolve in the same direction around the 
 sun, and that the sun and planets and satellites all rotate 
 on their axes in the same direction ; that the periods ol 
 revolution grow shorter in the planets and satellites as their 
 distances from their primary grow less ; that the sun rotates 
 on his axis in a shorter period than that employed in the 
 revolution of any planet ; that every planet accompanied by 
 satellites rotates on its axis in a less time than the period of 
 revolution of any satellite. The law of gravitation is not 
 responsible for any of these facts ; and in case we compute 
 the chances of such an organization coming into being by 
 accident, we shall find but one chance in so many millions, 
 that we are compelled to look to some higher cause than 
 mere accident to account for so great a multitude of com- 
 bined phenomena. 
 
 "We have said that gravitation is not responsible for the 
 facts above stated. In case a solitary planet be projected 
 with a given force, and in a given direction about the sun, 
 and at a given" distance, it will revolve, as we have seen, in 
 
THE NEBULAR HYPOTHESIS. 281 
 
 one of four curves, and in any one of these curves it will be 
 held equally by the law of gravitation. The plane in which 
 it revolves may assume any angle with a fixed plane, the 
 direction of the revolution may be the same or contrary to 
 that in which the sun rotates, the orbit may be a circle, an 
 ellipse, a parabola, or an hyperbola j and yet the planet shall 
 revolve, subject to the law of gravitation. It may rotate 
 on its own axis either with or against its revolution in its 
 orbit ; and in case we give to this planet a satellite, the 
 same statements are true with reference to this attendant. 
 So that, so far as the law of gravitation is concerned, there 
 might have been among the planets all the diversity in the 
 form of their orbits, in the angles of their inclination to a 
 fixed plane, and in the direction of their motions, as are 
 found among the comets, and yet each object would have 
 been subject to the great law of universal gravitation. 
 
 We cannot, therefore, affirm that the peculiar structure of 
 the solar system results from the laws of motion and 
 gravitation, without pre-supposing a condition of matter 
 entirely different from that now recognized as existing in 
 the planets and their satellites. We have already noticed 
 the wonderful constitution of the comets. In these bodies ^ 
 found a kind of matter which has been termed nebulous, in 
 which the minute particles are separated by some repulsive ^j_ 
 force, and the entire mass is but a vapour of the most refined / 
 tenuity. 
 
 Among the stellar regions the telescope has revealed 
 objects whose light is so faint and whose forms are so ill 
 defined, that they have been regarded by many astronomers 
 of high reputation to be analogous to the comets in their 
 material, exhibiting the primitive or primordial condition of 
 the matter composing the physical universe. This conjec- 
 ture (for it is nothing more) may be true or false ; but its 
 truth or falsehood cannot in any way affect the credibility 
 of the theory or hypothesis we are about to present. The 
 present condition of matter cannot in any way be assumed 
 to be the only condition in which it ever existed, since we 
 
282 POPULAR ASTRONOMY. 
 
 now know it to be subject to extraordinary changes and most 
 wonderful modifications. 
 
 Let us, then, suppose that a time once was, when the sun 
 and all its planets and their satellites existed as one mightj 
 globe of nebulous matter, whose diameter far exceeded the 
 present diameter of the orbit of Neptune ; that to this stu- 
 pendous globe a motion of rotation was given ; and that its 
 heat is slowly lost by radiation ; and let us endeavour to 
 follow the changes which must flow from the loss of heat and 
 the operation of the laws of motion and gravitation, and 
 learn whether from this parent-mass a scheme of planets and 
 satellites such as now exist can be generated. We prefer to 
 present the reasoning in the language of M. Pontecoulent, 
 one of the most eminent of the illustrious disciples of Newton 
 merely premising that, in case the central rotating mass 
 contracts by loss of heat, a time must come when, in conse- 
 quence of the increased velocity of rotation, the force of 
 gravity of a particle at the equator will be overcome by the 
 centrifugal force generated by the velocity of rotation ; and 
 hence flat zones or rings of vapour or nebulous matter must 
 eventually be formed in the plane of the equator of the 
 revolving globe : 
 
 " These zones must have begun by circulating round the 
 sun in the form of concentric rings, the most volatile mole- 
 cules of which have formed the superior part, and the most 
 condensed the inferior part. If all the nebulous molecules 
 of which these rings are composed had continued to cool 
 without disuniting, they would have ended by forming a 
 liquid or solid ring. But the regular constitution which all 
 parts of the ring would require for that, and which they 
 would have needed to preserve whilst cooling, would make 
 this phenomenon extremely rare. Accordingly, the solar 
 system presents only one instance of this, that of the rings 
 of Saturn. Generally the ring must have broken into 
 several parts, which have continued to circulate round the 
 sun, and with almost equal velocity, while at the same time, 
 01 consequence of their separation, they would acquire a 
 
THE NEBULAR HYPOTHESIS. 285 
 
 rotatory motion round their respective centres of gravity ; 
 and as the molecules of the superior part of the ring, that is 
 to say, those furthest from the centre of the sun, had neces- 
 sarily an absolute velocity greater than the molecules of the 
 inferior part which is nearest it, the rotatory motion, common 
 to all the fragments, must always have been in the same 
 direction as the orbitual motion. 
 
