PRESENTED BY 
 
 PROF. CHARLES A. KOFOID AND 
 MRS. PRUDENCE W. KOFOID 
 
 THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 OF CALIFORNIA 
 
The Great Telescope of tho Lick Observatory. Aperture, 36 inches; Length, 57 feet. 
 
LESSONS IN ASTRONOMY 
 
 INCLUDING URANOGRAPHY 
 
 A BEIEF INTEODUCTOEY COUESE 
 
 WITHOUT MATHEMATICS 
 
 FOR USE IN SCHOOLS AND SEMINARIES 
 
 BY 
 
 CHARLES A. YOUNG, PH.D., LL.D. 
 
 PROFESSOR OF ASTRONOMY IN THE COLLEGE OF NEW JERSEY (PRINCETON), 
 
 AUTHOR OF A " GENERAL ASTRONOMY FOR COLLEGES AND SCIENTIFIC 
 
 SCHOOLS," AND OF " ELEMENTS OF ASTRONOMY FOR 
 
 HIGH SCHOOLS AND ACADEMIES." 
 
 BOSTON, U.S.A., AND LONDON 
 
 GINN AND COMPANY, PUBLISHERS 
 
 1891 
 
VI PREFACE. 
 
 It has been thought wejl also to add brief notes on the legen- 
 dary mythology of the constellations for the benefit of such 
 pupils as are not likely to become familiar with it in the study 
 of classical literature. 
 
 In the preparation of the book great pains have been taken 
 not to sacrifice accuracy and truth to compactness ; and no less 
 to bring everything thoroughly down to date. The student 
 will find in their proper places the new results obtained by 
 Schiaparelli with respect to the rotation of Mercury and 
 Venus ; the identification of Brooks's comet with the long-lost 
 comet of Lexell, and the latest spectroscopic discoveries of 
 Pickering and Vogel. 
 
 The Appendix contains in its first chapter descriptions of 
 the most used astronomical instruments, and where time per- 
 mits, might profitably be brought into the course. The sec- 
 ond chapter of the Appendix is designed only for the use of 
 teachers and the more advanced pupils. Arts. 431-434, how- 
 ever, explaining how the sun's distance may be found in the 
 simplest way, might well be read by all. 
 
 My warmest thanks are due to my friend and assistant, Mr. 
 Taylor Reed, who has gone over all the proofs of the book, 
 and has given me many valuable suggestions. 
 
CONTENTS. 
 
 PAGE 8 
 
 CHAPTER I. INTRODUCTION : Fundamental Notions and Defi- 
 nitions. The Celestial Sphere and its Circles. Altitude 
 and Azimuth. Right Ascension and Declination. Celestial 
 Latitude and Longitude 1-16 
 
 CHAPTER II. URANOGRAPHY : Globes and Star- maps. Star 
 Magnitudes. Names and Designations of Stars. The Con- 
 stellations in Detail 17-54 
 
 CHAPTER III. FUNDAMENTAL PROBLEMS : Latitude and the 
 Aspect of the Celestial Sphere. Time, Longitude, and the 
 Place of a Heavenly Body . 55-67 
 
 CHAPTER IV. THE EARTH : Its Form and Dimensions ; its 
 Rotation, Mass, and Density; its Orbital Motion and the 
 Seasons. Precession. The Year and the Calendar . . 68-90 
 
 CHAPTER V. THE MOON : Her Orbital Motion and the Month. 
 
 Distance, Dimensions, Mass, Density, and Force of Grav- 
 ity. Rotation and Librations. Phases. Light and Heat. 
 
 Physical Condition. Telescopic Aspect and Surface . . 91-110 
 
 CHAPTER VI. THE SUN: Its Distance, Dimensions, Mass, and 
 Density. Its Rotation, Surface, and Spots. The Spectro- 
 scope and the Solar Spectrum ; the Chemical Constitution of 
 the Sun. The Chromosphere and Prominences. The Cor- 
 ona. The Sun's Light. Measurement and Intensity of the 
 Sun's Heat. Theory of its Maintenance, and Speculations 
 regarding the Age and Duration of the Sun . . . 111-141 
 
 vii 
 
Vlll CONTENTS. 
 
 CHAPTER VII. ECLIPSES AND THE TIDES : Form and Dimen- 
 sions of Shadows. Eclipses of the Moon. Solar Eclipses, 
 Total, Annular, and Partial. Number of Eclipses in a Year. 
 Recurrence of Eclipses, and the Saros. Occupations. 
 The Tides 142-156 
 
 CHAPTER VIII. THE PLANETARY SYSTEM: The Planets in 
 General. Their Number, Classification, and Arrangement. 
 Bode's Law. Orbits of the Planets. Kepler's Laws and 
 Gravitation. The Apparent Motions of the Planets and the 
 Systems of Ptolemy and Copernicus. Determination of the 
 Planets' Diameters, Masses, etc. Herschel's Illustration of 
 the System. Description of Individual Planets : the ' Ter- 
 restrial ' Planets, Mercury, Venus, and Mars . . . 157-186 
 
 CHAPTER IX. PLANETS (continued} : The Asteroids. Intra- 
 Mercurian Planets and the Zodiacal Light. The Major Plan- 
 ets, Jupiter, Saturn, Uranus, and Neptune. Ultra- Neptunian 
 Planet 187-207 
 
 CHAPTER X. COMETS AND METEORS : Comets, their Num- 
 ber, Designation, and Orbits ; their Constituent Parts and 
 Appearance ; their Spectra, Physical Constitution, and Proba- 
 ble Origin ; Remarkable Comets ; Aerolites, their Fall and 
 Characteristics ; Shooting Stars and Meteoric Showers ; Con- 
 nection between Meteors and Comets .... 208-242 
 
 CHAPTER XL THE STARS : Their Nature, Number, and Des- 
 ignation. Star Catalogues and Charts. Their Proper 
 Motions, and the Motion of the Sun in Space. Stellar Par- 
 allax. Star Magnitudes and Photometry. Variable Stars. 
 Stellar Spectra . 243-266 
 
 CHAPTER XII. THE STARS (continued) : Double and Multi- 
 ple Stars ; Clusters and Nebulae ; the Milky Way, and Distri- 
 bution of Stars in Space ; the Stellar Universe. Cosmogony 
 and the Nebular Hypothesis 267-293 
 
CONTENTS. IX 
 
 APPENDIX. 
 
 PAGES 
 
 CHAPTER XIII. ASTRONOMICAL INSTRUMENTS: The Telescope, 
 Simple Refracting, Achromatic, and Reflecting. The Equa- 
 torial. The Filar Micrometer. The Transit Instrument. 
 The Clock and the Chronograph. The Meridian Circle. 
 The Sextant 295-312 
 
 CHAPTER XIV. (FOR THE MOST PART SUPPLEMENTARY TO ARTI- 
 CLES IN THE TEXT). Hour-angle and Time. Twilight. 
 Determination of Latitude. Place of a Ship at Sea. Find- 
 ing the Form of the Earth's Orbit. The Ellipse. Illustra- 
 tions of Kepler's ' Harmonic ' Law. The Equation of Light, 
 and the Sun's Distance determined by it. Aberration of 
 Light. -De 1'Isle's Method of getting the Sun's Parallax from 
 a Transit of Venus. The Parabola and the Conic Sections. 
 Determination of Stellar Parallax. The Slitless Spectro- 
 scope 313-331 
 
 QUESTIONS FOR REVIEW 332 
 
 TABLES OF ASTRONOMICAL DATA: 
 
 I. Astronomical Constants 339 
 
 II. The Principal Elements of the Solar System ... 340 
 
 III. The Satellites of the Solar System 341 
 
 IV. The Principal Variable Stars 342 
 
 V. The Best Determined Stellar Parallaxes .... 343 
 
 VI. The Greek Alphabet and Miscellaneous Symbols . . 344 
 
 INDEX 345 
 
 STAR-MAPS 359 
 
CHAPTER I. 
 
 INTRODUCTION. FUNDAMENTAL NOTIONS AND DEFINI- 
 TIONS. THE CELESTIAL SPHERE AND ITS CIRCLES. 
 ALTITUDE AND AZIMUTH. RIGHT ASCENSION AND 
 DECLINATION. CELESTIAL LATITUDE AND LONGITUDE. 
 
 1. ASTRONOMY 1 is the science which deals with the heavenly 
 bodies. 
 
 As it is the oldest of the sciences, so also it is one of the 
 most perfect, and in certain aspects the noblest, as being the 
 most " unselfish " of them all. And yet, although not bearing 
 so directly upon the material interests of life as the more 
 modern sciences of Physics and Chemistry, it is of high utility. 
 By means of Astronomy the latitudes and longitudes of places 
 upon the earth's surface are determined, and by such determi- 
 nations alone is it possible to conduct vessels upon the sea. 
 Moreover, all the operations of surveying upon a large scale, 
 such as the determination of the boundaries of countries, de- 
 pend more or less upon astronomical observations. The same 
 is true of operations which, like the railway service, require 
 an accurate knowledge and observance of time ; for the funda- 
 mental timekeeper is the diurnal revolution of the heavens, as 
 determined by the astronomer's transit-instrument. 
 
 In ancient times the science was supposed to have a still higher 
 utility. It was believed that human affairs of every kind, the welfare 
 of nations, and the life history of individuals alike, were controlled, 
 
 1 The term is derived from two Greek words : astron, a star, and 
 wornos, a law. 
 
 1 
 
2 THE HEAVENLY BODIES. [ 1 
 
 or at least prefigured, by the motions of the stars and planets ; so 
 that from the study of the heavens it ought to be possible to predict 
 futurity. 
 
 2. The heavenly bodies include, first, the solar system, 
 that is, the sun and the planets which revolve around it, with 
 their attendant satellites ; second, the comets and the meteors, 
 which also revolve around the sun, but are bodies of a very 
 different nature from the planets, and move in different kinds 
 of orbits ; and, thirdly, the stars and nebulae. The earth on 
 which we live is one of the planets, and the moon is the earth's 
 satellite. The stars which we see are bodies of the same kind 
 as the sun, shining like him with fiery heat, while the planets 
 and the satellites are dark and cool like the earth, and visible 
 to us only by the sunlight they reflect. As for the comets and 
 nebulae, they appear to be mere clouds, composed of heated gas 
 or swarms of little particles of more solid substances, perhaps 
 not very hot, but luminous from some cause or other. It is 
 likely that besides the visible stars there are also multitudes 
 which, although too cool to shine, manifest their existence by 
 affecting the motion of certain of the stars which we can see. 
 It is hardly necessary to add that while with the naked eye 
 we see only a few thousand stars, the telescope makes millions 
 visible. 
 
 3. As we look off from the earth at night, the stars appear 
 to be all around us, like glittering points fastened to the inside 
 of a huge hollow globe. Really they are at very different dis- 
 stances, all enormous as compared with any distances with 
 which geography makes us familiar. Even the moon is eighty 
 times as far away as New York from Liverpool, and the sun 
 is nearly four hundred times as distant as the moon, and the 
 nearest of the stars is more than two hundred thousand times 
 as distant as the sun ; as to the remoter stars, some of them 
 are certainly thousands of times as far away as the nearer 
 ones, so far that light itself is thousands of years in coming 
 
3] THE HEAVENLY BODIES. 
 
 to us from them. These are facts which are certain, not mere 
 guesses or beliefs. 
 
 Then, too, as to their motions. Although the heavenly bodies 
 seem to us for the most part to be at rest, except as the earth's 
 rotation makes them appear to rise and set, yet really they are 
 all moving, and with a swiftness of which we can form no con- 
 ception. A cannon-ball is a snail to the slowest of them. The 
 earth itself in its revolution around the sun is flying eighteen 
 and a half miles in a second, which is more than fifty times as 
 fast as the swiftest rifle bullet. We fail to perceive the motion 
 simply because it is so smooth and so unresisted. The space 
 outside our air contains nothing that can sensibly obstruct 
 either sight or motion. 
 
 4. But this knowledge as to the real distance and motions 
 of the heavenly bodies was gained only after long centuries of 
 study. If we go out to look at the stars some moonless night 
 we find them apparently sprinkled over the dome of the sky 
 in groups or constellations, which are still substantially the 
 same as in the days of the earliest astronomers. At first these 
 constellations were figures of animals and other objects, and 
 many celestial globes and maps still bear grotesque pictures 
 representing them. At present, however, a constellation is 
 only a certain region of the sky, limited by imaginary lines 
 which divide it from the neighboring constellations, just as 
 countries are divided in geography. As to the exact boun- 
 daries of these constellations, and even their number, there is 
 no precise agreement among astronomers. Forty-eight of them 
 have come down to us from the time of Ptolemy, 1 and even in 
 his day many of them were already ancient. 
 
 About twenty more, which have been proposed by more 
 recent astronomers, are now recognized, besides a considerable 
 number which have been abandoned. 
 
 1 Ptolemy, the greatest astronomer of antiquity, flourished at Alexan- 
 dria about 130 A.D. 
 
4 UKANOGRAPHY. [ 5 
 
 5. TTranography, or Description of the Visible Heavens. 
 
 The study of the constellations, or the apparent arrangement 
 of the stars in the sky, is called Uranography. 1 It is not an 
 essential part of Astronomy, but it is an easy and pleasant 
 study ; and in becoming familiar with the constellations and 
 their principal stars, the pupil will learn more readily and 
 thoroughly than in any other way the most important facts in 
 relation to the apparent motions of the heavenly bodies, and 
 the principal points and circles of the celestial sphere. For 
 this reason the teacher is urged to take the earliest oppor- 
 tunity to have his pupils trace such of the constellations as 
 happen to be visible in the evening sky when they begin the 
 study of Astronomy. 
 
 6. The Celestial Sphere. 2 The sky appears like a hollow 
 vault, to which the stars seem to be attached, like specks of 
 gilding upon the inner surface of a dome. We cannot judge 
 of the distance of this surface from the eye, further than to 
 perceive that it must be very far away. It is therefore natural 
 and extremely convenient to regard the distance of the sky as 
 everywhere the same and unlimited. The ' celestial sphere,' as 
 it is called, is conceived of as so enormous that the whole world 
 of stars and planets lies in its centre like a few grains of sand 
 in the middle of the dome of the Capitol. Its diameter is 
 assumed to be immeasurably greater than any actual distance 
 known, and greater than any quantity assignable. In technical 
 language it is taken as mathematically infinite. 
 
 Since the celestial sphere is thus infinite, any two parallel 
 lines drawn from distant points on the surface of the earth, or 
 even from points as distant as the earth and the sun, will seem 
 to meet at one point on the surface of the sphere. If the two 
 
 1 From the Greek, ouranos (heavens), and graphe (description). 
 
 2 The study of the celestial sphere and its circles is greatly facilitated 
 by the use of a globe, or armillary sphere. Without some such appa- 
 ratus it is not easy for a young person to get clear ideas upon the subject. 
 
D 
 
 6] APPARENT PLACE OF A HEAVENLY BODY. 5 
 
 lines were anywhere a million miles apart, for instance, they 
 will, of course, still be a million miles apart when they reach 
 the surface of the sphere ; but at an infinite distance even a 
 million miles is a mere nothing, so that the two lines make 
 apparently but a single point 1 where they pierce the sphere. 
 
 7. The Apparent Place of a Heavenly Body. This is sim- 
 ply the point where a line drawn from the observer through 
 the body in question, continued 
 
 outward, pierces the celestial 
 sphere. It depends solely upon 
 the direction of the body, and 
 is in no way affected by its dis- 
 tance from us. Thus, in Fig. 1, 
 A, B, (7, etc., are the apparent 
 places of a, b, c, etc., the observ- 
 er being at 0. Objects that are 
 nearly in line with each other, 
 as Ji y i, k, will appear close to- 
 gether. The moon, for instance, 
 often looks to us very near a star, which is really of course at 
 an enormous distance beyond her. 
 
 8. Angular Measurement. It is clear that we cannot prop- 
 erly describe the apparent distance of two points upon the 
 celestial sphere from each other by feet or inches. To say 
 that two stars are about five feet apart, for instance, and it 
 is not very uncommon to hear such an expression, means 
 nothing unless we know how far from the eye the five-foot 
 measure is to be held. The proper units for expressing appar- 
 ent distance in the sky are those of angle, viz. : degrees (), 
 minutes ( f ), and seconds (") ; the circumference of a circle 
 being divided into 360 degrees, each degree into 60 minutes, 
 and each minute into 60 seconds. Thus, the Great Bear's tail, 
 
 FIG. i. 
 
 1 This is the same as the ' vanishing-point ' of perspective. 
 
6 CIRCLES OF THE CELESTIAL SPHERE. [ 8 
 
 or Dipper-handle, is about 16 long, and the long side of the 
 Dipper-bowl is about 10; the moon and the sun are each 
 about half a degree, or 30', in diameter. 
 
 It is very important that the student in Astronomy should become 
 accustomed as soon as possible to estimate celestial measures in this 
 way. A little practice soon makes it easy, though at first one is apt 
 to be embarrassed by the fact that the sky looks to the eye not like a 
 true hemisphere but like a flattened vault, so that the estimates of 
 distances for all objects near the horizon are apt to be too large. The 
 moon, when rising or setting, looks to most persons much larger than 
 when overhead ; and the Dipper-bowl, when underneath the pole, seems 
 to cover s^much larger area than when above it. 
 
 9. Circles and Principal Points of the Celestial Sphere. 
 
 Just as the surface of the earth in Geography is covered with 
 a net-work of imaginary lines, meridians and parallels of 
 latitude, so the sky is supposed to be marked off in a some- 
 what similar way. Two such sets of,,, points and reference 
 circles are in common use to describe the apparent places of 
 the stars, and a third was used by the ancients and is still em- 
 ployed for some purposes. The first system depends upon the 
 direction of the force of gravity shown by a plumb-line at the 
 point where the observer stands ; the second upon the direc- 
 tion of the axis of the earth, which points very near the so- 
 called Pole-star ; and the third depends upon the position of 
 the orbit in which the earth travels around the sun. 
 
 10. The Gravitational or Up-and-Down System. (a) The 
 
 Zenith and Nadir. The point in the sky directly above the 
 observer is called the zenith; the opposite point, under the 
 earth and of course invisible, the nadir. 1 
 
 (b) The Horizon (pronounced ho-ri'-zon, not hor'-i-zon). 
 
 1 These are Arabic terms. About 1100 A.D. the Arabs were the 
 world's chief astronomers, and have left their mark upon the science in 
 numerous names of stars and astronomical terms. 
 
10] 
 
 VERTICAL CIRCLES. 
 
 This is a l great circle ' * around the sky, half-way between the 
 zenith and the nadir, and therefore everywhere 90 from the 
 zenith. The word is derived from a Greek word which means 
 a 'boundary'; i.e., the line where the earth or sea limits the 
 sky. The actual line of division, which on the land is always 
 more or less irregular, is called the visible horizon, to distin- 
 guish it from the true horizon denned above. We may also 
 define the horizon as the great circle where a plane which 
 passes through the observer's eye perpendicular to the plumb- 
 line cuts the celestial sphere. 
 
 11. Vertical Circles and the Meridian; Altitude, and Azi- 
 muth. Circles drawn from the zenith to the nadir cut the 
 horizon at right angles, and are known as vertical circles. Each 
 star has at any moment its own vertical circle. 
 
 FIG. 2. The Horizon and Vertical Circles. 
 
 O, the place of the Observer. 
 OZ, the Observer's Vertical. 
 Z, the Zenith; P, the Pole. 
 S WNE, the Horizon. 
 SZPN, the Meridian. 
 EZW, the Prime Vertical. 
 
 M, some Star. 
 
 ZMH, arc of the Star's Vertical Circle. 
 
 TMIt, the Star's Almucantar. 
 
 Angle TZM, or arc Sff, Star's Azimuth. 
 
 Arc HM, Star's Altitude. 
 
 Arc ZM, Star's Zenith Distance. 
 
 That particular vertical circle which passes north and south 
 is known as the celestial MEKIDIAN ; while the vertical circle 
 at right angles to this is called the prime vertical. Small circles 
 
 1 ' Great Circles ' are those which divide the sphere into two equal 
 parts. 
 
8 DIURNAL ROTATION. [ H 
 
 drawn parallel to the horizon are known as parallels of alti- 
 tude. Fig. 2 illustrates these circles. 
 
 By their help we can easily define the apparent position of 
 a heavenly body. 
 
 Its Altitude is its apparent elevation above the horizon ; that 
 is, the number of degrees between it and the horizon measured 
 on a vertical circle. Thus, in Fig. 2, the vertical circle ZMH 
 passes through the point M. The arc MH 9 measured in 
 degrees, is the altitude of M, and the arc ZM is called its 
 zenith distance. 
 
 The Azimuth of a heavenly body is the same as its ' bearing ' 
 in Surveying, but measured from the true meridian and not 
 from the magnetic. 1 It is the arc of the horizon, measured in 
 degrees, intercepted between the south point and the foot of 
 the vertical circle which passes through the object. 
 
 There are various ways of reckoning azimuth. Many writ- 
 ers express it in the same way as the 'bearing 7 in Surveying, 
 i.e., so many degrees east or west of north or south. In the 
 figure, the azimuth of M thus expressed is about S, 50 E. 
 The more usual way at present, however, is to reckon clear 
 around from the south, through the west, to the point of be- 
 ginning. Expressed in this way the azimuth of M would be 
 about 310, i.e., the arc 8 WNEH. 
 
 Altitude and azimuth, however, are inconvenient for many 
 purposes, because they continually change for a celestial object 
 as it moves across the sky. 
 
 12, The Apparent Diurnal Rotation of the Heavens. If we 
 
 go out on some clear evening in the early autumn, say about 
 the 22d of September, and face the north, we shall find the ap- 
 pearance of that part of the heavens directly before us substan- 
 tially as shown in Fig. 3. In the north is the constellation of 
 
 1 The reader is reminded that the magnetic needle does not point 
 exactly north. Its direction varies widely at different parts of the earth, 
 and, moreover, is continually changing to some extent. 
 
12] 
 
 DIURNAL ROTATION. 
 
 9 
 
 the Great Bear (Ursa Major), characterized by the conspicuous 
 group of seven stars known as the " Great Dipper.' 7 It now 
 lies with its handle sloping upward to the west. The two 
 easternmost stars of the four which form its bowl are called 
 
 FIG. 3. The Northern Circumpolar Constellations. 
 
 the " Pointers," because they point to the Pole-star, which is a 
 solitary star not quite half-way from the horizon to the zenith 
 (in the latitude of New York), and about as bright as the 
 brighter of the two Pointers. 
 
 High up on the opposite side of the Pole-star from the 
 Great Dipper, and at nearly the same distance, is an irregular 
 
10 DIURNAL ROTATION. [ 12 
 
 zigzag of five stars, each about as bright as the Pole-star itself.. 
 This is the constellation of Cassiopeia. 
 
 If now we watch these stars for only a few hours, we shall 
 find that while all the forms remain unaltered, their places in 
 the sky are slowly changing. The Great Dipper slides down- 
 ward towards the north, so that by eleven o'clock (on Sept. 
 22) the Pointers are directly under the Pole-star. Cassiopeia 
 still keeps opposite^ however, rising towards the zenith ; and 
 if we continue the watch through the whole night, we shall 
 find that all the stars appear to be moving in circles around a 
 point near the Pole-star, revolving in the opposite direction to 
 the hands of a watch (as we look towards the north) with a 
 steady motion which takes them completely around once a day, 
 or, to be more exact, once in 23 h 56 m 4.1 s of ordinary time. 
 They behave just as if they were attached to the inner surface 
 of a huge revolving sphere. 
 
 To indicate the position of the stars as it will be at midnight of 
 Sept. 22, the figure must be held so that XII in the margin is at the 
 bottom; at 4 A.M. the stars will have come to the position indicated 
 by bringing XVI to the bottom, and so on. But at eight o'clock on 
 the next night we shall find things in their original position very 
 nearly. 
 
 If instead of looking toward the north we now look south- 
 ward, we shall find that in that part of the sky also the stars 
 appear to move in the same kind of way. All that are not too 
 near the Pole-star rise somewhere in the eastern horizon, 
 ascend obliquely to the meridian, and descend to their setting 
 at points on the western horizon. The next day they rise and 
 set again at precisely the same points, and the motion is 
 always in an arc of a circle, called the star's diurnal circle, the 
 size of which depends upon its distance from the pole. More- 
 over, all of these arcs are strictly concentric. 
 
 The ancients accounted for these fundamental and obvious 
 facts by supposing that the stars are really fastened to the 
 
12] DEFINITION OF THE POLES. 11 
 
 celestial sphere, and that this sphere really turns daily in the 
 manner indicated. According to this view there must really 
 be upon the sphere two opposite points which remain at rest, 
 and these are the poles. 
 
 13. Definition of the Poles. The Poles, therefore, may be 
 denned as those two points in the sky where a star would have 
 no diurnal motion. The exact position of either pole may be 
 determined with proper instruments, by finding the centre of 
 the small diurnal circle described by some star near it, as, for 
 instance, by the Pole-star. 
 
 The student must be careful not to confound the Pole with 
 the Pole-star.. The pole is an imaginary point; the Pole- 
 star is only that one of the conspicuous stars which happens 
 now to be nearest to that point. The Pole-star at present is 
 about 1 distant from it. If we draw an imaginary line from 
 the Pole-star to the star Mizar (the one at the bend of the 
 Dipper-handle), it will pass almost exactly through the pole 
 itself ; the distance of the pole from the Pole-star being very 
 nearly one-quarter of the distance between the two "Pointers." 
 
 This definition of the pole is that which would be given by 
 one familiar with the sky, but ignorant of the earth's rotation, 
 and it is still perfectly correct ; but knowing, as we now do, 
 that this apparent revolution of the celestial sphere is due to 
 the real spinning of the earth on its axis, we may also define 
 the poles as the two points where the earths axis of rotation, 
 produced indefinitely, would pierce the celestial sphere. 
 
 Since the two poles are diametrically opposite in the sky, only one 
 of them is usually visible from any given place. Observers north of 
 the earth's equator see only the north pole, and vice versa for observ- 
 ers in the southern hemisphere. 
 
 14. The Celestial Equator, or Equinoctial; Declination. 
 
 The Equator is a great circle of the celestial sphere drawn 
 half-way between the poles, everywhere 90 from each of them, 
 
12 HOUR-CIRCLES. [ 14 
 
 and is the great circle in which, the plane of the earth's equator 
 cuts the celestial sphere. It is often called the Equinoctial. 
 Fig. 4 shows how the plane of the earth's equator produced 
 far enough would mark out such a circle in the heavens. 
 
 Small circles drawn parallel 
 to the equinoctial, like the paral- 
 lels of latitude on the earth, are 
 known as 'Parallels of Decli- 
 nation,' the Declination of a star 
 being its distance in degrees 
 north or south of the celestial 
 equator, + if north, if south. 
 It corresponds precisely with 
 the latitude of a place on the 
 earth's surface ; but it cannot be 
 FIG. 4. The riane of the Earth's Equa- called celestial latitude, because 
 tor produced to cut the CeieBtiai Sphere. t h at term has been preoccupied 
 
 for an entirely different quantity (Art. 20). A star's parallel 
 of declination is identical with its diurnal circle. 
 
 15. Hour-circles. The great circles of the celestial sphere 
 which pass through the poles like the meridians on the earth, 
 and are therefore perpendicular to the celestial equator, are 
 called Hour-Circles. Some writers call them celestial merid- 
 ians, but the term is objectionable since it is sometimes used 
 to indicate an entirely different set of circles. That particu- 
 lar hour-circle which at any moment passes through the zenith 
 of course coincides with the celestial meridian already defined 
 in Art. 11. 
 
 16. The Celestial Meridian and the Cardinal Points. The 
 
 best definition of the celestial meridian is, however, the great 
 circle which passes through the zenith and the poles. The points 
 where this meridian cuts the horizon (the circle of level), are 
 the north and south points, and the east and west points of 
 
16] 
 
 THE VERNAL EQUINOX. 
 
 13 
 
 the horizon lie half-way between them, the fonr being known 
 as the " Cardinal Points." The student is especially cautioned 
 against confounding the north point with the north pole. The 
 north point is on the horizon ; the north pole is high up in the 
 sky. 
 
 FIG. 5. Equator, Hour-Circles, etc. 
 
 O, place of the Observer; Z, his Zenith. 
 
 SENW, the Horizon. 
 
 POP', line parallel to the axis of the Earth. 
 
 P and P' t the two Poles of the Heavens. 
 
 EQ WT, the Celestial Equator, or Equinoc- 
 tial. 
 
 X, the Vernal Equinox, or " First of 
 Aries." 
 
 PXP', the Equinoctial Colure, or Zero 
 Hour-Circle. 
 
 m, some Star. 
 
 Ym, the Star's Declination; Pm, its North- 
 Polar Distance. 
 
 Angle mPR =arc QY, the Star's (eastern) 
 Hour-Angle; = 24 h minus Star's 
 western Hour- Angle. 
 
 Angle XPm = arc X Y, Star's Right Ascen- 
 sion. 
 
 Sidereal time at the moment = 24 h minus 
 XPQ. 
 
 In Fig. 5, P is the north celestial pole, Z is the zenith, and 
 SQZPN is the celestial meridian. P and P 1 are the poles, 
 PmP is the hour-circle of m, and amRb V is its parallel of 
 declination, or diurnal circle. N and S are the north and 
 south points respectively. In the figure, m Y is the decimation 
 of m, and mP is called its polar distance. 
 
 17. The Vernal Equinox, or First of Aries. In order to 
 use this system of circles as a means of designating the places 
 
14 RIGHT ASCENSION. [ 17 
 
 of stars in the sky, it is necessary to fix upon some one hour- 
 circle, to be reckoned from in the same way that the meridian 
 of Greenwich is used on the earth's surface. The "Green- 
 wich of the sky " which has thus been fixed upon, is the point 
 where the sun crosses the celestial equator in the spring. 
 The sun and moon and the planets do not behave as if they, 
 like the stars, were firmly fixed upon the celestial sphere, but 
 rather as if they were glow-worms crawling slowly about upon 
 its surface while it carries them in its diurnal rotation. As 
 every one knows, the sun in winter is far to the south of the 
 equator, and in the summer far to the north, apparently com- 
 pleting a yearly circuit of the heavens on a path known as the 
 ecliptic. It crosses the equator, therefore, twice a year, pass- 
 ing from the south side of it to the north about March 20th, 
 and always at the same point (neglecting for the present the 
 effect of what is known as l precession '). This point is called 
 the ( Vernal Equinox,' and is made the starting-point. Unfor- 
 tunately it is not marked by any conspicuous star ; but a line 
 drawn from the Pole-star through Beta Cassiopei'ae (the west- 
 ernmost or " preceding " star in the zigzag) (see Map I.) and 
 continued 90 from the pole, strikes very near it. In Fig. 5, 
 X represents this point. It is often called the "First of 
 Aries." 
 
 18. Right Ascension. The right ascension of a star is the 
 arc of the celestial equator intercepted between the vernal equinox 
 and the point where the star's hour-circle cuts the equator, and is 
 reckoned always eastward from the equinox and completely 
 around the circle. It may be expressed either in degrees or 
 in hours. A star one degree west of the equinox has a right 
 ascension of 359, or of 23 h 56 m . Evidently the diurnal 
 motion does not affect the right ascension of a star, but this, 
 like the declination, remains practically unchanged for years. 
 In Fig. 5, if X be the vernal equinox the right ascension of m 
 is the arc XY measured from X eastward. 
 
19] SUMMARY. 15 
 
 19. Thus we can define the position of a star either by its 
 altitude and azimuth, which tell how high it is in the sky, and 
 how it " bears," as a sailor would say ; or we may use its 
 right ascension and declination, which do not change from 
 day to day (not perceptibly at least), and so are better adapted 
 to mapping purposes, corresponding as they do precisely to 
 latitude and longitude upon the surface of the earth. 
 
 Perhaps the easiest way to think of these celestial circles is 
 the following : Imagine a tall pole standing straight up from 
 the observer, having attached to it at the top (the zenith) two 
 half circles coming down to the level of the observer's eye, one 
 of them running north and south (the meridian), and the 
 other east and west (the prime vertical). The bottoms of 
 these two semicircles are connected by a complete circle, the 
 horizon, at the level of the eye. This framework, immense 
 but fortunately only imaginary and so not burdensome, the 
 observer takes with him wherever he goes, keeping always at 
 its centre, while over it turns the celestial sphere ; more 
 strictly, he and the earth and his framework turn together 
 under the celestial sphere. 
 
 The circles of the other set are drawn upon the celestial 
 sphere itself (the equator and the hour-circles) and are not 
 affected at all by the observer's journeys, but are as fixed as 
 the poles and meridians upon the earth ; the stars also, to all 
 ordinary observation, are fixed upon the sphere just as cities 
 are upon the earth. They really move, of course, and swiftly, 
 as has been said before, but they are so far away that it takes 
 centuries, as a rule, to produce the slightest apparent change 
 of place. 
 
 20. Celestial Latitude and Longitude. A different way of desig- 
 nating the positions of the heavenly bodies in the sky has come down 
 to us from very ancient times. Instead of the equator it makes use 
 of another circle of reference in the sky, known as the 'Ecliptic' 
 This is simply the apparent path described by the sun in its annual 
 motion among the stars ; for the sun appears to creep around the 
 
16 CELESTIAL LATITUDE AND LONGITUDE. t 2d 
 
 celestial sphere in a circle once every year, and the Ecliptic may be 
 defined as the intersection of the plane of the earth's orbit with the 
 celestial sphere, just as the celestial equator is the intersection of the 
 earth's equator; the vernal equinox is one of the points where the two 
 circles cross. Before the days of clocks, the Ecliptic was in many 
 respects a more convenient circle of reference than the equator and 
 was almost universally used as such by the old astronomers. Celestial 
 longitude and latitude are measured with reference to the Ecliptic, in 
 the same way that right ascension and declination are measured with 
 respect to the equator. Too much care can hardly be taken to avoid 
 confusion between terrestrial latitude and longitude and the celestial 
 quantities that bear the same name. 
 
URANOGRAPHY. 
 
 17 
 
 CHAPTER II 
 
 UKANOGRAPHY. 
 
 GLOBES AND STAR-MAPS. STAR MAGNITUDES. DESIG- 
 NATION OF THE STARS. THE CONSTELLATIONS. 
 
 NOTE. It is hardly necessary to say that this chapter is to be treated 
 by the teacher differently from the rest of the book. It is to be dealt 
 with, not as recitation matter, but as field-work : to be taken up at differ- 
 ent times during the course as the constellations make their appearance 
 in the evening sky. 
 
 For convenience of reference we add the following alphabetical list of 
 the constellations described or mentioned in the chapter : 
 
 Andromeda 
 Anser, see Vulpecula . 
 
 ARTICLE 
 . 35 
 . 69 
 
 Cepheus 
 Cetus . 
 
 ARTICLE 
 . 29 
 . 39 
 
 Antinoiis, see Aquila . 
 Antlia 
 Aquarius . 
 
 .71 
 
 . 62 
 
 . 78 
 
 Coma Berenices 
 Columba . 
 Corona Borealis . 
 
 . 57 
 .45 
 . 60 
 
 Aquila . 
 
 71 
 
 Corvus 
 
 . . .55 
 
 Argo Navis 
 Aries . . . 
 
 . 51 
 
 38 
 
 Crater 
 
 Cvsnus 
 
 . 55 
 
 . 68 
 
 Auriga . 
 Bootes 
 Camelopardus . 
 Cancer 
 Canes Venatici . 
 
 . 41 
 
 . 59 
 . 31 
 . 52 
 . 58 
 
 Delphmus . 
 Draco. 
 Equiileus . 
 Eridanus . 
 
 . 74 
 . . .30 
 . 75 
 . . 44 
 ... 47 
 
 Canis Major 
 Canis Minor 
 Capricornus 
 
 . .49 
 . 48 
 .73 
 
 Grus . 
 Hercules . 
 Hydra 
 
 . 79 
 . 66 
 . 55 
 
 Cassiopeia . 
 
 28 
 
 Lacerta 
 
 . 76 
 
 Centaurus . 
 
 . 62 
 
 Leo 
 
 . 63 
 
18 
 
 GLOBES AND STAR-MAPS. 
 
 [21 
 
 Leo Minor . 
 
 Lepus 
 
 Libra . 
 
 Lupus 
 
 Lynx . 
 
 Lyra . 
 
 Monoceros . 
 
 Norma 
 
 Ophiuchus . 
 
 Orion . 
 
 Pegasus . 
 
 Perseus 
 
 Phoanix 
 
 Pisces 
 
 Piscis Australis . 
 
 ARTICLE 
 
 . 54 
 
 . 45 
 
 . 61 
 
 . 62 
 
 . 46 
 
 . 67 
 
 . 50 
 
 . 64 
 
 . 65 
 
 . 43 
 
 . 77 
 
 . 40 
 
 . 39 
 
 . 36 
 
 , 79 
 
 A UTICLE 
 
 (Pleiades) 42 
 
 Sagitta 70 
 
 Sagittarius 72 
 
 Scorpio 63 
 
 Sculptor . . . .39 
 
 Serpens 65 
 
 Serpentarius, see Ophiuchus . 65 
 
 Sextans 54 
 
 Taurus 42 
 
 Taurus Poniatovii . . .65 
 Triangulum . . . .37 
 Ursa Major . . . .26 
 Ursa Minor . . . .27 
 
 Virgo 56 
 
 Vulp6cula 69 
 
 21. Globes and Star-Maps. In order to study the constel- 
 lations conveniently, it is necessary to have either a celestial 
 globe or a star-map, by which to identify the stars. The globe 
 is better and more accurate, if of sufficient size ; but is costly 
 and rather inconvenient. (For a figure and description of the 
 globe, see Appendix, Art. 400.) For most purposes a star-map 
 will answer just as well as the globe, but it can never repre- 
 sent any considerable portion of the sky correctly without 
 more or less distortion of all the lines and figures near the 
 margin of the map. Such maps are made on various systems, 
 each presenting its own advantages. In all of them the 
 heavens are represented as seen from the inside, and not as on 
 the globe, which represents the sky as seen from the outside. 
 
 22. Star-Maps of this Book. We present a series of four 
 small maps, which, though hardly on a large enough scale to 
 answer every purpose of a complete celestial atlas, are quite 
 sufficient to enable the student to trace out the constellations, 
 and to identify the principal stars. In the map of the north 
 circumpolar regions, Map I., the pole is in the centre, and at 
 the circumference are numbered the twenty-four right ascension 
 
22] STAR MAGNITUDES. 19 
 
 hours. The parallels of declination are represented by equi- 
 distant concentric circles. On the three other rectangular 
 maps, which show the equatorial belt of the heavens lying 
 between 50 north and 50 south of the equator, the parallels 
 of declination are horizontal lines, while the hour-circles are 
 represented by vertical lines, also equidistant, but spaced at 
 a distance which is correct, not at the equator but for declina- 
 tion 35. This keeps the distortion within reasonable bounds, 
 even near the margin of the map, and makes it very easy to 
 lay off the places of any object for which the right ascension 
 and declination are given. The ecliptic is the curved line 
 which extends across the middle of the map. The top of the 
 map is north ; and the east, instead of being at the right hand, 
 as in a map of the earth's surface, is to the left, so that if the 
 observer faces the south, and holds the map up before and 
 above him, the constellations which are near the meridian will 
 be pretty truly represented. 
 
 The hours of right ascension are indicated on the central horizontal 
 line, which is the celestial equator, and at the top of the map are given 
 the names of the months. The word " September," for instance, means 
 that the stars which are directly under it on the map will be near the 
 meridian about 9 o'clock in the evening during that month. 
 
 23. Star Magnitudes. To the eye the principal difference 
 in the appearance of the different stars is in their brightness, 
 or their so-called ' magnitude/ Hipparchus (B.C. 125) and 
 Ptolemy divided the visible stars into six classes, the brightest 
 fifteen or twenty being called first-magnitude stars, and the 
 faintest which can be seen by the naked eye being called 
 sixth. 
 
 It has since been found that the light of the average first-magnitude 
 star is just about 100 times as great as that of the sixth ; and at this 
 rate, the light of a first-magnitude star is just a trifle more than equal 
 to two and a half second-magnitude stars, and a second-magnitude 
 star to two and a half third-magnitude stars, etc. 
 
20 DESIGNATION OF THE STABS. [ 23 
 
 Our maps show all the stars down to about 4 magnitude, 
 about a thousand in number, and all which can be seen in a 
 moonlight night. A few smaller stars are also inserted where 
 they mark some particular configuration or point out some 
 interesting telescopic object. Such double stars as can be ob- 
 served by a three or four inch telescope are marked on the map 
 by underscoring : two underscoring lines denote a triple star, 
 and three a multiple. A variable star is denoted by a circle 
 enclosing the star symbol. A few clusters and nebulae are also 
 indicated. The letter M. against one of these stands for ' Mes- 
 sier/ who made the first catalogue of 103 such objects in 1784; 
 e.g., 97 M. designates No. 97 on Messier's list. 
 
 For reference purposes and for study of the heavens in detail, the 
 more elaborate star-atlases of Proctor, Heis, or Klein are recommended, 
 especially the latter, which contains a great amount of useful infor- 
 mation in addition to the maps, and is very cheap compared with the 
 others. The student or teacher who possesses a telescope will also find 
 an invaluable accessory to it in Webb's " Celestial Objects for Common 
 Telescopes." 
 
 24. Designation of the Stars. A few of the brighter stars 
 are designated by names of their own, and upon the map those 
 names which are in most common use are indicated. Generally, 
 however, the designation of visible stars is by the letters of 
 the Greek alphabet, on a plan proposed in 1603 by Bayer, and 
 ever since followed. The letters are ordinarily applied nearly 
 in the order of brightness, Alpha being the brightest star in 
 the constellation and Beta the next brightest ; but they are 
 sometimes applied to the stars in their order of position rather 
 than in that of brightness. When the stars of a constellation 
 are so numerous as to exhaust the letters of the Greek alpha- 
 bet, the Roman letters are next used, and then, if necessary, 
 we employ the numbers which Flamsteed assigned a century 
 later. At present every star visible to the naked eye can be 
 referred to and identified by its number or letter in the con- 
 
24] URSA MAJOR. 21 
 
 stellation to which it belongs. For the Greek Alphabet, see 
 page 344 (Appendix). 
 
 25. We begin our study of Uranography with the constel- 
 lations which are circumpolar (i.e., within 40 of the north 
 pole), because these are always visible in the United States 
 and so can be depended on to furnish land (or rather sky} 
 marks to aid in tracing out the others. Since in the latitude 
 of New York the elevation of the pole is about 41, it follows 
 that there (and this is nearly enough true of the rest of the 
 United States) all the constellations which are within 41 of 
 the north pole will move around it once in twenty-four hours 
 without setting. For this reason they are called circumpolar. 
 Map I. contains them all, 
 
 26. Ursa Major, the Great Bear (Map I.). Of these circum- 
 polar constellations none is more easily recognized than Ursa 
 Major. Assuming the time of observation as about 8 o'clock 
 in the evening on Sept. 22d, it will be found below the pole 
 and to the west. Hold the map so that VIII. is at the bottom 
 and it will be rightly placed for the time assumed. 
 
 The familiar Dipper is sloping downward in the northwest, 
 composed of seven stars, all of about the second magnitude, 
 excepting Delta (at the junction of the handle to the bowl), 
 which is of the third magnitude. The stars Alpha (Dubhe), 
 and Beta (Merati), are known as the "Pointers," because a 
 line drawn from Beta through Alpha and produced about 30 
 passes very near the Pole-star. The dimensions of the Dipper 
 furnish a convenient scale of angular measure. From Alpha 
 to Beta is 5 ; from Alpha to Delta is 10 ; and from Alpha to 
 Eta, at the extremity of the Dipper-handle, (which is also the 
 Bear's tail,) is 26. The Dipper (known also in England as 
 the " Plough " and as the " Wain," or wagon) comprises but a 
 small part of the whole constellation. The head of the Bear, 
 indicated by a small group of scattered stars, is nearly on the 
 
22 URSA MAJOR. [ 26 
 
 line from Delta through Alpha, carried on about 15 ; at the 
 time assumed (Sept. 22d, 8 o'clock) it is almost exactly under 
 the pole. 
 
 Three of the four paws of the creature are marked each by 
 a pair of third or fourth magnitude stars 1^ or 2 apart. The 
 three pairs are nearly equidistant, about 20 apart, and almost 
 on a straight line parallel to the diagonal of the Dipper-bowl 
 from Alpha to Gamma, but some 20 south of it. At the time 
 assumed they are all three very near the horizon for an ob- 
 server in latitude 40, but during the spring or summer, when 
 the constellation is high in the sky, they can be easily made 
 out. 
 
 The star Zeta (or Mizar), at the bend in the handle, is 
 easily recognized by the little star Alcor near it. Mizar it- 
 self is a double star, easily seen as double with a small tel- 
 escope, and one of the most interesting recent astronomical 
 results is the discovery that it is really triple, the larger of 
 the two stars being itself double, invisibly so to the telescope, 
 but revealing its double character by means of the lines in 
 its spectrum (see Art. 373). The star Xi, the southern one of 
 the pair, which marks the left-hand paw, is also double and 
 binary, i.e., the two stars which compose it revolve about their 
 common centre of gravity in about sixty-one years. (For 
 diagram of the orbit, see Fig. 77, Art. 369.) It was the first 
 binary whose orbit was computed. 
 
 According to the ancient legends, Ursa Major is Callisto, the daugh- 
 ter of Lycaon, king of Arcadia. The jealousy of Juno l changed her 
 into a bear, and afterwards Jupiter placed her among the constella- 
 tions with Areas her son, who became Ursa Minor. One of the quaint 
 
 1 We have followed throughout the Roman nomenclature of the gods 
 and heroes, as used by Virgil and Ovid ; but the reader should be reminded 
 that, in many important respects, these Roman personages differ from 
 the Greek divinities who were identified with them. It should be said, 
 also, that in many cases the old legends are greatly confused and often 
 contradictory, as, for instance, in the case of Hercules. 
 
27] URSA MINOR. 23 
 
 old authors explains the very un-bearlike length of the creatures' tails, 
 by saying that they stretched as Jupiter lifted them to the sky. 
 
 27. Ursa Minor, the Lesser Bear (Map I.). The line of the 
 "Pointers" unmistakably marks out the Pole-star (Polaris), 
 a star of the second magnitude, standing quite alone. It is 
 at the end of the tail of Ursa Minor, or at the extremity of 
 the handle of the " Little Dipper " ; for in Ursa Minor, also, 
 the seven principal stars form a dipper, though with the handle 
 bent in a different way from that of the other dipper. Begin- 
 ning at Polaris, a curved line (concave towards Ursa Major) 
 drawn through Delta and Epsilon brings us to Zeta, where the 
 handle joins the bowl. Two bright stars (second and third 
 magnitude), Beta and Gamma, correspond to the Pointers in 
 the large Dipper, and are known as the " Guardians of the 
 Pole " ; Beta is named Kochab. The pole now lies about 1J 
 from the Pole-star, on the line joining it to Mizar (at the 
 bend in the handle of the large Dipper). 
 
 It has not always been so. Some 4000 years ago the star Thuban 
 (Alpha Draconis) was the Pole-star, and 2000 years ago the present 
 Pole-star was very much farther from the pole than now. At present 
 the pole is coming nearer to the star, and towards the close of the 
 next century it will be within half a degree of it. Twelve thousand 
 years hence the bright star Alpha Lyrse will be the Pole-star, and 
 this not because the stars change their positions, but because the axis 
 of the earth slowly changes its direction, owing to 'precession ' (see 
 Art. 125). 
 
 The Greek name of the Pole-star was Cynosura, which 
 means the ' tail of the Dog,' indicating that at one time the 
 constellation was understood to represent a Dog instead of a 
 Bear. 
 
 As already said (Art. 26) this constellation is by many writers 
 identified with Areas, Callisto's son. But more generally Areas is 
 identified with Bootes. 
 
 The Pole-star is double, having a small companion barely 
 visible with a telescope of two or three inches diameter. 
 
24 CASSIOPEIA. [ 28 
 
 28. Cassiopeia (Map I.). This constellation lies on the op- 
 posite side of the pole from the Dipper, and at about the same 
 distance from it as the " Pointers." It is easily recognized by 
 the zigzag, " rail-fence " configuration of the five or six bright 
 stars that mark it. With the help of the rather inconspicuous 
 star Kappa, one can make out of them a pretty good chair with 
 the feet turned away from the pole. But this is wrong. In the 
 recognized figures of the constellation the lady sits with feet 
 towards the pole, and the bright star Alpha is in her bosom, 
 while Zeta and the other faint stars north of Alpha are in her 
 head and uplifted arms ; Iota, on the line from Delta to Epsilon 
 produced, is in the foot. The order of the principal stars is 
 easily remembered by the word 'Bagdei,' i.e., Beta, Alpha, 
 Gamma, Delta, Epsilon, Iota. 
 
 Alpha, which is slightly variable in brightness, is known as 
 Schedir ; Beta is called Caph. The little star Eta, which is 
 about half-way between Alpha and Gamma, a little off the 
 line, is a very pretty double star, the larger star orange, the 
 smaller one purple. It is binary (i.e., the two stars revolve 
 around each other), with a period of about 206 years. 
 
 In the year 1572 a famous temporary star made its appear- 
 ance in this constellation, at a point on the line drawn from 
 Gamma through Kappa, and extended about half its length. 
 It was carefully observed and described by Tycho Brahe, and 
 at one time was bright enough to be seen easily in broad day- 
 light. There has been an entirely unfounded notion that this 
 was identical with the Star of Bethlehem, and there has been 
 an equally unfounded impression that its reappearance may be 
 expected about the present time. 
 
 Cassiopeia was the wife of Cepheus, king of Libya, and the mother 
 of Andromeda, who was rescued from the sea-monster, Cetus, by Per- 
 seus, who came flying through the air, and used the head of Medusa, 
 (which he still holds in his hand,) to turn his adversaries to stone. 
 Cassiopeia had indulged in too great boasting of her daughter's beauty, 
 
29] CEPHEUS DRACO. 25 
 
 and thus excited the jealousy of the Nereids, at whose instigation the 
 sea-monster was sent by Neptune to ravage the kingdom. 
 
 29. Cepheus (Map I.). This constellation, though large, 
 contains very few bright stars. At the assumed time (8 
 o'clock, Sept. 22d) it is above Cassiopeia and to the west, not 
 having quite reached the meridian above the pole. A line 
 carried from Alpha Cassiopeia through Beta, and produced 20, 
 will pass very near to Alpha Cephei, a star of the third 
 magnitude in the king's right shoulder. Beta Cephei is about 
 8 north of Alpha, and Gamma about 12 from Beta, both also 
 of the third magnitude. Gamma is so placed that it is at the 
 obtuse angle of a rather flat isosceles triangle of which Beta 
 Cephei and the Pole-star form the other two corners. Cepheus 
 is represented as sitting behind Cassiopeia (his wife) with his 
 feet upon the tail of the Little Bear, Gamma being in his left 
 knee. His head is marked by a little triangle of fourth- 
 magnitude stars, of which Delta is a remarkable variable with 
 a period of 5J days. It is worth noting that there are several 
 other small variable stars in the same neighborhood (none of 
 them bright enough to be shown upon the map). Beta is a 
 very pretty double star. 
 
 30. Draco, the Dragon (Map I.). The constellation of 
 Draco is characterized by a long, winding line of stars, mostly 
 small, extending half-way around the pole and separating the 
 two Bears. A line from Delta Cassiopeia drawn through Beta 
 Cephei and extended about as far again will fall upon the head 
 of Draco, marked by an irregular quadrilateral of stars, two 
 of which are of the 2^ and 3 magnitude. These two bright 
 stars about 4 apart are Beta and Gamma. The latter (named 
 Etaniri), in its daily revolution, passes almost exactly through 
 the zenith of Greenwich, and it was by observations upon it 
 that the "aberration of light" was discovered (see Art. 435). 
 The nose of Draco is marked by a smaller star, Mu, some 
 5 beyond Beta, nearly on the line drawn through it from 
 
26 DKACO. [ 30 
 
 Gamma. From Gamma we trace the neck of Draco, eastward 
 and downward * toward the Pole-star, until we come to Delta 
 and Epsilon and some smaller stars near them. 
 
 There the direction of the line is reversed, as shown upon the 
 map, so that the body of the monster lies between its own head 
 and the bowl of the Little Dipper, and winds around this bowl 
 until the tip of the tail is reached, at the middle of the line 
 between the Pointers and the Pole-star. The constellation 
 covers more than 12 hours of right ascension. 
 
 One star deserves special notice, the star Alpha or Thuban, 
 a star of 3J magnitude, which lies half-way between Zeta Ursee 
 Majoris (Mizar) and Gamma Ursa Minoris. Four thousand 
 seven hundred years ago it was the Pole-star, and then within 
 a quarter of a degree of the pole, much nearer than Polaris is 
 at present or ever will be. It is probable also that its bright- 
 ness has considerably fallen off within the last 200 years, since 
 among the ancient astronomers it was always reckoned as of 
 the second magnitude and is not now much above the fourth. 
 The so-called 'Pole of the Ecliptic ' is in this constellation, 
 i.e., the point which is 90 distant from every point in the 
 Ecliptic, the circle annually described by the sun. This point 
 (see map) is the centre around which precession causes the 
 pole to move nearly in a circle (see Art. 126) once in 25,800 
 years. 
 
 The mythology of this constellation is doubtful. According to 
 some it is the dragon which Cadmus slew, afterwards sowing its teeth, 
 from which sprung up the harvest of armed men who fought and slew 
 each other, leaving only the five survivors who were the founders of 
 Thebes. Others say that it was the dragon who watched the golden 
 apples of the Hesperides, and was killed by Hercules when he cap- 
 tured that prize. This accords best with the fact that in the heavens 
 Hercules has his foot on the dragon's head. 
 
 1 The description applies strictly only at the time assumed, 8 o'clock, 
 Sept. 22d. 
 
31] THE MILKY WAY. 27 
 
 31. Camelopardus. This is the only remaining one of the strictly 
 circumpolar constellations, a modern one containing no stars above 
 fourth magnitude, and established by Hevelius (1611-1687) simply to 
 cover the great empty space between Cassiopeia and Perseus on one 
 side, and Ursa Major and Draco on the other. The animal stands on 
 the head and shoulders of Auriga, and his head is between the Pole- 
 star and the tip of the tail of Draco. 
 
 The two constellations of Perseus (which at the time assumed is 
 some 20 below Cassiopeia), and of Auriga, are partly circumpolar, but 
 on the whole can be more conveniently treated in connection with the 
 equatorial maps. Capella, the brightest star of Auriga, and next to 
 Vega and Arcturus the brightest star in the northern hemisphere, 
 is at the time assumed (Sept. 22d, 8 o'clock) a few degrees above 
 the horizon in the N.E. Between it and the nose of Ursa Major lies 
 part of the constellation of the Lynx, a modern one, made, like 
 Camelopardus, by Hevelius, merely to fill a gap, and without any 
 large stars. 
 
 32. The Milky Way in the Circumpolar Region. The only 
 circumpolar constellations traversed by the Milky Way are 
 Cassiopeia and Cepheus. It enters the circumpolar region from 
 the constellation of Cygnus, which at this time is just in the 
 zenith, sweeps down across the head and shoulders of Cepheus, 
 and on through Cassiopeia and Perseus to the northeastern 
 horizon in Auriga. There is one very bright patch a few 
 degrees north of Beta Cassiopeise, and half way between Delta 
 Cassiopeiae and Gamma Persei there is another bright cloud 
 in which is the famous double cluster of the " Sword-handle 
 of Perseus," a beautiful object for even the smallest tele- 
 scope. 
 
 33. For the most part the constellations shown upon the 
 circumpolar map (I.) will be visible every night in the north- 
 ern part of the United States. At places farther south the con- 
 stellations near the rim of the map will stay below the horizon 
 for a short time every twenty-four hours, since the height of 
 the pole always equals the latitude of the observer, and there- 
 fore only those stars which have a polar distance less than the 
 
28 TIMES FOR OBSERVATION [ 33 
 
 latitude will remain constantly visible. In other words, if, 
 with, the pole as a centre, we draw a circle with a radius equal 
 to the height of the pole above the horizon, all the stars within 
 this circle will remain continually above the horizon. This is 
 called the circle of ' Perpetual Apparition. 7 (Art. 85.) At 
 New Orleans, in latitude 30, its radius, therefore, is only 30, 
 and only those stars which are within 30 of the pole will 
 make a complete circle without setting. At stations in the 
 northern part of the United States, as Tacoma, it is nearly as 
 large as the whole map. 
 
 34. Before proceeding to consider the other constellations, 
 the student should be reminded that he will have to select 
 those that are conveniently visible at the time of the year 
 when he happens to be studying the subject, and that, if he 
 wishes to cover the whole sky, he will have to take up the sub- 
 ject more than once, and at various seasons of the year. The 
 constellations near the southern limits of the map especially 
 can be seen only a few weeks in each year. 
 
 He will also be likely to be occasionally perplexed by find- 
 ing in the heavens certain conspicuous stars not given on the 
 maps, stars much brighter than any that are given. These 
 are the planets Venus, Jupiter, Mars, and Saturn, called planets, 
 i.e., ' wandering stars,' just because they continually change 
 their place, and so cannot be mapped. The student will find 
 it interesting and instructive, however, to dot down upon the 
 star-map every clear night the places of any planets he may 
 notice, and thus to follow their motion for a month or two. 
 
 Remember also that on these maps east always lies on the 
 left hand, so that the map should be held between the eye and 
 the sky in order to represent things correctly. We begin with 
 Andromeda at the N.W. corner of Map II. 
 
 35. Andromeda (Map II.). November. Andromeda will 
 be found exactly overhead in our latitudes about 9 o'clock in 
 
35] ANDROMEDA PISCES. 29 
 
 the middle of November. Its characteristic configuration is the 
 line of three second-magnitude stars, Alpha, Beta, and Gamma, 
 extending east and north from Alpha, (Alpheratz) which 
 itself forms the N.E. corner of the so-called "Great Square 
 of Pegasus," and is sometimes lettered as Delta Pegasi. This 
 star may readily be found by extending an imaginary line from 
 Polaris through Beta Cassiopeise, and producing it about as 
 far again : Alpha is in the head of Andromeda, Beta (MiracJi) 
 in her waist, and Gamma (Almaach) in her left foot. A line 
 drawn northwesterly from Beta, nearly at right angles to 
 the line Beta Gamma, will pass through Mu at a distance of 
 about 5, and produced another 5 will strike the "great 
 nebula," which is visible to the naked eye like a little cloud of 
 light, and forms a small obtuse-angled triangle with Nu and 
 a little sixth-magnitude star. Andromeda has her mother, 
 Cassiopeia, close by on the north, with her father, Cepheus, 
 not far away, while at her feet is Perseus, her deliverer. Her 
 head rests upon the shoulder of Pegasus. In the south, 
 beyond the constellations of Aries and Pisces, Cetus, the sea- 
 monster, who was to have devoured her, stretches his ungainly 
 bulk. 
 
 We have already mentioned the nebula. Another very pretty 
 object is Gamma, which in a small instrument is a double star, the 
 larger one orange, the smaller a greenish blue. The small star is itself 
 double, making the system really triple, but as such is beyond the 
 reach of any but very large instruments. 
 
 When Neptune sent the leviathan, Cetus, to ravage Libya, the ora- 
 cle of Ammon announced that the kingdom could be delivered only 
 if Cepheus would give up his daughter. He assented and chained the 
 poor girl to a rock to await her destruction. But Perseus, returning 
 through the air from the slaying of the Gorgon, Medusa, saw her, 
 rescued her, won her love, and made her his wife. 
 
 36. Pisces, the Fishes (Map II.). November. Immediately 
 south of Andromeda lies Pisces, the first of the constellations 
 
30 TRIANGTJLUM. [ 36 
 
 of the Zodiac, 1 which is a belt 16 wide (8 on each side of 
 the ecliptic) encircling the heavens, and including the space 
 within the limits of which the sun, the moon, and all the prin- 
 cipal planets perform their apparent motions. At present, in 
 consequence of precession, it occupies the sign of Aries (see 
 Art. 126). It has not a single conspicuous star, and is notable 
 only as now containing the Vernal Equinox, or "First of 
 Aries," which lies near the southern boundary of the constel- 
 lation in a peculiarly starless region. A line from Alpha An- 
 dromedse through Gamma Pegasi, continued as far again, strikes 
 about 2 east of the point. The body of one of the two fishes 
 lies about 15 south of the middle of the southern side of the 
 "Great Square of Pegasus/' and is marked by an irregular 
 polygon of small stars, 5 or 6 in diameter. A long, crooked 
 "ribbon" of little stars runs eastward for more than 30, 
 terminating in Alpha Piscium, (called El Risclia, or 'the 
 knot,') a star of the fourth magnitude 20 south of the head 
 of Aries. From there another line of stars leads up north- 
 west in the direction of Delta Andromedse to the northern 
 fish, which lies in the vacant space south of Beta Andromedse. 
 
 Alpha is a very pretty double star, the two components being about 
 2" apart. 
 
 The mythology of this constellation is not very well settled. One 
 story is that the fishes are Venus and her son Cupid, who once were 
 thus transformed when endeavoring to escape from the giant Typhon. 
 The northern fish is Cupid, the southern his mother. 
 
 37. Triangulum or Deltoton, the Triangle (Map II.). De- 
 cember. This little constellation, insignificant as it is, is one 
 of Ptolemy's ancient -forty-eight. It lies half-way between 
 Gamma Andromedse and the head of Aries, and is character- 
 
 1 The word is derived from the Greek word zoon, a living creature, 
 and indicates that all the constellations in it (Libra alone excepted) are 
 animals. The zodiacal constellations are for the most part of remote 
 antiquity, antedating by many centuries even the Greek mythology. 
 
38] ARIES CETUS. 31 
 
 ized by three stars of the third and fourth magnitude, easily 
 made out by the help of the map. 
 
 It may be regarded as a canonization of " Divine Geometry," but 
 has no special mythological legend connected with it. 
 
 38. Aries, the Earn (Map II). December. This is the sec- 
 ond of the zodiacal constellations, now occupying the sign of 
 Taurus. It lies just south of Triangulum and Perseus. Its 
 characteristic star-group is that composed of Alpha (Hamal), 
 Beta, and Gamma (see map), about 20 due south of Gamma 
 Andromedse. Alpha, a star of 2^ magnitude, is fairly conspic- 
 uous, forming a large isosceles triangle with Beta and Gamma 
 Andromedse. 
 
 Gamma Arietis is a very pretty double star with the components 
 about 9" apart. It is probably the first double star discovered, hav- 
 ing been noticed by Hooke in 1664. 
 
 The star 41 Arietis (3} magnitude), which forms a nearly equilat- 
 eral triangle with Alpha Arietis and Gamma Trianguli, constitutes, 
 with two or three other stars near it, the constellation of Musca 
 (Borealis), a constellation, however, not now generally recognized. 
 
 According to the Greeks, Aries is the ram which bore the golden 
 fleece and dropped Helle into the Hellespont, when she and her brother, 
 Phrixus, were flying on its back to Colchis. Long afterwards the 
 Argonautic Expedition, with Jason as its head and Hercules as one 
 of its members, sailed from Greece to Colchis to recover the fleece, 
 and finally succeeded after long endeavors. 
 
 39. Cetus, the Sea-monster (Map II.). November-Decem- 
 ber. South of Aries and Pisces lies the huge constellation 
 of Cetus, the sea-monster, which backs up into the sky from 
 the southeastern horizon. The head lies some 20 southeast 
 of Alpha Arietis, and is marked by an irregular five-sided fig- 
 ure of stars, each side being some 5 or 6 long. The southern 
 edge of this pentagon is formed by the stars Alpha or Merikar 
 (21 magnitude) and Gamma (3J magnitude) ; Delta lies south- 
 west of Gamma. Beta (Deneb Ceti), the brightest star of the 
 
32 PERSEUS. [ 39 
 
 I 
 
 constellation (2 magnitude), stands by itself nearly 40 west 
 and south of Alpha. Gamma is a very pretty double star, but 
 rather close for a small telescope, the components being only 
 2.5" apart, yellow and blue. 
 
 Cetus is the leviathan that was sent by Neptune to ravage Libya 
 and devour Andromeda. Perseus turned him into stone by showing 
 him the head of the Gorgon, Medusa. On the globes he is usually 
 represented as a nondescript sort of beast, with a face like a puppy's, 
 and a tightly curled tail; as if the Gorgon's head had frightened out 
 all his savageness. 
 
 South of Cetus lies the modern constellation of Sculptoris Appa- 
 ratus (usually known simply as Sculptor), which, however, contains 
 nothing that requires notice here. South of Sculptor, and close to 
 the horizon, even when on the meridian, is Phoenix. It has some 
 bright stars, but none easily observable in the United States. 
 
 40. Perseus (Maps I. and II.). January. Keturning now 
 to the northern limit of the map, we come to the constella- 
 tion of Perseus. Its principal star is Alpha (Algenib), rather 
 brighter than the standard second magnitude, and situated 
 very nearly on the prolongation of the line of the three chief 
 stars of Andromeda. A very characteristic configuration is 
 the so-called " segment of Perseus " (Map I.), a curved line 
 formed by Delta, Alpha, Gamma, and Eta, with some smaller 
 stars, concave towards the northeast, and running along the 
 line of the Milky Way towards Cassiopeia. The remarkable 
 variable star, Beta, or Algol, is situated about 9 south and a 
 little west of Alpha, at the right angle of a right-angled triangle 
 which it forms with Alpha Persei and Gamma Andromedse. 
 Algol and a few small stars near it form " Medusa's Head," 
 which Perseus carries in his hand. For further particulars 
 and recent discoveries regarding this star, see Arts. 358 and 
 360. 
 
 Epsilon is a very pretty double star with the components about 8" 
 apart; but the most beautiful telescopic object in the constellation, 
 
40] AURIGA. 33 
 
 perhaps the finest, indeed, in the whole heavens for a small telescope, 
 is the pair of clusters about half-way between Gamma Persei and 
 Delta Cassiopeiae, visible to the naked eye as a bright knot in the 
 Milky Way, and already referred to in Art. 32. 
 
 Perseus was the sen of Danae by Jupiter, who won her in a shower 
 of gold. He was sent by his enemies on the desperate venture of 
 capturing the head of Medusa, the only mortal one of the three Gor- 
 gons, which were frightful female monsters with wings, tremendous 
 claws, and brazen teeth, and serpents for hair ; of such aspect that the 
 sight turned all who looked at them to stone. The gods helped Per- 
 seus by various gifts which enabled him to approach his victim, invis- 
 ible and unsuspected, and to deal the fatal blow without looking at the 
 sight himself. From the blood of Medusa, where her body fell, sprang 
 Pegasus, the winged horse, and where the drops fell on the sands of 
 Libya, as Perseus was flying across the desert, thousands of venomous 
 serpents swarmed. On his way, returning home, he saw and rescued 
 Andromeda, as already mentioned (Arts. 28 and 34). Hercules was 
 one of their descendants. 
 
 41. Auriga, the Charioteer (Maps I. and II.). January. 
 Proceeding east from Perseus we come to Auriga, who is 
 represented as holding in his arms a goat and her kids. The 
 constellation is instantly recognized by the bright yellow star, 
 Capella (the Goat), and her attendant 'Hoedi' (the Kids). 
 Alpha Aurigse (Capella) is, according to Pickering, precisely 
 of the same brightness as Vega, both of them being about of 
 a magnitude fainter than Arcturus, but distinctly brighter 
 than any other stars visible in our latitudes except Sirius itself. 
 The spectroscope shows that Capella is very similar in charac- 
 ter to our own sun, though probably vastly larger. About 10 
 east of Capella is Beta Aurigse (Menkalinan) of the second 
 magnitude ; Epsilon, Zeta, and Eta, which form a long triangle 
 4 or 5 south of Alpha, are the Kids. 
 
 There seems to be no well-settled mythological history for this 
 constellation, though some say that he is the charioteer of (Enomaus, 
 king of Elis; while others connect him with the story of Phaeton, 
 the son of Apollo, who borrowed the horses of his father and was over- 
 
34 TAURUS. [ 42 
 
 thrown in mid-heaven. The goat is supposed to be Amalthea, the goat 
 which suckled Jupiter in his infancy. Capella and the Kids were al- 
 ways regarded by astrologers as of kindly influence, especially towards 
 sailors. 
 
 42. Taurus, the Bull (Map III.). January. This, the 
 third of the zodiacal constellations, lies directly south of Per- 
 seus and Auriga, and north of Orion. It is unmistakably 
 characterized by the Pleiades, and by the V-shaped group of 
 the Hyades which forms the face of the bull, with the red 
 Aldebaran (Alpha Tauri), a standard first-magnitude star, 
 blazing in the creature's eye, as he charges down upon Orion. 
 His long horns reach out towards Gemini and Auriga, and 
 are tipped with the second and third magnitude stars, Beta 
 and Zeta. As in the case of Pegasus, only the head and 
 shoulders appear in the constellation. Six of the Pleiades 
 are easily visible, and on a dark night a fairly good eye will 
 count nine of them. With a three-irich telescope about 100 
 stars are visible in the cluster, which is more fully described 
 with a figure in Art. 376. The brightest of the Pleiades is 
 called ' Alcyone? and was assigned to the dignity of the 
 < Central Sun' by Maedler (Art. 386). 
 
 About 1 west and a little north of Zeta is a nebula (Messier 1), 
 which has many times been discovered by tyros with a small telescope 
 as a new comet : it is an excellent imitation of the real thing. 
 
 According to the Greek legends, Taurus is the milk-white bull into 
 which Jupiter changed himself when he carried away Europa from 
 Phoenicia to the island of Crete, where she became the mother of 
 Minos and the grandmother of Deucalion, the Noah of Greek my- 
 thology. But Taurus, like most of the other zodiacal constellations, is 
 really far older than the Greek mythology, and appears in the most 
 ancient zodiacs of Egypt, where it was probably connected with the 
 worship of the bull, Apis ; so also in the ancient Astronomy of Chal- 
 dea and India. 
 
 The Pleiades were daughters of the giant Atlas. Of the seven 
 sisters, one, who married a mortal, lost her brightness, according 
 
42] ORION. 35 
 
 to the legend, so that only six remain visible. Some say that Merope 
 was the one who thus gave up her immortality for love, but her star is 
 still visible, while Celaeno and Asterope are both faint. The now rec- 
 ognized names of the stars in the group (see map, Art. 376) include 
 Atlas and Pleione, the parents of the family, as well as the seven sis- 
 ters. As for the Hyades, who .were half-sisters of the Pleiades, there 
 is less legendary interest in their case. They are always called by 
 the poets " the rainy Hyades." 
 
 43. Orion (not O'rion) (Map II.). February. This is the 
 most splendid constellation in the heavens. As the giant 
 stands facing the bull, his shoulders are marked by the two 
 bright stars, Alpha (Betelgueze) and Gamma (Bellatrix), the 
 former of which in color closely matches Aldebaran, though 
 its brightness is somewhat variable. In his left hand he holds 
 up the lion skin, indicated by the curved line of little stars 
 between Gamma and the Hyades. The top of the club, which 
 he brandishes in his right hand, lies between Zeta Tauri and 
 Mu and Eta Geminorum. His head is marked by a little tri- 
 angle of stars of which Lambda is the chief. His belt, through 
 the northern end of which passes the celestial equator, consists 
 of three stars of the second magnitude, pointing obliquely 
 southeast toward Sirius. It is very nearly 3 in length, and 
 is known in England as the " Ell and Yard." From the belt 
 hangs the sword, composed of three smaller stars lying more 
 nearly north and south : the middle one of them is the mul- 
 tiple, Theta, in the great nebula, which even in a small tele- 
 scope is a beautiful object, the finest nebula in the sky. Beta 
 Orionis, or Rigel, a magnificent white star, is in the left foot, 
 and Kappa is in the right knee. Orion has no right foot, or if 
 he has, it is hidden behind Lepus. The quadrilateral Alpha, 
 Gamma, Beta, Kappa, with the diagonal belt, Delta, Eta, Zeta, 
 once learned can never be mistaken for anything else in the 
 heavens. 
 
 Rigel is a very pretty double star, the larger star having a very 
 small companion about 10" distant. The two stars at the extremities 
 of the belt are also double. 
 
36 LEPUS AND COLUMBA. [ 43 
 
 Orion was a giant and mighty hunter, son of Neptune, and beloved 
 by both Aurora and Diana. The legends of his life and exploits are 
 numerous, and often contradictory. He conquered every wild beast 
 except the Scorpion, which stung and killed him. As a winter con- 
 stellation his influence was counted stormy, and he was greatly dreaded 
 by sailors. 
 
 44. Eridanus, the River Po (Map II.). January. This con- 
 stellation lies south of Taurus, in the space between Cetus and Orion, 
 and extends far below the southern horizon. The portion near the 
 south pole has a pair of bright stars, which, of course, are never visi- 
 ble at the United States. Starting with Beta (Cursa, as it is called), 
 of the third magnitude, about 3 north and a little west of Rigel, one 
 can follow a sinuous line of stars westward to the paws of Cetus, 
 where the stream turns at right angles, and runs southward and south- 
 west to the horizon. One can trace it, however, only by the help of a 
 map on a larger scale than the one we present. 
 
 45. Lepus and Columba (Map II.). February. The con- 
 stellation of Lepus, the Hare, one of Orion's victims, is one 
 of the ancient forty-eight, and lies just south of the giant, 
 occupying a space of some 15 square. Its characteristic con- 
 figuration is a quadrilateral of third and fourth magnitude 
 stars, with sides from 3 to 5 long, about 10 south of Kappa 
 Orionis, and 15 west of Sirius. 
 
 Columba, the Dove, lies next south of Lepus, too far south 
 to be well seen in the Northern States. Its principal star, 
 Alpha (Phact) is of 2^ magnitude, and is readily found by 
 drawing a line from Procyon to Sirius and prolonging it 
 about the same distance. In passing, we may note that a 
 similar line drawn from Alpha Orionis through Sirius, and 
 produced, will strike near Zeta Argus, or Naos, a star about 
 as bright as Phact, the two lines which intersect at Sirius 
 making the so-called "Egyptian X." 
 
 Columba is a modern constellation, commemorating Noah's dove 
 returning to the ark with the olive branch. 
 
46] GEMINI CANIS MINOR. 37 
 
 46. Lynx (Maps I., II., and III.). February. Returning now 
 to the northern limit of the map, we find the modern constellation of 
 the Lynx lying just east of Auriga, and enveloping it on the north 
 and in the circumpolar region, as shown on the map. It contains no 
 stars above the fourth magnitude, and is of no importance except as 
 occupying an otherwise vacant space. 
 
 47. Gemini, the Twins (Map II.). February and March. 
 This is the fourth, of the zodiacal constellations, now lying 
 mostly in the sign of Cancer. It contains the summer solstitial 
 point the point where the sun turns from its northern mo- 
 tion to its southern in the summer. At present it is about 2 
 west and a little north of the star Eta. Gemini lies northeast 
 of Orion and southeast of Auriga, and is sufficiently character- 
 ized by the two stars Alpha and Beta (about 4J- apart), which 
 mark the heads of the twins. The southern one, Beta, or 
 Pollux, is now the brighter ; but Alpha, Castor, is much more 
 interesting, as being double (easily seen with a small tele- 
 scope). The feet are marked by the third-magnitude stars 
 Gamma and Mu, some 10 east of Zeta Tauri. 
 
 Castor and Pollux were the sons of Jupiter by Leda, and ancient 
 mythology, especially that of Rome, is full of legends relating to them. 
 Many of our readers will remember Macaulay's ballad of " The Bat- 
 tle of Lake Regillus," when they won the fight for Rome. They were 
 regarded as the special patrons of the sailor, who relied much on 
 their protection against the evil powers of Orion and the Hyades. 
 
 48. Canis Minor, the Little Dog (Map III.). March. 
 This constellation, about 20 south of Castor and Pollux, is 
 marked by the bright star Procyon, which means " before the 
 dog," because it rises about half an hour before the Dog 
 Star, Sirius. Alpha, Beta, and Gamma form together a config- 
 uration closely resembling that formed by Alpha, Beta, and 
 Gamma Arietis. Procyon, Alpha Orionis, and Sirius form 
 nearly an equilateral triangle, with sides of about 25. 
 
38 CANIS MAJOR. [ 49 
 
 The animal is supposed to have been one of Orion's dogs, though 
 some say the dog of Icarus, whom they identify with Bootes. 
 
 49. Canis Major, the Great Dog (Map II.). February. 
 This glorious constellation hardly needs description. Its 
 Alpha is the Dog Star, Sirius, beyond all comparison the 
 brightest star in the heavens, and one of our nearer neigh- 
 bors, so distant, however, that it requires more than eight 
 years for light to come to us from it. It is nearly pointed at 
 by a line drawn through the three stars of Orion's belt. Beta, 
 at the extremity of the uplifted paw, is of the second magni- 
 tude, and so are several of the stars farther south in the rump 
 and tail of the animal, who sits up watching his master Orion, 
 but with an eye out for Lepus. 
 
