| LI BRARY OF CONGRESS. V I *Lf. QB45 \\ $ / 'UNITED STATES OF AMKHICA.! m 1. Great Cluster of Stars in Hercules. 2. Whirlpool Nebula of Lord Rosse. SHELL'S OLMSTED'S SCHOOL ASTRONOMY. COMPENDIUM OF ASTEONOMT: gJbajjfeb to % $se of SCHOOLS AND ACADEMIES. BY DENISON* OLMSTED, LL.D., LATE PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE. KEVISED BY E, S. SNELL, LL.D., PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY IN AMHERST COLLEGE. C NEW YOEK : COLLINS & BBOTHEB, No. 106 LEONARD STREET. 1868. V Entered, according to Act of Congress, in the year 1S67, by JULIA M. OLMSTED, FOE THE CHILDREN OF DENISON OLMSTED, DECEASED, In the Clerk's Office of the District Court of the United States for the District of Connecticut. Electrotyped by Smith & McDougal, 82 and 84 Beekman St., N. Y. O" PEEFACB I have endeavored, in the present volume, to per- form a work for Professor Olmsted's School Astron- omy, similar to that which I performed a few years since for his School Philosophy. Besides bringing the science more fully down to the present time, I have made it my special aim to present the facts and principles of the subject in clear language, and in few words, believing such a style most profitable to the pupil and most satisfactory to the teacher. It is believed that a decided improvement will be found in the engravings. Those which in former editions were erroneous have given place to more correct ones, taken from the revised College As- tronomy, and a large proportion of the remain- der have been changed in their style, and newly drawn and engraved expressly for this edition. E. S. SNELL. Amherst College, October, 1867. CONTENTS CHAPTER I. GENERAL FORM AND DIMENSION'S OF THE EARTH — THE DIURNAL MOTION — ARTIFICIAL GLOBES. PAGE Astronomy 13 Form of the earth 14 Proofs that it is globular 14 The words up and down 15 Size of the earth 16 Inequalities of surface 16 The diurnal rotation IT The equator of the earth 17 Meridians ._ 17 Latitude and longitude 17 The terrestrial sphere 18 The celestial sphere 18 The horizon 18 The vertical circles 19 Altitude and azimuth 19 Celestial equator 19 PAGE The ecliptic 21 Equinoxes 21 Solstices 21 The colures 21 Signs of the ecliptic 22 Right ascension and declination 22 Celestial longitude and latitude 22 Apparent daily motion of the heavens 23 Rising, setting, culmination 23 Diurnal circles and horizon 24 The right sphere 25 The parallel sphere 26 The oblique sphere 26 Artificial globes 27 Problems on the terrestrial globe 29 Problems on the celestial globe 30 CHAPTER II. PARALLAX — ATMOSPHERIC REFRACTION TWILIGHT. Parallax 38 Diurnal parallax 33 Greatest at the horizon 35 Diminishes as distance increases 35 Horizontal parallax 35 Parallax of the moon 35 Atmospheric refraction 35 Its effect on rising and setting 36 Distortion of the sun's disk 37 Illumination of the sky 37 Twilight 38 Duration of twilight 39 CHAPTER IH. ASTRONOMICAL INSTRUMENTS — THE EARTH S MOTION ABOUT THE SUN — THE SEASONS FORM OF THE EARTH'S ORBIT. The equatorial telescope 40 The transit instrument 40 The astronomical clock 42 Sidereal time .- 42 To find right ascension 42 To find declination 42 The mural circle 43 The altitude and azimuth instru- ment 43 The sextant 44 Observations of the sun's place 45 The ecliptic and zodiac 46 Vlll CONTENTS PAGE The tropics and polar circles 46 Terrestrial zones 47 The annual motion observed without instruments 4S A motion of the earth, not the sun.. . 48 Cause of the change of seasons 49 Causes of heat in summer and of cold in winter 51 PAGE Time of greatest heat and greatest cold 52 Effect of no obliquity on seasons 52 Obliquity of 90° 53 To find the form of the earth's orbit. . 53 Perihelion, aphelion, etc 54 Line of apsides 55 Effect of sun's distance on the sea- sons 55 CHAPTER IV. SIDEREAL TIME — MEAN AND APPARENT SOLAR TIME THE CALENDAR. The sidereal day 57 The mean solar day 57 The apparent solar day 53 Causes of unequal solar days 58 The equation of time 59 Civil and astronomical timer 59 The Julian calendar 60 The Gregorian calendar 60 Days of the month and of the week... . 61 CHAPTER V. OBLATE FORM OF THE EARTH ITS MASS AND DENSITY PROOFS OF ITS ROTATION ON AN AXIS. Central forces 63 Illustrations 63 Loss of weight on the earth 64 Loss from a second cause 64 Oblate form of the earth 64 Equatorial belt 65 Weight and density of the earth. ..... 67 Proofs of the earth's rotation 67 CHAPTER VI. THE SUN — SOLAR SPOTS — CONDITION OF THE SUN'S SUR- FACE — THE ZODIACAL LIGHT. The form of the sun 69 The sun's distance and size 69 The sun's mass and strength of gravity 70 Diurnal rotation of the sun 70 Its apparent time 71 Its real time 71 Appearance of solar spots 71 Their motions and changes 72 Their nature 73 Herschel's theory 73 The zodiacal light 73 CHAPTER VII. GRAVITATION — KEPLER S LAWS MOTION IN AN ELLIPTICAL ORBIT — PRECESSION OF THE EQUINOXES. Gravitation . . : 75 First law of gravitation 75 Second law 76 Kepler's laws 76 The first law 76 The second law 77 The third law 78 Paths of projectiles 7S Effect of increased velocity 78 Why a planet returns from aphelion . . 79 Why a planet departs from aphelion.. 80 Precession of equinoxes 81 Signs of ecliptic displaced 81 Motion of the poles 82 Cause of precession 82 The tropical year 83 The sidereal year 83 C ONTENTS. IX CHAPTER VIII. THE MOON ITS EEVOLUTIONS — ITS PHASES THE CONDITION OF ITS SUEFACE. PAGE Distance and size of the moon 84 Eevolution about the earth 84 Months 85 Nodes t 85 Conj unction and opposition 85 Quadratures 86 Octants 86 Form of orbit 86 Diurnal motion 86 Libration of longitude 87 Libration of latitude 87 Diurnal libration 87 Eevolution round the sun 88 Phases of the moon 88 PAGE Moon running high or low 90 The harvest moon 90 Inequalities of moon's surface 91 Form of valleys 92 Volcanic appearance 92 Height of its mountains 93 No atmosphere or vapor 93 Changes of temperature on the moon. 94 View of the earth from the moon 94 As to magnitude 94 As to phase 94 As to position in the sky 95 As to surface 95 CHAPTER IX. ECLIPSES OF THE MOON AND SUN. General relations in eclipses 97 Eclipse months 98 Eclipse of the moon 99 Forms of shadows 99 Duration of eclipse 100 Appearance of moon 100 Eclipse of the sun 100 Total shadow and penumbra of the moon 101 Total and partial eclipses of the sun . 101 Annular eclipse 103 Velocity of the shadow 103 Eelative number of solar and lunar eclipses 103 Eclipses at the moon 104 True form of shadows 104 CHAPTER X. LONGITUDE — TIDES. Local time 105 Connection between longitude and local time 105 Longitude by the chronometer 106 Longitude by a lunar eclipse 106 By eclipses of Jupiter's satellites 106 By a solar eclipse 107 By occupations of stars 107 By the lunar method 107 By the magnetic telegraph 108 Change of days in going round the earth 109 Ambiguity as to days among the islands of the Pacific . >. 109 Tides, high and low water 110 Spring and neap tides Ill Opposite tides Ill Form of the water acted on by the moon Ill Direct and opposite tides 112 Tides by the sun 112 Joint action of sun and moon 113 Effect of inertia of water 113 Diurnal inequality 114 Effects of coasts 115 Cotidal lines 116 Tides in lakes 118 CONTENTS. CHAPTER XL THE PLANETS — TABULAR STATEMENTS — MERCURY — VENUS — MARS. PAGE Planetary bodies classified 119 Three groups 119 Inferior planets 120 Superior planets 120 Satellites 120 Table of distances 121 Table of revolutions 121 Table of magnitudes 122 Table of masses 122 Sun and planets compared 123 Diameters and distances compared. . 123 Direction of motions 123 Mercury — apparent motions 124 Modified by the earth's motions 125 Stationary points 127 PAGE Form and position of Mercury's orbit 127 Phases of Mercury 127 Point of greatest brightness 128 Transits of Mercury 12S Venus— its apparent motions 129 The phases and brightness of Venus. 129 Transits of Venus 129 Use made of them 130 Mars— its situation in the System... 130 Apparent motions 130 Phases and changes of apparent size. 132 Appearance of disk 132 Orbit and equator of Mars 133 Days on the small planets , 133 CHAPTER XII. THE PLANETOIDS JUPITER SATURN URANUS NEPTUNE DISTURBANCES OF THE PLANETS. Space between Mars and Jupiter 134 The planetoids 134 When discovered — number 134 Characteristics 134 Jupiter — its magnitude 136 Its place in the System 136 Its form and orbit 136 Belts of Jupiter 137 Satellites of Jupiter 138 Eclipses of Jupiter and its satellites. 138 Saturn— its disk 140 Rings of Saturn 140 Disappearance of rings 140 Phenomena of rings at the planet. . . 142 Satellites of Saturn 143 Uranus — discovery 143 Place in the System 143 Satellites of Uranus 144 Neptune — its discovery 144 Motions of the planets disturbed 145 Nodes retrograde . 146 Apsides advance 146 Eccentricity changes 146 Stability preserved 146 CHAPTER XIII. COMETS — SHOOTING STARS. Nucleus, coma, and envelope of a comet 148 Number of comets 148 Eccentricity of orbit 149 Form and direction of tail 149 Dimensions of comets 150 Light of comets 151 Mass of the comets 151 Directions of their motions 152 To find a comet's orbit 152 Comets of known period 153 Halley's comet 153 Remarkable comets 15*3 Comet of 1680 153 Of 1744 153 Of 1770 154 Of 1843 154 Of 1858 154 Of 1861 154 Shooting stars 155 Gaseous meteors 155 Solid meteors 156 Aerolites 156 CONTENTS XI CHAPTER XIV. THE FIXED STARS— CONSTELLATIONS. PAGE The stellar universe 158 The fixed stars and their magnitudes 158 Number included in the several mag- nitudes 159 Cause of unequal brightness 159 Constellations 160 Star catalogues 161 Descriptions of constellations 161 Constellations of the Zodiac described 161 Aries — Taurus — Gemini — Cancer — Leo— Virgo— Libra 161-165 Scorpio — Sagittarius 165 Capricorn us— Aquarius— Pisces 166 Constellations north of the Zodiac. . . 168 Ursa Minor — Ursa Major 168 Draco — Cepheus — Cassiopeia — Cam- elopardalus 168-171 PAGE Andromeda — Perseus 1T2 Auriga — Leo Minor — Canes Venatici — Coma Berenices— Bootes 173 Corona Borealis — Hercules — Lyra. . . 174 Cygnus — Vulpecula 175 Aquila — Antinous 176 Delphinus— Pegasus 176, 177 Ophiuchus 177 Constellations south of the Zodiac. . . 177 Cetus — Orion 177 Lepus — Canis Major — Canis Minor. . 178 Monoceros— Hydra 180 Evening constellations of autumn.. . 181 Of winter 182 Of spring 183 Of summer 183 CHAPTER XV. Effect of telescopic power on fixed stars 185 Annual parallax 185 Distances of the stars 186 Nature of the fixed stars 187 Double stars 188 Two ways of appearing double 188 Binary stars 189 Their periods 190 Dimensions of their orbits 190 Triple and quadruple stars 191 Periodic and temporary stars 191 Clusters of stars 192 Nebulae 192 Several forms 193 The galaxy. 193 COMPENDIUM OF ASTRONOMY, CHAPTEE I. GENEEAL FOEM AND DIMENSIONS OF THE EAETH — THE DIUENAL MOTION — AETTFICIAL GLOBES. 1, General Definitions. — Astronomy is the science which treats of the heavenly bodies ; that is, of the sun, the planets and their satellites, the comets, and the fixed stars. The sun, planets, satellites and comets constitute the Solar System, which is so called because the sun is the principal body belonging to it, and controls the movements of all the others. The Fixed Stars are at an immense distance out- side of the solar system ; and each fixed star is sup- posed to be the sun of a separate system. Nearly all the bright points seen in the sky in a clear night are fixed stars, the whole number of which has never yet been counted. 1. Define astronomy. What is the solar system ? What bodies are outside of the' solar system? 14 THE EARTH. 2. The Globular Form of the Earth, — The earth on which we live is one of the planets of the solar system. Its form, like that of all the other planets, is almost perfectly spherical. This is learned in sev- eral ways. 1. When the sun casts the shadow of the earth on the moon in a lunar eclipse, the edge of the shadow is always circular. 2. The earth shows its globular form by concealing the lower parts of objects when seen at a distance. Fig. 1. Thus, a person at A (Fig. 1) can see only the top of the mast of a ship, because the earth conceals all tne lower parts. If the surface of the ocean were perfectly flat, as in Fig. 2, then the whole ship could be seen, the lower part as well the upper, at any distance. 2. To what class of bodies does the earth belong ? Mention the first proof that it is spherical— the second — the third. WORDS "up" and "down." 15 Fig. 2. 3. The measurements made on various parts of the earth lead to the conclusion that the distance from the surface to the center is everywhere about the same. 3, Use of the words "up" and "dotvn." — "Wher- ever a person stands, up means from the earth, toward the highest point of the sky, and down means toward the center of the earth. Now, as the earth is a globe, the word up must express different directions in different places, though to us it always seems to be the same ; and so of the word dotvn, For example, the person at A (Fig. 3), sees the point E directly over his head, and calls that direction up; while at B, up is toward F, although directed 90° from AE. At 0, wp is toward G, precisely opposite to what it is at A. 3. Explain the meaning of up, and of dovm. How can up be in different directions ? 16 THE EAETH Fig. 3. In like manner, down, which is everywhere toward the center, is in all possible directions from the different places on the earth. 4, Size of the Earth. — If a person sails away from land till the ocean just conceals the whole height of a certain mountain, then, by means of its height and his distance from it, the Size of the earth can be easily calculated. For it is plain that the larger a globe is, the more nearly flat is its surface, and the farther off can the mountain be seen. In this and in other ways it is found that the diameter of the earth is 7,912 miles. Therefore the distance from the sur- face of the earth to its center is 3,956 miles, and the circumference is 24,857 miles. &. Inequalities of Surface. — As the surface of the earth is very uneven, and there are high mountains 4. How can the size of the earth be found ? ter ? its radius ? its circumference ? What is its diame- EQUATOR AND ITS SECONDARIES. 17 and deep valleys on many parts of it, it seems, at first, as though it could not have the regular form of a sphere. But we call an orange round, though it is covered with roughnesses ; and the mountains of the earth are comparatively a great deal smaller than the roughnesses on the outside of an orange. 6. The Diurnal notation. — The earth revolves continually from west to east on an imaginary line drawn through its center. This line is called the Earth's Axis. The ends of the axis are called the North and South Poles of the earth. The time occu- pied by the earth in revolving once round is called a Day ; and this is divided into 24 hours. 7» Tlie Earth's Equator and its Secondaries, — A great circle drawn round the earth, midway between its poles, is called the Equator. Meridians are great circles of the earth drawn through the poles, and therefore perpendicular to the equator. Since all great circles of a sphere which are perpendicular to a given great circle are called its Secondaries, there- fore the meridians are secondaries of the equator. The Latitude of a place is its distance north or south from the equator, measured on the meridian of that place, in degrees, minutes, and seconds. Parallels of latitude are small circles of the earth, parallel to the equator. 5. How can the earth be spherical, when there are high moun- tains and deep valleys upon it ? 6. Describe the earth's rotation. Define its axis — poles — a day. 7. Define the equator and the meridians. What are the secon- daries of a great circle ? Meridians are secondaries of what ? De- fine latitude — longitude. How is a place on the earth determined ? 18 THE EARTH. The Longitude of a place is the distance of its me- ridian, in degrees, minutes, and seconds, east or west from some standard meridian, as that of Greenwich, near London, or that of Washington. The situation of any place on the earth is determined by giving its latitude and longitude. 8. The earth is called the Terrestrial Sphere. The Celestial Sphere is that apparent vault, called the Sky, which surrounds the earth on every side> and to which the heavenly bodies seem to be attached. The -celestial sphere is often called The Heavens. For most purposes of astronomy, the eye of an observer may be considered as the center of the celestial sphere. 0* TJie Horizon and Ms Secondaries. — If the plumb-line (usually called the vertical), at any place on the earth, is supposed to be extended till it reaches the celestial sphere, it marks the Zenith above, and the Nadir below. And a plane passed through the center of the earth, perpendicular to the vertical, is called the Rational Horizon of that place. This is a great circle of the celestial sphere, and divides it into upper and lower hemispheres. The Sensible Hori- zon is parallel to the rational horizon, and passes through the place on the earth's surface. The planes of these two horizons are, therefore, nearly 4,000 miles apart ; but so great is the distance of the heav- 8. Describe the two spheres. What may be taken for the center of the celestial sphere ? 9. Define zenith — nadir. Define the rational horizon — the sensi- ble horizon. Why are they one in the sky ? What are the secon- THE CELESTIAL EQUATOR. 19 enly bodies, that the two planes seem to unite in the same great circle of the celestial sphere. The secondaries of the horizon intersect each other in the vertical line, and are called Vertical Circles. One of them is the meridian of the place. This cuts the horizon in the North and South Points of compass. The vertical circle, at right angles to the meridian, is called the Prime Vertical This cuts the horizon in the points called East and West The Altitude of a heavenly body is its elevation above the horizon, measured on the vertical circle passing through the body. The Zenith Distance of a body is the distance between it and the zenith, and is, therefore, the complement of its altitude. The Azimuth of a heavenly body is an arc of the horizon, measured from the meridian to the vertical circle, which passes through the body. The Ampli- tude is measured from the . vertical circle passing through the body to the prime vertical, and is, there- fore, the complement of the azimuth. The altitude, or zenith distance of a heavenly body, along with its azimuth or amplitude, determines its place in the vis- ible heavens. « 10, The Celestial Equator and its Secondaries, If the axis on which the earth revolves is produced to the heavens, it becomes the Axis of the Celestial Sphere, and marks the North and South Poles of that sphere. The north pole is at present in the constel- lation of Ursa Minor. If the plane of the equator be extended in like manner, it becomes the Celestial daries of the horizon ? How are the points of compass fixed Define altitude — zenith distance — azimuth — amplitude. 20 THE EAETH Equator. The secondaries to this circle are called meridians, as on the earth. They are also called Hour-circles, because the arcs of the equator inter- cepted between them are used as measures of time. Tii Let n (Fig. 4) represent the north pole of the earth, s its south pole, eq the equator (projected in a straight line), o a given place whose north latitude is eo. Then N, S, are the poles of the celestial sphere, EQ is the celestial equator, Z is the zenith of the place o, E is its nadir, and HO its rational horizon ; oesqn is the terrestrial meridian of the same place, and ZESQN is its celestial meridian, or hour-circle. 10. How are the celestial poles fixed? the celestial equator? What are the hour-circles ? Describe by the figure. THE ECLIPTIC. 21 11. The Ecliptic. — Besides tlie equator, there is' an important circle of the celestial sphere, called the Ecliptic. It is that in which the sun appears to make its annual circuit around the heavens. It is inclined to the equator at an angle of nearly 23J°, crossing it in two opposite points, called the Equinoctial Points, or Equinoxes. The word " equinoxes" is used, also, to express the times at which the sun crosses the equa- tor, because at those times the nights are equal to the days. The vernal equinox is the time when the sun passes the equator from south to north, as it occurs in the spring, about March 21st. The autumnal equi- nox occurs on or near September 22d, when the sun returns to the south of the equator. The Solstitial Points, or Solstices, are those points of the ecliptic which are furthest north or south from the equator, situated, therefore, midway between the equinoxes. They are so named because there the sun stops in his advance northward or southward, and begins to return. The summer solstice is the point ivhere, and also the time w hen, the sun is furthest north, about the 22d of June. He passes the winter solstice on or near the 22d of December. The Equinoctial Colure is that secondary to the equator which passes through the equinoxes. The Solstitial Colure is that which passes through the sol- stices. They are, therefore, at right angles to each other, and the latter is a secondary to the ecliptic, as well as to the equator. 11. Define the ecliptic — the equinoxes — and give their names. Define the solstices. When does the sun pass each of these four points ? Define the two colures. 22 THE EARTH. 12. Signs of the Ecliptic. — The ecliptic is divided into 12 equal parts of 30° each, called Signs, which beginning at the vernal equinox, succeed each other eastward in the following order : NORTHERN SOUTHERN. 1. Aries, . . . . . T 7. Libra, . . . . *== 2. Taurus, . . . . » 8. Scorpio, . . . . *l 3. Gemini, . . H 9. Sagittarius, . , . t 4. Cancer, . . . . 23 10. Capricornus, . . V? 5. Leo, . . . . . a 11. Aquarius, . . . ~ 6. Virgo, . . . . w 12. Pisces, . . . . X The vernal equinox being at the first point of Aries, the summer solstice is at the first of Cancer, the autumnal equinox at the first of Libra, and the winter solstice at the first of Capricorn. 13. Right Ascer&ion and Declination, — The right ascension of a heavenly body is the angular distance of its meridian from the vernal equinox, measured eastward on the equator. The declination of a body is its angular distance north or south from the equa- tor, measured on the meridian of the body. 14L. Celestial Longitude and Latitude* — On the celestial sphere, longitude and latitude are referred to the ecliptic, not to the equator. Suppose a second- ary to the ecliptic to pass through a heavenly body ; the distance of the body from the ecliptic, measured on the secondary, is its latitude ; and the distance of 12. What are signs of the ecliptic ? Name them in order. 13. What is the right ascension of a body ? its declination ? 14. Define celestial longitude and latitude. Which way is longi- tude reckoned ? right ascension ? BISING AND SETTING. 23 this secondary, measured eastward on the ecliptic, is its longitude. Bight ascension and longitude are reckoned only eastward, from 0° to 360°, the first on the equator, the other on the ecliptic. 15» Apparent Diurnal Motion of the Heavens. As the earth revolves from west to east on the axis ns, an observer, not being conscious of this motion, sees the heavenly bodies apparently revolving in the oppo- site direction ; that is, from east to west, about the axis NS. The sun, moon, and every planet, comet and star is observed to pass over from the eastern part of the sky toward the western, with a regular motion, reappearing again in the east, after the lapse of about one day, in the same, or nearly the same place. The fixed stars describe the circles, which are exactly parallel to the equator, and in precisely the same length of time. But the other bodies vary somewhat in their paths, and the periods of describing them, thus showing that they are affected by other motions besides the diurnal rotation. 16* Kising, Setting, and Culmination* — In Fig. 4, AB, DO, FG, &c, drawn parallel to EQ, represent the diurnal circles of stars, viewed edgewise, and, there- fore, appearing as straight lines. Some of these circles intersect the horizon PIO. These intersections are the points of rising or setting. Thus, a star de- 15. Explain the diurnal motion. 16. What are the points of a body's rising and setting ? What are the points of its culmination ? Are both culminations ever in sight ? Are both ever out of sight ? 24: THE EAETH. scribing the circle GF, rises in the northeast quarter, and sets in the northwest, at points which are both represented bj r. The star whose diurnal circle is IK, rises in the southeast, and sets in the southwest, at t. A star on the equator rises exactly in the east, and sets in the west, at the point 0. The points in which these circles cut the meridian are called the points of culmination. Thus, the star on FG makes its upper culmination at F, and its lower one at G. On AB, both the upper and lower culminations are above the horizon; on MP, they are both below. If both culminations of a star are above the horizon, it is always in view ; if both below, it never comes in sight. The number of stars which do not rise and set depends on the position of the celestial poles in relation to the horizon ; that is, on the latitude of the place. By the culmination of a body, in the ordinary use of the word, is meant its upper culmination. 17 • Relations of the Horizon to the Diurnal Circles. Every change of position on the earth changes the horizon. If an observer moves eastward, all the heavenly bodies which rise and set rise earlier, and also culminate and set earlier. If he moves west- ward, they rise, culminate and set later. If he moves toward the nearer pole of the earth, the correspond- ing pole of the celestial sphere becomes more ele- 17. Describe the effect of a person's moving east — west — toward the pole — toward the equator. Show what the elevation of one pole is equal to. Which pole is elevated ? How much is the other .? THE EIGHT SPHERE. 25 vated, and the other more depressed ; and the con- trary, if he moves from the nearer pole ; that is, toward the equator. In all north latitudes, the north pole is elevated, and the south pole depressed ; and the reverse in south latitudes. And the elevation of one pole, and the depression of the other, equals the latitude. For (Fig. 4) NO, the elevation of one pole (= HS, the depression of the other), equals EZ, since each is the complement of ZN. But EZ == eo, the latitude, because they subtend the same angle atC. The elevation of the celestial equator equals the complement of latitude. For EH is the complement of EZ, which equals eo, the latitude. Hence, the angle by which all the circles of diurnal motion are inclined to the plane of the horizon, equals the com- plement of latitude, since they are parallel to the equator. On account of this change of inclination between the horizon and the diurnal circles, the aspect of the diurnal rotation is very different in different parts of the earth. 18* The Might Sphere, — This name is given to those positions in which the diurnal circles cut the horizon at right angles. All points of the equator are so situated. As the latitude is zero, the poles, hav- ing no elevation or depression (Art. 17), are both in the horizon ; the celestial equator passes through the zenith, thus coinciding with the prime vertical ; and all the paths of daily motion, being parallel to the 18/ Describe tlie right sphere. 26 THE EAETH. equator, are perpendicular to the horizon. Every heavenly body, unless situated exactly at one of the poles, rises and sets during each revolution, and con- tinues above the horizon just as long as it remains below it, If a star rises in the east, it sets in the west, and culminates in the zenith and nadir. 19. TJie Parallel Sphere, — This term expresses the appearance of the heavens at those points of the earth where the circles of daily rotation are par- allel to the horizon. This aspect can be presented only at the poles. For, at those points the latitude being 90°, one pole must be elevated 90°; that is, to the zenith, and the other depressed 90°, or to the nadir. Hence, the diurnal circles, being perpendicu- lar to the axis, must be horizontal, and the equator must coincide with the horizon. Every star in view passes around the sky, maintaining the same eleva- tion at every point of its path, and, therefore, never rises or sets. At the north pole, that half the year in which the sun is north of the equator, is uninterrupted day. During the other half, the sun being south of the equator, it is constant night. 20. The Oblique Sphere. — At all latitudes, except 0° and 90°, the circles of daily motion are oblique to the horizon, since they incline at an angle equal to the complement of the latitude. Thus, at 42° north latitude, the celestial equator is elevated 48° above 19. Describe the parallel sphere. 20. Describe the oblique sphere. What bodies are more than half the time above the horizon ? below ? ARTIFICIAL GLOBES. 27 the southern horizon, as represented in Fig. 4 ; and all the diurnal circles, being parallel to the equator, make the same angle (48°) with the horizon. The circle OX), whose distance from the elevated pole equals its elevation, just touches the horizon at the lower culmination, and is the limit of that part of the sky which is always in view. This is called the circle of Perpetual Apparition. The circle HL, at the same distance from the depressed pole, also touches the horizon, and is called the circle of Perpetual Occulta- Hon, since it limits that part of the sky which is always concealed. The horizon HO bisects the equator EQ. Hence, a body on the equator is as long above the horizon as below it, in every part of the earth. But all bodies between the equator and the elevated pole are longer above the horizon than below, while on the opposite side they are longer below than above. 21c Artificial Globes. — They are of two kinds, ter- restrial and celestial. The terrestial globe is a minia- ture representation of the earth, having, also, the equator and several meridians and parallels of lati- tude traced upon it. The celestial globe exhibits the principal fixed stars in their relations to each other, and to the equator and ecliptic. The artificial globe is suspended in a strong brass ring by an axis passing through the north and south poles, on which it is free to revolve. This ring repre- sents the meridian of any place, and is supported 21. Describe the artificial globes. What is the quadrant of alti- tude? State the mode of adjusting the globe for the latitude. 