 " However, if, after their division, one of these fragments 
 has been sufficiently superior to the others to unite them 
 to it by its attraction, they will have formed only a mass of 
 vapour, which, by the continual friction of all its parts, must 
 have assumed the form of a spheroid flattened at the poles 
 and elongated in the direction of its equator. Here, then, 
 are rings of vapour left by the successive retreats of the 
 atmosphere of the sun, changed into so many planets in the 
 condition of vapour circulating round the sun, and possessing 
 a rotatory motion in the direction of their revolution. This 
 must have been the most common case ; but that in which 
 the fragments of some ring would form several distinct 
 planets possessing degrees of velocity must also have taken 
 place, and the telescopic planets discovered during the 
 present century seem to present an instance of this ; at least 
 if it is not admitted, with Olbers, that they are the frag- 
 ments of a single planet, broken by a strong interior 
 commotion. It is easy to imagine the successive changes 
 produced by cooling on the planets whose formation has been 
 just pointed out. Indeed, each of these planets, in the con- 
 dition of vapour, is, in every respect, like one of the nebulae 
 in the first stage ; they must, therefore, before arriving at a 
 state of solidity, pass through all the stages of change we 
 have just traced in the sun. At first, the condensation of 
 their atmosphere will form round the centre of the planet a 
 body composed of layers of unequal density, the densest 
 matter having, by its weight, approached the centre, and 
 ^he most volatile reached the surface, as we see in a vessel 
 different liquids ranged one above another, according to their 
 specific gravity to arrive at a state of equilibrium. The 
 
284 POPULAR ASTRONOMY. 
 
 atmosphere of each planet will, like that of the sun, leave 
 behind it zones -of vapour, which will form one or several 
 secondary planets, circulating round the principal planet as 
 the moon does round the earth, and the satellites round 
 Jupiter, Saturn, and Uranus ; or else .they form, by cooling 
 without dividing, a solid and continuous circle, of which we 
 have an instance in the ring of Saturn. In every case the 
 direction of the rotatory and orbitual motion of the satellites 
 or the ring will be the same as that of the rotatory motion 
 of the planet ; and this is completely confirmed by 
 observation. 
 
 " The wonderful coincidence of all the planetary motions 
 (a phenomenon which we cannot, without infringing the laws 
 of probability, regard as merely the effect of chance) must, 
 then, be the result even of the formation of the solar system 
 on this ingenious hypothesis ; we see also why the orbits of 
 the planets and satellites are so little eccentric, and deviate 
 so little from the plane of the solar equator. A perfect har- 
 mony between the density and temperature of their molecules 
 in a state of vapour would have rendered the orbits rigorously 
 circular and made to coincide with the plane of this equator ; 
 but this regularity could not exist in all parts of such large 
 masses ; there has resulted the slight eccentricities of the 
 orbits of the planets and satellites, and their deviation from 
 the plane of the solar equator. 
 
 " When in the zones abandoned by the solar atmosphere 
 there are found molecules too volatile either to unite with 
 each other or with the planets, they must continue to revolve 
 round the sun, without offering any sensible resistance to the 
 motions of the planetary bodies, either on account of their 
 extreme rarity, or because their motion is effected in the 
 same way as that of the bodies they encounter. These wan- 
 dering molecules must thus present all the appearances of the 
 zodiacal light. 
 
 . " We have seen that the figure of the heavenly bodies was 
 the necessary result of their fluidity at the beginning of time. 
 The singular phenomenon presented by tne rigorous equality 
 
THE NEBULAE HYPOTHESIS. 285 
 
 indicated by observation among the lesser motions of rotation 
 and revolution of each satellite, an equality rendering the 
 opposed hemisphere of the moon for ever invisible to us, is 
 another obvious consequence of this hypothesis. Indeed, 
 supposing that the slightest difference had existed between 
 the mean motion of rotation and revolution of our satellite, 
 while it was in the state of vapour or of fluidity, the attrac- 
 tion of the earth would have elongated the lunar spheroid in 
 the direction of its axis towards the earth. The same attrac- 
 tions would have tended to diminish insensibly the difference 
 between the rotatory and orbitual motions of the moon, so 
 as to confine to narrow limits a condition sufficient to cause 
 the axis of its equator, directed towards the earth, to be sub- 
 ject only to a species of periodical balancing constituting the 
 phenomenon of libration. If these oscillations are not now 
 observed, it is because they have ceased to exist in consequence 
 of the resistance they have encountered in the course of time ; 
 even as the oscillations of the terrestrial axis in the interior 
 of the earth, arising from the initial state of motion have 
 been destroyed ; and as indeed all the motions of the 
 heavenly bodies have disappeared which have not had a 
 permanent cause. 
 
 " The principal phenomena of the planetary system are 
 therefore explained with great facility by the hypothesis we 
 are examining ; and as these successive changes of a nebulous 
 mass and the leaving of a part of its substance by cooling, 
 agree with all the leading phenomena, it must be allowed a 
 high degree of probability. In this hypothesis the formation 
 of the planets would not have been simultaneous ; they have 
 been created successively at intervals of ages ; the oldest are 
 those which are furthest from the sun, and the satellites are 
 of a more recent date than their respective planets. It may 
 be, if we are ever permitted to reach so high, that, by an 
 examination of the constitution of each planet, we may go 
 back to the epoch of its formation, and assign to each its 
 place in the chronology of the universe. It is likewise seen 
 that the velocity of the orbitual motion of each planet, as it 
 
286 POPULAR ASTRONOMY. 
 
 is now, must differ little from that of the rotatory motion oi 
 the sun at the period when the planet was detached from its 
 atmosphere. And as the rotatory motion is accelerated in 
 proportion as the solar molecules are confined by cooling, so 
 that the sum of the areas which they describe round the centre 
 of gravity would remain always the same, it follows that revo- 
 lutionary motion must be so much more rapid as the planet 
 is nearer the sun ; as is seen by observation. It likewise 
 results that the duration of the rotation either of the sun or 
 of a planet must be shorter than the duration of the nearest 
 body which circulates round them ; this observation is com- 
 pletely confirmed even in those cases where the difference 
 between the duration of the two motions must be very 
 slight. Thus the interior ring of Saturn being very close 
 to the planet, the duration of its rotation must be almost 
 equal, but a little longer than that of the planet. 
 . " The observations of Herschel give, indeed, 0432 as the 
 duration of the rotation of the ring, and 0427 as that of the 
 planet ; why, then, should we not admit that this ring has 
 been formed by the condensation of the atmosphere of 
 Saturn, which formerly extended to it 1 We may perhaps 
 deduce from the laws of mechanics and the actual dimen- 
 sions of the sun, and the known duration of its rotation, the 
 relation existing between the radius-vector of its surface 
 and the time of its rotation in the different stages of con- 
 centration through which it has passed. The third law of 
 Kepler would be no longer the mere result of observation ; 
 it would be directly deduced from the primordial laws of 
 the heavenly bodies. 
 