 50. Monoceros, the Unicorn (Map II.). March. This is one 
 of the modern constellations organized by Hevelius to fill the gap 
 between Gemini and Canis Minor on the north, and Argo Navis and 
 Canis Major, on the south. It lies just east of Orion, and has no con- 
 spicuous stars, but is traversed by a brilliant portion of the Milky 
 Way. The Alpha of the constellation (fourth magnitude) lies about 
 half-way between Alpha Orionis and Sirius, a little west of the line 
 that joins them. 11 Monocerotis, a fine triple star (see Fig. 76, Art. 
 366), fourth magnitude, is very nearly pointed at by a line drawn from 
 Zeta Canis Majoris northward through Beta, and continued as far 
 
 51. Argo Navis, the Ship Argo (genitive Argus) (Maps 
 II. and III.). March. This is one of the largest, oldest, and 
 most important of the constellations, lying south and east of 
 Canis Major. Its brightest star, Alpha Argus, Canopus, ranks 
 next to Sirius, and is visible in the Southern States, but not 
 in the Northern. The constellation, huge as it is, is only a 
 half one, like Pegasus and Taurus, only the stern of a ves- 
 sel, with mast, sail, and oars ; the stem being wanting. In the 
 part of the constellation covered by our maps there are no 
 very conspicuous stars, though there are some of third and 
 
51] CANCER LEO. 39 
 
 fourth magnitude which lie east and southeast of the rump 
 and tail of Canis Major. We have already mentioned Zeta, or 
 Naos, at the southeast extremity of the " Egyptian X." 
 
 According to the Greek legends, this is the miraculous ship in 
 which Jason and his fifty companions sailed from Greece to Colchis 
 to recover the Golden Fleece. It had in its bow a piece of oak from 
 the sacred grove of Dodona, which enabled the ship to talk with its 
 commander and give him advice. 
 
 Some see in the constellation the ark of Noah. 
 
 52. Cancer, the Crab (Maps II. and III.) March. This 
 is the fifth of the zodiacal constellations, lying just east of 
 Canis Minor. It does not contain a single conspicuous star, 
 but is easily recognizable from its position, and in a dark night 
 by the nebulous cloud known as Prcesepe, or the "Manger," 
 with the two stars Gamma and Delta near it, the so-called 
 Aselli, or "Donkeys." Praesepe, sometimes also called the 
 "Beehive," is really a coarse cluster of seventh and eighth 
 magnitude stars, resolvable by an opera-glass. The line from 
 Castor through Pollux, produced about 12, passes near enough 
 to it to serve as a pointer. 
 
 The star Zeta is a very pretty triple star, though with a small tel- 
 escope it can be seen only as double. It is easily found by a line 
 from Castor through Pollux, produced 2J times as far. 
 
 By the Greeks this was identified as the Crab who attacked Hercu- 
 les when he was fighting the Lernaean Hydra. In the old Egyptian 
 zodiacs the Crab is replaced by the Scarabaeus, or Beetle ; and in some 
 of the more recent zodiacs by a pair of asses, still recognized in the 
 name, Aselli, given to the two stars Gamma and Delta. 
 
 53. Leo, the Lion (Map III.). April. East of Cancer 
 lies the noble constellation of Leo, which adorns the evening 
 sky in March and April ; it is the sixth of the zodiacal constel- 
 lations, now occupying the sign of Virgo. Its leading star, 
 Regulus, or "Cor Leonis," is of the first magnitude, and two 
 others, Beta (Denebola) and Gamma, are of the second mag- 
 
40 HYDEA. [ 53 
 
 nitude. Alpha, Gamma, Delta, and Beta form a conspicuous 
 irregular quadrilateral (see map), the line from Eegulus to 
 Denebola being about 26 long. Another characteristic con- 
 figuration is "the Sickle," of which Eegulus is the handle, 
 and the curved line Eta, Gamma, Zeta, Mu, and Epsilon, is the 
 blade, the cutting edge being turned towards Cancer. 
 
 The "radiant" of the November meteors lies between Zeta and 
 Epsilon. Gamma, in the Sickle, and at the southeast corner of the 
 quadrilateral, is a very pretty double star, binary, with a period of 
 about 400 years. 
 
 According to classic writers, this is the Nemaean Lion which was 
 killed by Hercules, as the first of his Twelve Labors ; but, like Aries 
 and Taurus, the constellation is far older than the Greeks, and stands 
 in its present form on all the ancient zodiacs. 
 
 54. Leo Minor and Sextans (Map II.). April. Leo Minor, 
 the Smaller Lion, is an insignificant modern constellation composed of 
 a few small stars north of Leo, between it and the feet of Ursa Major. 
 It contains nothing deserving special notice. The same remark holds 
 good as to Sextans, the Sextant, and even more emphatically. 
 
 55. Hydra (Map III.). March to June. This constellation, 
 with its riders, Crater (the Cup) and Corvus (the Raven), is a 
 large and important one, though not very brilliant. The head 
 is marked by a group of five or six fourth and fifth magnitude 
 stars just 15 south of Prsesepe. A curving line of small stars 
 leads down southeast to Alpha, Cor Hydras, or Alphard, a 2J 
 magnitude star standing very much alone. From there, as 
 the map shows, an irregular line of fourth-magnitude stars 
 running far south and then east, almost to the boundary of 
 Scorpio, marks the creature's body and tail, the whole cover- 
 ing almost six hours of right ascension, and very nearly 90 
 of the sky. About the middle of the length of Hydra, and 
 just below the hind feet of Leo (30 due south from Denebola), 
 we find the little constellation of Crater; and just east of it 
 the still smaller but much more conspicuous one of Corvus, 
 
55] VIRGO. 41 
 
 with two second-magnitude stars in it, and four of the third 
 and fourth magnitudes. It is well marked by a characteristic 
 quadrilateral (see map), with Delta and Eta together at its 
 northeast corner. The order of the letters in Corvus differs 
 widely from that of brightness, suggesting that changes may 
 have occurred since the letters were applied. 
 
 Epsilon Hydrae and Delta Corvi are pretty double stars, the latter 
 easily seen with a small telescope ; colors, yellow and purple. 
 
 Hydra, according to the Greeks, is the immense hundred-headed 
 monster which inhabited the Lernaean Marsh, and was killed by Her- 
 cules as his second labor. But the Hydra of the heavens has only one 
 head, and is probably much older than the legends of Hercules. 
 
 An old legend says that Corvus is Coronis, a nymph who was trans- 
 formed into a raven to escape the pursuit of Neptune. Another story 
 , is that she was changed into a crow for telling tales of some impru- 
 dent actions that came under her notice. 
 
 56. Virgo (Map III.). May. East and south of Leo lies 
 Virgo, the seventh zodiacal constellation, mostly in the sign 
 of Libra. Its Alpha, Spica Virginis, is of the 1^ magnitude, 
 and, standing rather alone, 10 south of the celestial equator, 
 is easily recognized as the southern apex of a nearly equilat- 
 eral triangle which it forms with Denebola (Beta Leonis) to 
 the northwest, and Arcturus northeast of it. Beta Virginis, of 
 the third magnitude, is 14 south of Denebola. A line drawn 
 eastward and a little south from Beta (third magnitude) and 
 then carried on, curving northward, passes successively (see 
 map) through Eta, Gamma, Delta, and Epsilon, of the third 
 magnitude. (Notice the word Begde, like Bagdei in Cassio- 
 peia, Art. 28.) 
 
 Gamma is a remarkable binary star, at present easily visible as 
 double in a small telescope. Its period is one hundred and eighty-five 
 years, and it has completed pretty nearly a full revolution since its 
 first discovery. For a diagram of its orbit, see Fig. 77, Art. 369. A 
 few degrees north of Gamma lies the remarkable nebulous region of 
 
42 CANES VENATICI. 
 
 [56 
 
 Virgo, containing hundreds of these curious objects ; but for the most 
 part they are very faint, and observable only with large telescopes. 
 
 The classic poets recognize Virgo as Astrsea, the goddess of justice, 
 who, last of all the old divinities, left the earth at the close of the 
 Golden Age. She holds the Scales of Justice (Libra) in one hand, 
 and in the other a sheaf of wheat. 
 
 Some identify her with Erigone, the daughter of Icarus or Bootes. 
 Others recognize in her the Egyptian Isis. 
 
 57. Coma Berenices, Berenice's Hair (Map III.). May. This 
 little constellation, composed of a great number of fifth and sixth 
 magnitude stars, lies 30 north of Gamma and Eta Virginis, and about 
 15 northeast of Denebola. It contains a number of interesting 
 double stars, but they are not easily found without the help of a tele- 
 scope equatorially mounted. 
 
 The constellation was established by the Alexandrian astronomer 
 Conon, in honor of the queen of Ptolemy Soter. She dedicated her 
 splendid hair to the gods, to secure her husband's safety in war. 
 
 58. Canes Venatici, the Hunting-Dogs (Map III.). May. 
 
 These are the dogs with which Bootes, the huntsman, is pursu- 
 ing the Great Bear around the pole : the northern of the two 
 is Asterion, the southern Chara. Most of the stars are small, 
 but Alpha is of the 2^ magnitude, and is easily found by draw- 
 ing from Eta Ursse Majoris (the star in the end of the Dipper- 
 handle) a line to the southwest, perpendicular to the line from 
 Eta to Zeta (Mizar), and about 15 long : in England it is gen- 
 erally known as Cor Caroli (the Heart of Charles), in allusion 
 to Charles I. With Arcturus and Denebola it forms a triangle 
 much like that which they form with Spica. 
 
 The remarkable whirlpool nebula of Lord Rosse is situated in this 
 constellation, about 3 west and somewhat south of the star Eta Ursse 
 Majoris. In a small telescope it is by no means conspicuous, but in a 
 large telescope is a wonderful object. 
 
 The constellation is modern, formed by Hevelius. 
 
 59. Bootes, the Huntsman (Maps I. and III.). June. This 
 fine constellation extends more than 60 in declination, from 
 
59] CORONA BOREALIS. 43 
 
 near the equator quite to Draco, where the uplifted hand hold- 
 ing the leash of the hunting-dogs overlaps the tail of the Bear. 
 Its principal star, Alpha, Arcturus (meaning ' bear-driver'), is 
 of a ruddy hue, and in brightness is excelled only by Sirius 
 among the stars visible in our latitudes. It is at once recog- 
 nizable by its forming with Spica and Denebola the great tri- 
 angle already mentioned (Art. 56). Six degrees west and a 
 little south of it is Eta, of the third magnitude, which forms 
 with it, in connection with Upsilon, a configuration like that 
 in the head of Aries. Epsilon is about 10 northeast of Arc- 
 turus, and in the same direction about 10 farther lies Delta. 
 The map shows the pentagon which is formed by these two 
 stars along with Beta, Gamma, and Rho. 
 
 Epsilon is a fine double star ; colors, orange and greenish blue ; 
 distance, about 3". 
 
 The legendary history of this constellation is very confused. One 
 legend makes it to be Icarus, the father of Erigone (Virgo). But the 
 one most usually accepted makes it to be Areas, son of Callisto. After 
 she was changed to a bear (Ursa Major), her son, not recognizing her, 
 hunted her with his dogs, and was on the point of killing her, when 
 Jupiter interfered and took them both to the stars. 
 
 60. Corona Borealis, the Northern Crown (Map III.). June. 
 This beautiful little constellation lies 20 northeast of Arc- 
 turus, and is at once recognizable as an almost perfect semi- 
 circle composed of half a dozen stars, among which the bright- 
 est, Alpha (Gemma or Alphacca), is of the second magnitude. 
 The extreme northern one is Theta ; next comes Beta, and the 
 rest follow in the Bagdei order, just as in Cassiopeia. About a 
 degree north of Delta, now visible with an opera-glass, is a 
 small star which in 1866 suddenly blazed out until it became 
 brighter than Alphacca itself (see Art. 355). 
 
 The little star Eta is a rapid binary with a period of less than forty- 
 two years. At times it can be easily divided by a small telescope. 
 
 The constellation is said to be the crown that Bacchus gave to 
 Ariadne, before he deserted her on the island of Naxos. 
 
44 LIBRA CENTAUR US. [ 61 
 
 61. Libra, the Balance (Map III.). June. This is the 
 eighth of the zodiacal constellations, lying east of Virgo, 
 bounded on the south by Centaurus and Lupus, on the east by 
 the upstretched claw of Scorpio, and on the north by Serpens 
 and Virgo. It is inconspicuous, the most characteristic figure 
 being the trapezoid formed by the lines joining the stars Alpha, 
 Iota, Gamma, and Beta. Beta, which is the northern one, is 
 about 30 due east from Spica, while Alpha is about 10 south- 
 west of Beta. The remarkable variable, Delta Librae, is 4 
 west and a little north from Beta. Most of the time it is of 
 the 4 or 5 magnitude, but runs down nearly two magnitudes, 
 to invisibility, at the minimum, once in 2J- days. 
 
 Libra is the Balance of Virgo, the goddess of justice, and was not 
 recognized by the classic writers as a separate constellation until the 
 time of Julius Caesar ; the space now occupied by Libra being then 
 covered by the extended claws of Scorpio. 
 
 62. Antlia, Centaurus, and Lupus (Map III.). April to 
 June. These constellations lie south of Hydra and Libra. 
 
 Antlia Pneumatica (the Air-Pump) is a modern constellation of no 
 importance and hardly recognizable by the eye, having only a single 
 star as bright as the 4 magnitude. 
 
 Centaurus, on the other hand, is an ancient and extensive 
 asterism, containing in its south (circumpolar) regions, not 
 visible in the United States, two stars of the first magnitude, 
 Alpha and Beta. Alpha Centauri stands next after Sirius and 
 Canopus in brightness, and, as far as present knowledge indi- 
 cates, is our nearest neighbor among the stars. The part of the 
 constellation which becomes visible in our latitudes is not 
 especially brilliant, though it contains several stars of the 2j- 
 and 3 magnitudes in the region lying south of Corvus and 
 Spica Virginis. 
 
 Lupus, the Wolf, also one of Ptolemy's constellations, lies due east 
 of Centaurus and just south of Libra. It contains a considerable 
 
62] SCOEPIO. 45 
 
 number of third and fourth magnitude stars ; but it is too low for 
 any satisfactory study in our latitudes. It is best seen late in June. 
 These constellations contain numerous objects interesting for a south- 
 ern observer, but not observable by us. 
 
 The Centaurs were a fabulous race, half man, half horse, who lived 
 in Thessaly and herded cattle. Chiron was the most distinguished of 
 them, the teacher of almost all the Greek heroes in every manly and 
 noble art, and the friend of Hercules, by whom, however, he was acci- 
 dentally killed. Jupiter transferred him to the stars. (See Sagitta- 
 rius, Art. 72.) The wolf is represented as transfixed by the Centaur's 
 spear. 
 
 63. Scorpio (or Scorpius; genitive Scorpii), the Scorpion 
 (Map IV.). July. This, the ninth of the zodiacal constel- 
 lations and the most brilliant of them all, lies southeast of 
 Libra, which in ancient times used to form its claws (Chelae). 
 It is recognized at once by the peculiar configuration of the 
 stars, which resembles a boy's kite, with a long streaming tail 
 extending far down to the south and east, and containing sev- 
 eral pairs of stars. The principal star of the constellation, 
 Antares, is of the first magnitude, and fiery red like the planet 
 Mars. From this it gets its name, which means "the rival 
 of Ares" (Mars). Antares is a very pretty double star, with 
 a beautiful little green companion just to the west of it, not 
 very easy to be seen, however, with a small telescope. Beta 
 (second magnitude) is in the arch of the kite bow, about 8 or 
 9 northwest of Antares, while the star which Bayer lettered 
 as Gamma Scorpii is well within Libra, 20 west of Antares. 
 (There is considerable confusion among uranographers as to 
 the boundary between the two constellations.) The other 
 principal stars of the constellation are easily found on the 
 map. 
 
 Many of them are of the second magnitude. One of the finest 
 clusters known, and easily seen with a small telescope, is Messier 80, 
 which lies about half-way between Alpha and Beta. 
 
 According to the Greek mythology, this is the scorpion that killed 
 
46 OPHIUCHUS AND SERPENS. [ 63 
 
 Orion. It was the sight of this monster of the heavens that frightened 
 the horses of the sun, when poor Phaeton tried to drive them and was 
 thrown out of his chariot. Among astrologers, the influence of Scorpio 
 has always been held as baleful to the last degree. 
 
 64. Norma Nilotica, the rule with which the height of the Nile 
 was measured, lies west of Scorpio, while Ara lies due south of Eta 
 and Theta. Both are old Ptolemaic constellations, but are small and 
 of little importance, at least to observers in our latitudes. 
 
 65. Ophiuchus and Serpens (Map IV.). July. Ophiuchus 
 means the " serpent-holder," and probably refers to the great 
 physician, JSsculapius. The hero is represented as standing 
 with his feet on Scorpio, and grasping the " serpent." The 
 two constellations, therefore, are best treated together. The 
 head of Serpens is marked by a group of small stars lying just 
 south of Corona and 20 due east of Arcturus. Beta and 
 Gamma are the two brightest stars in the group, their magni- 
 tudes 3^ and 4. Delta lies 6 southwest of Beta, and there 
 the Serpent's body bends southeast through Alpha and Epsilon 
 Serpentis (see map) to Delta and Epsilon Ophiuchi in the 
 giant's hand. The line of these five stars carried upwards 
 passes nearly through Epsilon Bootis, and downwards through 
 Zeta Ophiuchi. A line crossing this at right angles, nearly 
 midway between Epsilon Serpentis and Delta Ophiuchi, passes 
 through Mu Serpentis on the southwest and Lambda Ophiuchi 
 to the northeast. The lozenge-shaped figure formed by the 
 lines drawn from Alpha Serpentis and Zeta Ophiuchi to the 
 two stars last mentioned is one of the most characteristic 
 configurations of the summer sky. Alpha Ophiuchi (2} mag- 
 nitude) (Mas Alaghue) is easily recognizable in connection 
 with Alpha Herculis, since they stand rather isolated, about 6 
 apart, on the line drawn from Arcturus through the head of 
 Serpens, and produced as far again. Alpha Ophiuchi is the 
 eastern and the brighter of the two, and forms with Vega and 
 Altair a nearly equilateral triangle. Beta Ophiuchi lies about 
 9 southeast of Alpha. 
 
65] ^ HERCULES. 47 
 
 Five degrees east and a little south of Beta are five small stars in 
 the Milky Way, forming- a V with the point to the south, much like 
 the Hyades of Taurus. They form the head of the now discredited 
 constellation, " Poniatowski's Bull" (Taurus Poniatovii), proposed in 
 1777, and found in many maps. 70 Ophiuchi (the middle star in the 
 eastern leg of the V of Poniatowski's Bull) is a very pretty double star, 
 binary, with a period of ninety-three years. Just at present the star 
 is too close to be resolved by a small instrument, but it will soon open 
 up again. 
 
 Ophiuchus is identified with JEsculapius, who was the first great 
 physician, the son of Apollo and the nymph Coronis, educated in the 
 art of medicine by Chiron, the Centaur. The serpent and the cock 
 were sacred to him in his character as a deity. But the constellation 
 is older than the classic legends. 
 
 66. Hercules (Maps i. and IV.). July. This noble con- 
 stellation lies next north of Ophiuchus, between it and Draco. 
 The hero is represented as resting on one knee, with his foot 
 on the head of Draco, while his head is close to that of Ophiu- 
 chus. The constellation contains no stars of the first or even 
 of the second magnitude, but there are a number of the third. 
 The most characteristic figure is the keystone-shaped quadri- 
 lateral formed by the stars Epsilon, Zeta, Eta, with Pi and 
 Eho together at the northeast corner. It lies about midway 
 on the line from Vega to Corona. 
 
 On its western boundary, a third of the way from Eta towards Zeta, 
 lies the remarkable cluster, Messier 13, on the whole the finest of 
 all star clusters, barely visible to the naked eye on a dark night. 
 Alpha Herculis (Ras Algethi), in the head of the giant, is a very 
 beautiful double star, colors orange and blue, distance about 5". It 
 is slightly variable, and has a remarkable spectrum, characterized by 
 numerous dark bands. 
 
 Hercules, the son of Jupiter and Alcmena (a granddaughter of 
 Andromeda), was the Greek incarnation of gigantic strength. His 
 heroic actions and freaks occupy more space in their mythology than 
 those of any personage except Jupiter himself. He was the pupil of 
 Chiron, but by the will of Jupiter, his father, was subjected to the 
 
48 LYRA CYGNUS. [ 66 
 
 power of Eurystheus, the king of Tiryiis, for many years. At his 
 bidding he performed the great enterprises known as the Twelve 
 Labors of Hercules, for which we must refer the reader to the Classi- 
 cal Dictionaries. Among them we have already mentioned the con- 
 quest of the Nemaean Lion and of the Lernsean Hydra. Another was 
 to bring from the garden of the Hesperides the golden apples which 
 were guarded by the dragon that he killed, and on which his feet rest 
 in the sky. His last and greatest achievement was to bring to the 
 earth the three-headed dog, Cerberus, the guardian of the infernal 
 regions. 
 
 67. Lyra (Map IV.). August. This constellation is suffi- 
 ciently marked by the great white or blue star, Vega, one of 
 the finest stars in the whole sky, and certainly many times 
 larger than our own sun. It is attended on the east by two 
 fourth-magnitude stars, Epsilon and Zeta, which form with it 
 a little equilateral triangle having sides about 2 long. Epsi- 
 lon is a double-double or quadruple star. A sharp eye, even 
 unaided by a telescope, divides the star into two, and a large 
 telescope splits each of the components. It is a very pretty 
 object even to a small telescope. Beta" and Gamma, of the 
 third magnitude (Beta is variable), lie about 8 southeast from 
 Vega, 2y apart. (See Art. 357.) 
 
 On the line between Beta and Gamma, one-third of the way from 
 Beta, lies Messier 57, the Annular Nebula, which can be seen as a 
 small hazy ring even by a small telescope, though of course it is much 
 more interesting with a larger one. 
 
 According to the legends this constellation is the lyre of Orpheus, 
 with which he charmed the stern gods of the lower world, and per- 
 suaded them to restore to him his lost Eurydice. 
 
 68. Cygnus (Maps I. and IV.). September. This con- 
 stellation lies due east from Lyra, and is easily recognized by 
 the cross that marks it. The bright star Alpha (1^ magni- 
 tude) is at the top, and Beta (third magnitude) at the bottom, 
 while Gamma is where the cross-bar from Delta to Epsilon 
 intersects the main piece, which lies along the Milky Way 
 
68] VULPECULA ET ANSER. 49 
 
 from the northeast to the southwest. Beta (Albireo) is a 
 beautiful double star, orange and dark blue, one of the finest 
 of the colored pairs for a small telescope. 61 Cygni, which is 
 memorable as the first star to have its parallax determined (by 
 Bessel in 1838), is easily found by completing the parallelo- 
 gram of which Alpha, Gamma, and Epsilon are the other three 
 corners. Sigma and Tau form a little triangle with 61, which 
 is the faintest of the three. 61 is a fine double star. Delta 
 is also a fine double, but too difficult for an instrument of less 
 than six inches' aperture. 
 
 According to Ovid, Cygnus was a friend of Phaeton's, who mourned 
 his unhappy fate and was changed to a swan. Others see in the con- 
 stellation the swan in whose form Jupiter visited Leda, the mother of 
 Castor and Pollux and of Helen of Troy. 
 
 69. Vulpecula et Anser, the Fox and the Goose (Map IV.). 
 September. This little constellation is one of those originated by 
 Hevelius, and has obtained more general recognition among astrono- 
 mers than most of his creations. It lies just south of Cygnus, and is 
 bounded to the south by Delphinus, Sagitta, and Aquila. It has no 
 conspicuous stars, but it contains one very interesting telescopic 
 object, the " Dumb-bell Nebula" (see map). It may be found on a 
 line from Gamma Lyrae through Beta Cygni, produced as far again. 
 
 70. Sagitta (Map IV.). August. -This little constellation, though 
 very inconspicuous, is one of the old 48. It lies south of Vulpecula, 
 and the two stars Alpha and Beta, which mark the feather of the 
 arrow, lie nearly midway between Beta Cygni and Altair, while its 
 point is marked by Gamma, 5 farther east and north. Beta, the 
 middle star of the shaft of the arrow, is a very pretty double star, dis- 
 tance about 8" : the larger star is itself a close double. 
 
 71. A'quila (not A-qui'la) (Map IV.). August. This 
 constellation lies on the celestial equator, east of Ophiuchus 
 and north of Sagittarius and Capricornus. Its characteristic 
 configuration is that formed by Alpha, Altair, with Gamma to 
 the north and Beta to the south. It lies about 20 south of Beta 
 
50 SAGITTARIUS. [ 71 
 
 Cygni, and forms a fine triangle with Beta and Alpha Ophiu- 
 chi. Altair is taken as the standard first-magnitude star. Of 
 course, several of those which are called first magnitude, like 
 Sirius and Vega, are very much brighter than this, while others 
 fall considerably below it. 
 
 Aquila was the bird of Jupiter, which he kept by the side of his 
 throne and sent to bring Ganymede to him. 
 
 The southern part of the region allotted to Aquila on our maps has 
 been assigned to Antinoiis, which is recognized on some celestial 
 globes. The constellation existed even in Ptolemy's time, but he 
 declined to adopt it. Hevelius has appropriated the eastern part of 
 Antinoiis for his constellation of Scutum Sobieski. 
 
 72. Sagittarius, the Archer (Map IV.). August. This, 
 the tenth of the zodiacal constellations, contains no stars of the 
 first magnitude, but a number of the second and third magni- 
 tude, which make it reasonably conspicuous. The most char- 
 acteristic configuration is the little inverted " milk-dipper/' 
 formed by the five stars, Lambda, Phi, Sigma, Tau, and Zeta, 
 of which the last four form the bowl, while Lambda (in the 
 Milky Way) is the handle (see map). Delta, Gamma, and 
 Epsilon, which form a triangle, right-angled at Delta, lie south 
 and a little west of Lambda, the whole eight together forming 
 a very striking group. There is a curious disregard of any 
 apparent principle in the lettering of the stars of this con- 
 stellation ; Alpha and Beta are stars not exceeding in bright- 
 ness the fourth magnitude, about 4 apart on a north and south 
 line, and lying some 15 south and 5 east of Zeta (see map), 
 while Sigma is now a bright second-magnitude star, strongly 
 suspected of being irregularly variable. (The constellation 
 contains an unusual number of known variables.) The Milky 
 Way in Sagittarius is very bright and complicated in structure, 
 full of knots and streamers and dark pockets, and containing 
 many beautiful and interesting objects. 
 
 This constellation is said by many writers to commemorate the 
 Centaur, Chiron, but the same constellation appears on the ancient 
 
72J CAPRICORNUS DELPHINUS. 51 
 
 zodiacs of Egypt and India, and it seems probable, therefore, that, 
 like the Bull and the Lion, it was not representative of any particular 
 individual. 
 
 73. Capricornus (Map IV.). September. This, the eleventh 
 of the zodiacal constellations, follows Sagittarius on the east. 
 It has no bright stars, but the configuration formed by the two 
 Alphas (a x and a 2 ) with each other and with Beta, 3 south, is 
 characteristic, and not easily mistaken for anything else. The 
 two Alphas, a pretty double to the naked eye, lie on the line 
 drawn from Beta Cygni (at the foot of the cross) through 
 Altair, and produced about 25. 
 
 Some say that this constellation represents the god Pan, who was 
 represented by the Greeks as having the legs of a goat and the head of 
 a man. Others find in the goat, Amalthea (the foster-mother of the 
 infant Jupiter), who is also, it will be remembered, represented in the 
 constellation of Auriga. 
 
 74. Delphinus, the Dolphin (Map IV.). September. This 
 constellation, though small, is one of the ancient 48, and is 
 unmistakably characterized by the rhombus of third-magnitude 
 stars known as " Job's Coffin.' 7 It lies about 15 east of Altair. 
 There are a few stars visible to the naked eye, in addition to 
 the four that form the rhombus. Epsilon, about 3 to the 
 southwest, is the only conspicuous one. 
 
 Gamma, at the northwest angle of the rhombus, is a very pretty 
 double star. Beta is also a very close and rapid binary, beyond the 
 reach of all but large telescopes. 
 
 This is the Dolphin that preserved the life of the musician, Arion, 
 who was thrown into the sea by sailors, but carried safely to land 
 upon the back of the compassionate fish, who loved his music. 
 
 75. Equuleus, the Little Horse (Map IV.). This little con- 
 stellation, simply a horse's head, though still smaller than the Dolphin 
 and less conspicuous, is also one of Ptolemy's. It lies about 20 due 
 east of Altair, and 10 southeast of the Dolphin (see map) . 
 
52 PEGASUS AQUARIUS. [ 76 
 
 76. Lacerta, the Lizard (Maps I. and IV.). This is one of 
 Hevelius's modern constellations, lying between Cygnus and Androm- 
 eda, with no stars above the 4 magnitude, and of no importance for 
 our purposes. 
 
 77. Pe'gasus (not Pe-gas'us) (Map IV.). October. This 
 winged horse covers an immense space. Its most notable con- 
 figuration is the "great square," formed by the second-mag- 
 nitude stars, Alpha (Markab), Beta, and Gamma Pegasi, in 
 connection with Alpha Andromedse (sometimes lettered Delta 
 Pegasi), at its northeast corner. The stars of the square lie in 
 the body of the horse, which has no hindquarters. A line drawn 
 from Alpha Andromedae through Alpha Pegasi, and produced 
 about an equal distance, passes through Xi and Zeta in the 
 animal's neck, and reaches Theta in his ear. Epsilon (or 
 Enif), the bright star 8 northwest of Theta, marks his nose. 
 The forelegs are in the northwestern part of the constellation 
 just east of Cygnus, and are marked, one of them by the stars 
 Eta and Pi, and the other by Iota and Kappa. 
 
 This is the winged horse which sprang from the blood of Medusa, 
 after Perseus had cut off her head. He fixed his residence on Mt. 
 Helicon, where he was the favorite of the Muses, and after being 
 tamed by Minerva he was given to Bellerophon to aid him in conquer- 
 ing the Chimsera. After the destruction of the monster, Bellerophon 
 attempted to ascend to heaven upon Pegasus, but the horse threw off 
 his rider, and continued his flight to the stars. 
 
 78. Aquarins, the Water-bearer (Map IV.). October. 
 This, the twelfth and last of the zodiacal constellations, 
 extends more than 3^ h in right ascension, covering a con- 
 siderable region which by rights ought to belong to Capri- 
 cornus. The most notable configuration is the little Y of 
 third and fourth magnitude stars which marks the "water- 
 jar" from which Aquarius pours the stream that meanders 
 down to the southeast and south for 30, till it reaches the 
 Southern Fish. The middle of the Y is about 18 south and 
 
78] PISCIS AUSTRINUS. 53 
 
 west of Alpha Pegasi, and lies almost exactly on the celestial 
 equator. 
 
 Zeta, the central star of the Y, is a pretty and interesting double 
 star, distance about 4". The green nebula, nearly on the line from 
 Alpha through Beta, produced about its own length, 1 west of Nu, 
 is a planetary nebula, and curious from the vividness of its color (see 
 map). 
 
 There are various opinions respecting the origin of this constella- 
 tion. According to a Greek legend it represents Deucalion, the hero 
 of the Greek Deluge ; but among the Egyptians it evidently had refer- 
 ence to the rising and falling of the Nile. 
 
 79. Piscis Austrinus (or Australis), the Southern Fish (Map 
 IV.). October. This small constellation, lying south of Cap- 
 ricornus and Aquarius in the stream that issues from the 
 Water-bearer's urn, presents little of interest. It has one 
 bright star, Fomalhaut (pronounced Fomalo), of the 1|- mag- 
 nitude, which is easily recognized from its being nearly on the 
 same hour-circle with the western edge of the great square of 
 Pegasus, 45 to the south of Alpha Pegasi, and solitary, hav- 
 ing no star exceeding the fourth magnitude within 15 or 20. 
 
 This constellation is by some said to represent the transformation 
 of Venus into a fish, when fleeing from Typhon (but see Pisces). 
 
 South of the Southern Fish, barely rising above the southern hori- 
 zon, lie the constellations of Microscopium and Grus. The former is 
 of no account. In the southern hemisphere Grus is a conspicuous 
 constellation, and its two brightest stars, Alpha and Beta, of the sec- 
 ond magnitude, rise high enough to be seen in latitudes south of 
 Washington. They lie about 20 south and west of Fomalhaut. 
 
54 
 
 URANOGRAPHY. 
 
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80] 
 
 LATITUDE DEFINED. 
 
 55 
 
 CHAPTER III. 
 
 LATITUDE, AND THE ASPECT OF THE CELESTIAL SPHERE. 
 TIME. LONGITUDE. THE PLACE OF A HEAVENLY 
 BODY. 
 
 80. Latitude defined, In geography the latitude of a place 
 is usually defined simply as its distance north or south of the 
 equator, measured in degrees. This is not explicit enough, 
 unless it is stated how the degrees themselves are to be meas- 
 ured. There would be no difficulty if the earth were a perfect 
 sphere ; but since the earth is a little flattened at the poles, 
 the degrees (geographical) are of somewhat different lengths 
 at different parts of the earth. The exact definition of the 
 astronomical latitude of 
 a place is the angle be- 
 tween the direction of the 
 observer's plumb-line and 
 the plane of the earths 
 equator ; and this is the 
 same as the altitude of 
 the pole, as will be clear 
 from Fig. 6. Here the 
 angle ONQ is the lati- 
 tude as defined. If now 
 at we draw HH 1 per- 
 pendicular to OZ, it will 
 be a level line, and will point to the horizon. From also 
 draw OP", parallel to OP', the earth's axis. Since OP' and 
 OP" are parallel they will be directed apparently to the same 
 point in the celestial sphere (Art. 6), and this point is the 
 
 FIG. 6. Relation of Latitude to the Elevation 
 of the Pole. 
 
56 MEASURING THE LATITUDE. [ 80 
 
 celestial pole. The angle H'OP" is therefore the altitude of 
 the pole, as seen at 0, and it obviously equals ONQ ; and this 
 is true whether the earth be a sphere, or whatever its form. 
 This fundamental relation, THAT THE ALTITUDE OF THE POLE 
 
 IS IDENTICAL WITH THE OBSERVER'S LATITUDE, Cannot be tOO 
 
 strongly impressed on the mind. 
 
 81. Method of measuring the Latitude. The most obvious 
 method is to observe, with a suitable instrument, the altitude 
 of some star near the pole (a " circumpolar " star) at the 
 moment when it is crossing the meridian above the pole, and 
 again twelve hours later, when it is once more on the meridian 
 below the pole. In the first position, its elevation is the great- 
 est possible j in the second, the least. The average of these two 
 altitudes, when corrected for refraction, is the latitude of the 
 observer. It is exceedingly important that the student under- 
 stand this simple method of determining the latitude. 
 
 The instrument ordinarily used for making observations of this 
 kind at an observatory is called a meridian circle, and a brief descrip- 
 tion is given in the Appendix (see Art. 418). 
 
 82. Refraction. When we observe the altitude of a heav- 
 enly body with any instrument, we do not find it as it would 
 be if our atmosphere had no effect upon the rays of light. As 
 these rays enter the earth's atmosphere they are bent down- 
 ward by "refraction/ 7 excepting only such as come from 
 exactly overhead. Since the observer sees the object in the 
 direction in which the rays enter the eye, without any reference 
 to its real position, this bending down of the rays causes every 
 object seen through the air to look higher up in the sky than 
 it would be if the air were absent; and we must therefore 
 correct the observed altitude by diminishing it a certain 
 amount. Under ordinary conditions, refraction elevates a 
 body at the horizon about 35', so that the sun and moon in 
 rising appear clear of the horizon while they are still wholly 
 
82] THE BIGHT SPHERE. 57 
 
 below it. The refraction correction diminishes very rapidly 
 as the body rises. At an altitude of only 5 the refraction is 
 but 10'; at 44, it is about 1'; and at the zenith, zero, of 
 course. 
 
 Its amount at any given time is affected quite sensibly, however, by 
 the temperature and by the height of the barometer, increasing as the 
 thermometer falls or as the barometer rises ; so that whenever great 
 accuracy is required in measures of altitude we must have observa- 
 tions of both the barometer and thermometer to go with the reading 
 of the circle. In works on Practical Astronomy tables are given by 
 which the refraction can be computed for an object at any altitude 
 and in any state of the weather. It is hardly necessary to say that 
 this indispensable correction is very troublesome, and always involves 
 more or less error. 
 
 For other methods of determining the latitude, see Appendix, 
 Art. 424. 
 
 83. Effect of the Observer's Latitude upon the Aspect of the 
 Heavens ; the Eight Sphere. If the observer is situated at the 
 earth's equator, i.e., in latitude zero, the celestial poles will 
 evidently be on the horizon, and the celestial equator will pass 
 through the zenith and coincide with the prime vertical (Art. 
 11). At the earth's equator, therefore, all heavenly bodies 
 will rise and set vertically, and their diurnal circles will be 
 equally divided by the horizon, so that they will be twelve 
 hours above it and twelve hours below it, and the length of 
 the night will always equal that of the day. This aspect of 
 the heavens is called the right sphere. 
 
 84. Parallel Sphere. If the observer is at one of the poles 
 of the earth, where the latitude equals 90, then the corre- 
 sponding celestial pole will be exactly overhead, and the 
 celestial equator will coincide with the horizon. If he is at 
 the north pole, all the stars north of the celestial equator will 
 remain permanently visible, never rising or setting, but sailing 
 around the sky on parallels of altitude, while the stars south 
 
58 
 
 THE OBLIQUE SPHERE. 
 
 [84 
 
 K 
 
 of the equator will never rise to view. Since the sun and the 
 moon move in such a way that during half the time they are 
 north of the equator and half the time south of it, they will 
 therefore be half the time above the horizon and half the time 
 below it (that is, approximately, since refraction has a notice- 
 able effect). The moon will be visible for about a fortnight 
 at a time, and the sun for about six months. 
 
 85. The Oblique Sphere. At any station between the pole 
 and the equator the pole will be elevated above the horizon, 
 
 and the stars will rise and 
 set in oblique circles, as 
 shown in Fig. 7. Those 
 stars whose distance from 
 the elevated pole is less 
 than PN, the latitude of 
 the observer, will never 
 set, the radius of this " cir- 
 cle of perpetual appari- 
 tion" being just equal to 
 the height of the pole, and 
 becoming larger as the lat- 
 itude increases. On the 
 other hand, stars within 
 the same distance of the 
 
 FIG. 7. The Oblique Sphere. 
 
 depressed pole will lie within the " circle of perpetual occulta- 
 tion," and will never rise above the observer's horizon. An 
 object which is exactly on the celestial equator will have its 
 diurnal circle, EQWQ', equally divided by the horizon, and 
 will be above the horizon just as long as below it. 
 
 For an observer in the United States, a star north of the 
 equator will have more than half of its diurnal circle above the 
 horizon, and will be visible for more than twelve hours of each 
 day; as, for instance, the star at A. Whenever the sun is 
 north of the celestial equator, the day will therefore be longer 
 
85] THE OBLIQUE SPHERE. 59 
 
 than the night for all stations in northern latitude : how 
 much longer will depend both on the latitude of the place and 
 the sun's distance from the equator (its declination). 
 
 86. Moreover, when the sun is north of the equator, it will, 
 in the northern latitudes, rise at a point north of east, as at ~B 
 in the figure, and will continue to shine on the north side of 
 every wall that runs east and west until, as it ascends, it 
 crosses the prime vertical, EZW, at some point, as V. In the 
 latitude of New York the sun in June is south of the prime 
 vertical for only about six hours of the whole fifteen during 
 which it is above the horizon. During nine hours of the day, 
 therefore, it shines into north windows. 
 
 If the latitude of the observer is such that PN, in the figure, 
 is greater than the sun's polar distance at the time when it is 
 farthest north, the sun at midsummer will make a complete 
 circuit of the heavens without setting, thus producing the 
 phenomenon of the " midnight sun," visible at the North Cape 
 and at all stations within the Arctic Circle. 
 
 87. A celestial globe will be of great use in studying these 
 diurnal phenomena. The north pole of the globe must be 
 elevated to an angle equal to the latitude of the observer, 
 which can be done by means of the degrees marked on the 
 metal meridian ring. It will then be seen at once what stars 
 never set, which ones never rise, and during what part of the 
 twenty-four hours any heavenly body at a known distance 
 from the equator is above or below the horizon. For descrip- 
 tion of the celestial globe, see Appendix, Art. 400. 
 
 TIME. 
 
 Time is usually denned as " measured duration," and the 
 standard unit of time has always been obtained in some way 
 from the length of the day. 
 
60 SOLAE TIME. [88 
 
 88. Apparent Solar Time. The most natural way, since 
 we are obliged to regulate our lives by the sun, is to reckon 
 time by him ; i.e., to call it noon when the sun is on the merid- 
 ian and highest, and to divide the day from one noon to 
 another into its hours, minutes, and seconds. Time thus 
 reckoned is called apparent solar time (see Appendix, Art. 
 422), which is the time shown by a correctly adjusted sun- 
 dial. But because the sun's eastward motion in the sky is 
 not uniform (owing to the oval form of the earth's orbit, and 
 its inclination to the equator), these apparent solar days are not 
 exactly of the same length. Thus, for instance, the interval 
 from noon of Dec. 22d to noon of Dec. 23d is nearly a minute 
 longer than the interval between the noons of Sept. 15th and 
 16th. As a consequence, it is only by very complicated and 
 expensive machinery that a watch or clock can be made to 
 keep time precisely with the sundial, and the attempt was 
 long ago given up. Apparent solar time is now used only in 
 communities where clocks and watches are rare, and sundials 
 are the usual timepieces. 
 
 89. Mean Solar Time. At present, for civil and business 
 purposes, time is almost universally reckoned in days all of 
 which have precisely the same length, and are just equal to 
 the average apparent solar day ; and this time, called mean 
 solar time (Appendix, Art. 422), is that which is kept by all 
 good timepieces. 
 
 Sundial time agrees with mean time four times a year; viz., upon 
 April 15th, June 14th, Sept. 1st, and Dec. 24th. The greatest differ- 
 ences occur on Nov. 2d and Feb. llth, when the sundial is respec- 
 tively 16 m 20" fast of the clock and 14 m 30 s slow. During the summer 
 the difference never exceeds 6 m . This difference is called the Equation 
 of Time, and is given in the almanac for every day in the year. 
 
 90. The Civil Day and the Astronomical Day. The astro- 
 nomical day begins at noon ; the civil day at midnight, twelve hours 
 earlier. Astronomical mean time is reckoned around through the 
 
90] SIDEREAL TIME. 61 
 
 whole twenty-four hours, instead of being counted in two series of 
 twelve hours each. Thus 8 A.M. of Tuesday, Aug. 12th, civil reck- 
 oning, is Monday, Aug. llth, 20 h , astronomical reckoning. Beginners 
 need to bear this in mind in referring to the almanac. 
 
 91. Sidereal Time, or Time reckoned by the Stars. As has 
 been said (Art. 17), the sun is not fixed on the celestial sphere, 
 but appears to creep completely around it once a year. The 
 interval from noon to noon does not therefore correspond to 
 the true diurnal revolution of the heavens. If we reckoned by 
 the interval between two successive passages of any given 
 star across the .observer's meridian, we should find that the 
 true day, the sidereal day, as it is called, is nearly 4 m shorter 
 (3 m 56 8 .9) than the ordinary solar day, the relation being such 
 that in a year the number of sidereal days exceeds that of solar 
 by exactly one. For many purposes, astronomers find it much 
 more convenient to reckon by the stars than by the sun. 
 They count the time, however, not by any real star, but from 
 the Vernal Equinox^ the sidereal clock being so set and regu- 
 lated that it always shows zero hours, minutes, and seconds, 
 at the moment when the Vernal Equinox is on the meridian 
 (see Appendix, Art. 422). This kind of time, of course, would 
 not answer for business purposes, since its noon comes at all 
 hours of the day and night at different seasons of the year. 
 The almanac gives data by which sidereal time and mean solar 
 time can be easily converted into each other. 
 
 92. The Determination of Time. In practice, the problem 
 always takes the shape of finding the error of a timepiece of 
 some sort; i.e., ascertaining how many seconds it is fast or 
 slow. The instrument now ordinarily used for the purpose is 
 the transit instrument, which is a small telescope mounted on 
 an axis, placed exactly east and west, and level, so that as the 
 telescope is turned it will follow the meridian ; at least, the 
 middle cross-wire in the field of view will do so. It is the 
 
62 TIME FROM THE STARS. [ 92 
 
 same as the meridian circle, except that it does not require 
 the costly graduated circle with its appendages. For descrip- 
 tion, see Appendix, Art. 416. 
 
 To determine with the transit the error of the sidereal clock 
 which is ordinarily used in connection with it, it is only neces- 
 sary to observe the exact time indicated by the clock when 
 some star whose right ascension is known passes, or "tran- 
 sits," the middle wire of the instrument. 
 
 93. The right ascension of a star (Art. 18) is the number of 
 ' hours ' of arc (measured along the equator) by which the star 
 is east of the vernal equinox ; and therefore when the star is 
 on the meridian, the right ascension also equals the number 
 of hours, minutes, and seconds since the transit of the vernal 
 equinox. In other words, we may say that the right ascension 
 of a star is the sidereal time at the moment of its meridian tran- 
 sit. (This is often called the observatory definition of right 
 ascension.) For instance, the right ascension of Vega (Alpha 
 Lyrse) is 18 h 33 m . If we observe its transit to occur at 18 h 40 m 
 by the clock, the clock is obviously 7 m fast. 
 
 With a good instrument, a skilled observer can thus deter- 
 mine the clock-error within about -^ of a second of time. 
 
 To get solar time, we may observe the sun itself, the moment 
 of its transit being ' apparent noon/ But it is better, and it 
 is usual, to get the sidereal time first, and to deduce from that 
 the solar time by means of the necessary data which are fur- 
 nished in the almanac. 
 
 The method by the transit instrument is most used, and is, on the 
 whole, the most convenient ; but since the instrument requires to be 
 mounted upon a firm pier, it is not always available. When not, we 
 use some one of various other methods, for which reference must be 
 made to the General Astronomy. At sea, and by travellers on scien- 
 tific expeditions, the time is usually determined by observing the alti- 
 tude of the sun with a sextant some hours before or after noon. (See 
 Appendix, Art. 427.) 
 
94] DETEKMINAT10N OF LONGITUDE. 63 
 
 LONGITUDE. 
 
 94. The problem of finding the longitude is in many respects 
 the most important of what may be called the "economic" 
 problems of astronomy ; i.e., those of business utility to man- 
 kind. The great observatories of Greenwich and Paris were 
 founded for the express purpose of furnishing the necessary 
 data to enable the sailor to determine his longitude at sea; 
 and the English government has given great prizes for the 
 construction of clocks and chronometers fit to be used in such 
 determinations. 
 
 The longitude of a place on the earth is defined as the 
 arc of the equator intercepted between the meridian which passes 
 through the place and some meridian which is taken as the 
 standard. 1 
 
 Now since the earth turns on its axis at a uniform rate, this 
 arc is strictly proportional to, and may be measured by, the 
 time intervening between the transits of any given star across 
 the two meridians. The longitude of a place may therefore 
 be defined as the amount by which the time at Greenwich is ear- 
 lier or later than the time at the station of the observer, and this 
 whether we reckon by solar or by sidereal time. Accordingly, 
 terrestrial longitude is' usually reckoned in hours, minutes, 
 and seconds, rather than in degrees. Since the observer can 
 easily find his own local time by the transit instrument, or by 
 some of the many other methods, the knot of the problem is 
 simply this : To find the Greenwich time at any moment with- 
 out going to Greenwich ; then we get the longitude at once by 
 simply comparing it with our own time. 
 
 95. Methods of determining Longitude. Incomparably the 
 best method, whenever it is available, is to make a direct tele- 
 
 1 As to the standard meridian, there is a variation of usage among dif- 
 ferent nations. The French reckon from* the meridian of Paris, but most 
 other nations use the meridian of Greenwich, at least at sea. 
 
64 LOCAL AND STANDARD TIME. C 95 
 
 graphic comparison between the clock of the observer and that 
 of some station, the longitude of which is known. The differ- 
 ence between the two clocks, duly corrected for their ' errors ' 
 (Art. 92), will be the true difference of longitude. The astro- 
 nomical difference of longitude between the two places can 
 thus be determined by four or five nights 7 observations within 
 about O s .01 i.e., within ten feet or so, in the latitude of the 
 United States. In many cases the telegraphic method, how- 
 ever, is not available ; never at sea, of course. 
 
 96. A second method is to use a chronometer, which is 
 simply a very accurate watch. This is set to Greenwich time 
 at some place whose longitude is known, and afterwards is 
 supposed to keep that time wherever carried. The observer 
 has only to compare his own local time, determined with the 
 transit instrument or sextant, with the time shown by such a 
 chronometer, and the difference is his longitude from Green- 
 wich. 
 
 Practically, of course, no chronometer goes absolutely without gain- 
 ing or losing ; hence, it is always necessary to know and to allow for 
 its gain or loss since the time it was last set. Moreover, it is never 
 safe to trust a single chronometer, because of the liability of such in- 
 struments to change their rate in transportation. A number should 
 be used, if possible. 
 
 Before the days of telegraphs and chronometers, astronomers 
 were generally obliged to get their Greenwich time from the 
 moon, which may be regarded as a clock-hand with the stars 
 for dial figures ; but observations of this kind are troublesome, 
 and the results inaccurate, as compared with those obtained 
 by the telegraph and chronometer. (For further details, see 
 General Astronomy, Arts. 109-116.) 
 
 97. Local and Standard Time. Until recently it has been 
 always customary to use local time, each station determining 
 its own time by its own observations, and having, therefore, 
 
97] WHERE THE DAY BEGINS. 65 
 
 a time differing from that of all other stations not on the same 
 meridian. Before the days of the telegraph, and while travel- 
 ling was comparatively slow, this was best. At present there 
 are many reasons why it is better to give up the old system in 
 favor of a system of standard time. The change greatly facil- 
 itates all railway and telegraphic business, and makes it prac- 
 tically easy for everybody to have accurate time, since the 
 standard time can be daily wired from some headquarters to 
 every telegraph office. 
 
 According to the system now established in North America, 
 there are five such standard times in use, the colonial, the 
 eastern, the central, the mountain, and the Pacific, which 
 differ from Greenwich time by exactly four, five, six, seven, 
 and eight hours respectively, the minutes and seconds being 
 everywhere identical, and the same with those of the clock at 
 Greenwich. In order to determine the standard time by obser- 
 vation, it is only necessary to find the local time by one of the 
 methods given, and correct it according to the observer's longi- 
 tude from Greenwich. 
 
 98. Where the Day begins. It is clear that if a traveller 
 were to start from Greenwich on Monday noon, and travel 
 westward as fast as the earth turns to the east beneath his 
 feet, he would have the sun upon the meridian all day long, 
 and it would be continual noon. But what noon ? It was 
 Monday when he started, and when he gets back to London 
 twenty-four hours later it will be Tuesday noon there, and yet 
 he has had no intervening night. When did Monday noon 
 become Tuesday noon ? 
 
 It is agreed among mariners to make the change of date at 
 the 180th meridian from Greenwich. Ships crossing this line 
 from the east skip one day in so doing. If it is Monday after- 
 noon when a ship reaches the line, it becomes Tuesday after- 
 noon the moment she passes it, the intervening twenty-four 
 hours being dropped from the reckoning on the log-book. 
 
66 POSITION OF A HEAVENLY BODY. [98 
 
 Vice versa, when a vessel crosses the line from the western 
 side, it counts the same day twice, passing from Tuesday back 
 to Monday. 
 
 This 180th meridian passes mainly over the ocean, hardly touching 
 land anywhere. There is some irregularity as to the date actually 
 used on the different islands of the Pacific. Those which received 
 their earliest European inhabitants via the Cape of Good Hope, have, 
 for the most part, adopted the Asiatic date, even if they really lie east 
 of the 180th meridian, while those which were first approached via 
 Cape Horn have the American date. When Alaska was transferred 
 from Russia to the United States, it was necessary to drop one day of 
 the week from the official dates. 
 
 DETERMINATION OF THE POSITION OF A HEAVENLY 
 BODY. 
 
 As the basis of our investigations in regard to the motions 
 of the heavenly bodies, we require a knowledge of their 
 places in the sky at known times. By the " place " of a body, 
 we mean its right ascension and declination. 
 
 99. By the Meridian Circle (see Appendix, Art. 418). If a 
 body is bright enough to be seen by the telescope of the merid- 
 ian circle, and comes to the meridian in the night-time, its 
 right ascension and declination are best determined by that 
 instrument. If the instrument is in exact adjustment, the 
 right ascension of the body is simply the sidereal time when it 
 crosses the middle vertical wire of the reticle. The 'circle- 
 reading/ on the other hand, corrected for refraction, gives the 
 declination. A single complete observation with the meridian 
 circle determines accurately both the right ascension and the 
 declination of the object. 
 
 100. By the Equatorial. If the body a comet, for instance 
 is too faint to be observed by the telescope of the meridian 
 circle, seldom very powerful, or comes to the meridian only in 
 
100] DETERMINATION OF POSITION. 67 
 
 the daytime, we usually accomplish our object by using the 
 equatorial (Appendix, Art. 414), and determine the position 
 of the body by measuring with some kind of ' micrometer ? 
 the difference of right ascension and declination between it 
 and a neighboring star whose place is given in some star- 
 catalogue. 
 
 d 
 
 . i 
 
68 THE EARTH. [ 101 
 
 CHAPTER IV. 
 
 THE EARTH: ITS FORM AND DIMENSIONS; ITS ROTATION, 
 MASS, AND DENSITY; ITS ORBITAL MOTION AND THE 
 
 SEASONS. PRECESSION. THE YEAR AND THE CAL- 
 ENDAR. 
 
 101, In a science which deals with the ' heavenly bodies/ 
 there might seeni at first no place for the Earth. But certain 
 facts relating to the Earth, just such as we have to investi- 
 gate with respect to her sister planets, are ascertained by astro- 
 nomical methods, and a knowledge of them is essential as a 
 base of operations. In fact, Astronomy, like charity, "begins 
 at home," and it is impossible to go far in the study of the 
 bodies which are strictly " heavenly " until we have first ac- 
 quired some accurate knowledge of the dimensions and motions 
 of the Earth itself. 
 
 102. The astronomical facts relating to the Earth are 
 broadly these : 
 
 1. The earth is a great ball about 7920 miles in diameter. 
 
 2. It rotates on its axis once in twenty-four "sidereal" 
 hours. 
 
 3. It is not exactly spherical, but is slightly flattened at the 
 poles ; the polar diameter being nearly twenty-seven miles, or 
 ^ part less than the equatorial. 
 
 4. It has a mean density of about 5.6 times that of water, 
 and a mass represented in tons by 6 with twenty-one ciphers 
 following, (six thousand millions of millions of millions of 
 tons.) 
 
 5. It is flying through space in its orbital motion around 
 the sun, with a velocity of about eighteen and a half miles a 
 
102] THE EARTH'S FORM AND SIZE. 69 
 
 second; i.e., about seventy-five times as swiftly as an ordinary 
 cannon-ball. 
 
 103. The Earth's Approximate Form and Size. It is not 
 
 necessary to dwell on the ordinary proofs of the earth's globu- 
 larity. We simply mention them. 
 
 1. It can be sailed around. 
 
 2. The appearance of vessels coming in from the sea indi- 
 cates that the surface is everywhere convex. 
 
 3. The fact that as one goes from the equator towards the 
 north the elevation of the pole increases in proportion to the 
 distance from the equator, proves the same thing. 
 
 4. The outline of the earth's shadow, as seen upon the moon 
 during lunar eclipses, is such as only a sphere could cast. 
 
 We may add, as to the smoothness and roundness of the 
 earth, that if the earth be represented by an eighteen-inch 
 globe, the difference between its greatest and least diameters 
 would be only about one-sixteenth of an inch ; the highest 
 mountains would project only about one-ninetieth of an inch, 
 and the average elevation of continents and depths of the 
 ocean would be hardly greater than a film of varnish. Eela- 
 tively, the earth is really much smoother and rounder than 
 most of the balls in a bowling-alley. 
 
 104. One of the simplest methods of showing the curvature of the 
 earth is the following : 
 
 In an expanse of still, shallow water (a long reach of canal, for 
 instance), set a row of three poles about a mile apart, with their tops 
 projecting to exactly the same height above the surface. On sighting 
 across, it will then be found that the middle pole projects about eight 
 inches above the line that joins the tops of the two end ones, and from 
 this a rough estimate of the size of the earth can be made (see General 
 Astronomy, Art. 134). 
 
 105. Measure of the Earth's Diameter. The only accurate 
 method of measuring the diameter of the earth is the follow- 
 
70 
 
 THE EAETH'S DIAMETER. 
 
 [105 
 
 ing, the principle of which is very simple, and should be thor- 
 oughly mastered by the student : 
 
 It consists in finding the length in miles of an arc of the 
 earth's surface containing a known number of degrees. From 
 
 this we get the length of one degree, 
 and this gives the circumference of 
 the earth (since it contains 360), 
 and from this the diameter is ob- 
 tained by dividing it by 3.14159. 
 
 To do this, we select two sta- 
 tions, a and b (Fig. 8), some hun- 
 dreds of miles apart on the same 
 meridian, and determine the lati- 
 tude (or the altitude of the pole) at 
 each station by astronomical obser- 
 vation. The difference of latitude 
 (i.e., ECb ECa) is evidently the 
 number of degrees in the arc ab, 
 and the determination of this dif- 
 ference of latitude is the only astro- 
 nomical operation necessary. 
 
 Next, the distance in miles be- 
 tween the two stations must be 
 measured. This is geodetic work, and it is enough for our 
 purpose here to say that it can be done with great precision by 
 a process which is called ' triangulation.' 
 
 This measuring of arcs has been done on many parts of the 
 earth's surface, and the result is that the average length of a 
 degree is found to be a little more than sixty-nine miles, and 
 the mean diameter of the earth about 7918 miles. The reason 
 why we say average length and mean diameter is that the 
 earth, as has been said, is not quite a globe, but is slightly 
 flattened at its poles, so that the lengths of the degrees dif- 
 fer in different parts of the earth, as we shall soon see (Art. 
 110). 
 
 FIG. 8. Measuring the Earth's 
 Diameter. 
 
106] THE ROTATION OF THE EARTH. 71 
 
 106. The Rotation of the Earth. Ptolemy understood that 
 the earth was round, but he and all his successors deliberately 
 rejected the theory of its rotation. Though the idea that the 
 earth might turn upon an axis was not unfamiliar, they con- 
 sidered that there were conclusive reasons against it. At the 
 time when Copernicus of Thorn, in Poland (1473-1543), pro- 
 posed his theory of the solar system, the only argument he 
 could urge in favor of the earth's rotation 1 was that this 
 hypothesis was much more probable than the older one that 
 the heavens themselves revolve. All the phenomena then 
 known would be sensibly the same on either supposition. The 
 apparent daily motion of the heavenly bodies can be perfectly 
 accounted for (within the limits of such observations as were 
 then possible) either by supposing that they are actually at- 
 tached to the celestial sphere, which turns daily, or that the 
 earth itself spins upon an axis once in twenty-four hours ; and 
 for a long time the latter hypothesis did not seem to most 
 people so reasonable as the older and more obvious one. A 
 little later, after the telescope had been invented, analogy 
 could be appealed to ; for we can see with the telescope that 
 the sun and moon and many of the planets really rotate upon 
 axes. At present we can go still farther, and can absolutely 
 demonstrate the earth's rotation by experiments, some of 
 which even make it visible. 
 
 107. Foucault's Pendulum Experiment. Among these ex- 
 perimental proofs, the most impressive is the "pendulum 
 experiment" devised by Foucault in 1851. From the dome 
 of the Pantheon, in Paris, he hung a heavy iron ball by a 
 slender wire more than 200 feet long (Fig. 9). A circular rail, 
 
 1 The word rotation denotes a spinning motion, like that of a wheel on 
 its axis. The word revolve is more general, and may be used to describe 
 such a spinning motion, or (and this is the more common use in Astron- 
 omy) to describe the motion of a body travelling around another, as when 
 we say the earth revolves ' around the sun. 
 
FOUCAULT'S PENDULUM EXPERIMENT. 
 
 [107 
 
 with a little ridge of sand built upon it, was placed in such a 
 
 way that a pin attached to the swinging ball would just scrape 
 
 the sand and leave a mark at 
 each vibration. To put the 
 ball in motion, it was drawn 
 aside by a cotton cord and 
 left for some hours, until 
 it came absolutely to rest. 
 Then the cord was burned 
 off, and the pendulum started 
 to swing in a true plane. 
 
 But this plane at once be- 
 gan to deviate slowly towards 
 the right, so that the pin on 
 the pendulum ball cut the 
 sand ridge in a new place at 
 each swing, shifting at a rate 
 which would carry the line 
 fully around in about thirty- 
 two hours, if the pendulum 
 did not first come to rest. In 
 fact, the floor was actually 
 
 and visibly turning under the plane defined by the swinging 
 
 of the pendulum. 
 
 The experiment created great enthusiasm at the time, and has since 
 been frequently performed. The pendulum used in such experiments 
 must, in order to secure success, have a round ball, must be suspended 
 by a round wire or on a point, and must be very heavy, very long, and 
 very carefully protected against currents of wind. At the pole the 
 plane of the pendulum will shift completely around once in twenty- 
 four hours ; at the equator, it will not turn at all ; and in the interme- 
 diate regions, it will shift more or less rapidly according to the latitude 
 of the place where the experiment is performed. (For fuller descrip- 
 tion, see General Astronomy, Arts. 140, 141.) 
 
 There are a number of other experimental proofs of the earth's rota- 
 tion, which are really just as conclusive as the one above cited. (Gen- 
 eral Astronomy, Arts. 138-144.) 
 
 FIG. 9. Foucault's Pendulum Experiment. 
 
108 ] THE EARTH'S ROTATION. 73 
 
 108. Invariability of the Earth's Rotation, It is a question 
 of great importance whether the day ever changes its length. 
 Theoretically, it must almost necessarily do so. The friction 
 of the tides and the fall of meteors upon the earth both tend 
 to retard the rotation, while, on the other hand, the earth's 
 loss of heat by radiation and the consequent shrinkage of the 
 globe must tend to accelerate it, and to shorten the day. Then 
 geological changes, the elevation and subsidence of continents, 
 and the transportation of soil by rivers, act, some one way and 
 some the other. At present we can only say that the change, 
 if any change has occurred since Astronomy became accurate, 
 has been too small to be detected. The day is certainly not 
 longer or shorter by the y-^-g- part of a second than it was in 
 the days of Ptolemy; probably it has not changed by the 
 P ar t ^ a second, though of that we can hardly be sure. 
 
 109. Permanence of the Earth's Axis. Another equally in- 
 teresting question is whether the earth's axis is, or is not, absolutely 
 fixed in its position within the globe. Theoretically, any changes 
 which may occur in the distribution of matter upon the surface by 
 rivers or ocean currents, for instance, should displace the axis more 
 or less. But thus far, until very recently, the changes, if real, have 
 been too small for detection. In 1889, however, observers at several 
 stations in Germany, working together, seem to have proved that dur- 
 ing the summer of that year a small displacement of the north pole, 
 amounting to some forty or fifty feet, actually did occur, changing the 
 latitudes of German observatories by about 0".5. We mention this 
 mainly to prevent the student from conceiving of the earth's axis as a 
 real rod running through it, like the axle of a wheel. The axis is 
 only an imaginary line, like the axis of a base-ball which spins as it 
 flies through the air. There is nothing to prevent the axis from shift- 
 ing about within the earth if any force operates sufficient to displace 
 it. 
 
 110. Effect of the Earth's Rotation on its Form. The 
 
 whirling of the earth on its axis tends to make the globe 
 bulge at the equator and flatten at the poles, in the way illus- 
 
74 
 
 THE EARTH'S ROTATION. 
 
 [110 
 
 trated by the well-known little apparatus shown in Fig. 10. 
 
 That the equator does really bulge in this way is shown by 
 
 measuring the length of a 
 degree of latitude on the va- 
 rious parts of the earth's 
 surface between the equator 
 and the pole, in the manner 
 indicated a few pages back 
 (Art. 105). More than 
 twenty such arcs have been 
 measured, and it appears 
 that the length of the de- 
 
 }. 10. Effect of Earth's Rotation on its Form. OTPP.S increases regularly 
 
 from the equator towards the poles, as shown in the following 
 table: 
 
 At the equator, one degree = 68.704 miles 
 
 At lat. 20 
 
 (( II 4.QO 
 
 " 60 
 
 ( gQO 
 
 At the pole, 
 
 = 68.786 
 = 68.993 
 = 69.230 
 
 = 69.407 
 
 The difference between the equatorial and polar degree of 
 latitude is more than 0.7 of a mile, or over 3700 feet, while 
 the probable error of measurement cannot exceed a foot or 
 two to the degree. 
 
 From this table it can be calculated, by methods which 
 cannot be explained without assuming too much mathematical 
 knowledge in our readers, that the earth is orange-shaped, or 
 "an oblate spheroid," the diameter from pole to pole being 
 7899.74 miles, while the equatorial diameter is 7926.61 miles. 
 The difference, 26.87 miles, is about -g^-g- of the equatorial 
 diameter. This fraction, ^i-j, is called the oblateness or ellip- 
 ticity of the earth. 
 
 Scholars are often puzzled by the fact that although the pole is 
 nearer the centre of the earth than the equator, yet the degrees of lat- 
 
H] SURFACE AND VOLUME OF THE EARTH. 75 
 
 itude are longest at the pole. It is because the earth's surface there is 
 more nearly flat than anywhere else, so that a person has to travel 
 more miles to change the 
 direction of his plumb- 
 line one degree. Fig. 11 
 illustrates this. The an- 
 gles adb andfhg are equal, 
 but the arc ab is longer 
 than fg. 
 
 111. Effect of the 
 Earth's Rotation and 
 
 Ellipticlty Upon the Fm - n - Length of Degrees in Different Latitudes. 
 
 Force of Gravity. For two reasons the force of gravity is 
 less at the equator than at the poles. (1) The surface of the 
 earth is there 13^- miles farther from the centre, and this fact 
 diminishes the gravity at the equator by about -5-^. (2) The 
 centrifugal force of the earth's rotation reduces the gravity at 
 the equator by about -^-g- ; the whole reduction, therefore (-3-3-5- 
 -f 2-f^X i s ver y nearly equal to -^ ; i.e., an object which weighs 
 190 pounds at the equator would weigh 191 pounds near the pole, 
 weighed by an accurate spring-balance. (In an ordinary bal- 
 ance, the loss of weight would not show, simply because the 
 weights themselves would be affected as much as the body 
 weighed, so that the balance would not be disturbed.) The 
 effect of this variation of gravity from the pole to the equator 
 is especially evident in the going of a pendulum clock. Such 
 a clock, adjusted to keep accurate time at the equator, would 
 gain 3 m 37 s a day near the pole. In fact, one of the best ways 
 of determining the form of the earth is by experiments with a 
 pendulum at stations which differ considerably in latitude. 
 
 112. Surface and Volume of the Earth. The earth is so 
 nearly spherical that we can compute its surface and volume 
 with sufficient accuracy by the formula for a perfect sphere, 
 provided we put the earth's mean semi-diameter for the radius 
 
76 THE EARTH'S MASS AND DENSITY. [ 112 
 
 of the sphere. This mean semi-diameter is not the average of 
 the polar and equatorial diameters, but is found by adding the 
 polar diameter to twice the equatorial, and dividing by three. 
 It comes out 7917.66 miles. From this we find the earth's 
 surface to be, in round numbers, 197,000000 square miles, and 
 its volume, or bulk, 260000,000000 cubic miles. 
 
 113. The Earth's Mass and Density. The volume (or bulk) 
 of a globe is simply the number of cubic miles of space which 
 it contains. If the earth were all made of feathers or of lead, 
 its volume would remain the same, as long as the diameter 
 was not altered. The earth's mass, on the other hand, is the 
 quantity of matter in it the number of tons of rock and 
 water which compose it, and of course it makes a great dif- 
 ference with this whether the material be heavy or light. 
 The density of the earth is the number of times its mass 
 exceeds that of a sphere of pure water having the same 
 dimensions. 
 
 ^^*^\. 
 
 The methods by which the mass of the earth can be measured 
 depend upon a comparison between the attraction which the earth 
 exerts upon a body at its surface and the attraction which is exerted 
 upon the same body by another large body of known mass and at a 
 known distance. The experiments are delicate and difficult, and we 
 must refer for details to our larger book, General Astronomy, Arts. 
 164-179. 
 
 The most recent operations of the kind have been conducted 
 at Potsdam in 1887-88, and they show that the density of the 
 earth is about 5.58 times that of water, and its mass in tons 
 about 6000 millions of millions of millions, as before stated in 
 Art. 102. 
 
 114. Constitution of the Earth's Interior. Since the average 
 density of the earth's crust does not exceed three times that 
 of water, while the mean density of the whole earth is about 
 5.58, it is clear that at the earth's centre the density must be 
 
 
114] THE SUN AND THE EARTH. 77 
 
 very much, greater than at the surface. Very likely it is as 
 high as eight or ten times the density of water, and equal to 
 that of the heavier metals. 
 
 There is nothing surprising in this. If the earth were once fluid, it 
 is natural to suppose that the densest materials, in the process of 
 solidification, would settle towards the centre. 
 
 Whether the centre of the earth is now solid or fluid, it is difficult 
 to say with certainty. Certain tidal phenomena, to be mentioned 
 hereafter, have led Sir William Thomson to conclude that the earth as 
 a whole is solid throughout, and " more rigid than glass," volcanic cen- 
 tres being mere "pustules," so to speak, in the general mass. To this 
 most geologists demur, maintaining that at the depth of not many 
 hundred miles the materials of the earth must be fluid, or at least 
 semi-fluid. They infer this from the phenomena of volcanoes, and 
 from the fact that the temperature continually increases with the 
 depth, so far at least as we have yet been able to penetrate. 
 
 THE APPARENT MOTION OF THE SUN AND THE ORBITAL 
 MOTION OF THE EARTH, AND THEIR IMMEDIATE CON- 
 SEQUENCES. 
 
 115. The Sun's Apparent Motion among the Stars. The 
 
 sun's apparent motion among the stars, which makes it describe 
 the circuit of the heavens once a year, must have been among 
 the earliest recognized astronomical phenomena, as it is one 
 of the most important. The sun, starting in the spring, 
 mounts northward in the sky each day at noon for three 
 months, appears to stand still a few days at the summer sol- 
 stice, and then descends towards the south, reaching in autumn 
 the same noon-day elevation which it had in the spring. It 
 keeps on its southward course to the winter solstice (in Decem- 
 ber), and then returns to its original height at the end of a 
 year, by its course causing and marking the seasons. 
 
 Nor is this all. The sun's motion is not merely north and 
 south, but it also advances continually eastward among the stars. 
 It is true that we cannot see the stars near the sun in the 
 
78 THE ECLIPTIC. [ 115 
 
 same way that we can those about the moon, so as to be able 
 directly to perceive this motion ; but in the spring the stars 
 which are rising in the eastern horizon are different from 
 those which are found there in the summer or in the winter. 
 In March the most conspicuous of the eastern constellations 
 at sunset are Leo and Bootes. A little later Virgo appears ; in 
 the summer Ophiuchus and Libra ; still later Scorpio ; while 
 in midwinter Orion and Taurus are ascending as the sun goes 
 down. 
 
 So far as the obvious appearances are concerned, it is quite 
 indifferent whether we suppose the earth to revolve around 
 the sun, or vice versa. That the earth really moves, hoVever, 
 is absolutely demonstrated by two phenomena too minute and 
 delicate for observation without the telescope, but accessible 
 to modern methods. One of them is the aberration of light, 
 the other the annual parallax of the fixed stars. These can be 
 explained only by the actual motion of the earth, but we post- 
 pone their discussion for the present (see Art. 343, and Appen- 
 dix, 435). 
 
 116. The Ecliptic ; its Related Points and Circles. By ob- 
 serving daily with the meridian circle the sun's declination 
 and the difference between its right ascension and that of 
 some standard star, we obtain a series of positions of the sun's 
 centre which can be plotted on the globe, and we can thus 
 mark out the path of the sun among the stars. It turns out 
 to be a great circle, as is shown by its cutting the celestial equa- 
 tor at two points just 180 apart (the so-called " equinoctial 
 points" or "equinoxes"), where it makes an angle with the 
 equator of approximately 23y (23 27' 14" in 1890). 
 
 This great circle is called the Ecliptic, because, as was early 
 discovered, eclipses happen only when the moon is crossing 
 it. Its position among the constellations is shown upon the 
 equatorial star-maps. It may be defined as the circle in which 
 the plane of the earth's orbit cuts the celestial sphere. 
 
116] THE ZODIAC. 79 
 
 The angle which, the ecliptic makes with the equator at the 
 equinoctial points is called the obliquity of the Ecliptic. This 
 obliquity is evidently equal to the sun's greatest distance from 
 the equator; i.e., its maximum declination, which is reached in 
 December and June. 
 
 117. The two points in the ecliptic midway between the 
 equinoxes are called the solstices, because at these points the 
 sun " stands " ; that is, ceases to move north or south. Two 
 circles drawn through the solstices parallel to the equator are 
 called the tropics, or " turning-lines," because there the sun 
 turns from its northward motion to the southward, or vice 
 versa. The two points in the heavens 90 distant from the 
 ecliptic are called the poles of the ecliptic. The northern one 
 is in the constellation of Draco, about midway between the 
 stars Delta and Zeta Draconis, at a distance from the pole of 
 the heavens equal to the obliquity of the ecliptic, or about 
 23 y, and on the Solstitial Colure, the hour-circle which runs 
 through the two solstices, the hour-circle which passes through 
 the equinoxes being called the Equinoctial Colure. Great 
 circles drawn through the poles of the ecliptic, and therefore 
 perpendicular, or " secondaries," to the ecliptic, are known as 
 circles of latitude. It will be remembered (Art. 20) that celes- 
 tial longitude and latitude are measured with reference to the 
 ecliptic, and not to the equator. 
 
 118. The Zodiac and its Signs. A belt 16 wide (8 on 
 each side of the ecliptic) is called the Zodiac, or zone of ani- 
 mals, the constellations in it, excepting Libra, being all figures 
 of animals. It is taken of that particular width simply 
 because the moon and all the principal planets always keep 
 within it. It is divided into the so-called signs, each 30 in 
 length, having the following names and symbols : 
 
80 THE EARTH'S ORBIT. [ us 
 
 ( Aries T ( Libra =2= 
 
 Spring I Taurus 8 Autumn < Scorpio nt 
 
 ( Gemini n ( Sagittarius / 
 
 ( Cancer 05 ( Capricornus VJ 
 
 Summer < Leo SI Winter < Aquarius ^ 
 
 ( Virgo Ttj? ( Pisces X 
 
 The symbols are for the most part conventionalized pictures of the 
 objects. The symbol for Aquarius is the Egyptian character for 
 water. The origin of the signs for Leo, Capricornus, and Virgo is 
 not quite clear. 
 
 The zodiac is of extreme antiquity. In the zodiacs of the 
 earliest history, the Fishes, Ram, Bull, Lion, and Scorpion 
 appear precisely as now. 
 
 119. The Earth's Orbit. The ecliptic must not be con- 
 founded with the earth's orbit. It is simply a great circle of 
 the infinite celestial sphere, the trace made upon that sphere 
 by the plane of the earth's orbit, as was stated in its definition. 
 The fact that the ecliptic is a great circle gives us no informa- 
 tion about the earth's orbit itself, except that it lies in one 
 plane passing through the sun. It tells us nothing as to the 
 orbit's real form and size. 
 
 By reducing the observations of the sun's right ascension 
 and declination through the year to longitude and latitude 
 (the latitude would always be exactly zero except for some 
 slight perturbations due chiefly to the moon's revolution 
 around the earth), and combining these data with observations 
 of the sun's apparent diameter, we can, however, ascertain the 
 form of the earth's orbit and the law of its motion. The size 
 of the earth's orbit, i.e., its scale of miles, cannot be fixed until 
 we find the sun's distance. 
 
 The result is that the orbit is found to be very nearly a 
 circle, but not exactly so. It is an oval or ellipse, with the sun 
 at one of its foci (as illustrated in Fig. 12), but is much more 
 
119] 
 
 DEFINITION OF TERMS. 
 
 81 
 
 nearly circular than the oval there represented. Its eccen- 
 tricity is only about -fa ; that is to say, the distance from the 
 centre of the sun to the mid- 
 dle of the ellipse is only about 
 J^ of the average distance of 
 the sun from the earth. 
 
 The method by which we 
 proceed to ascertain the form 
 of the orbit may be found in 
 the Appendix, Art. 428. For 
 a description of the ellipse, 
 see Art. 429. FlQ - '-' rhe E1Ii P 8e - 
 
 120. Definition of Terms. The points where the earth is 
 nearest to and most remote from the sun are called respec- 
 tively the Perihelion and the Aphelion (Dec. 31st and June 
 30th), the line joining them being the major axis of the orbit. 
 This line, indefinitely produced in both directions, is called 
 the ( Line of Apsides' (pronounced Ap'-si-deez), the major axis 
 being a limited piece of it. A line drawn from the sun to the 
 earth, or to any other planet at any point in its orbit, as SP in 
 Fig. 12, is called the planet's Radius Vector. 
 
