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diff --git a/58810-0.txt b/58810-0.txt new file mode 100644 index 0000000..09a9b1d --- /dev/null +++ b/58810-0.txt @@ -0,0 +1,10187 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 58810 *** + + + +Note: Project Gutenberg also has an HTML version of this file + which includes the 466 original illustrations. + See 58810-h.htm or 58810-h.zip: + (http://www.gutenberg.org/files/58810/58810-h/58810-h.htm) + or + (http://www.gutenberg.org/files/58810/58810-h.zip) + + + Images of the original pages are available through + Internet Archive. See + https://archive.org/details/heavensabovepopu00gillrich + + + +Transcriber's note: + + Text enclosed by underscores is in italics (_italics_). + + Superscripts, such as P to the second power, are shown by + the caret character "^" before the superscript, such as P^2. + + Subscripts are similarly shown by an underscore before the + subscript which is wrapped in curly braces, such as M_{2}. + + + + + +[Illustration: SPECTRA OF VARIOUS SOURCES OF LIGHT.] + + The Heavens Above: A Popular Handbook of Astronomy + + +THE HEAVENS ABOVE: + +A Popular Handbook of Astronomy. + +by + +J. A. GILLET, + +Professor of Physics in the Normal College of the City of New York, + +and + +W. J. ROLFE, + +Formerly Head Master of the High School, Cambridge, Mass. + +With Six Lithographic Plates and Four Hundred +and Sixty Wood Engravings. + + + + + + +Potter, Ainsworth, & Co., +New York and Chicago. +1882. + +Copyright by +J. A. Gillet and W. J. Rolfe, +1882. + +Franklin Press: +Rand, Avery, and Company, +Boston. + + + + + PREFACE. + + +It has been the aim of the authors to give in this little book a brief, +simple, and accurate account of the heavens as they are known to +astronomers of the present day. It is believed that there is nothing in +the book beyond the comprehension of readers of ordinary intelligence, +and that it contains all the information on the subject of astronomy +that is needful to a person of ordinary culture. The authors have +carefully avoided dry and abstruse mathematical calculations, yet they +have sought to make clear the methods by which astronomers have gained +their knowledge of the heavens. The various kinds of telescopes and +spectroscopes have been described, and their use in the study of the +heavens has been fully explained. + +The cuts with which the book is illustrated have been drawn from all +available sources; and it is believed that they excel in number, +freshness, beauty, and accuracy those to be found in any similar work. +The lithographic plates are, with a single exception, reductions of the +plates prepared at the Observatory at Cambridge, Mass. The remaining +lithographic plate is a reduced copy of Professor Langley's celebrated +sun-spot engraving. Many of the views of the moon are from drawings made +from the photographs in Carpenter and Nasmyth's work on the moon. The +majority of the cuts illustrating the solar system are copied from the +French edition of Guillemin's "Heavens." Most of the remainder are from +Lockyer's "Solar Physics," Young's "Sun," and other recent authorities. +The cuts illustrating comets, meteors, and nebulæ, are nearly all taken +from the French editions of Guillemin's "Comets" and Guillemin's +"Heavens." + + + + + CONTENTS. + + +I. THE CELESTIAL SPHERE 3 + +II. THE SOLAR SYSTEM 41 + + I. THEORY OF THE SOLAR SYSTEM 41 + + The Ptolemaic System 41 + + The Copernican System 44 + + Tycho Brahe's System 44 + + Kepler's System 44 + + The Newtonian System 48 + + II. THE SUN AND PLANETS 53 + + I. The Earth 53 + + Form and Size 53 + + Day and Night 57 + + The Seasons 64 + + Tides 68 + + The Day and Time 74 + + The Year 78 + + Weight of the Earth and Precession 83 + + II. The Moon 86 + + Distance, Size, and Motions 86 + + The Atmosphere of the Moon 109 + + The Surface of the Moon 114 + + III. Inferior and Superior Planets 130 + + Inferior Planets 130 + + Superior Planets 134 + + IV. The Sun 140 + + I. Magnitude and Distance of the Sun 140 + + II. Physical and Chemical Condition of the Sun 149 + + Physical Condition of the Sun 149 + + The Spectroscope 152 + + Spectra 158 + + Chemical Constitution of the Sun 164 + + Motion at the Surface of the Sun 168 + + III. The Photosphere and Sun-Spots 175 + + The Photosphere 175 + + Sun-Spots 179 + + IV. The Chromosphere and Prominences 196 + + V. The Corona 204 + + V. Eclipses 210 + + VI. The Three Groups of Planets 221 + + I. General Characteristics of the Groups 221 + + II. The Inner Group of Planets 225 + + Mercury 225 + + Venus 230 + + Mars 235 + + III. The Asteroids 241 + + IV. Outer Group of Planets 244 + + Jupiter 244 + + The Satellites of Jupiter 250 + + Saturn 255 + + The Planet and his Moons 255 + + The Rings of Saturn 261 + + Uranus 269 + + Neptune 271 + + VII. Comets and Meteors 274 + + I. Comets 274 + + General Phenomena of Comets 274 + + Motion and Origin of Comets 281 + + Remarkable Comets 290 + + Connection between Meteors and Comets, 300 + + Physical and Chemical Constitution of Comets 314 + + II. The Zodiacal Light 318 + +III. THE STELLAR UNIVERSE 322 + + I. General Aspect of the Heavens 322 + + II. The Stars 330 + + The Constellations 330 + + Clusters 350 + + Double and Multiple Stars 355 + + New and Variable Stars 358 + + Distance of the Stars 364 + + Proper Motion of the Stars 365 + + Chemical and Physical Constitution of the Stars 371 + + III. Nebulæ 373 + + Classification of Nebulæ 373 + + Irregular Nebulæ 376 + + Spiral Nebulæ 384 + + The Nebular Hypothesis 391 + + IV. The Structure of the Stellar Universe 396 + + + + + I. + THE CELESTIAL SPHERE. + + +I. _The Sphere._--A _sphere_ is a solid figure bounded by a surface +which curves equally in all directions at every point. The rate at which +the surface curves is called the _curvature_ of the sphere. The smaller +the sphere, the greater is its curvature. Every point on the surface of +a sphere is equally distant from a point within, called the _centre_ of +the sphere. The _circumference_ of a sphere is the distance around its +centre. The _diameter_ of a sphere is the distance through its centre. +The _radius_ of a sphere is the distance from the surface to the centre. +The surfaces of two spheres are to each other as the squares of their +radii or diameters; and the volumes of two spheres are to each other as +the cubes of their radii or diameters. + +Distances on the surface of a sphere are usually denoted in _degrees_. A +degree is 1/360 of the circumference of the sphere. The larger a sphere, +the longer are the degrees on it. + +A curve described about any point on the surface of a sphere, with a +radius of uniform length, will be a circle. As the radius of a circle +described on a sphere is a curved line, its length is usually denoted in +degrees. The circle described on the surface of a sphere increases with +the length of the radius, until the radius becomes 90°, in which case +the circle is the largest that can possibly be described on the sphere. +The largest circles that can be described on the surface of a sphere are +called _great circles_, and all other circles _small circles_. + + Any number of great circles may be described on the surface of a + sphere, since any point on the sphere may be used for the centre of + the circle. The plane of every great circle passes through the + centre of the sphere, while the planes of all the small circles pass + through the sphere away from the centre. All great circles on the + same sphere are of the same size, while the small circles differ in + size according to the distance of their planes from the centre of + the sphere. The farther the plane of a circle is from the centre of + the sphere, the smaller is the circle. + + By a _section_ of a sphere we usually mean the figure of the surface + formed by the cutting; by a _plane section_ we mean one whose + surface is plane. Every plane section of a sphere is a circle. When + the section passes through the centre of the sphere, it is a great + circle; in every other case the section is a small circle. Thus, + _AN_ and _SB_ (Fig. 1) are small circles, and _MM'_ and _SN_ are + large circles. + +[Illustration: Fig. 1.] + + In a diagram representing a sphere in section, all the circles whose + planes cut the section are represented by straight lines. Thus, in + Fig. 2, we have a diagram representing in section the sphere of Fig. + 1. The straight lines _AN_, _SB_, _MM'_, and _SN_, represent the + corresponding circles of Fig. 1. + +The _axis_ of a sphere is the diameter on which it rotates. The _poles_ +of a sphere are the ends of its axis. Thus, supposing the spheres of +Figs. 1 and 2 to rotate on the diameter _PP'_, this line would be called +the axis of the sphere, and the points _P_ and _P'_ the poles of the +sphere. A great circle, MM', situated half way between the poles of a +sphere, is called the _equator_ of the sphere. + +Every great circle of a sphere has two poles. These are the two points +on the surface of the sphere which lie 90° away from the circle. The +poles of a sphere are the poles of its equator. + +[Illustration: Fig. 2.] + +2. _The Celestial Sphere._--The heavens appear to have the form of a +sphere, whose centre is at the eye of the observer; and all the stars +seem to lie on the surface of this sphere. This form of the heavens is a +mere matter of perspective. The stars are really at very unequal +distances from us; but they are all seen projected upon the celestial +sphere in the direction in which they happen to lie. Thus, suppose an +observer situated at _C_ (Fig. 3), stars situated at _a_, _b_, _d_, _e_, +_f_, and _g_, would be projected upon the sphere at _A_, _B_, _D_, _E_, +_F_, and _G_, and would appear to lie on the surface of the heavens. + +[Illustration: Fig. 3.] + +3. _The Horizon._--Only half of the celestial sphere is visible at a +time. The plane that separates the visible from the invisible portion is +called the _horizon_. This plane is tangent to the earth at the point of +observation, and extends indefinitely into space in every direction. In +Fig. 4, _E_ represents the earth, _O_ the point of observation, and _SN_ +the horizon. The points on the celestial sphere directly above and below +the observer are the poles of the horizon. They are called respectively +the _zenith_ and the _nadir_. No two observers in different parts of the +earth have the same horizon; and as a person moves over the earth he +carries his horizon with him. + +[Illustration: Fig. 4.] + +The dome of the heavens appears to rest on the earth, as shown in Fig. +5. This is because distant objects on the earth appear projected against +the heavens in the direction of the horizon. + +[Illustration: Fig. 5.] + +The _sensible_ horizon is a plane tangent to the earth at the point of +observation. The _rational_ horizon is a plane parallel with the +sensible horizon, and passing through the centre of the earth. As it +cuts the celestial sphere through the centre, it forms a great circle. +_SN_ (Fig. 6) represents the sensible horizon, and _S'N'_ the rational +horizon. Although these two horizons are really four thousand miles +apart, they appear to meet at the distance of the celestial sphere; a +line four thousand miles long at the distance of the celestial sphere +becoming a mere point, far too small to be detected with the most +powerful telescope. + +[Illustration: Fig. 6.] + +[Illustration: Fig. 7.] + +4. _Rotation of the Celestial Sphere._--It is well known that the sun +and the majority of the stars rise in the east, and set in the west. In +our latitude there are certain stars in the north which never disappear +below the horizon. These stars are called the _circumpolar_ stars. A +close watch, however, reveals the fact that these all appear to revolve +around one of their number called the _pole star_, in the direction +indicated by the arrows in Fig. 7. In a word, the whole heavens appear +to rotate once a day, from east to west, about an axis, which is the +prolongation of the axis of the earth. The ends of this axis are called +the _poles_ of the heavens; and the great circle of the heavens, midway +between these poles, is called the _celestial equator_, or the +_equinoctial_. This rotation of the heavens is apparent only, being due +to the rotation of the earth from west to east. + +5. _Diurnal Circles._--In this rotation of the heavens, the stars appear +to describe circles which are perpendicular to the celestial axis, and +parallel with the celestial equator. These circles are called _diurnal +circles_. The position of the poles in the heavens and the direction of +the diurnal circles with reference to the horizon, change with the +position of the observer on the earth. This is owing to the fact that +the horizon changes with the position of the observer. + +[Illustration: Fig. 8.] + +When the observer is north of the equator, the north pole of the heavens +is _elevated_ above the horizon, and the south pole is _depressed_ below +it, and the diurnal circles are _oblique_ to the horizon, leaning to the +south. This case is represented in Fig. 8, in which _PP'_ represents the +celestial axis, _EQ_ the celestial equator, _SN_ the horizon, and _ab_, +_cN_, _de_, _fg_, _Sh_, _kl_, diurnal circles. _O_ is the point of +observation, _Z_ the zenith, and _Z'_ the nadir. + +[Illustration: Fig. 9.] + +When the observer is south of the equator, as at _O_ in Fig. 9, the +south pole is _elevated_, the north pole _depressed_, and the diurnal +circles are _oblique_ to the horizon, leaning to the north. When the +diurnal circles are oblique to the horizon, as in Figs. 8 and 9, the +celestial sphere is called an _oblique sphere_. + +When the observer is at the equator, as in Fig. 10, the poles of the +heavens are on the horizon, and the diurnal circles are _perpendicular_ +to the horizon. + +When the observer is at one of the poles, as in Fig. 11, the poles of +the heavens are in the zenith and the nadir, and the diurnal circles are +_parallel_ with the horizon. + +[Illustration: Fig. 10.] + +[Illustration: Fig. 11.] + +6. _Elevation of the Pole and of the Equinoctial._--At the equator the +poles of the heavens lie on the horizon, and the celestial equator +passes through the zenith. As a person moves north from the equator, his +zenith moves north from the celestial equator, and his horizon moves +down from the north pole, and up from the south pole. The distance of +the zenith from the equinoctial, and of the horizon from the celestial +poles, will always be equal to the distance of the observer from the +equator. In other words, the elevation of the pole is equal to the +latitude of the place. In Fig. 12, _O_ is the point of observation, _Z_ +the zenith, and _SN_ the horizon. _NP_, the elevation of the pole, is +equal to _ZE_, the distance of the zenith from the equinoctial, and to +the distance of _O_ from the equator, or the latitude of the place. + +Two angles, or two arcs, which together equal 90°, are said to be +_complements_ of each other. _ZE_ and _ES_ in Fig. 12 are together equal +to 90°: hence they are complements of each other. _ZE_ is equal to the +latitude of the place, and _ES_ is the _elevation_ of the equinoctial +above the horizon: hence the elevation of the equinoctial is equal to +the complement of the latitude of the place. + +[Illustration: Fig. 12.] + +Were the observer south of the equator, the zenith would be south of the +equinoctial, and the south pole of the heavens would be the elevated +pole. + +[Illustration: Fig. 13.] + +_7. Four Sets of Stars._--At most points of observation there are four +sets of stars. These four sets are shown in Fig. 13. + +(1) The stars in the neighborhood of the elevated pole _never set_. It +will be seen from Fig. 13, that if the distance of a star from the +elevated pole does not exceed the elevation of the pole, or the latitude +of the place, its diurnal circle will be wholly above the horizon. As +the observer approaches the equator, the elevation of the pole becomes +less and less, and the belt of circumpolar stars becomes narrower and +narrower: at the equator it disappears entirely. As the observer +approaches the pole, the elevation of the pole increases, and the belt +of circumpolar stars becomes broader and broader, until at the pole it +includes half of the heavens. At the poles, no stars rise or set, and +only half of the stars are ever seen at all. + +(2) The stars in the neighborhood of the depressed pole _never rise_. +The breadth of this belt also increases as the observer approaches the +pole, and decreases as he approaches the equator, to vanish entirely +when he reaches the equator. The distance from the depressed pole to the +margin of this belt is always equal to the latitude of the place. + +(3) The stars in the neighborhood of the equinoctial, on the side of the +elevated pole, _set, but are above the horizon longer than they are +below it_. This belt of stars extends from the equinoctial to a point +whose distance from the elevated pole is equal to the latitude of the +place: in other words, the breadth of this third belt of stars is equal +to the complement of the latitude of the place. Hence this belt of stars +becomes broader and broader as the observer approaches the equator, and +narrower and narrower as he approaches the pole. However, as the +observer approaches the equator, the horizon comes nearer and nearer the +celestial axis, and the time a star is below the horizon becomes more +nearly equal to the time it is above it. As the observer approaches the +pole, the horizon moves farther and farther from the axis, and the time +any star of this belt is below the horizon becomes more and more unequal +to the time it is above it. The farther any star of this belt is from +the equinoctial, the longer the time it is above the horizon, and the +shorter the time it is below it. + +(4) The stars which are in the neighborhood of the equinoctial, on the +side of the depressed pole, _rise, but are below the horizon longer than +they are above it_. The width of this belt is also equal to the +complement of the latitude of the place. The farther any star of this +belt is from the equinoctial, the longer time it is below the horizon, +and the shorter time it is above it; and, the farther the place from the +equator, the longer every star of this belt is below the horizon, and +the shorter the time it is above it. + +At the equator every star is above the horizon just half of the time; +and any star on the equinoctial is above the horizon just half of the +time in every part of the earth, since the equinoctial and horizon, +being great circles, bisect each other. + +8. _Vertical Circles._--Great circles perpendicular to the horizon are +called _vertical circles_. All vertical circles pass through the zenith +and nadir. A number of these circles are shown in Fig. 14, in which +_SENW_ represents the horizon, and _Z_ the zenith. + +[Illustration: Fig. 14.] + +The vertical circle which passes through the north and south points of +the horizon is called the _meridian_; and the one which passes through +the east and west points, the _prime vertical_. These two circles are +shown in Fig. 15; _SZN_ being the meridian, and _EZW_ the prime +vertical. These two circles are at right angles to each other, or 90° +apart; and consequently they divide the horizon into four quadrants. + +[Illustration: Fig. 15.] + +9. _Altitude and Zenith Distance._--The _altitude_ of a heavenly body is +its distance above the horizon, and its _zenith distance_ is its +distance from the zenith. Both the altitude and the zenith distance of a +body are measured on the vertical circle which passes through the body. +The altitude and zenith distance of a heavenly body are complements of +each other. + +10. _Azimuth and Amplitude.--Azimuth_ is distance measured east or west +from the meridian. When a heavenly body lies north of the prime +vertical, its azimuth is measured from the meridian on the north; and, +when it lies south of the prime vertical, its azimuth is measured from +the meridian on the south. The azimuth of a body can, therefore, never +exceed 90°. The azimuth of a body is the angle which the plane of the +vertical circle passing through it makes with that of the meridian. + +The _amplitude_ of a body is its distance measured north or south from +the prime vertical. The amplitude and azimuth of a body are complements +of each other. + +11. _Alt-azimuth Instrument._--An instrument for measuring the altitude +and azimuth of a heavenly body is called an _alt-azimuth_ instrument. +One form of this instrument is shown in Fig. 16. It consists essentially +of a telescope mounted on a vertical circle, and capable of turning on a +horizontal axis, which, in turn, is mounted on the vertical axis of a +horizontal circle. Both the horizontal and the vertical circles are +graduated, and the horizontal circle is placed exactly parallel with the +plane of the horizon. + +When the instrument is properly adjusted, the axis of the telescope will +describe a vertical circle when the telescope is turned on the +horizontal axis, no matter to what part of the heavens it has been +pointed. + +The horizontal and vertical axes carry each a pointer. These pointers +move over the graduated circles, and mark how far each axis turns. + +To find the _azimuth_ of a star, the instrument is turned on its +vertical axis till its vertical circle is brought into the plane of the +meridian, and the reading of the horizontal circle noted. The telescope +is then directed to the star by turning it on both its vertical and +horizontal axes. The reading of the horizontal circle is again noted. +The difference between these two readings of the horizontal circle will +be the azimuth of the star. + +[Illustration: Fig. 16.] + +To find the _altitude_ of a star, the reading of the vertical circle is +first ascertained when the telescope is pointed horizontally, and again +when the telescope is pointed at the star. The difference between these +two readings of the vertical circle will be the altitude of the star. + +12. _The Vernier._--To enable the observer to read the fractions of the +divisions on the circles, a device called a _vernier_ is often employed. +It consists of a short, graduated arc, attached to the end of an arm _c_ +(Fig. 17), which is carried by the axis, and turns with the telescope. +This arc is of the length of _nine_ divisions on the circle, and it is +divided into _ten_ equal parts. If 0 of the vernier coincides with any +division, say 6, of the circle, 1 of the vernier will be 1/10 of a +division to the left of 7, 2 will be 2/10 of a division to the left of +8, 3 will be 3/10, of a division to the left of 9, etc. Hence, when 1 +coincides with 7, 0 will be at 6-1/10; when 2 coincides with 8, 0 will +be at 6-2/10; when 3 coincides with 9, 0 will be at 6-3/10, etc. + +[Illustration: Fig. 17.] + +To ascertain the reading of the circle by means of the vernier, we first +notice the zero line. If it exactly coincides with any division of the +circle, the number of that division will be the reading of the circle. +If there is not an exact coincidence of the zero line with any division +of the circle, we run the eye along the vernier, and note which of its +divisions does coincide with a division of the circle. The reading of +the circle will then be the number of the first division on the circle +behind the 0 of the vernier, and a number of tenths equal to the number +of the division of the vernier, which coincides with a division of the +circle. For instance, suppose 0 of the vernier beyond 6 of the circle, +and 7 of the vernier to coincide with 13 of the circle. The reading of +the circle will then be 6-7/10. + +13. _Hour Circles._--Great circles perpendicular to the celestial +equator are called _hour circles_. These circles all pass through the +poles of the heavens, as shown in Fig. 18. _EQ_ is the celestial +equator, and _P_ and _P'_ are the poles of the heavens. + +The point _A_ on the equinoctial (Fig. 19) is called the _vernal +equinox_, or the _first point of Aries_. The hour circle, _APP'_, which +passes through it, is called the _equinoctial colure_. + +[Illustration: Fig. 18.] + +14. _Declination and Right Ascension._--The _declination_ of a heavenly +body is its distance north or south of the celestial equator. The _polar +distance_ of a heavenly body is its distance from the nearer pole. +Declination and polar distance are measured on hour circles, and for the +same heavenly body they are complements of each other. + +[Illustration: Fig. 19.] + +The _right ascension_ of a heavenly body is its distance eastward from +the first point of Aries, measured from the equinoctial colure. It is +equal to the arc of the celestial equator included between the first +point of Aries and the hour circle which passes through the heavenly +body. As right ascension is measured eastward entirely around the +celestial sphere, it may have any value from 0° up to 360°. Right +ascension corresponds to longitude on the earth, and declination to +latitude. + +15. _The Meridian Circle._--The right ascension and declination of a +heavenly body are ascertained by means of an instrument called the +_meridian circle_, or _transit instrument_. A side-view of this +instrument is shown in Fig. 20. + +[Illustration: Fig. 20.] + +It consists essentially of a telescope mounted between two piers, so as +to turn in the plane of the meridian, and carrying a graduated circle. +The readings of this circle are ascertained by means of fixed +microscopes, under which it turns. A heavenly body can be observed with +this instrument, only when it is crossing the meridian. For this reason +it is often called the _transit circle_. + +To find the declination of a star with this instrument, we first +ascertain the reading of the circle when the telescope is pointed to the +pole, and then the reading of the circle when pointed to the star on its +passage across the meridian. The difference between these two readings +will be the polar distance of the star, and the complement of them the +declination of the star. + +To ascertain the reading of the circle when the telescope is pointed to +the pole, we must select one of the circumpolar stars near the pole, and +then point the telescope to it when it crosses the meridian, both above +and below the pole, and note the reading of the circle in each case. The +mean of these two readings will be the reading of the circle when the +telescope is pointed to the pole. + +16. _Astronomical Clock._--An _astronomical clock_, or _sidereal clock_ +as it is often called, is a clock arranged so as to mark hours from 1 to +24, instead of from 1 to 12, as in the case of an ordinary clock, and so +adjusted as to mark 0 when the vernal equinox, or first point of Aries, +is on the meridian. + +As the first point of Aries makes a complete circuit of the heavens in +twenty-four hours, it must move at the rate of 15° an hour, or of 1° in +four minutes: hence, when the astronomical clock marks 1, the first +point of Aries must be 15° west of the meridian, and when it marks 2, +30° west of the meridian, etc. That is to say, by observing an accurate +astronomical clock, one can always tell how far the meridian at any time +is from the first point of Aries. + +17. _How to find Right Ascension with the Meridian Circle._--To find the +right ascension of a heavenly body, we have merely to ascertain the +exact time, by the astronomical clock, at which the body crosses the +meridian. If a star crosses the meridian at 1 hour 20 minutes by the +astronomical clock, its right ascension must be 19°; if at 20 hours, its +right ascension must be 300°. + +To enable the observer to ascertain with great exactness the time at +which a star crosses the meridian, a number of equidistant and parallel +spider-lines are stretched across the focus of the telescope, as shown +in Fig. 21. The observer notes the time when the star crosses each +spider-line; and the mean of all of these times will be the time when +the star crosses the meridian. The mean of several observations is +likely to be more nearly exact than any single observation. + +[Illustration: Fig. 21.] + +[Illustration: Fig. 22.] + +18. _The Equatorial Telescope._--The _equatorial_ telescope is mounted +on two axes,--one parallel with the axis of the earth, and the other at +right angles to this, and therefore parallel with the plane of the +earth's equator. The former is called the _polar axis_, and the latter +the _declination axis_. Each axis carries a graduated circle. These +circles are called respectively the _hour circle_ and the _declination +circle_. The telescope is attached directly to the declination axis. +When the telescope is fixed in any declination, and then turned on its +polar axis, the line of sight will describe a diurnal circle; so that, +when the tube is once directed to a star, it can be made to follow the +star by simply turning the telescope on its polar axis. + +In the case of large instruments of this class, the polar axis is +usually turned by clock-work at the rate at which the heavens rotate; so +that, when the telescope has once been pointed to a planet or other +heavenly body, it will continue to follow the body and keep it steadily +in the field of view without further trouble on the part of the +observer. + +The great Washington Equatorial is shown in Fig. 22. Its object-glass is +26 inches in diameter, and its focal length is 32-1/2 feet. It was +constructed by Alvan Clark & Sons of Cambridge, Mass. It is one of the +three largest refracting telescopes at present in use. The Newall +refractor at Gateshead, Eng., has an objective 25 inches in diameter, +and a focal length of 29 feet. The great refractor at Vienna has an +objective 27 inches in diameter. There are several large refractors now +in process of construction. + +[Illustration: Fig. 23.] + +19. _The Wire Micrometer._--Large arcs in the heavens are measured by +means of the graduated circles attached to the axes of the telescopes; +but small arcs within the field of view of the telescope are measured by +means of instruments called _micrometers_, mounted in the focus of the +telescope. One of the most convenient of these micrometers is that known +as the _wire micrometer_, and shown in Fig. 23. + +The frame _AA_ covers two slides, _C_ and _D_. These slides are moved by +the screws _F_ and _G_. The wires _E_ and _B_ are stretched across the +ends of the slides so as to be parallel to each other. On turning the +screws _F_ and _G_ one way, these wires are carried apart; and on +turning them the other way they are brought together again. Sometimes +two parallel wires, _x_ and _y_, shown in the diagram at the right, are +stretched across the frame at right angles to the wires _E_, _B_. We may +call the wires _x_ and _y_ the _longitudinal_ wires of the micrometer, +and _E_ and _B_ the _transverse_ wires. Many instruments have only one +longitudinal wire, which is stretched across the middle of the focus. +The longitudinal wires are just in front of the transverse wires, but do +not touch them. + +To find the distance between any two points in the field of view with a +micrometer, with a single longitudinal wire, turn the frame till the +longitudinal wire passes through the two points; then set the wires _E_ +and _B_ one on each point, turn one of the screws, known as the +_micrometer screw_, till the two wires are brought together, and note +the number of times the screw is turned. Having previously ascertained +over what arc one turn of the screw will move the wire, the number of +turns will enable us to find the length of the arc between the two +points. + +The threads of the micrometer screw are cut with great accuracy; and the +screw is provided with a large head, which is divided into a hundred or +more equal parts. + +These divisions, by means of a fixed pointer, enable us to ascertain +what fraction of a turn the screw has made over and above its complete +revolutions. + +20. _Reflecting Telescopes._--It is possible to construct mirrors of +much larger size than lenses: hence reflecting telescopes have an +advantage over refracting telescopes as regards size of aperture and of +light-gathering power. They are, however, inferior as regards +definition; and, in order to prevent flexure, it is necessary to give +the speculum, or mirror, a massiveness which makes the telescope +unwieldy. It is also necessary frequently to repolish the speculum; and +this is an operation of great delicacy, as the slightest change in the +form of the surface impairs the definition of the image. These defects +have been remedied, to a certain extent, by the introduction of +silver-on-glass mirrors; that is, glass mirrors covered in front with a +thin coating of silver. Glass is only one-third as heavy as +speculum-metal, and silver is much superior to that metal in reflecting +power; and when the silver becomes tarnished, it can be removed and +renewed without danger of changing the form of the glass. + +_The Herschelian Reflector._--In this form of telescope the mirror is +slightly tipped, so that the image, instead of being formed in the +centre of the tube, is formed near one side of it, as in Fig. 24. The +observer can then view it without putting his head inside the tube, and +therefore without cutting off any material portion of the light. In +observation, he must stand at the upper or outer end of the tube, and +look into it, his back being turned towards the object. From his looking +directly into the mirror, it is also sometimes called the _front-view_ +telescope. The great disadvantage of this arrangement is, that the rays +cannot be brought to an exact focus when they are thrown so far to one +side of the axis, and the injury to the definition is so great that the +front-view plan is now entirely abandoned. + +[Illustration: Fig. 24.] + +_The Newtonian Reflector._--The plan proposed by Sir Isaac Newton was to +place a small plane mirror just inside the focus, inclined to the +telescope at an angle of 45°, so as to throw the rays to the side of the +tube, where they come to a focus, and form the image. An opening is made +in the side of the tube, just below where the image is formed; and in +this opening the eye-piece is inserted. The small mirror cuts off some +of the light, but not enough to be a serious defect. An improvement +which lessens this defect has been made by Professor Henry Draper. The +inclined mirror is replaced by a small rectangular prism (Fig. 25), by +reflection from which the image is formed very near the prism. A pair of +lenses are then inserted in the course of the rays, by which a second +image is formed at the opening in the side of the tube; and this second +image is viewed by an ordinary eye-piece. + +[Illustration: Fig. 25.] + +_The Gregorian Reflector._--This is a form proposed by James Gregory, +who probably preceded Newton as an inventor of the reflecting telescope. +Behind the focus, _F_ (Fig. 26), a small concave mirror, _R_, is placed, +by which the light is reflected back again down the tube. The larger +mirror, _M_, has an opening through its centre; and the small mirror, +_R_, is so adjusted as to form a second image of the object in this +opening. This image is then viewed by an eye-piece which is screwed into +the opening. + +[Illustration: Fig. 26.] + +_The Cassegrainian Reflector._--In principle this is the same with the +Gregorian; but the small mirror, _R_, is convex, and is placed inside +the focus, _F_, so that the rays are reflected from it before reaching +the focus, and no image is formed until they reach the opening in the +large mirror. This form has an advantage over the Gregorian, in that the +telescope may be made shorter, and the small mirror can be more easily +shaped to the required figure. It has, therefore, entirely superseded +the original Gregorian form. + +[Illustration: Fig. 27.] + +Optically these forms of telescope are inferior to the Newtonian; but +the latter is subject to the inconvenience, that the observer must be +stationed at the upper end of the telescope, where he looks into an +eye-piece screwed into the side of the tube. + +On the other hand, the Cassegrainian Telescope is pointed directly at +the object to be viewed, like a refractor; and the observer stands at +the lower end, and looks in at the opening through the large mirror. +This is, therefore, the most convenient form of all in management. + +[Illustration: Fig. 28.] + +The largest reflecting telescope yet constructed is that of Lord Rosse, +at Parsonstown, Ireland. Its speculum is 6 feet in diameter, and its +focal length 55 feet. It is commonly used as a Newtonian. This telescope +is shown in Fig. 27. + +The great telescope of the Melbourne Observatory, Australia, is a +Cassegranian reflector. Its speculum is 4 feet in diameter, and its +focal length is 32 feet. It is shown in Fig. 28. + +[Illustration: Fig. 29.] + +The great reflector of the Paris Observatory is a Newtonian reflector. +Its mirror of silvered glass is 4 feet in diameter, and its focal length +is 23 feet. This telescope is shown in Fig. 29. + +21. _The Sun's Motion among the Stars._--If we notice the stars at the +same hour night after night, we shall find that the constellations are +steadily advancing towards the west. New constellations are continually +appearing in the east, and old ones disappearing in the west. This +continual advancing of the heavens towards the west is due to the fact +that the sun's place among the stars is _continually moving towards the +east_. The sun completes the circuit of the heavens in a year, and is +therefore moving eastward at the rate of about a degree a day. + +[Illustration: Fig. 30.] + +This motion of the sun's place among the stars is due to the revolution +of the earth around the sun, and not to any real motion of the sun. In +Fig. 30 suppose the inner circle to represent the orbit of the earth +around the sun, and the outer circle to represent the celestial sphere. +When the earth is at _E_, the sun's place on the celestial sphere is at +_S'_. As the earth moves in the direction _EF_, the sun's place on the +celestial sphere must move in the direction _S'T_: hence the revolution +of the earth around the sun would cause the sun's place among the stars +to move around the heavens in the same direction that the earth is +moving around the sun. + +22. _The Ecliptic._--The circle described by the sun in its apparent +motion around the heavens is called the _ecliptic_. The plane of this +circle passes through the centre of the earth, and therefore through the +centre of the celestial sphere; the earth being so small, compared with +the celestial sphere, that it practically makes no difference whether we +consider a point on its surface, or one at its centre, as the centre of +the celestial sphere. The ecliptic is, therefore, a great circle. + +The earth's orbit lies in the plane of the ecliptic; but it extends only +an inappreciable distance from the sun towards the celestial sphere. + +[Illustration: Fig. 31.] + +23. _The Obliquity of the Ecliptic._--The ecliptic is inclined to the +celestial equator by an angle of about 23-1/2°. This inclination is +called the _obliquity of the ecliptic_. The obliquity of the ecliptic is +due to the deviation of the earth's axis from a perpendicular to the +plane of its orbit. The axis of a rotating body tends to maintain the +same direction; and, as the earth revolves around the sun, its axis +points all the time in nearly the same direction. The earth's axis +deviates about 23-1/2° from the perpendicular to its orbit; and, as the +earth's equator is at right angles to its axis, it will deviate about +23-1/2° from the plane of the ecliptic. The celestial equator has the +same direction as the terrestrial equator, since the axis of the heavens +has the same direction as the axis of the earth. + +[Illustration: Fig. 32.] + +Suppose the globe at the centre of the tub (Fig. 31) to represent the +sun, and the smaller globes to represent the earth in various positions +in its orbit. The surface of the water will then represent the plane of +the ecliptic, and the rod projecting from the top of the earth will +represent the earth's axis, which is seen to point all the time in the +same direction, or to lean the same way. The leaning of the axis from +the perpendicular to the surface of the water would cause the earth's +equator to be inclined the same amount to the surface of the water, half +of the equator being above, and half of it below, the surface. Were the +axis of the earth perpendicular to the surface of the water, the earth's +equator would coincide with the surface, as is evident from Fig. 32. + +[Illustration: Fig. 33.] + +24. _The Equinoxes and Solstices._--The ecliptic and celestial equator, +being great circles, bisect each other. Half of the ecliptic is north, +and half of it is south, of the equator. The points at which the two +circles cross are called the _equinoxes_. The one at which the sun +crosses the equator from south to north is called the _vernal_ equinox, +and the one at which it crosses from north to south the _autumnal_ +equinox. The points on the ecliptic midway between the equinoxes are +called the _solstices_. The one north of the equator is called the +_summer_ solstice, and the one south of the equator the _winter_ +solstice. In Fig. 33, _EQ_ is the celestial equator, _EcE'c'_ the +ecliptic, _V_ the vernal equinox, A the autumnal equinox, Ec the winter +solstice, and _E'c'_ the summer solstice. + +[Illustration: Fig. 34.] + +25. _The Inclination of the Ecliptic to the Horizon._--Since the +celestial equator is perpendicular to the axis of the heavens, it makes +the same angle with it on every side: hence, at any place, the equator +makes always the same angle with the horizon, whatever part of it is +above the horizon. But, as the ecliptic is oblique to the equator, it +makes different angles with the celestial axis on different sides; and +hence, at any place, the angle which the ecliptic makes with the horizon +varies according to the part which is above the horizon. The two extreme +angles for a place more than 23-1/2° north of the equator are shown in +Figs. 34 and 35. + +The least angle is formed when the vernal equinox is on the eastern +horizon, the autumnal on the western horizon, and the winter solstice on +the meridian, as in Fig. 34. The angle which the ecliptic then makes +with the horizon is equal to the elevation of the equinoctial _minus_ +23-1/2°. In the latitude of New York this angle = 49° - 23-1/2° = +25-1/2°. + +[Illustration: Fig. 35.] + +The greatest angle is formed when the autumnal equinox is on the eastern +horizon, the vernal on the western horizon, and the summer solstice is +on the meridian (Fig. 35). The angle between the ecliptic and the +horizon is then equal to the elevation of the equinoctial _plus_ +23-1/2°. In the latitude of New York this angle = 49° + 23-1/2° = +72-1/2°. + +Of course the equinoxes, the solstices, and all other points on the +ecliptic, describe diurnal circles, like every other point in the +heavens: hence, in our latitude, these points rise and set every day. + +26. _Celestial Latitude and Longitude._--_Celestial latitude_ is +distance measured north or south from the ecliptic; and _celestial +longitude_ is distance measured on the ecliptic eastward from the vernal +equinox, or the first point of Aries. Great circles perpendicular to the +ecliptic are called _celestial meridians_. These circles all pass +through the poles of the ecliptic, which are some 23-1/2° from the poles +of the equinoctial. The latitude of a heavenly body is measured by the +arc of a celestial meridian included between the body and the ecliptic. +The longitude of a heavenly body is measured by the arc of the ecliptic +included between the first point of Aries and the meridian which passes +through the body. There are, of course, always two arcs included between +the first point of Aries and the meridian,--one on the east, and the +other on the west, of the first point of Aries. The one on the _east_ is +always taken as the measure of the longitude. + +27. _The Precession of the Equinoxes._--The equinoctial points have a +slow westward motion along the ecliptic. This motion is at the rate of +about 50'' a year, and would cause the equinoxes to make a complete +circuit of the heavens in a period of about twenty-six thousand years. +It is called the _precession of the equinoxes_. This westward motion of +the equinoxes is due to the fact that the axis of the earth has a slow +gyratory motion, like the handle of a spinning-top which has begun to +wabble a little. This gyratory motion causes the axis of the heavens to +describe a cone in about twenty-six thousand years, and the pole of the +heavens to describe a circle about the pole of the ecliptic in the same +time. The radius of this circle is 23-1/2°. + +[Illustration: Fig. 36.] + + 28. _Illustration of Precession._--The precession of the equinoxes + may be illustrated by means of the apparatus shown in Fig. 36. The + horizontal and stationary ring _EC_ represents the ecliptic; the + oblique ring _E'Q_ represents the equator; _V_ and _A_ represent the + equinoctial point, and _E_ and _C_ the solstitial points; _B_ + represents the pole of the ecliptic, _P_ the pole of the equator, + and _PO_ the celestial axis. The ring _E'Q_ is supported on a pivot + at _O_; and the rod _BP_, which connects _B_ and _P_, is jointed at + each end so as to admit of the movement of _P_ and _B_. + + On carrying _P_ around _B_, we shall see that _E'Q_ will always + preserve the same obliquity to _EC_, and that the points _V_ and _A_ + will move around the circle _EC_. The same will also be true of the + points _E_ and _C_. + +29. _Effects of Precession._--One effect of precession, as has already +been stated, is the revolution of the pole of the heavens around the +pole of the ecliptic in a period of about twenty-six thousand years. The +circle described by the pole of the heavens, and the position of the +pole at various dates, are shown in Fig. 37, where o indicates the +position of the pole at the birth of Christ. The numbers round the +circle to the left of o are dates A.D., and those to the right of o are +dates B.C. It will be seen that the star at the end of the Little Bear's +tail, which is now near the north pole, will be exactly at the pole +about the year 2000. It will then recede farther and farther from the +pole till the year 15000 A.D., when it will be about forty-seven degrees +away from the pole. It will be noticed that one of the stars of the +Dragon was the pole star about 2800 years B.C. There are reasons to +suppose that this was about the time of the building of the Great +Pyramid. + +A second effect of precession is the shifting of the signs along the +zodiac. The _zodiac_ is a belt of the heavens along the ecliptic, +extending eight degrees from it on each side. This belt is occupied by +twelve constellations, known as the _zodiacal constellations_. They are +_Aries_, _Taurus_, _Gemini_, _Cancer_, _Leo_, _Virgo_, _Libra_, +_Scorpio_, _Sagittarius_, _Capricornus_, _Aquarius_, and _Pisces_. The +zodiac is also divided into twelve equal parts of thirty degrees each, +called _signs_. These signs have the same names as the twelve zodiacal +constellations, and when they were first named, each sign occupied the +same part of the zodiac as the corresponding constellation; that is to +say, the sign Aries was in the constellation Aries, and the sign Taurus +in the constellation Taurus, etc. Now the signs are always reckoned as +beginning at the vernal equinox, which is continually shifting along the +ecliptic; so that the signs are continually moving along the zodiac, +while the constellations remain stationary: hence it has come about that +the _first point of Aries_ (the _sign_) is no longer in the +_constellation_ Aries, but in Pisces. + +[Illustration: Fig. 37.] + +Fig. 38 shows the position of the vernal equinox 2170 B.C. It was then +in Taurus, just south of the Pleiades. It has since moved from Taurus, +through Aries, and into Pisces, as shown in Fig. 39. + +[Illustration: Fig. 38.] + +[Illustration: Fig. 39.] + +Since celestial longitude and right ascension are both measured from the +first point of Aries, the longitude and right ascension of the stars are +slowly changing from year to year. It will be seen, from Figs. 38 and +39, that the declination is also slowly changing. + +30. _Nutation._--The gyratory motion of the earth's axis is not +perfectly regular and uniform. The earth's axis has a slight tremulous +motion, oscillating to and fro through a short distance once in about +nineteen years. This tremulous motion of the axis causes the pole of the +heavens to describe an undulating curve, as shown in Fig. 40, and gives +a slight unevenness to the motion of the equinoxes along the ecliptic. +This nodding motion of the axis is called _nutation_. + +[Illustration: Fig. 40.] + +31. _Refraction._--When a ray of light from one of the heavenly bodies +enters the earth's atmosphere obliquely, it will be bent towards a +perpendicular to the surface of the atmosphere, since it will be +entering a denser medium. As the ray traverses the atmosphere, it will +be continually passing into denser and denser layers, and will therefore +be bent more and more towards the perpendicular. This bending of the ray +is shown in Fig. 41. A ray which started from _A_ would enter the eye at +_C_, as if it came from _I_: hence a star at _A_ would appear to be at +_I_. + +[Illustration: Fig. 41.] + +Atmospheric refraction displaces all the heavenly bodies from the +horizon towards the zenith. This is evident from Fig. 42. _OD_ is the +horizon, and _Z_ the zenith, of an observer at _O_. Refraction would +make a star at _Q_ appear at _P_: in other words, it would displace it +towards the zenith. A star in the zenith is not displaced by refraction, +since the rays which reach the eye from it traverse the atmosphere +vertically. The farther a star is from the zenith, the more it is +displaced by refraction, since the greater is the obliquity with which +the rays from it enter the atmosphere. + +[Illustration: Fig. 42.] + +At the horizon the displacement by refraction is about half a degree; +but it varies considerably with the state of the atmosphere. Refraction +causes a heavenly body to appear above the horizon longer than it really +is above it, since it makes it appear to be on the horizon when it is +really half a degree below it. + +The increase of refraction towards the horizon often makes the sun, when +near the horizon, appear distorted, the lower limb of the sun being +raised more than the upper limb. This distortion is shown in Fig. 43. +The vertical diameter of the sun appears to be considerably less than +the horizontal diameter. + +[Illustration: Fig. 43.] + +32. _Parallax._--_Parallax_ is the displacement of an object caused by a +change in the point of view from which it is seen. Thus in Fig. 44, the +top of the tower _S_ would be seen projected against the sky at _a_ by +an observer at _A_, and at _b_ by an observer at _B_. In passing from +_A_ to _B_, the top of the tower is displaced from _a_ to _b_, or by the +angle _aSb_. This angle is called the parallax of _S_, as seen from _B_ +instead of _A_. + +[Illustration: Fig. 44.] + +The _geocentric parallax_ of a heavenly body is its displacement caused +by its being seen from the surface of the earth, instead of from the +centre of the earth. In Fig. 45, _R_ is the centre of the earth, and _O_ +the point of observation on the surface of the earth. Stars at _S_, +_S'_, and _S''_, would, from the centre of the earth, appear at _Q_, +_Q'_, and _Q''_; while from the point _O_ on the surface of the earth, +these same stars would appear at _P_, _P'_ and _P''_, being displaced +from their position, as seen from the centre of the earth, by the angles +_QSP_, _Q'S'P'_, and _Q''S''P''_. It will be seen that parallax +displaces a body from the zenith towards the horizon, and that the +parallax of a body is greatest when it is on the horizon. The parallax +of a heavenly body when on the horizon is called its _horizontal +parallax_. A body in the zenith is not displaced by parallax, since it +would be seen in the same direction from both the centre and the surface +of the earth. + +[Illustration: Fig. 45.] + +The parallax of a body at _S'''_ is _Q'''S'''P_, which is seen to be +greater than _QSP_; that is to say, the parallax of a heavenly body +increases with its nearness to the earth. The distance and parallax of a +body are so related, that, either being known, the other may be +computed. + + 33. _Aberration._--_Aberration_ is a slight displacement of a star, + owing to an apparent change in the direction of the rays of light + which proceed from it, caused by the motion of the earth in its + orbit. If we walk rapidly in any direction in the rain, when the + drops are falling vertically, they will appear to come into our + faces from the direction in which we are walking. Our own motion has + apparently changed the direction in which the drops are falling. + + [Illustration: Fig. 46.] + + In Fig. 46 let _A_ be a gun of a battery, from which a shot is fired + at a ship, _DE_, that is passing. Let _ABC_ be the course of the + shot. The shot enters the ship's side at _B_, and passes out at the + other side at _C_; but in the mean time the ship has moved from _E_ + to _e_, and the part _B_, where the shot entered, has been carried + to _b_. If a person on board the ship could see the ball as it + crossed the ship, he would see it cross in the diagonal line _bC_; + and he would at once say that the cannon was in the direction of + _Cb_. If the ship were moving in the opposite direction, he would + say that the cannon was just as far the other side of its true + position. + + Now, we see a star in the direction in which the light coming from + the star appears to be moving. When we examine a star with a + telescope, we are in the same condition as the person who on + shipboard saw the cannon-ball cross the ship. The telescope is + carried along by the earth at the rate of eighteen miles a second: + hence the light will appear to pass through the tube in a slightly + different direction from that in which it is really moving: just as + the cannon-ball appears to pass through the ship in a different + direction from that in which it is really moving. Thus in Fig. 47, a + ray of light coming in the direction _SOT_ would appear to traverse + the tube _OT_ of a telescope, moving in the direction of the arrow, + as if it were coming in the direction _S'O_. + +[Illustration: Fig. 47.] + + As light moves with enormous velocity, it passes through the tube so + quickly, that it is apparently changed from its true direction only + by a very slight angle: but it is sufficient to displace the star. + This apparent change in the direction of light caused by the motion + of the earth is called _aberration of light_. + +34. _The Planets._--On watching the stars attentively night after night, +it will be found, that while the majority of them appear _fixed_ on the +surface of the celestial sphere, so as to maintain their relative +positions, there are a few that _wander_ about among the stars, +alternately advancing towards the east, halting, and retrograding +towards the west. These wandering stars are called _planets_. + +Their motions appear quite irregular; but, on the whole, their eastward +motion is in excess of their westward, and in a longer or shorter time +they all complete the circuit of the heavens. In almost every instance, +their paths are found to lie wholly in the belt of the zodiac. + +[Illustration: Fig. 48.] + +Fig. 48 shows a portion of the apparent path of one of the planets. + + II. + THE SOLAR SYSTEM. + + + I. THEORY OF THE SOLAR SYSTEM. + + +35. _Members of the Solar System._--The solar system is composed of the +_sun_, _planets_, _moons_, _comets_, and _meteors_. Five planets, +besides the earth, are readily distinguished by the naked eye, and were +known to the ancients: these are _Mercury_, _Venus_, _Mars_, _Jupiter_, +and _Saturn_. These, with the _sun_ and _moon_, made up the _seven +planets_ of the ancients, from which the seven days of the week were +named. + + + The Ptolemaic System. + + +36. _The Crystalline Spheres._--We have seen that all the heavenly +bodies appear to be situated on the surface of the celestial sphere. The +ancients assumed that the stars were really fixed on the surface of a +crystalline sphere, and that they were carried around the earth daily by +the rotation of this sphere. They had, however, learned to distinguish +the planets from the stars, and they had come to the conclusion that +some of the planets were nearer the earth than others, and that all of +them were nearer the earth than the stars are. This led them to imagine +that the heavens were composed of a number of crystalline spheres, one +above another, each carrying one of the planets, and all revolving +around the earth from east to west, but at different rates. This +structure of the heavens is shown in section in Fig. 49. + +[Illustration: Fig. 49.] + +37. _Cycles and Epicycles._--The ancients had also noticed that, while +all the planets move around the heavens from west to east, their motion +is not one of uniform advancement. Mercury and Venus appear to oscillate +to and fro across the sun, while Jupiter and Saturn appear to oscillate +to and fro across a centre which is moving around the earth, so as to +describe a series of loops, as shown in Fig. 50. + +[Illustration: Fig. 50.] + +The ancients assumed that the planets moved in exact circles, and, in +fact, that all motion in the heavens was circular, the circle being the +simplest and most perfect curve. To account for the loops described by +the planets, they imagined that each planet revolved in a circle around +a centre, which, in turn, revolved in a circle around the earth. The +circle described by this centre around the earth they called the +_cycle_, and the circle described by the planet around this centre they +called the _epicycle_. + +38. _The Eccentric._--The ancients assumed that the planets moved at a +uniform rate in describing the epicycle, and also the centre in +describing the cycle. They had, however, discovered that the planets +advance eastward more rapidly in some parts of their orbits than in +others. To account for this they assumed that the cycles described by +the centre, around which the planets revolved, were _eccentric_; that is +to say, that the earth was not at the centre of the cycle, but some +distance away from it, as shown in Fig. 51. _E_ is the position of the +earth, and _C_ is the centre of the cycle. The lines from _E_ are drawn +so as to intercept equal arcs of the cycle. It will be seen at once that +the angle between any pair of lines is greatest at _P_, and least at +_A_; so that, were a planet moving at the same rate at _P_ and _A_, it +would seem to be moving much faster at _P_. The point _P_ of the +planet's cycle was called its _perigee_, and the point A its _apogee_. + +[Illustration: Fig. 51.] + +As the apparent motion of the planets became more accurately known, it +was found necessary to make the system of cycles, epicycles, and +eccentrics exceedingly complicated to represent that motion. + + + The Copernican System. + + +39. _Copernicus._--Copernicus simplified the Ptolemaic system greatly by +assuming that the earth and all the planets revolved about the sun as a +centre. He, however, still maintained that all motion in the heavens was +circular, and hence he could not rid his system entirely of cycles and +epicycles. + + + Tycho Brahe's System. + + +40. _Tycho Brahe._--Tycho Brahe was the greatest of the early +astronomical observers. He, however, rejected the system of Copernicus, +and adopted one of his own, which was much more complicated. He held +that all the planets but the earth revolved around the sun, while the +sun and moon revolved around the earth. This system is shown in Fig. 52. + +[Illustration: Fig. 52.] + + + Kepler's System. + + +41. _Kepler._--While Tycho Brahe devoted his life to the observation of +the planets. Kepler gave his to the study of Tycho's observations, for +the purpose of discovering the true laws of planetary motion. He +banished the complicated system of cycles, epicycles, and eccentrics +forever from the heavens, and discovered the three laws of planetary +motion which have rendered his name immortal. + +42. _The Ellipse._--An _ellipse_ is a closed curve which has two points +within it, the sum of whose distances from every point on the curve is +the same. These two points are called the _foci_ of the ellipse. + +[Illustration: Fig. 53.] + +One method of describing an ellipse is shown in Fig. 53. Two tacks, _F_ +and _F'_, are stuck into a piece of paper, and to these are fastened the +two ends of a string which is longer than the distance between the +tacks. A pencil is then placed against the string, and carried around, +as shown in the figure. The curve described by the pencil is an ellipse. +The two points _F_ and _F'_ are the foci of the ellipse: the sum of the +distances of these two points from every point on the curve is equal to +the length of the string. When half of the ellipse has been described, +the pencil must be held against the other side of the string in the same +way, and carried around as before. + +The point _O_, half way between _F_ and _F'_, is called the _centre_ of +the ellipse; _AA'_ is the _major axis_ of the ellipse, and _CD_ is the +_minor axis_. + +43. _The Eccentricity of the Ellipse._--The ratio of the distance +between the two foci to the major axis of the ellipse is called the +_eccentricity_ of the ellipse. The greater the distance between the two +foci, compared with the major axis of the ellipse, the greater is the +eccentricity of the ellipse; and the less the distance between the foci, +compared with the length of the major axis, the less the eccentricity of +the ellipse. The ellipse of Fig. 54 has an eccentricity of 1/8. This +ellipse scarcely differs in appearance from a circle. The ellipse of +Fig. 55 has an eccentricity of 1/2, and that of Fig. 56 an eccentricity +of 7/8. + +[Illustration: Fig. 54.] + +[Illustration: Fig. 55.] + +[Illustration: Fig. 56.] + +44. _Kepler's First Law._--Kepler first discovered that _all the planets +move from west to east in ellipses which have the sun as a common +focus_. This law of planetary motion is known as _Kepler's First Law_. +The planets appear to describe loops, because we view them from a moving +point. + +The ellipses described by the planets differ in eccentricity; and, +though they all have one focus at the sun, their major axes have +different directions. The eccentricity of the planetary orbits is +comparatively small. The ellipse of Fig. 54 has seven times the +eccentricity of the earth's orbit, and twice that of the orbit of any of +the larger planets except Mercury; and its eccentricity is more than +half of that of the orbit of Mercury. Owing to their small eccentricity, +the orbits of the planets are usually represented by circles in +astronomical diagrams. + +[Illustration: Fig. 57.] + +45. _Kepler's Second Law._--Kepler next discovered that a planet's rate +of motion in the various parts of its orbit is such that _a line drawn +from the planet to the sun would always sweep over equal areas in equal +times_. Thus, in Fig. 57, suppose the planet would move from _P_ to +_P^1_ in the same time that it would move from _P^2_ to _P^3_, or from +_P^4_ to _P^5_; then the dark spaces, which would be swept over by a +line joining the sun and the planet, in these equal times, would all be +equal. + +A line drawn from the sun to a planet is called the _radius vector_ of +the planet. The radius vector of a planet is shortest when the planet is +nearest the sun, or at _perihelion_, and longest when the planet is +farthest from the sun, or at _aphelion_: hence, in order to have the +areas equal, it follows that a planet must move fastest when at +perihelion, and slowest at aphelion. + +_Kepler's Second Law_ of planetary motion is usually stated as follows: +_The radius vector of a planet describes equal areas in equal times in +every part of the planet's orbit_. + +46. _Kepler's Third Law._--Kepler finally discovered that the periodic +times of the planets bear the following relation to the distances of the +planets from the sun: _The squares of the periodic times of the planets +are to each other as the cubes of their mean distances from the sun_. +This is known as _Kepler's Third Law_ of planetary motion. By _periodic +time_ is meant the time it takes a planet to revolve around the sun. + +These three laws of Kepler's are the foundation of modern physical +astronomy. + + + The Newtonian System. + + +47. _Newton's Discovery._--Newton followed Kepler, and by means of his +three laws of planetary motion made his own immortal discovery of the +_law of gravitation_. This law is as follows: _Every portion of matter +in the universe attracts every other portion with a force varying +directly as the product of the masses acted upon, and inversely as the +square of the distances between them._ + +48. _The Conic Sections._--The _conic sections_ are the figures formed +by the various plane sections of a right cone. There are four classes of +figures formed by these sections, according to the angle which the plane +of the section makes with the axis of the cone. + +_OPQ_, Fig. 58, is a right cone, and _ON_ is its axis. Any section, +_AB_, of this cone, whose plane is perpendicular to the axis of the +cone, is a _circle_. + +[Illustration: Fig. 58.] + +Any section, _CD_, of this cone, whose plane is oblique to the axis, but +forms with it an angle greater than _NOP_, is an _ellipse_. The less the +angle which the plane of the section makes with the axis, the more +elongated is the ellipse. + +Any section, _EF_, of this cone, whose plane makes with the axis an +angle equal to _NOP_, is a _parabola_. It will be seen, that, by +changing the obliquity of the plane _CD_ to the axis _NO_, we may pass +uninterruptedly from the circle through ellipses of greater and greater +elongation to the parabola. + +Any section, _GH_, of this cone, whose plane makes with the axis _ON_ an +angle less than _NOP_, is a _hyperbola_. + +[Illustration: Fig. 59.] + +It will be seen from Fig. 59, in which comparative views of the four +conic sections are given, that the circle and the ellipse are _closed_ +curves, or curves which return into themselves. The parabola and the +hyperbola are, on the contrary, _open_ curves, or curves which do not +return into themselves. + + 49. _A Revolving Body is continually Falling towards its Centre of + Revolution._--In Fig. 60 let _M_ represent the moon, and _E_ the + earth around which the moon is revolving in the direction _MN_. It + will be seen that the moon, in moving from M to N, falls towards the + earth a distance equal to _mN_. It is kept from falling into the + earth by its orbital motion. + +[Illustration: Fig. 60.] + + The fact that a body might be projected forward fast enough to keep + it from falling into the earth is evident from Fig. 61. _AB_ + represents the level surface of the ocean, _C_ a mountain from the + summit of which a cannon-ball is supposed to be fired in the + direction _CE_. _AD_ is a line parallel with _CE_; _DB_ is a line + equal to the distance between the two parallel lines _AD_ and _CE_. + This distance is equal to that over which gravity would pull a ball + towards the centre of the earth in a minute. No matter, then, with + what velocity the ball _C_ is fired, at the end of a minute it will + be somewhere on the line _AD_. Suppose it were fired fast enough to + reach the point _D_ in a minute: it would be on the line _AD_ at the + end of the minute, but still just as far from the surface of the + water as when it started. It will be seen, that, although it has all + the while been falling towards the earth, it has all the while kept + at exactly the same distance from the surface. The same thing would + of course be true during each succeeding minute, till the ball came + round to _C_ again, and the ball would continue to revolve in a + circle around the earth. + +[Illustration: Fig. 61.] + +50. _The Form of a Body's Orbit depends upon the Rate of its Forward +Motion._--If the ball _C_ were fired fast enough to reach the line _AD_ +beyond the point _D_, it would be farther from the surface at the end of +the second than when it started. Its orbit would no longer be circular, +but _elliptical_. If the speed of projection were gradually augmented, +the orbit would become a more and more elongated ellipse. At a certain +rate of projection, the orbit would become a _parabola_; at a still +greater rate, a _hyperbola_. + +51. _The Moon held in her Orbit by Gravity._--Newton compared the +distance _mN_ that the moon is drawn to the earth in a given time, with +the distance a body near the surface of the earth would be pulled toward +the earth in the same time; and he found that these distances are to +each other inversely as the squares of the distances of the two bodies +from the centre of the earth. He therefore concluded that _the moon is +drawn to the earth by gravity_, and that the _intensity of gravity +decreases as the square of the distance increases_. + +[Illustration: Fig. 62.] + +52. _Any Body whose Orbit is a Conic Section, and which moves according +to Kepler's Second Law, is acted upon by a Force varying inversely as +the Square of the Distance._--Newton compared the distance which any +body, moving in an ellipse, according to Kepler's Second Law, is drawn +towards the sun in the same time in different parts of its orbit. He +found these distances in all cases to vary inversely as the square of +the distance of the planet from the sun. Thus, in Fig. 62, suppose a +planet would move from _K_ to _B_ in the same time that it would move +from _k_ to _b_ in another part of its orbit. In the first instance the +planet would be drawn towards the sun the distance _AB_, and in the +second instance the distance _ab_. Newton found that _AB : ab = (SK)^2 : +(Sk)^2_. He also found that the same would be true when the body moved +in a parabola or a hyperbola: hence he concluded that _every body that +moves around the sun in an ellipse, a parabola, or a hyperbola, is +moving under the influence of gravity_. + +[Transcriber's Note: In Newton's equation above, (SK)^2 means to group S +and K together and square their product. In the original book, instead +of using parentheses, there was a vinculum, a horizontal bar, drawn over +the S and the K to express the same grouping.] + +[Illustration: Fig. 63.] + +53. _The Force that draws the Different Planets to the Sun Varies +inversely as the Squares of the Distances of the Planets from the +Sun._--Newton compared the distances _jK_ and _eF_, over which two +planets are drawn towards the sun in the same time, and found these +distances to vary inversely as the squares of the distances of the +planets from the sun: hence he concluded that _all the planets are held +in their orbits by gravity_. He also showed that this would be true of +any two bodies that were revolving around the sun's centre, according to +Kepler's Third Law. + +54. _The Copernican System._--The theory of the solar system which +originated with Copernicus, and which was developed and completed by +Kepler and Newton, is commonly known as the _Copernican System_. This +system is shown in Fig. 64. + +[Illustration: Fig. 64.] + + + II. THE SUN AND PLANETS. + + + I. THE EARTH. + + + Form and Size. + + +55. _Form of the Earth._--In ordinary language the term _horizon_ +denotes the line that bounds the portion of the earth's surface that is +visible at any point. + +(1) It is well known that the horizon of a plain presents the form of a +circle surrounding the observer. If the latter moves, the circle moves +also; but its form remains the same, and is modified only when mountains +or other obstacles limit the view. Out at sea, the circular form of the +horizon is still more decided, and changes only near the coasts, the +outline of which breaks the regularity. + +Here, then, we obtain a first notion of the rotundity of the earth, +since a sphere is the only body which is presented always to us under +the form of a circle, from whatever point on its surface it is viewed. + +(2) Moreover, it cannot be maintained that the horizon is the vanishing +point of distinct vision, and that it is this which causes the +appearance of a circular boundary, because the horizon is enlarged when +we mount above the surface of the plain. This will be evident from Fig. +65, in which a mountain is depicted in the middle of a plain, whose +uniform curvature is that of a sphere. From the foot of the mountain the +spectator will have but a very limited horizon. Let him ascend half way, +his visual radius extends, is inclined below the first horizon, and +reveals a more extended circular area. At the summit of the mountain the +horizon still increases; and, if the atmosphere is pure, the spectator +will see numerous objects where from the lower stations the sky alone +was visible. + +[Illustration: Fig. 65.] + +This extension of the horizon would be inexplicable if the earth had the +form of an extended plane. + +(3) The curvature of the surface of the sea manifests itself in a still +more striking manner. If we are on the coast at the summit of a hill, +and a vessel appears on the horizon (Fig. 66), we see only the tops of +the masts and the highest sails; the lower sails and the hull are +invisible. As the vessel approaches, its lower part comes into view +above the horizon, and soon it appears entire. + +[Illustration: Fig. 66.] + +In the same manner the sailors from the ship see the different parts of +objects on the land appear successively, beginning with the highest. The +reason of this will be evident from Fig. 67, where the course of a +vessel, seen in profile, is figured on the convex surface of the sea. + +[Illustration: Fig. 67.] + +As the curvature of the ocean is the same in every direction, it follows +that the surface of the ocean is _spherical_. The same is true of the +surface of the land, allowance being made for the various inequalities +of the surface. From these and various other indications, we conclude +that _the earth is a sphere_. + +56. _Size of the Earth._--The size of the earth is ascertained by +measuring the length of a degree of a meridian, and multiplying this by +three hundred and sixty. This gives the circumference of the earth as +about twenty-five thousand miles, and its diameter as about eight +thousand miles. We know that the two stations between which we measure +are one degree apart when the elevation of the pole at one station is +one degree greater than at the other. + +57. _The Earth Flattened at the Poles._--Degrees on the meridian have +been measured in various parts of the earth, and it has been found that +they invariably increase in length as we proceed from the equator +towards the pole: hence the earth must curve less and less rapidly as we +approach the poles; for the less the curvature of a circle, the larger +the degrees on it. + +[Illustration: Fig. 68.] + +58. _The Earth in Space._--In Fig. 68 we have a view of the earth +suspended in space. The side of the earth turned towards the sun is +illumined, and the other side is in darkness. As the planet rotates on +its axis, successive portions of it will be turned towards the sun. As +viewed from a point in space between it and the sun, it will present +light and dark portions, which will assume different forms according to +the portion which is illumined. These different appearances are shown in +Fig. 69. + +[Illustration: Fig. 69.] + + + Day and Night. + + +59. _Day and Night._--The succession of day and night is due to _the +rotation of the earth on its axis_, by which a place on the surface of +the earth is carried alternately into the sunshine and out of it. As the +sun moves around the heavens on the ecliptic, it will be on the +celestial equator when at the equinoxes, and 23-1/2° north of the +equator when at the summer solstice, and 23-1/2° south of the equator +when at the winter solstice. + +60. _Day and Night when the Sun is at the Equinoxes._--When the sun is +at either equinox, the diurnal circle described by the sun will coincide +with the celestial equator; and therefore half of this diurnal circle +will be above the horizon at every point on the surface of the globe. At +these times _day and night will be equal in every part of the earth_. + +[Illustration: Fig. 70.] + +[Illustration: Fig. 71.] + + The equality of days and nights when the sun is on the celestial + equator is also evident from the following considerations: one-half + of the earth is in sunshine all of the time; when the sun is on the + celestial equator, it is directly over the equator of the earth, and + the illumination extends from pole to pole, as is evident from Figs. + 70 and 71, in the former of which the sun is represented as on the + eastern horizon at a place along the central line of the figure, and + in the latter as on the meridian along the same line. In each + diagram it is seen that the illumination extends from pole to pole: + hence, as the earth rotates on its axis, every place on the surface + will be in the sunshine and out of it just half of the time. + +61. _Day and Night when the Sun is at the Summer Solstice._--When the +sun is at the summer solstice, it will be 23-1/2° north of the celestial +equator. The diurnal circle described by the sun will then be 23-1/2° +north of the celestial equator; and more than half of this diurnal +circle will be above the horizon at all places north of the equator, and +less than half of it at places south of the equator: hence _the days +will be longer than the nights at places north of the equator, and +shorter than the nights at places south of the equator_. At places +within 23-1/2° of the north pole, the entire diurnal circle described by +the sun will be above the horizon, so that the sun will not set. At +places within 23-1/2° of the south pole of the earth, the entire diurnal +circle will be below the horizon, so that the sun will not rise. + +[Illustration: Fig. 72.] + +[Illustration: Fig. 73.] + + The illumination of the earth at this time is shown in Figs. 72 and + 73. In Fig. 72 the sun is represented as on the western horizon + along the middle line of the figure, and in Fig. 73 as on the + meridian. It is seen at once that the illumination extends 23-1/2° + beyond the north pole, and falls 23-1/2° short of the south pole. As + the earth rotates on its axis, places near the north pole will be in + the sunshine all the time, while places near the south pole will be + out of the sunshine all the time. All places north of the equator + will be in the sunshine longer than they are out of it, while all + places south of the equator will be out of the sunshine longer than + they are in it. + +62. _Day and Night when the Sun is at the Winter Solstice._--When the +sun is at the winter solstice, it is 23-1/2° south of the celestial +equator. The diurnal circle described by the sun is then 23-1/2° south +of the celestial equator. More than half of this diurnal circle will +therefore be above the horizon at all places south of the equator, and +less than half of it at all places north of the equator: hence _the days +will be longer than the nights south of the equator, and shorter than +the nights at places north of the equator_. At places within 23-1/2° of +the south pole, the diurnal circle described by the sun will be entirely +above the horizon, and the sun will therefore not set. At places within +23-1/2° of the north pole, the diurnal circle described by the sun will +be wholly below the horizon, and therefore the sun will not rise. + + The illumination of the earth at this time is shown in Figs. 74 and + 75, and is seen to be the reverse of that shown in Figs. 72 and 73. + +[Illustration: Fig. 74.] + +[Illustration: Fig. 75.] + +63. _Variation in the Length of Day and Night._--As long as the sun is +north of the equinoctial, the nights will be longer than the days south +of the equator, and shorter than the days north of the equator. It is +just the reverse when the sun is south of the equator. + +The farther the sun is from the equator, the greater is the inequality +of the days and nights. + +The farther the place is from the equator, the greater the inequality of +its days and nights. + +When the distance of a place from the _north_ pole is less than the +distance of the sun north of the equinoctial, it will have _continuous +day without night_, since the whole of the sun's diurnal circle will be +above the horizon. A place within the same distance of the _south_ pole +will have _continuous night_. + +When the distance of a place from the _north_ pole is less than the +distance of the sun south of the equinoctial, it will have _continuous +night_, since the whole of the sun's diurnal circle will then be below +the horizon. A place within the same distance of the _south_ pole will +then have _continuous day_. + +At the _equator_ the _days and nights are always equal_; since, no +matter where the sun is in the heavens, half of all the diurnal circles +described by it will be above the horizon, and half of them below it. + +64. _The Zones._--It will be seen, from what has been stated above, that +the sun will at some time during the year be directly overhead at every +place within 23-1/2° of the equator on either side. This belt of the +earth is called the _torrid zone_. The torrid zone is bounded by circles +called the _tropics_; that of _Cancer_ on the north, and that of +_Capricorn_ on the south. + +It will also be seen, that, at every place within 23-1/2° of either +pole, there will be, some time during the year, a day during which the +sun will not rise, or on which it will not set. These two belts of the +earth's surface are called the _frigid zones_. These zones are bounded +by the _arctic_ circles. The nearer a place is to the poles, the greater +the number of days on which the sun does not rise or set. + +Between the frigid zones and the torrid zones, there are two belts on +the earth which are called the _temperate zones_. The sun is never +overhead at any place in these two zones, but it rises and sets every +day at every place within their limits. + +65. _The Width of the Zones._--The distance the frigid zones extend from +the poles, and the torrid zones from the equator, is exactly equal to +_the obliquity of the ecliptic_, or the deviation of the axis of the +earth from the perpendicular to the plane of its orbit. Were this +deviation forty-five degrees, the obliquity of the ecliptic would be +forty-five degrees, the torrid zone would extend forty-five degrees from +the equator, and the frigid zones forty-five degrees from the poles. In +this case there would be no temperate zones. Were this deviation fifty +degrees, the torrid and frigid zones would overlap ten degrees, and +there would be two belts of ten degrees on the earth, which would +experience alternately during the year a torrid and a frigid climate. + +Were the axis of the earth perpendicular to the plane of the earth's +orbit, there would be no zones on the earth, and no variation in the +length of day and night. + +66. _Twilight._--Were it not for the atmosphere, the darkness of +midnight would begin the moment the sun sank below the horizon, and +would continue till he rose again above the horizon in the east, when +the darkness of the night would be suddenly succeeded by the full light +of day. The gradual transition from the light of day to the darkness of +the night, and from the darkness of the night to the light of day, is +called _twilight_, and is due to the _diffusion of light from the upper +layers of the atmosphere_ after the sun has ceased to shine on the lower +layers at night, or before it has begun to shine on them in the morning. + +[Illustration: Fig. 76.] + +Let _ABCD_ (Fig. 76) represent a portion of the earth, _A_ a point on +its surface where the sun _S_ is setting; and let _SAH_ be a ray of +light just grazing the earth at _A_, and leaving the atmosphere at the +point _H_. The point _A_ is illuminated by the whole reflective +atmosphere _HGFE_. The point _B_, to which the sun has set, receives no +direct solar light, nor any reflected from that part of the atmosphere +which is below _ALH_; but it receives a twilight from the portion _HLF_, +which lies above the visible horizon _BF_. The point _C_ receives a +twilight only from the small portion of the atmosphere; while at _D_ the +twilight has ceased altogether. + +67. _Duration of Twilight._--The astronomical limit of twilight is +generally understood to be the instant when stars of the sixth magnitude +begin to be visible in the zenith at evening, or disappear in the +morning. + + Twilight is usually reckoned to last until the sun's depression + below the horizon amounts to eighteen degrees: this, however, + varies; in the tropics a depression of sixteen or seventeen degrees + being sufficient to put an end to the phenomenon, while in England a + depression of seventeen to twenty-one degrees is required. The + duration of twilight differs in different latitudes; it varies also + in the same latitude at different seasons of the year, and depends, + in some measure, on the meteorological condition of the atmosphere. + When the sky is of a pale color, indicating the presence of an + unusual amount of condensed vapor, twilight is of longer duration. + This happens habitually in the polar regions. On the contrary, + within the tropics, where the air is pure and dry, twilight + sometimes lasts only fifteen minutes. Strictly speaking, in the + latitude of Greenwich there is no true night from May 22 to July 21, + but constant twilight from sunset to sunrise. Twilight reaches its + minimum three weeks before the vernal equinox, and three weeks after + the autumnal equinox, when its duration is an hour and fifty + minutes. At midwinter it is longer by about seventeen minutes; but + the augmentation is frequently not perceptible, owing to the greater + prevalence of clouds and haze at that season of the year, which + intercept the light, and hinder it from reaching the earth. The + duration is least at the equator (an hour and twelve minutes), and + increases as we approach the poles; for at the former there are two + twilights every twenty-four hours, but at the latter only two in a + year, each lasting about fifty days. At the north pole the sun is + below the horizon for six months, but from Jan. 29 to the vernal + equinox, and from the autumnal equinox to Nov. 12, the sun is less + than eighteen degrees below the horizon; so that there is twilight + during the whole of these intervals, and thus the length of the + actual night is reduced to two months and a half. The length of the + day in these regions is about six months, during the whole of which + time the sun is constantly above the horizon. The general rule is, + _that to the inhabitants of an oblique sphere the twilight is longer + in proportion as the place is nearer the elevated pole, and the sun + is farther from the equator on the side of the elevated pole_. + + + The Seasons. + + +68. _The Seasons._--While the sun is north of the celestial equator, +places north of the equator are receiving heat from the sun by day +longer than they are losing it by radiation at night, while places south +of the equator are losing heat by radiation at night longer than they +are receiving it from the sun by day. When, therefore, the sun passes +north of the equator, the temperature begins to rise at places north of +the equator, and to fall at places south of it. The rise of temperature +is most rapid north of the equator when the sun is at the summer +solstice; but, for some time after this, the earth continues to receive +more heat by day than it loses by night, and therefore the temperature +continues to rise. For this reason, the heat is more excessive after the +sun passes the summer solstice than before it reaches it. + +69. _The Duration of the Seasons._--Summer is counted as beginning in +June, when the sun is at the summer solstice, and as continuing until +the sun reaches the autumnal equinox, in September. Autumn then begins, +and continues until the sun is at the winter solstice, in December. +Winter follows, continuing until the sun comes to the vernal equinox, in +March, when spring begins, and continues to the summer solstice. In +popular reckoning the seasons begin with the first day of June, +September, December, and March. + +The reason why winter is counted as occurring after the winter solstice +is similar to the reason why the summer is placed after the summer +solstice. The earth north of the equator is losing heat most rapidly at +the time of the winter solstice; but for some time after this it loses +more heat by night than it receives by day: hence for some time the +temperature continues to fall, and the cold is more intense after the +winter solstice than before it. + +[Illustration: Fig. 77.] + +Of course, when it is summer in the northern hemisphere, it is winter in +the southern hemisphere, and the reverse. Fig. 77 shows the portion of +the earth's orbit included in each season. It will be seen that the +earth is at perihelion in the winter season for places north of the +equator, and at aphelion in the summer season. This tends to mitigate +somewhat the extreme temperatures of our winters and summers. + +[Illustration: Fig. 78.] + +70. _The Illumination of the Earth at the different Seasons._--Fig. 78 +shows the earth as it would appear to an observer at the sun during each +of the four seasons; that is to say, the portion of the earth that is +receiving the sun's rays. Figs. 79, 80, 81, and 82 are enlarged views of +the earth, as seen from the sun at the time of the summer solstice, of +the autumnal equinox, of the winter solstice, and of the vernal equinox. + +[Illustration: Fig. 79.] + +[Illustration: Fig. 80.] + +[Illustration: Fig. 81.] + +[Illustration: Fig. 82.] + +[Illustration: Fig. 83.] + +Fig. 83 is, so to speak, a side view of the earth, showing the limit of +sunshine on the earth when the sun is at the summer solstice; and Fig. +84, showing the limit of sunshine when the sun is at the autumnal +equinox. + +[Illustration: Fig. 84.] + +71. _Cause of the Change of Seasons._--Variety in the length of day and +night, and diversity in the seasons, depend upon _the obliquity of the +ecliptic_. Were there no obliquity of the ecliptic, there would be no +inequality in the length of day and night, and but slight diversity of +seasons. The greater the obliquity of the ecliptic, the greater would be +the variation in the length of the days and nights, and the more extreme +the changes of the seasons. + + + Tides. + + +72. _Tides._--The alternate rise and fall of the surface of the sea +twice in the course of a lunar day, or of twenty-four hours and +fifty-one minutes, is known as the _tides_. When the water is rising, it +is said to be _flood_ tide; and when it is falling, _ebb_ tide. When the +water is at its greatest height, it is said to be _high_ water; and when +at its least height, _low_ water. + + 73. _Cause of the Tides._--It has been known to seafaring nations + from a remote antiquity that there is a singular connection between + the ebb and flow of the tides and the diurnal motion of the moon. + +[Illustration: Fig. 85.] + + This tidal movement in seeming obedience to the moon was a mystery + until the study of the law of gravitation showed it to be due to + _the attraction of the moon on the waters of the ocean_. The reason + why there are two tides a day will appear from Fig. 85. Let _M_ be + the moon, _E_ the earth, and _EM_ the line joining their centres. + Now, strictly speaking, the moon does not revolve around the earth + any more than the earth around the moon; but the centre of each body + moves around the common centre of gravity of the two bodies. The + earth being eighty times as heavy as the moon, this centre is + situated within the former, about three-quarters of the way from its + centre to its surface, at the point _G_. The body of the earth + itself being solid, every part of it, in consequence of the moon's + attraction, may be considered as describing a circle once in a + month, with a radius equal to _EG_. The centrifugal force caused by + this rotation is just balanced by the mean attraction of the moon + upon the earth. If this attraction were the same on every part of + the earth, there would be everywhere an exact balance between it and + the centrifugal force. But as we pass from _E_ to _D_ the attraction + of the moon diminishes, owing to the increased distance: hence at + _D_ the centrifugal force predominates, and the water therefore + tends to move away from the centre _E_. As we pass from _E_ towards + _C_, the attraction of the moon increases, and therefore exceeds the + centrifugal force: consequently at _C_ there is a tendency to draw + the water towards the moon, but still away from the centre _E_. At + _A_ and _B_ the attraction of the moon increases the gravity of the + water, owing to the convergence of the lines _BM_ and _AM_, along + which it acts: hence the action of the moon tends to make the waters + rise at _D_ and _C_, and to fall at _A_ and _B_, causing two tides + to each apparent diurnal revolution of the moon. + + 74. _The Lagging of the Tides._--If the waters everywhere yielded + immediately to the attractive force of the moon, it would always be + high water when the moon was on the meridian, low water when she was + rising or setting, and high water again when she was on the meridian + below the horizon. But, owing to the inertia of the water, some time + is necessary for so slight a force to set it in motion; and, once in + motion, it continues so after the force has ceased, and until it has + acted some time in the opposite direction. Therefore, if the motion + of the water were unimpeded, it would not be high water until some + hours after the moon had passed the meridian. The free motion of the + water is also impeded by the islands and continents. These deflect + the tidal wave from its course in such a way that it may, in some + cases, be many hours, or even a whole day, behind its time. + Sometimes two waves meet each other, and raise a very high tide. In + some places the tides run up a long bay, where the motion of a large + mass of water will cause an enormous tide to be raised. In the Bay + of Fundy both of these causes are combined. A tidal wave coming up + the Atlantic coast meets the ocean wave from the east, and, entering + the bay with their combined force, they raise the water at the head + of it to the height of sixty or seventy feet. + +75. _Spring-Tides and Neap-Tides._--The sun produces a tide as well as +the moon; but the tide-producing force of the sun is only about +four-tenths of that of the moon. At new and full moon the two bodies +unite their forces, the ebb and flow become greater than the average, +and we have the _spring-tides_. When the moon is in her first or third +quarter, the two forces act against each other; the tide-producing force +is the difference of the two; the ebb and flow are less than the +average; and we have the _neap-tides_. + +[Illustration: Fig. 86.] + +[Illustration: Fig. 87.] + +[Illustration: Fig. 88.] + +Fig. 86 shows the tide that would be produced by the moon alone; Fig. +87, the tide produced by the combined action of the sun and moon; and +Fig. 88, by the sun and moon acting at right angles to each other. + +The tide is affected by the distance of the moon from the earth, being +highest near the time when the moon is in perigee, and lowest near the +time when she is in apogee. When the moon is in perigee, at or near the +time of a new or full moon, unusually high tides occur. + + 76. _Diurnal Inequality of Tides._--The height of the tide at a + given place is influenced by the declination of the moon. When the + moon has no declination, the highest tides should occur along the + equator, and the heights should diminish from thence toward the + north and south; but the two daily tides at any place should have + the same height. When the moon has north declination, as shown in + Fig. 89, the highest tides on the side of the earth next the moon + will be at places having a corresponding north latitude, as at _B_, + and on the opposite side at those which have an equal south + latitude. Of the two daily tides at any place, that which occurs + when the moon is nearest the zenith should be the greatest: hence, + when the moon's declination is north, the height of the tide at a + place in north latitude should be greater when the moon is above the + horizon than when she is below it. At the same time, places south of + the equator have the highest tides when the moon is below the + horizon, and the least when she is above it. This is called the + _diurnal inequality_, because its cycle is one day; but it varies + greatly in amount at different places. + +[Illustration: Fig. 89.] + +77. _Height of Tides._--At small islands in mid-ocean the tides never +rise to a great height, sometimes even less than one foot; and the +average height of the tides for the islands of the Atlantic and Pacific +Oceans is only three feet and a half. Upon approaching an extensive +coast where the water is shallow, the height of the tide is increased; +so that, while in mid-ocean the average height does not exceed three +feet and a half, the average in the neighborhood of continents is not +less than four or five feet. + + + The Day and Time. + + +78. _The Day._--By the term _day_ we sometimes denote the period of +sunshine as contrasted with that of the absence of sunshine, which we +call _night_, and sometimes the period of the earth's rotation on its +axis. It is with the latter signification that the term is used in this +section. As the earth rotates on its axis, it carries the meridian of a +place with it; so that, during each complete rotation of the earth, the +portion of the meridian which passes overhead from pole to pole sweeps +past every star in the heavens from west to east. The _interval between +two successive passages of this portion of the meridian across the same +star_ is the exact period of the complete rotation of the earth. This +period is called a _sidereal day_. The sidereal day may also be defined +as _the interval between two successive passages of the same star across +the meridian_; the passage of the meridian across the star, and the +passage or _transit_ of the star across the meridian, being the same +thing looked at from a different point of view. The interval _between +two successive passages of the meridian across the sun_, or _of the sun +across the meridian_, is called a _solar day_. + +79. _Length of the Solar Day._--The solar day is a little longer than +the sidereal day. This is owing to the sun's eastward motion among the +stars. We have already seen that the sun's apparent position among the +stars is continually shifting towards the east at a rate which causes it +to make a complete circuit of the heavens in a year, or three hundred +and sixty-five days. This is at the rate of about one degree a day: +hence, were the sun and a star on the meridian together to-day, when the +meridian again came around to the star, the sun would appear about one +degree to the eastward: hence the meridian must be carried about one +degree farther in order to come up to the sun. The solar day must +therefore be _about four minutes longer_ than the sidereal day. + +[Illustration: Fig. 90.] + +[Illustration: Fig. 91.] + +The fact that the earth must make more than a complete rotation is also +evident from Figs. 90 and 91. In Fig. 90, _ba_ represents the plane of +the meridian, and the small arrows indicate the direction the earth is +rotating on its axis, and revolving in its orbit. When the earth is at +1, the sun is on the meridian at _a_. When the earth has moved to 2, it +has made a complete rotation, as is shown by the fact that the plane of +the meridian is parallel with its position at 1; but it is evident that +the meridian has not yet come up with the sun. In Fig. 91, _OA_ +represents the plane of the meridian, and _OS_ the direction of the sun. +The small arrows indicate the direction of the rotation and revolution +of the earth. In passing from the first position to the second the earth +makes a complete rotation, but the meridian is not brought up to the +sun. + +80. _Inequality in the Length of Solar Days._--The sidereal days are all +of the same length; but the solar days differ somewhat in length. This +difference is due to the fact that the sun's apparent position moves +eastward, or _away from the meridian_, at a variable rate. + + There are three reasons why this rate is variable:-- + + (1) The sun's eastward motion is due to the revolution of the earth + in its orbit. Now, the earth's orbital motion is _not uniform_, + being fastest when the earth is at perihelion, and slowest when the + earth is at aphelion: hence, other things being equal, solar days + will be longest when the earth is at perihelion, and shortest when + the earth is at aphelion. + +[Illustration: Fig. 92.] + +[Illustration: Fig. 93.] + + (2) The sun's eastward motion is along the ecliptic. Now, from Figs. + 92 and 93, it will be seen, that, when the sun is at one of the + equinoxes, it will be moving away from the meridian _obliquely_; + and, from Figs. 94 and 95, that, when the sun is at one of the + solstices, it will be moving away from the meridian + _perpendicularly_: hence, other things being equal, the sun would + move away from the meridian _fastest_, and the days be _longest_, + when the sun is at the _solstices_; while it would move away from + the meridian _slowest_, and the days be _shortest_, when the sun is + at the _equinoxes_. That a body moving along the ecliptic must be + moving at a variable angle to the meridian becomes very evident on + turning a celestial globe so as to bring each portion of the + ecliptic under the meridian in turn. + +[Illustration: Fig. 94.] + +[Illustration: Fig. 95.] + + (3) The sun, moving along the ecliptic, always moves _in a great + circle_, while the point of the meridian which is to overtake the + sun moves in a diurnal circle, which is _sometimes a great circle_ + and _sometimes a small circle_. When the sun is at the equinoxes, + the point of the meridian which is to overtake it moves in a great + circle. As the sun passes from the equinoxes to the solstices, the + point of the meridian which is to overtake it moves on a smaller and + smaller circle: hence, as we pass away from the celestial equator, + the points of the meridian move slower and slower. Therefore, other + things being equal, the meridian will gain upon the sun _most + rapidly_, and the days be _shortest_, when the sun is at the + _equinoxes_; while it will gain on the sun _least rapidly_, and the + days will be _longest_, when the sun is at the _solstices_. + +The ordinary or _civil day_ is the mean of all the solar days in a year. + +81. _Sun Time and Clock Time._--It is noon by the sun when the sun is on +the meridian, and by the clock at the middle of the civil day. Now, as +the civil days are all of the same length, while solar days are of +variable length, it seldom happens that the middles of these two days +coincide, or that sun time and clock time agree. The difference between +sun time and clock time, or what is often called _apparent solar time_ +and _mean solar time_, is called the _equation of time_. The sun is said +to be _slow_ when it crosses the meridian after noon by the clock, and +_fast_ when it crosses the meridian before noon by the clock. Sun time +and clock time coincide four times a year; during two intermediate +seasons the clock time is ahead, and during two it is behind. + + * * * * * + +The following are the dates of coincidence and of maximum deviation, +which vary but slightly from year to year:-- + + February 10 True sun fifteen minutes slow. + April 15 True sun correct. + May 14 True sun four minutes fast. + June 14 True sun correct. + July 25 True sun six minutes slow. + August 31 True sun correct. + November 2 True sun sixteen minutes fast. + December 24 True sun correct. + +One of the effects of the equation of time which is frequently +misunderstood is, that the interval from sunrise until noon, as given in +the almanacs, is not the same as that between noon and sunset. The +forenoon could not be longer or shorter than the afternoon, if by "noon" +we meant the passage of the sun across the meridian; but the noon of our +clocks being sometimes fifteen minutes before or after noon by the sun, +the former may be half an hour nearer to sunrise than to sunset, or +_vice versa_. + + + The Year. + + +82. _The Year._--The _year_ is the time it takes the earth to revolve +around the sun, or, what amounts to the same thing, _the time it takes +the sun to pass around the ecliptic_. + +(1) The time it takes the sun to pass from a star around to the same +star again is called a _sidereal year_. This is, of course, the exact +time it takes the earth to make a complete revolution around the sun. + +[Illustration: Fig. 96.] + +(2) The time it takes the sun to pass around from the vernal equinox, or +the _first point of Aries_, to the vernal equinox again, is called the +_tropical_ year. This is a little shorter than the sidereal year, owing +to the precession of the equinoxes. This will be evident from Fig. 96. +The circle represents the ecliptic, _S_ the sun, and _E_ the vernal +equinox. The sun moves around the ecliptic _eastward_, as indicated by +the long arrow, while the equinox moves slowly _westward_, as indicated +by the short arrow. The sun will therefore meet the equinox before it +has quite completed the circuit of the heavens. The exact lengths of +these respective years are:-- + + Sidereal year 365.25636=365 days 6 hours 9 min 9 sec + Tropical year 365.24220=365 days 5 hours 48 min 46 sec + +Since the recurrence of the seasons depends on the tropical year, the +latter is the one to be used in forming the calendar and for the +purposes of civil life generally. Its true length is eleven minutes and +fourteen seconds less than three hundred and sixty-five days and a +fourth. + +It will be seen that the tropical year is about twenty minutes shorter +than the sidereal year. + + (3) The time it takes the earth to pass from its perihelion point + around to the perihelion point again is called the _anomalistic + year_. This year is about four minutes longer than the sidereal + year. This is owing to the fact that the major axis of the earth's + orbit is slowly moving around to the east at the rate of about ten + seconds a year. This causes the perihelion point _P_ (Fig. 97) to + move _eastward_ at that rate, as indicated by the short arrow. The + earth _E_ is also moving eastward, as indicated by the long arrow. + Hence the earth, on starting at the perihelion, has to make a little + more than a complete circuit to reach the perihelion point again. + +[Illustration: Fig. 97.] + + 83. _The Calendar._--The _solar year_, or the interval between two + successive passages of the same equinox by the sun, is 365 days, 5 + hours, 48 minutes, 46 seconds. If, then, we reckon only 365 days to + a common or _civil year_, the sun will come to the equinox 5 hours, + 48 minutes, 46 seconds, or nearly a quarter of a day, later each + year; so that, if the sun entered Aries on the 20th of March one + year, he would enter it on the 21st four years after, on the 22d + eight years after, and so on. Thus in a comparatively short time the + spring months would come in the winter, and the summer months in the + spring. + + Among different ancient nations different methods of computing the + year were in use. Some reckoned it by the revolution of the moon, + some by that of the sun; but none, so far as we know, made proper + allowances for deficiencies and excesses. Twelve moons fell short of + the true year, thirteen exceeded it; 365 days were not enough, 366 + were too many. To prevent the confusion resulting from these errors, + Julius Cæsar reformed the calendar by making the year consist of 365 + days, 6 hours (which is hence called a _Julian_ year), and made + every fourth year consist of 366 days. This method of reckoning is + called _Old Style_. + + But as this made the year somewhat too long, and the error in 1582 + amounted to ten days, Pope Gregory XIII., in order to bring the + vernal equinox back to the 21st of March again, ordered ten days to + be struck out of that year, calling the next day after the 4th of + October the 15th; and, to prevent similar confusion in the future, + he decreed that three leap-years should be omitted in the course of + every four hundred years. This way of reckoning time is called _New + Style_. It was immediately adopted by most of the European nations, + but was not accepted by the English until the year 1752. The error + then amounted to eleven days, which were taken from the month of + September by calling the 3d of that month the 14th. The Old Style is + still retained by Russia. + + According to the Gregorian calendar, _every year whose number is + divisible by four_ is a _leap-year_, except, that, _in the case of + the years whose numbers are exact hundreds, those only are + leap-years which are divisible by four after cutting off the last + two figures_. Thus the years 1600, 2000, 2400, etc., are leap-years; + 1700, 1800, 1900, 2100, 2200, etc., are not. The error will not + amount to a day in over three thousand years. + + 84. _The Dominical Letter._--The _dominical letter_ for any year is + that which we often see placed against Sunday in the almanacs, and + is always one of the first seven in the alphabet. Since a common + year consists of 365 days, if this number is divided by seven (the + number of days in a week), there will be a remainder of one: hence a + year commonly begins one day later in the week than the preceding + one did. If a year of 365 days begins on Sunday, the next will begin + on Monday; if it begins on Thursday, the next will begin on Friday; + and so on. If Sunday falls on the 1st of January, the _first_ letter + of the alphabet, or _A_, is the _dominical letter_. If Sunday falls + on the 7th of January (as it will the next year, unless the first is + leap-year), the _seventh_ letter, _G_, is the dominical letter. If + Sunday falls on the 6th of January (as it will the third year, + unless the first or second is leap-year), the _sixth_ letter, _F_, + will be the dominical letter. Thus, if there were no leap-years, the + dominical letters would regularly follow a retrograde order, _G_, + _F_, _E_, _D_, _C_, _B_, _A_. + + But _leap_-years have 366 days, which, divided by seven, leaves two + remainder: hence the years following leap-years will begin two days + later in the week than the leap-years did. To prevent the + interruption which would hence occur in the order of the dominical + letters, leap-years have _two_ dominical letters, one indicating + Sunday till the 29th of February, and the other for the rest of the + year. + +By _Table I._ below, the dominical letter for any year (New Style) for +four thousand years from the beginning of the Christian Era may be +found; and it will be readily seen how the Table could be extended +indefinitely by continuing the centuries at the top in the same order. + +To find the dominical letter by this table, _look for the hundreds of +years at the top, and for the years below a hundred, at the left hand_. + +Thus the letter for 1882 will be opposite the number 82, and in the +column having 1800 at the top; that is, it will be _A_. In the same way, +the letters for 1884, which is a leap-year, will be found to be _FE_. + +Having the dominical letter of any year, _Table II._ shows what days of +every month of the year will be _Sundays_. + +To find the Sundays of any month in the year by this table, _look in the +column, under the dominical letter, opposite the name of the month given +at the left_. + +From the Sundays the date of any other day of the week can be readily +found. + +Thus, if we wish to know on what day of the week Christmas falls in +1889, we look opposite December, under the letter _F_ (which we have +found to be the dominical letter for the year), and find that the 22d of +the month is a Sunday; the 25th, or Christmas, will then be Wednesday. + +In the same way we may find the day of the week corresponding to any +date (New Style) in history. For instance, the 17th of June, 1775, the +day of the fight at Bunker Hill, is found to have been a _Saturday_. + +These two tables then serve as a _perpetual almanac_. + +TABLE I. + + 100 200 300 400 + 500 600 700 800 + 900 1000 1100 1200 + 1300 1400 1500 1600 + 1700 1800 1900 2000 + 2100 2200 2300 2400 + --- --- --- ---- + C E G BA + + 1 29 57 85 B D F G + 2 30 58 86 A C E F + 3 31 59 87 G B D E + 4 32 60 88 FE AG CB DC + 5 33 61 89 D F A B + 6 34 62 90 C E G A + 7 35 63 91 B D F G + 8 36 64 92 AG CB ED FE + 9 37 65 93 F A C D + 10 38 66 94 E G B C + 11 39 67 95 D F A B + 12 40 68 96 CB ED GF AG + 13 41 69 97 A C E F + 14 42 70 98 G B D E + 15 43 71 99 F A C D + 16 44 72 .. ED GF BA CB + 17 45 73 .. C E G A + 18 46 74 .. B D F G + 19 47 75 .. A C E F + 20 48 76 .. GF BA DC ED + 21 49 77 .. E G B C + 22 50 78 .. D F A B + 23 51 79 .. C E G A + 24 52 80 .. BA DC FE GF + 25 53 81 .. G B D E + 26 54 82 .. F A C D + 27 55 83 .. E G B C + 28 56 84 .. DC FE AG BA + +TABLE II. + + A B C D E F G + + 1 2 3 4 5 6 7 + Jan. 31. 8 9 10 11 12 13 14 + 15 16 17 18 19 20 21 + Oct. 31. 22 23 24 25 26 27 28 + 29 30 31 .. .. .. .. + + Feb. 28-29. .. .. .. 1 2 3 4 + 5 6 7 8 9 10 11 + March 31. 12 13 14 15 16 17 18 + 19 20 21 22 23 24 25 + Nov. 30. 26 27 28 29 30 31 .. + + .. .. .. .. .. .. 1 + April 30. 2 3 4 5 6 7 8 + 9 10 11 12 13 14 15 + July 31 16 17 18 19 20 21 22 + 23 24 25 26 27 28 29 + 30 31 .. .. .. .. .. + + .. .. 1 2 3 4 5 + 6 7 8 9 10 11 12 + Aug. 31. 13 14 15 16 17 18 19 + 20 21 22 23 24 25 26 + 27 28 29 30 31 .. .. + + .. .. .. .. .. 1 2 + Sept. 30. 3 4 5 6 7 8 9 + 10 11 12 13 14 15 16 + 17 18 19 20 21 22 23 + Dec. 31. 24 25 26 27 28 29 30 + 31 .. .. .. .. .. .. + + .. 1 2 3 4 5 6 + 7 8 9 10 11 12 13 + May. 31. 14 15 16 17 18 19 20 + 21 22 23 24 25 26 27 + 28 29 30 31 .. .. .. + + .. .. .. .. 1 2 3 + 4 5 6 7 8 9 10 + June 30. 11 12 13 14 15 16 17 + 18 19 20 21 22 23 24 + 25 26 27 28 29 30 .. + + + Weight of the Earth and Precession. + + +85. _The Weight of the Earth._--There are several methods of +ascertaining the weight and mass of the earth. The simplest, and perhaps +the most trustworthy method is to compare the pull of the earth upon a +ball of lead with that of a known mass of lead upon it. The pull of a +known mass of lead upon the ball may be measured by means of a torsion +balance. One form of the balance employed for this purpose is shown in +Figs. 98 and 99. Two small balls of lead, _b_ and _b_, are fastened to +the ends of a light rod _e_, which is suspended from the point _F_ by +means of the thread _FE_. Two large balls of lead, _W_ and _W_, are +placed on a turn-table, so that one of them shall be just in front of +one of the small balls, and the other just behind the other small ball. +The pull of the large balls turns the rod around a little so as to bring +the small balls nearer the large ones. The small balls move towards the +large ones till they are stopped by the torsion of the thread, which is +then equal to the pull of the large balls. The deflection of the rod is +carefully measured. The table is then turned into the position indicated +by the dotted lines in Fig. 99, so as to reverse the position of the +large balls with reference to the small ones. The rod is now deflected +in the opposite direction, and the amount of deflection is again +carefully measured. The second measurement is made as a check upon the +accuracy of the first. The force required to twist the thread as much as +it was twisted by the deflection of the rod is ascertained by +measurement. This gives the pull of the two large balls upon the two +small ones. We next calculate what this pull would be were the balls as +far apart as the small balls are from the centre of the earth. We can +then form the following proportion: the pull of the large balls upon the +small ones is to the pull of the earth upon the small ones as the mass +of the large balls is to the mass of the earth, or as the weight of the +large balls is to the weight of the earth. Of course, the pull of the +earth upon the small balls is the weight of the small balls. In this way +it has been ascertained that the mass of the earth is about 5.6 times +that of a globe of water of the same size. In other words, the _mean +density_ of the earth is about 5.6. + +[Illustration: Fig. 98.] + +[Illustration: Fig. 99.] + +The weight of the earth in pounds may be found by multiplying the number +of cubic feet in it by 62-1/2 (the weight, in pounds, of one cubic foot +of water), and this product by 5.6. + +[Illustration: Fig. 100.] + +86. _Cause of Precession._--We have seen that the earth is flattened at +the poles: in other words, the earth has the form of a sphere, with a +protuberant ring around its equator. This equatorial ring is inclined to +the plane of the ecliptic at an angle of about 23-1/2°. In Fig. 100 this +ring is represented as detached from the enclosed sphere. _S_ represents +the sun, and _Sc_ the ecliptic. As the point _A_ of the ring is nearer +the sun than the point _B_ is, the sun's pull upon _A_ is greater than +upon _B_: hence the sun tends to pull the ring over into the plane of +the ecliptic; but the rotation of the earth tends to keep the ring in +the same plane. The struggle between these two tendencies causes the +earth, to which the ring is attached, to wabble like a spinning-top, +whose rotation tends to keep it erect, while gravity tends to pull it +over. The handle of the top has a gyratory motion, which causes it to +describe a curve. The axis of the heavens corresponds to the handle of +the top. + + + II. THE MOON. + + + Distance, Size, and Motions. + + +87. _The Distance of the Moon._--The moon is the nearest of the heavenly +bodies. Its distance from the centre of the earth is only about sixty +times the radius of the earth, or, in round numbers, two hundred and +forty thousand miles. + + The ordinary method of finding the distance of one of the nearer + heavenly bodies is first to ascertain its horizontal parallax. This + enables us to form a right-angled triangle, the lengths of whose + sides are easily computed, and the length of whose hypothenuse is + the distance of the body from the centre of the earth. + +[Illustration: Fig. 101.] + + Horizontal parallax has already been defined (32) as the + displacement of a heavenly body when on the horizon, caused by its + being seen from the surface, instead of the centre, of the earth. + This displacement is due to the fact that the body is seen in a + different direction from the surface of the earth from that in which + it would be seen from the centre. Horizontal parallax might be + defined as the difference in the directions in which a body on the + horizon would be seen from the surface and from the centre of the + earth. Thus, in Fig. 101, _C_ is the centre of the earth, _A_ a + point on the surface, and _B_ a body on the horizon of _A_. _AB_ is + the direction in which the body would be seen from _A_, and _CB_ the + direction in which it would be seen from _C_. The difference of + these directions, or the angle _ABC_, is the parallax of the body. + + The triangle _BAC_ is right-angled at _A_; the side _AC_ is the + radius of the earth, and the hypothenuse is the distance of the body + from the centre of the earth. When the parallax _ABC_ is known, the + length of _CB_ can easily by found by trigonometrical computation. + + We have seen (32) that the parallax of a heavenly body grows less + and less as the body passes from the horizon towards the zenith. The + parallax of a body and its altitude are, however, so related, that, + when we know the parallax at any altitude, we can readily compute + the horizontal parallax. + + The usual method of finding the parallax of one of the nearer + heavenly bodies is first to find its parallax when on the meridian, + as seen from two places on the earth which differ considerably in + latitude: then to calculate what would be the parallax of the body + as seen from one of these places and the centre of the earth: and + then finally to calculate what would be the parallax were the body + on the horizon. + +[Illustration: Fig. 102.] + + Thus, we should ascertain the parallax of the body _B_ (Fig. 102) as + seen from _A_ and _D_, or the angle _ABD_. We should then calculate + its parallax as seen from _A_ and _C_, or the angle _ABC_. Finally + we should calculate what its parallax would be were the body on the + horizon, or the angle _AB'C_. + + The simplest method of finding the parallax of a body _B_ (Fig. 102) + as seen from the two points _A_ and _D_ is to compare its direction + at each point with that of the same fixed star near the body. The + star is so distant, that it will be seen in the same direction from + both points: hence, if the direction of the body differs from that + of the star 2° as seen from one point, and 2° 6' as seen from the + other point, the two lines _AB_ and _DB_ must differ in direction by + 6'; in other words, the angle _ABD_ would be 6'. + + The method just described is the usual method of finding the + parallax of the moon. + +88. _The Apparent Size of the Moon._--The _apparent size_ of a body is +the visual angle subtended by it; that is, the angle formed by two lines +drawn from the eye to two opposite points on the outline of the body. +The apparent size of a body depends upon both its _magnitude_ and its +_distance_. + +The apparent size, or _angular diameter_, of the moon is about +thirty-one minutes. This is ascertained by means of the wire micrometer +already described (19). The instrument is adjusted so that its +longitudinal wire shall pass through the centre of the moon, and its +transverse wires shall be tangent to the limbs of the moon on each side, +at the point where they are cut by the longitudinal wire. The micrometer +screw is then turned till the wires are brought together. The number of +turns of the screw needed to accomplish this will indicate the arc +between the wires, or the angular diameter of the moon. + +[Illustration: Fig. 103.] + +In order to be certain that the longitudinal wire shall pass through the +centre of the moon, it is best to take the moon when its disc is in the +form of a crescent, and to place the longitudinal wire against the +points, or _cusps_, of the crescent, as shown in Fig. 103. + +[Illustration: Fig. 104.] + +89. _The Real Size of the Moon._--The real diameter of the moon is a +little over one-fourth of that of the earth, or a little more than two +thousand miles. The comparative sizes of the earth and moon are shown in +Fig. 104. + +[Illustration: Fig. 105.] + + The distance and apparent size of the moon being known, her real + diameter is found by means of a triangle formed as shown in Fig. + 105. _C_ represents the centre of the moon, _CB_ the distance of the + moon from the earth, and _CA_ the radius of the moon. _BAC_ is a + triangle, right-angled at _A_. The angle _ABC_ is half the apparent + diameter of the moon. With the angles _A_ and _B_, and the side _CB_ + known, it is easy to find the length of _AC_ by trigonometrical + computation. Twice _AC_ will be the diameter of the moon. + +The volume of the moon is about one-fiftieth of that of the earth. + +90. _Apparent Size of the Moon on the Horizon and in the Zenith._.