28 THE EAETH. vertically within a horizontal wooden ring which stands upon a tripod. The wooden ring represents the horizon. The brass ring may be slid around in its own plane, so as to elevate or depress either pole to any angle with the horizon. It is graduated from the equator each way to the poles, for measuring lati- tude and declination ; while the horizon ring has near its inner edge two graduated circles, one for azimuth, and the other for amplitude. On this ring, also, for convenient reference, are delineated the signs of the ecliptic, and the sun's place in it for every day of the year. Around the north pole is a small circle, marked with the hours of the day ; and at the same pole a brass index is attached to the meridian, which can be set at any hour of the circle. The Quadrant of Altitude is a flexible strip of brass, graduated into 90 parts, each equal to a degree of the globe. This can be used for measuring angular dis- tances in any direction on the sphere ; and when applied to a vertical circle of the celestial globe, it determines the altitude, or zenith distance of a heav- enly body. To adjust either globe for any place on the earth, elevate the corresponding pole to a height equal to the latitude. By moving the tripod, the axis can then be made parallel to that of the earth or the heavens. And if the globe is turned (the celestial westward, or the terrestrial eastward), the diurnal motion will be truly represented. 22. Tell how to find the latitude and longitude of a place. The latitude and longitude of a place being given, how is it found? PROBLEMS. 29 22* Problems on the Terrestrial Globe* 1. To find tJie Latitude and Longitude of a Place. Turn the globe so as to bring the place to the brass meridian ; then the degree and minute on the merid- ian over the place shows its latitude, and the point of the equator, under the meridian, shows its longitude. Example. What are the latitude and longitude of New York ? 2. To find a Place by its given Latitude and Longitude. Eind the given longitude on the equator, and bring it to the meridian ; then under the meridian, at the given latitude, will be found the required place. Ex. What place is in latitude 39° N., and longitude 77° W. ? 3. To find tlie Bearing and Distance of one Place from another Adjust the globe for one of the places, and bring it to the meridian ; screw the quadrant of altitude directly over the place, and bring its edge to the other place. Then the azimuth will be the bearing of the second place from the first, and the number of degrees beween them, multiplied by 69J, will give their distance apart in miles. Ex. Find the bearing of New Orleans from New York, and the distance between them. How is the bearing of one place from another found? Find the difference of time at different places. When it is 2 P. M. in Paris, what time is it in Boston ? 30 THE EAETH. 4. To find the Difference of Time at Different Places. Bring to the meridian the place which lies west of the other, and set the hour-index at XII. Turn the globe westward, until the other place comes to the meridian, and the index will show the hour at the second place when it is noon at the first. The hour thus found is the difference required. Ex. "When it is noon at New York, what time is it at London ? 5. The Hour being given at any Place, to find ivhat Hour it is at any other Place. Find the difference of time between the two places, as in (4) ; then, if the place whose time is required is east of the other, add this difference to the given time ; but if west, subtract it. Ex. What time is it in Boston, when it is 2 P. M. in Paris ? 23, Problems on the Celestial Globe. 1. To find the Right Ascension and Declination of a Heavenly Body. Bring the place of the body to the meridian ; then the point directly over it shows its declination, and the point of the equator under the meridian, its right ascension. Ex. Find the right ascension and declination of Alpha Lyrse. Also, of the sun on the 3d of May. 23. How are the riglit ascension and declination of a star found ? Describe the manner of adjusting tho globe to represent the heav- PROBLEMS. 31 2. To Represent the Appearance of the Heavens at any Time. Adjust the globe for the place (Art. 21). On the wooden horizon find the day of the month, and against it is given the sun's place in the ecliptic. On the ecliptic find the same sign and degree, and bring the point to the meridian. The globe then presents the positions of the stars at noon. Set the hour- index at XII, and turn the globe till the index points to the required hour. The aspect of the heavens at that hour is then represented. Ex. Kequired the aspect of the stars at Lat. 51°, December 5th, at 10 P. M. 3. To find the Time of the Rising and Setting of any Heavenly Body at a given Blace. Having adjusted for the latitude, bring the sun's place in the ecliptic to the meridian, and set the index at XII. Turn the globe eastward, and then westward, till the given body meets the horizon, and the index will show the times of rising and setting. The times of the sun's rising and setting may be found in the same manner on the terrestrial globe, since the ecliptic is usually represented on it. Ex. At what time does the sun rise and set on the 4th of July? Eind the time of the rising and setting of Arcturus on the 10th of November. ens at a given time. How are the times of rising and setting of a body found ? How are the altitude and azimuth of a body found ? The distance between two stars ? Find the height of the sun at noon, August 1st, Lat. 28° 30' N. 32 THE EARTH. 4. To find the Altitude and Azimuth of a Star for a given Latitude and Time. Adjust the globe for the aspect of the heavens (2) ; screw the quadrant of altitude to the zenith, and direct it through the place of the star ; then, the arc between the star and the horizon is the altitude, and the arc of the horizon between the quadrant of alti- tude and the meridian is the azimuth. Ex. Find the altitude and azimuth of Sirius, De- cember 25th, at 9 p. m. Lat. 43°. 5. To find the Angular Distance between two Stars. Lay the quadrant of altitude across the two stars, so that the zero shall fall on one of them ; then, the degree at the other will show their distance from each other. Ex. Find the distance between Arcturus and Alpha Lyrae. 6. To find the Suns Meridian Altitude for a given Lati- tude and Day. Find the sun's place, and bring it to the meridian. The degree over it will show its declination. If the declination and latitude are both north or south, add the declination to the co-latitude ; if not, subtract it. Ex. Find the sun's meridian altitude at noon, Aug. 1st, Lat. 38° 30' K CHAPTEE II. PARALLAX — ATMOSPHERIC REFRACTION — TWILIGHT. 24. Parallax Defined. — When a person changes his place, objects about him in general appear in dif- ferent directions from him. This change of direction is called Parallax. If, for example, he moves north, an object which was directly ivest of him is moved by parallax towards the soidhivest ; and an object which was east now appears in the southeast quarter. The direction of every thing is more or less altered, except those objects which are directly before, or directly behind him. It is easily perceived, also, that objects which are near change their direction very rapidly ; while distant things change slowly, or even appear to remain at rest, unless the person moves a great way. The par- allax of a body may, therefore, be used to enable us to find out how far off it is. 25. Diurnal Parallax. — While a person travels over the earth, or is carried about it by the diurnal rotation, the heavenly bodies must in the same way suffer some change of direction. 24. Define parallax. Illustrate it. Compare near and distant objects. 34 THE EARTH. By the true place of a heavenly body is meant that which it would seem to occupy if viewed from the center of the earth. At the surface, therefore, it ap- pears generally displaced from its true position ; and this displacement is called the Diurnal Parallax, Thus, the true place of the "body M (Fig. 5) is in the direction CK ; but at A it appears in the line AH ; and the parallax is the angle AMO. So, the true place of M is Q, its apparent place is P, and the par- allax is AM'C. But the body M"' appears at Z, whether viewed from A or C, and the parallax in this case is zero. Since the earth's radius, in each instance, subtends the angle of parallax, we have the following definition : The diurnal parallax of a body is the angle at that body subtended by the semi-diameter of the earth. 25. What is diurnal parallax ? What is the true place of a body ? Show the effect of parallax by the figure. ATMOSPHEEIC EEFKACTION. 35 2G* On what Diurnal Parallax Depends. — At the horizon, the angle M, being subtended perpendicu- larly by the earth's radius AC, is larger than M', or M", which are subtended obliquely. And it is plain, that the higher the body in the sky, the less is its parallax, till at M m , when seen in the zenith, it has no parallax at all. Again, if the body were further removed from the earth, it is obvious that the angle M, subtended by the same line AC, would be smaller. Hence, the par- allax of a body is greatest at the horizon, and varies in- versely as the distance of the body from the earth's center. The parallax of a body at the horizon is called its Horizontal Parallax. 7. TJie Parallax of the 3Ioon. — There is no one of the heavenly bodies which has so great a parallax as the moon. It is, therefore, the nearest of them all. But even the moon's parallax is less than one degree; that is, if a person were to travel over the line AC, which is about 4,000 miles long, the direction of the moon would not be changed so much as one degree. This shows that the moon, though nearer than any other body, is yet at a very great distance from us. 28* Atmospheric Hefraction. — The atmosphere of the earth refracts or bends the rays of light as they come through it from the heavenly bodies. Let DD (Fig. 6) be a part of the surface of the earth, and AA 20. On what does parallax depend? Where is it nothing? Where is it greatest ? What i3 it called ? £7. What heavenly body has the greatest parallax ? How much ? 36 THE EAKTH the top of the atmosphere. If a person is at O, the light of the star S does not come to hLn in a straight line, but first strikes at a, and is bent downward to b, then to c, and finally to O. Therefore it does not seem to come from S, but from S', in the line Oc pro- duced. Thus, the star appears elevated above its ABCD DOBA true place. In this figure, the effect of refraction is very much exaggerated. The greatest refraction takes place at the horizon ; but even there it elevates an object only about 34', or a little more than the breadth of the sun. As the height above the horizon increases, the refraction becomes less, and is nothing at the zenith. 29* Time of Rising and Setting Affected by Re- fraction. — Since a body at the horizon appears raised 28. Show by the figure how light from a star comes to a person. What effect is produced? Where is refraction greatest? How much is it ? ILLUMINATION OF THE SKY. 37 above its true place about the breadth of the sun or moon, it must appear to rise earlier and to set later than it really does. This circumstance causes the sun and all the bodies which rise and set to be seen above the horizon at least four minutes longer than they would do if there were no atmosphere. 30, Distortion of the Sun's and Bloon's Disk by Refraction. — The change in the amount of refraction is so rapid near the horizon, that when the sun has just risen, or is just about to set, the lower limb is elevated more than the upper by a very perceptible quantity. Its form, therefore, does not appear circu- lar, but nearly elliptical, the vertical diameter being shortened about 5' or 6'. The lower half, however, appears more flattened than the upper half, because the difference of refraction between the lower limb and the center is greater than that between the center and the upper limb. SI, Illumination of the Sky. — During the day the atmosphere is illuminated by the light of the sun, which penetrates every part of it, and is reflected in all directions. If there were no air, the sky, instead of appearing luminous by day, would exhibit the same blackness as by night, and the stars would be visible alike at all times. "We should, in that case, lose a great part of that generally diffused light which illuminates the interior of buildings and other 29. Its effect on the time of rising and setting ? 30. Describe and explain the effect on the disk of the sun. 31. How would the sky appear if there were no air ? Why ? 38 THE EAETH. places screened from the direct rays of the sun. The earth's surface, and all terrestrial objects on which the sunlight falls directly, would indeed, by radiant reflection, cause a degree of illumination, but it would be far less than we now enjoy. It has been observed, in ascending to great heights, either on mountains or in balloons, where, of course, the air which is most dense and reflects most abundantly is left below, that the sky assumes a very dark hue, and the general illumination is greatly diminished. 32, Twilight. — The illumination of the sky begins before the sun rises, and continues after it sets. It is then called twilight. More or less of it is visible as long as the sun is not more than 18° vertically below the horizon. Those parts of the atmosphere are most luminous which lie nearest to the direction of the sun. Thus, in Fig. 7, let A be a place on the earth where the sun is just setting. The whole sky, IEFH, is illuminated. But, to a place further east, as B, the twilight extends from E to H, the part of the sky HK, remote from the sun being in the* shadow of the 32. Explain twilight by Fig. 7. DUBATION OF TWILIGHT. 39 earth. At C, only FH is illuminated, and HL is dark. At D, the twilight is entirely gone. Though the twilight terminates at H, there is no abrupt transition from light to shade at that point, since the reflection from those high and rare parts of the air is exceedingly feeble ; and, also, because the thickness of the illuminated segment, through which we look, diminishes gradually to that limit, as is obvi- ous from an inspection of the figure. S3. Duration of Twilight. — To an observer at the equator, at those times of the year when the sun is on the celestial equator, the twilight continues Ih. 12m. For, in the diurnal motion, 15° are described in an hour, and, therefore, 18° in l^h. = lh. 12m. This is the shortest duration possible. For, if the sun were north or south of the equator, the degrees of diurnal motion would be shorter than those on a great circle. And, if the observer were on some par- allel of latitude, the circles of daily motion would be oblique to his horizon, and the sun must, therefore, pass over more than 18° in order to move 18° verti- cally. An extreme case occurs at the poles, where twilight lasts several months. 33. How long does it last in different cases. CHAPTEE III. ASTRONOMICAL INSTRUMENTS- THE SUN — THE SEASONS — FOKM OF THE EARTH'S ORBIT. 34, The Equatorial Telescope. — In order that the telescope may be used to the best advantage for astronomical purposes, it is often mounted equator- idtty ; that is, it can be turned on tivo axes, one par- allel to the earth's axis, and the other perpendicular to it. And, besides this, a clock is connected with the first axis in such a way as to revolve the telescope just as fast as the earth revolves, and in the opposite direction. Thus, any heavenly body to which the telescope is directed remains steadily in the field of view, and can be examined leisurely and with care. 35. The Transit Instrument. — This is a telescope so mounted as to observe a heavenly body at the instant when it crosses the meridian. AD (Fig. 8) represents the telescope supported by a horizontal axis, which consists of two hollow cones placed base to base, so as to combine lightness and strength. The ends of the axis rest in sockets, attached to two stone piers, E and W. That the instrument may re- ceive no tremors from the building, the piers stand 34. Describe the equatorial telescope. Why so mounted ? ASTEONOMICAL INSTKUMENTS 41 on a firm foundation in the ground, passing through the floor without contact. The axis being placed east and west horizontally, the telescope, which is perpen- dicular to it, will, when turned, revolve in the plane of Fig. 8. the meridian. A graduated circle, N, is attached to one end of the axis, for marking altitudes or zenith distances. The whole instrument can be raised from the sockets, and the axis inverted, so that the east end shall rest on the pier "W, and the west end on the 35. Describe the transit instrument.. Why so called ? 42 THE SAETH. pier E. In the focus of the eye-glass there is a fine horizontal wire, and several vertical wires, of which the middle one is on the meridian. "When a star which is crossing the field of view is seen on the middle wire, it is at that moment making a transit of the meridian. SO. TJie Astronomical Clock. — A clock must be near the transit instrument, to show the exact time of the transit. The clock of the observatory is made to keep sidereal time ; that is, star time instead of sun time. One sidereal day is the length of time from the moment a star passes the meridian till it passes it again ; and it is about four minutes shorter than a day as measured by the sun. The sidereal day be- gins and ends at the moment when the vernal equinox is on the meridian. 37* To find the Might Ascension and Declination of a Heavenly Body. — Observe the exact sidereal time when the body makes its transit. That time ex- presses its right ascension, or its distance east of the vernal equinox, in hours, minutes, and seconds. This may be changed into degrees, minutes, and seconds. For, since a star makes an apparent revolution of 360° in 24 sidereal hours, it describes 15° in one hour, 15' in one minute, and 15" in one second. Bight ascension is measured either in time or in arc. The declination of the body is found by observing 36. What accompanies it ? Wliat kind of time is kept ? 37. State "how to find the right ascension of a body. In what denominations is it measured? How is its declination found? What other instrument is sometimes used for this? ASTRONOMICAL INSTRUMENTS 43 its height above the horizon, as indicated on the circle N, and then finding the difference between this height and the height of the equator, which is known by the latitude of the place. A separate instrument, called the Mural Circle, is sometimes employed in the observatory for finding the declination. 38* The Altitude and Azimuth Instrument. — The essential parts of this instrument are a telescope and two graduated circles, one vertical, the other horizon- Fra. 9. tal. Fig. 9 presents one of its more simple forms. The telescope AB is movable on a horizontal axis, 88. Describe the altitude and azimuth instrument, and its use. 44 THE EARTH. at the center of the vertical circle abc, and also on a vertical axis, passing through the center of the hori- zontal circle EFG. The levels g and h, placed at right angles to each other, show when the circle EFG is brought to a horizontal position by the tripod screws. The tangent screws, d and e, give slow mo- tions, one in a vertical, the other in a horizontal plane. If the reading of the vertical circle is taken when the telescope is horizontal, and again when it is directed to a star, the difference of the readings is equal to the altitude of the star. In a similar manner, if the hori- zontal circle is read when the telescope is directed to the north, and read again when it is directed to a star, the difference is its azimuth. 39o The Sextant. — This is an instrument for meas- uring the angular distance between two points situ- ated in any plane whatever. It is represented in Fig. 10. I and H are two small mirrors, and T a small telescope. ID is a movable radius or index, carrying the index mirror at the center of motion, I, and a vernier at the extremity, D. The horizon glass, H, is silvered only on one-half of its surface. When the zero of the vernier coincides with that of the arc at F, the mirrors are precisely parallel. If now we direct the telescope to a star, it may be seen in the transparent part of the horizon glass, and its image in close contact with it, in the silvered part. In order to measure an angle, as, for example, that between the moon M and the star S, direct the tele- 39. Describe the sextant, and how to measure the distance be- tween the mocn and a star. THE SUN'S PLAGE, Fig. 10. 45 scope to S, and turn the index from F toward E, till the moon is seen to touch the star. The vernier will then show on the graduated arc the size of the angle between the star and the moon's limb. 40, Observations of the Sun's Place. — If we em- ploy the instruments of the observatory in measuring from day to day the right ascension and declination of the sun, at the moment of its crossing the merid- ian, it will be discovered that these quantities are constantly changing ; or, in other words, that the sun is constantly shifting its place in relation to the stars. 40. What motion has the sun in right ascension ? What in de- clination? When is It furthest north? When furthest south? 46 THE EAETH. In right ascension, the sun gains nearly a degree every day ; that is, it moves eastivard nearly a degree each day ; so that, in 365 or 366 days, it comes round again to the same place among the stars. But in declination, it moves alternately north and south, crossing the equator on the 21st of March, as it moves northward, and again on the 22d of Septem- ber, as it returns southward. On the 22d of June it is furthest north, and on the 22d of December it is furthest south. Its greatest distance north and south of the equator is about 23 J°. 41. The Ecliptic and Zodiac* — The apparent an- nual path of the sun is found, by the foregoing ob- servations, to lie in a ptarw, cutting the celestial sphere" in a circle called the Ecliptic (Art. 11), and inclined to the plane of the equator at an angle of about 23° 27'. The Zjdiac is the name given to a zone of the heavens, 16° wide, extending along the circle of the ecliptic, 8° on each side of it. The paths of the prin- cipal planets lie within this zone. Its length is divided into 12 signs of 30° each, having the same names and arranged in the same order as those of the ecliptic (Art. 12), though not coincident with them. The signs of the zodiac are distinguished from each other by the stars which occupy them. 42. The Tropics and Polar Circles. — Through the two points of the ecliptic most distant from the equa- Wlien does it cross the equator ? How far north, and how far south does it go ? 41. How does the sun's path lie? What is the zodiac? How divided ? THE ANNUAL MOTION. 47 tor, called the solstices, (Art. 11), we imagine circles to be drawn parallel to the equator, called the Tropics. The northern circle, passing through the first of Can- cer on the ecliptic, is called the tropic of Cancer ; the southern one, for a like reason, is called the tropic of Capricorn. Two other parallels to the equator, pass- ing through the poles of the ecliptic, and therefore 23° 27' from the poles of the equator, are called the Polar Circles. 43. Terrestrial Zones. — On the terrestrial sphere, a similar system of circles divides the earth's surface into the well-known zones of geography, called the torrid, temperate, and frigid zones. The tropics are the limits of vertical sunshine in mid-summer. The polar circles are the limits within which the sun makes a diurnal revolution in mid-summer and mid- winter without rising or setting. 44:, The Annual Motion Observed without Instru- mentsm — If the stars were visible in the daytime, we should perceive the sun making progress among them toward the east, by a distance equal to nearly twice its own breadth every day, since the apparent diame- ter of the sun is a little more than half a degree. But, as they are invisible by day, we detect the same fact, when we notice that at a given hour of the night all the stars are further west than on a previous night. For example, at 9 o'clock p. m. — that is, 9 hours after 42. Define the tropics — the polar circles. 43. The zones of the earth. 44. How is the annual motion of the sun perceived without in- struments? How far each day does it move ? 48 THE EAETH. noon — it is easily observed that there is, from one evening to another, a regular progress of all the stars westward, as long as we choose to watch them. In other words, the sun is at the same rate advancing eastward relatively to the stars. 43. The Annual 3Iotion is a Motion of the Earth, not of the Sun. — There is abundant evidence that the motion of the sun around the earth, above described, is only apparent, and results from a real motion of the earth about the sun. Thus, suppose the earth to pass Fig. 11. around the sun S (Fig. 11) in the orbit ABPC, in the order of the signs. If we were unconscious of this motion, the sun would appear to us to move about 45. Is this really the sun's motion ? Use Fig. 11. CHANGE OF SEASONS. 49 the earth in the same order of the signs, though, at any given moment, in a contrary direction. When the earth is at B (in the sign T, as seen from the sun), we could see the sun in the sign ^= ; when we reach b , the sun is seen in fit ; and so on. 46. Catise of the Change of Seasons. — The phe- nomena of the seasons are due to the fact that the two revolutions of the earth, one on its axis, and the other around the sun, are in different planes ; in other words, that the equator and the ecliptic make an angle with each other. In Fig. 12, let the ecliptic be represented by the large circle in the plane of the paper. And suppose the earth to pass round the sun in the order of the signs, °P, s , n, etc., occupying the position A on the 21st of March, B on June 22d, C on September 22d, and D on December 22d. Next, suppose the plane of the equator (represented by the straight line eq) to be inclined to the plane of the paper by an angle of 23J°, and always in the same direction. The axis ns, which is perpendicular to eq, will, therefore, be parallel to itself in all posi- tions of the earth. In the figure, it is represented as everywhere leaning to the right. At A, the earth's position, March 21st, the rays of the sun just reach to n and s ; so that, if the earth revolves on ns at that place, every spot on its surface will be one-half the time in the light, and the other half in darkness. The days and nights are, therefore, equal. In this position, the plane eq, if extended, passes through 46. By Fig. 12, show how the seasons are caused. Position A ; position B, C, D. 3 * 50 THE BAETH. the sun; that is, the sun is in the equator of the heavens, and it is the time of the vernal equinox. Fig. 12. In the position B, the circle of illumination, as represented, reaches beyond n to the polar circle, and falls short of s by the same distance, the sun being seen north of the equator eq. As the earth revolves on ns, it is evident that all places north of eq are longer in light than in darkness ; and the reverse is true of all places south of eq. It is now summer in the northern hemisphere, and winter in the southern. HEATANDCOLD. 51 At C, the earth has reached the autumnal equinox ; the circle of illumination passes through n and s, and the phenomena are the same as at A. At D, the north pole is turned as far as possible into the shade, and the south pole into the sunlight. The sun is at the tropic of Capricorn ; and as the earth rotates on ns 9 all places north of the equator experience the short days and the long nights of winter, and the reverse at all places south of the equator. 47 • Causes of Seat in Summer and Cold in Win- ter. — These are two. 1st. The length of the day compared with the night. The heat of the earth is passing off by radi- ation during the whole time, whether the sun shines or not. But the earth receives heat from the sun only while the sun is above the horizon. Hence, the longer the period of sunshine, compared with the time of a diurnal revolution, the greater the heat. For this reason, therefore, the summer is warmer than the winter. 2d. The greater altitude of the sun in summer than in winter. The greater the sun's height is, the more numerous are the rays which fall on a given area. Between March and September the northern hemi- sphere has its summer, both because the days are longest and the sun is highest. And for a similar reason the southern hemisphere has its summer be- tween September and March. Of course the winter 47. Give the first reason for heat in summer, and cold in winter, the second. 52 THEEAETH. of each hemisphere occurs at the same time as the summer of the other. 48. Wliy the Greatest Heat is Later than the Sum- mer Solstice, and the Greatest Cold Later than the Whiter Solstice. — If the sun sheds on a given surface more heat each day than the surface loses by radi- ation, then the heat accumulates from day to day. This is the case during the long days of summer; and more heat is gained than lost till a month or more after the summer solstice. For a like reason, during the middle hours of the day, heat is received from the sun more rapidly than it is lost by radiation, so that the hottest hour is 2 or 3 o'clock p. M. In the winter, on the contrary, the loss by radiation exceeds the quantity received from the sun during all the shortest days, so that the temperature descends till many weeks after the winter solstice. 49» iVo Change of Seasons if there were no Obli- quity. — The angle between the planes of the two mo- tions of the earth being the cause of the change of seasons, it follows that there would be no such change if those motions were in the same plane. If, while the earth advances in its orbit about the sun, it should rotate in the same direction on its axis, then the sun would always be in the plane of the equator, and would, every day of the year, describe the equator as its diurnal circle, rising exactly in the east, culmi- 48. Why is it hottest after the longest days ? Why coldest after the shortest days ? 