 The variations in the sun's apparent diameter due to our 
 changing distance are too small to be detected without a 
 telescope, so that the ancients failed to perceive them. Hip- 
 parchus, however, about 120 B.C., discovered that the earth is 
 not in the centre 1 of the circular orbit which he supposed the 
 sun to describe around it with uniform velocity. 
 
 Obviously the sun's apparent motion is not uniform, because 
 it takes 186 days for the sun to pass from the vernal equinox, 
 
 1 Hipparchus (and every one else until the time of Kepler, 1607) 
 assumed on metaphysical grounds that the sun^s orbit must necessarily 
 be a circle, and described with a uniform motion, because (they said) the 
 circle is the only perfect curve, and uniform motion is the only perfect 
 motion proper for heavenly bodies. 
 
82 LAW OF THE EARTH'S MOTION. [ 120 
 
 March 20th, to the autumnal, Sept. 22d and only 179 days to 
 return. Hipparchus explained this on the hypothesis that the 
 earth is out of the centre of the circle. 
 
 121. The Law of the Earth's Motion. By combining the 
 measured apparent diameter of the sun with the differences of 
 longitude from day to day, we can deduce mathematically not 
 
 only the form of the earth's or- 
 bit, but the law of her motion in 
 it. It can be shown from the 
 comparison that the earth moves 
 in such a way that its radius 
 vector describes areas proportional 
 to the time, a law which Kepler 
 first brought to light in 1609 j 
 that is to say, if ab, cd } ef (Fig. 
 
 Fio.l3.-E q uableDe 8 criptionof Areas. ^ ^ portions Q f the orbit de _ 
 
 scribed by the earth in different weeks, the areas of the ellip- 
 tical sectors aSb, cSd, and eSf are all equal. A planet near 
 perihelion moves faster than at aphelion in just such propor- 
 tion as to preserve this relation. 
 
 As Kepler left the matter, this is a mere fact of observation. 
 Newton afterwards proved that it is the necessary mechanical 
 consequence of the fact that the earth moves under the action 
 of a force always directed towards the sun. 
 
 It is true in every case of the elliptical motion of a heavenly body, 
 and enables us to find the position of the earth or of any planet, when 
 we once know the time of its orbital revolution (technically the 
 "period "), and the time when it was last at perihelion. The solution 
 of the problem, first worked out by Kepler, lies, however, quite beyond 
 the scope of the present work. 
 
 122. Changes in the Earth's Orbit. The orbit of the earth 
 changes slowly in form and position, though in the long run 
 it is absolutely unchangeable as regards the length of its 
 major axis and the duration of the year. 
 
122] 
 
 THE SEASONS. 
 
 83 
 
 These so-called "secular changes" are due to "perturba- 
 tions" caused by the action of the other planets upon the 
 earth. Were it not for their attraction the earth would keep 
 her orbit with reference to the sun and stars absolutely 
 unaltered from age to age. 
 
 Besides these secular perturbations of the earth's orbit, the 
 earth itself is also continually being slightly disturbed in its 
 orbit. On account of its connection with the moon, it oscil- 
 lates each month a few hundred miles above and below the 
 true plane of the ecliptic, and by the action of the other 
 planets is sometimes set backwards or forwards in its orbit to 
 the extent of some thousands of miles. Of course every such 
 displacement of the earth produces a corresponding slight 
 change in the apparent position of the sun and of the nearer 
 planets. 
 
 Autumnal Equinox 
 
 Perihelia 
 
 Vernal Equinox 
 FIG. 14. The Seasons. 
 
 123. The Seasons. The earth in its motion around the sun 
 always keeps its axis nearly parallel to itself during the whole 
 year, for the mechanical reason that a spinning globe main- 
 
84 THE SEASONS. [ 123 
 
 tains the direction of its axis invariable, unless disturbed by 
 some outside force (very prettily illustrated by the gyro- 
 scope). Fig. 14 shows the way in which the north pole of 
 the earth is tipped with reference to the sun at different 
 seasons of the year. At the vernal equinox (March 20th) the 
 earth is situated so that the plane of its equator passes 
 through the sun. At that time, therefore, the circle which 
 bounds the illuminated portion of the earth passes through 
 the two poles, as shown in Fig. 15, B, and day and night are 
 
 therefore equal, as implied by the 
 term ' equinox.' The same is again 
 true on the 22d of September. 
 About the 21st of June the earth is 
 so situated that its north pole is 
 inclined towards the sun by about 
 FIG. is. -Position of Pole at Solstice 23, as shown in Fig. 15, A. The 
 and Equinox. south pole is then in the unlighted 
 
 half of the earth's globe, while the north pole receives sunlight 
 all day long, and in all portions of the northern hemisphere 
 the day is longer than the night. In the southern hemi- 
 sphere, on the other hand, the reverse is true. 
 
 At the time of the winter solstice the southern pole has per- 
 petual sunshine, and the north pole is in the night. At the 
 equator of the earth, day and night are equal at all times of 
 the year, and at that part of the earth there are no seasons in 
 the proper sense of the word. Everywhere else the day and 
 night are unequal, except when the sun is at one of the 
 equinoxes. 
 
 In high latitudes the inequality between the lengths of the 
 day in summer and in winter is very great; and at places 
 within the polar circle there are always days in winter when 
 the sun does not rise at all, and others in the summer when it 
 does not set, but we have the phenomenon of the " midnight 
 sun," as it is called. At the pole itself, the summer is one 
 perpetual day, six months in length, while the winter is a six- 
 months night. 
 
123] EFFECTS ON TEMPERATURE. 85 
 
 Perhaps the student will get a better idea by thinking of the earth 
 as a globe floating, just half immersed, on a sheet of still water, and so 
 weighted that its poles dip at an angle of 23 , while it swims in a 
 circle around the sun, a much larger globe, also floating on the same 
 surface. The sheet of water corresponds to the ecliptic, while the 
 plane of the equator is a circle on the globe itself, drawn square to the 
 axis. If, now, the axis is kept pointing always the same way while 
 the globe swims around, things will correspond to the motion of the 
 earth around the sun. 
 
 124. Effects on Temperature. The changes in the dura- 
 tion of insolation (exposure to sunshine) at any place involve 
 changes of temperature, thus producing the seasons. It is 
 clear that the surface of the soil at any place in the northern 
 hemisphere will receive daily from the sun more than the. 
 average amount of heat when- 
 ever he is north of the celestial 
 equator, and for two reasons : 
 
 1. Sunshine lasts more than 
 half the day. 
 
 2. The mean altitude of the 
 sun during the day is greater 
 
 than the average, since he is FIG 16 
 
 higher at noon than at the time Effect of Sun's Elevation on Amount of 
 
 of the equinox, and in any case Heat im P arte <* to ^ sou. 
 
 reaches the horizon at rising and setting. 
 
 Now the more obliquely the rays strike, the less heat they 
 bring to each square inch of surface, as is obvious from Fig. 
 16. A beam of sunshine which would cover the surface AC, 
 if received squarely, will be spread over a much larger sur- 
 face, Ac, if it falls at the angle h. The difference in favor of 
 vertical rays is further exaggerated by the absorption of heat 
 in our atmosphere, because the rays that are nearly horizontal 
 have to traverse a much greater thickness of air before reach- 
 ing the ground. 
 
 For these two reasons, therefore, the temperature rises 
 
86 PRECESSION OF THE EQUINOXES. [ 124 
 
 rapidly for a place in the northern hemisphere as the sun 
 comes north of the equator. We, of course, recei\e the most 
 heat in twenty-four hours at the time of the summer solstice ; 
 but this is not the hottest time of the summer. The weather 
 is then getting hotter, and the maximum will not be reached 
 until the increase ceases ; i.e., not until the amount of heat 
 lost in twenty-four hours equals that received in the same 
 time. This maximum is reached in our latitude about the 1st 
 of August. For similar reasons the minimum temperature in 
 winter occurs about Feb. 1st. 
 
 125. Precession of the Equinoxes. This is a slow westward 
 motion of the equinoxes along the ecliptic. In explaining the 
 seasons we have said (Art. 123) that the earth keeps its axis 
 nearly parallel to itself during its annual revolution. It does 
 not maintain strict parallelism, however, but owing to the 
 attraction of the sun and moon on that portion of the mass of 
 the earth which projects, like an equatorial ring, beyond the 
 true spherical surface, the earth's axis continually but slowly 
 shifts its place, keeping always nearly the same inclination to 
 the plane of the ecliptic, so that its pole revolves in a small 
 circle of 23^- radius around the pole of the ecliptic once in 
 25,800 years. Of course the celestial equator must move also, 
 since it has to keep everywhere just 90 from the celestial 
 pole ; and, as a consequence, the equinoxes move westward on 
 the ecliptic about 50".2 each year, as if to meet the sun. 
 This motion of the equinox was called ' precession ' by Hip- 
 parchus, who discovered 1 it about 125 B.C., but could not 
 explain it. The explanation was not reached until the time of 
 Newton, about 200 years ago. 
 
 126. Effect of Precession upon the Pole and the Zodiac. 
 
 At present the Pole-star, Alpha Ursae Minoris, is about 1^ 
 
 1 He discovered it by finding that in his time the place of the equinox 
 among the stars was no longer the same that it used to be in the days of 
 Homer and Hesiod, several hundred years before. 
 
126] THE YEAR AND THE CALENDAR. 87 
 
 from the pole, while in the time of Hipparchus the distance 
 was fully 12. During the next century the distance will 
 diminish to about 30', and then begin to increase. 
 
 If upon the celestial globe we trace a circle of 23^- radius, 
 around the pole of the ecliptic as a centre, it will mark the 
 track of the celestial pole among the stars. 
 
 It passes not very far from Alpha Lyrse (Vega), on the opposite 
 side of the circle from the present Pole-star ; about 12,000 years hence 
 Vega will, therefore, be the Pole-star. Reckoning backwards, we find 
 that some 4000 years ago Alpha Draconis (Thuban) was the Pole-star, 
 and about 3 from the pole. 
 
 Another effect of precession is that the signs of the zodiac 
 do not now agree with the constellations which bear the same 
 name. The sign of Ares is now in the constellation of Pisces, 
 and so on ; each sign having " backed " bodily, so to speak, 
 into the constellation west of it. 
 
 The forces which cause precession do not act quite uni- 
 formly, and as a result the rapidity of the precession varies 
 somewhat, and there is also a slight tipping or nodding of the 
 earth's axis which is called nutation. (For a fuller account of 
 the whole matter, see General Astronomy, Arts. 209-215.) 
 
 THE YEAE AND THE CALENDAR 
 
 127. Three different kinds of "year" are now recognized, 
 the Sidereal, the Tropical (or Equinoctial)) and the Anom- 
 alistic. 
 
 The sidereal year, as its name implies, is the time occu- 
 pied by the sun in apparently completing the circuit from a 
 given star to the same star again. Its length is 365 days, 
 6 hours, 9 minutes, 9 seconds. From the mechanical point of 
 view, this is the true year ; i.e., it is the time occupied by the 
 earth in completing its revolution around the sun from a given 
 direction in space to the same direction again. 
 
88 THE CALENDAR. [ 127 
 
 The tropical year is the time included between two successive 
 passages of the vernal equinox by the sun. Since the equinox 
 moves yearly 50".2 towards the west, the tropical year is 
 shorter than the sidereal by about 20 minutes, its length being 
 365 days, 5 hours, 48 minutes, 36 seconds. Since the seasons 
 depend on the sun's place with respect to the equinox, the tropical 
 year is the year of chronology and civil reckoning. 
 
 The third kind of year is the anomalistic year, the time between 
 two successive passages of the perihelion by the earth. Since the line 
 of apsides of the earth's orbit makes an eastward revolution once in 
 about 108,000 years, this kind of year is nearly 5 minutes longer than 
 the sidereal, its length being 365 days, 6 hours, 13 minutes, 48 sec- 
 onds. It is but little used except in calculations relating to perturba- 
 tions of the planets. 
 
 128. The Calendar. The natural units of time are the 
 day, the month and the year. The day is too short for con- 
 venience in dealing with considerable periods, such as the life 
 of a man, for instance ; and the same is true even of the 
 month ; so that for all chronological purposes the tropical year 
 (the year of the seasons) has always been employed. At the 
 same time, so many religious ideas and observations have been 
 connected with the changes of the moon, that there has been a 
 constant struggle to reconcile the month with the year. Since 
 the two are incommensurable, no really satisfactory solution is 
 possible, and the modern calendar of civilized nations entirely 
 disregards the lunar phases. In early times the calendar was 
 in the hands of the priesthood, and was mainly lunar, the 
 seasons being either disregarded, or kept roughly in place 
 by the occasional putting in or dropping of a month. The 
 Mohammedans still use a purely lunar calendar, having a 
 " year " of twelve months, which contains alternately 354 and 
 355 days. In their reckoning the seasons fall continually in 
 different months, and their calendar gains on ours about one 
 year in thirty-three. 
 
129] THE JULIAN CALENDAR. 89 
 
 129. The Julian Calendar. When Julius Caesar came into 
 power, he found the Roman calendar in a state of hopeless 
 confusion. He, therefore, with the advice of Sosigenes, the 
 astronomer, established (B.C. 45) what is known as the Julian 
 Calendar, which still, either untouched or with a trifling mod- 
 ification, continues in use among civilized nations. Sosigenes 
 discarded all reference to the moon's phases, and adopting 
 365J days as the true length of the year, he ordained that 
 every fourth year should contain 366 days, the extra day 
 being inserted by repeating the sixth day before the Calends 
 of March (whence such a year is called " Bissextile "). He 
 also transferred the beginning of the year, which before 
 Caesar's time had been in March (as is indicated by the names 
 of several of the months, December, the tenth month, for 
 instance), to Jan. 1st. 
 
 Caesar also took possession of the month Quintilis, naming it July 
 after himself. His successor, Augustus, in a similar manner appropri- 
 ated the next month, Sextilis, calling it August, and to vindicate his 
 dignity and make his month as long as his predecessor's he added to 
 it a day stolen from February. 
 
 The Julian calendar is still used unmodified in the Greek 
 Church, and also in many astronomical reckonings. 
 
 130. The Gregorian Calendar. The true length of the 
 tropical year is not 365^ days, but 365 days, 5 hours, 48 min- 
 utes, 46 seconds, leaving a difference of 11 minutes and 14 
 seconds by which the Julian year is too long. This difference 
 amounts to a little more than three days in 400 years. As a 
 consequence the date of the vernal equinox comes continually 
 earlier and earlier in the Julian calendar, and in 1582 it had 
 fallen back to the llth of March instead of occurring on the 
 21st, as it did at the time of the Council of Nice (A.D. 325). 
 Pope Gregory, therefore, under the astronomical advice of 
 Clavius, ordered that the calendar should be restored by add- 
 ing ten days, so that the day following Oct. 4th, 1582, should 
 
90 THE GEEGOBIAN CALENDAR. [ 130 
 
 be called the 15th. instead of the 5th ; further, to prevent any 
 future displacement of the equinox, he decreed that thereafter 
 only such century years should be leap years as are divisible 
 by 400. Thus 1700, 1800, 1900, and 2100 are not leap 
 years, but 1600 and 2000 are. The change was immediately 
 adopted by all Catholic countries, but the Greek Church and 
 most Protestant nations refused to recognize the Pope's au- 
 thority. The new calendar was, however, at last adopted in 
 England in 1752. At present (since the year 1800 was a leap 
 year in the Julian calendar and not in the Gregorian) the dif- 
 ference between the two calendars is twelve days ; but it will 
 become thirteen in 1900, which will not be a leap year with 
 us, though it will in Eussia. 
 
131] THE MOON. 91 
 
 CHAPTER V. 
 
 THE MOON. HER ORBITAL MOTION AND THE MONTH. 
 DISTANCE, DIMENSIONS, MASS, DENSITY, AND FORCE OF 
 GRAVITY. ROTATION AND ITERATIONS. PHASES. 
 LIGHT AND HEAT. PHYSICAL CONDITION. TELE- 
 SCOPIC ASPECT AND PECULIARITIES OF THE LUNAR 
 SURFACE. 
 
 131. NEXT to the sun, the moon is the most conspicuous, 
 and to us the most important, of the heavenly bodies ; in fact, 
 she is the only one except the sun, which exerts the slightest 
 perceptible influence upon the interests of human life. She 
 owes her conspicuousness and her importance, however, solely 
 to her nearness ; for she is really a very insignificant body as 
 compared with stars and planets. 
 
 132. The Moon's Apparent Motion ; Definition of Terms, etc. 
 
 One of the earliest observed of astronomical phenomena 
 must have been the eastward motion of the moon with refer- 
 ence to the sun and stars, and the accompanying change of 
 phase. If, for instance, we note the moon to-night as very 
 near some conspicuous star, we shall find her to-morrow night 
 at a point considerably farther east, and the next night 
 farther yet ; she changes her place about 13 daily, and makes 
 the complete circuit of the heavens, from star to star again, in 
 about 27J days. In other words, she revolves around the 
 earth in that time, while she accompanies us in our annual 
 journey around the sun. Since the moon moves eastward 
 among the stars so much faster than the sun (which takes a 
 year in going once around), she overtakes and passes him at 
 
92 SIDEREAL AND SYNODIC MONTHS. C ^ 
 
 regular intervals ; and as her phases depend upon her apparent 
 position with reference to the sun, this interval from new 
 moon to new moon is specially noticeable, and is what we 
 ordinarily understand as the " month." 
 
 The angular distance of the moon east or west of the sun at 
 any time is called her Elongation. At new moon it is zero, 
 and the moon is said to be in Conjunction. At full moon the 
 elongation is 180, and she is said to be in Opposition. In 
 either case the moon is in Syzygy. (Syzygy means "yoked 
 together," the sun, moon, and earth being then nearly in line.) 
 When the elongation is 90, she is said to be in Quadrature. 
 
 133. Sidereal and Synodic Months. The sidereal month is 
 the time it takes the moon to make her revolution from a given 
 star to the same star again ; its length is 27^ days (27 days, 7 
 hours, 43 minutes, 11.545 seconds). The mean daily motion, 
 therefore, is 360 divided by this, or 13 11' (nearly). The 
 sidereal month is the true month from the mechanical point 
 of view. 
 
 The synodic month is the time between two successive con- 
 junctions or oppositions; i.e., between two successive new or 
 full moons. It.; average length is about 29^- days (29 days, 
 12 hours, 44 minutes, 2.864 seconds), but it varies consider- 
 ably on account of the eccentricity of the moon's orbit. 
 
 If M be the length of the moon's sidereal period in days, E the 
 length of the sidereal year, and S that of the synodic month, the three 
 
 quantities are connected by a simple relation easily demonstrated. 
 
 M 
 is the fraction of a circumference moved over by the moon in a day. 
 
 Similarly, is the apparent daily motion of the sun. The difference 
 
 E 
 
 is the amount which the moon gains on the sun daily. Now it gains 
 a whole revolution in one synodic month of S days, and therefore 
 
 must gain daily of a circumference. Hence we have the important 
 
 S 
 
 equation _1 __L_J: 
 
 M E S 
 
133] MOON'S PATH AMONG THE STABS. 93 
 
 which is known as the equation of synodic motion. In a sidereal year 
 the number of sidereal months is exactly one greater than the num- 
 ber of synodic months, the numbers being respectively 13.369 + and 
 12.369 +. 
 
 134. The Moon's Path among the Stars. By observing the 
 moon's right ascension and declination daily with suitable 
 instruments, we can map out its apparent path, just as in the 
 case of the sun (Art. 116) . This path turns out to be (very 
 nearly) a great circle, inclined to the ecliptic at an angle of 
 5 8'. The two points where it cuts the ecliptic are called the 
 "nodes," the ascending node being where the moon passes 
 from the south side to the north side of the ecliptic, while the 
 opposite node is called the descending node. 
 
 The moon at the end of the month never comes back exactly to the 
 point of beginning among the stars, on account of the so-called " per- 
 turbations" of her orbit, due mostly to the attraction of the sun. 
 One of the most important of these perturbations is the " regression 
 of the nodes." These slide westward on the ecliptic just as the vernal 
 equinox does (precession), but much faster, completing their circuit 
 in about 19 years instead of 26,000. 
 
 135. Interval between the Moon's Successive Transits ; Daily 
 Retardation. Owing to the eastward motion of the moon it 
 comes to the meridian about 51 minutes later each day, on 
 the average ; but the retardation ranges all the way from 38 
 minutes to 66 minutes, on account of the variation in the rate 
 of the moon's motion. 
 
 The average retardation of the moon's rising and setting is 
 also, of course, the same 51 minutes ; but the actual retarda- 
 tion is still more variable than that of the meridian transits, 
 depending to some extent on the latitude of the observer as 
 well as on the variations in the moon's motion. At New 
 York the range is from 23 minutes to 1 hour and 17 minutes ; 
 that is to say, on some nights the rising of the moon is only 
 23 minutes later than on the preceding night, while at other 
 
94 HARVEST AND HUNTER'S MOON. [ 135 
 
 times it is more than an hour and a quarter behindhand. In 
 high latitudes the differences are still greater. In very high 
 latitudes the moon, when it has its greatest possible declina- 
 tion, becomes circumpolar for a certain time each month, 
 and remains visible without setting at all (like the midnight 
 sun) for a greater or less number of days, according to the 
 latitude of the observer. 
 
 136. Harvest and Hunter's Moon. The full moon that 
 occurs nearest the autumnal equinox is called the ' harvest 
 moon ' ; the one next following, the ' hunter's moon.' At that 
 time of the year the moon, while nearly full, rises for several 
 consecutive nights almost at the same hour, so that the moon- 
 light evenings last for an unusually long time. The phenome- 
 non, however, is much more striking in Northern Europe and 
 in Canada than in the United States. 
 
 137. Form of the Moon's Orbit. By observation of the 
 moon's apparent diameter in connection with observations of 
 her place in the sky, we can determine the form of her orbit 
 around the earth in the same way that the form of the earth's 
 orbit around the sun was worked out (see Appendix, Art. 
 428). The moon's apparent diameter ranges from 33' 33", 
 when as near the earth as possible, to 29' 24", when most 
 remote ; and her orbit turns out to be an ellipse like that of 
 the earth around the sun, but of much greater eccentricity, 
 averaging about ^ (as against -g^). We say " averaging " be- 
 cause the actual eccentricity is variable, on account of pertur- 
 bations. 
 
 The point of the moon's orbit nearest the earth is called the 
 Perigee, that most remote the Apogee, and the indefinite line 
 passing through these points the Line of Apsides, while the 
 major axis is that portion of this line which lies between the 
 perigee and apogee. This line of apsides is in continual 
 motion, on account of perturbations (just as the line of nodes 
 
137] THE MOON^S DISTANCE. 05 
 
 is, Art. 134), but it moves eastward instead of westward, com- 
 pleting its revolution in about nine years. In her revolution 
 about the earth, the moon observes the same law of equal 
 areas that the earth does in her orbit around the sun (Art. 
 121). 
 
 THE MOON'S DISTANCE. 
 
 138. In the case of any heavenly body, one of the first and 
 most fundamental inquiries relates to its distance from us : 
 until the distance has been somehow measured we can get no 
 knowledge of the real dimensions of its orbit, nor of the size, 
 mass, etc., of the body itself. The problem is usually solved 
 by measuring the apparent " parallactic " displacement of the 
 body, as seen by observers at widely separated stations. 
 Before proceeding farther, we must, therefore, say a few 
 words upon the subject of parallax. 
 
 139. Parallax. In general the word "parallax" means 
 the difference between the directions of a heavenly body as 
 seen by the observer, and as seen from some standard point 
 of reference. The annual or heliocentric parallax of a star is 
 the difference of the star's direction as seen from the earth 
 and from the sun. The diurnal or geocentric parallax of the 
 sun, the moon, or a planet, is the difference between its direc- 
 tion as seen from the centre of the earth and from the obser- 
 ver's station on the earth's surface ; or, what comes to the same 
 thing, the geocentric parallax is the angle at the body made by 
 two lines drawn from it, one to the observer, the other to the centre 
 of the earth. (Stars have no geocentric parallax j the earth as 
 seen from them is a mere point.) 
 
 In Fig. 17, the parallax of the body P is the angle OPC. 
 Obviously this diurnal parallax is zero for a body directly over- 
 head at Z, and is the greatest possible for a body on the hori- 
 zon, as at P h . 
 
96 
 
 PARALLAX AND DISTANCE. 
 
 [139 
 
 Moreover, and this is to be specially noted, this parallax of 
 a body at the horizon the " horizontal parallax " is simply 
 the wngular semi-diameter of the earth as seen from the body. 
 When, for instance, we say that the moon's horizontal parallax 
 is 57', it is equivalent to saying that seen from the moon the 
 earth appears to have a diameter of 114'. In the same way, 
 since the sun's parallax is 8".8, the diameter of the earth as 
 seen from the sun is 17".6. 
 
 140. Relation between Parallax and Distance. When the 
 horizontal parallax of any heavenly body is ascertained, its dis- 
 tance follows at once through 
 our knowledge of the earth's 
 dimensions. If we know how 
 large a ball of given size 
 appears, we can tell how far 
 away it is ; if we know how 
 large the earth looks from the 
 moon, we can find the distance 
 between them. Thus, when in 
 the triangle CP h O, Fig. 17, we 
 know the angle at P^ and the 
 side CO, the radius of the 
 earth, we can compute CP h by 
 a very easy trigonometrical 
 
 calculation. Evidently the more remote the body, the smaller 
 its parallax. 
 
 Since the radius of the earth varies slightly in different lati- 
 tudes, we take the equatorial radius as a standard, and the 
 equatorial horizontal parallax is the earth's equatorial semi- 
 diameter as seen from the body. It is this which is usually 
 meant when we speak simply of " the parallax " of the moon, 
 of the sun, or of a planet without adding any qualification 
 (but never when we speak of the parallax of a star ; then we 
 always mean the annual parallax). 
 
 FIG. 17. Diurnal Parallax. 
 
141] DIAMETER, ETC., OF THE MOON. 97 
 
 141. Parallax, Distance, and Velocity of the Moon. The 
 
 moon's equatorial horizontal parallax found by corresponding 
 observations made at different parts of the earth, is 3422" (57' 
 2") according to Neison, but varies considerably on account of 
 the eccentricity of the orbit. From this parallax we find 
 that the moon's average distance from the earth is about 60.3 
 times the earth's equatorial radius, or 238,840 miles, with an 
 uncertainty of perhaps 20 miles. 
 
 The maximum and minimum values of the moon's distance are 
 given by Neison as 252,972 and 221,617 miles. It will be noted that 
 the average distance is not the mean of the two extremes. 
 
 Knowing the size and form of the moon's orbit, the velocity 
 of her motion is easily computed. It averages a little less 
 than 2300 miles an hour, or about 3350 feet per second. Her 
 mean apparent angular velocity among the stars is about 33', 
 which is just a little greater than the apparent diameter of 
 the moon itself. 
 
 142. Diameter, Area, and Bulk of the Moon. The mean 
 apparent diameter of the moon is 31' 7". Knowing its dis- 
 tance, its real diameter comes out 2163 miles. This is 0.273 
 of the earth's diameter. 
 
 Since the surfaces of globes vary as the squares of their 
 diameters, and their volumes as the cubes, this makes the sur- 
 face area of the moon equal to about J T of the earth's, and the 
 volume (or bulk) almost exactly -fa of the earth's. 
 
 No other satellite is nearly as large as the moon in comparison with 
 its primary planet. The earth and moon together, as seen from a dis- 
 tance, are really in many respects more like a double planet than like 
 a planet and satellite of ordinary proportions. At a time, for instance, 
 when Venus happens to be nearest the earth (at a distance of about 
 twenty-five millions of miles), her inhabitants (if she has any) would 
 see the earth just about as brilliant as Venus herself at her best 
 appears to us, and the moon would be about as bright as Sirius, oscil- 
 
98 MASS, DENSITY, ETC., OF THE MOON. [ 143 
 
 lating backwards and forwards about half a degree each side of the 
 earth, once a month. 
 
 143. Mass, Density, and Superficial Gravity of the Moon. 
 
 Her mass is about ^5- of the earth's mass (0.0125). The 
 actual measurement of the moon's mass is an extremely diffi- 
 cult problem, and the methods pursued are quite beyond the 
 
 scope of this book. Since the density is equal to TT i ass , the 
 
 Volume 
 
 density of the moon as compared to that of the earth is found 
 to be 0.613, or about 3.4 the density of water (the earth's 
 density being 5.58). This is a little above the average den- 
 sity of the rocks which compose the crust of the earth. 
 
 The ' superficial gravity,' or the attraction of the moon for 
 bodies at its surface, is about one-sixth that at the surface of 
 the earth. This is a fact that must be borne in mind in con- 
 nection with the enormous scale of the craters on the moon. 
 Volcanic forces there would throw materials to a vastly greater 
 distance than on the earth. 
 
 144. Rotation of the Moon. The moon turns on its axis 
 once a month, in exactly the time occupied by its revolution 
 around the earth : its day and night are, therefore, each nearly 
 a fortnight in length, and in the long run it keeps the same 
 
 Oside always toward the earth. We see to- 
 day precisely the same face of the moon 
 ' '^\ which Galileo did when he first looked at it 
 with his telescope. The opposite face has 
 never been seen from the earth, and prob- 
 ably never will be. 
 
 tf 
 
 It is difficult for some to see why a motion of 
 this sort should be considered a rotation of the 
 moon, since it is essentially like the motion of a 
 
 FIG. 18. ball carried on a revolving crank (Fig. 18). Such 
 
 a ball, they say, " revolves around the shaft, but does not rotate on 
 its own axis." It does rotate, however j for if we mark one side of 
 
144] THE MOON'S PHASES. 99 
 
 the ball, we shall find the marked side presented successively to every 
 point of the compass as the crank turns around, so that the ball turns 
 on its own axis as really as if it were whirling upon a pin fastened to 
 the table. By virtue of its connection with the crank, the ball has 
 two distinct motions, (1) the motion of translation, which carries its 
 centre in a circle around the shaft ; (2) an additional motion of rota- 
 tion around a line drawn through its centre of gravity parallel to the 
 shaft. 
 
 Rotation consists essentially in this : A line connecting any two points 
 in the rotating body, and produced to the celestial sphere, will sweep out a 
 circle upon it. In every rotating body, one line can be drawn through 
 the centre of the body, however, so that the circle described by it in 
 the sky will be infinitely small. This is the axis of the body. 
 
 145. Librations. While in the long run the moon keeps the 
 same face towards the earth, it is not so from day to day. With refer- 
 ence to the centre of the earth, it is continually oscillating a little, 
 and these oscillations constitute what are called "Librations," of 
 which we distinguish three; viz., (1) the libration in latitude, by 
 which the north and south poles are alternately presented to the earth ; 
 (2) the libration in longitude, by which the east and west sides of the 
 moon are alternately tipped a little towards us ; and (3) the diurnal 
 libration, which enables us to look over whatever edge of the moon is 
 uppermost when it is near the horizon. Owing to these librations we 
 see considerably more than half of the moon's surface at one time 
 and another. About 41 per cent of it is always visible ; 41 per cent 
 never visible, and a belt at the edge of the moon, covering about 18 
 per cent is rendered alternately visible and invisible by libration. 
 
 146. Phases of the Moon. Since the moon is an opaque 
 globe shining merely by reflected light, we can only see that 
 hemisphere of her surface on which the sun is shining, and of 
 the. illuminated hemisphere only that portion which happens 
 to be turned towards the earth. 
 
 When the moon is between the earth and the sun (new 
 moon), the side presented to us is dark, and the moon, is 
 then invisible. A week later, at the end of the first quarter, 
 half of the illuminated hemisphere is visible, and we have the 
 
100 
 
 THE MOON'S PHASES. 
 
 [U6 
 
 half-moon just as we do a week after the full. Between the 
 new moon and the half-moon, during the first and last quarters 
 of the lunation, we see less than half of the illuminated por- 
 tion, and then have the "crescent" phase. Between half- 
 moon and the full moon, during the second and third quarters 
 
 FIG. 19. The Moon's Phases. 
 
 of the lunation, we see more than half of the moon's illumi- 
 nated side, and we have then what is called the " gibbous " 
 phase. 
 
 Fig. 19 (in which the light is supposed to come from a point far 
 above the circle which represents the moon's orbit) shows the way in 
 which the phases are distributed through the month. 
 
146] EARTH-SHINE ON THE MOON. 101 
 
 The line which separates the dark portion of the disc from 
 the bright is called the Terminator, and is always a semi- 
 ellipse, since it is a semicircle viewed obliquely, as shown by 
 Fig. 20, A. Draughtsmen sometimes incorrectly represent the 
 crescent form by a construction like Fig. 20, J5, in which a 
 smaller circle has a portion cut out of it by an arc of a larger 
 one. It is to be noticed also that a&, 
 the line which joins the " cusps " or 
 points of the crescent, is always perpen- d<( J[ \ n ]f 
 dicular to a line drawn from the moon 
 to the sun, so that the horns are always 
 turned directly away from the sun. The 
 precise position in which they will stand 
 at any time is, therefore, perfectly predictable, and has nothing 
 whatever to do with the weather. (Pupils have probably 
 heard of the " wet moon " and " dry moon " superstition.) 
 
 147. Earth-shine on the Moon. Near the time of new 
 moon, the portion of the moon's disc which does not get the 
 sunlight is easily visible, illuminated by a pale reddish light. 
 This light is earth-shine, the earth as seen from the moon 
 being then nearly full. The red color is due to the fact that 
 the light sent to the moon from the earth has passed twice 
 through our atmosphere, and so has acquired the sunset tinge. 
 Seen from the moon, the earth would be itself a magnificent 
 moon about 2 in diameter, showing the same phases as the 
 moon does itself. 
 
 Taking everything into account, the earth-shine is probably fifteen 
 to twenty times as strong as the light of the moon at similar phases. 
 Since the moon keeps always the same face towards the earth, the 
 earth is visible only from that part of the moon which faces us, and 
 remains nearly stationary in the lunar sky, neither rising nor setting. 
 It is easy to see that she would be a very beautiful object, on account 
 of the changes which would be continually going on upon her surface 
 due to snow-storms, clouds, growth of vegetation, etc. 
 
102 ABSENCE OF AIR AND WATER. [ 148 
 
 PHYSICAL CHARACTERISTICS OF THE MOON. 
 
 148. Absence of Air and Water. The moon's atmosphere, 
 if there is any, is extremely rare, its density at the moon's 
 surface being probably not more than -3-^ part of that of our 
 own atmosphere. 
 
 The evidence on the point is twofold : First, the telescopic appear- 
 ance. There is no haze, shadows are perfectly black ; there is no 
 sensible twilight at the points of the crescent, and all outlines are visi- 
 ble sharply and without the least blurring such as would be due to 
 the intervention of an atmosphere. Second, the absence of refraction 
 when the moon intervenes between us and any distant body. When 
 the moon * occults ' a star, for instance, there is no distortion or dis- 
 coloration of the star-disc, but both the disappearance and the reap- 
 pearance are practically instantaneous. 
 
 Of course if there is no air, there can be no liquid water, 
 since the water would immediately evaporate and form an 
 atmosphere of vapor if air were not present. It is not impos- 
 sible, however, nor perhaps improbable, that solid water (ice 
 and snow) may exist on the moon's surface. Although ice and 
 snow liberate a certain amount of vapor, yet at a low temper- 
 ature the quantity would be insufficient to make an atmos- 
 phere dense enough to be observed from the earth. 
 
 If the moon once formed a portion of the earth, as is likely, 
 the absence of air and water requires explanation, and there 
 have been many interesting speculations on the subject into 
 which we cannot enter. 
 
 149. The Moon's Light. In its quality moonlight is simply 
 sunlight, showing a spectrum identical in every detail with 
 that of the light coming from the sun itself, except as the 
 intensity of different portions of the spectrum is slightly 
 altered by its reflection from the lunar surface. 
 
 The brightness of full moonlight as compared with sunlight 
 is about one six-hundred-thousandth. According to this, if the 
 
1*9] HEAT OF THE MOON. 103 
 
 whole visible hemisphere were packed with full moons, we 
 should receive from it only about one-eighth of the light of the 
 sun. 
 
 The half-moon does not give nearly half as much light as 
 the full moon. Near the full the brightness is suddenly and 
 greatly increased, probably because at any time except the 
 full the moon's visible surface is more or less darkened by 
 shadows which disappear at the moment of full. 
 
 The average "albedo," or reflecting power, of the moon's 
 surface is given by Zollner as 0.174; i.e., the moon's surface 
 reflects a little more than one-sixth of the light that falls 
 upon it. There are, however, great differences in the bright- 
 ness of the different portions of the moon's surface. Some 
 spots are nearly as white as snow or salt, and others as dark 
 as slate. 
 
 150. Heat of the Moon. For a long time it was impossible 
 to detect the moon's heat by observation. Even when concen- 
 trated by a large lens, it is too feeble to be shown by the most 
 delicate thermometer. With modern apparatus, however, it is 
 easy enough to perceive the heat of lunar radiation, though the 
 measurement is extremely difficult. The total amount of heat 
 sent by the full moon to the earth appears to be about 170 1 007 of 
 that sent by the sun; i.e., the full moon in two days sends 
 us about as much heat as the sun does in one second. 
 
 A considerable portion of the lunar heat seems to be simply 
 reflected from the surface like light, while the rest, perhaps 
 three-fourths of the whole, is "obscure heat"; i.e., heat which 
 has first been absorbed by the moon's surface and then radi- 
 ated, like the heat from a brick surface that has been warmed 
 by the sunshine. 
 
 As to the temperature of the moon's surface, it is impossible 
 to be very certain. During the long lunar night of fourteen 
 days, the temperature must inevitably fall appallingly low, 
 perhaps 200 or 300 below zero. On the other hand, the 
 
104 LUNAR INFLUENCES. [ 15 
 
 lunar rocks are exposed to the sun's rays in a cloudless sky 
 for fourteen days at a time, so that if they were protected by 
 air, like the rocks upon the earth, they would certainly become 
 intensely heated. But there is no air, and, on the whole, it is 
 probable that the temperature never rises much above the 
 freezing-point of water, since in the absence of air the heat 
 would be lost about as fast as it is received, and the condition 
 of things may be supposed to be somewhat like that on the 
 highest mountains of the earth (where there is perpetual snow 
 and ice), only more so. 
 
 151. Lunar Influences on the Earth. The most important 
 effect produced upon the earth by the moon is the generation 
 of the tides in co-operation with the sun. There are also cer- 
 tain well-ascertained disturbances of the terrestrial magnetism 
 connected with the approach and recession of the moon in its 
 oval orbit; and this ends the chapter of proved lunar influ- 
 ences. 
 
 The multitude of current beliefs as to the controlling influ- 
 ence of the moon's phases and changes upon the weather and 
 the various conditions of life are mostly unfounded. It is 
 quite certain that if the moon has any influence at all of the 
 sort imagined, it is extremely slight ; so slight that it has not 
 yet been demonstrated, though numerous investigations have 
 been made expressly for the purpose of detecting it. Different 
 workers continually come to contradictory results. 
 
 152. The Moon's Telescopic Appearance. Even to the 
 naked eye the moon is a beautiful object, diversified with curi- 
 ous markings connected with numerous popular legends. In 
 a powerful telescope these naked-eye markings vanish, and 
 are replaced by a multitude of smaller details which make the 
 moon, on the whole, the most interesting of all telescopic 
 objects especially to instruments of moderate size, say from 
 six to ten inches in diameter, which generally give a more 
 
152] THE MOON'S SURFACE. 105 
 
 pleasing view than instruments either much larger or much 
 smaller. An instrument of this size, with magnifying powers 
 between 250 and 500, virtually brings the moon within a dis- 
 tance ranging from 1000 to 500 miles. Any object half a 
 mile in diameter on the moon is distinctly visible. A long 
 line or streak even less than a quarter of a mile across can 
 easily be seen. 
 
 For most purposes the best time to look at the moon is when it is 
 between six and ten days old : at the time of full moon few parts of 
 the surface are well seen. It is evident that while with the telescope 
 we should be able to see such objects as lakes, rivers, forests, and 
 great cities, if they existed on the moon, it would be hopeless to 
 expect to distinguish any of the minor indications of life, such as 
 buildings or roads. 
 
 153. The Moon's Surface Structure. The moon's surface 
 for the most part is extremely broken. The earth's mountains 
 are mainly in long ranges, like the Andes and Himalayas. 
 On the moon the ranges are few in number ; but, on the other 
 hand, the surface 
 is pitted all over 
 with great craters, 
 which resemble 
 very closely the 
 volcanic craters on 
 the earth's surface, 
 though on an im- 
 mensely greater 
 scale. The largest 
 terrestrial craters FlG< 21> " A Norraal Lunar Crater ( Nasra y th )- 
 
 do not exceed six or seven miles in diameter ; many of those 
 on the moon are fifty or sixty miles across, and some have a 
 diameter of more than a hundred miles, while smaller ones 
 from five to twenty miles in diameter are counted by the 
 hundred. 
 
 The normal lunar crater (Fig. 21) is nearly circular, sur- 
 
106 LUNAR CRATERS AND MOUNTAINS. [ 153 
 
 rounded by a mountain ring, which rises anywhere from 1000 
 to 20,000 feet above the neighboring country. The floor within 
 the ring may be either above or below the outside level ; some 
 craters are deep, and some are rilled nearly to the brim. Fre- 
 quently, in the centre of the crater, there rises a group of 
 peaks which attain the same elevation as the encircling ring, 
 and these central peaks often show holes or minute craters 
 in their summits. 
 
 On some portions of the moon these craters stand very 
 thickly. This is especially the case near the moon's south 
 
 pole. It is noticeable, 
 also, that as on the 
 earth the youngest 
 mountains are gener- 
 ally the highest, so on 
 the moon the most re- 
 cent craters are gener- 
 ally deepest and most 
 precipitous. * 
 
 The height of a lu- 
 nar mountain can be 
 measured with consid- 
 erable accuracy by 
 means of its shadow. 
 
 The striking resem- 
 blance of these lunar 
 craters to terrestrial vol- 
 canoes makes it natural 
 to assume that they have 
 
 FIG. 22. Gaesendi (JSTasmyth). . . ,, . 
 
 a similar origin. This, 
 
 however, is not quite certain, for there are considerable difficulties in 
 the way of the volcanic theory, especially in the case of what are 
 called the great " Bulwark Plains," so extensive that a person stand- 
 ing in the centre could not even see the summit of the surrounding 
 ring at any point; and yet there is no line of distinction between 
 them and the smaller craters, the series is continuous. Moreover, 
 
153] 
 
 OTHER LUNAR FORMATIONS. 
 
 107 
 
 on the earth, volcanoes necessarily require the action of air and water, 
 which do not now exist on the moon ; so that if these lunar craters 
 are really the result of volcanic eruptions, they must be ancient forma- 
 tions, for there is absolutely no evidence of any present volcanic 
 activity. Fig. 22 represents one of the finest lunar craters, Gassendi, 
 which is best seen about two days after the half moon. 
 
 154. Other Lunar Formations. The craters and mountains 
 are not the only interesting features on the moon's surface. 
 There are many deep, narrow, crooked valleys which go by the 
 name of "rills/' and 
 may once have been 
 water-courses (see Fig. 
 23). Then there are 
 many straight "clefts " 
 half a mile or so wide, 
 and of unknown depth, 
 running in some cases 
 several hundred miles 
 straight through moun- 
 tain and valley, with- 
 out any apparent re- 
 gard for the accidents 
 of the surface. 
 
 Most curious of all 
 are the light-colored 
 streaks, or "rays," 
 which radiate from cer- 
 tain of the craters, ex- 
 tending in some cases 
 a distance of many hundred miles. They are usually from five 
 to ten miles wide, and neither elevated nor depressed to any 
 considerable extent with reference to the general surface. 
 Like the clefts, they pass across valley and mountain, and 
 sometimes straight through craters, without any change in 
 width or color. No satisfactory explanation of them has yet 
 
 FIG. 23. Archimedes and the Apennines (Nasmyth). 
 
108 
 
 MAP OF THE MOON. 
 
 [154 
 
 been given. The most remarkable of these " ray-systems " is 
 the one connected with the great crater Tycho, not very far 
 from the moon's south pole. The rays are not very conspic- 
 uous until within a few days of full moon, but at that time 
 they, and the crater from which they diverge, constitute by 
 far the most striking feature of the telescopic view. 
 
 FIG. 24. Map of the Moon, reduced from Nelson. 
 
 155. Changes on the Moon. It is certain that there are 
 no conspicuous changes on the moon's surface ; no such trans- 
 formations as would be presented by the earth viewed with a 
 telescope from the moon, no clouds, no storms, no snow of 
 
155] CHANGES ON THE MOON. 109 
 
 winter, and 110 spread of verdure in the spring. At the same 
 time it is confidently maintained by some observers that here 
 and there alterations do take place in the details of the lunar 
 surface, while others as stoutly dispute it. The difficulty in 
 settling the question arises from the great changes which take 
 place in the appearance of a lunar object, according to 'the 
 angle at which the sunlight strikes it. Other conditions also, 
 such as the height of the moon above the horizon and the 
 clearness and steadiness of the air, affect the appearance ; and 
 it is very difficult to secure a sufficient identity of conditions 
 at different times of observation to be sure that apparent 
 changes are real. It is probable that the question will finally 
 be settled by photography. For further discussion of this 
 subject, see General Astronomy, Art. 272. 
 
 KEY TO THE PRINCIPAL OBJECTS INDICATED IN FIG. 24. 
 
 A. Mare Humorum. K. Mare Nubium. 
 
 B. Mare Nectaris. L. Mare Frigoris. 
 
 C. Oceanus Procellarum. T. Leibnitz Mountains. 
 
 D. Mare Fecunditatis. U. Doerfel Mountains. 
 
 E. Mare Tranquilitatis. V. Rook Mountains. 
 
 F. Mare Crisium. W. D'Alembert Mountains. 
 
 G. Mare Serenitatis. X. Apennines. 
 //. Mare Imbrium. Y. Caucasus. 
 
 /. Sinus Iridum. Z. Alps. 
 
 1. Clavius. 14. Alphonsus. 27. Eratosthenes, 
 
 2. Schiller. 15. Theophilus. 28. Proclus. 
 
 3. Maginus. 16. Ptolemy. 28'. Pliny. 
 
 4. Schickard. 17. Langrenus. 29. Aristarchus. 
 
 5. Tycho. 18. Hipparchus. 30. Herodotus. 
 
 6. Walther. 19. Grimaldi. 31. Archimedes. 
 
 7. Purbach. 20. Flam steed. 32. Cleomedes. 
 
 8. Petavius. 21. Messier. 33. Aristillus. 
 
 9. "The Railway." 22. Maskelyne. 34. Eudoxus. 
 
 10. Arzachel. 23. Triesnecker. 35. Plato. 
 
 11. Gassendi. 24. Kepler. 36. Aristotle. 
 
 12. Catherina. 25. Copernicus. 37. Endymion. 
 
 13. Cyrillus. 26. Stadius. 
 
110 NOMENCLATURE. [156 
 
 156. Lunar Maps and Nomenclature. A number of maps 
 of the moon have been constructed by different observers. 
 The most recent and extensive is that by Schmidt of Athens, 
 on a scale of seven feet in diameter ; it was published by the 
 Prussian government in 1878. Perhaps the best for ordinary 
 observers is that given in Webb's " Celestial Objects for Com- 
 mon Telescopes." We present here (Fig. 24) a skeleton map, 
 which indicates the position of about fifty of the leading 
 objects. 
 
 As for the names of the lunar objects, the great plains upon 
 the surface were called by Galileo " oceans," or " seas " (Maria), 
 because he supposed that these grayish surfaces, which are 
 visible to the naked eye and conspicuous in a small telescope, 
 though not with a large one, were covered with water. Thus we 
 have the "Oceanus Procellarum" (Sea of Storms), the "Mare 
 Imbrium" (Sea of Showers), etc. The ten mountain ranges 
 on the moon are mostly named for terrestrial mountains, as 
 Caucasus, Alps, Apennines, though two or three bear the 
 names of astronomers, like Leibnitz, Doerfel, etc. The con- 
 spicuous craters bear the names of ancient and mediaeval 
 astronomers and philosophers, as Plato, Archimedes, Tycho, 
 Copernicus, Kepler, and Gassendi. This system of nomencla- 
 ture seems to have originated with Kiccioli, who made the first 
 map of the moon in 1650. 
 
157] THE SUN. Ill 
 
 CHAPTER VI. 
 
 THE SUN. ITS DISTANCE, DIMENSIONS, MASS, AND DEN- 
 SITY. ITS ROTATION, SURFACE, AND SPOTS. THE 
 SPECTROSCOPE AND THE CHEMICAL CONSTITUTION OF 
 THE SUN. THE CHROMOSPHERE AND PROMINENCES. 
 THE CORONA. THE SUN'S LIGHT. MEASUREMENT 
 AND INTENSITY OF THE SUN'S HEAT. THEORY OF ITS 
 MAINTENANCE AND SPECULATIONS REGARDING THE 
 AGE OF THE SUN. 
 
 157. THE sun is a star, the nearest of them; a hot, self- 
 luminous globe, enormous as compared with the earth and 
 moon, though probably only of medium size as a star ; but to 
 the earth and the other planets which circle around it, it is 
 the grandest and most important of all the heavenly bodies. 
 Its attraction controls their motions, and its rays supply the 
 energy which maintains every form of activity upon their 
 surfaces. 
 
 158. The Sun's Distance. The mean distance of the sun 
 from the earth (the astronomical unit of distance) is a little 
 less than 93,000000 miles. There are many methods of deter- 
 mining it, some of which depend on a knowledge of the Ve- 
 locity of Light (Appendix, Arts. 434 and 436), while others 
 depend on finding the sun's horizontal parallax. (For a 
 resumt of the subject, see General Astronomy, Chap. XIV.) 
 The mean value of this parallax is very nearly 8 ".8. In other 
 words, as seen from the sun, the earth has an apparent diam- 
 eter of about 17".6 (Art. 139). The distance is variable, to 
 
112 DIMENSIONS OF THE SUN. [ 158 
 
 the extent of about 1,500000 miles, on account of the eccen- 
 tricity of the earth's orbit, the earth being almost 3,000000 
 miles nearer to the sun on Dec. 31st than on July 1st. 
 
 Knowing the distance of the earth from the sun, the earth's 
 orbital velocity follows at once by dividing the circumference 
 of the orbit by the number of seconds in a year. It comes out 
 18.5 miles per second. (Compare this with the velocity of a 
 cannon-ball, which seldom exceeds 2000 feet per second.) In 
 travelling this 18|- miles, the deflection of the earth's motion from 
 a perfectly straight line amounts to less than one-ninth of an inch. 
 
 159. The distance of the sun is of course enormous compared with 
 any distance upon the earth's surface. Perhaps the simplest illustra- 
 tion which will give us any conception of it is that drawn from the 
 motion of a railway train, which, going a thousand miles a day 
 (nearly forty-two miles an hour without stops) would take 254i years 
 to make the journey. If sound were transmitted through interplan- 
 etary space, and at the same rate as in our own air, it would make the 
 passage in about fourteen years ; i.e., an explosion on the sun would 
 be heard by us fourteen years after it actually occurred. Light trav- 
 erses the distance in 499 seconds. 
 
 160. Dimensions of the Sun. The sun's mean apparent 
 diameter is 33' 4". Since at its distance, 1" equals 450.36 
 miles, its diameter is 866,500 miles, or 109|- times that of the 
 earth. If we suppose the sun to be hollowed out, and the 
 earth placed at the centre of it, the sun's surface would be 
 433,000 miles away. Now since the distance of the moon 
 from the earth is about 239,000 miles, she would be only 
 a little more than half-way out from the earth to the inner 
 surface of the hollow globe, which would thus form a very 
 good background for the study of the lunar motions. 
 
 If we represent the sun by a globe two feet in diameter, the earth on 
 the same scale would be 0.22 of an inch in diameter, the size of a very 
 small pea. Its distance from the sun would be just about 220 feet, 
 and the nearest star, still on the same scale, would be 8000 miles away, 
 on the other side of the earth. 
 
160] SUN'S MASS, DENSITY, ETC. 113 
 
 Since the surfaces of globes are proportional to the squares 
 of their radii, the surface of the sun exceeds that of the earth 
 in the ratio of (109.5) 2 : 1 ; i.e., the area of its surface is about 
 12,000 times the surface of the earth. 
 
 The volumes of spheres are proportional to the cubes of 
 their radii, hence the sun's volume or bulk is (109.5) 3 , or 
 1,300000 times that of the earth. 
 
 161. The Sun's Mass, Density, and Superficial Gravity. 
 
 The mass of the sun is nearly 332,000 times that of the earth. 
 There are various ways of getting at this result, but they lie 
 rather beyond the mathematical scope of this work. 
 
 Its density, as compared with that of the earth, is found by 
 simply dividing its mass by its bulk (both as compared with the 
 
 ooo C\C)C\ 
 
 earth); i.e., the sun's density equals ' - = 0.255, a 
 
 1,300000 
 
 little more than a quarter of the earth's density. 
 
 To get its 'specific gravity' (i.e., its density compared with 
 water), we must multiply this by the earth's mean specific 
 gravity, 5.58. This gives 1.41. In other words, the sun's 
 mean density is only about 1.4 times that of water, a very 
 significant result as bearing on its physical condition, espe- 
 cially when we know that a considerable portion of its mass is 
 composed of metals. 
 
 Of course this low density depends upon the fact that the tempera- 
 ture is enormously high, and the materials are mainly in a state of 
 cloud, vapor, or gas. 
 
 The superficial gravity is about 27.6 as great as gravity on 
 the earth ; that is to say, a body which weighs one pound on 
 the surface of the earth would there weigh 27.6 pounds, and 
 a person who weighs 150 pounds here would there weigh 
 nearly two tons. A body would fall 444 feet in the first 
 second, and a pendulum which vibrates seconds on the earth 
 would vibrate in less than a fifth of a second there. 
 
114 
 
 THE SUN S ROTATION. 
 
 [162 
 
 162. The Sun's Rotation. Dark spots are often visible 
 upon the sun's surface, which pass across the disc from east 
 
 to west and indicate an axial 
 rotation. The average time 
 occupied by a spot in passing 
 around the sun and return- 
 ing to the same apparent po- 
 sition, as seen from the earth, 
 is 27.25 days. This interval, 
 however, is not the true time 
 of the sun's rotation, but the 
 synodic, as is evident from 
 Fig. 25. Suppose an obser- 
 ver on the earth at E sees a 
 spot on the centre of the 
 
 E' 
 
 FIG. 25. 
 
 Synodic and Sidereal Revolutions of the Sun. sun's disc at S ', while the 
 
 sun rotates, E will also move forward in its orbit, and the 
 observer, the next time he sees the spot on the centre of the 
 disc, will be at E', the spot having gone around the whole 
 circumference plus the arc SS'. 
 
 The equation by which the true period is deduced from the synodic 
 is the same as in the case of the moon ; viz., 
 
 !=:!_ 1 
 
 S T E' 
 
 T being the true period of the sun's rotation, E the length of the year, 
 and S the observed synodic rotation. This gives !T=25.35. Differ- 
 ent observers get slightly different results. 
 
 The paths of the spots across the sun's disc are usually more 
 or less oval, showing that the sun's axis is inclined to the 
 ecliptic, and so inclined that the north pole is tipped about 
 7^ towards the position which the earth occupies near the 
 first of September. Twice a year the paths become straight, 
 when the earth is in the plane of the sun's equator, June 3d 
 and Dec. 5th (Fig. 26). 
 
163] LAW OF THE SUN'S ROTATION. 115 
 
 163. Peculiar Law of the Sun's Rotation. It was noticed 
 quite early that different spots give different results for the 
 
 DEC. MARCH. JUNE. SEPT. 
 
 FIG. 26. Path of Spots across the Sun's Disc. 
 
 period of rotation, but the researches of Carrington, about 
 thirty years ago, first brought out the fact that the differences 
 are systematic, so that at the solar equator the time of solar 
 rotation is less than on either side of it. For spots near the 
 sun's equator it is about 25 days ; for solar latitude 30, 
 26.5 days ; and in solar latitude 40, 27 days. The time of 
 rotation of the sun's surface in latitude 45 is fully two days 
 longer than at the equator ; but we are unable to follow the 
 law further towards the poles of the sun, because spots are 
 almost never found beyond the parallel of 45. No really 
 satisfactory explanation of this strange acceleration of the 
 spots at the sun's equator has yet been found. 
 
 164. Study of the Sun's Surface. The heat and light of 
 the sun are so intense that we cannot look directly at it with 
 a telescope, as we do at the moon, 
 and it is necessary, therefore, to 
 provide either a special eye-piece 
 with suitable shade-glass, or arrange 
 the telescope, as in Fig. 27, so as to 
 throw an image of the sun upon a 
 screen. 
 
 In the study of the sun's surface, 
 
 photography is for Some purposes FIG. 27. -Telescope and Screen. 
 
 very advantageous and much used. The instrument must, 
 however, have lenses specially constructed for photographic 
 
116 
 
 GREAT SUN SPOT. 
 
 [164 
 
 operations, since an object-glass which would give admirable 
 results for visual purposes would be worthless photograph- 
 
 FIG. 28. The Great Sun Spot of September, 1870, and the Structure of the Photo- 
 sphere. From a Drawing by Professor Langley. From the " New Astronomy " by 
 permission of the Publishers. 
 
 ically. The exposure required to form a photographic picture 
 is practically instantaneous. The negatives are usually from 
 
164] THE PHOTOSPHERE. 117 
 
 two inches up to eight or ten inches in diameter, and some 
 of the best of them bear enlarging up to forty inches. 
 
 Photographs have the great advantage of freedom from preposses- 
 sion on the part of the observer, and in an instant of time they secure 
 a picture of the whole surface of the sun such as would require a skil- 
 ful draughtsman hours to copy. But, on the other hand, they take no 
 advantage of the instants of fine seeing, but represent the solar sur- 
 face as it happened to appear at the moment when the plate was 
 uncovered, affected by all the momentary distortions due to atmos- 
 pheric disturbances. 
 
 165. The Photosphere. The sun's surface seen with a tele- 
 scope, under a medium magnifying power, appears to be of 
 nearly uniform texture, though distinctly darker at the edges, 
 and usually marked here and there with certain dark spots. 
 With a higher power it is evident that the visible surface 
 (called the photosphere) is by no means uniform, but is made 
 up, as shown in Fig. 28, of a comparatively darkish background 
 sprinkled over with grains, or "nodules," as Herschel calls 
 them, of something more brilliant, "like snowflakes on a 
 gray cloth," according to Langley. These nodules or " rice- 
 grains" are from 400 to 600 miles across, and, when the seeing 
 is best, themselves break up into more minute "granules." For 
 the most part, the nodules are about as broad as they are long, 
 though of irregular form; but here and there, especially in 
 the neighborhood of the spots, they are drawn out into long 
 streaks, known as "filaments," "willow leaves," or "thatch 
 straws." 
 
 Certain bright streaks called " f aculse " are also usually visi- 
 ble here and there upon the sun's surface, and though not very 
 obvious near the centre of the disc, they become conspicuous 
 near the " limb," or edge of the disc, especially in the neigh- 
 borhood of the spots, as shown in Fig. 29. These faculae are 
 masses of the same material as the rest of the photosphere, 
 but elevated above the general level and intensified in bright- 
 
118 THE PHOTOSPHERE. [ 165 
 
 ness. When one of them passes off the edge of the disc, it is 
 sometimes seen as a little projection. 
 
 In their nature, the photospheric "nodules " and faculae are 
 in all probability luminous clouds, floating in a less luminous 
 atmosphere, just as a snow or rain-cloud, which has been 
 
 FIG. 29. Faculse at Edge of the Sun (De La Rue). 
 
 formed by the condensation of water-vapor, floats in the earth's 
 atmosphere. Such a cloud, while at a temperature even lower 
 than that of the surrounding gases, has a vastly greater power 
 of emitting light, and therefore appears very brilliant in com- 
 parison with the gas in which it floats. 
 
 166, Sun Spots, Sun spots, whenever visible, are the most 
 interesting and conspicuous objects upon the solar surface. 
 The appearance of a normal sun spot (Fig. 30), fully formed 
 and not yet beginning to break up, is that of a dark central 
 "umbra," more or less circular, with a fringing "penumbra" 
 composed of converging filaments. The umbra itself is not 
 uniformly dark throughout, but is overlaid with filmy clouds, 
 
166] 
 
 SUN SPOTS. 
 
 119 
 
 which usually are rather hard to see, but sometimes are con- 
 spicuous, as in the figure. Usually, also, within the umbra 
 there are a number of round and very black spots, sometimes 
 called "vortices," but often referred to as " Dawes's holes," 
 after the name of their first discoverer. 
 
 Even the darkest portions of the umbra, however, are dark 
 only by contrast. Photometric observations show that the 
 
 FIG. 30. A Normal Sun Spot (Secchi; modified). 
 
 nucleus of a spot gives about one per cent as much light as 
 a corresponding area of the photosphere ; the blackest portion 
 of a sun spot is really more brilliant than a calcium light. 
 
 Very few spots are strictly normal. Frequently the umbra 
 is out of the centre of the penumbra, or has a penumbra on 
 one side only, and the penumbral filaments, instead of con- 
 verging regularly towards the nucleus, are often distorted in 
 every conceivable way. Spots are often gathered in groups 
 within a common penumbra, separated from each other by 
 brilliant "bridges," which extend across from the outside 
 
120 SUN SPOTS. [ 166 
 
 photosphere. Occasionally a spot has no penumbra at all, and 
 sometimes we have what are called " veiled " spots, in which 
 there seems to be a penumbra without any central nucleus. 
 
 167. Nature of Sun Spots. The spots are unquestionably 
 cavities or hollows in the photosphere, and are filled with gases 
 and vapors which are cooler than the surrounding regions, and 
 therefore absorb a considerable portion of light, and make the 
 spot look dark. The fact that they are depressions is shown 
 by the change in their appearance as they approach the 
 "limb" of the disc. Here the penumbra becomes wider on 
 the outer edge, and narrower on the inner edge, and just before 
 the spot goes out of sight around the edge of the sun, the 
 penumbra on the inner edge entirely disappears. The appear- 
 ance is precisely such as would be shown by a saucer-shaped 
 
 FIG. 31. Sun Spots as Cavities. 
 
 cavity in the surface of a globe, the bottom of the cavity being 
 painted black to represent the umbra, and the sloping sides 
 gray for the penumbra (see Fig. 31). 
 
 Observations upon a single spot would hardly be sufficient to prove 
 this, because the spots are so irregular in their form ; but by observ- 
 ing the behavior of several hundred, the truth comes out clearly. 
 Occasionally when a very large spot passes off the sun's limb, the 
 depression can be seen with the telescope. 
 
 That the nucleus of a spot is cooler as well as darker than 
 the rest of the sun's surface, has been proved by several 
 observers by direct experiments. 
 
167] DIMENSIONS OF SUN SPOTS. 121 
 
 The penumbra is usually composed of " thatch straws/ 7 or 
 long drawn out filaments, and these, as has been said, con- 
 verge in a general way towards the centre of the spot. In the 
 neighborhood of the spot, the surrounding photosphere is 
 usually much disturbed and elevated into faculse. 
 
 168. Dimensions of Sun Spots, etc. The diameter of the 
 umbra of a sun spot varies all the way from 500 miles, in the 
 case of a very small one, to 50,000 miles in the case of a very 
 large one. The penumbra surrounding a group of spots is 
 sometimes 150,000 miles across, though that is an exceptional 
 size. Quite frequently sun spots are large enough to be visi- 
 ble with the naked eye, and can actually be thus seen at sun- 
 set or through a fog, or by the help of a simple colored glass. 
 The depth of the bottom of a spot is very difficult to deter- 
 mine, but according to Faye, Carrington, and some others, it 
 seldom exceeds 2500 miles, and more often is between 500 and 
 1500. 
 
 The duration of sun spots is very various, but they are 
 always short-lived phenomena from the astronomical point of 
 view, sometimes lasting only for a few days, though more fre- 
 quently for a month or two. In one instance a spot group 
 attained the age of eighteen months. 
 
 Very little can be said as to their cause. Numerous theo- 
 ries, more or less satisfactory, have been proposed. On the 
 whole, perhaps the most probable view is that, they are the 
 effect of eruptions. It is not likely, however, that they are 
 the holes or craters through which the eruptions break out, as 
 Secchi at one time thought, and as Mr. Proctor maintained to 
 the very last : it is more probable, in accordance with Secchi' s 
 later views, that when an eruption takes place, a hollow, or 
 sink, results in the photospheric cloud-surface somewhere near 
 it, in which hollow the cooler gases and vapors collect. 
 
 169. Distribution of Spots, and their Periodicity. It is a 
 
 significant fact that the spots are confined mostly to two zones 
 
122 INFLUENCE OF SUN SPOTS. [ 169 
 
 of the sun's surface between 5 and 40 of north and south 
 solar latitude. Practically none are ever found beyond the 
 latitude of 45, but at the time when spots are most numerous, 
 a few are found near the equator. In 1843 Schwabe of Dessau, 
 by the comparison of an extensive series of observations cover- 
 ing nearly twenty years, showed that the sun spots are probably 
 periodic, being at some times much more numerous than at 
 others, with a roughly regular recurrence every ten or eleven 
 years. A few years later he fully established this remarkable 
 result. Wolf of Zurich has collected all the observations dis- 
 coverable, and has obtained a pretty complete record back to 
 1610, when Galileo first discovered these objects. The aver- 
 age period is 11.1 years, but the maxima are somewhat irregu- 
 lar, both in time and as to the extent of the surface covered 
 by spots. The last maximum occurred in 1883-4. During 
 the maximum the sun is never free from spots, from 25 to 50 
 being frequently visible at once. During the minimum, on the 
 contrary, weeks and even months pass without the appearance 
 of even a single one. The cause of this periodicity is not yet 
 known. 
 
 170. Terrestrial Influence of Sun Spots. One influence of 
 sun spots on the earth is perfectly demonstrated. When the 
 spots are numerous, magnetic disturbances (magnetic storms) 
 are most numerous and most violent upon the earth a fact not 
 to be wondered at, since notable disturbances upon the sun's 
 surface have been immediately followed by magnetic storms 
 with brilliant exhibitions of the Aurora Borealis, as in 1859 
 and 1883. But no one has yet been able to explain the nature 
 of the connection by which disturbances upon the sun's sur- 
 face affect the magnetic condition of the earth, though the fact 
 is beyond doubt. 
 
 It has been attempted, also, to show that the periodical disturbance 
 of the sun's surface is accompanied by effects upon the earth's mete- 
 orology, upon its temperature, barometric pressure, storminess, and 
 
170] THE SOLAR SPECTRUM. 123 
 
 the amount of rainfall. On the whole, it can only be said that while 
 it is possible that real effects are produced, they must be very slight, 
 and are almost entirely covered up by the effect of purely terrestrial 
 causes. The results obtained thus far in attempting to co-ordinate 
 sun-spot phenomena with meteorological phenomena are unsatisfac- 
 tory and often contradictory. We may add that the spots cannot 
 produce any sensible effect by their direct action in diminishing the 
 light and heat of the sun. They do not directly alter the amount of 
 solar radiation at any time by so much as one part in a thousand. 
 
 THE SOLAR SPECTRUM AND ITS REVELATIONS. 
 
 About 1860 the spectroscope appeared in the field as a new 
 and powerful instrument for astronomical research, resolving 
 at a glance many problems which before did not seem even 
 open to investigation. 
 
 171. Principle of the Spectroscope. The essential part of 
 the apparatus is either a prism or a train of prisms, or else a 
 diffraction " grating/' * which is capable of performing the 
 same office of " dispersing " (i.e., of spreading and sending in 
 different directions) the light rays of different colors. 
 
 If with such a " dispersion piece," as we may call it (either 
 prism or grating), one looks at a distant point of light, he will 
 see instead of a point a long, bright streak, red at one end and 
 violet at the other. If the object looked at is a line of light, 
 parallel to the edge of the prism or to the lines of the grating, 
 then instead of a colored streak without width, he gets a 
 colored band or ribbon of light, the spectrum, which may show 
 markings which will give him much valuable information. It 
 is usual to form this line of light by admitting the rays 
 through a narrow " slit " placed at one end of a tube, which 
 carries at the other end an achromatic object-glass having 
 
 1 The " grating " is merely a piece of glass or speculum metal, ruled with 
 many thousand straight, equidistant lines, from 5000 to 20,000 in the 
 inch. 
 
124 
 
 THE SPECTROSCOPE. 
 
 [171 
 
 the slit in the principal focus. This tube, with slit and lens, 
 constitutes the " collimator." Instead of looking at the spec- 
 trum with the naked eye, it is better also in most cases to use 
 a small " view telescope," so called to distinguish it from the 
 large telescope to which the spectroscope is often attached. 
 
 172. Construction of the Spectroscope. The instrument, 
 therefore, as usually constructed, and shown in Fig. 32, con- 
 sists of three parts, collimator, dispersion-piece, and view 
 
 Prism-Spectroscope 
 
 Grating-Spectroscope 
 Collimator \S 2 
 
 Grating 
 
 
 S, 
 
 Direct-Vision Spectroscope 
 FIG. 32. Different Forms of Spectrum. 
 
 telescope, although in the "direct-vision" spectroscope, 
 shown in the figure, the view telescope is omitted. If the slit 
 S be illuminated by strictly homogeneous light (i.e., light all 
 of one color), say yellow, the "real image" of the slit will be 
 found at Y. If, at the same time, light of a different color 
 red for instance be also admitted, a second image will be 
 formed at jR, and the observer will then see a spectrum with 
 
172] SPECTRUM ANALYSIS. 125 
 
 two bright lines, the lines being really nothing more than images 
 of the slit. 
 
 If violet light be admitted, a third image will be formed at 
 F, and there will be three bright lines. If light from a candle 
 be admitted, there will be an infinite number of these slit- 
 images close together, like the pickets in a fence, without 
 interval or break, and we then get what is called a i continu- 
 ous ? spectrum. If, however, we look at sunlight or moonlight 
 or the light of a star, we shall find a spectrum continuous in 
 the main, but crossed by numerous dark lines, or missing slit- 
 images (as if some of the fence-pickets had been knocked off, 
 leaving gaps). 
 
 173. Principles upon which Spectrum Analysis depends. 
 
 These, substantially, as announced by Kirchhoff in 1858, are 
 the three following : 
 
 1st. A continuous spectrum is given by bodies which are so 
 dense that the molecules interfere with each other in such a 
 way as to prevent their free vibration ; i.e., by bodies which 
 are either solid or liquid, or, if gaseous, are under pressure. 
 
 2d. The spectrum of a luminous gas under low pressure is 
 discontinuous, that is, it is made up of bright lines or bands, and 
 these lines are characteristic. The same substance under simi- 
 lar conditions always gives the same set of lines, and usually 
 it does so even under conditions which differ rather widely ; 
 but when the circumstances differ too much, it may give two 
 or more different spectra. 
 
 3d (and most important for our purpose just now). A gas or 
 vapor absorbs from a beam of white light passing through it 
 precisely those rays of which its own spectrum consists; so that 
 the spectrum of white light which has been transmitted 
 through such a vapor, if the vapor is cooler than the original 
 source of light, exhibits a " reversed " spectrum of the gas ; 
 i.e., we get a spectrum which shows dark lines in place of the 
 characteristic bright lines. 
 
126 
 
 SPECTRUM ANALYSIS. 
 
 [173 
 
 We therefore infer that the sun is covered by an envelope 
 of gases, not so hot as the luminous clouds which form the 
 photosphere, and that these gases by their absorption produce 
 the dark lines which we see. 
 
 174. Experiment illustrating Reversal of Spectrum. The 
 
 principle of reversal is illustrated by Fig. 33. Suppose that 
 in front of the spectroscope we place a spirit lamp with a little 
 
 FIG. 33. Reversal of the Spectrum. 
 
 carbonate of soda and some salt of thallium upon the wick. 
 We shall then get a spectrum showing the two yellow lines of 
 sodium and the green line of thallium, all bright, as in the 
 upper of the two spectra. If now the liine light be started 
 behind the flame, we shall at once get the effect shown in the 
 lower figure, a continuous spectrum crossed by three black 
 lines which exactly replace the bright ones. Thrust a screen 
 between the lamp flame and the lime, and the dark lines 
 instantly turn bright again. 
 
175] 
 
 SPECTRUM ANALYSIS. 
 
 127 
 
 175. Chemical Constituents of the Solar Atmosphere. By 
 
 taking advantage of these principles, we can detect a large 
 number of well-known terrestrial elements in the sun. The 
 solar spectrum is crossed by dark lines, 1 which with an instru- 
 ment of high power number several thousand. 
 
 By proper arrangements it is possible to identify among 
 these lines many which are due to the presence in the sun's 
 atmosphere of known terrestrial elements in the state of 
 vapor. To effect the comparison necessary for this purpose, 
 the spectroscope must be so arranged that the observer can 
 confront the spectrum of sunlight with that of the substance 
 to be tested. In order to do this, half of the slit is covered 
 by a little reflector or " comparison prism," which reflects into 
 the tube the light of the sun, while the other half of the 
 slit receives directly the light of some flame or electric 
 spark. On looking into the spectroscope, the observer will 
 then see a spectrum, the lower half of which, for instance, is 
 
 FIG. 34. Comparison of the Spectrum of Iron with the Solar Spectrum. From a 
 Negative by Professor Trowbridge. 
 
 made by sunlight, while the upper half is made by light com- 
 ing from an electric spark between two metal points, say of 
 iron. This latter spectrum will show the bright lines of iron 
 vapor, and the observer can then easily see whether they do 
 or do not correspond exactly with the dark lines of the solar 
 spectrum. 
 
 1 They are generally referred to as Fraunhofer's lines, because Fraun- 
 hofer was the first to map them. To some of the principal ones he 
 assigned letters of the alphabet, which are still retained; thus A is a 
 strong red line at the extreme end of the spectrum ; C, one in the scarlet ; 
 D, one in the yellow ; and H, one in the violet. 
 
128 THE CHROMOSPHERE. [ 175 
 
 In such comparisons photography may be most effectively used 
 instead of the eye. Fig. 34 is a rather unsatisfactory reproduction, 
 on a reduced scale, of a negative made by Professor Trowbridge of 
 Cambridge. The lower half is the violet portion of the sun's spec- 
 trum, and the upper half that of an electric arc charged with the 
 vapor of iron. 1 The reader can see for himself with what absolute 
 certainty such a photograph indicates the presence of iron in the solar 
 atmosphere. A few of the lines in the photograph which do not show 
 corresponding lines in the solar spectrum are due to impurities in the 
 carbon, and not to iron. 
 
 176. Elements known to exist in the Sun. As the result of 
 such comparisons, we have the following list of sixteen ele- 
 ments which are now (1890) known to exist in the sun : 
 Barium, Manganese, 
 
 Calcium, Nickel, 
 
 Chromium, Platinum, 
 
 Cobalt, Silicon, 
 
 Copper, Silver, 
 
 Hydrogen, Sodium, 
 
 Iron, Titanium, 
 
 Magnesium, Vanadium. 
 
 There are evidences, perhaps not quite conclusive, of the 
 presence of several more, viz. 
 
 Aluminium, Lead(?), 
 
 Cadmium, Molybdenum (?), 
 
 Carbon, Palladium (?), 
 
 Zinc, Uranium (?). 
 
 As to carbon, its spectrum is so peculiar, consisting of bands 
 rather than lines, that it is very difficult to be sure ; but the 
 tendency of the latest investigations is to establish its place 
 in the upper list. These bodies must, of course, in the sun all 
 be in a condition of vapor, and vapor somewhat cooler than the 
 clouds which form the photosphere. It will be noticed that 
 
 1 Of course, in the negative, dark lines show bright, and vice versa. 
 
176] THE REVERSING LAYER. 129 
 
 the elements named in the lists, carbon alone excepted, are 
 all metals (chemically, hydrogen is as much a metal as any of 
 the others), and that a number of the elements which are most 
 important in the constitution of the earth's surface fail to 
 appear. As yet oxygen, nitrogen, chlorine, bromine, iodine, 
 sulphur, phosphorus, and boron are all missing. 
 
 We must be cautious, however, in drawing negative con- 
 clusions. It is quite conceivable that the spectra of these 
 bodies in their solar conditions may be so different from their 
 spectra as presented in our laboratories, that we cannot easily 
 recognize them ; for it is now unquestionable that many sub- 
 stances, under different conditions, give two or more widely 
 differing spectra. 
 
 177. The Reversing Layer. According to Kirchhoff's theory 
 the dark lines are formed by the passing of light emitted by 
 minute solid or liquid particles of photospheric clouds through 
 the somewhat cooler vapors which compose the substances 
 that we recognize by the dark lines in the spectrum. If this 
 is so, the spectrum of the gaseous envelope, which by its 
 absorption forms the dark lines, ought to show a spectrum of 
 corresponding bright lines when seen by itself. The oppor- 
 tunities are rare when it is possible to obtain a spectrum of 
 this gaseous envelope separate from that of the photosphere ; 
 but at the time of a total eclipse, at the moment when the 
 sun's disc has just been obscured by the moon, and the sun's 
 atmosphere is still visible beyond the moon's limb, the ob- 
 server ought to see this bright-line spectrum, if the slit of the 
 spectroscope be carefully directed to the proper point ; land the 
 observation has actually been made. The lines of the solar 
 spectrum, which up to the time of the total obscuration of the 
 sun remain dark as usual, are suddenly reversed, and the whole 
 field of the spectroscope is filled with brilliant colored lines, 
 which flash out quickly, and then gradually fade away, disap- 
 pearing in about two seconds. 
 