--The +moon is nearly four thousand miles farther from the observer when she is +on the horizon than when she is in the zenith. This is evident from Fig. +106. _C_ is the centre of the earth, _M_ the moon on the horizon, _M'_ +the moon in the zenith, and _O_ the point of observation. _OM_ is the +distance of the moon when she is on the horizon, and _OM'_ the distance +of the moon from the observer when she is in the zenith. _CM_ is equal +to _CM'_, and _OM_ is about the length of _CM_; but _OM'_ is about four +thousand miles shorter than _CM'_: hence _OM'_ is about four thousand +miles shorter than _OM_. + +[Illustration: Fig. 106.] + + Notwithstanding the moon is much nearer when at the zenith than at + the horizon, it seems to us much larger at the horizon. + + This is a pure illusion, as we become convinced when we measure the + disc with accurate instruments, so as to make the result independent + of our ordinary way of judging. When the moon is near the horizon, + it seems placed beyond all the objects on the surface of the earth + in that direction, and therefore farther off than at the zenith, + where no intervening objects enable us to judge of its distance. In + any case, an object which keeps the same apparent magnitude seems to + us, through the instinctive habits of the eye, the larger in + proportion as we judge it to be more distant. + + 91. _The Apparent Size of the Moon increased by Irradiation._--In + the case of the moon, the word _apparent_ means much more than it + does in the case of other celestial bodies. Indeed, its brightness + causes our eyes to play us false. As is well known, the crescent of + the new moon seems part of a much larger sphere than that which it + has been said, time out of mind, to "hold in its arms." The bright + portion of the moon as seen with our measuring instruments, as well + as when seen with the naked eye, covers a larger space in the field + of the telescope than it would if it were not so bright. This effect + of _irradiation_, as it is called, must be allowed for in exact + measurements of the diameter of the moon. + +[Illustration: Fig. 107.] + +92. _Apparent Size of the Moon in Different Parts of her Orbit._--Owing +to the eccentricity of the moon's orbit, her distance from the earth +varies somewhat from time to time. This variation causes a corresponding +variation in her apparent size, which is illustrated in Fig. 107. + +93. _The Mass of the Moon._--The moon is considerably less dense than +the earth, its mass being only about one-eightieth of that of the earth; +that is, while it would take only about fifty moons to make the bulk of +the earth, it would take about eighty to make the mass of the earth. + + One method of finding the mass of the moon is to compare her effect + in producing the _tides_ with that of the sun. We first calculate + what would be the moon's effect in producing the tides, were she as + far off as the sun. We then form the following proportion: as the + sun's effect in producing the tides is to the moon's effect at the + same distance, so is the mass of the sun to the mass of the moon. + + The method of finding the mass of the sun will be given farther on. + +94. _The Orbital Motion of the Moon._--If we watch the moon from night +to night, we see that she moves eastward quite rapidly among the stars. +When the new moon is first visible, it appears near the horizon in the +west, just after sunset. A week later the moon will be on the meridian +at the same hour, and about a week later still on the eastern horizon. +The moon completes the circuit of the heavens in a period of about +thirty days, moving eastward at the rate of about twelve degrees a day. +This eastward motion of the moon is due to the fact that she is +revolving around the earth from west to east. + +[Illustration: Fig. 108.] + +95. _The Aspects of the Moon._--As the moon revolves around the earth, +she comes into different positions with reference to the earth and sun. +These different positions of the moon are called the _aspects_ of the +moon. The four chief aspects of the moon are shown in Fig. 108. When the +moon is at _M_, she appears in the opposite part of the heavens to the +sun, and is said to be in _opposition_; when at _M'_ and at _M'''_, she +appears ninety degrees away from the sun, and is said to be in +_quadrature_; when at _M''_, she appears in the same part of the heavens +as the sun, and is said to be in _conjunction_. + +96. _The Sidereal and Synodical Periods of the Moon._--The _sidereal +period_ of the moon is the time it takes her to pass around from a star +to that star again, or the time it takes her to _make a complete +revolution around the earth_. This is a period of about twenty-seven +days and a third. It is sometimes called the _sidereal month_. + +The _synodical period_ of the moon is the time that it takes the moon to +_pass from one aspect around to the same aspect again_. This is a period +of about twenty-nine days and a half, and it is sometimes called the +_synodical month_. + +[Illustration: Fig. 109.] + +The reason why the synodical period is longer than the sidereal period +will appear from Fig. 109. _S_ represents the position of the sun, _E_ +that of the earth, and the small circle the orbit of the moon around the +earth. The arrow in the small circle represents the direction the moon +is revolving around the earth, and the arrow in the arc between _E_ and +_E'_ indicates the direction of the earth's motion in its orbit. When +the moon is at _M_{1}_, she is in conjunction. As the moon revolves +around the earth, the earth moves forward in its orbit. When the moon +has come round to _m_{1}_, so that _m_{3}m_{1}_ is parallel with +_M_{3}M_{1}_, she will have made a complete or _sidereal_ revolution +around the earth; but she will not be in conjunction again till she has +come round to _M_, so as again to be between the earth and sun. That is +to say, the moon must make more than a complete revolution in a +synodical period. + +[Illustration: Fig. 110.] + + The greater length of the synodical period is also evident from Fig. + 110. _T_ represents the earth, and _L_ the moon. The arrows indicate + the direction in which each is moving. When the earth is at _T_, and + the moon at _L_, the latter is in conjunction. When the earth has + reached _T'_, and the moon _L'_, the latter has made a sidereal + revolution; but she will not be in conjunction again till the earth + has reached _T''_, and the moon _L''_. + +97. _The Phases of the Moon._--When the new moon appears in the west, it +has the form of a _crescent_, with its convex side towards the sun, and +its horns towards the east. As the moon advances towards quadrature, the +crescent grows thicker and thicker, till it becomes a _half-circle_ at +first quarter. When it passes quadrature, it begins to become convex +also on the side away from the sun, or _gibbous_ in form. As it +approaches opposition, it becomes more and more nearly circular, until +at opposition it is a _full_ circle. From full moon to last quarter it +is again gibbous, and at last quarter a half-circle. From last quarter +to new moon it is again crescent; but the horns of the crescent are now +turned towards the west. The successive phases of the moon are shown in +Fig. 111. + +[Illustration: Fig. 111.] + +98. _Cause of the Phases of the Moon._--Take a globe, half of which is +colored white and the other half black in such a way that the line which +separates the white and black portions shall be a great circle which +passes through the poles of the globe, and rotate the globe slowly, so +as to bring the white half gradually into view. When the white part +first comes into view, the line of separation between it and the black +part, which we may call the _terminator_, appears concave, and its +projection on a plane perpendicular to the line of vision is a concave +line. As more and more of the white portion comes into view, the +projection of the terminator becomes less and less concave. When half of +the white portion comes into view, the terminator is projected as a +straight line. When more than half of the white portion comes into view, +the terminator begins to appear as a convex line, and this line becomes +more and more convex till the whole of the white half comes into view, +when the terminator becomes circular. + +[Illustration: Fig. 112.] + +The moon is of itself a dark, opaque globe; but the half that is towards +the sun is always bright, as shown in Fig. 112. This bright half of the +moon corresponds to the white half of the globe in the preceding +illustration. As the moon revolves around the earth, different portions +of this illumined half are turned towards the earth. At new moon, when +the moon is in conjunction, the bright half is turned entirely away from +the earth, and the disc of the moon is black and invisible. Between new +moon and first quarter, less than half of the illumined side is turned +towards the earth, and we see this illumined portion projected as a +crescent. At first quarter, just half of the illumined side is turned +towards the earth, and we see this half projected as a half-circle. +Between first quarter and full, more than half of the illumined side is +turned towards the earth, and we see it as gibbous. At full, the whole +of the illumined side is turned towards us, and we see it as a full +circle. From full to new moon again, the phases occur in the reverse +order. + +99. _The Form of the Moon's Orbit._--The orbit of the moon around the +earth is an ellipse of slight eccentricity. The form of this ellipse is +shown in Fig. 113. _C_ is the centre of the ellipse, and _E_ the +position of the earth at one of its foci. The eccentricity of the +ellipse is only about one-eighteenth. It is impossible for the eye to +distinguish such an ellipse from a circle. + +[Illustration: Fig. 113.] + +100. _The Inclination of the Moon's Orbit._--The plane of the moon's +orbit is inclined to the ecliptic by an angle of about five degrees. The +two points where the moon's orbit cuts the ecliptic are called her +_nodes_. The moon's nodes have a westward motion corresponding to that +of the equinoxes, but much more rapid. They complete the circuit of the +ecliptic in about nineteen years. + +The moon's latitude ranges from 5° north to 5° south; and since, owing +to the motion of her nodes, the moon is, during a period of nineteen +years, 5° north and 5° south of every part of the ecliptic, her +declination will range from 23-1/2° + 5° = 28-1/2° north to 23-1/2° + 5° += 28-1/2° south. + +101. _The Meridian Altitude of the Moon._--The _meridian altitude_ of +any body is its altitude when on the meridian. In our latitude, the +meridian altitude of any point on the equinoctial is forty-nine degrees. +The meridian altitude of the summer solstice is 49° + 23-1/2° = 72-1/2°, +and that of the winter solstice is 49° - 23-1/2° = 25-1/2°. The greatest +meridian altitude of the moon is 72-1/2° + 5° = 77-1/2°, and its least +meridian altitude, 25-1/2° - 5° = 20-1/2°. + +When the moon's meridian altitude is greater than the elevation of the +equinoctial, it is said to run _high_, and when less, to run _low_. The +full moon runs high when the sun is south of the equinoctial, and low +when the sun is north of the equinoctial. This is because the full moon +is always in the opposite part of the heavens to the sun. + + 102. _Wet and Dry Moon._--At the time of new moon, the cusps of the + crescent sometimes lie in a line which is nearly perpendicular with + the horizon, and sometimes in a line which is nearly parallel with + the horizon. In the former case the moon is popularly described as a + _wet_ moon, and in the latter case as a _dry_ moon. + +[Illustration: Fig. 114.] + + The great circle which passes through the centre of the sun and moon + will pass through the centre of the crescent, and be perpendicular + to the line joining the cusps. Now the ecliptic makes the least + angle with the horizon when the vernal equinox is on the eastern + horizon and the autumnal equinox is on the western. In our latitude, + as we have seen, this angle is 25-1/2°: hence in our latitude, if + the moon were at new on the ecliptic when the sun is at the autumnal + equinox, as shown at _M_{3}_ (Fig. 114), the great circle passing + through the centre of the sun and moon would be the ecliptic, and at + New York would be inclined to the horizon at an angle of 25-1/2°. If + the moon happened to be 5° south of the ecliptic at this time, as at + _M_{4}_, the great circle passing through the centre of the sun and + moon would make an angle of only 20-1/2° with the horizon. In either + of these cases the line joining the cusps would be nearly + perpendicular to the horizon. + +[Illustration: Fig. 115.] + + If the moon were at new on the ecliptic when the sun is near the + vernal equinox, as shown at _M_{1}_ (Fig. 115), the great circle + passing through the centres of the sun and moon would make an angle + of 72-1/2° with the horizon at New York; and were the moon 5° north + of the ecliptic at that time, as shown at _M_{2}_, this great circle + would make an angle of 77-1/2° with the horizon. In either of these + cases, the line joining the cusps would be nearly parallel with the + horizon. + + At different times, the line joining the cusps may have every + possible inclination to the horizon between the extreme cases shown + in Figs. 114 and 115. + +103. _Daily Retardation of the Moon's Rising._--The moon rises, on the +average, about fifty minutes later each day. This is owing to her +eastward motion. As the moon makes a complete revolution around the +earth in about twenty-seven days, she moves eastward at the rate of +about thirteen degrees a day, or about twelve degrees a day faster than +the sun. Were the moon, therefore, on the horizon at any hour to-day, +she would be some twelve degrees below the horizon at the same hour +to-morrow. Now, as the horizon moves at the rate of one degree in four +minutes, it would take it some fifty minutes to come up to the moon so +as to bring her upon the horizon. Hence the daily retardation of the +moon's rising is about fifty minutes; but it varies considerably in +different parts of her orbit. + + There are two reasons for this variation in the daily retardation:-- + + (1) The moon moves at a _varying rate in her orbit_; her speed being + greatest at perigee, and least at apogee: hence, other things being + equal, the retardation is greatest when the moon is at perigee, and + least when she is at apogee. + +[Illustration: Fig. 116.] + +[Illustration: Fig. 117.] + + (2) The moon moves at a _varying angle to the horizon_. The moon + moves nearly in the plane of the ecliptic, and of course she passes + both equinoxes every lunation. When she is near the autumnal + equinox, her path makes the greatest angle with the eastern horizon, + and when she is near the vernal equinox, the least angle: hence the + moon moves away from the horizon fastest when she is near the + autumnal equinox, and slowest when she is near the vernal equinox. + This will be evident from Figs. 116 and 117. In each figure, _SN_ + represents a portion of the eastern horizon, and _Ec_, _E'c'_, a + portion of the ecliptic. _AE_, in Fig. 116, represents the autumnal + equinox, and _AEM_ the daily motion of the moon. _VE_, in Fig. 117, + represents the vernal equinox, and _VEM'_ the motion of the moon for + one day. In the first case this motion would carry the moon away + from the horizon the distance _AM_, and in the second case the + distance _A'M'_. Now, it is evident that _AM_ is greater than + _A'M'_: hence, other things being equal, the greatest retardation of + the moon's rising will be when the moon is near the autumnal + equinox, and the least retardation when the moon is near the vernal + equinox. + +The least retardation at New York is twenty-three minutes, and the +greatest an hour and seventeen minutes. The greatest and least +retardations vary somewhat from month to month; since they depend not +only upon the position of the moon in her orbit with reference to the +equinoxes, but also upon the latitude of the moon, and upon her nearness +to the earth. + +[Illustration: Fig. 118.] + +The direction of the moon's motion with reference to the ecliptic is +shown in Fig. 118, which shows the moon's motion for one day in July, +1876. + +104. _The Harvest Moon_--The long and short retardations in the rising +of the moon, though they occur every month, are not likely to attract +attention unless they occur at the time of full moon. The long +retardations for full moon occur when the moon is near the autumnal +equinox at full. As the full moon is always opposite to the sun, the sun +must in this case be near the vernal equinox: hence the long +retardations for full moon occur in the spring, the greatest retardation +being in March. + +The least retardations for full moon occur when the moon is near the +vernal equinox at full: the sun must then be near the autumnal equinox. +Hence the least retardations for full moon occur in the months of +August, September, and October. The retardation is, of course, least for +September; and the full moon of this month rises night after night less +than half an hour later than the previous night. The full moon of +September is called the "Harvest Moon," and that of October the +"Hunter's Moon." + +105. _The Rotation of the Moon._--A careful examination of the spots on +the disc of the moon reveals the fact that she always presents the same +side to the earth. In order to do this, she must rotate on her axis +while making a revolution around the earth, or in about twenty-seven +days. + +106. _Librations of the Moon._--The moon appears to rock slowly to and +fro, so as to allow us to see alternately a little farther around to the +right and the left, or above and below, than we otherwise could. This +apparent rocking of the moon is called _libration_. The moon has three +librations:-- + +(1) _Libration in Latitude._--This libration enables us to see +alternately a little way around on the northern and southern limbs of +the moon. + + This libration is due to the fact that the axis of the moon is not + quite perpendicular to the plane of her orbit. The deviation from + the perpendicular is six degrees and a half. As the axis of the + moon, like that of the earth, maintains the same direction, the + poles of the moon will be turned alternately six degrees and a half + toward and from the earth. + +(2) _Libration in Longitude._--This libration enables us to see +alternately a little farther around on the eastern and western limbs of +the moon. + +[Illustration: Fig. 119.] + + It is due to the fact that the moon's axial motion is uniform, while + her orbital motion is not. At perigee her orbital motion will be in + advance of her axial motion, while at apogee the axial motion will + be in advance of the orbital. In Fig. 119, _E_ represents the earth, + _M_ the moon, the large arrow the direction of the moon's motion in + her orbit, and the small arrow the direction of her motion of + rotation. When the moon is at _M_, the line _AB_, drawn + perpendicular to _EM_, represents the circle which divides the + visible from the invisible portion of the moon. While the moon is + passing from _M_ to _M'_, the moon performs less than a quarter of a + rotation, so that _AB_ is no longer perpendicular to _EM'_. An + observer on the earth can now see somewhat beyond _A_ on the western + limb of the moon, and not quite up to _B_ on the eastern limb. While + the moon is passing from _M'_ to _M''_, her axial motion again + overtakes her orbital motion, so that the line _AB_ again becomes + perpendicular to the line joining the centre of the moon to the + centre of the earth. Exactly the same side is now turned towards the + earth as when the moon was at _M_. While the moon passes from _M''_ + to _M'''_, her axial motion gets in advance of her orbital motion, + so that _AB_ is again inclined to the line joining the centres of + the earth and moon. A portion of the eastern limb of the moon beyond + _B_ is now brought into view to the earth, and a portion of the + western limb at _A_ is carried out of view. While the moon is + passing from _M'''_ to _M_, the orbital motion again overtakes the + axial motion, and _AB_ is again perpendicular to _ME_. + +(3) _Parallactic Libration._--While an observer at the centre of the +earth would get the same view of the moon, whether she were on the +eastern horizon, in the zenith, or on the western horizon, an observer +on the surface of the earth does not get exactly the same view in these +three cases. When the moon is on the eastern horizon, an observer on the +surface of the earth would see a little farther around on the western +limb of the moon than when she is in the zenith, and not quite so far +around on the eastern limb. On the contrary, when the moon is on the +western horizon, an observer on the surface of the earth sees a little +farther around on the eastern limb of the moon than when she is in the +zenith, and not quite so far around on her western limb. + +[Illustration: Fig. 120.] + + This will be evident from Fig. 120. _E_ is the centre of the earth, + and _O_ a point on its surface. _AB_ is a line drawn through the + centre of the moon, perpendicular to a line joining the centres of + the moon and the earth. This line marks off the part of the moon + turned towards the centre of the earth, and remains essentially the + same during the day. _CD_ is a line drawn through the centre of the + moon perpendicular to a line joining the centre of the moon and the + point of observation. This line marks off the part of the moon + turned towards _O_. When the moon is in the zenith, _CD_ coincides + with _AB_; but, when the moon is on the horizon, _CD_ is inclined to + _AB_. When the moon is on the eastern horizon, an observer at _O_ + sees a little beyond _B_, and not quite to _A_; and, when she is on + the western horizon, he sees a little beyond _A_, and not quite to + _B_. _B_ is on the western limb of the moon, and _A_ on her eastern + limb. + + Since this libration is due to the point from which the moon is + viewed, it is called _parallactic_ libration; and, since it occurs + daily, it is called _diurnal_ libration. + +[Illustration: Fig. 121.] + + 107. _Portion of the Lunar Surface brought into View by + Libration._--The area brought into view by the first two librations + is between one-twelfth and one-thirteenth of the whole lunar + surface, or nearly one-sixth of the hemisphere of the moon which is + turned away from the earth when the moon is at her state of mean + libration. Of course a precisely equal portion of the hemisphere + turned towards us during mean libration is carried out of view by + the lunar librations. + + If we add to each of these areas a fringe about one degree wide, due + to the diurnal libration, and which we may call the _parallactic_ + fringe, we shall find that the total area brought into view is + almost exactly one-eleventh part of the whole surface of the moon. A + similar area is carried out of view; so that the whole region thus + swayed out of and into view amounts to two-elevenths of the moon's + surface. This area is shown in Fig. 121, which is a side view of the + moon. + +[Illustration: Fig. 122.] + + 108. _The Moon's Path through Space._--Were the earth stationary, + the moon would describe an ellipse around it similar to that of Fig. + 113; but, as the earth moves forward in her orbit at the same time + that the moon revolves around it, the moon is made to describe a + sinuous path, as shown by the continuous line in Fig. 122. This + feature of the moon's path is greatly exaggerated in the upper + portion of the diagram. The form of her path is given with a greater + degree of accuracy in the lower part of the figure (the broken line + represents the path of the earth); but even here there is + considerable exaggeration. The complete serpentine path of the moon + around the sun is shown, greatly exaggerated, in Fig. 123, the + broken line being the path of the earth. + +[Illustration: Fig. 123.] + + The path described by the moon through space is much the same as + that described by a point on the circumference of a wheel which is + rolled over another wheel. If we place a circular disk against the + wall, and carefully roll along its edge another circular disk (to + which a piece of lead pencil has been fastened so as to mark upon + the wall), the curve described will somewhat resemble that described + by the moon. This curve is called an _epicycloid_, and it will be + seen that at every point it is concave towards the centre of the + larger disk. In the same way the moon's orbit is _at every point + concave towards the sun_. + +[Illustration: Fig. 124.] + + The exaggeration of the sinuosity in Fig. 123 will be more evident + when it is stated, that, on the scale of Fig. 124, the whole of the + serpentine curve would lie _within the breadth_ of the fine circular + line _MM'_. + +109. _The Lunar Day._--The lunar day is twenty-nine times and a half as +long as the terrestrial day. Near the moon's equator the sun shines +without intermission nearly fifteen of our days, and is absent for the +same length of time. Consequently, the vicissitudes of temperature to +which the surface is exposed must be very great. During the long lunar +night the temperature of a body on the moon's surface would probably +fall lower than is ever known on the earth, while during the day it must +rise higher than anywhere on our planet. + +[Illustration: Fig. 125.] + + It might seem, that, since the moon rotates on her axis in about + twenty-seven days, the lunar day ought to be twenty-seven days long, + instead of twenty-nine. There is, however, a solar, as well as a + sidereal, day at the moon, as on the earth; and the solar day at the + moon is longer than the sidereal day, for the same reason as on the + earth. During the solar day the moon must make both a _synodical + rotation_ and a _synodical revolution_. This will be evident from + Fig. 125, in which is shown the path of the moon during one complete + lunation. _E_, _E'_, _E''_, etc., are the successive positions of + the earth; and 1, 2, 3, 4, 5, the successive positions of the moon. + The small arrows indicate the direction of the moon's rotation. The + moon is full at 1 and 5. At 1, _A_, at the centre of the moon's + disk, will have the sun, which lies in the direction _AS_, upon the + meridian. Before _A_ will again have the sun on the meridian, the + moon must have made a synodical revolution; and, as will be seen by + the dotted lines, she must have made more than a complete rotation. + The rotation which brings the point _A_ into the same relation to + the earth and sun is called a _synodical_ rotation. + + It will also be evident from this diagram that the moon must make a + synodical rotation during a synodical revolution, in order always to + present the same side to the earth. + +110. _The Earth as seen from the Moon._--To an observer on the moon, the +earth would be an immense moon, going through the same phases that the +moon does to us; but, instead of rising and setting, it would only +oscillate to and fro through a few degrees. On the other side of the +moon it would never be seen at all. The peculiarities of the moon's +motions which cause the librations, and make a spot on the moon's disk +seem to an observer on the earth to oscillate to and fro, would cause +the earth as a whole to appear to a lunar observer to oscillate to and +fro in the heavens in a similar manner. + +It is a well-known fact, that, at the time of new moon, the dark part of +the moon's surface is partially illumined, so that it becomes visible to +the naked eye. This must be due to the light reflected to the moon from +the earth. Since at new moon the moon is between the earth and sun, it +follows, that, when it is new moon at the earth, it must be _full earth_ +at the moon: hence, while the bright crescent is enjoying full sunlight, +the dark part of its surface is enjoying the light of the full _earth_. +Fig. 126 represents the full earth as seen from the moon. + +[Illustration: Fig. 126.] + + + The Atmosphere of the Moon. + + +111. _The Moon has no Appreciable Atmosphere._--There are several +reasons for believing that the moon has little or no atmosphere. + +(1) Had the moon an atmosphere, it would be indicated at the time of a +solar eclipse, when the moon passes over the disk of the sun. If the +atmosphere were of any considerable density, it would absorb a part of +the sun's rays, so as to produce a dusky border in front of the moon's +disk, as shown in Fig. 127. In reality no such dusky border is ever +seen; but the limb of the moon appears sharp, and clearly defined, as in +Fig. 128. + +[Illustration: Fig. 127.] + +[Illustration: Fig. 128.] + +If the atmosphere were not dense enough to produce this dusky border, +its refraction would be sufficient to distort the delicate cusps of the +sun's crescent in the manner shown at the top of Fig. 125; but no such +distortion is ever observed. The cusps always appear clear and sharp, as +shown at the bottom of the figure: hence it would seem that there can be +no atmosphere of appreciable density at the moon. + +(2) The absence of an atmosphere from the moon is also shown by the +absence of twilight and of diffused daylight. + +Upon the earth, twilight continues until the sun is eighteen degrees +below the horizon; that is, day and night are separated by a belt twelve +hundred miles in breadth, in which the transition from light to darkness +is gradual. We have seen (66) that this twilight results from the +refraction and reflection of light by our atmosphere; and, if the moon +had an atmosphere, we should notice a similar gradual transition from +the bright to the dark portions of her surface. Such, however, is not +the case. The boundary between the light and darkness, though irregular, +is sharply defined. Close to this boundary the unillumined portion of +the moon appears just as dark as at any distance from it. + +The shadows on the moon are also pitchy black, without a trace of +diffused daylight. + +[Illustration: Fig. 129.] + + (3) The absence of an atmosphere is also proved by the absence of + refraction when the moon passes between us and the stars. Let _AB_ + (Fig. 129) represent the disk of the moon, and _CD_ an atmosphere + supposed to surround it. Let _SAE_ represent a straight line from + the earth, touching the moon at _A_, and let _S_ be a star situated + in the direction of this line. If the moon had no atmosphere, this + star would appear to touch the edge of the moon at _A_; but, if the + moon had an atmosphere, a star behind the edge of the moon, at _S'_, + would be visible at the earth; for the ray _S'A_ would be bent by + the atmosphere into the direction _AE'_. So, also, on the opposite + side of the moon, a star might be seen at the earth, although really + behind the edge of the moon: hence, if the moon had an atmosphere, + the time during which a star would be concealed by the moon would be + less than if it had no atmosphere, and the amount of this effect + must be proportional to the density of the atmosphere. + + The moon, in her orbital course across the heavens, is continually + passing before, or _occulting_, some of the stars that so thickly + stud her apparent path; and when we see a star thus pass behind the + lunar disk on one side, and come out again on the other side, we are + virtually observing the setting and rising of that star upon the + moon. The moon's apparent diameter has been measured over and over + again, and is known with great accuracy; the rate of her motion + across the sky is also known with perfect accuracy: hence it is easy + to calculate how long the moon will take to travel across a part of + the sky exactly equal in length to her own diameter. Supposing, + then, that we observe a star pass behind the moon, and out again, it + is clear, that, if there is no atmosphere, the interval of time + during which it remains occulted ought to be exactly equal to the + computed time which the moon would take to pass over the star. If, + however, from the existence of a lunar atmosphere, the star + disappears too late, and re-appears too soon, as we have seen it + would, these two intervals will not agree; the computed time will be + greater than the observed time, and the difference will represent + the amount of refraction the star's light has sustained or suffered, + and hence the extent of atmosphere it has had to pass through. + + Comparisons of these two intervals of time have been repeatedly + made, the most extensive being executed under the direction of the + Astronomer Royal of England, several years ago, and based upon no + less than two hundred and ninety-six occultation observations. In + this determination the measured or telescopic diameter of the moon + was compared with the diameter deduced from the occultations; and it + was found that the telescopic diameter was greater than the + occultation diameter by two seconds of angular measurement, or by + about a thousandth part of the whole diameter of the moon. This + discrepancy is probably due, in part at least, to _irradiation_ + (91), which augments the apparent size of the moon, as seen in the + telescope as well as with the naked eye; but, if the whole two + seconds were caused by atmospheric refraction, this would imply a + horizontal refraction of one second, which is only one + two-thousandth of the earth's horizontal refraction. It is possible + that an atmosphere competent to produce this refraction would not + make itself visible in any other way. + + But an atmosphere two thousand times rarer than our air can scarcely + be regarded as an atmosphere at all. The contents of an air-pump + receiver can seldom be rarefied to a greater extent than to about a + thousandth of the density of air at the earth's surface; and the + lunar atmosphere, if it exists at all, is thus proved to be twice as + attenuated as what we commonly call a vacuum. + + + The Surface of the Moon. + + +[Illustration: Fig. 130.] + +112. _Dusky Patches on the Disk of the Moon._--With the naked eye, large +dusky patches are seen on the moon, in which popular fancy has detected +a resemblance to a human face. With a telescope of low power, these dark +patches appear as smooth as water, and they were once supposed to be +seas. This theory was the origin of the name _mare_ (Latin for _sea_), +which is still applied to the larger of these plains; but, if there were +water on the surface of the moon, it could not fail to manifest its +presence by its vapor, which would form an appreciable atmosphere. +Moreover, with a high telescopic power, these plains present a more or +less uneven surface; and, as the elevations and depressions are found to +be permanent, they cannot, of course, belong to the surface of water. + + The chief of these plains are shown in Fig. 130. They are _Mare + Crisium_, _Mare Foecunditatis_, _Mare Nectaris_, _Mare + Tranquillitatis_, _Mare Serenitatis_, _Mare Imbrium_, _Mare + Frigoris_, and _Oceanus Procellarum_. All these plains can easily be + recognized on the surface of the full moon with the unaided eye. + +113. _The Terminator of the Moon._--The terminator of the moon is the +line which separates the bright and dark portions of its disk. When +viewed with a telescope of even moderate power, the terminator is seen +to be very irregular and uneven. Many bright points are seen just +outside of the terminator in the dark portion of the disk, while all +along in the neighborhood of the terminator are bright patches and dense +shadows. These appearances are shown in Figs. 131 and 132, which +represent the moon near the first and last quarters. They indicate that +the surface of the moon is very rough and uneven. + +[Illustration: Fig. 131.] + +[Illustration: Fig. 132.] + +As it is always either sunrise or sunset along the terminator, the +bright spots outside of it are clearly the tops of mountains, which +catch the rays of the sun while their bases are in the shade. The bright +patches in the neighborhood of the terminator are the sides of hills and +mountains which are receiving the full light of the sun, while the dense +shadows near by are cast by these elevations. + +114. _Height of the Lunar Mountains._--There are two methods of finding +the height of lunar mountains:-- + +(1) We may measure the length of the shadows, and then calculate the +height of the mountains that would cast such shadows with the sun at the +required height above the horizon. + + The length of a shadow may be obtained by the following method: the + longitudinal wire of the micrometer (19) is adjusted so as to pass + through the shadow whose length is to be measured, and the + transverse wires are placed one at each end of the shadow, as shown + in Fig. 133. The micrometer screw is then turned till the wires are + brought together, so as to ascertain the length of the arc between + them. We may then form the proportion: the number of seconds in the + semi-diameter of the moon is to the number of seconds in the length + of the shadow, as the length of the moon's radius in miles to the + length of the shadow in miles. + +[Illustration: Fig. 133.] + + The height of the sun above the horizon is ascertained by measuring + the angular distance of the mountain from the terminator. + +(2) We may measure the distance of a bright point from the terminator, +and then construct a right-angled triangle, as shown in Fig. 134. A +solution of this triangle will enable us to ascertain the height of the +mountain whose top is just catching the level rays of the sun. + +[Illustration: Fig. 134.] + + _B_ is the centre of the moon, _M_ the top of the mountain, and + _SAM_ a ray of sunlight which just grazes the terminator at _A_, and + then strikes the top of the mountain at _M_. The triangle _BAM_ is + right-angled at _A_. _BA_ is the radius of the moon, and _AM_ is + known by measurement; _BM_, the hypothenuse, may then be found by + computation. _BM_ is evidently equal to the radius of the moon + _plus_ the height of the mountain. + +By one or the other of these methods, the heights of the lunar mountains +have been found with a great degree of accuracy. It is claimed that the +heights of the lunar mountains are more accurately known than those of +the mountains on the earth. Compared with the size of the moon, lunar +mountains attain a greater height than those on the earth. + +115. _General Aspect of the Lunar Surface._--A cursory examination of +the moon with a low power is sufficient to show the prevalence of +crater-like inequalities and the general tendency to _circular_ shape +which is apparent in nearly all the surface markings; for even the large +"seas" and the smaller patches of the same character repeat in their +outlines the round form of the craters. It is along the terminator that +we see these crater-like spots to the best advantage; as it is there +that the rising or setting sun casts long shadows over the lunar +landscape, and brings elevations into bold relief. They vary greatly in +size; some being so large as to bear a sensible proportion to the moon's +diameter, while the smallest are so minute as to need the most powerful +telescopes and the finest conditions of atmosphere to perceive them. + +[Illustration: Fig. 135.] + +The prevalence of ring-shaped mountains and plains willbe evident from +Fig. 135, which is from a photograph of a model of the moon constructed +by Nasmyth. + +This same feature is nearly as marked in Figs. 131 and 132, which are +copies of Rutherfurd's photographs of the moon. + +116. _Lunar Craters._--The smaller saucer-shaped formations on the +surface of the moon are called _craters_. They are of all sizes, from a +mile to a hundred and fifty miles in diameter; and they are supposed to +be of volcanic origin. A high telescopic power shows that these craters +vary remarkably, not only in size, but also in structure and +arrangement. Some are considerably elevated above the surrounding +surface, others are basins hollowed out of that surface, and with low +surrounding ramparts; some are like walled plains, while the majority +have their lowest depression considerably below the surrounding surface; +some are isolated upon the plains, others are thickly crowded together, +overlapping and intruding upon each other; some have elevated peaks or +cones in their centres, and some are without these central cones, while +others, again, contain several minute craters instead; some have their +ramparts whole and perfect, others have them broken or deformed, and +many have them divided into terraces, especially on their inner sides. + +A typical lunar crater is shown in Fig. 136. + +[Illustration: Fig. 136.] + +It is not generally believed that any active volcanoes exist on the moon +at the present time, though some observers have thought they discerned +indications of such volcanoes. + +[Illustration: Fig. 137.] + +117. _Copernicus._--This is one of the grandest of lunar craters (Fig. +137). Although its diameter (forty-six miles) is exceeded by others, +yet, taken as a whole, it forms one of the most impressive and +interesting objects of its class. Its situation, near the centre of the +lunar disk, renders all its wonderful details conspicuous, as well as +those of objects immediately surrounding it. Its vast rampart rises to +upwards of twelve thousand feet above the level of the plateau, nearly +in the centre of which stands a magnificent group of cones, three of +which attain a height of more than twenty-four hundred feet. + +Many ridges, or spurs, may be observed leading away from the outer banks +of the great rampart. Around the crater, extending to a distance of more +than a hundred miles on every side, there is a complex network of bright +streaks, which diverge in all directions. These streaks do not appear in +the figure, nor are they seen upon the moon, except at and near the full +phase. They show conspicuously, however, by their united lustre on the +full moon. + +This crater is seen just to the south-west of the large dusky plain in +the upper part of Fig. 132. This plain is _Mare Imbrium_, and the +mountain-chain seen a little to the right of Copernicus is named the +_Apennines_. Copernicus is also seen in Fig. 135, a little to the left +of the same range. + +Under circumstances specially favorable, myriads of comparatively minute +but perfectly formed craters may be observed for more than seventy miles +on all sides around Copernicus. The district on the south-east side is +specially rich in these thickly scattered craters, which we have reason +to suppose stand over or upon the bright streaks. + +118. _Dark Chasms._--Dark cracks, or chasms, have been observed on +various parts of the moon's surface. They sometimes occur singly, and +sometimes in groups. They are often seen to radiate from some central +cone, and they appear to be of volcanic origin. They have been called +_canals_ and _rills_. + +[Illustration: Fig. 138.] + +One of the most remarkable groups of these chasms is that to the west of +the crater named _Triesneker_. The crater and the chasms are shown in +Fig. 138. Several of these great cracks obviously diverge from a small +crater near the west bank of the great one, and they subdivide as they +extend from the apparent point of divergence, while they are crossed by +others. These cracks, or chasms, are nearly a mile broad at the widest +part, and, after extending full a hundred miles, taper away till they +become invisible. + +[Illustration: Fig. 139.] + +119. _Mountain-Ranges._--There are comparatively few mountain-ranges on +the moon. The three most conspicuous are those which partially enclose +Mare Imbrium; namely, the _Apennines_ on the south, and the _Caucasus_ +and the _Alps_ on the east and north-east. The Apennines are the most +extended of these, having a length of about four hundred and fifty +miles. They rise gradually, from a comparatively level surface towards +the south-west, in the form of innumerable small elevations, which +increase in number and height towards the north-east, where they +culminate in a range of peaks whose altitude and rugged aspect must form +one of the most terribly grand and romantic scenes which imagination can +conceive. The north-east face of the range terminates abruptly in an +almost vertical precipice; while over the plain beneath, intensely black +spire-like shadows are cast, some of which at sunrise extend full ninety +miles, till they lose themselves in the general shading due to the +curvature of the lunar surface. Many of the peaks rise to heights of +from eighteen thousand to twenty thousand feet above the plain at their +north-east base (Fig. 139). + +[Illustration: Fig. 140.] + +Fig. 140 represents an ideal lunar landscape near the base of such a +lunar range. Owing to the absence of an atmosphere, the stars will be +visible in full daylight. + +[Illustration: Fig. 141.] + +120. _The Valley of the Alps._--The range of the _Alps_ is shown in Fig. +141. The great crater at the north end of this range is named _Plato_. +It is seventy miles in diameter. + +The most remarkable feature of the Alps is the valley near the centre of +the range. It is more than seventy-five miles long, and about six miles +wide at the broadest part. When examined under favorable circumstances, +with a high magnifying power, it is seen to be a vast flat-bottomed +valley, bordered by gigantic mountains, some of which attain heights of +ten thousand feet or more. + +[Illustration: Fig. 142.] + +121. _Isolated Peaks._--There are comparatively few isolated peaks to be +found on the surface of the moon. One of the most remarkable of these is +that known as _Pico_, and shown in Fig. 142. Its height exceeds eight +thousand feet, and it is about three times as long at the base as it is +broad. The summit is cleft into three peaks, as is shown by the +three-peaked shadow it casts on the plain. + +122. _Bright Rays._--About the time of full moon, with a telescope of +moderate power, a number of bright lines may be seen radiating from +several of the lunar craters, extending often to the distance of +hundreds of miles. These streaks do not arise from any perceptible +difference of level of the surface, they have no very definite outline, +and they do not present any sloping sides to catch more sunlight, and +thus shine brighter, than the general surface. Indeed, one great +peculiarity of them is, that they come out most forcibly when the sun is +shining perpendicularly upon them: hence they are best seen when the +moon is at full, and they are not visible at all at those regions upon +which the sun is rising or setting. They are not diverted by elevations +in their path, but traverse in their course craters, mountains, and +plains alike, giving a slight additional brightness to all objects over +which they pass, but producing no other effect upon them. "They look as +if, after the whole surface of the moon had assumed its final +configuration, a vast brush charged with a whitish pigment had been +drawn over the globe in straight lines, radiating from a central point, +leaving its trail upon every thing it touched, but obscuring nothing." + +[Illustration: Fig. 143.] + +The three most conspicuous craters from which these lines radiate are +_Tycho_, _Copernicus_, and _Kepler_. Tycho is seen at the bottom of +Figs. 143 and 130. Kepler is a little to the left of Copernicus in the +same figures. + +It has been thought that these bright streaks are chasms which have been +filled with molten lava, which, on cooling, would afford a smooth +reflecting surface on the top. + +123. _Tycho._--This crater is fifty-four miles in diameter, and about +sixteen thousand feet deep, from the highest ridge of the rampart to the +surface of the plateau, whence rises a central cone five thousand feet +high. It is one of the most conspicuous of all the lunar craters; not so +much on account of its dimensions as from its being the centre from +whence diverge those remarkable bright streaks, many of which may be +traced over a thousand miles of the moon's surface (Fig. 143). Tycho +appears to be an instance of a vast disruptive action which rent the +solid crust of the moon into radiating fissures, which were subsequently +filled with molten matter, whose superior luminosity marks the course of +the cracks in all directions from the crater as their common centre. So +numerous are these bright streaks when examined by the aid of the +telescope, and they give to this region of the moon's surface such +increased luminosity, that, when viewed as a whole, the locality can be +distinctly seen at full moon by the unassisted eye, as a bright patch of +light on the southern portion of the disk. + + + III. INFERIOR AND SUPERIOR PLANETS. + + + Inferior Planets. + + +124. _The Inferior Planets._--The _inferior planets_ are those which lie +between the earth and the sun, and whose orbits are included by that of +the earth. They are _Mercury_ and _Venus_. + +[Illustration: Fig. 144.] + +125. _Aspects of an Inferior Planet._--The four chief _aspects_ of an +inferior planet as seen from the earth are shown in Fig. 144, in which +_S_ represents the sun, _P_ the planet, and _E_ the earth. + +When the planet is between the earth and the sun, as at _P_, it is said +to be in _inferior conjunction_. + +When it is in the same direction as the sun, but beyond it, as at _P''_, +it is said to be in _superior conjunction_. + +When the planet is at such a point in its orbit that a line drawn from +the earth to it would be tangent to the orbit, as at _P'_ and _P'''_, it +is said to be at its _greatest elongation_. + +[Illustration: Fig. 145.] + +126. _Apparent Motion of an Inferior Planet._--When the planet is at +_P_, if it could be seen at all, it would appear in the heavens at _A_. +As it moves from _P_ to _P'_, it will appear to move in the heavens from +_A_ to _B_. Then, as it moves from _P'_ to _P''_, it will appear to move +back again from _B_ to _A_. While it moves from _P''_ to _P'''_, it will +appear to move from _A_ to _C_; and, while moving from _P'''_ to _P_, it +will appear to move back again from _C_ to _A_. Thus the planet will +appear to oscillate to and fro across the sun from _B_ to _C_, never +getting farther from the sun than _B_ on the west, or _C_ on the east: +hence, when at these points, it is said to be at its _greatest western_ +and _eastern elongations_. This oscillating motion of an inferior planet +across the sun, combined with the sun's motion among the stars, causes +the planet to describe a path among the stars similar to that shown in +Fig. 145. + +[Illustration: Fig. 146.] + +127. _Phases of an Inferior Planet._--An inferior planet, when viewed +with a telescope, is found to present a succession of phases similar to +those of the moon. The reason of this is evident from Fig. 146. As an +inferior planet passes around the sun, it presents sometimes more and +sometimes less of its bright hemisphere to the earth. When the earth is +at _T_, and Venus at superior conjunction, the planet turns the whole of +its bright hemisphere towards the earth, and appears _full_; it then +becomes _gibbous_, _half_, and _crescent_. When it comes into _inferior +conjunction_, it turns its dark hemisphere towards the earth: it then +becomes _crescent_, _half_, _gibbous_, and _full_ again. + +128. _The Sidereal and Synodical Periods of an Inferior Planet._--The +time it takes a planet to make a complete revolution around the sun is +called the _sidereal period_ of the planet; and the time it takes it to +pass from one aspect around to the same aspect again, its _synodical +period_. + +[Illustration: Fig. 147.] + +The synodical period of an inferior planet is longer than its sidereal +period. This will be evident from an examination of Fig. 147. _S_ is the +position of the sun, _E_ that of the earth, and _P_ that of the planet +at inferior conjunction. Before the planet can be in inferior +conjunction again, it must pass entirely around its orbit, and overtake +the earth, which has in the mean time passed on in its orbit to _E'_. + +While the earth is passing from _E_ to _E'_, the planet passes entirely +around its orbit, and from _P_ to _P'_ in addition. Now the arc _PP'_ is +just equal to the arc _EE'_: hence the planet has to pass over the same +arc that the earth does, and 360° more. In other words, the planet has +to gain 360° on the earth. + +The synodical period of the planet is found by direct observation. + + 129. _The Length of the Sidereal Period._--The length of the + sidereal period of an inferior planet may be found by the following + computation:-- + + Let _a_ denote the synodical period of the planet, + Let _b_ denote the sidereal period of the earth, + Let _x_ denote the sidereal period of the planet. + Then _360°/b_ = the daily motion of the earth, + And _360°/x_ = the daily motion of the planet, + And _360°/x - 360°/b_ = the daily gain of the planet: + Also _360°/a_ = the daily gain of the planet: + Hence _360°/x - 360°/b = 360°/a_. + Dividing by 360°, we have _1/x - 1/b = 1/a_; + Clearing of fractions, we have _ab - ax = bx_: + Transposing and collecting, we have _(a + b)x = ab_: + + Therefore _x = ab/a+b_. + + 130. _The Relative Distance of an Inferior Planet._--By the + _relative distance_ of a planet, we mean its distance from the sun + compared with the earth's distance from the sun. The relative + distance of an inferior planet may be found by the following + method:-- + +[Illustration: Fig. 148.] + + Let _V_, in Fig. 148, represent the position of Venus at its + greatest elongation from the sun, _S_ the position of the sun, and + _E_ that of the earth. The line _EV_ will evidently be tangent to a + circle described about the sun with a radius equal to the distance + of Venus from the sun at the time of this greatest elongation. Draw + the radius _SV_ and the line _SE_. Since _SV_ is a radius, the angle + at _V_ is a right angle. The angle at _E_ is known by measurement, + and the angle at _S_ is equal to 90°- the angle _E_. In the + right-angled triangle _EVS_, we then know the three angles, and we + wish to find the ratio of the side _SV_ to the side _SE_. + + The ratio of these lines may be found by trigonometrical computation + as follows:-- + + _VS : ES = sin SEV : 1._ + + Substitute the value of the sine of SEV, and we have + + _VS : ES = .723 : 1._ + + Hence the relative distances of Venus and of the earth from the sun + are .723 and 1. + + + Superior Planets. + + +131. _The Superior Planets._--The _superior planets_ are those which lie +beyond the earth. They are _Mars_, the _Asteroids_, _Jupiter_, _Saturn_, +_Uranus_, and _Neptune_. + +[Illustration: Fig. 149.] + +132. _Apparent Motion of a Superior Planet._--In order to deduce the +apparent motion of a superior planet from the real motions of the earth +and planet, let _S_ (Fig. 149) be the place of the sun; 1, 2, 3, etc., +the orbit of the earth; _a_, _b_, _c_, etc., the orbit of Mars; and +_CGL_ a part of the starry firmament. Let the orbit of the earth be +divided into twelve equal parts, each described in one month; and let +_ab_, _bc_, _cd_, etc., be the spaces described by Mars in the same +time. Suppose the earth to be at the point 1 when Mars is at the point +_a_, Mars will then appear in the heavens in the direction of 1 _a_. +When the earth is at 3, and Mars at _c_, he will appear in the heavens +at _C_. When the earth arrives at 4, Mars will arrive at _d_, and will +appear in the heavens at _D_. While the earth moves from 4 to 5 and from +5 to 6, Mars will appear to have advanced among the stars from _D_ to +_E_ and from _E_ to _F_, in the direction from west to east. During the +motion of the earth from 6 to 7 and from 7 to 8, Mars will appear to go +backward from _F_ to _G_ and from _G_ to _H_, in the direction from east +to west. During the motion of the earth from 8 to 9 and from 9 to 10, +Mars will appear to advance from _H_ to _I_ and from _I_ to _K_, in the +direction from west to east, and the motion will continue in the same +direction until near the succeeding opposition. + +The apparent motion of a superior planet projected on the heavens is +thus seen to be similar to that of an inferior planet, except that, in +the latter case, the retrogression takes place near inferior +conjunction, and in the former it takes place near opposition. + +[Illustration: Fig. 150.] + +133. _Aspects of a Superior Planet._--The four aspects of a superior +planet are shown in Fig. 150, in which _S_ is the position of the sun, +_E_ that of the earth, and _P_ that of the planet. + +When the planet is on the opposite side of the earth to the sun, as at +_P_, it is said to be in _opposition_. The sun and the planet will then +appear in opposite parts of the heavens, the sun appearing at _C_, and +the planet at _A_. + +When the planet is on the opposite side of the sun to the earth, as at +_P''_, it is said to be in _superior conjunction_. It will then appear +in the same part of the heavens as the sun, both appearing at _C_. + +When the planet is at _P'_ and _P'''_, so that a line drawn from the +earth through the planet will make a right angle with a line drawn from +the earth to the sun, it is said to be in _quadrature_. At _P'_ it is in +its western quadrature, and at _P'''_ in its eastern quadrature. + +[Illustration: Fig. 151.] + +134. _Phases of a Superior Planet._--Mars is the only one of the +superior planets that has appreciable phases. At quadrature, as will +appear from Fig. 151, Mars does not present quite the same side to the +earth as to the sun: hence, near these parts of its orbit, the planet +appears slightly gibbous. Elsewhere in its orbit, the planet appears +full. + +All the other superior