IMAGE EVALUATION TEST TARGET (MT-3) 4^s ^ d Z • o 1.0 I.I IL25 i 1.4 lAiiZS |2.5 lUUu 1.6 Hiotographic Sciences Corporation n WEST MAIN STREET WEBSTER, N.y. 14SM (716)S72-'S03 •17 '<^ CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques Technical and Bibliographic Notes/Notes techniques et bibliographiques The Institute has attempted to obtain the best original copy available for filming. Features of this copy which may be bibliographically unique, which may alter any of the images in the reproduction, or which may significantly change the usual method of filming, are checked below. D Coloured covers/ Couverture de couleur I I Covers damaged/ D Couverture endommagde Covers restored and/or laminated/ Couverture restaur^e et/ou pelliculde I I Cover title missing/ D D Le titre de couverture manque Coloured maps/ Cartes gdographiques en couleur Coloured ink (i.e. other than blue or black)/ Encre de couleur (i.e. autre que bleue ou noire) □ Coloured plates and/or illustrations/ Plane \1 D n iches et/ou illustrations en couleur Bound with other material/ Reli6 avec d'autres documents Tight binding may cause shadows or distortion along interior margin/ La reliure serr^e peut causer de I'ombre ou de la distortion le long de la marge intdrieure Blank leaves added during restoration may appear within the text. Whenever possible, these have been omitted from filming/ II se peut que certaines pages blanchet ijouties lors d'une restauration apparaissent dans le texte, mais, lorsque cela 6tait possible, ces pages n'ont pas 6td film^es. Additional comments:/ Commentaires suppldmentaires; L'Institut a microfilmd le meilleur exemplaire qu'il lui a 6t6 possible de se procurer. Les details de cet exemplaire qui sont peut-dtre uniques du point de vue bibliographiqua, qui peuvent modifier une image reproduite, ou qui peuvent exiger une modification dans la mdthode normale de filmage sont indiquds ci-ciessous. D D □ □ Coloured pages/ Pages de couleur Pages damaged/ Pages endommagdes Pages restored and/or laminated/ Pages restaurdes et/ou pelMcul6es Pages discoloured, stained or foxed/ Pages d6color6es, tachet^es ou piqudes Pages detached/ Pages ddtach^es r7p( Showthrough/ I I Transparence I I Quality of print varies/ Quality in^gale de I'impression Includes supplementary material/ Comprend du materiel supplementaire D Only edition available/ Seule Edition disponible Pages wholly or partially obscured by errata slips, tissues, etc., have been refilmed to ensure the best possible image/ Les pages totalement ou partiellement obscurcies par un feuillet d'errata, une pelure, etc., ont 6t6 film6es d nouveau de faqon d obtenir la meilleure image possible. This item is filmed at the reduction ratio checked belo'jv/ Ce document est filmd au taux de reduction indiquA ci-dessous. 10X 14X 18X 22X 26X 30X 7 12X 16X 20X 24X 28X 32X 1 i The copy filmed here hes been reproduced thenks to the generosit. of: University of British Columbia Library L'exempleire film6 fut reproduit grflce A la gAnArositi de: University of British Columbia Library The Images appearing here are the best quality possible considering the condition and legibility of the original copy and in keeping with the filming contract specifications. Les images sulvantes ont 6tL LEGES Horj>>:\ ij T^ -v-.,\ 1 AMERICAN SCIENCE SERIES-ADVANCED COURSE ASTEONOMY FOR HIGH SCHOOLS AND COLLEGES BY SIMON NEWCOMB, LL.D., PROFESSOR OP MATHEMATICS) IN THE JOHNS HOPKINS UNIVERSITY, AND EDWARD S. HOLDEX, LL.D., DIRECTOR OF THE LICK OBSERVATORY. SIXTH EDITION, REVISED NEW YORK HENRY HOLT AND COMPANY 1893. Copyright, 1879, BV Henry Holt & Co. t I C s li a u n t] g \i\ ai m m VI de ed Cj PREFACE. The following work is designed principally for the use of those who desire to pursue the study of Astronomy as a brancli of liberal education. To facilitate its use by stu- dents of different grades, the subject-matter is divided into two classes, distinguished by the size of the type. The portions in large type form a complete coui*se for the use of those who desire only such a general knowledge of the subject as car be acquired without the application of ad- vanced mathematics. Sometimes, especially in the ear- lier chapters, a knowledge of eleraentaiy trigonometry and natural philosophy will be found necessary to the full understanding of this course, but it is believed that it can nearly all be mastered by one having at command only those geometrical ideas which are familiar to most intelli- gent students in our advanced schools. The portions in small type comprise additions for the use of those students who either desire a more detailed and precise knowledge of the subject, or who intend to make astronomy a special study. In this, as in the ele- mentary course, the rule has been never to use more ad- vanced mathematical methods than are necessary to the development of the subject, but in some cases a knowl- edge of Analytic Geometry, in others of the Differential Calculus, and in others of elementary Mechanics, is neces- PREFACE. * sarily presupposed. The object aimed at has been to lay a broad foundation for further study rather than to at- tempt the detailed presentation of any special branch. As some students, especially in seminaries, may not de- sire so extended a knowledge of the subject as that em- braced in the course in large type, tlie following liints are added for their benetit : Chapter I., on the relation of the earth to the heavens, Chapter III., on the motion of the earth, and the chapter on Chronology sliould, so far as pos- sible, be mastered by ail. The remaining parts of the course may be left to the selection of the teacher or student. Most persons will desire to know something of the tele- scope (Chapter II.), of the arrangement of the solar system (Chapter IV. , §§ 1-2, and Par" " I. , Chapter II.), of eclipses, of the phases of the moon, of the physical constitution of the sun (Part II., Chapter II.), and of the constellations (Part III,, Chapter I.). It is to be expected that all will be interested in the subjects of the planets, comets, and meteors, treated in Part II., the study of which involves no difficulty. An acknowledgment is due to the managers of the Clarendon Press, Oxford, who have allowed the use of a number of electrotypes from Chambers's Descriptive Astronomy. Messrs. Fauth & Co., instrument-makers, of Washington, have also lent electrotypes of instruments, and a few electrotypes have been kindly furnished by the editors of the American Journal of Science and of the Popular Science Monthly. The greater part of the illus- trations have, however, been prepared expressly for the work. CONTENTS. PART I. Introduction. PAOR . 1 CHAPTER I. THE RELATION OF THE BARTn TO THE HEAVK''^. The Earth— The Celestial Sphere— Relation of tlie Spber's to the Horizon — Plane of the Horizon — The Diurnal Mt)tion — The Diurnal Motion in different Latitudes — Corresj ondence of the Terrestrial and Celestial Spheres — Ri^ht Ancension and Dec- lination ,- -Relation of Time to the Sphere — Determination of Terrestrial Longitudes — Mathematical Theory of the ('elestial Sphere — Determination of Latitudes on the Earth by Astro- nomical Observations — Parnllax and Semidiamoter 9 CHAPTER 11. ASTRONOMICAL INSTRUMENTS. The Refracting Telescope — Reflecting Telescopes — Chronometers and Clocks — The Transit Instrument — Graduated Circles — The Meridian Circle — The Equatorial — The Zenith Tele.scope —The Sextant 63 CHAPTER in. MOTION OF THE EARTH. Ancient Ideas of the Planets — Annual Revolution of the Earth — The Sun's apparent Path — Obliquity of the Ecliptic — The Seasons 96 CHAPTER rv. THK PLANETARY MOTIONS. Apparent and Real Motions of the Planets — Gravitation in the Heavens — Kepler's Laws of Planetary Motion 113 vm CONTENTS. CHAPTER V. UNIVERSAL GRAVITATION. PASS Newton's Laws of Motion — Problems of Oravitation— Results of Gravitation — Remarks on the Theory of Gravitation 131 CHAPTER VI. THE MOTION AND ATTRACTION OP THE MOON. The Moon's Motion and Phases — The Sun's disturbing Force- Motion of the Moon's Nodes — Motion of the Perigee — Rotation of the Moon— The Tides 169 ' I i If! CHAPTER VII. ECLIPSES OF THE SUN AND MOON. The Earth's Shadow and Penumbra — Eclipses of the Moon- Eclipses of the Sun — The Recurrence of Eclipses — Character of Eclipses 168 CHAPTER VIII. THE EARTH. Mass and Density of the Earth — Laws of Terrestrial Gravitation- Figure and Magnitude of the Earth — Cliange of Gravity with the Latitude — Motion of the Earth's Axis, or Precession of the Equinoxes 188 CHAPTER IX. CELESTIAL MEASUREMENTS OF MASS AND DISTANCE. The Celestial Scale of Measurement — Measures of the Solar Parallax — Relative Masses of the Sun and Planets 213 CHAPTER X. THE REFRACTION AND ABERRATION OF LIGHT. Atmospheric Refraction — Aberration and the Motion of Light 234 CHAPTER XL CHRONOLOGY. Astronomical Measures of Time — Formation of Calendars — Division of the Day — Remarks on improving the Calendar — The .'.stronomical Ephemeris or Nautical Almanac 245 CONTENTS. IX PAET II. THE «OLAR SYSTEM IN DETAIL. CHAPTER I. FAOB Stbcctube of the Solab System ^ 207 CHAPTER II. THE sua. General Summary — The Photosphere — Sun-Spots and Faculse — The Sun's Chromosphere and Corona — Sources of the Sun's Heat 278 CHAPTER III. THE INFERIOR PLANETS. Motions and Aspects — Aspect and Rotation of Mercury — The Aspect ana supposed Rotation of Venus — Transits of Mercury and Venus — Supposed intramercurial Planets 810 CHAPTER IV. The Moon 326 CHAPTER V. THE PLANET MARS. The Description of the Planet — Satellites of Mars 884 CHAPTER VI. The Minor Planets 840 CHAPTER VII. JUPITER AND HIS SATELLITES. The Planet Jupiter— The Satellites of Jupiter 848 CHAPTER VIII. SATURN AND HIS SYSTEM. General Description— The Rings of Saturn— Satellites of Saturn. . 863 I i I X CONTENTS. CHAPTER IX. The Planet Uranus— Satellites of Uraaas. 363 CHAPTER X. The Planet Neptune— Satellite of Neptune 865 CHAPTER XI. The PH78ICAL Constitution of the Planets 370 CHAPTER XIL meteors. Phenomena and Causes of Meteors — Meteoric Showers 375 CHAPTER XIII. COMETS. Aspect of Comets — The Vaporous Envelopes — The Physical Con- stitution of Comets — Motion of Comets — Origin of Comets — Remarkable Comets 388 PAET III. THE UNIVERSE AT LARGE. Introduction 411 CHAPTER I. THE constellations. General Aspect of the Heavens— Majirnitude of the Stars — The Constellations and Names of the Stars — Description of Con» stellations — Numbering and Cataloguing the Stars 415 CHAPTER IL variable and temporary stars. Stan Regularly Variable— Temporary or New Stars— Theory of Variable Stars 440 CONTENTS. xi CHAPTER III. MULTIPLE STABS. FAGB Character of Double and Multiple Stars — Orbits of Binary Stars. . 44ti CHAPTER IV. NEBULA AND CLUSTERS. Discovery of Nebul» — Clabsification of Nebulaa and Clusters — Star Clusters — Spectra of Nebulae and Clusters — Distribution of Nebulee and Clusters on the Surface of the Celestial Sphere 457 CHAPTER V. SPECTRA OF FIXED STARS. Characters of Stellar Spectra — Motion of Stars in the Line of Sight. 468 CHAPTER VI. MOTIONS AND DISTANCES OF THE STARS. Proper Motions — Prop<'if Motion of the Sun — Distances of the Fixed Stars 47» CHAPTER VII. CONSTRUCTION OF THE HEAVENS 478 CHAPTER VIII. Cosmogony 492 Index 503 *;'- , m s n t] rj o ir b. ti g cc oi; m fr( ti tO] rei vri. pr( ASTRONOMY. INTRODUCTION. Astronomy {aatr/p — a star, and vopio? — a law) is the science which has to do with the heavenly bodies, their appearances, their nature, and the laws governing their real and their apparent motions. In approaching the study of this, the most ancient of the sciences depending upon observation, it must be borne in mind that its progress is most intimately connected with that of the race, it having always been the basis of geog- raphy and navigation, and the soul of chronology. Some of the chief advances and discoveries in abstract mathe- matics have been made in its service, and the methods both of observation and analysis once peculiar to its prac- tice now furnish the firm bases upon which rest that great group of exact sciences which we call physics. It is more important to the student that he should be- come penetrated with the spirit of the methods of astron- omy than that he should recollect its minutiae, and it is most important that the knowledge which he may gain from this or other books should be referred by him to its ti sources. For example, it will often be necessary to speak of certain planes or circles, the ecliptic, the equa- tor, the meridian, etc. , and of the relation of the appa- rent positions of stars and planets to them ; but his labor will be useless if it has not succeeded in giving him a precise notion of these circles and planes as they exist in 2 ASTROAOMV. m the sky, and not merely in tlie figures of his text-book. Above all, the study of this science, in which not a single step could have been taken without careful and painstak- ing observation of the heavens, should lead its student himself to attentively regard the phenomena daily and hourl}'^ presented to him by the heavens. Does the sun set daily in the same point of the hori- zon ? Does a change of his own station affect this and other aspects of the sky ? At what time does the full moon rise ? Which way fire the horns of the young moon pointed ? These and a thousand other questions are already answered by the observant eyes, of the an- cients, who discovered not only the existence, but the motions, of the various planets, and gave special names to no less than fourscore stars. The modern pupil is more richly equipped for observation tlian the ancient philoso- pher. If one could have put a mere opera-glass in the hands of Hippakcuus the world need not have waited two thousand years to know the nature of tliat early mystery, the Milky Way, nor would it have required a Galileo to discover the phases of Vemis and the spots on the sun. From the earliest times the science has steadily progress- ed by means of faithful observation and sound reasoning upon the data which • 'i)servation gives. The advances in our special knowledge of this science have made it con- venient to regard it as divided into certain portions, which it is often convenient to consider separately Jthough the boundaries cannot be precisely fixed. Spherical and Practical Astronomy — First in logical order we have the instruments and methods by which the positions of the heavenly bodies are determined from obser- vation, and by which geographical positions are also fixed. The branch M^hich treats of these is v lied spherical and practical astronomy. Spherical astronomy provides the mathematical theory, and practical astronomy (which is almost as much an art as a science) treats of the applica- tion of this theory. '4 DIVISIONS OF THE SUBJECT. 3 Theoretical Astronomy deals with the laws of motion of the celestial bodies as determined by repeated observations of their positions, and by the laws according to which they ought to move under the influence of their mutual gravi- tation. The purely mathematical part of the science, by which the laws of the celestial motions are deduced from the theory of gravitation alone, is also called Celestial Mechanics^ a term first applied by La Place in the title of his great work Mecanique Celeste. Gosmioal Physics.