130 
 
 SUN-SPOT SPECTRUM. 
 
 The natural interpretation of this phenomenon is that the 
 formation of the dark lines in the solar spectrum is, mainly at 
 least, produced by a very thin stratum closely covering the 
 photosphere, since the moon's motion in two seconds would 
 correspond to a thickness of only 500 miles. 
 
 There are reasons, however, to doubt whether the lines are all 
 produced in such a thin layer. According to Mr. Lockyer, the solar 
 atmosphere is very extensive, and certain lines of the spectrum appear 
 to be formed only in the regions of lower temperature high up above 
 the surface of the photosphere. 
 
 178. Sun-Spot Spectrum. The spectrum of a sun spot 
 differs from the general solar spectrum not only in its dimin- 
 ished brilliancy, but in the great widening of certain lines, the 
 thinning of others, and the change of some (especially the lines 
 of hydrogen) to bright lines on some occasions. The majority 
 of the Fraunhofer lines, however, are not much affected either 
 way. 
 
 Sometimes, in connection with sun spots, certain lines of the 
 spectrum are bent and broken, as shown in Fig. 35. These 
 
 distortions are explained by 
 the swift motion towards or 
 from the observer of the 
 gaseous matter, which by 
 its absorption produces the 
 line in question. In the case 
 
 2* 43" 2M6" 2^51-" .,, /" , . ,, 
 
 Pie. 35. - The c line in the Spectrum of a illustrated in the figure, hy- 
 Sun Spot. drogen was the substance, 
 
 and its motion was towards the observer, nearly at the rate of 
 300 miles a second at one point. 
 
 179. Doppler's Principle. The principle upon which the 
 explanation of this displacement and distortion of lines de- 
 pends was first enunciated by Doppler in 1842. It is this: 
 when the distance between us and a body which is emitting regular 
 
179] THE CHROMOSPHERE. 131 
 
 vibrations, either of sound or of light, is decreasing, then the 
 number of pulsations received by us in each second is increased, 
 and the length of the tvaves is correspondingly diminished. Thus 
 the pitch of a musical tone rises in the case supposed, and in 
 the same way the refrangibility of a light wave, which depends 
 upon its wave length, is increased, so that it will fall nearer 
 the violet end of the spectrum. This principle finds numerous 
 applications in modern astronomical spectroscopy, and it is of 
 extreme importance that the student should clearly under- 
 stand it. 
 
 180. The Chromosphere. Outside the photosphere, or shin- 
 ing surface of the sun, lies the so-called chromosphere, of which 
 the stratum of gases that produce the dark lines in the solar 
 spectrum is the hottest and densest portion. The word is 
 derived from the Greek, chroma (color), and means "color- 
 sphere." It is so-called because it is brilliantly scarlet, owing 
 this color to the hydrogen gas which is its most conspicuous 
 component. In structure, it is like a sea of flame, covering 
 the photosphere to a depth of from 5000 to 10,000 miles, and 
 as seen through a telescope at the time of a total eclipse, it 
 has been well described as looking like a "prairie on fire." 
 There is, however, no real burning in the case ; i.e., no heat- 
 producing combination of hydrogen with oxygen, or with any 
 other element. 
 
 Under ordinary circumstances the chromosphere is invisible, 
 drowned in the light of the photosphere. It can be seen with 
 the telescope only for a few seconds at a time, during the fleet- 
 ing moments of a total eclipse ; but with the spectroscope it 
 can be studied at other times, as we shall see. 
 
 181. Prominences. The prominences, or protuberances, are 
 scarlet clouds which are seen during a total eclipse, projecting 
 from behind the edge of the moon. They are simply exten- 
 sions of the chromosphere, or isolated clouds of the same 
 
132 PROMINENCES AND CHROMOSPHERE. [ 181 
 
 gaseous substances, chiefly hydrogen. Their true nature was 
 first established at an eclipse in 1868, when their spectrum 
 was first satisfactorily made out. This spectrum is com- 
 posed of numerous bright lines, conspicuous among which are 
 the lines of hydrogen, together with a brilliant yellow line 
 (sometimes called D 3 because near the two so-called D lines). 
 It is due to some substance not yet recognized, but provision- 
 ally called helium, that is, ' the metal of the sun/ from the 
 Greek, helios (the sun). 
 
 182. Spectroscopic Observations of the Prominences and Chro- 
 mosphere. Since the spectrum of these objects is composed 
 of a small number of brilliant lines, it is possible to observe 
 them with a spectroscope in full daylight. The explanation 
 of the way in which the spectroscope effects this lies rather 
 beyond our limitations ; but it is sufficient for our purpose to 
 say that by attaching a spectroscope to a good telescope the 
 prominences can now be studied at leisure any clear day. They 
 are wonderfully interesting and beautiful objects. Some of 
 them, the so-called " quiescent " prominences, are of enormous 
 size, 50,000 or even 100,000 miles in height, faint and diffuse, 
 remaining almost unchanged for days. Others are much more 
 brilliant and active, especially those that are associated with 
 sun spots, as many of them are. These "eruptive" promi- 
 nences often alter their appearance very rapidly, so fast 
 that one can sometimes actually see the motion: velocities 
 from 50 to 200 miles a second are frequently met with. As a 
 rule the eruptive prominences are not so large as the quiescent 
 ones, but occasionally they surpass them, and a few have been 
 observed to attain elevations of more than 200,000 miles. 
 Fig. 36 gives specimens of both kinds. 
 
 183. The Corona. Probably the most beautiful and im- 
 pressive of all natural phenomena is the corona, the " glory " 
 of light which surrounds the sun at a total eclipse. The por- 
 
183] 
 
 THE CORONA. 
 
 133 
 
 tion of it near the sun is dazzlingly bright and of a pearly 
 lustre, contrasting beautifully with the scarlet prominences, 
 which stud it like rubies. It seems to be mainly composed 
 
 Quiescent Prominences. 
 
 Flames. Jets and Spikes near Sun's Limb, Oct. 5, 1571. 
 
 % Eruptive Prominences. 
 
 FIG. 36. 
 
 of projecting filaments of light, which near the sun are 
 pretty well defined, but at a little distance fade out and melt 
 into the general radiance. Near the poles of the sun the 
 corona does not usually extend very far and has a pretty 
 definite outline, but in the spot regions and near the sun's 
 equator faint streams sometimes extend to a distance of sev- 
 eral degrees; and at the distance of the sun every degree 
 means more than a million of miles. 
 
 A very striking and perplexing feature is the existence of 
 
134 
 
 THE CORONA. 
 
 [ 183 
 
 perfectly straight dark rays or rifts, which reach clear down 
 
 to the very edge of the sun. 
 
 The corona varies very greatly in brightness at different 
 
 eclipses, according to the apparent diameter of the moon at 
 
 the time. The portion of 
 the corona nearest the sun 
 is so much brighter than 
 the outer regions that 
 a little increase of the 
 moon's diameter cuts off 
 a very large proportion of 
 the light. The total light 
 of the corona is always at 
 least two or three times 
 as great as that of the full 
 moon. 
 
 Fig. 37 represents the 
 corona as seen in the 
 eclipse of 1882. 
 
 184. Spectrum of the 
 Corona. A characteris- 
 tic feature of its spectrum 
 is a bright green line, 
 generally known as the 
 "1474" line. 1 This line was at first supposed to be due to 
 iron, and the coincidence was for a long time puzzling (since 
 the vapor of iron is a very improbable substance to be found 
 at an elevation above the hydrogen of the chromosphere), until 
 it was discovered that the line is really a close double. One of 
 the two components of the dark line is due to iron, while the 
 other, the true corona line, is due to some unknown gaseous 
 
 1 So-called because it coincides with a dark line on Kirchhoff's map of 
 the solar spectrum, which was the chart in use when the line was first 
 discovered, in 1869. 
 
 FIG. 37. 
 Corona of the Egyptian Eclipse, 1882. 
 
184] THE CORONA. 135 
 
 element (probably lighter than hydrogen), which has been 
 called coronium, after the analogy of helium. 
 
 Besides this conspicuous green line, the hydrogen lines are 
 also faintly visible in the corona spectrum ; and by means of 
 photography it has been found that the violet and ultra-violet 
 portions of the spectrum are also rich in bright lines, the two 
 wide lines or bands, known as H and K in the ordinary solar 
 spectrum, being especially bright and conspicuous. 
 
 185. The corona is_ proved to be a true appendage of the 
 sun, and not, as has been at times supposed, a mere optical 
 phenomenon, nor one due to the atmosphere of the earth or 
 moon, by two established facts : 
 
 1st. That its spectrum is not that of reflected sunlight, but 
 of a self-luminous gas j and 
 
 2d. Because photographs of the corona, made at widely dif- 
 ferent stations along the track of an eclipse, agree exactly in 
 details. 
 
 Its real nature and relation to the sun is very difficult to 
 explain. It is a gaseous envelope, at least mainly gaseous, as 
 our atmosphere is, but it does not stand in any such relations 
 to the globe beneath as does the air. Its phenomena are not 
 yet satisfactorily explained, and remind us far more of auroral 
 streamers and of comets' tails than of anything that occurs in 
 the lower regions of the earth's atmosphere. The material of 
 the corona is of excessive rarity, as is shown by the fact that 
 in a number of cases comets have passed directly through it 
 (as, for instance, in 1882) without the slightest perceptible 
 disturbance. Its density, therefore, must be almost incon- 
 ceivably less than that of the best vacuum which we are able 
 to produce. 
 
 SUN'S LIGHT AND HEAT. 
 
 186. The Sun's Light. By photometric measures, which 
 we cannot explain here, it is found that the sun gives us 1575 
 
136 SUN'S LIGHT AND HEAT. [ 186 
 
 billions of billions (1575 followed by 24 ciphers) times as 
 much light as a standard candle * would do at that distance. 
 
 The amount of light received from the sun is about 600,000 
 times that given by the full moon, about 7000,000000 times 
 that of Sirius, the brightest of the fixed stars, and fully 
 200,000,000000 times that of the Pole-star. As to the inten- 
 sity of sunlight, or the intrinsic brightness of the sun's sur- 
 face, we find that it is about 190,000 times as bright as that 
 of the candle flame, and fully 150 times as bright as the lime 
 of a calcium light ; so that even the darkest part of a sun spot 
 outshines the lime light. The brightest part of an electric arc- 
 light comes nearer sunlight in intensity than anything else we 
 know of, being from a half to a quarter as bright as the solar 
 surface itself. 
 
 The sun's disc is brightest near the centre, but the variation 
 is slight until we get pretty near the edge, where the light 
 falls off rapidly. Just at the sun's limb, the brightness is not 
 much more than a third as great as at the centre. The color 
 is there modified also, becoming a sort of an orange-red. This 
 darkening and change of color are due to the general absorp- 
 tion of light by the lower portions of the sun's atmosphere. 
 According to Langley, if this atmosphere were suddenly re- 
 moved the surface would shine out somewhere from two to 
 five times as brightly as now, and its tint would become 
 strongly blue, like the color of an electric arc. 
 
 187. The Quantity of Solar Heat ; the Solar Constant. The 
 
 " solar constant " is the number of heat units which a square 
 unit of the earth's surface, unprotected by any atmosphere and 
 squarely exposed to the sun's rays, would receive from the sun 
 in a unit of time. The heat-unit most used at present is the 
 " calory," which is the quantity of heat required to raise the 
 
 1 The standard candle is a sperm candle weighing one- sixth of a pound 
 and burning 120 grains an hour. An ordinary gas-burner usually gives a 
 light equivalent to from ten to fifteen candles. 
 
187] THE SUN'S HEAT. 137 
 
 temperature of one kilogram of water 1 C. j and as the result 
 of the best observations thus far made, it appears that the 
 ' Solar Constant 7 is between twenty-five and thirty of these 
 calories to a square metre in a minute. At the earth's surface 
 a square metre, owing to the absorption of a large percentage 
 of heat by the air, would, however, seldom actually receive 
 more than from ten to fifteen calories in a minute. 
 
 The method of determining the solar constant is simple, as 
 far as the principle goes, but the practical difficulties are 
 serious, and thus far have prevented our obtaining all the 
 accuracy desirable. The determination is made by allowing a 
 beam of sunlight of known diameter to fall upon a known 
 quantity of water for a known time, and measuring how much 
 the water rises in temperature. The principal difficulty lies 
 in determining the proper allowance to be made for absorption 
 of the sun's heat in passing through the air. Besides this it 
 is necessary to measure, and allow for, the heat which is re- 
 ceived by the water during the experiment from other sources 
 than the sun. 
 
 188. Solar Heat at the Earth's Surface. Since it requires 
 about eighty calories of heat to melt one kilogram of ice, it 
 follows that, taking the solar constant at twenty-five, the heat 
 received from the sun when overhead would melt in an hour a 
 sheet of ice about three-quarters of an inch thick. From this 
 it is easily computed that the amount of heat received by the 
 earth from the sun in a year would melt a shell of ice 137 feet 
 thick all over the earth's surface. 
 
 If we accept the larger value of the solar constant, assigned by 
 Langley (thirty instead of twenty-five), this would be 165 feet. 
 
 Solar heat can, of course, be used as power, and so-called 
 "solar engines" have been constructed within the last few 
 years, in which the heat received upon a large reflector is 
 made to evaporate water in a suitable boiler and to drive a 
 
138 RADIATION FROM THE SUN'S SURFACE. [ 188 
 
 steam engine. It is found that the heat received upon a re- 
 flector ten feet square can be made to give practically about 
 one horse-power. 
 
 189. Radiation from the Sun's Surface. If we attempt to 
 estimate the intensity of the radiation from the surface of the 
 sun itself, we reach results which are simply amazing. We 
 must multiply the solar constant observed at the earth by the 
 square of the ratio between the earth's distance from the sun 
 and the distance of the sun's surface from its own centre ; i.e., 
 
 by the square of f 93 ' OOOOQO \ or about 46,000 : in other words, 
 y 43,250 J 
 
 the amount of heat emitted in a minute by a square foot of 
 the sun's surface is about 46,000 times as great as that received 
 by a square foot of surface at the distance of the earth. Car- 
 rying out the figures, we find that if the sun were frozen 
 over completely to a depth of over fifty feet, the heat it emits 
 would be sufncient to melt the ice in one minute ; that if a 
 bridge of ice could be formed from the earth to the sun by an 
 ice-column 2^ miles square, and if in some way the entire solar 
 radiation could be concentrated upon it, it would be melted in 
 one second, and in seven more would be dissipated in vapor. 
 
 Expressing it in terms of energy, we find that the solar radi- 
 ation is more than 100,000 horse-power continuously, for each 
 square metre of the sun's surface. 
 
 So far as we can now see, only a very small fraction of this whole 
 radiation ever reaches a resting-place. The earth intercepts about 
 ??oo ooooTrg- an d the other planets of the solar system receive in all 
 perhaps from ten to twenty times as much. Something like Tinnnnmnr 
 seems to be utilized within the limits of the solar system. 
 
 190. The Sun's Temperature. We can determine with some 
 accuracy the amount of heat which the sun gives ; to find its 
 temperature is a very different thing, and we really have very 
 little knowledge about it, except that it must be extremely 
 
190] CONSTANCY OF THE SUN'S HEAT. 139 
 
 high, far higher than that of any terrestrial source of heat 
 now known. The difficulty is that our laboratory experiments 
 do not give the necessary data from which we can determine 
 what temperature substances like those of which the sun is 
 composed must have, in order to enable them to send out 
 heat at the rate which we observe. Of two bodies at precisely 
 the same temperature, one may send out heat a hundred times 
 more rapidly than the other. 
 
 The estimates as to the temperature of the photosphere run 
 all the way from the very low ones of some of the French 
 physicists (who set it at about 2500 C.) to those of Secchi 
 and Ericsson, who put the figure among the millions. The 
 prevailing opinion sets it between 5000 and 10,000 C., or 
 from 9000 to 18,000 F. 
 
 A very impressive demonstration of the intensity of the 
 sun's heat is found in the fact that in the focus of a powerful 
 burning lens all known substances melt and vaporize ; and yet 
 it can be shown that at the focus of the lens the temperature 
 can never even nearly equal that of the source from which the 
 heat is derived. 
 
 191. Constancy of the Sun's Heat. It is still a question 
 whether the total amount of the sun's radiation does or does 
 not vary from time to time. There may be considerable fluc- 
 tuations in the hourly or daily quantity of heat, without our 
 being able to detect them with our present means of obser- 
 vation. 
 
 As to any steady progressive increase or decrease in the 
 amount of heat received from the sun, it is quite certain that 
 no considerable change has occurred for the past 2000 years, 
 because the distribution of plants and animals on the earth's 
 surface is practically the same as in the earliest days of his- 
 tory. It is, however, rather probable than otherwise that the 
 great changes of climate, which Geology indicates as having 
 formerly taken place on the earth, may ultimately be traced 
 to changes in the condition of the sun. 
 
140 MAINTENANCE OF THE SOLAR HEAT. [ 192 
 
 192. Maintenance of the Solar Heat. We cannot here dis- 
 cuss the subject fully, but must content ourselves with saying, 
 first, negatively, that this maintenance cannot be accounted 
 for on the supposition that the sun is a hot body, solid or 
 liquid, simply cooling ; nor by combustion j nor (adequately) 
 by the fall of meteors on the sun's surface, though this cause 
 undoubtedly operates to a limited extent. Second, we can say 
 positively that the solar radiation can be accounted for on the 
 hypothesis first proposed by Helmholtz, that the sun is mainly 
 gaseous, and shrinking slowly but continuously. While we 
 cannot see any such shrinkage, because it is too slow, it is a 
 matter of demonstration that if the sun's diameter should con- 
 tract about 300 feet a year, heat enough would be generated 
 to keep up its radiation without any lowering of its tem- 
 perature. If the shrinkage were more than about 300 feet, 
 the sun would be hotter at the end of the year than it was at 
 the beginning. 
 
 We can only say that while no other theory meets the con- 
 ditions of the problem,- this appears to do so perfectly, and 
 therefore has probability in its favor. 
 
 193. Age and Duration of the Sun. Of course if this 
 theory is correct, the sun's heat must ultimately come to an 
 end ; and looking backward it must have had a beginning. If 
 the sun keeps up its present rate of radiation, it must, on this 
 hypothesis, shrink to about half its diameter in some 5,000000 
 years at the longest. It will then be eight times as dense as 
 now, and can hardly continue to be mainly gaseous, so that 
 the temperature must begin to fall quite sensibly. It is not, 
 therefore, likely, in the opinion of Professor Newcomb, that 
 the sun will continue to give heat sufficient to support the 
 present conditions upon the earth for much more than 
 10,000000 years, if so long. 
 
 On the other hand, it is certain that the shrinkage of the 
 sun to its present dimensions from a diameter larger than that 
 
193] CONSTITUTION OF THE SUN. 141 
 
 of the orbit of Neptune, the remotest of the planets, would 
 produce about 18,000000 times as much heat as the sun now 
 throws out in a year ; hence, IF the sun's heat has been, and 
 still is, wholly due to the contraction of its mass, it cannot have 
 been emitting heat at the present rate, on this shrinkage hy- 
 pothesis, for more than 18,000000 years. But notice the 'if.' 
 It is quite possible that the solar system may have received 
 in the past supplies of heat other than that due to the con- 
 traction of the sun's mass. If so, it may be much older. 
 
 194. Constitution of the Sun. To sum up : The received 
 opinion as to the constitution of the sun is that the central 
 mass, or nucleus, is probably gaseous, under enormous pressure, 
 and at an enormous temperature. 
 
 The photosphere is probably a sheet of luminous clouds, con- 
 stituted mechanically like terrestrial clouds ; that is, of small, 
 solid, or liquid particles floating in gas. 
 
 These photospheric clouds float in an atmosphere composed 
 of those gases which do not condense into solid or liquid par- 
 ticles at the temperature of the solar surface. This atmos- 
 phere is laden, of course, with the vapors out of which the 
 clouds have been condensed, and constitutes the reversing layer 
 which produces the dark lines of the solar spectrum. 
 
 The chromosphere and prominences appear to be composed of 
 permanent gases, mainly hydrogen and helium, which are min- 
 gled with the vapors in the region of the photosphere, but rise 
 to far greater elevations. For the most part the prominences 
 appear to be formed by jets of hydrogen, ascending through 
 the interstices between the photospheric clouds, like flames 
 playing over a coal fire. 
 
 As to the corona, it is as yet impossible to give any satis- 
 factory explanation of all the phenomena that it presents, and 
 since thus far it has been possible to observe it only during 
 the brief moments of total eclipses, progress in its study has 
 been necessarily slow. 
 
142 ECLIPSES. [ 195 
 
 CHAPTER VII. 
 
 ECLIPSES AND THE TIDES. FORM AND DIMENSIONS OF 
 SHADOWS. ECLIPSES OF THE MOON. SOLAR ECLIPSES, 
 TOTAL, ANNULAR, AND PARTIAL. NUMBER OF 
 ECLIPSES IN A YEAR. RECURRENCE OF ECLIPSES 
 AND THE SAROS. OCCULTATIONS. THE TIDES. 
 
 195. The word Eclipse (literally a ' swoon 7 ) is a term ap- 
 plied to the sudden darkening of a heavenly body, especially 
 of the sun or moon. An eclipse of the moon is caused by its 
 passing through the shadow of the earth; an eclipse of the 
 sun by the moon's passing between the sun and the observer, 
 or, what comes to the same thing, by the passage of the 
 moon's shadow over the observer. The l Shadow/ in Astron- 
 omy, is the space from which sunlight is excluded by an inter- 
 vening body ; speaking geometrically, it is a solid, not a surface. 
 If we regard the sun and the other heavenly bodies as spheri- 
 cal, which, of course, they are very nearly, these shadows are 
 cones with their axes in the line which joins the centres of the 
 sun and the shadow-casting body, the point being always 
 directed away from the sun. If interplanetary space were a 
 little hazy, we should see every planet accompanied by its 
 shadow, like a black tail behind it. 
 
 ECLIPSES OF THE MOON. 
 
 196. Dimensions of the Earth's Shadow. The length of 
 the shadow is easily found. In Fig. 38, is the centre of the 
 sun and E the centre of the earth, and aCb is the shadow of 
 
196] 
 
 THE EARTH S SHADOW. 
 
 143 
 
 the earth cast by the sun. It is readily shown by Geometry 
 that if we call EC, the length of the shadow, L, and OE, the 
 distance of the earth from the sun, D, then 
 
 L = D x ( r \ R being OA the radius of the sun, and r 
 v ~~ T J 
 
 the radius of the earth Ea. This fraction, ( _ - \ is about 
 
 \R - rj 
 
 L : , so that L = -r--U: D. 
 
 108.5' 108.5 
 
 This gives 857,000 miles for the length of the earth's 
 shadow. The length varies about 14,000 miles on each side 
 
 FIG. 38. The Earth's Shadow. 
 
 of the mean, in consequence of the variation of the earth's dis- 
 tance from the sun at different times of the year. 
 
 From the cone aCb all sunlight is excluded, or would be were it not 
 for the fact that the atmosphere of the earth bends gome of the rays 
 which pass near the earth's surface into its shadow. The effect of 
 this atmospheric refraction is to increase the diameter of the shadow 
 about two per cent, but to make it less perfectly dark. 
 
 If we draw the lines, Be and Ad, crossing at P, between the 
 earth and the sun, they will bound the penumbra, within 
 which a part, but not the whole, of the sunlight is cut off : an 
 observer outside of the shadow, but within this partly shaded 
 space, would see the earth as a black body encroaching on the 
 sun's disc, but not covering it. 
 
144 LUNAR ECLIPSES. [ 197 
 
 197. Lunar Eclipses. The axis, or central line, of the 
 earth's shadow is always directed to a point directly opposite 
 the sun. If, then, at the time of full moon the moon happens 
 to be near the ecliptic, i.e., not far from one of the nodes (the 
 points where her orbit cuts the ecliptic), she will pass through 
 the shadow and be eclipsed. Since, however, the moon's orbit 
 is inclined 5 &' to the ecliptic, lunar eclipses do not happen 
 very frequently, seldom more than twice a year ; because the 
 moon at the full usually passes north or south of the shadow, 
 without touching it. 
 
 Lunar eclipses are of two kinds, partial and total; total 
 when she passes completely into the shadow; partial when 
 she only partly enters it, going so far to the north or south of 
 the centre that only a portion of the disc is obscured. An 
 eclipse of the moon when central (i.e., when the moon crosses 
 the centre of the shadow) may continue total for about two 
 hours, the interval from the first to the last contact being 
 about two hours more. This depends upon the facts that the 
 moon's hourly motion is nearly equal to its own diameter, and 
 that the diameter of the earth's shadow where the moon 
 crosses it is between two and three times the diameter of the 
 moon itself. The duration of an eclipse that is not central varies 
 of course with the part of the shadow traversed by the moon. 
 
 198. Phenomena of Total Eclipses of the Moon. Half an 
 hour or so before the moon reaches the shadow, its edge begins 
 to be sensibly darkened by the penumbra, and the edge of the 
 shadow itself, when it first touches the moon, appears nearly 
 black by contrast with the bright parts of the moon's surface. 
 To the naked eye the outline of the shadow looks fairly sharp, 
 but even with a small telescope it appears indefinite, and with 
 a large telescope of high magnifying power the edge of the 
 shadow becomes entirely indistinguishable, so that it is impos- 
 sible to determine within half a minute or so the time when 
 it reaches any particular point. 
 
198] COMPUTATION OF A LUNAR ECLIPSE. 145 
 
 After the moon has wholly entered the shadow, her disc is 
 usually distinctly visible, illuminated with a dull copper- 
 colored light, which is sunlight deflected around the earth into 
 the shadow by the refraction of our atmosphere, as illustrated 
 by Fig. 39. The brightness of the moon's disc during a total 
 eclipse of the moon differs greatly at different times, according 
 
 A 
 A' 
 
 FIG. 39. Light bent into Earth's Shadow by Refraction. 
 
 to the condition of the weather on the parts of the earth which 
 happen to lie at the edges of the earth's disc as seen from the 
 moon. If it is cloudy and stormy there, little light will reach 
 the moon ; if it happens to be clear, the quantity of light 
 deflected into the shadow may be very considerable. In the 
 lunar eclipse of 1884, the moon was for a time absolutely 
 invisible to the naked eye, a very unusual circumstance. 
 
 During the eclipse of Jan. 28th, 1888, although the moon was 
 pretty bright to the eye, Pickering found that its photographic power, 
 when centrally eclipsed, was only about rrrnnnnr f what it had been 
 before the shadow covered it. 
 
 199. Computation of a Lunar Eclipse. The computation of 
 a lunar eclipse is not at all complicated, though we do not propose to 
 enter into it. Since all its phases are seen everywhere at the same 
 absolute instant wherever the moon is above the horizon, it follows 
 that a single calculation giving the Greenwich times of the different 
 phenomena is all that is needed. Such computations are made and 
 published in the Nautical Almanac. The observer needs only to cor- 
 rect the predicted time by simply adding or subtracting his longitude 
 from Greenwich, in order to get the true local time. With an eclipse 
 of the sun the case is very different. 
 
146 
 
 ECLIPSES OF THE STJK. 
 
 [200 
 
 ECLIPSES OF THE SUN. 
 
 200. The Length of the Moon's Shadow is very nearly 
 of its distance from the sun, and averages 232,150 miles. 
 It varies not quite 4000 miles, ranging from 236,050 to 
 238,300. 
 
 Since the mean length of the shadow is less than the mean 
 distance from the earth (238,800 miles), it is evident that on 
 the average the shadow will fall short of the earth. The eccen- 
 tricity of the moon's orbit, however, is so great that she is 
 sometimes more than 30,000 miles nearer than at others. If 
 when the moon is nearest the earth, the shadow happens to 
 have at the same time its greatest possible length, its point 
 may reach nearly 18,400 miles beyond the earth's surface. In 
 
 .. > To Sun 
 
 FIG. 40. The Moon's Shadow on the Earth. 
 
 M' 
 
 this CLse the " cross-section " of the shadow, where the earth's 
 surface cuts it (at o in Fig. 40) will be about 168 miles in 
 diameter, which is the largest value possible. On the other 
 hand, when the moon is farthest from the earth, we may have 
 the state of things indicated by placing the earth at B, in Fig. 
 40. The vertex, V, of the shadow will then fall 24,700 miles 
 short of the earth's surface, and the cross-section of the 
 "shadow produced" will have a diameter of 206 miles at o r , 
 where the earth's surface cuts it. 
 
 201 . Total and Annular Eclipses. To an observer within 
 the shadow-cone (i.e., between V and the moon, Fig. 40), the 
 sun will be totally eclipsed. An observer in the " produced " 
 cone, beyond V, will see the moon apparently smaller than the 
 
201] PARTIAL ECLIPSES. 147 
 
 sun, leaving a ring of the sun uneclipsed ; this is what is 
 called an "annular" eclipse. These annular eclipses are con- 
 siderably more frequent than the total, and now and then an 
 eclipse is annular in part of its course across the earth, and 
 total in part. This is when the point of the moon's shadow 
 extends beyond the surface of the earth, but does not reach as 
 far as its centre. 
 
 The track of the eclipse across the earth will of course be a 
 narrow stripe having its width equal to the cross-section of 
 the shadow, and extending across the hemisphere which is 
 turned towards the moon at the time, though not necessarily 
 passing the centre of that hemisphere. Its course is always 
 from the west towards the east, but usually with considerable 
 motion toward the north or south. 
 
 202. The Penumbra and Partial Eclipses. The penumbra 
 can easily be shown to have a diameter on the line CD (Fig. 
 40) a little more than twice the diameter of the moon, or over 
 4000 miles. An observer situated within this penumbra has a 
 partial eclipse. If he is near to the cone of the shadow, the 
 sun will be mostly covered by the moon; if near the outer 
 edge of the penumbra, the moon will but slightly encroach on 
 the sun's disc. While, therefore, a total or annular eclipse is 
 visible as such only by observers within the narrow path trav- 
 ersed by the shadow-spot, the same eclipse will be visible as a 
 partial one anywhere within 2000 miles on each side of the 
 path ; and the 2000 miles must be reckoned square to the axis 
 of the shadow, and may correspond to a much greater distance 
 when reckoned around upon the spherical surface of the earth. 
 
 203. Velocity of the Shadow, and Duration of an Eclipse. 
 
 Were it not for the earth's rotation, the moon's shadow 
 would pass the observer at the rate of about 2100 miles an 
 hour. The earth, however, is rotating towards the east in the 
 same general direction as that in which the shadow moves, 
 so that the relative velocity is usually much less. 
 
148 PHENOMENA OF A SOLAR ECLIPSE. [ 203 
 
 A total eclipse of the sun observed at a station near the 
 equator, under the most favorable conditions possible, may 
 continue total for 7 m 58". In latitude 40 the duration can 
 barely equal 6J- m . At the equator an annular eclipse may 
 last for 12 m 24", the maximum width of the ring of the sun 
 visible around the moon being 1' 37". 
 
 In the observation of an eclipse, four contacts are recognized : the 
 first, when the edge of the moon first touches the edge of the sun ; the 
 second, when the eclipse becomes total or annular ; the third, at the ces- 
 sation of the total or annular phase ; and the fourth, when the moon 
 finally leaves the solar disc. From the first contact to the fourth the 
 time may be a little over two hours. In a partial eclipse, only the 
 first and fourth are observable, and the interval between them may be 
 very small when the moon just grazes the edge of the sun. 
 
 The magnitude of an eclipse is usually reckoned in " digits," the 
 digit being T *y of the sun's diameter. An eclipse of nine digits is 
 one in which the disc of the moon covers three-fourths of the sun's 
 diameter at the middle of the eclipse. 
 
 204. Phenomena of a Solar Eclipse. There is nothing of 
 special interest until the sun is mostly covered, though before 
 that time the shadows cast by the foliage begin to be peculiar. 
 
 The light shining through every small interstice among the leaves, 
 instead of forming as usual a circle on the ground, makes a little cres- 
 cent an image of the partly covered sun. 
 
 About ten minutes before totality the darkness begins to be 
 felt, and the remaining light, coming as it does from the edge 
 of the sun, is not only faint but yellowish, more like that of a 
 calcium light than sunshine. Animals are perplexed and 
 birds go to roost. The temperature falls, and dew appears. 
 In a few moments, if the observer is so situated that his view 
 commands the distant western horizon, the moon's shadow is 
 seen coming, much like a heavy thunder shower, and advanc- 
 ing with almost terrifying swiftness. As soon as the shadow 
 arrives, and sometimes a little before, the corona and promi- 
 
204] CALCULATION OF A SOLAR ECLIPSE. 149 
 
 nences become visible, while the brighter planets and stars of 
 the first three magnitudes make their appearance. 
 
 The suddenness with which the darkness pounces upon the 
 observer is startling. The sun is so brilliant that even the 
 small portion which remains visible up to the moment of 
 total obscuration so dazzles the eye that it is unprepared for 
 the sudden transition. In a few moments, however, the eye 
 adjusts itself, and it is found that the darkness is really not 
 very intense. If the totality is of short duration, say not 
 more than two minutes, there is not much difficulty in reading 
 an ordinary watch-face. In an eclipse of long duration (four 
 or five minutes) it is much darker, and lanterns become 
 necessary. 
 
 205. Calculation of a Solar Eclipse. A solar eclipse cannot 
 be dealt with in any such summary way as a lunar eclipse, because 
 the times of contact and the phenomena are different at every differ- 
 ent station. The path which the shadow of a total eclipse will 
 describe upon the earth is roughly mapped out in the Nautical Alma- 
 nacs several years beforehand, and with the chart are published the 
 data necessary to enable one to calculate with accuracy the phenomena 
 for any given station ; but the computation is rather long and some- 
 what complicated. 
 
 Oppolzer, a Viennese astronomer, published a few years ago a 
 remarkable book entitled "The Canon of Eclipses," containing the 
 elements of all eclipses (8000 solar and 5200 lunar) occurring between 
 the year 1207 B.C. and 2162 A.D., with maps showing the approximate 
 tracks of all the solar eclipses. 
 
 206. Frequency of Eclipses and Number in a Year. The 
 
 least possible number in a year is two, both of the sun ; the 
 largest seven, five solar and two lunar : the most usual number 
 is four. The eclipses of a given year always take place at two 
 opposite seasons, which may be called the " eclipse months " 
 of the year, near the times when the sun crosses the nodes of 
 the moon's orbit. Since the nodes move westward around the 
 ecliptic once in about nineteen years (Art. 134), the time oc- 
 
150 RECURRENCE OF ECLIPSES. [ 206 
 
 cupied by the sun in passing from a node to the same node 
 again is only 346.62 days, which is sometimes called the 
 " eclipse year." 
 
 Taking the whole earth into account, the solar eclipses are 
 the more numerous, nearly in the ratio of 3:2. It is not so, 
 however, with those that are visible at a given place. A solar 
 eclipse can be seen only by persons who happen to be on the 
 track described by the moon's shadow in its passage across 
 the globe, while a lunar eclipse is visible over considerably 
 more than half the earth, either at its beginning or end, 
 if not throughout its whole duration, and this more than 
 reverses the proportion; i.e., at any given place lunar eclipses 
 are considerably more frequent than solar. Solar eclipses that 
 are total somewhere or other on the earth's surface are not 
 very rare, averaging about one for every year and a half. But 
 at any given place a total eclipse happens only once in about 
 360 years in the long run. 
 
 During the 19th century, six shadow-tracks have already traversed 
 the United States, and one more will do so on May 27th, 1900, the 
 path in this case running from Texas to Virginia. 
 
 207. Recurrence of Eclipses ; the Saros. It was known to 
 the Egyptians, even in prehistoric times, that eclipses occur 
 at regular intervals of 18 years and 11-J- days (10^ days if there 
 happen to be five leap years in the interval). They named 
 this period the " Saros." It consists of 223 synodic months, 
 containing 6585.32 days, while 19 "eclipse years" contain 
 6585.78. The difference is only about 11 hours, in which time 
 the sun moves on the ecliptic about 28'. If, therefore, a solar 
 eclipse should occur to-day with the sun exactly at one of the 
 moon's nodes, at the end of 223 months the new moon will 
 find the sun again close to the node (only 28' west of it), and 
 a very similar eclipse will occur again ; but the track of this 
 new eclipse will lie about 8 hours of longitude farther west on 
 the earth, on account of the odd .32 of a day in the Saros. 
 
207] CAUSE OF THE TIDES. 151 
 
 The usual number of eclipses in a Saros is a little over 70, 
 varying two or three one way or the other. 
 
 In the Saros closing Dec. 22d, 1889, the total number was 72, 29 
 lunar and 43 solar. Of the latter, 29 were central (13 total, 16 annu- 
 lar), and 14 were only partial. 
 
 THE TIDES. 
 
 208. Cause of the Tides. Since the tides depend upon the 
 action of the sun and of the moon upon the waters of the 
 earth, they may properly be considered here before we deal 
 with the planetary system. We do not propose to go into the 
 mathematical theory of the 
 phenomena at all, as it lies 
 far beyond our limitations ; 
 but any person can see that 
 a liquid globe falling freely 
 towards an attracting body, 
 which attracts the nearer por- 
 tions more powerfully than 
 
 .__ . J , FIG. 41. The Tides. 
 
 the more remote, will be drawn 
 
 out into an elongated lemon-shaped form, as illustrated in 
 Fig. 41 ; and if the globe, instead of being liquid, is mainly 
 solid, but has large quantities of liquid on its surface, substan- 
 tially the same result will follow. Now the earth is free in 
 space, and though it has other motions, it is also falling towards 
 the moon and towards the sun, and is affected precisely as it 
 would be if its other motions did not exist. The consequence 
 is that at any time there is a tendency to elongate those diam- 
 eters of the earth which are pointed towards the moon and 
 towards the sun. The sun is so much farther away than the 
 moon that its effect in thus deforming the surface of the 
 earth is only about two-fifths as great as that of the moon. 
 
152 DEFINITIONS. [ 209 
 
 209. The tides consist in a regular rise and fall of the ocean 
 surface, the average interval between corresponding high 
 waters on successive days at any given place being twenty- 
 four hours and fifty-one minutes, which is precisely the same 
 as the average interval between two successive passages of the 
 moon across the meridian ; and since this coincidence is main- 
 tained indefinitely, it of itself makes it certain that there must 
 be some causal connection between the moon and the tides. 
 Some one has said that the odd fifty-one minutes is the moon's 
 " ear mark." 
 
 That the moon is largely responsible for the tides is also 
 shown by the fact that when the moon is in perigee, at the 
 nearest point to the earth, the tides are nearly twenty per cent 
 higher than when she is in apogee. 
 
 210, Definitions. While the water is rising, it is flood tide ; 
 while falling, it is ebb tide. It is high water at the moment 
 when the water level is highest, and low water when it is 
 lowest. The spring tides are the largest tides of the month, 
 which occur near the times of new and full moon, while the 
 neap tides are the smallest, and occur at half moon, the rela- 
 tive heights of spring and neap tides being about as 7 : 3. At 
 the time of the spring tides, the interval between the corre- 
 sponding tides of successive days is less than the average, 
 being only about 24 hours, 38 minutes (instead of 24 hours, 
 51 minutes), and then the tides are said to prime. At the neap 
 tides, the interval is greater than the mean, about 25 hours, 
 6 minutes, and the tide lags. The establishment of a port is 
 the mean interval between the time of high water at that port 
 and the next preceding passage of the moon across the merid- 
 ian. The "establishment" of New York, for instance, is 8 
 hours, 13 minutes. The actual interval between the moon's 
 transit and high water varies, however, nearly half an hour 
 on each side of this mean value at different times of the 
 month, and under varying conditions of the weather. 
 
211] MOTION OF THE TIDES. 153 
 
 211. Motion of the Tides. If the earth were wholly com- 
 posed of water, and if it kept always the same face towards the 
 moon, as the moon does towards the earth, then (leaving out 
 of account the sun's action for the present) a permanent tide 
 would be raised upon the earth, as indicated in Fig. 41. The 
 difference between the water level at A and D would be a 
 little less than two feet. Suppose, now, the earth put in rota- 
 tion. It is easy to see that the two tidal waves A and B would 
 move over the earth's surface, following the moon at a certain 
 angle dependent on the inertia of the water, and tending to 
 move with a westward velocity equal to the earth's eastward 
 rotation, about a thousand miles an hour at the equator. 
 The sun's action would produce similar tides superposed upon 
 the moon's tide, and about two-fifths as large, and at different 
 times of the month these two pairs of tides would sometimes 
 conspire and sometimes be opposed. 
 
 If the earth were entirely covered with deep water, the tide 
 waves would run around the globe regularly ; and if the depth 
 of the water were not less than thirteen miles, the tide crests, 
 as can be shown (though we do not undertake it here), would 
 follow the moon at an angle of just 90 : it would be high water 
 just where it might at first be supposed we should get low 
 water, the place of high water being shifted 90 by the rota- 
 tion of the earth. 
 
 If the depth of the water were, as it really is, much less 
 than thirteen miles, the tide wave in the ocean could not keep 
 up with the moon, and this would complicate the results. 
 Moreover, the continents of North and South America, with 
 the southern Antarctic continent, make a barrier almost from 
 pole to pole, leaving only a narrow passage at Cape Horn. As 
 a consequence it is quite impossible to determine by theory 
 what the course and character of tide waves must be. We 
 have to depend upon observations, and observations are 
 more or less inadequate, because, with the exception of a 
 few islands, our only possible tide stations are on the shores 
 
154 FREE AND FOECED OSCILLATIONS. [ 211 
 
 of continents where local circumstances largely control the 
 phenomena. 
 
 212. Free and Forced Oscillations. If the water of the 
 ocean is suddenly disturbed, as, for instance, by an earth- 
 quake, and then left to itself, a " free wave " is formed, which, 
 if the horizontal dimensions of the wave are large as compared 
 with the depth of the water (i.e., if it is many hundred miles 
 in length), will travel at a rate which depends simply on the 
 depth of the water. 
 
 Its velocity is equal, as can be proved, to the velocity acquired by a 
 body in falling through half the depth of the ocean. Observations 
 upon waves caused by certain earthquakes in South America and 
 Japan have thus informed us that between the coasts of those coun- 
 tries the Pacific averages between two and one-half and three miles in 
 depth. 
 
 Now as the moon in its apparent diurnal motion passes 
 across the American continent each day and comes over the 
 Pacific Ocean, it starts such a "parent" wave in the Pacific, 
 and a second one is produced twelve hours later. These waves, 
 once started, move on nearly (but not exactly) like a free earth- 
 quake wave : not exactly, because the velocity of the earth's 
 rotation being about 1040 miles at the equator, the moon 
 moves (relatively) westward faster than the wave can natu- 
 rally follow it ; and so for a while the moon slightly acceler- 
 ates the wave. The tidal wave is thus, in its origin, a " forced 
 oscillation " : in its subsequent travel it is very nearly, but 
 not entirely, " free." 
 
 Of course as the moon passes on over the Indian and Atlan- 
 tic oceans, it starts waves in them also, which combine with 
 the parent wave coming in from the Pacific. 
 
 213. Course of Travel of the Tide Wave. The parent wave 
 appears to start twice a day in the Pacific Ocean, off Callao, on the 
 
213] HEIGHT OF THE TIDES. 155 
 
 coast of South America. From this point the wave travels northwest 
 through the deep water of the Pacific, at the rate of about 850 miles an 
 hour, reaching Kamtchatka in ten hours. Through the shallow water 
 to the west and southwest the velocity is only from 400 to 600 miles an 
 hour, so that the wave is six hours old when it reaches New Zealand. 
 Passing on by Australia and combining with the small wave which the 
 moon starts in the Indian Ocean, the resultant tide crest reaches the 
 Cape of Good Hope in about twenty-nine hours, and enters the 
 Atlantic. Here it combines with a smaller tide wave, twelve hours 
 younger, which has " backed " into the Atlantic around Cape Horn, 
 and it is also modified by the direct tide produced by the moon's 
 action upon the Atlantic. The tide resulting from the combination of 
 these three then travels northward through the Atlantic at the rate of 
 about 700 miles an hour. It is about forty hours old when it first 
 reaches the coast of the United States in Florida ; and our coast lies 
 in such a direction that it arrives at all the principal ports within two 
 or three hours of the same time. It is forty-one or forty-two hours 
 old when it reaches New York and Boston. To reach London, it has 
 to travel around the northern end of Scotland and through the North 
 Sea, and is nearly sixty hours old when it arrives at that port. 
 
 In the great oceans there are three or four such tide crests, follow- 
 ing nearly in the same track, but with continual minor changes. 
 
 214. Height of the Tides. In mid-ocean the difference 
 between high and low water is usually between two and three 
 feet, as observed on isolated islands in the deep water. On 
 the continental shores the height is ordinarily much greater. 
 
 j^ ^_c^ ^ ^ A r 
 
 ^ ^^ ^ ^ ^^ v v v 
 
 PIG. 42. Increase in Height of Tide on approaching the Shore. 
 
 As soon as the tide wave "touches bottom/ 7 so to speak, the 
 velocity* is diminished, the tide crests are crowded more closely 
 together, and the height of the tide is very much increased, as 
 indicated in Fig. 42. 
 
156 TIDES IN RIVEKS. [ 214 
 
 Theoretically it varies inversely as the fourth root of the depth ; i.e., 
 where the water is 100 feet deep, the tide wave should be twice as 
 high as at the depth of 1600 feet. 
 
 Where the configuration of the shore forces the tide into a 
 corner, it sometimes rises very high. At Annapolis on the 
 Bay of Fundy, tides of seventy feet are not uncommon, and an 
 altitude of 100 feet is said to occur sometimes. At Bristol 
 in the English Channel, tides of forty or fifty feet are reached ; 
 at the same time on the coast of Ireland, just opposite, the 
 tide is very small. 
 
 215. Tides in Rivers. The tide wave ascends a river at a rate 
 which depends upon the depth of the water, the amount of friction, 
 and the swiftness of the stream. It may, and generally does, ascend 
 until it cornes to a rapid where the velocity of the current is greater 
 than that of the wave. In shallow streams, however, it dies out 
 earlier. Contrary to what is usually supposed, it often ascends to an 
 elevation far above that of the highest crest of the tide wave at the 
 river's mouth. In the La Plata and Amazon, the tide goes up to an 
 elevation of at least 100 feet above the sea-level. The velocity of a 
 tide wave in a river seldom exceeds ten or twenty miles an hour, and 
 is ordinarily much less. 
 
216] THE PLANETS IN GENERAL. 157 
 
 CHAPTER VIII. 
 
 THE PLANETAEY SYSTEM. 
 
 THE PLANETS IN GENERAL. THEIR NUMBER, CLASSI- 
 FICATION, AND ARRANGEMENT. BODE'S LAW. THEIR 
 ORBITS. KEPLER'S LAWS AND GRAVITATION. AP- 
 PARENT MOTIONS AND THE SYSTEMS OF PTOLEMY 
 AND COPERNICUS. DETERMINATION OF DATA RELAT- 
 ING TO THE PLANETS, THEIR DIAMETER, MASS, ETC. 
 
 HERSCHEL'S ILLUSTRATION OF THE SOLAR SYSTEM. 
 
 DESCRIPTION OF THE TERRESTRIAL PLANETS, MERCURY, 
 VENUS, AND MARS. 
 
 216. THE earth is one of a number of bodies called planets 
 which revolve around the sun in oval orbits that are nearly 
 circular and lie nearly in one plane or level. There are eight 
 of them which are of considerable size, besides a group of sev- 
 eral hundred minute bodies called the asteroids, which seem 
 to represent in some way a ninth planet, either broken to 
 pieces or somehow ruined in the making. 
 
 217. Classification of the Planets. The four inner ones 
 have been called by Humboldt the terrestrial planets, because 
 the earth is one of them, and the others resemble it in size 
 and density. In the order of distance from the sun they are 
 Mercury, Venus, the earth, and Mars. The four outer ones 
 Humboldt calls the major planets, because they are much 
 larger and move in larger orbits. They seem to be bodies of 
 a different sort from the earth, very much less dense and 
 
158 
 
 BODE'S LAW. 
 
 [217 
 
 probably of higher temperature. They are Jupiter, Saturn, 
 Uranus, and Neptune. The asteroids (from the Greek aster- 
 eidos, i.e., star-like planets), called by some planetoids, or 
 minor planets, all lie in the vacant space between Mars and 
 Jupiter, and appear to contain in the aggregate about as much 
 material as would make a planet not far from the size of Mars. 
 All of the planets except Mercury and Venus have satellites. 
 The earth has one, Mars two, Jupiter four, Saturn eight, 
 Uranus four, Neptune one, twenty in all. 
 
 218. The following little table contains in round numbers 
 the principal numerical facts as to the planets : 
 
 NAME. 
 
 DISTANCE IN 
 ASTRONOMICAL 
 UNITS. 
 
 PERIOD. 
 
 DIAMETER. 
 
 Mercury 
 
 04 
 
 3 months 
 
 3000 miles 
 
 Venus 
 
 07 
 
 7^ months 
 
 7700 " 
 
 Earth . 
 
 10 
 
 1 year 
 
 7918 " 
 
 Mars 
 
 1 5 
 
 1 yr 10 mos 
 
 4200 " 
 
 Asteroids 
 
 3.0 
 
 3 years to 9 years 
 
 200 to 10 miles 
 
 Jupiter 
 
 52 
 
 11 9 years 
 
 86,000 miles 
 
 Saturn 
 
 95 
 
 295 " 
 
 73 000 " 
 
 Uranus 
 
 192 
 
 8^0 " 
 
 32 000 " 
 
 Neptune 
 
 301 
 
 1648 " 
 
 35 000 " 
 
 
 
 
 
 This table should be learned by heart. More accurate data 
 will be given hereafter, but the round numbers are quite suf- 
 ficient for all ordinary purposes, and are much more easily 
 remembered. 
 
 219. Bode's Law. If we set down a row of 4's, to the 
 second 4 add 3, to the third 6, to the fourth 12, etc., a series of 
 numbers will result which, divided by 10, will represent the 
 planetary distances very nearly, except in the case of Neptune, 
 
219] KEPLER'S LAWS. 159 
 
 whose distance is only 30 instead of 38, as the rule would 
 make it. Thus 
 
 444444 4 4 4 
 
 3 6 12 24 48 96 192 384 
 
 4 7 10 16 [28] 52 100 196 388 
 
 $ 2 :y b v 
 
 (The characters below the numbers are the symbols of the 
 planets, used in almanacs instead of their names.) 
 
 This law seems to have been first noticed by Titius of Wittenberg, 
 but bears the name of Bode, Director of the Observatory of Berlin, 
 who first secured general attention to it. 
 
 No logical reason can yet be given for it. It may be a mere con- 
 venient coincidence, or it may be the result of the process of develop- 
 ment which brought the solar system into its present state. 
 
 220. Kepler's Laws. Three famous laws discovered by 
 Kepler (1607-1620) govern the motions of the planets : 
 
 I. The orbit of each planet is an ellipse with the sun in one 
 of its foci. (See Appendix, Art. 429, for a description of the 
 ellipse.) 
 
 II. In the motion of each planet around the sun, the radius 
 vector describes equal areas in equal times. (See Art. 121, 
 Fig. 13, for illustration.) 
 
 III. The squares of the periods of the planets are propor- 
 tional to the cubes of their mean distances from the sun. This 
 is known as the Harmonic Law. Stated as a proportion it 
 reads : P-f : P 2 2 : : A-f : A 2 S , or in words : The square of the period 
 of planet No. 1 : square of the period of planet No. 2 : : cube of 
 the mean distance of planet No. 1 : cube of the mean distance of 
 planet No. 2. Planets No. 1 and No. 2 are any pair of planets 
 selected at pleasure. (For fuller illustration, see Appendix, 
 Art. 430.) 
 
 It was the discovery of this law which so filled Kepler with 
 enthusiasm that he wrote, " If God has waited 6000 years for 
 a discoverer, I can wait as long for a reader." 
 
160 GRAVITATION. [ 221 
 
 221. Gravitation. When Kepler discovered these three 
 laws he could give no reason for them no more than we 
 can now for Bode's law ; but some sixty years later Newton 
 discovered that they all follow necessarily as the consequence 
 of the law of gravitation, which he had discovered ; namely, 
 that "every particle of matter in the universe attracts every 
 other particle with a force that varies directly as the masses of the 
 particles, and inversely as the square of the distance between 
 them" It would take us far beyond our limits to attempt to 
 show how Kepler's laws follow from this, but they do. The 
 only mystery in the case is the mystery of the " attraction " 
 itself; for this word "attraction' 7 is to be taken as simply 
 describing an effect without in the least explaining it. 
 
 Things take place as if the atoms had in themselves intelligence to 
 recognize each other's positions, and power to join hands in some way, 
 and pull upon each other through the intervening space, whether it 
 be great or small. But neither Newton nor any one else supposes that 
 atoms are really endowed with any such power, and the explanation 
 of gravity remains to be found : very probably it is somehow involved 
 in that constitution of the material universe which makes possible the 
 transmission through space of light and heat, and electric and mag- 
 netic forces. 
 
 222. Sufficiency of Gravitation to explain the Planetary 
 Motions. We wish to impress as distinctly as possible upon 
 the student one idea; this namely, that given a planet once in 
 motion, nothing further than gravitation is required to explain 
 perfectly all its motions forever after. Many half-educated 
 people have an idea that some other force or mechanism must 
 act to keep the planets going. This is not so : not a single 
 motion in the whole planetary system has ever yet been de- 
 tected for which gravitation fails to account. 
 
 223. Map of the Orbits. Fig. 43 shows the smaller orbits 
 of the system (including the orbit of Jupiter) drawn to scale, 
 
223] 
 
 SMALLER PLANETARY ORBITS. 
 
 161 
 
 the radius of the earth's orbit being taken as four-tenths of an 
 inch. 
 
 On this scale, the diameter of Saturn's orbit would be 7.4 inches, 
 that oi' Uranus would be 13.4: inches, and that of Neptune about two 
 
 FIG. 43. Plan of the Smaller Planetary Orbits. 
 
 feet. The nearest fixed star, on the same scale, would be a mile and 
 a quarter away. 
 
 It will be seen that the orbits of Mercury, Mars, Jupiter, 
 and several of the asteroids are quite distinctly " out of cen- 
 
162 INCLINATION OF THE ORBITS. [ 223 
 
 tre " with respect to the sun. The orbits are so nearly cir- 
 cular that there is no noticeable difference between their 
 length and their breadth, but the eccentricity shows plainly 
 in the position of the sun. 
 
 224. Inclination of the Orbits. The orbits are drawn as if 
 they all lay on the plane of the ecliptic ; i.e., on the surface of 
 the paper. This is not quite correct. The orbit of the asteroid 
 Pallas should be really tipped up at an angle of nearly 30, 
 and that of Mercury, which is more inclined to the ecliptic 
 than the orbit of any other of the principal planets, is sloped 
 at an angle of 7. The inclinations, however, are so small 
 
 (excepting the asteroids) 
 that they may be neg- 
 lected for ordinary pur- 
 poses. On the scale of 
 the diagram, Neptune, 
 ~ which rises and falls the 
 
 _ ,. . . __ _ most of all with refer- 
 
 FIG. 44. Inclination ana Line of Nodes. 
 
 ence to the plane of the 
 
 ecliptic, would never be more than a third of an inch above 
 or below the level of the paper. 
 
 The line in which the plane of a planet's orbit cuts the 
 plane of the earth's orbit at the ecliptic is called the Line of 
 Nodes. Fig. 44 shows how the line of nodes and the inclina- 
 tion of the two orbits are related. 
 
 225. Geocentric Motions of the Planets; i.e., their motions 
 with respect to the earth regarded as the centre of observation. 
 
 While the planets revolve regularly in nearly circular orbits 
 around the sun, with velocities * which depend upon their dis- 
 tance from it, the motions relative to the earth are very dif- 
 ferent, being made up of the planet's real motion combined 
 
 1 A planet's velocity in miles per second equals very nearly 
 
225] 
 
 DIRECT AND RETROGRADE MOTION. 
 
 163 
 
 with, the apparent motion due to that of the earth in her own 
 orbit. 
 
 If, for instance, we keep up observations, for a long time, of 
 the direction of Jupiter as seen from the earth, at the same 
 time watching the changes 
 of its distance by measur- 
 ing the alterations of the 
 planet's apparent size as 
 seen in the telescope, and 
 then plot the results to get 
 the form of the orbit of 
 Jupiter with reference to 
 the earth, we get a path 
 like that shown in Fig. 45, 
 which represents his mo- 
 tion relative to the earth 
 during a term of about 
 twelve years. The appear- 
 ances are all the same as if 
 the earth were really at rest while the planet moved in this 
 odd way. 
 
 The procedure for finding this relative orbit of Jupiter is the same 
 as that indicated in Appendix, Art. 428, for finding the form of the 
 earth's orbit around the sun. 
 
 226. Direct and Retrograde Motion. With the eye alone 
 the changes in a planet's diameter would not be visible, and 
 we should notice only the alternating direct (eastward) 
 and retrograde (westward) motion of the planet among the 
 stars. If we watch one of the planets (say Mars) for a few 
 weeks, beginning at the time when it rises at sunset, we shall 
 find that each night it has travelled some little distance to the 
 west ; and it will keep up this westward or retrograde motion 
 for some weeks, when it will stop or become " stationary," and 
 will then reverse its motion and begin to move eastward. If 
 
 FIG. 45. 
 Apparent Geocentric Motion of Jupiter. 
 
164 
 
 ELONGATION AND CONJUNCTION. 
 
 [226 
 
 we watch long enough (i.e., for several years) we shall find 
 that it keeps up this oscillating motion all the time, the length 
 of its eastward swing being always greater than that of the 
 corresponding westward one. All the planets, without excep- 
 tion, behave alike in this respect, as to their alternate direct 
 and retrograde motion among the stars. 
 
 227. Elongation and Conjunction. The visibility of a 
 planet does not, however, depend upon its position among 
 
 Conjunction 
 
 Greatest W. Elongation 
 
 Opposition 
 FIG. 46. Planetary Configurations. 
 
 the stars, but upon its position in the sky with reference to 
 the sun's place. If it is very near the sun, it will be above 
 the horizon only by day, and generally we cannot see it. The 
 Elongation of a planet is the apparent distance from the sun 
 in degrees, as seen from the earth, of course. In Fig. 46, for 
 the planet P, it is the angle PES. When the planet is in line 
 
227] SYNODIC PERIOD. 165 
 
 with, the sun as seen from the earth, at B, C, or / in the figure, 
 the elongation is zero, and the planet is said to be in conjunc- 
 tion; inferior conjunction, if the planet is between the earth 
 and the sun, as at /; superior, if beyond the sun, as at B or O. 
 When the elongation is 180, as at A, the planet is said to be 
 in opposition. When the planet is at an elongation of 90, as 
 at F or G, it is in quadrature. Evidently only those planets 
 which lie within the earth's orbit, and are called < inferior' 
 planets, can have an inferior conjunction; and only those 
 which are outside the earth's orbit (the superior planets) can 
 come to quadrature or opposition. 
 
 228. Synodic Period. The synodic period of a planet is 
 the time occupied by it in passing from conjunction to con- 
 junction again, or from opposition to opposition; so called 
 because the word " synod " is derived from two Greek words 
 which mean ' a coming together.' The relation of the synodic 
 period to the sidereal is the same for planets as in the case of 
 the moon. If E is the length of the true (sidereal) year, and 
 P the planet's period, S being the length of the synodic period, 
 then 
 
 !=!_! 
 SEP 
 
 (The difference between and is to be taken without regard 
 E P 
 
 to which of the two is the larger.) 
 
 229. The Synodic Motion, or Apparent Motion of a Planet 
 with respect to ' Elongation ' or to the Sun's Place in the Sky. 
 
 In this respect there is a marked difference between the 
 superior and inferior planets. 
 
 (a) The inferior planets are never seen very far from the 
 sun, but appear to oscillate back and forth in front of and 
 behind him. Venus, for instance, starting at superior con- 
 junction at C (Fig. 46), seems to come out eastward from the 
 
166 PTOLEMAIC AND COPERNICAN SYSTEMS. [ 229 
 
 sun as an evening star, until, at the point V, she reaches her 
 greatest eastern elongation, about 47 from the sun. Then she 
 begins to dimmish her elongation, and approaches the sun, 
 until she comes to inferior conjunction, at /. From there 
 she continues to move westward as morning star, until she 
 comes to V, her greatest western elongation, and there she 
 begins to diminish her western elongation until, at the end 
 of the synodic period, she is back at superior conjunction. 
 The time taken to move from V' to V through C is, in her 
 case, more than three times that required to slide back from 
 V to V through I. The gain of eastern elongation is up-hill 
 work, as she is then, so to speak, pursuing the sun, which 
 itself moves eastward nearly a whole degree every day along 
 the ecliptic. 
 
 (b) The superior planets may be found at all elongations, 
 and do not oscillate back and forth with reference to the 
 apparent place of the sun, but continually increase their 
 western elongation or decrease their eastern. They always 
 come to the meridian earlier on each successive night } though the 
 difference is not uniform. 
 
 230. Ptolemaic and Coperniean Systems. Until the time 
 of Copernicus (about 1540) the Ptolemaic System prevailed 
 unchallenged. It rejected the idea of the earth's rotation 
 (though Ptolemy accepted the rotundity of the earth), placing 
 her at the centre of things and teaching that the apparent 
 motions of the stars and planets were real ones. It taught 
 that the celestial sphere revolves daily around the earth, carry- 
 ing the stars and planets with it, and that besides this diurnal 
 motion, the moon, the sun, and all the planets revolve around 
 the earth within the sphere, the two former steadily, but the 
 planets with the peculiar looped motion shown in Fig. 45. 
 
 Copernicus put the sun at the centre, and made the earth 
 revolve on its axis and travel around the sun, and showed that 
 it was possible in this simple way to account for all the other- 
 
230] THE PLANETS THEMSELVES. 167 
 
 wise hopelessly complicated phenomena of the planetary and 
 diurnal motions, so far as then known. It was not until after 
 the invention of the telescope, and the introduction of new 
 methods of observation, that the facts which absolutely demon- 
 strate the orbital motion of the earth were brought to light ; 
 viz., Aberration of Light (Appendix, Art. 435) and Stellar 
 Parallax (Art. 433). 
 
 THE PLANETS THEMSELVES. 
 
 231. In studying the planetary system we meet a number 
 of inquiries which refer to the planet itself and not to its 
 orbit ; relating, for instance, to its magnitude; its mass, density, 
 and surface-gravity; its diurnal rotation and ellipticity ; its 
 brightness, phases, and reflecting power, or " albedo " ; the pecul- 
 iarities of its spectrum; its atmosphere; its surface-markings and 
 topography ; and, finally, its satellite system. 
 
 232. Magnitude. The size of a planet is found by measur- 
 ing its apparent diameter (in seconds of arc) with some form 
 of "micrometer" (see Appendix, Art. 415). Since we can 
 find the distance of a planet from the earth at any moment 
 when we know its orbit, this micrometric measure will give us 
 the means of finding at once the planet's diameter in miles. 
 
 If we take r to represent the number of times by which the 
 planet's semi-diameter exceeds that of the earth, then the area 
 of the planet's surface compared with that of the earth equals 
 r 2 , and its volume or bulk equals r 3 . The nearer the planet, 
 other things being equal, the more accurately r and the quanti- 
 ties to be derived from it can be determined. An error of O'M 
 in measuring the apparent diameter of Venus, when nearest us, 
 counts for less than thirteen miles ; while in Neptune's case, 
 the same error would correspond to more than 1300 miles. 
 
 233. Mass, Density, and Gravity. If the planet has a 
 satellite, its mass is very easily and accurately found from the 
 
168 THE EOTATION PERIOD. [ 233 
 
 following proportion, which we simply state without demon- 
 stration (see General Astronomy, Arts. 536, 539) j viz. : 
 
 AS a 3 
 
 Mass of JSun : mass of Planet : : 2 : , 
 
 in which A is the mean distance of the planet from the sun and 
 T its sidereal period of revolution, while a is the distance of 
 the satellite from the planet, and t its sidereal period ; whence 
 
 Mass of Planet = Sun x ( X \ 
 \ t 2 A 3 J 
 
 Substantially the same proportion may be used to compare the 
 planet with the earth ; viz. : 
 
 (Earth + Moon) : (Planet + Satellite) : : -\ : ^L, 
 
 t\ l* 
 
 a^ and < a being here the period and distance of the moon, and a 2 and 
 t z those of the planet's satellite. 
 
 If the planet has no satellite, the determination of its mass is a dif- 
 ficult matter, depending upon perturbations produced by it in the 
 motions of the other planets. 
 
 Having the planet's mass compared with the earth, we get 
 its density by dividing the mass by the volume, and the super- 
 ficial gravity is found by dividing by r 2 the mass of the planet 
 compared with that of the earth. 
 
 234. The Rotation Period and Data connected with it. 
 
 The length of the planet's day, when it can be determined at 
 all, is ascertained by observing with the telescope some spot 
 on the planet's disc and noting the interval between its returns 
 to the same apparent position. The inclination of the planet's 
 equator to the plane of its orbit, and the position of its equi- 
 noxes, are deduced from the same observations that give the 
 planet's diurnal rotation ; we have to observe the path pursued 
 by a spot in its motion across the disc. Only Mars, Jupiter, 
 and Saturn permit us to find these elements with any consider- 
 able accuracy. 
 
 The ellipticity or oblateness of the planet, due to its rota- 
 
234] SATELLITE SYSTEM. 169 
 
 tion, is found by taking measures of its polar and equatorial 
 diameters. 
 
 235. Data relating to the Planet's Light. A planet's 
 brightness and its reflecting power, or "albedo," are deter- 
 mined by photometric observations, and the spectrum of the 
 planet's light is of course studied with the spectroscope. The 
 question of the planet's atmosphere is investigated by means of 
 various effects upon the planet's appearance and light, and by 
 the phenomena that occur when the planet comes very near to 
 a star or to some other heavenly body which lies beyond. The 
 planet's surface-markings and topography are studied directly 
 with the telescope, by making careful drawings of the appear- 
 ances noted at different times. Photography, also, is begin- 
 ning to be used for the purpose. If the planet has any well- 
 marked and characteristic spots upon its surface by which the 
 time of rotation can be found, then it soon becomes easy to 
 identify such as are really permanent, and after a time we can 
 chart them more or less perfectly; but we add at once that 
 Mars is the only planet of which, so far, we have been able to 
 make anything which can be fairly called a map. 
 
 236. Satellite System. The principal data to be ascer- 
 tained are the distances and periods of the satellites. These 
 are obtained by micrometric measures of the apparent distance 
 and direction of each satellite from the planet, followed up for 
 a considerable time. In a few cases it is possible to make 
 observations by which we can determine the diameters of the 
 satellites, and when there are a number of satellites together 
 their masses may sometimes be ascertained from their mutual 
 perturbations. With the exception of our moon and lapetus, 
 the outer satellite of Saturn, all the satellites of the solar sys- 
 tem move almost exactly in the plane of the equator of the planet 
 to which they belong ; at least, so far as known, for we do not 
 know with certainty the position of the equators of Uranus 
 
170 PLANETARY DATA. [ 236 
 
 and Neptune. Moreover, all the satellites, except the moon 
 and Hyperion, the seventh satellite of Saturn, move in orbits 
 that are practically circular. 
 
 237. Tables of Planetary Data. In the Appendix we pre- 
 sent tables of the different numerical data of the solar system, 
 derived from the best authorities and calculated for a solar 
 parallax of 8".80, the sun's mean distance being, therefore, 
 taken as 92,897000 miles. These tabulated numbers, however, 
 differ widely in accuracy. The periods of the planets and 
 their distances in ' astronomical units' are very accurately 
 known ; probably the last decimal in the table may be trusted. 
 Next in certainty come the masses of such planets as have 
 satellites, expressed in terms of the sun's mass. The masses 
 of Venus and Mercury are much more uncertain. 
 
 The distances of the planets in miles, their masses in terms 
 of the earth's mass, and their diameter in miles, all involve the 
 solar parallax, and are affected by the slight uncertainty in its 
 amount. For the remoter planets, diameters, volumes, and 
 densities are all subject to a very considerable percentage of 
 error. The student need not be surprised, therefore, at finding 
 serious discrepancies between the values given in these tables 
 and those given in others, amounting in some cases to ten or 
 twenty per cent, or even more. Such differences merely indi- 
 cate the actual uncertainty of our knowledge. Fig. 47 gives 
 an idea of the relative sizes of the planets. 
 
 The sun, on the scale of the figure, would be about a foot in 
 diameter. 
 
 238. Sir John Herschel's Illustration of the Dimensions of 
 the Solar System. In his "Outlines of Astronomy," Herschel 
 gives the following illustration of the relative magnitudes and dis- 
 tances of the members of our system : 
 
 " Choose any well-levelled field. On it place a globe two feet in diame- 
 ter. This will represent the sun. Mercury will be represented by a grain 
 
RELATIVE SIZE OF THE PLANETS. 
 
 171 
 
 of mustard seed on the circumference of a circle 164 feet in diameter for 
 its orbit ; Venus, a pea, on a circle of 284 feet in diameter ; the Earth, 
 also a pea, on a circle of 430 feet ; Mars, a rather large pin's head, on a 
 circle of 654 feet ; the asteroids, grains of sand, on orbits having a diame- 
 ter of 1000 to 1200 feet ; Jupiter, a moderate- sized orange, on a circle 
 nearly half a mile across ; Saturn, a small orange, on a circle of four- fifths 
 
 FIG. 47. Relative Size of the Planets. 
 
 of a mile ; Uranus, a full-sized cherry or small plum, upon a circumfer- 
 ence of a circle more than a mile in diameter ; and, finally, Neptune, a 
 good-sized plum, on a circle about 2| miles in diameter." 
 
 We may add that, on this scale, the nearest star would be on the 
 opposite side of the globe, 8000 miles away. 
 
 THE TERRESTRIAL PLANETS, MERCURY, VENUS, AND 
 
 MARS. 
 
 239. Mercury has been known from the remotest antiquity, 
 and among the Greeks it had for a time two names, Apollo 
 when it was morning star, and Mercury when it was evening 
 star. It is so near the sun that it is comparatively seldom 
 
172 MEBCTJR. t 239 
 
 seen with the naked eye, but when near its greatest elongation 
 it is easily enough visible as a brilliant reddish star of the 
 first magnitude, low down in the twilight. It is best seen in 
 the evening at such eastern elongations as occur in the spring. 
 When it is morning star, it is best seen in the autumn. 
 
 It is exceptional in the solar system in various ways. It is 
 the nearest planet to the sun, receives the most light and heat, 
 is the swiftest in its movement, and (excepting some of the 
 asteroids) has the most eccentric orbit, with the greatest inclina- 
 tion to the ecliptic. It is also the smallest in diameter (again 
 excepting the asteroids), has the least mass, and (probably) 
 the greatest density of all the planets. 
 
 240. Its Orbit. The planet's mean distance from the sun 
 is 36,000000 miles, but the eccentricity of its orbit is so great 
 (0.205) that the sun is 7,500000 miles out of the centre, 
 and the distance ranges all the way from 281 millions to 43^ 
 millions, while the planet's velocity in the different parts of 
 its orbit varies from 36 miles a second to only 23. A given 
 area upon its surface receives on the average nearly seven 
 times as much light and heat as it would on the earth ; but 
 the heat received when the planet is at perihelion is 2\ times 
 greater than at aphelion. For this reason there must be at 
 least two seasons in its year, due to the changing distance of 
 the planet from the sun, whatever may be the position of its 
 equator or the length of its day. The sidereal period is 88 
 days, and the synodic period (or time from conjunction to con- 
 junction) is 116 days. The greatest elongation ranges from 
 18 to 28, and occurs about 22 days before and after the in- 
 ferior conjunction. The inclination of the orbit to the ecliptic 
 is about 7. 
 
 241. Planet's Magnitude, Mass, etc. The apparent diam- 
 eter of Mercury varies from 5" to about 13", according to its 
 distance from us ; and its real diameter is very near 3000 
 
TELESCOPIC APPEARANCE. 
 
 173 
 
 miles. This makes its surface about one-seventh that of the 
 earth, and its bulk or volume one-eighteenth. The planet's 
 mass is very difficult to determine, since it has no satellite, 
 and it is not accurately known. Probably it is not far from 
 one-fifteenth of the earth's mass ; it is certainly smaller than 
 that of any planet (asteroids , excepted). Our uncertainty as 
 to the mass prevents us from assigning certain values to its 
 density or superficial gravity, though it is probably somewhat 
 denser than the earth, and the force of gravity upon it about 
 one-half what it is upon the earth. 
 
 242. Telescopic Appearances, Phases, etc. Seen through 
 the telescope the planet looks like a little moon, showing 
 
 FIG. 48. Phases of Mercury and Venus. 
 
 phases precisely similar to those of our satellite. At inferior 
 conjunction the dark side is towards us ; at superior conjunc- 
 tion the illuminated surface. At greatest elongation, the 
 planet appears as a half-moon. It is gibbous between superior 
 conjunction and greatest elongation, while between inferior 
 conjunction and greatest elongation it is crescent. Fig. 48 
 illustrates these phases. 
 
 The atmosphere of the planet cannot be as dense as that of 
 the earth or Venus, because at a transit it shows no encircling 
 ring of light, as Venus does (Art. 248); both Huggins and 
 Vogel, however, report that the spectrum of the planet, in 
 
174 DIURNAL ROTATION OF MERCURY. [242 
 
 addition to the ordinary dark lines belonging to the spectrum 
 of reflected sunlight, shows certain bands known to be due to 
 water-vapor, thus indicating that water exists in the planet's 
 atmosphere. 
 
 Generally, Mercury is so near the sun that it can be observed 
 only by day ; but when proper precautions are taken to screen 
 the object-glass of the telescope from direct sunlight, the ob- 
 servation is not especially difficult. The surface presents very 
 little of interest. The disc is brighter at the edge than at the 
 centre, but the markings are not well enough denned to give 
 us any really satisfactory information as to its topography. 
 
 The albedo, or reflecting power, of the planet is very low, 
 only 0.13, somewhat inferior to that of the moon and very 
 much below that of any other of the planets. No satellite is 
 known, and there is no reason to suppose that it has any. 
 
 243. Diurnal Rotation of the Planet. In 1889, Schiaparelli, 
 the Italian astronomer, announced that he had discovered cer- 
 tain markings upon the planet, and that they showed that the 
 planet rotates on its axis only once during its orbital period of 
 eighty-eight days, thus keeping the same face always turned 
 towards the sun, in the same way that the moon behaves with 
 respect to the earth. Owing to the eccentricity of the planet's 
 orbit, however, it must have a large libration (Art. 145), 
 amounting to about 23 on each side of the mean ; i.e., seen 
 from a favorable station on the planet's surface, the sun, 
 instead of rising and setting, as with us, would seem to oscil- 
 late back and forth through an arc of 47 once in 88 days. 
 
 This asserted discovery is very important and has excited 
 great interest. Schiaparelli is probably correct, but it may be 
 well to wait for confirmation of his observations by others 
 before absolutely accepting the conclusion. 
 
 244. Transits of Mercury. At the time of inferior con- 
 junction, the planet usually passes north or south of the sun; 
 
244] VENUS. 175 
 
 the inclination of its orbit being 7; but if the conjunction 
 occurs when the planet is very near its node (Art. 224), it 
 crosses the sun's disc and becomes visible upon it as a small 
 black spot ; not, however, large enough to be seen without a 
 telescope, as Venus can under similar circumstances. Since 
 the earth passes the planet's line of nodes on May 7th and 
 Nov. 9th, transits can occur only near those days. 
 
 The transits of the last half of the present century are as follows : 
 May Transits. May 6th, 1878; May 9th, 1891 ; visible in the 
 United States. November Transits. Nov. 12th, 1861; Nov. 5th, 
 1868; Nov. 7th, 1881; Nov. 10th, 1894. 
 
 Transits of Mercury are of no particular astronomical importance, 
 except as furnishing accurate determinations of the planet's place in 
 the sky at a given time. 
 
 VENUS. 
 
 245. The second planet in order from the sun is Venus, the 
 brightest and most conspicuous of all. It is so brilliant that 
 at times it casts a shadow, and is easily seen by the naked eye 
 in the daytime. Like Mercury it had two names among the 
 Greeks, Phosphorus as morning star, and Hesperus as even- 
 ing star. 
 
 Its mean distance from the sun is 67,200000 miles, and its 
 distance from the earth ranges from 26,000000 miles (93 67) 
 to 160,000000 (93 + 67). No other body ever comes so near 
 the earth except the moon, and occasionally a comet. The 
 eccentricity of the orbit of Venus is the smallest in the plane- 
 tary system, only 0.007, so that the greatest and least dis- 
 tances of the planet from the sun differ from the mean less 
 than 500,000 miles. Its sidereal period is 225 days, or seven 
 and a half months ; and its synodic period 584 days, a year 
 and seven months. From superior conjunction to greatest 
 elongation is only 71 days. The inclination of its orbit is not 
 quite 3y, less than half that of Mercury. 
 
176 MAGNITUDE, MASS, ETC. t 2 ^ 
 
 246. Magnitude, Mass, Density, etc. The apparent diam- 
 eter of the planet varies from 67", at the time of inferior con- 
 junction, to only 11", at superior ; the great difference arising 
 from the enormous variation in the distance of the planet from 
 the earth. The real diameter of the planet in miles is about 
 7700. Its surface compared with that of the earth is T 9 ^ ; its 
 volume, -j^. By means of the perturbations she produces 
 upon the earth, the mass of Venus is found to be a little less 
 than four-fifths of the earth's mass, so that her mean density 
 is a little less than the earth's. In magnitude she is the 
 earth's twin sister. 
 