planets are so far away from the sun and earth, +that the sides which they turn towards the sun and the earth in every +part of their orbit are so nearly the same, that no change in the form +of their disks can be detected. + +135. _The Synodical Period of a Superior Planet._--During a synodical +period of a superior planet the earth must gain one revolution, or 360°, +on the planet, as will be evident from an examination of Fig. 152, in +which _S_ represents the sun, _E_ the earth, and _P_ the planet at +opposition. Before the planet can be in opposition again, the earth must +make a complete revolution, and overtake the planet, which has in the +mean time passed on from _P_ to _P'_. + +[Illustration: Fig. 152.] + +In the case of most of the superior planets the synodical period is +shorter than the sidereal period; but in the case of Mars it is longer, +since Mars makes more than a complete revolution before the earth +overtakes it. + +The synodical period of a superior planet is found by direct +observation. + + 136. _The Sidereal Period of a Superior Planet._--The sidereal + period of a superior planet is found by a method of computation + similar to that for finding the sidereal period of an inferior + planet:-- + + Let _a_ denote the synodical period of the planet, + Let _b_ denote the sidereal period of the earth, + Let _x_ denote the sidereal period of the planet. + Then will _360°/b_ = daily motion of the earth, + And _360°/x_ = daily motion of the planet; + Also _360°/b - 360°/x_ = daily gain of the earth. + But _360°/a_ = daily gain of the earth: + Hence _360°/b - 360°/x = 360°/a_ + + _1/b - 1/x = 1/a_ + + _ax - ab = bx_ + + _(a-b)x = ab_ + + _x = ab/(a-b)_. + +[Illustration: Fig. 153.] + + 137. _The Relative Distance of a Superior Planet._--Let _S_, _e_, + and _m_, in Fig. 153, represent the relative positions of the sun, + the earth, and Mars, when the latter planet is in opposition. Let + _E_ and _M_ represent the relative positions of the earth and Mars + the day after opposition. At the first observation Mars will be seen + in the direction _emA_, and at the second observation in the + direction _EMA_. + + But the fixed stars are so distant, that if a line, _eA_, were drawn + to a fixed star at the first observation, and a line, _EB_, drawn + from the earth to the same fixed star at the second observation, + these two lines would be sensibly parallel; that is, the fixed star + would be seen in the direction of the line _eA_ at the first + observation, and in the direction of the line _EB_, parallel to + _eA_, at the second observation. But if Mars were seen in the + direction of the fixed star at the first observation, it would + appear back, or west, of that star at the second observation by the + angular distance _BEA_; that is, the planet would have retrograded + that angular distance. Now, this retrogression of Mars during one + day, at the time of opposition, can be measured directly by + observation. This measurement gives us the value of the angle _BEA_; + but we know the rate at which both the earth and Mars are moving in + their orbits, and from this we can easily find the angular distance + passed over by each in one day. This gives us the angles _ESA_ and + _MSA_. We can now find the relative length of the lines _MS_ and + _ES_ (which represent the distances of Mars and of the earth from + the sun), both by construction and by trigonometrical computation. + + Since _EB_ and _eA_ are parallel, the angle _EAS_ is equal to _BEA_. + + _SEA = 180° - (ESA + EAS)_ + _ESM = ESA - MSA_ + _EMS = 180° - (SEA + ESM)_. + + We have then + + _MS : ES = sin SEA : sin EMS._ + + Substituting the values of the sines, and reducing the ratio to its + lowest terms, we have + + _MS : ES = 1.524 : 1._ + + Thus we find that the relative distances of Mars and the earth from + the sun are 1.524 and 1. By the simple observation of its greatest + elongation, we are able to determine the relative distances of an + inferior planet and the earth from the sun; and, by the equally + simple observation of the daily retrogression of a superior planet, + we can find the relative distances of such a planet and the earth + from the sun. + + + IV. THE SUN. + + + I. MAGNITUDE AND DISTANCE OF THE SUN. + + +[Illustration: Fig. 154.] + +138. _The Volume of the Sun._--The apparent diameter of the sun is about +32', being a little greater than that of the moon. The real diameter of +the sun is 866,400 miles, or about a hundred and nine times that of the +earth. + +As the diameter of the moon's orbit is only about 480,000 miles, or some +sixty times the diameter of the earth, it follows that the diameter of +the sun is nearly double that of the moon's orbit: hence, were the +centre of the sun placed at the centre of the earth, the sun would +completely fill the moon's orbit, and reach nearly as far beyond it in +every direction as it is from the earth to the moon. The circumference +of the sun as compared with the moon's orbit is shown in Fig. 154. + +The volume of the sun is 1,305,000 times that of the earth. + +139. _The Mass of the Sun._--The sun is much less dense than the earth. +The mass of the sun is only 330,000 times that of the earth, and its +density only about a fourth that of the earth. + + To find the mass of the sun, we first ascertain the distance the + earth would draw the moon towards itself in a given time, were the + moon at the distance of the sun, and then form the proportion: as + the distance the earth would draw the moon towards itself is to the + distance that the sun draws the earth towards itself in the same + time, so is the mass of the earth to the mass of the sun. + +Although the mass of the sun is over three hundred thousand times that +of the earth, the pull of gravity at the surface of the sun is only +about twenty-eight times as great as at the surface of the earth. This +is because the distance from the surface of the sun to its centre is +much greater than from the surface to the centre of the earth. + +[Illustration: Fig. 155.] + +140. _Size of the Sun Compared with that of the Planets._--The size of +the sun compared with that of the larger planets is shown in Fig. 155. +The mass of the sun is more than seven hundred and fifty times that of +all of the planets and moons in the solar system. In Fig. 156 is shown +the apparent size of the sun as seen from the different planets. The +apparent diameter of the sun decreases as the distance from it +increases, and the disk of the sun decreases as the square of the +distance from it increases. + +[Illustration: Fig. 156.] + +141. _The Distance of the Sun._--The mean distance of the sun from the +earth is about 92,800,000 miles. Owing to the eccentricity of the +earth's orbit, the distance of the sun varies somewhat; being about +3,000,000 miles less in January, when the earth is at perihelion, than +in June, when the earth is at aphelion. + + "But, though the distance of the sun can easily be stated in + figures, it is not possible to give any real idea of a space so + enormous: it is quite beyond our power of conception. If one were to + try to walk such a distance, supposing that he could walk four miles + an hour, and keep it up for ten hours every day, it would take + sixty-eight years and a half to make a single million of miles, and + more than sixty-three hundred years to traverse the whole. + + "If some celestial railway could be imagined, the journey to the + sun, even if our trains ran sixty miles an hour day and night and + without a stop, would require over a hundred and seventy-five years. + Sensation, even, would not travel so far in a human lifetime. To + borrow the curious illustration of Professor Mendenhall, if we could + imagine an infant with an arm long enough to enable him to touch the + sun and burn himself, he would die of old age before the pain could + reach him; since, according to the experiments of Helmholtz and + others, a nervous shock is communicated only at the rate of about a + hundred feet per second, or 1,637 miles a day, and would need more + than a hundred and fifty years to make the journey. Sound would do + it in about fourteen years, if it could be transmitted through + celestial space; and a cannon-ball in about nine, if it were to move + uniformly with the same speed as when it left the muzzle of the gun. + If the earth could be suddenly stopped in her orbit, and allowed to + fall unobstructed toward the sun, under the accelerating influence + of his attraction, she would reach the centre in about four months. + I have said if she could be stopped; but such is the compass of her + orbit, that, to make its circuit in a year, she has to move nearly + nineteen miles a second, or more than fifty times faster than the + swiftest rifle-ball; and, in moving twenty miles, her path deviates + from perfect straightness by less than an eighth of an inch. And + yet, over all the circumference of this tremendous orbit, the sun + exercises his dominion, and every pulsation of his surface receives + its response from the subject earth." (Professor C. A. Young: The + Sun.) + + 142. _Method of Finding the Sun's Distance._--There are several + methods of finding the sun's distance. The simplest method is that + of finding the actual distance of one of the nearer planets by + observing its displacement in the sky as seen from widely separated + points on the earth. As the _relative_ distances of the planets from + each other and from the sun are well known, we can easily deduce the + actual distance of the sun if we can find that of any of the + planets. The two planets usually chosen for this method are Mars and + Venus. + + (1) The displacement of Mars in the sky, as seen from two + observatories which differ considerably in latitude, is, of course, + greatest when Mars is nearest the earth. Now, it is evident than + Mars will be nearer the earth when in opposition than when in any + other part of its orbit; and the planet will be least distant from + the earth when it is at its perihelion point, and the earth is at + its aphelion point, at the time of opposition. This method, then, + can be used to the best advantage, when, at the time of opposition, + Mars is near its perihelion, and the earth near its aphelion. These + favorable oppositions occur about once in fifteen years, and the + last one was in 1877. + +[Illustration: Fig. 157.] + + Suppose two observers situated at _N'_ and _S'_ (Fig. 157), near the + poles of the earth. The one at _N'_ would see Mars in the sky at + _N_, and the one at _S'_ would see it at _S_. The displacement would + be the angle _NMS_. Each observer measures carefully the distance of + Mars from the same fixed star near it. The difference of these + distances gives the displacement of the planet, or the angle _NMS_. + These observations were made with the greatest care in 1877. + + (2) Venus is nearest the earth at the time of inferior conjunction; + but it can then be seen only in the daytime. It is, therefore, + impossible to ascertain the displacement of Venus, as seen from + different stations, by comparing her distances from a fixed star. + Occasionally, at the time of inferior conjunction, Venus passes + directly across the sun's disk. The last of these _transits_ of + Venus occurred in 1874, and the next will occur in 1882. It will + then be over a hundred years before another will occur. + +[Illustration: Fig. 158.] + + Suppose two observers, _A_ and _B_ (Fig. 158), near the poles of the + earth at the time of a transit of Venus. The observer at _A_ would + see Venus crossing the sun at _V_{2}_, and the one at _B_ would see + it crossing at _V_{1}_. Any observation made upon Venus, which would + give the distance and direction of Venus from the centre of the sun, + as seen from each station, would enable us to calculate the angular + distance between the two chords described across the sun. This, of + course, would give the displacement of Venus on the sun's disk. This + method was first employed at the last transits of Venus which + occurred before 1874; namely, those of 1761 and 1769. + + There are three methods of observation employed to ascertain the + apparent direction and distance of Venus from the centre of the sun, + called respectively the _contact method_, the _micrometric method_, + and the _photographic method_. + + (_a_) In the _contact_ method, the observation consists in noting + the exact time when Venus crosses the sun's limb. To ascertain this + it is necessary to observe the exact time of external and internal + contact. This observation, though apparently simple, is really very + difficult. With reference to this method Professor Young says,-- + + "The difficulties depend in part upon the imperfections of optical + instruments and the human eye, partly upon the essential nature of + light leading to what is known as diffraction, and partly upon the + action of the planet's atmosphere. The two first-named causes + produce what is called irradiation, and operate to make the apparent + diameter of the planet, as seen on the solar disk, smaller than it + really is; smaller, too, by an amount which varies with the size of + the telescope, the perfection of its lenses, and the tint and + brightness of the sun's image. The edge of the planet's image is + also rendered slightly hazy and indistinct. + +[Illustration: Fig. 159.] + + "The planet's atmosphere also causes its disk to be surrounded by a + narrow ring of light, which becomes visible long before the planet + touches the sun, and, at the moment of internal contact, produces an + appearance, of which the accompanying figure is intended to give an + idea, though on an exaggerated scale. The planet moves so slowly as + to occupy more than twenty minutes in crossing the sun's limb; so + that even if the planet's edge were perfectly sharp and definite, + and the sun's limb undistorted, it would be very difficult to + determine the precise second at which contact occurs. But, as things + are, observers with precisely similar telescopes, and side by side, + often differ from each other five or six seconds; and, where the + telescopes are not similar, the differences and uncertainties are + much greater.... Astronomers, therefore, at present are pretty much + agreed that such observations can be of little value in removing the + remaining uncertainty of the parallax, and are disposed to put more + reliance upon the micrometric and photographic methods, which are + free from these peculiar difficulties, though, of course, beset with + others, which, however, it is hoped will prove less formidable." + + (_b_) Of the _micrometric_ method, as employed at the last transit, + Professor Young speaks as follows:-- + + "The micrometric method requires the use of a heliometer,--an + instrument common only in Germany, and requiring much skill and + practice in its use in order to obtain with it accurate measures. At + the late transit, a single English party, two or three of the + Russian parties, and all five of the German, were equipped with + these instruments; and at some of the stations extensive series of + measures were made. None of the results, however, have appeared as + yet; so that it is impossible to say how greatly, if at all, this + method will have the advantage in precision over the contact + observations." + + (_c_) The following observations, with reference to the + _photographic_ method, are also taken from Professor Young:-- + + "The Americans and French placed their main reliance upon the + photographic method, while the English and Germans also provided for + its use to a certain extent. The great advantage of this method is, + that it makes it possible to perform the necessary measurements + (upon whose accuracy every thing depends) at leisure after the + transit, without hurry, and with all possible precautions. The + field-work consists merely in obtaining as many and as good pictures + as possible. A principal objection to the method lies in the + difficulty of obtaining good pictures, i.e., pictures free from + distortion, and so distinct and sharp as to bear high magnifying + power in the microscopic apparatus used for their measurement. The + most serious difficulty, however, is involved in the accurate + determination of the scale of the picture; that is, of the number of + seconds of arc corresponding to a linear inch upon the plate. + Besides this, we must know the exact Greenwich time at which each + picture is taken, and it is also extremely desirable that the + _orientation_ of the picture should be accurately determined; that + is, the north and south, the east and west points of the solar image + on the finished plate. There has been a good deal of anxiety lest + the image, however accurate and sharp when first produced, should + alter, in course of time, through the contraction of the collodion + film on the glass plate; but the experiments of Rutherfurd, Huggins, + and Paschen, seem to show that this danger is imaginary.... The + Americans placed the photographic telescope exactly in line with a + meridian instrument, and so determined, with the extremest + precision, the direction in which it was pointed. Knowing this and + the time at which any picture was taken, it becomes possible, with + the help of the plumb-line image, to determine precisely the + orientation of the picture,--an advantage possessed by the American + pictures alone, and making their value nearly twice as great as + otherwise it would have been. + + "The figure below is a representation of one of the American + photographs reduced about one-half. _V_ is the image of Venus, + which, on the actual plate, is about a seventh of an inch in + diameter; _aa'_ is the image of the plumb-line. The centre of the + reticle is marked with a cross." + +[Illustration: Fig. 160.] + + The English photographs proved to be of little value, and the + results of the measurements and calculations upon the American + pictures have not yet been published. There is a growing + apprehension that no photographic method can be relied upon. + +The most recent determinations by various methods indicate that the +sun's distance is such that his parallax is about eighty-eight seconds. +This would make the linear value of a second at the surface of the sun +about four hundred and fifty miles. + +[Illustration: Plate 1.] + + + II. PHYSICAL AND CHEMICAL CONDITION OF THE SUN. + + + Physical Condition of the Sun. + + +143. _The Sun Composed mainly of Gas._--It is now generally believed +that the sun is mainly a ball of gas, or vapor, powerfully condensed at +the centre by the weight of the superincumbent mass, but kept from +liquefying by its exceedingly high temperature. + +The gaseous interior of the sun is surrounded by a layer of luminous +clouds, which constitutes its visible surface, and which is called its +_photosphere_. Here and there in the photosphere are seen dark _spots_, +which often attain an immense magnitude. + +These clouds float in the _solar atmosphere_, which extends some +distance beyond them. + +The luminous surface of the sun is surrounded by a _rose-colored_ +stratum of gaseous matter, called the _chromosphere_. Here and there +great masses of this chromospheric matter rise high above the general +level. These masses are called _prominences_. + +Outside of the chromosphere is the _corona_, an irregular halo of faint, +pearly light, mainly composed of filaments and streamers, which radiate +from the sun to enormous distances, often more than a million of miles. + +In Fig. 161 is shown a section of the sun, according to Professor Young. + +The accompanying lithographic plate gives a general view of the +photosphere with its spots, and of the chromosphere and its prominences. + +144. _The Temperature of the Sun._--Those who have investigated the +subject of the temperature of the sun have come to very different +conclusions; some placing it as high as four million degrees Fahrenheit, +and others as low as ten thousand degrees. Professor Young thinks that +Rosetti's estimate of eighteen thousand degrees as the _effective +temperature_ of the sun's surface is probably not far from correct. By +this is meant the temperature that a uniform surface of lampblack of the +size of the sun must have in order to radiate as much heat as the sun +does. The most intense artificial heat does not exceed four thousand +degrees Fahrenheit. + +[Illustration: Fig. 161.] + +145. _The Amount of Heat Radiated by the Sun._--A unit of heat is the +amount of heat required to raise a pound of water one degree in +temperature. It takes about a hundred and forty-three units of heat to +melt a pound of ice without changing its temperature. A cubic foot of +ice weighs about fifty-seven pounds. According to Sir William Herschel, +were all the heat radiated by the sun concentrated on a cylinder of ice +forty-five miles in diameter, it would melt it off at the rate of about +a hundred and ninety thousand miles a second. + +Professor Young gives the following illustration of the energy of solar +radiation: "If we could build up a solid column of ice from the earth to +the sun, two miles and a quarter in diameter, spanning the inconceivable +abyss of ninety-three million miles, and if then the sun should +concentrate his power upon it, it would dissolve and melt, not in an +hour, nor a minute, but in a single second. One swing of the pendulum, +and it would be water; seven more, and it would be dissipated in vapor." + +[Illustration: Fig. 162.] + +This heat would be sufficient to melt a layer of ice nearly fifty feet +thick all around the sun in a minute. To develop this heat would require +the hourly consumption of a layer of anthracite coal, more than sixteen +feet thick, over the entire surface of the sun; and the _mechanical +equivalent_ of this heat is about ten thousand horse-power on every +square foot of the sun's surface. + +146. _The Brightness of the Sun's Surface._--The sun's surface is a +hundred and ninety thousand times as bright as a candle-flame, a hundred +and forty-six times as bright as the calcium-light, and about three +times and a half as bright as the voltaic arc. + +The sun's disk is much less bright near the margin than near the centre, +a point on the limb of the sun being only about a fourth as bright as +one near the centre of the disk. This diminution of brightness towards +the margin of the disk is due to the increase in the absorption of the +solar atmosphere as we pass from the centre towards the margin of the +sun's disk; and this increased absorption is due to the fact, that the +rays which reach us from near the margin have to traverse a much greater +thickness of the solar atmosphere than those which reach us from the +centre of the disk. This will be evident from Fig. 162, in which the +arrows mark the paths of rays from different parts of the solar disk. + + + The Spectroscope. + + +[Illustration: Fig. 163.] + +147. _The Spectroscope as an Astronomical Instrument._--The +_spectroscope_ is now continually employed in the study of the physical +condition and chemical constitution of the sun and of the other heavenly +bodies. It has become almost as indispensable to the astronomer as the +telescope. + +148. _The Dispersion Spectroscope._--The essential parts of the +_dispersion_ spectroscope are shown in Fig. 163. These are the +_collimator tube_, the _prism_, and the _telescope_. The collimator tube +has a narrow slit at one end, through which the light to be examined is +admitted, and somewhere within the tube a lens for condensing the light. +The light is dispersed on passing through the prism: it then passes +through the objective of the telescope, and forms within the tube an +image of the spectrum, which is examined by means of the eye-piece. The +power of the spectroscope is increased by increasing the number of +prisms, which are arranged so that the light shall pass through one +after another in succession. Such an arrangement of prisms is shown in +Fig. 164. One end of the collimator tube is seen at the left, and one +end of the telescope at the right. Sometimes the prisms are made long, +and the light is sent twice through the same train of prisms, once +through the lower, and once through the upper, half of the prisms. This +is accomplished by placing a rectangular prism against the last prism of +the train, as shown in Fig. 165. + +[Illustration: Fig. 164.] + +[Illustration: Fig. 165.] + +149. _The Micrometer Scale._--Various devices are employed to obtain an +image of a micrometer scale in the tube of the telescope beside that of +the spectrum. + +[Illustration: Fig. 166.] + +One of the simplest of these methods is shown in Fig. 166. _A_ is the +telescope, _B_ the collimator, and _C_ the micrometer tube. The opening +at the outer end of _C_ contains a piece of glass which has a micrometer +scale marked upon it. The light from the candle shines through this +glass, falls upon the surface of the prism _P_, and is thence reflected +into the telescope, where it forms an enlarged image of the micrometer +scale alongside the image of the spectrum. + +[Illustration: Fig. 167.] + +150. _The Comparison of Spectra._--In order to compare two spectra, it +is desirable to be able to see them side by side in the telescope. The +images of two spectra may be obtained side by side in the telescope tube +by the use of a little rectangular prism, which covers one-half of the +slit of the collimator tube, as shown in Fig. 167. The light from one +source is admitted directly through the uncovered half of the slit, +while the light from the other source is sent through the covered +portion of the slit by reflection from the surface of the rectangular +prism. This arrangement and its action will be readily understood from +Fig. 167. + +[Illustration: Fig. 168.] + +151. _Direct-Vision Spectroscope._--A beam of light may be dispersed, +without any ultimate deflection from its course, by combining prisms of +crown and flint glass with equal refractive, but unequal dispersive +powers. Such a combination of prisms is called a _direct-vision_ +combination. One of three prisms is shown in Fig. 168, and one of five +prisms in Fig. 169. + +[Illustration: Fig. 169.] + +[Illustration: Fig. 170.] + +A _direct-vision spectroscope_ (Fig. 170) is one in which a +direct-vision combination of prisms is employed. _C_ is the collimator +tube, _P_ the train of prisms, _F_ the telescope, and _r_ the comparison +prism. + +[Illustration: Fig. 171.] + +152. _The Telespectroscope._--The spectroscope, when used for +astronomical work, is usually combined with a telescope. The compound +instrument is called a _telespectroscope_. The spectroscope is mounted +at the end of the telescope in such a way that the image formed by the +object-glass of the telescope falls upon the slit at the end of the +collimator tube. A telespectroscope of small dispersive power is shown +in Fig. 171; _a_ being the object-glass of the telescope, _cc_ the tube +of the telescope, and _e_ the comparison prism at the end of the +collimator tube. A more powerful instrument is shown in Fig. 172. _A_ is +the telescope, _C_ the collimator tube of the spectroscope, _P_ the +train of prisms, and _E_ the telescope tube. Fig. 173 shows a still more +powerful spectroscope attached to the great Newall refractor (18). + +[Illustration: Fig. 172.] + +[Illustration: Fig. 173.] + +153. _The Diffraction Spectroscope._--A _diffraction_ spectroscope is +one in which the spectrum is produced by reflection of the light from a +finely ruled surface, or _grating_, as it is called, instead of by +dispersion in passing through a prism. The essential parts of this +instrument are shown in Fig 174. This spectroscope may be attached to +the telescope in the same manner as the dispersion spectroscope. When +the spectroscope is thus used, the eye-piece of the telescope is +removed. + +[Illustration: Fig. 174.] + + + Spectra. + + +154. _Continuous Spectra._--Light from an incandescent solid or liquid +which has suffered no absorption in the medium which it has traversed +gives a spectrum consisting of a continuous colored band, in which the +colors, from the red to the violet, pass gradually and imperceptibly +into one another. The spectrum is entirely free from either light or +dark lines, and is called a _continuous spectrum_. + +155. _Bright-Lined Spectra._--Light from a luminous gas or vapor gives a +spectrum composed of bright lines separated by dark spaces, and known as +a _bright-lined spectrum_. It has been found that the lines in the +spectrum of a substance in the state of a gas or vapor are the most +characteristic thing about the substance, since no two vapors give +exactly the same lines: hence, when we have once become acquainted with +the bright-lined spectrum of any substance, we can ever after recognize +that substance by the spectrum of its luminous vapor. Even when several +substances are mixed, they may all be recognized by the bright-lined +spectrum of the mixture, since the lines of all the substances will be +present in the spectrum of the mixture. This method of identifying +substances by their spectra is called _spectrum analysis_. + +The bright-lined spectra of several substances are given in the +frontispiece. The number of lines in the spectra of the elements varies +greatly. The spectrum of sodium is one of the simplest, while that of +iron is one of the most complex. The latter contains over six hundred +lines. Though no two vapors give identical spectra, there are many cases +in which one or more of the spectral lines of one element coincide in +position with lines of other elements. + + 156. _Methods of rendering Gases and Vapors Luminous._--In order to + study the spectra of vapors and gases it is necessary to have some + means of converting solids and liquids into vapor, and also of + rendering the vapors and gases luminous. There are four methods of + obtaining luminous vapors and gases in common use. + +[Illustration: Fig. 175.] + +(1) _By means of the Bunsen Flame._--This is a very hot but an almost +non-luminous flame. If any readily volatilized substance, such as the +compounds of sodium, calcium, strontium, etc., is introduced into this +flame on a fine platinum wire, it is volatilized in the flame, and its +vapor is rendered luminous, giving the flame its own peculiar color. The +flame thus colored may be examined by the spectroscope. The arrangement +of the flame is shown in Fig. 175. + +[Illustration: Fig. 176.] + +(2) _By means of the Voltaic Arc._--An electric lamp is shown in Fig. +176. When this lamp is to be used for obtaining luminous vapors, the +lower carbon is made larger than the upper one, and hollowed out at the +top into a little cup. The substance to be volatilized is placed in this +cup, and the current is allowed to pass. The heat of the voltaic arc is +much more intense than that of the Bunsen flame: hence substances that +cannot be volatilized in the flame are readily volatilized in the arc, +and the vapor formed is raised to a very high temperature. + +(3) _By means of the Spark from an Induction Coil._--The arrangement of +the coil for obtaining luminous vapors is shown in Fig. 177. + +[Illustration: Fig. 177.] + +The terminals of the coil between which the spark is to pass are brought +quite close together. When we wish to vaporize any metal, as iron, the +terminals are made of iron. On the passage of the spark, a little of the +iron at the ends of the terminals is evaporated; and the vapor is +rendered luminous in the space traversed by the spark. A condenser is +usually placed in the circuit. With the coil, the temperature may be +varied at pleasure; and the vapor may be raised even to a higher +temperature than with the electric lamp. To obtain a low temperature, +the coil is used without the condenser. By using a larger and larger +condenser, the temperature may be raised higher and higher. + +By means of the induction coil we may also heat gases to incandescence. +It is only necessary to allow the spark to pass through a space filled +with the gas. + +[Illustration: Fig. 178.] + +(4) _By means of a Vacuum Tube._--The form of the vacuum tube commonly +used for this purpose is shown in Fig. 178. The gas to be examined, and +which is contained in the tube, has very slight density: but upon the +passage of the discharge from an induction coil or a Holtz machine, +through the tube, the gas in the capillary part of the tube becomes +heated to a high temperature, and is then quite brilliant. + +157. _Reversed Spectra._--If the light from an incandescent cylinder of +lime, or from the incandescent point of an electric lamp, is allowed to +pass through luminous sodium vapor, and is then examined with a +spectroscope, the spectrum will be found to be a bright spectrum crossed +by a single _dark_ line in the position of the yellow line of the sodium +vapor. The spectrum of sodium vapor is _reversed_, its bright lines +becoming dark and its dark spaces bright. With a spectroscope of any +considerable power, the yellow line of sodium vapor is resolved into a +double line. With a spectroscope of the same power, the dark sodium line +of the reversed spectrum is seen to be a double line. + +It is found to be generally true, that the spectrum of the light from an +incandescent solid or liquid which has passed _through a luminous vapor_ +on its way to the spectroscope is made up of a bright ground crossed by +dark lines; there being a dark line for every bright line that the vapor +alone would give. + +158. _Explanation of Reversed Spectra._--It has been found that gases +absorb and quench rays of the same degree of refrangibility as those +which they themselves emit, and no others. When a solid is shining +through a luminous vapor, this absorbs and quenches those rays from the +solid which have the same degrees of refrangibility as those which it is +itself emitting: hence the lines of the spectrum receive light from the +vapor alone, while the spaces between the lines receive light from the +solid. Now, solids and liquids, when heated to incandescence, give a +very much brighter light than vapors and gases at the same temperature: +hence the lines of a reversed spectrum, though receiving light from the +vapor or gas, appear dark by contrast. + +159. _Effect of Increasing the Power of the Spectroscope upon the +Brilliancy of a Spectrum._--An increase in the power of a spectroscope +diminishes the brilliancy of a _continuous_ spectrum, since it makes the +colored band longer, and therefore spreads the light out over a greater +extent of surface; but, in the case of a _bright-lined_ spectrum, an +increase of power in the spectroscope produces scarcely any alteration +in the brilliancy of the lines, since it merely separates the lines +farther without making the lines themselves any wider. In the case of a +_reversed_ spectrum, an increase of power in the spectroscope dilutes +the light in the spaces between the lines without diluting that of the +lines: hence lines which appear dark in a spectroscope of slight +dispersive power may appear bright in an instrument of great dispersive +power. + +160. _Change of the Spectrum with the Density of the Luminous +Vapor._--It has been found, that, as the density of a luminous vapor is +diminished, the lines in its spectrum become fewer and fewer, till they +are finally reduced to one. On the other hand, an increase of density +causes new lines to appear in the spectrum, and the old lines to become +thicker. + +161. _Change of the Spectrum with the Temperature of the Luminous +Vapor._--It has also been found that the appearance of a bright-lined +spectrum changes considerably with the temperature of the luminous +vapor. In some cases, an increase of temperature changes the relative +intensities of the lines; in other cases, it causes new lines to appear, +and old lines to disappear. + +In the case of a compound vapor, an increase of temperature causes the +colored bands (which are peculiar to the spectrum of the compound) to +disappear, and to be replaced by the spectral lines of the elements of +which the compound is made up. The heat appears to _dissociate_ the +compound; that is, to resolve it into its constituent elements. In this +case, each elementary vapor would give its own spectral lines. As the +compound is not completely dissociated at once, it is possible, of +course, for one or more of the spectral lines of the elementary vapors +to co-exist in the spectrum with the bands of the compound. + +It has been found, that, in some cases, the spectra of the elementary +gases change with the temperature of the gas; and Lockyer thinks he has +discovered conclusive evidence, in the spectra of the sun and stars, +that many of the substances regarded as elementary are really resolved +into simpler substances by the intense heat of the sun; in other words, +that our so-called elements are really compounds. + + + Chemical Constitution of the Sun. + + +162. _The Solar Spectrum._--The solar spectrum is crossed transversely +by a great number of fine dark lines, and hence it belongs to the class +of _reversed_ spectra. + +These lines were first studied and mapped by Fraunhofer, and from him +they have been called _Fraunhofer's lines_. + +[Illustration: Fig. 179.] + + A reduced copy of Fraunhofer's map is shown in Fig. 179. A few of + the most prominent of the dark solar lines are designated by the + letters of the alphabet. The other lines are usually designated by + the numbers at which they are found on the scale which accompanies + the map. This scale is usually drawn at the top of the map, as will + be seen in some of the following diagrams. The two most elaborate + maps of the solar spectrum are those of Kirchhoff and Angström. The + scale on Kirchhoff's map is an arbitrary one, while that of Angström + is based upon the wave-lengths of the rays of light which would fall + upon the lines in the spectrum. + +[Illustration: Fig. 180.] + + The appearance of the spectrum varies greatly with the power of the + spectroscope employed. Fig. 180 shows a portion of the spectrum as + it appears in a spectroscope of a single prism: while Fig. 181 shows + the _b_ group of lines alone, as they appear in a powerful + diffraction spectroscope. + +[Illustration: Fig. 181.] + +163. _The Telluric Lines._--There are many lines of the solar spectrum +which vary considerably in intensity as the sun passes from the horizon +to the meridian, being most intense when the sun is nearest the horizon, +and when his rays are obliged to pass through the greatest depth of the +earth's atmosphere. These lines are of atmospheric origin, and are due +to the absorption of the aqueous vapor in our atmosphere. They are the +same lines that are obtained when a candle or other artificial light is +examined with a spectroscope through a long tube filled with steam. +Since these lines are due to the absorption of our own atmosphere, they +are called _telluric lines_. A map of these lines is shown in Fig. 182. + +[Illustration: Fig. 182.] + +164. _The Solar Lines._--After deducting the telluric lines, the +remaining lines of the solar spectrum are of solar origin. They must be +due to absorption which takes place in the sun's atmosphere. They are, +in fact, the reversed spectra of the elements which exist in the solar +atmosphere in the state of vapor: hence we conclude that the luminous +surface of the sun is surrounded with an atmosphere of luminous vapors. +The temperature of this atmosphere, at least near the surface of the +sun, must be sufficient to enable all the elements known on the earth to +exist in it as vapors. + +[Illustration: Fig. 183.] + +165. _Chemical Constitution of the Sun's Atmosphere._--To find whether +any element which exists on the earth is present in the solar +atmosphere, we have merely to ascertain whether the bright lines of its +gaseous spectrum are matched by dark lines in the solar spectrum when +the two spectra are placed side by side. In Fig. 183, we have in No. 1 a +portion of the red end of the solar spectra, and in No. 2 the spectrum +of sodium vapor, both as obtained in the same spectroscope by means of +the comparison prism. It will be seen that the double sodium line is +exactly matched by a double dark line of the solar spectrum: hence we +conclude that sodium vapor is present in the sun's atmosphere. Fig. 184 +shows the matching of a great number of the bright lines of iron vapor +by dark lines in the solar spectrum. This matching of the iron lines +establishes the fact that iron vapor is present in the solar atmosphere. + +[Illustration: Fig. 184.] + + The following table (given by Professor Young) contains a list of + all the elements which have, up to the present time, been detected + with certainty in the sun's atmosphere. It also gives the number of + bright lines in the spectrum of each element, and the number of + those lines which have been matched by dark lines in the solar + spectrum:-- + + Elements. Bright Lines Reversed. Observer. + Lines. + + 1. Iron 600 460 Kirchhoff. + + 2. Titanium 206 118 Thalen. + + 3. Calcium 89 75 Kirchhoff. + + 4. Manganese 75 57 Angström. + + 5. Nickel 51 33 Kirchhoff. + + 6. Cobalt 86 19 Thalen. + + 7. Chromium 71 18 Kirchhoff. + + 8. Barium 26 11 Kirchhoff. + + 9. Sodium 9 9 Kirchhoff. + + 10. Magnesium 7 7 Kirchhoff. + + 11. Copper? 15 7? Kirchhoff. + + 12. Hydrogen 5 5 Angström. + + 13. Palladium 29 5 Lockyer. + + 14. Vanadium 54 4 Lockyer. + + 15. Molybdenum 27 4 Lockyer. + + 16. Strontium 74 4 Lockyer. + + 17. Lead 41 3 Lockyer. + + 18. Uranium 21 3 Lockyer. + + 19. Aluminium 14 2 Angström. + + 20. Cerium 64 2 Lockyer. + + 21. Cadmium 20 2 Lockyer. + + 22. Oxygen a 42 12 ± bright H. Draper. + + Oxygen b 4 4? Schuster. + + In addition to the above elements, it is probable that several other + elements are present in the sun's atmosphere; since at least one of + their bright lines has been found to coincide with dark lines of the + solar spectrum. There are, however, a large number of elements, no + traces of which have yet been detected; and, in the cases of the + elements whose presence in the solar atmosphere has been + established, the matching of the lines is far from complete in the + majority of the cases, as will be seen from the above table. This + want of complete coincidence of the lines is undoubtedly due to the + very high temperature of the solar atmosphere. We have already seen + that the lines of the spectrum change with the temperature; and, as + the temperature of the sun is far higher than any that we can + produce by artificial means, we might reasonably expect that it + would cause the disappearance from the spectrum of many lines which + we find to be present at our highest temperature. + + Lockyer maintains that the reason why no trace of the spectral lines + of certain of our so-called elements is found in the solar + atmosphere is, that these substances are not really elementary, and + that the intense heat of the sun resolves them into simpler + constituents. + + + Motion at the Surface of the Sun. + + +166. _Change of Pitch caused by Motion of Sounding Body._--When a +sounding body is moving rapidly towards us, the pitch of its note +becomes somewhat higher than when the body is stationary; and, when such +a body is moving rapidly from us, the pitch of its note is lowered +somewhat. We have a good illustration of this change of pitch at a +country railway station on the passage of an express-train. The pitch of +the locomotive whistle is considerably higher when the train is +approaching the station than when it is leaving it. + +167. _Explanation of the Change of Pitch produced by Motion._--The pitch +of sound depends upon the rapidity with which the pulsations of sound +beat upon the drum of the ear. The more rapidly the pulsations follow +each other, the higher is the pitch: hence the shorter the sound-waves +(provided the sound is all the while travelling at the same rate), the +higher the pitch of the sound. Any thing, then, which tends to shorten +the waves of sound tends also to raise its pitch, and any thing which +tends to lengthen these waves tends to lower its pitch. + +When a sounding body is moving rapidly forward, the sound-waves are +crowded together a little, and therefore shortened; when it is moving +backward, the sound-waves are drawn out, or lengthened a little. + + The effect of the motion of a sounding body upon the length of its + sonorous waves will be readily seen from the following illustration: + Suppose a number of persons stationed at equal intervals in a line + on a long platform capable of moving backward and forward. Suppose + the men are four feet apart, and all walking forward at the same + rate, and that the platform is stationary, and that, as the men + leave the platform, they keep on walking at the same rate: the men + will evidently be four feet apart in the line in front of the + platform, as well as on it. Suppose next, that the platform is + moving forward at the rate of one foot in the interval between two + men's leaving the platform, and that the men continue to walk as + before: it is evident that the men will then be three feet apart in + the line after they have left the platform. The forward motion of + the platform has the effect of crowding the men together a little. + Were the platform moving backward at the same rate, the men would be + five feet apart after they had left the platform. The backward + motion of the platform has the effect of separating the men from one + another. + + The distance between the men in this illustration corresponds to the + length of the sound-wave, or the distance between its two ends. Were + a person to stand beside the line, and count the men that passed him + in the three cases given above, he would find that more persons + would pass him in the same time when the platform is moving forward + than when it is stationary, and fewer persons would pass him in the + same time when the platform is moving backward than when it is + stationary. In the same way, when a sounding body is moving rapidly + forward, the sound-waves beat more rapidly upon the ear of a person + who is standing still than when the body is at rest, and less + rapidly when the sounding body is moving rapidly backward. + + Were the platform stationary, and were the person who is counting + the men to be walking along the line, either towards or away from + the platform, the effect upon the number of men passing him in a + given time would be precisely the same as it would be were the + person stationary, and the platform moving either towards or away + from him at the same rate. So the change in the rapidity with which + pulsations of sound beat upon the ear is precisely the same whether + the ear is stationary and the sounding body moving, or the sounding + body is stationary and the ear moving. + +168. _Change of Refrangibility due to the Motion of a Luminous +Body._--Refrangibility in light corresponds to pitch in sound, and +depends upon the length of the luminous waves. The shorter the luminous +waves, the greater the refrangibility of the waves. Very rapid motion of +a luminous body has the same effect upon the length of the luminous +waves that motion of a sounding body has upon the length of the sonorous +waves. When a luminous body is moving very rapidly towards us, its +luminous waves are shortened a little, and its light becomes a little +more refrangible; when the luminous body is moving rapidly from us, its +luminous waves are lengthened a little, and its light becomes a little +less refrangible. + +[Illustration: Fig. 185.] + +169. _Displacement of Spectral Lines._--In examining the spectra of the +stars, we often find that certain of the dark lines are _displaced_ +somewhat, either towards the red or the violet end of the spectrum. As +the dark lines are in the same position as the bright lines of the +absorbing vapor would be, a displacement of the lines towards the red +end of the spectrum indicates a lowering of the refrangibility of the +rays, due to a motion of the luminous vapor away from us; and a +displacement of the lines towards the violet end of the spectrum +indicates an increase of refrangibility, due to a motion of the luminous +vapor towards us. From the amount of the displacement of the lines, it +is possible to calculate the velocity at which the luminous gas is +moving. In Fig. 185 is shown the displacement of the _F_ line in the +spectrum of Sirius. This is one of the hydrogen lines. _RV_ is the +spectrum, _R_ being the red, and _V_ the violet end. The long vertical +line is the bright _F_ line of hydrogen, and the short dark line to the +left of it is the position of the _F_ line in the spectrum of Sirius. It +is seen that this line is displaced somewhat towards the red end of the +spectrum. This indicates that Sirius must be moving from us; and the +amount of the displacement indicates that the star must be moving at the +rate of some twenty-five or thirty miles a second. + +[Illustration: Fig. 186.] + +170. _Contortion of Lines on the Disk of the Sun._--Certain of the dark +lines seen on the centre of the sun's disk often appear more or less +distorted, as shown in Fig. 186, which represents the contortion of the +hydrogen line as seen at various times. 1 and 2 indicate a rapid motion +of hydrogen away from us, or a _down-rush_ at the sun; 3 and 4 (in which +the line at the centre is dark on one side, and bent towards the red end +of the spectrum, and bright on the other side with a distortion towards +the violet end of the spectrum) indicate a _down-rush_ of _cool_ +hydrogen side by side with an _up-rush_ of _hot and bright_ hydrogen; 5 +indicates local _down-rushes_ associated with _quiescent_ hydrogen. + +The contorted lines, which indicate a violently agitated state of the +sun's atmosphere, appear in the midst of other lines which indicate a +quiescent state. This is owing to the fact that the absorption which +produces the dark lines takes place at various depths in the solar +atmosphere. There may be violent commotion in the lower layers of the +sun's atmosphere, and comparative quiet in the upper layers. In this +case, the lines which are due to absorption in the lower layers would +indicate this disturbance by their contortions; while the lines produced +by absorption in the upper layers would be free from contortion. + +It often happens, too, that the contortions are confined to one set of +lines of an element, while other lines of the same element are entirely +free from contortions. This is undoubtedly due to the fact that +different layers of the solar atmosphere differ greatly in temperature; +so that the same element would give one set of lines at one depth, and +another set at another depth: hence commotion in the solar atmosphere at +any particular depth would be indicated by the contortion of those lines +of the element only which are produced by the temperature at that +particular depth. + +A remarkable case of contortion witnessed by Professor Young is shown in +Fig. 187. Three successive appearances of the _C_ line are shown. The +second view was taken three minutes after the first, and the third five +minutes after the second. The contortion in this case indicated a +velocity ranging from two hundred to three hundred miles a second. + +[Illustration: Fig. 187.] + +171. _Contortion of Lines on the Sun's Limb._--When the spectroscope is +directed to the centre of the sun's disk, the distortion of the lines +indicates only vertical motion in the sun's atmosphere; but, when the +spectroscope is directed to the limb of the sun, displacements of the +lines indicate horizontal motions in the sun's atmosphere. When a +powerful spectroscope is directed to the margin of the sun's disk, so +that the slit of the collimator tube shall be perpendicular to the sun's +limb, one or more of the dark lines on the disk are seen to be prolonged +by a bright line, as shown in Fig. 188. But this prolongation, instead +of being straight and narrow, as shown in the figure, is often widened +and distorted in various ways, as shown in Fig. 189. In the left-hand +portion of the diagram, the line is deflected towards the red end of the +spectrum; this indicates a violent wind on the sun's surface blowing +away from us. In the right-hand portion of the diagram, the line is +deflected towards the violet end of the spectrum; this indicates a +violent wind blowing towards us. In the middle portion of the figure, +the line is seen to be bent both ways; this indicates a cyclone, on one +side of which the wind would be blowing from us, and on the other side +towards us. + +[Illustration: Fig. 188.] + +[Illustration: Fig. 189.] + +The distortions of the solar lines indicate that the wind at the surface +of the sun often blows with a velocity of _from one hundred to three +hundred miles a second_. The most violent wind known on the earth has +velocity of a hundred miles an hour. + + + III. THE PHOTOSPHERE AND SUN SPOTS. + + + The Photosphere. + + +[Illustration: Fig. 190.] + +172. _The Granulation of the Photosphere._--When the surface of the sun +is examined with a good telescope under favorable atmospheric +conditions, it is seen to be composed of minute grains of intense +brilliancy and of irregular form, floating in a darker medium, and +arranged in streaks and groups, as shown in Fig. 190. With a rather low +power, the general effect of the surface is much like that of rough +drawing-paper, or of curdled milk seen from a little distance. With a +high power and excellent atmospheric conditions, the _grains_ are seen +to be irregular, rounded masses, some hundreds of miles in diameter, +sprinkled upon a less brilliant background, and appearing somewhat like +snow-flakes sparsely scattered over a grayish cloth. Fig. 191 is a +representation of these grains according to Secchi. + +[Illustration: Fig. 191.] + +With a very powerful telescope and the very best atmospheric conditions, +the grains themselves are resolved into _granules_, or little luminous +dots, not more than a hundred miles or so in diameter, which, by their +aggregation, make up the grains, just as they, in their turn, make up +the coarser masses of the solar surface. Professor Langley estimates +that these granules constitute about one-fifth of the sun's surface, +while they emit at least three-fourths of its light. + +173. _Shape of the Grains._--The grains differ considerably in shape at +different times and on different parts of the sun's surface. Nasmyth, in +1861, described them as _willow-leaves_ in shape, several thousand miles +in length, but narrow and with pointed ends. He figured the surface of +the sun as a sort of basket-work formed by the interweaving of such +filaments. To others they have appeared to have the form of +_rice-grains_. On portions of the sun's disk the elementary structure is +often composed of long, narrow, blunt-ended filaments, not so much like +willow-leaves as like bits of straw lying roughly parallel to each +other,--a _thatch-straw_ formation, as it has been called. This is +specially common in the immediate neighborhood of the spots. + +174. _Nature of the Grains._--The grains are, undoubtedly, incandescent +_clouds_ floating in the sun's atmosphere, and composed of partially +condensed metallic vapors, just as the clouds of our atmosphere are +composed of partially condensed aqueous vapor. Rain on the sun is +composed of white-hot drops of molten iron and other metals; and these +drops are often driven with the wind with a velocity of over a hundred +miles a second. + +As to the forms of the grains, Professor Young says, "If one were to +speculate as to the explanation of the grains and thatch-straws, it +might be that the grains are the upper ends of long filaments of +luminous cloud, which, over most of the sun's surface, stand +approximately vertical, but in the neighborhood of a spot are inclined +so as to lie nearly horizontal. This is not certain, though: it may be +that the cloud-masses over the more quiet portions of the solar surface +are really, as they seem, nearly globular, while near the spots they are +drawn out into filamentary forms by atmospheric currents." + +175. _Faculæ._--The _faculæ_ are irregular streaks of greater brightness +than the general surface, looking much like the flecks of foam on the +surface of a stream below a waterfall. They are sometimes from five to +twenty thousand miles in length, covering areas immensely larger than a +terrestrial continent. + +These faculæ are _elevated regions_ of the solar surface, ridges and +crests of luminous matter, which rise above the general level of the +sun's surface, and protrude through the denser portions of the solar +atmosphere. When one of these passes over the edge of the sun's disk, it +can be seen to project, like a little tooth. Any elevation on the sun to +be perceptible at all must measure at least half a second of an arc, or +two hundred and twenty-five miles. + +The faculæ are most numerous in the neighborhood of the spots, and much +more conspicuous near the limb of the sun than near the centre of the +disk. Fig. 192 gives the general appearance of the faculæ, and the +darkening of the limb of the sun. Near the spots, the faculæ often +undergo very rapid change of form, while elsewhere on the disk they +change rather slowly, sometimes undergoing little apparent alteration +for several days. + +[Illustration: Fig. 192.] + +176. _Why the Faculæ are most Conspicuous near the Limb of the +Sun._--The reason why the faculæ are most conspicuous near the limb of +the sun is this: The luminous surface of the sun is covered with an +atmosphere, which, though not very thick compared with the diameter of +the sun, is still sufficient to absorb a good deal of light. Light +coming from the centre of the sun's disk penetrates this atmosphere +under the most favorable conditions, and is but slightly reduced in +amount. The edges of the disk, on the other hand, are seen through a +much greater thickness of atmosphere; and the light is reduced by +absorption some seventy-five per cent. Suppose, now, a facula were +sufficiently elevated to penetrate quite through this atmosphere. Its +light would be undimmed by absorption on any part of the sun's disk; but +at the centre of the disk it would be seen against a background nearly +as bright as itself, while at the margin it would be seen against one +only a quarter as bright. It is evident that the light of any facula, +owing to the elevation, would be reduced less rapidly as we approach the +edge of the disk than that of the general surface of the sun, which lies +at a lower level. + + + Sun-Spots. + + +177. _General Appearance of Sun-Spots._--The general appearance of a +well-formed sun-spot is shown in Fig. 193. The spot consists of a very +dark central portion of irregular shape, called the _umbra_, which is +surrounded by a less dark fringe, called the _penumbra_. The penumbra is +made up, for the most part, of filaments directed radially inward. + +[Illustration: Fig. 193.] + +There is great variety in the details of form in different sun-spots; +but they are generally nearly circular during the middle period of their +existence. During the period of their development and of their +disappearance they are much more irregular in form. + +There is nothing like a gradual shading-off of the penumbra, either +towards the umbra on the one side, or towards the photosphere on the +other. The penumbra is separated from both the umbra and the photosphere +by a sharp line of demarcation. The umbra is much brighter on the inner +than on the outer edge, and frequently the photosphere is excessively +bright at the margin of the penumbra. The brightness of the inner +penumbra seems to be due to the crowding together of the penumbral +filaments where they overhang the edge of the umbra. + +There is a general antithesis between the irregularities of the outer +and inner edges of the penumbra. Where an angle of the penumbral matter +crowds in upon the umbra, it is generally matched by a corresponding +outward extension into the photosphere, and _vice versa_. + +The umbra of the spot is far from being uniformly dark. Many of the +penumbral filaments terminate in little detached grains of luminous +matter; and there are also fainter veils of a substance less brilliant, +but sometimes rose-colored, which seem to float above the umbra. The +umbra itself is made up of masses of clouds which are really intensely +brilliant, and which appear dark only by contrast with the intenser +brightness of the solar surface. Among these clouds are often seen one +or more minute circular spots