— A third branch which has received its greatest developments in quite recent times may be called Cosmical Physics. Physical astronomy might be a better appellation, were it not sometimes applied to celestial mechanics. This branch treats of the physical constitution and aspects of the heavenly bodies as investi- gated with the telescope, the spectroscope, etc. We thus have three great branches which run into each other by insensible gradations, but undei which a large part of the astronomical research of the present day may be included. In a work like the present, however, it will not be advisable to follow strictly this order of sub- jects ; we shall rather strive to present the whole subject in the order in which it can best be understood. This order will be somewhat like that in which the knowl- edge has been actually acquired by the astronomers of different ages. Owing to the frequency with which we have to use terms expressing angular measure, or referring to circles on a sphere, it may be admissible, at the outset, to give an idea of these terms, and to recapitulate some prop- erties of the sphere. Angular Measures. — The unit of angular measure most used for considerable angles, is the degree, 360 of which extend round the circle. The reader knows that it is 90° from tlie horizon to the zenith, and that two objects 180* apart are diametrically opposite. An idea of distances of ASTRONOMY. a few degrees may be obtained by looking at the two Btars which form tlie pointers in the constellation Ursa Major (the Dipper), soon to be described. These stars are 5" apart. The angular diameters of the sun and moon are each a little more than half a degree, or 30'. An object subtending an angle of only one minute ap- pears as a point rather than a disk, but is still plainly vis- ible to the ordinary eye. Helmholtz finds that if two minute points are nearer together than about V 12", no eye can any longer distinguish them as two. If the ob- jects are not plainly visible — if they are small stars, for instance, they may have to be separated 3', 5', or even 10', to be seen as separate objects. Near the star a Lyrm are a pair of stars 3^^' apart, which can be separated only by very good eyes. If the object be not a point, but a long line, it may be Been by a good eye when its breadth subtends an angle of only a fraction of a minute ; the limit probably ranges from 10" to 15". If the object be much brighter than the background on which it is seen, there is no limit below which it is neces- sarily invisible. Its visibility then depends solely on the quantity of light which it sends to the ej'e. It is not likely that the brightest stars subtend an angle of -j-J^ of a second. So long as the angle subtended by an object is small, we may regard it as varying directly as the linear magnitude of the body, and inversely as its distance from the ob- server. A line seen perpendicularly subtends an angle of 1° when it is a little less than 60 times its length dis- tant from the observer (more exactly when it is 57-3 lengths distant) ; an angle of 1' when it is 3438 lengths distant, and of 1' when it is 206265 lengths distant. These numbers are obtained by dividing the number of degrees, minutes, and seconds, respectively, in the cir- cumference, by. 2 X 3.14159265, the ratio of the circum- ference of a circle to the radius. PLANES AND CIRCLES OF A SPHERE. 5 Planes and Circles of a Sphere. — Let Fig. 1 represent tlie outline of a sphere, of which is the centre. Imagine a plane ^ ^ to pass through the centre O and cut the sphere. This plane will divide the sphere into two equal parts called hemispheres. It will intersect the sphere in a circle A E B F^ called a great circle of the sphere. FlO. 1.— SECTIONS OF A BPHBRB BT FLANBS. Through O let a straight line P P' he passed per- pendicular to the plane. The points P and P\ in which it intersects the surface of the sphere, are everywhere 90° from the circle A E B F. They are called poles of that circle. Imagine another plane CEDE., to cut the sphere in a great circle. Its poles will be Q and Q' . The following relations between the angles made by the figures will then hold : I. The angle P Q between the poles will he equal to the inclination of the planes to each other. II. The arc B I), which measures the greatest distance between the two great circles^ will he equal to this same inclination. III. The points E and F, in which ihe two great circles intersect each other., are the poles of the great circle P Q A OP' Q'B Dy which pass through the poles ofthejwst ci/rcle. SYMBOLS AND ABBREVIATIONS. SIGNS OF THB PLANETS, ETC. i Mara. V Jupiter. % Saturn. $ Uranua. ^ Neptune. The asteroids aredistingnislied by a circle inclosing a number, which number indicates the order of discovery, or by their names, or by both, na@}ill€eate The Sun. unds. pounds, grains. 8 ^lain. BB tlian I of g 1. THE EARTH. The following are fundamental propositions of modern astronomy : I. The earth is approximately a sphere. — Besides the proofs of this proposition familiar to the student of geography, we have the fact that portions of the earth's surface visible from ele- vated positions appear to be bounded by circles. This property belongs only to the surface of a sphere. H. The directions which we call up and down are not invariable, ltd are always toward or from the centre of the earth. — Therefore, tlipyare different at different points of the earth's surface. HI. The earth is completely isolated in space. — The most obvious proof of this is that men have visited nearly every part of its surface without finding any communica- tion with other bodies. IV. The earth is one of a vast number of globular bodies, familiarly known a^ stars and planets, moving according to certain laws and separated hy distances IlIiiBtrating the fact that the portions of th« eiirth vinihle from eleviited ponitioiw, S. S, /S", etc., arc bounded by circles. 10 ASTRONOMY. 80 immense, that the magnitudes of the bodies themselves are insignificant in comparison. Tlie fii-st conception tlie student of astronomy lias to form is that of living on the surface of a spherical earth, which, although it seems of immei.se size to him, is really but a point in comparison witli the distances which sepa- rate him from the stars which he sees in the heavens. § 2. THE CELESTIAL SPHERE. The directions of the heavenly bodies are defined by their positions on an imaginary sphere called the celestial sphere. The celestial sphere is an imaginary hollo v>" sphere, hav- ing the earth in its centre, and of dimensions so great that the earth may be considered a point in comparison. One half of the celestial sphere is represented by the vault above our heads, connnonly called the sky, in which the heavenly bodies appear to be set. This vault is called the visible hemisphere^ and is bounded on all sides by the horizon. To complete the sphere it is supposed to extend below the horizon on all sides, our view of it being cut off by the earth on which we stand. The hemisphere in- visible to us is visible -to those upon the opposite side of the earth. We may imagine a complete view of the sphere to be obtained by travelling around the earth. The celestial sphere being imaginary, may be supposed to have dimensions as great as we please. Convenience is gained by supposing it so large as to include all the heavenly bodies within it. The latter will then appear as if upon its interior surface, as shown in Fig. 8. Here the observer is supposed to be stationed in the centre 0, and to have around him the bodies p, q, r, s, ty etc. The sphere itself being supposed to extend outside of all these bodies, we may imagine lines drawn from the centre through each of them, directly away from the observer, until they inter- sect the sphere in the points P Q R S T, etc. These THE CELKISTIAL SPHERE. 11 hemselves ny lias to cial earth, , is really liicli sepa- vens. lefined by e celestial here, hav- great that on. ,ed by the , in vvliich It is called des by the to extend being cut sphere in- lite side of of the arth. supposed enience is 3 heavenly as if upon observer id to have here itself )odie8, we ;h each of hev inter- These latter points will represent the apparent positions of the bodies, as seen by the observer at O. c. Fm. 3.— STARS SEEN ON THE CELESTIAL SPHERE. If several of tlie bodies, as those marked ^, t\ t'\ are in the same straight line from the observer, they will appear as one body, and will be projected on the same point of the sphere. Hence positions on the celestial sphere rejyresent the directions of the heavenly lodies from the olser'ver, hut not their distances. To iix the appari.'nt positions of the heavenly bodies on tlie celestial sphere, certain circles are supjtosed to be drawn upon it, to which these positions are referred. The following propositions flow from the doctrine of the sphere. In Figs. 1 and 3, suppose the earth to be at 0, and the circles to represent the outlines of the celestial sphere, then : I. Every straight line through the earth., lohen produced indefinitely^ intersects the celestial sphere in tvjo opposite points. 12 ASTRONOMY. Since the earth is supposed to be a point in comparison with the sphere, the points in which a line intersects the sphere may be supposed opposite, whether the line passes through the centre or the surface of the earth. II. Every plane through the earth intersects the sphere in a great circle. III. For every such plane tJiere is one line thrmigh the centre of the earth intersecting the plane at right angles. This line meets the sphere at tlie poles of the great circle in which the plane intersects the sphere. Example. — P P\ Fig. 1, is the line through perpen- dicular to the plane A B. P and P' are the poles of A B. IV. Every line through the centre has one plane per- pendicular to itf which plane intersects the sphere in the great circle whose poles are the intersections of the line with the sphere. Example. — The line Q Q' has the one plane CD through O perpendicular to it. § 3. RELATION OF THE SFHEBE TO THE HOBI- ZON-PLANB OP THE HORIZON. A level plane touching the spherical earth at the point where an observer stands is called thr plane of the horizon. If we imagine this plane extended out indefinitely on all sides so as to reach the celestial sphere, it will inter- sect the latter in a great circle, called the celestial horizon. The celestial horizon is therefore the boundary between the visible and invisible heini8j)heres, the view of the lat- ter being cut off by the earth. We may also imagine a plane passing through the cen- tre of the earth, parallel to the horizon of the observer. This plane will intersect the celestial sphere in a circle below that of the observer's horizon by an amount equal to the radius of the earth. This circle is called the rational horizon., while that first defined is called the sensible horizon. But when the celestial sphere is con- sidered so imr^.ense that the earth may be regarded as a RELATIONS OF THE JiUlilZON. 13 Fig. 4. The Visible Hemisphere— 5 iV. the horizon ; Z, the zenith ; \vs that ler they lifEerent Inch the ies from thence and up [•idian is )oles of fne pole e/' meri- \^r meri- to the leridian kneauing earth's |nigh the Naval DIUHNAL MOTION IX DIFFKHKST LATITUDES, 'il < 5 THE DIURNAL MOTION IN DIFFERENT LATI- TUDES. As wo have seen, the celestial horizon of an observer will change its place on the celestial .sphere as the observer travels from place to place on the surface of the earth. If lie moves directly toward the noith his zenith will aj)- i)roacii the north pole, but as the zenith is not a visible ])(»int, the motion M'ill be naturally attributed to the pole, which will seem to approach the point overhead. The new apparent i)osition of the pole will change the aspect of tlie observer's sky, as the higher the pole appears above i the honzc)n the greater the circle of perpetual apparition, ^ and tlierefore the greater the number of stare, which never set. ZP f I -- ' \ " f — 1 I i ^'f^jj'f '■■^ H< iL/LUU / \\ • / / ^^^-^ ^ _— - ^ / 1 FlO. 8. — THK PAKALLEL SIMIKKE. If the observer is at the north pole his zenith and the bole itself will coincide : half of the stars onlv will be vis- Jble, and these will never rise or set, but appear to move Tioimd in circles parallel to the horizon. The horizon jrid equator will coincide. The meridian Avill be indeter- liuate since Zand P coincide ; there will l>e no east and post line, and no direction but south. The sphere in this pso is called a parallel sphere. If iristeiid of travellin^"^ to the nortli tlie ohscrver elionld go toward the c'«jiiator, the iiortli pole wouM seein to aj)- proacli liin liori/on. When lie readied tlie equator both poles would lie in the horizon, one north antl the otlier south. All the ntars in HUcee.ssion would then he visible, and eat'h would be an equal time above and below thj horizon. FlU. 9. — TICK UIOilT 81*11 KllE. The sphere in this case is called a 7'i(/ht pphere, because the (linrnal motion is at riijrht auijles to the horizon. If now the observer travels southward from the equator, the soutli pole will become elevated above his horizon, and in the southern hemis])here appearances will be reproduced'! M'liich we have already described for the northern, except that the direction of the motion will, in one respect, he | different. The heavenly bodies will still rise in the eatit and set in the west, but thoKo near the e([uator will pass|| north of the zenith instead ol south of it, as in our lati- tudes. The sun, instead of movinoj from left to riglit,| there uioves from right to left. The bounding line be- tween the two directions of motion is the equator, wherei the sun culminates north of the zenith from March tiilf September, and south of it from September till Marcli. If the observer travels west or east, the characteij of the diurnal motion will not change. CIIiCLh'S OF TJIh: ^"H'llHUl':. 88 I to ap- or both u other viwible, low thj 3S because If now le soutli in the M'odnced 1, except pect, be the east will V^^i our lati- to right I line bo- wbere| ylarch tillj Marcli. character] or, § 6. CORRESPONDENCE OF THE TERRESTRIAL AND CELESTIAL SPHERES. Fiiiiihimfnttd propoHtfion.— The (iltltu(Je of the pole iihoir tin' horizon in equal to the lotitnde of thej)lace. This may be Hhown an follows : Let L be a place on the earth PKpQ^ Pp being the earth's axis, and E Q its equator, Z is the zenith, and 11 It tlie liorizon of L. L O Q is the latitude of L .iccord- iii<; to ordinary geographical defiiiitions : i.e.^ it is its an- jjjular distance from the equa- tor. Prolong O I* indefinitely to P' anil (b'aw L P" par- allel to it. To an observer at L, the elevated pole of the lieavuns will bo seen along tlie line L P'\ because at an iiitiiiite distance the distance P' P" will appear like a point. JILZ = POQ, and P" LII—LOQ — that is, the elevation of the pole above the celestial horizon L II is ecpuil to the latitude of the place as stated. Correspondence of zeniths. — The zenith of any point on the surface of the earth is considered as a corresponding point of the celestial sphere. If for a moment we suppose both spheres at rest, an observer travelling over the earth would find his zenith to mark out a path on the celestial sphere corresponding to his path on the earth. To un- dei-stand the relation, we may imagine that the observer's zenith is marked out by an infinitely long pencil, extending vertically above his head to the celestial sphere. Let Fig. 11 represent the celestial sphere, with the earth 111 the centre. Fig. 10. ZLP" = ZOP\ hence 24 ASTliONOMT. At either pole of the eaitlt (« or n), the vertical line will extend to the celestial pole, JV jH or /S J*f and the Pio. 11. Correspondence of Circles on the Celestial and Terrestrial Spherci;. i^er'th will remain the srlne from day to day, l)eeaase the position of the observer is not changed by tlie rota- tion oi tlie earth. If the observ^er is in latitude 45", he will in tw"ent3'-fonr hours, by the rotation of the earth, be carried around on a parallel of -terrestrial latitude, 45° from the north pole of the earth. His zenith will, during the same time, describe a circle 31 L on the celestial sphere, corresponding to this parallel of latitude on the earth ; that is, a circle 45° from the celestial pole and 45° from the coi.