 247. General Telescopic Appearance ; Phases, etc. The 
 
 general telescopic appearance of Venus is striking on account 
 of her great brilliancy, but exceedingly unsatisfactory because 
 nothing is distinctly outlined upon the disc. 
 
 When about midway between greatest elongation and infe- 
 rior conjunction, the planet has an apparent diameter of 40", 
 so that with a magnifying power of only 45 she looks exactly 
 like the moon four days old, and of the same apparent size. 
 (Very few persons, however, would think so on the first view 
 through the telescope; the novice always underrates the 
 apparent size of a telescopic object.) 
 
 The phases of Venus were first discovered by Galileo in 1610, and 
 afforded important evidence as to the truth of the Copernican system 
 as against the Ptolemaic. Fig. 49 represents the planet's disc as seen 
 at five points in its orbit. 1, 3, and 5 are taken at superior conjunc- 
 tion, greatest elongation, and near inferior conjunction, respectively; 
 while 2 and 4 are at intermediate points. (No. 2 is badly engraved, 
 however ; the sharp corners are impossible.) 
 
 The planet attains its maximum brightness when its appar- 
 ent area is at a maximum, about thirty-six days before and 
 after inferior conjunction. According to Zollner, the ' albedo ' 
 of the planet is 0.50; i.e., it reflects about half the light 
 which falls upon it, the reflecting power being about three 
 
247] 
 
 TELESCOPIC APPEARANCES OF VENUS. 
 
 177 
 
 times that of the moon, and almost four times that of Mer- 
 cury. It is, however, slightly exceeded by the reflecting 
 power of Uranus and Jupiter, while that of Saturn is about 
 
 FIG. 49. Telescopic Appearances of Venus. 
 
 the same. This high albedo probably indicates a surface 
 mostly covered with clouds, since few rocks or soils could 
 match its brightness. Like Mercury, Mars, and the moon, the 
 disc of Venus is brightest at the edge, in contrast with the 
 appearance of Jupiter and Saturn. 
 
 248. Atmosphere of the Planet. When the planet is near 
 inferior conjunction, the horns of the crescent extend notably 
 beyond the diameter ; and when very near conjunction, a thin 
 line of light has been seen by some observers to complete the 
 whole circumference of the disc. This is due to the refrac- 
 tion of sunlight bent around the planet's globe by its atmos- 
 phere, a phenomenon still better seen when the planet is 
 entering upon the sun's disc at a transit. The black disc is 
 
178 
 
 ATMOSPHERE OP VENUS. 
 
 [248 
 
 then encircled by a delicate luminous ring, as illustrated by 
 Fig. 50. The planet's atmosphere is probably from one and 
 
 one-half to two times as 
 dense as our own, and 
 the spectrum shows 
 evidence of water-va- 
 por in it. Many ob- 
 servers have also re- 
 ported faint lights as 
 visible at times on the 
 dark portions of the 
 planet's disc. These 
 cannot be accounted 
 for by any mere reflec- 
 tion or refraction of 
 sunlight, but must orig- 
 inate on the planet it- 
 self. They recall the 
 Aurora Borealis and 
 other electrical mani- 
 festations on the earth, though it is impossible to give a certain 
 explanation of them as yet. 
 
 249. Surface-markings, Rotation, etc. As has been said, 
 Venus is a very unsatisfactory telescopic object. She pre- 
 sents no obvious surface-markings, nothing but occasional 
 indefinite shadings : sometimes, however, when in the crescent 
 phase, intensely bright spots have been reported near the 
 points of the crescent, which may perhaps be " ice-caps " like 
 those which are seen on Mars. The darkish shadings may 
 possibly be continents and oceans, dimly visible, or they may 
 be atmospheric objects ; observations do not yet decide. From 
 certain irregularities occasionally observed upon the "termi- 
 nator " (Art. 146), various observers have concluded that there 
 are high mountains upon the planet. 
 
 FIG. 50. Atmosphere of Venus as seen during a 
 Transit. (Vogel, 1882.) 
 
249] TRANSITS. 179 
 
 As to the rotation-period of the planet, nothing is yet cer- 
 tainly known. The length of its day has been set, on very 
 insufficient grounds, at about 23 hours and 21 minutes ; but the 
 recent work of Schiaparelli makes it quite certain that this 
 result cannot be trusted, and renders it rather probable that 
 Venus behaves like Mercury in its diurnal rotation, the length 
 of its sidereal day being equal to the time of its orbital revolu- 
 tion. The planet's disc shows no sensible oblateness. 
 
 No satellite has ever been discovered; not, however, for 
 want of earnest searching. 
 
 250. Transits. Occasionally Venus passes between the 
 earth and the sun at inferior conjunction, giving us a so- 
 called "transit." She is then visible, even to the naked eye, 
 as a black spot on the sun's disc, crossing it from east to west. 
 When the transit is central it occupies about eight hours, but 
 when the track lies near the edge of the disc the duration 
 is correspondingly shortened. Since the earth passes the 
 nodes of the orbit on June 5th and Dec. 7th, all the transits 
 occur near these days, but they are ex- 
 tremely rare phenomena. Their special 
 interest consists in their availability for 
 the purpose of finding the sun's parallax 
 (see Appendix, Art. 437, and General 
 Astronomy, Chap. XVI.). 
 
 The first observed transit in 1639 was seen 
 by only two persons, Horrox and Crabtree in FlG - 51> 
 
 England, -but the four which have occurred n 
 since then have been observed in all parts of the world by scientific 
 expeditions sent out for the purpose by the different governments. 
 The transits of 1869 and 1882 were visible in the United States. 
 Transits of Venus have occurred or will occur at the following 
 dates : 
 
 ( Dec. 7th, 1631. < June 5th, 1761. 
 
 1 Dec. 4th, 1639. ( June 3d, 1769. 
 
180 MARS. [ 250 
 
 5 Dec. 9th, 1874. ( June 8th, 2004. 
 
 ( Dec. 6th, 1882. < June 6th, 2012. 
 
 Fig. 51 shows the tracks of Venus across the sun's disc in the tran- 
 sits of 1874 and 1882. 
 
 MARS. 
 
 251. This planet, also, has always been known. It is so 
 conspicuous on account of its fiery red color and brightness, 
 as well as the rapidity and apparent capriciousness of its 
 movement among the stars, that it could not have escaped the 
 notice of the very earliest observers. 
 
 Its mean distance from the sun is a little more than one and 
 a half times that of the earth (141,500000 miles), and the ec- 
 centricity of its orbit is so considerable (0.093) that its radius 
 vector varies more than 26,000000 miles. At opposition the 
 planet's average distance from the earth is 48,600000 miles ; 
 but when opposition occurs near the planet's perihelion, this 
 distance is reduced to less than 36,000000 miles, while near 
 aphelion it is over 61,000000 miles. At conjunction the aver- 
 age distance from the earth is 234,000000 miles. 
 
 The apparent diameter and brightness of the planet of 
 course vary enormously with these great changes of distance. 
 At a favorable opposition (when the planet's distance from us 
 is the least possible) it is more than fifty times as bright as at 
 conjunction, and fairly rivals Jupiter; when most remote, it is 
 hardly as bright as the Pole-star. 
 
 The favorable oppositions occur always in the latter part of August, 
 and at intervals of fifteen or seventeen years. The last such opposi- 
 tion was in 1877, and the next will be in 1892. 
 
 The inclination of the orbit is small, 1 51'. The planet's 
 sidereal period is 687 days (one year, ten and a half months) j 
 its synodic period is much the longest in the planetary system, 
 being 780 days, or nearly two years and two months. During 
 
251] TELESCOPIC ASPECT. 181 
 
 710 of these 780 days it moves towards the east, and retro- 
 grades during 70. 
 
 252. Magnitude, Mass, etc. The apparent diameter of the 
 planet ranges from 3".6, at conjunction, to 25" at a favorable 
 opposition. Its real diameter is very closely 4230 miles, with 
 an error of perhaps 20 miles one way or the other. This 
 makes its surface about two-sevenths, and its volume one- 
 seventh of the earth's. Its mass is a little less than one-ninth 
 of the earth's mass. This makes its density 0.73, and its super- 
 ficial gravity 0.38 ; i.e., a body which here weighs 100 pounds 
 would have a weight of only 38 pounds on the surface of Mars. 
 
 253. General Telescopic Aspect, Phases, etc. When the 
 planet is nearest, it is more favorably situated for telescopic 
 observation than any other heavenly body, the moon alone 
 excepted. It then shows a ruddy disc, 
 
 which, with a magnifying power of 75, 
 is as large as the moon. Since its orbit 
 is outside the earth's, it never exhibits 
 the crescent phases like Mercury and 
 Venus ; but at quadrature it appears 
 distinctly gibbous, as in Fig. 52, about 
 like the moon three days from full. Like 
 Mercury, Venus, and the moon, its disc 
 is brightest at the limb (i.e.. at its circu- 
 
 Mars at Quadrature. 
 
 lar edge) ; but at the " terminator," or 
 boundary between day and night upon the planet's surface, 
 there is a slight shading, which, taken in connection with cer- 
 tain other phenomena, indicates the presence of an atmosphere. 
 This atmosphere, however, is probably much less dense than 
 that at the earth, as indicated by the infrequency of clouds 
 and of other atmospheric phenomena familiar to us on the 
 earth. Huggins reports, however, that the planet's spectrum 
 shows the lines of water-vapor. 
 
182 MARS. [ 2 53 
 
 Zollner gives the albedo of Mars as 0.26, just double that of 
 Mercury, and much higher than that of the moon, but only 
 about half that of Venus and the major planets. Near oppo- 
 sition the brightness of the planet suddenly increases in the 
 same way as that of the moon near the full (Art. 149). 
 
 254. Rotation, etc. The spots upon the planet's disc 
 enable us to determine its period of rotation with great pre- 
 cision. Its sidereal day is found to be 24 hours, 37 minutes, 
 22.67 seconds, with a probable error not to exceed one-fiftieth 
 of a second. It is the only one of the planets which has the 
 length of its day determined with any such accuracy. The 4 
 exactness is obtained by comparing the drawings of the planet 
 made two hundred years ago with others made recently. 
 
 The inclination of the planet's equator to the plane of its 
 orbit is very nearly 24 50 f (26 21' to the ecliptic). So far, 
 therefore, as depends upon that circumstance, Mars should 
 have seasons substantially the same as our own, and certain 
 phenomena make it evident that such is the case. 
 
 The planet's rotation causes a slight flattening of the poles, 
 about Y^-Q-, according to the latest determinations. (Larger 
 values, now known to be erroneous, are given in many text- 
 books.) 
 
 255. Surface and Topography. With even a small tele- 
 scope, not more than four or five inches in diameter, the planet 
 is a very beautiful object, showing a surface diversified with 
 markings, light and dark, which for the most part are found to 
 be permanent. Occasionally, however, we see others of a tem- 
 porary character, supposed to be clouds; but these are sur- 
 prisingly rare, compared with clouds upon the earth. The 
 permanent markings are broadly divisible into three classes : 
 
 First, the white patches, two of which are specially con- 
 spicuous near the planet's poles, and are generally supposed 
 to be masses of snow or ice, since they behave just as would 
 
255] SCHIAPARELLI'S OBSERVATIONS. 183 
 
 be expected if such were the case. The northern one dwin- 
 dles away during the northern summer, when the north pole is 
 turned towards the sun, while the southern one grows rapidly 
 larger ; and vice versa during the southern summer. 
 
 Second) patches of bluish gray or greenish shade, covering 
 about three-eighths of the planet's surface, and generally sup- 
 posed to be bodies of water. 
 
 Third, extensive regions of various shades of orange and 
 yellow, covering nearly five-eighths of the surface, and inter- 
 preted as land. 
 
 These markings, of course, are best seen when near the 
 centre of the planet's disc ; near the limb they are lost in the 
 
 FIG. 53. Telescopic Views of Mars. 
 
 brilliant light which there prevails, and at the terminator they 
 fade out in the shade. Fig. 53 gives an idea of the planet's 
 general appearance, though without pretending to minute 
 accuracy. 
 
 256. Schiaparelli's Observations. In addition to these three 
 classes of markings, the Italian astronomer, Schiaparelli, reports the 
 observation of a net-work of fine, straight, dark lines, or " canals," as 
 he calls them, crossing the " continents " in every direction. He is so 
 careful and experienced an observer that his results cannot be lightly 
 rejected ; and yet it is not easy to banish a vague suspicion of some 
 error or illusion, partly because his observations have thus far received 
 so little confirmation from others, and partly because his "canals" 
 are so difficult to explain. They can hardly be rivers, because they 
 
184 SCHIAPAKtiLLl's OBSERVATIONS. [ 2 ^6 
 
 are quite straight; nor can they be artificial waterways, since the 
 narrowest of them are at least 100 miles wide. To add to the mys- 
 tery, he finds that at certain times many of them become " doubled," 
 the two which replace the former single one running parallel to 
 each other sometimes for thousands of miles, with a space of 200 or 
 300 miles between them; and this "gemination" seems to follow the 
 course of the planet's seasons. No satisfactory explanation for such 
 phenomena appears as yet. 
 
 Schiaparelli and some other observers report also, within a year or 
 two, certain phenomena which look as if large regions of land were 
 subject to periodic inundations. It is hoped that in 1892 the great 
 telescopes of the world will throw some light on these peculiar prob- 
 lems; and possibly photography may take a hand in the affair by 
 that time. 
 
 257. Maps of the Planet. A number of maps of Mars have 
 been constructed by different observers since the first one was made 
 by Maedler in 1830. Fig. 54 is reduced from one which was published 
 in 1888 by Schiaparelli, and shows most of his "canals" and their 
 " geminations." While there may be some doubt as to the accuracy 
 of the minor details, there can be no doubt that the main features of 
 the planet's surface are substantially correct. The nomenclature, 
 however, is in a very unsettled state. Schiaparelli has taken his 
 names mostly from ancient geography, while the English areogra- 
 phers, 1 following the analogy of the lunar maps, have mainly used the 
 names of astronomers who have contributed to our knowledge of the 
 planet's surface. 
 
 If the prevailing interpretations of the markings upon the planet 
 are correct, it is certain that the temperature of Mars must be higher 
 than that of the earth, notwithstanding his smaller supply of solar 
 heat (somewhat less than half) . Otherwise, the snow and ice in the 
 winter would not be limited to mere polar caps, but would extend far 
 into the lower latitudes, as they do upon the earth. 
 
 258. Satellites. The planet has two satellites, discovered 
 by Professor Hall, at Washington, in 1877. They are ex- 
 
 lr The Greek name of Mars is Ares; hence " Areography " is the de- 
 scription of the surface of Mars. 
 
258] 
 
 CHART OF MARS. 
 
 185 
 
186 HABITABILITY OF MARS. [ 258 
 
 tremely small, and observable only with very large telescopes. 
 The outer one, Deiinos, is at a distance of 14,600 mi]es from 
 the planet's centre, and has a sidereal period of 30 hours, 18 
 minutes ; while the inner one, Phobos, is at a distance of only 
 5800 miles, and its period is only 7 hours, 39 minutes, less 
 than one-third of the planet's day. (This is the only case of a 
 satellite with a period shorter than the day of its primary.) 
 Owing to this circumstance, it rises in the west, as seen from 
 the planet's surface, and sets in the east, completing its 
 strange, backward, diurnal revolution in about eleven hours. 
 Deimos, on the other hand, rises in the east, but takes nearly 
 132 hours in its diurnal circuit, which is more than four of its 
 months. Both the Orbits are sensibly circular, and lie very 
 closely in the plane of the planet's equator. 
 
 Micrometric measures of the diameters of such small objects are im- 
 possible; but from photometric observations, Professor E. C. Pick- 
 ering, assuming that they have the same reflecting power as that of 
 Mars itself, estimates the diameter of Phobos as about seven miles, 
 and that of Deimos as five or six. According to this, Phobos, at the 
 time of full moon, as seen from the planet's surface, would have an 
 apparent diameter of about one-fifth that of our moon, and would 
 probably give about one-fiftieth as much light. Deimos would be 
 hardly more than a brilliant star, like Venus. 
 
 259. Habitability of Mars. As to this question, we can only 
 say that, while the conditions on Mars are very different from those 
 prevailing on the earth, the difference is less than in the case of any 
 other heavenly body with which we are acquainted ; and if life, such 
 as we know life upon the earth, can exist anywhere else, Mars is the 
 place. But there is at present no scientific ground for belief one way 
 or the other as to the habitability of " other worlds than ours," pas- 
 sionately as the doctrine has been affirmed and denied by men of 
 opposite opinions. 
 
260] THE ASTEROIDS. 187 
 
 CHAPTER IX. 
 
 THE PLANETS CONTINUED. 
 
 THE ASTEROIDS. INTRA-MERCURIAN PLANETS AND THE 
 ZODIACAL LIGHT. THE MAJOR PLANETS, JUPITER, 
 SATURN, URANUS, AND NEPTUNE. 
 
 THE ASTEROIDS, OR MINOR PLANETS. 
 
 260. THE asteroids 1 are a multitude of small planets cir- 
 cling around the sun in the space between Mars and Jupiter. 
 It was early noticed that between Mars and Jupiter there is a 
 gap in the series of planetary distances, and when Bode's Law 
 (Art. 219) was published in 1772, the impression became very 
 strong that there must be a missing planet in the space, an 
 impression greatly strengthened when Uranus was discovered 
 in 1781, at a distance precisely corresponding to that law. 
 
 The first member of the group was found by the Sicilian as- 
 tronomer, Piazzi, on the very first night of the present century 
 (Jan. 1, 1801). He named it Ceres, after the tutelary divinity 
 of Sicily. The next year Pallas was discovered by Olbers. 
 Juno was found in 1804 by Harding, and in 1807 Olbers, who 
 had broached the theory of an exploded planet, discovered the 
 fourth, Vesta, the only one which is bright enough ever to be 
 easily seen by the naked eye. The search was kept up for 
 some years longer, but without success, because the searchers 
 
 1 They were first called "asteroids" (i.e., "star-like" bodies) by Sir 
 William Herschel early in the century, because, though really planets, 
 the telescope shows them only as stars, without a sensible disc. 
 
188 ORBITS OF THE ASTEROIDS. [ 26 ^ 
 
 did not look for small enough objects. The fifth asteroid 
 (Astraea) was found in 1845 by Hencke, an amateur who had 
 resumed the subject afresh by studying the smaller stars. In 
 1847 three more were discovered, and every year since then 
 has added from one to twenty. ' In November, 1890, the list 
 included 300. They all have names, but more generally they 
 are designated by numbers in the order of their discovery. 
 Thus, Ceres is , Thule is (279), etc. 
 
 Of the 300, 113 were discovered in Germany, 80 in France, 76 
 in the United States, 20 by English observers, and 11 by Italians. 
 
 Palisa, who stands far ahead of all the other planet-hunters, is alone 
 responsible for 71 of them, and the late Dr. Peters of Clinton, N.Y., 
 for 48.i 
 
 261. Their Orbits. The mean distances of the different 
 asteroids from the sun differ pretty widely, and the periods, of 
 course, correspond. Medusa, (UQ), is the nearest to the sun of 
 those at present known, its distance being 2.13 (astronomical 
 units), or 198,000000 miles, with a period of 3 years and 40 
 days. Thule, (279), is the most remote, with a mean distance 
 of 4.30 (400,000000 miles) and a period only 10 days less than 
 9 years. 
 
 The inclinations of the orbits to the ecliptic average nearly 
 8. The orbit of Pallas, @, is inclined at an angle of 35, 
 and seven others exceed 25. The eccentricity of the orbits is 
 very large in many cases. Aethra, (132), has the largest eccen- 
 tricity (0.38), and ten others have an eccentricity exceeding 
 0.30. 
 
 1 These figures are from the lists given in the Annuaire du Bureau des 
 Longitudes. Other lists differ somewhat in the assignment of the discov- 
 eries, as there are a number of cases where the same planet has been dis- 
 covered independently, and almost simultaneously, by more than one 
 observer. 
 
262] THE BODIES THEMSELVES. 189 
 
 262. The Bodies Themselves. The four first discovered, 
 and one or two others, when examined with a powerful tele- 
 scope, show a perceptible disc, not large enough, however, for 
 accurate measurement. By photometric observations, assum- 
 ing what is by no means certain that their albedo is 
 about the same as that of Mars, it is estimated that Vesta, the 
 largest and brightest, has a diameter of about 320 miles. The 
 other three of the first four may be two-thirds as large. None 
 of the rest can well exceed 100 miles in diameter; and the 
 more newly discovered ones, which are just fairly visible in a 
 telescope with an aperture of 10 or 12 inches, cannot be many 
 times larger than the moons of Mars, say from 10 to 20 
 miles in diameter. 
 
 As to the individual masses and densities, we have no certain 
 knowledge. 
 
 Assuming that the density of Vesta is about the same as that of 
 the rocks which compose the earth's crust, her mass may be as great 
 3(8 strVffo that of the earth. If so, gravity on her surface would be about 
 ^ of gravity here, so that a body would fall about six inches in the 
 first second. Of course, on the smaller asteroids it would be much 
 less. 
 
 From the perturbations of Mars, Leverrier has estimated 
 that the aggregate mass of the whole swarm cannot exceed 
 one-fourth the mass of the earth, something more than double 
 that of Mars. 
 
 The united mass of those at present known would make only a 
 small fraction of such a body, hardly a thousandth of it; prob- 
 ably, however, those still undiscovered are very numerous. 
 
 263. Origin. As to this we can only speculate. It is 
 hardly possible to doubt, however, that this swarm of little 
 rocks in some way represents a single planet of the " terres- 
 trial" group. A commonly accepted view is that the mate- 
 rial, which, according to the nebular hypothesis, once formed 
 
190 INTRA-MERCTJRIAN PLANETS. [263 
 
 a ring (like one of the rings of Saturn), and ought to have col- 
 lected to make a single planet, has failed to be so united ; and 
 the failure is ascribed to the perturbations produced by the 
 next neighbor, the giant Jupiter, whose powerful attraction is 
 supposed to have torn the ring to pieces, and thus prevented 
 its normal development into a planet. 
 
 Another view is that the asteroids may be fragments of an 
 exploded planet. If so, there must have been not one, but 
 many, explosions, first of the original body, and then of the 
 separate pieces ; for it is demonstrable that no single explo- 
 sion could account for the present tangle of orbits. 
 
 INTRA-MERCURIAN PLANETS AND THE ZODIACAL 
 LIGHT. 
 
 264. Intra-Mercurian Planets. It is very probable, indeed 
 nearly certain, that there is a considerable quantity of matter circu- 
 lating around the sun inside the orbit of Mercury. This is indicated 
 by an otherwise unexplained perturbation of its orbit. It has been 
 somewhat persistently supposed that this intra-Mercurian matter is 
 concentrated into one, or possibly two, planets of considerable size, 
 and such a planet has several times been reported as discovered, and 
 has even been named Vulcan. The supposed discoveries have never 
 been confirmed, however, and the careful observations of total solar 
 eclipses during the past ten years make it practically certain that 
 there is no " Vulcan." Probably, however, there is a family of intra- 
 Mercurian asteroids ; but they must be very minute, or some of them 
 would certainly have been found either during eclipses or crossing the 
 sun's disc ; a planet as much as 200 miles in diameter could hardly 
 have escaped discovery. 
 
 265. The Zodiacal Light This is a faint beam of light 
 extending from the sun both ways along the ecliptic. In the 
 evening it is best seen in the early spring, and in our latitude 
 then extends about 90 eastward from the sun ; in the tropics, 
 it is said that it can be followed quite across the sky. The 
 
265] JUPITER. 191 
 
 region near the sun is fairly bright and even conspicuous, but 
 the more distant portions are extremely faint and can be 
 observed only in places where there is no illumination of the 
 air by artificial lights. Its spectrum is a simple, continuous 
 spectrum, without markings of any kind, so far as can be 
 observed. 
 
 We emphasize this, because of late it has been mistakenly reported 
 that the bright line which characterizes the spectrum of the Aurora 
 Borealis appears in the spectrum of the zodiacal light. 
 
 The cause of the phenomenon is not certainly known. Some 
 imagine that the zodiacal light is only an extension of the 
 solar corona (whatever that may be), which is not perhaps 
 unlikely ; but on the whole the more prevalent opinion seems 
 to be that it is due to sunlight reflected from myriads of small 
 meteoric bodies circling around the sun, nearly in the plane of 
 the ecliptic, thus forming a thin, flat sheet (something like one 
 of Saturn's rings), which extends far beyond the orbit of the 
 earth. 
 
 THE MAJOR PLANETS. JUPITER. 
 
 266. Jupiter, the nearest of the major planets, stands next 
 to Venus in the order of brilliance among the heavenly bodies, 
 being fully five or six times as bright as Sirius, and decidedly 
 superior to Mars, even when Mars is nearest. It is not, like 
 Venus, confined to the twilight sky, but at the time of opposi- 
 tion dominates the heavens all night long. 
 
 Its orbit presents no marked peculiarities. The mean dis- 
 tance of the planet from the sun is a little more than five astro- 
 nomical units (483,000000 miles), and the eccentricity of the 
 orbit is not quite -fa, so that the actual distance ranges about 
 21,000000 miles each side of the mean. At an average oppo- 
 sition, the planet's distance from the earth is about 390,000000 
 miles, while at conjunction it is distant about 580,000000. 
 
192 DIMENSIONS, MASS, ETC. [ 266 
 
 The inclination of its orbit to the ecliptic is only 1 19'. Its 
 sidereal period is 11.86 years, and the synodic is 399 days (a 
 figure easily remembered), a little more than a year and a 
 month ; i.e., each year Jupiter comes to opposition a month 
 and four days later than in the preceding year. 
 
 267. Dimensions, Mass, Density, etc. The planet's appar- 
 ent diameter varies from 50" to 32", according to its distance 
 from the earth. The disc, however, is distinctly oval, so that 
 while the equatorial diameter is 88,200 miles, the polar diam- 
 eter is only 83,000. The mean diameter (see Art. 112) is 
 86,500 miles, or very nearly eleven times that of the earth. 
 
 Its surface, therefore, is 119, and its volume or bulk 1300 
 times that of the earth. It is by far the largest of all the 
 planets, larger, in fact, than all the rest united. 
 
 Its mass is very accurately known, both by means of its 
 satellites and from the perturbations it produces upon certain 
 asteroids. It is j-^Vs of the sun's mass, or about 316 times 
 that of the earth. 
 
 Comparing this with its volume, we find its mean density to 
 be 0.24; i.e., less than one-fourth the density of the earth, and 
 almost precisely the same as that of the sun. Its surface 
 gravity is about 2| times that of the earth, but varies nearly 
 20 per cent between the equator and poles of the planet on 
 account of the rapid rotation. 
 
 268. General Telescopic Aspect, Albedo, etc. In a small 
 telescope the planet is a fine object ; for a magnifying power 
 of only 60 makes its apparent diameter, even when remotest, 
 equal to that of the moon. With a large instrument and a 
 magnifying power of 200 or 300, it is magnificent, the disc 
 being covered with an infinite variety of detail, interesting in 
 outline and rich in color, changing continually as the planet 
 turns on its axis. For the most part the markings are 
 
268] 
 
 arranged in 
 in Fig. 55. 
 
 TELESCOPIC VIEWS OF JUPITER. 
 
 193 
 
 belts " parallel to the planet's equator, as shown 
 
 The left-hand one of the two larger figures is from a drawing by 
 Trouvelot (1870), and the other from one by Vogel (1880). The 
 smaller figure below represents the planet's ordinary appearance in 
 a three-inch telescope. 
 
 Near the limb the light is less brilliant than in the centre of 
 the disc, and the belts there fade out. The planet shows no 
 
 FIG. 55. Telescopic Views of Jupiter. 
 
 perceptible phases, but the edge which is turned away from 
 the sun is usually sensibly darker than the other. According 
 to Zollner, the mean albedo of the planet is 0.62, which is ex- 
 tremely high, that of white paper being only 0.78. The ques- 
 tion has been raised whether Jupiter is not to some extent 
 
194 JUPITER. [268 
 
 self-luminous, but there is DO proof and little probability that 
 such is the case. 
 
 269. Atmosphere and Spectrum. The planet's atmosphere 
 must be very extensive. The forms which we see with the 
 telescope are all evidently atmospheric. In fact, the low mean 
 density of the planet makes it very doubtful whether there is 
 anything solid about it anywhere, whether it is anything 
 more than a ball of fluid overlaid by cloud and vapor. 
 
 The spectrum of the planet differs less from that of mere 
 reflected sunlight than might have been expected, showing 
 that the light is not obliged to penetrate the atmosphere to 
 any great depth before it encounters the reflecting envelope of 
 cloud. There are, however, certain unexplained dark shadings 
 in the red and orange parts of the spectrum that are prob- 
 ably due to the planet's atmosphere, and seem to be identical 
 in position with certain bands which, in the spectra of Uranus 
 and Neptune, are much more intense. 
 
 270. Rotation. Jupiter rotates on its axis more swiftly 
 than any other of the planets. Its sidereal day has a length 
 of about 9 hours, 55 minutes, but the time can be given only 
 approximately, because different results are obtained from dif- 
 ferent spots, according to their nature and their distance from 
 the equator, the differences amounting to six or seven min- 
 utes. Speaking generally, spots near the equator indicate a 
 shorter period of rotation than those near the poles, just as is 
 the case with the sun. 
 
 In consequence of the swift rotation, the planet's oblateness 
 or " polar compression " is quite noticeable, about -^-. The 
 plane of rotation nearly coincides with that of the orbit, the 
 inclination being only 3, so that there can be no well-marked 
 seasons on the planet due to the causes which produce our 
 own seasons. 
 
271] PHYSICAL CONDITION SATELLITES. 195 
 
 271, Physical Condition. This is obviously very different 
 from that of the earth or Mars. No permanent markings are 
 found upon the disc, though occasionally there are some which 
 may be called " sub-permanent " as, for instance, the great 
 red spot shown in Fig. 55. This was first noticed in 1878, 
 became extremely conspicuous for several years, and still 
 (1890) remains visible as a faded ghost of itself. Were it not 
 that during the 12 years of its visibility it has changed the 
 length of its apparent rotation by about six seconds (from 9 
 hours, 55 minutes, 34.9 seconds to 9 hours, 55 minutes, 40.2 
 seconds), we might suppose it permanently attached to the 
 planet's surface, and evidence of a coherent mass underneath. 
 As it is, opinion is divided on this point ; the phenomenon is 
 as puzzling as the canals of Mars. 
 
 Many things in the planet's appearance indicate a high 
 temperature, as, for instance, the abundance of clouds, and 
 the swiftness of their transformations ; and since on Jupiter 
 the solar light and heat are only -^ as intense as here, we are 
 forced to conclude that it gets very little of its heat from the 
 sun, but is probably hot on its own account, and for the same 
 reason that the sun is hot ; viz., as the result of a process of 
 condensation. In short, it appears very probable that the 
 planet is a sort of semi-sun, hot, though not so hot as to be 
 sensibly self-luminous. 
 
 272. Satellites. Jupiter has a retinue of four large satel- 
 lites, the first heavenly bodies ever discovered. Galileo 
 found them in January, 1610, within a very few weeks after 
 his invention of the telescope. 
 
 They are now usually known as the first, second, etc., in the 
 order of their distance from the planet. The distances range 
 from 262,000 to 1,169,000 miles, being respectively 6, 9, 15, 
 and 26 radii of the planet (nearly). Their sidereal periods 
 range from 42 hours to 16f days. Their orbits are sensibly 
 circular, and lie very nearly in the plane of the equator. The 
 
196 SATELLITES OF JUPITER. [272 
 
 third satellite is much the largest, having a diameter of about 
 3600 miles, while the others are between 2000 and 3000. 
 
 For some reason, the fourth satellite is a very dark-complexioned 
 body, so that when it crosses the planet's disc it looks like a black 
 spot hardly distinguishable from its own shadow : the others, under 
 similar circumstances, appear bright, dark, or invisible, according 
 to the brightness of the part of the planet which happens to form 
 the background. In Fig. 55 a satellite and its shadow are visible 
 together near the eastern limb of the planet. In the case of the 
 fourth satellite, a certain regularity in its changes of brightness sug- 
 gests that it probably follows the example of our moon in always 
 keeping the same face towards the planet. 
 
 273. Eclipses and Transits. The orbits of the satellites are 
 so nearly in the plane of the planet's orbit that with the ex- 
 ception of the fourth, which sometimes escapes, they are 
 eclipsed at every revolution. When the planet is either at 
 opposition or conjunction, the shadow, of course, is directly 
 behind it, and we cannot see the eclipse at all. At other times 
 we ordinarily see only the beginning or the end ; but when the 
 planet is very near quadrature the shadow projects so far to 
 one side that the whole eclipse of every satellite, except the 
 first, takes place clear of the disc, and both the disappearance 
 and reappearance can be seen. 
 
 Two important uses have been made of these eclipses : they 
 have been employed for the determination of longitude, and 
 they furnish the means of ascertaining the time required by light 
 to traverse the space between the earth and the sun. (See Appen- 
 dix, Arts. 431-434.) 
 
 SATURN. 
 
 X 
 274, This is the most remote of the planets known to the 
 
 ancients. It appears as a star of the first magnitude (out- 
 shining all of them, indeed, except Sirius), with a steady, 
 
274] SATURN. 197 
 
 yellowish light, not varying much in appearance from month 
 to month, though in the course of 15 years it alternately gains 
 and loses nearly 50 per cent of its brightness with the chang- 
 ing phases of its rings ; for it is unique among the heavenly 
 bodies, a great globe attended by eight satellites and sur- 
 rounded by a system of rings, which has no counterpart else- 
 where in the universe so far as known. 
 
 Its mean distance from the sun is about 9|- astronomical 
 units, or 886,000000 miles; but the distance varies over 
 100,000000 miles on account of the considerable eccentricity of 
 the orbit (0.056). Its least distance from the earth is about 
 774,000000 miles, the greatest, about 1028,000000. The incli- 
 nation of the orbit to the ecliptic is 2^-. The sidereal period 
 is about 29^ years, the synodic period being 378 days, or a year 
 and a fortnight nearly. 
 
 275. Dimensions, Mass, etc. The apparent mean diameter 
 of the planet varies according to the distance from 14" to 20". 
 The planet is more flattened at the poles than any other 
 (nearly y 1 -^), so that while the equatorial diameter is about 
 75,000 miles, the polar is pnly 68,000 : the mean diameter 
 (Art. 112) being not quite 73,000, a little more than nine 
 times that of the earth. Its surface is about 84 times that of 
 the earth, and its volume 770 times. Its mass is found (by 
 means of its satellites) to be 95 times that of the earth, so 
 that its mean density comes out only one-eighth that of the 
 earth, actually less than that of water ! It is by far the least 
 dense of all the planetary family. 
 
 Its mean superficial gravity is about 1.2 times as great as 
 gravity upon the earth, varying, however, nearly 25 per cent 
 between the equator and the pole, so that at the planet's 
 equator it is practically the same as upon the earth. It 
 rotates on its axis in about 10 hours, 14 minutes, but there 
 is reason to suspect that different spots would give results 
 varying with their latitude, as in the case of Jupiter. 
 
198 
 
 SATURN. 
 
 [275 
 
 FIG. 56. Saturn and his Rings. 
 
SURFACE, ALBEDO, SPECTRUM. 199 
 
 The equator of the planet is inclined about 27 to the plane 
 of its orbit about 28 to the ecliptic. 
 
 276. Surface, Albedo, Spectrum. The disc of the planet, 
 like that of Jupiter, is shaded at the edge, and like Jupiter it 
 shows a number of belts arranged parallel to the equator. 
 The equatorial belt is very bright, and is often of a delicate 
 pinkish tinge. The belts in higher latitudes are comparatively 
 faint and narrow, while just at the pole there is usually a cap 
 of olive green (see Fig. 56). 
 
 Zollner makes the mean albedo of the planet 0.52, about the 
 same as that of Venus. 
 
 The planet's spectrum is substantially like that of Jupiter, 
 but the dark bands are more pronounced. These bands, how- 
 ever, do not appear in the spectrum of the ring, which prob- 
 ably has very little atmosphere. As to its physical condition 
 and constitution, the planet is probably much like Jupiter, 
 though it does not seem to be " boiling " quite so vigorously. 
 
 277. The Rings. The most remarkable peculiarity of the 
 planet is its ring system. The globe is surrounded by three 
 thin, flat, concentric rings, like circular discs of paper pierced 
 through the centre. They are generally referred to as A, B, 
 and C, A being the exterior one. 
 
 Galileo half discovered them in 1610 ; i.e., he saw with his little 
 telescope two appendages, one on each side of the planet ; but he could 
 make nothing of them, and after a while he lost them. The problem 
 remained unsolved for nearly fifty years, until Huyghens explained 
 the mystery in 1655. Twenty years later D. Cassini discovered that 
 the ring is double ; i.e., composed of two concentric rings, with a dark- 
 line of separation between them ; and in 1850, Bond of Cambridge, 
 U.S., discovered the third "dusky" or "gauze" ring between the 
 principal ring and the planet. (It was discovered a fortnight later, 
 independently, by Dawes, in England.) 
 
200 SATURN'S RINGS. [277 
 
 The outer ring, A, has a diameter of about 168,000 miles, 
 and a width of about 10,000. Cassini's division is about 1000 
 miles wide; the ring B, which is much the broadest of the 
 three, is about 17,000. The semi-transparent ring, (7, has a 
 width of about 9000 miles, leaving a clear space of from 9000 
 to 10,000 miles in width between the planet's equator and its 
 inner edge. The thickness of the rings is extremely small, 
 probably not over 100 miles, as proved by the appearance 
 presented, when once in 15 years we view them edgewise. 
 
 278. Phases of the Rings. The plane of the rings coin- 
 cides with the plane of the planet's equator, and is inclined 
 
 FIG. 57. The Phases of Saturn's Rings. 
 
 about 28 to the ecliptic. It, of course, remains parallel 
 to itself at all times. Twice in a revolution of the planet, 
 therefore, this plane sweeps across the orbit of the earth (too 
 small to be shown in the figure Fig. 57), occupying nearly a 
 year in so doing ; and whenever the plane passes between the 
 earth and the sun the dark side of the ring is towards us, and 
 the edge alone is visible, as when the planet is at 1 or 2; 
 when it is at the intermediate points 3 and 4 the rings present 
 their widest opening. 
 
278] SATELLITES. . 201 
 
 When the ring is exactly edgewise towards us only the largest tele- 
 scopes can see it, like a fine needle of light piercing the planet's ball, 
 as in the uppermost engraving of Fig. 56. It becomes obvious at 
 such times that the thickness of the rings is not uniform, since con- 
 siderable irregularities appear upon the line of light at different 
 points. The last period of disappearance was in 1877-78 ; the next 
 will be in 1892-93. 
 
 279. Structure of the Rings. It is now universally ad- 
 mitted that they are not continuous sheets, either solid or 
 liquid, but mere swarms of separate particles, each particle pur- 
 suing its own independent orbit around the planet, though all 
 moving nearly in a common plane. 
 
 The idea was first suggested by J. Cassini in 1715, but was lost 
 sight of until again suggested by Bond in connection with his dis- 
 covery of the semi-transparent or dusky ring ; it has finally been estab- 
 lished by the researches of Pierce, Maxwell, and others, who have 
 shown that no solid or liquid sheet could maintain itself for any 
 length of time under the circumstances. 
 
 The recent investigations of H. Struve show that the aggre- 
 gate mass of the rings is extremely small, so small that 
 they exert no sensible influence on the motion of the satellites. 
 
 It is a question not yet settled whether the rings constitute 
 a permanently stable system, or are liable ultimately to be 
 broken up. 
 
 280. Satellites. Saturn has eight of these attendants, the 
 largest of which was discovered by Huyghens in 1655. It 
 looks like a star of the ninth magnitude, and is easily seen 
 with a three-inch telescope. The smallest one, the seventh in 
 order of distance from the planet, was discovered by Bond, at 
 Cambridge (U.S.) in 1848. 
 
 Since the order of discovery does not agree with that of distance, it 
 has been found convenient to designate them by the names assigned 
 
202 - URANUS. [280 
 
 by Sir John Herschel, as follows, beginning with the most remote 
 viz. : 
 
 lapetus (Hyperion), Titan, Rhea, Dione, Tethys; 
 
 Enceladus, Mimas. 
 
 The range of the system is enormous. lapetus has a distance of 
 2,225,000 miles, with a period of 79 days, nearly as long as that of 
 Mercury. On the western side of the planet, this satellite is always 
 much brighter than upon the eastern, showing that, like our own 
 moon, it keeps the same face towards its primary. 
 
 Titan, as its name suggests, is by far the largest. Its distance is 
 about 770,000 miles, and its period a little less than 16 days. It is 
 probably 3000 or 4000 miles in diameter, and, according to Stone, its 
 mass is ^^7 of Saturn's, or about double that of our moon. The orbit 
 of lapetus is inclined nearly 10 to the plane of the rings, but all of 
 the other satellites move almost exactly in their plane, and all the five 
 inner ones in orbits nearly circular. 
 
 URANUS. 
 
 281. Uranus (not U-ra'nus) was the first planet ever "dis- 
 covered," and the discovery created great excitement and 
 brought the highest honors to the astronomer. It was found 
 accidentally by the elder Herschel on March 13, 1781, while 
 " sweeping " for interesting objects with a seven-inch reflector 
 of his own construction. He recognized it at once by its disc 
 as something different from a star, but supposed it to be a 
 peculiar sort of a comet, and its planetary character was not 
 demonstrated until nearly a year had passed. It is easily 
 visible to a good eye as a star of the sixth magnitude. 
 
 Its mean distance from the sun is about 19 times that of the 
 earth, or about 1800,000000 miles, and the eccentricity of its 
 orbit is about the same as that of Jupiter's. The inclination 
 of the orbit to the ecliptic is very slight only 46'. The side- 
 real period is 84 years, and the synodic, 369^ days. 
 
 In the telescope it shows a greenish disc about 4" in diam- 
 eter, which corresponds to a real diameter of about 32,000 
 
281 1 SATELLITES OF URANUS. 203 
 
 miles. This makes its bulk about 66 times that of the earth. 
 The planet's mass is found from its satellites to be about 14.6 
 times that of the earth ; its density, therefore, is 0.22 about 
 the same as that of Jupiter and the sun. 
 
 The albedo of the planet, according to Zollner, is very high, 
 0.64, even a little above that of Jupiter. The spectrum 
 exhibits intense dark bands in the red, due to some unidenti- 
 fied substance in the planet's atmosphere. These bands explain 
 the marked greenish tint of the planet's light. The atmos- 
 phere is probably dense. 
 
 The disc is obviously oval, with an ellipticity of about T \. 
 There are no clear markings upon it, but there seem to be 
 faint traces of something like belts. No spots are visible from 
 which to determine the planet's diurnal rotation. 
 
 282. Satellites. The planet has four satellites, Ariel, 
 Umbriel, Titania, and Oberon, Ariel being the nearest to the 
 planet. 
 
 The two brightest, Oberon and Titania, were discovered by Sir 
 William Herschel a few years after his discovery of the planet; 
 Ariel and Umbriel, by Lassell, in 1851. 
 
 They are among the smallest bodies in the solar system, and 
 the most difficult to see. 
 
 Their orbits are sensibly circular, and all lie in one plane, 
 which ought to be, and probably is, coincident with the plane 
 of the planet's equator. 
 
 They are very close packed also, Oberon having a distance of only 
 375,000 miles, and a period of 13 days, 11 hours, while Ariel has a 
 period of 2 days, 12 hours, at a distance of 120,000 miles. Titania, 
 the largest and brightest of them, has a distance of 280,000 miles, 
 somewhat greater than that of the moon from the earth, with a period 
 of 8 days, 17 hours. 
 
 The most remarkable thing about this system remains to be 
 mentioned. The plane of their orbits is inclined 82.2, or 
 
204 DISCOVERY OF NEPTUNE. [ 282 
 
 almost perpendicularly, to the plane of the ecliptic j and in 
 that plane they revolve backwards. 
 
 NEPTUNE. 
 
 283. Discovery. The discovery of this planet is reckoned 
 the greatest triumph of mathematical astronomy. Uranus 
 failed to move precisely in the path computed for it, and was 
 misguided by some unknown influence to an extent which 
 could almost be seen with the naked eye. The difference 
 between the actual and computed places in 1845 was the " in- 
 tolerable quantity " of nearly two minutes of arc. 
 
 This is a little more than half the distance between the two prin- 
 cipal components of the double-double star, Epsilon Lyrae, the north- 
 ern one of the two little stars which form the small equilateral triangle 
 with Vega (Arts. 67 and 375). A very sharp eye detects the duplicity 
 of Epsilon without the aid of a telescope. 
 
 One might think that such a minute discrepancy between 
 observation and theory was hardly worth minding, and that 
 to consider it " intolerable " was putting the case very strongly. 
 But just these minute discrepancies supplied the data which 
 were found sufficient for calculating the position of a great 
 unknown world, and bringing it to light. As the result of a 
 most skilful and laborious investigation, Leverrier (born 1811, 
 died 1877) wrote to Galle in substance : 
 
 "Direct your telescope to a point on the ecliptic in the constellation of 
 Aquarius, in longitude 326, and you will find within a degree of that 
 place a new planet, looking like a star of about the ninth magnitude, and 
 having a perceptible disc." 
 
 The planet was found at Berlin on the night of Sept. 23, 
 1846, in exact accordance with this prediction, within half an 
 hour after the astronomers began looking for it, and within 
 52' of the precise point that Leverrier had indicated. 
 
283] THE PLANET AND ITS ORBIT. 205 
 
 We cannot here take the space for a historical statement, further 
 than to say that the English Adams (now Professor of Astronomy at 
 Cambridge, England) fairly divides with Leverrier the credit for the 
 mathematical discovery of the planet, having solved the problem and 
 deduced the planet's approximate place even earlier than his competi- 
 tor. The planet was being searched for in England at the time it was 
 found in Germany. In fact, it had already been observed, and the 
 discovery would necessarily have followed in a few weeks, upon the 
 reduction of the observations. 
 
 284. Error of the Computed Orbit. Both Adams and Lever- 
 rier, besides calculating the planet's position in the sky, had deduced 
 elements of its orbit and a value for its mass, which turned out to be 
 seriously wrong, and certain high authorities have therefore character- 
 ized the discovery as a " happy accident." This is not so, however. 
 While the data and methods employed were not sufficient to deter- 
 mine the planet's orbit with accuracy, they were adequate to ascertain 
 the planet's direction from the earth. The computers informed the 
 observers where to point their telescopes, and this was all that was neces- 
 sary for finding the planet. 
 
 285. The Planet and its Orbit. The planet's mean distance 
 from the sun is a little more than 2800,000000 miles (800,- 
 000000 miles nearer the sun than it should be according to 
 Bode's Law). The orbit is very nearly circular, its eccentricity 
 being only 0.009. The inclination of* the orbit is about 1|. 
 The period of the planet is about 164 years (instead of 217, as 
 as it should have been according to Leverrier's computed 
 orbit), and the orbital velocity is about 3^ miles per second. 
 
 Neptune appears in the telescope as a small star of between 
 the eighth and ninth magnitudes, absolutely invisible to the 
 naked eye, though easily seen with a good opera-glass. Like 
 Uranus, it shows a greenish disc, having an apparent diameter 
 of about 2 ".6. The real diameter of the planet is about 35,000 
 miles, and the volume a little more than 90 times that of the 
 earth. 
 
 Its mass, as determined by means of its satellite, is about 
 18 times that of the earth, and its density 0.20. 
 
206 NEPTUNE'S SATELLITE. [ 285 
 
 The planet's albedo, according to Zollner, is 0.46, a trifle 
 less than that of Saturn and Venus. 
 
 There are no visible markings upon its surface, and nothing 
 certain is known as to its rotation. 
 
 The spectrum of the planet appears to be like that of 
 Uranus, but of course is rather faint. 
 
 It will be noticed that Uranus and Neptune form a " pair of twins," 
 very much as the earth and Venus do, being almost alike in magni- 
 tude, density, and many other characteristics. 
 
 286. Satellite. Neptune has one satellite, discovered by 
 Lassell within a month after the discovery of the planet 
 itself. Its distance is about 223,000 miles, and its period 
 5 d 21 h . Its orbit is inclined to the ecliptic at an angle of 34 
 48', and it moves backward in it from east to west, like the 
 satellites of Uranus. From its brightness, as compared with 
 that of Neptune itself, its diameter is estimated as about the 
 same as that of our own moon. 
 
 287. The Solar System as seen from Neptune. At Nep- 
 tune's distance the sun itself has an apparent diameter of 
 only a little more thai\ one minute of arc, about the diam- 
 eter of Venus when nearest us, and too small to be seen as a 
 disc by the naked eye, if there are eyes on Neptune. The 
 solar light and heat are there only ^ of what we get at the 
 earth. 
 
 Still, we must not imagine that the Neptunian sunlight is 
 feeble as compared with starlight, or even moonlight. Even 
 at the distance of Neptune the sun gives a light nearly equal 
 to 700 full moons. This is about 80 times the light of a 
 standard candle at one metre's distance, and is abundant for 
 all visual purposes. In fact, as seen from Neptune, the sun 
 would look very like a large electric arc lamp, at a distance of 
 a few yards. 
 
288] ULTRA-NEPTUNIAN PLANETS, ETC. 207 
 
 288. Ultra-Neptunian Planets. Perhaps the breaking down of 
 Bode's Law at Neptune may be regarded as an indication that the 
 solar system terminates there, and that there is no remoter planet ; 
 but of course it does not make it certain. If such a planet exists, it 
 is sure to be found sooner or later, either by means of the disturbances 
 it produces in the motion of Uranus and Neptune, or else by the 
 methods of the asteroid hunters, although its slow motion will render 
 its discovery in that way difficult. Quite possibly such a discovery 
 may come within a few years as a result of the photographic star- 
 charting operations now in progress. 
 
 288*. Stability of the Solar System. It is an interesting and 
 important question, once long and warmly discussed, whether the so- 
 called "perturbations" which result from the mutual attractions of 
 the planets can ever seriously derange the system. It is now nearly 
 a century since Laplace and Lagrange first demonstrated that they 
 cannot. The system is stable in itself, all the planetary disturbances 
 due to gravitation being either of such a character, or so limited in 
 extent, that they can never do any harm. 
 
 It does not follow, however, that because the mutual attractions of 
 the planets are thus harmless, there may not be other causes which 
 would act disastrously. Many such are conceivable, such, for in- 
 stance, as the retardation of the speed of the planets which would be 
 caused by the presence of a resisting medium in space, or by the en- 
 counter of the system with a sufficiently dense and extended cloud of 
 meteors. 
 
 But so far as we can now judge, the ultimate cooling of the sun 
 (Art. 193) is likely to extinguish life upon the planets long before the 
 mechanical destruction of the system can occur from any such exter- 
 nal causes. 
 
208 COMETS. [ 289 
 
 CHAPTER X. 
 
 COMETS AND METEOKS. 
 
 THE NUMBER, DESIGNATION, AND ORBITS OF COMETS. 
 THEIR CONSTITUENT PARTS AND APPEARANCE. THEIR 
 SPECTRA AND PHYSICAL CONSTITUTION. THEIR PROB- 
 ABLE ORIGIN. REMARKABLE COMETS. AEROLITES, 
 THEIR FALL AND CHARACTERISTICS. SHOOTING STARS, 
 METEORIC SHOWERS. CONNECTION BETWEEN COMETS 
 AND METEORS. 
 
 289. Comets their Appearance and Number. The word 
 " comet" (derived from the Greek kom) means a "hairy star." 
 The appearance is that of a rounded cloud of luminous fog 
 with a star shining through it, often accompanied by a long 
 fan-shaped train or " tail " of hazy light. They present them- 
 selves from time to time in the heavens, mostly when unex- 
 pected, move across the constellations in a path longer or 
 shorter according to circumstances, and remain visible for some 
 weeks or months, until they fade out and vanish in the dis- 
 tance. The large ones are magnificent objects, sometimes as 
 bright as Venus, and visible by day ; with a head as large as 
 the moon, and having a train which extends from the horizon 
 to the zenith, and is really long enough to reach from the earth 
 to the sun. Such comets are rare, however. The majority are 
 faint wisps of light, visible only with the telescope. Fig. 58 
 is a representation of Donati's comet of 1858, which was one of 
 the finest ever seen. 
 
289] 
 
 COMETS. 
 
 209 
 
 Fi0. 58. Naked-eye View of Donati's Comet, Oct. 4, 1858. (Bond.) 
 
 In ancient times, comets were always regarded with terror, as at 
 least presaging evil, if not actively malignant, and the notion still 
 survives in certain quarters, though the most careful research goes to 
 
210 DESIGNATION OF COMETS, [289 
 
 prove that they really do not exert upon the earth the slightest per- 
 ceptible influence of any kind. 
 
 Thus far our lists contain about 650, about 400 of which 
 were observed before the invention of the telescope, and there- 
 fore must have been fairly bright. Of the 250 observed since 
 then, only a small proportion have been conspicuous to the 
 naked eye, perhaps one in five. The total number that visit 
 the solar system must be enormous ; for there is seldom a time 
 when one at least is not in sight, and even with the telescope 
 we see only the few which come near the earth and are favor- 
 ably situated for observation. 
 
 290. Designation of Comets. A remarkable comet gener- 
 ally bears the name of its discoverer or of some one who has 
 "acquired its ownership," so to speak, by some important 
 research concerning it. Thus we have Halley's, Encke's, and 
 Donati's comets. The ordinary telescopic comets are desig- 
 nated only by the year of discovery with a letter indicating 
 the order of discovery in that year, as comet " 1890 a " ; or still 
 again, with the year and a Eoman numeral denoting the order 
 of perihelion passage, as 1890 I, the latter method being the 
 most used. In some cases a comet bears a double name, as 
 the Lexell-Brooks comet (1889 V), which was investigated by 
 Lexell in 1770, and discovered by Brooks on its recent return in 
 1889. 
 
 291. Duration of Visibility and Brightness. The great 
 comet of 1811 was observed for seventeen months, and the 
 little comet, known as 1889 I, for more than two years, the 
 longest period of visibility on record. On the other hand, 
 the whole appearance sometimes lasts only a week or two. The 
 average is probably not far from three months. 
 
 As to brightness, comets differ widely. About one in five 
 reaches the naked-eye limit, and a very few, say four or five in 
 
291] THEIR ORBITS. 211 
 
 a century, are bright enough to be seen in the day-time. The 
 great comet of 1882 was the last one so visible. 
 
 292. Their Orbits. A large majority of the comets move 
 in orbits that are sensibly parabolas (see Appendix, Arts. 439- 
 440). A comet moving in such an orbit approaches the sun 
 from an enormous distance, far beyond the limits of the solar 
 system, sweeps once around the sun, and goes off, never to 
 come back. The parabola does not return into itself and form a 
 closed curve, like the circle and ellipse, but recedes to infinity. 
 Of the 270 orbits that have been computed, more than 200 
 appear to be of this kind. About 60 orbits are more or less 
 distinctly elliptical, and about half a dozen are perhaps hyper- 
 bolas (see Appendix, Art. 440) ; but the hyperbolas differ so 
 slightly from parabolas that the hyperbolic character is not 
 really certain in a single case. 
 
 Comets which have elliptical orbits of course return at regu- 
 lar intervals. Of the 60 elliptical orbits, there are about a 
 dozen to which computation assigns periods near to or exceed- 
 ing 1000 years. These orbits approach parabolas so closely 
 that their real character is still rather doubtful. About 50 
 comets, however, have orbits which are distinctly and certainly 
 elliptical, and 28 have periods of less than one hundred years. 
 Fourteen of these 28 have been actually observed at two or 
 more returns at perihelion. As to the rest of them, some are 
 now due within a few years, and some have probably been lost 
 to observation, either like Biela's comet (Art. 312), or by hav- 
 ing their orbits transformed by perturbations. 
 
 293. The first comet ascertained to move in an elliptical orbit was 
 that known as Halley's, with a period of about seventy-six years, its 
 periodicity having been discovered by Halley in 1681. It has since 
 been observed in 1759 and 1835, and is expected again about 1911. 
 The second of the periodic comets (in the order of discovery) is 
 Encke's, with the shortest period known, only three and one-half 
 years. Its periodicity was discovered in 1819, though the comet itself 
 
212 
 
 COMET GROUPS. 
 
 [293 
 
 had been observed several times before. Fig. 59 shows the orbits of a 
 number of short period comets (it would cause confusion to insert 
 more of them), and also a part of the orbit of Halley's comet. These 
 comets all have periods ranging from three and one-half to eight years, 
 and it will be noticed that they all pass very near to the orbit of 
 Jupiter. Moreover, each comet's orbit crosses that of Jupiter near 
 one of its nodes, the node being marked by a short cross-line on the 
 
 FIG. 59. Orbits of Short-period Comets. 
 
 comet's orbit. The fact is very significant, showing that these comets 
 at times come very near to Jupiter, and it points to an almost certain 
 connection between that planet and these bodies. 
 
 294. Comet Groups. There are several instances in which a 
 number of comets, certainly distinct, chase each other along almost 
 exactly the same path, at an interval usually of a few months or years, 
 though they sometimes appear simultaneously. The most remarkable 
 of these "comet groups " is that composed of the great comets of 1668, 
 1843, 1880, 1882, and 1887. It is of course nearly certain that the 
 comets of such a " group " have a common origin. 
 
295] PERIHELION DISTANCE. 213 
 
 295. Perihelion Distance, etc. Eight of -the 270 cometary 
 orbits, thus far determined, approach the sun within less than 
 6,000000 miles, and four have a perihelion distance exceeding 
 200,000000. A single comet (that of 1729) had a perihelion 
 distance of more than four ' astronomical units/ or 375,000000 
 miles. It must have been an enormous one, to be visible at 
 all under the circumstances. There may, of course, be any 
 number of comets with still greater perihelion distances, 
 because as a rule we are only able to see such as come reason- 
 ably near the earth, and this is probably only a small percent- 
 age of the total number that visit the sun. 
 
 The inclinations of cometary orbits range all the way from 
 zero to 90. As regards the direction of motion, all the ellip- 
 tical comets having periods of less than 100 years move direct, 
 i.e., from west to east, except Halley's comet and TempePs 
 comet of 1886. Other comets show no decided preponderance 
 either way. 
 
 296. Parabolic Comets are Visitors. The fact that the 
 orbits of most comets are sensibly parabolic, and that their 
 planes have no evident relation to the ecliptic, indicates 
 (though it does not absolutely prove) that these bodies do not 
 in any proper sense belong to the solar system. They are only 
 visitors. Such comets come to us precisely as if they simply 
 dropped towards the sun from an enormous distance among 
 the stars ; and they leave the system with a velocity which, 
 if no force but the sun's attraction acts upon them, will 
 carry them away to an infinite distance, or until they encoun- 
 ter the attraction of some other sun. Their motions are just 
 what might be expected of ponderable masses moving among 
 the stars under the law of gravitation. 
 
 297. Origin of Periodic Comets. But while the parabolic 
 comets are thus unquestionably strangers and visitors, there is 
 a question as to the periodic comets, which move in elliptical 
 
214 THE CAPTURE THEORY. [ 297 
 
 orbits. Are we to regard them as native citizens, or only as 
 naturalized foreigners, so to speak ? It is evident that, some- 
 how or other, many of them stand in peculiar relations to 
 Jupiter, Saturn, and other planets, as already indicated in Art. 
 293. All short period comets (those which have periods 
 ranging from three to eight years) pass very close to the orbit 
 of Jupiter, and are now recognized and spoken of as Jupiter's 
 " family of comets " ; eighteen of them are known at present. 
 Similarly, Saturn is credited with two comets, and Uranus 
 with three, one of them being Tempel's comet, which is closely 
 connected with the November meteors, and is due on its next 
 return in 1900. Finally, Neptune has a family of six, among 
 them Halley's comet, and two others which have returned a 
 second time to perihelion since 1880. 
 
 298. The Capture Theory. The generally accepted theory 
 as to the origin of these " comet-families " is one first suggested 
 by Laplace nearly 100 years ago, that the comets which com- 
 pose them have been captured by the planet to which they 
 stand related. A comet entering the system in a parabolic 
 orbit, and passing near a planet, will be disturbed, either 
 accelerated or retarded. If it is accelerated, it is easy to 
 prove that the original parabolic orbit will be changed to an 
 hyperbola, and the comet will never be seen again, but will 
 pass out of the system forever ; but if it is retarded, the orbit 
 becomes elliptical) and the comet will return at each successive 
 revolution to the place where it was first disturbed. 
 
 But this is not the end. After a certain number of revo- 
 lutions, the planet and the comet will come together a second 
 time at or near the place where they met before. The result 
 may then be an acceleration, which will send the comet out 
 of the system finally ; but it is an even chance at least, that 
 it may be a second retardation, and that the orbit and period 
 may thus be further diminished : and this may happen over and 
 over again, until the comet's orbit falls so far inside that of the 
 
298] THE LEXELL-BROOKS COMET. 215 
 
 planet that there is no further disturbance to speak of. Given 
 time enough and comets enough, and the result would inevi- 
 tably be such a comet-family as really exists. We may add 
 that certain researches of Professor Newton of New Haven 
 and others, upon the position and distribution of cometary 
 orbits, decidedly favor the idea that these bodies do not 
 originate in the solar system, but come to us from interstellar 
 space. 
 
 The late R. A. Proctor declined to accept this capture theory, and 
 maintained with much vigor and ability the theory that comets and 
 meteor-swarms have been ejected from the great planets by eruptions 
 of some sort. We cannot take space here to discuss the theory, which 
 is really not quite so wild as at first it seems ; but the objections to it 
 are serious, and we think fatal. 
 
 299. The Lexell-Brooks Comet. The " capture " theory 
 has recently received a remarkable corroboration in the case 
 of a little comet, 1889 V, discovered by Mr. Brooks of Geneva, 
 N.Y., in July, 1889. It was soon found to be moving with a 
 period of about seven years, in an elliptical orbit which passes 
 very near to that of Jupiter. (We remark in passing that 
 this comet in August divided into four fragments ; see Art. 
 314.) On investigating the orbit more carefully, Mr. S. C. 
 Chandler of Cambridge (U.S.) discovered that, in 1886, the 
 comet and the planet had been close together for some months, 
 and that as a consequence the comet's orbit must have been 
 completely transformed, the previous orbit having been a much 
 larger one with a period of nearly twenty-seven years. 
 
 Now, in 1770, a famous comet appeared, which is known as 
 LexelFs, because Lexell computed its orbit. It was bright, 
 and came very near the earth, and, according to Lexell' s cal- 
 culations, was then moving in an orbit with a period of only five 
 and a half years, the first instance of a short-period comet on 
 record ; but it was never seen again. Its failure to reappear, 
 in 1776, was easily accounted for by the fact that its orbit did 
 
216 PHYSICAL CONSTITUTION OF COMETS. [ 299 
 
 not then bring it anywhere near the earth. But it should 
 have reappeared in 1781, and for a long time its disappear- 
 ance was very mysterious, until Laplace, some years later, 
 showed that, in 1779, the comet must have come very close 
 to Jupiter, perhaps as near as some of its satellites, and that 
 in consequence the attraction of that planet had probably 
 sent it into a new orbit, not observable from the earth. 
 
 More recent investigations by Leverrier, some thirty years 
 ago, show that while the data are insufficient to determine the 
 comet's subsequent orbit with certainty, one of the possible 
 orbits would have had a period a little less than twenty-seven 
 years. This would bring it back, in 1886, after four revolu- 
 tions, to the same place which it had occupied in 1779 ; now 
 nine of Jupiter's periods are 106|- years, so that he, also, would 
 have returned to the same place. 
 
 To make a long story short, Mr. Chandler shows that it is 
 extremely probable that Brooks's comet, 1889 V, is identical 
 with Lexell's comet of 1770. Jupiter first transformed its 
 orbit from a parabola to an ellipse, with a period of five and a 
 half years ; then removed it from our sphere of observation ; 
 and, again, after a century' or more, has brought it back. 
 What will happen at the next encounter of the comet with the 
 planet it is not yet possible to predict. 
 
 PHYSICAL CONSTITUTION OF COMETS. 
 
 300. Constituent Parts of a Comet. (a) The essential part 
 of a comet, that which is always present and gives the comet 
 its name, is the coma, or nebulosity, a hazy cloud of faintly 
 luminous transparent matter. 
 
 (b) Next we have the nucleus, which, however, is wanting 
 in many comets, and makes its appearance only as the comet 
 comes near the sun. It is a bright, more or less star-like 
 point near the centre of the comet. In some cases it is double, 
 or even multiple. 
 
300] DIMENSIONS OF COMETS. 217 
 
 (c) The tail or train is a stream of light which commonly 
 accompanies a bright comet, and is sometimes present even 
 with a telescopic one. As the comet approaches the sun, the 
 tail follows it ; but as the comet moves away from the sun, it 
 precedes. It is always, speaking broadly, directed away from 
 the sun, though its precise form and position are determined 
 partly by the comet's motion. It is practically certain that 
 it consists of extremely rarefied matter which is thrown off by 
 the comet and powerfully repelled by the sun. 
 
 It certainly is not like the smoke of a locomotive or train of a 
 meteor simply left behind by the comet, because as the comet is 
 receding, from the sun the tail goes before it, as has been said. 
 
 (d) Jets and Envelopes. The head of a comet is often 
 veined by short jets of light, which appear to be spurted out 
 from the nucleus ; and sometimes the nucleus throws off a 
 series of concentric envelopes, like hollow shells, one within 
 the other. These phenomena, however, are seldom observed 
 in telescopic comets. 
 
 301. Dimensions of Comets. The volume or bulk of a comet 
 is often enormous, almost inconceivably so, if the tail is in- 
 cluded in the estimate. The head, as a rule, is from 40,000 to 
 50,000 miles in diameter (comets less than 10,000 miles in 
 diameter would stand little chance of discovery). Comets 
 exceeding 150,000 miles are rather rare, though there are 
 several on record. 
 
 The comet of 1811 at one time had a diameter of fully 1,200000 
 miles, 40 per cent larger than that of the sun. The head of the comet 
 of 1680 was 600,000 miles in diameter, and that of Donati's comet, of 
 1858, about 250,000. 
 
 The diameter of the head keeps changing all the time ; and 
 what is singular is that while the comet is approaching the 
 sun the head usually contracts, and expands again as it recedes. 
 
218 MASS OF COMETS. [ 3 1 
 
 No entirely satisfactory explanation is known for this behavior, but 
 Sir John Herschel has suggested that the change is merely optical ; 
 that near the sun a part of the nebulous matter is evaporated by the 
 solar heat and so becomes invisible, condensing and reappearing again 
 when the comet gets to cooler regions. 
 
 The nucleus ordinarily has a diameter ranging from 100 miles 
 up to 5000 or 6000, or even more. Like the comet's head it 
 also varies greatly in diameter, even from day to day, so that it 
 is probably not a solid body. Its changes, however, do not 
 seem to depend in any regular 'way upon the comet's distance 
 from the sun, but rather upon its activity in throwing off jets 
 and envelopes. 
 
 The tail of a comet, as regards simple magnitude, is by 
 far the most imposing feature. Its length is seldom less 
 than from 5,000000 to 10,000000 miles. It frequently attains 
 50,000000, and there are several cases where it has exceeded 
 100,000000; while its diameter at the end remote from the 
 comet varies from 1,000000 to 15,000000. 
 
 302. Mass of Comets. While the bulk of comets is thus 
 enormous, their masses are apparently insignificant, in no case 
 at all comparable with that of our little earth, even. The evi- 
 dence on this point, however, is purely negative ; it does not 
 enable us in any case to say just what the mass really is, but 
 only to say how great it is not; i.e., it only proves that a 
 comet's mass is less than 1 ^ ^ of the earth's, 1 how much 
 less we cannot yet find out. The evidence is derived from the 
 fact that no sensible perturbations are produced in the motions 
 of a planet when a comet comes even very near it, although 
 in such a case the comet itself is fairly "sent kiting," thus 
 showing that gravitation has its full effect between the two 
 bodies. 
 
 1 One one-hundred-thousandth of the earth's mass is about ten times 
 the mass of the earth's whole atmosphere, and is equivalent to the mass 
 of an iron ball about 150 miles in diameter. 
 
302] DENSITY OF COMETS. 219 
 
 Lexell's comet, in 1770, and Biela's comet on several occasions, 
 have come so near the earth that the length of the comet's period was 
 changed by several weeks, while the year was not altered by so much 
 as a single second. It would have been changed by many seconds if 
 the comet's mass were as much as that of the earth. 
 
 303. Density of Comets. This is, of course, almost incon- 
 ceivably small, the mass of comets being so minute and their 
 volumes so enormous. If the head of a comet, 50,000 miles in 
 diameter, has a mass yrnnnnF ^ at ^ the eartn > ^s mean density 
 must be about -g-^-tf that of the air at the sea-level, far below 
 that of the best air-pump vacuum. As for the tail, the density 
 must be almost infinitely lower yet. It is nearer to an " airy 
 nothing " than anything else we know of. 
 
 The extremely low density of comets is shown also by their 
 transparency. Small stars can be seen through the head of a 
 comet 100,000 miles in diameter, even very near its nucleus, 
 and with, hardly a perceptible diminution of their lustre. 
 
 We must bear in mind, however, that the low mean density of a 
 comet does not necessarily imply a low density of its constituent parti- 
 cles. A comet may be to a considerable extent composed of small 
 heavy bodies, and still have a low mean density, provided they are far 
 enough apart. There is much reason, as we shall see, for supposing 
 that such is really the case, that the comet is largely composed of 
 small meteoric stones, carrying with them a certain quantity of envel- 
 oping gas. 
 
 Another point should be referred to. Students often find it 
 impossible to conceive how such impalpable "dust clouds" 
 can move in orbits like solid masses, and with such enormous 
 velocities. They forget that in a vacuum a feather falls as 
 swiftly as a stone. Interplanetary space is a vacuum far 
 more perfect than anything we can produce by air-pumps, and 
 in it the lightest bodies move as freely and swiftly as the 
 densest, since there is nothing to resist their motion. If all 
 the earth were suddenly annihilated except a single feather, 
 
220 
 
 THE LIGHT OF COMETS. 
 
 [303 
 
 the feather would keep right on and continue the same orbit, 
 with unchanged speed. 
 
 304. The Light of Comets. To some extent their light 
 may be mere reflected sunlight; but in the main it is light 
 emitted by the comet itself under the stimulus of solar action. 
 That the light depends in some way on the sun is shown by 
 
 FIG. 60. Comet Spectra. 
 
 (For convenience in engraving, the dark lines of the solar spectrum in the lowest strip 
 of the figure are represented as bright.) 
 
 the fact that its brightness usually varies with its distance 
 from the sun, according to the same law as that of a planet. 
 
 But the brightness frequently varies rapidly and capri- 
 ciously without any apparent reason ; and that the comet is 
 self-luminous when near the sun is proved by its spectrum, 
 which is not at all like the spectrum of reflected sunlight, but 
 is a spectrum of bright bands, three of which are usually seen, 
 
304] 
 
 DONATI S COMET. 
 
 221 
 
 and have been identified repeatedly and certainly with the 
 spectrum of gaseous hydrocarbons. (All the different hydro- 
 carbon gases give the same spectrum at the temperature of a 
 Bunsen burner.) This spectrum is absolutely identical with 
 that given by the blue base of a candle flame, or, better, by 
 a Bunsen burner consuming ordinary coal gas. 
 
 Occasionally a fourth band is seen in the violet, and when the 
 comet approaches unusually near the sun, the bright lines of sodium, 
 and other metals (probably iron), sometimes appear. There seem to 
 be cases, also, when different bands replace the ordinary ones. Fig. 60 
 represents the ordinary comet spectrum, compared with the solar spec- 
 
 FIG. 61. Head of Donati's Comet, Oct. 5, 1858. (Bond.) 
 
 trum and with that of a candle flame. Two anomalous comet-spectra 
 are also shown in the figure. The spectrum makes it almost cer- 
 tain that hydrocarbon gases are present in considerable quantity, 
 
222 
 
 FORMATION OF TAIL. 
 
 [304 
 
 and that these gases are somehow rendered luminous ; not probably 
 by any general heating, however, for there is no reason to think that 
 the general temperature of a comet is very high. We must not infer 
 that the hydrocarbon gas, because it is so conspicuous in the spec- 
 trum, necessarily constitutes most of the comet's mass: more likely 
 it is only a very small fraction of the whole. 
 
 305. Phenomena that accompany a Comet's Approach to the 
 Sun. When the comet is first discovered, it is usually a mere 
 round, hazy cloud of faint nebulosity, a little brighter near the 
 middle. As it approaches the sun it brightens rapidly, and 
 the nucleus appears. Then on the sunward side the nucleus 
 begins to emit luminous jets, or else to throw off more or less 
 symmetrical envelopes, which follow each other at intervals of 
 some hours, expanding or growing fainter, until they are lost 
 in the nebulosity of the head. 
 
 Fig. 61 shows the envelopes as they appeared in the head of 
 Donati's comet of 1858. At one time seven of them were vis- 
 ible together : very few com- 
 ets, however, exhibit this phe- 
 nomenon with such symmetry. 
 More frequently the emissions 
 from the nucleus take the form 
 of jets and streamers. 
 
 To Sun 
 
 306. Formation of Tail. 
 
 The tail appears to be formed 
 of material which is first pro- 
 jected from the nucleus of the 
 comet towards the sun, and 
 then afterwards repelled by 
 the sun, as illustrated by Fig. 
 62. At least this theory has 
 the great advantage over all others which have been proposed 
 that it not only accounts for the phenomenon in a general way, 
 but admits of being worked out in detail and verified mathe- 
 
 FIG. 62. Formation of a Comet's Tail by 
 Matter expelled from the Head. 
 
306] TYPES OF COMETS' TAILS. 223 
 
 matically, by comparing the actual size and form of the planet's 
 tail, at different points in the orbit, with that indicated by the 
 theory j and the accordance is generally very satisfactory. 
 
 The tail is curved because the repelled particles, after leav- 
 ing the comet's head, retain their original motion, so that they 
 are arranged not along a straight line drawn from the sun to 
 
 FIG. 63. A Comet's Tail at Different Points in its Orbit near Perihelion. 
 
 the comet, but on a curve convex to the comet's motion, as 
 shown in Fig. 63 ; but the stronger the repulsion the less the 
 curvature, and the straighter the tail. The nature of the force 
 which repels the particles of a comet is, of course, only a 
 matter of speculation ; but the idea that it is electrical gener- 
 ally prevails, though the detailed explanation is not easy. 
 There is no reason to suppose that the matter driven off to 
 form the tail is ever recovered by the comet. 
 
 307. Types of Comets' Tails. Bredichin, of Moscow, has 
 found that the trains of comets may be classified under three 
 different types, as indicated by Fig. 64. 
 
 First, the long, straight rays, composed of matter upon which the 
 solar repulsion is from ten to fifteen times as great as the attraction 
 
224 
 
 TYPES OF COMETS' TAILS. 
 
 [307 
 
 enormous. 
 
 of gravity, so that the particles leave the comet with a velocity of four 
 or five miles a second, which is afterwards increased until it becomes 
 The nearly straight rays, shown in Fig. 58, belong to 
 
 this type. For plausible 
 reasons, which, however, 
 we cannot stop to explain, 
 Bredichin supposes these 
 straight rays to be com- 
 posed of hydrogen. 
 
 The second type is the 
 ordinary, curved, plume- 
 like train, like the principal 
 tail of Donati's comet. In 
 trains of this type, sup- 
 posed to be due to hydro- 
 carbon vapors, the repulsive 
 force varies from 2.2 times 
 the attraction of gravity for 
 particles on the convex edge 
 of the train, to half that 
 amount for those on the 
 inner edge. The spectrum 
 is the same as that of the 
 comet's head. 
 
 Third, a few comets show 
 tails of still a third type, 
 short, stubby brushes, vio- 
 lently curved, and due to 
 matter on which the repul- 
 sive force is feeble as com- 
 pared with gravity. These 
 are assigned by Bredichin 
 to metallic vapors of con- 
 siderable density, with an 
 FIG. 64. , . , . ;. 
 
 admixture of sodium, etc. 
 
 Bredichin's Three Types of Cometary Tails. 
 
 308. Unexplained and Anomalous Phenomena. A curious 
 phenomenon, not yet explained, is the dark stripe which, in a 
 
308] THE NATURE OF COMETS. 225 
 
 large comet approaching the sun, runs down the centre of the 
 tail, looking very much as if it were a shadow of the comet's 
 head. It is certainly not a shadow, however, because it usually 
 makes more or less of an angle 
 with the sun's direction. It is 
 well shown in Fig. 61. When the 
 comet is at a greater distance from 
 the sun, this central stripe is usu- 
 ally bright, as in Fig. 65. 
 
 Not unfrequently, moreover, FIG. 65. 
 