49. If the ecliptic coincided with the equator, what would be the seasons ? FORM OF THE EARTH'S ORBIT. 53 nating at a zenith distance equal to the latitude of the place, and setting exactly in the west. At the equator, the sun would always follow the prime verti- cal, and at either pole it would always be passing round in the horizon. oO» The Greatest Changes of Season if the Obli- quity were 90\ — If, while the earth revolves on its axis from west to east, it should pass around the sun in a plane lying north and south, then the ecliptic would pas§ through the north and south poles, and the solstices would be at the poles. Hence, at a station on the equator, the sun would, during the year, describe the prime vertical and various small circles parallel to it, down to the north and south points of the horizon, where it would be stationary alternately at the times of the solstices. At the equator, therefore, there would be an alternation from summer to winter, or the reverse, every three months. SI • Mode of Determining the Form of the JEqrth's Orbit. — The earth's orbit is an ellipse described about the sun, which is situated in one of its foci. This is ascertained by observing the changes in the sun's apparent diameter throughout the year. "When the sun appears smallest, it is most distant; and when largest, it is nearest. And its distance, in all cases, varies inversely as its apparent diameter. Therefore, if the sun's apparent diameter be accu- rately measured as frequently as possible, we can from these measurements find the relative distances ; and these distances determine the form of the orbit. 50. What if the obliquity were 90°? 54 THE EAETH. Thus, suppose the earth to be at E (Fig. 13), and that the sun's apparent diameter is measured when in the direction Ea. After it has advanced eastward some days, so as to be seen in the direction E6, let it be measured again : and so on, at every opportunity through the year. Then the proportion of the lines Fig. 13. Ea, W), Ec, etc., will be known ; and if they are laid down of the proper length, and in the proper direc- tions, the dotted line abmv, passing through their extremities, will be the true form of the sun's ap- parent orbit about the earth, and, therefore, of the earth's orbit about the sun. This form is found to be an ellipse, having the sun in one of its foci. 52. Definitions Relating to a Planetary Orbit, Let E be the focus occupied by the sun, and am the 51. What observations are made to find the form of the earth's orbit ? Describe by the figure. What is the form ? LINE OE APSIDES. 55 the major axis of an elliptical orbit described about it ; the nearest point, a, is called the 'perihelion, and the most distant point, m, the aphelion. The two points a and m are also called the apsides. The varying dis- tance, Ea, E&, Wi, etc., is called the radius vector. If the major axis, am,, is bisected in C, the ratio of EG to the semi-major axis, aC, is called the eccentricity of the orbit. The less EC is, compared with aC, the less is the eccentricity, and the nearer does the ellipse approach to a circle. If E coincides with C, the eccentricity is nothing, and the orbit is a circle. The eccentricity of the earth's orbit is only g 1 ^ ; that is, EC is ^ of aC. If the figure were drawn in that proportion, it could not be distinguished from a circle. 53, Position of the Line of Apsides. — The direc- tion of the major axis of the earth's orbit, or the line of apsides, is slowly changing ; but at present it passes through the 10th degree of Cancer and Capri- corn, as represented in Eig. 11. The earth is at peri- helion on the 1st of January, and at aphelion on the 1st of July. We are, therefore, nearest to the sun in the winter of the northern hemisphere, and furthest from it in the summer. 54. Distance from the Sun, as Affecting the Sea- sons. — The intensity of the sun's heat at the earth, as well as that of its light, varies inversely as the square 52. Define the several parts of an orbit. How much is the eccen- tricity of the earth's orbit ? It is nearly of what shape ? 53. When does the earth pass the perihelion and the aphelion ? 56 THE EAETH. of our distance from it. On this account, the inten- sity of heat at perihelion is to that at aphelion as 6V : 59 3 , which is nearly as 31 : 29. Therefore, so far as distance is concerned, the earth receives -^- s more heat on the 1st of January than on the 1st of July. This produces a slight effect to mitigate the severity of cold in winter and of heat in summer, in the northern hemisphere, and to aggravate the same in the southern hemisphere. 54. Why is it not colder when we are furthest from the sun ? CHAPTEE IY. SIDEEEAL TIME — MEAN AND APPAEENT SOLAE TIME — THE CALENDAE. ££• Hie Sidereal Day. — This is the interval of time which elapses between two successive culmina- tions of a star (Art. 36). The length of this interval appears to be invariable, whatever star is observed, or in whatever season or year the observation is made. On this account, the sidereal day is regarded as the true period of the earth's rotation on its axis. In order to reckon by sidereal time, the moment chosen for the beginning of each sidereal day is the moment when the vernal equinox culminates. The sidereal clock, if correct, then points to 0/?. 0m. 0s. Each sidereal day is divided into 24 sidereal hours, each hour into 60 sidereal minutes, and each minute into 60 sidereal seconds. £8. Hie Mean Solar Bay. — This is the mean in- terval between two successive culminations of the Sun. It will be shown, presently, that these inter- vals vary throughout the year. As the sun, by the annual motion, is advancing eastward continually 55. What is a sidereal day ? When does it begin ? 56. What is the mean solar day ? How does it differ from the sidereal day? 58 THE EAETH. among the stars, the solar day must always be longer than the sidereal day. For, if the sun and a star were on the meridian of a place together, then, while that place passes around eastward till its meridian meets the star again, the sun has advanced eastward nearly a degree, and the place must revolve nearly a degree more than one revolution before its meridian will reach the sun. This will require nearly 4 minutes of time ; for, in the diurnal motion, 15° correspond to one hour, and, therefore, 1° to -^ of an hour ; that is, 4 minutes. «57. The Apparent Solar Day. — This is the actual interval between two successive culminations of the sun. And this interval changes its length from day to day through the entire year, being sometimes greater and sometimes less than the mean solar day. In keeping solar time by clocks and watches, it is customary, for convenience, to aim to keep the mean rather than the apparent time, and to regard the sun as going alternately too fast and too slow. $8, Causes of Unequal Solar Daus. — After the earth has completed a sidereal day, it must always revolve a little further to bring the meridian of a place to the sun, which has advanced nearly one degree eastward. Now, if the sun advanced east- ward exactly the same distance every day, then the solar days, as well as the sidereal days, would all 57. What is the apparent solar day ? Which is used in keeping time? 58. What makes the solar days unequal ? CIVIL AND ASTRONOMICAL TIME. 59 be equal. But it does not ; for sometimes the annual motion is faster, and sometimes slower; and some- times it is parallel to the daily motion, and again it is oblique. Hence, the arc of right ascension, to be added to the sidereal day in order to complete the solar day, varies in its length ; and, therefore, the solar days themselves must be of different lengths. S9. The Equation of Time. — The difference be- tween mean time and apparent time, on any given day, is the equation of time for that day. If the sun is slow, the equation must be added to the apparerst time ; if fast, it must be subtracted, in order to give mean time. The mean and apparent time agree four times in a year — April 15th, June 15th, September 1st, and December 24th. The two largest equations are, +14 minutes, February 11th, and —16 minutes, November 2d. S0» Civil and Astronomical Time* — -The mean solar day, when employed for civil purposes, is sup- posed to begin and end at midnight, and is divided into hours, numbering from 1 to 12 A. M., and then from 1 to 12 P. M. But the astronomical day (which is also the mean solar day) begins and ends at noon, 12 hours later than the corresponding civil day, and its hours are counted from 1 to 24. Thus, the astronom- ical date, April 12c/, 207*., is the same as the civil date, April 13th, 8 o'clock A. m. 59. What is tlie equation of time ? How large does it ever be- come ? 60. State the diffsrencs between civil and astronomical time. 60 THE EARTH. Gl, Tlie Julian Calendar. — The period in which the sun passes from the vernal equinox to the same point again, is called the Tropical Year. In that period the round of the seasons is exactly completed. The length of the tropical year is 365c?. 5h. 4.8m. 46.155. This is so near 3 65 J days, that in the adjust- ment of the calendar made by Julius Caesar (hence called the Julian calendar), three successive years were made to contain 365 days each, and the fourth 366 days. The additional day is called the intercalary day. In this calendar it was introduced by reckoning twice the 6th day before the Kalends of March ; and hence the year containing this additional day was called the Bissextile. The intercalary day is now the 29fch of February, and the year containing such a day is called Leap Year. 62. The Gregorian Calendar. — By calling the tropical year 365 \ days, the Julian calendar makes it more than 11 minutes too long, and the intercalation of one day in four years is, therefore, too great. This excess amounts to more than 18 hours in a cen- tury. Hence, by dropping the intercalary day three times in four centuries, the adjustment is nearly com- plete. The Julian calendar, thus amended, is called the Gregorian calendar, because adopted under Pope Gregory XIII. At that time, 1582, the vernal equi- nox, by the error of the Julian calendar, had fallen 61. What is the tropical year? Describe the Julian calendar. What is meant by leap year ? 62. What was the defect in the Julian calendar ? Describe the Gregorian calendar. Will it always be correct? What is old style? HOW TO COMPAEE DAYS. 61 back to March, 11th. To bring the equinox to its proper date, 10 days were first dropped (the 5th being called the 15th), and then the following system was adopted : Every year not exactly divisible by 4, has 365 days. Every year divisible by 4, and not by 100, has 366 days. Every year divisible by 100, and not by 400, has 365 days. Every year divisible by 400, has 366 days. The Gregorian calendar will not be correct perpet- ually, but the error will not amount to a day in 4,000 years. The nation of Russia has not yet adopted the Gre- gorian calendar, so that there is now a discrepancy of 12 days between their dates and those of other na- tions. The reckoning still used by them is known as Old Style, and is distinguished by appending the let- ters O. S. to every date. OS. JEEoiv to Compare Days of the Month and of the Week in Passing from one Year to Another, — A common year of 365 days contains 52 weeks and one day ; a leap-year contains 52 weeks and two days. Hence, a year usually begins a day later in the week than the year previous. And, generally, any day of any month is one day later in the week than the same day of the preceding year. Thus, July 4th, 1365, 63. What is tlie change in a given day of the month, in passing from one year to another? Why does it fall a day later in the week ? When does it fall two days later, and why ? 62 THE EAETH. falls on Tuesday; 1866, on "Wednesday; 1867, on Thursday. But, in leap-year, this rule applies only till the end of February. From that time to the same date in the year following, every day of a month falls two days later in the week than in the previous year. Thus, July 14th, 1871, is Tuesday ; 1872, Thursday ; and February 22d, 1872, is Thurs- day ; 1873, it is Saturday. CHAPTEE V. OBLATE FORM OF THE EAETH — ITS MASS AND DENSITY — PKOOFS OF ITS ROTATION ON AN AXIS. 64. Central Forces. — When a body is revolving on an axis, the parts, on account of their inertia, tend to move in straight lines, tangent to their respective cir- cles, and thus leave the rest of the body ; and they would do so, unless restrained by some force. The force which tends to carry the particles off in a tan- gent is called the projectile force ; that which holds them in is called the centripetal force ; and that com- ponent of the projectile force which acts directly away from the center is called the centrifugal force. All these are frequently called central forces. 65. Illustrations. — We see an illustration of the projectile force when a wheel is revolved, having water on its edge. The drops are thrown off in tan- gent lines. If a ball is whirled by a string, the projectile force is prevented from carrying the body away by the 64. What is the projectile force? the centripetal? the centrifiii gal ? What common name is given to them all ? 65. Illustrate by wheel — by ball and string — by the curve of a railroad. 64 THE EAETH. strength of tlie string, which is the centripetal force. But the string is strained, and may possibly be broken by the centrifugal force, which is a part of the projectile force. When a train of cars turns a curve, there is a cen- trifugal force tending to throw it off from the track on the convex side. Hence, the outside rail is laid highest, so that the cars may lean in the opposite direction. 66, Loss of Weight on the Earth. — As the earth revolves on its axis, all objects upon it are affected by the centrifugal force, and lose a little of their weight. The loss is greatest at the equator, where the motion is swiftest ; but even there it is very small, only - 2 -|-g of the whole. At all other places the loss of weight is less than this, according as the dis- tance from the equator is greater. At the poles there is no loss at all. There is an additional loss of weight at the equa- tor, arising from the oblate form mentioned in the next article. The whole loss amounts to T ^ ¥ of the weight. Therefore, a body on the equator, which would weigh 194 pounds if the earth were a sphere and at rest, actually weighs only 193 pounds. 67, Oblate Form of the Earth. — The centrifugal force on the earth produces another effect upon all the yielding parts, such as the water of the oceans. 66. How are bodies on the earth affected by its rotation ? Where is loss of weight greatest ? How much is the loss by centrifugal force ? In what other way is there a loss ? How great is the whole loss? OBLATE FORM OE THE EAETH 65 They tend to flow away from the poles, and all places near the poles, towards the equator, until the water at the equator is about 13 miles further from the center than the poles are. Thus, the earth, as a whole, is not an exact sphere, but is flattened in the polar re- gions, and has the form which is called an Oblate Fig. ( 14. /& \ WW /UrP \\\Y\ n i \ \ \\\ Jiiv i 1 G 1 Ell v\ I 1 I i vaVA / rrn \w\ \ n^z/y \\ \ ■r£z?y D Spheroid. Fig. 14 will give an idea of the earth's form, C and D being the poles, and AEGFB the equator. The diameter AB of the equator is about 26 miles longer than CD, the axis on which the earth revolves. If we imagine a sphere constructed on the polar diameter of the earth, the difference between the sphere and spheroid will be a sort of shell or ling, 13 miles thick at the equator, and growing thin- ner on every side to the poles. This is sometimes called the Equatorial Ring or Belt of the earth, and it 67. What is the earth's form? equatorial belt ? Why ? What is meant by the 66 THE EARTH produces sensible effects on the earth's relations to the moon and sun. 08* Weight and Density of the Earth. — The weight of the whole earth has been found, by comparing its attraction with the attraction of a mountain of given Fig. 15. size. Thus, if the mountain M exerted no attraction, the plumb-lines AB and CD would hang towards the center of the earth. But if the mountain alone attracted them, they would be drawn directly towards the center of gravity of the mountain. But since the earth and the mountain both attract, they hang a little sideways towards the mountain, as in the dotted lines. By carefully measuring the deviation of the plumb-lines, it may be learned how much greater the 68. Describe the mode of finding the weight of the whole earth. How great is it ? What is its density, or specific gravity ? ROTATION OF THE EARTH. 67 earth's attraction is than that of the mountain. The weight of the earth is about 6,000,000,000,000,000,- 000,000 tons. The size and weight of the earth being both known, its density, or specific gravity, is easily found. It is expressed by the number 5.67 ; that is, it weighs 5.67 times as much as the same bulk of water. 09* Proofs that the Earth Revolves on its Axis, The early belief of all people is that the earth is im- movable, and that the heavenly bodies revolve about it. It is only a few centuries since the wisest philos- ophers began to teach that the earth itself revolves. But there are several independent proofs that the earth really revolves once round every day. 1. This is the only reasonable way of explaining the fact that all the millions of fixed stars, at various and immense distances from us, in large and in small circles of the sphere, perform their apparent revolu- tions about us in precisely the same length of time, viz., one sidereal day. 2. Without supposing the earth to rotate on its axis, we cannot account for the oblate form of the waters of the ocean. Whatever form the solid parts might have, the movable portion would be spherical, if the earth were at rest. Moreover, the degree of oblateness is exactly that which is required on a sphere having the diameter and mass of the earth, if it be supposed to rotate once in 24 hours. 69. Did ancient philosophers believe that the earth revolves? What is the first proof that it does ? the second ? the third ? the fourth ? the fifth ? the' sixth 1 68 THE EARTH. 3. The weight of a body at the equator, compared with that at the poles, is too small to be wholly ac- counted for by increased distance. Centrifugal force, arising from rotation, can alone explain the remain- ing difference. 4. A body dropped from a great height strikes/wr- tlier east than the vertical line in which it began to fall. If the earth rotates, the top of a tower moves faster than the base ; and, therefore, a body let fall from the top, retaining the eastward motion of that point, will strike further east -than the base. At the equator, this distance would be near 2 inches for a fall of 500 feet. Numerous experiments on the fall of bodies through great distances have been very care- fully made by different individuals, and in different latitudes ; and they all concur in proving that a body in falling deviates from a vertical line toward the east. 5. It is also proved by FoucauWs pendulum experi- ment If a very long pendulum be set vibrating north and south, it will slowly change to the northeast and southwest, thus showing its tendency to preserve, as nearly as possible, the original direction of its vibra- tion in space. 6. The precession of the equinoxes can be explained only on the supposition that the earth rotates on an axis. CHAPTEE VI. THE SUN — SOLAE SPOTS— CONDITION OF THE SUN'S SUEEACE — THE ZODIACAL LIGHT. 70* The Form of the Sun. — As the sun revolves on an axis, the centrifugal force must produce some oblateness. It is, however, too slight to be perceived, because the velocity of rotation is small, and the force of attraction very great. Hence, the appear- ance of the sun is that of a perfect sphere. 71» Tlie Sun's Distance and Size.— The horizontal parallax of the son is so small that there is much dif- ficulty in measuring it accurately. According to the best determinations, it is about 8.6", from which it is calculated that the earth's distance from the sun is a little more than 95,000,000 miles. The distance of the sun being found, and its appa- rent breadth being measured, it is easy to compute its diameter. This is found to be 887,000 miles, which is 112 times as great as the diameter of the earth. In 70. What appears to be tiie form of the sun ? What is its real form ? Why does it not appear so ? 71 . What is the sun's horizontal parallax ? Is it easily found ? What is our distance from the sun ? What is the sun's diameter ? Compare it with the earth. Compare the sun's and the earth's bulk. 70 THE SUN. bulk, therefore, the sun is 1,400,000 times as large as the earth. 72o The Sun's Mass, and Strength of Gravity, — In respect to quantity of matter, the sun does not ex- ceed the earth nearly as much as in size ; for while its volume is 1,400,000 times as great as that of the earth, its mass is only 355,000 times as great as the mass of the earth. It follows that its density is only one-fourth as great as the earth's density. The strength of gravity on the sun is 28 times as great as it is on the earth ; so that, what weighs 100 pounds here, if transported to the sun, would weigh 2,800 pounds; and a body there would fall through 450 feet in the first second of its descent, while on the earth it falls only 16 feet. 73. Diurnal notation of the Sun. — By means of spots on the sun, it is found that it revolves on its axis in about 25 days, from west to east, nearly in the same plane in which the earth revolves about the sun. After a spot has presented itself on the edge of the sun's disk, it occupies almost two weeks in going across, and then is out of sight as much longer, re- appearing in the same place as at first, in 27J- days. If the earth were at rest, then 27 J- days would be the period of the sun's rotation on its axis ; but since the earth revolves about the sun in the same direction, it requires more than one revolution of the sun to bring 72. Compare them in respect to mass. Which is the most dense ? How many times ? What is the strength of gravity at the sun ? 73. How is it found that the sun revolves on its axis ? In what time, and in what direction, does it revolve? What is the appa- SOLAE SPOTS, 71 the spot again to the edge. Suppose the earth at rest at the point E (Fig. 16). Then a spot coming into Fig. 16. view at A would go round through B, D, and H, to A again, when it would reappear. But while it goes round, the earth in fact advances in its orbit from E to F. The edge of the sun's disk is changed to B, and the spot mast move so much further before it comes in sight again. As it requires about tivo days to go over AB, the time of one revolution of the sun on its axis is a little more than 25 days. 74. Appearance of the Solar Spots. — Nearly every spot on the sun consists of two parts — a black center of irregular form, called the nucleus, and a surround- ing part of lighter shade, called the umbra (Fig. 17). These parts are distinct, and do not shade into each other. The spots not only move across the disk, but rent time of revolution ? Describe the cause of the difference, by Fig. 16. 72 THE SUN. Fig. 17. # July 9 " W 1844. July 11 change their form and appearance from day to day. Sometimes a large spot divides into two or more, smaller ones ; and, again, a group unites into one or two larger spots. A spot sometimes diminishes and disappears, first the nucleus, then the umbra. The reverse also happens; a spot is seen in the midst of the disk, where there was none the day before. Though only a few are commonly in sight at once, yet in some instances they have been counted by tens, and even hundreds. Yery rarely a spot is so large as to be seen by the naked eye. They do not cross all parts of the disk, but appear chiefly in two zones, one on each side of the equator, from 10° to 35° of latitude, as shown by the dotted lines in Fig. 17. 74. Describe a solar spot. What is the nucleus ? the umbra ? State what changes the spots undergo. What parts of the disk do they pass across ? THE ZODIACAL LIGHT. 73 The same figure exhibits the change which took place in a group of spots in the course of two days. 7&. The Nature of the Spots. — From the changes which the spots undergo in passing near the edge of the disc, it is found that they are cavities in the lumi- nous atmosphere of the sun, the nucleus being deeper than the umbra which surrounds it. Sir William Herschel proposed the theory that an atmosphere of flaming gas forms the outer surface of the sun, having a less luminous stratum beneath, while lower down is the liquid or solid surface of the sun, which is still darker. When an opening is rent in the outer stratum, we look in upon the second stratum, and this forms the umbra of a spot» And, supposing a smaller rent to exist in that, we are able to see the more dense portion below, as the nucleus of the spot. Sir John Herschel has suggested that these openings, one below the other, may be occasioned by rotating storms in the solar atmosphere, resembling some which take place on the earth. 76* The Zodiacal Light* — This name is given to a faint, ill-defined light, extending along the zodiac, either in the west, after sunset, or in the east, before sunrise. It so much resembles the twilight that it is not ordinarily noticed, because it appears as a mere upward extension of it. It is projected on the sky as a triangle, inclined to the horizon at the same angle as the ecliptic (Fig. 18). In the evening, it is best seen 75. What is the nature of the spots ? What is Sir William Her- Bchel's theory ? 4 74 THE SUN. at the season when the ecliptic is most nearly perpen- dicular to the horizon, after twilight has ceased. It is, therefore, most conspicuous, at evening, in the month of February. When the air is clear, and there Fig. 18 is no moon, it is visible till after 9 o'clock. For a like reason, the best time for seeing it before morning twi- light is the month of October. The apparent extent of it, both in breadth and height, is much increased by indirect vision. 76. Describe the zodiacal light. When does it appear in the morning? When in the evening? CHAPTEE VII. GEAVTTATTON — KEPLEE'S LAWS — MOTION LN AN ELLIPTICAL OEBIT — PEECESSION OE THE EQUINOXES. 77 o Gravitation. — AH portions oi matter in the universe show a tendency towards each other. This tendency is called gravity or gravitation. It is by this force that bodies fall to the earth, when left at rest in the air, or when thrown in any direction. And it is discovered that the same force causes the moon to go round the earth, and the planets to go round the sun, instead of moving off in straight lines, as they would do if there were no such force as gravitation. 78. First Laiv of Gravitation. — When the distance is the same, gravity varies as the quantity of matter. Bodies fall as swiftly as they do, because the earth contains so great a quantity of matter ; and if it con- tained more or less, bodies would fall faster or slower in the same proportion. So, also, bodies fall toward the earth, instead of falling toward a mountain, be- cause the earth contains vastly more matter than the mountain. Again, we see that gravity varies as the quantity of 77. What is gravitation ? Where do we observe its operations 78. What is the first, law of gravitation ? Give the proofs. 76 GKAVITATION. matter, in the fact that the weight of a body increases as the quantity of matter in it ; for weight is only another name for strength of gravity. 79. Second Law of Gravitation. — When the quan- tity of matter is the same, gravity varies inversely as the square of the distance. Hence, if the distance is twice as great, gravity is four times less ; if three times as great, it is nine times less, and so on. It can be demonstrated that this must be the law of gravitation in regard to distance, in order that a planet may de- scribe an ellipse about the sun, or a satellite about a planet, while the central body is situated in the focus. 80. Kepler's Laws. — From the observed motions of the planets about the sun, Kepler deduced the three following laws, which are applicable to all bodies revolving about a central body. Though Kep- ler discovered them as facts in the solar system, they were afterwards proved by Newton to be necessarily involved in the laws of inertia and gravitation : 81. (1.) The Areas Described about the Sun by the Madias Vector vary as the Times of Describing Them. Of course, if equal times are spent, the areas passed over are also equal. This is illustrated by a reference to Fig. 13. If the sun is at E, and a planet describes the orbit aemt, and passes over ah, be, cd, &c, in equal times, then the areas dEb, bEc, cEd, &c, are equal. 79. The second law ? Illustrate by numbers. 80. Who proved the truth of Kepler's laws mathematically? Why are the following laws called Kepler's laws? 81. State the first law of Kepler. Illustrate by Fig. 13. OEBITS OF THE PLANETS. 77 This implies that the planet moves fastest when it is nearest the central body ; for there the areas are shortest, and need to be widest. The velocity is, therefore, greatest at a, the perihelion, and least at m, the aphelion. 82, (2,) TJie Orbit of each Planet is an Ellipse, the Sun being in one Focus. — Thus, ACBD may represent the orbit of a planet, the sun being at E or F, which are the two foci. If the foci are nearer the center, the ellipse approaches more nearly to the form of a cir- cle, in which case it is said to be less eccentric. But a more eccentric ellipse is one whose foci are further from the center. The figure is then narrower, and differs more from a circle. The orbits of the comets are generally very eccentric, while those of the planets 82. State the second law. Where is the sun in a planet's orbit ? What is the eccentricity of an orbit? Are the orbits of the planets very eccentric ? 78 GEAVXTATION. have very little eccentricity, and, if correctly repre- sented, could not be distinguished from circles. 83. (3.) Tlie Squares of the Periodic Times vary as the Cubes of the Mean Distances. — The periodic time is the time occupied by a planet in making a complete revolution. And, according to this third law, the times increase faster than the distances ; for the distances must be raised to the third power, in order to vary as fast as the second power of the times. Hence, the further off a planet is from the sun, the slower it moves. 