^stial equator. Next, let us suppose the observer on the earth's equator at e or q^. His zenith will then be 90° from each pole. As the earth revolves o:i its axis, his zenith will describe u V: CIRCLES OF THE SPHERE. 25 preat circle, E Q, around the celestial sphere. This circle is, in fact, the celestial equator. The line from the centni of the earth through the observer to his zenith will de- peribe a plane, namely, the plane of the equator. (Cf. Fig. 5.) ^ An observer in 45° south latitude, will be half way be- tween the equator and the south pole. By the diurnal motion of the earth, he will be carried around on the paral- lel of 45^ south terrestri .1 latitude. Since his zenith is con- tinually 45° from the pole, it will describe a circle, S 0, in the celeiitial sphere of 45° south polar distance. Thus, for each parallel of latitude on the earth, we have a corresponding circle on the celestial sphere, having its pole at the celestial pole. Let us now inquire how far the same thing t«; true of the meridians. The relation of the meridians is complicated by the earth's rotation, in consequence of which tlie celestial meridian of any place is continually in motion from west to east on the celestial t])liere. To express the same thing in another form, tho celestial sphere is apparently in motion from east to west, across the terrestrial meridian, the latter, it will be re- membered, remaining at rest relative to any given place on the earth. A north and south wall on the earth is al- ways ill the common plane of the terrestrial and celestial meridians of the place where it stands. Suppose now that we couhi by a sweep of a pencil in a moment mark out the semicircle of our meridian upon the heavens by a line from the north pole through the zenith and south horizon, to the south pole. At the end of an hour this semicircle would h? e apparently moved 15° toward the west by the diurnal motion. Then im- agine that we again mark our meridian on the celestial sphere. The two semicircles will meet at each pole and be widest apart at the equator. Continuing the process for twenty-four hours, we should have twenty-four semi- circles, all diverging from one pole and meeting at the 26 ASTRONOMI. other, as shown in Fig. 11. The circles thus formed are called hour circles. Hence the definition : Hour circlea on the celestial sphere are circles passing through the two poles and therefore cutting the equator at right angles. The Jiour circle of any particular star is the hour circle [lassing through that star. In Figure 11a let the outline represent the celestial sphere ; Z being the zenith and P Fig. 11a.— circles of the sphere. the north pole. Let A be the position of a star. Then PAB is, by definition, part of the hour circle of the star A. The angle ZPA its then called the hour angle of the star. Hence the definirion : The hour angle of a star is the angle which its hour circle makes with the meridian of the place. The hour angle of a star is, therefore, continually chang- ing in consequence of the diurnal motion. The declination of a etar is its distance from the equa- tor north or south. Thus, in the figure, CWDE is the C3lestial equator and the arc ^ -4 is the declination of 6- AIOIIT ASCENSION AND DECLINATION 37 the star A. By tlie previous definition, P Ah the polar distance of the star. Because P B is 90°, it follows that the sum of the polar distance and declination of a star make 90°. Therefore, if we put p, the polar distance of the star, and 6 its declination, we shall have : p-^S = 90°. (5 = 90°—^. The declination and hour angle of a star are two co ordinates which completely define its position. From Figure 11a it can at once be seen that the lati- tude of a place on the earth's surface is equal to the declination of the zenitli of that place, since the declina- tion of the zenith is equal to the altitude of the elevated I'ole. § 7. RIGHT ASCENSION AND DECLINATION. Since the hour angle of a heavenly body is continually dianging in consequence of the diurnal motion, it is necessary to have fixed circles on the sphere to which we may refer the position of a star. The circles already dc- fiicribed will enable us to do this. We call to mind that to determine the longitude of a ])lace, we choose some meridian, that of Greenwich or Washin. . I LONarruDK n r viihonometicrs. 37 cation, but necofisarily limited to places in telegraphic c'oiiiiminication with each other. Longitude by Motion of the Moon. — When we de- ecribe the motion of the moon, we Hhall hoc that it moves eastward among the stars at the rate of about thirteen de- grees per day, more or less. In other words, its right as- cension is constantly increjising at the rate of a degree in istiiiething less than two hours. If, then, its right ascension can be predicted in advance for each hour of (Greenwich or Washington time, an observer at any point of the earth, by noting the local time at his station, wlien the moon has any given right ascension, can thence determine the corresponding moment of Green wicli time ; and hence, from the difference of the local times, the longitude of his ])lace. The moon will thus serve the purpose of a sort of clock running on (irrcenwich time, upon the face of which any observer with the proper appliances can read the (ircenwich hour. This method of determining longitudes ^ , whether of angles or lines, which define its pjslilon. For in! fix a position on a sphere or other surface, two co-ordl- uuiu.'4 are nuce» COS or we may use : sin'i^ COS ( — 6) — sin a cos COS 6 Having thus found h, wo have Sidereal time = h + u, a being the star's right ascension, and the hour angle A being changed into time by dividing by 15. nr. An interesting form of this last problem arises when we sup- pose a = 0, which is the same thing as supposing the star to be io ASTRONOMY. 45 the horizor and thererore to be rising or setting. The vnlue of A will then be the liour angle at which it rises or sets ; or being changed to time by dividing by 15, it will be the interval of sidereal tiint; lietween its rising and its passage over the meridian, or be- tween this passage and its setting. This interval is called the semi- iliurnal arc, and by doubling it we have the time between the risin<; and setting of the star or other object. Putting « = in the preceding expression for cos h we find for the semi-diurnal arc A, CCS h = — Pig. 15. — UPPER AND LOWEK DIUR- NAL ARCS, sin sin d cos ?» cos 6 =^ — tan ^ tan (J, and the arc during which the star is above the horizon is 3 h. From this formula may be deduced at once many of the results given in the preceding sections. (I). At the poles = 90% tan 6 = infinity, and therefore cos h = infinity. But the cosine of an angle can never be greater than unity ; there is therefore no valufr of h which fulfils the condition. Hence, a star at the pole can neither rise nor set. (2). At the earth's equator * = 0% tan = 0, whence cos 7t = 0, h = 90\ and 2 h = 180', whatever be r5. This being a semicircum- ferenceall the heavenly bodies are hilf the time above the horizon n> an observer on the equator. (3). If d = 0° (that is, if the star is on the celestial equator), then tan (5 = 0, and cos 7* = 0, A = 90% 2 A = 180°, so that all stars on (he equator are half the time above the horizon, whatever be the lati- tude of the observer. Here we except the pole, where, in this case, tan p tan (J = a x 0, an indeterminate quantity. In fact, a star on the celestial equator will, at the pole of the earth, seem to move round in the horizon. (4). The above value of cos A may be expressed in the form : cos A = — tan i cot tan f? tan (l»0 — «) This shows that when 6 lies outside the limits + (90° — (p) and — (90° — 90°, 2 A > 180*. Witli '■ t f la ASTRONOMY. negative S, cos h is positive, h < 90°, 2 A < 180'. Hence, in north- ern latitudes, a northern star is more than half of the time above the horizon, and a southern star less. In the southern hemisphere,

= Ig sin (J = — Ig sin ^ sin 6 = — sin sin 8 = sm a = a — sin sin 8 = Ig cos cos 6 — = 9 9 Ig cos cos 6 = Ig (sin a— sin sin ^,) = Ig cos h = h = A -f- 15 = a = sidereal time = 332478 797879 161681 959560 091109 215020 806129 891151 995379 886530 485905 9-599375 66° 34' 33" 4'' 26" 18'.20 5h 8'»44'.27 9'' 35" 2'.47 (2). Had the star been observed at the same altitude in the east, what would have been the sidereal time ? Ana. a — h = 0^ 42" 26'.07. DETERMINA TION OF LA TITUDE. 47 (3). At what sidereal time does Rigol rise, and at what sidereal tinif does it set in the latituue of Wasliington ? — tg0 = — 9- 906728 tgd = _ 9166301 cos /< = — 9 073029 A ^ 15 = a = 83 12' 19' 51, 32... 4y».27 51. 8"'44-.27 rises 23'' 35'" 55\00 sets 10''41'"33\54 (4). What is the greatest altitude of Rigel above the horizon of Washington, and what is its fjjrcatest depression below it V Ans. Altitude=42^ 45' 45' ; (lepression=5» 26' 67'. (5). What is the greatest altitude of a star on the equator in the meridian of Washington V Ans. 51" 6' 21". (6). The declination of the pointer in the Great Bear which is nearest the pole is 62^ 30' N., at what altitude does it pass above the pole at Washnigton, and at what altitude does it pass below it V Ans. 66' 23' 39" above the pole, and 11' 23' 39' when below it. (7). If the declination of a star is 50" N., what length of sidereal time is it above the horizon of Washington and what length below it (luring its apparent diurnal circuit'/ Ans. Above, 21'' 52'" j below, 2'' H'". Ml. DBTBKMINATION OF LATITUDES ON THE EABTH BY ASTBONOMICAIi OB3EBVATIONS. Latitude from circumpolar stars. — In Fig. 16 let ^ represent the zenith of the place of observation, Pthe pole, and IIPZ li the me- ridian, the observer being at the centre of the sphere. Suppose (Sand ti' to be the two pouits at which a circumpolar star crosses the meridian in the de- scription of its apparent diurnal orbit. Then, since P is midway between 8 and 8\ ZS + ZS' „„ -„- = ZP=9O"-0, or, Z + Z' = 90" - = li[(,^ + 6') + {Z-Z')]. It will be noted that m this meth- od the latitude depends sim))ly upon the mean of two declinations which can be determined before- hand, and only recjuires the (f{ft'er- eiice of zenith distances to be ac- curately measured, while the ab- solute values of these are unknown. In this consists its advantage. Latitude by a Single Aititude of a Star.— In the trian{>;le Z I'S (Fig. 14) the sides are Zl = 90° - ; P 8 = 90° - (5 ; Z1S = Z = 90° — a\ Z PS = h = the hour-angle. If we can measure ut any known sidereal time the altitude a of the star sin 6 + cos <> cos 6 cos h (ll a and is not absolutely constant for all parts of the earth, and its greatest value is usually taken as that to which the hori- zontal value shall be referred. This greatest value is, as we shall hereafter see, the radius of the equator, and the I '. 52 ASTRONOMY. correp ponding value of the parallax is therefore called the equator kd horizontal parallax. When tlie distance /• of tlie body is known, the fvi'i^- torial iiorizontal parallax can be found by the first of the above equations ; when the parallax can be observed, the distance r is found from tlie second equation. How this is done will be described in treating the subject of celep- tial measurement. It is easily seen that the equatorial horizontal parallax, or the angle C P S, is the same as the angular semi- diameter of the earth seer, from the object P. In fact, if we draw the line P ^ tangent to the earth at S', the angle S P S' will be the apparent atigular diameter of the earth as seen from P, and will also be double the angle OPS. The apparent semi-diameter of a heavenly body is therefore given by the same formulte as the parallax, its own radius being substituted for that of the earth. If we put, p, the radius of the body in linear measure ; r, the distance of its centre from the observer, expressed in the same measure ; 8. its angular semi-diameter, as seen by the observer j we sl"\ll have, sm 8 — -. r If we measure the semi-diameter .v, and know the dis- tance, r, the radius of the body will be /o = r sin s. Generally the angular semi-diameters of the heavenly bodies are so small that they may be considered the same as their sines. We may tlierefore say that the apparent angular diameter of a iieavenly body vares inversely as its distance. CHAPTER II. - 1 •". ASTRONOMICAL INSTRUMENTS. § 1. THE BEFBACTINa TELESCOPE. In explaining the theory and use of the refracting tele- 6eo})e, we shall assume that the reader is acquainted with tlio fundamental p'^inciples of the refraction and disper- sion of light, so chat the simple enumeration of them will recall them to his mind. These principles, so far as wo have occasion to refer to them, are, th^t when a ray of light passing through a vacuum cntera a trans- parent medium, it is refrac*^od or hent from its course in a direction toward a lino perpendicular to the sur- face at the point wiion5 the ray enters ; that this bend- iii<]^ follows a certain law known as the law of sines ; that when a pencil of rays emanating from a luminous point falls nearly perpendicularly upon a convex lens, the rays, after pjissing through it, all converge toward a point on the other side called a focus : that light is com- poimded of rays of various degrees of refrangibility, so that, when thus refracted, the component rays pursue slightly different courses, and in passing through a lens come to slightly diflFerent foci ; and finally, that the ap- parent angular magnitude subtended by an object when viewed from any point is inversely proportional to its distance.* * More exactly, In the case of a globe, the sine of the angle is In- vcibuly as the distance of the object, as shown un the preceding page. We shall ^4 ASTRONOMY. first describe the telescope in its simplest form, showing the principles upon which its action depends, leaving out of considera- tion the defects of aberration which require special devices in order to avoid them. In the simplest form in which we can conceive i of a telescope, it consists of two lenses of I unequal focal lengths. The purpose of one \ of these lenses (called the objective, or object I glass) is to bring the rays of light from a I distant object at which the telescope is I pointed, to a focus and there to form an I image of the object. The purpose of the I other lens (called the eye-piece) is to view ! this object, or, more precisely, to form an- , other enlarged image of it on the retina of the eye. i The figure gives a representation of the 1 course of one pencil of the rays which go to ' fonn the image A 1' of an object / B after i passing through the objective 0', The ; pencil chosen is that composed of all the j rays emanating from / which can possibly i fall on the objective 0'. All these are, , by the action of the objective, concentrated ! at the point /. In the same way each point j of the image out of the optical axis A B \ emits an oblique pencil of diverging rays which are made to converge to some point \ of the image by the lens. The image of ; the point B of the object is the point A of the image. "We must conceive the image of any object in the focus of any lens (or mirror) to be formed by separate bundles of rays as in the figure. The image thus formed becomes, in its turn, an object to be viewed by the eye-piece. After the rays meet to form MAGNIFYING POWER OF TELESCOPE. 