 " In this system the particular form of the planets, the 
 flattening at the poles, and bulging out at the equator, is 
 only the necessary consequence of the laws of the equili- 
 brium of fluids, and easily explains the greater part of the 
 phenomena observed by geologists in the constitution of the 
 terrestrial globe, which appear ir explicable, if it is not 
 admitted that the earth and planets have been originally 
 fluid. 
 
THE NEBULAR HYPOTHESIS. 287 
 
 " Let us now see what is the origin and part assigned to 
 comets by this hypothesis. La Place supposes that they do 
 not belong to the planetary system ; and he regards them 
 as masses of vapour formed by the agglomeration of the 
 luminous matter diffused in all parts of the universe, and 
 wandering by chance in the various solar systems. Comets 
 would thus be, in relation to the planetary system, what the 
 aerolites are in. relation to the earth, with which they seem 
 to have no original connection. When a comet approaches 
 sufficiently near the regions of space occupied by our system 
 to enter into the sphere of the sun's influence, the attraction 
 of that luminary, combined with the velocity acquired by 
 the comet causes it to describe an elliptic or hyperbolic orbit. 
 But as the direction of this velocity is quite arbitrary, comets 
 must move in every direction, and in every part of the sky. 
 
 " The cometary orbits will, then, have every inclination to 
 the ecliptic ; and this hypothesis explains equally well the 
 great eccentricity by which they are usually affected. 
 Indeed, if the curves described by comets are ellipses, they 
 must be greatly elongated, since their major axes are at 
 least equal to the radius of the sphere of the sun's attrac- 
 tion ; and we must consequently be able to see only those 
 whose eccentricity is very great, and perihelion distance 
 inconsiderable ; all others, on account of their minuteness 
 and distance, must always be invisible ; unless at least the 
 resistance of the ether, the 'attraction of the planets, or 
 other unknown causes diminish their perihelion-distance, 
 and bring them nearer the terrestrial orbit. The same cir- 
 cumstances may change the primitive orbits of some comets 
 into ellipses, whose major axes are comparatively small ; 
 and this has probably happened to the periodical comets of 
 1759, 1819, and 1832. The laws of the curvilinear motion 
 likewise show, that the eccentricity of the orbit chiefly 
 depends on the direction of the comet's motion on its enter- 
 ing the sphere of the sun's attraction ; and as this motion 
 is possible in every direction, there are i o limits to the 
 eccentricities of the orbits of comets. 
 
288 POPULAR ASTBONOMY. 
 
 " If at the formation of the planets, some comets pene- 
 trated the atmospheres of the sun and planets, the resistance 
 they met would gradually destroy their velocity; they 
 would then fall on those bodies, describing spirals; and 
 their fall would have the effect of causing the planes of the 
 orbits and equators of the planets to remove from the plane 
 of the solar equator. It is, therefore, partly to this cause, 
 and partly to those we have developed above, that the blight 
 deviations we now perceive must be attributed. 
 
 " Such is a summary of the hypothesis of La Place on 
 the origin of the solar system. This hypothesis explains, in 
 the most satisfactory manner, the three most remarkable 
 phenomena presented by the planetary motions. 
 
 " 1st. The motion of the planets in the same direction, 
 
 d nearly in the same plane. 
 
 " 2nd. The motion of the satellites in the same direction 
 as their planets. 
 
 " 3rd. The singular coincidence in direction of the rotatory 
 and orbitual motions of the planets and the sun, which in 
 other systems would present inexplicable difficulties. 
 
 " The no less remarkable phenomena of the smallness of 
 the eccentricities and inclinations of the planetary orbits are 
 also a necessary consequence of it, while we see at the same 
 time why the orbits of the comets depart from this general 
 law, and may be very eccentric, and have any inclination 
 whatever to the ecliptic. The flattening of the form of the 
 planets, shown on the earth by the enlargement of degrees 
 of the meridian, and by the regular increase of weight in 
 going from the equator to the poles, is only the result of the 
 attraction of their molecules while they were yet in a state 
 of vapour, combined with the centrifugal force produced by 
 the rotatory motion impressed on the fluid mass. In short, 
 among the phenomena presented by the motions and the 
 form of the heavenly bodies, there are none which cannot 
 be explained with extreme facility by the successive con- 
 densation of the solar system ; and the more this svstem 
 
THE NEBULAR HYPOTHESIS. 289 
 
 is examined, the more we are led to acknowledge its pro- 
 bability. 
 
 " Undoubtedly, if, as La Place has himself said, a hypo- 
 thesis not founded on observation or calculation must always 
 be presented with extreme diffidence, this, it will be granted, 
 acquires, at least by the union and agreement of so many 
 different facts, all the marks of probability. But what, in 
 my opinion, principally distinguishes it from the ordinary 
 theories concerning the formation of systems, is the identity 
 which it establishes between the solar system and the stars 
 spread so profusely through the sky. 
 