much darker than the rest of the umbra. +These darker portions are called _nuclei_. They seem to be the mouths of +tubular orifices penetrating to unknown depths. The faint veils +mentioned above continually melt away, and are replaced by others in +some different position. The bright granules at the tips of the +penumbral filaments seem to sink and dissolve, while fresh portions +break off to replace them. There is a continual indraught of luminous +matter over the whole extent of the penumbra. + +At times, though very rarely, patches of intense brightness suddenly +break out, remain visible for a few minutes, and move over the spot with +velocities as great as a hundred miles _a second_. + +The spots change their form and size quite perceptibly from day to day, +and sometimes even from hour to hour. + +178. _Duration of Sun-Spots._--The average life of a sun-spot is two or +three months: the longest on record is that of a spot observed in 1840 +and 1841, which lasted eighteen months. There are cases, however, where +the disappearance of a spot is very soon followed by the appearance of +another at the same point; and sometimes this alternate disappearance +and re-appearance is several times repeated. While some spots are thus +long-lived, others endure only a day or two, and sometimes only a few +hours. + +179. _Groups of Spots._--The spots usually appear not singly, but in +groups. A large spot is often followed by a train of smaller ones to the +east of it, many of which are apt to be irregular in form and very +imperfect in structure, sometimes with no umbra at all, often with a +penumbra only on one side. In such cases, when any considerable change +of form or structure shows itself in the principal spot, it seems to +rush westward over the solar surface, leaving its attendants trailing +behind. When a large spot divides into two or more, as often happens, +the parts usually seem to repel each other, and fly apart with great +velocity. + +180. _Size of the Spots._--The spots are sometimes of enormous size. +Groups have often been observed covering areas of more than a hundred +thousand miles square, and single spots occasionally measure from forty +to fifty thousand miles in diameter, the umbra being twenty-five or +thirty thousand miles across. A spot, however, measuring thirty thousand +miles over all, may be considered a large one. Such a spot can easily be +seen without a telescope when the brightness of the sun's surface is +reduced by clouds or nearness to the horizon, or by the use of colored +glass. During the years 1871 and 1872 spots were visible to the naked +eye for a considerable portion of the time. The largest spot yet +recorded was observed in 1858. It had a breadth of more than a hundred +and forty-three thousand miles, or nearly eighteen times the diameter of +the earth, and covered about a thirty-sixth of the whole surface of the +sun. + +[Illustration: Fig. 194.] + +Fig. 194 represents a group of sun-spots observed by Professor Langley, +and drawn on the same scale as the small circle in the upper left-hand +corner, which represents the surface of half of our globe. + +[Illustration: Fig. 195.] + +181. _The Penumbral Filaments._--Not unfrequently the penumbral +filaments are curved spirally, indicating a cyclonic action, as shown in +Fig. 195. In such cases the whole spot usually turns slowly around, +sometimes completing an entire revolution in a few days. More +frequently, however, the spiral motion lasts but a short time; and +occasionally, after continuing for a while in one direction, the motion +is reversed. Very often in large spots we observe opposite spiral +movements in different portions of the umbra, as shown in Figs. 196 and +197. + +[Illustration: Fig. 196.] + +Neighboring spots show no tendency to rotate in the same direction. The +number of spots in which a decided cyclonic motion (like that shown in +Fig. 198) appears is comparatively small, not exceeding two or three per +cent of the whole. + +[Illustration: Fig. 197.] + +[Illustration: Fig. 198.] + +[Illustration: Plate 2.] + +Plate II. represents a typical sun-spot as delineated by Professor +Langley. At the left-hand and upper portions of this great spot the +filaments present the ordinary appearance, while at the lower edge, and +upon the great overhanging branch, they are arranged very differently. +The feathery brush below the branch, closely resembling a frost-crystal +on a window-pane, is as rare as it is curious, and has not been +satisfactorily explained. + +[Illustration: Fig. 199.] + +182. _Birth and Decay of Sun-Spots._--The formation of a spot is +sometimes gradual, requiring days or even weeks for its full +development; and sometimes a single day suffices. Generally, for some +time before its appearance, there is an evident disturbance of the solar +surface, indicated especially by the presence of many brilliant faculæ, +among which _pores_, or minute black dots, are scattered. These enlarge, +and between them appear grayish patches, in which the photospheric +structure is unusually evident, as if they were caused by a dark mass +lying below a thin veil of luminous filaments. This veil seems to grow +gradually thinner, and finally breaks open, giving us at last the +complete spot with its penumbra. Some of the pores coalesce with the +principal spot, some disappear, and others form the attendant train +before described (179). The spot when once formed usually assumes a +circular form, and remains without striking change until it disappears. +As its end approaches, the surrounding photosphere seems to crowd in, +and overwhelm the penumbra. Bridges of light (Fig. 199), often much +brighter than the average of the solar surface, push across the umbra; +the arrangement of the penumbra filaments becomes confused; and, as +Secchi expresses it, the luminous matter of the photosphere seems to +tumble pell-mell into the chasm, which disappears, and leaves a +disturbed surface marked with faculæ, which, in their turn, gradually +subside. + +[Illustration: Fig. 200.] + +183. _Motion of Sun-Spots._--The spots have a regular motion across the +disk of the sun from east to west, occupying about twelve days in the +transit. A spot generally appears first on or near the east limb, and, +after twelve or fourteen days, disappears at the west limb. At the end +of another fourteen days, or more, it re-appears at the east limb, +unless, in the mean time, it has vanished from sight entirely. This +motion of the spots is indicated by the arrow in Fig. 200. The interval +between two successive appearances of the same spot on the eastern edge +of the sun is about twenty-seven days. + +[Illustration: Fig. 201.] + +184. _The Rotation of the Sun._--The spots are evidently carried around +by the rotation of the sun on its axis. It is evident, from Fig. 201, +that the sun will need to make more than a complete rotation in order to +bring a spot again upon the same part of the disk as seen from the +earth. _S_ represents the sun, and _E_ the earth. The arrows indicate +the direction of the sun's rotation. When the earth is at _E_, a spot at +_a_ would be seen at the centre of the solar disk. While the sun is +turning on its axis, the earth moves in its orbit from _E_ to _E'_: +hence the sun must make a complete rotation, and turn from _a_ to _a'_ +in addition, in order to bring the spot again to the centre of the disk. +To carry the spot entirely around, and then on to _a'_, requires about +twenty-seven days. From this _synodical period_ of the spot, as it might +be called, it has been calculated that the sun must rotate on its axis +in about twenty-five days. + +[Illustration: Fig. 202.] + +185. _The Inclination of the Sun's Axis._--The paths described by +sun-spots across the solar disk vary with the position of the earth in +its orbit, as shown in Fig. 202. We therefore conclude that the sun's +axis is not perpendicular to the plane of the earth's orbit. The sun +rotates on its axis from west to east, and the axis leans about seven +degrees from the perpendicular to the earth's orbit. + +186. _The Proper Motion of the Spots._--When the period of the sun's +rotation is deduced from the motion of spots in different solar +latitudes, there is found to be considerable variation in the results +obtained. Thus spots near the equator indicate that the sun rotates in +about twenty-five days; while those in latitude 20° indicate a period +about eighteen hours longer; and those in latitude 30° a period of +twenty-seven days and a half. Strictly speaking, the sun, as a whole, +has no single period of rotation; but different portions of its surface +perform their revolutions in different times. The equatorial regions not +only move more rapidly in miles per hour than the rest of the solar +surface, but they _complete the entire rotation in shorter time_. + +[Illustration: Fig. 203.] + +There appears to be a peculiar surface-drift in the equatorial regions +of the sun, the cause of which is unknown, but which gives the spots a +_proper_ motion; that is, a motion of their own, independent of the +rotation of the sun. + +[Illustration: Fig. 204.] + +187. _Distribution of the Sun-Spots._--The sun-spots are not distributed +uniformly over the sun's surface, but occur mainly in two zones on each +side of the equator, and between the latitudes of 10° and 30°, as shown +in Fig. 203. On and near the equator itself they are comparatively rare. +There are still fewer beyond 35° of latitude, and only a single spot has +ever been recorded more than 45° from the solar equator. + +Fig. 204 shows the distribution of the sun-spots observed by Carrington +during a period of eight years. The irregular line on the left-hand side +of the figure indicates by its height the comparative frequency with +which the spots occurred in different latitudes. In Fig. 205 the same +thing is indicated by different degrees of darkness in the shading of +the belts. + +[Illustration: Fig. 205.] + +188. _The Periodicity of the Spots._--Careful observations of the solar +spots indicate a period of about eleven years in the spot-producing +activity of the sun. During two or three years the spots increase in +number and in size; then they begin to diminish, and reach a minimum +five or six years after the maximum. Another period of about six years +brings the return of the maximum. The intervals are, however, somewhat +irregular. + +[Illustration: Fig. 206.] + +Fig. 206 gives a graphic representation of the periodicity of the +sun-spots. The height of the curve shows the frequency of the sun-spots +in the years given at the bottom of the figure. It appears, from an +examination of this sun-spot curve, that the average interval from a +minimum to the next following maximum is only about four years and a +half, while that from a maximum to the next following minimum is six +years and six-tenths. The disturbance which produces the sun-spots is +developed suddenly, but dies away gradually. + +189. _Connection between Sun-Spots and Terrestrial Magnetism._--The +magnetic needle does not point steadily in the same direction, but is +subject to various disturbances, some of which are regular, and others +irregular. + +(1) One of the most noticeable of the regular magnetic changes is the +so-called _diurnal oscillation_. During the early part of the day the +north pole of the needle moves toward the west in our latitude, +returning to its mean position about ten P.M., and remaining nearly +stationary during the night. The extent of this oscillation in the +United States is about fifteen minutes of arc in summer, and not quite +half as much in winter; but it differs very much in different localities +and at different times, and the average diurnal oscillation in any +locality increases and decreases pretty regularly during a period of +about eleven years. The maximum and minimum of this period of magnetic +disturbance are found to coincide with the maximum and minimum of the +sun-spot period. This is shown in Fig. 206, in which the dotted lines +indicate the variations in the intensity of the magnetic disturbance. + +(2) Occasionally so-called _magnetic storms_ occur, during which the +compass-needle is sometimes violently disturbed, oscillating five +degrees, or even ten degrees, within an hour or two. These storms are +generally accompanied by an aurora, and an aurora is _always_ +accompanied by magnetic disturbance. A careful comparison of aurora +observations with those of sun-spots shows an almost perfect parallelism +between the curves of auroral and sun-spot frequency. + +(3) A number of observations render it very probable that every intense +disturbance of the solar surface is propagated to our terrestrial +magnetism with the speed of light. + +[Illustration: Fig. 207.] + +Fig. 207 shows certain of the solar lines as they were observed by +Professor Young on Aug. 3, 1872. The contortions of the _F_ line +indicated an intense disturbance in the atmosphere of the sun. There +were three especially notable paroxysms in this distortion, occurring at +a quarter of nine, half-past ten, and ten minutes of twelve, A.M. + +[Illustration: Fig. 208.] + +Fig. 208 shows the curve of magnetic disturbance as traced at Greenwich +on the same day. It will be seen from the curve that it was a day of +general magnetic disturbance. At the times of the three paroxysms, which +are given at the bottom of the figure, it will be observed that there is +a peculiar shivering of the magnetic curve. + +190. _The Spots are Depressions in the Photosphere._--This fact was +first clearly brought out by Dr. Wilson of Glasgow, in 1769, from +observations upon the penumbra of a spot in November of that year. He +found, that when the spot appeared at the eastern limb, or edge of the +sun, just moving into sight, the penumbra was well marked on the side of +the spot nearest to the edge of the disk; while on the other edge of the +spot, towards the centre of the sun, there was no penumbra visible at +all, and the umbra itself was almost hidden, as if behind a bank. When +the spot had moved a day's journey toward the centre of the disk, the +whole of the umbra came into sight, and the penumbra on the inner edge +of the spot began to be visible as a narrow line. After the spot was +well advanced upon the disk, the penumbra was of the same width all +around the spot. When the spot approached the sun's western limb, the +same phenomena were repeated, but in the inverse order. The penumbra on +the _inner_ edge of the spot narrowed much faster than that on the +outer, disappeared entirely, and finally seemed to hide from sight much +of the umbra nearly a whole day before the spot passed from view around +the limb. This is precisely what would occur (as Fig. 209 clearly shows) +if the spot were a saucer-shaped depression in the solar surface, the +bottom of the saucer corresponding to the umbra, and the sloping sides +to the penumbra. + +[Illustration: Fig. 209.] + +[Illustration: Fig. 210.] + +191. _Sun-Spot Spectrum._--When the image of a sun-spot is thrown upon +the slit of the spectroscope, the spectrum is seen to be crossed +longitudinally by a continuous dark band, showing an increased general +absorption in the region of the sun-spot. Many of the spectral lines are +greatly thickened, as shown in Fig. 210. This thickening of the lines +shows that the absorption is taking place at a greater depth. New lines +and shadings often appear, which indicate, that, in the cooler nucleus +of the spot, certain compound vapors exist, which are dissociated +elsewhere on the sun's surface. These lines and shadings are shown in +Fig. 211. + +[Illustration: Fig. 211.] + +It often happens that certain of the spectral lines are reversed in the +spectrum of the spot, a thin bright line appearing over the centre of a +thick dark one, as shown in Fig. 212. These reversals are due to very +bright vapors floating over the spot. + +[Illustration: Fig. 212.] + +At times, also, the spectrum of a spot indicates violent motion in the +overlying gases by distortion and displacement of the lines. This +phenomenon occurs oftener at points near the outer edge of the penumbra +than over the centre of the spot; but occasionally the whole +neighborhood is violently agitated. In such cases, lines in the spectrum +side by side are often affected in entirely different ways, one being +greatly displaced while its neighbor is not disturbed in the least, +showing that the vapors which produce the lines are at different levels +in the solar atmosphere, and moving independently of each other. + +[Illustration: Fig. 213.] + +192. _The Cause and Nature of Sun-Spots._--According to Professor Young, +the arrangement and relations of the photospheric clouds in the +neighborhood of a spot are such as are represented in Fig. 213. "Over +the sun's surface generally, these clouds probably have the form of +vertical columns, as at _aa_. Just outside the spot, the level of the +photosphere is the most part, overtopped by eruptions of hydrogen and +usually raised into faculæ, as at _bb_. These faculæ are, for metallic +vapors, as indicated by the shaded clouds.... While the great clouds of +hydrogen are found everywhere upon the sun, these spiky, vivid outbursts +of metallic vapors seldom occur except just in the neighborhood of a +spot, and then only during its season of rapid change. In the penumbra +of the spot the photospheric filaments become more or less nearly +horizontal, as at _pp_; in the umbra at _u_ it is quite uncertain what +the true state of affairs may be. We have conjecturally represented the +filaments there as vertical also, but depressed and carried down by a +descending current. Of course, the cavity is filled by the gases which +overlie the photosphere; and it is easy to see, that, looked at from +above, such a cavity and arrangement of the luminous filaments would +present the appearances actually observed." + +Professor Young also suggests that the spots may be depressions in the +photosphere caused "by the _diminution of upward pressure_ from below, +in consequence of eruptions in the neighborhood; the spots thus being, +so to speak, _sinks_ in the photosphere. Undoubtedly the photosphere is +not a strictly continuous shell or crust; but it is _heavy_ as compared +with the uncondensed vapors in which it lies, just as a rain-cloud in +our terrestrial atmosphere is heavier than the air; and it is probably +continuous enough to have its upper level affected by any diminution of +pressure below. The gaseous mass below the photosphere supports its +weight and the weight of the products of condensation, which must always +be descending in an inconceivable rain and snow of molten and +crystallized material. To all intents and purposes, though nothing but a +layer of clouds, the photosphere thus forms a constricting shell, and +the gases beneath are imprisoned and compressed. Moreover, at a high +temperature the viscosity of gases is vastly increased, so that quite +probably the matter of the solar nucleus resembles pitch or tar in its +consistency more than what we usually think of as a gas. Consequently, +any sudden diminution of pressure would propagate itself slowly from the +point where it occurred. Putting these things together, it would seem, +that, whenever a free outlet is obtained through the photosphere at any +point, thus decreasing the inward pressure, the result would be the +sinking of a portion of the photosphere somewhere in the immediate +neighborhood, to restore the equilibrium; and, if the eruption were kept +up for any length of time, the depression in the photosphere would +continue till the eruption ceased. This depression, filled with the +overlying gases, would constitute a spot. Moreover, the line of fracture +(if we may call it so) at the edges of the sink would be a region of +weakness in the photosphere, so that we should expect a series of +eruptions all around the spot. For a time the disturbance, therefore, +would grow, and the spot would enlarge and deepen, until, in spite of +the viscosity of the internal gases, the equilibrium of pressure was +gradually restored beneath. So far as we know the spectroscopic and +visual phenomena, none of them contradict this hypothesis. There is +nothing in it, however, to account for the distribution of the spots in +solar latitudes, nor for their periodicity." + + + IV. THE CHROMOSPHERE AND PROMINENCES. + + +193. _The Sun's Outer Atmosphere._--What we see of the sun under +ordinary circumstances is but a fraction of his total bulk. While by far +the greater portion of the solar _mass_ is included within the +photosphere, the larger portion of his _volume_ lies without, and +constitutes a gaseous envelope whose diameter is at least double, and +its bulk therefore sevenfold, that of the central globe. + +This outer envelope, though mainly gaseous, is not spherical, but has an +exceedingly irregular and variable outline. It seems to be made up, not +of regular strata of different density, like our atmosphere, but rather +of flames, beams, and streamers, as transient and unstable as those of +the aurora borealis. It is divided into two portions by a boundary as +definite, though not so regular, as that which separates them both from +the photosphere. The outer and far more extensive portion, which in +texture and rarity seems to resemble the tails of comets, is known as +the _coronal atmosphere_, since to it is chiefly due the _corona_, or +glory, which surrounds the darkened sun during an eclipse. + +194. _The Chromosphere._--At the base of the coronal atmosphere, and in +contact with the photosphere, is what resembles a sheet of scarlet fire. +It appears as if countless jets of heated gas were issuing through vents +over the whole surface, clothing it with flame, which heaves and tosses +like the blaze of a conflagration. This is the _chromosphere_, or +color-sphere. It owes its vivid redness to the predominance of hydrogen +in the flames. The average depth of the chromosphere is not far from ten +or twelve seconds, or five thousand or six thousand miles. + +195. _The Prominences._--Here and there masses of this hydrogen, mixed +with other substances, rise far above the general level into the coronal +regions, where they float like clouds, or are torn to pieces by +conflicting currents. These cloud-masses are known as solar +_prominences_, or _protuberances_. + +196. _Magnitude and Distribution of the Prominences._--The prominences +differ greatly in magnitude. Of the 2,767 observed by Secchi, 1,964 +attained an altitude of eighteen thousand miles; 751, or nearly a fourth +of the whole, reached a height of twenty-eight thousand miles; several +exceeded eighty-four thousand miles. In rare instances they reach +elevations as great as a hundred thousand miles. A few have been seen +which exceeded a hundred and fifty thousand miles; and Secchi has +recorded one of three hundred thousand miles. + +[Illustration: Fig. 214.] + +The irregular lines on the right-hand side of Fig. 214 show the +proportion of the prominences observed by Secchi, that were seen in +different parts of the sun's surface. The outer line shows the +distribution of the smaller prominences, and the inner dotted line that +of the larger prominences. By comparing these lines with those on the +opposite side of the circle, which show the distribution of the spots, +it will be seen, that, while the spots are confined mainly to two belts, +the prominences are seen in all latitudes. + +197. _The Spectrum of the Chromosphere._--The spectrum of the +chromosphere is comparatively simple. There are eleven lines only which +are always present; and six of these are lines of hydrogen, and the +others, with a single exception, are of unknown elements. There are +sixteen other lines which make their appearance very frequently. Among +these latter are lines of sodium, magnesium, and iron. + +Where some special disturbance is going on, the spectrum at the base of +the chromosphere is very complicated, consisting of hundreds of bright +lines. "The majority of the lines, however, are seen only occasionally, +for a few minutes at a time, when the gases and vapors, which generally +lie low (mainly in the interstices of the clouds which constitute the +photosphere), and below its upper surface, are elevated for the time +being by some eruptive action. For the most part, the lines which appear +only at such times are simply _reversals_ of the more prominent dark +lines of the ordinary solar spectrum. But the selection of the lines +seems most capricious: one is taken, and another left, though belonging +to the same element, of equal intensity, and close beside the first." +Some of the main lines of the chromosphere and prominences are shown in +Fig. 215. + +[Illustration: Fig. 215.] + +198. _Method of Studying the Chromosphere and Prominences._--Until +recently, the solar atmosphere could be seen only during a total eclipse +of the sun; but now the spectroscope enables us to study the +chromosphere and the prominences with nearly the same facility as the +spots and faculæ. + +The protuberances are ordinarily invisible, for the same reason that the +stars cannot be seen in the daytime; they are hidden by the intense +light reflected from our own atmosphere. If we could only get rid of +this aerial illumination, without at the same time weakening the light +of the prominences, the latter would become visible. This the +spectroscope enables us to accomplish. Since the air-light is reflected +sunshine, it of course presents the same spectrum as sunlight,--a +continuous band of color crossed by dark lines. Now, this sort of +spectrum is weakened by increase of dispersive power (159), because the +light is spread out into a longer ribbon, and made to cover a greater +area. On the other hand, the spectrum of the prominences, being composed +of bright lines, undergoes no such diminution by increased dispersion. + +[Illustration: Fig. 216.] + +When the spectroscope is used as a means of examining the prominences, +the slit is more or less widened. The telescope is directed so that the +image of that portion of the solar limb which is to be examined shall be +tangent to the opened slit, as in Fig. 216, which represents the +slit-plate of the spectroscope of its actual size, with the image of the +sun in the proper position for observation. + +[Illustration: Fig. 217.] + +If, now, a prominence exists at this part of the solar limb, and if the +spectroscope itself is so adjusted that the _C_ line falls in the centre +of the field of view, then one will see something like Fig. 217. "The +red portion of the spectrum will stretch athwart the field of view like +a scarlet ribbon with a darkish band across it; and in that band will +appear the prominences, like scarlet clouds, so like our own terrestrial +clouds, indeed, in form and texture, that the resemblance is quite +startling. One might almost think he was looking out through a +partly-opened door upon a sunset sky, except that there is no variety or +contrast of color; all the cloudlets are of the same pure scarlet hue. +Along the edge of the opening is seen the chromosphere, more brilliant +than the clouds which rise from it or float above it, and, for the most +part, made up of minute tongues and filaments." + +199. _Quiescent Prominences._--The prominences differ as widely in form +and structure as in magnitude. The two principal classes are the +_quiescent_, _cloud-formed_, or _hydrogenous_, and the _eruptive_, or +_metallic_. + +[Illustration: Plate 3.] + +The _quiescent_ prominences resemble almost exactly our terrestrial +clouds, and differ among themselves in the same manner. They are often +of enormous dimensions, especially in horizontal extent, and are +comparatively permanent, often undergoing little change for hours and +days. Near the poles they sometimes remain during a whole solar +revolution of twenty-seven days. Sometimes they appear to lie upon the +limb of the sun, like a bank of clouds in the terrestrial horizon, +probably because they are so far from the edge that only their upper +portions are in sight. When fully seen, they are usually connected to +the chromosphere by slender columns, generally smallest at the base, and +often apparently made up of separate filaments closely intertwined, and +expanding upward. Sometimes the whole under surface is fringed with +pendent filaments. Sometimes they float entirely free from the +chromosphere; and in most cases the larger clouds are attended by +detached cloudlets. Various forms of quiescent prominences are shown in +Plate III. Other forms are given in Figs. 218 and 219. + +[Illustration: Fig. 218.] + +Their spectrum is usually very simple, consisting of the four lines of +hydrogen and the orange _D_^3: hence the appellation _hydrogenous_. +Occasionally the sodium and magnesium lines also appear, even near the +tops of the clouds. + +[Illustration: Fig. 219.] + +200. _Eruptive Prominences._--The _eruptive_ prominences ordinarily +consist of brilliant spikes or jets, which change very rapidly in form +and brightness. As a rule, their altitude is not more than twenty +thousand or thirty thousand miles; but occasionally they rise far higher +than even the largest of the quiescent protuberances. Their spectrum is +very complicated, especially near their base, and often filled with +bright lines. The most conspicuous lines are those of sodium, magnesium, +barium, iron, and titanium: hence Secchi calls them _metallic_ +prominences. + +[Illustration: Fig. 220.] + +They usually appear in the immediate vicinity of a spot, never very near +the solar poles. They change with such rapidity, that the motion can +almost be seen with the eye. Sometimes, in the course of fifteen or +twenty minutes, a mass of these flames, fifty thousand miles high, will +undergo a total transformation; and in some instances their complete +development or disappearance takes no longer time. Sometimes they +consist of pointed rays, diverging in all directions, as represented in +Fig. 220. "Sometimes they look like flames, sometimes like sheaves of +grain, sometimes like whirling water-spouts capped with a great cloud; +occasionally they present most exactly the appearance of jets of liquid +fire, rising and falling in graceful parabolas; frequently they carry on +their edges spirals like the volutes of an Ionic column; and continually +they detach filaments, which rise to a great elevation, gradually +expanding and growing fainter as they ascend, until the eye loses them." + +[Illustration: Fig. 221.] + +201. _Change of Form in Prominences._--Fig. 221 represents a prominence +as seen by Professor Young, Sept. 7, 1871. It was an immense quiescent +cloud, a hundred thousand miles long and fifty-four thousand miles high. +At _a_ there was a brilliant lump, somewhat in the form of a +thunder-head. On returning to the spectroscope less than half an hour +afterwards, he found that the cloud had been literally blown into shreds +by some inconceivable uprush from beneath. The prominence then presented +the form shown in Fig. 222. The _débris_ of the cloud had already +attained a height of a hundred thousand miles. While he was watching +them for the next ten minutes, they rose, with a motion almost +perceptible to the eye, till the uppermost reached an altitude of two +hundred thousand miles. As the filaments rose, they gradually faded away +like a dissolving cloud. + +[Illustration: Fig. 222.] + +Meanwhile the little thunder-head had grown and developed into what +appeared to be a mass of rolling and ever-changing flame. Figs. 223 and +224 give the appearance of this portion of the prominence at intervals +of fifteen minutes. Other similar eruptions have been observed. + +[Illustration: Fig. 223.] + +[Illustration: Fig. 224.] + + + V. THE CORONA. + + +202. _General Appearance of the Corona._--At the time of a total eclipse +of the sun, if the sky is clear, the moon appears as a huge black ball, +the illumination at the edge of the disk being just sufficient to bring +out its rotundity. "From behind it," to borrow Professor Young's vivid +description, "stream out on all sides radiant filaments, beams, and +sheets of pearly light, which reach to a distance sometimes of several +degrees from the solar surface, forming an irregular stellate halo, with +the black globe of the moon in its apparent centre. The portion nearest +the sun is of dazzling brightness, but still less brilliant than the +prominences which blaze through it like carbuncles. Generally this inner +corona has a pretty uniform height, forming a ring three or four minutes +of arc in width, separated by a somewhat definite outline from the outer +corona, which reaches to a much greater distance, and is far more +irregular in form. Usually there are several _rifts_, as they have been +called, like narrow beams of darkness, extending from the very edge of +the sun to the outer night, and much resembling the cloud-shadows which +radiate from the sun before a thunder-shower; but the edges of these +rifts are frequently curved, showing them to be something else than real +shadows. Sometimes there are narrow bright streamers, as long as the +rifts, or longer. These are often inclined, occasionally are even nearly +tangential to the solar surface, and frequently are curved. On the +whole, the corona is usually less extensive and brilliant over the solar +poles, and there is a recognizable tendency to accumulations above the +middle latitudes, or spot-zones; so that, speaking roughly, the corona +shows a disposition to assume the form of a quadrilateral or four-rayed +star, though in almost every individual case this form is greatly +modified by abnormal streamers at some point or other." + +[Illustration: Fig. 225.] + +203. _The Corona as seen at Recent Eclipses._--The corona can be seen +only at the time of a total eclipse of the sun, and then for only a few +minutes. Its form varies considerably from one eclipse to another, and +apparently also during the same eclipse. At least, different observers +at different stations depict the same corona under very different forms. +Fig. 225 represents the corona of 1857 as observed by Liais. In this +view the _petal-like_ forms, which have been noticed in the corona at +other times, are especially prominent. + +[Illustration: Fig. 226.] + +Fig. 226 shows the corona of 1860 as it was observed by Temple. + +[Illustration: Fig. 227.] + +Fig. 227 shows the corona of 1867. This is interesting as being a corona +at the time of sun-spot minimum. + +[Illustration: Fig. 228.] + +Fig. 228 represents the corona of 1868. This is a larger and more +irregular corona than usual. + +[Illustration: Fig. 229.] + +The corona of 1869 is shown in Fig. 229. + +[Illustration: Fig. 230.] + +Fig. 230 is a view of the corona of 1871 as seen by Capt. Tupman. + +[Illustration: Fig. 231.] + +Fig. 231 shows the same corona as seen by Foenander. + +[Illustration: Fig. 232.] + +Fig. 232 shows the same corona as photographed by Davis. + +[Illustration: Fig. 233.] + +Fig. 233 shows the corona of 1878 made up from several views as combined +by Professor Young. + +204. _The Spectrum of the Corona._--The chief line in the spectrum of +the corona is the one usually designated as 1474, and now known as the +_coronal_ line. It is seen as a dark line on the disk of the sun; and a +spectroscope of great dispersive power shows this dark line to be +closely double, the lower component being one of the iron lines, and the +upper the coronal line. This dark line is shown at _x_, Fig. 234. + +[Illustration: Fig. 234.] + +Besides this bright line, the hydrogen lines appear faintly in the +spectrum of the corona. The 1474 line has been sometimes traced with the +spectroscope to an elevation of nearly twenty minutes above the moon's +limb, and the hydrogen lines nearly as far; and the lines were just as +strong _in the middle of a dark rift_ as anywhere else. + +The substance which produces the 1474 line is unknown as yet. It seems +to be something with a vapor-density far below that of hydrogen, which +is the lightest substance of which we have any knowledge. It can hardly +be an "allotropic" form of any terrestrial element, as some scientists +have suggested; for in the most violent disturbances in prominences and +near sun-spots, when the lines of hydrogen, magnesium, and other metals, +are contorted and shattered by the rush of the contending elements, this +line alone remains fine, sharp, and straight, a little brightened, but +not otherwise affected. For the present it remains, like a few other +lines in the spectrum, an unexplained mystery. + +Besides bright lines, the corona shows also a faint continuous spectrum, +in which have been observed a few of the more prominent _dark_ lines of +the solar spectrum. + +This shows, that, while the corona may be in the main composed of +glowing gas (as indicated by the bright lines of its spectrum), it also +contains considerable matter in such a state as to reflect the sunlight, +probably in the form of dust or fog. + + + V. ECLIPSES. + + +[Illustration: Fig. 235.] + +205. _The Shadows of the Earth and Moon._--The shadows cast by the earth +and moon are shown in Fig. 235. Each shadow is seen to be made up of a +dark portion called the _umbra_, and of a lighter portion called the +_penumbra_. The light of the sun is completely excluded from the umbra, +but only partially from the penumbra. The umbra is in the form of a +cone, with its apex away from the sun; though in the case of the earth's +shadow it tapers very slowly. The penumbra surrounds the umbra, and +increases in size as we recede from the sun. The axis of the earth's +shadow lies in the plane of the ecliptic, which in the figure is the +surface of the page. As the moon's orbit is inclined five degrees to the +plane of the ecliptic, the axis of the moon's shadow will sometimes lie +above, and sometimes below, the ecliptic. It will lie on the ecliptic +only when the moon is at one of her nodes. + +206. _When there will be an Eclipse of the Moon._--The moon is eclipsed +_whenever it passes into the umbra of the earth's shadow_. It will be +seen from the figure that the moon can pass into the shadow of the earth +only when she is in opposition, or _at full_. Owing to the inclination +of the moon's orbit to the ecliptic, the moon will pass either above or +below the earth's shadow when she is at full, unless she happens to be +near her node at this time: hence there is not an eclipse of the moon +every month. + +When the moon simply passes into the penumbra of the earth's shadow, the +light of the moon is somewhat dimmed, but not sufficiently to attract +attention, or to be denominated an eclipse. + +[Illustration: Fig. 236.] + +207. _The Lunar Ecliptic Limits._--In Fig. 236 the line _AB_ represents +the plane of the ecliptic, and the line _CD_ the moon's orbit. The large +black circles on the line _AB_ represent sections of the umbra of the +earth's shadow, and the smaller circles on _CD_ represent the moon at +full. It will be seen, that, if the moon is full at _E_, she will just +graze the umbra of the earth's shadow. In this case she will suffer no +eclipse. Were the moon full at any point nearer her node, as at _F_, she +would pass into the umbra of the earth's shadow, and would be +_partially_ eclipsed. Were the moon full at _G_, she would pass through +the centre of the earth's shadow, and be _totally_ eclipsed. + +It will be seen from the figure that full moon must occur when the moon +is within a certain distance from her node, in order that there may be a +lunar eclipse; and this space is called the _lunar ecliptic limits_. + +The farther the earth is from the sun, the less rapidly does its shadow +taper, and therefore the greater its diameter at the distance of the +moon; and, the nearer the moon to the earth, the greater the diameter of +the earth's shadow at the distance of the moon. Of course, the greater +the diameter of the earth's shadow, the greater the ecliptic limits: +hence the lunar ecliptic limits vary somewhat from time to time, +according to the distance from the earth to the sun and from the earth +to the moon. The limits within which an eclipse is inevitable under all +circumstances are called the _minor ecliptic limits_; and those within +which an eclipse is possible under some circumstances, the _major +ecliptic limits_. + +[Illustration: Fig. 237.] + +208. _Lunar Eclipses._--Fig. 237 shows the path of the moon through the +earth's shadow in the case of a _partial eclipse_. The magnitude of such +an eclipse depends upon the nearness of the moon to her nodes. The +magnitude of an eclipse is usually denoted in _digits_, a digit being +one-twelfth of the diameter of the moon. + +[Illustration: Fig. 238.] + +Fig. 238 shows the path of the moon through the earth's shadow in the +case of a _total eclipse_. It will be seen from the figure that it is +not necessary for the moon to pass through the centre of the earth's +shadow in order to have a total eclipse. When the moon passes through +the centre of the earth's shadow, the eclipse is both _total_ and +_central_. + +At the time of a total eclipse, the moon is not entirely invisible, but +shines with a faint copper-colored light. This light is refracted into +the shadow by the earth's atmosphere, and its amount varies with the +quantity of clouds and vapor in that portion of the atmosphere which the +sunlight must graze in order to reach the moon. + +The duration of an eclipse varies between very wide limits, being, of +course, greatest when the eclipse is central. A total eclipse of the +moon may last nearly two hours, or, including the _partial_ portions of +the eclipse, three or four hours. + +Every eclipse of the moon, whether total or partial, is visible at the +same time to the whole hemisphere of the earth which is turned towards +the moon; and the eclipse will have exactly the same magnitude at every +point of observation. + +209. _When there will be an Eclipse of the Sun._--There will be an +eclipse of the sun _whenever any portion of the moon's shadow is thrown +on the earth_. It will be seen from Fig. 235 that this can occur only +when the moon is in conjunction, or at _new_. It does not occur every +month, because, owing to the inclination of the moon's orbit to the +ecliptic, the moon's shadow is usually thrown either above or below the +earth at the time of new moon. There can be an eclipse of the sun only +when new moon occurs at or near one of the nodes of her orbit. + +210. _Solar Ecliptic Limits._--The distances from the moon's node within +which a new moon would throw some portion of its shadow on the earth so +as to produce an eclipse of the sun are called the _solar ecliptic +limits_. As in the case of the moon, there are _major_ and _minor_ +ecliptic limits; the former being the limits within which an eclipse of +the sun is _possible_ under some circumstances, and the latter those +under which an eclipse is _inevitable_ under all circumstances. + +The limits within which a solar eclipse may occur are greater than those +within which a lunar eclipse may occur. This will be evident from an +examination of Fig. 235. Were the moon in that figure just outside of +the lines _AB_ and _CD_, it will be seen that the penumbra of her shadow +would just graze the earth: hence the moon must be somewhere within the +space bounded by these lines in order to cause an eclipse of the sun. +Now, these lines mark the prolongation to the sun of the cone of the +umbra of the earth's shadow: hence, in order to produce an eclipse of +the sun, new moon must occur somewhere within this prolongation of the +umbra of the earth's shadow. Now, it is evident that the diameter of +this cone is greater on the side of the earth toward the sun than on the +opposite side: hence the solar ecliptic limits are greater than the +lunar ecliptic limits. + +211. _Solar Eclipses._--An observer in the umbra of the moon's shadow +would see a _total_ eclipse of the sun, while one in the penumbra would +see only a _partial_ eclipse. The magnitude of this partial eclipse +would depend upon the distance of the observer from the umbra of the +moon's shadow. + +[Illustration: Fig. 239.] + +[Illustration: Fig. 240.] + +The umbra of the moon's shadow is just about long enough to reach the +earth. Sometimes the point of this shadow falls short of the earth's +surface, as shown in Fig. 239, and sometimes it falls upon the earth, as +shown in Fig. 240, according to the varying distance of the sun and moon +from the earth. The diameter of the umbra at the surface of the earth is +seldom more than a hundred miles: hence the belt of a total eclipse is, +on the average, not more than a hundred miles wide; and a total eclipse +seldom lasts more than five or six minutes, and sometimes only a few +seconds. Owing, however, to the rotation of the earth, the umbra of the +moon's shadow may pass over a long reach of the earth's surface. Fig. +241 shows the track of the umbra of the moon's shadow over the earth in +the total eclipse of 1860. + +[Illustration: Fig. 241.] + +[Illustration: Fig. 242.] + +Fig. 242 shows the track of the total eclipse of 1871 across India and +the adjacent seas. + +[Illustration: Fig. 243.] + +[Illustration: Fig. 244.] + +In a partial eclipse of the sun, more or less of one side of the sun's +disk is usually concealed, as shown in Fig. 243. Occasionally, however, +the centre of the sun's disk is covered, leaving a bright ring around +the margin, as shown in Fig. 244. Such an eclipse is called an _annular_ +eclipse. An eclipse can be annular only when the cone of the moon's +shadow is too short to reach the earth, and then only to observers who +are in the central portion of the penumbra. + +212. _Comparative Frequency of Solar and Lunar Eclipses._--There are +more eclipses of the sun in the year than of the moon; and yet, at any +one place, eclipses of the moon are more frequent than those of the sun. + +There are more lunar than solar eclipses, because, as we have seen, the +limits within which a solar eclipse may occur are greater than those +within which a lunar eclipse may occur. There are more eclipses of the +moon visible at any one place than of the sun; because, as we have seen, +an eclipse of the moon, whenever it does occur, is visible to a whole +hemisphere at a time, while an eclipse of the sun is visible to only a +portion of a hemisphere, and a total eclipse to only a very small +portion of a hemisphere. A total eclipse of the sun is, therefore, a +very rare occurrence at any one place. + +The greatest number of eclipses that can occur in a year is seven, and +the least number, two. In the former case, five may be of the sun and +two of the moon, or four of the sun and three of the moon. In the latter +case, both must be of the sun. + + + VI. THE THREE GROUPS OF PLANETS. + + + I. GENERAL CHARACTERISTICS OF THE GROUPS. + + +213. _The Inner Group._--The _inner group_ of planets is composed of +_Mercury_, _Venus_, the _Earth_, and _Mars_; that is, of all the planets +which lie between the asteroids and the sun. The planets of this group +are comparatively small and dense. So far as known, they rotate on their +axes in about twenty-four hours, and they are either entirely without +moons, or are attended by comparatively few. + +The comparative sizes and eccentricities of the orbits of this group are +shown in Fig. 245. The dots round the orbits show the position of the +planets at intervals of ten days. + +[Illustration: Fig. 245.] + +214. _The Outer Group._--The _outer group_ of planets is composed of +_Jupiter_, _Saturn_, _Uranus_, and _Neptune_. These planets are all very +large and of slight density. So far as known, they rotate on their axes +in about ten hours, and are accompanied with complicated systems of +moons. Fig. 246, which represents the comparative sizes of the planets, +shows at a glance the immense difference between those of the inner and +outer group. Fig. 247 shows the comparative sizes and eccentricities of +the orbits of the outer planets. The dots round the orbits show the +position of the planets at intervals of a thousand days. + +[Illustration: Fig. 246.] + +[Illustration: Fig. 247.] + +215. _The Asteroids._--Between the inner and outer groups of planets +there is a great number of very small planets known as the _minor +planets_, or _asteroids_. Over two hundred planets belonging to this +group have already been discovered. Their orbits are shown by the dotted +lines in Fig. 247. The sizes of the four largest of these planets, +compared with the earth, are shown in Fig. 248. + +[Illustration: Fig. 248.] + +The asteroids of this group are distinguished from the other planets, +not only by their small size, but by the great eccentricities and +inclinations of their orbits. If we except Mercury, none of the larger +planets has an eccentricity amounting to one-tenth the diameter of its +orbit (43), nor is any orbit inclined more than two or three degrees to +the ecliptic; but the inclinations of many of the minor planets exceed +ten degrees, and the eccentricities frequently amount to an eighth of +the orbital diameter. The orbit of Pallas is inclined thirty-four +degrees to the ecliptic, while there are some planets of this group +whose orbits nearly coincide with the plane of the ecliptic. + +[Illustration: Fig. 249.] + +Fig. 249 shows one of the most and one of the least eccentric of the +orbits of this group as compared with that of the earth. + +[Illustration: Fig. 250.] + +The intricate complexity of the orbits of the asteroids is shown in Fig. +250. + + + II. THE INNER GROUP OF PLANETS. + + + Mercury. + + +216. _The Orbit of Mercury._--The orbit of Mercury is more eccentric +than that of any of the larger planets, and it has also a greater +inclination to the ecliptic. Its eccentricity (43) is a little over a +fifth, and its inclination to the ecliptic somewhat over seven degrees. +The mean distance of Mercury from the sun is about thirty-five million +miles; but, owing to the great eccentricity of its orbit, its distance +from the sun varies from about forty-three million miles at aphelion to +about twenty-eight million at perihelion. + +[Illustration: Fig. 251.] + +217. _Distance of Mercury from the Earth._--It is evident, from Fig. +251, that an inferior planet, like Mercury, is the whole diameter of its +orbit nearer the earth at inferior conjunction than at superior +conjunction: hence Mercury's distance from the earth varies +considerably. Owing to the great eccentricity of its orbit, its distance +from the earth at inferior conjunction also varies considerably. Mercury +is nearest to the earth when its inferior conjunction occurs at its own +aphelion and at the earth's perihelion. + +[Illustration: Fig. 252.] + +218. _Apparent Size of Mercury._--Since Mercury's distance from the +earth is variable, the apparent size of the planet is also variable. +Fig. 252 shows its apparent size at its extreme and mean distances from +the earth. Its apparent diameter varies from five seconds to twelve +seconds. + +[Illustration: Fig. 253.] + +219. _Volume and Density of Mercury._--The real diameter of Mercury is +about three thousand miles. Its size, compared with that of the earth, +is shown in Fig. 253. The earth is about sixteen times as large as +Mercury; but Mercury is about one-fifth more dense than the earth. + +220. _Greatest Elongation of Mercury._--Mercury, being an _inferior_ +planet (or one within the orbit of the earth), appears to oscillate to +and fro across the sun. Its greatest apparent distance from the sun, or +its _greatest elongation_, varies considerably. The farther Mercury is +from the sun, and the nearer the earth is to Mercury, the greater is its +angular distance from the sun at the time of its greatest elongation. +Under the most favorable circumstances, the greatest elongation amounts +to about twenty-eight degrees, and under the least favorable to only +sixteen or seventeen degrees. + +221. _Sidereal and Synodical Periods of Mercury._--Mercury accomplishes +a complete revolution around the sun in about eighty-eight days; but it +takes it a hundred and sixteen days to pass from its greatest elongation +east to the same elongation again. The orbital motion of this planet is +at the rate of nearly thirty miles a second. + +In Fig. 251, _P'''_ represents elongation east of the sun, and _P'_ +elongation west. It will be seen that it is much farther from _P'_ +around to _P'''_ than from _P'''_ on to _P'_. Mercury is only about +forty-eight days in passing from greatest elongation east to greatest +elongation west, while it is about sixty-eight days in passing back +again. + +222. _Visibility of Mercury._--Mercury is too close to the sun for +favorable observation. It is never seen long after sunset, or long +before sunrise, and never far from the horizon. When visible at all, it +must be sought for low down in the west shortly after sunset, or low in +the east shortly before sunrise, according as the planet is at its east +or west elongation. It is often visible to the naked eye in our +latitude; but the illumination of the twilight sky, and the excess of +vapor in our atmosphere near the horizon, combine to make the telescopic +study of the planet difficult and unsatisfactory. + +[Illustration: Fig. 254.] + +223. _The Atmosphere and Surface of Mercury._--Mercury seems to be +surrounded by a dense atmosphere. One proof of the existence of such an +atmosphere is furnished at the time of the planet's _transit_ across the +disk of the sun, which occasionally happens. The planet is then seen +surrounded by a border, as shown in Fig. 254. A bright spot has also +been observed on the dark disk of the planet during a transit, as shown +in Fig. 255. The border around the planet seems to be due to the action +of the planet's atmosphere; but it is difficult to account for the +bright spot. + +[Illustration: Fig. 255.] + +[Illustration: Fig. 256.] + +Schröter, a celebrated German astronomer, at about the beginning of the +present century, thought that he detected spots and shadings on the disk +of the planet, which indicated both the presence of an atmosphere and of +elevations. The shading along the terminator, which seemed to indicate +the presence of a twilight, and therefore of an atmosphere, are shown in +Fig. 256. It also shows the blunted aspect of one of the cusps, which +Schröter noticed at times, and which he attributed to the shadow of a +mountain, estimated to be ten or twelve miles high. Fig. 257 shows this +mountain near the upper cusp, as Schröter believed he saw it in the year +1800. By watching certain marks upon the disk of Mercury, Schröter came +to the conclusion that the planet rotates on its axis in about +twenty-four hours. Modern observers, with more powerful telescopes, have +failed to verify Schröter's observations as to the indications of an +atmosphere and of elevations. Nothing is known with certainty about the +rotation of the planet. + +[Illustration: Fig. 257.] + +The border around Mercury, and the bright spot on its disk at the time +of the transit of the planet across the sun, have been seen since +Schröter's time, and the existence of these phenomena is now well +established; but astronomers are far from being agreed as to their +cause. + +224. _Intra-Mercurial Planets._--It has for some time been thought +probable that there is a group of small planets between Mercury and the +sun; and at various times the discovery of such bodies has been +announced. In 1859 a French observer believed that he had detected an +intra-Mercurial planet, to which the name of _Vulcan_ was given, and for +which careful search has since been made, but without success. During +the total eclipse of 1878 Professor Watson observed two objects near the +sun, which he thought to be planets; but this is still matter of +controversy. + + + Venus. + + +225. _The Orbit of Venus._--The orbit of Venus has but slight +eccentricity, differing less from a circle than that of any other large +planet. It is inclined to the ecliptic somewhat more than three degrees. +The mean distance of the planet from the sun is about sixty-seven +million miles. + +226. _Distance of Venus from the Earth._--The distance of Venus from the +earth varies within much wider limits than that of Mercury. When Venus +is at inferior conjunction, her distance from the earth is ninety-two +million miles _minus_ sixty-seven million miles, or twenty-five million +miles; and when at superior conjunction it is ninety-two million miles +_plus_ sixty-seven million miles, or a hundred and fifty-nine million +miles. Venus is considerably more than _six times_ as far off at +superior conjunction as at inferior conjunction. + +[Illustration: Fig. 258.] + +227. _Apparent Size of Venus._--Owing to the great variation in the +distance of Venus from the earth, her apparent diameter varies from +about ten seconds to about sixty-six seconds. Fig. 258 shows the +apparent size of Venus at her extreme and mean distances from the earth. + +228. _Volume and Density of Venus._--The real size of Venus is about the +same as that of the earth, her diameter being only about three hundred +miles less. The comparative sizes of the two planets are shown in Fig. +259. The density of Venus is a little less than that of the earth. + +[Illustration: Fig. 259.] + +229. _The Greatest Elongation of Venus._--Venus, like Mercury, appears +to oscillate to and fro across the sun. The angular value of the +greatest elongation of Venus varies but slightly, its greatest value +being about forty-seven degrees. + +230. _Sidereal and Synodical Periods of Venus._--The _sidereal_ period +of Venus, or that of a complete revolution around the sun, is about two +hundred and twenty-five days; her orbital motion being at the rate of +nearly twenty-two miles a second. Her _synodical_ period, or the time it +takes her to pass around from her greatest eastern elongation to the +same elongation again, is about five hundred and eighty-four days, or +eighteen months. Venus is a hundred and forty-six days, or nearly five +months, in passing from her greatest elongation east through inferior +conjunction to her greatest elongation west. + +231. _Venus as a Morning and an Evening Star._--For a period of about +nine months, while Venus is passing from superior conjunction to her +greatest eastern elongation, she will be east of the sun, and will +therefore set after the sun. During this period she is the _evening +star_, the _Hesperus_ of the ancients. While passing from inferior +conjunction to superior conjunction, Venus is west of the sun, and +therefore rises before the sun. During this period of nine months she is +the _morning star_, the _Phosphorus_, or _Lucifer_, of the ancients. + +232. _Brilliancy of Venus._--Next to the sun and moon, Venus is at times +the most brilliant object in the heavens, being bright enough to be seen +in daylight, and to cast a distinct shadow at night. Her brightness, +however, varies considerably, owing to her phases and to her varying +distance from the earth. She does not appear brightest when at full, for +she is then farthest from the earth, at superior conjunction; nor does +she appear brightest when nearest the earth, at inferior conjunction, +for her phase is then a thin crescent (see Fig. 258). She is most +conspicuous while passing from her greatest eastern elongation to her +greatest western elongation. After she has passed her eastern +elongation, she becomes brighter and brighter till she is within about +forty degrees of the sun. Her phase at this point in her orbit is shown +in Fig. 260. Her brilliancy then begins to wane, until she comes too +near the sun to be visible. When she re-appears on the west of the sun, +she again becomes more brilliant; and her brilliancy increases till she +is about forty degrees from the sun, when she is again at her brightest. +Venus passes from her greatest brilliancy as an evening star to her +greatest brilliancy as a morning star in about seventy-three days. She +has the same phase, and is at the same distance from the earth, in both +cases of maximum brilliancy. Of course, the brilliancy of Venus when at +the maximum varies somewhat from time to time, owing to the +eccentricities of the orbits of the earth and of Venus, which cause her +distance from the earth, at her phase of greatest brilliancy, to vary. +She is most brilliant when the phase of her greatest brilliancy occurs +when she is at her aphelion and the earth at its perihelion. + +[Illustration: Fig. 260.] + +233. _The Atmosphere and Surface of Venus._--Schröter believed