55 tlic image of an object, as at Ty tliey continue on their coui*se, diverging from I' as if tlie latter were a material object reflecting the liglit. There is, however, this excep- tion : that the rays, instead of diverging in every direction, only form a small cone having its vertex at T, and having its angle equal to O I' 0'. The reason of this is that only those rays whicli pass through the objective can form the image, and they must continue on their course in straight lines after forming the image. This image can now be viewed by a lens, or even by the unassisted eye, if the observer places himself behind it in the direction Aj so that the pencil of rays shall enter his eye. For the pres- ent we may consider the eye-piece as a simple lens of short focus like a common hand- magnifier, a more com- plete description being given later. Magnifying Power.— To undei*stand the manner in which the telescope magnifies, we remark that if an eye at tlie object-glass could view the image, it would appear of the same size as the actual object, the image and the object subtending the same angle, but lying in opposite direc- tions. This angular magnitude being the same, M'hatever tlie focal distance at which the image is fonued, it follows that the size of the image varies directly as the focal length of the object-glass. But when we view an object with a lens of small focal distance, its apparent magnitude is the same as if it were seen at that focal distance. Consequently tJie apparent angular magnitude will be inversely as the focal distance of the lens. Hence the focal imagre as seen with the eye-piece will appear larger than it would when viewed from the objective, in the ratio of the focal distance of the objective to that of the eye-piece. But we have said that, seen through the objective, the image and tlie real object subtend the same angle. Hence the angu- lar magnifying power is equal to the focal distance of the objective, divided by that of the eye piece. If we simply turn the telescope end for end, the objective becomes the eye-piece and the latter the objective. The ratio is in- 56 ASTRONOMT. I V verted, and the object is diminished in size in the same ratio tliat it is increased when viewed in the ordinary way. If we should form a telescope of two lenses of equal focal length, by placing them at double their focal distance, it would not magnify at all. The image formed by a convex lens, being upside down, and appearing in the same position when viewed with the eye-piece, it follo^rs that the telescope, when constructed in the simplest manner, shows all objects in- verted, or upside down, and right side left. This is the case with all refracting telescopes made for astronomical uses. Light-gathering Power.— It is not merely by magnify- ing that the telescope assists the vision, but also by in- creasing the quantity of light which reaches the eye from the object at which we look. Indeed, should we view an object through an instrument which magnified, but did not increase the amount of light received by the eye, it is evident that the brilliancy would be diminished in propor- tion as the surface of the object was enlarged, since a con- stant amount of light would be spread over an increased surface ; and thus, unless the light were brilliant, the object might become so darkened as to be less plainly seen than with the naked eye. How the telescope increases the quantity of light will be seen by considering that when tlie unaided eye looks at any object, the retina can only re- ceive so many rays as fall upon the pupil of the eye. i^y the use of the telescope, it is evident that as many rays can be brought to the retina as fall on the entire object- glass. The pupil of the human eye, in its normal state, has a diameter of alwut one fifth of an inch ; and by the use of the telescope it is virtually increased in surface in the ratio of the square of the diameter of the objective to the square of one fifth of an inch. Thus, with a two-inch aperture to our telescope, the number of rays collected is one hundred times as great as the number collected with the naked eye. POWER OF TELESCOPE. With a 5-inch object-glass, the ratio is (( 1Q (( (i (( (( t( <( 25 '^ '' '' " '< (( 20 " '^ " " '' i( 26 '' '' '* '' '' 57 625 to 1 2,500 to 1 5,625 to 1 10,000 to 1 16,900 to 1 ; i; "When a minute object, like a star, is viewed, it is necessary that a certain number of rays should fall on the retina in order that the star may be visible at all. It is therefore plain that the use of the telescope enables an observer to see much fainter stars than he could detect M'itli the naked eye, and also to see faint objects much better than by unaided vision alone. Thus, with a 26- iiieli telescope we may see stars so minute that it would require many thousands to be visible to the unaided eye. An important remark is, however, to be made here. Inspecting Fig. 20 we see that the cone of rays passing through the object-glass converges to a focus, then diverges at the same angle iinally passing through the eye-piece. After this passage the rays emerge from the eye-piece parallel, as shown in Fig. 22. It is evident that the diameter of this cylinder of parallel rays, or " emergent pencil," as it is called, is less than the diameter of the object-glass, in the same ratio that the focal length of the eye-piece is less than that of the object-glass. For the central ray / T is the common axis of two cones, A F and T 0\ having the same angle, and equal in length to tiie respective focal distances of the glasses. But this ratio is also the magnifying power. Hence the diameter of the emergent pencil of rays is found by dividing the (liiinieter of the object-glass by the magnifying power. Now it is clear that if the magnifying power is so small tliat this emergent pencil is larger than the pupil of the fye, all the light which falls on the object-glass cannot enter the pupil. This will be the case whenever the magnifying power is less than five for every inch of ai)erture of the glasf . If, for example, the observer should VO' ^it i fit 1 k w ff 58 ASTRONOMY. look through a twelve-inch telescope with an eye-pieco BO large that the magnifying power was only 30, tho emergent pencil would be two fifths of an inch in diani- eter, and only so much of tho light could enter tlie pupil as fell on the central six inches of the object-glass. Practically, therefore, the observer would only be using a six-inch telescope, all the light which fell outside of tho six-inch circle being lost. In order, thei-efore, that he may get the advantage of all his object-glass, he must use a magnifying power at least five times the diameter of his objective in inches. When the magnifying power is carried beyond this limit, the action of a telescope will depend partly on the nature of the object one is looking at. Viewing a star, the increase of power will give no increase of Hght, and therefore no increjise in the apparent brightness of the star. If one is looking at an object having a sensible surface, as the moon, or a planet, the light coming from a given portion of the surface will be spread over a larger portion of the retina, as the magnifying power is increased. All magnifying must then be gained at the expense of the apparent illumination of the surface. "Whether this loss of illumination is important or not will depend entirely on how much light is to spare. In a general way wo may say that the moon and all the plan- ets nearer than Saturn are so brillianily illuminated by the sun that the magnifying power can be carried many times above the limit without any loss in the distinctness of vision. The Telescope in Measiirement. — A telescope is gen- erally thought of only as an instrument to assist the eye by its magnifying and light-gathering power in the man- ner we have described. But it has a very important additional function in astronomical measurements by en- abling the astronomer to point at a celestial object with a certainty and accuracy otherwise unattainable. This func- tion of the telescope was not recognized for more than USE OF TELESCOPE. 60 fialf a century after its invention, and after a long and rather acrimonious contest between two scliools of astron- oiriers. Until the middle of the seventeenth century, when an astronomer wislied to determine the altitude of a celestial object, or to measure the angular distance be- tween two stara, he was obliged to point his quadrant or other measuring instrument at the object by means of " pinnules. " These served the same purpose as the sights on a rifle. In using them, however, a difliculty arose. It was impossible for the observer to have distinct vision both of the object and of the pinnules at the same time, because when the eye was focused on either pinnule, or on tlie object, it was necessarily out of focus for the others. The only way to diminish this difficulty was to lengtlien the arm on which the pinnules were fastened so that the latter should be as far apart as possible. Thus Tyciio Bkahk, before the year 1600, had measuring in- struments very much larger than any in use at the pres- ent time. But this plan only diminished the difficulty and could not entirely obviate it, because to be manageable tlie instrument must not be very large. About 1670 the English and French astronomers found that by simply inserting fine threads or wires exactly in tlie focus of the telescope, and then pointing it at the ob- ject, the image of that object formed in the focus could be made to coincide with the threads, so that the observer could see the two exactly superimposed upon each other. AVhen thus brought into coincidence, it was known that the point of the object on which the wires were set was in a straight line passing through the wires, and through the centre of the object-glass. So exactly could such a point- i:ig be made, that if the telescope did not magnify at all (the eye-piece and object-glass being of equal focal length), a very important advance would still be made in the ac- curacy of astronomical measurements. This line, passing centrally through the telescope, we call the line of col- Umation of the telescope, A B in Fig. 20. If we have *:i ^i ru "■ it T?--'. [L' ! .V no ASTltONOMY. any way of determining it we at once realize the idea ex. pressed in the opening chapter of this book, of a pencil ex- tended in a definite direction from the earth to the heav- ens. If the observer simply sets his telescope in a fixed position, looks through it and notices what stars piiss alon^r the threads in the eye-piece, he knows that those stars all lie in the line of collimation of his telescope at that instant. By the diurnal motion, a pencil-mark, as it were, is thus being made in the heavens, the direction of which can be determined with far greater precision than by any meas- urements with the unaided eye. The direction of this line of collimation can be determined by methods which we need not now describe in detail. The Aohromatio Telescope. — The simple form of tele- scope which we have described is rather a geometrical conception than an actual instrument. Only the earli- est instruments of this class were made with so few as two lenses. Galileo's telescope was not made in the form which we have described, for instead of two convex lenses having a common focus, the eye-piece was concave, and was placed at the proper distance inside of the focus of tiie objective. This form of instrument is still used in opera- glasses, but is objectionable in large instruments, owing to the smallness of the field of view. The use of two con- vex lenses was, we believe, first propcsed by Kepleu. Although telescopes of this simple form were wonderful instrumants in their day, yet they would not now be re- garded as serving any of the purposes of such an instru- ment, owing to the aberrations with which a single lens is affected. We know that when ordinary light passes through a simple lens it is partially decomposed, the differ- ent rays coming to a focus at different distances. The focus for red rays is most distant from the object-glass, and that for violet rays the nearest to it. Thus arises the ohromatic aberration of a lens. But this is not all. Even if the light is but of a single degree of refrangi- bility, if the surfaces of our lens are spherical, the rayii A CimOMA no OBJECTOLASS. 61 wliicli pass near the edge will come to a shorter focus than tliose whicli pass near the centre. Thus arises tijihi'i-ical aherration. This aberration might be avoided if lenses could be ground with a proper gradation of curvature from the centre to the circumference. Prac- tically, however, this is impossible ; the deviation from uniform sphericity, which an optician can produce, is too email to neutralize the defect. Of tliese two defects, the chromatic al)erration is much the more serious ; and no viray of avoiding it was known until the latter part of the last century. The fact had, indeed, been recognized by inuthematicians and physicists, that if two glasses could be found having very different ratios of refractive to dispereive powei*s,* the defect could be cured by combining lenses made of these different kinds of glass. But this idea was not realized until tho time of DoLLOND, an English optician M'ho lived during the last century. This artist found that a concave lens of Hint glass could be combined with a convex lens of crown of double the curvature in such a manner that the dispersive pouers of the two lenses should neutralize each other, being equal and acting in opposite di- rections. But the crown glass having the greater refractive power, owing to its greater cur- vature, the rays would be brought to a focus without dispersion. Such is the construction of the achromatic objective. As now made, the outer or crown glass lens is double convex ; the inner or flint one is generally nearly plano-concave. Fig. 21 shows the section of such an objective jis made by Alvan Clark & Sons, the inner curves of the crown and flint being nearly equal. * By the refractive power of a glass is meant its power of bending tlie rays out of tlieir course, so as to bring tliem to a foeiis. By its dittper- dve lumer is meant its power of separating tlie colors so as to form a spectrum, or to produce cliromatic aberration. Pig. 21.