84. Paths of Projectiles. — When a stone is thrown, or a ball is fired, its path (if undisturbed by the air) is part of an elliptic orbit, one of whose foci is at the center of the earth. This ellipse, however, is one of extreme eccentricity, and is, therefore, usually called a parabola. Making use of the time and distance of the moon's revolution, it is calculated, by Kepler's third law, that if there were nothing to- obstruct the motion of the projectile, it would complete its orbit, and return to the place from which it was thrown, in about 31 minutes. The perihelion of this orbit would be only a few feet beyond the center of the earth. 85. Effect of Increased Velocity of Projection. Suppose that P (Fig. 20) is a point near the earth, 83. State Kepler's third law. What planets have the swiftest motion ? 84. When a stone is thrown, what is the form of its path ? What is it usually called ? Why ? When would it return if uninter- rupted ? Which focus is at the earth's center ? WHY PLANETS RETURN AND DEPART. 79 ADE, and that the velocity of projection, in the direc- tion PB, is so greatly increased that the projectile strikes the earth at D. By a still greater increase of velocity it might meet the earth at E. In these cases the earth's center would be in the most remote focus of the orbit. But if we suppose the velocity so much increased that the centrifugal force just equals the force of gravity, then the body would describe the circular orbit PFG. Any increase of the velocity of projection beyond this will again produce an ellipse, as PK, whose nearer focus is at the earth's center. And we can imagine the velocity increased till the ellipse becomes one of extreme eccentricity. SG» Why a Planet at Aphelion begins to Return, or at Perihelion begins to Depart, — It might be thought 85. What is the effect of increasing the velocity of projection? When will the orbit "become a circle ? What if the velocity is still more increased ? 80 GRAVITATION that a planet at its aphelion, C (Fig. 21), being less attracted toward the sun than at any other point, would continue to withdraw, instead of commencing to return ; and that when at its perihelion, G, being more attracted than elsewhere, it would continue to approach till it falls to the sun. The reason why a planet begins to return after reaching the aphelion is to be found in its diminished velocity. As the planet recedes through H, K, and A, the centripetal force toward S draws it back, and causes continual retard- ation, till at C the velocity is so much diminished that the attraction of S, though less than elsewhere, is still sufficient to curve the path so that it falls within a circle about the centre S, and the planet begins to approach the sun. Again, as the planet passes through D, E, and F, 86. Explain by Fig. 21 why a planet returns from aphelion, or departs from perihelion. PEECESSION OF EQUINOXES. 81 the attraction toward S partly conspires with its iner- tia, and it is continually accelerated, till, at Gr, its velocity has become so great that its path strikes outside of a circle about the center S, and it begins again to depart as before. 87* Precession of Equinoxes Described, — The points in which the equator intersects the ecliptic on the celestial sphere are not stationary, but have a slow retrograde movement ; that is, they revolve from east to west. The sun, therefore, in its annual progress eastward, crosses the equator each year a little fur- ther west than it did the year previous. This motion is called the Precession of the Equinoxes. These points move about 50 J" in a year. At this rate, it will re- quire 25,800 years to make a complete circuit of the heavens. 88* Signs of the Ecliptic Displaced from the Signs of the Zodiac. — The want of coincidence between the signs of the ecliptic and the signs of the zodiac was noticed (Art. 41). They coincided at the time the division was made, about 2,000 years ago ; and the precession, during this period, has moved the equi- noxes backward 2,000 x 50J" = 28°, nearly. Hence, Aries, of the zodiac, almost coincides with Taurus, of the ecliptic ; Taurus, of the zodiac, with Gemini, of the ecliptic, &c. 87. What is meant by the precession of equinoxes? How fast do they recede ? 88. What effect has precession produced on the position of the signs of the ecliptic ? How much are they now displaced? 82 GBAVITATION. 89* Motion of the North and South Poles. — Con- sidering the plane of the ecliptic as fixed, its poles, of course, occupy fixed positions among the stars. But this is not true of the poles of the equator. Their distance from the poles of the ecliptic is equal to the obliquity of the two circles ; that is, 23° 27'. As this angle remains nearly constant, and the points of in- tersection move around westward, the poles of the equator must likewise move round those of the eclip- tic in the same direction, and occupy the same period, 25,800 years, in completing their revolution. The north pole of the equator is now near the star in Ursa Minor known as the pole-star. According to the ear- liest catalogues, the pole was 12° distant from the pole-star. It is now somewhat more than 1° distant, and will, at the nearest, pass within J° of it. In about 13,000 years the pole will be on the opposite side of the pole of the ecliptic, near the bright star Alpha Lyrse, which will then be the pole-star. 90o Cause of Precession. — The precession of the equinoxes is a disturbance produced by the sun's and moon's attraction upon the equatorial ring of the earth. The sun being always in the plane of the ecliptic, and the moon always near it, both bodies act upon the equatorial ring to tip it into the same plane. This action, in connection with the inertia of the earth as it revolves on its axis, causes the equinoxes to move backward. 89. What is the effect on the poles of the equator ? What is said respecting the pole-star ? 90. Explain how precession i3 caused. TROPICAL AND SIDEREAL YEAR. 83 91> The Tropical and Sidereal Year, — Tlie fact of precession shows that the year has two different values, according as we reckon from a star or from an equinox. Hence, the Sidereal Year is defined to be the period occupied by the sun in passing eastward around the heavens from a star to the same star again ; and the Tropical Tear, the time of passing around from one equinox to the same equinox again (Art. 61). vAs the equinox moves westward, the sun reaches it sooner than if it were stationary, and thus makes the tropical year shorter than the sidereal, by the time required to pass over 50J", which is 20m. 22.9s. As the tropical year is 365c?. 5k 4.8m. 46.155. (Art. 61), the sidereal year, therefore, is 365d. 6h. 9771. 9s. Though the sidereal year is the true period of the earth's revolution about the sun, yet the tropical year possesses by far the greatest interest, because it is the period in which the seasons are completed. 91. What two kinds of year are described ? "Why are there two? Which is the true period of the earth's revolution ? CHAPTEE VIII. THE MOON— ITS INVOLUTIONS— ITS PHASES — THE CONDITION OF ITS SUKFACE. 02, Distance and Dimensions of the Moon* — The moon is a satellite of the earth, revolving about it within a comparatively small distance, and accom- panying it in its orbit around the sun. The mean horizontal parallax of the moon at the earth's equator being 57' 5", its mean distance is found to be 238,650 miles. As its apparent diameter is 31' 6", its real diameter must be 2,161 miles. Therefore, the surface of the moon is 13 times less, and its volume 49 times less, than the surface and volume of the earth. But in respect to mass, the moon is 80 times less than the earth. 93. Revolution about the Earth. — The slightest attention to the position of the moon, from night to night, shows that it moves eastward, among the stars, several degrees every day. If the instruments of the observatory be employed to measure its right ascen- 92. What is the moon's parallax? its distance from the earth? its diameter ? Compare its surface and volume with the earth s ; also its mass. 93. How does the moon move in relation to the earth ? Telescopic view of the Moon. Telescopic view of the Moon when five days old. THE NODES. 85 sion and declination, it is ascertained that the moon describes nearly a great circle, inclined about 5° to the ecliptic, and occupies 27.32 days in returning to the same place among the stars. 94. Months. — The period just mentioned, in which the moon makes a revolution from a star to the same star again, is called the Sidereal Month. The time occupied in making a revolution relatively to the sun, instead of a star, is called a Synodical Month. This is more than two days longer than the sidereal month ; for the moon's daily progress is about 13°; and during the 27 days of its revolution, the sun, at the rate of 1° per day, will advance 27°, requiring more than two additional days for the moon to over- take it. The mean length of the synodical month is 29.53 days. 95. Nodes. — The points where the moon's path cuts the circle of the ecliptic are called the moon's nodes. The ascending node is the one through which the moon passes from the south to the north side of the ecliptic ; the other, 180° from it, is called the de- scending node. 96. The Moon's Positions in Relation to the Sun. The moon is said to be in Conjunction with the sun, when both bodies have the same longitude ; in Oppo- sition, when their longitudes differ by 180°. The con- 94. What kinds of month are described ? Explain them. 95. Name and describe the nodes. 86 THE MOON. junction and opposition are called by the common name of Syzygies. When the longitude of the moon is 90°, or 270° greater than that of the sun, it is said to be in Quad- rature. The points midway between syzygies and quadra- tures are called Octants. The period in which the moon passes from any one of these points to the same point again (that is, a synodical month), is also called a Lunation. 07* Form of the Moon's Orbit. — It is ascertained by the same method as was described (Art. 51), that the moon's orbit is an ellipse, one of whose foci is at the earth. But its eccentricity is 4J times greater than that of the earth's orbit. The point of the moon's orbit nearest the earth is called the Perigee; the most distant point, the Apogee. 08* T7ie Moon's Diurnal Motion. — The moon not only revolves about the earth, but also on its own axis, in the same length of time ; that is, once in 27.32 days ; and its axis is nearly perpendicular to the plane of its orbit. This rotation is indicated by the fact that the same side of the moon is always pre- sented toward the earth. If it should pass around the earth, and not turn upon an axis, it would obvi- 96. Name and describe the several positions of the moon in rela- tion to the sun. 97. What is the shape of the moon's orbit ? What is apogee ? What is perigee ? 98. What other motion has the moon 1 Do we see all sides of the moon? THE MOON'S LIBEATIONS. 87 ously present all sides to us in the course of each revolution. . But though it keeps the same side toward the earth, it presents all sides to the sun once in each synodical month. Therefore, the days and nights on the moon are nearly 30 (29.53) times the length of those on the earth. 99* The Moon's Librations. — Though the same side of the moon is turned to us on the whole, yet there are slight apparent oscillations, by which nar- row portions of the other hemisphere alternately come into view. These are called Librations. They are of three kinds — the libration in longitude, the libration in latitude, and the diurnal libration. By the libration in longitude, we see a little way round upon the back side, first on the eastern edge, and then on the western. This arises from the un- equal velocity of the moon in its elliptical orbit. By the libration in latitude, we at one time see a little beyond the moon's north pole, then beyond its south pole. This is because the moon's axis is not exactly perpendicular to the plane of its orbit. Both these librations are completed in one sidereal month. By the diurnal libration, we see a little beyond the moon's western limb at its rising, and a little beyond its eastern limb at setting; on account of our being elevated 4,000 miles above the earth's center. 99. Do we see any of the back side ? In how many ways ? De- scribe the libration of longitude — the libration of latitude — the diurnal libration. 88 THE MOON. 100. TJie 3Ioon's Revolution about the Sun. — While the moon revolves about the earth, the earth revolves about the sun, at a distance 400 times as great. Therefore the moon really has a third revolution; namely, that in company with the earth around the sun. And this is far greater than its other revolu- tions, which have been described. Since the moon goes round the earth, its path jnust lie outside of the earth's orbit one-half of the time, and the other half within it. The path is, therefore, a waving line, which crosses the earth's path 25 times in a year. But the moon's orbit is so small, and the earth's motion so swift, that the waves are very long and narrow, and everywhere concave toward the sun. 101. Phases of the Moon. — The moon is not self- luminous, and is seen only as it reflects to us the light which falls upon it. The several forms which the part illuminated by the sun presents to our view, are called Phases. The Circle of Illumination, or the Terminator, is the circle which separates the hemisphere enlightened by the sun from the dark hemisphere, and is perpendicu- lar to the sun's rays which fall on the moon. The Circle of tlie Disk is that which separates the hemi- sphere turned toward the earth from the opposite one, and is perpendicular to our line of vision. The phase depends on the size of the angle formed at the moon, between the solar ray and our visual line. Let the earth be at E (Fig. 22), and the moon in 100. What third revolution lias the moon ? What kind of a path is it ? How can it be everywhere concave toward the sun ? PHASES OF THE MOON. 89 several positions, A, B, &c., and let the lines AS, BS, &c, be directed toward the sun. At A, the moon is in conjunction, and wholly invisible — this is called Neiv Moon; and the angle SAE, between the solar ray and visual ray, is 180°. From A to C (as at B), the phase is called Crescent; and the angle SBE is obtuse. The First Quarter occurs at C, the quadrature, where SCE is a right angle. From to F (as at D), the Fig. 22. O phase is called Gibbous. In this phase, the angle SDE is always acute. At F, the moon is in opposition, and wholly illuminated. This is called Full Moon. The angle SFE is 0°. From F to A, the phases are repeated in reverse order, the Last Quarter being at H. The outer figures at B, C, &c, show the corres- ponding phase. 101. What is meant by phases' using Fig. 22. Explain the several phases, 90 THEMOON. 102. Moon Munning High or JLoiv. — It is gener- ally observed that, at a given age of the moon, for instance, at the full, its meridian altitude is very dif- ferent at different seasons of the year ; that is, that the full moon runs high at some seasons, and low at others. This is readily explained by noticing the moon's relations to the sun. As the moon's path is everywhere near the ecliptic, the new moon will cul- minate at a high point when the sun does ; that is, in the summer. But, in the same season, the full moon, being opposite to the sun, will culminate low. On the contrary, when the sun is in the most southern part of the ecliptic, and culminates low, as is the case in win- ter, the new moon will do so likewise ; but the full moon will culminate at a high point. In the polar winter, therefore, when the sun is absent for months, the moon, whenever near the full, circulates round the sky without setting. 103. The Harvest Moon, — This name is given to the full moon which occurs nearest to the autumnal equinox, September 22d, and which rises from evening to evening with a less interval of time than the full moon of any other season. The sun being at the autumnal equinox, the moon is near the vernal equinox, and at sunset the southern half of the ecliptic is above the horizon, and makes the smallest possible angle with it. It is this small If 2. When does the full moon run high ? when low ? Show why. Where does the full moon shine all the time for many days with- out setting? 103. Which moon is called harvest moon ? Explain the small difference in the time of rising. Why not noticed every month ? THE MOON'S SUE3TACE. 91 angle, made by the ecliptic, and, therefore, by the moon's orbit with the horizon, which causes the small interval in the time of the moon's rising from one evening to another ; for, as the moon advances 13° each day in its orbit, this arc is so^oblique to the horizon, that its two extremities rise with only a few minutes' difference of time ; but the 'place of rising moves rapidly northward. The harvest moon attracts most attention in high latitudes, where the angle between the ecliptic and horizon is smaller, and, therefore, the intervals of time are less. The moon passes the vernal equinox every month, and, therefore, rises with the same small intervals. But when the moon is not full at the same time, the circumstance is unnoticed. 104. Inequalities of the Moon's Surface. — These are clearly revealed by the changing direction of the sun's rays. As the terminator advances over the disc, the light strikes the highest peaks, which appear as bright points a little way upon the dark part of the moon. After the terminator has passed over them, they project shadows away from the sun, which cor- respond to the apparent shape of the elevations, and grow shorter as the rays fall more nearly vertical. And again, in the waning of the moon, the shadows are cast in the opposite direction, lengthening until the dark part of the disc reaches them, and the sum- mits once more become isolated bright points, and then disappear. 104. How do we know the moon is mountainous ? 92 THE MOON. 105. Forms of Valleys. — The most striking char- acteristic of the moon's surface is its numerous circu- lar valleys. The smaller and more regular ones are of all sizes, from one or two miles in diameter up to sixty miles. These are numbered by hundreds. The mountain ridge which surrounds one of these cavities is a ring, very steep and precipitous on the inner side ; but externally it falls off by a rugged but grad- ual slope. These ridges are called Ring Mountains. In the central part of the cavity are generally one or more steep, conical mountains. There is another class of larger but less regular cavities, sometimes called Bulwark Plains. Their diameters are often more than one hundred miles. These are also surrounded by rough mountain masses arranged in a circle. Over these plains are sparsely scattered small conical and ring mountains. There are still larger tracts, more level than the general lunar surface, and of a darkish hue, which still retain the name of seas, formerly given them, though they are covered with permanent inequalities, and show no signs of being fluid. At the time of full moon, there are seen around a few of the principal ring mountains a great many luminous stripes, radiating in straight lines, and ex- tending, in some cases, hundreds of miles. These are sometimes called Lava Lines. 10G» Volcanic Appearance of the Moon, — Every part of the moon's surface has the appearance of 105. Describe the valleys. What is meant by the seas ? What appearance at full moon ? NO ATMOSPHERE OE VAPOR. 93 rocky hardness. The interior slopes of the ring mountains are steep, rough, and angular. The coni- cal peaks within them appear like isolated rocks, resembling the needles of the Alps. The surface nowhere gives indication of having been softened down by the action of water. The circular cavities, with steep and rugged sides, appear like vast craters, and the mountains within them like volcanic cones, more recently thrown up. Nearly every part of the hemisphere presented to our view exhibits these indi- cations of former volcanic action, on a scale far be- yond anything on the earth. But there is no evidence of volcanic action at present. % 107 • Height of the Lunar Mountains. — The height of a mountain on the moon can be determined either by observing how far from the terminator it is when the sunlight just touches its summit, or by measuring the length of its shadow. The highest of the lunar mountains are from three to four and a half miles high. "While the diameter of the moon is not much more than one-fourth as great as the earth's diame- ter, its mountains are nearly equal in height to the mountains of the earth. 10S» Wo Atmosphere or Vapor. — If any kind of atmosphere were spread over the disk of the moon, it would reflect the sun's light so strongly as to dim the features of the solid surface. Nothing of the kind is ever perceived. No terrestrial objects, however near, 106. What are tlie proofs of past volcanic action ? 107. How is the height of lunar mountains found ? How high are they ? 94 THE MOON. ever exhibit greater sharpness of outline than the in- equalities of the moon ; and they never vary in this respect, except in a manner which is obviously occa- sioned by our own atmosphere. A still better proof that there is no atmosphere on the moon is the fact that when its edge passes be- tween us and the stars, they are not dimmed, nor their position disturbed in the least. 100. Changes of Temperature on the Moon. — The moon's equator makes an angle of only 1J° with the ecliptic, and, therefore, experiences no perceptible change of seasons ; but its diurnal rotation is so slow that the extremes of heat and cold during each day are excessive. A place on the moon is exposed to the full power of the sun's rays for about two weeks, and then is for as long a time turned away from the sun, without clouds, or even air, to prevent the free radia- tion of heat. 110. View of the Earth from the Moon, 1. As to Magnitude. — The apparent dimensions of the two bodies, as seen one from the other, are pro- portional to their real dimensions. Hence, in diame- ter, the earth, as seen from the moon, is 3f times as large as the moon, viewed from the earth, and in area is about 13 times as large. 2. As to Phase. — It is obvious, from Fig. 22, that when the full moon is presented to the earth, the earth's dark side is toward the moon, and the reverse. 108. Has the moon an atmosphere ? How proved ? 109. What is said of changes of temperature on the moon ? VIEW OF THE EAETH. 95 Also, that when we see the gibbous phases of the moon, a spectator on the moon would see crescent phases of the earth ; for the angle SED or SEG would then be obtuse. In like manner, the relative phases are in every case supplementary to each other. This relation explains the well-known fact that near the time of new moon, the part of the moon not directly enlightened by the sun is distinctly visi- ble. It is then illuminated indirectly by the earth, which is nearly full, as seen from the moon, and re- flects a strong light upon it. For the same reason, the moon can be faintly seen in a total solar eclipse. 3. As to Position in the SJcy.—The earth, seen from the moon, has no apparent diurnal rotation, as all other heavenly bodies have, but. remains nearly fixed in the same part of the sky. This is owing to the fact that the moon's monthly motion and its diurnal motion are at the same rate in the same direction, so that one apparent motion of the earth neutralizes the other. Hence, a spectator occupying the middle of the moon's disk sees the earth perpetually near his zenith. Another, at the edge of the disk, sees it always near the same point of the horizon. The first and second librations of the moon, since they vary the spectator's position a little in relation to the disk, merely cause small oscillations of the earth's place in the sky. 4 As to Surface. — The earth, by its rotation, pre- sents all its parts to the view of the nearer hemi- 110. State how the earth appears, seen from the moon — as to magnitude — as to phase — as to position in the sky — as to surface. 96 THE MOON. sphere of the moon once in 25 hours. To the other hemisphere it never appears at all. On account of its nearness, and its great size, we might suppose that the geographical features of the earth would be very conspicuous to a spectator on the moon, and that the nature of its surface in nearly all respects could be thoroughly observed. But the deep and dense atmosphere of the earth would reflect an intense light, so as probably to render the inequal- ities of the terrestrial surface nearly invisible ; and whenever clouds prevail over a country, that portion of the earth's surface would, of course, be entirely hidden from view. CHAPTEE IX. ECLIPSES OF THE MOON AND SUN. 1 11, General Relations in Eclipses. — The moon is eclipsed when it is obscured wholly or in part by the earth's shadow. It can occur, therefore, only at op- position, or full moon. The sun is eclipsed when it is either wholly or partially concealed from view by the moon coming between it and the earth. This can happen only at conjunction, or new moon. If the moon's orbit and the ecliptic were coincident planes, there must be an eclipse of the moon at every full moon, and an eclipse of the sun at every new moon ; for at those times the three bodies would be in a straight line. But as the moon's orbit and the ecliptic make an angle of 5° with each other, the moon generally passes opposition and conjunction so far north or south of the sun, that there is no eclipse. That an eclipse may occur, the syzygies must happen near the line of nodes, so that, as the moon comes into conjunction or opposition, some parts of the three bodies may be in a straight line. Fig. 23 will illustrate this. Let NA be a small portion of the ecliptic, and KB, of the moon's orbit. N is the 111. When is the moon eclipsed ? the sun ? Why are there not eclipses every month ? Show by Fig. 23. 98 ECLIPSES. ascending node. If the sun is at N, when the moon is in conjunction, the latter will come exactly between the sun and the center of the earth, and cause a cen- tral eclipse. But if the sun has passed by the node Fig. 23. to E, when the moon comes to conjunction at F, then it will conceal only the north limb of the sun. If the sun is still further from the node, as at C or A, then the moon will pass by at D or B, without appearing to overlap the sun, and no eclipse will occur. 112. Eclipse Months. — As there are two nodes on opposite sides of the heavens, the sun, in its annual progress, must pass through both of them every year, at intervals of about six months. And as the moon comes into the line of syzygies every two weeks, the sun will certainly be near enough to a node for one or two eclipses, and possibly for three, every six months. Thus, the eclipses of any year always occur in clus- ters, at opposite seasons. If two or three are in Jan- uary, the others are in July. These are called the 112. How are the eclipses of any year arranged ? Why ECLIPSE OF THE MOON 99 Node Months of that year. In 1866, for example, the node months are parts of March and April, and parts of September and October. On account of the retro- grade motion of the nodes, the sun passes from a node to the same one again in less than a year, so that the node months occur earlier each successive year perpetually. 113. Eclipse of the Moon. — When the moon is eclipsed, there is nothing interposed to hide it from our view ; but it merely falls into the shadow of the earth, and is obscured. This obscuration may possi- bly continue for several hours. Fig. 24. The sun being vastly larger than the earth, the total shadow of the latter is a cone, as represented in Fig. 24, where the cone of the earth's shadow extends to the extreme right hand. It is found by calculation 113. What is the shape of the earth's total phadow? How long is it ? Where does the nioon pass it ? What is the penumbra? 100 ECLIPSES. to be nearly 900,000 miles long ; and the moon is so near the earth as to go through the broader part of the shadow. But besides the total shadow, there is a partial shadow, called the Penumbra, surrounding the other. It has the form of an increasing cone. When the moon is eclipsed, it must pass through the penumbra before it reaches the total shadow, and again after leaving it. In Fig. 24, the moon enters the penumbra at a, and finally leaves it at b. 114. Length of Lunar Eclipses, and Appearance of the Moon. — The breadth of the total shadow, where the moon passes it, is nearly three times, and that of the penumbra nearly five times, the breadth of the moon. Now the moon moves over its own breadth in about an hour. Hence, when the eclipse is central, it continues between five and six hours. The penum- bra, however, is so faint that its effect is scarcely no- ticeable ; so that the whole apparent duration of a central eclipse is only about four hours. But even when buried in the total shadow, the moon is not invisible, but shines very dimly, appear- ing of a dull red color. This is owing to the sun's fight which the earth's atmosphere refracts into the shadow. Some of the sunlight thus falls on the face of the moon all the while it is in eclipse, and renders it visible. 115. Eclipse of the Sun, — An eclipse of the sun is of a different character from an eclipse of the moon. 114. How long can a lunar eclipse last ? How does the moon ap- pear in eclipse ? Why ? ECLIPSE OE THE SUN. 101 "When the moon is eclipsed, it is obscured by the earth's shadow falling on it. The moon itself is affected. But the sun is said to be eclipsed when the moon intervenes between it and the earth, and hides it from our view. The sun itself suffers no change, but we are placed in circumstances which prevent our seeing it. The phenomenon would more properly be called an Occultation of the sun. 110. Total Shadow and Penumbra of the Moon. The moon's total shadow is a cone of tne same form as the earth's ; but its mean length is only about 232,000 miles, and does not generally quite reach the earth. The moon's total shadow is also surrounded by a penumbra. These are both represented in Fig. 24, where the moon at m stretches its total shadow nearly to the earth's surface, while the penumbra spreads over a large portion of it. "When the moon is nearest, and its shadow longest, it reaches so far as to be cut off by the earth's surface, and form a dark circle, 170 miles in diameter. The penumbra gener- ally covers a circle 4,000 miles in diameter, repre- sented by cd in the figure. The circle of the penum- bra is faintly shaded at the edges, and grows darker towards the center, where the dark circle is situated. 