 COmetS pOSSeSS anomalous tails, Bright-centred Tail of Coggia's Comet, 
 , ., ,. .j . , , June, 1874. 
 
 tails directed sometimes straight 
 
 towards the sun, and sometimes at right angles to that direc- 
 tion. Then sometimes there are luminous sheaths, which seem 
 to envelop the head of the comet and project towards the sun 
 (Fig. 66), or little clouds of cometary matter which leave the 
 main comet like puffs of smoke from a bursting bomb, and 
 travel off at an angle until they fade away (see Fig. 66). 
 None of these appearances are contradictory to the theory 
 above stated, though they are not yet clearly included 
 in it. 
 
 309. The Nature of Comets. All things considered, the 
 most probable hypothesis as to the constitution of a comet, so 
 far as we can judge at present, is that its head is a swarm of 
 small meteoric particles, widely separated (say pin-heads, many 
 yards apart), each carrying with it an envelope of rarefied gas 
 and vapor, in which light is produced either by electric dis- 
 charges between the solid particles, or by some action due to 
 the rays of the sun. As to the size of the constituent par- 
 ticles, opinions differ widely. Some maintain that they are 
 large rocks : Professor Newton calls a comet a " gravel bank " : 
 others say that it is a mere "dust-cloud." The unquestion- 
 able close connection between meteors and comets (Art. 327) 
 almost compels some " meteoric hypothesis." 
 
226 DANGER FROM COMETS. [ 310 
 
 310. Danger from Comets. In all probability there is none. 
 It has been supposed that comets might do us harm in two ways, 
 either by actually striking the earth, or by falling into the sun and 
 thus producing such an increase of solar heat as to burn us up. 
 
 As regards the possibility of a collision between a comet and the 
 earth, the event is certainly possible. In fact, if the earth lasts long 
 enough, it is practically sure to happen, for there are several comet's 
 orbits which pass nearer to the earth's orbit than the semi-diameter 
 of the comet's head. As to the consequence of such a collision, it is 
 impossible to speak with absolute confidence for want of certain knowl- 
 edge as to the constitution of a comet. If the theory presented in the 
 preceding article is true, everything depends on the size of the separate 
 solid particles which form the main portion of the comet. If they 
 weigh tons, the bombardment experienced by the earth when struck 
 by the comet would be a very serious matter. If they are most of 
 them not larger than pin-heads, the result would be only a meteoric 
 shower. 
 
 The encounters, however, will be very rare. If we accept the esti- 
 mate of Babinet, they will occur on the average once in about 
 15,000000 years. 
 
 If a comet actually strikes the sun, which would necessarily be a 
 very rare phenomenon, it is not likely that the least harm will be 
 done. The collision might generate about as much heat as the sun 
 radiates in eight or nine hours; but the cometary particles would 
 pierce the photosphere, and their heat would be liberated mostly below 
 the solar surface, simply expanding by some slight amount the diam- 
 eter of the sun, but making no particular difference in the amount of 
 its radiation for the time being. There might be, and very likely 
 would be, a flash of some kind at the solar surface when the shower 
 of meteors struck it ; but probably nothing that the astronomer would 
 not take delight in observing. 
 
 311. Remarkable Comets. Our space does not permit us 
 to give full accounts of any considerable number. We limit 
 ourselves to two, which for various reasons are of special 
 interest. 
 
 Biela's comet is, or rather was, a small comet some 40,000 
 miles in diameter, at times barely visible to the naked eye, 
 
311] BIELA'S COMET. 227 
 
 and sometimes showing a short tail. It had a period of 6.6 
 years, and was the second comet of short period known, hav- 
 ing been discovered by Biela, an Austrian officer, in 1826 
 (the periodicity of Encke's comet had been discovered seven 
 years earlier). Its orbit comes within a few thousand miles 
 of the earth's orbit, the distance varying somewhat, of course, 
 on account of perturbations ; but the approach is sometimes 
 so close that, if the comet and the earth should happen to 
 arrive at the same time, there would be a collision. At its 
 return, in 1846, it split into two. When first seen on Nov. 28th, 
 it was one and single. On Dec. 19th it was distinctly pear- 
 shaped, and ten days later it was divided. 
 
 The twin comets travelled along for four months, at an almost 
 unchanging distance of about 165,000 miles, without any apparent 
 effect upon each other's motions, but both very active from the physical 
 point of view, showing remarkable variations and alterations of bright- 
 ness entirely unexplained. In August, 1852, the twins were again 
 observed, then separated by a distance of about 1,500000 miles; but 
 it was impossible to tell which was which. Neither of them has ever 
 been seen again, though they must have returned many times, and 
 more than once in a very favorable position. 
 
 312. There remains, however, another remarkable chapter 
 in the story of this comet. In 1872, on Nov. 27th, just as the 
 earth was crossing the track of the lost comet, but some mil- 
 lions of miles behind where the comet ought to be, she en- 
 countered a wonderful meteoric shower. As Miss Clerke 
 expresses it, perhaps a little too positively, " it became evident 
 that Biela's comet was shedding over us the pulverized prod- 
 ucts of its disintegration." A similar meteoric shower oc- 
 curred again in 1885, when the earth once more crossed the 
 track of the comet. 
 
 It is not certain whether the meteor swarms thus encountered were 
 the remains of the comet itself, or whether they were other small bodies 
 merely following in its path. The comet must have been several mil- 
 
228 THE GREAT COMET OF 1882. [ 312 
 
 lions of miles ahead of the place where these meteor swarms were 
 met, unless it has been set back in its orbit since 1852 by some unex- 
 plained and improbable perturbations. But the comet cannot be 
 found, and if it still exists and occupies the place it ought to, it must 
 have somehow lost the power of shining. 
 
 313. The Great Comet of 1882. This is the most recent 
 of the brilliant comets that have been observed, and will long 
 be remembered not only for its magnificent beauty, but for the 
 great number of unusual phenomena which it presented. It 
 was first seen in the southern hemisphere about Sept. 3d, but 
 not in the northern until the 17th, the day on which it arrived 
 at perihelion. On that day it was independently discovered 
 within 2 or 3 of the sun, near noon, by several observers, who 
 had not before heard of its existence. It was visible to the 
 naked eye in full sunshine for more than a week after its peri- 
 helion passage. It then became a splendid object in the morn- 
 ing sky, and continued to be observed for six months. 
 
 That portion of the orbit visible from the earth coincides 
 almost exactly with the orbits of four other comets, those 
 of 1668, 1843, 1880, and 1887, with which it forms a " comet 
 group," as already mentioned (Art. 294). The perihelion dis- 
 tances of the comets of this group are' all less than 750,000 
 miles, so that they pass within 300,000 miles of the sun's 
 surface ; i.e., right through the corona, and with a velocity 
 exceeding 300 miles a second ; and yet this passage through 
 the corona does not disturb their motion perceptibly. 
 
 The orbit of the comet of 1882 turns out to be a very elon- 
 gated ellipse with a period of about 800 years. The period of 
 the comet of 1880 appears to be only seventeen years, while 
 the orbits of the other three are sensibly parabolic. 
 
 314. Early in October the comet presented the ordinary 
 features. The nucleus was round, a number of well-marked 
 envelopes were visible in the head^ and the dark stripe down 
 
314] 
 
 THE "SHEATH. 
 
 the centre of the tail was sharply defined. Two weeks later 
 the nucleus had been broken up and transformed into a 
 crooked stream, some 50,000 miles in length, of five or six 
 bright points : the envelopes had vanished from the head, and 
 the dark stripe was replaced by a bright central spine. 
 
 At the time of perihelion the comet's spectrum was filled 
 with countless bright lines. Those of sodium were easily 
 recognizable, and continued visible for weeks ; the other lines 
 
 Fio. 66. The " Sheath," and the Attendants of the Comet of 1882. 
 
 continued only a few days and were not certainly identified, 
 although the general aspect of the spectrum indicated that 
 iron, manganese, and calcium were probably present. By the 
 middle of October it had become simply the normal comet 
 spectrum, with the ordinary hydrocarbon bands. 
 
230 METEORS AND SHOOTING-STARS. [ 3 *4 
 
 The comet was so situated that the tail was directed nearly 
 away from the earth, and so was not seen to good advantage, 
 never having an apparent length exceeding 35. The actual 
 length, however, at one time was more than 100,000000 miles. 
 
 A unique, and so far unexplained, phenomenon was a faint, 
 straight-edged "sheath" of light, which enveloped the por- 
 tions of the comet near the head, and projected 3 or 4 in 
 front of it, as shown in Fig. 66. Moreover, there were certain 
 shreds of cometary matter accompanying the comet, at a dis- 
 tance of 3 or 4 when first seen, but gradually receding and 
 growing fainter. This also was something new in cometary 
 history, though the Lexell-Brooks comet, 1889 V, has since 
 done the same thing. 
 
 
 METEORS AND SHOOTING-STARS. 
 
 315. Meteorites. Occasionally bodies fall upon the 
 out of the sky. Such a body during its flight through the air 
 is called a " Meteorite " or " Bolide," and the pieces which fall 
 to the earth are called "Meteorites," "Aerolites/' "Urano- 
 liths," or simply "meteoric stones." 
 
 If the fall occurs at night, a ball of fire is seen, which moves 
 with an apparent velocity depending upon the distance of the 
 meteor and the direction of its motion. The fire-ball is gener- 
 ally followed by a luminous train, which sometimes remains 
 visible for many minutes after the meteor itself has disap- 
 peared. The motion is usually somewhat irregular, and here 
 and there along its path the meteor throws off sparks and frag- 
 ments, and changes its course more or less abruptly. Some- 
 times it vanishes by simply fading out in the air, sometimes 
 by bursting like a rocket. If the observer is near enough, the 
 flight is accompanied by a heavy, continuous roar, emphasized 
 now and then by violent detonations. 
 
 The observer must not expect to hear the explosion at the moment 
 when he sees it, since sound travels only about twelve miles a minute. 
 
315] 
 
 THE AEROLITES THEMSELVES. 
 
 231 
 
 If the fall occurs by day, the luminous appearances are 
 mainly wanting, though sometimes a white cloud is seen, and 
 the train may be visible. In a few cases aerolites have fallen 
 almost silently, and without warning. 
 
 316. The Aerolites themselves. The mass that falls is 
 sometimes a single piece, but more usually there are many 
 fragments, sometimes numbering thousands ; so that, as the 
 old writers say, " it rains stones." The pieces weigh from 500 
 pounds to a few grains, 
 the aggregate mass 
 sometimes amounting 
 to a number of tons. 
 By far the greater num- 
 ber of aerolites are 
 stones, but a few, per- 
 haps three or four per 
 cent of the whole num- 
 ber, are masses of near- 
 ly pure iron more or 
 less alloyed with nickel 
 
 The total number of 
 meteorites which have 
 fallen and been gathered 
 into cabinets since 1800 
 is about 250, only 10 
 of which are iron masses. 
 Nearly all, however, con- 
 tain a large percentage of 
 iron, either in the metal- 
 lic form or as sulphide. 
 Between 25 and 30 of the 
 250 fell within the United States, the most remarkable being those 
 of Weston, Conn., in 1807; New Concord, Ohio, 1860; Amana, Iowa, 
 1875 ; Emmett County, Iowa, 1879 (mainly iron) ; and Johnson 
 County, Ark., 1886 (iron). 
 
 FIG. 67. 
 Fragment of one of the Amana Meteoric Stones. 
 
232 PATH AND MOTION. [ 316 
 
 Twenty-four of the chemical elements have been found in 
 these bodies, but not one new element, though a large number 
 of new minerals appear in them, and seem to be characteristic 
 of aerolites. 
 
 The most distinctive external feature of a meteorite is the 
 thin, black, varnish-like crust that covers it. It is formed by 
 the melting of the surface during the meteor's swift flight 
 through the air, and in some cases penetrates the mass in 
 cracks and veins. The surface is generally somewhat uneven, 
 having "thumb-marks" upon it, hollows, probably formed 
 by the fusion of some of the softer minerals. Fig. 67 is from 
 a photograph given in Langley's "New Astronomy," where 
 the body is designated, perhaps a little too positively, as " part 
 of a comet." 
 
 317. Path and Motion. When a meteor has been observed 
 from a number of different stations, its path can be computed. 
 It usually is first seen at an altitude of between 80 and 100 
 miles, and disappears at an altitude of between 5 and 10. 
 The length of the path may be anywhere from 50 to 500 miles. 
 In the earlier part of its course, the velocity ranges from 10 
 to 40 miles a second, but this is greatly reduced before the 
 meteor disappears. 
 
 In observing these bodies, the object should be to obtain as accurate 
 an estimate as possible of the altitude and azimuth of the meteor, at 
 moments which can be identified, and also of the time occupied in 
 traversing definite portions of the path. The altitude and azimuth 
 will enable us to determine the height and position of the meteor, 
 while the observations of the time are necessary in computing its 
 velocity. By night the stars furnish the best reference points from 
 which to determine its position. By day, one must take advantage of 
 natural objects or buildings to define the meteor's place, the observer 
 marking the precise spot where he stood. By taking the proper 
 instrument to the place afterwards, it is then easy to ascertain the 
 bearings and altitude. As to the time of flight, it is usual for the 
 observer to begin to repeat rapidly some familiar verse of doggerel 
 
317] LIGHT AND HEAT OF METEORS. 233 
 
 when the meteor is first seen, reiterating it until the meteor disap- 
 pears. Then by rehearsing the same before a clock, the number of 
 seconds can be pretty accurately determined. 
 
 318. The Light and Heat of Meteors. These are due 
 simply to the destruction of the meteor's velocity by the fric- 
 tion and resistance of the air. When a body moving with a 
 high velocity is stopped by the resistance of the air, by far the 
 greater part of its energy is transformed into heat. Sir Wil- 
 liam Thomson has shown that the heating effect in the case of 
 a body moving through the air with a velocity exceeding ten 
 miles a second, is the same as if it were " immersed in a flame 
 having a temperature at least as high as the oxyhydrogen 
 blow-pipe " ; and, moreover, this temperature is independent 
 of the density of the air, depending only on the velocity of 
 the meteor. Where the air is dense, the total quantity of 
 heat (i.e., the number of calories developed in a given time) is 
 of course greater than where the air is rarified ; but the virtual 
 temperature of the air itself where it rubs against the surface 
 is the same in either case. During the meteor's flight, its sur- 
 face, therefore, is raised to a white heat and melted, and the 
 liquefied portions are swept off by the rush of air, condensing 
 as they cool to form the train. In some cases this train 
 remains visible for many minutes, a fact not easily ex- 
 plained. It seems probable that the material must be phos- 
 phorescent. 
 
 319. Origin of Meteors. They cannot be, as some have 
 maintained, the immediate product of eruptions from volca- 
 noes, either terrestrial or lunar, since they reach our atmo- 
 sphere with a velocity which makes it certain that they come 
 to us from the depths of space. There is no proof that they 
 have originated in any way different from the larger heavenly 
 bodies. At the same time many of them resemble each other 
 so closely as almost to compel the surmise that these, at least, 
 
234 SHOOTING-STARS. [ 319 
 
 had a common source. It is not perhaps impossible that such 
 may be fragments which long ago were shot out from now 
 extinct lunar volcanoes, with a velocity which made planets 
 of them for the time being. If so, they have since been trav- 
 elling in independent orbits until they encountered the earth 
 at the point where her orbit crosses theirs. Nor is it impos- 
 sible that some of them were thrown out by terrestrial erup- 
 tions when the earth was young; or that they have been 
 ejected from the planets, or even from the stars. It is only 
 certain that during the period immediately preceding their 
 arrival upon the earth, they have been travelling in long 
 ellipses, or parabolas, around the sun. 
 
 SHOOTING-STARS. 
 
 320. Their Nature and Appearance. These are the evanes- 
 cent, swiftly moving, star-like points of light which may be 
 seen every few minutes on any clear moonless night. They 
 make no sound, nor has anything been known to reach the 
 earth's surface from them. 
 
 For this reason it is probably best to retain, provisionally, at least, 
 the old distinction between them and the great meteors from which 
 aerolites fall. It is quite possible that the distinction has no real 
 ground, that shooting-stars, as is maintained by many, are just like 
 other meteors, except that being so small they are entirely consumed 
 in the air ; but then, on the other hand, there are some things which 
 rather favor the idea that the two classes differ in about the same way 
 as asteroids do from comets. We know that an aerolitic meteor is a 
 compact mass of rock. It is possible, or even likely, that a shooting- 
 star, on the contrary, is a little dust-cloud, like a puff of smoke. 
 
 321. Number of Shooting-stars. Their number is enor- 
 mous. A single observer averages from four to eight an hour ; 
 but if the observers are sufficiently numerous, and so placed 
 as to be sure of noting all that are visible from a given station. 
 
321] ELEVATION", PATH, AND VELOCITY. 235 
 
 about eight times as many are counted. From this it has 
 been estimated that the total number which enter our atmo- 
 sphere daily must be between 10,000000 and 20,000000, the 
 average distance between them being some 200 miles. 
 
 Besides those which are visible to the naked eye, there is a still 
 larger number of meteors which are so small as to be observable only 
 with the telescope. 
 
 The average hourly number about 6 o'clock in the morning 
 is double the hourly number in the evening ; the reason being 
 that in the morning we are in front of the earth, as regards its 
 orbital motion, while in the evening we are in the rear. In 
 the evening we see only such as overtake us ; in the morning 
 we see all that we either meet or overtake. 
 
 322. Elevation, Path, and Velocity. By observations made 
 at stations 30 or 40 miles apart, it is easy to determine these 
 data with some accuracy. It is found that on the average the 
 shooting-stars appear at a height of about 74 miles, and dis- 
 appear at an elevation of about 50 miles, after traversing a 
 course 40 or 50 miles long, with a velocity from 10 to 50 miles 
 a second, about 25 on the average. They do not begin to 
 be visible at so great a height as the aerolitic meteors ; and 
 they are more quickly consumed, and therefore do not pene- 
 trate the atmosphere so deeply. 
 
 323. Brightness, Material, and Mass. Now and then a 
 shooting-star rivals Jupiter, or even Venus, in brightness. A 
 considerable number are like first-magnitude stars ; but the 
 great majority are faint. The bright ones generally leave 
 trains. Occasionally it has been possible to get a "snap 
 shot," so to speak, at the spectrum of a meteor, and in it the 
 bright lines of sodium and magnesium (probably) are fairly 
 conspicuous among many others which cannot be identified by 
 such a hasty glance. 
 
236 MATERIAL AND MASS OF SHOOTING-STARS. [ 323 
 
 Since these bodies are consumed in the air, all that we can 
 hope to get of their material is their " ashes.' 7 
 
 In most places its collection and identification is, of course, hope- 
 less ; but the Swedish naturalist Nordenskiold thought that it might 
 be found in the polar snows. In Spitzbergen he therefore melted 
 several tons of snow, and on filtering the water he actually detected 
 in it a sediment containing minute globules of oxide and sulphide of 
 iron. Similar globules have also been found in the products of deep- 
 sea dredging. They may be meteoric, but what we now know of the 
 distance to which smoke and fine volcanic dust is carried by the wind 
 make it not improbable that they may be of purely terrestrial origin. 
 
 We have no way of determining the exact mass of a shoot- 
 ing-star, but from the light it emits as seen from a known dis- 
 tance, an approximate estimate can be formed, since we know 
 roughly how much energy corresponds to the production of 
 a given amount of light. It is likely, on the whole, that an 
 ordinary meteor and a good electric incandescent lamp do not 
 differ widely in what is called their 'luminous efficiency 7 ; i.e., 
 the percentage of their total energy which is converted into 
 visible light. Calculations on this basis indicate that ordinary 
 shooting-stars are very minute, weighing only a small fraction 
 of an ounce, from less than a grain up to 50 or 100 grains 
 for a very large one. 
 
 324. Meteoric Showers. There are occasions when these 
 bodies, instead of showing themselves here and there in the 
 sky at intervals of several minutes, appear in showers of thou- 
 sands ; and at such times they do not move at random, but all 
 their paths diverge or radiate from a single point in the sky 
 known as the radiant; i.e., their paths produced backward all 
 pass through this point, though they do not usually start 
 there. Meteors which appear near the radiant are apparently 
 stationary, or describe paths which are very short, while those 
 in the more distant regions of the sky pursue long courses. 
 The radiant keeps its place among the stars sensibly un- 
 
324] 
 
 METEORIC SHOWEBS. 
 
 237 
 
 changed during the whole continuance of the shower ; it may 
 be for hours and even days, and the shower is named accord- 
 ingly from the place of the radiant. Thus we have the 
 
 FIG. 68. The Meteoric Radiant in Leo, Nov. 13, 1866. 
 
 "Leonids," or meteors whose radiant is the constellation of 
 Leo ; the " Andromedes " (or Bielids) ; the " Perseids " ; the 
 "Lyrids," etc. 
 
 Fig. 68 represents the tracks of a large number of the Leonids of 
 1866, showing the positions of the radiant near Zeta Leonis. 
 
 The radiant is explained as a mere effect of perspective. 
 The meteors are all moving in lines nearly parallel with each 
 other when encountered by the earth, and the radiant is 
 simply the perspective " vanishing-point " of this system of 
 parallels. Its position depends entirely on the direction of 
 the motion of the meteors with respect to the earth. For 
 various reasons, however, the paths of the meteors, after they 
 
238 DATES OF METEORIC SHOWERS. [ 324 
 
 enter the air, are not exactly parallel, and in consequence the 
 radiant is not a mathematical point, but a " spot " in the sky, 
 often covering an area of 3 or 4 square. 
 
 Probably the most remarkable of all the meteoric showers 
 that ever occurred was that of the Leonids on Nov. 12th, 
 1833. The number of meteors at some stations was estimated 
 as high as 100,000 an hour, for five or six hours. " The sky 
 was as full of them as it ever is of snow-flakes in a storm." 
 
 325. Dates of Meteoric Showers. Such meteoric showers 
 are caused by the earth's encounter with a swarm of little 
 meteors ; and since this swarm pursues a regular orbit around 
 the sun, the earth can meet it only when she is at the point 
 where her orbit cuts this path. The encounter, therefore, 
 must always happen on or near the same day of the year, 
 except as in time the meteoric orbits shift their positions on 
 account of perturbations. The Leonid showers, therefore, 
 always appear on the 13th of November, within a day or two ; 
 and the Andromedes on the 27th or 28th of the same month. 
 
 In some cases the meteors are distributed along their whole 
 orbit, forming a sort of elliptical ring, and are rather widely 
 scattered. In that case the shower recurs every year, and 
 may~eontinue for several days, as is the case with the Per- 
 seids, which appear in early August. On the other hand, 
 the flock may be concentrated, and then the shower will occur 
 only when the earth and the meteor swarm both arrive at the 
 orbit-crossing together. This is the case with both the Leo- 
 nids and the Andromedes. The showers then occur not every 
 year, but only at intervals of several years, though always on 
 or near the same day of the month. For the Leonids, the 
 interval is about thirty-three years, and for the Bielids about 
 thirteen years. 
 
 326. The meteors which belong to the same group have a 
 marked family resemblance. The Perseids are yellow, and 
 
326] COMETS AND METEORS. 239 
 
 move with, medium velocity. The Leonids are very swift (we 
 meet them), and they are of a bluish green tint, with vivid 
 trains. The Bielids are sluggish (they overtake the earth), 
 are reddish, being less intensely heated than the others, and 
 they usually have only feeble trains. During these showers 
 no sound is heard, no sensible heat perceived, nor do any 
 masses of matter reach the ground : with one exception, how- 
 ever, that on Nov. 27th, 1885, a piece of meteoric iron fell at 
 Mazapil, in Northern Mexico, during the shower of Androme- 
 des, which occurred that evening. The coincidence may be 
 accidental, but is certainly interesting. Many high author- 
 ities speak confidently of this piece of iron as a piece of Biela's 
 comet itself ; and this brings us to one of the most important 
 astronomical discoveries of the last half-century. 
 
 327. The Connection between Comets and Meteors. At the 
 
 time of the great meteoric shower of 1883, Professors Olmsted 
 and Twining of New Haven were the first to recognize the 
 " radiant," and to point out its significance as indicating that 
 the meteors must be members of a swarm of bodies revolving 
 around the sun in a permanent orbit. In 1864 Professor 
 Newton of New Haven, taking up the subject anew, showed 
 by an examination of the old records that there had been a 
 number of great meteoric showers about the middle of Novem- 
 ber at intervals of thirty-three or thirty-four years j and he 
 predicted confidently the repetition of the shower on Nov. 
 13th or 14th, 1866. It occurred as predicted, and was ob- 
 served in Europe ; and it was followed by another, in 1867, 
 which was visible in America, the meteoric swarm being ex- 
 tended in so long a procession as to require more than two 
 years to cross the earth's orbit. The researches of Newton 
 and Adams showed that the flock was moving in a long ellipse 
 with a period of thirty-three years. 
 
 328. Identification of Meteoric and Cometary Orbits. 
 
 Within a few weeks after the shower of 1866 it was found 
 
240 
 
 ORBITS OF METEORIC SWARMS. 
 
 [328 
 
 that the orbit pursued by these meteors was identical with 
 that of a comet, known as Tempel's, which had been visible 
 about a year before; and about the same time Schiaparelli 
 showed that the Perseids, or August meteors, move in an orbit 
 identical with that of the bright comet of 1862. Now a single 
 coincidence might be accidental, but hardly two. Five years 
 later came the shower of Andromedes, following in the track 
 of Biela's comet ; and among the more than a hundred distinct 
 
 FIG. 69. Orbits of Meteoric Swarms. 
 
 meteor swarms now recognized, Professor Alexander Herschel 
 finds five others which are similarly related, each to its special 
 comet. It is no longer possible to doubt that there is a real 
 and close connection between these comets and their attend- 
 ant meteors. Fig. 69 represents four of the orbits of these 
 cometo-meteoric bodies. 
 
 329. Nature of the Connection. This cannot be said to be 
 ascertained. In the case of the* Leonids and Andromedes, the 
 
329] 
 
 ORIGIN OF THE LEONIDS. 
 
 241 
 
 meteoric swarm follows the comet, but this does not seem to 
 be so in the case of the Perseids, which scatter along more or 
 less abundantly every year. The prevailing belief is that the 
 comet itself is only the thickest part of the meteoric swarm, 
 and that the clouds of meteors scattered along its path are the 
 result of its disintegration; but this is by no means certain. 
 
 It is easy to show that if the comet really is such a swarm, it must 
 at each return to perihelion gradually break up more and more, and dis- 
 perse its constituent particles along its path, until the compact swarm 
 has become a diffuse ring. The longer the comet has been moving 
 
 FIG. 70. Origin of the Leonids. 
 
 around the sun, the more uniformly the particles will be distributed. 
 The Perseids, therefore, are supposed to have been in the system for a 
 long time, while the Leonids and Andromedes are believed to be com- 
 paratively new comers. Leverrier, indeed, has gone so far as to indicate 
 the year 126 B.C. as the time at which Uranus captured Tempel's 
 comet, and brought it into the system, as illustrated by Fig. 70. But 
 the theory that meteoric swarms are the product of cometary disinte- 
 gration assumes the premise that comets enter the system as compact 
 clouds, which, to say the least, is not yet certain. 
 
242 MR. LOCKYER'S METEORIC HYPOTHESIS. t 330 
 
 330. Mr. Lockyer's Meteoric Hypothesis. Within the last 
 few years Mr. Lockyer has been enlarging the astronomical impor- 
 tance of meteors. The probable meteoric constitution of the zodiacal 
 light, as well as of Saturn's rings, and of the comets, has long been 
 recognized; but he goes much farther, and maintains that all the 
 heavenly bodies are either meteoric swarms, more or less condensed, 
 or the final products of such condensation ; and upon this hypothesis 
 he attempts to explain the evolution of the planetary system, the 
 phenomena of variable and colored stars, the various classes of stellar 
 spectra, and the forms and structure of the nebulse, indeed pretty 
 much everything in the heavens from the Aurora Borealis to the sun. 
 As a " working hypothesis," his theory is unquestionably important, 
 and has attracted much attention, but it does not bear criticism in all 
 its details. 
 
331] THE STARS. 243 
 
 CHAPTER XL 
 
 THE STARS. 
 
 THEIR NATURE, NUMBER, AND DESIGNATION. STAR 
 CATALOGUES AND CHARTS. PROPER MOTIONS AND 
 THE MOTION OF THE SUN IN SPACE. STELLAR PAR- 
 ALLAX. STAR MAGNITUDES. VARIABLE STARS. 
 STELLAR SPECTRA. 
 
 331. THE solar system is surrounded by an immense void 
 peopled only by stray meteors. The nearest star, as far as 
 our present knowledge goes, is one whose distance is more 
 than 200,000 times as great as our distance from the sun, 
 so remote that from it the sun would look no brighter than 
 the Pole-star, and no telescope yet constructed would be able 
 to show a single one of all the planets. As to the nature of 
 the stars, their spectra indicate that they are bodies resem- 
 bling our sun, that is, incandescent, and each shining with 
 its own peculiar light. Some are larger and hotter than the 
 sun, others smaller and cooler; some, perhaps, large but 
 hardly luminous at all. They differ enormously among them- 
 selves, not being, as once thought, as much alike as individuals 
 of the same race, but differing as widely as animalcules from 
 elephants. 
 
 332. Number of Stars. Those which are visible to the eye, 
 though numerous, are by no means countless. If we take a 
 limited region, for instance, the bowl of the Dipper, we shall 
 find that the number we can see within it is not very large, 
 
244 NUMBER OF STABS. [ 332 
 
 hardly a dozen. In the whole celestial sphere, the number of 
 stars bright enough to be distinctly seen by an average eye is 
 only between 6000 and- 7000, even in a perfectly clear and 
 moonless sky; a little haze or moonlight will cut down the 
 number fully one-half. At any one time not more than 2000 
 or 2500 are fairly visible, since near the horizon the small stars 
 (which are vastly the more numerous) all disappear. The 
 total number which could be seen by the ancient astronomers 
 well enough to be observable with their instruments is not 
 quite 1100. With even the smallest telescope, however, the 
 number is enormously increased. A common opera-glass 
 brings out at least 100,000, and with a 2-J- inch telescope Arge- 
 lander made his " Durchmusterung " of the stars north of the 
 equator, more than 300,000 in number. The Lick telescope, 
 36 inches in diameter, probably makes visible at least 
 100,000/)00. 
 
 333. Constellations. The stars are grouped in so-called 
 "constellations," many of which are extremely ancient. All 
 of those of the zodiac and most of those near the north pole 
 antedate history. Their names are, for the most part, drawn 
 from the Greek and Roman mythology, many of them being 
 connected in some way or other with the Argonautic Expedi- 
 tion. In some cases the eye, with the help of a lively imagi- 
 nation, can trace in the arrangement of the stars a vague 
 resemblance to the object which gives the name to the constel- 
 lation ; but generally no reason is obvious for either name or 
 boundaries. 
 
 We have already, in Chapter II., given a brief description 
 of those constellations which are visible in the United States, 
 with maps and directions for tracing them. 
 
 334. Designation of the Stars. In Art. 24 we have already 
 indicated the different methods by which the brighter stars 
 are designated, by proper names, position in the constellation, 
 
334] STAB-CATALOGUES. 245 
 
 or by letters of the Greek and Eoman alphabets. But these 
 methods do not apply to the telescopic stars, at least to any 
 considerable extent. Such stars we identify by their cata- 
 logue number ; that is, we refer to them as No. so-and-so in 
 some one's star-catalogue. Thus LI., 21,185 is read " Lalande, 
 21,185," and means the star that is so numbered in Lalande's 
 catalogue. At present not far from 800,000 stars are cata- 
 logued, so that, except in the Milky Way, every star visible 
 in a three-inch telescope can be found and identified. Of 
 course all the bright stars which have names, have letters also, 
 and are sure to be found in every catalogue which covers their 
 part of the heavens. A conspicuous star, therefore, has usu- 
 ally many " aliases," and sometimes great care is necessary to 
 avoid mistakes on this account. 
 
 335. Star-catalogues are carefully arranged lists of stars, 
 giving their positions (i.e., their right ascensions and declina- 
 tions, or latitudes and longitudes) for a given date, and usually 
 also indicating their so-called magnitudes or brightness. The 
 earliest of these star-catalogues was made about 125 B.C. by 
 Hipparchus of Bithynia, the first of the world's great astrono- 
 mers, and gives the latitudes and longitudes of 1080 stars. 
 This catalogue was republished by Ptolemy 250 years later, 
 the longitudes being corrected for precession ; and during the 
 Middle Ages several other catalogues were made by Arabic 
 astronomers and those that followed them. The modern cata- 
 logues are numerous ; some, like Argelander's " Durchmuster- 
 ung," give the places of a great number of stars rather roughly, 
 merely as a means of ready identification. Others are " cata- 
 logues of precision," like the Pulkowa and Greenwich cata- 
 logues, which give the places of only a few hundred so-called 
 "fundamental" stars, determined as accurately as possible, 
 each star by itself. Finally, we have the so-called "zones," 
 which give the place of many thousands of stars, determined 
 accurately but not independently ; that is, their positions are 
 
246 STAB-CHARTS AND STELLAR PHOTOGRAPHY. [ 335 
 
 determined by reference to the fundamental stars in the same 
 region of the sky. 
 
 336. Mean and Apparent Places of the Stars. The mod- 
 ern star-catalogue contains the mean right ascension and declination 
 of its stars at the beginning of some designated year ; i.e., the place 
 the star would occupy if there were no nutation, or aberration (Art. 
 126, and Appendix, 435). To get the actual (apparent) right ascen- 
 sion and declination of a star for some given date, which is what we 
 always want in practice, the catalogue place must be "reduced" to 
 that date; i.e., it must be corrected for precession, etc. The opera- 
 tion is an easy one with modern tables and formulae, but tedious when 
 many stars are in question. 
 
 337. Star-charts and Stellar Photography. For some pur- 
 poses, accurate star-charts are even more useful than cata- 
 logues. The old-fashioned and laborious way of making such 
 charts was by "plotting" the results of zone observations, but 
 at present it is being done by means of photography, vastly 
 better and more rapidly. A co-operative international cam- 
 paign is now in progress, the object of which is to secure a 
 photographic chart of all the stars down to the 14th magni- 
 tude. The work is expected to occupy a dozen instruments in 
 different countries for the next six or seven years. One of 
 the most remarkable things about the photographic method is 
 that there appears to be no limit to the faintness of the stars 
 that can be photographed with a good instrument. By in- 
 creasing the time of exposure, smaller and smaller stars are 
 continually reached. With the ordinary plates and exposure- 
 times not exceeding twenty minutes, it is now possible to get 
 distinct photographs of stars that the eye cannot possibly see 
 with the same telescope. 
 
 Fig. 71 represents the photographic telescope (fourteen 
 inches diameter, and eleven feet focus, of the Paris observa- 
 tory). The other instruments engaged in the star-chart cam- 
 paign are substantially like it, though differing more or less 
 in minor details. 
 
338] STELLAR PHOTOGRAPHY. 247 
 
 FIG. 71. Photographic Telescope of the Paris Observatory. 
 
248 STAR MOTIONS. [337 
 
 Professor Pickering of Cambridge, U.S., is also planning an inde- 
 pendent work of the same kind, with an instrument which is to have 
 a four-lens object-glass of twenty-four inches diameter and eleven feet 
 focus. It will take much larger plates and require much shorter 
 exposures than the Paris instrument, and so will do the work much 
 more rapidly. It is intended to erect it upon some mountain, first in 
 the northern hemisphere and then in the southern. 
 
 STAR MOTIONS. 
 
 338. The stars are ordinarily called " fixed/' in distinction 
 from the planets, or "wanderers/' because they keep their 
 positions and configurations sensibly unchanged with respect 
 to each other for long periods of time. Delicate observations, 
 however, demonstrate that the fixity is not absolute, but that 
 the stars are really in motion. Moreover, by the spectroscope 
 their rate of motion towards or from the earth can in some 
 cases be approximately measured. In fact, it appears that the 
 velocities of the stars are of the same order as those of the 
 planets. The stars are flying through space far more swiftly 
 than cannon-balls, and it is only because of their enormous dis- 
 tance from us that they appear to change their positions so 
 slowly. 
 
 339. Proper Motion. If we compare a star's position 
 (right ascension and declination) as determined to-day with 
 that observed 100 years ago, it will always be found to have 
 changed considerably. The difference is due in the main to 
 precession (Art. 125) ; but after allowing for all such merely 
 apparent motions of a star, it generally turns out that within a 
 century the star has really altered its place more or less with 
 reference to others near it, and this real shifting of its place is 
 called its " proper motion." Of two stars side by side in the 
 same telescopic field of view, the proper motions may be 
 directly opposite, while, of course, the apparent motions (due 
 to precession, etc.) will be sensibly the same. 
 
VELOCITY OF STAR MOTIONS. 249 
 
 Even the largest of these proper motions is very small. 
 The largest at present known, that of the so-called " run-away 
 star," 1830 Groombridge, is only 7" a year. (This star is not 
 visible to the naked eye.) About a dozen stars are known to 
 have an annual proper motion exceeding 3", and about 150, so 
 far as known at present, exceed 1". The proper motions of 
 the bright stars average higher than those of the faint, as 
 might be expected, since on the average the bright ones are 
 probably nearer. For the first-magnitude stars, the average is 
 about J" annually; and for the sixth-magnitude stars, the 
 smallest visible to the naked eye, it appears to be about ^". 
 
 Motions of this kind were first detected in 1718 by Halley, who 
 found that since the time of Hipparchus the star Arcturus had moved 
 towards the south nearly a whole degree, and Sirius about half as 
 much. 
 
 340. Velocity of Star Motions. The proper motion of a 
 star gives us very little knowledge as to the star's real motion 
 in miles per second. The proper motion derived from the 
 comparison of star-catalogues of different dates is only the 
 value in seconds of arc of that part of its whole motion which 
 is perpendicular to the line of sight. A star moving straight 
 towards us or from us has no proper motion at all ; i.e., no 
 change of apparent place which can be detected by comparing 
 observations of its position. 
 
 We can, however, in some cases fix a minor limit to the 
 velocity of a star. We know, for instance, that the distance 
 of the star, 1830 Groombridge, is certainly not less than 
 2,000000 ' astronomical units/ and, therefore, since its yearly 
 path subtends an angle of 7" at the earth, the length of the 
 path must at least equal sixty-nine astronomical units a year, 
 which corresponds to a velocity of over 200 miles a second. 
 The real velocity must be more than this, but how much 
 greater we cannot determine until we know how much the 
 star's distance exceeds 2,000000 units, and how fast it is mov- 
 ing towards or from us. 
 
250 MOTION IN THE LINE OF SIGHT. [ 340 
 
 In many cases a number of stars in the same region of the 
 sky have a motion practically identical, making it almost cer- 
 tain that they are real neighbors and in some way connected, 
 probably by community of origin. In fact, it seems to be 
 the rule rather than the exception that stars which are appar- 
 ently near each other are real comrades j they show, as Miss 
 Clerke expresses it, a distinctly " gregarious " tendency. 
 
 341. Motion in the Line of Sight. Within the last thirty 
 years a method 1 has been developed by which any swift 
 motion of a star, directly towards or from us, may be detected 
 by means of the spectroscope. 
 
 If a star is approaching us, the lines of its spectrum will 
 apparently be shifted towards the violet, according to Doppler's 
 principle (Art. 197), and vice versa, if it is receding from us. 
 Visual observations of this sort, first made by Huggins in 
 1868, and since then by many others, have succeeded in dem- 
 onstrating the reality of these motions in the line of sight 
 and in roughly measuring some of them. Recently Vogel of 
 Potsdam has taken up the investigation photographically, and 
 has obtained results that are far more satisfactory than any 
 before reached. He photographs the spectrum of the star and 
 the spectrum of hydrogen gas, or some other substance whose 
 lines appear in the star spectrum, together upon the same 
 plate, the light from both being admitted through the same 
 slit. If the star is not moving towards or from us, its lines 
 will coincide precisely with those of the comparison spectrum ; 
 otherwise, they will deviate one way or the other. 
 
 1 It is not, as students sometimes think, by changes in the apparent 
 size and brightness of a star. Theoretically, of course, a star which is 
 approaching us must grow brighter, but even the nearest star of all, Alpha 
 Centauri (Art. 343) is so far away that if it were coming directly towards 
 us at the rate of 100 miles a second, it would require more than 8000 years 
 to make the journey ; so that in a century its brightness would only 
 change about two per cent, far too little to be observed. 
 
341] THE SUN'S WAY. 251 
 
 Fig. 72 is from one of his negatives of the spectrum of Beta Orionis 
 (Rigel), in which one of its dark lines is compared with the corre- 
 sponding bright lines in the spectrum 
 
 of hydrogen. The dark line of the Blue | Red 
 
 stellar spectrum (bright in the nega- 
 tive) is shifted towards the red by an 
 amount which indicates that at the Spectrum of Rigel 
 
 time the star was rapidly receding. ^ 72 . _ D i8placem ent of H y Line 
 
 For the most part, these motions in the Spectrum f ' rioni8 ' 
 of the stars, so far as ascertained, seem to range between zero 
 and fifty miles a second, with still higher speeds in a few 
 exceptional cases. 
 
 342. The "Sun's Way." The proper motions of the stars 
 are due partly to their own real motions, but partly also to the 
 motion of the sun, which, like the other stars, is travelling 
 through space, taking with it its planets. Sir William Her- 
 schel was the first to investigate and determine the direction 
 of this motion a century ago. The principle involved is this : 
 On the whole the stars appear to drift bodily in a direction 
 opposite to the sun's real motion. Those in that quarter of 
 the sky which we are approaching open out from each other, 
 and those in the rear close up behind us. The motions of the 
 individual stars lie in all possible directions, but when we 
 deal with them by thousands, the individual is lost in the 
 general, and the prevailing drift appears. 
 
 About twenty different determinations of the point, towards 
 which the sun's motion is directed, have been made by various 
 astronomers. There is a reasonable and almost surprising 
 accordance of results, and they all show that the sun is mov- 
 ing towards a point in the constellation of Hercules, having a 
 right ascension of about 267 (17 h 48 m ), and a declination of 
 about 32 north. This point is called the " apex of the sun's 
 way." As to the velocity of this motion of the sun, it comes 
 out as about 0".05 annually, seen from the average distance of 
 
252 PARALLAX OF A STAR. [ 342 
 
 the standard sixth-magnitude star. It is assumed by high 
 authorities, on grounds that we cannot stop to discuss, that 
 this distance is about 20,000000 astronomical units; and on 
 that assumption, the speed of the sun's motion is about sixteen 
 miles a second. But the result is to be taken as hardly more 
 than a reasonable guess. 
 
 THE PARALLAX AND DISTANCE OF STARS. 
 
 343. When we speak of the " parallax " of the sun, of the 
 moon, or of a planet, we always mean the " diurnal " or " geo- 
 centric " parallax (Art. 139) ; i.e., the apparent semi-diameter 
 of the earth as seen from the body. In the case of a star, this 
 kind of parallax is practically nothing, never reaching ^-J-^-g- 
 of a second of arc. The expression, "parallax of a star," 
 always refers, on the contrary, to its "annual" or "helio- 
 
 E 
 
 PIG. 73. The Annual Parallax of a Star. 
 
 centric " parallax ; i.e., the apparent semi-diameter, not of the 
 earth, but of the earth's orbit, as seen from the star. In 
 Fig. 73 the angle at the star is its parallax. 
 
 Even this heliocentric parallax, in the case of most stars, is 
 far too small to be detected by our present instruments : it 
 never reaches a single second of arc. But in a few instances 
 it has been actually measured. Alpha Centauri, which is our 
 nearest neighbor, so far as yet known, has a parallax of about 
 0".9, according to the earlier observers, or only 0".T5, accord- 
 ing to the latest authorities. There are but four or five other 
 stars at present known which have a parallax more than half 
 as great as this. (For the method of determining stellar 
 parallax, see Appendix, Arts. 441-443.) 
 
344] THE LIGHT-YEAB. 253 
 
 344. Unit of Stellar Distance; the Light-year. The dis- 
 tances of the stars are so enormous that even the radius of 
 the earth's orbit, the " astronomical unit " hitherto employed, 
 is far too small for convenience. It is better, and now usual, 
 to take as the unit of stellar distance the so-called light-year; 
 i.e., the distance which light travels in a year. This is about 
 63,000 times the distance of the earth from the sun. 
 
 This number is found by dividing the number of seconds in a year 
 by 499, the number of seconds required by light to make the journey 
 from the sun to the earth (Appendix, Art. 432). 
 
 A star with a parallax of 1" is at a distance of 3.26 light- 
 
 O OJ 
 
 years, and in general the distance in light-years equals -^y-, 
 
 where p" is the parallax of the star expressed in seconds. 
 
 So far as can be judged from the scanty data, it appears 
 that few if any stars are nearer than four light-years from the 
 solar system ; that the naked-eye stars are probably, for the 
 most part, within 200 or 300 years ; and that many of the re- 
 moter stars must be thousands, or even tens of thousands, of 
 light-years away. 
 
 For the parallaxes of a number of stars, see Table V., 
 Appendix. 
 
 THE LIGHT OF THE STARS. 
 
 345. Star Magnitudes. As has already been mentioned 
 (Art. 23), Hipparchus and Ptolemy arbitrarily divided the 
 stars into six "magnitudes" according to their brightness, 
 the stars of the sixth magnitude being those which are barely 
 perceptible by an ordinary eye, while the first class comprise 
 about twenty of the brightest. After the invention of the 
 telescope the same system was extended to the smaller stars, 
 though without any special plan, so that the "magnitudes" 
 assigned to telescopic stars by different observers are very 
 discordant. 
 
254 SCALE OF STAR MAGNITUDES. [345 
 
 Heis enumerates the stars clearly visible to the naked eye, north of 
 the 35th parallel of south declination, as follows : 
 
 First Magnitude, 14. Fourth Magnitude, 313. 
 
 Second " 48. Fifth 854. 
 
 Third " 152. Sixth 2010. 
 
 Total, 3391. 
 
 It will be noticed how rapidly the numbers increase for the smaller 
 magnitudes. Nearly the same holds good also for the telescopic stars, 
 though below the tenth magnitude the rate of increase falls off. 
 
 346. Light-ratio and "Absolute Scale" of Star Magnitudes. 
 
 The scale of magnitudes ought to be such that the "light- 
 ratio," or number of times by which the brightness of any 
 star exceeds that of a star which is one magnitude smaller, 
 should be the same throughout the whole extent of the scale. 
 This relation was roughly, but not accurately, observed by the 
 older astronomers, and very recently Professor Pickering of 
 Cambridge, U. S., and Professor Pritchard of Oxford, England, 
 have made photometric measurements of the brightness of all 
 the naked-eye stars visible in our latitude, and have re-classified 
 them according to the so-called " absolute scale," which uses 
 a light-ratio equal to the fifth root of 100, (2.51) ; i.e., upon 
 this scale a star of the third magnitude is just 2.51 times 
 brighter than one of the fourth. 
 
 This ratio is based upon an old determination of Sir John Her- 
 schel's, who found that the average first-magnitude star is just about 
 a hundred times as bright as a star of the sixth magnitude, five mag- 
 nitudes fainter. 
 
 On this scale, Altair (Alpha Aquilse) and Aldebaran (Alpha 
 Tauri) may be taken as standard first-magnitude stars, while 
 the Pole-star and the two pointers are very nearly of the stand- 
 ard second magnitude. 
 
 Of course, in indicating the brightness of stars with precision, frac- 
 tional numbers must be used ; that is, we have stars of 2.4 magni- 
 tude, etc. 
 
346] STARLIGHT COMPARED WITH SUNLIGHT. 255 
 
 Stars that are brighter than Aldebaran or Altair have their bright- 
 ness denoted by a, fraction, or even by a negative number; thus the 
 absolute magnitude of Vega is 0.2, and of Sirius 1.4. The necessity 
 of these negative and fractional magnitudes for bright stars is rather 
 unfortunate, but not really of much importance. 
 
 347. Magnitudes and Telescopic Power. If a good telescope 
 just shows a star of a certain magnitude, we must have a telescope 
 with its aperture larger in the ratio of 1.58 : 1, in order to show stars 
 one magnitude smaller; (1.58= V2.51). A tenfold increase in the 
 diameter of an object-glass theoretically carries the power of vision 
 just five magnitudes lower. 
 
 It is usually estimated that the 12th magnitude is the limit of vision 
 for a 4-inch glass. It would require, therefore, a 40-inch glass to reach 
 the 17th magnitude of the absolute scale. 
 
 Our space does not permit any extended discussion of the methods 
 by which the brightness of stars is measured, a subject which has of 
 late attracted much attention (see General Astronomy, Arts. 823-829). 
 
 348. Starlight compared with Sunlight. Zollner and 
 others have endeavored to determine the amount of light l re- 
 ceived by us from certain stars, as compared with the light of 
 the sun. According to him, Sirius gives us about yinrrwffTJUiF 
 as much light as the sun does, and Capella and Vega about 
 
 ^ ^ n ^ s ra te> the standard first-magnitude star, 
 
 like Altair, should give us about sinnnroooooo? and ^ would 
 take, therefore, about nine million million stars of the sixth 
 magnitude to equal the sun. These numbers, however, are 
 very uncertain. The various determinations for Vega vary 
 more than fifty per cent. 
 
 Assuming what is roughly true, that Argelander's magnitudes agree 
 with the absolute scale, it appears that the 324,000 stars of his " Durch- 
 
 1 Undoubtedly, the stars send us heat also, and attempts have been 
 made to measure it ; but there is no reason for supposing that the propor- 
 tion of stellar heat to solar differs much from the proportion of starlight to 
 sunlight ; and if so, the heat of a star must be far below the possibility of 
 measurement by any apparatus yet at our command. 
 
256 LIGHT OF CERTAIN STABS. [ 348 
 
 musterung," all of them north of the celestial equator, give a light 
 about equivalent to 240 or 250 first-magnitude stars. How much 
 light is given by stars smaller than the 9| magnitude (which was his 
 limit) is not certain. It must greatly exceed that given by the larger 
 stars. As a rough guess we may estimate that the total starlight of 
 both the northern and southern hemispheres is equivalent to about 
 3000 stars like Vega, or 1500 at any one time. According to this, the 
 starlight on a clear night is about ^ of the light of a full moon, or 
 about ^j-jnhn^ that of sunlight. More than 95 per cent of it comes 
 from stars which are entirely invisible to the naked eye. 
 
 349. Amount of Light emitted by Certain Stars. When 
 we know the distance of a star in astronomical units, it is easy 
 to compute the amount of light it really emits as compared 
 with that given off by the sun. It is only necessary to mul- 
 tiply the light we now get from it (expressed as a fraction of 
 sunlight) by the square of the star's distance in astronomical 
 units. Thus, the distance of Sirius is about 550,000 units, and 
 the light we receive from it is yooo oooooo ^ sunlight. Mul- 
 tiplying this fraction by the square of 550,000, we find that 
 Sirius is really radiating more than forty times as much light 
 as the sun. As for several other stars, whose distance and 
 light have been measured, some turn out brighter, and some 
 darker than the sun. The range of variation is very wide, 
 and in brilliance the sun holds apparently about a medium 
 rank among its kindred. 
 
 350. Why the Stars differ in Brightness. The apparent 
 brightness of a star, as seen from the earth, depends both on 
 its distance and on the quantity of light it emits, and the 
 latter depends on the extent of its luminous surface and upon 
 the brightness of that surface. As Bessel long ago suggested, 
 " there may be as many dark stars as bright ones." Taken as 
 a class, the bright stars undoubtedly average nearer to us than 
 the fainter ones, and just as undoubtedly they also average 
 larger in diameter and more intensely luminous ; but when we 
 
350] VARIABLE STARS. 257 
 
 compare any particular bright star with another fainter one, 
 we can seldom say to which of these different causes it owes 
 its superiority. We cannot assert that the faint star is smaller 
 or darker or more distant than that particular bright star, 
 unless we know something more about it than the simple fact 
 that it is fainter. 
 
 351. Dimensions of the Stars. The stars are so far away 
 that their apparent diameters are altogether too small to be 
 measured by any known form of micrometer. The sun at the 
 distance of the nearest star would measure 1 not quite 0".01 
 across. Micrometers, therefore, do not help us in the matter, 
 and until very recently we were absolutely without any posi- 
 tive knowledge as to the real size of a single one of the stars. 
 But in 1889, by a spectroscopic method, more fully explained 
 in Art. 360, Vogel succeeded in showing that the bright vari- 
 able star, Algol (Beta Persei) (Art. 358), must have a diam- 
 eter of about 1,160,000 miles, while its invisible companion is 
 about 840,000 miles in diameter, or just about the size of 
 the sun. 
 
 VARIABLE STARS. 
 
 352. Classes of Variables. Many stars are found to change 
 their brightness more or less, and are known as "variable." 
 They may be classed as follows : 
 
 I. Stars which change their brightness slowly and con- 
 tinuously. 
 II. Those that fluctuate irregularly. 
 
 III. Temporary stars which blaze out suddenly and then 
 
 disappear. 
 
 IV. Periodic stars of the type of " Omicron Ceti," usually 
 
 having a period of several months. 
 
 1 This does not refer, of course, to the " spurious disc " of the star 
 (Appendix, Art. 408), which is many times larger. 
 
258 GRADUAL CHANGES. [ 352 
 
 V. Periodic stars of the type of " Beta Lyrae," usually hav- 
 ing short periods. 
 
 VI. Periodic stars of the " Algol " type, in which the period 
 is usually short, and the variation is like what might 
 be produced if the star were periodically " eclipsed " 
 by some intervening object. 
 
 353. Gradual Changes. The number of stars which are 
 certainly known to be gradually changing in brightness is sur- 
 prisingly small. On the whole, the stars present not only in 
 position, but in brightness also, sensibly the same relations as 
 in the catalogues of Hipparchus and Ptolemy. 
 
 There are, however, a few instances in which it can hardly be 
 doubted that considerable alteration has occurred even within the last 
 two or three centuries. Thus, in 1610 Bayer lettered Castor as Alpha 
 Geminorum, while Pollux, which he called Beta Geminorum, is now 
 considerably brighter. There are about a dozen other similar cases 
 known, and a much larger number is suspected. 
 
 It is commonly believed that a considerable number of stars have 
 disappeared since the first catalogues were made, and that many new 
 ones have come into existence. While it is unsafe to deny absolutely 
 that such things may have happened, it can be said, on the other 
 hand, that not a single case of the kind is certainly known. The dis- 
 crepancies between the older and newer catalogues are all accounted 
 for by some error or other that has already been discovered. 
 
 354. Irregular Fluctuations. The most conspicuous star 
 of the second class is Eta Argus (not visible in the United 
 States). It varies all the way from above the first magnitude 
 (in 1843 it stood next to Sirius) down to the seventh magni- 
 tude (invisible to the eye), which has been its status ever 
 since 1865, though recently it is reported as slightly brighten- 
 ing up again. Alpha Orionis and Alpha Cassiopeise behave in 
 a similar way, except that their variation of brightness is 
 
 small, not much exceeding half a magnitude. 
 
355] TEMPORARY STARS. 259 
 
 355. Temporary Stars. There are eleven well-authenti- 
 cated instances of stars which have blazed up suddenly, and 
 then gradually faded away (see General Astronomy, Arts. 
 842-845). The most remarkable of these is that known as 
 Tycho's, which appeared in the constellation of Cassiopeia 
 (Art. 28) in November, 1572, was for some days as bright as 
 Venus at her best, and then gradually faded away, until at 
 the end of sixteen months it became invisible. (There were 
 no telescopes then.) It is not certain whether it still exists as 
 a telescopic star: so far as we can judge it may be either of 
 half a dozen which are near the place determined by Tycho. 
 
 There has been a curious and utterly unfounded notion that this 
 star was the " Star of Bethlehem " and would reappear to herald the 
 second advent. 
 
 A temporary star which appeared in the constellation Corona 
 Borealis, in May, 1866, is interesting as having been spectro- 
 scopically examined when near its brightest (second magni- 
 tude). It then showed the same bright lines of hydrogen 
 which are conspicuous in the solar prominences. Before its 
 outburst it was an eighth-magnitude star of Argelander's cata- 
 logue, and within a few months it returned to its former low 
 estate, which it still retains. 
 
 The most recent instance is that of a sixth-magnitude star 
 which in August, 1885, suddenly appeared in the midst of the 
 great nebula of Andromeda (Art. 377). In a few months it 
 totally disappeared, even to the largest telescopes. 
 
 356. Variables of the "Omicron Ceti" Type. These ob- 
 jects behave almost exactly like a temporary star in remain- 
 ing most of the time faint, suddenly blazing out, and then 
 gradually fading away, but they do it periodically. Omicron 
 Ceti, or Mira (i.e., " the wonderful ") is the type. It was dis- 
 covered in 1596, and was the first variable star known. Dur- 
 ing most of the time it is of the ninth magnitude, but at 
 intervals of about eleven months it runs up to the fourth, 
 
260 
 
 TYPES OF VARIABLE STARS. 
 
 [356 
 
 third, or even second magnitude, and then back again, the 
 whole change occupying about 100 days, and the rise being 
 much more rapid than the fall. It remains at its maximum 
 about a week or ten days. The maximum brightness varies 
 very considerably, and its period, while always about eleven 
 
 oCeti 
 (Mira) 
 
 Period 11 months 
 
 
 FIG. 74. Light-curves of Variable Stars. 
 
 months, varies to the extent of two or three weeks. The 
 spectrum of the star when brightest is very beautiful, show- 
 ing a large number of intensely bright lines, some of which 
 are due to hydrogen. Its light-curve is A in Fig. 74. 
 
 Nearly half of all the known variables belong to this class, 
 and a large proportion of them- have periods which do not 
 differ very widely from a year. Most of the periods, how- 
 ever, are more or less irregular. Some writers include the 
 temporary stars in this class, maintaining that the only differ- 
 ence is in the length of their period. 
 
 357. Class V. The variables of Class V. are mostly of 
 short period, and are characterized by a continual rising and 
 
357] EXPLANATION OF VARIABLE STARS. 261 
 
 falling of brightness, running through the whole period. 
 Sometimes there are two, or even three, maxima before the 
 cycle is completed. The light-curve of Beta Lyrse, the type- 
 star of this class (period about thirteen days) is B in Fig. 74. 
 
 358. The "Algol" Type. In the stars of Class VI. the 
 variation is precisely the reverse of that in Class IV. The 
 star remains bright for most of the time, but apparently suffers 
 a periodical eclipse. The periods are mostly very short, 
 only a few days, and one little star in the constellation of 
 Antlia has a period of less than eight hours. 
 
 Algol (Beta Persei) is the type-star. During most of the 
 time it is of the second magnitude, and it loses about five- 
 sixths of its light at the time of obscuration. The fall of 
 brightness occupies about 4 hours. The minimum lasts about 
 20 minutes, and the recovery of light takes about 3 hours. 
 The period, a little less than three days, is known with great 
 precision, to a single second indeed, and is given in connec- 
 tion with the light-curve of the star in Fig. 74. At present 
 the period seems to be slowly shortening. Less than a dozen 
 stars are as yet known in this class. 
 
 359. Explanation of Variable Stars. No single explana- 
 tion will cover the whole ground. As to progressive changes, 
 no explanation may be looked for. The wonder rather is that 
 as the stars grow old, such changes are not more notable than 
 they are. 
 
 As for irregular changes, no sure account can yet be given. 
 Where the range of variation is small (as it is in most cases), 
 one thinks of spots upon the surface of the star, more or less 
 like sun spots ; and if we suppose these spots to be much more 
 extensive and numerous than are the sun spots, and also, like 
 them, to have a regular period of frequency, and also that the 
 star revolves upon its axis, we find in the combination a pos- 
 sible explanation of a large proportion of all the variable stars. 
 
262 EXPLANATION OF THE ALGOL TYPE. [359 
 
 For the temporary stars, we may imagine either great erup- 
 tions of glowing matter, like solar prominences on an enor- 
 mous scale, or, with Mr. Lockyer, we may imagine that most 
 of the variable stars are only swarms of meteors, rather com- 
 pact, but not yet having reached the condensed condition 
 of our own sun. Stars of the Mira type, according to this 
 theory, owe their regular outbursts of brightness to the collis- 
 ions, due to the passage of a smaller swarm through the outer 
 portions of a larger one, around which the smaller is supposed 
 to revolve in a long oval. But the great irregularity in the 
 periods of variables belonging to this class is hard to recon- 
 cile with a true orbital revolution, which usually keeps time 
 accurately. 
 
 360. Explanation of the Algol Type. The natural and 
 most probable explanation of the behavior of these stars is that 
 the periodical darkening is produced by the interposition of 
 some opaque body between us and the star. This eclipse theory 
 has lately received a striking confirmation from the spectro- 
 scopic work of Vogel, who has found by the method indicated 
 in Art. 341 that about seventeen hours before the obscuration, 
 Algol is receding from us at the rate of nearly twenty-seven 
 miles a second, while seventeen hours after the minimum it 
 approaches us at the same rate. This is just what it ought to 
 do, if it had a large, dark companion, and the two were revolv- 
 ing around their common centre of gravity in an orbit nearly 
 edgewise to the earth. When the dark star is rushing for- 
 ward to interpose itself between us and Algol, Algol itself 
 must be moving backwards, and vice versa when the dark star 
 is receding after the eclipse. Vogel's conclusions are, that the 
 distance of the dark star from Algol is about 3,250000 miles ; 
 that their diameters are respectively about 840,000 and 
 1,160000 miles; that their united mass is about two-thirds 
 that of the sun ; and their density about one-fifth that of the 
 sun, not much greater than that of cork. 
 
361] STAR SPECTRA. 263 
 
 361. Number and Designation of Variables, and their Range 
 of Variation. Mr. Chandlers catalogue of known variables, 
 with its recent supplement, includes 238 objects, and there is 
 also a considerable number of suspected variables. 
 
 169 of the 238 are distinctly periodic. The rest of them are 
 some irregular, some temporary, and in respect to many we 
 have not yet certain knowledge whether the variation is or is 
 not periodic. 
 
 Table IV., Appendix, contains a list of the naked-eye vari- 
 ables visible in the United States. 
 
 Such variable stars as had not names of their own before their 
 variability was discovered are at present generally indicated by the 
 letters R, S, T, etc.; i.e., R Sagittarii is the first discovered variable in 
 the constellation of Sagittarius, S Sagittarii is the second, etc. 
 
 In a considerable number of the earlier discovered variables, 
 the range of brightness is from two to eight magnitudes ; 
 that is, the maximum brightness exceeds the minimum from 
 6 to 1000 times. In the majority, however, the range is much 
 less, only a fraction of a magnitude. 
 
 It is worth noting that a large proportion of the variables, 
 especially those of Classes IV. and V., are reddish in their 
 color. This is not true of the Algol type. 
 
 STAR SPECTRA. 
 
 <r 
 
 362. As early as 1824 Fraunhofer observed the spectra of a 
 number of bright stars by looking at them with a small tele- 
 scope with a prism in front of the object-glass. In 1864, as 
 soon as the spectroscope had taken its place as a recognized 
 instrument of research, it was applied to the stars by Huggins 
 and Secchi. The former studied very few spectra, but very 
 thoroughly, with reference to the identification of the chemi- 
 cal elements in certain stars. He found with certainty in 
 their spectra the lines of sodium, magnesium, calcium, iron, 
 
264 SECCHl's CLASSES OF SPECTRA. [ 362 
 
 and hydrogen, and more or less doubtfully a number of other 
 metals. Secchi, on the other hand, examined great numbers 
 of spectra, less in detail, but with reference to a classification 
 of the stars from the spectroscopic point of view. 
 
 363. Secchi's Classes of Spectra. He made four classes, 
 as follows : 
 
 I. Those which have a spectrum characterized by great in- 
 tensity of the dark lines of hydrogen, all other lines being 
 comparatively feeble or absent. This class comprises more 
 than half of all the stars, nearly all the white or bluish 
 stars. Sirius and Vega are its types. 
 
 II. Those which show a spectrum resembling that of the 
 sun; i.e.) marked with a great number of fine dark lines. 
 Capella (Alpha Aurigse) and Pollux (Beta Geminorum) are 
 conspicuous examples. The stars of this class are also numer- 
 ous. The first and second classes together comprise fully 
 seven-eighths of all the stars whose spectra are known. 
 
 Certain stars, like Procyon and Altair, seem to be intermediate 
 between the first and second classes. The line of demarcation is by 
 no means sharp. 
 
 ' III. Stars which show a spectrum characterized by dark 
 bands, sharply defined at the upper or more refrangible edge, 
 aad shading out towards the red. Most of the red stars, and 
 a large number of the variable stars, belong to this class. 
 Some of them show, also, bright lines in their spectra. 
 
 IV. This class comprises only a few small stars, which, like 
 the preceding, show dark bands, but shading in the opposite 
 direction. Usually they also show a few bright lines. 
 
 This classification is by no means entirely satisfactory, and various 
 modifications have been proposed for it by Vogel, Lockyer, and others. 
 On the whole, however, we let it stand as the best known and simplest, 
 and sufficient for most purposes. 
 
364] PHOTOGRAPHY OF STELLAR SPECTRA. 265 
 
 364. Photography of Stellar Spectra. The observation of 
 these spectra by the eye is very tedious and difficult, and pho- 
 tography has of late been brought in most effectively. Hug- 
 gins, in England, and Henry Draper, in this country, were the 
 pioneers, but incomparably the finest results in this line are 
 those that have been obtained by Professor E. C. Pickering, of 
 Cambridge, in connection with the Draper Memorial Fund. 
 Pickering has recurred to the old method of Fraunhofer, using 
 a prism, or prisms, in front of the object-glass of his photo- 
 graphic telescope, thus forming a "slitless spectroscope." 
 The edges of the prism, or prisms, are placed east and west. 
 If the clock-work of the instrument followed the star exactly, 
 the spectrum formed on the sensitive plate would be a mere nar- 
 row streak ; but by allowing the clock to gain or lose slightly, 
 the image of the star will move to the east or west by a 
 very small quantity during the exposure, converting the streak 
 into a band. With his large apparatus, consisting of the 
 eleven-inch telescope formerly belonging to Dr. Draper, and a 
 battery of four enormous prisms placed in front of the object- 
 glass, spectra are obtained with an exposure of thirty minutes, 
 which before enlargement are fully three inches long from 
 the F line to the ultra-violet extremity. They easily bear 
 
 KH h Hy jr 
 
 FIG. 75. Photographic Spectrum of Vega. 
 
 tenfold enlargement, and show many hundreds of lines in the 
 spectra of the stars which belong to Secchi's second class. 
 Fig. 76 is from one of these photographs of the spectrum of 
 Vega. Of course the photograph fails to show the lower por- 
 tion of the spectrum, i.e., the red, yellow, and green. 
 
266 TWINKLING OF THE STARS. [ 365 
 
 365. Twinkling or Scintillation of the Stars. This phe- 
 nomenon is purely physical, and not in the least astronomical. It 
 depends both upon the irregularities of refraction in the air traversed 
 by the light on its way to the eye (due to winds and differences of 
 temperature), and also on the fact that the star is optically a luminous 
 point without apparent size, a fact which, under the circumstances, 
 gives rise to the optical phenomenon known as "interference." Plan- 
 ets which have discs measurable with a micrometer do not sensibly 
 twinkle. 
 
 The scintillation is of course greatest near the horizon, and on a 
 good night it practically disappears at the zenith. When the image 
 of a twinkling star is examined with the spectroscope, dark inter- 
 ference-bands are seen moving back and forth in its spectrum. 
 
3t5<j -l DOUBLE STARS. 267 
 
 CHAPTER XII. 
 
 DOUBLE AND MULTIPLE STARS AND CLUSTERS. NEBULAE. 
 DISTRIBUTION OF STARS AND CONSTITUTION OF THE 
 STELLAR UNIVERSE. COSMOGONY AND THE NEBULAR 
 HYPOTHESIS. 
 
 366. Double Stars. The telescope shows numerous cases 
 in which two stars lie so near each other that they can be 
 separated only by a high magnifying power. These are 
 " double stars," and at present more than 10,000 such couples 
 are known. There is also a considerable number of triple 
 stars, and a few which are quadruple. Fig. 76 represents a 
 few of the best known objects of each class. The apparent 
 distances generally range from 30" downwards, very few tele- 
 scopes being able to separate stars closer than a quarter of a 
 second. In a large proportion of cases (perhaps a third of all) 
 the two components are nearly equal in brightness, but in 
 many they are very unequal ; in that case (never when they 
 are equal) they often present contrasts of color, and when they 
 do, the smaller star (for some reason not known) always has a 
 tint higher in the spectrum than that of the larger : if the larger 
 is reddish or yellow, the small star will be green, blue, or 
 purple. 
 
 Gamma Andromedae and Beta Cygni are fine examples of colored 
 doubles for a small telescope. 
 
 367. Stars Optically and Physically Double. Stars may 
 be double in two ways, optically or physically. In the first 
 case they are merely approximately in line with each other, as 
 
268 DOUBLE STARS. t 367 
 
 seen from the earth ; in the second case, they are really near 
 each other. In the case of stars that are only optically double, 
 it usually happens that after some years we can detect their 
 mutual independence in the fact that their relative motion is in 
 
 FIG. 76. Double and Multiple Stars. 
 
 a straight line and uniform; i.e., one of them drifts by the other 
 in a line which is perfectly straight. This is a simple conse- 
 quence of the combination of their independent "proper 
 motions." If they are physically connected, we find on the 
 contrary that the relative motion is in a concave curve; i.e., 
 taking one of them as a centre, the other one moves around it 
 in a curve. 
 
 The doctrine of chances shows what direct observation con- 
 firms, that optical pairs must be comparatively rare, and that 
 the great majority of double stars must be really physically 
 
367] BINARY STABS. 269 
 
 connected, probably by the same attraction of gravitation 
 which controls the solar system. 
 
 368. Binary Stars. Stars thus physically connected are 
 also known as "binary" stars. They revolve in elliptical 
 orbits around their common centre of gravity, in periods which 
 range from 14 years to 1500 (so far as at present known), 
 while the apparent length of the ovals ranges from 40" to 0".5. 
 The older Herschel, a little more than a century ago, first dis- 
 covered this orbital motion of " binaries " in trying to ascertain 
 the parallax of some of the few double stars which were known 
 at his time. It was then supposed that they were simply opti- 
 cal pairs, and he expected to detect an annual displacement of 
 one member of the pair with reference to the other, from 
 which he could infer its annual parallax (Art. 343). He 
 failed in this, but found instead a true orbital motion. The 
 apparent orbit is always an ellipse ; but this apparent orbit is 
 the true orbit seen more or less obliquely ; so that the larger 
 star is not usually in the focus of the relative orbit pursued by 
 the smaller one. If we assume what is probable, though cer- 
 tainly not proved as yet, that the orbital motion of the pair is 
 under the law of gravitation, we know that the larger star 
 must be in the focus of the true relative orbit of the smaller, 
 and, moreover, that the latter must describe around it equal 
 areas in equal times. By the help of these principles we can 
 deduce from the apparent oval the true orbital ellipse; but 
 the calculation is troublesome and delicate. 
 
 369. At present the number of pairs in which this kind of motion 
 has been certainly detected is about 200, and it is continually increas- 
 ing as our study of the double stars goes on. About fifty pairs have 
 progressed so far, either having completed an entire revolution or a 
 large part of one, that it is possible to determine their orbits with 
 some accuracy. 
 
 The case of Sirius is peculiar. Nearly forty years ago it had been 
 found from meridian-circle observations to be moving, for no assign- 
 
270 
 
 SIZE OF THE ORBITS. 
 
 [ 360 
 
 able reason, in a small orbit, with a period of about fifty years. In 
 1862, Clark, the telescope-maker in Cambridge, U.S., found near it a 
 
 minute companion, which 
 explains everything; only 
 we have to admit that this 
 faint attendant, which does 
 not give T 2^<r as much 
 light as Sirius itself, has a 
 mass more than a quarter 
 part as great. It seems to 
 be one of Bessel's dark 
 stars. Fig. 77 represents 
 
 FIG. 77. - Orbits of Binary Stare. the apparent Qrbits of twQ 
 
 of the best determined double-star systems, Gamma Virginis and Xi 
 Ursse Majoris. 
 
 370. Size of the Orbits. The real dimensions of a double- 
 star orbit can easily be obtained when we know its distance 
 from us. Fortunately, a number of stars whose parallaxes 
 have been ascertained are also binary ; and assuming the best 
 available data, we have the results, given in the little table 
 which follows, the real semi-major axis of the orbit (in astro- 
 
 n" 
 nomical units) being always equal to the fraction , in which 
 
 a" is the angular semi-major axis of the double star orbit in 
 seconds of arc, and p" the parallax of the star. 
 
 NAME. 
 
 Assumed 
 Parallax. 
 
 Angular 
 Serai-axis. 
 
 Real 
 Semi-axis. 
 
 Period. 
 
 Mass. 
 
 0=1. 
 
 17 Cassiopeia 
 Sirius 
 
 0".15 
 
 0.38 
 
 8".64 
 8.58 
 
 57.6 
 22.6 
 
 195.y2 
 52.0? 
 
 5.0 
 
 4.26? 
 
 a Geminorum .... 
 a Centauri ... 
 
 0.20? 
 075 
 
 5.54 
 1750 
 
 27.7? 
 233 
 
 266 
 770 
 
 0.30? 
 2 14 
 
 70 Ophiuchi 
 61 Cveni 
 
 0.16 
 0.43 
 
 4.79 
 1540? 
 
 29.9 
 358? 
 
 94.5 
 4500? 
 
 3.0 
 0.23? 
 
 
 
 
 
 
 
^70] MASSES OF BINARY STARS. 271 
 
 These double-star orbits are evidently comparable in magni- 
 tude with the larger orbits of the planetary system, none of 
 those given being smaller than the orbit of Uranus, and none 
 twice as large as that of Neptune. 
 
 371. Masses of Binary Stars. If we assume that the 
 binary stars move under the law of gravitation, then when we 
 know the semi-major axis of the orbit and the period of revolu- 
 tion, we can easily find the mass of the pair as compared with 
 that of the sun ; much more easily, indeed, than we can deter- 
 mine the mass of Mercury or the moon, strange as it may 
 seem. It is done simply by the following equation, which we 
 give without demonstration (see General Astronomy, Arts. 576 
 and 838): 
 
 (If +m) = * 
 
 in which (M + m) is the united mass of the two stars, S is the 
 mass of the sun, a is the semi-major axis of the orbit of the 
 double star in astronomical units, and t its period in years. 
 The final column of the preceding table gives the masses of 
 the star-pairs, resulting from such data as we now possess ; 
 but the reader must bear in mind that the margin of error is 
 very considerable, because of the uncertainty of the orbits and 
 parallaxes in question. A very slight error in the parallax 
 makes a very great error in the resulting mass. 
 
 372. Planetary Systems attending Stars. It is a natural ques- 
 tion whether some of the small companions that we see near large 
 stars may not be the " Jupiters " of their planetary systems. We can 
 only say as to this that no telescope ever constructed could even come 
 near to making visible a planet which bears to its primary any such 
 relations of size, distance, and brightness, as Jupiter bears to the sun. 
 Viewed from our nearest neighbor among the stars, Jupiter would be 
 a little star of about the 21st magnitude, not quite 5" distance from 
 the sun, which itself would look like a star of the second magnitude. 
 To render a star of the 21st magnitude barely visible (apart from all 
 the difficulties raised by the nearness of a larger star) would require 
 
272 SPECTROSCOPIC BINARIES. [ 372 
 
 01 
 
 a telescope more fAan twenty feet in diameter. If any of the stars have 
 planetary systems accompanying them, we shall never be likely to see 
 them until our telescopes have attained a magnitude and power as yet 
 undreamed of. 
 
 373. Spectroscopic Binaries. One of the most interesting 
 of recent astronomical results is the detection by the spectro- 
 scope of several pairs of double stars so close that no telescope 
 can separate them. In 1889 the bright component of the well- 
 known double star Mizar (Zeta Ursse Majoris, Fig. 76) was 
 found by Pickering to show the dark lines double in the photo- 
 graphs of its spectrum, at regular intervals of about fifty-two 
 days. The obvious explanation is that this star is composed 
 of two, which revolve around their common centre of gravity 
 in an orbit which is turned nearly edgewise towards us. (If it 
 was exactly edgewise, the star would be variable like Algol.) 
 
 When the stars are at right angles to the line from them to 
 us, one of the two will be moving towards us, while the. other 
 is moving in an opposite direction ; and as a consequence, 
 the lines in their spectra will be shifted opposite ways, accord- 
 ing to Doppler's principle (Art. 179). Now since the two 
 stars are so close that their spectra overlie each other, the 
 result will be simply to make the lines in the compound spec- 
 trum look double. From the distance apart of the lines, the 
 relative velocity of the stars can be found, and from this the 
 size of the orbit and the mass of the stars. Thus it appears 
 that in the case of Mizar the relative velocity of the two 
 components is about 100 miles per second, the period about 
 104 days, and the distance between the two stars about the 
 same as the diameter of the orbit of Mars ; from which it fol- 
 lows that their united mass is about forty times that of the 
 sun. 
 
 This makes Mizar really a triple star, the larger of the two that are 
 seen with a small telescope being the one that is thus spectroscopically 
 split. 
 
374] SPECTROSCOPIC BINARIES. 273 
 
 374. The lines in the spectrum of Beta Aurigae exhibit the 
 same peculiarity, but the doubling occurs once in four days ; 
 the velocity being about 150 miles a second, and the diameter 
 of the orbit about 8,000000 miles, while the united mass of the 
 two stars is about two and a half times that of the sun. 
 