— section of object- glass ¥ n' I €2 ASTRONOMY. A great advantage of the achromatic o])jectiv(' is that it may be made to correct the splierical lus well as the c'lro- matic aberration. Tliis is effected by giving the propiT curvature to the various surfaces, and by making such slight deviations ^rom perfect sphericity that rays passinj^ through all parts of the glass shall come to the same focus. The Seoondary Speotmm. — It m now known that tlio cliromatic aberration of an objective cannot be perfectly corrected with any combination of glasses yet discovered. In the best telescopes the brightest rays of the spectrum, wliich are the yellow and green ones, are all brought to the same focus, but the red and blue ones reacli a focus a httle farther from the objective, and the violet ones a focus still farther. Hence, if we look at a bright star through a large telescope, it will be seen surrounded by a blue or violet light. If we push the eye-piece in a little the enlarged inuige of the star will be yellow in the centre and purple around the border. This sepai on of colors by a pair of lenses is called a secondary spectram. Eye-Fieoe. — In the skeleton form of telescope before described the eye-piece as well as the objective was con- sidered as consisting of but a single lens. But with such an eye -piece vision is imperfect, except in the centre of the field, from the fact that the image does not throw rays in every direction, but only in straight lines away from the objective. Hence, the rays from near the edges of the focal image fall on or near the edge of the eye- piece, whence arises distortion of the image formed on the retina, and loss of light. To remedy this ditHculty a lens is inserted at or very near the place where the focal image is formed, for the purpose of throwing the different pencils of rays which emanate from the several parts of the image toward the axis of the telescope, so that they shall all pass nearly through the centre of the eye lens pro- per. These two lenses are together called the eye-piece. There are some small differences of detail in the con- struction of eye-pieces, but the general principle is the TUEORT OF ODJECru LASS. eri same in all. The two rccop^nized chwscfi are tlio powi- tive and negative, the i'urnier being thuKe in which the iiiiiige is formed before tlie liglit readies tin- field lens ; the iKirative those in which it is formed between the lenses. TliP figure shows the positive oyc-piorc! (lr:iwnnoniriitp|y to srnle. () / is one of the conver( the eye-pieei,' us ii real oi»j('ct, ami the shadeil nincil l)etween F and A' shows the courHC! of these rays after de- viiition hy F. If tliere were no I'lic-len^ K an eye properly placed btyond /' would see an image at / a . The eye-len^ K receives the pencil of rays, and deviates it to the observer's eye pifr cd at such a point that the whole incident pencil will pxss thuM|M;|| the pupil uuse A n, F\ft. 2''\, to l)u II li'tis or coinhiiiiition of Iciihoh on wliicli \\\v light fulls from the left hiuul and pasHos through to the right. HuppoHc ruyn parullil to Ji I' to fall on evt-ry part of thu first surface of the glass. After passing through it they are all supposed to converge nearly or vy. actly to the same point li". Among nil these rays there is one, ami one only, the course of which, after emerging from the glass at (^, will he parallel to its original direction li J\ Let li P Q li' be this central ray, which will be completely determined by the direction from which it comes. Next, let \\h take a ray coming from another direction as S I*. Among all the rays parallel to S I\ let us take that unvi which, after emerging from the glass at 7', moves in a lino parallel to its original direction, ('ontinuing the process, let us suppose isolated rays coming from all parts of a distant object sub- ject to the single condition that the course of each, after passim; through the glass or system of glasses, shall be parallel to its original course. Tliese rays we may call eciitrid nn/H. They have this re- markable property, pointed out by Uauhs : tliut they uli converge if:! Fkj. 23. toward a single point, P, in coming to the glass, and diverge from another point, 7*^, after passing through the last lens. Those points were termed by Gauss " Ilauptpunkte," or principal points. But they will probably be better understood if we call the tint one tlic centre of convergence, and the second the centre of divergence. It must not be understood that the central rays necessarily pass through these centres. If one of them lies outside the first or last refracting surface, then the central rays must actually pass through it. But if they lie between the surfaces, they will be fixed by the continuation of the straight line in which the rays move, the latter being refracted out of their course by passing through the surface, and thus avoiding the points in question. If the lens or system of lenses be turned arouna, or if the light pas.ses through them in an opposite direction, the centre of convergence in the first case be- comes the centre of divergence in the second, and vice verm. The necessity of this will be clearly seen by reflecting that a return ray of light will always keep on the course of the original ray in the opposite direction. 1 1 TIIKORY OF (WJECr.OLASS. 65 The flffuro reprcscntH a plano-convex Icnn with lif?Iit fallinfif on the (onvfx side. In thin case tlu; centre of converfjence will bo oil tlx^ on vex surface, and that of divergence inside the glass iilMHit one third or two Hfths of the way from the convex to the pliiiic surface, the positions varying with the refractive index of the frh\sn. Ill u double convex lens, both i)oints will lie inside the glass, wliilc if u glass is concave on one side and convex on the other, one of the points will be outside the glass on the concave side. It must be remembered that the positions of these (;entres of conver- gence and divergence depend solaly on the form and size of the •s and their refractive indices, an ' do not refe IfllM': jfer in any way to tlic distances of the objects whose iinii^ cs they form. The principal pro]»erties of a lens or objective, by which the size of iiii ii^es are determined, are as follows : Since the angle .S' 1*' li' nuuli' i)y the diverging rays is equal to li 1* S, made by the con- vcrjriiig ones, it follows, that if a lens form the image of an object, till' si/e of the image will be to that of the object as their respec- tive distances from the centres of convergence and divergence. In other words, the ooject seen from the centre of convergence /'will lie of the Slime angular magnitude as the image seen from tlie ciiitrc of divergence J". Uy roiijugnte fori of a lens or system of lenses we mean a pair of ]i(iiiits such that if rays diverge from the one, they will converge to the ftther. Hence if an object is in one of a pair of such foci, the iinii>,'e will be formed in the other. By the refrdctice power of a lens or combination of lenses, we mean its influence in refr»»,.:tinj.' parallel rays to u focus which we may measure by the reciprocal of its focal distance or 1 -^-f. Thus, ilic power of a piece of plain glass is 0, because it cannot bring rays to a focus at all. The power of a convex lens is positive, while tliat of a concave lens is negative. In the latter case, it will be iciiH'inbered by the student of optics that the virtual focus is on the same side of the lens from which the rays proceed. It is to lie noted that when we speak of the focal distance of a lens, we nuan the distance from the centre of divergence to the focus for liaialh.'l rays. In astronomical language this fo(!Us is called the stellar focus, being that for celestial objects, all of which we may re<,'ard as infinitely distant. If, now, we put /', the power of the lens ; /'. its stellar focal distance ; f, tlie distance of an object from tlie centre of convergence ; /', the distance of its image from the centre of divergence ; then the eijuatiou which determines/ will be 1 1 1 f+f-j-P/ or. ff_ j'-f /' = t;'-S From these equations may be found the focal length, having the ilistance at whicti the image of an object is fomied, or vice verta. 89 ASTKONOMY. % 2. BEFLECTING TELESCOPES. Ab wc have seen, the most essential part of a refracting telescope is the objective, which brings all the incident rays from an object to one focus, fonning there an imago of tlui object. In reflecting telesco])e8 (i-ctlectoi's) the objective is a mirror of speculum metal or silvered glass ground to the shape of a jjaraboloid. The tigure shown the action of such a mirroi on a bundle of ])arallel rays, which, after imj)inging on it, are brought hy retlection to one focus 1\ The image formed at this focus may be viewed with an eye-])iece, as in the case of the refracting telescope. The eye-pieces used with such a mirror arc of the kinds already described. In the ligm*e the eye-piece would Pig. 24. — concave Minnon fohmtno an image. have to be placed to the right of the point F, and the observer's head would thus interfere with the incident light. Various devices have been ])ropoi?e(i to remedy this inconvenience, of which we will des'jribe the two most common. The Wewtonian Telescope. — In this form the rays of light reflected from the mirror are made to fall on a small phuio mirror placed diagonally just before they reach tho principal focus. Tho rays are thus reflected out laterally through an opening in the telescope tube, and are theie brought to a focus, and the image formed at the point inarlvcd by a heavy white line in Fig. 25, instead of at Uie point inside tho telescope marked by a dotted lino Tills focfl 'h'nary ey of tlie tel Tiiis de nbwtoniai The Cassef arv convex n REFLECTINO TKL ESC OPES. 67 This focal image is tlien ex.imined l\v means of an or- HiKiry eye-piece, the licad of tlie observer being outside of tlie telescop? tube. This device is the invention of Sir Isaac Nkwton. I Y\n. 25. NEWTONIAN TKI.EWOPK. Fro. 2«. CASSKftnAIX I A N TKI.KSrOPK The Cassegrainian Telesoope. — In this form a second- ary convex mirror is placed in the tube of the telescope r>8 A arm NO MY about three foiirtlis of the way from the large Bpecuiuni to the focus. The rays, after being reflected from the large speculum, fall on this mirror before reaching the focus, and are reflected back again to the speculum ; an opening is nuide in the centre of the latter to let the rays pass through. The position and curvature of the secondary mirror are adjusted so that the focus shall be formed just after passing through the opening in the speculum. In this telescope the observer stands behind or under the speculum, and, with the eye-piece, looks through the opening in the centre, in the direction of the object. Tliis form of reflector is much more convenient in use than the Newtonian, in using which the observer has to be near the top of the tul)e. This form wjis devised by Casseorain in 1072. The advantages of reflectoi*s are found in tlieir cheap- ness, and in the fact that, supposing tlie mirrors perfect in figure, all the rays of tlie spectrum are brought to one focus. Thus the reflector is suitable for spectroscopic or ])]u)tographic researches without any change from its or- dinary form. This is not true of the "efractor, since the rays by which we now photograph (the blue and vluht rays) are, in that instrument, owing to the secondarv spectrum, brought to a focus sliglitly different from that of the yellow and adjacent rays by means of which wo see. Keflectors have been made as large as six feet in aper- ture, the greatest being that of Lord Rosse, but those which have been most successful have hardly ever been larger than two or three feet. The smallest satellite of Satmn {Mimas) was discovered by Sir William Hkrsciiki- with a four-foot speculum, but all the other satellites dis- covered by him were seen with mirrors of iibout eighteen inches in aperture. With these the vast majority of his fa'nt nebuljF were also discovered. The satell' tes of Neptune and f^ranua were discovered by Lassell with a two-foot speculum, and much of the nEFLKVTINQ TELESCOPES. 69 [er- lost' of llis- Iceii his fcred Itbo v.-i-ik of Lord Riisse has been done with liis three-foot Tiiirror, instead of his celebrated six-foot one. From the time of Newton till quite recently it was usual to make the large mirror or objective out of specu- lum metal, a brilliant alloy liable to tarnish. When the mirror was once tarnished through exposure to the weather, it could be renewed only by a process of polish- 'wv^ almost equivalent to figuring and p(/lishing the mirror anew. Consequently, in such a siieculum, after the cor- rect form and j)olish were attained, there wjis great diffi- culty in preserving them. In recent years this difficulty lias l)oen largely overcome in two ways : first, by im- liriivcments in the composition of the alloy, by which its lialiility to tarnish under exposure is greatly diminished, and, secondly, by a plan proposed by Foucault, which consists in making, once for all, a mirror of glass which will always retain its good figure, and depositing upon it a tliiu film of silver which may be removed and restored with little lr.b*M' as often as it becomes tarnished. In this wa^, one important defect \i\ the reflector has lieen avoided. Another great defect has been less success- fully treated. It is not a process of exceeding difficulty to irive to the reflecting surface of either metal or glass the correct parabolic shape by wliieh the incident rays are hrouijht accurately to one focus. But to nuiintain this t^hape constantly when the mirror is mounted in a tube, and when this tube is directed in succession to various parts of the sky, is a mechanical problem of extreme diffi- culty. However the mirror may be BU])i>orted, all the unsupported points tend by their weight to sag away from the }>roper position. When the mirror is pointed near the horizon, this effect of flexure is quite different from what it is when pointed near the zenith. As bug as the mirror is small (not grccater than eight to twelve inches in diameter), it is found easy to supjjort it 60 that these variations in the strains of flexure have little praeti(;al effect. As we increase its diameter up to 48 or 1 'I v^-. 70 ASTRONOMY. 72 inches, tlie eflfect of flexure rapidly increases, and special devices liavo to be used to counterbalance tlio injury done to the shape of the mirror. § 3. CHBONOMETEBS AISTD CLOCKS. In Chapter I., § 8, we described how the right ascen- sions of the heavenly bodies .are measured by the times of their transits over the meridian, tliis quantity increas- ing by a minute of arc in four seconds of time. In order to determine it with all required accuracy, it is jiecessary that the time-pieces with which it is measured shall go with the greatest possible precision. There is no great difficulty in making astronomical measures to a second of arc, and a star, by its diurnal motion, ])asses over this space in one tiftecnth of a second of time. It is there- fore desirable that the astronomical clock shall not vary from a unifonii rate more than a few hundredths of a second in the course of a day. It is not, however, necessary that it should be perfectly correct ; it may go too fast or too slow without detracting from its char- acter for accuracy, if the intervals of time which it tells o'ff — houi*s, minutes, or seconds — are always of e.c- actly the same length, or, in other words, if it gains or loses exactly the same amount every hour and every day. The time-pieces used in .astronomical observation arc the chronometer and the clock. The chronomctfr is merely a very perfect time-piece with a balance-wheel so constrncted that changes of tein- per.ature have the lejist possible effect upon the time of its oscillation. Such a balance is called a coinpensation baK ance. The ordinary house clock goes f.aster in cold than in warm weather, because the pendnlum rod shortens under the influence of cold. This eff'j''*^^ is such tluit the clock will gain about one second a day for e\ ury fall of 3° Cent, (r)'*.4 Fahr.) in the temperature, supposing the penduluiu <^''il use for a THE ASTltONOMICAL CLOCK. 