117. Total and Partial Eclipses of the Sun.— When the moon's total shadow reaches the earth, and forms a dark circle on it, a person within that circle wit- 115. How does a solar eclipse differ in character from a lunar eclipse ? What is the appropriate name ? 116. State the form and length of the moon's total shadow. How much of the earth's surface can it possibly cover ? How much can the penumbra cover ? 102 ECLIPSES nesses a total eclipse of the sun. This is one of the most sublime and impressive phenomena of nature. The sun is completely hidden from view, though the sky may be perfectly clear. The whole heavens have something of the appearance of night, and the bright- est stars are visible. The chill of evening is also felt, and animals retire to their resting places. But those who are situated outside of the total shadow, and within the penumbra, perceive the sun 'partially hidden, one side of it being covered up by the circular edge of the moon. A partial eclipse of the sun usually attracts no great attention, because, unless nearly the whole of it is covered, its light is not so much diminished as it often is by clouds. Fig. 25. 117. Describe a total eclipse of the sun. What persons see it ? And what persons see a partial eclipse ? NUMBEE OE ECLIPSES. 103 118* Annular Eclipse. — When the moon's shadow does not reach the earth, those who are in the direc- tion of it see a partial eclipse of a very peculiar form. The sun is all covered by the moon, except a narrow ring around its edge. As the visible part of the sun has the form of a ring, this kind of eclipse is called Annular. (See Fig. 25.) 119* Velocity of the Shadow, and Duration of an Eclipse. — The moon moves in its orbit at the rate of about 2,000 miles in an hour. Therefore its shadow crosses the whole breadth of the earth in a little less than 4 hours. But since the earth revolves on its axis in nearly the same direction, and with one-half the same velocity at the equator, the shadow passes by a place at the rate of a little more than 1,000 miles per hour. Of course, all total and annular eclipses are short, the former not more than 8 minutes, and the latter not more than 13 minutes ; but the whole duration of an eclipse, at a place where it is central, may be about 2 hours. 120, Relative Number of Solar and Lunar Eclipses. On the whole earth there are only about two- thirds as many eclipses of the moon as of the sun ; but, because one is really an eclipse, and the other an occultation, eclipses of the moon at a given place are more frequent than those of the sun. An eclipse of 118. What is an annular eclipse ? In what circumstances does it occur ? 119. How swiftly does the shadow move over the earth ? How long can a total eclipse continue ? an annular ? a partial ? 120. Which kind of eclipses occurs most frequently on the whole earth ? at any given place ? Explain the reason. 104 ECLIPSES. the moon is visible to all on the hemisphere nearest to it, without regard to locality. But an eclipse of the sun is not seen at a place, unless the moon's shadow falls at that place. 121. Eclipses at the 3Ioon. — When we witness a solar eclipse, a spectator at the moon would notice only a small, dimly-defined circular shadow passing over the earth's disk. It would be a partial eclipse of the earth. But when we see a total lunar eclipse, the phenom- enon at the moon would be one of great interest, and of very strange appearance. A dim red light from all parts of the sun's disk is spread over the moon, being refracted thither by the earth's atmosphere. Hence, a spectator there would see the sun expanded out into a thin dull red ring, surrounding the earth, and, therefore, having nearly four times the usual diameter of the sun's disk. 122, True Form of SJiadoivs. — It is impossible, in ordinary diagrams, to present the shadows of the earth and moon in their true proportions. The dis- tance of the sun is so very great, compared with its diameter, that the shadows are exceedingly slender, having a length about 110 times the diameter of the base. The earth being represented as in Fig. 24, the length of its shadow, if rightly proportioned, ought to be more than five feet long. 121. When we see a solar eclipse, what can be seen at the moon ? And what, when we see a total lunar eclipse ? 122. What is the true form of the shadows of earth and moon ? Why not exhibited in diagrams ? CHAPTEE X. LONGITUDE — TIDES. 123. Local Time,— Time is reckoned at every place from the moment when the sun crosses the meridian at either the upper or the lower culmination. This is called local time ; for at the same absolute instant, the time thus reckoned at any place differs from that on every other meridian. 124:* Connection between Longitude and Local Time. — The earth turns uniformly on its axis toward the east through 15° every hour. Therefore, a place lying eastward of another will have the sun earlier on its meridian, and, consequently, in respect to the hour of the day, will be in advance of the other at the rate of one hour for every 15°. Thus, to a place 15° east of Greenwich observatory, it is 1 o'clock P. M. when it is noon at Greenwich ; and to a place 15° west of that meridian, it is 11 o'clock A. m. at the same instant. Hence, the difference of local time at any two places indicates their difference of longitude. 123. What is local time ? 124. How is it connected with longitude ? Illustrate. 106 LONGITUDE — TIDES. 12o, Longitude by the Chronometer. — If a person leaves London with a chronometer accurately ad- justed to Greenwich time, and travels eastward till he finds his own time slower than the local time of the place by Hi. 30???., then he knows the place to be 22° 30' east longitude. For 15° x 1J = 22J . On the contrary, if he travels westward, and at length finds his time-piece at Qh. 44m., when the local time is 4/?. 32m. (in other words, that his Greenwich time is 2/?. 12??2. too fast), then the longitude of the place is 33° W. In the same manner, the longitudes of any two places may be compared with each other. For the use of navigators, chronometers are made which run with very great accuracy, and may be relied on during long voyages. There is always a probability, however, that a chronometer may change its rate somewhat, when it comes to be transported from place to place. It is, therefore, safer, on long voyages, to use several chronometers, and employ the mean of all their indications. 126o Longitude by Eclipses of the Moon, and of Jupiter's Satellites. — In one respect, these eclipses are very favorable for the comparison of longitudes. They are distant phenomena, seen at the same abso- lute instant by all. Hence, any difference of time in the observations at different places is entirely due to difference of longitude. But in another respect, they are quite unfitted for 125. How is longitude found by a chronometer ? 126. How found by eclipses of moon and Jupiter's satellites ? What is the advantage, and what the disadvantage of this method ? THE LUNAR METHOD. 107 the purpose. On account of the penumbra, there is no definite edge to the shadow which passes over the disk, and, consequently, there is great uncertainty as to the time of beginning or end of the eclipse. This method is but little depended on for accurate results. 127 • Longitude by a Solar Eclipse, — In both the above particulars, a solar eclipse differs from a lunar. It is not an event at a distance, seen at once by all, but on the earth's surface, happening to one place at one instant, and to another place at another. The time of beginning or end of a solar eclipse depends on the position of the observer. On the other hand, the phenomenon is very defi- nite, and the moments of immersion and emersion of the sun's limb can be quite accurately fixed by observation* , Occultations of stars by the moon are much more frequent than the occultation of the sun; and these are phenomena of the same general character, and may be used in the same way for finding the longi- tude of a place. 128* Longitude by the Lunar Method. — This is a method particularly useful to navigators, because the observations are made by the sextant. It consists in measuring the angular distance between the moon and some conspicuous heavenly body, as the sun, or a large planet or star, and then correcting the ob- 127. How is a solar eclipse favorable, and how -unfavorable, for finding longitude ? 128. What is the lunar method ? 108 LONGITUDE — TIDES. servation for parallax or refraction, so as to have the true distance between the bodies, as seen from the center of the earth. The observer must also note the local time when this measurement is made. Having with him the Nautical Almanac, in which the distances, as seen from the earth's center, are pre- dicted for every day and hour of Greenwich time, he looks for the Greenwich time at which the distance agrees with the distance as he has obtained it. The absolute time is the same ; hence, the difference of time shows his longitude from Greenwich. The bodies whose angular distances from the moon the Nautical Almanac gives for every three hours, with proportional numbers for interpolation, are the Sun, Venus, Mars, Jupiter, Saturn, and nine bright fixed stars. 129. Longitude by the Telegraph. — Since the in- vention of the magnetic telegraph, it has been em- ployed to determine the differences of longitude between fixed stations on land with a precision which was before altogether unattainable. Suppose two stations to be connected by the telegraphic line, and that there is at each a clock keeping the local time. The observers make signals at certain times agreed on ; and each notes on his own clock the times of the signals given by the other. Electricity moves so swiftly, that a signal may be considered as received at the same absolute instant in which it is given. Hence, the difference of the clocks is merely a dif- ference of longitude. 129. State how the telegraph is used for this purpose. AMBIGUITY AS TO DAYS. 109 130* Change of Days in Circumnavigating the Earth* — While a person travels westward, he length- ens his days by one hour for every 15°, or 4 minutes for every degree, since he moves along with the ap- parent diurnal motion of the sun. In traveling east- ward, on the contrary, he shortens the days at the same rate, by moving in opposition to the sun's daily progress. If we suppose him to go westward entirely round the earth to the same meridian again, whether he takes a longer or a shorter time for the journey, he will lengthen the individual days sufficiently to make the whole number just one day less than if he had remained where he was. The 5th of a month is to him the 4th ; and Tuesday, according to his reck- oning, is Monday. The reason is obvious ; for during his journey, the earth has made a certain number of diurnal revolutions from west to east; but he, by going round from east to west, has, in respect to him- self, diminished that number by one. All this is exactly reversed when one goes round the globe from west to east. He gains just a day by making all the days of his travel a little shorter. It is plain that he makes one more diurnal revolution from west to east than the earth does. Of course, if these two individuals meet at their place of starting, they differ from each other just two days in their reckoning. ~L31., Ambiguity as to Days among the Islands of the Pacific Ocean, — If an island in the Pacific were 130. What change of day is there to a person who goes round the earth to the east ? to the west ? How will they differ from each other ? 110 LONGITUDE — TIDES. settled by navigators, who had gone westward, and also by others, who had sailed eastward, the reckoning of these two parties would differ by one day. To the former, a day will be the first of a month when it is the 2d to the latter. It is, in fact, true that there are islands lying contiguous to each other which have this difference of reckoning. If inhabited land extended entirely round the earth, it would be necessary to fix arbitrarily on some me- ridian on which the change of day should be made. For it is impossible that the reckoning of days should go on unbroken around the earth. The arbitrary meridian would separate between places which differ a day from each other ; so that, on the west side of it, the time is one day later, both in the month and the week, than on the east side. 132. Definitions Melating to Tides. — The Tides are the daily rising and falling of the waters of the ocean. When the water, in this dailv oscillation, has reached its highest point, it is called High Water; at its lowest point, it is called Low Water. Y/hile the water is rising, it is called Flood; and while falling, El)b. A Lunar Bay is the time between two successive culminations of the moon. Its length is about 24 7 ?. 52m., being nearly an hour longer than a solar day on account of the rapid eastward motion of the moon. The tides make their revolutions within the lunar day. 131. What difference of days occurs among the islands of the Pacific ocean ? 132. Define the terms in this article. How long is the lunar day ? OPPOSITE TIDES. Ill Twice in a lunation high water is at a maximum, and twice it is at a minimum. The former are called Spring Tides ; the latter, Neap Tides. The spring tides occur near the time of syzygies ; the neap tides near the time of quadratures. 133* Opposite Tides. — There are two tide-waves on opposite sides of the globe, moving around it from east to west, and arriving at any place at intervals, whose mean value is 12h. 26m., or half a lunar day. Since the mean diurnal motion of each of the two opposite tides is the same as that of the moon, the action of the moon must be regarded as the principal cause of the tides. 134. Form of the Water acted on by the 3Ioon, If the earth were covered with water, and no force were exerted except gravitation toward the earth itself, its form would be exactly spherical, as repre- sented in Fig. 26. But if a distant body, as the moon, should also attract it, the sphere would be changed into a Prolate Spheroid ; that is, into a form produced by revolving an ellipse about its major axis. Let the moon be in the direction of CE produced, and suppose the center of gravity of the nearer half of the water, DEF, to be at A, and that of the remote half at B, while the center of the earth, as a whole, is at 0. Since A is more attracted than C, and C more than B, the form of equilibrium must be dis- turbed, and some of the water will flow toward E, and 133. What is meant by opposite tides ? 134. How would tho moon change the form of the globe if cov- ered with water ? Explain by Fig. 26. 112 LONGITUDE — TIDES oilier parts toward G, till the particles are in equi- librio between their unequal tendencies to the moon and their gravity on the inclined surface of the spheroid. E and G are the highest points of the spheroid, and all points on the circle DF (perpen- dicular to EG) are the lowest. Every section through EG is an ellipse, whose major axis is EG, and whose minor axis is equal to DF. The ellipticity of the section will obviously depend not only on the strength of the moon's attraction, but also on the difference between the attractions on the nearer and remoter parts. In the case of the earth and moon, it is computed that the major axis would exceed the minor by 5 feet ; that is, the tides would be only 2J feet high, and on opposite sides of the earth, one directed toward the moon, the other from it. The tide on the side nearest the moon is sometimes called the direct tide ; the one on the remote side, the opposite tide. '135, Tides by the Sun. — The same kind of effect is produced by the sun as by the moon. But the dis- INERTIA OF WATER. 113 tance of the sun is so great, that though it attracts the earth more than the moon does, yet the difference of its attractions on the several parts is less. The power of the moon to raise a tide is to that of the sun about as 5 to 2. ISO. Joint Action of the Sun and 31oon. — At the time of conjunction, the moon and sun attract in the same direction, and, therefore, the tides are equal to the sum of the lunar and solar tides. The same is true at opposition, because each body produces two tides at once ; and the direct lunar tide coincides with the opposite solar tide, and vice versa. These are the spring tides which occur at the syzygies. At quadratures, each body raises a tide at the ex- pense of that raised by the other. For if the moon is in the direction of EG produced (Fig. 26), it causes high water at E and G, and low water at D and F. And if the sun is in the direction of DF produced, it causes high water at D and F, and Ioy/ water at E and G. As the lunar tides are the highest, E and G are the neap tides, made less by this action of the sun than if the moon had acted alone. 137. Effect of the Inertia of Water. — If the moon and earth were at rest, the tides would be directed exactly to and from the moon. But while the waters are flowing toward these points, the moon, by the diurnal motion, passes westward, and causes them to 135. Compare the sun's action with the moon's. 186. When will the sun and moon conspire in their action? When will they counteract each other ? 137. What is the effect of the inertia of the water ? 114 LONGITUDE — TIDES, change the places at which they tend to accumulate. Thus, even if the waves were unchecked by the shores of continents and islands, the summit would be two or three hours behind the moon in passing a given meridian. 138. Diurnal inequality. — At a given place, the two tides which follow the culmination of the moon will vary in height, according to the relation between the latitude of the place and the mioon's declination. Fig. 27. If the moon, M (Fig. 27), is on the equator, it is clear that the tides on the equator, EQ,~are greatest, and that in other places they are less, as the latitude is greater. But the two successive tides at any place are equal ; for, by the rotation on NS, the tide at B in 12 -J hours will come round to A, and be equal to the tide now there. The same is true of the tides C and D, or F and G. Hence, when the moon has no declination, there is no diurnal inequality. 138. Describe the diurnal inequality. When will the direct tide be greater than the opposite tide? When will the opposite tide be the greatest ? EFFECT OF COAST; 115 But suppose the moon has a northern declination, as in Fig. 28. Then the highest points of the tide are at A in north latitude, and D in south. At A, where the direct tide is large, the opposite tide, now at B, will arrive in 12J hours, and will be small. But afc 0, this is reversed ; the direct tide is small, and Fig. 28. the opposite one (now at D, and arriving at C 12J hours later), is large. Therefore, when the declina- tion and the latitude are both north, or both south, the direct tide (that is, the tide which first succeeds the upper culmination of the moon) is larger than the opposite tide ; but if one is north, and the other south, the direct tide is smaller than the opposite tide. This difference in the height of the two suc- cessive tides is called the diurnal inequality. 130o Change of Direction and Velocity caused by Coasts. — The tide-wave, which would move regularly westward around the earth, if it were wholly covered by deep water, is exceedingly broken up and changed, 139. Explain how coasts affect the direction and velocity of tides. 116 LONGITUDE — TIDES both in direction and velocity, by coasts and shoals. Its general direction is westward ; but as it can pass the continents only at their southern extremities, it bears to the northwest, and then to the north, in the Atlantic and Pacific oceans ; and when it enters seas or channels, it usually bends its course in the direc- tion of their length. 140. Cotidal Lines. — These are lines drawn on a chart of the oceans, showing the position of the sum- mit of the tide-wave for each hour of a day. Such a system of lines expresses to the eye the direction and velocity of' the tide at all places. Thus, on the open Fig. ocean, the figures 1, 2, 3, 4 (Fig. 29), show the situa- tion of one and the same tide-wave at those hours, 140. Describe the cotidal lines. Why is the tide-wave convex forward in channels ? How can there be four tides in a day at any- place ? EFFECT OF COASTS. 117 respectively. And in the channel which extends northward, the wave, having separated from the ocean tide, advances northward, and occupies the places marked at the hours indicated. The wave advances most rapidly in the deepest water. Hence, the front is generally convex, as in Eig. 29, since it moves fast- est in the central part, where the water is deepest. For this reason, also, the tide may occupy as long a time in running through a long channel of shallow water as in advancing half round the earth. The greatest velocity of tide in the deep open ocean is near 1,000 miles per hour. Some channels are affected by tides entering at both extremities. For example, the German Ocean and English Channel receive the Atlantic tide both at the north and at the south end. As a consequence, the tide system is doubled, causing, at some points, four tides per day. 141. Modification in the Height of the Tide caused by Coasts. — The relation of coast lines to each other also very much affects the height of the tide at partic- ular places. When the tide directly enters a broad- mouthed bay, it grows higher as the bay contracts in breadth ; and at the head of the bay there is usually found the greatest height of all. One of the most remarkable examples is the Bay of Eundy. The western extremity of the Atlantic tide-wave, after en- tering this bay, is gradually contracted by the shores as it advances, till, at the head of the bay, it some- times rises to 70 feet. 141. How is the height of the tide affected by the coasts ? Where is the tide likely to he highest in a hay ? 118 LONGITUDE — TIDES. The height of the tide on the coast is generally greater than in the open ocean, owing to the effect of shoal water. The most advanced part of the wave moves slower than the hinder portion ; so that the cross-section of the ridge becomes shorter, and, there- fore, higher, as the depth of water diminishes. The mean height of the spring tides at any place is called the Unit of Altitude for that place. 142. Tides of Lalces and Inland Seas. — In general, the tides of lakes and inland seas are scarcely per- ceptible. The reason is, their extent is so small that all parts are to be considered as almost equi-distant from the moon. There is little opportunity for water to be attracted from the more distant to the nearer part. The largest North American lakes have tides but an inch or two in height. In the Mediterranean, however, which derives no tide from the ocean, the tide-wave reaches 1^ or 2 feet. 142. Why is there so little tide in inland seas ? CHAPTER XI. THE PLANETS — TABULAR STATEMENTS— MERCURY— "VENUS — MARS. 143, Names and Classification of the Planets.— The Planets are solid spherical bodies revolving about the sun in orbits which are nearly circular. The name "planet" signifies a wanderer, and was given to these bodies because they continually change their places among the fixed stars, generally moving from west to east, but sometimes from east to west. These appar- ently irregular motions are fully explained by our own annual motion, the earth on which we live being one of the planets. The planets are naturally arranged in three classes. 1. Four small planets near the sun, of which the earth is the largest, namely : Mercury, Venus, Earth, Mars. 2. The Planetoids, an indefinite number of bodies, too small to be measured with certainty, and occupy- ing a ring outside of the first class. They are also called Asteroids and Minor Planets. 143. What are planets ? State and describe the three groups. 120 THE PLANETS. 3. Four large planets, moving outside of the ring of planetoids, widely separated from each other, and at vast distances from the sun. These are Jupiter, Saturn, Uranus, Neptune, Two planets of the first class, Mercury and Yenus, revolve in orbits within the earth's orbit. These are called inferior planets, being loiver down in the solar system than the earth is. All the others, including the planetoids, are called superior planets ; because, in relation to the sun, the great center of attraction, they are higher than the earth, and revolve in orbits exterior to the earth's orbit. 144. Satellites.— There is another class of spheri- cal bodies, holding a subordinate place in the solar system, since they revolve around the planets as cen- ters. These are called Satellites. The moon, already described in Chapter VIII, is a satellite of the earth. They are distributed as follows : • The earth has 1 ; Jupiter, 4 ; Saturn, 8 ; Uranus, 4 ; Neptune, 1. Mer- cury, Yenus, and Mars, have no satellites. The satellites are also called secondary planets; and the planets, in distinction from them, primary planets. 145. Distances of the Planets from the Sun. — The following table presents the mean distances of the planets from the sun in millions of miles, and also their relative distances, the earth's being called 1 : 144. V\That are satellites j What planets do they attend ? 145. Give the distances of the planets from the sun. PEEIODIC TIMES. 121 I. Mean Relative Distances. Distances. Mercury 37,000,000 0.39 Venus 69,000,000 0.72 Earth 95,000,000 1.00 Mars 145,000,000 1.52 Planetoids 254,000 000 2.67 Jupiter 496,000,000 5.20 Saturn . . . . 909,000,000 9.54 Uranus 1,828,000,000 19.18 Neptune 2,862,000,000 30.04 It appears, by this table, that the remotest planet is 77 times as far from the sun as the nearest. Hence it is that orreries, unless of inconvenient size, always fail of truly representing the planetary distances. The same is generally true of diagrams. 146* Periodic Times of the Planets. — The follow- ing table contains the length of the sidereal revolu- tions in months and years, which is the most con- venient form for the memory ; their length in days and decimals, for calculations ; and their mean daily motion : IL Sidereal Sidereal Revolu- Mean Daily Revolution. tion in Days. Motion. Mercury 3 months. 87.969 4° 5' 22.6" Venus 7± ■ " 224.701 1° 36' 7.7" Earth 1 year. 365.256 0° 59' 8.3" Mars 2 "• 686.980 0° 31' 26.5" Planetoids 4-|- " Jupiter 12 " 4,332.585 0° 4' 59.1" Saturn 29 " 10,759.220 0° 2' 0.5" Uranus 84 " 30,686.821 0° 0' 42.2" Neptune 164 " 60,126.720 0° 0' 21.6" 146. State the periods of revolution. Diameters. Volumes. 82' 2" 1,405,000 0' 8" * 0' 17" ft 1 0' 6" t 0' 37" 1,521 0' 16" 921 0' 4" 87 0' 2" 79 122 THE PLANETS. 147* Magnitudes of the Planets, — Table III gives the diameters of trie sun and planets in miles, with their mean apparent diameters, and their volumes compared with the earth : III. Diameters. Sun 886,000 Mercury 3,100 Venus 7,800 Earth 7,912 Mars 4,500 Jupiter 91,000 Saturn 77,000 Uranus 35,000 Neptune 34,000 148* Masses and Densities of the Planets. — Table IV exhibits the masses and densities of the sun and planets, the earth being called I. It appears, from this table, that the small planets are much more dense than the large planets and the sun : iv. Masses. Density. Sun 355,000.00 0.25 Mercury 0.12 1.97 Venus 0.88 0.92 Earth 1.00 1.00 Mars 0.13 0.72 Jupiter 338.03 0.22 Saturn 101.06 0.11 Uranus 14.79 0.15 Neptune 24.65 0.31 147. Give their diameters and volumes. 148. Also their inasses. Which aie the most dense ? PLANETARY MOTIONS. 123 149. The Sun and Planets Compared. — By Table III, we see that the sun has 10 times the diameter, and 1,000 times the volume, of Jupiter, the largest planet in the system. Table IY shows that the mass of the sun is also more than 1,000 times as great as that of Jupiter, and 700 times greater than the united masses of all the planets. Its attraction mainly con- trols the movements of all the planets, satellites, and comets. Hence, these bodies describe their various paths about it, scarcely disturbing it from a state of rest. For this reason, this system of bodies is called the Solar System. ISO* Diameters of Planets, and their Distances from the Sun. — One of the most remarkable facts relating to the planets is brought to view in com- paring the distances in Table I with the diameters in Table III. "While the diameters of the planets are only a few thousands of miles, their distances from the sun are many millions. The diameter of Nep- tune's orbit is more than 20,000 times the diameters of all the planets added together. To attempt to represent both the distances a*ad magnitudes of the planets in their proportions, by an orrery or diagram, is out of the question. 151. Directions of the Planetary Motions, — It has been stated in preceding chapters that all the mo- tions of the sun, earth and moon are from west to 149. Compare the sun with the planets in diameter, in volume, and in mass. Why is the system called the solar system ? 150. Compare the diameters of the planets and their distances from the sun. 124 THE PLANETS. east. The same thing is true, in general, of all the planets and satellites ; and in nearly every case the inclination to the ecliptic is very small. Since the motions in the solar system are so generally from west to east, this is regarded as direct motion ; and any motions, real or apparent, which are from east to west, are called retrograde. MERCURY. 152. Apparent 3Iotions. — Mercury is an inferior planet, whose orbit is far within the earth's ; for it is seen alternately east and west of the sun, and never Fig more than 29° from it. Let E (Fig. 30), be the earth, supposed, for the present, to be at rest ; the circle 151. What is the general direction of the planetary motions ? MEKCUKY. 