 " All the phenomena of nature are connected, all flow 
 from a few simple and general laws, and the task of the man 
 of genius consists in discovering those secret connections, 
 those unknown relations, which connect the phenomena 
 which appear to the vulgar to have no analogy. In going 
 from a phenomenon of which the primitive law is easily 
 perceived, to another in which particular circumstances com- 
 plicate it so as to conceal it from us, he sees them all flowing 
 from the same source, and the secret of nature becomes his 
 possession. Thus the laws of the elliptic motion of the 
 planets led Newton to the great principle of universal 
 gravitation, which he would have sought for in vain in the 
 less simple phenomena of the rotatory motion of the earth, 
 or the flux and reflux of the sea. But this great principle 
 being once discovered, all the circumstances of the planetary 
 motions were explained, even in their minutest details, and 
 the stability of the solar system was itself only the necessary 
 consequence of its conformation, without which, as Newton 
 thought, God would be constantly obliged to retouch his 
 work, in order to render it secure. La Place, extending to 
 all the stars, and consequently to the sun, the mode of con- 
 densation by which the nebulae are changed into stars, has 
 connected the origin of the planetary system with the 
 primordial laws of motion, without recurring to any hypo- 
 thesis but that of attraction. He has, therefore, extended 
 to the fixed stars the great law of universal gravitation, 
 
 u 
 
290 POPULAR ASTRONOMY. 
 
 which is probably the only efficient principle of the creation 
 of the physical world, as it is of its preservation." 
 
 Such is a brief outline of one of the most sublime specu- 
 lations that has ever resulted from the efforts of human 
 thought. It carries us back to that grand epoch when " in 
 the beginning God created the heavens and the earth," when 
 matter was first called into being in its unformed nebulous 
 condition, and " the earth was without form and void," and 
 darkness covered the mighty deep of unfathomable space. 
 But the Spirit of God moved on the boundless flood of 
 vaporous matter scattered through the dark profound, and 
 gave to each particle its now eternal function, impressed the 
 laws of gravitation and motion, selected the grand centres 
 about which the germs of suns and systems should form, and 
 in infinite wisdom drew the plan of that one scheme which 
 we have attempted to examine, among the millions that 
 ehine in splendour throughout the boundless empire of 
 space. 
 
APPENDIX. 
 
 TABLES OF ELEMENTS. 
 
 SOLAR ELEMENTS, EPOCH IST JAN., 1801. 
 
 Mean Longitude 280 39' 10"'2 
 
 Longitude of the perigee 270 V> 30' 05"'0 
 
 Greatest equation of centre 1 55' 27"'3 
 
 Decrease of same in one year 0"'173 
 
 Inclination of axis to the ecliptic 82 40' 00"'0 
 
 Motion in a mean solar day 7 30' 00" - 
 
 Motion of perigee in 365 days 1' 01" '9 
 
 Apparent diameter 32' 12"'6 
 
 Mean horizontal parallax 8"'6 
 
 Rotation in mean solar hours 607h 48m Os 
 
 Time of passing over one degree of mean longitude . . 24h 20m 58 'Is 
 
 Eccentricity of orbit (semi-axis major 1) '01685318 
 
 Volume (earth as 1) 1,415,225 
 
 Mass (earth as 1) 354,936 
 
 Mean distance in miles 95,000,000 
 
 Same (earth's radius 1) 23,984 
 
 Density (earth as 1) 0'250 
 
 Diameter in miles 888,646 
 
 Gravity at equator 28'7 
 
 In one second of time bodies fall in feet 462'0'/ 
 
 ELEMENTS OF THE ORBIT OF MERCURY, 
 EPOCH IST JAN., 1801. 
 
 Mean distance from the sun in miles 36,725,000 
 
 Same (earth's distance as 1) -3870984 
 
 Greatest distance, same unit '4666927 
 
 Least distance, same unit '3075041 
 
 Eccentricity (semi-axis major as l\ -2056178 
 
 Annual variation of same (decrease) 0*00000003866 
 
 Sidereal revolution in days 87*9692824 
 
 Synodical revolution in days 115*877 
 
 Longitude of perihelion at epoch 74 57' 27"'00 
 
 Annual variation of same (increase) 5'81 
 
 Longitude of ascending node 46 23' 55' K 00 
 
 Annual variation of same 10 "'07 
 
 u 2 
 
2P2 APPENDIX. 
 
 Inclination of orbit to ecliptic 7 00' 13"'30 
 
 Annual variation of same 00"'18 
 
 Mean daily motion in orbit 245' 32 " - 6 
 
 Time of rotation on axis 24h 05m 28s 
 
 Inclination of axis to ecliptic Uncertain 
 
 Apparent diameter 6"'69 
 
 Diameter in miles 3,089 
 
 Diameter (earth's being 1) 0'398 
 
 Volume (earth's being 1) 0'0595 
 
 Density (earth's being 1) 1'225 
 
 Light received at perihelion (earth's being 1) 10'58 
 
 Same at aphelion (earth's 'being 1) 4 '59 
 
 Weight of a terrestrial pound 0'48 
 
 Space fallen through in one second of time, in feet 7'70 
 
 1) 0-0769 
 
 ELEMENTS OF VENUS FOE THE IST JAN., 1840. 
 
 Mean distance from the sun in miles 68,713,500 
 
 Same (earth's distance as 1) '7233317 
 
 Greatest distance, same unit '7282636 
 
 Least distance, same unit '7183998 
 
 Eccentricity (semi-axis major as 1) -0068183 
 
 Annual variation of same (decrease) '0000006271 
 
 Sidereal revolution in days 224'7007754 
 
 Synodical revolution in days 583'920 
 
 Longitude of the perihelion 124 14' 25"'6 
 
 Annual variation of same (decrease) 3" '24 
 
 Longitude of the ascending node 75 11' 29 "'8 
 
 Annual variation of same (decrease) 20 "'50 
 
 Inclination of orbit to the ecliptic 3 23' 31 "'4 
 
 Annual variation of same (increase) 0"'07 
 
 Mean daily motion in orbit 96' 7"'8 
 
 Time of rotation on axis 23h 21m 21s 
 
 Inclination of axis to the ecliptic Uncertain 
 
 Apparent diameter 17"'10 
 
 Diameter in miles 7,896 
 
 Diameter (earth's being 1) 0'925 
 
 Volume (earth's being 1) -9960 
 
 Mass or weight (earth's being 1) *894 
 
 Density (earth's being 1) 0'923 
 
 Light received at perihelion (earth's being 1) T94 
 
 Same at aphelion (earth's being 1) 1-91 
 
 Weight of a terrestrial pound, or gravity 0'90 
 
 Space fallen through in one second of time > in feet 14*5 
 
 ELEMENTS OF THE EAETH, IST JAN., 1801. 
 