 These observations of Professor Pickering's were made by 
 photographing the spectrum with the slitless spectroscope (Art. 
 364), and are possible only where the stars which compose the 
 binary are both of them reasonably bright. 
 
 With his slit-spectroscope, Vogel (Art. 341), as has already 
 been stated (Art. 360), has been able to detect a similar orbital 
 motion in Algol, although the companion of the brighter star 
 is itself invisible. More recently, in the case of the bright 
 star Alpha Virginis (Spica), he has found a result of the same 
 kind. At first the photographic observations of the spectrum 
 of this star appeared very discordant. Some days they indi- 
 cated that the star was moving toivards us quite rapidly, and 
 then again from us ; but it is found that everything can be 
 explained by the simple supposition that the star is double 
 with a small companion, like that of Algol, not bright enough 
 to show itself by its light, but heavy enough to make its part- 
 ner swing around in an orbit about 6,000000 miles in diameter, 
 once in four days, the orbit not being quite edgewise to the 
 earth, so that the dark companion does not eclipse Spica, as 
 Algol is eclipsed by its attendant. Bigel (Beta Orionis) also 
 shows traces of a similar periodic variation, though the obser- 
 vations have not yet been continued long enough to deter- 
 mine its period precisely. It is likely that a large number of 
 similar double stars will thus be found by the spectroscope 
 before very long. These orbits, of course, are very much 
 smaller than those of most of the telescopic binaries. 
 
 375. Multiple Stars (see Fig. 76). In a considerable 
 number of cases we find three or more stars connected in one 
 system. Zeta Cancri consists of a close pair revolving in a 
 
274 MULTIPLE STARS CLUSTERS. [ 3 ?5 
 
 nearly circular orbit, with a period somewhat less than sixty 
 years, while a third star revolves in the same direction around 
 them, at a much greater distance, and with a period not less 
 than 500 years (not yet fully determined). Moreover, this 
 third star is subject to a peculiar irregularity in its motion, 
 which seems to indicate that it has an invisible companion 
 very near the system, the system being really quadruple. 
 
 In Epsilon Lyrse we have a most beautiful quadruple sys- 
 tem, composed of two pairs, each binary with a period of over 
 200 years. Moreover, since they have a common proper 
 motion, it is probable that the two pairs revolve around 
 each other in a period which can be reckoned only in thou- 
 sands of years. In Theta Orionis, we have a remarkable object, 
 in which the six components are not organized in pairs, but 
 are at not very unequal distances from each other. 
 
 376. Clusters. There are in the sky numerous groups of 
 stars, containing from a hundred to many thousand members. 
 A few of them are resolvable by the naked eye, as, for in- 
 stance, the Pleiades (Fig. 78) ; some, like Praesepe in Cancer, 
 break up under the power of even an opera-glass (Art. 52); 
 but most of them require a large telescope to show the sepa- 
 rate components. To the naked eye or small telescopes, if 
 visible at all, they look like faint clouds of shining haze ; but 
 in a great telescope they are among the most magnificent 
 objects the heavens afford. The cluster known as "13 Mes- 
 sier," not far from the " apex of the sun's way," is perhaps 
 the finest. 
 
 The question at once arises whether the stars in such a 
 cluster are comparable with our own sun in magnitude, and 
 separated from each other by distances like that between the 
 sun and Alpha Centauri, or whether they are really small (for 
 stars) and closely packed, whether the swarm is about the 
 same distance . from us as the rest of the stars, or far beyond 
 them. 
 
376] THE PLEIADES. 275 
 
 Forty years ago the prevalent view was that these clusters 
 were stellar universes, galaxies, like the group of stars to 
 which it was supposed the sun belongs, but so inconceivably 
 remote that they dwindled to mere shreds of cloud. It is now, 
 
 Astcrope 
 
 +K 
 
 \ : , , Q Taygeta 
 
 "" 
 
 ^c. Pleione ..-'' A * /I M V . 
 
 '" - Jf>- .;.:.-"/ '-'..::: ^T?^-- 
 
 Alcyone ; S" Electro, 
 
 M. * :.' .,; :^.:^\r::.v::.vf-'--- 
 
 ,;:>'' /v/Merope 
 
 FIG. 78. The Pleiades. 
 
 however, quite certain that the opposite view is correct. The 
 star clusters are among our stars, and form a part of our own 
 stellar universe. Large and small stars are so associated in 
 the same group as to leave no doubt on this point, although 
 it has not yet been possible to determine the actual parallax 
 and distance of any cluster. 
 
276 
 
 GREAT NEBULA IN ANDROMEDA. 
 
 [377 
 
 NEBULAE. 
 
 377. Besides the luminous clouds which, under the tele- 
 scope, break up into separate stars, there are others which no 
 telescopic power resolves, and among them some which are 
 brighter than many of the clusters. These irresolvable <5b- 
 
 jects, which now number 
 more than 8000, are "neb- 
 ulae." Two or three of 
 them are visible to the 
 naked eye ; one, the bright- 
 est of all, and the one in 
 which the temporary star 
 of 1885 appeared, is in the 
 constellation of Androm- 
 eda (see Fig. 79). An- 
 other most conspicuous 
 and very beautiful nebula 
 is that in the sword of 
 Orion. 
 
 The larger and brighter 
 nebulae are, for the most 
 part, irregular in form, 
 sending out sprays and 
 streams in all directions, 
 and containing dark openings and "lanes." Some of them 
 are of enormous volume. The great nebula of Orion (which 
 includes within its boundary the multiple star, Theta Orionis) 
 covers several square degrees. 1 
 
 The nebula of Andromeda is not quite so extensive, but is 
 rather more regular in its form. 
 
 1 Very recently photographs taken at Wilson's Peak, Cal., show that 
 nearly the whole constellation is enveloped in nebulosity, the wisps attach- 
 ing themselves especially to most of the principal stars. 
 
 FIG. 79. Telescopic View of the Great Nebula 
 in Andromeda. 
 
377] 
 
 ANNULAR NEBULA IN LYRA. 
 
 277 
 
 The smaller nebulae are, for the most part, more or less 
 nearly oval, and brighter in the centre. In tfie so-called 
 " nebulous stars,' 7 the cen- 
 tral nucleus is like a star 
 shining through a fog. 
 The "planetary nebulae" 
 are about circular and 
 have nearly a uniform 
 brightness throughout, 
 while the rare " annular " 
 or "ring nebulae" are 
 darker in the centre. Fig. 
 80 is a representation of 
 the finest of these annular 
 nebulae, that in the con- 
 stellation of Lyra. There 
 are a number of nebulae 
 which exhibit a remark- 
 able spiral structure in 
 large telescopes. There 
 are several double nebulae, 
 and a few that are variable in brightness, though no regular- 
 ity has yet been ascertained in their variation. 
 
 The great majority of the 8000 nebulae are extremely faint, 
 even in large telescopes, but the few that are reasonably bright 
 are very interesting objects. 
 
 378, Drawings and Photographs of Nebulae, Until very 
 lately the correct representation of a nebula was an extremely 
 difficult task. More or less elaborate engravings exist of per- 
 haps fifty of the more conspicuous of them, but photography 
 has now taken possession of the field. The first success in 
 this line was by Henry Draper of New York, in 1880, in pho- 
 tographing the nebula of Orion. Since his death, in 1882, 
 great progress has been made both in Europe and in this 
 
 FIG. 80. The Annular Nebula in Lyra. 
 
278 
 
 PHOTOGRAPHS OF NEBULA. 
 
 [378 
 
 country, and at present the photographs are continually 
 bringing out new and before unsuspected features. Fig. 81, 
 
 FIG. 81. Mr. Roberts's Photograph of the Nebula of Andromeda. 
 
 for instance, is from a photograph of the nebula of Androm- 
 eda, taken by Mr. Roberts of Liverpool in 1888, and shows 
 
378] PHOTOGRAPHS OF NEBULA. 279 
 
 that the so-called " dark lanes," which hitherto had been seen 
 only as straight and wholly mysterious markings (Fig. 79), 
 are really curved ovals, like the divisions in Saturn's rings. 
 The photograph brings out clearly a distinct annular structure 
 pervading the whole nebula, which as yet has never been 
 made out satisfactorily by the eye with any telescope. 
 
 The photographs not only show new features in old nebulae, but 
 they reveal numbers of new nebulae invisible to the eye with any tele- 
 scope. Thus, in the Pleiades it has been found that almost all the 
 larger stars have wisps of nebulosity attached to them, as indicated by 
 the dotted lines in Fig. 78 ; and in a small territory, in and near the 
 constellation of Orion, Pickering, with an eight-inch telescope, found 
 upon his star-plates nearly as large a number of new nebulae as of 
 those that were previously known within the same boundary. 
 
 The photographs of nebulse require generally an exposure of from 
 one to two hours. The images of all the brighter stars that fall upon 
 the plate, are, therefore, always immensely over-exposed, and seriously 
 injure the picture from an artistic point of view. 
 
 The photographic brightness of a nebula, to use such an expression, 
 is many times greater than its brightness to the eye, owing to the fact 
 that its light consists mainly in rays which belong to the upper or 
 blue portion of the spectrum. It has very little red or yellow in it. 
 At least, this is so with all the nebulae whose spectra are characterized 
 by bright lines. 
 
 379. Changes in Nebulae. It cannot be stated with certainty 
 that sensible changes have occurred in any of the nebulse since they 
 first began to be observed, the early instruments were so inferior to 
 modern ones that the older drawings cannot be trusted ; but some of 
 the differences between the older and more recent representations make 
 it extremely likely that real changes are going on. Probably after a 
 reasonable interval of time photography will settle the question. 
 
 380. Spectra of Nebulae. One of the most important of 
 the early achievements of the spectroscope was the proof that 
 the light of many nebulae, if not all, proceeds from glow- 
 ing gas of low density, and not from aggregations of stars. 
 
280 SPECTRA OF NEBULAE. [ 380 
 
 Huggins, in 1864, first made the decisive observation by find- 
 ing bright lines in their spectra. Thus far the spectra of all the 
 nebulae that show lines at all appear to be substantially the 
 same. Four lines are usually easily observed, two of which 
 are due to hydrogen ; but the other two, which are brighter 
 than the hydrogen lines, are not yet identified. 
 
 At one time the brightest of the four lines was thought to be due 
 to nitrogen, and even yet the statement that such is the case is found 
 in many books ; but it is now certain that, whatever it may be, nitro- 
 gen is not the substance. Very recently Mr. Lockyer has ascribed this 
 line to magnesium, in connection with his meteoric hypothesis. But 
 recent elaborate observations of Huggins and others show that this 
 identification also is probably incorrect. 
 
 Fig. 82 shows the position of the principal lines so far as observed. 
 In the brighter nebulae a number of others are also sometimes seen. 
 Mr. Huggins's recent photographic spectrum of the nebula of Orion 
 
 FIG. 82. Spectrum of the Gaseous Nebulas. 
 
 shows, in addition to those that are visible to the eye, a number of 
 bright lines in the ultra-violet; and, what is interesting, these lines 
 seem to pertain also to the spectrum of the stars in the so-called 
 " Trapezium " (Theta Orionis), as if (which is very likely) the stars 
 themselves were mere condensations of nebulous matter. 
 
 381. Not all nebulae show the bright-line spectrum. Those 
 which do (about half the whole number) are of a greenish tint, 
 at once recognizable in a large telescope. The white nebulae, 
 with the nebula of Andromeda, the brightest of all, at their 
 head, present only a plain continuous spectrum, unmarked by 
 
381] DISTANCE AND DISTRIBUTION OF NEBULAE. 281 
 
 lines of any kind. This, however, does not necessarily indicate 
 that the luminous matter is not gaseous, for a gas under pres- 
 sure gives a continous spectrum, like an incandescent solid or 
 liquid. The telescopic evidence as to the non-stellar consti- 
 tution of nebulae is the same for all; no nebula resists all 
 attempts at resolution (i.e., breaking up into stars) mojre stub- 
 bornly than that of Andromeda. 1 
 
 As to the real constitution of those bodies, we can only 
 speculate. The fact that the luminous matter in them is 
 mainly gaseous does not at all make it certain that they do 
 not also contain dark matter, either liquid or solid. What 
 proportion of it there may be, we have at present no means 
 of knowing. 
 
 382. Distance and Distribution of Nebulae. As to the dis- 
 tance, we can only say that, like the star clusters, they are 
 within the stellar universe and not beyond its boundaries. 
 This is clearly shown by the nebulous stars, first pointed out 
 and discussed by the older Herschel. We find all gradations, 
 from a star with a little faint nebulosity around it, to nebulae 
 which show only the faintest spot of light in the centre. It is 
 confirmed also by such peculiar associations of the stars and 
 nebulae as we find in the Pleiades. Moreover, in certain curi- 
 ous luminous masses, known as the "Nubeculae," near the 
 south pole, we have stars, star clusters, and nebulae promis- 
 cuously intermingling. 
 
 Taking the sky generally, however, the distribution of the 
 nebulae is in contrast with that of the stars. The stars, as we 
 shall see, crowd together near the Milky Way. The nebulae, 
 on the other hand, are most numerous just where the stars are 
 fewest, as if the stars had somehow used up the substance of 
 which the nebulae are made. 
 
 1 Some years ago it was stated that Lord Rosse's telescope had partially 
 resolved the nebula of Andromeda and the nebula of Orion. This turned 
 out to be a mistake. 
 
282 THE MILKY WAY. [ 383 
 
 THE SIDEREAL HEAVENS. 
 
 383. The Galaxy, or Milky Way. This is a luminous belt 
 of irregular width and outline, which surrounds the heavens 
 nearly in a great circle. It is very different in brightness in 
 different parts, and is marked here and there by dark bars and 
 patches, which at night look like overlying clouds. For about 
 a third of its length (between Cygnus and Scorpio) it is 
 divided into two roughly parallel streams. The telescope 
 shows it to be made up almost entirely of small stars from 
 the eighth magnitude down ; it contains, also, numerous star 
 clusters, but very few true nebulae. 
 
 The galaxy intersects the ecliptic at two opposite points not 
 far from the solstices, and at an angle of nearly 60, the north 
 " galactic pole " being, according to Herschel, in the constella- 
 tion of Coma Berenices. As Herschel remarks, 
 
 "The 'galactic plane' is to the sidereal universe much what the 
 plane of the ecliptic is to the solar system, a plane of ultimate refer- 
 ence, and the ground plan of the stellar system." 
 
 384. Distribution of Stars in the Heavens. It is obvious 
 that the distribution of the stars is not even approximately 
 uniform. They gather everywhere into groups and streams ; 
 but, besides this, the examination of any of the great star- 
 catalogues shows that the average number to a square degree 
 increases rapidly and pretty regularly from the galactic pole to 
 the galaxy itself, where they are most thickly packed. This 
 is best shown by the "star-gauges " of the older Herschel, each 
 of which consists merely in an enumeration of the stars visi- 
 ble in a single field of view. He made 3400 of these gauges, 
 and his son followed up the work at the Cape of Good Hope 
 with 2300 more in the south circumpolar regions. From 
 these data it appears that near the pole of the galaxy, the 
 average number of stars in a single field of view is only 
 
384] STRUCTURE OF THE STELLAR UNIVERSE. 283 
 
 about 4 ; at 45 from the galaxy, a little over 10 ; while on the 
 galactic circle itself it is 122. 
 
 Herschel, starting from the unsound assumption that the stars are 
 all of about the same size and brightness and separated by approxi- 
 mately equal distances, drew from his observations numerous untenable 
 conclusions as to the form and structure of the " galactic cluster " to 
 which the sun was supposed to belong, theories for a time widely 
 accepted, and even yet more or less current in popular text-books, 
 though in many points certainly incorrect. 
 
 But although the apparent brightness of the stars does not 
 depend entirely, or even mainly, upon their distance, it is cer- 
 tain that as a class the faint stars are really more remote, as 
 well as smaller and darker than the brighter ones. We may, 
 therefore, safely draw a few inferences, which, so far as they 
 go, in the main agree with those of Herschel. 
 
 385. Structure of the Stellar Universe. I. The great ma- 
 jority of the stars we see are included within a space having, 
 roughly, the form of a rather thin, flat disc, like a watch, with 
 a diameter eight or ten times as great as its thickness, our 
 sun being not very far from its centre. 
 
 II. Within this space the naked-eye stars are distributed 
 with some uniformity, but not without a tendency to cluster, 
 as shown in the Pleiades. The smaller stars, on the other 
 hand, are strongly " gregarious," and are largely gathered into 
 groups and streams which have comparatively vacant spaces 
 between them. 
 
 III. At right angles to the galactic plane the stars are 
 scattered more evenly and thinly than in it, and we find on 
 the sides of the disc the comparatively starless region of the 
 nebulae. 
 
 IV. As to the Milky Way itself, it is not certain whether 
 the stars which compose it form a sort of thin, flat, continu- 
 ous sheet, or whether they are arranged in a sort of ring with 
 
284 DO THE STAES FORM A SYSTEM ? [ 385 
 
 a comparatively empty space in the middle, where the sun is 
 situated, not far from its centre. 
 
 As to the size of the disc-like space which contains most of the 
 stars, very little can be said positively. Its diameter must be as great 
 as 20,000 or 30,000 light-years, how much greater it may be we can- 
 not even guess; and as to the "beyond," we are still more ignorant. 
 If, however, there are other stellar systems of the same order as our 
 own, these systems are neither the nebulae, nor the clusters which the 
 telescope reveals, but are far beyond the reach of any instrument at 
 present existing. 
 
 386. Do the Stars form a System ? It is probable (though 
 not certain) that gravitation operates between the stars, as 
 indicated by the motion of the binaries. The stars are cer- 
 tainly moving very swiftly in various directions, and the 
 question is whether these motions are governed by gravita- 
 tion, and are " orbital " in the ordinary sense of the word. 
 
 There has been a very persistent belief that somewhere 
 there is an enormous central sun, around which the stars are 
 all circulating in the same way as the planets of the solar 
 system move about our own sun. This belief has been abun- 
 dantly proved to be unfounded. It is now certain that there 
 is no such great body dominating the stellar universe. 
 
 387. Maedler's Hypothesis. Another less improbable doc- 
 trine is that there is a general revolution of the mass of stars 
 around the centre of gravity of the whole, a revolution nearly 
 in the plane of the Milky Way. Some years ago, Maedler, in 
 his speculations, concluded (though without sufficient reason) 
 that this centre of gravity of the stellar system was not far 
 from Alcyone, the brightest of the Pleiades, and, therefore, 
 that this star was in a sense the 'central sun'; and the idea 
 is frequently met with in popular writings. It has no basis of 
 reason, however, nor is there yet proof or probability of any 
 such general revolution. 
 
388] COSMOGONY. 285 
 
 388. On the whole, the most reasonable view seems to be 
 that the stars are moving much as bees do in a swarm, each 
 star mainly under the control of the attraction of its nearest 
 neighbors, though influenced more or less, of course, by that 
 of the general mass. If so, the paths of the stars are not 
 " orbits " in the strict sense ; that is, they are not paths which 
 return into themselves, the forces which at any moment act 
 upon a given star being so nearly balanced that its motion 
 must be sensibly in a straight line for thousands of years at 
 a time. 
 
 The solar system is an absolute despotism, the sun supreme. 
 Among the stars, on the other hand, there is no central power, 
 but the system is a pure democracy, in which the individuals 
 are controlled by the influence of their neighbors, and by the 
 authority of the whole community to which they themselves 
 belong. 
 
 COSMOGONY. 
 
 389. One of the most interesting topics of speculation re- 
 lates to the process by which the present state of things has 
 come about. In a forest, to use an old comparison of Her- 
 schel's, we see around us trees in all stages of their life-his- 
 tory, from the sprouting seedlings to the prostrate and decaying 
 trunks of the dead. Is the analogy applicable to the heavens, 
 and can we hope by a study of the present condition and 
 behavior of the bodies around us to come to an understanding 
 of their past history and probable future ? Possibly to some 
 extent. But human life is so short that the processes of 
 change are hardly perceptible, and our telescopes and spectro- 
 scopes reveal but little of the " true inwardness " of things, so 
 that speculation is continually baffled, and its results can 
 seldom be accepted as secure. Still, some general conclusions 
 seem to have been reached, which are likely to be true ; but 
 the pupil is warned that they are not to be regarded as estab- 
 
GENESIS OF THE PLA>TETARY SYSTEM. 
 
 listed in any such sense as the law of gravitation and the 
 theory of planetary motion. 
 
 In a general way we may say that the shrinkage of clouds 
 of rarefied matter into more compact masses under the force of 
 gravitation, the production of heat by this shrinkage, the effect 
 of this heat upon the mass itself and upon neighboring bodies, 
 these principles cover nearly all the explanations that can 
 thus far be given for the present condition of the heavenly 
 bodies. 
 
 390. Genesis of the Planetary System. Ourplanetar; 
 tern is clearly no accidental aggregation of bodies. Masses of 
 matter coining haphazard to the sun would move (as comets 
 actually do move) in orbits which, though necessarily conic 
 sections, would have every degree of inclination and eccen- 
 tricity. In the planetary system this is not so. Numerous 
 relations exist for which gravitation does not at all account, 
 and for which the mind demands an explanation. 
 
 We note the following as the principal : 
 
 1. The orbits of the planets are all nearly circular (i.e-, never very 
 eccentric). 
 
 2. They are all nearly in one plane (excepting those of some of the 
 asteroids). 
 
 3. The revolution of all, without exception, is in the same direction. 
 
 4. There is a curious and regular progression of distances (ex- 
 pressed by Bode's Law; which, however, breaks down with Xeptone). 
 
 As regards the planets themselves : 
 
 5. The plane of erery planet's rotation nearly coincides with that 
 of its orbit (probably excepting Uranus). 
 
 6. The direction of rotation is the same as that of the orbital revo- 
 lution (excepting, probably, Uranus and Neptune). 
 
 7. The plane of orbital revolution of the planet's satellites coincides 
 nearly with that of the planet's rotation, wherever this has been ascer- 
 tained. 
 
 8. The direction of the satellites' revolution also coincides with that 
 of the planet's revolution (with the same limitation). 
 
 9. The largest planets rotate most swiftly. 
 
391] LAPLACE'S NEBULAE HYPOTHESIS. 
 
 391. Sow this arrangement is certainly an admirable one 
 for a planetary system, and therefore some hare argued that 
 the Deity constructed the system in that way, perfect from 
 the first. But to one who considers the way in which other 
 perfect works usually attain their perfection, their processes 
 of growth and development, this explanation seems improba- 
 ble. It appears far more likely that the planetary system was 
 formed by growth than that it was built outright. The theory 
 which, in its main features, is now generally accepted, as sup- 
 plyiiig an intelligible explanation of the facts, is that known 
 as the "nebular hypothesis." In a more or less crude and 
 unscientific form, it was first suggested by Swedenborg and 
 Kant, and afterwards, about the beginning of the present cen- 
 tury, was worked out in mechanical detail by Laplace. On the 
 whole, we may say that while, in its main outlines, the theory 
 is probably true, it also probably needs serious modifications in 
 its details. 
 
 392. Laplace's Nebular Hypothesis. He maintained (a) 
 that at some time in the past 1 the matter which is now 
 gathered into the sun and planets was in the form of a 
 "nebula." 
 
 (6) This nebula, according to him, was a cloud of intensely 
 heated gas (questionable). 
 
 (c) Under the action of its own gravitation, the nebula 
 assumed a form approximately globular, with a motion of rota- 
 tion, the whirling motion depending upon the accidental differ- 
 ences in the original velocities and densities of the different 
 
 1 As to the origin of the nebula itself, he did not speculate. There was 
 no assumption on his part, as is often supposed, that the matter was first 
 created in the nebulous condition. He assumed only that as the egg may 
 be taken as the starting-point in the life-history of an animal, so the 
 nebula is to be regarded as the starting-point of the life history of the 
 planetary system. He did not raise the question whether the egg is older 
 than the hen or not. 
 
288 LAPLACE'S NEBULAR HYPOTHESIS. [ 392 
 
 parts of the nebula. As the contraction proceeded, the swift- 
 ness of the rotation would necessarily increase for mechanical 
 reasons. 
 
 (d) In consequence of its whirling motion, the globe would 
 necessarily become flattened at the poles, and ultimately, as 
 the contraction went on, the centrifugal force at the equator 
 would there become equal to gravity, and rings of nebulous 
 matter would be detached from the central mass, like the rings 
 of Saturn. In fact, Saturn's rings suggested this feature of 
 the theory. 
 
 (e) The ring thus formed would for a time revolve as a 
 whole, but would ultimately break, and the material would col- 
 lect into a globe revolving around the central nebula as a planet. 1 
 
 Laplace supposed that the ring would revolve as if it were 
 solid, the particles at the outer edge moving more swiftly than 
 those at the inner (questionable). If this were always so, the 
 planet formed would necessarily rotate in the same direction 
 in which the ring had revolved. 
 
 (/) The planet thus formed would throw off rings of its 
 own, and so form for itself a system of satellites. 
 
 393. This theory obviously explains most of the facts of the 
 solar system, which were enumerated in the preceding article, 
 though some of the exceptional facts (such as the short 
 periods of the satellites of Mars, and the retrograde motions of 
 those of Uranus and Neptune) cannot be explained by it alone 
 in its original form. But even these exceptions do not contra- 
 dict it, as is sometimes supposed. 
 
 As to the modifications required by the theory, while they 
 alter the mechanism of the development in some respects, they 
 do not touch the main results. It is rather more likely, for 
 instance, that the original nebula was a cloud of ice-cold dust 
 
 1 It has been suggested by Huggins and others that the two small neb- 
 ulae near the great nebula of Andromeda (Fig. 81) may be planets in 
 process of formation. 
 
393] LOCKYER'S METEORIC HYPOTHESIS. 289 
 
 than incandescent gas and "fire-mist/' to use a favorite expres- 
 sion; and it is likely that planets and satellites were often 
 separated from the mother-orb otherwise than in the form of 
 rings. 
 
 Nor is it possible that a thin, wide ring could revolve in 
 the same way as a solid mass; the particles near the inner 
 edge must make their revolution in periods much shorter than 
 those upon the circumference, or the ring would tear to pieces. 
 But this very fact makes it possible to account for the peculiar 
 backward motion of the satellites of Uranus and Neptune, 
 thus removing one of the main objections to the theory in its 
 original form. 
 
 Many things, also, make it questionable whether the outer 
 planets are so much older than the inner ones, as Laplace's 
 theory would indicate. It is not impossible that they may 
 even be younger. 
 
 Our limits do not permit us to enter into a discussion of Darwin's 
 " tidal theory " of satellite formation, which may be regarded as in a 
 sense supplementary to the nebular hypothesis ; nor can we more than 
 mention Faye's proposed modification of it. According to him, the 
 inner planets are the oldest. 
 
 394. Lockyer's Meteoric Hypothesis. Within the last two 
 years Mr. Lockyer has vigorously revived a theory which has 
 been from time to time suggested before; viz., that all the 
 heavenly bodies in their present state are mere clouds of 
 meteors, or have been formed by the condensation of such 
 clouds ; and it is an interesting fact, as Professor G. H. Dar- 
 win has recently shown, that a large swarm of meteors, in 
 which the individuals move swiftly in all directions, would, in 
 the long run and as a whole, behave almost exactly, from a 
 mechanical point of view, in the same way as one of Laplace's 
 hypothetical gaseous nebulae. 1 
 
 1 This is not very strange, after all. According to the modern "kinetic 
 theory of gases " (Rolfe's "Physics," page 157), a meteor cloud is mechani- 
 
290 STARS, STAR-CLUSTERS, AND NEBTTLJE. [ 394 
 
 The spectroscopic observations upon which Mr. Lockyer rests his 
 attempted demonstration are many of them very doubtful ; but that 
 does not really discredit the main idea, except so far as the question 
 of the origin and nature of the light of the heavenly bodies is con- 
 cerned. He makes the light in all cases depend upon the collisions 
 between the meteors, and finds in the spectra of the heavenly bodies 
 evidence of the presence of materials with which we are familiar in the 
 meteorites which fall upon the earth's surface. These identifications 
 are in many cases questionable, and it seems much more likely that 
 the luminosity depends to a great degree upon other than mere 
 mechanical actions. 
 
 395. Stars, Star-clusters, and Nebulae. It is obvious that 
 the nebular hypothesis in all its forms applies to the explana- 
 tion of the relations of these different classes of bodies to 
 each, other. In fact, Herschel, appealing only to the "law 
 of continuity," had concluded, before Laplace published his 
 theory, that the nebulae develop sometimes into clusters, some- 
 times into double or multiple stars, and sometimes into single 
 stars. He showed the existence in the sky of all the inter- 
 mediate forms between the nebula and the finished star. For 
 a time, about forty years ago, while it was generally believed 
 that -all the nebulas were only star-clusters, too remote to be 
 resolved by existing telescopes, his views fell rather into abey- 
 ance ; but they regained acceptance in their essential features 
 when the spectroscope demonstrated the substantial difference 
 between gaseous nebulae and the star-clusters. 
 
 396. Conclusions from the Theory of Heat. Kant and La- 
 place, as Newcomb says, seem to have reached their results by 
 reasoning forwards. Modern science comes to very similar 
 
 cally just the same thing as a mass of gas magnified. The kinetic theory 
 asserts that gas is only a swarm of minute molecules, the peculiar gaseous 
 properties depending upon the collisions of these molecules with each 
 other and with the walls of the enclosing vessel. Magnify sufficiently the 
 molecules and the distances between them, and you have a meteoric cloud. 
 
396] AGE OF THE SYSTEM. 291 
 
 conclusions by working backwards from the present state of 
 things. 
 
 Many circumstances go to show that the earth was once 
 much hotter than it now is. As we penetrate below the sur- 
 face, the temperature rises nearly a degree (Fahrenheit) for 
 every sixty feet, indicating a white heat at the depth of a few 
 miles ; the earth at present, as Sir William Thomson says, " is 
 in the condition of a stone that has been in the fire and has 
 cooled at the surface." 
 
 The moon bears apparently on its surface the marks of the 
 most intense igneous action, but seems now to be entirely 
 chilled. 
 
 The planets, so far as we can make out with the telescope, 
 exhibit nothing at variance with the view that they were once 
 intensely heated, while many things go to establish it. Jupi- 
 ter and Saturn, Uranus and Neptune, do not seem yet to have 
 cooled off to anything like the earth's condition. 
 
 As to the sun, we have in it a body continuously pouring 
 forth an absolutely inconceivable quantity of heat without any 
 visible source of supply. As has been explained already (Art. 
 192), the only rational explanation of the facts, thus far pre- 
 sented, is that which makes it a huge, cloud-mantled ball of 
 elastic substance, slowly shrinking under its own central grav- 
 ity, and thus generating heat. 1 A shrinkage of about 300 feet 
 a year in the sun's diameter will account for the whole annual 
 output of radiant heat and light. 
 
 397. Age of the System. Looking backward, then, and 
 trying to imagine the course of time and of events reversed, 
 we see the sun growing larger and larger, until at last it has 
 
 1 So far we have no decisive evidence whether the sun has passed its 
 maximum of temperature or not. Mr. Lockyer thinks its spectrum 
 (resembling as it does that of Capella and the stars of the second class) 
 proves that it is now on the downward grade and growing cooler; but 
 others do not consider the evidence conclusive. 
 
292 FUTURE DURATION OF THE SYSTEM. [ 397 
 
 expanded to a huge globe that fills the largest orbit of our 
 system. How long ago this may have been, we cannot state 
 with certainty. If we could assume that the amount of heat 
 yearly radiated by the solar surface had remained constantly 
 the same through all those ages, and, moreover, that all the 
 radiated heat came solely from the slow contraction of the 
 sun's mass, apart from any considerable original capital in 
 the form of a high initial temperature, and without any re- 
 enforcement of energy from outside sources, if we could 
 assume these premises, it is easy to show that the sun's past 
 history must cover about 15,000000 or 20,000000 years. But 
 such assumptions are at least doubtful ; and if we discard 
 them, all that can be said is that the sun's age must be 
 greater, and probably many times greater, than the limit we 
 have named. 
 
 398. Future Duration of the System. Looking forward, 
 on the other hand, from the present towards the future, it is 
 easy to conclude with certainty that if the sun continues its 
 present rate of radiation and contraction, and receives no sub- 
 sidies of energy from without, it must, within 5,000000 or 
 10,000000 years, become so dense that its constitution will be 
 radically changed. Its temperature will fall and its function 
 as a sun will end. Life on the earth, as we know life, will be 
 no longer possible when the sun has become a dark, rigid, 
 frozen globe. At least this is the inevitable consequence of 
 what now seems to be the true account of the sun's condition 
 and activity. 
 
 399. The System not Eternal. One conclusion seems to 
 be clear : That the present system of stars and worlds is 
 not an eternal one. We have before us everywhere evidence 
 of continuous, irreversible progress from a definite beginning 
 towards a definite end. Scattered particles and masses are 
 gathering together and condensing, so that the great grow con- 
 
399] THE SYSTEM NOT ETERNAL. 293 
 
 tinually larger by capturing and absorbing the smaller. At 
 the same time the hot bodies are losing their heat and distrib- 
 uting it to the colder ones, so that there is an unremitting 
 tendency towards a uniform, and therefore useless, temperature 
 throughout our whole universe : for heat is available as energy 
 (i.e., it can do ivork) only when it can pass from a warmer 
 body to a colder one. The continual warming up of cooler 
 bodies at the expense of hotter ones always means a loss, 
 therefore, not of energy, for that is indestructible, but of 
 available energy. To use the ordinary technical term, energy 
 is continually "dissipated " by the processes which constitute 
 and maintain life on the universe. This dissipation of energy 
 can have but one ultimate result, that of absolute stagnation 
 when the temperature has become everywhere the same. 
 
 If we carry our imagination backwards, we reach " a begin- 
 ning of things," which has no intelligible antecedent ; if for- 
 wards, we come to an end of things in dead stagnation. That 
 in some way this end of things will result in a " new heavens 
 and a new earth " is, of course, probable, but science as yet 
 can present no explanation of the method. 
 
APPENDIX. 
 
 CHAPTER XIII. 
 
 ASTRONOMICAL INSTRUMENTS. 
 
 THE CELESTIAL GLOBE. THE TELESCOPE : SIMPLE, ACHRO- 
 MATIC, AND REFLECTING. THE EQUATORIAL. THE 
 FILAR MICROMETER. THE TRANSIT INSTRUMENT. - 
 THE CLOCK AND CHRONOGRAPH. THE MERIDIAN CIR- 
 CLE. THE SEXTANT. 
 
 400, The Celestial Globe. The celestial globe is a ball, 
 usually of papier-mache", upon which are drawn the circles of 
 the celestial sphere and a map of the stars. It is ordinarily 
 mounted in a framework which represents the horizon and the 
 meridian, in the manner shown in Fig. 83. 
 
 The "horizon," HH' in the figure, is usually a wooden 
 ring three or four inches wide and perhaps three-quarters of 
 an inch thick, directly supported by the pedestal. It carries 
 upon its upper surface at the inner edge a circle marked with 
 degrees for measuring the azimuth of any heavenly body, and 
 outside this the so-called zodiacal circles, which give the sun's 
 longitude and the equation of time for every day of the year. 
 
 The meridian ring, MM' , is a circular ring of metal which 
 carries the bearings upon which the globe revolves. Things 
 are so arranged, or ought to be, that the mathematical axis 
 of the globe is exactly in the same plane as the graduated face 
 
 295 
 
296 
 
 APPENDIX. 
 
 [400 
 
 of the ring, which is divided into degrees. The meridian ring 
 is held underneath the globe by a support, with a clamp which 
 enables us to fix it securely in any desired position. 
 
 The surface of the globe is marked first with the celestial 
 equator, next with the ecliptic, crossing the equator at an 
 
 FIG. 83. The Celestial Globe. 
 
 angle of 23 J at F(as the figure is drawn, V happens to be the 
 autumnal equinox, not the vernal), and each of these circles is 
 divided into degrees. The equinoctial and solstitial colures 
 are also always represented. As to the other circles, usage 
 differs. The ordinary way at present is to mark the globe 
 with twenty-four hour-circles 15 apart (the colures, Art. 117, 
 being four of them), and with parallels of declination 10 
 
400] TO RECTIFY A GLOBE. 297 
 
 apart. On the surface of the globe are plotted the positions 
 of the stars and the outlines of the constellations. 
 
 It is perhaps worth noting that many of the spirited figures of the 
 constellations upon our present globes are copied from designs drawn 
 by Albert Diirer for a star-map published in his time. 
 
 The Hour-index is a small circle of thin metal, about four 
 inches in diameter, which is fitted to the northern pole of the 
 globe with a stiffish friction, so that it can be set like the 
 hands of a clock, and when once set will turn with the globe 
 without shifting. 
 
 401. To rectify a Globe, i.e., to set it so as to show the 
 aspect of the heavens at any time : 
 
 (1) Elevate the north pole of the globe to an angle equal 
 to the observer's latitude by means of the graduation on 
 the meridian ring, and clamp the ring securely. 
 
 (2) Look up the day of the month on the horizon of the 
 globe, and opposite to the day find on the zodiacal circle the 
 sun's longitude for that day. 
 
 (3) On the ecliptic (upon the surface of the globe) find 
 the degree of longitude thus indicated, and bring it to the 
 graduated face of the meridian ring. The globe is thus set to 
 correspond to apparent noon of the day in question. 
 
 It may be well to mark the place of the sun temporarily with a bit 
 of paper gummed on at the proper place in the ecliptic. It can easily 
 be wiped off after using. 
 
 (4) Hold the globe fast, so as to keep the place of the sun 
 exactly on the meridian, and turn the hour-index until it shows 
 at the edge of the meridian ring the mean time of apparent 
 noon (i.e., 12 h the equation of time given on the wooden 
 horizon for the day in question). 
 
 If standard time is used, the hour-index must be set to the standard 
 time for apparent noon instead of the local mean time. 
 
298 APPENDIX. [ 401 
 
 (5) Finally, turn the globe upon its axis until the hour- 
 index shows at the meridian the hour for which it is to be 
 set. The globe will then represent the true aspect of the 
 heavens at that time. 
 
 The positions of the moon and planets are not given by this opera- 
 tion, since they have no fixed places in the sky, and therefore cannot 
 be put in by the globe-maker. If one wants them represented, he 
 must look up their right ascensions and declinations in some almanac, 
 and mark the proper places on the globe with bits of wax or paper. 
 
 TELESCOPES. 
 
 402. Telescopes are of two kinds, refracting and reflecting. 
 The refractor was first invented, early in the seventeenth 
 
 century, and is much more used, but the largest instruments 
 ever made dfre reflectors. In both, the fundamental principle 
 is the same. The large lens of the instrument (or else its 
 concave mirror) forms a real image of the object looked at, 
 and this image is then examined and magnified by the eye- 
 piece, which in principle is only a magnifying-glass. 
 
 In the form of instrument, however, which was originally devised 
 by Galileo and is still used as the " opera-glass," the rays from the 
 object-glass are intercepted, and brought to parallelism, by the concave 
 lens which serves as an eye-glass, before they form the image. Tele- 
 scopes of this construction are never made of much power, being 
 inconvenient on account of the smallness of the field of view. 
 
 403. The Simple Refracting Telescope. This consists 
 essentially, as shown in Fig. 84, of two convex lenses : one, 
 the object-glass A, of large size and long focus ; the other, the 
 eye-glass B, of short focus, the two being set at a distance 
 nearly equal to the sum of their focal lengths. Recalling the 
 optical principles relating to the formation of images by lenses, 
 we see that if the instrument is pointed towards the moon, for 
 instance, all the rays that strike the object-glass from the top 
 
403] MAGNIFYING POWER. 299 
 
 of the crescent will be collected to a focus at a, while those 
 from the bottom will come to a focus at b ; and similarly with 
 rays from the other points on the surface of the moon. We 
 shall, therefore, get in the "focal plane " of the object-glass a 
 small inverted "image" of the moon. The image is a real 
 
 FlQ. 84. The Simple Refracting Telescope. 
 
 one; i.e., the rays really meet at the focal points, so that if we 
 insert a photographic plate in the focal plane at ab and prop- 
 erly expose it, we shall get a picture of the object. The size 
 of the picture will depend upon the apparent angular diameter 
 of the object and the distance from the object-glass to the 
 image ab. 
 
 If the focal length of the lens A is ten feet, then the image of the 
 moon will be a little more than one inch in diameter. 
 
 404. Magnifying Power. If we use the naked .eye, we 
 cannot see the image distinctly from a distance much less than 
 a foot, but if we use a magnifying lens of, say, one inch focus, 
 we can view it from a distance of only an inch, and it will 
 look correspondingly larger. Without stopping to prove the 
 principle, we may say that the magnifying power is simply 
 equal to the quotient obtained by dividing the focal length of the 
 object-glass by that of the eye-lens. 
 
 It is to be noted, however, that a magnifying power of unity is 
 sometimes spoken of as no magnifying power at all, since the image 
 appears of the same size as the object. 
 
 The magnifying power of a telescope is changed at pleasure by 
 simply interchanging the eye-pieces, of which every telescope of any 
 pretensions always has a considerable stock, giving various powers. 
 
300 APPENDIX. [ 405 
 
 405, Brightness of the Image. This depends not upon the 
 focal length of the object-glass, but upon its diameter; or, 
 more strictly, its area. If we estimate the diameter of the 
 pupil of the eye at one-fifth of an inch, as it is usually reck- 
 oned, then (neglecting the loss from want of perfect transpar- 
 ency in the lenses) a telescope one inch in diameter collects 
 into the image of a star 25 times as much light as the naked 
 eye receives ; and the great Lick telescope of 36 inches in 
 diameter, 32,400 times as much, or about 30,000 after allow- 
 ing for the losses. The amount of light is proportional to the 
 square of the diameter of the object-glass. 
 
 The apparent brightness of an object which, like the moon or 
 a planet, shows a disc, is not, however, increased in any such 
 ratio, because the light gathered by the object-glass is spread 
 out by the magnifying power of the eye-piece. But the total 
 quantity of light in the image of the object greatly exceeds 
 that which is available for vision with the naked eye, and 
 objects which, like the stars, are mere luminous points, have 
 their brightness immensely increased, so that with the tele- 
 scope millions otherwise invisible are brought to light. With 
 the telescope, also, the brighter stars are easily seen in the 
 daytime. 
 
 406. The Achromatic Telescope. A single lens cannot 
 bring the rays which emanate from a single point in the object 
 to any exact focus, since the rays of each different color are 
 differently refracted, the blue more than the green, and this 
 more than the red. In consequence of this so-called " chro- 
 matic aberration," the simple refracting telescope is a very 
 poor 1 instrument. 
 
 1 By making it extremely long in proportion to its diameter, the indis- 
 tinctness of the image is considerably diminished, and in the middle of the 
 seventeenth century instruments more than 100 feet in length were used 
 by Huyghens and others. Saturn's rings and several of his satellites were 
 discovered with instruments of this kind. 
 
406] ACHROMATISM NOT PERFECT. 301 
 
 About 1760, it was discovered in England that by making 
 the object-glass of two or more lenses of different kinds of 
 glass, the chromatic aberration can be nearly corrected. Object- 
 glasses so made none others are now in common use are 
 called achromatic. In practice, only two lenses are ordinarily 
 used in the construction of an astronomical glass, a convex 
 of crown glass, and a concave of flint glass, the curves of the 
 two lenses and the distances between them being so chosen as 
 to give the most perfect possible correction of the " spherical " 
 aberration (" Physics," p. 363) as well as of the chromatic. 
 
 407. Achromatism not Perfect. It is not possible with the 
 kinds of glass hitherto available to obtain a perfect correction 
 of color. Even the best achromatic telescopes show a purple 
 halo around the image of a bright star, which, though usually 
 regarded as "very beautiful" by tyros, seriously injures the 
 definition, and is especially obnoxious in large instruments. 
 
 This imperfection of achromatism makes it impossible to get satis- 
 factory photographs with an ordinary object-glass, corrected for vision. 
 An instrument for photography must have an object-glass specially 
 corrected for the purpose, since the rays most efficient in impressing 
 the image upon the photographic plate are the blue and violet rays, 
 which in the ordinary object-glass are left to wander very wildly. 
 
 Much is hoped from the new kinds of glass now being made for 
 optical purposes at Jena, Germany, as the results of the experiments 
 conducted by Professor Abbe at the expense of the German govern- 
 ment. Though the new glass is especially intended for use in the con- 
 struction of microscopes, a few telescope lenses from three to six inches 
 in diameter have been already made with it, which appear to be nearly 
 perfect in their color correction. 
 
 408. Diffraction and Spurious Discs. Even if a lens were 
 absolutely perfect as regards the correction of aberrations, 
 both spherical and chromatic, it would still be unable to give 
 vision absolutely distinct. Since light consists of waves of 
 finite length, the image of a luminous point can never be also 
 
302 APPENDIX. [ 408 
 
 a point, but must of mathematical necessity be a disc of finite 
 diameter surrounded by a series of 'diffraction' rings. The 
 diameter of the "'spurious disc" of a star, as it is called, 
 varies inversely with the diameter of the object-glass : the 
 larger the telescope, the smaller the image of a star with a 
 given magnifying power. 
 
 With a good telescope and a power of about 30 to the inch of aper- 
 ture (120 for a 4-inch telescope) the image of a star, when the air is 
 steady (a condition unfortunately seldom fulfilled), should be a clean, 
 round disc, with a bright ring around it, separated from the disc by 
 a clear black space. According to Dawes, the disc of a star with a 
 4^-inch telescope should be about 1" in diameter; with a 9-inch instru- 
 ment 0".5, and |" for a 36-inch glass. 
 
 409. Eye-pieces. For some purposes the simple convex 
 lens is the best " eye-piece " possible ; but it performs well 
 only for a small object, like a close double star, placed exactly 
 
 Huyghenian in the C6Iltre f the field f 
 
 view. Generally, therefore, we 
 employ " eye-pieces " composed 
 of two or more lenses, which 
 give a larger field of view than 
 a single lens, and define satis- 
 
 FIG. 85. Telescope Eye-pieces. 
 
 tactorily over the whole extent 
 
 of the field. They fall into two general classes, the positive 
 and the negative. 
 
 The positive eye-pieces are much more generally useful. They act 
 as simple magnifying-glasses, and can be taken out of the telescope 
 and used as hand-magnifiers if desired. The image of the object 
 formed by the object-glass lies outside of this kind of eye-piece, between 
 it and the object-glass. 
 
 In the negative eye-piece, on the other hand, the rays from the 
 object-glass are intercepted by the so-called " field-lens " before reach- 
 ing the focus, and the image is formed between the two lenses of the 
 eye-piece. It cannot therefore be used as a hand-magnifier. 
 
 Fig. 85 shows the two most usual forms of eye-piece. 
 
409] THE REFLECTING TELESCOPE. 303 
 
 These eye-pieces show the object in an inverted position; 
 but this is of no importance as regards astronomical obser- 
 vations. 
 
 410. Reticle. When the telescope is used for pointing 
 upon an object, as it is in most astronomical instruments, it 
 must be provided with a ' reticle ' of some sort. The simplest 
 form is a metallic frame with spider lines stretched across it, 
 the intersection of the spider lines being the point of reference. 
 This reticle is placed not at or near the object-glass, as is often 
 supposed, but -MI its focal plane, as ab in Fig. 84. Sometimes a 
 glass plate with fine lines ruled upon it is used instead of 
 spider lines. Some provision must be made for illuminating 
 the lines, or " wires," as they are usually called, by reflecting 
 into the instrument a faint light from a lamp suitably placed. 
 
 411. The Reflecting Telescope. About 1670, when the 
 chromatic aberration of refractors first came to be understood 
 (in consequence of Newton's discovery of the " decomposition 
 of light "), the reflecting telescope was invented. For nearly 
 150 years it held its place as the chief instrument for star- 
 gazing, until about 1820, when large achromatics began to be 
 made. There are several varieties of reflecting telescope, dif- 
 fering in the way in which the image formed by the mirror is 
 brought within reach of the magnifying eye-piece. 
 
 Until about 1870, the large mirror (technically " speculum ") 
 was always made of speculum metal, a composition of copper 
 and tin. It is now usually made of glass, silvered on the front 
 by a chemical process. When new, these silvered films reflect 
 much more light than the old speculum metal : they tarnish 
 rather easily, but fortunately can be easily renewed. 
 
 412. Large Telescopes. The largest telescopes ever made have 
 been reflectors. At the head stands the enormous instrument of Lord 
 Rosse of Birr Castle, Ireland, six feet in diameter and sixty feet long, 
 
304 APPENDIX. [ 412 
 
 made in 1842, and still used. Next in size, but probably superior in 
 power, comes the five-foot silver-on-glass reflector of Mr. Common, at 
 Baling, England, completed in 1889 ; and then follow a number (four 
 or five) of four-foot telescopes, that of Herschel (erected in 1789, but 
 long ago dismantled) being the first, while the great instrument at 
 Melbourne is the only instrument of this size now in active use. 
 
 Of the refractors, the largest is that of the Lick Observatory (see 
 frontispiece), which has an aperture of 36 inches and a length of 
 nearly 60 feet. The next in size is that of Pulkowa, 30 inches in diam- 
 eter, and this is nearly equalled by the great telescope at Nice, with 
 an aperture of 29 inches. Then come the Vienna telescope, 27 
 inches ; the two telescopes at Washington and the University of Vir- 
 ginia, 26^ inches aperture; the Newhall telescope (just presented to 
 the University of Cambridge, England), 25 inches ; and the Princeton 
 telescope, 23 inches. These are at present (1890) all the refractors 
 which have an aperture exceeding 20 inches, but a number of others 
 are now under construction. All these large object-glasses were made 
 by the Clarks of Cambridge (U.S.), excepting those at Nice, Vienna, 
 and Cambridge (England). 
 
 413. Relative Advantages of Reflectors and Refractors. 
 
 There is no little discussion on this point, each form of instrument 
 having its earnest partisans. 
 
 In favor of the reflector we have Jirst, its comparative ease of con- 
 struction and cheapness, since there is but one surface to grind and 
 polish, as against four in an achromatic object-glass ; second, the fact 
 that reflectors can be made larger than refractors ; third, the reflector 
 is absolutely achromatic. 
 
 On the other hand, a refractor gives a much brighter image than a 
 reflector of the same size; it also generally defines much better, 
 because, for optical reasons into which we cannot enter here, any 
 slight distortion or malformation of the speculum of a reflector dam- 
 ages the image many times more than the same amount of distortion 
 of an object-glass. Then a lens hardly deteriorates at all with age, 
 while a speculum soon tarnishes, and must be re-silvered or re-polished 
 every few years. 
 
 As a rule, also, refractors are lighter and more convenient than 
 reflectors of equal power. 
 
414] 
 
 MOUNTING OF A TELESCOPE. 
 
 305 
 
 414. Mounting of a Telescope, the Equatorial. A tele- 
 scope, however excellent optically, is not good for much unless 
 firmly and conveniently mounted. 1 
 
 At present some form of equatorial mounting is practically 
 universal. Fig. 86 represents schematically the ordinary ar- 
 rangement of the instrument. Its essential feature is that its 
 "principal axis" (i.e., the one which turns in fixed bearings 
 attached to the pier, and is called the polar aocis) is placed par- 
 allel to the earth's axis, pointing to 
 the celestial pole, so that the circle 
 H t attached to it, is parallel to the 
 celestial equator. This circle is 
 sometimes called the hour-circle, 
 sometimes the right-ascension circle. 
 At the extremity of the polar axis a 
 " sleeve " is fastened, which carries 
 within it the declination axis D, 
 and to this declination axis is at- 
 tached the telescope tube T, and 
 also the declination circle C. 
 
 The advantages of this mount- 
 ing are very great. In the first 
 place, when the telescope is once 
 pointed upon an object, it is not 
 necessary to move the declination axis at all in order to keep 
 the object in the field, but only to turn the polar axis with a 
 perfectly uniform motion, which motion can be, and usually is, 
 given by clock-work (not shown in the figure). 
 
 In the next place, it is very easy to find an object even if 
 
 FIG. 86. The Equatorial. 
 
 1 We may add that it must, of course, be mounted where it can be 
 pointed directly at the stars, without any intervening window-glass be- 
 tween it and the object. We have known purchasers of telescopes to 
 complain bitterly because they could not see Saturn well through a closed 
 window. 
 
306 
 
 APPENDIX. 
 
 [414 
 
 invisible to the eye (like a faint comet, or a star in the day- 
 time), provided we know its right ascension and declination, 
 and have the sidereal time, a sidereal clock or chronometer 
 being an indispensable accessory of the instrument. 
 
 The frontispiece shows the actual mounting of the Lick telescope. 
 Fig. 71, Art. 337, represents another form of equatorial mounting, 
 which has been adopted for the instruments of the photographic 
 campaign. 
 
 415. The Micrometer. This is an instrument for measur- 
 ing small angles, usually not exceeding 15' or 20'. Various 
 
 kinds are employed, all of 
 them small pieces of ap- 
 paratus, which, when used, 
 are secured to the eye-end 
 of a telescope. The most 
 common is the parallel- 
 wire micrometer, which is 
 a pair of parallel spider 
 threads, one or both of 
 which can be moved with 
 a fine screw with a grad- 
 uated head, so that the 
 distance between the two 
 1 wires J can be varied at 
 pleasure, and then " read 
 off" by looking at the 
 micrometer head. Fig. 87 
 represents such an instru- 
 ment attached to a telescope : the spider threads are in the 
 box BB, and are viewed through the eye-piece. 
 
 416. The Transit Instrument (Fig. 88). This consists of 
 a telescope carrying at the eye-end a reticle, and mounted on 
 a stiff axis with pivots that are perfectly true. They turn in 
 
 Fio. 87. The Filar Position Micrometer. 
 
416] 
 
 THE ASTRONOMICAL CLOCK, ETC. 
 
 307 
 
 Y's, which are firmly set upon some sort of framework or on 
 the top of solid piers, and so placed that the axis will be ex- 
 actly east and west and precisely level. When the telescope 
 is turned on its axis, the mid- 
 dle wire of the reticle, if 
 everything is correctly ad- 
 justed, will follow the celes- 
 tial meridian, and whenever a 
 star crosses the wire, we know 
 that it is exactly on the me- 
 ridian. Instead of a single 
 wire, the reticle generally con- 
 tains a number of wires 
 equally spaced, as shown in 
 Fig. 89. The object is then 
 observed upon each of the 
 wires, and the mean of the 
 observations is taken as giv- 
 ing the moment when the star crossed the middle wire. 
 
 A delicate spirit-level, to be placed 
 on the pivots and test the horizon- 
 tality of the axis, is an indispensable 
 accessory. 
 
 So far as the theory of the instru- 
 ment is concerned, a graduated circle 
 is not essential ; but practically it is 
 necessary to have one attached to 
 the axis in order to enable the ob- 
 server to set for a star in preparing 
 for the observation. 
 
 FIG. 88. The Transit Instrument. 
 
 FIG. 89. Reticle of the Transit 
 Instrument. 
 
 417. The Astronomical Clock, Chronometer, and Chrono- 
 graph. A good timepiece is an essential adjunct of the tran- 
 sit instrument, and equally so of most other astronomical 
 instruments. The invention of the pendulum clock by Huy- 
 
308 APPENDIX. [ 417 
 
 ghens was almost as important an event in the history of 
 practical astronomy as that of the telescope itself. 
 
 The astronomical clock differs in no essential respect from 
 any other, except that it is made with extreme care, and has a 
 " compensated " pendulum so constructed that the rate of the 
 clock will not be affected by changes of temperature. It is 
 almost invariably made to beat seconds, and usually has its 
 face divided into twenty-four hours instead of twelve. 
 
 Excellence in a clock consists essentially in the constancy of 
 its 'rate' ; i.e., it should gain or lose precisely the same amount 
 each day, and as a matter of convenience the daily rate should 
 be small, not to exceed a second or two. The rate is adjusted 
 by slightly raising or lowering the pendulum bob, or putting 
 little weights upon a small shelf attached to the rod ; the 
 ' error/ when necessary, by simply setting the hands. 
 
 The error of a timepiece is the difference between the time shown 
 by the clock-face and the true time at the moment ; the rate is the 
 amount it gains or loses in twenty-four hours. 
 
 The chronometer is simply a carefully made watch, and has 
 the advantage of portability, though in 'accuracy it cannot 
 quite compete with a well-made clock. 
 
 Formerly transit-instrument observations were made by sim- 
 ply noting with eye and ear the time indicated by the clock at 
 the moment when the star observed was crossing the wire or 
 reticle. A skilful observer can do this within about a tenth 
 of a second. At present the observer usually presses a tele- 
 graph-key at the moment of the transit, and so telegraphs 
 the instant to an instrument called a "chronograph" which 
 makes a permanent record of the observation upon a sheet 
 of paper, thus making the observation much more accurate 
 as well as easier. (For the description of the chronograph, 
 see General Astronomy, Art. 56.) 
 
 418. The Meridian Circle. In many respects this is the 
 fundamental instrument of a working observatory. It is 
 
418] 
 
 THE MERIDIAN CIRCLE. 
 
 309 
 
 simply the transit instrument plus a finely graduated circle 
 
 or circles attached to the axis, and provided with microscopes 
 
 for reading the graduation with precision. In the accurate 
 
 construction of the pivots 
 
 of the instrument and of 
 
 the circles, with their 
 
 graduation, the utmost re- 
 
 sources of the mechanical 
 
 art are taxed. Fig. 90 
 
 shows the instrument in 
 
 principle. Fig. 91 is a 
 
 small meridian circle, as 
 
 actually constructed, with 
 
 a four-inch telescope and 
 
 twenty-four-inch circles. 
 
 Its main purpose is to 
 determine the right ascen- 
 sion and declination of 
 objects as they cross the 
 meridian. The declination is determined by measuring how 
 many degrees the object is north or south of the celestial equa- 
 tor at the moment of transit. The " circle-reading " for the 
 equator must first be determined as a zero point; and this is 
 done by observing a star near the pole and getting the circle- 
 reading as it crosses the meridian above the pole, and twelve 
 hours later, when it crosses again below it. The mean of these 
 two readings, corrected for refraction, will be the circle-reading 
 for the pole, or the polar point, which is, of course, just 90 
 from the equatorial zero point. 
 
 419. The Nadir Point. To get the latitude of the observer 
 with this instrument (Art. 81), it is necessary also to have the. 
 nadir point as a zero; i.e., the circle-reading which corresponds 
 to the vertical position of the telescope. This point is found 
 by pointing the telescope down towards a basin of mercury 
 
 F '' 90 ' ~ Tbe Merld "" 1 oircle 
 
310 
 
 APPENDIX. 
 
 [419 
 
 beneath it, and setting it so that the image of the east and 
 west wire in the reticle coincides with itself. Then the tele- 
 scope will be exactly vertical. The horizontal point is just 
 90 from the nadir point, and the difference between the 
 
 FIG. 91. A Meridian Circle. 
 
 (north) horizontal point and the polar point is the latitude of 
 the observatory. 
 
 Obviously the instrument can also be used as a simple tran- 
 sit instrument in connection with a clock, so that (Art. 99) the 
 
419] 
 
 THE SEXTANT. 
 
 311 
 
 observer can determine both the right ascension and declination 
 of any object which is visible when it crosses the meridian. 
 
 420. The Sextant. All the instruments so far mentioned, 
 except the chronometer, require firmly fixed supports, and are, 
 therefore, useless at sea. The sextant is the only instrument 
 for measurement upon which the mariner can rely. By means 
 of it he can measure the angular distance between any two 
 points (as, for instance, the sun and the visible horizon), not 
 
 JM 
 8 
 
 S' 
 
 FIG. 92. The Sextant. 
 
 by pointing first on one and afterwards on the other, but by 
 sighting them both simultaneously and in apparent coincidence. 
 This observation can be accurately made even if he has no 
 stable footing, but is swinging about on the deck of a vessel. 
 Fig. 92 represents the instrument. For a detailed description 
 and explanation, see General Astronomy, Arts. 76-80. 
 
 421. Use of the Instrument. The principal use of the in- 
 strument is in measuring the altitude of the sun. At sea, an 
 
312 APPENDIX. [ 421 
 
 observer holding the instrument in his right hand, and keep- 
 ing the plane of the arc vertical, looks directly towards the 
 visible horizon through the horizon-glass, H, at the point under 
 the sun. Then by moving the index, N, with his left hand, 
 he inclines the index mirror upward, until he sees the re- 
 flected image of the sun, and the lower edge of this image is 
 brought to touch the horizon-line. The reading of the gradu- 
 ation, after due correction for refraction, etc., gives the sun's 
 true altitude at the moment. If the observation is made near 
 noon, for the purpose of determining the latitude, it will not 
 be necessary to read the chronometer at the same . time. If, 
 however, the observation is made for the purpose of determin- 
 ing the longitude (Art. 497), the instant of observation, as 
 shown by the chronometer, must be carefully noted. 
 
 The skilful use of the sextant requires considerable dexterity, 
 and from the small size of the telescope, the angles measured 
 are less precisely measured than with large fixed instruments ; 
 but the portability of the instrument and its applicability at 
 sea render it absolutely invaluable. It was invented by 
 Gregory, of Philadelphia, in 1730. 
 
422] HOUR-ANGLE AND TIME. 313 
 
 CHAPTER XIV. 
 
 MISCELLANEOUS. 
 
 HOUR-ANGLE AND TIME. TWILIGHT. DETERMINATION 
 OF LATITUDE. SHIP'S PLACE AT SEA. FINDING THE 
 FORM OF THE EARTH'S ORBIT. THE ELLIPSE. ILLUS- 
 TRATIONS OF KEPLER'S THIRD LAW. THE EQUATION 
 
 OF LIGHT AND THE SUN'S DISTANCE. ABERRATION OF 
 LIGHT. DE L'ISLE'S METHOD OF GETTING THE SOLAR 
 PARALLAX FROM THE TRANSIT OF VENUS. THE 
 CONIC SECTIONS. STELLAR PARALLAX. THE SLIT- 
 LESS SPECTROSCOPE. 
 
 422. Hour-angle and Time (supplementary to Arts. 89-91). 
 There is another way of looking at the matter of time, 
 which has great advantages. If we face towards the north 
 pole and consider the star ra (Fig. 93) as carried at the end 
 of the arc mP of the hour-circle, which connects it to the 
 pole, we may regard this arc as a sort of clock-hand ; and if 
 we produce it to the celestial equator and mark off the equa- 
 tor into 15 spaces, or ' hours/ the angle QPm, or the arc Q Y, 
 will measure the time which has elapsed since m was on the 
 meridian PQ. The angle mPQ is called the Iwur-angle of the 
 star w. It is the angle at the pole between the meridian and 
 the hour-circle which passes through the body. 
 
 Having now this definition of the hour-angle, we may define 
 sidereal time (Art. 91) at any moment as the hour-angle of the 
 vernal equinox at that moment. In the same way, the apparent 
 solar time (Art. 88) is the hour-angle of the sun's centre ; the 
 
314 
 
 APPENDIX. 
 
 [422 
 
 FIG. 93. Hour-Angle. 
 
 mean solar time (Art. 89) is the hour-angle of a fictitious sun 
 which moves around the heavens uniformly, once a year, in 
 
 the equator, keeping its 
 right ascension equal to the 
 mean longitude of the real 
 sun. For some purposes, 
 as in dealing with the tides, 
 it is convenient to use lunar 
 time, which is simply the 
 hour-angle of the moon at 
 any moment. 
 
 423. Twilight is caused 
 by the reflection of sunlight 
 from the upper portions of the 
 earth's atmosphere. After the 
 sun has set, its rays still con- 
 tinue to shine through the air above the observer's head, and twilight 
 continues as long as any portion of this illuminated air can be seen 
 from where he stands. It is considered to end when stars of the 
 sixth magnitude become visible near the zenith, which does not occur 
 until the sun is about 18 below the horizon ; but this is not strictly 
 the same for all places. 
 
 The duration of twilight varies with the season and with the 
 observer's latitude. In latitude 40 it is about 90 minutes on March 
 1st and Oct. 12th; but more than two hours at the summer solstice. 
 In latitudes above 50, when the days are longest, twilight never quite 
 disappears, even at midnight. On the mountains of Peru, on the 
 other hand, it is said never to last more than half an hour. 
 
 424. Methods of determining Latitude by Other Observa- 
 tions than those of Circumpolar Stars (supplementary to Art. 
 81). To determine the latitude by observations of a circum- 
 polar star, the observer must remain at the same station at 
 least twelve hours. The latitude can be determined, however, 
 with a good instrument, with almost equal precision, by ob- 
 serving the meridian altitude, or zenith distance, of a body whose 
 
424] DETEKMINATION OF LATITUDE. 315 
 
 declination is accurately known. In Fig. 94 the circle AQPB 
 
 is the meridian, Q and P being respectively the equator and 
 
 the pole, and Z the zenith. QZ is evidently the declination 
 
 of the zenith (i.e., the distance of 
 
 the zenith from the celestial 
 
 equator) and is equal to PB, the 
 
 latitude of the observer, or height 
 
 of the pole. Suppose now that 
 
 we observe Zs, i.e., the zenith 
 
 distance of the star s, south of 
 
 ,1 ,-! ., ,-1 FIG. 94. Determination of Latitude. 
 
 the zenith, as it crosses the me- 
 ridian, and that we know Qs, the declination of the star. 
 Evidently QZ = Qs + sZ-, i.e., the latitude equals the declina- 
 tion of the star plus its zenith distance. If the star were at s', 
 south of the equator, the same equation would hold good 
 algebraically, because the declination, Qs', is a minus quantity. 
 If the star were at n, between the zenith and the pole, we 
 should have : Latitude equals the declination of the star minus 
 the zenith distance. This is the method actually used at sea 
 (Art. 426), the sun being the object observed. 
 
 There are many other methods in use, as, for instance, that 
 by the zenith telescope and that by the prime-vertical instru- 
 ment, which are practically more convenient and more accurate 
 than either of the two described, but they are more compli- 
 cated, and their explanation would take us too far. The 
 reader is referred to General Astronomy, Arts. 104-107. 
 
 FINDING THE PLACE OF A SHIP. 
 
 425. The determination of the place of a ship at sea is, 
 from the economic point of view, the most important problem 
 of Astronomy. National observatories and nautical almanacs 
 were established, and are maintained, principally to supply the 
 mariner with the data needed to make this determination 
 accurately and promptly. The methods employed are neces- 
 
316 APPENDIX. [ 425 
 
 sarily such that the required observations can be made with 
 the sextant and chronometer, since fixed instruments, like the 
 transit instrument and meridian circle, are obviously out of 
 the question on board a vessel. 
 
 426. Latitude at Sea. This is obtained by observing with 
 the sextant the sun's maximum altitude, which is reached 
 when the sun is crossing the meridian. 
 
 Since at sea the sailor seldom knows beforehand the precise 
 time which will be shown by his chronometer at noon, he 
 takes care not to be too late, and begins to measure the sun's 
 altitude a little before noon, repeating his observations every 
 minute or two. At first the altitude will keep increasing, but 
 when noon comes the sun will cease rising, and then begin to 
 descend. The observer uses, therefore, the maximum altitude 
 obtained, which, with due allowance for refraction and some 
 other corrections (for details, see larger works) gives him the 
 true altitude of the sun's centre. Taking this from 90, we 
 get its zenith distance. 
 
 Eef erring now to Fig. 94, in which the circle AQZPB is 
 the meridian, P the pole, Z the zenith, and OQ the celestial 
 equator seen edgewise, we see that PB, the altitude of the 
 pole, is necessarily equal to ZQ, the distance from the zenith 
 to the equator. Now from the almanac we find the declina- 
 tion of the sun, Qs, for the day on which the observations are 
 made. 1 We have only to add to this, Zs, the measured dis- 
 tance of the sun from the zenith, to obtain QZ, which is the 
 observer's latitude. 
 
 It is easy in this way, with a good sextant, to get the lati- 
 tude within about half a minute of arc, or, roughly, about 
 half a mile, which is quite sufficiently accurate for nautical 
 purposes. 
 
 1 If the sun happened to be south of the equator (in the winter), as at 
 s', we should have ZQ equals Zs s'Q. 
 
427] LOCAL TIME AND LONGITUDE AT SEA. 317 
 
 427. Determination of Local Time and Longitude at Sea. 
 
 The usual method now employed for the longitude depends 
 upon the chronometer. This is carefully 'rated' in port; 
 i.e., its error and its daily gain or loss are determined by com- 
 parisons with an accurate clock for a week or two, the clock 
 itself being kept correct to Greenwich time by transit obser- 
 vations. By merely allowing for the gain or loss since leaving 
 port, and adding this gain or loss to the ' error' (Art. 417), 
 which the chronometer had when brought on board, the sea- 
 man at once obtains the error of the chronometer on Green- 
 wich time at any moment ; and allowing for this error, he has 
 the Greenwich time itself, with an accuracy which depends 
 only pn the constancy of the chronometer's rate : it makes no 
 difference whether it is gaining much or little, provided its 
 daily rate is steady. 
 
 He must also determine his own local time; and this must 
 be done with the sextant, since, as was said before, an instru- 
 ment like the transit cannot be used at sea. He does it by 
 measuring the altitude of the sun, not at or near noon, as often 
 supposed, but when the sun is as near due east or west as cir- 
 cumstances permit. From such an observation the sun's hour- 
 angle, i.e., the apparent solar time (Art. 422), is easily found, 
 by a trigonometrical calculation, provided the ship's latitude 
 is known. (For the method of calculation, see General As- 
 tronomy, Art. 116.) 
 
 The longitude follows at once, being simply the difference 
 between the Greenwich time and the local time. 
 
 In certain cases where the chronometers have been for 
 some reason disturbed, the mariner is obliged to get his Green- 
 wich time by observing with a sextant the distance of the 
 moon from some neighboring fixed star, but the results thus 
 obtained are comparatively inaccurate and unsatisfactory. 
 
 428. To find the Form of the Earth's Orbit (supplementary 
 to Art. 119). Take the point S (Fig. 95) for the sun, and 
 
318 
 
 APPENDIX. 
 
 [428 
 
 draw from it a line, SO, directed toward the vernal equinox, 
 from which longitudes are measured. Lay off from S lines 
 indefinite in length, making angles with 80 equal to the 
 
 earth's longitude as seen 
 from the sun on each 
 of the days when the 
 observations are made 
 (earth's longitude equals 
 sun's longitude + 180). 
 We shall thus get a sort 
 of "spider," showing the 
 direction of the earth as 
 seen from the sun on 
 each of those days. 
 
 10 / 11 / Next, as to the dis- 
 
 tances. While the ap- 
 parent diameter of the 
 sun does not tell us its 
 
 absolute distance from the earth, unless we know his diameter 
 in miles, yet the changes in the apparent diameter do inform 
 us as to the relative distance at different times, since the nearer 
 we are to the sun, the larger it looks. If, then, on the legs of 
 the " spider " we lay off distances inversely proportional to the 
 number of seconds of arc in the sun's measured diameter at 
 each date, these distances will be proportional to the true dis- 
 tance of the earth from the sun, and the curve joining the 
 points thus obtained will be a true map of the earth's orbit, 
 though without any scale of miles. When the operation is 
 performed, we find that the orbit is an ellipse of small eccen- 
 tricity, with the sun not at the centre, but in one of the two 
 foci. 
 
 FIG. 95. 
 Determination of the Form of the Earth's Orbit. 
 
 429. The Ellipse, and Definitions relating to it (supplemen- 
 tary to Arts. 119, 120). If we drive two pins into a board, as 
 at F and S in Fig. 96, and put a looped thread around the 
 
429] 
 
 DEFINITIONS RELATING TO THE ELLIPSE. 
 
 319 
 
 pins, attached to the point of a pencil, P, then on carrying 
 
 the pencil around it will mark out an ellipse. The pins, F 
 
 and S, are the " foci " of the 
 
 ellipse, and C is its centre. 
 
 From the manner in which 
 
 the ellipse is constructed, . it 
 
 is clear that at any point, P, 
 
 on its outline, the sum of the 
 
 two lines, PS and PF, will 
 
 always be the same, and equal 
 
 to the line AA'. The length 
 
 of the ellipse, AA', is called FlG " 96 - The Ellip8e ' 
 
 its major axis, and AC its semi-major axis, which is usually 
 
 designated by a, while the semi-minor axis, BC, is lettered &. 
 
 CS 
 The fraction, -, is called the eccentricity of the ellipse, and 
 
 AC 
 
 determines the shape of the oval. Its usual symbol is e. If e 
 is nearly unity, i.e. t if CS is nearly equal to CA, the oval 
 will be very narrow compared with its length ; but if CS is 
 very small compared with CA, the ellipse will be almost round. 
 Taken together, a and e determine the size and form of the 
 oval. The ellipse is called a ' conic/ because when a cone is 
 cut across obliquely the section is elliptical (see Art. 440). 
 
 430. Problems illustrating the Harmonic Law ' (supple- 
 mentary to Art. 220). To aid the student in apprehending the 
 meaning and scope of Kepler's third law, we give a few simple exam- 
 ples of its application. 
 
 1. What would be the period of a planet having a mean distance 
 from the sun of one hundred astronomical units ; i.e., a distance a 
 hundred times that of the earth ? 
 
 P:100 3 =l 2 (year):X 2 ; 
 whence, X (in years) = VlOO 8 = 1000 years. 
 
 2. What would be the distance from the sun of a planet having a 
 period of 125 years ? 
 
 I 2 (year) : 125 2 = 1 : Z 8 ; whence X = v/125 2 = 25 astron. units. 
 
320 APPENDIX. [ 430 
 
 3. What would be the period of a satellite revolving close to the 
 earth's surface ? 
 
 (Moon's Dist.) 8 : (Dist. of Satellite) 8 = (27.3 days) 2 : X\ 
 or, 60 8 : I 8 = 27.3 2 : X 2 ; 
 
 whence, X = 27 j 2 days - 1" 24 m . 
 
 V60 8 
 
 4. How much would an increase of 10 per cent in the earth's dis- 
 tance from the sun lengthen the year? 
 
 100 8 : HO 8 = (365}) 2 : X*, whence Z 2 = X 
 
 X being the new length of the year. X is found by logarithmic com- 
 putation to be 421.38 days. The increase is 56.13 days. 
 
 5. What is the distance from the sun of an asteroid with a period 
 of 3 years ? 
 
 I 2 (year): 3.5 2 = 1 : Dist. 3 
 
 .-. Dist. = \/(3^T 2 = v/12^5 = 2.305 astron. units. 
 
 431. The Equation of Light. When we observe a celestial 
 body, we see it not as it is at the moment of observation, but 
 as it was at the moment when the light which we see left it. 
 If we know its distance in astronomical units, and know how 
 long light takes to traverse that unit, we can at once correct 
 our observation by simply dating it back to the time when the 
 light started from the object. The necessary correction is 
 called the " equation of light," and the time required by light to 
 traverse the astronomical unit of distance is called the "Con- 
 stant of the Light-equation" (not quite 500 seconds, as 
 we shall see). 
 
 It was in 1675 that Roemer, the Danish astronomer (the inventor 
 of the transit instrument, meridian-circle, and prime-vertical instru- 
 ment, a man almost a century in advance of his day), found that 
 the eclipses of Jupiter's satellites show a peculiar variation in their 
 times of occurrence, which he explained as due to the time taken by 
 light to pass through space. His bold and original suggestion was 
 
431] 
 
 THE EQUATION OF LIGHT. 
 
 321 
 
 neglected for more than fifty years, until long after his death, when 
 Bradley 's discovery of aberration (Art. 435) proved the correctness of 
 his views. 
 
 432. Determination of the Constant of the Equation of 
 Light. Eclipses of the satellites of Jupiter recur at intervals 
 which are really almost exactly equal (the perturbations being 
 very slight), and the interval can easily be determined and the 
 times tabulated. But if we thus predict the times of the 
 eclipses during a whole synodic period of the planet, then, be- 
 ginning at the time of opposition, it is found that as the planet 
 recedes from the earth, the eclipses, as observed, fall constantly 
 more and more behindhand, and by precisely, the same amount 
 for all four satellites. The 
 difference between the pre- 
 dicted and observed time 
 continues to increase until 
 the planet is near conjunc- 
 tion, when the eclipses are 
 about 16 m 38 s later than the 
 prediction. After the con- 
 junction they quicken their 
 pace, and make up the loss, 
 so that when opposition is 
 reached once more they are 
 again on time. 
 
 It is easy to see from 
 Fig. 97 that at opposition 
 the planet is nearer the earth than at conjunction by just two 
 astronomical units. At opposition the distance between Jupi- 
 ter and the earth is JA, while six and a half months later,, 
 at the time of Jupiter's superior conjunction, it is JB. The 
 difference between JA and JB is just twice the distance from 
 8 to A. 
 
 The whole apparent retardation of eclipses between opposi- 
 
 FIG. 97. The Equation of Light. 
 
322 APPENDIX. [ 432 
 
 tion and conjunction must therefore be exactly twice the time 1 
 required for light to come from the sun to the earth. In this way 
 the " light-equation constant " is found to be very nearly 499 
 seconds, or 8 minutes 19 seconds, with a probable error of 
 perhaps two seconds. 
 
 433. Since these eclipses are gradual phenomena, the determination 
 of the exact moment of a satellite's disappearance or reappearance is 
 very difficult, and this renders the result somewhat uncertain. Prof. E. 
 C. Pickering of Cambridge has proposed to utilize photometric observa- 
 tions for the purpose of making the determination more precise, and 
 two series of observations of this sort, and for this purpose, are now 
 in progress, one in Cambridge, United States, and the other at 
 Paris under the direction of Cornu, who has devised a similar plan. 
 Pickering has also applied photography to the observation of these 
 eclipses with encouraging success. 
 