125 ABD, the orbit of Mercury ; S, the sun ; and BA/, the sky, on which the bodies are seen projected. When Mercury is at B, it is seen at B' ; as it passes through D to A, it appears to advance to A ; as it is now coming toward the earth, it seems to be station- ary at A' ; then from A through C to B, it appears to retrograde from A to B', where it is again stationary, as it moves away from us. Since the sun appears at S f , the planet passes by it, both when advancing and when retrograding. When the planet is at D and C, it is in conjunction with the sun ; at C, between the earth and sun, it is said to be in the inferior conjunction ; at D, in supe- rior conjunction. B and A are called the points of greatest elongation. At superior conjunction, the mo- tion of Mercury appears to be forward ; at the infe- rior conjunction, backward ; and if the earth were at rest, as we are now supposing, the planet would ap- pear stationary at the points of greatest elongation, 153. The Motions of Mercury as Modified by the Earth's Motion. — To simplify the case, it was sup- posed, in the preceding article, that the earth is at rest. But the earth moves in nearly the same direc- tion as Mercury, making about one revolution while Mercury makes four (Table II). The effect is to lengthen the arc of apparent advance, and shorten that of retrogradation. Thus, let the earth be at A (Fig. 31), when Mercury is at F ; then it will appear in the sky at L. While the earth is advancing to B, 152. Describe the apparent motions of Mercury, the earth being at rest. Define superior and inferior conjunctions, and greatest elongations. 126 THE PLANETS. Mercury passes the inferior conjunction, and arrives at G, and appears at M, having moved apparently backward from L to M. As the earth moves to C, Mercury describes GKE, and is at superior conjunc- tion N. Again, while the earth moves to D, Mercury Fig. 31. passes round to G, still advancing in the sky to O. But while the earth describes DE, Mercury again passes the inferior conjunction from G to K, and ap- parently retrogrades from O to P; after which, it begins once more to advance. Thus, by the earth's motion, the planet is made to retrograde through a shorter arc, and to advance through a longer one, than if the earth were at rest. 153. Show how the earth's motion modifies the apparent motions of Mercury. MEECUEY. 127 154. Stationary Points. — If the earth were at rest, as supposed in Fig. 30, the points where the planet would appear to be stationary, in relation to the stars, would be A and B, at which tangents drawn from the earth would meet the orbit. But the earth's motion removes the apparently stationary points a little way toward the inferior conjunction. For, in order to appear stationary, the advance which the earth's motion causes must be just neutralized by the retrogradation of Mercury. This planet appears sta- tionary when its elongation from the sun is 15° or 20°, according as it is nearer the perihelion or the aphelion. 155. Form and Position of Mercury' s Orbit. — The orbit of Mercury is more eccentric, and more inclined to the ecliptic than that of any other of the eight planets. While the eccentricity of the earth's orbit is only ■£$, that of Mercury is nearly ^. Yet this ren- ders the minor only -^ shorter than the major axis ; so that the form of the most eccentric of the plane- tary orbits, if correctly drawn, would appear to the eye to be a circle. The inclination of Mercury's orbit to the plane of the ecliptic is 7°. 156. Phases of Mercury. — At the inferior con- junction, C (Fig. 30), the unilluminated side of Mer- cury is turned toward the earth, so that, like the new moon, it is invisible. At the superior conjunction, D, 154. Where would Mercury appear stationary, if the earth were at rest ? Where, if the earth is in motion ? 155. State the form and position of Mercury's orbit. 128 THE PLANETS. its illuminated side is toward us, and it is full. At A or B, where the ray AS, and our line of vision, AE, are at right angles, the phase is a semicircle. On the arc ACB occur the crescent phases ; on BDA, the gibbous phases. 157. Point of Greatest Brightness. — Mercury is not brightest when full, because it is then too far dis- tant. It is not brightest when nearest, because its dark side is toward us. Nor is it brightest at the place of greatest elongation ; but beyond it, toward the superior conjunction, when about 22° from the sun. Its apparent diameter, when nearest the earth, and when most distant from it, is as 2J to 1. 158. Transits of 3Iercury. — As Mercury, at the inferior conjunction, passes nearly between the earth and sun, it may possibly come exactly in a line with them, and thus be seen as a black round spot going across the sun's disk. This phenomenon is called a transit of Mercury. If the plane of its orbit were coincident with that of the ecliptic, a transit would obviously occur at every inferior conjunction. Since the angle between the two planes is 7°, the planet cannot be seen on the disk unless near the node. The nodes of Mercury's orbit lie in those parts of the heavens which the sun passes through in May and 156. Describe the phases of Mercury, and when they respectively occur. 157. Where is Mercury when brightest ? Why not at the point nearest to us ? 158. What is a transit of Mercury ? Why does not a transit oc- cur at every inferior conjunction ? In what months do they occur ? VENUS. 129 November. Therefore, a transit of that planet can occur only in those months. The shortest interval between two transits of Mercury is 3J years. VENUS. 159* Apparent Motions. — Like Mercury, Venus appears to pass back and forth by the sun, reaching a distance of 47° at its greatest elongation. This proves it to be an inferior planet, between Mercury and the earth. Its sidereal period approaches so near to that of the earth that its synodic period is lengthened to nearly If years. Hence, after making an apparent retrograde motion, as LM (Fig. 31), it advances once and two-thirds round the heavens be- fore it commences the next retrograde arc, OP. 160* Phases and Brightness of Venus, — Venus passes through the same changes of phase as Mer- cury. But its apparent diameter, when the crescent phase is narrowest, is more than 6 times as great as when at full, because it is more than 6 times as near. Venus is the brightest of the planets, and has been known from ancient times as the morning and evening star, according as it west of the sun, or east of it. The place of greatest brightness for Venus is when about 40° from the sun, between the point of great- est elongation and the inferior conjunction. In this situation, it is frequently visible all day. 161. Transits of Venus. — The orbit of Venus is inclined to the ecliptic about 3J degrees. The sun 159. Describe the apparent motions of Venus. 160. State respecting its phases and its greatest brightness. 130 THE PLANETS. passes its nodes in June and December. Therefore, the transits of that planet always occur in those months. The shortest interval between two transits of Venus is 8 years ; but after the occurrence of two such, there cannot be another for more than a cen- tury. Between 1800 and 1900 there are two transits of Yenus, viz. : December 8th, 1878, and December 6fch, 1882. A transit of Venus is an occurrence of great inter- est to astronomers, because it furnishes the best method known for determining the sun's horizontal parallax, and, therefore, the earth's distance from the sun. MAES. 102. Situation of Mars in the Solar System.— This is the most remote planet of the first group described in Art. 258, namely : Mercury, Venus, Earth, Mars. It is also the nearest to the earth of those planets which are called superior. As Mars revolves in an orbit outside of the earth's, it can come into Opposition to the sun, as well as into conjunction with it, appearing at every degree of elongation from 0° to 180°. 163. Apparent Motions.— The real motion of Mars is from west to east ; and during most of the year, its apparent motion is in the same direction, sometimes 161. What is the shortest interval between two transits of Venus? After two such transits, how long before another ? Why is a tran- sit of Venus important ? 162. Where is Mars in the solar system ? What is the opposition of Mars ? MAES. 131 accelerated, and sometimes retarded, by the earth's motion. Near opposition, however, when the earth overtakes and passes by Mars, its motion appears re- trograde. Thus, let the earth make one revolution Fm. 32. from F to F again (Fig. 32), while Mars describes nearly a half revolution from G to N. When the earth is at F, Mars appears in the direction FG; when at A, Mars, at H, appears in the sky at O ; when the earth is at B, Mars, at I, appears at P. Thus far the motion has been in advance, though becoming re- tarded near P. But as the earth passes from B, through C, to D, Mars, passing over the shorter arc IKL, appears to retrograde from P to Q ; after which it again advances, appearing at B, when the earth is at E, and in the direction FN when the earth is at F. For the same reason, all the superior planets have a retrograde motion at the time of opposition. 163. By Fig. 32, describe" tlie apparent motions of Mars, When will it appear to go backwards ? 132 THE PLANET 164. Phases, and Changes of Apparent Size, — At opposition, M (Fig. 33), and at conjunction, M', it is obvious that Mars appears full, since we look in the same direction in which the sun shines upon it. In other positions, the angle between the sun's rays and our visual line is acute, and the phase is gibbous (Art. 101). The planet is so near us that the phase differs perceptibly from the full, when about half-way from conjunction to opposition, as at Q, Q'. The least possible distance of Mars from the earth, at opposition, is 35,000,000 miles ; and the greatest possible distance, at conjunction, is 255,000,000 miles. 165. Appearance of Disk. — Mars is remarkable among the planets for its redness. The telescope 164. What changes of phase has Mars? How near the earth, and how far from it, can Mars be ? MARS. 133 reveals some permanent inequalities of surface, by which its diurnal rotation has been determined more satisfactorily than in the cases of Mercury and Ye- nus. And there are other appearances, which change as the relation of the equator to the sun changes. The polar regions, when turned away from the sun, exhibit a whiteness which is supposed to be the effect of ice and snow ; and this whiteness disappears grad- ually when the pole is turned again toward the sun. 166. Orbit and Equator of Mars. — The orbit of Mars is inclined to the ecliptic nearly 2°, and has an eccentricity equal to T \. In its diurnal rotation, it considerably resembles the earth, having about the same length of day, and its equator being inclined nearly 29° to its orbit. Hence, the seasons vary somewhat more than those on the earth. The four small planets are all nearly alike as to the length of their day. Mercury revolves in 24Ji. 5rn. } Yenus in 23h. 21m., the earth in 23k 56m., and Mars in 24Ji. 37m. 165. Describe its telescopic appearance. 166. What are the form and position of its orbit ? What is the length of day on the four planets nearest the sun ? CHAPTER XII. THE PLANETOIDS — JUPITER— SATURN — URANUS — NEP- TUNE — DISTURBANCES OF THE PLANETS. 107 • Hie Space between the Four Small Planets and the Four Large Ones. — There is a wide space between Mars and Jupiter, within which the astrono- mers of the last century conjectured there might re- volve another planet. The search for such a planet at length led to the discovery of those bodies called the Planetoids, known, also, by the name of Asteroids. THE PLANETOIDS. 108* Their Number, and the Time of their Dis- covery. — Four of these bodies were discovered within the first seven years of the present century, namely : Ceres, Pallas, Juno, and Yesta. Since 1845, others have been found nearly every year, till their number at the present time (1867) is between 90 and 100. The whole number of planetoids may be regarded as in- definitely great. 169. Characteristics.— -They are distinguished from the eight planets in the following particulars : 167. What is said of the space between Mars and Jupiter? What was discovered in it ? 168. Give an account of the discovery. THE PLANETOIDS, 135 1. By their Diminutive Size. — They are invisible to the naked eye, and by the telescope cannot be distin- guished from faint fixed stars, except by their motion. They are generally too small to show a sensible disk, and hence cannot be measured with any certainty. The largest of them is believed to be only about 200 miles in diameter. And it is estimated, by the slight disturbing influence which they exert, that their entire mass is equal only to a small fraction of the earth. 2. By the Large Eccentricity and Obliquity of their Orbits. — The eccentricity of most of them is much greater than that of any of the eight planets. The obliquity of the orbit of Hebe is 14°, and that of Pallas is 34°, which is the greatest yet discovered. 3. By their being Clustered in a Ring. — The orbits vary considerably in size, and, therefore, the periodic times are various. But as they are generally quite eccentric, every planetoid is nearer the sun at perihe- lion than any other one is at aphelion. The orbits are, therefore, all linked together, and pass through each other. Thus, the planetoids are to be regarded as moving among each other about the sun, within the limits of a ring, whose breadth, in the direction of the radius vector, is more than 100,000,000 miles. Flora, which moves in the smallest orbit yet discov- ered, performs its revolution in 3 J years ; Cybele, the most remote, in 6J years. Their mean periodic time is 4J years ; and their mean distance from the sun is 254,000,000 miles. 169. What is the first particular which distinguishes the planet- oids from the planets? the second? the third? What are the longest and shortest periods of the planetoids ? 136 THE PLANETS. JUPITER. 17 Oo Jupiter's Magnitude and Place in the Solar System. — Jupiter is the nearest of the large planets outside of the planetoids, and its orbit is not far from 200,000,000 miles beyond the ring which includes them. On account of its great distance from the sun, compared with the earth's, Jupiter presents to us no visible change of phase, appearing always full. Its disk, as presented to us, is almost the same as if we were at the sun. The same is, of course, true of all the planets still more remote. Jupiter greatly surpasses all the other planets in magnitude. In volume, it is about 1| times the sum of all the others, and in mass, more than 2-J times their united mass. 171. Its Form and Orbit. — Though the diameter of Jupiter is 11 times that of the earth, yet it rotates on its axis in less than 10 hours ; so that the equa- torial velocity is about 27 times as great as the earth's. This rapidity of rotation produces a sensi- ble oblateness of the planet. Its ellipticity is T \ ; and so considerable a deviation from the spherical form is perceptible to the eye without measurement. The orbit of Jupiter is nearly in the plane of the ecliptic, and has an eccentricity of J-q, which is three times that of the earth's orbit. The equator of the 170. Where is Jupiter in the solar system? Does it present changes of phase ? Why ? Compare its size and mass with those of the other planets. 1 71 , How swiftly does it rotate on its axis ? What is the effect ? Is there a change of seasons on Jupiter ? Why ? JUPITER. 137 planet is inclined only about 3° to the plane of its orbit, so that there is no perceptible change of seasons. 172. The Belts of Jtipiter. — This name is given to bands or stripes of darker shade than the rest of the disk, stretching across it in the direction of its rota- Fig. 34. tion (Fig. 34). xhey vary, from time to time, in num- ber and in breadth, often covering a large part of the surface. A belt usually appears of uniform breadth entirely across, but not always ; its edge is occasion- ally broken, and sometimes it is much wider on one part of the disk than on the other, the change of breadth being commonly quite abrupt, and thereby revealing the rotation of the planet. There are, ordi- narily, two conspicuous belts, lying near the equator, one north, and the other south of it. Jupiter is supposed to have an atmosphere, in which there are always many clouds floating. These, 172. Describe tlio belts. Explain their formation. 138 THE PLANETS. by the swift rotation of the planet, are thrown into stripes parallel with the equator ; and the dark belts are considered to be the spaces between the clouds, through which we look upon the planet itself. 173. Satellites of Jupiter. — These are four in num- ber, revolving in orbits very nearly circular, and in planes which make small angles, both with the orbit and the ecliptic. They are called the first, second, third, and fourth, reckoning outward from the planet. Their orbits being presented edgewise to us, they seem to move back and forth across the place of Ju- piter, one way in front of the planet, and the other w^ay behind it, and always appear nearly in a straight line. (See Tig. 34.) Jupiter's satellites are all somewhat larger than the moon, but on account of their great distance from us, they are too small to be seen except by a telescope. Because of the great attraction of Jupiter, exerted upon them, they revolve a great deal quicker than the moon about the earth, as shown in the following table : Satellites. Diameters. Distances. Sidereal Revolutions. 1 2,440 275,000 Id. lSd. 28m 2 2,190 438,000 M. ISh. 15m 8 3,580 698,000 7d. Sh. 43m. 4 3,060 1,229,000 16d. 16A. 32m. . 174:. Eclipses of Jupiter and its Satellites, — On account of the great size of Jupiter and its shadow, 173. How many satellites lias Jupiter ? How do they appear to move ? Give their sises and times of revolution. Why do they re- volve so swiftlv ? JUPITEK. 139 and the small inclination between its own orbit and those of its satellites, most of them are eclipsed at every revolution, when on the opposite side of the planet from the sun ; and they generally eclipse Jupi- ter itself in passing between it and the sun. And since they revolve very rapidly, these eclipses are oc- curring every day. When Jupiter is eclipsed by one of its moons, there is seen only a small dark spot going across its disk. Both kinds of eclipses will be Fig. 35. understood by reference to Fig. 35, where J repre- sents Jupiter, 1, 2, 3, 4, the orbits of the satellites, and A, B, C, D, different positions of the earth in its own orbit. At a, the first satellite is just entering the shadow ; at b, it has just emerged ; and when any satellite comes between J and the sun, its shadow will fall on the planet. By means of the eclipses of Jupiter's satellites it has been discovered how swiftly light moves. For, when the earth is at A, it is observed that an eclipse 174. What phenomena do they present ? Describe and explain the eclipses of the satellites and of the planet. What discovery was made by these means ? 140 THE PLANETS. is seen about 16 minutes earlier than if it were at C. And this must be because it requires 16 minutes for the light to cross the earth's orbit. SATURN. .175, Saturn's Disk. — Saturn is the second planet in size ; and being the second in order beyond the planetoids, is not too far from the earth to present a large disk. Its form is seen to be elliptical, and it is faintly striped with belts in the direction of the major axis. Both these appearances are explained by the rapid rotation of the planet on its axis, as in the case of Jupiter. It ellipticity is ^ revolves in about 10J hours, and its 176, Saturn's Mings. — The distinguishing feature of this planet is the system of broad thin rings which Fig. 36 surround it. They lie in a plane inclined about 28° to the ecliptic, and, therefore, generally present an 175. Where is Saturn's place in respect to distance from the sun ? In respect to size ? What is the appearance of its disk ? SATURN. 141 elliptical appearance to the earth (Fig. 36). The ring, as usually seen, consists of two rings, the inner of which is the widest. The inner edge is 20,000 miles from the surface of the planet ; and the diame- ter from outside to outside is 176,000 miles. The line in which the plane of the ring intersects the plane of Saturn's orbit is called the line of the nodes. The rings revolve in the same time as the planet ; that is, in about 10 J hours. 177. Disappearance of the Mings. — Saturn re- volves about the sun once in 29 years, and its rings always remain parallel to themselves, as represented Fig. 37. in 'Fig. 37, where GO is Saturn's orbit, and db the earth's. As Saturn moves from A, through C, to E, we look upon the northern side of the rings ; and 176. What distinguishes Saturn? Describe the rings and their motions. 177. What is Saturn's period ? What are the changes in the as- pect of the rings ? Can the rings disappear more than once during the year of disappearance ? Why ? 142 THE PLANETS. from E to A, upon the southern side. At A and E, the rings present their edge toward us, and can scarcely be seen at all. Thus, the rings disappear once in about 15 years. But it requires about a year for the plane of the rings to pass by the whole breadth of the earth's orbit. It, therefore, happens that, during the year of the edge-view, the plane will pass once through the sun, and perhaps two or three times through the earth ; and, during a portion of the year, the plane will He between the sun and the earth, so that the dark side of the rings will be presented toward us. 1 78, Phenomena of the Mings at the Planet. — On that hemisphere of the planet to which the luminous side of the rings is presented, there is the appearance of splendid arches spanning the sky, having a breadth and elevation according to the latitude of the place. At latitude 30° the breadth is about 18°, and the ele- vation of the lower edge on the meridian about 22°. Near the poles, however, it is below the horizon. The luminous side is presented to the northern hemisphere near 15 years, and then the same length of time to the southern hemisphere, in regular alternation. A part of the rings is generally eclipsed by the shadow of the planet falling on it. Also, during the 15 years in which the dark side of the rings is turned toward a hemisphere, its shadow is cast across a zone of it, which causes an eclipse of the sun. And at a given place, a total solar eclipse may continue from day to day, without interruption, for several years. 178. How do tlie rings appear on the planet itself? UEANUS. 143 179, Satellites of Saturn, — Saturn is attended by eight satellites. Their periods of revolution vary from less than one day to 79 days. Their diameters vary from 500 to 3,000 miles ; but on account of their immense distance from the earth, they are seen only with the best instruments. They are all external to the rings, at distances from the planet varying from 129,000 to 2,478,000 miles. Their orbits are nearly in the plane of the rings, and make an angle of about 28° with the orbit of the planet. Hence, they are not very liable to be eclipsed. The principal time for eclipses is that at which the rings disappear ; for then the sun is nearly in the plane of their orbits, as well as of the rings. URANUS. 180* Discovery, and Place in the System. — Uranus was unknown to the ancient astronomers ; and to them, therefore, Saturn's orbit was the boundary of the solar system. Uranus was discovered by Sir William Herschel, in 1781, and has made but little more than one revolution since that time ; for its periodic time is 84 years. It was, however, repeat- edly seen by earlier astronomers, and recorded in their catalogues as a fixed star. By this discovery, the diameter of the known solar system was doubled. Uranus is the third of the four great planets, both in size and in order of distance. But its distance from us is so immense that it appears only as a faint 179. Describe the satellites of Saturn. 180. When, and by whom, was Uranus discovered ? How dees it appear ? 144 THE PLANETS. star, and presents no inequalities by widen its diurnal motion can be discovered. Its orbit is very nearly circular, and is inclined less than a degree to the ecliptic. 181. The Satellites of Uranus. — Sir William Her- schel announced the discovery of six satellites belong- ing to Uranus. But only four have been identified by later astronomers. The remarkable facts relating to these satellites are, that their orbits are nearly at right angles to the plane of the ecliptic, and that in the orbits the motions of the satellites are retrograde; that is, from east to west. Their periods of revolu- tion vary from 2J days to 13J days, and their dis- tances from 130,000 to 396,000 miles. NEPTUNE. 182. Discovery. — Neptune was discovered in 1846. The circumstances which led to the discovery were briefly as follows : After the orbit of Uranus had been carefully computed, and corrections made for the disturbing influence of Jupiter and Saturn, the planet was found to depart from the calculated path in a manner not to be accounted for except by sup- posing some other disturbing force. It was for some time suspected that there must be a planet superior to Uranus, whose attraction caused the change of its orbit. At length, two mathematicians, Le Verrier, of France, and Adams, of England, each without any knowledge of what the other was attempting, engaged 181. By what is it attended ? NEPTUNE. 145 in the arduous labor of calculating what must be the elements of a planet which should produce the given disturbance of the motions of Uranus. They reached results which agreed remarkably with each other D Le Verrier communicated to Galle, of the Berlin ob- servatory, the place in the sky in which the disturb- ing body should be situated ; and in the evening of the same day, Galle found it within a degree of the predicted longitude. The planet thus discovered explains fully the dis- turbances in the motions of Uranus. It soon appeared that Neptune had repeatedly been entered in catalogues as a fixed star. The ear- liest of these records, in 1795, afforded material aid at once in determining its mean distance and its peri- odic time. Neptune is attended by one satellite, which was also discovered in 1846. It is nearly as far from the primary as the moon is from the earth, and revolves in 5d. 21h. So far as known, Neptune is the most remote- planet of the solar system, its distance from the sur being 30 times as great as that of the earth. Its time of revolution is 164 years. MUTUAL ACTION OF THE PLANETS. 183. Motions of the Planets Disturbed. — On ac- count of the universal gravitation of matter, it mighl be expected that the planets, in describing theii 182. When was Neptune discovered? What led to the discov ry? Give an account of it. State other particulars respecting Neptune. 146 THE PLANETS. orbits about the sun, would disturb each other's mo- tions. It is true that they do ; and one of the most difficult and laborious parts of practical astronomy is to calculate and allow for these disturbances. No one of all the planets pursues the same elliptic orbit which it would describe if the sun were the only other body in the system. One kind of disturbance is this : The plane of an orbit changes its position in such a manner that the nodes, in which the planet cuts the plane of the ecliptic, move backward ; that is, from east to west. Another is, that the perihelion and aphelion of most planetary orbits advance, or move from west to east. Still another disturbance is, that the eccentricity of an orbit changes, becoming at one time greater, and at another time less. And others beside these might be named. 184. Stability of the System, — Notwithstanding these disturbances, it has been proved that they do not tend to cause the destruction of the system, as was once supposed. The reasons why the stability and permanency of the system are not endangered are the following : 1. The planets are exceedingly small compared with the central body, the sun being more than 700 times greater than all of them together. 2. The largest planets are very distant from the 183. What effect do the planets produce on each other? State the different kinds of disturbance caused by them. 184. Do they tend to destroy the system ? Why ? The first rea- son — the second. STABILITY OF THE SYSTEM. 147 small ones and from each other, and move in orbits very nearly circular, and very nearly in one plane. For these ' reasons the disturbances are all very small ; and such of them as might ultimately become dangerous by accumulating for a long time, are pre- vented from accumulating by oscillating back and forth ; that is, they increase for a time in one direc- tion, and then in the opposite. CHAPTEK XIII. COMETS — SHOOTING STARS. 185. A Comet Defined. — A comet is a body which consists of nebulous matter, and revolves about the sun in a very eccentric orbit. Most comets present a roundish ill-defined appearance, often having a bright central part, called the Nucleus. The fainter part, surrounding the nucleus, is called the Coma (hair) ; and the Tail, which distinguishes many comets, is merely the extension of the coma. It is the stream- ing appearance of the tail, resembling hair, which gave the name " comet" to this class of bodies. The nucleus has been sometimes supposed to be solid ; but it probably consists always of nebulous matter in a more condensed state than the other parts. The nucleus and coma are called the Bead of the comet. 186. Number of Comets. — Many hundreds of com- ets have been recorded, most of them, of course, vis- ible to the naked eye. But lately it is observed that most comets are telescopic objects. And many, which would otherwise be seen, escape observation by being above the horizon only in the daytime. The whole number, therefore, belonging to the solar system is 185. Define a comet and its parts. 186. What is said of the number of comets TAILS OF COMETS 149 undoubtedly to be reckoned by thousands, or tens of thousands. 187. Eccentricity of Orbit. — All known cometary orbits are more eccentric than any planetary orbit ; and most of them are exceedingly so, their perihelion being as near the sun as Mercury and Yenus, or nearer, and their aphelion as far off as the most dis- tant planets, or even beyond. And some appear to be ellipses of infinite length. On account of this great eccentricity, comets are not seen except when they are near the perihelion. 188. Form and Direction of Tails of Comets.