 Mean distance in miles 95,000,000 
 
 Greatest distance (mean distance 1) I -01 67751 
 
 Least distance, same unit 0*9832249 
 
APPENDIX. 293 
 
 Mean sidereal revolution (solar days) 365d 06h 09m 09s'6 
 
 Mean tropical revolution 365d 05h 48m 49s*7 
 
 Mean animalistic revolution 365d 06h 13m 49s*3 
 
 Revolution of the sun's perigee (solar days) 7,645,793 
 
 Mean longitude (20" for aberration) 100 39' 10" '2 
 
 Earth's motion in perihelio in a mean solar day 1 01' 09" '9 
 
 Mean motion in a solar day 59' 08"*33 
 
 Mean motion in a sidereal day 59' 58"*64 
 
 Motion in aphelion in a mean solar day 57' 11 "'50 
 
 Mean longitude of perihelion 99 30' 05" '0 
 
 Annual motion of perihelion (east) 11"*8 
 
 Same referred to the ecliptic 1' 01 "'9 
 
 Complete tropical revolution of same in years 20.984 
 
 Obliquity of the ecliptic 23 27' 56"*5 
 
 Annual diminution of same 0" '457 
 
 Nutation (semi-axis major) 9"*4 
 
 Precession (annual) ; luni-solar 50"'4 
 
 Precession in longitude 50'' '1 
 
 Complete revolution of vernal equinox in years 25,868 
 
 Lunar nutation in longitude 17"*579 
 
 Solar nutation in longitude , . . 1"*137 
 
 Eccentricity of orbit (semi-axis major 1) 0*01678356 
 
 Annual decrease 0*0000004163 
 
 Daily acceleration of sidereal over mean solar time 3' 55 "'91 
 
 From vernal equinox to summer solstice 92d 21h 50m 
 
 From summer solstice to autumnal equinox 93d 13h 44m 
 
 From autumnal equinox to winter solstice 89d 16h 44m 
 
 From winter solstice to vernal equinox 89d Olh 33m 
 
 Mass (sun as 1) 0*0000028173 
 
 Density (water as 1) 5'6747 
 
 Mean diameter in miles 7,916 
 
 Polar diameter in miles 7,898 
 
 Equatorial diameter in miles 7,924 
 
 Centrifugal force at equator 0*00346 
 
 Light arrives from the sun in 8' 13" '3 
 
 Aberration 20 "'25 
 
 ELEMENTS OF THE MOON. EPOCH IST JAN., 1801. 
 
 Mean distance from the earth (earth's radius 1) 60-273433 
 
 Mean sidereal revolution in days 27*321 661 
 
 Mean synodical revolution in days 29 '5305887 
 
 Eccentricity of orbit 0*054908070 
 
 Mean revolution of nodes in days 6793*391080 
 
 Mean revolution of apogee in days 3232*575343 
 
 Mean longitude of node at epoch 13 53' 17"'7 
 
 Mean longitude of perigee 266 10' 07" P 5 
 
 Mean inclination of orbit 5 08' 39"*9? 
 
 Mean longitude of moon at epoch 118 17' 08 "*3 
 
 Mass (earth as 1) 0'011364 
 
 Diameter in miles 2164*6 
 
294 APPENDIX. 
 
 Density (earth as 1) 0'556 
 
 Gravity, or weight of one terrestrial pound 0*16 
 
 Bodies fall in one second, in feet 2*6 
 
 Diameter (earth as 1) 0*264 
 
 Density (water as 1) 3'37 
 
 Inclination of axis 1 30' 10"*8 
 
 Maximum evection 1 20' 29"*9 
 
 Maximum variation 35' 42" -0 
 
 Maximum annual equation 11' 12"*0 
 
 , Maximum horizontal parallax 1 01' 24"'0 
 
 Mean horizontal parallax 57' 00"*9 
 
 Minimum horizontal parallax 63' 48"*0 
 
 Maximum apparent diameter 33' 31 "'1 
 
 Mean apparent diameter 31' 07"*0 
 
 Minimum apparent diameter 29' 21"*9 
 
 ELEMENTS OF MARS FOR THE IST JAN., 1840 
 
 Mean distance from the sun in miles 145,750,000 
 
 Same (ekrth's distance as 1) 1-523691 
 
 Greatest distance, same unit 1'6657795 
 
 Least distance, same unit 1-3816025 
 
 Eccentricity (semi-axis major as 1) '0932528 
 
 Annual variation of same (increase) -0000090176 
 
 Sidereal revolution in days 686*9794561 
 
 Synodical revolution in days 779*836 
 
 Longitude of the perihelion 333 6' 38 "'4 
 
 Annual variation of same (increase) 15"'46 
 
 Longitude of the ascending node 48 16' 18 "'0 
 
 Annual variation of same (decrease) 25""22 
 
 Inclination of orbit to the ecliptic 1 51' 5" '7 
 
 Annual variation of same (decrease) 0" '01 
 
 Iklean daily motion in orbit 31' 26"'7 
 
 Time of rotation on axis 24h 37m 22a 
 
 Inclination of axis to the ecliptic 59 41' 49" 
 
 Apparent diameter 5"*8 
 
 Diameter in miles 4,070 
 
 Diameter (earth's being 1) 0*519 
 
 Volume (earth's being 1) 0*1364 
 
 Mass or weight (earth's being 1) 0*134 
 
 Density (earth's being 1) , 0*948 
 
 Light received at perihelion (earth's being 1) 0*524 
 
 Same at aphelion (earth's being 1) 0'360 
 
 Weight of a terrestrial pound, or gravity 0*49 
 
 Space fallen through in one second of time, in feet 7*9 
 
APPENDIX. 
 