that he +saw shadings and markings on Venus similar to those on Mercury, +indicating the presence of an atmosphere and of elevations on the +surface of the planet. Fig. 261 represents the surface of Venus as it +appeared to this astronomer. By watching certain markings on the disk of +Venus, Schröter came to the conclusion that Venus rotates on her axis in +about twenty-four hours. + +[Illustration: Fig. 261.] + +It is now generally conceded that Venus has a dense atmosphere; but +Schröter's observations of the spots on her disk have not been verified +by modern astronomers, and we really know nothing certainly of her +rotation. + +234. _Transits of Venus._--When Venus happens to be near one of the +nodes of her orbit when she is in inferior conjunction, she makes a +transit across the sun's disk. These transits occur in pairs, separated +by an interval of over a hundred years. The two transits of each pair +are separated by an interval of eight years, the dates of the most +recent being 1874 and 1882. Venus, like Mercury, appears surrounded with +a border on passing across the sun's disk, as shown in Fig. 262. + +[Illustration: Fig. 262.] + + + Mars. + + +235. _The Orbit of Mars._--The orbit of Mars is more eccentric than that +of any of the larger planets, except Mercury; its eccentricity being +about one-eleventh. The inclination of the orbit to the ecliptic is +somewhat under two degrees. The mean distance of Mars from the sun is +about a hundred and forty million miles; but, owing to the eccentricity +of his orbit, the distance varies from a hundred and fifty-three million +miles to a hundred and twenty-seven million miles. + +[Illustration: Fig. 263.] + +236. _Distance of Mars from the Earth._--It will be seen, from Fig. 263, +that a _superior_ planet (or one outside the orbit of the earth), like +Mars, is nearer the earth, by the whole diameter of the earth's orbit, +when in opposition than when in conjunction. The mean distance of Mars +from the earth, at the time of opposition, is a hundred and forty +million miles _minus_ ninety-two million miles, or forty-eight million +miles. Owing to the eccentricity of the orbit of the earth and of Mars, +the distance of this planet when in opposition varies considerably. When +the earth is in aphelion, and Mars in perihelion, at the time of +opposition, the distance of the planet from the earth is only about +thirty-three million miles. On the other hand, when the earth is in +perihelion, and Mars in aphelion, at the time of opposition, the +distance of the planet is over sixty-two million miles. + +The mean distance of Mars from the earth when in conjunction is a +hundred and forty million miles _plus_ ninety-two million miles, or two +hundred and thirty-two million miles. It will therefore be seen that +Mars is nearly five times as far off at conjunction as at opposition. + +[Illustration: Fig. 264.] + +237. _The Apparent Size of Mars._--Owing to the varying distance of Mars +from the earth, the apparent size of the planet varies almost as much as +that of Venus. Fig. 264 shows the apparent size of Mars at its extreme +and mean distances from the earth. The apparent diameter varies from +about four seconds to about thirty seconds. + +[Illustration: Fig. 265.] + +238. _The Volume and Density of Mars._--Among the larger planets Mars is +next in size to Mercury. Its real diameter is somewhat more than four +thousand miles, and its bulk is about one-seventh of that of the earth. +Its size, compared with that of the earth, is shown in Fig. 265. + +[Illustration: Plate 4.] + +The density of Mars is only about three-fourths of that of the earth. + +239. _Sidereal and Synodical Periods of Mars._--The _sidereal_ period of +Mars, or the time in which he makes a complete revolution around the +sun, is about six hundred and eighty-seven days, or nearly twenty-three +months; but he is about seven hundred and eighty days in passing from +opposition to opposition again, or in performing a _synodical_ +revolution. Mars moves in his orbit at the rate of about fifteen miles a +second. + +240. _Brilliancy of Mars._--When near his opposition, Mars is easily +recognized with the naked eye by his fiery-red light. He is much more +brilliant at some oppositions than at others, for reasons already +explained (236), but always shines brighter than an ordinary star of the +first magnitude. + +241. _Telescopic Appearance of Mars._--When viewed with a good telescope +(see Plate IV.), Mars is seen to be covered with dusky, dull-red +patches, which are supposed to be continents, like those of our own +globe. Other portions, of a greenish hue, are believed to be tracts of +water. The ruddy color, which overpowers the green, and makes the whole +planet seem red to the naked eye, was believed by Sir J. Herschel to be +due to an ochrey tinge in the general soil, like that of the red +sandstone districts on the earth. In a telescope, Mars appears less red, +and the higher the power the less the intensity of the color. The disk, +when well seen, is mapped out in a way which gives at once the +impression of land and water. The bright part is red inclining to +orange, sometimes dotted with brown and greenish points. The darker +spaces, which vary greatly in depth of tone, are of a dull gray-green, +having the aspect of a fluid which absorbs the solar rays. The +proportion of land to water on the earth appears to be reversed on Mars. +On the earth every continent is an island; on Mars all seas are lakes. +Long, narrow straits are more common than on the earth; and wide +expanses of water, like our Atlantic Ocean, are rare. (See Fig. 266.) + +[Illustration: Fig. 266.] + +[Illustration: Fig. 267.] + +Fig. 267 represents a chart of the surface of Mars, which has been +constructed from careful telescopic observation. The outlines, as seen +in the telescope, are, however, much less distinct than they are +represented here; and it is by no means certain that the light and dark +portions are bodies of land and water. + +In the vicinity of the poles brilliant white spots may be noticed, which +are considered by many astronomers to be masses of snow. This conjecture +is favored by the fact that they appear to diminish under the sun's +influence at the beginning of the Martial summer, and to increase again +on the approach of winter. + +242. _Rotation of Mars._--On watching Mars with a telescope, the spots +on the disk are found to move (as shown in Fig. 268) in a manner which +indicates that the planet rotates in about twenty-four hours on an axis +inclined about twenty-eight degrees from a perpendicular to the plane of +its orbit. The inclination of the axis is shown in Fig. 269. It is +evident from the figure that the variation in the length of day and +night, and the change of seasons, are about the same on Mars as on the +earth. The changes will, of course, be somewhat greater, and the seasons +will be about twice as long. + +[Illustration: Fig. 268.] + +[Illustration: Fig. 269.] + +[Illustration: Fig. 270.] + +243. _The Satellites of Mars._--In 1877 Professor Hall of the Washington +Observatory discovered that Mars is accompanied by two small moons, +whose orbits are shown in Fig. 270. The inner satellite has been named +_Phobos_, and the outer one _Deimos_. It is estimated that the diameter +of the outer moon is from five to ten miles, and that of the inner one +from ten to forty miles. + +Phobos is remarkable for its nearness to the planet and the rapidity of +its revolution, which is performed in seven hours thirty-eight minutes. +Its distance from the centre of the planet is about six thousand miles, +and from the surface less than four thousand. Astronomers on Mars, with +telescopes and eyes like ours, could readily find out whether this +satellite is inhabited, the distance being less than one-sixtieth of +that of our moon. + +It will be seen that Phobos makes about three revolutions to one +rotation of the planet. It will, of course, rise in the west; though the +sun, the stars, and the other satellite rise in the east. Deimos makes a +complete revolution in about thirty hours. + + + III. THE ASTEROIDS. + + +244. _Bode's Law of Planetary Distances._--There is a very remarkable +law connecting the distances of the planets from the sun, which is +generally known by the name of _Bode's Law_. Attention was drawn to it +in 1778 by the astronomer Bode, but he was not really its author. + +To express this law we write the following series of numbers:-- + + 0, 3, 6, 12, 24, 48, 96; + +each number, with the exception of the first, being double the one which +precedes it. If we add 4 to each of these numbers, the series becomes-- + + 4, 7, 10, 16, 28, 52, 100; + +which series was known to Kepler. These numbers, with the exception of +28, are sensibly proportional to the distances of the principal planets +from the sun, the actual distances being as follows:-- + + Mercury. Venus. Earth. Mars. ---- Jupiter. Saturn. + + 3·9 7·2 10 15·2 52·9 95·4 + +245. _The First Discovery of the Asteroids._--The great gap between Mars +and Jupiter led astronomers, from the time of Kepler, to suspect the +existence of an unknown planet in this region; but no such planet was +discovered till the beginning of the present century. _Ceres_ was +discovered Jan. 1, 1801, _Pallas_ in 1802, _Juno_ in 1804, and _Vesta_ +in 1807. Then followed a long interval of thirty-eight years before +_Astræa_, the fifth of these minor planets, was discovered in 1845. + +246. _Olbers's Hypothesis._--After the discovery of Pallas, Olbers +suggested his celebrated hypothesis, that the two bodies might be +fragments of a single planet which had been shattered by some explosion. +If such were the case, the orbits of all the fragments would at first +intersect each other at the point where the explosion occurred. He +therefore thought it likely that other fragments would be found, +especially if a search were kept up near the intersection of the orbits +of Ceres and Pallas. + + Professor Newcomb makes the following observations concerning this + hypothesis:-- + + "The question whether these bodies could ever have formed a single + one has now become one of cosmogony rather than of astronomy. If a + planet were shattered, the orbit of each fragment would at first + pass through the point at which the explosion occurred, however + widely they might be separated through the rest of their course; + but, owing to the secular changes produced by the attractions of the + other planets, this coincidence would not continue. The orbits would + slowly move away, and after the lapse of a few thousand years no + trace of a common intersection would be seen. It is therefore + curious that Olbers and his contemporaries should have expected to + find such a region of intersection, as it implied that the explosion + had occurred within a few thousand years. The fact that the required + conditions were not fulfilled was no argument against the + hypothesis, because the explosion might have occurred millions of + years ago; and in the mean time the perihelion and node of each + orbit would have made many entire revolutions, so that the orbits + would have been completely mixed up.... A different explanation of + the group is given by the nebular hypothesis; so that Olbers's + hypothesis is no longer considered by astronomers." + +247. _Later Discoveries of Asteroids._--Since 1845 over two hundred +asteroids have been discovered. All these are so small, that it requires +a very good telescope to see them; and even in very powerful telescopes +they appear as mere points of light, which can be distinguished from the +stars only by their motions. + +To facilitate the discovery of these bodies, very accurate maps have +been constructed, including all the stars down to the thirteenth +magnitude in the neighborhood of the ecliptic. A reduced copy of one of +these maps is shown in Fig. 271. + +[Illustration: Fig. 271.] + +Furnished with a map of this kind, and with a telescope powerful enough +to show all the stars marked on it, the observer who is searching for +these small planets will place in the field of view of his telescope six +spider-lines at right angles to each other, and at equal distances +apart, in such a manner that several small squares will be formed, +embracing just as much of the heavens as do those shown in the map. He +will then direct his telescope to the region of the sky he wishes to +examine, represented by the map, so as to be able to compare +successively each square with the corresponding portion of the sky. Fig. +272 shows at the right hand the squares in the telescopic field of view, +and at the left hand the corresponding squares of the map. + +[Illustration: Fig. 272.] + +He can then assure himself if the numbers and positions of the stars +mapped, and of the stars observed, are identical. If he observes in the +field of view a luminous point which is not marked in the map, it is +evident that either the new body is a star of variable brightness which +was not visible at the time the map was made, or it is a planet, or +perhaps a comet. If the new body remains fixed at the same point, it is +the former; but, if it changes its position with regard to the +neighboring stars, it is the latter. The motion is generally so +sensible, that in the course of one evening the change of position may +be detected; and it can soon be determined, by the direction and rate of +the motion, whether the body is a planet or a comet. + + + IV. OUTER GROUP OF PLANETS. + + + Jupiter. + + +248. _Orbit of Jupiter._--The orbit of Jupiter is inclined only a little +over one degree to the ecliptic; and its eccentricity is only about half +of that of Mars, being less than one-twentieth. The mean distance of +Jupiter from the sun is about four hundred and eighty million miles; +but, owing to the eccentricity of his orbit, his actual distance from +the sun ranges from four hundred and fifty-seven to five hundred and +three million miles. + +249. _Distance of Jupiter from the Earth._--When Jupiter is in +opposition, his mean distance from the earth is four hundred and eighty +million miles _minus_ ninety-two million miles, or three hundred and +eighty-eight million miles, and, when he is in conjunction, four hundred +and eighty million miles _plus_ ninety-two million miles, or five +hundred and seventy-two million miles. It will be seen that he is less +than twice as far off in conjunction as in opposition, and that the +ratio of his greatest to his least distance is very much less than in +the case of Venus and Mars. This is owing to his very much greater +distance from the sun. Owing to the eccentricities of the orbits of the +earth and of Jupiter, the greatest and least distances of Jupiter from +the earth vary somewhat from year to year. + +[Illustration: Fig. 273.] + +250. _The Brightness and Apparent Size of Jupiter._--The apparent +diameter of Jupiter varies from about fifty seconds to about thirty +seconds. His apparent size at his extreme and mean distances from the +earth is shown in Fig. 273. + +Jupiter shines with a brilliant white light, which exceeds that of every +other planet except Venus. The planet is, of course, brightest when near +opposition. + +251. _The Volume and Density of Jupiter._--Jupiter is the "giant planet" +of our system, his mass largely exceeding that of all the other planets +combined. His mean diameter is about eighty-five thousand miles; but the +equatorial exceeds the polar diameter by five thousand miles. In volume +he exceeds our earth about thirteen hundred times, but in mass only +about two hundred and thirteen times. His specific gravity is, +therefore, far less than that of the earth, and even less than that of +water. The comparative size of Jupiter and the earth is shown in Fig. +274. + +[Illustration: Fig. 274.] + +252. _The Sidereal and Synodical Periods of Jupiter._--It takes Jupiter +nearly twelve years to make a _sidereal_ revolution, or a complete +revolution around the sun, his orbital motion being at the rate of about +eight miles a second. His _synodical_ period, or the time of his passage +from opposition to opposition again, is three hundred and ninety-eight +days. + +253. _The Telescopic Aspect of Jupiter._--There are no really permanent +markings on the disk of Jupiter; but his surface presents a very +diversified appearance. The earlier telescopic observers descried dark +belts across it, one north of the equator, and the other south of it. +With the increase of telescopic power, it was seen that these bands were +of a more complex structure than had been supposed, and consisted of +stratified, cloud-like appearances, varying greatly in form and number. +These change so rapidly, that the face of the planet rarely presents the +same appearance on two successive nights. They are most strongly marked +at some distance on each side of the planet's equator, and thus appear +as two belts under a low magnifying power. + +Both the outlines of the belts, and the color of portions of the planet, +are subject to considerable changes. The equatorial regions, and the +spaces between the belts generally, are often of a rosy tinge. This +color is sometimes strongly marked, while at other times hardly a trace +of it can be seen. A general telescopic view of Jupiter is given in +Plate V. + +[Illustration: Plate 5.] + +254. _The Physical Constitution of Jupiter._--From the changeability of +the belts, and of nearly all the visible features of Jupiter, it is +clear that what we see on that planet is not the solid nucleus, but +cloud-like formations, which cover the entire surface to a great depth. +The planet appears to be covered with a deep and dense atmosphere, +filled with thick masses of clouds and vapor. Until recently this +cloud-laden atmosphere was supposed to be somewhat like that of our +globe; but at present the physical constitution of Jupiter is believed +to resemble that of the sun rather than that of the earth. Like the sun, +he is brighter in the centre than near the edges, as is shown in the +transits of the satellites over his disk. When the satellite first +enters on the disk, it commonly seems like a bright spot on a dark +background; but, as it approaches the centre, it appears like a dark +spot on the bright surface of the planet. The centre is probably two or +three times brighter than the edges. This may be, as in the case of the +sun, because the light near the edge passes through a greater depth of +atmosphere, and is diminished by absorption. + +It has also been suspected that Jupiter shines partly by his own light, +and not wholly by reflected sunlight. The planet cannot, however, emit +any great amount of light; for, if it did, the satellites would shine by +this light when they are in the shadow of the planet, whereas they +totally disappear. It is possible that the brighter portions of the +surface are from time to time slightly self-luminous. + +[Illustration: Fig. 275.] + +Again: the interior of Jupiter seems to be the seat of an activity so +enormous that it can be ascribed only to intense heat. Rapid movements +are always occurring on his surface, often changing its aspect in a few +hours. It is therefore probable that Jupiter is not yet covered by a +solid crust, and that the fiery interior, whether liquid or gaseous, is +surrounded by the dense vapors which cease to be luminous on rising into +the higher and cooler regions of the atmosphere. Figs. 275 and 276 show +the disk of Jupiter as it appeared in December, 1881. + +[Illustration: Fig. 276.] + +255. _Rotation of Jupiter_.--Spots are sometimes visible which are much +more permanent than the ordinary markings on the belts. The most +remarkable of these is "the great red spot," which was first observed in +July, 1878, and is still to be seen in February, 1882. It is shown just +above the centre of the disk in Fig. 275. By watching these spots from +day to day, the time of Jupiter's axial rotation has been found to be +about nine hours and fifty minutes. + +The axis of Jupiter deviates but slightly from a perpendicular to the +plane of its orbit, as is shown in Fig. 277. + +[Illustration: Fig. 277.] + + + THE SATELLITES OF JUPITER. + + +[Illustration: Fig. 278.] + +256. _Jupiter's Four Moons._--Jupiter is accompanied by four moons, as +shown in Fig. 278. The diameters of these moons range from about +twenty-two hundred to thirty-seven hundred miles. The second from the +planet is the smallest, and the third the largest. The smallest is about +the size of our moon; the largest considerably exceeds Mercury, and +almost rivals Mars, in bulk. The sizes of these moons, compared with +those of the earth and its moon, are shown in Fig. 279. + +[Illustration: Fig. 279.] + +The names of these satellites, in the order of their distance from the +planet, are _Io_, _Europa_, _Ganymede_, and _Callisto_. Their times of +revolution range from about a day and three-fourths up to about sixteen +days and a half. Their orbits are shown in Fig. 280. + +[Illustration: Fig. 280.] + +257. _The Variability of Jupiter's Satellites._--Remarkable variations +in the light of these moons have led to the supposition that violent +changes are taking place on their surfaces. It was formerly believed, +that, like our moon, they always present the same face to the planet, +and that the changes in their brilliancy are due to differences in the +luminosity of parts of their surface which are successively turned +towards us during a revolution; but careful measurements of their light +show that this hypothesis does not account for the changes, which are +sometimes very sudden. The satellites are too distant for examination of +their surfaces with the telescope: hence it is impossible to give any +certain explanation of these phenomena. + +[Illustration: Fig. 281.] + +258. _Eclipses of Jupiter's Satellites._--Jupiter, like the earth, casts +a shadow away from the sun, as shown in Fig. 281; and, whenever one of +his moons passes into this shadow, it becomes eclipsed. On the other +hand, whenever one of the moons throws its shadow on Jupiter, the sun is +eclipsed to that part of the planet which lies within the shadow. + +To the inhabitants of Jupiter (if there are any, and if they can see +through the clouds) these eclipses must be very familiar affairs; for in +consequence of the small inclinations of the orbits of the satellites to +the planet's equator, and the small inclination of the latter to the +plane of Jupiter's orbit, all the satellites, except the most distant +one, are eclipsed in every revolution. A spectator on Jupiter might +therefore witness during the planetary year forty-five hundred eclipses +of the moons, and about the same number of the sun. + +[Illustration: Fig. 282.] + +259. _Transits of Jupiter's Satellites._--Whenever one of Jupiter's +moons passes in front of the planet, it is said to make a _transit_ +across his disk. When a moon is making a transit, it presents its bright +hemisphere towards the earth, as will be seen from Fig. 282: hence it is +usually seen as a bright spot on the planet's disk; though sometimes, on +the brighter central portions of the disk, it appears dark. + +[Illustration: Fig. 283.] + +It will be seen from Fig. 282 that the shadow of a moon does not fall +upon the part of the planet's disk that is covered by the moon: hence we +may observe the transit of both the moon and its shadow. The shadow +appears as a small black spot, which will precede or follow the moon +according to the position of the earth in its orbit. Fig. 283 shows two +moons of Jupiter in transit. + +260. _Occultations of Jupiter's Satellites._--The eclipse of a moon of +Jupiter must be carefully distinguished from the _occultation_ of a moon +by the planet. In the case of an eclipse, the moon ceases to be visible, +because the mass of Jupiter is interposed between the sun and the moon, +which ceases to be luminous, because the sun's light is cut off; but, in +the case of an occupation, the moon gets into such a position that the +body of Jupiter is interposed between it and the earth, thus rendering +the moon invisible to us. The third satellite, _m''_ (Fig. 282), is +invisible from the earth _E_, having become _occulted_ when it passed +behind the planet's disk; but it will not be _eclipsed_ until it passes +into the shadow of Jupiter. + +261. _Jupiter without Satellites._--It occasionally happens that every +one of Jupiter's satellites will disappear at the same time, either by +being eclipsed or occulted, or by being in transit. In this event, +Jupiter will appear without satellites. This occurred on the 21st of +August, 1867. The position of Jupiter's satellites at this time is shown +in Fig. 284. + +[Illustration: Fig. 284.] + + + Saturn. + + + + + THE PLANET AND HIS MOONS. + + +262. _The Orbit of Saturn._--The orbit of Saturn is rather more +eccentric than that of Jupiter, its eccentricity being somewhat more +than one-twentieth. Its inclination to the ecliptic is about two degrees +and a half. The mean distance of Saturn from the sun is about eight +hundred and eighty million miles. It is about a hundred million miles +nearer the sun at perihelion than at aphelion. + +263. _Distance of Saturn from the Earth._--The mean distance of Saturn +from the earth at opposition is eight hundred and eighty million miles +_minus_ ninety-two million miles, or seven hundred and eighty-eight +million; and at conjunction, eight hundred and eighty million miles +_plus_ ninety-two million, or nine hundred and seventy-two million. +Owing to the eccentricity of the orbit of Saturn, his distance from the +earth at opposition and at conjunction varies by about a hundred million +miles at different times; but he is so immensely far away, that this is +only a small fraction of his mean distance. + +264. _Apparent Size and Brightness of Saturn._--The apparent diameter of +Saturn varies from about twenty seconds to about fourteen seconds. His +apparent size at his extreme and mean distances from the earth is shown +in Fig. 285. + +[Illustration: Fig. 285.] + +The planet generally shines with the brilliancy of a moderate +first-magnitude star, and with a dingy, reddish light, as if seen +through a smoky atmosphere. + +265. _Volume and Density of Saturn._--The real diameter of Saturn is +about seventy thousand miles, and its volume over seven hundred times +that of the earth. The comparative size of the earth and Saturn is shown +in Fig. 286. This planet is a little more than half as dense as Jupiter. + +[Illustration: Fig. 286.] + +266. _The Sidereal and Synodical Periods of Saturn._--Saturn makes a +complete revolution round the sun in a period of about twenty-nine years +and a half, moving in his orbit at the rate of about six miles a second. +The planet passes from opposition to opposition again in a period of +three hundred and seventy-eight days, or thirteen days over a year. + +267. _Physical Constitution of Saturn._--The physical constitution of +Saturn seems to resemble that of Jupiter; but, being twice as far away, +the planet cannot be so well studied. The farther an object is from the +sun, the less it is illuminated; and, the farther it is from the earth, +the smaller it appears: hence there is a double difficulty in examining +the more distant planets. Under favorable circumstances, the surface of +Saturn is seen to be diversified with very faint markings; and, with +high telescopic powers, two or more very faint streaks, or belts, may be +discerned parallel to its equator. These belts, like those of Jupiter, +change their aspect from time to time; but they are so faint that the +changes cannot be easily followed. It is only on rare occasions that the +time of rotation can be determined from a study of the markings. + +268. _Rotation of Saturn._--On the evening of Dec. 7, 1876, Professor +Hall, who had been observing the satellites of Saturn with the great +Washington telescope (18), saw a brilliant white spot near the equator +of the planet. It seemed as if an immense eruption of incandescent +matter had suddenly burst up from the interior. The spot gradually +spread itself out into a long light streak, of which the brightest point +was near the western end. It remained visible until January, when it +became faint and ill-defined, and the planet was lost in the rays of the +sun. + +From all the observations on this spot, Professor Hall found the period +of Saturn to be ten hours fourteen minutes, reckoning by the brightest +part of the streak. Had the middle of the streak been taken, the time +would have been less, because the bright matter seemed to be carried +along in the direction of the planet's rotation. If this motion was due +to a wind, the velocity of the current must have been between fifty and +a hundred miles an hour. The axis of Saturn is inclined twenty-seven +degrees from the perpendicular to its orbit. + +[Illustration: Fig. 287.] + +269. _The Satellites of Saturn._--Saturn is accompanied by eight moons. +Seven of these are shown in Fig. 287. The names of these satellites, in +the order of their distances from the planet, are given in the +accompanying table:-- + + Number. Name. Distance Sidereal Discoverer. + from Period. + Planet + + 1 Mimas 120,800 0 22 37 0.94 Herschel + + 2 Enceladus 155,000 1 8 53 1.37 Herschel + + 3 Tethys 191,900 1 21 18 1.88 Cassini + + 4 Dione 245,800 2 17 41 2.73 Cassini + + 5 Rhea 343,400 4 12 25 4.51 Cassini + + 6 Titan 796,100 15 22 41 15.94 Huyghens + + 7 Hyperion 963,300 21 7 7 21.29 Bond + + 8 Japetus 2,313,800 79 7 53 79.33 Cassini + +The apparent brightness or visibility of these satellites follows the +order of their discovery. The smallest telescope will show Titan, and +one of very moderate size will show Japetus in the western part of its +orbit. An instrument of four or five inches aperture will show Rhea, and +perhaps Tethys and Dione; while seven or eight inches are required for +Enceladus, even at its greatest elongation from the planet. Mimas can +rarely be seen except at its greatest elongation, and then only with an +aperture of twelve inches or more. Hyperion can be detected only with +the most powerful telescopes, on account of its faintness and the +difficulty of distinguishing it from minute stars. + +_Japetus_, the outermost satellite, is remarkable for the fact, that +while, in one part of its orbit, it is the brightest of the satellites +except Titan, in the opposite part it is almost as faint as Hyperion, +and can be seen only in large telescopes. When west of the planet, it is +bright; when east of it, faint. This peculiarity has been accounted for +by supposing that the satellite, like our moon, always presents the same +face to the planet, and that one side of it is white and the other +intensely black; but it is doubtful whether any known substance is so +black as one side of the satellite must be to account for such +extraordinary changes of brilliancy. + +[Illustration: Fig. 288.] + +_Titan_, the largest of these satellites, is about the size of the +largest satellite of Jupiter. The relative sizes of the satellites are +shown in Fig. 288, and their orbits in Fig. 289. + +[Illustration: Fig. 289.] + +[Illustration: Fig. 290.] + +Fig. 290 shows the transit of one of the satellites, and of its shadow, +across the disk of the planet. + + + THE RINGS OF SATURN. + + +270. _General Appearance of the Rings._--Saturn is surrounded by a thin +flat ring lying in the plane of its equator. This ring is probably less +than a hundred miles thick. The part of it nearest Saturn reflects +little sunlight to us; so that it has a dusky appearance, and is not +easily seen, although it is not quite so dark as the sky seen between it +and the planet. The outer edge of this dusky portion of the ring is at a +distance from Saturn of between two and three times the earth's +diameter. Outside of this dusky part of the ring is a much brighter +portion, and outside of this another, which is somewhat fainter, but +still so much brighter than the dusky part as to be easily seen. The +width of the brighter parts of the ring is over three times the earth's +diameter. To distinguish the parts, the outer one is called ring _A_, +the middle one ring _B_, and the dusky one ring _C_. Between _A_ and _B_ +is an apparently open space, nearly two thousand miles wide, which looks +like a black line on the ring. Other divisions in the ring have been +noticed at times; but this is the only one always seen with good +telescopes at times when either side of the ring is in view from the +earth. The general telescopic appearance of the ring is shown in Fig. +291. + +[Illustration: Fig. 291.] + +[Illustration: Fig. 292.] + +Fig. 292 shows the divisions of the rings as they were seen by Bond. + +271. _Phases of Saturn's Ring._--The ring is inclined to the plane of +the planet's orbit by an angle of twenty-seven degrees. The general +aspect from the earth is nearly the same as from the sun. As the planet +revolves around the sun, the axis and plane of the ring keep the same +direction in space, just as the axis of the earth and the plane of the +equator do. + +When the planet is in one part of its orbit, we see the upper or +northern side of the ring at an inclination of twenty-seven degrees, the +greatest angle at which the ring can ever be seen. This phase of the +ring is shown in Fig. 293. + +[Illustration: Fig. 293.] + +When the planet has moved through a quarter of a revolution, the edge of +the ring is turned towards the sun and the earth; and, owing to its +extreme thinness, it is visible only in the most powerful telescopes as +a fine line of light, stretching out on each side of the planet. This +phase of the ring is shown in Fig. 294. + +[Illustration: Fig. 294.] + +All the satellites, except Japetus, revolve very nearly in the plane of +the ring: consequently, when the edge of the ring is turned towards the +earth, the satellites seem to swing from one side of the planet to the +other in a straight line, running along the thin edge of the ring like +beads on a string. This phase affords the best opportunity of seeing the +inner satellites, Mimas and Enceladus, which at other times are obscured +by the brilliancy of the ring. + +[Illustration: Fig. 295.] + +Fig. 295 shows a phase of the ring intermediate between the last two. + +When the planet has moved ninety degrees farther, we again see the ring +at an angle of twenty-seven degrees; but now it is the lower or southern +side which is visible. When it has moved ninety degrees farther, the +edge of the ring is again turned towards the earth and sun. + +[Illustration: Fig. 295.] + +The successive phases of Saturn's ring during a complete revolution are +shown in Fig. 296. + +It will be seen that there are two opposite points of Saturn's orbit in +which the rings are turned edgewise to us, and two points half-way +between the former in which the ring is seen at its maximum inclination +of about twenty-seven degrees. Since the planet performs a revolution in +twenty-nine years and a half, these phases occur at average intervals of +about seven years and four months. + +[Illustration: Fig. 297.] + +[Illustration: Fig. 298.] + +272. _Disappearance of Saturn's Ring._--It will be seen from Fig. 297 +that the plane of the ring may not be turned towards the sun and the +earth at exactly the same time, and also that the earth may sometimes +come on one side of the plane of the ring while the sun is shining on +the other. In the figure, _E_, _E'_, _E''_, and _E'''_ is the orbit of +the earth. When Saturn is at _S'_, or opposite, at _F_, the plane of the +ring will pass through the sun, and then only the edge of the ring will +be illumined. Were Saturn at _S_, and the earth at _E'_, the plane of +the ring would pass through the earth. This would also be the case were +the earth at _E'''_, and Saturn at _S''_. Were Saturn at _S_ or at +_S''_, and the earth farther to the left or to the right, the sun would +be shining on one side of the ring while we should be looking on the +other. In all these cases the ring will disappear entirely in a +telescope of ordinary power. With very powerful telescopes the ring will +appear, in the first two cases, as a thin line of light (Fig. 298). It +will be seen that all these cases of disappearance must take place when +Saturn is in the parts of his orbit intercepted between the parallel +lines _AC_ and _BD_. These lines are tangent to the earth's orbit, which +they enclose, and are parallel to the plane of Saturn's ring. As Saturn +passes away from these two lines on either side, the rings appear more +and more open. When the dark side of the ring is in view, it appears as +a black line crossing the planet; and on such occasions the sunlight +reflected from the outer and inner edges of the rings _A_ and _B_ +enables us to see traces of the ring on each side of Saturn, at least in +places where two such reflections come nearly together. Fig. 299 +illustrates this reflection from the edges at the divisions of the +rings. + +[Illustration: Fig. 299.] + +273. _Changes in Saturn's Ring._--The question whether changes are going +on in the rings of Saturn is still unsettled. Some observers have +believed that they saw additional divisions in the rings from time to +time; but these may have been errors of vision, due partly to the +shading which is known to exist on portions of the ring. + +Professor Newcomb says, "As seen with the great Washington equatorial in +the autumn of 1874, there was no great or sudden contrast between the +inner or dark edge of the bright ring and the outer edge of the dusky +ring. There was some suspicion that the one shaded into the other by +insensible gradations. No one could for a moment suppose, as some +observers have, that there was a separation between these two rings. All +these considerations give rise to the question whether the dusky ring +may not be growing at the expense of the inner bright ring." + +Struve, in 1851, advanced the startling theory that the inner edge of +the ring was gradually approaching the planet, the whole ring spreading +inwards, and making the central opening smaller. The theory was based +upon the descriptions and drawings of the rings by the astronomers of +the seventeenth century, especially Huyghens, and the measures made by +later astronomers up to 1851. This supposed change in the dimension of +the ring is shown in Fig. 300. + +[Illustration: Fig. 300.] + +274. _Constitution of Saturn's Ring._--The theory now generally held by +astronomers is, that the ring is composed of a cloud of satellites too +small to be separately seen in the telescope, and too close together to +admit of visible intervals between them. The ring looks solid, because +its parts are too small and too numerous to be seen singly. They are +like the minute drops of water that make up clouds and fogs, which to +our eyes seem like solid masses. In the dusky ring the particles may be +so scattered that we can see through the cloud, the duskiness being due +to the blending of light and darkness. Some believe, however, that the +duskiness is caused by the darker color of the particles rather than by +their being farther apart. + + + Uranus. + + +275. _Orbit and Dimensions of Uranus._--Uranus, the smallest of the +outer group of planets, has a diameter of nearly thirty-two thousand +miles. It is a little less dense than Jupiter, and its mean distance +from the sun is about seventeen hundred and seventy millions of miles. +Its orbit has about the same eccentricity as that of Jupiter, and is +inclined less than a degree to the ecliptic. Uranus makes a revolution +around the sun in eighty-four years, moving at the rate of a little over +four miles a second. It is visible to the naked eye as a star of the +sixth magnitude. + +As seen in a large telescope, the planet has a decidedly sea-green +color; but no markings have with certainty been detected on its disk, so +that nothing is really known with regard to its rotation. Fig. 301 shows +the comparative size of Uranus and the earth. + +[Illustration: Fig. 301.] + +276. _Discovery of Uranus._--This planet was discovered by Sir William +Herschel in March, 1781. He was engaged at the time in examining the +small stars of the constellation _Gemini_, or the Twins. He noticed that +this object which had attracted his attention had an appreciable disk, +and therefore could not be a star. He also perceived by its motion that +it could not be a nebula; he therefore concluded that it was a comet, +and announced his discovery as such. On attempting to compute its orbit, +it was soon found that its motions could be accounted for only on the +supposition that it was moving in a circular orbit at about twice the +distance of Saturn from the sun. It was therefore recognized as a new +planet, whose discovery nearly doubled the dimensions of the solar +system as it was then known. + +277. _The Name of the Planet._--Herschel, out of compliment to his +patron, George III., proposed to call the new planet _Georgium Sidus_ +(the Georgian Star); but this name found little favor. The name of +_Herschel_ was proposed, and continued in use in England for a time, but +did not meet with general approval. Various other names were suggested, +and finally that of _Uranus_ was adopted. + +[Illustration: Fig. 302.] + +278. _The Satellites of Uranus._--Uranus is accompanied by four +satellites, whose orbits are shown in Fig. 302. These satellites are +remarkable for the great inclination of their orbits to the plane of the +planet's orbit, amounting to about eighty degrees, and for their +_retrograde_ motion; that is, they move _from east to west_, instead of +from west to east, as in the case of all the planets and of all the +satellites previously discovered. + + + Neptune. + + +279. _Orbit and Dimensions of Neptune._--So far as known, Neptune is the +most remote member of the solar system, its mean distance from the sun +being twenty-seven hundred and seventy-five million miles. This distance +is considerably less than twice that of Uranus. Neptune revolves around +the sun in a period of a little less than a hundred and sixty-five +years. Its orbit has but slight eccentricity, and is inclined less than +two degrees to the ecliptic. This planet is considerably larger than +Uranus, its diameter being nearly thirty-five thousand miles. It is +somewhat less dense than Uranus. Neptune is invisible to the naked eye, +and no telescope has revealed any markings on its disk: hence nothing is +certainly known as to its rotation. Fig. 303 shows the comparative size +of Neptune and the earth. + +[Illustration: Fig. 303.] + +280. _The Discovery of Neptune._--The discovery of Neptune was made in +1846, and is justly regarded as one of the grandest triumphs of +astronomy. + +Soon after Uranus was discovered, certain irregularities in its motion +were observed, which could not be explained. It is well known that the +planets are all the while disturbing each other's motions, so that none +of them describe perfect ellipses. These mutual disturbances are called +_perturbations_. In the case of Uranus it was found, that, after making +due allowance for the action of all the known planets, there were still +certain perturbations in its course which had not been accounted for. +This led astronomers to the suspicion that these might be caused by an +unknown planet. Leverrier in France, and Adams in England, independently +of each other, set themselves the difficult problem of computing the +position and magnitude of a planet which would produce these +perturbations. Both, by a most laborious computation, showed that the +perturbations were such as would be produced by a planet revolving about +the sun at about twice the distance of Uranus, and having a mass +somewhat greater than that of this planet; and both pointed out the same +part of the heavens as that in which the planet ought to be found at +that time. Almost immediately after they had announced the conclusion to +which they had arrived, the planet was found with the telescope. The +astronomer who was searching for the planet at the suggestion of +Leverrier was the first to recognize it: hence Leverrier has obtained +the chief credit of the discovery. + +The observed planet is proved to be nearer than the one predicted by +Leverrier and Adams, and therefore of smaller magnitude. + +281. _The Observed Planet not the Predicted One._--Professor Peirce +always maintained that the planet found by observation was not the one +whose existence had been predicted by Leverrier and Adams, though its +action would completely explain all the irregularities in the motion of +Uranus. His last statement on this point is as follows: "My position is, +that there were _two possible planets_, either of which might have +caused the observed irregular motions of Uranus. Each planet excluded +the other; so that, if one was, the other was not. They coincided in +direction from the earth at certain epochs, once in six hundred and +fifty years. It was at one of these epochs that the prediction was made, +and at no other time for six centuries could the prediction of the one +planet have revealed the other. The observed planet was not the +predicted one." + +282. _Bode's Law Disproved._--The following table gives the distances of +the planets according to Bode's law, their actual distances, and the +error of the law in each case:-- + + Planet. Numbers of Actual Errors. + Bode. Distances. + + + Mercury 0 + 4 = 4 3.9 0.1 + + Venus 3 + 4 = 7 7.2 0.2 + + Earth 6 + 4 = 10 10.0 0.0 + + Mars 12 + 4 = 16 15.2 0.8 + + Minor 24 + 4 = 28 20 to 35 + planets + + Jupiter 48 + 4 = 52 52.0 0.0 + + Saturn 96 + 4 = 100 95.4 4.6 + + Uranus 192 + 4 = 196 191.9 4.1 + + Neptune 384 + 4 = 388 300.6 87.4 + +It will be seen, that, before the discovery of Neptune, the agreement +was so close as to indicate that this was an actual law of the +distances; but the discovery of this planet completely disproved its +existence. + +[Illustration: Fig. 304.] + +283. _The Satellite of Neptune._--Neptune is accompanied by at least one +moon, whose orbit is shown in Fig. 304. The orbit of this satellite is +inclined about thirty degrees to the plane of the ecliptic, and the +motion of the satellite is retrograde, or from east to west. + + + VII. COMETS AND METEORS. + + + I. COMETS. + + + General Phenomena of Comets. + +284. _General Appearance of a Bright Comet._--Comets bright enough to be +seen with the naked eye are composed of three parts, which run into each +other by insensible gradations. These are the _nucleus_, the _coma_, and +the _tail_. + +The _nucleus_ is the bright centre of the comet, and appears to the eye +as a star or planet. + +The _coma_ is a nebulous mass surrounding the nucleus on all sides. +Close to the nucleus it is almost as bright as the nucleus itself; but +it gradually shades off in every direction. The nucleus and coma +combined appear like a star shining through a small patch of fog; and +these two together form what is called the _head_ of the comet. + +The _tail_ is a continuation of the coma, and consists of a stream of +milky light, growing wider and fainter as it recedes from the head, till +the eye is unable to trace it. + +[Illustration: Fig. 305.] + +The general appearance of one of the smaller of the brilliant comets is +shown in Fig. 305. + +[Illustration: Fig. 306.] + +[Illustration: Fig. 307.] + +285. _General Appearance of a Telescopic Comet._--The great majority of +comets are too faint to be visible with the naked eye, and are called +_telescopic_ comets. In these comets there seems to be a development of +coma at the expense of nucleus and tail. In some cases the telescope +fails to reveal any nucleus at all in one of these comets; at other +times the nucleus is so faint and ill-defined as to be barely +distinguishable. Fig. 306 shows a telescopic comet without any nucleus +at all, and another with a slight condensation at the centre. In these +comets it is generally impossible to distinguish the coma from the tail, +the latter being either entirely invisible, as in Fig. 306, or else only +an elongation of the coma, as shown in Fig. 307. Many comets appear +simply as patches of foggy light of more or less irregular form. + +[Illustration: Fig. 308.] + +286. _The Development of Telescopic Comets on their Approach to the +Sun._--As a rule, all comets look nearly alike when they first come +within the reach of the telescope. They appear at first as little foggy +patches, without any tail, and often without any visible nucleus. As +they approach the sun their peculiarities are rapidly developed. Fig. +308 shows such a comet as first seen, and the gradual development of its +nucleus, head, and tail, as it approaches the sun. + +[Illustration: Fig. 309.] + +[Illustration: Fig. 310.] + +[Illustration: Fig. 311.] + +If the comet is only a small one, the tail developed is small; but these +small appendages have a great variety of form in different comets. Fig. +309 shows the singular form into which _Encke's_ comet was developed in +1871. Figs. 310 and 311 show other peculiar developments of telescopic +comets. + +287. _Development of Brilliant Comets on their Approach to the +Sun._--Brilliant comets, as well as telescopic comets, appear nearly +alike when they come into the view of the telescope; and it is only on +their approach to the sun that their distinctive features are developed. +Not only do these comets, when they first come into view, resemble each +other, but they also bear a close resemblance to telescopic comets. + +As the comet approaches the sun, bright vaporous jets, two or three in +number, are emitted from the nucleus on the side of the sun and in the +direction of the sun. These jets, though directed towards the sun, are +soon more or less carried backward, as if repelled by the sun. Fig. 312 +shows a succession of views of these jets as they were developed in the +case of _Halley's_ comet in 1835. + +[Illustration: Fig. 312.] + +The jets in this case seemed to have an oscillatory motion. At 1 and 2 +they seemed to be attracted towards the sun, and in 3 to be repelled by +him. In 4 and 5 they seemed to be again attracted, and in 6 to be +repelled, but in a reverse direction to that in 3. In 7 they appeared to +be again attracted. Bessel likened this oscillation of the jets to the +vibration of a magnetic needle when presented to the pole of a magnet. + +In the case of larger comets these luminous jets are surrounded by one +or more envelops, which are thrown off in succession as the comet +approaches the sun. The formation of these envelops was a conspicuous +feature of _Donati's_ comet of 1858. A rough view of the jets and the +surrounding envelops is given in Fig. 313. Fig. 314 gives a view of the +envelops without the jets. + +[Illustration: Fig. 313.] + +[Illustration: Fig. 314.] + +288. _The Tails of Comets._--The _tails_ of brilliant comets are rapidly +formed as the comet approaches the sun, their increase in length often +being at the rate of several million miles a day. These appendages seem +to be formed entirely out of the matter which is emitted from the +nucleus in the luminous jets which are at first directed towards the +sun. The tails of comets are, however, always directed away from the +sun, as shown in Fig. 315. + +[Illustration: Fig. 315.] + +It will be seen that the comet, as it approaches the sun, travels head +foremost; but as it leaves the sun it goes tail foremost. + +The apparent length of the tail of a comet depends partly upon its real +length, partly upon the distance of the comet, and partly upon the +direction of the axis of the tail with reference to the line of vision. +The longer the tail, the nearer the comet; and the more nearly at right +angles to the line of vision is the axis of the tail, the greater is the +apparent length of the tail. In the majority of cases the tails of +comets measure only a few degrees; but, in the case of many comets +recorded in history, the tail has extended half way across the heavens. + +The tail of a comet, when seen at all, is usually several million miles +in length; and in some instances the tail is long enough to reach across +the orbit of the earth, or twice as far as from the earth to the sun. + +The tails of comets are apparently hollow, and are sometimes a million +of miles in diameter. So great, however, is the tenuity of the matter in +them, that the faintest stars are seen through it without any apparent +obscuration. See Fig. 316, which is a view of the great comet of 1264. + +[Illustration: Fig. 316.] + +[Illustration: Fig. 317.] + +[Illustration: Fig. 318.] + +[Illustration: Fig. 319.] + +[Illustration: Fig. 320.] + +The tails of comets are sometimes straight, as in Fig. 316, but usually +more or less curved, as in Fig. 317, which is a view of _Donati's_ comet +as it appeared at one time. The tail of a comet is occasionally divided +into a number of streamers, as in Figs. 318 and 319. Fig. 318 is a view +of the great comet of 1744, and Fig. 319 of the great comet of 1861. No. +1, in Fig. 320, is a view of the comet of 1577; No. 2, of the comet of +1680; and No. 3, of the comet of 1769. + +[Illustration: Fig. 321.] + +Fig. 321 shows some of the forms which the imagination of a +superstitious age saw depicted in comets, when these heavenly visitants +were thought to be the forerunners of wars, pestilence, famine, and +other dire calamities. + +289. _Visibility of Comets._--Even the brightest comets are visible only +a short time near their perihelion passage. When near the sun, they +sometimes become very brilliant, and on rare occasions have been visible +even at mid-day. It is seldom that a comet can be seen, even with a +powerful telescope, during its perihelion passage, unless its perihelion +is either inside of the earth's orbit, or but little outside of it. + + + Motion and Origin of Comets. + + +290. _Recognition of a Telescopic Comet._--It is impossible to +distinguish telescopic comets by their appearance from another class of +heavenly bodies known as _nebulæ_. Such comets can be recognized only by +their motion. Thus, in Fig. 322, the upper and lower bodies look exactly +alike; but the upper one is found to remain stationary, while the lower +one moves across the field of view. The upper one is thus shown to be a +nebula, and the lower one a comet. + +[Illustration: Fig. 322.] + +291. _Orbits of Comets._--All comets are found to move in _very +eccentric ellipses_, in _parabolas_, or in _hyperbolas_. + +Since an ellipse is a _closed_ curve (48), all comets that move in +ellipses, no matter how eccentric, are permanent members of the solar +system, and will return to the sun at intervals of greater or less +length, according to the size of the ellipses and the rate of the +comet's motion. + +Parabolas and hyperbolas being _open_ curves (48), comets that move in +either of these orbits are only temporary members of our solar system. +After passing the sun, they move off into space, never to return, unless +deflected hither by the action of some heavenly body which they pass in +their journey. + +[Illustration: Fig. 323.] + + Since a comet is visible only while it is near the sun, it is + impossible to tell, by the form of the portion of the orbit which it + describes during the period of its visibility, whether it is a part + of a very elongated ellipse, a parabola, or a hyperbola. Thus in + Fig. 323 are shown two orbits, one of which is a very elongated + ellipse, and the other a parabola. The part _ab_, in each case, is + the portion of the orbit described by the comet during its + visibility. While describing the dotted portions of the orbit, the + comet is invisible. Now it is impossible to distinguish the form of + the visible portion in the two orbits. The same would be true were + one of the orbits a hyperbola. + + Whether a comet will describe an ellipse, a parabola, or a + hyperbola, can be determined only by its _velocity_, taken in + connection with its _distance from the sun_. Were a comet ninety-two + and a half million miles from the sun, moving away from the sun at + the rate of twenty-six miles a second, it would have just the + velocity necessary to describe a _parabola_. Were it moving with a + greater velocity, it would necessarily describe a _hyperbola_, and, + with a less velocity, an _ellipse_. So, at any distance from the + sun, there is a certain velocity which would cause a comet to + describe a parabola; while a greater velocity would cause it to + describe a hyperbola, and a less velocity to describe an ellipse. If + the comet is moving in an ellipse, the less its velocity, the less + the eccentricity of its orbit: hence, in order to determine the form + of the orbit of any comet, it is only necessary to ascertain its + distance from the sun, and its velocity at any given time. + + Comets move in every direction in their orbits, and these orbits + have every conceivable inclination to the ecliptic. + +292. _Periodic Comets._--There are quite a number of comets which are +known to be _periodic_, returning to the sun at regular intervals in +elliptic orbits. Some of these have been observed at several returns, so +that their period has been determined with great certainty. In the case +of others the periodicity is inferred from the fact that the velocity +fell so far short of the parabolic limit that the comet must move in an +ellipse. The number of known periodic comets is increasing every year, +three having been added to the list in 1881. + +The velocity of most comets is so near the parabolic limit that it is +not possible to decide, from observations, whether it falls short of it, +or exceeds it. In the case of a few comets the observations indicate a +minute excess of velocity; but this cannot be confidently asserted. It +is not, therefore, absolutely certain that any known comet revolves in a +hyperbolic orbit; and thus it is possible that all comets belong to our +system, and will ultimately return to it. It is, however, certain, that, +in the majority of cases, the return will be delayed for many centuries, +and perhaps for many thousand years. + +293. _Origin of Comets._--It is now generally believed that the original +home of the comets is in the stellar spaces outside of our solar system, +and that they are drawn towards the sun, one by one, in the long lapse +of ages. Were the sun unaccompanied by planets, or were the planets +immovable, a comet thus drawn in would whirl around the sun in a +parabolic orbit, and leave it again never to return, unless its path +were again deflected by its approach to some star. But, when a comet is +moving in a parabola, the slightest _retardation_ would change its orbit +to an ellipse, and the slightest _acceleration_ into a hyperbola. Owing +to the motion of the several planets in their orbits, the velocity of a +comet would be changed on passing each of them. Whether its velocity +would be accelerated or retarded, would depend upon the way in which it +passed. Were the comet accelerated by the action of the planets, on its +passage through our system, more than it was retarded by them, it would +leave the system with a more than parabolic orbit, and would therefore +move in a hyperbola. Were it, on the contrary, retarded more than +accelerated by the action of the planets, its velocity would be reduced, +so that the comet would move in a more or less elongated ellipse, and +thus become a permanent member of the solar system. + +In the majority of cases the retardation would be so slight that it +could not be detected by the most delicate observation, and the comet +would return to the sun only after the expiration of tens or hundreds of +thousands of years; but, were the comet to pass very near one of the +larger planets, the retardation might be sufficient to cause the comet +to revolve in an elliptical orbit of quite a short period. The orbit of +a comet thus captured by a planet would have its aphelion point near the +orbit of the planet which captured it. Now, it happens that each of the +larger planets has a family of comets whose aphelia are about its own +distance from the sun. It is therefore probable that these comets have +been captured by the action of these planets. As might be expected from +the gigantic size of Jupiter, the Jovian family of comets is the +largest. The orbits of several of the comets of this group are shown in +Fig. 324. + +[Illustration: Fig. 324.] + +294. _Number of Comets._--The number of comets recorded as visible to +the naked eye since the birth of Christ is about five hundred, while +about two hundred telescopic comets have been observed since the +invention of the telescope. The