— -The forms of tails belonging to different comets are ex- ceedingly varied. In general, however, the sides diverge from the head, so that the most distant and faintest part is broadest, as in the comets of 1680 and Fig. 38. COMET OF 1680. 187. What is the form of their orbits? When are the comets invisible ? 188. Describe the general appearance and direction of the tail. COMET OF 1811. 1811 (Figs. 38, 39). But sometimes the divergence is very slight, as in the comet of 1843 (see Fig. 40). In a few instances, the tail has appeared to be divided into two or more branches diverging from each other. The general direction of the tail is from the sun; so that, as a comet approaches the sun, the tail follows it; but as it recedes, the tail is directed forward. The axis of the tail is not, however, a straight line, but more or less curved backward, so that the convex side of the curve is foremost in the motion. 189. Dimensions of Comets. — The dimensions of comets are various, and, on account of their nebulous character, they never admit of accurate measurement. The nucleus of a large comet is sometimes 5.000 miles, and the coma 200,000 miles, in diameter, while the tail has, in one case, attained the extraordinary length of 200,000,000 miles. 189. What is said of tlie dimensions of comets ? Over how long an arc does the tail sometimes extend ? MATTER IN COMETS. 151 The apparent length of a comet's tail is often suf- ficient to span an arc of 20° or 30° on the sky, and sometimes much more than this. The comet of 1680 extended 97°, and that of 1861, 106°. The fainter part, in all cases, is seen only by indirect vision. It is obvious that the real length cannot be inferred from the apparent, until the distance from us, and the obliquity to our line of vision, are obtained. 190. Light of the Comets. — These bodies, like the planets and satellites, shine by solar light which they reflect to us. But, unlike all planetary bodies, they are in a condition so attenuated that the sun's rays penetrate every part of them without obstruction. The brightness of a star is not diminished in the least when seen through the tail or coma of a comet. In a few instances, a star has been seen through the nu- cleus, and even then was not essentially dimmed. 191. Quantity of Matter in Comets.— Though some of the largest comets surpass all other bodies in the solar system in magnitude, yet in respect to their mass they are too small to have produced, as yet, the slightest perceptible effect. They sometimes come very near planets and their satellites, but are never known to exert the least influence on them. They do, of course, attract the planets, because they are attracted by them, and suffer great disturbances from them. But until they themselves produce some effect which is appreciable, their mass must be regarded as infinitely small. 190. What is said of tlie light of the comets ? 191. What proof is given that their mass is very small ? Do we ka / that they attract at all? 152 COMETS. 192, Directions of Cometary 3Iotions. — The com- etary orbits are unlike the planetary, not only in the degree of their eccentricity, but in the varied posi- tions of their planes. Instead of being limited to a narrow zone like the zodiac, they make every variety of angle with the ecliptic, so that a comet is as likely to pass round the sun from north to south as from west to east. And whether the orbit is much or little inclined, the comet's motion in it is as often retro- grade as direct. 193* T7ie Determination of a Comet's Orbit,— From. the observations of right ascension and declination of a comet, which are repeatedly made while it is in sight near the perihelion, the form of its orbit and the time of describing it can be calculated. But the part in which it is visible is so small, compared with the whole orbit, that the results of calculation are quite uncertain, until the comet is identified on its re- turn. "When a comet is thus identified, its periodic time is, of course, known ; and from that the length and form of its orbit can be computed. The periods of most comets, however, appear to be so long that only a few have returned since the time when accurate observations began to be made. Hence it is that by far the greater part of all the recorded comets are unknown in respect to the extent of their orbits and the time of describing them. And the few which are known have com- 192. How are their orbits situated ? 193. What observations are made in order to calculate their or- bits ? Are the results certain ? When can the orbits be exactly determined ? Have many been determined? EEMAKKABLE COMETS. 153 paratively small orbits, and describe them in short periods. 194. Comets of Known Period. — The following table contains the names of the only comets whose periodic times are certainly known : Period Perihelion Aphelion Comet. in years. Distance. Distance. Halley's 75 56,000,000 3,400,000,000 Encke's 3£ 32,000,000 390,000,000 Biela's 6-J 85,000,000 570,000,000 Faye's 7i 161,000,000 565,000,000 Brorsen's 5^ 62,000,000 538,000,000 D' Arrest's 6i 111,000,000 546,000,000 Winnecke's 5£ 73,000,000 526,000,000 Of the above, Halley's is by far the most interest- ing, on account of its brightness and length of tail, and also on account of its long period. Its last re- turn to the perihelion was in 1835, and it will not be seen again till 1910. The other six contained in the table considerably resemble each other. Their pe- riods are short, they are accompanied by little or no tail, and they are all too faint to be seen except by a telescope. Hence, they are of little interest except to the astronomer. 195. Other Remarkable Comets. — The comet of 1680 was unusually brilliant, and was the first whose orbit was calculated by Sir Isaac Newton. (See Fig. 38.) The comet of 1744 was so bright as to be seen in 194. Name the comets whose orbits are known. Which is the most interesting ? Why ? What is said of the others ? 154 COMETS. the daytime. Its tail was divided into six distinct and divergent parts. The comet of 1770 was remarkable for having its orbit twice changed by the attraction of Jupiter ; first from a period of 48 years to one of 6 years, and then again to one of 20 years. While its period was six years, it came twice to the perihelion, but was never seen before, and has never been seen since. The comet of 1843 was so bright as to be seen by day, and passed so near the sun at perihelion as to Fig. 40 touch it. Its tail was very slender and straight, as shown in Fig. 40. The comet of 1858, called, also, Donati's comet, presented a series of envelopes, one within another. Its period is computed to be about 2,000 years. The comet of 1861 was remarkable for the great apparent length of its tail, viz., 106°. It came so 195. Describe tlie comet of 1680— of 1744— of 1770— of 1843— of 1858— of 1861. GASEOUS ETEORS. 155 near the earth that the latter is supposed to have passed through a part of its tail. Its appearance is presented in Fig. 41. Fig. 41. 196. Shooting Stars.— This is the popular name given to those bodies which appear like stars or planets moving across some part of the sky, and then vanishing. They are equally well known by the name of meteors. They may be seen in any clear night, by watching an hour or two, especially if the moon is not shining. The heights of meteors are found to be generally about 50 miles, and their velocities 20 or 30 miles per second. Coming into the air with such great velocity, they are almost instantly set on fire, and their substance becomes incorporated with the atmosphere. From the meteors, it is found that they around the sun. Jill! 1 Iftllillljll: I m i;?%-..;. m :'■*. iBl'ili 11111 jiiii observed motions of are bodies revolving 197. Gaseous Meteors. — If the ordinary meteors 196. What are shooting stars ? How high are they generally ? What is their velocity ? Around what do they revolve ? 156 SHOOTING STARS. were more dense than a gas, they would hardly lose all their motion, as they do, before reaching the earth. The most interesting fact relating to this class of bodies is, that they sometimes come in showers; that is, hundreds of thousands of them are seen in a single night. These showers seem to have periodical returns. The most remarkable date is November 12th or 13th, at which time, every 33 or 34 years, they appear in immense numbers on some part or other of the earth's surface. 1799, 1833, and 1866 were the three last times of great meteoric showers. 198. Solid Meteors. — There is another class of meteoric bodies which afford indubitable evidence of being solid. Like the gaseous meteors, they plunge into the atmosphere with great velocity, and are in- flamed by the violent friction. Before reaching the earth they usually explode, and scatter their frag- ments. Some of them, however, appear to lose only small portions of their mass by explosion, and pass on in their orbits round the sun, greatly disturbed, of course, by the earth's attraction. 199. Aerolites. — This is the name usually given to the fragments thrown down by solid meteors ; though, in rare instances, an aerolite obviously constitutes the entire meteor itself. Aerolites consist of iron, silex, and a few other materials, which are all known among terrestrial substances. But they are always distinguishable from terrestrial bodies by their pecu- 197. Describe meteoric showers. What are the dates of their occurrence ? 198. How is it known that any meteors are solid ? AEEOLITES. 157 liar structure. Since the great velocities of meteors, solid as well as gaseous, have become known, the former theories as to the origin of meteoric stones, or aerolites, have been abandoned. Such velocities, if they could be generated at all on the earth, could never exist in horizontal or downward directions. Both solid and gaseous meteors are, therefore, con- sidered as describing orbits about the sun. The inter- planetary spaces, which have been generally reckoned as vacant, may perhaps be to a great extent occupied by innumerable bodies, of a grade far below that of comets and planetoids. 199. What are aerolites ? Of what do they consist ? How is their material distinguishable from terrestrial substances ? CHAPTEB XIV. THE EJXED STAES— CONSTELLATIONS. 200. The Stellar Universe. — The bodies described in the foregoing chapters all belong to the solar sys- tem. If our investigations are extended outside of this system, we find that there are other systems, greater or less than this, unlimited in number, and separated from the solar system and from each other by solitudes so vast that each system is only a point in comparison with the distances between them. The central sun in each of these countless systems is a fixed star. The word "universe" is employed to express the sum total of all these systems, the number of which, and the extent of space occupied by them, are utterly beyond the reach of human comprehension. 201* The Fixed Stars, and their Magnitudes. — The fixed stars are so called because, to common observa- tion, they always maintain the same situations with respect to each other. All the thousands of bright points ordinarily seen in the sky by night are fixed stars, with the exception of two or three, possibly four, which are planets. SCO. What is there outside of the solar system? What is the meaning of universe ? UNEQUAL BEIGHTNESS. 159 The fixed stars are classified according to magni- tudes, though the word, when thus used, signifies only degrees of brightness. The stars which can be seen by the naked eye, in the most favorable circumstances, are divided into six magnitudes. Those which can be seen only by the aid of the telescope, called tele- scopic stars, are arranged into several more ; so that all the magnitudes are 16 or 18. Stars of the same magnitude are not equally bright ; for there is a continual gradation in respect to bright- ness ; so that, if the intensity were accurately meas- ured, probably the light of but very few would be found exactly equal. Stars of the first magnitude are fewest in number, and, generally, the smaller the magnitude, the larger the number of stars included under it. The limits of the successive magnitudes differ somewhat, according to different astronomers ; but the following round numbers do not vary widely from any of them : First magnitude 20 Second magnitude 40 Third magnitude 140 Fourth magnitude 300 Fifth magnitude 950 Sixth magnitude 4,450 In all, near 6,000, visible to the naked eye. The numbers of the telescopic stars increase at so rapid a rate that they have to be reckoned by millions. 202. Cause of Unequal Brightness. — "We might suppose either that the stars are themselves unequal in respect to the quantity of light which they emit, or 201. Why are the fixed stars so called ? How are they classified? What are telescopic stars ? Give the numbers included under each of the first six magnitudes. 160 CONSTELLATIONS. tliat they appear unequally bright on account of their different distances. It is undoubtedly true that there is some diversity in the bodies themselves ; and yet, the rapid increase of numbers as the magnitudes are less, indicates that difference of distance is the chief cause of inequality in brightness. If there is any approach to a uniform distribution of the stars in space, those which are nearest should be fewest in number, and should, in general, appear brightest. 203. Constellations. — The fixed stars are also classed topographically in constellations. This divi- sion is very ancient ; and some of the constellations are mentioned by the earliest writers. The names given to them are those of the animals, heroes, and other objects of pagan mythology. "Within each constellation, the brightest stars are designated by the letters of the Greek alphabet in the order of brightness. Thus, Alpha Lyrse is the brightest star in Lyra ; Beta Scorpionis, the brightest but one in Scorpio, &c. After the Greek letters are all used, Roman letters, and then numerals, are em- ployed. In some cases the order of brightness does not accord with the order of the alphabet. This may result from a change of brightness which has taken place since the stars were first named. When a cap- ital letter follows a number, there is reference to the catalogue of some astronomer. Thus, 84H is the star 84, of a certain constellation in Herschel's catalogue. A few conspicuous stars are still known by the indi- 202. What is the principal cause of unequal brightness in stars ? 203. What are constellations ? How are stars in each designated ? THE ZODIAC. 161 vidual names given to them in ancient times ; as Arc- turus, Antares, Sirius, Yega, &c. 204, Star Catalogues. — The first catalogue of stars was made by Hipparchus, before the time of Christ, and contained 1,022 of the most conspicuous stars. Catalogues of the present day contain hundreds of thousands of stars, whose right ascensions and de- clinations are given for a certain date. 203. Descriptions of Constellations. — The remain- der of this chapter is devoted to brief descriptions of the most prominent constellations which can be seen in about latitude 40° N., accompanied by a few dia- grams to show the relative position of some of the principal stars contained in them. These are in- tended to afford the learner some aid in studying the constellations in the sky. But in order to become well acquainted with this branch of astronomy, a celestial globe or a series of star maps is necessary. CONSTELLATIONS OF THE ZODIAC. 206. Aries (The Main) the first Aeies. constellation of the Zodiac, is known &. by two bright stars, Alpha, on the a fi% northeast, and Beta, on the southwest, 4° apart, forming the head. . South of 7 Beta, at the distance of 2°, is a smaller star, Gamma. 204. Who made the first catalogue of stars ? Compare the num- ber in that and modern catalogues. 205. What is the purpose of the following descriptions ? What more is needed, in order to learn the constellations thoroughly ? 206. Describe Aries. 162 CONSTELLATIONS. The next brightest star of the Kam, Delta, is in the tail, 15° southeast of Alpha. The feet of the figure rest on the head of the Whale. t 207. Taurus (The Bull) will be readily found by the seven stars, or Pleiades, which lie in the neck, 24° eastward of Alpha Arietis. The largest star in Tau- rus is Aldebaran, of the first magnitude, in the Bull's eye, 10° southeast of the Pleiades. It has a reddish color, and resembles the planet Mars. The other eye Taurus. Pleiades. 6% of the figure is Epsilon, 3° northwest of Aldebaran. Five small stars, situated a little west of Aldeba- ran, in the face of the Bull, constitute the Hyades. Although the Pleiades are usually denominated the seven stars, yet it has been remarked, from a high an : tiquity, that only six are present. Some persons, however, of remarkable powers of vision, are still able to recognize seven, and even a greater number. With a moderate telescope, not less than 50 or 60 stars, of considerable brightness, may be counted in this group, and a much larger number of very small stars are revealed to the more pow- erful telescopes. The beautiful allusion, in the Book of Job, to the " sweet influences of the Pleiades," and 207. Describe Taurus. THE ZODIAC. 163 the special mention made of this group by Homer and Hesiod, show how early it had attracted the attention of mankind. The liorns of the Bull are two stars, Beta and Zeta, situated 25° east of the Pleiades, being 8° apart. The northern horn, Beta, also forms one of the feet of Auriga, the Charioteer. 208. Gemini (The Twins) is re- The Twins. presented by two well-known stars, „ " Castor and Pollux, in the head of * the figure, 5° asunder. Castor, the northern, is of the first, and Pollux of the second magnitude. Four conspicuous stars, extending in a line from south to north, 25° south- west of Castor, form the feet, and two others, parallel to these, at the distance of 6° or 7° northeastward, are in the knees. 7# 209. Cancer (The Crab). — There are no large stars in this constellation, and it is regarded as less re- markable than any other in the Zodiac. The two most conspicuous stars, Alpha and Beta, are in the southern claws of the figure ; and in its body are the northern and southern Asellus, which may be readily found on a celestial globe. But the most remark- able object in this constellation is a misty group of very small stars, so close together, when seen by the naked eye, as to resemble a comet, but easily sep- arated by the telescope into a beautiful collection of brilliant points. It is called Prossepe, or the Beehive. 208—209. Describe Gemini— Cancer. 164: CONSTELLATIONS. 210. Leo (The Lion) is a very large constellation, and has many interesting members. Regulus (Alpha Leonis) is a star of the first magnitude, which lies The L*ion. j very near the ecliptic, and is much used in astronom- ical observations. North of Regulus lies a semicircle of five bright stars, arranged in the form of a sickle, of which Regulus is the handle, and extending over the shoulder and neck of the Lion. Denebola, a con- spicuous star in the Lion's tail, lies 25° east of Regu- lus. Twenty bright stars in all help to compose this beautiful constellation. It ranges from west to east along the Zodiac, over more than 40° of longitude, all parts of the figure excepting the feet lying north of the ecliptic. 211, Virgo (Hie Virgin) extends along the Zodiac eastward from the Lion, covering an equally wide re- gion of the heavens, although less distinguished by brilliant stars. Spica, however, is a star of the first magnitude, and lies a little east of the vernal equi- nox. Vindemiatrix, in the arm of Virgo, 18° east of Denebola, and 23° north of Spica, is easily found ; and directly south of Denebola 13°, is Beta Virgims; 210—211. Describe Leo— Virgo. THE ZODIAC. 165 while four other conspicuous stars, in the form of a trapezium, between this and Vindemiatrix, lie in the wing and shoulders of the figure. The feet are near the Balance. 212* Libra (TJie Balance) is composed of a few scattered members situated between the feet of Yirgo and the head of Scorpio, but has no very distinctive marks. Two stars of the second magnitude, Alpha, on the south, and Beta, 8° northeast of Alpha, to- gether with a few smaller stars, form the scales. 213, Scorpio (TJie Scorpion) is one of the finest of the constellations of the Zodiac, and is manifestly so called from its resemblance to the animal whose The Scorpion. * * * *v * « # name it bears. The head is composed of five stars, arranged in a line slightly curved, which is crossed in 212—213. Describe Libra— Scorpio. 166 CONSTELLATIONS. the center by the ecliptic, nearly at right angles, a degree south of the brightest of the group, Beta Seor- pionis. Nine degrees southeast of this is a remarka- ble star of the first magnitude, called Antares, and sometimes the Heart of the Scorpion. It is of a red cjlor, resembling the planet Mars. South and east of this, a succession of not less than nine bright stars sweep round in a semicircle, terminating in several small stars forming the sting of the Scorpion. The tail of the figure extends into the Milky Way. 214. Sagittarius (The Archer). — Ten degrees east- ward of the Scorpion's tail, on the eastern margin of Milky Way, we come to the hoiv of Sagittarius, con- sisting of three stars, about 6° apart, the middle one being the brightest, and situated in the bend of the bow, while a fourth star, 4° westward of it, consti- tutes the arrow. The archer is represented by the figure of a Centaur (half horse and half man) ; and proceeding about 10° east from the bow, we come to a collection of seven or eight stars of the second and third magnitudes, which lie in the human or upper part of the figure. 215. Capricornus (The Goat), represented with the head of a goat and the tail of a fish, comes next to Sagittarius, about 20° eastward of the group that form the upper portions of that constellation. Two stars of the second magnitude, Alpha, on the north, and Beta, on the south, 3° apart, constitute the head of Capricornus, while a collection of stars of the 214 — 215, Describe Sagittarius — Capricornus. THE ZODIAC. 167 third magnitude, lying 20° southeast of these, form the tail. 216. Aquarius (The Water Bearer) is closely in contact with the tail of Capricornus, immediately north of which, at the distance of 10°, is the western shoulder (Beta), and 10° further east is the eastern shoulder (Alpha) of Aquarius. About 3° southeast of Alpha is Gamma Aquarii, which, together with the other two, makes an acute triangle, of which Beta forms the vertex. In the eastern arm of Aquarius are found four stars, which together make the figure T, the open part being westward, or towards the shoulders of the constellation. Aquarius ranges nearly 30° from north to south, being nearly bisected by the ecliptic. 217. Pisces (TJie Fishes). — Three figures of this kind, at a great distance apart, two north and one south of the ecliptic, compose this constellation. The southern Fish, Piscis Australia, otherwise called Fo- malhaut, lies directly below the feet of Aquarius, and being the only conspicuous star in that part of the heavens, is much used in astronomical measurements. It is 30° south of the equator. About 12° east of the figure Y in the arm of Aqua- rius, is an assemblage of five stars, forming a pretty regular pentagon, which is one of the northern mem- bers of the Constellation Pisces ; and far to the northeast of this figure, north of the head of Aries, lies the third member, the three being represented as 216 — 217. Describe Aquarius — Pisces. 168 CONSTELLATIONS. connected together by a ribbon, or wavy band, com- posed of minute stars. CONSTELLATIONS NORTH OF THE ZODIAC. 218. Ursa Minor (The Little Bear).— The Pole-star (Polaris) is in the extremity of the tail of the Little Bear. It is of the third magnitude, and being within less than a degree and a half of the North Pole of The Little Beak, 7 < *>' ""••.. "Pole Star the heavens, it serves, at present, to Indicate the po- sition of the pole. It will be recollected, however, that on account of the precession of the equinoxes, the pole of the heavens is constantly shifting its place from east to west, revolving about the pole of the ecliptic, and will in time recede so far from the pole- star that this will no longer retain its present distinc- tion. Three stars in a straight line, 4° or 5° apart, commencing with Polaris, lead to a trapezium of four stars, the whole seven together forming the figure of a dipper, the trapezium being the body, and the three first-mentioned stars being the handle. 219. Ursa Major (The Great Bear) is one of the 218. Describe Ursa Minor. NORTH OF THE ZODIAC. 169 largest and most celebrated of the constellations. It is usually recognized by the figure of a larger and more perfect dipper than the one in the Little Bear ; The Gkeat Beab. £*- .* 4 a f \ * Ms- y P three stars, as before, constituting the handle, and four others, in the form of a trapezium, the body of the figure. The two western stars of the trapezium, ranging nearly with the North Star, are called the Pointers ; and beginning with the northern of these two, and following round from left to right through the whole seven, they correspond in rank to the suc- cession of the first seven letters of the Greek alpha- bet — Alpha, Beta, Gamma, Delta, Epsilon, Zeta, Eta. Several of them also are known by their Arabic names. Thus, the first in the tail, corresponding to Epsilon, is Alioth, the next (Zeta) Mizar, and the last (Eta) Benetnascli. These are all bright and beautiful stars, -Alpha being of the first magnitude, Beta, Gamma, Delta, of the second, and the three forming the tail, of the third. But it must be remarked that this very remarkable figure of a dipper, or ladle, com- poses but a small part of the entire constellation, be- ing merely the hinder half of the body and the tail of the Bear. The head and breast of the figure, lying 219. Describe Ursa Major. 170 CONSTELLATIONS. about ten or twelve degrees west of the Pointers, con- tain a great number of minute stars in a triangular group. One of the fourth magnitude, Omicron, is in the mouth of the Bear. The feet of the figure may be looked for about 15° south of those already de- scribed, the two hinder paws consisting each of two stars very similar in appearance, and only a degree and a half apart. The two paws are distant from each other about 18°; and following westward about the same number of degrees, we come to another very similar pair of stars, which constitute one of the fore paws, the other foot being without any corresponding pair. In a clear winter's night, when the whole constella- tion is above the pole, these various parts may be easily recognized, and the entire figure will be seen to resemble a large animal, readily accounting for the name given to this constellation from the earliest 220. Draco (The Dragon) is also a very large con- stellation) extending for a great length from east to west. Beginning at the tail, which lies half way be- tween the Pointers and the Pole-star, and winding round between the Great and the Little Bear, by a continued succession of bright stars from 5° to 10° asunder, it coils around under the feet of the Little Bear, sweeps round the pole of the ecliptic, and ter- minates in a trapezium formed by four conspicuous stars, from 30° to 35° from the North Pole. A few of the members of this constellation are of the second, 220. Describe Draco. \ NORTH OF THE ZODIAC. 171 but the greater part of the third magnitude, and be- low it. 221. Cepheus (The King) is bounded north by the Little Bear, east by Cassiopeia, south by the Lizard, and west by the Dragon. The head lies in the Milky Way, and the feet extend toward the pole. It con- tains no stars above the third magnitude. 222. Cassiopeia is bounded north and west by Cepheus, east by Camelopardalus, and south by An- dromeda, and is one of the constellations of the Milky Way. It is readily distinguished by the figure of a Cassiopeia. H / " J chair inverted, of which two stars constitute the back, and four, in the form of a square, the body of the chair. It is on the opposite side of the pole from the Great Bear, and nearly at the same distance from it. 223. Camelopardalus (The Giraffe) is bounded north by the Little Bear, east by the head of the Great Bear, south by Auriga and Perseus, and west by Cassiopeia. Although this constellation occupies a large space, yet it has no conspicuous stars. 221 — 222 — 223. Describe Cepheus — Cassiopeia — Camelopardalus. 172 CONSTELLATIONS. 224. Andromeda is bounded north by Cassiopeia, east by Perseus, south by Pegasus, and west by the Lizard. The direction of the figure is from south- west to northeast, the head coming down within 30° of the equator, and being recognized by a star of the second magnitude, which forms the northeastern corner of the great square in Pegasus, to be described hereafter. At the distance of six or seven degrees from the head are three conspicuous stars in a row, ranging from north to south, which he in the breast of the figure ; and about the same distance from these, and parallel to them, three more, which constitute the girdle of Andromeda. Near the northernmost of the three is a faint, misty object, often mistaken for a comet, but is a nebula, and one of the most remarka- ble in the heavens. 225. Perseus is bounded north by Cassiopeia, east by Auriga, south by Taurus, and west by Andromeda. The figure extends from north to south, and is repre- sented by a giant holding aloft a sword in his right hand, while his left grasps the head of Medusa, a group of stars on the western side of the figure, embracing the celebrated star Algol. A series of bright stars descend along the shoulders and the waist, and there divide into the two legs. The western foot is 8° north of the Pleiades. The eastern leg is bent at the knee, which is distinguished by a group of small stars. Near the sword handle, under Cassiopeia's chair, is a fine cluster of stars, so close together as scarcely to be separable by the eye. 224 — 225. Describe Andromeda — Perseus. NORTH OF THE ZODIAC. 173 228. Auriga {Tlie Wagoner) is bounded north by Camelopardalus, east by the Lynx, south by Taurus, and west by Perseus. He is represented as bearing on his left shoulder the little Goat Capella, a white and beautiful star of the first magnitude, while Beta forms the right shoulder, 8° east of Capella. These two bright stars form, with the northern horn of the Bull, at the distance of 18°, an isosceles triangle. 