 295 
 
 111 
 
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APPENDIX. 297 
 
 ELEMENTS OF JUPITEE FOE THE IST JAN., 1840. 
 
 Mean distance from the sun in miles 494,256,000 
 
 Same (earth's distance as 1) 5'202767 
 
 Greatest distance, same unit , 5 '453663 
 
 Xieast distance, same unit 4'951871 
 
 Eccentricity (semi-axis major as 1) '0482235 
 
 Annual variation of same (increase) "000001593 
 
 Sidereal revolution in days 4332*5848032 
 
 Synodical revolution in days 398*867 
 
 Longitude of the perihelion 11 45' 32"'8 
 
 Annual variation of same (increase) 6" '65 
 
 Longitude of the ascending node 98 48' 37 "'8 
 
 Annual variation of same (decrease) 15" '90 
 
 Inclination of orbit to the ecliptic 1 18' 42 "'4 
 
 Annual variation of same (decrease) 0"'23 
 
 Mean daily motion in orbit 4' 59"'3 
 
 Time of rotation on axis 9h 55m 26s 
 
 Inclination of axis to the ecliptic 86 54' 30" 
 
 Apparent diameter 38" '4 
 
 Diameter in miles 92,164 
 
 Diameter (earth's being 1) 11 '225 
 
 Volume (earth's being 1) 1491 
 
 Mass or weight (earth's being 1) 342'738 
 
 Density (earth's being 1) 0'238 
 
 Light received at perihelion (earth's being 1) '0408 
 
 Same at aphelion (earth's being 1) "0336 
 
 Weight of a terrestrial pound, or gravity 2 '45 
 
 Space fallen through in one second of time, in feet 39'4 
 
 ELEMENTS OF JUPITER'S SATELLITES. 
 
 No. 1. No ECCENTRICITY. 
 
 Sidereal revolution in days Id 18h 27m 33'506s 
 
 Mean distance (Jupiter's radius 1) 6'04853 
 
 Inclination of orbit to a fixed plane 00' 00" '0 
 
 Inclination of this plane to Jupiter's equator .... 00' 06"'0 
 Mass, that of Jupiter being 1,000,000,000 17328 
 
 NO. 2. No ECCENTEICITY. 
 
 Sidereal revolution in days. 3d 13h 14m 36'393s 
 
 Mean distance (Jupiter's radius 1) 9 '62347 
 
 Inclination of orbit to a fixed plane 27' 50" 
 
 Inclination of this plane to Jupiter's equator 01' 05" 
 
 Eetrograde revolution of nodes on fixed plane in years 29'9142 
 
 Mass, Jupiter's being 1,000,000,000 25235 
 
 No. 3. ECCENTRICITY SMALL. 
 
 Sidereal revolution in days 7d 03h 42m 33'362s 
 
 Mean distance (Jupiter's radius 1) 15'35024 
 
 Inclination of orbit to a fixed plane 12' 20" 
 
298 APPENDIX. 
 
 Inclination of this plane to Jupiter's equator 05' 02* 
 
 Retrograde revolution of nodes on fixed plane in years 141 '7390 
 No. 4. ECCENTRICITY SMALL. 
 
 Sidereal revolution in days 16d 16h 31m 49'702a 
 
 Mean distance (Jupiter's radius being 1) 26*99835 
 
 Inclination of orbit to a fixed plane 14' 58" 
 
 Inclination of this plane to Jupiter's equator 24' 04" 
 
 Retrograde revolution of node on fixed plane in years 531,000 
 
 ELEMENTS OF SATURN FOR THE 1ST JAN., 1840. 
 
 Mean distance from the sun in miles 906,205,000 
 
 Same (earth's distance as 1) 9'53S850 
 
 Greatest distance, same unit 10'073278 
 
 Least distance, same unit 9'004422 
 
 Eccentricity (semi-axis major as 1) '0560265 
 
 Annualvanation of same (decrease) 0*000003124 
 
 Sidereal revolution in days 10759*2197 106 
 
 Synodical revolution in days 378*090 
 
 Longitude of the perihelion 89 54' 41"'2 
 
 Annual variation of same (increase) 19 "'31 
 
 Longitude of the ascending node 112 16' 34 "'2 
 
 Annual variation of same (decrease) 19"'54 
 
 Inclination of orbit to the ecliptic 2 29' 29" '9 
 
 Annual variation of same (decrease) 0" '15 
 
 Mean daily motion in orbit 2' 0"'6 
 
 Time of rotation on axis lOh 29m 17s 
 
 Inclination of axis to the ecliptic 61 49' 
 
 Apparent diameter 17" '1 
 
 Diameter in miles 75,070 
 
 Diameter (earth's being 1) 9'022 
 
 Volume (earth's being 1) 772'0 
 
 Mass or weight (earth's being 1) 102*682 
 
 Density (earth's being 1) 0'138 
 
 Light received at perihelion (earth's being 1) '0123 
 
 Same at aphelion (earth's being 1) '0099 
 
 Weight of a terrestrial pound, or gravity 1-09 
 
 Space fallen through in one second of time, in feet 17 '6 
 
 ELEMENTS OF SATURN'S SATELLITES. 
 
 No. 1. MIMAS. 
 
 Sidereal revolution in days Od 22h 37m 27'9a 
 
 Mean distance (Saturn's radius 1) 3'3607 
 
 Epoch 1790-0 
 
 Mean longitude at epoch 256 58' 48" 
 
 Eccentricity and Peri-Saturnium Unknown 
 
 No. 2. ENCELADUS. 
 
 Sidereal revolution in days Id 08h 53m 06 7a 
 
 Mean distance (Saturn's radius 1) 4'3125 
 
APPENDIX. 299 
 
 Epoch 1836-0 
 
 Mean longitude at epoch 67 41' 36" 
 
 Eccentricity and Peri-Saturrium , Unknown 
 
 No. 3. TETHTS. 
 