total number of comets observed since +the Christian era is therefore about seven hundred. It is certain, +however, that only an insignificant fraction of all existing comets have +ever been observed. Since they can be seen only when near their +perihelion, and since it is probable that the period of most of those +which have been observed is reckoned by thousands of years (if, indeed, +they ever return at all), our observations must be continued for many +thousand years before we have seen all which come within range of our +telescopes. Besides, as already stated (289), a comet can seldom be seen +unless its perihelion is either inside the orbit of the earth, or but +little outside of it; and it is probable that the perihelia of the great +majority of comets are beyond this limit of visibility. + + + Remarkable Comets. + + +295. _The Comet of 1680._--The great comet of 1680, shown in Fig. 320, +is one of the most celebrated on record. It was by his study of its +motions that Newton proved the orbit of a comet to be one of the conic +sections, and therefore that these bodies move under the influence of +gravity. This comet descended almost in a direct line to the sun, +passing nearer to that luminary than any comet before known. Newton +estimated, that, at its perihelion point, it was exposed to a +temperature two thousand times that of red-hot iron. During its +perihelion passage it was exceedingly brilliant. Halley suspected that +this comet had a period of five hundred and seventy-five years, and that +its first recorded appearance was in 43 B.C., its third in 1106, and its +fourth in 1680. If this is its real period, it will return in 2255. The +comet of 43 B.C. made its appearance just after the assassination of +Julius Cæsar. The Romans called it the _Julian Star_, and regarded it as +a celestial chariot sent to convey the soul of Cæsar to the skies. It +was seen two or three hours before sunset, and continued visible for +eight successive days. The great comet of 1106 was described as an +object of terrific splendor, and was visible in close proximity to the +sun. The comet of 1680 has become celebrated, not only on account of its +great brilliance, and on account of Newton's investigation of its orbit, +but also on account of the speculation of the theologian Whiston in +regard to it. He accepted five hundred and seventy-five years as its +period, and calculated that one of its earlier apparitions must have +occurred at the date of the flood, which he supposed to have been caused +by its near approach to the earth; and he imagined that the earth is +doomed to be destroyed by fire on some future encounter with this comet. + +[Illustration: Fig. 325.] + +296. _The Comet of 1811._--The great comet of 1811, a view of which is +given in Fig. 325, is, perhaps, the most remarkable comet on record. It +was visible for nearly seventeen months, and was very brilliant, +although at its perihelion passage it was over a hundred million miles +from the sun. Its tail was a hundred and twenty million miles in length, +and several million miles through. It has been calculated that its +aphelion point is about two hundred times as far from the sun as its +perihelion point, or some seven times the distance of Neptune from the +sun. Its period is estimated at about three thousand years. It was an +object of superstitious terror, especially in the East. The Russians +regarded it as presaging Napoleon's great and fatal war with Russia. + +[Illustration: Fig. 326.] + +[Illustration: Fig. 327.] + +297. _Halley's Comet._--Halley's comet has become one of the most +celebrated of modern times. It is the first comet whose return was both +predicted and observed. It made its appearance in 1682. Halley computed +its orbit, and compared it with those of previous comets, whose orbits +he also computed from recorded observations. He found that it coincided +so exactly with that of the comet observed by Kepler in 1607, that there +could be no doubt of the identity of the two orbits. So close were they +together, that, were they both drawn in the heavens, the naked eye would +almost see them joined into one line. There could therefore be no doubt +that the comet of 1682 was the same that had appeared in 1607, and that +it moved in an elliptic orbit, with a period of about seventy-five +years. He found that this comet had previously appeared in 1531 and in +1456; and he predicted that it would return about 1758. Its actual +return was retarded somewhat by the action of the planets on it in its +passage through the solar system. It, however, appeared again in 1759, +and a third time in 1835. Its next appearance will be about 1911. The +orbit of this comet is shown in Fig. 326. Fig. 327 shows the comet as it +appeared to the naked eye, and in a telescope of moderate power, in +1835. This comet appears to be growing less brilliant. In 1456 it +appeared as a comet of great splendor; and coming as it did in a very +superstitious age, soon after the fall of Constantinople, and during the +threatened invasion of Europe by the Turks, it caused great alarm. Fig. +328 shows the changes undergone by the nucleus of this comet during its +perihelion passage in 1835. + +[Illustration: Fig. 328.] + +[Illustration: Fig. 329.] + +[Illustration: Fig. 330.] + +298. _Encke's Comet._--This telescopic comet, two views of which are +given in Figs. 329 and 330, appeared in 1818. Encke computed its orbit, +and found it to lie wholly within the orbit of Jupiter (Fig. 324), and +the period to be about three years and a third. By comparing the +intervals between the successive returns of this comet, it has been +ascertained that its orbit is continually growing smaller and smaller. +To account for the retardation of this comet, Olbers announced his +celebrated hypothesis, that the celestial spaces are filled with a +subtile _resisting medium_. This hypothesis was adopted by Encke, and +has been accepted by certain other astronomers; but it has by no means +gained universal assent. + +299. _Biela's Comet._--This comet appeared in 1826, and was found to +have a period of about six years and two thirds. On its return in 1845, +it met with a singular, and as yet unexplained, accident, which has +rendered the otherwise rather insignificant comet famous. In November +and December of that year it was observed as usual, without any thing +remarkable about it; but, in January of the following year, it was found +to have been divided into two distinct parts, so as to appear as two +comets instead of one. The two parts were at first of very unequal +brightness; but, during the following month, the smaller of the two +increased in brilliancy until it equalled its companion; it then grew +fainter till it entirely disappeared, a month before its companion. The +two parts were about two hundred thousand miles apart. Fig. 331 shows +these two parts as they appeared on the 19th of February, and Fig. 332 +as they appeared on the 21st of February. On its return in 1852, the +comets were found still to be double; but the two components were now +about a million and a half miles apart. They are shown in Fig. 333 as +they appeared at this time. Sometimes one of the parts appeared the +brighter, and sometimes the other; so that it was impossible to decide +which was really the principal comet. The two portions passed out of +view in September, and have not been seen since; although in 1872 the +position of the comet would have been especially favorable for +observation. The comet appears to have become completely broken up. + +[Illustration: Fig. 331.] + +[Illustration: Fig. 332.] + +[Illustration: Fig. 333.] + +[Illustration: Fig. 334.] + +300. _The Comet of 1843._--The great comet of 1843, a view of which is +given in Fig. 334, was favorably situated for observation only in +southern latitudes. It was exceedingly brilliant, and was easily seen in +full daylight, in close proximity to the sun. The apparent length of its +tail was sixty-five degrees, and its real length a hundred and fifty +million miles, or nearly twice the distance from the earth to the sun. +This comet is especially remarkable on account of its near approach to +the sun. At the time of its perihelion passage the distance of the comet +from the photosphere of the sun was less than one-fourteenth of the +diameter of the sun. This distance was only one-half that of the comet +of 1680 when at its perihelion. When at perihelion, this comet was +plunging through the sun's outer atmosphere at the rate of one million, +two hundred and eighty thousand miles an hour. It passed half way round +the sun in the space of _two hours_, and its tail was whirled round +through a hundred and eighty degrees in that brief time. As the tail +extended almost double the earth's distance from the sun, the end of the +tail must have traversed in two hours a space nearly equal to the +circumference of the earth's orbit,--a distance which the earth, moving +at the rate of about twenty miles a second, is a _whole year_ in +passing. It is almost impossible to suppose that the matter forming this +tail remained the same throughout this tremendous sweep. + +301. _Donati's Comet._--The great comet of 1858, known as _Donati's_ +comet, was one of the most magnificent of modern times. When at its +brightest it was only about fifty million miles from the earth. Its tail +was then more than fifty million miles long. Had the comet at this time +been directly between the earth and sun, the earth must have passed +through its tail; but this did not occur. The orbit of this comet was +found to be decidedly elliptic, with a period of about two thousand +years. This comet is especially celebrated on account of the careful +telescopic observations of its nucleus and coma at the time of its +perihelion passage. Attention has already been called (287) to the +changes it underwent at that time. Its tail was curved, and of a curious +feather-like form, as shown in Fig. 335. At times it developed lateral +streamers, as shown in Fig. 336. Fig. 337 shows the head of the comet as +it was seen by Bond of the Harvard Observatory, whose delineations of +this comet have been justly celebrated. + +[Illustration: Fig. 335.] + +[Illustration: Fig. 336.] + +[Illustration: Fig. 337.] + +302. _The Comet of 1861._--The great comet of 1861 is remarkable for its +great brilliancy, for its peculiar fan-shaped tail, and for the probable +passage of the earth through its tail. Sir John Herschel declared that +it far exceeded in brilliancy any comet he had ever seen, not excepting +those of 1811 and 1858. Secchi found its tail to be a hundred and +eighteen degrees in length, the largest but one on record. Fig. 338 +shows this comet as it appeared at one time. Fig. 339 shows the position +of the earth at _E_, in the tail of this comet, on the 30th of June, +1861. Fig. 340 shows the probable passage of the earth through the tail +of the comet on that date. As the tail of a comet doubtless consists of +something much less dense than our atmosphere, it is not surprising that +no noticeable effect was produced upon us by the encounter, if it +occurred. + +[Illustration: Fig. 338.] + +[Illustration: Fig. 339.] + +[Illustration: Fig. 340.] + +303. _Coggia's Comet._--This comet, which appeared in 1874, looked very +large, because it came very near the earth. It was not at all brilliant. +Its nucleus was carefully studied, and was found to develop a series of +envelops similar to those of Donati's comet. Figs. 341 and 342 are two +views of the head of this comet. Fig. 343 shows the system of envelops +that were developed during its perihelion passage. + +[Illustration: Fig. 341.] + +[Illustration: Fig. 342.] + +[Illustration: Fig. 343.] + +304. _The Comet of June, 1881._--This comet, though far from being one +of the largest of modern times, was still very brilliant. It will ever +be memorable as the first brilliant comet which has admitted of careful +examination with the spectroscope. + + + Connection between Meteors and Comets. + + +305. _Shooting-Stars._--On watching the heavens any clear night, we +frequently see an appearance as of a star shooting rapidly through a +short space in the sky, and then suddenly disappearing. Three or four +such _shooting-stars_ may, on the average, be observed in the course of +an hour. They are usually seen only a second or two; but they sometimes +move slowly, and are visible much longer. These stars begin to be +visible at an average height of about seventy-five miles, and they +disappear at an average height of about fifty miles. They are +occasionally seen as high as a hundred and fifty miles, and continue to +be visible till within thirty miles of the earth. Their visible paths +vary from ten to a hundred miles in length, though they are occasionally +two hundred or three hundred miles long. Their average velocity, +relatively to the earth's surface, varies from ten to forty-five miles a +second. + +The average number of shooting-stars visible to the naked eye at any one +place is estimated at about _a thousand an hour_; and the average number +large enough to be visible to the naked eye, that traverse the +atmosphere daily, is estimated at _over eight millions_. The number of +telescopic shooting-stars would of course be much greater. + +Occasionally, shooting-stars leave behind them a trail of light which +lasts for several seconds. These trails are sometimes straight, as shown +in Fig. 344, and sometimes curved, as in Figs. 345 and 346. They often +disappear like trails of smoke, as shown in Fig. 347. + +[Illustration: Fig. 344.] + +[Illustration: Fig. 345.] + +[Illustration: Fig. 346.] + +[Illustration: Fig. 347.] + +Shooting-stars are seen to move in all directions through the heavens. +Their apparent paths are, however, generally inclined downward, though +sometimes upward; and after midnight they come in the greatest numbers +from that quarter of the heavens toward which the earth is moving in its +journey around the sun. + +306. _Meteors._--Occasionally these bodies are brilliant enough to +illuminate the whole heavens. They are then called _meteors_, although +this term is equally applicable to ordinary shooting-stars. Such a +meteor is shown in Fig. 348. + +[Illustration: Fig. 348.] + +Sometimes these brilliant meteors are seen to explode, as shown in Fig. +349; and the explosion is accompanied with a loud detonation, like the +discharge of cannon. + +[Illustration: Fig. 349.] + +Ordinary shooting-stars are not accompanied by any audible sound, though +they are sometimes seen to break in pieces. Meteors which explode with +an audible sound are called _detonating meteors_. + +307. _Aerolites._--There is no certain evidence that any deposit from +ordinary shooting-stars ever reaches the surface of the earth; though a +peculiar dust has been found in certain localities, which has been +supposed to be of meteoric origin, and which has been called _meteoric +dust_. But solid bodies occasionally descend to the earth from beyond +our atmosphere. These generally penetrate a foot or more into the earth, +and, if picked up soon after their fall, are found to be warm, and +sometimes even hot. These bodies are called _aerolites_. When they have +a stony appearance, and contain but little iron, they are called +_meteoric stones_; when they have a metallic appearance, and are +composed largely of iron, they are called _meteoric iron_. + +There are eighteen well-authenticated cases in which aerolites have +fallen in the United States during the last sixty years, and their +aggregate weight is twelve hundred and fifty pounds. The entire number +of known aerolites the date of whose fall is well determined is two +hundred and sixty-one. There are also on record seventy-four cases of +which the date is more or less uncertain. There have also been found +eighty-six masses, which, from their peculiar composition, are believed +to be aerolites, though their fall was not seen. The weight of these +masses varies from a few pounds to several tons. The entire number of +aerolites of which we have any knowledge is therefore about four hundred +and twenty. + +Aerolites are composed of the same elementary substances as occur in +terrestrial minerals, not a single new element having been found in +their analysis. Of the sixty or more elements now recognized by +chemists, about twenty have been found in aerolites. + +While aerolites contain no new elements, their appearance is quite +peculiar; and the compounds found in them are so peculiar as to enable +us by chemical analysis to distinguish an aerolite from any terrestrial +substance. + +Iron ores are very abundant in nature, but iron in the metallic state is +exceedingly rare. Now, aerolites invariably contain metallic iron, +sometimes from ninety to ninety-six per cent. This iron is malleable, +and may be readily worked into cutting instruments. It always contains +eight or ten per cent of nickel, together with small quantities of +cobalt, copper, tin, and chromium. This composition _has never been +found in any terrestrial mineral_. Aerolites also contain, usually in +small amount, a compound of iron, nickel, and phosphorus, which has +never been found elsewhere. + +Meteorites often present the appearance of having been fused on the +surface to a slight depth, and meteoric iron is found to have a peculiar +crystalline structure. The external appearance of a piece of meteoric +iron found near Lockport, N.Y., is shown in Fig. 350. Fig. 351 shows the +peculiar internal structure of meteoric iron. + +[Illustration: Fig. 350.] + +[Illustration: Fig. 351.] + +308. _Meteoroids._--Astronomers now universally hold that +shooting-stars, meteors, and aerolites are all minute bodies, revolving, +like the comets, about the sun. They are moving in every possible +direction through the celestial spaces. They may not average more than +one in a million of cubic miles, and yet their total number exceeds all +calculation. Of the nature of the minuter bodies of this class nothing +is certainly known. The earth is continually encountering them in its +journey around the sun. They are burned by passing through the upper +regions of our atmosphere, and the shooting-star is simply the light of +that burning. These bodies, which are invisible till they plunge into +the earth's atmosphere, are called _meteoroids_. + +309. _Origin of the Light of Meteors._--When one of these meteoroids +enters our atmosphere, the resistance of the air arrests its motion to +some extent, and so converts a portion of its energy of motion into that +of heat. The heat thus developed is sufficient to raise the meteoroid +and the air around it to incandescence, and in most cases either to +cause the meteoroid to burn up, or to dissipate it as vapor. The +luminous vapor thus formed constitutes the luminous train which +occasionally accompanies a meteor, and often disappears as a puff of +smoke. When a meteoroid is large enough and refractory enough to resist +the heat to which it is exposed, its motion is sufficiently arrested, on +entering the lower layers of our atmosphere, to cause it to fall to the +earth. We then have an _aerolite_. A brilliant meteor differs from a +shooting-star simply in magnitude. + +310. _The Intensity of the Heat to which a Meteoroid is Exposed._--It +has been ascertained by experiment that a body moving through the +atmosphere at the rate of a hundred and twenty-five feet a second raises +the temperature of the air immediately in front of it one degree, and +that the temperature increases as the square of the velocity of the +moving body; that is to say, that, with a velocity of two hundred and +fifty feet, the temperature in front of the body would be raised four +degrees; with a velocity of five hundred feet, sixteen degrees; and so +on. To find, therefore, the temperature to which a meteoroid would be +exposed in passing through our atmosphere, we have merely to divide its +velocity in feet per second by a hundred and twenty-five, and square the +quotient. With a velocity of forty-four miles a second in our +atmosphere, a meteoroid would therefore be exposed to a temperature of +between three and four million degrees. The air acts upon the body as if +it were raised to this intense heat. At such a temperature small masses +of the most refractory or incombustible substances known to us would +flash into vapor with the evolution of intense light and heat. + +If one of these meteoric bodies is large enough to pass through the +atmosphere and reach the earth, without being volatilized by the heat, +we have an aerolite. As it is only a few seconds in making the passage, +the heat has not time to penetrate far into its interior, but is +expended in melting and vaporizing the outer portions. The resistance of +the denser strata of the atmosphere to the motion of the aerolite +sometimes becomes so enormous that the body is suddenly rent to pieces +with a loud detonation. It seems like an explosion produced by some +disruptive action within the mass; but there can be little doubt that it +is due to the velocity--perhaps ten, twenty, or thirty miles a +second--with which the body strikes the air. + +If, on the other hand, the meteoroid is so small as to be burned up or +volatilized in the upper regions of the atmosphere, we have a common +shooting-star, or a meteor of greater or less brilliancy. + +[Illustration: Fig. 352.] + +311. _Meteoric Showers._--On ordinary nights only four or five +shooting-stars are seen in an hour, and these move in every direction. +Their orbits lie in all possible positions, and are seemingly scattered +at random. Such meteors are called _sporadic_ meteors. On occasional +nights, shooting-stars are more numerous, and all move in a common +direction. Such a display is called a _meteoric shower_. These showers +differ greatly in brilliancy; but during any one shower the meteors all +appear to radiate from some one point in the heavens. If we mark on a +celestial globe the apparent paths of the meteors which fall during a +shower, or if we trace them back on the celestial sphere, we shall find +that they all meet in the same point, as shown in Fig. 352. This point +is called the _radiant point_. It always appears in the same position, +wherever the observer is situated, and does not partake of the diurnal +motion of the earth. As the stars move towards the west, the radiant +point moves with them. The point in question is purely an effect of +perspective, being the "vanishing point" of the parallel lines in which +the meteors are actually moving. These lines are seen, not in their real +direction in space, but as projected on the celestial sphere. If we look +upwards, and watch snow falling through a calm atmosphere, the flakes +which fall directly towards us do not seem to move at all, while the +surrounding flakes seem to diverge from them on all sides. So, in a +meteoric shower, a meteor coming directly towards the observer does not +seem to move at all, and marks the point from which all the others seem +to radiate. + +312. _The August Meteors._--A meteoric shower of no great brilliancy +occurs annually about the 10th of August. The radiant point of this +shower is in the constellation _Perseus_, and hence these meteors are +often called the _Perseids_. The orbit of these meteoroids has been +pretty accurately determined, and is shown in Fig. 353. + +[Illustration: Fig. 353.] + +It will be seen that the perihelion point of this orbit is at about the +distance of the earth from the sun; so that the earth encounters the +meteors once a year, and this takes place in the month of August. The +orbit is a very eccentric ellipse, reaching far beyond Neptune. As the +meteoric display is about equally brilliant every year, it seems +probable that the meteoroids form a stream quite uniformly distributed +throughout the whole orbit. It probably takes one of the meteoroids +about a hundred and twenty-four years to pass around this orbit. + +[Illustration: Fig. 354.] + +313. _The November Meteors._--A somewhat brilliant meteoric shower also +occurs annually, about the 13th of November. The radiant point of these +meteors is in the constellation _Leo_, and hence they are often called +the _Leonids_. Their orbit has been determined with great accuracy, and +is shown in Fig. 354. While the November meteors are not usually very +numerous or bright, a remarkably brilliant display of them has been seen +once in about thirty-three or thirty-four years: hence we infer, that, +while there are some meteoroids scattered throughout the whole extent of +the orbit, the great majority are massed in a group which traverses the +orbit in a little over thirty-three years. A conjectural form of this +condensed group is shown in Fig. 355. The group is so large that it +takes it two or three years to pass the perihelion point: hence there +may be a brilliant meteoric display two or three years in succession. + +[Illustration: Fig. 355.] + +The last brilliant display of these meteors was in the years 1866 and +1867. The display was visible in this country only a short time before +sunrise, and therefore did not attract general attention. The display of +1833 was remarkably brilliant in this country, and caused great +consternation among the ignorant and superstitious. + +[Illustration: Fig. 356.] + +314. _Connection between Meteors and Comets._--It has been found that a +comet which appeared in 1866, and which is designated as 1866, I., has +exactly the same orbit and period as the November meteors, and that +another comet, known as the 1862, III., has the same orbit as the August +meteors. It has also been ascertained that a third comet, 1861, I., has +the same orbit as a stream of meteors which the earth encounters in +April. Furthermore, it was found, in 1872, that there was a small stream +of meteors following in the train of the lost comet of Biela. These +various orbits of comets and meteoric streams are shown in Fig. 356. The +coincidence of the orbits of comets and of meteoric streams indicates +that these two classes of bodies are very closely related. They +undoubtedly have a common origin. The fact that there is a stream of +meteors in the train of Biela's comet has led to the supposition that +comets may become gradually disintegrated into meteoroids. + + + Physical and Chemical Constitution of Comets. + + +315. _Physical Constitution of Telescopic Comets._--We have no certain +knowledge of the physical constitution of telescopic comets. They are +usually tens of thousands of miles in diameter, and yet of such tenuity +that the smallest stars can readily be seen through them. It would seem +that they must shine in part by reflected light; yet the spectroscope +shows that their spectrum is composed of bright bands, which would +indicate that they are composed, in part at least, of incandescent +gases. It is, however, difficult to conceive how these gases become +sufficiently heated to be luminous; and at the same time such gases +would reflect no sunlight. + +It seems probable that these comets are really made up of a combination +of small, solid particles in the form of minute meteoroids, and of gases +which are, perhaps, rendered luminous by electric discharges of slight +intensity. + +316. _Physical Constitution of Large Comets._--In the case of large +comets the nucleus is either a dense mass of solid matter several +hundred miles in diameter, or a dense group of meteoroids. Professor +Peirce estimated that the density of the nucleus is at least equal to +that of iron. As such a comet approaches the sun, the nucleus is, to a +slight extent, vaporized, and out of this vapor is formed the coma and +the tail. + +That some evaporating process is going on from the nucleus of the comet +is proved by the movements of the tail. It is evident that the tail +cannot be an appendage carried along with the comet, as it seems to be. +It is impossible that there should be any cohesion in matter of such +tenuity that the smallest stars could be seen through a million of miles +of it, and which is, moreover, continually changing its form. Then, +again, as a comet is passing its perihelion, the tail appears to be +whirled from one side of the sun to another with a rapidity which would +tear it to pieces if the movement were real. The tail seems to be, not +something attached to the comet, and carried along with it, but a stream +of vapor issuing from it, like smoke from a chimney. The matter of which +it is composed is continually streaming outwards, and continually being +replaced by fresh vapor from the nucleus. + +The vapor, as it emanates from the nucleus, is repelled by the sun with +a force often two or three times as great as the ordinary solar +attraction. The most probable explanation of this phenomenon is, that it +is a case of electrical repulsion, the sun and the particles of the +cometary mist being similarly electrified. With reference to this +electrical theory of the formation of comets' tails, Professor Peirce +makes the following observation: "In its approach to the sun, the +surface of the nucleus is rapidly heated: it is melted and vaporized, +and subjected to frequent explosions. The vapor rises in its atmosphere +with a well-defined upper surface, which is known to observers as an +_envelop_.... The electrification of the cometary mist is analogous to +that of our own thunder-clouds. Any portion of the coma which has +received the opposite kind of electricity to the sun and to the repelled +tail will be attracted. This gives a simple explanation of the negative +tails which have been sometimes seen directed towards the sun. In cases +of violent explosion, the whole nucleus might be broken to pieces, and +the coma dashed around so as to give varieties of tail, and even +multiple tails. There seems, indeed, to be no observed phenomenon of the +tail or the coma which is not consistent with a reasonable modification +of the theory." Professor Peirce regarded comets simply as the largest +of the meteoroids. They appear to shine partly by reflected sunlight, +and partly by their own proper light, which seems to be that of vapor +rendered luminous by an electric discharge of slight intensity. + +[Illustration: Fig. 357.] + +317. _Collision of a Comet and the Earth._--It sometimes happens that +the orbit of a comet intersects that of the earth, as is shown in Fig. +357, which shows a portion of the orbit of Biela's comet, with the +positions of the comet and of the earth in 1832. Of course, were a comet +and the earth both to reach the intersection of their orbits at the same +time, a collision of the two bodies would be inevitable. With reference +to the probable effect of such a collision, Professor Newcomb remarks,-- + +"The question is frequently asked, What would be the effect if a comet +should strike the earth? This would depend upon what sort of a comet it +was, and what part of the comet came in contact with our planet. The +latter might pass through the tail of the largest comet without the +slightest effect being produced; the tail being so thin and airy that a +million miles thickness of it looks only like gauze in the sunlight. It +is not at all unlikely that such a thing may have happened without ever +being noticed. A passage through a telescopic comet would be accompanied +by a brilliant meteoric shower, probably a far more brilliant one than +has ever been recorded. No more serious danger would be encountered than +that arising from a possible fall of meteorites; but a collision between +the nucleus of a large comet and the earth might be a serious matter. +If, as Professor Peirce supposes, the nucleus is a solid body of +metallic density, many miles in diameter, the effect where the comet +struck would be terrific beyond conception. At the first contact in the +upper regions of the atmosphere, the whole heavens would be illuminated +with a resplendence beyond that of a thousand suns, the sky radiating a +light which would blind every eye that beheld it, and a heat which would +melt the hardest rocks. A few seconds of this, while the huge body was +passing through the atmosphere, and the collision at the earth's surface +would in an instant reduce everything there existing to fiery vapor, and +bury it miles deep in the solid earth. Happily, the chances of such a +calamity are so minute that they need not cause the slightest +uneasiness. There is hardly a possible form of death which is not a +thousand times more probable than this. So small is the earth in +comparison with the celestial spaces, that if one should shut his eyes, +and fire a gun at random in the air, the chance of bringing down a bird +would be better than that of a comet of any kind striking the earth." + +[Illustration: Fig. 358.] + +[Illustration: Fig. 359.] + +318. _The Chemical Constitution of Comets._--Fig. 358 shows the bands of +the spectrum of a telescopic comet of 1873, as seen by two different +observers. Fig. 359 shows the spectrum of the coma and tail of the comet +of 1874; and the spectrum of the bright comet of 1881 showed the same +three bands for the coma and tail. Now, these three bands are those of +certain hydrocarbon vapors: hence it would seem that the coma and tails +of comets are composed chiefly of such vapors (315). + + + II. THE ZODIACAL LIGHT. + + +319. _The General Appearance of the Zodiacal Light._--The phenomenon +known as the _zodiacal light_ consists of a very faint luminosity, which +may be seen rising from the western horizon after twilight on any clear +winter or spring evening, also from the eastern horizon just before +daybreak in the summer or autumn. It extends out on each side of the +sun, and lies nearly in the plane of the ecliptic. It grows fainter the +farther it is from the sun, and can generally be traced to about ninety +degrees from that luminary, when it gradually fades away. In a very +clear, tropical atmosphere, it has been traced all the way across the +heavens from east to west, thus forming a complete ring. The general +appearance of this column of light, as seen in the morning, in the +latitude of Europe, is shown in Fig. 360. + +[Illustration: Fig. 360.] + +Taking all these appearances together, they indicate that it is due to a +lens-shaped appendage surrounding the sun, and extending a little beyond +the earth's orbit. It lies nearly in the plane of the ecliptic; but its +exact position is not easily determined. Fig. 361 shows the general form +and position of this solar appendage, as seen in the west. + +[Illustration: Fig. 361.] + +320. _The Visibility of the Zodiacal Light._--The reason why the +zodiacal light is more favorably seen in the evening during the winter +and spring than in the summer and fall is evident from Fig. 362, which +shows the position of the ecliptic and the zodiacal light with reference +to the western horizon at the time of sunset in March and in September. +It will be seen that in September the axis of the light forms a small +angle with the horizon, so that the phenomenon is visible only a short +time after sunset and low down where it is difficult to distinguish it +from the glimmer of the twilight; while in March, its axis being nearly +perpendicular to the horizon, the light may be observed for some hours +after sunset and well up in the sky. Fig. 363 gives the position of the +ecliptic and of the zodiacal light with reference to the eastern horizon +at the time of sunrise, and shows why the zodiacal light is seen to +better advantage in the morning during the summer and fall than during +the winter and spring. It will be observed that here the angle made by +the axis of the light with the horizon is small in March, while it is +large in September; the conditions represented in the preceding figure +being thus reversed. + +[Illustration: Fig. 362.] + +[Illustration: Fig. 363.] + +321. _Nature of the Zodiacal Light._--Various attempts have been made to +explain the phenomena of the zodiacal light; but the most probable +theory is, that it is due to an immense number of meteors which are +revolving around the sun, and which lie mostly within the earth's orbit. +Each of these meteors reflects a sensible portion of sunlight, but is +far too small to be separately visible. All of these meteors together +would, by their combined reflection, produce a kind of pale, diffused +light. + + + + + III. THE STELLAR UNIVERSE. + + + I. GENERAL ASPECT OF THE HEAVENS. + + +322. _The Magnitude of the Stars._--The stars that are visible to the +naked eye are divided into six classes, according to their brightness. +The brightest stars are called stars of the _first magnitude_; the next +brightest, those of the _second magnitude_; and so on to the _sixth +magnitude_. The last magnitude includes the faintest stars that are +visible to the naked eye on the most favorable night. Stars which are +fainter than those of the sixth magnitude can be seen only with the +telescope, and are called _telescopic stars_. Telescopic stars are also +divided into magnitudes; the division extending to the _sixteenth_ +magnitude, or the faintest stars that can be seen with the most powerful +telescopes. + +The classification of stars according to magnitudes has reference only +to their brightness, and not at all to their actual size. A sixth +magnitude star may actually be larger than a first magnitude star; its +want of brilliancy being due to its greater distance, or to its inferior +luminosity, or to both of these causes. + +None of the stars present any sensible disk, even in the most powerful +telescope: they all appear as mere points of light. The larger the +telescope, the greater is its power of revealing faint stars; not +because it makes these stars appear larger, but because of its greater +light-gathering power. This power increases with the size of the +object-glass of the telescope, which plays the part of a gigantic pupil +of the eye. + +The classification of the stars into magnitudes is not made in +accordance with any very accurate estimate of their brightness. The +stars which are classed together in the same magnitude are far from +being equally bright. + +The stars of each lower magnitude are about two-fifths as bright as +those of the magnitude above. The ratio of diminution is about a third +from the higher magnitude down to the fifth. Were the ratio two-fifths +exact, it would take about + + 2-1/2 stars of the 2d magnitude to make one of the 1st. + 6 stars of the 3d magnitude to make one of the 1st. + 16 stars of the 4th magnitude to make one of the 1st. + 40 stars of the 5th magnitude to make one of the 1st. + 100 stars of the 6th magnitude to make one of the 1st. + 10,000 stars of the 11th magnitude to make one of the 1st. + 1,000,000 stars of the 16th magnitude to make one of the 1st. + +323. _The Number of the Stars._--The total number of stars in the +celestial sphere visible to the average naked eye is estimated, in round +numbers, at five thousand; but the number varies much with the +perfection and the training of the eye and with the atmospheric +conditions. For every star visible to the naked eye, there are thousands +too minute to be seen without telescopic aid. Fig. 364 shows a portion +of the constellation of the Twins as seen with the naked eye; and Fig. +365 shows the same region as seen in a powerful telescope. + +[Illustration: Fig. 364.] + +[Illustration: Fig. 365.] + +Struve has estimated that the total number of stars visible with +Herschel's twenty-foot telescope was about twenty million. The number +that can be seen with the great telescopes of modern times has not been +carefully estimated, but is probably somewhere between thirty million +and fifty million. + +The number of stars between the north pole and the circle thirty-five +degrees south of the equator is about as follows:-- + + Of the 1st magnitude about 14 stars. + Of the 2d magnitude about 48 stars. + Of the 3d magnitude about 152 stars. + Of the 4th magnitude about 313 stars. + Of the 5th magnitude about 854 stars. + Of the 6th magnitude about 2010 stars. + ---- + Total visible to naked eye 3391 stars. + +The number of stars of the several magnitudes is approximately in +inverse proportion to that of their brightness, the ratio being a little +greater in the higher magnitudes, and probably a little less in the +lower ones. + +324. _The Division of the Stars into Constellations._--A glance at the +heavens is sufficient to show that the stars are not distributed +uniformly over the sky. The larger ones especially are collected into +more or less irregular groups. The larger groups are called +_constellations_. At a very early period a mythological figure was +allotted to each constellation; and these figures were drawn in such a +way as to include the principal stars of each constellation. The heavens +thus became covered, as it were, with immense hieroglyphics. + +There is no historic record of the time when these figures were formed, +or of the principle in accordance with which they were constructed. It +is probable that the imagination of the earlier peoples may, in many +instances, have discovered some fanciful resemblance in the +configuration of the stars to the forms depicted. The names are still +retained, although the figures no longer serve any astronomical purpose. +The constellation Hercules, for instance, no longer represents the +figure of a man among the stars, but a certain portion of the heavens +within which the ancients placed that figure. In star-maps intended for +school and popular use it is still customary to give these figures; but +they are not generally found on maps designed for astronomers. + +325. _The Naming of the Stars._--The brighter stars have all proper +names, as _Sirius_, _Procyon_, _Arcturus_, _Capella_, _Aldebaran_, etc. +This method of designating the stars was adopted by the Arabs. Most of +these names have dropped entirely out of astronomical use, though many +are popularly retained. The brighter stars are now generally designated +by the letters of the Greek alphabet,--_alpha_, _beta_, _gamma_, +etc.,--to which is appended the genitive of the name of the +constellation, the first letter of the alphabet being used for the +brightest star, the second for the next brightest, and so on. Thus +_Aldebaran_ would be designated as _Alpha Tauri_. In speaking of the +stars of any one constellation, we simply designate them by the letters +of the Greek alphabet, without the addition of the name of the +constellation, which answers to a person's surname, while the Greek +letter answers to his Christian name. The names of the seven stars of +the "Dipper" are given in Fig. 366. When the letters of the Greek +alphabet are exhausted, those of the Roman alphabet are employed. The +fainter stars in a constellation are usually designated by some system +of numbers. + +[Illustration: Fig. 366.] + +326. _The Milky-Way, or Galaxy._--The Milky-Way is a faint luminous +band, of irregular outline, which surrounds the heavens with a great +circle, as shown in Fig. 367. Through a considerable portion of its +course it is divided into two branches, and there are various vacant +spaces at different points in this band; but at only one point in the +southern hemisphere is it entirely interrupted. + +[Illustration: Fig. 367.] + +The telescope shows that the Galaxy arises from the light of countless +stars too minute to be separately visible with the naked eye. The +telescopic stars, instead of being uniformly distributed over the +celestial sphere, are mostly condensed in the region of the Galaxy. They +are fewest in the regions most distant from this belt, and become +thicker as we approach it. The greater the telescopic power, the more +marked is the condensation. With the naked eye the condensation is +hardly noticeable; but with the aid of a very small telescope, we see a +decided thickening of the stars in and near the Galaxy, while the most +powerful telescopes show that a large majority of the stars lie actually +in the Galaxy. If all the stars visible with a twelve-inch telescope +were blotted out, we should find that the greater part of those +remaining were in the Galaxy. + +[Illustration: Fig. 368.] + +The increase in the number of the stars of all magnitudes as we approach +the plane of the Milky-Way is shown in Fig. 368. The curve _acb_ shows +by its height the distribution of the stars above the ninth magnitude, +and the curve _ACB_ those of all magnitudes. + +327. _Star-Clusters._--Besides this gradual and regular condensation +towards the Galaxy, occasional aggregations of stars into _clusters_ may +be seen. Some of these are visible to the naked eye, sometimes as +separate stars, like the "Seven Stars," or Pleiades, but more commonly +as patches of diffused light, the stars being too small to be seen +separately. The number visible in powerful telescopes is, however, much +greater. Sometimes hundreds or even thousands of stars are visible in +the field of view at once, and sometimes the number is so great that +they cannot be counted. + +328. _Nebulæ._--Another class of objects which are found in the +celestial spaces are irregular masses of soft, cloudy light, known as +_nebulæ_. Many objects which look like nebulæ in small telescopes are +shown by more powerful instruments to be really star-clusters. But many +of these objects are not composed of stars at all, being immense masses +of gaseous matter. + +[Illustration: Fig. 369.] + +The general distribution of nebulæ is the reverse of that of the stars. +Nebulæ are thickest where stars are thinnest. While stars are most +numerous in the region of the Milky-Way, nebulæ are most abundant about +the poles of the Milky-Way. This condensation of nebulæ about the poles +of the Milky-Way is shown in Figs. 367 and 369, in which the points +represent, not stars, but nebulæ. + + + II. THE STARS. + + + The Constellations. + + +[Illustration: Fig. 370.] + +[Illustration: Fig. 371.] + +329. _The Great Bear._--The Great Bear, or _Ursa Major_, is one of the +circumpolar constellations (4), and contains one of the most familiar +_asterisms_, or groups of stars, in our sky; namely, the _Great Dipper_, +or _Charles's Wain_. The positions and names of the seven prominent +stars in it are shown in Fig. 370. The two stars Alpha and Beta are +called the _Pointers_. This asterism is sometimes called the _Butcher's +Cleaver_. The whole constellation is shown in Fig. 371. A rather faint +star marks the nose of the bear, and three equidistant pairs of faint +stars mark his feet. + +330. _The Little Bear, Draco, and Cassiopeia._--These are all +circumpolar constellations. The most important star of the Little Bear, +or _Ursa Minor_, is _Polaris_, or the _Pole Star_. This star may be +found by drawing a line from Beta to Alpha of the Dipper, and prolonging +it as shown in Fig. 372. This explains why these stars are called the +_Pointers_. The Pole Star, with the six other chief stars of the Little +Bear, form an asterism called the _Little Dipper_. These six stars are +joined with Polaris by a dotted line in Fig. 372. + +[Illustration: Fig. 372.] + +The stars in a serpentine line between the two Dippers are the chief +stars of _Draco_, or the _Dragon_; the trapezium marking its head. Fig. +373 shows the constellations of Ursa Minor and Draco as usually figured. + +[Illustration: Fig. 373.] + +To find _Cassiopeia_, draw a line from Delta of the Dipper to Polaris, +and prolong it about an equal distance beyond, as shown in Fig. 372. +This line will pass near Alpha of Cassiopeia. The five principal stars +of this constellation form an irregular _W_, opening towards the pole. +Between Cassiopeia and Draco are five rather faint stars, which form an +irregular _K_. These are the principal stars of the constellation +_Cepheus_. These two constellations are shown in Fig. 374. + +[Illustration: Fig. 374.] + +[Illustration: Fig. 375.] + +331. _The Lion, Berenice's Hair, and the Hunting-Dogs._--A line drawn +from Alpha to Beta of the Dipper, and prolonged as shown in Fig. 375, +will pass between the two stars _Denebola_ and _Regulus_ of _Leo_, or +the _Lion_. Regulus forms a _sickle_ with several other faint stars, and +marks the heart of the lion. Denebola is at the apex of a right-angled +triangle, which it forms with two other stars, and marks the end of the +lion's tail. This constellation is visible in the evening from February +to July, and is figured in Fig. 376. + +[Illustration: Fig. 376.] + +In a straight line between Denebola and Eta, at the end of the Great +Bear's tail, are, at about equal distances, the two small constellations +of _Coma Berenices_, or _Berenice's Hair_, and _Canes Venatici_, or the +_Hunting-Dogs_. These are shown in Fig. 377. The dogs are represented as +pursuing the bear, urged on by the huntsman _Boötes_. + +[Illustration: Fig. 377.] + +332. _Boötes, Hercules, and the Northern Crown._--_Arcturus_, the +principal star of _Boötes_, may be found by drawing a line from Zeta to +Eta of the Dipper, and then prolonging it with a slight bend, as shown +in Fig. 378. Arcturus and Polaris form a large isosceles triangle with a +first-magnitude star called _Vega_. This triangle encloses at one corner +the principal stars of Boötes, and the head of the Dragon near the +opposite side. The side running from Arcturus to Vega passes through +_Corona Borealis_, or the _Northern Crown_, and the body of _Hercules_, +which is marked by a quadrilateral of four stars. + +[Illustration: Fig. 378.] + +_Boötes_, who is often represented as a husbandman, _Corona Borealis_, +and _Hercules_, are delineated in Fig. 379. These constellations are +visible in the evening from May to September. + +[Illustration: Fig. 379.] + +[Illustration: Fig. 380.] + +333. _The Lyre, the Swan, the Eagle, and the Dolphin._--_Altair_, the +principal star of _Aquila_, or the _Eagle_, lies on the opposite side of +the Milky-Way from Vega. Altair is a first-magnitude star, and has a +faint star on each side of it, as shown in Fig. 380. Vega, also of the +first magnitude, is the principal star of _Lyra_, or the _Lyre_. Between +these two stars, and a little farther to the north, are several stars +arranged in the form of an immense cross. The bright star at the head of +this cross is called _Deneb_. The cross lies in the Milky-Way, and +contains the chief stars of the constellation _Cygnus_, or the _Swan_. A +little to the north of Altair are four stars in the form of a diamond. +This asterism is popularly known as _Job's Coffin_. These four stars are +the chief stars of _Delphinus_, or the _Dolphin_. These four +constellations are shown together in Fig. 381. The _Swan_ is visible +from June to December, in the evening. + +[Illustration: Fig. 381.] + +334. _Virgo._--A line drawn from Alpha to Gamma of the Dipper, and +prolonged with a slight bend at Gamma, will reach to a first-magnitude +star called _Spica_ (Fig. 382). This is the chief star of the +constellation _Virgo_, or the _Virgin_, and forms a large isosceles +triangle with _Arcturus_ and _Denebola_. + +[Illustration: Fig. 382.] + +_Virgo_ is represented in Fig. 383. To the right of this constellation, +as shown in the figure, there are four stars which form a trapezium, and +mark the constellation _Corvus_, or the _Crow_. This bird is represented +as standing on the body of _Hydra_, or the _Water-Snake_. _Virgo_ is +visible in the evening, from April to August. + +[Illustration: Fig. 383.] + +[Illustration: Fig. 384.] + +[Illustration: Fig. 385.] + +335. _The Twins._--A line drawn from Delta to Beta of the Dipper, and +prolonged as shown in Fig. 384, passes between two bright stars called +_Castor_ and _Pollux_. The latter of these is usually reckoned as a +first-magnitude star. These are the principal stars of the constellation +_Gemini_, or the _Twins_, which is shown in Fig. 385. The constellation +_Canis Minor_, or the _Little Dog_, is shown in the lower part of the +figure. There are two conspicuous stars in this constellation, the +brightest of which is of the first magnitude, and called _Procyon_. + +The region to which we have now been brought is the richest of the +northern sky, containing no less than seven first-magnitude stars. These +are _Sirius_, _Procyon_, _Pollux_, _Capella_, _Aldebaran_, _Betelgeuse_, +and _Rigel_. They are shown in Fig. 386. + +[Illustration: Fig. 386.] + +_Betelgeuse_ and _Rigel_ are in the constellation _Orion_, being about +equally distant to the north and south from the three stars forming the +_belt_ of Orion. Betelgeuse is a red star. _Sirius_ is the brightest +star in the heavens, and belongs to the constellation _Canis Major_, or +the _Great Dog_. It lies to the east of the belt of Orion. _Aldebaran_ +lies at about the same distance to the west of the belt. It is a red +star, and belongs to the constellation _Taurus_, or the _Bull_. +_Capella_ is in the constellation _Auriga_, or the _Wagoner_. These +stars are visible in the evening, from about December to April. + +336. _Orion and his Dogs, and Taurus._--_Orion_ and his _Dogs_ are shown +in Fig. 387, and _Orion_ and _Taurus_ in Fig. 388. _Aldebaran_ marks one +of the eyes of the bull, and is often called the _Bull's Eye_. The +irregular _V_ in the face of the bull is called the _Hyades_, and the +cluster on the shoulder the _Pleiades_. + +[Illustration: Fig. 387.] + +[Illustration: Fig. 388.] + +[Illustration: Fig. 389.] + +337. _The Wagoner._--The constellation _Auriga_, or the _Wagoner_ +(sometimes called the _Charioteer_), is shown in Fig. 389. _Capella_ +marks the _Goat_, which he is represented as carrying on his back, and +the little right-angled triangle of stars near it the _Kids_. The five +chief stars of this constellation form a large, irregular pentagon. +Gamma of _Auriga_ is also Beta of _Taurus_, and marks one of the horns +of the _Bull_. + +[Illustration: Fig. 390.] + +338. _Pegasus, Andromeda, and Perseus._--A line drawn from Polaris near +to Beta of _Cassiopeia_ will lead to a bright second-magnitude star at +one corner of a large square (Fig. 390). Alpha belongs both to the +_Square of Pegasus_ and to _Andromeda_. Beta and Gamma, which are +connected with Alpha in the figure by a dotted line, also belong to +Andromeda. _Algol_, which forms, with the last-named stars and with the +_Square of Pegasus_, an asterism similar in configuration to the _Great +Dipper_, belongs to _Perseus_. _Algenib_, which is reached by bending +the line at Gamma in the opposite direction, is the principal star of +_Perseus_. + +[Illustration: Fig. 391.] + +[Illustration: Fig. 392.] + +[Illustration: Fig. 393.] + +_Pegasus_ is shown in Fig. 391, and _Andromeda_ in Fig. 392. _Cetus_, +the _Whale_, or the _Sea Monster_, shown in Fig. 393, belongs to the +same mythological group of constellations. + +[Illustration: Fig. 394.] + +339. _Scorpio, Sagittarius, and Ophiuchus._--During the summer months a +brilliant constellation is visible, called _Scorpio_, or the _Scorpion_. +The configuration of the chief stars of this constellation is shown in +Fig. 394. They bear some resemblance to a boy's kite. The brightest star +is of the first magnitude, and called _Antares_ (from _anti_, instead +of, and _Ares_, the Greek name of Mars), because it rivals Mars in +redness. The stars in the tail of the Scorpion are visible in our +latitude only under very favorable circumstances. This constellation is +shown in Fig. 395, together with _Sagittarius_ and _Ophiuchus_. +_Sagittarius_, or the _Archer_, is to the east of _Scorpio_. It contains +no bright stars, but is easily recognized from the fact that five of its +principal stars form the outline of an inverted dipper, which, from the +fact of its being partly in the Milky-Way, is often called the _Milk +Dipper_. + +[Illustration: Fig. 395.] + +_Ophiuchus_, or the _Serpent-Bearer_, is a large constellation, filling +all the space between the head of _Hercules_ and _Scorpio_. It is +difficult to trace, since it contains no very brilliant stars. This +constellation and _Libra_, or the _Balances_, which is the zodiacal +constellation to the west of Scorpio, are shown in Fig. 396. + +[Illustration: Fig. 396.] + +[Illustration: Fig. 397.] + +340. _Capricornus, Aquarius, and the Southern Fish._--The two zodiacal +constellations to the east of Sagittarius are _Capricornus_ and +_Aquarius_. _Capricornus_ contains three pairs of small stars, which +mark the head, the tail, and the knees of the animal. + +_Aquarius_ is marked by no conspicuous stars. An irregular line of +minute stars marks the course of the stream of water which flows from +the Water-Bearer's Urn into the mouth of the _Southern Fish_. This mouth +is marked by the first-magnitude star _Fomalhaut_. These constellations +are shown in Fig. 397. + +[Illustration: Fig. 398.] + +341. _Pisces and Aries._--The remaining zodiacal constellations are +_Pisces_, or the _Fishes_, _Aries_, or the _Ram_ (Fig. 398), and +_Cancer_, or the _Crab_. + +The _Fishes_ lie under _Pegasus_ and _Andromeda_, but contain no bright +stars. _Aries_ (between _Pisces_ and _Taurus_) is marked by a pair of +stars on the head,--one of the second, and one of the third magnitude. +_Cancer_ (between _Leo_ and _Gemini_) has no bright stars, but contains +a remarkable cluster of small stars called _Præsepe_, or the _Beehive_. + + + Clusters. + + +342. _The Hyades._--The _Hyades_ are a very open cluster in the face of +_Taurus_ (334). The three brightest stars of this cluster form a letter +_V_, the point of the _V_ being on the nose, and the open ends at the +eyes. This cluster is shown in Fig. 399. The name, according to the most +probable etymology, means _rainy_; and they are said to have been so +called because their rising was associated with wet weather. They were +usually considered the daughters of Atlas, and sisters of the Pleiades, +though sometimes referred to as the nurses of Bacchus. + +[Illustration: Fig. 399.] + +343. _The Pleiades._--The _Pleiades_ constitute a celebrated group of +stars, or a miniature constellation, on the shoulder of _Taurus_. Hesiod +mentions them as "the seven virgins of Atlas born," and Milton calls +them "the seven Atlantic sisters." They are referred to in the Book of +Job. The Spaniards term them "the little nanny-goats;" and they are +sometimes called "the hen and chickens." + +[Illustration: Fig. 400.] + +[Illustration: Fig. 401.] + +Usually only six stars in this cluster can be seen with the naked eye, +and this fact has given rise to the legend of the "lost Pleiad." On a +clear, moonless night, however, a good eye can discern seven or eight +stars, and some observers have distinguished as many as eleven. Fig. 400 +shows the _Pleiades_ as they appear to the naked eye under the most +favorable circumstances. Fig. 401 shows this cluster as it appears in a +powerful telescope. With such an instrument more than five hundred stars +are visible. + +344. _Cluster in the Sword-handle of Perseus._--This is a somewhat dense +double cluster. It is visible to the naked eye, appearing as a hazy +star. A line drawn from _Algenib_, or _Alpha_ of _Perseus_ (338), to +_Delta_ of _Cassiopeia_ (330), will pass through this cluster at about +two-thirds the distance from the former. This double cluster is one of +the most brilliant objects in the heavens, with a telescope of moderate +power. + +[Illustration: Fig. 402.] + +345. _Cluster of Hercules._--The celebrated globular cluster of +_Hercules_ can be seen only with a telescope of considerable power, and +to resolve it into distinct stars (as shown in Fig. 402) requires an +instrument of the very highest class. + +[Illustration: Fig. 403.] + +346. _Other Clusters._--Fig. 403 shows a magnificent globular cluster in +the constellation _Aquarius_. Herschel describes it as appearing like a +heap of sand, being composed of thousands of stars of the fifteenth +magnitude. + +[Illustration: Fig. 404.] + +Fig. 404 shows a cluster in the constellation _Toucan_, which Sir John +Herschel describes as a most glorious globular cluster, the stars of the +fourteenth magnitude being immensely numerous. There is a marked +condensation of light at the centre. + +[Illustration: Fig. 405.] + +[Illustration: Fig. 406.] + +Fig. 405 shows a cluster in the _Centaur_, which, according to the same +astronomer, is beyond comparison the richest and largest object of the +kind in the heavens, the stars in it being literally innumerable. Fig. +406 shows a cluster in _Scorpio_, remarkable for the peculiar +arrangement of its component stars. + +Star clusters are especially abundant in the region of the Milky-Way, +the law of their distribution being the reverse of that of the nebulæ. + + + Double and Multiple Stars. + + +347. _Double