7J by whicli the disturbing eflEects of rod to be of iron. Such changes of rate would be entirelj inadmissible in a clock used for astronomical purposes. The astronomical clock is therefore provided with a com peusation pendulum, changes of temperature are avoided. Tliere are two forms now in use, the Harrison (grid' iron) and the mercurial. In the gridiron pendulum the rod is composed in part of a number of parallel bars of steel and brass, so connected together that while the expansion of the steel bars produced by an increase of temperature tends to depress the hoh of the pendulum, the greater (expansion of the brass bars tends to raise it. When the total lengths of the steel and brjiss bars liave been properly adjusted a nearly perfect compensation occurs, and the centre of oscillation remains at a con- stant distance from tlio point of sus- pension. Tlie rate of the clock, so lar as it depends on the length of the j»enduhim, will therefore be constant. In the mercurial pendulum the weiglit which forms the bob is a cyhndric glass vessel nearly filled with mercury. With an increase of temperature the steel suspension rod lengthens, thus throwing the centre of oscilhition away from the point of suspension ; at the same time the expanding mercury rises in the cylinder, and tends therefore to raise the centre of oscillation. Wlien the length of the rod and the dimensions of the cylinder of mercury are properly proportioned, the centre of oscillation is kept at a constant distance from tlie point (if snspension. Other metliods of making this compensa- tion have been used, but these are the two in most ^,g\\- eral nse for jistronomical clocks. Fio. 27.— oniDinoN PENDULUM. 7a ASTRONOMY. The correction of a chronometer (or clock) is the quantity of time (expressed in hours, minutes, seconds, and decimals of a secomiy which it is necessary to add algebraically to the indication of tlie hands, in order that the sum may be the correct time. Thus, if at sidereal 0'', May 18, at New York, a sidereiil clock or chronomettr indicates 28'' 58'" 20' 7, its correction is + 1'" 39'- 3; if atO'' (sidereal noon), of May 17, its correction was + 1'" 38' -8, its daily rate or tlie change of its correction in a sidereal day is + I'-O: in other words, this clock is luHiug V daily. For clock itloiB the sign of the correction is 4- ; •' is - ; rate is — ; is + . A clock or chronometer may be well compensated for temperaturi!. and yet its rate may be gaining or losing on the tiniK it is intendeii to keep: it is not even necessary that the rate should be small (ex- cept that a small rate is practically convenient), provided only tiiut it is constant. It is continually n(;nessarv to compute the clock cor rection at a given time from its known correction at some other tiiiit'. and its known rate. If for some definite instant we denote the time as shown by the clock (technically "the clock-face") by 'J\ the trut time by T and the clock correction by a 7', we have tl " fant " tl ti tl it •' gaining " li it tl it " lo«ing " It t. tl T = AT' = T + r - A 7\ and T. In all observatories and at sea observations are made daily to do- termine A T. At the instant of the observation the time T'is noted by the clock; from the data of the observation the time 7" is (•oiii- putcd. If these agree, the clock is correct. If they differ, A /'i^ found from the above e(|uations. If by observation we have found A To = the clock correction at a clock-time Ta, AT — the clock correction at a clock-tune Z", (^7' ~ the cluck ratu in a unit of time, A 7'= A7'„ + .!7'(7'- n) we have where T — T,, must bo expressed in days, hours, etc., according: as (5 7' is the rate in one day, one hour, etc When, ihorefore, the clock correction A To and rate •57' have been determined for a certain instant, 7^0, we call deduce the true liiiit> from the clock-face 7' at any other instant by the e(|iiation 7" - / -f A 7'o + iST {T — T„). If the clock correction has beeu dctir mined at two (liHerent times, 7'u and T to be A 7'u and A 7', the u\^' is inferred front the equation 6T = AT- ATo T - TJ THE ASTltONOAflCAL CLOCK. 78 Thene equations apply only 8o long as wc can regard the rate as toiislitnt. As observations can be ti.<.vio only in clear weather, it is plain that during periods of overcast sky we must depend on these fi|ti:i(ion3 for our knowledge of T — /.«., the true time at a clock- liiiu' T. 'I'liu intervals between the determination of the clock correction siioiild be small, since even with the best clocks and chronometers too iniich dependence must not be placed upon the rate. The follow- ing example from Ciiauvenet's Astronomy will illustrate the pructi- (•ill jirocesses: •• Kxinnph. — At sidereal noon, May 5, the correction of a sidereal rlook is— 16'" 47"0; at sidereal noon, May Vi, it is — 1(J"' 13*-50; wliut is the sidereal time on May 25, when the clock-face is 11" 13'" 1 2' -6, supposing the rate to be uniform V May .'), correction = - 16'" 47*. 30 " 12, '* = - 16'" 13'.50 7 days' rate = -|- 6 7' = -f 4V785 Taking then as our starting-point 7'u = May 12, 0'', we have for the iiitcrviil to T = May 25, li'' 13'" 12".6, T - 1\ = IS"* 11" 13'" 12'.6 - i;5'i.407. Hence we iiiive a7o = - 16'" 13'. 50 6T{T- To) =+ 1'" 4*44 A 2'= - 15'" »'.(>0 T= 11'' l:>"' 12'.C>0 T = T0"^5«"' 3'.r)4 Rut in this example the rate is obtained for one true sidereal day, whik' tlie unit of the interval 13''.467 is a sidereal day as shown by the dock. The proper interval with which to compute the rate in this case is Vi^ 10'' 58'" 4M3 = 13''.457, with which we find a7'„=:- 16'" 13'. 50 dTX 18.457 = -f- 1'" 4'.39 A 7'=- 15'" J)', n 7' = ll^KV" 12'. 60 7""^ T(F5b"' 3\4» Tills repetition will bo iciidercd unnecessary by alwnys giving the rate in ii unit of' fhe ilnik. Tlius, suppose that on .lime it, iil 4'' 11" \'i'.',\i) l)y the clock, we have found the correction -(- 2"' I0'.14; Jinil HI) .June 4, at 14'' 17"' 49'. 82 we have found the correction -f 3'" 111'. Mil; the rate in one hour of the clock will be W ASTRONOMY. 8 4. THE TRANSIT INSTRXTMEirF. The meridian tra/nsit instritmentf or briefly the ** tran. ait," is used to observe the transits of the heavenly bodies, H^^ FlO. 28.— A TRANSIT INSTRUMENT. and from the times of these transits as read from the clock to determine either the corrections of the clock or the right ascension of the observed body, as explained in Chaptei' I., §8. TlIK TRANSIT INSTRUMENT. 75 Tt has two general forms, one (Fig. 28) for use in fixed (discrvatories and one (Fig. 20) for use in tlio field. It consists essentially of a telescope T T (Fig. 28) mounted on an axis V V oX. right angles to it. Fig. 29.— poutahlk tuansit instuumknt. The ends of this axis terminate in accurately cylindrical steel pivots which rest in metallic bearings V F, in shape like the letter Y, and hence called the Ys. 76 ASTUONOMY. ThcBC are fastened to two ])lllur8 of stone, l»nek, ur iron. Two coiinterpoigcs W W are eonnec^ted with the axis as in the plate, so as to take a hir<>[o portion of the weight of the axis and telescope ironi the Ys, and thus to diminish the friction upon these and to render the rota- tion about V V more easy and regular. In the onlinarv use of the transit, the line V V is placed accurately level and ])erpcndicular to the meridian, or in the east and west line. To elTect this " adjustment," there are two sett* of adjusting screws, by which the ends of V V in the Ys siiay be moved eitlier up and down or north and south. The plate gives the form of transit used in permanent observa- tories, and shows the observing chair ( ', the reversing car- riage 7?, and the level L. The arms of the latter have Y's, which can be placed over the pivots V V. The line of eollimatlon of the transit telescope is tlie line drawn through the centre of the objective perpendic- ular to the rotation axis V V. The reticle is a network of fine spider lines placed in the focus of the objective. In Fig. 30 the circle represents the field of view of a transit as seen through the eve-piece. The seven ver- tical Unes, I, II, III, IV, V, VI. VII, are seven fine spider lines tightly stretched across a metal jjlato or diaphragm, and so adjusted as to be peri)endicular to the direction of a star's a[)i)arent diurnal motion. This metal ])late can be moved right and left by line screws. The hori- zontal wires, guide-wires^ a and /', mark the centre of the field. The field is illuminated at night by a lamp at the end of tlie axis which shines through tiie hollow interior of the lat- ter, and causes the field to a])pear bright. The wires arc dark against a bnght ground. Tiie line of sight is a line joining the centre of the objective and the central one, IV, of the seven vertical wires. Tin: TiiANsrr ixsrnuxfHST. Tt The wliolo traiiHit i.s in adjustiiierit wlitMi, first, tlio axi» r V h liorizoiitul ; He(;oiiiiiit f this difference gives a II IMAGE EVALUATION TEST TARGET (MT-3) v.. 1.0 1.1 UiUl 12.5 |50 "^~ ■■■ !!: Ii£ 12.0 1.8 1 1.25 |||,.4 ,,.6 ^ 6" ► Photographic Sdences Corporation sj v iV ;\ \ 33 WfST MAIN STREIT WEBSTSi.N.Y. MS80 , 16) 873-4503 ;\ I Ua 78 ASTRONOMY. means of deducing the deviation oi A A from an east and west line. In a similar way the effect of a given error of level on the time of the transit of a star of declination 6 is found. Methods of Observing with the Transit Instrument.— We have so far assunied that the time of a star's transit over the middle thread was known, or could be noted. It is necessary to speak more in detail of how it is noted. When the telescope is pointed to any star the earth's diurnal motion will carry the image of the star slowly across the field of view of the telescope (which is kept fixed), as before explained. As it crosses each of the threads, the time at which it is exactly on the thread is noted from the clock, which must be near the transit. The mean of these times gives the time at which this star was on the middle thread, the threads being at equal intervals ; or on the " lamn thread," if, as is the case in practice, they are at unequal intervals. If it were po.ssible for an astronomer to note the exact instant of the transit of a star over a thread, it is plain that one thread would be sufficient ; but, as all estima- tions of this time are, from the very nature of the case, but approximations, several threads are inserted in order that the accidental errors of estimations maybe eliminated as far as possible. Five, or at most seven, threads are sufticient for this purpose. In the fijrure of the reticle of a transit instru- ment the star (the planet Venus in this case) may enter on the right hand in the figure, and may be supposed to cross each of the wires, the time of its tran- sit over each of them, or over a suffi- cient number, being noted. The method of noting this time may be best understood by referring to the next figure. Suppose that the line in the middle of Fig. 32 is one of the transit- threads, and that the star is passing from the right hand of the figure toward the left ; if it h on this wire at an Fig. 31. THE TRANSIT INSTRUMENT. 79 Pig. 83. exact second by the clock (which is always near the ob- server, beating seconds audibly), this second must be writ- ten down as the time of the transit over tliis thread. As a rule, however, the transit cnnnot occur on the exact beat of the clock, but at the seventeenth second (for exam- ple) the Ltar may be on the right of the wire, say at a \ while at the eighteenth second it will have passed this wire and may be at h. If the distance of a from the wire is six tenths of the distance ah, then the time of transit is t<^ be recorded as — hour? — mil ites (to be taken from the clock-facf^), and seven- teen and six tenths seconds / and in this way the transit over each wire is observed. This is the method of " eye- and-ear" observation, the basis of such work as we have described, and it is so called from the part which both the eye and the ear play in the appreciation of intervals of time. The ear catches the beat of the clock, the eye fixes the place of the star at a ; at the next beat of the clock, the eye fixes the star at 5, and subdivides the space a h into tenths, at the same time appreciating the ratio which th-j distance from the thread to a bears to the distance a h. This is recorded as above. This method, which is still used in many observatories, was introduced by the celebrated Bradley, astronomer royal of England in 1750, and per- fected by Maskelyne, his successor. A practiced observer can note the time within a tenth of a second in three cases out of four. Tliere is yet another method now in common use, which it is necessary to understand. This is called the American or chronographic method, and consists, in the present prjictice, in the use of a sheet of a paper wound about and fastened to a horizontal cylindrical barrel, which is caused to revolve by machinery once in one min- ute of time. A pen of glass which will make a continu- so ASTIiONOMF. OU8 line is allowed to rest on the paper, and to this pen a continuous motion of translation in the direction of the length of the cylinder is given. Now, if the pen is allow- ed to mark, it is evident that it will trace on the paper an endless spiral line. An electric current is caused to run through the observing clock, through a key which is held in the observer's hand and through an electro- magnet comiected with the pen. A simple device ynables the clock every second to give a, slight lateral motion to the pen, wliich lasts about a thirtieth of a second. Thus every second is automatically marked by the clock on the chronograph paper. The ob- server also has the power to make a signal by his key (easily distinguished from the clock-signal by its different length), which is likewise permanently registered on the sheet. In this way, after the chronograph is in motion, the observer has merely to notice the instant at which the star is 07i the thread, and to press the key at that moment. At any subsequent time, ho must mark some hour, miu- nte, and second, taken from the clock, on the sheet at its appropriate place, and the translation of the spaces on the sheet into times may be done at leisure. § 5. GRADUATED CIBCLES. T^carly every datum in practical astronomy depends either directly or indirectly upon the measure of an angle. To make the necessary measures, it is customary to em- ploy what are called graduated or divided circles. These are made of metal, as light and yet as rigid as possible, and they have at their circumferences a narrow flat band of silver, gold, or platinum on which fine radial lines called "divisions" are cut by a "dividing engine" at regular and equal intervals. These intervals may be of 10', 5 \ or 2', according to the size of the circle and the degree of accuracy desired. The narrow band is called the divided Imib, and the circle is said to be di- 4 THE VKRNIKR. 