 Sidereal revolution in days Id 21h 18m 25'7e 
 
 Mean distance (Saturn's radius 1) 5*3396 
 
 Epoch 1836-C- 
 
 Mean longitude at epoch 313 43' 48" 
 
 Eccentricity and Peri-Saturnium Uncertain 
 
 No. 4. DIONE. 
 
 Sidereal revolution in days 2d 17h 41m 08'9s 
 
 Mean distance (Saturn's radius 1) 6'8398 
 
 Epoch 1836-0 
 
 Mean longitude at epoch 327 40' 48" 
 
 Eccentricity and Peri-Saturnium Uncertain 
 
 No. 5. RHEA. 
 
 Sidereal revolution in days 4d 12h 25m 10'8s 
 
 Mean distance (Saturn's radius 1) 9 '55 28 
 
 Epoch 1836-0 
 
 Longitude at epoch 353 44' 00" 
 
 Eccentricity and Peri-Saturnium Uncertain 
 
 No. 6. TITAN. 
 
 Sidereal revolution 15d 22h 41m 25 '2s 
 
 Mean distance (Saturn's radius 1) 22-1450 
 
 Epoch 1830-0 
 
 Mean longitude at epoch 187 21' 24" 
 
 Eccentricity 0-02934 
 
 Longitude of Peri-Saturnium 256 38' 11" 
 
 No. 7. HYPEEION. 
 
 Sidereal revolution 21d 07h 07m 40'8s 
 
 Mean distance (Saturn's radius 1) 267834 
 
 Other elements unknown. 
 
 Discovered (Sept. 19, 1848) by Bond of Cambridge, 
 and by Lassell of Liverpool. 
 
 No. 8. JAPETUS. 
 
 Sidereal revolution 79d 7h 53m 40'4s 
 
 Mean distance (Saturn's radius 1) 64*3590 
 
 Epoch 1790-0 
 
 Mean longitude at epoch 269 37' 48" 
 
 Eccentricity and Peri-Saturnium Unknown 
 
 ELEMENTS OF URANUS FOR THE IST JAN., 1840. 
 
 Mean distance from the sun in miles 1,822,328,000 
 
 Same (earth's distance as 1) 19-18239 
 
 Greatest distance, same unit 20*07630 
 
 Least distance, same unit 18-28848 
 
 Eccentricity (semi-axis major as 1) -0466006 
 
 Annual variation of same Unknown 
 
 Sidereal revolution in days 30686'8205556 
 
300 APPEND!^ 
 
 Synodical revolution in days 369*656 
 
 Longitude of the penhelion 168 5' 24" 
 
 Annual variation of same (increase) 2 "'28 
 
 Longitude of the ascending node 73 8' 47"'8 
 
 Annual variation of same (decrease) 36" '05 
 
 Inclination of orbit to the ecliptic 46' 29 "'2 
 
 Annual variation of same (increase) 0" '03 
 
 Mean daily motion in orbit 42"'4 
 
 Time of rotation on axis Unknown 
 
 Inclination of axis to the ecliptic Unknown 
 
 Apparent dmmeter 4" *1 
 
 Diameter in miles 36,216 
 
 Diameter (earth's being 1) 4'344 
 
 Volume (earth's being 1) 86'5 
 
 Mass or weight (earth's being 1) 17'551 
 
 Density (earth's being 1) 0'180 
 
 Light received at perihelion (earth's being 1) '0027 
 
 Same at aphelion (earth's being 1) '0025 
 
 Weight of a terrestrial pound, or gravity 0'76 
 
 Space fallen through in one second of time, in feet 12'3 
 
 ELEMENTS OF URANUS' SATELLITES. 
 
 No. 1. ARIEL. 
 
 Sidereal revolution in days 2d 12h 29m 20 '66s 
 
 Mean distance 7'40 
 
 No. 2. UMBRIEL. 
 
 Sidereal revolution in days 4d 3h 28m 8'OOs 
 
 Mean distance 10'31 
 
 No. 3. TITANIA. 
 
 Sidereal revolution in days 8d 16h 56m 31 '30s 
 
 Mean distance 16'92 
 
 No. 4. OBERON. 
 
 Sidereal revolution in days 13d llh 7m 12 -6s 
 
 Mean distance 22'56 
 
 ELEMENTS OF NEPTUNE FOR THE 1ST JAN., 1854. 
 
 Mean distance from the sun in miles 2,853,420,000 
 
 Same (earth's distance as 1) 30'03627 
 
 Greatest distance, same unit 30-29816 
 
 Least distance, same unit 29'77438 
 
 Eccentricity (semi-axis major as 1) '00.87193 
 
 Annual variation of same Unknown 
 
 Sidereal revolution in days 60126722 
 
 Synodical revolution in days 367 '488 
 
 Longitude of the perihelion 47 17' 58" 
 
 Annual variation of same Unknown 
 
 Longitude of the ascending node 130 10' 12"'3 
 
 Annual variation of same Unknown 
 
APPENDIX. 301 
 
 Inclination of orbit to the ecliptic 1 46' 59" -0 
 
 Annual variation of same Unknown 
 
 Mean daily motion in orbit 21"'6 
 
 Time of rotation on axis Unknown 
 
 Inclination of axis to the ecliptic Unknown 
 
 Apparent diameter 2"'4 
 
 Diameter in miles 33,610 
 
 Diameter (earth's being 1) 4'719 
 
 Volume (earth's being 1) 76'6 
 
 Mass or weight (earth's being 1) 19'145 
 
 Density (earth's being ]) 0'222 
 
 Light received at perihelion (earth's being 1) -0011 
 
 Same at aphelion (earth's being 1) '0011 
 
 Weight of a terrestrial pound or gravity 1'36 
 
 Space fallen through in one second of time, in feet 21*8 
 
 ELEMENTS OF NEPTUNE'S SATELLITES. 
 No. 1. 
 