Stars._--The telescope shows that many stars which appear +single to the naked eye are really _double_, or composed of a pair of +stars lying side by side. There are several pairs of stars in the +heavens which lie so near together that they almost seem to touch when +seen with the naked eye. + +[Illustration: Fig. 407.] + +[Illustration: Fig. 408.] + +Pairs of stars are not considered double unless the components are so +near together that they both appear in the field of view when examined +with a telescope. In the majority of the pairs classed as double stars +the distance between the components ranges from half a second to fifteen +seconds. + +[Illustration: Fig. 409.] + +_Epsilon Lyræ_ is a good example of a pair of stars that can barely be +separated with a good eye. Figs. 407 and 408 show this pair as it +appears in telescopes magnifying respectively four and fifteen times; +and Fig. 409 shows it as seen in a more powerful telescope, in which +each of the two components of the pair is seen to be a truly double +star. + +[Illustration: Fig. 410.] + +[Illustration: Fig. 411.] + +348. _Multiple Stars._--When a star is resolved into more than two +components by a telescope, it is called a _multiple_ star. Fig. 410 +shows a _triple_ star in _Pegasus_. Fig. 411 shows a quadruple star in +_Taurus_. Fig. 412 shows a _sextuple_ star, and Fig. 413 a _septuple_ +star. Fig. 414 shows the celebrated septuple star in _Orion_, called +_Theta Orionis_, or the _trapezium_ of Orion. + +349. _Optically Double and Multiple Stars._--Two or more stars which are +really very distant from each other, and which have no physical +connection whatever, may appear to be near together, because they happen +to lie in the same direction, one behind the other. Such accidental +combinations are called _optically_ double or multiple stars. + +[Illustration: Fig. 412.] + +[Illustration: Fig. 413.] + +350. _Physically Double and Multiple Stars._--In the majority of cases +the components of double and multiple stars are in reality comparatively +near together, and are bound together by gravity into a physical system. +Such combinations are called _physically_ double and multiple stars. The +components of these systems all revolve around their common centre of +gravity. In many instances their orbits and periods of revolution have +been ascertained by observation and calculation. Fig. 415 shows the +orbit of one of the components of a double star in the constellation +_Hercules_. + +[Illustration: Fig. 414.] + +351. _Colors of Double and Multiple Stars._--The components of double +and multiple stars are often highly colored, and frequently the +components of the same system are of different colors. Sometimes one +star of a binary system is _white_, and the other _red_; and sometimes a +_white_ star is combined with a _blue_ one. Other colors found in +combination in these systems are _red_ and _blue_, _orange_ and _green_, +_blue_ and _green_, _yellow_ and _blue_, _yellow_ and _red_, etc. + +[Illustration: Fig. 415.] + +If these double and multiple stars are accompanied by planets, these +planets will sometimes have two or more suns in the sky at once. On +alternate days they may have suns of different colors, and perhaps on +the same day two suns of different colors. The effect of these changing +colored lights on the landscape must be very remarkable. + + + New and Variable Stars. + + +352. _Variable Stars._--There are many stars which undergo changes of +brilliancy, sometimes slight, but occasionally very marked. These +changes are in some cases apparently irregular, and in others +_periodic_. All such stars are said to be _variable_, though the term is +applied especially to those stars whose variability is _periodic_. + +[Illustration: Fig. 416.] + +353. _Algol._--_Algol_, a star of _Perseus_, whose position is shown in +Fig. 416, is a remarkable variable star of a short period. Usually it +shines as a faint second-magnitude star; but at intervals of a little +less than three days it fades to the fourth magnitude for a few hours, +and then regains its former brightness. These changes were first noticed +some two centuries ago, but it was not till 1782 that they were +accurately observed. The period is now known to be two days, twenty +hours, forty-nine minutes. It takes about four hours and a half to fade +away, and four hours more to recover its brilliancy. Near the beginning +and end of the variations, the change is very slow, so that there are +not more than five or six hours during which an ordinary observer would +see that the star was less bright than usual. + +This variation of light was at first explained by supposing that a large +dark planet was revolving round Algol, and passed over its face at every +revolution, thus cutting off a portion of its light; but there are small +irregularities in the variation, which this theory does not account for. + +354. _Mira._--Another remarkable variable star is _Omicron Ceti_, or +_Mira_ (that is, the _wonderful_ star). It is generally invisible to the +naked eye; but at intervals of about eleven months it shines forth as a +star of the second or third magnitude. It is about forty days from the +time it becomes visible until it attains its greatest brightness, and is +then about two months in fading to invisibility; so that its increase of +brilliancy is more rapid than its waning. Its period is quite irregular, +ranging from ten to twelve months; so that the times of its appearance +cannot be predicted with certainty. Its maximum brightness is also +variable, being sometimes of the second magnitude, and at others only of +the third or fourth. + +[Illustration: Fig. 417.] + +355. _Eta Argus._--Perhaps the most extraordinary variable star in the +heavens is _Eta Argus_, in the constellation _Argo_, or the _Ship_, in +the southern hemisphere (Fig. 417). The first careful observations of +its variability were made by Sir John Herschel while at the Cape of Good +Hope. He says, "It was on the 16th of December, 1837, that, resuming the +photometrical comparisons, my astonishment was excited by the appearance +of a new candidate for distinction among the very brightest stars of the +first magnitude in a part of the heavens where, being perfectly familiar +with it, I was certain that no such brilliant object had before been +seen. After a momentary hesitation, the natural consequence of a +phenomenon so utterly unexpected, and referring to a map for its +configuration with other conspicuous stars in the neighborhood, I became +satisfied of its identity with my old acquaintance, _Eta Argus_. Its +light was, however, nearly tripled. While yet low, it equalled Rigel, +and, when it attained some altitude, was decidedly greater." It +continued to increase until Jan. 2, 1838, then faded a little till April +following, though it was still as bright as Aldebaran. In 1842 and 1843 +it blazed up brighter than ever, and in March of the latter year was +second only to _Sirius_. During the twenty-five years following it +slowly but steadily diminished. In 1867 it was barely visible to the +naked eye; and the next year it vanished entirely from the unassisted +view, and has not yet begun to recover its brightness. The curve in Fig. +418 shows the change in brightness of this remarkable star. The numbers +at the bottom show the years of the century, and those at the side the +brightness of the star. + +[Illustration: Fig. 418.] + +356. _New Stars._--In several cases stars have suddenly appeared, and +even become very brilliant; then, after a longer or shorter time, they +have faded away and disappeared. Such stars are called _new_ or +_temporary_ stars. For a time it was supposed that such stars were +actually new. They are now, however, classified by astronomers among the +variable stars, their changes being of a very irregular and fitful +character. There is scarcely a doubt that they were all in the heavens +as very small stars before they blazed forth in so extraordinary a +manner, and that they are in the same places still. There is a wide +difference between these irregular variations, or the breaking-forth of +light on a single occasion in the course of centuries, and the regular +and periodic changes in the case of a star like _Algol_; but a long +series of careful observation has resulted in the discovery of stars of +nearly every degree of irregularity between these two extremes. Some of +them change gradually from one magnitude to another, in the course of +years, without seeming to follow any law whatever; while in others some +slight tendency to regularity can be traced. _Eta Argus_ may be regarded +as a connecting link between new and variable stars. + +357. _Tycho Brahe's Star._--An apparently new star suddenly appeared in +_Cassiopeia_ in 1572. It was first seen by Tycho Brahe, and is therefore +associated with his name. Its position in the constellation is shown in +Fig. 419. It was first seen on Nov. 11, when it had already attained the +first magnitude. It became rapidly brighter, soon rivalling Venus in +splendor, so that good eyes could discern it in full daylight. In +December it began to wane, and gradually faded until the following May, +when it disappeared entirely. + +[Illustration: Fig. 419.] + +A star showed itself in the same part of the heavens in 945 and in 1264. +If these were three appearances of the same star, it must be reckoned as +a periodic star with a period of a little more than three hundred years. + +358. _Kepler's Star._--In 1604 a new star was seen in the constellation +_Ophiuchus_. It was first noticed in October of that year, when it was +of the first magnitude. In the following winter it began to fade, but +remained visible during the whole year 1605. Early in 1606 it +disappeared entirely. A very full history of this star was written by +Kepler. + +One of the most remarkable things about this star was its brilliant +scintillation. According to Kepler, it displayed all the colors of the +rainbow, or of a diamond cut with multiple facets, and exposed to the +rays of the sun. It is thought that this star also appeared in 393, 798, +and 1203; if so, it is a variable star with a period of a little over +four hundred years. + +359. _New Star of 1866._--The most striking case of this kind in recent +times was in May, 1866, when a star of the second magnitude suddenly +appeared in _Corona Borealis_. On the 11th and 12th of that month it was +observed independently by at least five observers in Europe and America. +The fact that none of these new stars were noticed until they had nearly +or quite attained their greatest brilliancy renders it probable that +they all blazed up very suddenly. + +360. _Cause of the Variability of Stars._--The changes in the brightness +of variable and temporary stars are probably due to operations similar +to those which produce the spots and prominences in our sun. We have +seen (188) that the frequency of solar spots shows a period of eleven +years, during one portion of which there are few or no spots to be seen, +while during another portion they are numerous. If an observer so far +away as to see our sun like a star could from time to time measure its +light exactly, he would find it to be a variable star with a period of +eleven years, the light being least when we see most spots, and greatest +when few are visible. The variation would be slight, but it would +nevertheless exist. Now, we have reason to believe that the physical +constitution of the sun and the stars is of the same general nature. It +is therefore probable, that, if we could get a nearer view of the stars, +we should see spots on their disks as we do on the sun. It is also +likely that the varying physical constitution of the stars might give +rise to great differences in the number and size of the spots; so that +the light of some of these suns might vary to a far greater degree than +that of our own sun does. If the variations had a regular period, as in +the case of our sun, the appearances to a distant observer would be +precisely what we see in the case of a periodic variable star. + +The spectrum of the new star of 1866 was found to be a continuous one, +crossed by bright lines, which were apparently due to glowing hydrogen. +The continuous spectrum was also crossed by dark lines, indicating that +the light had passed through an atmosphere of comparatively cool gas. +Mr. Huggins infers from this that there was a sudden and extraordinary +outburst of hydrogen gas from the star, which by its own light, as well +as by heating up the whole surface of the star, caused the extraordinary +increase of brilliancy. Now, the spectroscope shows that the red flames +of the solar chromosphere (197) are largely composed of hydrogen; and it +is not unlikely that the blazing-forth of this star arose from an action +similar to that which produces these flames, only on an immensely larger +scale. + + + Distance of the Stars. + + +361. _Parallax of the Stars._--Such is the distance of the stars, that +only in a comparatively few instances has any displacement of these +bodies been detected when viewed from opposite parts of the earth's +orbit, that is, from points a hundred and eighty-five million miles +apart; and in no case can this displacement be detected except by the +most careful and delicate measurement. Half of the above displacement, +or the displacement of the star as seen from the earth instead of the +sun, is called the _parallax_ of the star. In no case has a parallax of +one second as yet been detected. + +362. _The Distance of the Stars._--The distance of a star whose parallax +is one second would be 206,265 times the distance of the earth from the +sun, or about nineteen million million miles. It is quite certain that +no star is nearer than this to the earth. Light has a velocity which +would carry it seven times and a half around the earth in a second; but +it would take it more than three years to reach us from that distance. +Were all the stars blotted out of existence to-night, it would be at +least three years before we should miss a single one. + +_Alpha Centauri_, the brightest star in the constellation of the +_Centaur_, is, so far as we know, the nearest of the fixed stars. It is +estimated that it would take its light about three years and a half to +reach us. It has also been estimated that it would take light over +sixteen years to reach us from _Sirius_, about eighteen years to reach +us from _Vega_, about twenty-five years from _Arcturus_, and over forty +years from the _Pole-Star_. In many instances it is believed that it +would take the light of stars hundreds of years to make the journey to +our earth, and in some instances even thousands of years. + + + Proper Motion of the Stars. + + +363. _Why the Stars appear Fixed._--The stars seem to retain their +relative positions in the heavens from year to year, and from age to +age; and hence they have come universally to be denominated as _fixed_. +It is, however, now well known that the stars, instead of being really +stationary, are moving at the rate of many miles a second; but their +distance is so enormous, that, in the majority of cases, it would be +thousands of years before this rate of motion would produce a sufficient +displacement to be noticeable to the unaided eye. + +[Illustration: Fig. 420.] + +364. _Secular Displacement of the Stars._--Though the proper motion of +the stars is apparently slight, it will, in the course of many ages, +produce a marked change in the configuration of the stars. Thus, in Fig. +420, the left-hand portion shows the present configuration of the stars +of the Great Dipper. The small arrows attached to the stars show the +direction and comparative magnitudes of their motion. The right-hand +portion of the figure shows these stars as they will appear thirty-six +thousand years from the present time. + +[Illustration: Fig. 421.] + +Fig. 421 shows in a similar way the present configuration and proper +motion of the stars of _Cassiopeia_, and also these stars as they will +appear thirty-six thousand years hence. + +[Illustration: Fig. 422.] + +Fig. 422 shows the same for the constellation _Orion_. + +365. _The Secular Motion of the Sun._--The stars in all parts of the +heavens are found to move in all directions and with all sorts of +velocities. When, however, the motions of the stars are averaged, there +is found to be an apparent proper motion common to all the stars. The +stars in the neighborhood of _Hercules_ appear to be approaching us, and +those in the opposite part of the heavens appear to be receding from us. +In other words, all the stars appear to be moving away from Hercules, +and towards the opposite part of the heavens. + +[Illustration: Fig. 423.] + +This apparent motion common to all the stars is held by astronomers to +be due to the real motion of the sun through space. The point in the +heavens towards which our sun is moving at the present time is indicated +by the small circle in the constellation Hercules in Fig. 423. As the +sun moves, he carries the earth and all the planets along with him. Fig. +424 shows the direction of the sun's motion with reference to the +ecliptic and to the axis of the earth. Fig. 425 shows the earth's path +in space; and Fig. 426 shows the paths of the earth, the moon, Mercury, +Venus, and Mars in space. + +[Illustration: Fig. 424.] + +[Illustration: Fig. 425.] + +[Illustration: Fig. 426.] + +Whether the sun is actually moving in a straight line, or around some +distant centre, it is impossible to determine at the present time. It is +estimated that the sun is moving along his path at the rate of about a +hundred and fifty million miles a year. This is about five-sixths of the +diameter of the earth's orbit. + +366. _Star-Drift._--In several instances, groups of stars have a common +proper motion entirely different from that of the stars around and among +them. Such groups probably form connected systems, in the motion of +which all the stars are carried along together without any great change +in their relative positions. The most remarkable case of this kind +occurs in the constellation _Taurus_. A large majority of the brighter +stars in the region between _Aldebaran_ and the _Pleiades_ have a common +proper motion of about ten seconds per century towards the east. Proctor +has shown that five out of the seven stars which form the Great Dipper +have a common proper motion, as shown in Fig. 427 (see also Fig. 420). +He proposes for this phenomenon the name of _Star-Drift_. + +[Illustration: Fig. 427.] + +367. _Motion of Stars along the Line of Sight._--A motion of a star in +the direction of the line of sight would produce no displacement of the +star that could be detected with the telescope; but it would cause a +change in the brightness of the star, which would become gradually +fainter if moving from us, and brighter if approaching us. Motion along +the line of sight has, however, been detected by the use of the +tele-spectroscope (152), owing to the fact that it causes a displacement +of the spectral lines. As has already been explained (169), a +displacement of a spectral line towards the red end of the spectrum +indicates a motion away from us, and a displacement towards the violet +end, a motion towards us. + + * * * * * + +By means of these displacements of the spectral lines, Huggins has +detected motion in the case of a large number of stars, and calculated +its rate:-- + +STARS RECEDING FROM US. + + Sirius 20 miles per second. + Betelgeuse 22 miles per second. + Rigel 15 miles per second. + Castor 25 miles per second. + Regulus 15 miles per second. + +STARS APPROACHING US. + + Arcturus 55 miles per second. + Vega 50 miles per second. + Deneb 39 miles per second. + Pollux 49 miles per second. + Alpha Ursæ Majoris 46 miles per second. + +These results are confirmed by the fact that the amount of motion +indicated is about what we should expect the stars to have, from their +observed proper motions, combined with their probable distances. Again: +the stars in the neighborhood of Hercules are mostly found to be +approaching the earth, and those which lie in the opposite direction to +be receding from it; which is exactly the effect which would result from +the sun's motion through space. The five stars in the Dipper, which have +a common proper motion, are also found to have a common motion in the +line of sight. But the displacement of the spectral lines is so slight, +and its measurement so difficult, that the velocities in the above table +are to be accepted as only an approximation to the true values. + + + Chemical and Physical Constitution of the Stars. + + +368. _The Constitution of the Stars Similar to that of the Sun._--The +stellar spectra bear a general resemblance to that of the sun, with +characteristic differences. These spectra all show Fraunhofer's lines, +which indicate that their luminous surfaces are surrounded by +atmospheres containing absorbent vapors, as in the case of the sun. The +positions of these lines indicate that the stellar atmospheres contain +elements which are also found in the sun's, and on the earth. + +[Illustration: Fig. 428.] + +369. _Four Types of Stellar Spectra._--The spectra of the stars have +been carefully observed by Secchi and Huggins. They have found that +stellar spectra may be reduced to four types, which are shown in Fig. +428. In the spectrum of _Sirius_, a representative of _Type I._, very +few lines are represented; but the lines are very thick. + +Next we have the solar spectrum, which is a representative of _Type +II._, one in which more lines are represented. In _Type III._ fluted +spaces begin to appear, and in _Type IV._, which is that of the red +stars, nothing but fluted spaces is visible; and this spectrum shows +that something is at work in the atmosphere of those red stars different +from what there is in the simpler atmosphere of _Type I._ + +Lockyer holds that these differences of spectra are due simply to +differences of temperature. According to him, the red stars, which give +the fluted spectra, are of the lowest temperature; and the temperature +of the stars of the different types gradually rises till we reach the +first type, in which the temperature is so high that the dissociation +(161) of the elements is nearly if not quite complete. + + + + + III. NEBULÆ. + + + Classification of Nebulæ. + + +370. _Planetary Nebulæ._--Many nebulæ (328) present a well-defined +circular disk, like that of a planet, and are therefore called +_planetary_ nebulæ. Specimens of planetary nebulæ are shown in Fig. 429. + +[Illustration: Fig. 429.] + +371. _Circular and Elliptical Nebulæ._--While many nebulæ are circular +in form, others are elliptical. The former are called _circular_ nebulæ, +and the latter _elliptical_ nebulæ. Elliptical nebulæ have been +discovered of every degree of eccentricity. Examples of various circular +and elliptical nebulæ are given in Fig. 430. + +[Illustration: Fig. 430.] + +372. _Annular Nebulæ._--Occasionally ring-shaped nebulæ have been +observed, sometimes with, and sometimes without, nebulous matter within +the ring. They are called _annular_ nebulæ. They are both circular and +elliptical in form. Several specimens of this class of nebulæ are given +in Fig. 431. + +[Illustration: Fig. 431.] + +373. _Nebulous Stars._--Sometimes one or more minute stars are enveloped +in a nebulous haze, and are hence called _nebulous stars_. Several of +these nebulæ are shown in Fig. 432. + +[Illustration: Fig. 432.] + +374. _Spiral Nebulæ._--Very many nebulæ disclose a more or less spiral +structure, and are known as _spiral_ nebulæ. They are illustrated in +Fig. 433. There are, however, a great variety of spiral forms. We shall +have occasion to speak of these nebulæ again (381-383). + +[Illustration: Fig. 433.] + +375. _Double and Multiple Nebulæ._--Many _double_ and _multiple_ nebulæ +have been observed, some of which are represented in Fig. 434. + +[Illustration: Fig. 434.] + +Fig. 435 shows what appears to be a double annular nebula. Fig. 436 +gives two views of a double nebula. The change of position in the +components of this double nebula indicates a motion of revolution +similar to that of the components of double stars. + +[Illustration: Fig. 435.] + +[Illustration: Fig. 436.] + + + Irregular Nebulæ. + + +376. _Irregular Forms._--Besides the more or less regular forms of +nebulæ which have been classified as indicated above, there are many of +very irregular shapes, and some of these are the most remarkable nebulæ +in the heavens. Fig. 437 shows a curiously shaped nebula, seen by Sir +John Herschel in the southern heavens; and Fig. 438, one in _Taurus_, +known as the _Crab_ nebula. + +[Illustration: Fig. 437.] + +[Illustration: Fig. 438.] + +377. _The Great Nebula of Andromeda._--This is one of the few nebulæ +that are visible to the naked eye. We see at a glance that it is not a +star, but a mass of diffused light. Indeed, it has sometimes been very +naturally mistaken for a comet. It was first described by Marius in +1614, who compared its light to that of a candle shining through horn. +This gives a very good idea of the impression it produces, which is that +of a translucent object illuminated by a brilliant light behind it. With +a small telescope it is easy to imagine it to be a solid like horn; but +with a large one the effect is more like fog or mist with a bright body +in its midst. Unlike most of the nebulæ, its spectrum is a continuous +one, similar to that from a heated solid, indicating that the light +emanates, not from a glowing gas, but from matter in the solid or liquid +state. This would suggest that it is really an immense star-cluster, so +distant that the highest telescopic power cannot resolve it; yet in the +largest telescopes it looks less resolvable, and more like a gas, than +in those of moderate size. If it is really a gas, and if the spectrum is +continuous throughout the whole extent of the nebula, either it must +shine by reflected light, or the gas must be subjected to a great +pressure almost to its outer limit, which is hardly possible. If the +light is reflected, we cannot determine whether it comes from a single +bright star, or a number of small ones scattered through the nebula. + +With a small telescope this nebula appears elliptical, as in Fig. 439. +Fig. 440 shows it as it appeared to Bond, in the Cambridge refractor. + +[Illustration: Fig. 439.] + +[Illustration: Fig. 440.] + +378. _The Great Nebula of Orion._--The nebula which, above all others, +has occupied the attention of astronomers, and excited the wonder of +observers, is the _great nebula of Orion_, which surrounds the middle +star of the three which form the sword of Orion. A good eye will +perceive that this star, instead of looking like a bright point, has a +hazy appearance, due to the surrounding nebula. This object was first +described by Huyghens in 1659, as follows:-- + +"There is one phenomenon among the fixed stars worthy of mention, which, +so far as I know, has hitherto been noticed by no one, and indeed cannot +be well observed except with large telescopes. In the sword of Orion are +three stars quite close together. In 1656, as I chanced to be viewing +the middle one of these with the telescope, instead of a single star, +twelve showed themselves (a not uncommon circumstance). Three of these +almost touched each other, and with four others shone through a nebula, +so that the space around them seemed far brighter than the rest of the +heavens, which was entirely clear, and appeared quite black; the effect +being that of an opening in the sky, through which a brighter region was +visible." + +[Illustration: Fig. 441.] + +The representation of this nebula in Fig. 441 is from a drawing made by +Bond. In brilliancy and variety of detail it exceeds any other nebula +visible in the northern hemisphere. In its centre are four stars, easily +distinguished by a small telescope with a magnifying power of forty or +fifty, together with two smaller ones, requiring a nine-inch telescope +to be well seen. Besides these, the whole nebula is dotted with stars. + +In the winter of 1864-65 the spectrum of this nebula was examined +independently by Secchi and Huggins, who found that it consisted of +three bright lines, and hence concluded that the nebula was composed, +not of stars, but of glowing gas. The position of one of the lines was +near that of a line of nitrogen, while another seemed to coincide with a +hydrogen line. This would suggest that the nebula is a mixture of +hydrogen and nitrogen gas; but of this we cannot be certain. + +[Illustration: Fig. 442.] + +379. _The Nebula in Argus._--There is a nebula (Fig. 442) surrounding +the variable star _Eta Argus_ (355), which is remarkable as exhibiting +variations of brightness and of outline. + +In many other nebulæ, changes have been suspected; but the +indistinctness of outline which characterizes most of these objects, and +the very different aspect they present in telescopes of different +powers, render it difficult to prove a change beyond a doubt. + +380. _The Dumb-Bell Nebula._--This nebula was named from its peculiar +shape. It is a good illustration of the change in the appearance of a +nebula when viewed with different magnifying powers. Fig. 443 shows it +as it appeared in Herschel's telescope, and Fig. 444 as it appears in +the great Parsonstown reflector (20). + +[Illustration: Fig. 443.] + +[Illustration: Fig. 444.] + + + Spiral Nebulæ. + + +381. _The Spiral Nebula in Canes Venatici._--The great spiral nebula in +the constellation _Canes Venatici_, or the _Hunting-Dogs_, is one of the +most remarkable of its class. Fig. 445 shows this nebula as it appeared +in Herschel's telescope, and Fig. 446 shows it as it appears in the +Parsonstown reflector. + +[Illustration: Fig. 445.] + +[Illustration: Fig. 446.] + +382. _Condensation of Nebulæ._--The appearance of the nebula just +mentioned suggests a body rotating on its axis, and undergoing +condensation at the same time. + +It is now a generally received theory that nebulæ are the material out +of which stars are formed. According to this theory, the stars +originally existed as nebulæ, and all nebulæ will ultimately become +condensed into stars. + +[Illustration: Fig. 447.] + +[Illustration: Fig. 448.] + +[Illustration: Fig. 449.] + +383. _Other Spiral Nebulæ._--Fig. 447 represents a spiral nebula of the +_Great Bear_. This nebula seems to have several centres of condensation. +Fig. 448 is a view of a spiral nebula in _Cepheus_, and Fig. 449 of a +singular spiral nebula in the _Triangle_. This also appears to have +several points of condensation. Figs. 450 and 451 represent oval and +elliptical nebulæ having a spiral structure. + +[Illustration: Fig. 450.] + +[Illustration: Fig. 451.] + +_THE MAGELLANIC CLOUDS._ + +[Illustration: Fig. 452.] + +384. _Situation and General Appearance of the Magellanic Clouds._--The +_Magellanic clouds_ are two nebulous-looking bodies near the southern +pole of the heavens, as shown in the right-hand portion of Fig. 452. In +the appearance and brightness of their light they resemble portions of +the Milky-Way. + +[Illustration: Fig. 453.] + +The larger of these clouds is called the _Nubecula Major_. It is visible +to the naked eye in strong moonlight, and covers a space about two +hundred times the surface of the moon. It is shown in Fig. 453. The +smaller cloud is called the _Nubecula Minor_. It has only about a fourth +the extent of the larger cloud, and is considerably less brilliant. It +is visible to the naked eye, but it disappears in full moonlight. This +cloud is shown in Fig. 454. The region around this cloud is singularly +bare of stars; but the magnificent cluster of _Toucan_, already +described (346), is near, and is shown a little to the right of the +cloud in the figure. + +[Illustration: Fig. 454.] + +[Illustration: Fig. 455.] + +385. _Structure of the Nubeculæ._--Fig. 455 shows the structure of these +clouds as revealed by a powerful telescope. The general ground of both +consists of large tracts and patches of nebulosity in every stage of +resolution,--from that which is irresolvable with eighteen inches of +reflecting aperture, up to perfectly separated stars, like the Milky-Way +and clustering groups. There are also nebulæ in abundance, both regular +and irregular, globular clusters in every state of condensation, and +objects of a nebulous character quite peculiar, and unlike any thing in +other regions of the heavens. In the area occupied by the _nubecula +major_ two hundred and seventy-eight nebulæ and clusters have been +enumerated, besides fifty or sixty outliers, which ought certainly to be +reckoned as its appendages, being about six and a half per square +degree; which very far exceeds the average of any other part of the +nebulous heavens. In the _nubecula minor_ the concentration of such +objects is less, though still very striking. The nubeculæ, then, +combine, each within its own area, characters which in the rest of the +heavens are no less strikingly separated; namely, those of the galactic +and the nebular system. Globular clusters (except in one region of small +extent) and nebulæ of regular elliptic forms are comparatively rare in +the Milky-Way, and are found congregated in the greatest abundance in a +part of the heavens the most remote possible from that circle; whereas +in the nubeculæ they are indiscriminately mixed with the general starry +ground, and with irregular though small nebulæ. + + + THE NEBULAR HYPOTHESIS. + + + 386. _The Basis of the Nebular Hypothesis._--We have seen that the + planets all revolve around the sun from west to east in nearly the + same plane, and that the sun rotates on his axis from west to east. + The planets, so far as known, rotate on their axes from west to + east; and all the moons, except those of Uranus and Neptune, revolve + around their planets from west to east. These common features in the + motion of the sun, moons, and planets, point to the conclusion that + they are of a common origin. + + 387. _Kant's Hypothesis._--Kant, the celebrated German philosopher, + seems to have the best right to be regarded as the founder of the + modern nebular hypothesis. His reasoning has been concisely stated + thus: "Examining the solar system, we find two remarkable features + presented to our consideration. One is, that six planets and nine + satellites [the entire number then known] move around the sun in + circles, not only in the same direction in which the sun himself + revolves on his axis, but very nearly in the same plane. This common + feature of the motion of so many bodies could not by any reasonable + possibility have been a result of chance: we are therefore forced to + believe that it must be the result of some common cause originally + acting on all the planets. + + "On the other hand, when we consider the spaces in which the planets + move, we find them entirely void, or as good as void; for, if there + is any matter in them, it is so rare as to be without effect on the + planetary motions. There is, therefore, no material connection now + existing between the planets through which they might have been + forced to take up a common direction of motion. How, then, are we to + reconcile this common motion with the absence of all material + connection? The most natural way is to suppose that there was once + some such connection, which brought about the uniformity of motion + which we observe; that the materials of which the planets are formed + once filled the whole space between them. There was no formation in + this chaos, the formation of separate bodies by the mutual + gravitation of parts of the mass being a later occurrence. But, + naturally, some parts of the mass would be more dense than others, + and would thus gather around them the rare matter which filled the + intervening spaces. The larger collections thus formed would draw + the smaller ones into them, and this process would continue until a + few round bodies had taken the place of the original chaotic mass." + + Kant, however, failed to account satisfactorily for the motion of + the sun and planets. According to his system, all the bodies formed + out of the original nebulous mass should have been drawn to a common + centre so as to form one sun, instead of a system of revolving + bodies like the solar system. + + 388. _Herschel's Hypothesis._--The idea of the gradual transmutation + of nebulæ into stars seems to have been suggested to Herschel, not + by the study of the solar system, but by that of the nebulæ + themselves. Many of these bodies he believed to be immense masses of + phosphorescent vapor; and he conceived that these must be gradually + condensing, each around its own centre, or around the parts where it + is most dense, until it should become a star, or a cluster of stars. + On classifying the nebulæ, it seemed to him that he could see this + process going on before his eyes. There were the large, faint, + diffused nebulæ, in which the condensation had hardly begun; the + smaller but brighter ones, which had become so far condensed that + the central parts would soon begin to form into stars; yet others, + in which stars had actually begun to form; and, finally, + star-clusters in which the condensation was complete. The + spectroscopic revelations of the gaseous nature of the true nebulæ + tend to confirm the theory of Herschel, that these masses will all, + at some time, condense into stars. + + 389. _Laplace's Hypothesis._--Laplace was led to the nebular + hypothesis by considering the remarkable uniformity in the direction + of the rotation of the planets. Believing that this could not have + been the result of chance, he sought to investigate its cause. This, + he thought, could be nothing else than the atmosphere of the sun, + which once extended so far out as to fill all the space now occupied + by the planets. He begins with the sun, surrounded by this immense + fiery atmosphere. Since the sum total of rotary motion now seen in + the planetary system must have been there from the beginning, he + conceives the immense vaporous mass forming the sun and his + atmosphere to have had a slow rotation on its axis. As the intensely + hot mass gradually cooled, it would contract towards the centre. As + it contracted, its velocity of rotation would, by the laws of + mechanics, constantly increase; so that a time would arrive, when, + at the outer boundary of the mass, the centrifugal force due to the + rotation would counterbalance the attractive force of the central + mass. Then those outer portions would be left behind as a revolving + ring, while the next inner portions would continue to contract until + the centrifugal and attractive forces were again balanced, when a + second ring would be left behind; and so on. Thus, instead of a + continuous atmosphere, the sun would be surrounded by a series of + concentric revolving rings of vapor. As these rings cooled, their + denser materials would condense first; and thus the ring would be + composed of a mixed mass, partly solid and partly vaporous, the + quantity of solid matter constantly increasing, and that of vapor + diminishing. If the ring were perfectly uniform, this condensation + would take place equally all around it, and the ring would thus be + broken up into a group of small planets, like the asteroids. But if, + as would more likely be the case, some portions of the ring were + much denser than others, the denser portions would gradually attract + the rarer portions, until, instead of a ring, there would be a + single mass composed of a nearly solid centre, surrounded by an + immense atmosphere of fiery vapor. This condensation of the ring of + vapor around a single point would not change the amount of rotary + motion that had existed in the ring. The planet with its atmosphere + would therefore be in rotation; and would be, on a smaller scale, + like the original solar mass surrounded by its atmosphere. In the + same way that the latter formed itself first into rings, which + afterwards condensed into planets, so the planetary atmospheres, if + sufficiently extensive, would form themselves into rings, which + would condense into satellites. In the case of Saturn, however, one + of the rings was so uniform throughout, that there was no denser + portion to attract the rest around it; and thus the ring of Saturn + retained its annular form. + + [Illustration: Fig. 456.] + + Such is the celebrated nebular hypothesis of Laplace. It starts, not + with a purely nebulous mass, but with the sun, surrounded by an + immense atmosphere, out of which the planets were formed by gradual + condensation. Fig. 456 represents the condensing mass according to + this theory. + + 390. _The Modern Nebular Hypothesis._--According to the nebular + hypothesis as held at the present time, the sun, planets, and + meteoroids originated from a purely nebulous mass. This nebula first + condensed into a nebulous star, the star being the sun, and its + surrounding nebulosity being the fiery atmosphere of Laplace. The + original nebula must have been put into rotation at the beginning. + As it contracted and became condensed through the loss of heat by + radiation into space, and under the combined attraction of gravity, + cohesion, and affinity, its speed of rotation increased; and the + nebulous envelop became, by the centrifugal force, flattened into a + thin disk, which finally broke up into rings, out of which were + formed the planets and their moons. According to Laplace, the rings + which were condensed into the planets were thrown off in succession + from the equatorial region of the condensing nebula; and so the + outer planets would be the older. According to the more modern idea, + the nebulous mass was first flattened into a disk, and subsequently + broken up into rings, in such a way that there would be no marked + difference in the ages of the planets. The sun represents the + central portion of the original nebula, and the comets and + meteoroids its outlying portion. At the sun the condensation is + still going on, and the meteoroids appear to be still gradually + drawn in to the sun and planets. + + The whole store of energy with which the original solar nebula was + endowed existed in it in the potential form. By the condensation and + contraction this energy was gradually transformed into the kinetic + energy of molar motion and of heat; and the heat became gradually + dissipated by radiation into space. This transformation of potential + energy into heat is still going on at the sun, the centre of the + condensing mass, by the condensation of the sun itself, and by the + impact of meteors as they fall into it. + + It has been calculated, that, by the shrinking of the sun to the + density of the earth, the transformation of potential energy into + heat would generate enough heat to maintain the sun's supply, at the + present rate of dissipation, for seventeen million years. A + shrinkage of the sun which would generate all the heat he has poured + into space since the invention of the telescope could not be + detected by the most powerful instruments yet constructed. + + The least velocity with which a meteoroid could strike the sun would + be two hundred and eighty miles a second; and it is easy to + calculate how much heat would be generated by the collision. It has + been shown, that, were enough meteoroids to fall into the sun to + develop its heat, they would not increase his mass appreciably + during a period of two thousand years. + + The sun's heat is undoubtedly developed by contraction and the fall + of meteoroids; that is to say, by the transformation of the + potential energy of the original nebula into heat. + + It must be borne in mind that the nebular hypothesis is simply a + supposition as to the way in which the present solar system may have + been developed from a nebula endowed with a motion of rotation and + with certain tendencies to condensation. Of course nothing could + have been developed out of the nebula, the germs of which had not + been originally implanted in it by the Creator. + + + IV. THE STRUCTURE OF THE STELLAR UNIVERSE. + + +391. _Sir William Herschel's View._--Sir William Herschel assumed that +the stars are distributed with tolerable uniformity throughout the space +occupied by our stellar system. He accounted for the increase in the +number of stars in the field of view as he approached the plane of the +Milky-Way, not by the supposition that the stars are really closer +together in and about this plane, but by the supposition that our +stellar system is in the form of a flat disk cloven at one side, and +with our sun near its centre. A section of this disk is shown in Fig. +457. + +[Illustration: Fig. 457.] + +An observer near _S_, with his telescope pointed in the direction of _S +b_, would see comparatively few stars within the field of view, because +looking through a comparatively thin stratum of stars. With his +telescope pointed in the direction _S a_, he would see many more stars +within his field of view, even though the stars were really no nearer +together, because he would be looking through a thicker stratum of +stars. As he directed his telescope more and more nearly in the +direction _S f_, he would be looking through a thicker and thicker +stratum of stars, and hence he would see a greater and greater number of +them in the field of view, though they were everywhere in the disk +distributed at uniform distances. He assumed, also, that the stars are +all tolerably uniform in size, and that certain stars appear smaller +than others, only because they are farther off. He supposed the faint +stars of the Milky-Way to be merely the most distant stars of the +stellar disk; that they are really as large as the other stars, but +appear small owing to their great distance. The disk was assumed to be +cloven on one side, to account for the division of the Milky-Way through +nearly half of its course. This theory of the structure of the stellar +universe is often referred to as the _cloven disk_ theory. + +[Illustration: Fig. 458.] + +392. _The Cloven Ring Theory._--According to Mädler, the stars of the +Milky-Way are entirely separated from the other stars of our system, +belonging to an outlying ring, or system of rings. To account for the +division of the Milky-Way, the ring is supposed to be cloven on one +side: hence this theory is often referred to as the _cloven ring_ +theory. According to this hypothesis, the stellar system viewed from +without would present an appearance somewhat like that in Fig. 458. The +outlying ring cloven on one side would represent the stars of the +Milky-Way; and the luminous mass at the centre, the remaining stars of +the system. + +393. _Proctor's View._--According to Proctor, the Milky-Way is composed +of an irregular spiral stream of minute stars lying in and among the +larger stars of our system, as represented in Fig. 459. The spiral +stream is shown in the inner circle as it really exists among the stars, +and in the outer circle as it is seen projected upon the sky. According +to this view, the stars of the Milky-Way appear faint, not because they +are distant, but because they are really small. + +[Illustration: Fig. 459.] + +394. _Newcomb's View._--According to Newcomb, the stars of our system +are all situated in a comparatively thin zone lying in the plane of the +Milky-Way, while there is a zone of nebulæ lying on each side of the +stellar zone. He believes that so much is certain with reference to the +structure of our stellar universe; but he considers that we are as yet +comparatively ignorant of the internal structure of either the stellar +or the nebular zones. The structure of the stellar universe, according +to this view, is shown in Fig. 460. + +[Illustration: Fig. 460.] + + + + + INDEX + + + A. + + Aberration of light, 38. + + Aerolites, 304. + + Aldebaran, star in Taurus, 340, 342. + + Algol, a variable star, 343, 358. + + Almanac, perpetual, 82. + + Alps, lunar mountains, 126. + + Altair, star in Aquila, 336. + + Alt-azimuth instrument, 13. + + Altitude, 12. + + Andromeda (constellation), 343, 346. + nebula in, 376. + + Angström's map of spectrum, 164. + + Antares, star in Scorpio, 347. + + Apennines, lunar mountains, 122, 124. + + Aphelion, 47. + + Apogee, 44. + + Aquarius, or the Water-Bearer, 350. + cluster in, 354. + + Aquila, or the Eagle, 336. + + Arcturus, star in Boötes, 335, 365, 370. + + Argo, or the Ship, 360. + nebula in, 383. + variable star in, 360. + + Aries, or the Ram, 350. + + Asteroids, 223, 241. + + Astræa, an asteroid, 241. + + Auriga, or the Wagoner, 342. + + Azimuth, 13. + + + B. + + Betelgeuse, star in Orion, 340, 370. + + Berenice's Hair (constellation), 334. + + Bode's law, 241. + disproved, 273. + + Boötes (constellation), 334, 335. + + + C. + + Calendar, the, 80. + + Callisto, moon of Jupiter, 250. + + Cancer, or the Crab, 350. + tropic of, 61. + + Canes Venatici, or the Hunting-Dogs, 334. + + Canes Venatici, nebula in, 384. + + Canis Major, or the Great Dog, 342. + + Canis Minor, or the Little Dog, 340. + + Capella, star in Auriga, 340, 343. + + Capricorn, tropic of, 61. + + Capricornus, or the Goat, 350. + + Cassiopeia (constellation), 332. + new star in, 362. + + Castor, star in Gemini, 340, 370. + + Caucasus, a lunar range, 124. + + Centaurus, star-cluster in, 355. + + Cepheus (constellation), 334. + nebula in, 387. + + Ceres, the planet, 241. + + Cetus, or the Whale, 346. + variable star in, 359. + + Charles's Wain, 330. + + Circles, great, 4. + diurnal, 8. + hour, 16. + small, 4. + vertical, 12. + + Clock, astronomical, 18. + time, 78. + + Coma Berenices, or Berenice's Hair, 334. + + Comet, Biela's, 293. + and earth, collision of, 316. + Coggia's, 297. + Donati's, 296. + Encke's, 293. + Halley's, 291. + of 1680, 290. + of 1811, 290. + of 1843, 295. + of 1861, 297. + of June, 1881, 300. + + Comets, appearance of, 274. + and meteors, 313. + bright, 274. + chemical constitution of, 318. + development of, 277. + number of, 288. + orbits of, 282. + origin of, 287. + periodic, 286. + physical constitution of, 314. + tails of, 279. + telescopic, 275, 281. + visibility of, 281. + + Conic sections, 48. + + Conjunction, 91. + inferior, 130. + superior, 130, 136. + + Constellations, 325. + zodiacal, 32. + + Copernican system, the, 44, 53. + + Copernicus, a lunar crater, 120, 129. + + Corona Borealis, or the Northern Crown, 336. + + Corona Borealis, new star in, 363. + + Corvus, or the Crow, 339. + + Crystalline spheres, 41. + + Cycles and epicycles, 42. + + Cygnus, or the Swan, 338. + + + D. + + Day and night, 57. + civil, 77. + lunar, 108. + sidereal, 74. + solar, 74. + + Declination, 16. + + Deimos, satellite of Mars, 239. + + Delphinus, or the Dolphin, 338. + + Deneb, star in Cygnus, 338, 370. + + Dione, satellite of Saturn, 259. + + Dipper, the Great, 330, 366, 369, 370. + the Little, 331. + the Milk, 347. + + Dissociation, 163. + + Dominical Letter, the, 81. + + Draco, or the Dragon, 331. + + + E. + + Earth, density of, 85. + flattened at poles, 55. + form of, 53. + in space, 56. + seen from moon, 109. + size of, 55. + weight of, 83. + + Eccentric, the 43. + + Eccentricity, 46. + + Eclipses, 210. + annular, 219. + lunar, 210, 214. + solar, 216. + + Ecliptic, the, 27. + obliquity of, 28. + + Ellipse, the, 45, 49. + + Elongation, of planet, 130. + + Enceladus, moon of Saturn, 259. + + Epicycles, 42. + + Epicycloid, 107. + + Epsilon Lyræ, a double star, 356. + + Equator, the celestial, 7. + + Equinoctial, the, 7. + colure, 16. + elevation of, 9. + + Equinox, autumnal, 29. + vernal, 16, 29. + + Equinoxes, precession of, 31, 85. + + Eta Argus, a variable star, 360, 383. + + Europa, moon of Jupiter, 250. + + F. + + Faculæ, solar, 177. + + Fomalhaut, star in Southern Fish, 350. + + Fraunhofer's lines, 164, 371. + + + G. + + Galaxy, the, 326. + + Ganymede, moon of Jupiter, 250. + + Gemini, or the Twins, 340. + + Georgium Sidus, 271. + + + H. + + Hercules (constellation), 336. + cluster in, 353. + orbit of double star in, 357. + solar system moving towards, 367. + + Herschel, the planet (see Uranus). + + Herschel's hypothesis, 392, 396. + + Horizon, the, 5. + + Hyades, the, 342, 350. + + Hydra, or the Water-Snake, 340. + + Hyperbola, the, 49. + + Hyperion, moon of Saturn, 259. + + + I. + + Io, moon of Jupiter, 250. + + Irradiation, 90, 113. + + + J. + + Japetus, moon of Saturn, 259. + + Job's Coffin (asterism), 338. + + Juno, the planet, 241. + + Jupiter, apparent size of, 245. + distance of, 245. + great red spot of, 249. + orbit of, 244. + periods of, 246. + physical constitution of, 246. + rotation of, 248. + satellites of, 250. + eclipses of, 252. + transits of, 254. + volume of, 245. + without satellites, 255. + + + K. + + Kant's hypothesis, 391. + + Kepler, a lunar crater, 129. + + Kepler's system, 44. + laws, 46. + star, 362. + + Kirchhoff's map of spectrum, 164. + + L. + + Laplace's hypothesis, 392. + + Latitude, celestial, 30. + + Leap year, 81. + + Leo, or the Lion, 334. + + Leonids (meteors), 312. + + Libra, or the Balances, 347. + + Libration, 102. + + Longitude, celestial, 30. + + Lyra, or the Lyre, 338. + double star in, 356. + + + M. + + Magellanic clouds, the, 389. + + Magnetic storms, 190. + + Magnetism and sun-spots, 190. + + Mars, apparent size of, 236. + brilliancy of, 237. + distance of, 235. + orbit of, 235. + periods of, 237. + rotation of, 239. + satellites of, 239. + volume of, 236. + + Mercury, apparent size of, 226. + atmosphere of, 228. + distance of, 225. + elongation of, 227. + orbit of, 225. + periods of, 227. + volume of, 226. + + Meridian, the, 12. + + Meridian circle, 17. + + Meridians, celestial, 31. + + Meteoric iron, 305, 307. + showers, 310. + stones, 305. + + Meteors, 300. + August, 311. + light of, 309. + November, 312. + sporadic, 310. + + Meteoroids, 308. + + Micrometers, 20, 153. + + Milky-Way, the, 326. + + Mimas, moon of Saturn, 259. + + Mira, a variable star, 359. + + Moon, apparent size of, 87, 89. + aspects of, 91. + atmosphere of, 109. + chasms in, 123. + craters in, 119. + day of, 108. + distance of, 86. + eclipses of, 210. + form of orbit, 97. + harvest, 101. + hunter's, 102. + inclination of orbit, 97. + kept in her path by gravity, 51. + librations of, 102. + mass of, 90. + meridian altitude of, 98. + mountains of, 116. + orbital motion of, 91. + phases of, 93. + real size of, 88. + rising of, 99. + rotation of, 102. + sidereal period of, 92. + surface of, 115. + synodical period of, 92. + terminator of, 115. + wet and dry, 98. + + + N. + + Nadir, the, 6. + + Neap-tides, 72. + + Nebula, in Andromeda, 376. + crab, 376. + dumb-bell, 383. + in Argus, 383. + in Canes Venatici, 384. + in Cepheus, 387. + in Orion, 378. + in the Triangle, 387. + in Ursa Major, 386. + + Nebulæ, 281, 330, 373. + annular, 373. + circular, 373. + condensation of, 385. + double, 375. + elliptical, 373. + irregular, 376. + multiple, 375. + spiral, 373, 384. + + Nebular hypothesis, the, 391. + + Neptune, discovery of, 271. + orbit of, 271. + satellite of, 274. + + New style, 80. + + Newcomb's theory of the stellar universe, 398. + + Newton's system, 48. + + Nodes, 97. + + Nubecula, Major, 389. + Minor, 389. + + Nutation, 34. + + + O. + + Olbers's hypothesis, 241. + + Old style, 80. + + Ophiuchus (constellation), 347. + new star in, 362. + + Opposition, 91, 136. + + Orion, 341. + nebula in, 378. + the trapezium of, 356. + + + P. + + Pallas, the planet, 241. + + Parabola, the, 49. + + Parallax, 37. + + Pegasus (constellation), 343, 346. + triple star in, 356. + + Perigee, 44. + + Perihelion, 47. + + Perseids (meteors), 311. + + Perseus (constellation), 346. + cluster in, 353. + + Phobos, satellite of Mars, 239. + + Pico, a lunar mountain, 127. + + Pisces, or the Fishes, 350. + + Piscis Australis, or the Southern Fish, 350. + + Planets, 39. + inferior, 130. + periods of, 132. + phases of, 132. + inner group of, 221. + intra-Mercurial, 230. + minor, 223. + outer group of, 222, 244. + superior, 134. + motion of, 134. + periods of, 137. + phases of, 137. + three groups of, 221. + + Pleiades, the, 328, 342, 351. + + Pointers, the, 330. + + Polar distance, 16. + + Pole Star, the, 7, 330, 365. + + Poles, celestial, 7, 9. + + Pollux, star in Gemini, 340, 370. + + Præsepe, or the Beehive, 350. + + Precession of equinoxes, 31, 85. + + Prime vertical, the, 12. + + Proctor's theory of the stellar universe, 398. + + Procyon, star in Canis Minor, 340. + + Ptolemaic system, the, 41. + + + Q. + + Quadrature, 91, 137. + + + R. + + Radiant point (meteors), 310. + + Radius vector, 47. + + Refraction, 35. + + Regulus, star in Leo, 334, 370. + + Rhea, moon of Saturn, 259. + + Rigel, star in Orion, 340, 370. + + Right ascension, 16. + + + S. + + Sagittarius, or the Archer, 347. + + Saturn, apparent size of, 256. + distance of, 256. + orbit of, 255. + periods of, 256. + physical constitution of, 257. + ring of, 261. + changes in, 268. + constitution of, 269. + phases of, 263. + rotation of, 258. + satellites of, 259. + volume of, 256. + + Scorpio, or the Scorpion, 347. + cluster in, 355. + + Seasons, the, 64. + + Sirius, the Dog-Star, 340, 342, 365, 370, 371. + + Solar system, the, 41. + + Solstices, 29, 59, 60. + + Sound, effect of motion on, 168. + + Spectra, bright-lined, 158. + comparison of, 154. + continuous, 158. + displacement of lines in, 171. + of comets, 318. + reversed, 161. + sun-spot, 193. + types of stellar, 371. + + Spectroscope, the, 152. + diffraction, 157. + direct-vision, 155. + dispersion, 152. + + Spectrum analysis, 159. + solar, 164. + + Sphere, defined, 3. + the celestial, 5. + rotation of, 7. + + Spring-tides, 72. + + Stars, circumpolar, 7. + clusters of, 328, 350. + color of, 357. + constellations of, 325. + constitution of, 371. + distance of, 364. + double, 355. + drift of, 368. + four sets of, 10. + magnitude of, 322. + motion of, in line of sight, 369. + multiple, 356. + names of, 325. + nebulous, 373. + new, 361. + number of, 323. + parallax of, 364. + proper motion of, 365. + secular displacement of, 366. + temporary, 361. + variable, 358. + + Sun, atmosphere of, 149. + brightness of, 151. + chemical constitution of, 164. + chromosphere of, 149, 196. + corona of, 149, 196, 204. + distance of, 142. + faculæ of, 177. + heat radiated by, 150. + inclination of axis of, 187. + mass of, 140. + motion of, among the stars, 26. + at surface of, 168. + in atmosphere of, 172. + secular, 366. + photosphere of, 149, 175. + prominences of, 149, 197. + rotation of, 186. + spectrum of, 164, 171. + temperature of, 149. + volume of, 140. + winds on, 174. + + Sun-spots, 179. + and magnetism, 190. + birth and decay of, 185. + cause of, 194. + cyclonic motion in, 182. + distribution of, 188. + duration of, 181. + groups of, 181. + periodicity of, 189. + proper motion of, 187. + size of, 181. + spectrum of, 193. + + + T. + + Taurus, or the Bull, 342. + quadruple star in, 356. + + Telescope, Cassegrainian, 23. + equatorial, 19. + front-view, 22. + Gregorian, 23. + Herschelian, 22. + Lord Rosse's, 25. + Melbourne, 25. + Newall, 20. + Newtonian, 22. + Paris, 26. + reflecting, 21. + Washington, 20. + Vienna, 20. + + Telespectroscope, the, 155. + + Telluric lines of spectrum, 165. + + Tethys, moon of Saturn, 259. + + Tides, 67. + + Time, clock, 78. + sun, 78. + + Titan, moon of Saturn, 259, 261. + + Toucan, star cluster in, 354, 389. + + Transit instrument, 17. + + Transits of Venus, 145. + + Triesneker, lunar formation, 123. + + Tropics, 61. + + Twilight, 62. + + Tycho Brahe's star, 361. + system, 44. + + Tycho, a lunar crater, 129. + + + U. + + Universe, structure of the stellar, 396. + + + Uranus, discovery of, 271. + name of, 270. + orbit of, 269. + satellites of, 271. + + Ursa Major, or the Great Bear, 330. + nebula in, 386. + + Ursa Minor, or the Little Bear, 330. + + + V. + + Vega, star in Lyra, 336, 365, 370. + + Venus, apparent size of, 231. + atmosphere of, 234. + brilliancy of, 232. + distance of, 231. + elongation of, 231. + orbit of, 230. + periods of, 232. + volume of, 231. + transits of, 145, 234. + + Vernier, the, 15. + + Virgo, or the Virgin, 338. + + Vesta, the planet, 241. + + Vulcan, the planet, 230. + + + Y. + + Year, the, 78. + anomalistic, 79. + Julian, 80. + sidereal, 79. + tropical, 79. + + + Z. + + Zenith, the, 6. + distance, 12. + + Zodiac, the, 32. + + Zodiacal constellations, 32. + light, 318. + + Zones, 61. + + + + + * * * * * * + + + + +Transcriber's note: + +Missing or obscured punctuation was corrected. + +Typographical errors were silently corrected. + + + +*** END OF THE PROJECT GUTENBERG EBOOK 58810 *** |