81 Pig. 38. vided to 10', 5', 2'. The separate divisions are numbered consecutively from 0° to 360° or from 0° to 90°, etc. The graduated circle has an axis at its centre, and to this may be attached the telescope by which to view the points wliose angular distance is to be determined. To this centre is also attached an arm which revolves with it, and by its motion past a certain number of divi- f^iuns on the c'rcle, determines the angle through which the centre has been rotated. This arm is called the index arm, and it usually carries a vernier on its extremity, l)y means of which the spaces on the graduated circle are subdivided. The readiny of the circle when the J ^ iiulex arm is in any position is the number of degrees, minutes, and seconds M^hich correspond to that po- sition ; when the index arrr is in an- other position there is a different reading, and the differences of the two readings S'—S', S'—S% S'—ST are the angles through which the index arm has turned. The process of measuring the angle between the objects by means of a divided circle consists then of pointing the telescope at the first object and reading the position of the index arm, and then turning the telescope (the index arm turning with it) until it points at the second object, and again reading the position of the index arm. The difference of these readings is the angle sought. To facilitate the determination of the exact readiiig of the circle, we have to employ special devices, as tl e vernier and the reading microscope. The Vernier. — In Fig. 34, J/ iV *3 a portion of the divided limb of a graduated circle ; CD is the index arm which revolves with the telescope about the centre of the circle. The end ah oi C D h also a part of a circle con- centric with MJV, and it is divided into n parts or divi- sions. The length of these n parts is so chosen that it is 82 ASTRONOMY. the same as that of {n — 1) parts on tlie divided limb 31 i\' or the reverse. The first stroke a is the zero of the vernier, and the reading is always determined by the position of this zero or pointer. If tliis has revolved past exactly twenty di- visions of the circle, then the angle to be measured is 20 X d, d being the value of one division on the limb {JV 31) in arc. Fig. 34.'— the vernier. Call the angular value of one division on the vernier d': ^ — 1 7 17 7' ^ J a, and a— a =-a: n n {71 — l)d = n- d\ or d' = d — d' is, called the least count of tlie vernier which is one n*"* part of a circle division. If the zero a does not fall exactly on a division on the circle, but ia at some other point (as in the figure), for ex- ample between two divisions whose numbers are P and {P + 1), the whole reading of the circle in this position is P X d + the fraction of a division from P to a. If the m*'' division of the vernier is in the prolongation of a division on the limb, then this fraction Pa is m THE MElilDIAN CIRCLE. 83 7/2/ {jl ^(T) = --d. In the figure n = 10, and as the 4i division is ahnost exactly in coincidence, m = 4, so that 4 tlie whole reading of the circle is P X d + -ry d. If d h 10', for example, and if the division J* is numbered 297° 40', then this reading would be 297° 44', the least count being 1', and so in other cases. If the zero had started from tlie reading 28U° 20', it must have moved past 17° 24', and this is the angle which has been measured. ^ 6. THE MERIDIAN CIRCLE. The meridian circle is a combination of the transit in- strument with a graduated circle fastened to its axis and moving with it. The meridian circle made by Repsold for the United States Naval Academy at Annapolis is shown in the figure. It has two circles, c c and c' c\ finely divided on their sides. The graduation of each circle is viewed by four microscopes, two of which, li A*, are shown in the cut. The microscopes are 90° apart. The cut slmws also the hanging level L Z, by which the error of level of the axis ^ ^ is found. Tiie instrument can be used as a transit to determine right ascensions, as before described. It can be also nsed to measure declinations in the following way. If the tele- scope is pointed to the nadir, a certain division of the cir- cles, as N^ is under the first microscope. If it is pointed to the pole, the reading will change by the angular distance between the nadir and the pole, or by 90° -|- 0, being the latitude of the place (supposed to be known). The polar reading P is thus known when the nadir reading N is found. If the telescope is then pointed to various stars of unknown polar distances, p\ p'\p"\ etc., as they successively cross the meridian, and if the circle readings for these stars are P', P\ P'" , etc., it follows that V' = P'~P ; p" == P" - P J p'" = P' - P, etc. H ASTRONOMY, Fro. 85.— THE MBRIDIAN CIRCLB. TUE MERIDIAN CIRCLE. 85 To determine the readings P, I", P", etc, we use the micro- Bcopes It, a, etc. Tlie observer, after having -ict the telescope so that one of the stars shall cross the field of view exactly at its cen- tre (which may be here marked by a Kingic horizontal thread in the reticle), goes to each of the microwro|iC)« in succession and places his eye at A (see Fig. 1, i)age W). He sees in the field of the microscope the image of the divisions of the graduated scale (Fig. 2) formed at D (Fig. 1), the common focus of the lenses A and G. Just at that focus is placed a notched m:h\c (Fig. 2) and two crossed spider lines. These lines are fixed to a sliding frame a a, which can be moved by turning the graduat<:d head F. This head is divided usually into sixty parts, each of which is 1'' of arc on *.lie circle, one whole revolution of the head serving to move the sliding frame a a, and its crossed wires through 60" or 1' on the graduated circle. The notched scale is not movable, but serves to count the number of complete revolutions made by the screw, there being one notch for each revolution. The index i (Fig. 1) is fixed, and serves to count the number of parts of /'wliich are carried past it by the revolution of this head. If on setting the crossed threads at the centre of the motion of F^ and looking into the microscope, a division on the circle coin- cides with the cross, the reading of the circle P is the exact num- ber of degrees and minutes corresjwnding to that particular divi- sion on the divided circle. Usually, however, the cross has been apparently carried past one of tlie exact divisions of the circle by a certain quantity, which is now to be measured and added to the reading corresponding to this adjacent division. This measure can be made by turning the screw back say four revolutions (measured on the notched scale) ;)Z(/s 37"3 parts (measured by the index i). If the division of the circle in question was 179' 50', for example, the complete reading would be in this case 179° 50' + 4' 37'" -3 or 179" 54' 37" -3. Such a reading is made by each microscope, and tlie mean of the min- utes and seconds from all four taken as the circle reading. We now know how to obtain the readings of our circle when directed to any point. We require some zero of reference, as the nadir reading (iV), the polar reading (P), the equator reading, {Q), or the zenith reading (Z). Any one of these being known, the circle readings for any stars as P, P', P'', etc., t;an be turned into polar distances p\ p", p"\ etc. Tiie nadir reading (iV) is the zero commonly employed. It can be determined by pointing the telesco|)e vertically downward at a basin of mercury plac. -» immediately beneath the instrument, and turning the whole instrument about the axis until the middle wire of the reticle seen directly exactly coincides with the image of wire seen by reflection from the surface of the quicksUver this When this is the case, the telescope is vertical, as can be easily seen, and the nadir reading may be found from the circles. The meridian circle thus serves to determine both the right ascen- sion and declination of a given star at the same culmination. Zone observations are made with it by clamping the telescope in one 86 ASTRONOMY. n«i. C D It' *k W«.3. T,g.4. Fig. 3G. — readino microscope, micrometeH and levei^ THE KQUATOlilAL. 87 (Unction, and obsorvincf successively the stars which j^ass through Its field of view. It is by tins rapid method of observing that tlio liirgest catalogues of stars have been formed. % 7. THE EQUATORIAL. To complete tlio enumeration and description of the ])iiiicipal instruments of astronomy, we require an account of the equatorial. Tiiis term, properly speaking, refers to a form of mounting, but it is commonly used to in- clude both mounting and telescope. In this class of instruments the object to bo attained is in general the easy finding and following of any celestial object whose apparent place in the heavens is known by its right as- cension and declination. The equatorial mounting con- sists essentially of a pair of axes at riglit angles to each otlior. One of these S N (the polar axis) is directed to- ward the elevated pole of the heavens, and it therefore makes an angle with the horizon equal to the latitude of the place (p. 73). This axis can be turned about its own axial line. On one extremity it carries another axis Z D (tlie declination a.ris)^ which is fixed at right angles to it, but wliich can again be rotated about its axial line. To tliis last axis a telescope is attached, which may eitlier be a reflector or a refractor. It is plain that such a telescope may be directed to any point of the heavens ; for we can rotate the declination axis until the telescope points to any given polar distance or declination. Then, keeping the telescope fixed in respect to the declination axis, we can rotate the whole instrument as one mass about the polar axis until the telescope points to any por- tion of the parallel of declination defined by the given right ascension or hour-angle. Fig. 37 is an equatorial of six-inch aperture which can be moved from place to place. If we point such a telescope to a star when it is rising (doing this by rotating the telescope first about its decli- nation axis, and then about the polar axis), and fix the telescope in this position, we can, by simply r '"ting the 8S A8TR0N0MT. \vho] trace wliic^ ting. that i same of rot tclc'sc as Ion tlio asi Pig. 87. — ^equatorial telescope roiNXED towakd the pole. THE MWllOMKTKR. 80 wliole apparatus on tlie polar axis, cause the telescope to trace out on the celestial Hpliere the apparent diurnal path which this star will appear to foMow from rising to set- ling, lu such tele8C0j)e8 a driving-dock is so arranged that it can turn the telescope round tlie polar axis at the same rate at which the earth itself turns about its own axis (if rotation, hut in a contrary directioii. llenco such a telescope once j)ointed at a star will continue to })oint at it as long as the driving-clock is in oj)L'ration, thus enabling the astronomer to observe it at his leisure. Pig. 38.— MEA8UUKMENT OF POSITION-ANaLK. Every equatorial telescope intended for making exact measures 1ms a filar micrometer^ which is precisely the same in principle as the reading microscope in Fig. 2, page 86, except that its two wires are parallel. A figure of this instrument is given in Fig. 3, page 86. One of tlie wires is fixed and the other is movable by the screw. To measure the distance apart, of two objects A and B, wire 1 (the tixed wire) is placed on A and wire 2 (movable by the screw) is jtlaced on B. The number of revolutions and parts of a revolution of the screw is noted, say 10'"-267 ; then wires I and 2 are placed in coincidence, and this zero-reading noted, say 5'''143. The dis- tance J. J? is equal to 5'- 124. Placing wires 1 and 2 a known num- ber of revolutions apart, we may observe the transits of a star in the equator over them ; and from the interval of time required for this star to move over say fifty revolutions, the value of one revolution 90 ASTRONOMY. is known, and can always be used to turn distances measured in revoiut'ons to distances in time or arc. By tlie filar micrometer we can determine the distance apart in seconds of arc of any two stars A and B. To completely fix the relative position of A and B, we require not only this distance, but also the angle which the line A B makes with some fixed direction in space. We assume as the fixed direction that of the meridian passing through A. Suppose in Fig. 38 A and B to be two stars visible in the field of the equatorial. The clock-work is detached, and by the diurnal motion of the earth the two stars will cross the field slowly in the direction of the parallel of declination passing through A, or in the direction of the arrow in the figure from E. to W., east to west. The filar micrometer is con- structed so that it can be rotated bodily about the axis of the tele- scope, and a graduated circle measures the amount of this rotation. The micrometer is then rotated until the star A will pass along one of its wires. This wire marks the direction of the parallel. The wire perpendicular to this is then in the meridian of the star. The position angle of B with respect to A is then the angle which A B makes with the meridian A N passing through A toward the north. It is zero when B is north of A, 90° when B is east, 180 when B is south, and 270° when B is west of A. Knowing p, the position angle (N A Bm the figure), and « (^4 B) the distance of B, we can find the difference of right ascension (A a), and the differ- ence of declination (AfJ) of. B from A by the formulse, Aa = 8 sin p ; A^ = s cos p. Conversely knowing Aa and A(5, we can deduce s and p from these formulae. The angle p is measured while the clock-work keeps the star A in the centre of the field. Q § 8. THE ZEIHTH TELESCOPE. The accompanying figure gives a view of the zenith telescope in the form in which it is used by the United States Coast Survey. It consists of a vertical pillar which supports two Ys. In these rests the horizontal axis of the instrument which carries the tele- scope at one end, and a counterpoise at the other. The whole in- strument can revolve 180° in azimuth about this pillar. The tele- scope has a micrometer at its eye-end, and it also carries a divided circle provided with a fine level. A second level is provided, whose use is to make the rotation axis horizontal. The peculiar features of the zenith telescope are the divided circle and its at- tached level. The level is, as shown in the cut, in the plane of motion of the telescope (usually the plane of the meridian), and it can be independently rotated on the axis of the divided circle, and set by means of it to any angle with the optical axis of the telescope. The circle is divided from zero (0°) at its lowest point to 90° in each direction, and is firmly attached to the telescope tube, and moves with it. By setting the vernier or index-arm of the circle to any degree and minute as a, and clamping it there (the level moving with it) THE ZENITH TELESCOPE. 91 1^! Fig. 39.— the zenith telescope. 99 ASTRONOMY. and then rotating the telescope and the whole system about the horizontal axis until the bubble of the level is in the centre of the level-tube, the axis of the telescopes will be directed to the zenith distance a. The filar micrometer is so adjusted that a motion of its screw measures differences of zenith distance. The use of the ze- nith telescope is for determining the latitude by Talcott's method. The theory of this operation has been already given on page 48. A description of the actual process of observation will illustrate the excellences of this method. Two stars, A and B, are selected beforehand (from Star Cata- logues), which culminate, A south of the zenith of the place of ob- servation, B north of it. They are chosen at nearly equal zenith dis- tances i* and {■, and so that |* — $' is less than the breadth of the field of view. Their right ascensions are also chosen so as to be about the same. The circle is then set to the mean zenith distance of the two stars, and the telescope is pointed so that the bubble is nearly in the middle of the level. Suppose the right ascension of A is the smaller, it will then culminate first. The telescope is then turned to the south. As A passes near the centre of the field its distance from the centre is measured by the micrometer. The level and micrometer are read, the whole instrument is revolved 180°, and star B is observed in the same way. By these operations we have determined the ditference of the zenith distances of two stars whose declinations d* and <5" are known. But ^ being the latitude, ^ = 6* -f $^ and = «i" — |", whence = ^ (d^ + «)' ')+i(«" 1°). The first term of this is known ; the second is measured ; so that each pair of stars so observed gives a value of the latitude which depends on the measure of a very small arc with the micrometer, and as this arc can be measured with great precision, the exactness of the determination of the latitude is equally great. 