 Sidereal revolution 5d 21h 2m 43s 
 
 Longitude of the ascending node 175 40' 
 
 Longitude of perihelion 177 30' 
 
 Inclination to ecliptic , 151 0' 
 
 Eccentricity 0'10597 
 
 ELEMENTS OF PERIODICAL COMETS. 
 
 H ALLEY'S COMET, 1835, Nov. 15. 
 
 Time of perihelion passage 22h 41m 22s 
 
 Longitude of perihelion .'.... . . 304 81' 32" 
 
 Longitude of the ascending node 55 9' 59" 
 
 Inclination to the ecliptic 17 45' 5" 
 
 The semi-axis 17*98796 
 
 Eccentricity 0'967391 
 
 Period in days 27,865d'74 
 
 Retrograde 
 
 ENCKE'S COMET, 1845, AUG. 9. 
 
 Time of perihelion passage 15h llm 11s 
 
 Longitude of perihelion 157 44' 21" 
 
 Longitude of the ascending node 334 19' 33" 
 
 Inclination to the ecliptic 13 7' 34" 
 
 The semi-axis * 2-21640 
 
 Eccentricity ; 0'847436 
 
 Period in days l,205d'23 
 
 Direct 
 
 BIELA'S COMET, 1846, FEB. 11.* 
 
 Time of perihelion passage Oh 2m 50s 
 
 Longitude of perihelion 109 5' 47" 
 
 Longitude of the ascending node 245 56' 58" 
 
 * This comet, which was observed double in 1846, was still divided at its return in 
 1852. 
 
302 APPENDIX, 
 
 Inclination to the ecliptic 12 34' 14* 
 
 The serai-axis 3'50182 
 
 Eccentricity 0'755471 
 
 Period in days 2,393d'52 
 
 Direct 
 
 FATE'S COMET, 1843, OCT. 17. 
 
 Time of perihelion passage 3h 42m 16s 
 
 Longitude of perihelion 49 34' 19" 
 
 Longitude of the ascending node 209 29' 19" 
 
 Inclination to the ecliptic 11 22' 31" 
 
 The semi- axis 3'81179 
 
 Eccentricity 0*555962 
 
 Period in days 2,7l8d'26 
 
 Direct 
 
 DB Vice's COMET, 1844, SEPT. 2. 
 
 Time of perihelion passage llh 36m 53s 
 
 Longitude of perihelion 342 31' 15" 
 
 Longitude of the ascending node 63 49' 31" 
 
 Inclination to the ecliptic. 2 54' 45" 
 
 The semi-axis 3'09946 
 
 Eccentricity 0'617256 
 
 Period in days l,93d'09 
 
 Direct 
 
 BRORSEN'S COMET, 1846, FEB. 25. 
 
 Time of perihelion passage 9h 13m 35a 
 
 Longitude of perihelion 116 28' 34" 
 
 Longitude of the ascending node 102 39' 36" 
 
 Unclination to the ecliptic 30 55' 7" 
 
 The semi-axis 3'15021 
 
 Eccentricity 0'793629 
 
 Periodindays 2,042d'24 
 
 Direct 
 
A SHORT GLOSSAEY OF WOEDS USED, BUT NOT FULLY 
 EXPLAINED IN THE BODY OF THE WORK. 
 
 ANOMALISTIC. Referring to the unequal motion of a planet in au 
 elliptic orbit ; so that, in the course of a year, the planet has not 
 only to move from apogee to the same point again, but also to move 
 on about 11" besides, owing to the progressive motion of the apogee. 
 
 AZIMUTHAL. Referring to the deviation of a transit-instrument from 
 the plane of the meridian. 
 
 COMPLEMENT. That which sunvlies what is wanting. 
 
 COMPONENT. In Mechanics, a force acting in unison with another 
 force, to make up a whole, or integral force. 
 
 DIAPHRAGM. A screen to intercept a part of the rays from any body. 
 
 DYNAMICAL. In Mechanics, relating to the action of forces. 
 
 ELIMINATION. Simplification, by getting rid of superfluous quantities. 
 
 EQUATION. The exhibition of one or more terms, making a certain 
 quantity, as being of the same value as one or more other terms. 
 
 EVECTION. A perturbation of the Moon in the line of the radius- 
 vector, owing to the irregularity of motion of the perigee, and to 
 the alternate increase and decrease ot the eccentricity. 
 
 FACUL.E. Peculiarly bright spots on the surface of the sun, or other 
 heavenly body. 
 
 FioccuLENT. Having the appearance of wool. 
 
 HELIACAL. Near to the sun at its rising or setting. 
 
 HYPOTHESIS. A supposition. 
 
 INFINITESIMAL ANALYSIS. A mathematical method for examining the 
 continuous changes of a quantity for very small increments or decre- 
 ments. 
 
 LENTICULAR. Doubly convex ; in the nature of a lens. 
 
 LINE OF COLLIMATION. The line joining the centres of the eye-glass 
 and object-glass of a telescope. 
 
 LUNATION. The time from new moon to new moon again. 
 
 NORMAL. Elementary ; such as to serve for a rule or pattern. It is 
 generally used in philosophical language to signify a line drawn 
 perpendicularly to the surface of a body. 
 
304 GLOSSARY. 
 
 PARALLAX. An apparent change of place in a heavenly body, owing 
 
 to the observer altering his position. 
 PENUMBRA. A partial shadow, resulting from the diminished light of 
 
 the sun to the earth or moon, during a solar or lunar eclipse,. 
 
 appearing as partial. 
 
 PHENOMENA. Appearances, varying from the common course of things. 
 PHOTOSPHERE. A globe of light. 
 
 PRIMORDIAL. Eelating to the first beginnings of things. 
 RADIUS- VECTOR. A line drawn from the sun to any one of the planets. 
 SYNODICAL. Coming together ; referring to the conjunctions of heavenly 
 
 bodies. 
 
 THE CfD. 
 
 Woodfall & Kinder, Printers, 70 to 76, Long Acre, London, W.Q, 
 
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