 434. The Distance of the Sun determined by the "Light- 
 equation." Until 1849 our only knowledge of the velocity of 
 light was obtained from such observations of Jupiter's satel- 
 lites. By assuming as known the earth's distance from the sun, 
 the velocity of light can be obtained when we know the time 
 occupied by light in coming from the sun. 
 
 At present, however, the case is reversed. We can deter- 
 mine the velocity of light by two independent experimental 
 methods, and with a surprising degree of accuracy. Then, 
 knowing this velocity and the "light-equation constant," we 
 can deduce the distance of the sun. According to the latest 
 determinations the velocity of light is 186,330 miles per second. 
 Multiplying this by 499 we get 92,979,000 miles for the sun's 
 distance (compare Art. 436). 
 
 1 The student's attention is specially directed to the point that the ob- 
 servations of the eclipses of Jupiter's satellites give directly neither the 
 velocity of light nor the distance of the sun : they give only the time re- 
 quired by light to make the journey from the sun. Many elementary 
 text-books, especially the older ones, state the case carelessly. 
 
435] 
 
 ABERRATION OF LIGHT. 
 
 323 
 
 435. Aberration of Light. The fact that light is not trans- 
 mitted instantaneously causes the apparent displacement of 
 an object viewed from any moving station, unless the motion 
 is directly towards or from that object. If the motion of 
 the observer is not rapid, this displacement, or "aberration," 
 is insensible ; but the earth moves so swiftly (18J miles 
 per second) that it is easily observable in the case of the 
 stars. Astronomical aberration may be defined, therefore, as 
 the apparent displacement of a heavenly body due to the combina- 
 tion of the orbital motion of the earth with that of light the 
 direction in which we have to point our telescope in observing 
 a star is not the same as if the earth were at rest. 
 
 We may illustrate this by considering what would happen in the 
 case of falling rain-drops. Suppose the observer standing with a tube 
 in his hand while the drops 
 are falling straight down: if 
 he wishes to have the drops 
 descend through the middle of 
 the tube without touching the 
 sides, he must keep it vertical 
 so long as he stands still ; but 
 if he advances in any direction 
 the drops will strike the side of 
 the tube, and he must thrust 
 forward its upper end (Fig. 98) 
 by an amount which equals 
 
 m 
 
 u 
 
 FIG. 98. Aberration. 
 
 the advance he makes while a 
 
 drop is falling through it ; i.e., 
 
 he must incline the tube forward at an angle, depending both upon 
 
 the velocity of the rain-drop and the swiftness of his own motion, 
 
 so that when the drop, which entered the tube at B, reaches A', the 
 
 bottom of the tube will be there also. 
 
 It is true that this illustration is not a demonstration, because light 
 does not consist of particles coming towards us, but of waves trans- 
 mitted through the ether of space. But it has been shown (though 
 the proof is by no means elementary) that within very narrow limits, 
 the apparent direction of a wave is affected in precisely the same way 
 as that of a moving projectile. 
 
324 APPENDIX. [ 435 
 
 The best observations show that a star situated on a line at 
 right angles to the direction of the earth's motion, is thus 
 apparently displaced by an angle of about 20".5. The latest 
 and most trustworthy determination by Nyren of Pulkowa 
 makes it 20".492. 
 
 This is the so-called " CONSTANT OF ABERRATION/' 
 If the star is in a different part of the sky, its displacement 
 will be less, the amount being easily calculated when the star's 
 position is given. 
 
 436. Determination of the Sun's Distance by Means of the 
 Aberration of Light. The constant of aberration, a, and 
 the two velocities, that of the earth in its orbit, u, and the 
 velocity of light, V, are connected by the very simple equation 
 
 a = 206265 x ; whence = x V. 
 
 When, therefore, we have ascertained the value of a (20". 492) 
 from observations of the stars, and of V (186,330 miles, ac- 
 cording to the most recent determinations by Michelson and 
 Newcomb) by physical experiments, we can immediately find 
 u, the velocity of the earth in her orbit. The circumference of 
 the earth's orbit is then found by multiplying this velocity, w, 
 by the number of seconds in a sidereal year (Art. 127) ; and 
 from this we get the radius of the orbit, or the earth's mean dis- 
 tance from the sun, by dividing the circumference by 2?r (?r = 
 3.14159). Using the values above given, the mean distance of 
 the sun comes out 92,975500 miles. 
 
 But the uncertainty of a is probably as much as 0".03, and 
 this affects the distance proportionally, say one part in 600, or 
 150,000 miles. Still, the method is one of the very best of 
 all that we possess for determining in miles the value of " the 
 Astronomical Unit." 
 
 437. De 1'Isle's Method of determining the Sun's Parallax 
 by a Transit of Venus. We have thus (Arts. 434 and 436) 
 
437] DETERMINING THE SUN'S PARALLAX. 325 
 
 two methods by which the mean distance of the sun from the 
 earth can be determined. They both depend upon a knowl- 
 edge of the velocity of light, and of course were unavailable 
 before 1849, when Fizeau first succeeded in actually measuring 
 it. Before that time it was necessary to rely entirely upon 
 observations of either Mars or Venus, made at times when 
 they come specially near us. 
 
 Most of the methods of getting the sun's parallax and dis- 
 tance from such observations depend upon our having a pre- 
 vious knowledge of the relative distances of the planets from 
 the sun. These relative distances were ascertained centuries 
 ago. Copernicus knew them nearly as accurately as we have 
 them now; but since we have not explained in this book how 
 
 E 
 
 FIG. 99. Transit of Venue. 
 
 they are found (the explanation involves a little Trigonom- 
 etry), we limit ourselves to giving here a single very simple 
 method, which requires a previous knowledge not of the rela- 
 tive distances of Venus and the earth from the sun, but only 
 of the synodic period of the planet (Art. 228) ; i.e., the time in 
 which she gains one entire revolution upon the earth. This 
 is 584 days, as has been known from remote antiquity. 
 
 Fig. 99 represents things at a transit of Venus, as they would 
 be seen by one looking down from an infinitely distant point 
 above the earth's north pole. As seen from the earth itself, 
 Venus would appear to cross the sun, striking the disc on 
 the east side and moving straight across to the west, mak- 
 ing four ' contacts ' with the edge of the sun as shown in 
 Fig. 100. 
 
326 APPENDIX. [ 438 
 
 438. Suppose, now, that two observers, E and W (Fig. 99), 
 are stationed opposite each, other, and near the earth's equator. 
 
 E will see Venus strike the sun's 
 disc before W does, and if they 
 both observe the moment of con- 
 tact, in Greenwich time, the differ- 
 ence between their records will be 
 the time it takes Venus to move 
 over the arc from V\ to F 2 . From 
 the figure it is clear that the angle, 
 ViDVz, is the same as EDW, the 
 ,. 100. earth's apparent diameter seen from 
 
 Contacts in a Transit of Venus. tJ te SUU} an( J this is at Once known 
 
 when we have the time from Vi to F 2 . 
 
 Since Venus gains one revolution in 584 days, in one day 
 she will gain -^^ of a revolution, or 37' (very nearly), and 
 this will make her gain 1".54 in one minute. Now it is found 
 that the difference between the moments of contact at two 
 stations situated like E and W is about ll m 25 s , and hence that 
 the diameter of the earth as seen from the sun is 17".6, or the 
 sun's horizontal parallax (Art. 139) is 8".8 ; from which its 
 distance is easily found (Art. 140). 
 
 The reader will see that the two observers must know their 
 longitudes accurately, in order to be sure of the correct Green- 
 wich time. Moreover, the two stations can never be quite 
 exactly opposite each other, but stations a little nearer together 
 must be taken and proper allowances made. Finally, we are 
 very sorry to add that the necessary observations of the mo- 
 ment when Venus reaches the edge of the sun's disc cannot be 
 made with the accuracy which is desirable, owing to the effect 
 of the planet's atmosphere (see Art. 248) ; so that practically 
 the method is less accurate than might be hoped. For fur- 
 ther details, see General Astronomy, Chapter XVI. 
 
 439. The Parabola (supplementary to Arts. 292-298). This 
 differs from the ellipse in never coming around into itself. 
 
439] 
 
 THE PAEABOLA. 
 
 327 
 
 In Fig. 101, the curves PA l} PA 2 and PA 3 , are ellipses of dif- 
 ferent length, all having S at one of their foci. The first and 
 smallest of the ellipses is nearly circular, and shaped about 
 like the orbit of Mercury ; the next, more eccentric than the 
 orbit of any asteroid ; and the third still more so. Now if we 
 
 FIG. 101. Ellipse, Parabola, and Hyperbola. 
 
 imagine the point F carried farther and farther to the right, 
 the ellipse will grow larger and longer, until when F is infi- 
 nitely far away the curve will become a parabola. 
 
 Of course if the point F is very distant, even if not infinitely 
 so, the part of the curve near S will agree with the parabola 
 so closely that no one could distinguish between them. 
 
 All ellipses that have S for the focus and P for the perihe- 
 lion lie inside of the parabola, while another set of conic curves 
 called hyperbolas, with the same focus and perihelion, lie en- 
 tirely outside of it, which is, so to speak, a sort of boundary 
 or division line between the ellipses and hyperbolas which 
 have this focus and perihelion. 
 
328 
 
 APPENDIX. 
 
 [440 
 
 440. The Conic Sections. The way in which these curves, 
 the ellipse, parabola, and hyperbola are formed by sec- 
 tions of the cone is shown by Fig. 102. 
 
 (a) If the cone be cut by a 
 plane which makes with its 
 axis, VC, an angle greater than 
 BVC, the plane of the section 
 will cut completely across the 
 cone, and the section EF will 
 be an ellipse, which will vary 
 in shape and size according to 
 the position of the plane. The 
 circle is simply a special case 
 when the cutting plane is per- 
 pendicular to the axis, as NM. 
 
 (b) When the cutting plane 
 makes with the axis an angle 
 less than B VC (the semi-angle 
 of the cone), it plunges contin- 
 ually deeper and deeper into 
 the cone and never comes out 
 on the other side (the cone is 
 supposed to be indefinitely 
 prolonged). The section in 
 this case is an hyperbola, GHK. 
 If the plane of the section be 
 produced upward, however, it 
 encounters the "cone pro- 
 duced," cutting out from it 
 a second hyperbola, G'H'K', 
 precisely like the original one, 
 
 but turned in the opposite direction. 
 
 The axis of the hyperbola is always reckoned as negative, 
 lying outside of the curve itself : in the figure, it is the line 
 HH'. The centre of the hyperbola is the middle point of this 
 axis, a point also outside of the curve. 
 
 FIG. 102. The Conies. 
 
440] STELLAK PARALLAX. 329 
 
 (c) When the angle made by the cutting plane with the 
 axis is exactly equal to the cone's semi-angle, the plane will 
 be parallel to the side of the cone, and we then get the special 
 case of the parabola, RPO, which forms a partition, so to 
 speak, between the infinite variety of ellipses and hyperbolas 
 which can be cut from a given cone. All parabolas are of the 
 same shape, just as all circles are, differing only in size. The 
 fact is by no means self-evident, and we cannot stop to prove 
 it, but it is true. 
 
 441. Determination of the Parallax of a Star (supplemen- 
 tary to Art. 343). The determination of the parallax of stars 
 had been attempted over and over again from the time of 
 Tycho Brahe down, but without success until, in 1838, Bessel 
 at last demonstrated and measured the parallax of 61 Cygni ; 
 and the next year Henderson, of the Cape of Good Hope, 
 determined that of Alpha Centauri. The operation of measur- 
 ing the parallax of a star is on the whole the most delicate 
 in the whole range of practical Astronomy. Two methods 
 have been used so far, known as the absolute and the differential. 
 
 442. The Absolute Method consists in making the most scru- 
 pulously precise observations of the star's right ascension 
 and declination with the meridian circle at different times 
 through the course of an entire year, applying rigidly all 
 known corrections (for precession, aberration, proper motion, 
 etc.), and then examining the deduced positions. If the star 
 is without parallax, these positions will all agree. If the star 
 has a sensible parallax, they will show, on the other hand, 
 when plotted on a chart, an apparent annual orbital motion of 
 the star in a little ellipse, the major axis of which is twice the 
 star's annual parallax, as can easily be shown. 
 
 Theoretically, the method is perfect ; practically, it seldom 
 gives satisfactory results, because the annual changes of tem- 
 perature and moisture disturb the instrument in such a way 
 
330 APPENDIX. [ 44i 
 
 that the instrumental errors intertwine themselves with the 
 parallax of a star in a manner that defies disentanglement. 
 No process of multiplying observations and taking averages 
 helps the matter very much, because the instrumental errors 
 are themselves periodic annually, just as is the parallax ; 
 still, in a few cases the method has proved successful, as in 
 the case of Alpha Centauri, above cited. 
 
 443. The Differential Method. This, the method which 
 has principally proved successful thus far, consists in meas- 
 uring the annual displacement of the star whose parallax we 
 are seeking, with respect to other small stars near it in appar- 
 ent position (i.e., within a few minutes of arc), but presuma- 
 bly so far beyond as to have no sensible parallax of their own. 
 
 If, for instance, the observer notes the apparent place of an 
 object at no great distance from him with reference to the 
 trees on a distant hill-side, and then moves a few feet one way 
 or the other, he will see that the nearer object shifts its posi- 
 tion with reference to the trees. In the same way, on account 
 of the earth's orbital motion, those stars which are very near 
 the earth appear every year to shift slightly backwards and 
 forwards with respect to those that are far beyond them ; and 
 by measuring the amount of this shift it is possible to deduce 
 approximately the parallax and distance of the nearer stars. 
 
 We say approximately, because the shift thus measured is 
 not really the whole parallax of the nearer star, but only 
 the difference between that parallax and the parallax of the 
 remote objects with which it is compared; so that observa- 
 tions, if accurately made, will always give us for the nearer 
 star a parallax too small, if anything, never too large ; and, 
 as a consequence, the distance of the nearer star determined 
 in this way will come out a little too large, and never too small. 
 
 444. The necessary measurements, if the comparison stars 
 are within a minute or two of arc, may be made with the wire 
 
444] THE SLITLESS SPECTROSCOPE. 331 
 
 micrometer (Art. 415) ; but if the distance exceeds a few min- 
 utes, we must resort to the " heliometer " (see General Astron- 
 omy, Art. 677), with which Bessel first succeeded ; or we may 
 employ photography, which Professor Pritchard at Oxford 
 has recently been doing with remarkable success. 
 
 On the whole, the differential method, notwithstanding the 
 fundamental objection to it, that it never gives us the entire 
 parallax of the star, is at present more trustworthy than the 
 other. 
 
 It is obviously necessary to choose for observation by either 
 method those stars that are presumably near us. The most 
 important indication of nearness in a star is a large proper 
 motion ; brightness, also, is of course confirmatory. Still, 
 neither of these indications is certain. A star which happens 
 to be moving directly towards or from us shows no proper 
 motion at all, however near it may be ; and the faint stars are 
 so very much more numerous than the brighter ones that 
 among their millions it is quite likely that we shall ultimately 
 find individuals which are even nearer than Alpha Centauri. 
 
 445, (Supplementary to Art. 364.) The slitless spectroscope 
 has three great advantages : (1) it saves all the light which 
 comes from the star, much of which in the usual form of the 
 instrument is lost in the jaws of the slit ; (2) by taking advan- 
 tage of the length of a large telescope, it produces a long spec- 
 trum with even a single prism ; (3) and most important of all, 
 it gives on the same plate, and with a single exposure, the 
 spectra of all the many stars (sometimes more than a hun- 
 dred) whose images fall upon the plate. 
 
 On the other hand, the giving up of the slit precludes the 
 usual methods of identifying the lines and measuring their 
 displacements, by actually confronting them with comparison 
 spectra. For instance, it has not yet been found possible to 
 use the slitless spectroscope for determining the absolute 
 motions of the stars in the line of sight. 
 
332 APPENDIX. 
 
 SUGGESTIVE QUESTIONS 
 
 FOR USE IN REVIEWS. 
 
 To many of these questions direct answers will not be 
 found in the book ; but the principles upon which the answers 
 depend have been given, and the student will have to use his 
 own thinking in order to make the proper application. 
 
 1. What point in the celestial sphere has both its right ascension 
 and declination zero ? 
 
 2. What angle does the (celestial) equator make with the horizon 
 at this place ? 
 
 3. Name the (fourteen) principal points in the celestial sphere 
 (zenith, etc.). 
 
 4. What important circles in the heavens have no correlatives on 
 the surface of the earth ? 
 
 5. What constellation of the zodiac rises at sunset to-day, and 
 which one is then on the meridian ? (Use the star-maps.) 
 
 6. If Vega comes to the meridian at 8 o'clock to-night, at what 
 time (approximately) will it transit eight days hence? 
 
 7. What bright star can I observe on the meridian between 3 and 
 4 P.M., in the middle of August? (See star-maps.) 
 
 8. Would twilight be longer or shorter at the summit of the Peak 
 of Teneriffe than at its base ? Why ? 
 
 9. The declination of Vega is 38 41' ; does it pass the meridian 
 north of your zenith, or south of it? 
 
 10. What are the right ascension and declination of the north pole 
 of the ecliptic ? 
 
 11. What are the longitude and latitude (celestial) of the north 
 celestial pole (the one near the Pole-star) ? 
 
SUGGESTIVE QUESTIONS. 333 
 
 12. Can the sun ever be directly overhead where you live ? If not, 
 why not ? 
 
 13. What is the zenith distance of the sun at noon on June 22d in 
 New York City (lat. 40 42') ? 
 
 14. What are the greatest and least angles made by the ecliptic 
 with the horizon at New York ? Why does the angle vary ? 
 
 15. If the obliquity of the ecliptic were 30, how wide would the 
 temperate zone be? How wide if the obliquity were 50? What 
 must the obliquity be to make the two temperate zones each as wide 
 as the torrid zone V 
 
 16. Does the equinox always occur on the same days of March and 
 September ? If not, why not ; and how much c*an the date vary ? 
 
 17. Was the sun's declination at noon on March 10th, 1887, pre- 
 cisely the same as on the same date in 1889 ? 
 
 18. In what season of the year is New Year's Day in Chili? 
 
 19. When the sun is in the constellation Taurus, in what sign of 
 the zodiac is he ? 
 
 20. In what constellation is the sun when he is vertically over the 
 tropic of Cancer ? Near what star? (See star-map.) 
 
 21. When are day and night most unequal? 
 
 22. In what part of the earth are the days longest on March 20th ? 
 On June 20th ? On Dec. 20th ? 
 
 23. Why is it warmest in the United States when the earth is 
 farthest from the sun? 
 
 24. What will be the Russian date corresponding to Feb. 28th, 
 1900, of our calendar ? To May 28th ? 
 
 25. Why are the intervals from sunrise to noon and from noon to 
 sunset usually unequal as given in the almanac ? (For example, see 
 Feb. 20th and Nov. 20th.) 
 
 26. If the earth were to shrink to half its present diameter, what 
 would be its mean density ? 
 
 27. Is it absolutely necessary, as often stated, to know the diameter 
 of the earth in order to find the distance of the sun from the earth ? 
 
 28. How will a projectile fired horizontally on the earth deviate 
 from the line it would follow if the earth did not rotate on its axis ? 
 
 29. If the earth were to contract in diameter, how would the weight 
 of bodies on its surface be affected ? 
 
 30. What keeps up the speed of the earth in its motion around the 
 sun? 
 
334 APPENDIX. 
 
 31. Why is the sidereal month shorter than the synodic? 
 
 32. Does the moon rise every day of the month ? 
 
 33. If the moon rises at 11.45 Tuesday night, when will it rise 
 next? 
 
 34. How many times does the moon turn on its axis in a year ? 
 
 35. What determines the direction of the horns of the moon ? 
 
 36. Does the earth rise and set for an observer on the moon ? If so, 
 at what intervals ? 
 
 37. How do we know that the moon is not self-luminous ? 
 
 38. How do we know that there is no water on the moon ? 
 
 39. How much information does the spectroscope give us about the 
 moon ? 
 
 40. What conditions must concur to produce a lunar eclipse ? 
 
 41. Can an eclipse of the rnoon occur in the daytime ? 
 
 42. Why can there not be an annular eclipse of the moon ? 
 
 43. Which are most frequent at New York, solar eclipses or lunar? 
 
 44. Can an occultation of Venus by the moon occur during a lunar 
 eclipse ? Would an occultation of Jupiter be possible under the same 
 circumstances ? 
 
 45. Which of the heavenly bodies are not self-luminous ? 
 
 46. When is a planet an evening star ? 
 
 47. What planets have synodic periods longer than their sidereal 
 periods ? 
 
 48. When a planet is at its least distance from the earth, what is 
 its apparent motion in right ascension ? 
 
 49. A planet is seen 120 distant from the sun ; is it an inferior or 
 a superior planet ? 
 
 50. Can there be a transit of Mars across the sun's disc ? 
 
 51. When Jupiter is visible in the evening, do the shadows of the 
 satellites precede or follow the satellites themselves as they cross the 
 planet's disc ? 
 
 52. What would be the length of the month if the moon were four 
 times as far away as now ? (Apply Kepler's third law.) 
 
 53. What is the distance from the sun of an asteroid which has a 
 period of eight years ? (Kepler's third law.) 
 
 54. Upon what circumstances does the apparent length of a comet's 
 tail depend ? 
 
 55. How can the distance of a meteor from the observer, and its 
 height above the earth, be determined ? 
 
SUGGESTIVE QUESTIONS. 335 
 
 56. What heavenly bodies are not included in the solar system? 
 
 57. How do we know tiiat stars are suns ? How much is meant by 
 the assertion that they are ? 
 
 58. Suppose that in attempting to measure the parallax of a bright 
 star by the differential method (Art. 443) it should turn out that the 
 small star taken as the point to measure from, and supposed to be far 
 beyond the bright one, should really prove to be nearer. How would 
 the measures show the fact ? 
 
 59. If Alpha Centauri were to travel straight towards the sun with 
 a uniform velocity equal to that of the earth in its orbit, how long 
 would the journey take, on the assumption that the star's parallax is 
 0".75? 
 
 60. If Altair were ten times as distant from us, what would be its 
 apparent "magnitude"? What, if it were a thousand times as 
 remote? (See Arts. 436, 437; and remember that the apparent 
 brightness varies inversely with the square of the distance.) 
 
TABLES OF ASTRONOMICAL DATA. 
 
TABLES. 339 
 
 TABLE I. ASTRONOMICAL CONSTANTS. 
 TIME CONSTANTS. 
 
 The sidereal day = 23 h 56 m 4 8 .090 of mean solar time. 
 The mean solar day = 24 h 3 m 56 s . 556 of sidereal time. 
 
 To reduce a time interval expressed in units of mean solar 
 time to units of sidereal time, multiply by 1.00273791; Log. of 
 0.00273791 =[7.4374191]. 
 
 To reduce a time interval expressed in units of sidereal 
 time to units of mean solar time, multiply by 0.99726957 = 
 (1 - 0.00273043) ; Log. 0.00273043 = [7.4362316]. 
 
 Tropical year (Leverrier, reduced to 1900), 365 d 5 h 48 m 45 8 .51. 
 Sidereal year " " " 365 6 9 8.97. 
 
 Anomalistic year " " 365 6 13 48.09. 
 
 Mean synodical month (new moon to new), 29 d 12 h 44 m 2 s . 684. 
 
 Sidereal month, 27 7 43 11.545. 
 
 Tropical month (equinox to equinox) , .27 7 43 4.68. 
 Anomalistic month (perigee to perigee), . 27 13 18 37.44. 
 Nodical month (node to node), . . 27 5 5 35.81. 
 
 Obliquity of the ecliptic (Leverrier), 
 
 23 27' 08".0 - 0".4757 (t - 1900). 
 
 Constant of precession (Struve), 
 
 50".264 + 0".000227 (t -1900). 
 
 Constant of nutation (Peters), 9".223. 
 
 Constant of aberration (Nyr6n), 20".492. 
 
 Equatorial semi-diameter of the earth (Clarke's spheroid of 
 1878) , 20 926 202 feet = 6 378 190 metres = 3963.296 miles . 
 
 Polar semi-diameter, 
 
 20 854 895 feet = 6 356 456 metres = 3949.790 mUefl . 
 Ellipticity, or Polar Compression, 29 s. 46 - 
 
340 
 
 APPENDIX. 
 
 i a 
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 i. 
 
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 gg 
 
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 OC OO t- CO 
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 Ills 
 
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 111 
 
 13 
 
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TABLES. 
 
 341 
 
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 Sidereal Period. 
 
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 rH rH tO CO "^ CO rH 
 
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 tL t~to oow 110 <NOO 
 
 5. rH i-l CO t- O rH 
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 CT^rHC^^rH ScoS 10 3! 
 
 rHt~<N<NtOt- WCOtOrH rH 
 rHIM^tOrHCJl C^-^OOCO tO 
 
 S 8 
 
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 mi i 
 
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 5 ^s^igss 
 
 SliSil SSgi 
 
 
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 Tt< fN O GO rH r-( j CQ 
 
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 Discovery. 
 
 1 
 
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 ' hj = 1 fe 
 
 3 ^ 1 
 
 1 I J .- 1 = 
 
 ft - s 1 fi I s w : 1 
 
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 1 
 
 gg 8, B i 1 
 
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 C0^.0t0l-C0 rlweOTK J?5 
 
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 f <0 ^f 
 
342 
 
 APPENDIX. 
 
 TABLE IV. THE PRINCIPAL VARIABLE STARS. 
 
 A selection from S. C. Chandler's catalogue of 225 variables (Astronomical Journal, 
 Sept., 1888), containing such as, at the maximum, are easily visible to the naked eye, have 
 a range of variation exceeding half a magnitude, and can be seen in the United States. 
 
 1 
 
 NAME. 
 
 Place, 1900. 
 
 Range of 
 Variation. 
 
 Period (days). 
 
 Remarks. 
 
 a 
 
 1 
 
 
 
 h m 
 
 
 
 
 
 1 
 
 R Andromedae 
 
 18.8 
 
 + 38 1' 
 
 5.6 to 13 
 
 411.2 
 
 (Mira. Varia- 
 
 2 
 
 oCeti. . . . 
 
 2 14.3 
 
 - 3 26 
 
 1.7 9.5 
 
 331.3363 
 
 | tions in length 
 
 3 
 4 
 
 p Persei . . . 
 /3 Persei . . . 
 
 2 58.7 
 3 1.6 
 
 + 38 27 
 + 40 34 
 
 3.4 4.2 
 2.3 3.5 
 
 33 
 2* 20h 48* 55'.43 
 
 ( of period. 
 ( Algol. Period 
 \ now shortening. 
 
 5 
 
 ATauri . . . 
 
 3 55.1 
 
 + 12 12 
 
 3.4 4.2 
 
 3d 22> 52 m 12" 
 
 ( Algol type, but 
 
 6 
 
 Aurigae . . 
 
 4 54.8 
 
 + 43 41 
 
 3 4.5 
 
 Irregular 
 
 \ irregular 
 
 7 
 
 a Orionis . . 
 
 5 49.7 
 
 + 7 23 
 
 1 1.6 
 
 196 ? 
 
 Irregular. 
 
 8 
 
 i) Geminorum . 
 
 6 8.8 
 
 + 22 32 
 
 3.2 4.2 
 
 229.1 
 
 
 9 
 
 Geminorum . 
 
 6 58.2 
 
 + 20 43 
 
 3.7 4.5 
 
 10* 3h 4im 3Q8 
 
 
 10 
 
 RCanisMaj. . 
 
 7 14.9 
 
 -16 12 
 
 5.9 6.7 
 
 Id 3h 15"" 55" 
 
 Algol type. 
 
 11 
 
 R Leonis . . 
 
 9 42.2 
 
 + 11 54 
 
 5.2 10 
 
 312.87 
 
 
 12 
 
 U Hydras . . 
 
 10 32.6 
 
 -12 52 
 
 4.5 6.3 
 
 194.65 
 
 
 13 
 
 R Hydrse . . 
 
 13 24.2 
 
 -22 46 
 
 3.5 9.7 
 
 496.91 
 
 Period short'ing 
 
 14 
 
 fi Librae . . . 
 
 14 55.6 
 
 -87 
 
 5.0 6.2 
 
 2d 7h 5im 22^.8 
 
 Algol type. 
 
 15 
 
 R Coronse . . 
 
 15 44.4 
 
 + 28 28 
 
 5.8 13 
 
 Irregular 
 
 
 16 
 
 R Serpentis . 
 
 15 46.1 
 
 + 15 26 
 
 5.6 13 
 
 357.6 
 
 
 17 
 
 a Herculis . . 
 
 17 10.1 
 
 + 14 30 
 
 3.1 3.9 
 
 Two or three mon 
 
 ths, but very irreg. 
 
 18 
 
 U Ophiuchi . 
 
 17 11.5 
 
 + 1 19 
 
 6.0 6.7 
 
 2 0h 7m 418.6 
 
 
 19 
 
 X Sagittarii . 
 
 17 41.3 
 
 -27 48 
 
 4 6 
 
 7.01185 
 
 
 20 
 
 W Sagittarii . 
 
 17 58.6 
 
 -29 35 
 
 5 6.5 
 
 7.59445 
 
 
 21 
 
 R Scuti . . . 
 
 18 42.1 
 
 - 5 49 
 
 4.7 9 
 
 71.10 
 
 ( Secondary mini- 
 
 22 
 
 /SLyrae . . . 
 
 18 46.4 
 
 + 33 15 
 
 3.4 4.5 
 
 12 d 21> 46- 58'.3 
 
 J mum about mid- 
 
 23 
 
 X Cygni . . . 
 
 19 46.7 
 
 + 32 40 
 
 4.0 13.5 
 
 406.045 
 
 ( way. 
 Period length'ng 
 
 24 
 
 7) Aquilro . . 
 
 19 47.4 
 
 + 45 
 
 3.5 4.7 
 
 7d 4h i4m o.0 
 
 
 25 
 
 S Sagittse . . 
 
 19 51.4 
 
 + 16 22 
 
 5.6 6.4 
 
 8* 9> ll m 
 
 
 26 
 
 T Vulpeculaa . 
 
 20 47.2 
 
 + 27 52 
 
 5.5 6.5 
 
 4d iQh 29"> 
 
 
 27 
 
 TCephei . . 
 
 21 8.2 
 
 + 68 5 
 
 5.6 9.9 
 
 383.20 
 
 
 28 
 
 /u. Cephei . . 
 
 21 40.4 
 
 + 58 19 
 
 4 5 
 
 432? 
 
 
 29 
 
 6 Cephei . . 
 
 22 25.4 
 
 + 57 54 
 
 3.7 4.9 
 
 5* 8> 47" 39.97 
 
 
 30 
 
 pPegasi. . . 
 
 22 58.9 
 
 + 27 32 
 
 2.2 2.7 
 
 Irregular 
 
 
 31 
 
 R Cassiopeiae . 
 
 23 53.3 
 
 + 50 50 
 
 4.8 12 
 
 429.00 
 
 
TABLES. 
 
 343 
 
 TABLE V. STELLAR PARALLAXES AND PROPER MOTIONS. 
 
 (From Oudeman's Table, Ast. Nach., Aug., 1889.) 
 
 No. 
 
 NAME. 
 
 Mag. 
 
 Proper Motion. 
 
 Annual 
 Parallax. 
 
 Distance 
 Light Years. 
 
 1 
 
 a Centauri . 
 
 0.7 
 
 3".67 
 
 0".75 
 
 4 
 
 2 
 
 LI. 21185 . . 
 
 6.9 
 
 4.75 
 
 0.50 
 
 6.5 
 
 3 
 
 61 Cygni . . 
 
 5.1 
 
 5.16 
 
 0.40 
 
 8 
 
 4 
 
 Sirius . . . 
 
 -1.4 
 
 1.31 
 
 0.39 
 
 8.3 
 
 5 
 
 22398. . . 
 
 8.2 
 
 2.40 
 
 0.35 
 
 9.3 
 
 6 
 
 LI. 9352 . . 
 
 7.5 
 
 6.96 
 
 0.28 
 
 12 
 
 7 
 
 Procyon . . 
 
 0.5 
 
 1.25 
 
 0.27 
 
 12.3 
 
 8 
 
 LI. 21258 . . 
 
 8.5 
 
 4.40 
 
 0.26 
 
 12.5 
 
 9 
 
 Altair . . . 
 
 1.0 
 
 0.65 
 
 0.20 
 
 16.3 
 
 10 
 
 e Indi . . . 
 
 5.2 
 
 4.60 
 
 0.20 
 
 16.3 
 
 11 
 
 o 2 Eridani 
 
 4.5 
 
 4.05 
 
 0.19 
 
 17 
 
 12 
 
 Vega . . . 
 
 0.2 
 
 0.36 
 
 0.16 
 
 20 
 
 13 
 
 /? Cassiopeiae, 
 
 2.4 
 
 0.55 
 
 0.16 
 
 20 
 
 14 
 
 70 Ophiuclii . 
 
 4.1 
 
 1.13 
 
 0.15 
 
 21 
 
 15 
 
 e Eridani . . 
 
 4.4 
 
 3.03 
 
 0.14 
 
 23 
 
 16 
 
 Aldebaran 
 
 1.0 
 
 0.19 
 
 0.12 
 
 27 
 
 17 
 
 Capella . . 
 
 0.2 
 
 0.43 
 
 0.11 
 
 29 
 
 18 
 
 Kegulus . . 
 
 1.4 
 
 0.27 
 
 0.10 
 
 32 
 
 19 
 
 Polaris . . 
 
 2.1 
 
 0.05 
 
 0.07 
 
 47 
 
 These are not all the stars upon Oudeman's list which are given as hav- 
 ing parallaxes exceeding 0".l ; but they are probably the best determined 
 ones. 
 
THE GEEEK ALPHABET. 
 
 Letters. 
 
 Name. 
 
 Letters. 
 
 Name. 
 
 A, a, 
 
 Alpha. 
 
 I, i, 
 
 Iota. 
 
 B, ft 
 
 Beta. 
 
 K, K, 
 
 Kappa. 
 
 r, y, 
 
 Gamma. 
 
 A, X, 
 
 Lambda. 
 
 A, 8, 
 
 Delta. 
 
 M,.JA, 
 
 Mu. 
 
 E, c, 
 
 Epsilon. 
 
 N, v, 
 
 Nu. 
 
 z, t 
 
 Zeta. 
 
 H,*, 
 
 Xi. 
 
 H, 77, 
 
 Eta. 
 
 0,o, 
 
 Omicron. 
 
 , 0, *, 
 
 Theta. 
 
 H, 7T, TO, 
 
 Pi. 
 
 Letters. Name. 
 
 P, P) & Kho. 
 
 2, o-, ?, Sigma. 
 
 T, T, Tau. 
 
 Y, v, Upsilon 
 
 $, ^>, Phi. 
 
 X, x , Chi. 
 
 ^, \[r, Psi. 
 
 O, w, Omega. 
 
 MISCELLANEOUS SYMBOLS. 
 
 6 , Conjunction. A.R., or a, Eight Ascension. 
 
 D, Quadrature. Decl., or 8, Declination. 
 
 <?, Opposition. A, Longitude (Celestial). 
 
 &, Ascending Node. /?, Latitude (Celestial). 
 
 5? Descending Node. <, Latitude (Terrestrial). 
 
 <o, Angle between line of .nodes and line of apsides j also 
 the obliquity of the ecliptic. 
 
 344 
 
INDEX 
 
INDEX. 
 
 [All references, unless expressly stated to the contrary, are to articles, not to pages.] 
 
 A. 
 
 Aberration, of light, 435 ; determining 
 distance of sun, 436. 
 
 Absolute scale of star magnitudes, 346. 
 
 Acceleration of rotation at the sun's 
 equator, 163. 
 
 Achromatic telescope, 406, 407. 
 
 ADAMS, J. C. (and LEVERRIBR), dis- 
 covery of Neptune, 283; orbit of the 
 Leonids, 327. 
 
 Aerolite. See Meteorite. 
 
 Age of the sun and planetary system, 
 193, 397-399. 
 
 Albedo denned, 149, 235 ; of the moon 
 (Zolluer), 149; of the planets (Z611- 
 ner), 242, 247, 253, 268, 276, 281, 285. 
 
 Algol, or 3 Persei, 40, 351, 358, 360. 
 
 Alphabet, the Greek, page 344. 
 
 Altitude defined, 11; parallels of, 11; 
 of the pole equals latitude, 80. 
 
 Andromeda, constellation of, 35 ; neb- 
 ula of, 377, 378, 392, note; nebula of, 
 temporary star in, 355. 
 
 Andromedes, or Bielids, 312, 326. 
 
 Angular measurements, units of, 8. 
 
 Annual or heliocentric parallax de- 
 fined, 343; methods of determining 
 it for the stars by observation, 441- 
 444. 
 
 Annular eclipses, 201. 
 
 Anomalistic year, 127. 
 
 Anomalous phenomena in comets, 308 
 
 Apex of the sun's way, 342. 
 
 Aphelion defined, 120. 
 
 Apogee defined, 137. 
 
 Apparent motion of a planet, 225-229 ; 
 motion of the sun, 115-117; solar 
 time, 88. 
 
 Apsides, line of, defined, 120, 137; of 
 the moon's orbit, 137. 
 
 Aquarius, 78, 118. 
 
 Aquila, 71. 
 
 Arcs of meridian, measurement of, 105, 
 110. 
 
 Areas, equal, law of, 121, 137, 220. 
 
 Argo Navis, 51. 
 
 Ariel, a satellite of Uranus, 282. 
 
 Aries, first of, defined, 17; constella- 
 tion of, 38, 118. 
 
 Asteroids, or minor planets, 260-263. 
 
 Astronomical constants, table of, page 
 339; day, beginning of, 90; symbols, 
 page 344 ; unit, see Distance of the 
 sun. 
 
 Astronomy, utility of, 1. 
 
 Atmosphere of the moon, 148 ; of Mars, 
 253 ; of Mercury, 242 ; of Venus, 248. 
 
 Attraction of gravitation, its law, 
 220, 221. 
 
 Auriga, 41. 
 
 Axis of the earth, 13, 109; its per- 
 manence, 109. 
 
 Azimuth defined, 11. 
 
 B. 
 
 BAYER, his system of lettering the 
 stars, 24. 
 
 Beginning of the century (Ceres dis- 
 covered) , 260 ; of the day, 90, 98. 
 
 BESSEL, dark stars, 350, 360; first 
 measures stellar parallax, 441, 444. 
 347 , 
 
348 
 
 INDEX. 
 
 [All references, unless expressly stated to the contrary, are to articles, not to pages.} 
 
 Bethlehem, the star of, 355. 
 
 BIKLA'S comet, 311, 312. 
 
 Bielids, or Andromedes, 312, 324, 328. 
 
 Binary stars, 368-371. 
 
 Bissextile year, 129. 
 
 BODE'S law, 219. 
 
 BOND, W. C., discovery cf the " gauze 
 ring" of Saturn, 277; discovery of 
 Hyperion, 280. 
 
 Bootes, 59. 
 
 BREDICHIN, his theory of comets' tails, 
 307. 
 
 Brightness of comets, 291 ; of meteors, 
 318; of stars, and causes of differ- 
 ence, 345-350. 
 
 BROOKS, his comets, 290, 299. 
 
 CAESAR, JULIUS, reformation of the 
 
 calendar, 129. 
 Calendar, the, 128-130. 
 Calory, the, denned, 187. 
 Camelopardus, 31. 
 Canals of Mars, 256. 
 Cancer, 52, 118. 
 Canes Venatici, 58. 
 Canis Major, 49. 
 Canis Minor, 48. 
 Capricornus, 73, 118. 
 Capture theory of comets, 298. 
 Cardinal points denned, 16. 
 CARRINGTON, discovery of the peculiar 
 
 law of the sun's rotation, 163. 
 CASSINI, J. D., discovers division in 
 
 Saturn's ring, 277. 
 Cassiopeia, 28. 
 Catalogues of stars, 335. 
 Celestial globe described, 400, 401; 
 
 sphere, infinite, 6. 
 Centaurus, 62. 
 
 Centrifugal force due to earth's rota- 
 tion, 111. 
 Cepheus, 29. 
 
 Ceres, the first of the asteroids, 260. 
 Cetus, 39. 
 CHANDLER, S. C., identification of 
 
 Lexell's comet, 299; his catalogue 
 
 of variable stars, 361. 
 
 ^ 
 
 Changes, gradual, in the brightness 
 of stars, 353; on the surface of the 
 moon, 155. 
 
 Chemical constitution of the sun, 175, 
 176. 
 
 Chromosphere of the sun, 180, 194; 
 and prominences made visible by the 
 spectroscope, 182. 
 
 Chronograph, the, 417. 
 
 Chronometer, the, 417 ; longitude by, 
 96, 427. 
 
 Circle, meridian, the, 81, 99, 418. 
 
 Circles, hour, defined, 15. 
 
 Circumpolar stars, latitude by, 81. 
 
 Civil day and astronomical day, 90. 
 
 Classification of the planets, Hum- 
 boldt, 217; of stellar spectra, Secchi, 
 363 ; of variable stars, 352. 
 
 Clock, the astronomical, 417; its rate 
 and error, 92, 93, 417. 
 
 Clusters of stars, 376. 
 
 Columba, 45. 
 
 Colures defined, 117. 
 
 Coma Berenices, 57. 
 
 Comet, Biela's, 311, 312; Donati's, 289; 
 Encke's, 293, 311; Lexell-Brooks, 
 299; Halley's, 293; of 1882, 313, 
 314. 
 
 Comets, anomalous phenomena shown 
 by, 308; attendant companions, 314; 
 brightness and visibility, 291; cap- 
 ture theory of their origin, 298; cen- 
 tral stripe in tail, 308; connection 
 with meteors, 327-329; constitution 
 of, 300; danger fjjpm, 310; density 
 of, 303; designation and nomencla- 
 ture, 290; dimensions of, 301 ; elliptic, 
 293, 297 ; envelopes in head, 305; fam- 
 ilies of, 297; formation of the tail, 
 306; their light and spectra, 304; 
 mass of, 302; nature of, 309; num- 
 ber of, 289; orbits of, 292, 293; peri- 
 odic, their origin, 297, 298; sheath 
 of comet of 1882, 314; tails or trains, 
 300, 306-308; visitors to the solar 
 system, 296. 
 
 Comet-groups, 294. 
 
 Conic sections, the, 440. 
 
 Conjunction defined, 132, 227. 
 
INDEX. 
 
 849 
 
 [All references, unless expressly stated to the contrary, are to articles, not to pages.] 
 
 Constant, solar, defined and discussed, 
 
 187. 
 
 Constellations, the, 4, 333. (For de- 
 tailed description, see Chap. II.) 
 Constitution of comets, 300; of the 
 
 sun, 194. 
 Contraction of a comet nearing the 
 
 sun, 301; of the sun, Helmholtz's 
 
 theory, 192, 396, 397. 
 COPERNICUS, rotation of the earth, 
 
 106 ; his system, 230. 
 Corona Borealis, 60. 
 Corona, the solar, 183-185. 
 Coronium, hypothetical element of the 
 
 corona, 184. 
 Correction or error of a timepiece, 92, 
 
 427. 
 
 Corvus, 55. 
 Cosmogony, 389-396. 
 Crater, 55. 
 Cygnus, 68. 
 
 D. 
 
 Dark stars, 350, 360. 
 
 DARWIN, G. H., demonstrates that a 
 meteoric swarm behaves like a gas- 
 eous nebula, 394. 
 
 Day, beginning of, 98 ; civil and astro- 
 nomical, 90. 
 
 Decimation defined, 14; determina- 
 tion of, 99, 100 ; parallels of, 14. 
 
 Degrees of latitude, length of, 110. 
 
 Deimos, a satellite of Mars, 258. 
 
 DE L'ISLE, his method of observing a 
 transit of Venus, 437, 438. 
 
 Delphinus, 74. 
 
 Density of comets, 303; of the earth, 
 113; of the moon, 143; of the sun, 
 161. 
 
 Designation and nomenclature of 
 comets, 290; and nomenclature of 
 the stars, 24, 334 ; and nomenclature 
 of variable stars, 361. 
 
 Diameter of a planet, how determined, 
 232. 
 
 Difference of brightness in stars, its 
 causes, 350. 
 
 Diffraction, telescopic, 408. 
 
 Diffraction grating, the, 171, note. 
 
 Dione, a satellite of Saturn, 280. 
 
 Disc, spurious, of a star, 408. 
 
 Displacement of spectrum lines by 
 motion in line of sight, 179, 341, 373. 
 
 Distance of a body as depending on 
 its parallax, 140; of the moon, 141; 
 of the nebulae, 382; of the planets 
 from the sun, Table II., page 340; of 
 the stars, 343, 441-444; of the sun, 
 by aberration of light, 436; of the 
 sun, by the equation of light, 434; 
 of the sun, by its parallax, 437. 
 
 Distribution of the nebulae, 382; of 
 the stars in the heavens, 384; of sun 
 spots, 169. 
 
 Diurnal or geocentric parallax defined, 
 139 ; rotation of the heavens, 12. 
 
 DOPPLER'S principle, 179. 
 
 Double stars, 366, 367; optical and 
 physical, distinguished, 367. 
 
 Draco, 30. 
 
 DRAPER, H., photograph of the nebu- 
 la of Orion, 378 ; photographs of star 
 spectra, 364. 
 
 Duration of solar eclipses, 203 ; prob- 
 able, of the solar system, 193, 397- 
 399. 
 
 K. 
 
 Earth, the, astronomical facts relating 
 to it, 102; its density, 113; dimen- 
 sions of, 105, 110, Table I.; ellip- 
 ticity or oblateness determined, 110; 
 its interior constitution, 114; mass, 
 113; orbital motion of, 115-122,428; 
 its orbit, changes in, 122; its rota- 
 tion, invariability of, 108; its rota- 
 tion, proofs of, 107; shadow of, its 
 dimensions, 196; surface area and 
 volume, 112; velocity in its orbit, 
 158. 
 
 Earth-shine on the moon, 147. 
 
 Ebb defined, 210. 
 
 Eccentricity of the earth's orbit, 119; 
 of an ellipse defined, 119, 429. 
 
 Eclipses, frequency of, 206; of Jupi- 
 ter's satellites, 273; lunar, 197-199; 
 Oppolzer's canon of, 205 ; number in 
 a year, 206; recurrence of, 207; so- 
 
350 
 
 INDEX. 
 
 [All references, unless expressly stated to the contrary, are to articles, not to pages.] 
 
 lar, duration'of , 203 ; solar, phenom- 
 ena of, 204; solar, varieties of, total 
 
 annular, and partial, 201, 202. 
 Ecliptic, the, defined, 116; obliquity 
 
 of, 116; poles of, 117. 
 Elements, chemical, recognized in the 
 
 stars, 362; chemical, recognized in 
 
 the sun, 176; of the planets' orbits 
 
 Table II., page 340. 
 Ellipse, the, defined and described, 
 
 429, 439, 440. 
 
 Elliptic comets, 292, 293. 
 Ellipticity, or oblateness of the earth, 
 
 110. 
 
 Elongation defined, 132, 227. 
 Enceladus, a satellite of Saturn, 280. 
 ENCKE'S comet, 293, 311. 
 
 Energy 
 189. 
 
 of the solar radiation, 188, 
 
 Envelopes in the head of a comet, 305, 
 
 314. 
 
 Equation of light, 431^33 ; of time, 89. 
 Equator, celestial or equinoctial, de- 
 
 fined, 14. 
 Equatorial acceleration of the sun's 
 
 surface rotation, 163; instrument, 
 
 the, 414; use in determining the 
 
 place of a heavenly body, 100. 
 Equinoctial, the, or celestial equator, 
 
 defined, 14. 
 
 Equinox, vernal, defined, 17, 116. 
 Equinoxes, precession of, 125, 126. 
 Equuleus, 75. 
 Eridanus, 44. 
 Error or correction of a timepiece, 92, 
 
 93, 417. 
 
 Eruptive prominences on the sun, 182. 
 Establishment of a port, 210. 
 Eye-pieces, telescopic, various forms, 
 
 409. 
 
 Faculae, solar, 165. 
 
 Families of comets, 297. 
 
 FAYE, depth of sun spots, 168 ; modi- 
 
 fication of the nebular hypothesis, 
 
 393. 
 
 Filar micrometer, the, 415. 
 Flood tide, 210. 
 
 Form of the earth's orbit determined 
 428. 
 
 FOUCAULT, his pendulum experiment, 
 107. 
 
 FRAUNHOFER lines in the solar spec- 
 trum, 175, note. 
 
 Frequency of eclipses, 206. 
 
 O. 
 
 Galaxy, the, 383. 
 
 GALILEO, his discovery of Jupiter's 
 satellites, 272; discovery of phases 
 of Venus, 247 ; discovery of Saturn's 
 ring, 277; discovery of sun spots, 
 169; his telescope, 402. 
 
 Gemination of the canals of Mars, 256. 
 
 Gemini, 47, 118. 
 
 Genesis of the planetary system, 390, 
 391. 
 
 Geocentric parallax, 139. 
 
 Gibbous phase defined, 146. 
 
 Globe, the celestial, described, 400, 401. 
 
 Grating, diffraction, 171, note. 
 
 Gravitation, 221, 222. 
 
 Gravity, at the moon's surface, 143; 
 at the pole and equator of the earth, 
 111 ; at the sun's surface, 161; super- 
 ficial, of a planet, how determined, 
 233. 
 
 Greek alphabet, the, page 344. 
 
 Gregorian calendar, the, 130. 
 
 Groups, cometary, 294. 
 
 Grus, 79. 
 
 Gyroscope illustrating the cause of the 
 seasons, 123. 
 
 H. 
 
 Habitability of Mars, 259. 
 
 HALL, A., discovery of the satellites of 
 Mars, 258. 
 
 HALLEY discovers the proper motion 
 of stars, 339 ; his periodic comet, 293. 
 
 Harmonic law, Kepler's, 220, 430. 
 
 Harvest and hunter's moons, the, 136. 
 
 Heat of meteors, its explanation, 318 ; 
 from the moon, 150; from the stars, 
 348, note; of the sun, its constancy, 
 191; of the sun, its intensity, 190; 
 of the sun, its maintenance, 192; of 
 the sun, its quantity, 187, 189.- 
 
INDEX. 
 
 351 
 
 [All references, unless expressly stated to the contrary, are to articles, not 
 
 Heavenly bodies defined and enumer- 
 ated, 2; apparent place of, 7. 
 
 Heliocentric, or annual parallax, de- 
 fined, 139, 343. 
 
 Helium, hypothetical element in the 
 sun, 181. 
 
 HELMHOLTZ, his theory of the sun's 
 heat, 192. 
 
 Hercules, 66. 
 
 HERSCHEL, SIR J., illustration of the 
 solar system, 238; his names for the 
 satellites of Saturn and Uranus, 280, 
 282. 
 
 HERSCHEL, SIR W., discovery of Ura- 
 nus, 281 ; his great telescope, 412 ; re- 
 lation between nebulae and stars, 395. 
 
 HERSCHELS, the, their star-gauges, 
 384. 
 
 HIPPARCHUS, 120, 125, 335, 345. 
 
 Horizon defined, rational and visible, 
 10. 
 
 Horizontal parallax, 139. 
 
 Hour-angle defined, 422. 
 
 Hour-Circles defined, 15. 
 
 Hourly number of meteors, 321. 
 
 HUGGINS, W., observes spectrum of 
 Mars, 253; observes spectrum of 
 Mercury, 242; observes spectrum 
 of nebulse, 380; observes spectrum 
 of stars, 362; observes spectrum of 
 temporary star of 1866, 355 ; spectro- 
 scopic measures of star motions, 341. 
 
 HUMSOLDT, his classification of the 
 planets, 217. 
 
 Hunter's moon, the, 136. 
 
 HUYGHENS, his discovery of Saturn's 
 ring, 277; discovery of Titan, 280; 
 invention of the pendulum clock, 
 417. 
 
 Hydra, 55. 
 
 Hyperbola, the, 439, 440. 
 
 Hyperion, a satellite of Saturn, 280. 
 
 lapetus, the remotest satellite of Sat- 
 urn, 280. 
 
 Identification of the orbits of certain 
 comets and meteors, 328. 
 
 Illuminating power of a telescope, 
 
 405. 
 
 Illumination of the moon's disc dur- 
 ing a lunar eclipse, 198. 
 Illustration of the proportions of the 
 
 solar system, 238. 
 Influence of the moon on the earth, 
 
 151 ; of sun spots on the earth, 170. 
 Intensity of the sun's heat, 189-190; 
 
 of the sun's light, 186. 
 Intra-Mercurian planets, 264. 
 Invariability of the earth's rotation, 
 
 108; of the length of the year and 
 
 distance from the sun, 122. 
 Iron in comets, 314; in meteorites, 
 
 316; in stars, 362; in the sun, 175. 
 
 Julian calendar, the, 129. 
 
 Juno, the third asteroid, 260. 
 
 Jupiter (the planet) , 266-271 ; his belts, 
 red spot, and other markings, 268, 
 271; his rotation, 270; his satellites, 
 and their eclipses, 272, 273. 
 
 Jupiter's family of comets, 297. 
 
 K. 
 
 KANT, a proposer of the nebular hy- 
 pothesis, 391. 
 
 KEPLER, his laws of planetary motion, 
 121, 220, 430. 
 
 KIRCHHOFF, fundamental principles of 
 spectrum analysis, 173. 
 
 I*. 
 
 Lacerta, 76. 
 
 LANGLEY, S. P., his value of the solar 
 constant, 188. 
 
 LAPLACE, his capture theory of comets, 
 298 ; his nebular hypothesis, 392, 393; 
 stability of the solar system, 288*. 
 
 LASSELL, his discovery of Ariel and 
 Umbriel, 282; his discovery of the 
 satellite of Neptune, 286. 
 
 Latitude (celestial) defined, 20; (ter- 
 restrial) defined, 80; length of de- 
 grees, 110 ; methods of determining, 
 81, 424,426; variations of, 109. 
 
 Law, Bode's, 219 ; of the earth's orbital 
 motion, 121 ; of gravitation, 221, 222. 
 
352 
 
 INDEX. 
 
 [All references, unless expressly stated to the contrary, are to articles, not lo pages.] 
 
 Laws, Kepler's, 121, 220, 430. 
 
 Leap-year, 129, 130. 
 
 Leo, 53, 118. 
 
 Leo minor, 54. 
 
 Leonids, the, 324, 325, 326, 329. 
 
 Lepus, 45. 
 
 LEVERRIER (and ADAMS), discovery 
 of Neptuue, 283 ; on the origin of the 
 Leonids, 329. 
 
 Libra, 61, 118. 
 
 Librations of the moon, 145. 
 
 LICK telescope, the, 412. 
 
 Light, aberration of, 435, 436 ; of com- 
 ets, 291; equation of, the, 432, 433; 
 of the moon, 149; of the sun, its in- 
 tensity, 186; of the stars, 348-350; 
 velocity of, used to determine the 
 distance of the sun, 434, 436; the 
 zodiacal, 265. 
 
 Light-ratio of the scale of stellar mag- 
 nitude, 346. 
 
 Light-year, the, 344. 
 
 Local time, 97 ; time from altitude of 
 the sun, 427; time by transit instru- 
 ment, 93, 416. 
 
 LOCKYER, J. N., his meteoric hypothe- 
 sis, 330, 394; on spectra of nebulae, 
 380. 
 
 Longitude and latitude (celestial) 20; 
 (terrestrial), defined, 94; (terres- 
 trial), methods of determining it, 
 95, 96, 427. 
 
 Lunar. See Moon. 
 
 Lupus, 62. 
 
 Lynx, 46. 
 
 Lyra, 67. 
 
 91. 
 
 Magnesium in nebulae (Lockyer) , 380 ; 
 in the stars, 362 ; in the sun, 176. 
 
 Magnifying power of a telescope, 404. 
 
 Magnitudes, star, 345-347 ; star, abso- 
 lute scale of, 346; star, and tele- 
 scopic power, 347. 
 
 Mars (the planet), 251-257; habita- 
 bility of, 259; map of the planet, 
 257; satellites, 258; Schiaparelli's 
 observations, etc., 256; telescopic 
 aspect, rotation, etc., 253, 254. 
 
 Mass, definition, 113; of comets, 302; 
 of earth, 113; of the moou, 143; of a 
 planet, how determined, 233; of 
 shooting stars, how estimated, 323; 
 of the sun, 161. 
 
 Masses of binary stars, 371. 
 
 Mazapil, meteorite of, 326. 
 
 Mean and apparent places of stars, 
 336 ; and apparent solar time, 88-89. 
 
 Melbourne reflector, 412. 
 
 Mercury (the planet), 239-244; rota- 
 tion of, 243; transits of, 244. 
 
 Meridian (celestial) defined, 11, 15, 16 ; 
 (terrestrial), arcs of, measured, 105, 
 110; circle, the, 81, 99, 418. 
 
 Meteoric hypothesis (Lockyer), 330, 
 394; showers, 324-326. 
 
 Meteorite of Mazapil, 326. 
 
 Meteorites, 315; their constituents, 
 316; their fall, 315. 
 
 Meteors, ashes of, 323; connection 
 with comets, 327-329 ; heat and light, 
 318; observation of, 317; origin of, 
 319 ; path and velocity, 317. 
 
 Micrometer, the, 415. 
 
 Midnight sun, the, 86. 
 
 Milky Way, the, 383. 
 
 Mimas, the inner satellite of Saturn, 
 280. 
 
 Mira Ceti, 356. 
 
 Missing and new stars, 353. 
 
 Monoceros, 50. 
 
 Month, sidereal and synodic, 133* 
 
 Moon, its albedo, 149 ; its atmosphere 
 discussed, 148; changes on its sur- 
 face, 155; character of its surface, 
 153; density, 143; diameter, surface 
 area and bulk, 142; distance and 
 parallax, 141 ; eclipses of, 195-199; 
 heat, 150; influence on the earth, 
 151; librations,145; light and albedo, 
 149; map, 154, 156 ; mass, density, and 
 gravity, 143; motion (in general), 
 132-135 ; nomenclature of objects on 
 surface, 156; perturbations of, 134; 
 phases, 146; rotation, 144; shadow 
 of, 200; surface structure, 153; tele- 
 scopic appearance, 152; tempera- 
 ture, 150 ; water not present, 148. 
 
INDEX. 
 
 353 
 
 [All references, unless expressly stated to the contrary, are to articles, not to pages.] 
 
 Motion, apparent diurnal, of the 
 heavens, 12, 13; of the moon, 132-134; 
 of a planet, 225, 220, 229 ; of the sun, 
 115-117; in line of vision, effect on 
 spectrum, 179, 341; of the sun in 
 space, 342. 
 
 Motions of stars, 338-341. 
 
 Mountains, lunar, 153, 156. 
 
 Mounting of a telescope, 414. 
 
 Multiple stars, 375. 
 
 Pi. 
 
 Nadir defined, 10. 
 
 Nadir-point of meridian circle, 419. 
 
 Names of planets, 218 ; of satellites of 
 Saturn, 280 ; of satellites of Uranus, 
 282. 
 
 Neap tide, 210. 
 
 Nebulae, the, 377-382; changes in, 379; 
 distance and distribution, 382 ; spec- 
 tra of, 380, 381. 
 
 Nebular hypothesis, the, 392, 393. 
 
 Negative eye-pieces, 409. 
 
 Neptune (the planet), 283-287. 
 
 NEWCOMB, S., on the age and duration 
 of the system, 193 ; and MICHELSON, 
 the velocity of light, 436. 
 
 NEWTON, H. A., estimate of the daily 
 number of meteors, 321 ; investiga- 
 tion of the orbit of the Leonids, 327 ; 
 nature of comets, 309. 
 
 NEWTON, SIR ISAAC, law of gravita- 
 tion, 221, 222. 
 
 Nodes of the moon's orbit and their 
 regression, 134; of the planetary 
 orbits, 224. 
 
 NORDENSKIOLD, ashes of meteors, 323. 
 
 Norma, 64. 
 
 Number of comets, 289 ; of eclipses in 
 a saros, 207; of eclipses in a year, 
 206; of the stars, 332. 
 
 NYREN, his value of the aberration 
 constant, 435. 
 
 O. 
 
 Oberon, a satellite of Uranus, 282. 
 
 Oblateness or ellipticity of the earth 
 defined, 110. 
 
 Oblique sphere, 85. 
 
 Obliquity of the ecliptic, 116. 
 
 OLBERS, discovers Pallas and Vesta, 
 260. 
 
 Ophiuchus, 65. 
 
 OPPOLZER, his canon of eclipses, 205. 
 
 Opposition defined, 132, 227. 
 
 Orbit of the earth, its form, etc., 115, 
 122, 428 ; of the moon, 137 ; parallac- 
 tic, of a star, 442. 
 
 Orbital motion of the earth, proof of 
 it, 115. 
 
 Orbits of binary stars, 370; of comets, 
 292 ; of the planets, 223. 
 
 Origin of the asteroids, 263 ; of mete- 
 ors, 319 ; of periodic comets, 297. 
 
 Orion, 43. 
 
 PALISA, discovery of asteroids, 260. 
 Pallas, the second asteroid, 260. 
 Parabola, the, 439, 440. 
 Parallax, annual or heliocentric, of 
 
 the stars, 139, 343, 441-444 ; diurnal 
 
 or geocentric, 139 ; solar, by transit 
 
 of Venus, de 1'Isle's method, 437; 
 
 stellar, how determined, 441-444. 
 Parallaxes, stellar, table of, Table V., 
 
 page 343. 
 
 Parallel sphere, 84. 
 Pegasus, 77. 
 Pendulum used to determine earth's 
 
 form, 111 ; Foucault, 107. 
 Perigee defined, 137. 
 Perihelion defined, 120. 
 Periodicity of sun spots, 169. 
 Periods of the Planets, 218; sidereal 
 
 and synodic, 133, 162, 228. 
 Perseids, the, 324-326, 328, 329. 
 Perseus, 40. 
 Perturbations, lunar, 134 ; planetary, 
 
 122, 288*. 
 
 PETERS, asteroid discoveries, 260. 
 Phase of Mars, 253. 
 Phases of Mercury and Venus, 242, 
 
 247 ; of the moon, 146 ; of Saturn's 
 
 rings, 278. 
 
 Phobos, a satellite of Mars, 258. 
 Phomix, 39. 
 Photographic power of eclipsed moon, 
 
 198; star-charts, 337; telescopes, 337. 
 
354 
 
 INDEX. 
 
 [All references, unless expressly stated to the contrary, are to articles, not to pages.] 
 
 Photographs of nebulae, 378 ; of star- 
 spectra, 341, 364. 
 
 Photography, solar, 164. 
 
 Photometry, stellar, 348, 349. 
 
 Photosphere, the, 165, 194. 
 
 PIAZZI discovers Ceres, 260. 
 
 PICKERING, E. C., photographs of star- 
 spectra, 364, 373 ; photometric obser- 
 vations of eclipses of Jupiter's satel- 
 lites, 433; photometric measures of 
 stellar magnitudes, 346. 
 
 Pisces, 36, 118. 
 
 Piscis Australis, 79. 
 
 Place of a heavenly body denned, 7 ; 
 of a heavenly body, how determined 
 by observation, 99, 100; of a ship, 
 how determined, 426, 427. 
 
 Planet, albedo of, denned, 231, 235; 
 apparent motion of, 225-229 ; diame- 
 ter and volume, how measured, 232; 
 mass and density, how determined, 
 233; rotation on axis determined, 
 234; satellite system, how investi- 
 gated, 236 ; superficial gravity deter- 
 mined, 233. 
 
 Planetary data, their relative accu- 
 racy, 237; system, its genesis, age, 
 and duration, 390-398 ; its stability, 
 288*. 
 
 Planetoids. See Asteroids. 
 
 Planets, Humboldt's classification, 
 217; the list of, 218; intra-Mercurian, 
 264 ; minor, 260-263 ; possibly attend- 
 ing stars, 372; table of elements, 
 Appendix, Table II., page 340; table 
 of names, symbols, etc., 218. 
 
 Pleiades, the, 42, 376. 
 
 Pointers, the, 12, 26. 
 
 Pole (celestial), altitude of, equals 
 latitude, 80; defined, 13; effect of 
 precession, 126; (terrestrial), diur- 
 nal phenomena near it, 83. 
 
 Pole-star, former, a Draconis, 126; 
 how recognized, 12. 
 
 Positive eye-pieces, 409. 
 
 Precession of the equinoxes, 125, 126. 
 
 Prime vertical, the, 11. 
 
 PROCTOR, sun spots, 168; theory of 
 comets, 298. 
 
 Prominences, the solar, 181, 182, 194. 
 Proper motion of stars, 339. 
 Ptolemaic system, the, 230. 
 PTOLEMY, 4, 230. 
 
 Q. 
 
 Quadrature defined, 132, 227. 
 Quiescent prominences, 182. 
 
 Radiant, the, of a meteoric shower, 
 324. 
 
 Radius vector defined, 120. 
 
 Rate of a timepiece defined, 417. 
 
 Rectification of a globe, 401. 
 
 Recurrence of eclipses, 207. 
 
 Red spot of Jupiter, 271. 
 
 Reflecting telescope, the, 411, 413. 
 
 Refracting telescope, the, 403-407, 413. 
 
 Refraction, astronomical, 82. 
 
 Reticle, the, 410, 416. 
 
 Retrograde and retrogression defined, 
 226. 
 
 Reversing layer, 177. 
 
 Rhea, a satellite of Saturn, 280. 
 
 Right ascension defined, 18, 93; how 
 determined by observation, 99, 100. 
 
 Right sphere, the, 83. 
 
 Rings of Saturn, the, 277-279. 
 
 ROBERTS., photographs of nebulae, 378. 
 
 ROSSE, LORD, his great reflector, 412. 
 
 Rotation, apparent diurnal, of the 
 heavens, 12; definition of, 144; dis- 
 tinguished from revolution, 106, note ; 
 of earth, its effect on gravity, 111; 
 of earth, proofs of, 107; of earth, 
 variability of, 108; of the moon, 144; 
 of the sun, 162, 163. 
 
 Rotation -period of Jupiter, 270; of 
 Mars, 254; of Mercury, 243; of a 
 planet, how ascertained, 234; of 
 Saturn, 275; of Venus, 249. 
 
 Sagitta, 70. 
 Sagittarius, 72, 118. 
 Saros, the, 207. 
 
INDEX. 
 
 355 
 
 [All references, unless expressly stated to the contrary, are to articles, 
 
 Satellite system, how investigated, 
 236; systems, table of, Table III., 
 page 341. 
 
 Satellites of Jupiter, 272; of Mars, 
 258; of Neptune, 286; of Saturn, 
 280 ; of Uranus, 282. 
 
 Saturn (the planet), 274-280. 
 
 Scale of stellar magnitudes, 346. 
 
 SCHIAPARELLI, identification of come- 
 tary and meteoric orbits, 328 ; obser- 
 vations of Mars, 256; rotation of 
 Mercury and Venus, 243, 249. 
 
 SCHWABE, discovers periodicity of sun 
 spots, 169. 
 
 Scintillation of the stars, 365. 
 
 Scorpio, 63, 118. 
 
 Sea, position at, how found, 426, 427. 
 
 Seasons, explanation of, 123-124. 
 
 SECCHI, on stellar spectra, 363; on 
 sun spots, 168. 
 
 Secondary spectrum of achromatic 
 object-glass, 407. 
 
 Serpens, 65. 
 
 Serpentarius, 65. 
 
 Sextant, the, 420, 421. 
 
 Shadow of the earth, its dimensions, 
 196; of the moon, its dimensions, 
 200 ; of the moon, its velocity, 203. 
 
 Ship at sea, determination of its posi- 
 tion, 426, 427. 
 
 Shooting stars (see also Meteors) 320- 
 324; ashes of, 323; brightness of, 
 323; elevation and path, 322; mass 
 of, 323; materials of, 323; nature of, 
 320 ; number, daily and hourly, 321 ; 
 radiant, 324; showers of, 324-326; 
 spectrum of, 323 ; velocity of, 322. 
 
 Showers, meteoric, 324-326. 
 
 Sidereal and synodic months, 133 ; and 
 synodic periods of planets, 228 ; time 
 defined, 91; year, 127. 
 
 Signs of the zodiac, 118 ; effect of pre- 
 cession on them, 126. 
 
 Sirius, its companion, 369; light com- 
 pared with that of the sun, 349; its 
 mass compared with that of the sun, 
 370. 
 
 Solar constant, the, 187; parallax, 158 ; 
 time, mean and apparent, 88, 89. 
 
 Solstice defined, 117. 
 
 SOSIGENES and the calendar, 129. 
 
 Spectroscope, its principle and con- 
 struction, 171, 172 ; slitless, 364, 445 ; 
 used to observe the solar promi- 
 nences, 182 ; used to measure motions 
 in line of sight, 178, 179, 341, 373, 
 374. 
 
 Spectrum of the chromosphere and 
 prominences, 181 ; of comets in gen- 
 eral, 304; of the comet of 1882, 314; 
 of meteors, 323; of nebulae, 380, 
 381; of a shooting star, 323; of 
 stars, 362-364 ; the solar, 172-175 ; of 
 the solar corona, 184 ; of a sun spot, 
 178. 
 
 Spectrum analysis, fundamental prin- 
 ciples, 173. 
 
 Speculum of a reflecting telescope, 
 411. 
 
 Sphere, celestial, the, 6; doctrine of 
 the, 9-20. 
 
 Spots, solar. See Sun spots. 
 
 Spring tide defined, 210. 
 
 Stability of the planetary system, 288*. 
 
 Standard time, 97. 
 
 Stars, binary, 368-371; catalogues of, 
 335 ; charts of, 337 ; clusters of, 376 ; 
 dark, 350, 360 ; designation and no- 
 menclature, 24, 334; dimensions of, 
 351, 360; distance of, 343, 344; distri- 
 bution of, 384; double, 366, 367; 
 gravitation among them, 368, 371, 
 386 ; heat from them, 348, note ; light 
 of certain stars compared with sun- 
 light, 348, 349; magnitudes and 
 brightness, 345-350; mean and ap- 
 parent places of, 336; missing and 
 new, 353 ; motions of, 338-342 ; mul- 
 tiple, 375; new, 353; number of, 
 332 ; parallax of, 343, 441^44 ; Table 
 V., page 343; shooting (see Shoot- 
 ing stars, also Meteors) ; spectra of, 
 362-364; system of the, 386; tem- 
 porary, 355; total amount of light 
 from the, 348; twinkling of, 365; 
 variable, 352-361 ; Table IV., page 
 342. 
 
 Star- gauges of the Herschels, 384. 
 
356 
 
 INDEX. 
 
 [All references, unless expressly stated to the contrary, are to articles, no 
 
 Starlight, its total amount, 348. 
 
 Stellar parallaxes, table of, Table V., 
 page 343 ; photometry, 348, 349. 
 
 Structure of the stellar universe, 385. 
 
 Sun, the age and duration of, 193, 397, 
 398 ; apparent motion in the heavens, 
 115-117; its chromosphere, 180; its 
 constitution, 194; its corona, 183- 
 185 ; its density, 161 ; dimensions of, 
 160; distance of, 158, 159, 434-438; 
 elements recognized in it, 176 ; f ac- 
 ulae, 165 ; gravity on its surface, 161 ; 
 heat of, quantity, intensity, and 
 maintenance, 187-192; light of, its 
 intensity, 186 ; mass of, 161 ; motion 
 in space, 342; parallax of, 159; 
 prominences, 181, 182, 194; reversing 
 layer, the, 177, 194 ; rotation of, 162, 
 163 ; spectrum of, 172, 175 ; temper- 
 ature of, 190; temperature dimin- 
 ishing, Lockyer, 396, note. 
 
 Sun spots, appearance and nature, 
 166, 170 ; cause of, 168 ; distribution 
 of, 169 ; influence on the earth, 170 ; 
 periodicity of, 169 ; spectrum of, 178. 
 
 Superficial gravity of a planet, how 
 determined, 233. 
 
 Surface structure of the moon, 153, 
 154. 
 
 Swarms, meteoric, 324-329. 
 
 Synodic and sidereal months, 133 ; and 
 sidereal periods of planets, 228. 
 
 System, planetary, its age and dura- 
 tion, 397-399; its genesis and evo- 
 lution, 390-393; its stability, 288*; 
 stellar, its probable nature, 386-388. 
 
 Syzygy denned, 132. 
 
 X. 
 
 Tables, astronomical constants, Table 
 I., page 339; astronomical symbols, 
 page 344; binary stars, orbits and 
 masses, 370; Bode's law, 219; con- 
 stellations, showing place in heavens, 
 page 54 ; Greek alphabet, page 344 ; 
 moon, names of principal objects, 
 155; planet's elements, Table II., 
 page 340 ; planet's names, distances, 
 
 etc., approximate, 218; satellite sys- 
 tems, Table III., page 341; stellar 
 parallaxes and proper motions, Table 
 V., page 343; variable stars, Table 
 IV., page 342. 
 
 Tails of comets, 300, 301, 305-308. 
 
 Taurus, 42. 
 
 Telegraph, longitude by, 95. 
 
 Telescope, achromatic, 406, 407; eye- 
 pieces of, 409 ; general principles of, 
 402; illuminating power, 405; mag- 
 nifying power, 404; magnitude of 
 stars visible with a given aperture, 
 347; mounting of, 414; reflecting, 
 411 ; simple refracting, 403. 
 
 Telescopes, great, 412. 
 
 Temperature of the moon, 150; of the 
 sun, 190. 
 
 Temporary stars, 355. 
 
 Terminator, the, defined and described, 
 146. 
 
 Tethys, a satellite of Saturn, 280. 
 
 THOMSON, SIB W., the internal heat of 
 the earth, 396 ; the heat of meteors, 
 318 ; the rigidity of the earth, 114. 
 
 Tidal-wave, course of, 213. 
 
 Tides, the definitions relating to, 210; 
 due mainly to moon's action, 209; 
 explanation of, 208, 209, 211, 212; 
 height of, 214 ; motion of, 211, 213 ; in 
 rivers, 215. 
 
 Time, equation of, 89 ; local, from sun's 
 altitude, 427; methods of determin- 
 ing, 92, 93, 427; relation to hour- 
 angle, 422 ; sidereal, defined, 91 ; 
 solar mean and apparent, 88, 89; 
 standard, defined, 97. 
 
 Titan, satellite of Saturn, 280. 
 
 Titania, satellite of Uranus, 282. 
 
 Total and annular eclipses, 201. 
 
 Trains of meteors, 315. 
 
 Transit or meridian circle, 81, 99, 418. 
 
 Transit instrument, the, 92, 416. 
 
 Transits of Mercury, 244; of Venus, 
 250. 
 
 Triangulum, 37. 
 
 Tropical year, the, 127. 
 
 Twinkling of the stars, 365. 
 
 TYCHO BRAKE, his temporary star, 355. 
 
357 
 
 [All references, unless expressly stated to the contrary, are to articles, not to pages.] 
 
 U. Volcanoes on the moon, 153. 
 
 Vulcan, the hypothetical intra-Mercu- 
 
 rian planet, 264. 
 Vulpecula, 69. 
 
 Ultra-Neptunian planet, 288. 
 Umbriel, a satellite of Uranus, 282. 
 Universe, stellar, its structure, 385. 
 Uranography denned, 5. 
 Uranolith, or Uranolite. See Meteor- 
 ite. 
 
 Uranus (the planet), 281, 282. 
 Ursa Major, 26. 
 Ursa Minor, 27. 
 Utility of astronomy, 1. 
 
 Vanishing point, 6, note. 
 
 Variable stars, 352-361; table of, 
 Table IV., page 342. 
 
 Velocity of earth in its orbit, 102, 158 ; 
 of light, 436; of moon's shadow, 
 203; of meteors and shooting stars, 
 317, 322 ; of star motions, 340, 341. 
 
 Venus (the planet), 245-250; phases 
 of, 247 ; transits of, 250. 
 
 Vernal equinox, the, 17, 36, 116. 
 
 Vertical circles, 11. 
 
 Vesta, the fourth asteroid, 260. 
 
 Virgo, 56, 118. 
 
 Visible horizon denned, 10. 
 
 VOGBL, H. C., spectroscopic determina- 
 tion of star motions in the line of 
 sight, 341; spectroscopic observa- 
 tions of Algol and Spica, 360, 374. 
 
 W. 
 
 Water absent from the moon, 148. 
 Wave-length of a light-ray affected 
 
 by motion in the line of sight, Dop- 
 
 pler's principle, 179, 341. 
 Wave, tidal, its course, 213. 
 Way, the sun's, 342. 
 Weather, the moon's influence on, 151. 
 Weight, loss of, between pole and 
 
 equator, 111. 
 
 Y. 
 
 Year, the sidereal, tropical, and anom- 
 alistic, 127, and Table I., page 339. 
 
 Zenith, the, denned, 10. 
 Zenith distance denned, 11. 
 Zero-points of the meridian circle, 418, 
 
 419. 
 Zodiac, the, and its signs, 118 ; its signs 
 
 as affected by precession, 126. 
 Zodiacal light, the, 265. 
 ZOLLNER, determination of planets' 
 
 albedoes, 242, 247, 253, 268, 276, 281, 
 
 285 ; measurement of moonlight, 149 ; 
 
 measures of light of stars, 348.