227. Leo Minor {The Lesser Lion) is bounded north by Ursa Major, east by Coma Berenices, south by Leo, and west by the Lynx. It lies directly under the hind feet of the Great Bear, and over the sickle in Leo, and is easily distinguished. Four stars in the central part of the figure, from 4° to 5° apart, form a pretty regular parallelogram. 228. Canes Venatici {The Greyhounds,)- -This con- stellation lies between the hind legs of the Great Bear, on the west, and Bootes, on the east. Cor Caroli, a solitary star of the third magnitude, 18° south of Alioth, in the tail of the Great Bear, will serve to mark this constellation. 229. Coma Berenices {Berenice's Hair) is a cluster of small stars, composing a rich group, 15° northeast of Denebola, in the Lion's tail, in a line between this star and Cor Caroli, and half way between the two. 230. Bootes is bounded north by Draco, east by the Crown and the head of Serpentarius, south by 226—227—228—229. Describe Auriga— Leo Minor— Canes Vena- tici — Coma Berenices. 174: CONSTELLATIONS. Virgo, and west by Coma Berenices and the Hounds. It reaches for a great distance from north to south, the head being within 20° of the Dragon, and the feet extending to the Zodiac. In the knee of Bootes is Arcturus, a star of the first magnitude. The next brightest star, Beta, is in the head of Bootes, 23° north of Arcturus, and 15° east of the last star in the tail of the Great Bear. *.£ 231, Corona Bor calls (The The Crown. Northern Crown) is bounded effc north and east by Hercules, / south by the head of Serpenta- 7^ f° rius, and west by Bootes. It \ %' Q is formed of a semicircle of -$£ ■ bright stars, six in number, of which Gamma, near the center of the curve, is of the second magnitude. 232, Hercules is bounded north by Draco, east by Lyra, south by Ophiuchus, and west by Corona Bore- alis. It is a very large constellation, and contains some brilliant objects for the telescope, although its components are generally very small. The figure lies north and south, with the head near the head of Ophiuchus, and the feet under the head of Draco. Being between the Crown and the Lyre, its locality is easily determined. The eastern foot of Hercules forms an isosceles triangle with the two southern stars of the trapezium in the head of Draco ; while the head of Hercules is far in the south, within 15° of the equator, being 6° west of a similar star which constitutes the head of Ophiuchus. 230 — 231 — 232. Describe Bootes — Corona Borealis — Hercules. NOETH OF THE ZODIAC. 175 233. Lyra {The Lyre) is bounded north by the head of Draco, east by the Swan, south and west by Hercules. Alpha Lyrce, or Vega, is of the first mag- nitude. It is accompanied by a small acute triangle of stars. Its color is a shining white, resembling Ca- pella and the Eagle. 234. Cygnus {The Swan) extends along the Milky Way, below Cepheus, and immediately eastward of The Swan. the Lyre, and has the figure of a large bird flying along the Milky Way from north to south, with out- stretched wings and long neck. Commencing with the tail, 25° east of Lyra, and following down the Milky Way, we pass along a line of conspicuous stars which form the body and neck of the figure; and then returning to the second of the series, we see two bright stars at 8° or 9° on the right and left (the three together ranging across the Milky Way), which form the wings of the Swan. This constellation is among the few which exhibit some resemblance to the ani- mals whose names they bear. 233—234. Describe Lyra— Cygnus. 176 CONSTELLATIONS. 235. Vulpecula {The Little Fox) is a small constel- lation, in which a fox is represented as holding a goose in his mouth. It lies in the Milky Way, be- tween the Swan, on the north, and the Dolphin and the Arrow, on the south. 236* Aquila {The Eagle) stretches across the Milky Way, and is bounded north by Sagitta, a small con- stellation which separates it from the Fox, east by the Dolphin, south by Antinous, and west by Taurus Poniatowski (the Polish Bull), which separates it from Ophiuchus. It is distinguished by three bright stars in the neck, known as the " three stars," which lie in a straight line about 2° apart, on the eastern margin of the Milky Way. The central star is of the first magnitude. Its Arabic name is Altair. 237. Antinous lies across the equator, between the Eagle, on the north, and the head of Capricorn, on the south. 238. Delphinns (Tlie Dolphin) is situated east and north of Altair, and is composed of five stars of the third magnitude, of which four, in the form of a rhombus, compose the head, and the fifth forms the tail. 230. Pegasus (TJie Flying Horse) is a very large constellation, and is bounded north by the Lizard and Andromeda, east and south by Pisces, west by the Dolphin. The head is near the Dolphin, while the 235—236—237—238—239. Describe Vulpecula — Aquila — Anti- nous — Delpliinus — Pegasus. SOUTH OF THE ZODIAC. 177 back rests on Pisces, and the feet extend towards Andromeda. A large square, composed of four conspicuous mem- bers, one (Marhab) of the first, and three others of the second magnitude, distinguish this constellation. The corners of the square are about 15° apart, the northeastern corner being in the head of Andromeda. 240. Ophiuchus is another very large constella- tion, the head being near the head of Hercules, and the feet reaching to Scorpio, the western foot being almost in contact with Antares. The figure is that of a giant holding a serpent in his hands. The head of the serpent is a little south of the Crown, and the tail reaches far eastward towards the Eagle. CONSTELLATIONS SOUTH OF THE ZODIAC. 241. Cetus {The Whale) is distinguished rather for its extent than its brilliancy, occupying a large tract of the sky south of the constellations Pisces and Aries. The head is directly below the head of Aries, and the tail reaches westward 45°, being about 10° south of the vernal equinox. Menhir (Alpha Ceti), the largest of its components, is situated in the mouth, 25° southeast of Alpha Arietis ; and Mira (Omicron Ceti), in the neck, 14° west -of Menkar, is celebrated as a variable star, which exhibits different magnitudes at different times. 242. Orion is one of the most magnificent of the constellations, and one of those that have longest 240—241. Describe Ophiuchus — Cetus 178 CONSTELLATIONS. attracted the admiration of mankind, being alluded to in the Book of Job, and mentioned by Homer. The head of Orion lies southeast of Taurus, 15° from Aldebaran, and is composed of a cluster of small stars. Two very bright stars, Betelgeuse, of the first, «#■ Orion. * * 7* ft* and Bellatrix, of the second magnitude, form the shoulders ; three more, resembling the three stars of the Eagle, compose the girdle ; and three smaller stars, in a line inclined to the girdle, form the sword. Bigel, of the first magnitude, makes the west foot, but the corresponding star, 9° southeast of this, which is sometimes taken for the other foot, is above the knee, this foot being concealed behind the Hare. Orion's club is marked by three stars of the fifth magnitude, close together, in the Milky "Way, just below the southern horn of the Bull. Orion is a favorite constellation with the practical astronomer, 242. Describe Orion. SOUTH OF THE ZODIAC. 179 abounding, as it does, in addition to the splendor of its components, with fine nebulse, double stars, and other objects of peculiar interest, when viewed with the telescope. It embraces 70 stars, plainly visible to the naked eye, including two of the first, four of the second, and three of the third magnitude. 243, Lepus {TJie Hare). — Below Bigel, the western foot of Orion, is a small trapezium of stars, which forms the ears of the Hare ; and an assemblage of nine stars, of the third and fourth magnitudes, south and east of these, make up the remaining parts of the figure. 244, Cants Major {The Greater Dog) lies directly east of the Hare, and is highly distinguished by con- taining Sirius, the most splendid of all the fixed stars, which lies in the mouth of the figure. In the fore paw, 6° west of Sirius, is a star of the second magnitude {Beta Ganis Majoris), and from 10° to 15° south of Sirius is a collection of stars of the second and third magnitude, which make up the hinder por- tions of the figure. The Egyptians, who anticipated the rising of the Nile by the appearance of Sirius in the morning sky, represented the constellation by the figure of a dog, the symbol of a faithful watchman. 245* Canis Minor {The Lesser Dog). — About 25° north of Sirius is the bright star Procyon, also of the first magnitude, which marks the side of the Lesser Dog. A star of the third magnitude (Beta), 4° north- west of this, in the head of the figure, forms, with 243 — 244 — 245. Describe Lepus — Canis Major — Canis Minor. 180 CONSTELLATIONS. Procyon, the lower side of an elongated parallelo- gram, of which Castor and Pollux, 25° north, form the upper side. 246. Monoceros is a large constellation, occupying the space between the Greater and the Lesser Dog, but has no conspicuous members. 247. Hydra occupies a long space south of Leo, Virgo, and Libra. Its head, which is south of the fore paws of the Lion, consists of four stars of the fourth magnitude, of nearly uniform appearance ; and about 15° southeast of these is the Heart (Cor Hydrce), 23° south of Eegulus. Besting on Hydra, and south of the hind feet of Leo, is Crater (the Cup), consist- ing of six stars of the fourth magnitude, arranged in the form of a semicircle ; and a little further east, also perched on the back of Hydra, is Corvus (the Crow), the two brightest components of which are situated in one of the wings of the figure, in a line between Crater and Spica Yirginis. EVENING CONSTELLATIONS OF THE DIFFERENT SEASONS. 248. Since the sun passes from west to east round the heavens once in a year, the constellations of the evening sky will continually vary with the season. Hence one portion of the heavens can be best studied in the spring, another in the summer, a third in the autumn, and the fourth and remaining part in the 246 — 247. Describe Monoceros — Hydra. 248. Why do we see different constellations in the evenings of each season ? EVENING CONSTELLATIONS. 181 winter. The following general descriptions, adapted to the times of the equinoxes and solstices, may afford some aid in these studies : 249» Evening Constellations of Autumn* — For the Middle of September, from 8 to 10 d clock. — At 8 o'clock Scorpio is near setting in the southwest, Antares be- ing near 10° high. The bow of Sagittarius is on the eastern margin of the Milky Way, the arrow being directed to a point a little below Antares. At 9 o'clock the horns of the Goat come upon the me- ridian ; and at 10 o'clock, the western shoulder of Aquarius. The other shoulder, and the figure Y in the a*rm, may also be easily found from the descrip- tion given (Art. 216) ; also, the Pentagon, in Pisces, and Fomalhaut (the Southern Fish), a solitary bright star far in the south, only 16° above the horizon. The head of Aries appears in the east, and the Pleiades are but little above the horizon, while Aldebaran is just rising. Keturning now to the west (at 10 o'clock), the Crown is seen a little north of west, about 20° high ; Lyra is 30° west of the zenith ; the Swan is nearly overhead ; and following down the Milky Way, the Eagle is seen on its eastern margin over against Lyra on the western ; and the Dolphin, a little east- ward of the Eagle, and as far above the horns of Oapricornus as the latter are above the southern horizon. Following on the east of the meridian, the great square in Pegasus may next be identified ; and since the northeastern corner of the square is in the head of Andromeda, this constellation may next be 249. Describe the appearance in a September evening. 182 CONSTELLATIONS. learned ; and then Perseus and Auriga, which appear still further east. Directly north of Perseus is Cas- siopeia's chair; and next to that we may take the Pole-star, the Little Bear, and the Great Bear, the Dipper only being traced for the present. Com- mencing now at the tail of the Dragon, we may trace round this figure, between the two Bears, to the head, which brings us back to Lyra and the feet of Hercules. 250, Evening Constellations of Winter, — For the Middle of December, from 7 to 10 o clock. — Of the con- stellations of the Zodiac, Taurus and Gemini are now favorably situated for observation in the east. At 7 o'clock the tail of Cetus just reaches the meridian, its head being seen below the feet of Aries. Orion is just risen in the southeast. At 9 o'clock, just above the western horizon, are seen in succession, from south to north, Aquarius, the Dolphin, the Eagle, the Lyre, and the Dragon's head. Between the Eagle and the Lyre, at a little higher altitude, we perceive the Swan, flying directly downwards. Between the tail of the Swan and the Pole-star is Cepheus ; and from the pole, along the meridian, we trace Cassio- peia, the feet of Andromeda, the head of Aries, and the neck of the Whale. At 10 o'clock Perseus has reached the meridian, the star Algol, in the head of Medusa, being directly overhead. The Pleiades are but little eastward of the zenith ; and following along south from the pole, at the interval of from one to two hours east of the meridian, we may trace in suc- 250. Describe tlio appearance in a December evening. EVENING CONSTELLATIONS. 183 cession, Camelopard, Auriga, Taurus, Orion, and the Hare. Turning along the eastern horizon, we find Canis Major, Monoceros, Canis Minor, the head of Hydra (just rising), Cancer, Leo, the sickle just ap- pearing about 3° north of the east point. Leo Minor and Ursa Major complete the survey ; and we may now advantageously trace out the various parts of the Great Bear, as described (Art. 219) ; the two stars composing its hindmost paw being scarcely above the horizon. 251. Evening Constellations of Spring. — For the Middle of March, from 8 to 10 o'clock. — At 8 o'clock we see the Twins nearly overhead, and Procyon and Sirius, at different intervals, towards the south. Along the west we recognize the neck and head of the Whale, the head of Aries, and the head of An- dromeda ; next above these, Orion, Taurus, Perseus, Cassiopeia, and Cepheus ; and north of the head of Orion, we see Auriga and Camelopard. In the south, Hydra is now fully displayed ; and following on north, we obtain fine views of the Greater and the Lesser Lion, and the Great Bear. At 9 o'clock Crater and Corvus appear in the southeast, on the back of Hydra ; Yirgo extends from Leo down to the horizon, Spica Yirginis being about 5° high ; and north of Virgo, we trace in succession Coma Bere- nices, Cor Caroli, Bootes, with Arcturus and the Crown lying far in the northeast. 252. Evening Constellations of Summer. — For the Middle of June, from 9 to 10 o'clock. — At 9 o'clock, 251. Describe tlie appearance in a March evening. 184: CONSTELLATIONS. Bootes, Corona Borealis, the head of Libra, the Ser- pent, and Scorpio, lie along on either side of the me- ridian. Castor and Pollux are just setting, and Leo is about an hour high. East of Leo, Yirgo is seen extending along towards the meridian, Spica being about 30° above the southern horizon. North of Leo and Yirgo, we recognize Leo Minor, Coma Berenices, Cor Caroli, and Ursa Major. At 10 o'clock, we trace along the eastern side of the meridian, Draco, Her- cules, and Ophiuchus ; and east of these, the Lyre, the Eagle, Antinous, Sagittarius, and Capricornus. North of the Eagle, and round to the east, we find Cepheus and Cassiopeia, Andromeda rising in the northeast, Pegasus in the east, and Aquarius in the southeast. 252. Describe tlie appearance in a June evening. CHAPTEE XV. DISTANCES AND MOTIONS OF STARS — DOUBLE STAES, CLUSTERS, AND NEBULAE. 253. Effect of Telescopic Power on Fixed Stars. One indication of the vast distance of fixed stars is, that no power of a telescope has ever sensibly magni- fied them. Even under a power which increases the diameter of a body 5,000 times, they appear no larger than to the naked eye. It is inferred that they fill an angle so small that 5,000 times that angle is still too minute to be perceived. Any appearance of dish which a star presents, either with a telescope or with- out, is the effect of the light upon the retina of the eye. It is called a spurious disk, since an increase of magnifying power causes no increase of its diameter. 254:. Annual Parallax. — Another proof that the fixed stars are at an immense distance from us is the fact that while we shift our position every six months from one side of the earth's orbit to the opposite, a distance of 190,000,000 miles, there is no perceptible change in the relation of the stars to each other. It is only after long-continued and most accurate ob- 253. Wiiat is the effect of the telescope on the fixed stars ? 186 DISTANCES OF THE STAES. servation that a few stars have been discovered to suffer an annual change of position, which is clearly of the nature of parallax. The annual parallax of a star is the angle, at the star, subtended by the radius of the earth's orbit. As this angle is, in almost all cases, too small to be detected, it shows that the earth's orbit, seen from the distance of the stars, appears as a mere point. It is justly reckoned among the greatest achieve- ments in practical astronomy that the annual parallax has, in a few cases, not only been clearly detected as existing, but has been satisfactorily measured, though it is never so great as 1". The greatest parallax yet measured is that of Alpha Centauri, which is 0.91". The parallax of a star is most satisfactorily deter- mined when it is in the same telescopic field with other stars ; for then the distances between the stars may be measured with great precision by a microme- ter, and all errors arising from refraction and other disturbing causes are wholly avoided, because all the stars in the same field are affected alike. Parallax is is the only circumstance which can produce an an- nual change in their relative positions. The star 61 Cygni is, in this respect, very favorably situated, and its parallax is thought to be quite accurately deter- mined. It is 0.35". 255. Distances of the Stars. — When the parallax of a body is found, its distance can be computed by trigonometry. It is thus ascertained that Alpha Cen- 254. What is annual parallax ? What is the greatest parallax of a star ? NATURE OF FIXED STARS. 187 tauri, the nearest star, is about 22,000,000,000,000 miles from us ; and 61 Cygni, the next nearest, is 57,000,000,000,000 miles distant. Light, moving at the rate of 192,500 miles per second, would require about 3J years to come to us from Alpha Centauri, and 9 J years from 61 Cygni. As to all other stars, it is only known that they are still more distant. There is no improbability that, from the remotest telescopic stars yet seen, light may occupy thousands of years in coming to us. There- fore, we see all the stars as they were years ago ; per- haps not as they are now. And if at any time a change has been detected in the aspect or place of a star, that change occurred, not when it was seen, but 10, 100, or 1,000 years before, according to its distance. 256* Nature of the Fixed Stars. — The stars are situated at such vast distances from the solar system that if they merely reflected the light of the sun, they would be invisible. In order to exhibit such brightness as they do, they must not only shed light, but a very intense light of their own. They cannot be compared with any one of the bodies in the solar sys- tem except the sun itself. All the fixed stars, there- fore, are to be considered as suns, and probably the centers of systems resembling the solar system. It is 255. Which, is the nearest star ? What is its distance ? Which is the next nearest ? Its distance ? How long would light require to come from each ? What is known of other stars ? 258. What is the nature of the stars? Why are they suns? Compare Alpha Centauri and Sirius with the sun. At the distance of the stars, how would the sun appear ? 188 DOUBLE STAES. ascertained, respecting some of those stars whose dis- tance is known, that they shed more light than the sun. For example, Alpha Centanri has been found to shed near four times as much light as the sun ; and Sirius one hundred times as much. On the other hand, if the sun were removed from us to the nearest fixed star, its apparent diameter would be only T |V'> an ^» therefore, it would be a star having no sensible mag- nitude, and having only J- of the brightness of Sirius. 257* Double Stars. — It is discovered, in a great number of instances, that a fixed star, when exam- ined by the telescope, really consists of two stars, very close to each other. If the distance between them does not exceed 32", such stars are called double stars. Their distance apart is often less than 1'', and some are so close that the highest power of the tele- scope and the most acute vision are requisite to sepa- rate them. Hence, certain double stars are habitu- ally used as tests of the excellence of an instrument. "When Sir "William Herschel first began his observa- tions on this class of objects, in 1780, he knew of only four ; but he extended the list to 500 himself, and the number now known exceeds 6,000. The two stars which compose a doable star usually differ from each other in magnitude, and sometimes in color. 258* Ttvo Ways in ivliich Stars might- Appear Double. — The two stars which compose a double star 257. What are double stars ? Speak of their discovery. What is their number ? How do the two members of a double star often differ? BINAEY STABS. 189 may be supposed either to be really near each other, or only to appear near together, because they fall almost into the same line of vision, while one is actu- ally at an immense distance beyond the other. In the latter case, the stars are said to be optically double. "When Sir William Herschel commenced examining double stars, he very naturally supposed that, in the very few cases known, one star happened thus to be nearly in the same visual line with the other ; and he began the work of observing them with the expectation of detecting annual parallax in objects so favorably situated. For, if the nearer star is perceptibly affected by parallax, it would exhibit an annual motion relatively to the more distant star in a manner not to be mistaken. 259. Binary Stars, — It soon became evident, how- ever, that double stars are too numerous to allow the supposition that they appear near to each other acci- ' dentally. But the question was soon set at rest by another most interesting discovery, namely, that some of the double stars exhibit motions which indicate a revolution of one around the other ; or, rather, of the two around a common center, and in periods of vari- ous lengths, having no connection whatever with the earth's annual motion. Such motion cannot be par- allactic ; it must be real ; and such stars are not opti- cally, but physically double. They are called Binary 258. In what two ways might stars appear double ? What did Herschel anticipate when he first saw them ? 259. What did he discover ? What are binary stars ? What are their orbits ? What law prevails among the stars ? 190 STELLAE OEBITS. Stars, and are to be regarded as the centers of double stellar systems. The orbits of the binary stars are ellipses. It is known, therefore, that the law of gravitation outside of the solar system is the same as within it. 260. Periods of Binary Stars. — The shortest pe- riod known is that of Zeta Herculis, about 31 years. The period of Eta Coronae is 43 years; that of Xi UrssB Majoris 58 years. These, and a few others of short period, have completed their revolutions once or twice since they were discovered. The orbits of such are quite accurately determined. Alpha Cen- tauri has not yet made a revolution since its discov- ery. Its period is calculated to be 77 years. A large number of binary stars, whose periods are computed to be some hundreds or thousands of years, have been observed as yet only through a short arc ; hence their periodic times, and the forms of their orbits, are quite uncertain. 261. Dimensions of Stellar Orbits. — There are two binary stars whose parallax has been so satisfactorily measured that their distances from us may be consid- ered as well known. These are Alpha Centauri and 61 Cygni. Hence, by the angular length of the semi- major axes of their orbits, we may find the mean radius vector of each. That of Alpha Centauri is about 1,500,000,000 miles, and that of 61 Cygni is about 4,200,000,000 miles. 260. State the periods of some of the double stars. 261. What orbits of double stars are known ? How large are they? TEMPORARY STARS. 191 262. Triple and Quadruple Stars. — There are a few instances of three or four stars, which are known to be physically connected, and to constitute a sys- tem. Zeta Cancri is triple, and Epsilon Lyrse is quadruple. In each of these, the component stars have a slow motion about each other. 263 o Periodic and Temporary Stars. — There are among the fixed stars several instances in which there appear to be revolutions of another sort, the nature of which is not understood. Stars which exhibit these changes are called periodic stars. A remarka- ble example occurs in the star Omicron Ceti. It passes through its changes of brightness in about 11 months. When brightest, it is of the second magni- tude, and remains so for two weeks. It then dimin- ishes during three months to the tenth magnitude, remains thus five months, and increases again during three months to its maximum of brightness. Algol (Beta Persei) has a very short period, occu- pying only 2d. 20h. 48m. Its changes succeed each other with great regularity, thus : During 2d. 14A. Qm it remains of the second magnitude. " Qd. %Ji. 24m. diminishes from second to fourth. " Qd. Sh. 24m. increases from fourth to second. 2d. 207i. 48m. whole period. iSome of this class of stars have periods of only a few days, while in others the changes go on very 262. Are there any combinations more complex still ? 263. State what is meant by periodic stars. Describe two. What others are probably of this class ? 192 NEBULA. slowly, and appear to require several years. The periods of some are quite uniform, and of others irregular. To this class probably belong those stars which are called temporary stars. That of 1572 is celebrated. It appeared so suddenly, and of such brilliancy, as to attract the attention of common people, and rapidly increased, till in a few weeks it surpassed Jupiter in brightness. It then faded slowly, and, after about 1 J years, entirely disappeared. Several other cases less marked than this are on record. And the earlier catalogues contain numerous stars which are not to be found at the present day. 264. Clusters of Stars.— The fixed stars are fre- quently grouped together in clusters; such as the Pleiades, in Taurus ; Presepe, in Cancer ; and Coma Berenices. If a telescope of low power is used, the number of stars appears greatly increased. There are others which, to the naked eye, appear to be nebulous, but, by the use of the telesccope, are plainly seen to be clusters ; and in some of them the stars are so numerous as not to be easily counted. The clusters in Perseus and Hercules are fine exam- ples. For the latter, see Fig. 1, frontispiece. 285. Nehulw. — These are faint patches of light, having generally an ill-defined edge, and, in ordinary telescopes, presenting the same nebulous aspect which the closer clusters do to the naked eye. As the powers of the telescope are increased, many neb- 264. Mention some clusters of stars. THE GALAXY. 193 ulae are resolved into clusters of stars, while many others retain their nebulous appearance under every power yet employed. The number of nebulae now known exceeds 4,000. The forms of nebulae are vari- ous, and may be classified as follows *. 1. Globular, — These appear circular in their outline, and generally grow brighter from the edges toward the center. The Planetary Nebvke have a well defined edge, and no bright center. The Nebulous Stars have only a bright point at the center, and a uniform nebu- losity about it. 2. Elliptical. — A large number of the nebulae have this form, the most remarkable example of which is the great nebula of Andromeda. 3. Spiral. — This form is becoming more frequent as telescopes are improved, and the more delicate fea- tures traced. The whirlpool nebula, near the tail of the Great Bear, is a fine example. See Fig. 2, frontispiece. 4. Annular. — A few nebulae appear ring-like, being more luminous on the edges than in the center. The nebula of Lyra is annular. 5. Irregular. — All the previous forms imply the existence of revolution in the material of which the nebula is composed. But there are others which are wholly irregular. None is more remarkable than the great nebula of Orion. 268. TJie Galaxy, — This is a belt, or zone, of neb- ulous appearance, which encircles the heavens, nearly 265. What are nebulae? Name the several forms. What re- markable ones of these forms ? 194 THE GALAXY. coincident with a great circle, and cuts the plane of the equator afc an angle of 63°. It is usually called the Milky Way. Near the constellation Cygnus, it divides into two parts, which continue separate nearly a semicircle (150°), and then reunite. Its edges are generally ill-defined, and also quite crooked and irregular, having many projections and indentations. The telescope shows that the whiteness of the galaxy is due to unnumbered stars, too faint to be seen individually. Their distribution is quite un- equal ; the stars, in some parts, being crowded very closely together, while here and there spaces occur which contain but few. These inequalities are most marked in the southern hemisphere. In the most luminous parts, Sir William Herschel estimated that, within an area of less than T \$ part of the hemi- sphere, there passed the field of his telescope 50,000 stars, large enough to be distinctly seen. The whole number of stars in the Milky Way is to be reckoned by millions. 266. What is the galaxy? Describe its extent. What does it consist of?