6 § 9. THE SEXTANT. Tlie sextant is a portable instrument by which the altitudes of celestial bodies or the angular distances between them may be measured. It is used chiefly by navigators for determining tlie latitude and the local time of the position of the ship. Knowing the local time, and comparing it with a chronometer regulated on Greenwich time, the longitude becomes known and the ship's place is fixed. It consists of the arc of a divided circle usually 60° in extent, whence the name. This arc is in fact divided into 120 equal parts, each marked as a degree, and these are again divided into smaller spaces, so that by means of the vernier at the end of the index-arm M 8axi arc of 10" (usually) may be read. The index-arm M 8 carries the index-glass M, which is a silvered plane mirror set perpendicular to the plane of the divided arc. The THE SEXTANT, 93 hmzMv-gloM m is also n plane mirror fixed perpendicular to the plane of the divided circle. This last glass is fixed in position, while the first revolves with the index-arm. The horizon-glass is divided into two parts, of which the lower one is silvered, the upper half being transparent. ^ is a telescope of low power pointed toward the horizon-glass. By it any object to which it is directed can be seen through the un- eilvered half of the horizon-glass. Any other object in the same plane can be brought into the same field by rotating the index-arm Fig. 40.— the sextant. (and the index-glass with it), ao that a beam of light from this second object shall strike the index-glass at the proper angle, there to be reflected to the horizon-glass, and again reflected down the telescope E. Thus the images of any two objects in the plane of the sextant may be brought together in the telescope by viewing one directly, and the other by reflection. The principle upon which the sextant depends is the following, which IS proved in optical works. The angle between thejirnt and the last direction of a ray which has suffered two reflections in the same 94 ASTRONOMY. plane is equal to twice the angle which the two reflecting surfaces make with each other. In the figure 8 A is the ray incident upon A, and this ray is by reflection brought to the direction B E. The theorem declares that the angle BE Sie equal to twice D C P, or twice the angle of the mirrors, since B G and D G are perpendicular to B and A. To measure the altitude of a star (or the sun) at sea, the sextant is held in the hand, and the telescope is pointed to the sea-horizon, which appears like a definite line. The index-arm is then moved until the reflected image of the sun or of the star coincides with the 43. — ARTIFICIAIi HORIZON. image of the sea-liorizon seen directly. When this occurs the time is to be noted from a chronometer. If a star is observed, the read- ing of the divided limb gives the altitude directly ; if it is the sun or moon which has been observed, the lower limb of these is brought to coinciue with the horizon, and the altitude of the centre THE SEXTANT. 95 is found by applying the semi-diameter as found in the Nautical Almanac to the observed altitude of the limb. The angular distance apart of a star and the moon can be meas- ured by pointing the telescope at the star, revolving the whole sex- tant about the sight-line of the telescope until the plane of the di- vided arc passes through both star and moon, and then by moving the index-arm until the reflected moon is just in contact with the star's image seen directly. On shore the horizon is broken up by buildings, trees, etc., and the observer is therefore obliged to have recourse to an artificial horizon, which consists usually of the reflecting surface of some liquid, as mercury, contained in a small vessel A, whose upper surface is necessarily parallel to the horizon D A C. A ray of light 8 A, from a star at 8, incident on the mercury at A, will be reflected in the direction A E, making the angle S A C = C A S' (A S' be- ing E A produced), and the reflected image of the star will appear to an eye at E as far below the horizon as the real star is above it. With a sextant whose index and horizon -glasses are at /and //, the angle S E S' may be measured ; but /S E S' = S A S' — A S E, and if .^ ^ is exceedingly small as compared with A S, as it is for all celestial bodies, the angle A 8 E may be neglected, and 8 E S^ will equal 8 A 8', or double the altitude of the object : hence one half *^'' reading of the instrument will give the apparent altitude. CHAPTER III. MOTION OF THE EARTH. § 1. ANCIENT IDEAS OF THE PLANETS. It was observed by the ancients that while the great mass of tlio stars maintained their positions relatively to each other not only during each diurnal revolution, but month after month and year after year, there were visi- ble to them seven heavenly bodies which changed their positions relatively to the stars and to each other. These they called planets or wandering stars. Still calling the apparent crystalline vault in which the stars seem to be set the celestial sphere, and imagining it as at rest, it was found that the seven planets performed a very slow revolution around the sphere from west to east, in periods ranging from one month in the case of the moon, to thirty years in that of Saturn. It was evident that these bodies could not be considered as set in the same solid sphere with the stars, because uney could not then change their positions among the stars. Various ways of accounting for their motions were therefore pro- posed. One of the earliest conceptions is associated with the name of Pythagoras. He is said to have taught that each of the seven planets had its own sphere inside of and concentric with that of the fixed stars, and that these seven hollow spheres each performed its own revolution, independently of the others. This idea of a immber of con- centric solid spheres was, however, apparently given up THE SOLAR SYSTEM. 97 without any one having talcen the trouhlo to refute it by argument. Although at first sight plausible enough, a close examination would show it to be entirely inconsis- tent with the observed facts. The idea of the fixed stars being set in a solid sphere was, indeed, in seemingly perfect accord with their diurnal revolution as observed bv the naked eye. But it was not so with the planets. The latter, after continued observation, were found to move sometimes backward and sometimes forward ; and it was quite evident that at certain periods they were nearer the earth than at other periods. These motions were entirely inconsistent with the theory that they were fixed in solid spheres. Still the old language continued in use — the word sphere meaning, not a solid body, but the space or region within which the planet moved. These several conceptions, as well as those which fol- lowed, were all steps toward the truth. The planets were riijhtlv considered as bodies nearer to us than the fixed stars. It was also rightly judged that those which moved most slowly were the most distant, and thus their order of distance from the earth was correctly given, except in the case of Mercury and Venus. We now know that these seven planets, together with the earth, and a number of other bodies which the tele- scope has made known to us, form a family or system by themselves, the dimensions of whicii, although inconceiv- ably greater than any which we have to deal with at the surface of the earth, are quite insignificant when com- pared with the distance whi 'h separates us from the fixed stars. The sun being the great central body of this sys- tem, it is called the Solar System,. It is to the motions of its several bodies and the consequences which flow from them that the attention of the reader is directed in the following chapters. We premise that there are now known to be eight large planets, of which the earth is the third in the order of distance from the sun, and that these bodies all perform a regular revolution around the sun. 98 ASTRONOMY, Mercury^ the nearest, performs its revolution in threo montlis ; Neptune^ the farthest, in 164 years. First in importance to ns, among the heavenly bodies which \vc see from the earth, stands the sun, the supporter of life and motion upon the earth. At first sight it miglit seem curious that the sun and seeming stars like Mars and Saturn should have been classified togetlier as planets bv the ancients, while the fixed stars were considered as forming another class. That the ancients were acute enough to do this tends to impress ns with a favorable sense of the scientific character of their intellect. To any but the most careful theorists and observers, the star-like planets, if we may call them so, would never have seemed to belong in the same class with the sun, but rather in that of the stars ; especially when it was found that they were never visible at the same time with the sun. But before the times of which we have any historic record, there were men who saw that, in a motion from west to east among the fixed stars, these several bodies showed a common character, which was more essential in a theory of the nniverse than their immense differences of asju'ct and lustre, striking though these were. It must, however, be remembered that we no longer consider the sun as a planet. We have modified the an- cient system by making the sun and the earth change places, so that the latter is now regarded as one of the eight large phmets, while the former has taken the place of the earth as the central body of the system. In consequence of the revolution of the planets round the sun, each of them seems to perform a corresponding circuit in the heavens around the celestial sphere, when viewed from any other planet or from the earth. § 2. ANNUAL BEVOLUTION OP THE EAKTH. To an observer on the earth, the sun seems to perform an annual revolution among the stars, a fact which has been known from early ages. We now know that this motion MOTION OF Tin: EAllTIL 99 is due to the annual revolution of the earth round the sun. It is to the nature and efTccts of \\\\a annual revolu- tion of the earth that the aitentioii of the reader is now directed. Our first lesson is to show the relations between it and the corresponding apparent revolution of the sun, which is its counterpart. In Fig. 43, let S represent the sun, A B (J D the orbit of the earth around it, and KFO II the sphere of the Fig. 43. — kevolution ok thk eaktu. fixed stars. This sphere, being supposed infinitely dis- tant, must be considered as infinitely larger than the circle A B CD. Suppose now that 1, 2, 3, 4, 5, 6 are a number of consecutive positions of the earth. The line 1^9 drawn from the sun to the earth in the first position is called the radius vector of the earth. Suppose this line extended infinitely so as to meet the celestial sphere in the point V. It is evident that to an observer on the 100 ASTHONOMT. oartli at 1 tlio sun will appear projected on the sphere in the direction of 1'. When the earth reaches 2, it will appear in the direction of 2', and so on. In other words, as the earth revolves around the sun, the latter will seem to perform a revolution among the fixed stars, which are immensely more distant than itself. It is also evident that the point in which the earth would he projected, if viewed from the sun, is always exactly opposite that in which the sun appears as projected from the earth. Moreover, if the earth moves more rapidly in some points of its orbit than in others, it is evident that the sun will also appear to move more rapidly among the Btars, and that the two motions must always accurately correspond to each other. We now have the following definitions : The radius vector oi the earth is the straight line from the centre of the sun to the centre of the earth. As the earth describes its annual revolution around tlie sun, its radius vector describes a plane. This plane is called the plane of the ecliptic. If the plane of the ecliptic, beihg- continued indefinitely in all directions, the great circle in which it cuts the ce- lestial spliere is called the circle of the ecliptic, or sim])]}' the ecliptic. The axis of the ecliptic is a straight line passing througli the centre of the sun at right angles to the plane of tlie ecliptic. The 2)oles of the ecliptic are the two opposite points in which the axis of the ecliptic intersects the celestial sphere. Every point of the circle of the ecliptic is necessarily '90° from each pole. .Effect of the sun\t annual motion upon the rising and setting of the stars. — It is evident from Fig. 43 that tlie sun appears to perform an annual revolution from webt to east among the stars. Hence, if we watch any star for a few weeks, we shall find it to rise, cross the iK^ridian, and i f THE SUIT'S APPARENT PATIf. 101 eet about 4 minutes earlier every day than it did the day before. Let U8 take, for example, the bright reddish star. Aide- fMiriffi, which, on a winter evening, we may see north- ^^ost of Orion. Near the end of February this star crosses the meridian about six o'clock in the evening, and sets about midnight. If we watch it night after night through the months of March and April, we shall find that it is far- ther and farther toward the west on each successive even- ing at the same hour. By the end of April we shall bare- ly be able to see it about the close of the evening twilight. At the end of May it will be so close to the sun as to be entirely invisible. This shows that during the months we liave been watching it, the sun has been approaching the star from the west. If in July wo watch the eastern liorizon in the early morning, we shall sec this star rising before the sun. Tlie sun has therefore passed by the star, and is now east of it. At the end of November we will find it rising at sunset and settinor at sunrise. The sun is therefore directly opposite the star. During the winter months it approaches it again from the west, and passes it about the end of May, as before. Any other star south of the zenith shows a similar change, since the relative positions of the stars do not vary. § 3. THE SUN'S APPABENT PATH. It is evident that if the apparent path of the sun lay in the equator, it would, during the entire year, rise exactly in tlie east and set in the west, and would always cross the meridian at the same altitude. The days would always be twelve hours long, for the same reason that a star in the equator is always twelve hours above the hori- zon and twelve hours below it. But we know that this is net the case, the sun being sometimes north of the equator and sometimes south of it, and therefore having a motion in declination. To nndei*stand this motion. 103 ASTRONOMY. siippoHc that oil March IDth, 1879, tho sun liail heen ohserved with a meridian cirule and a sidereal clocic at the moment of transit over tlie meridian of Washington. Its positio!! wouhl have heen found to be this : lljght Ascension, 2;)'' 55"' 23* j Declination, 0° 30' south. Had the observation been repeated on tho 20tli and following days, the results would have been : March 20, U. Ascen. 23" SI)"" 2" ; Dec. 0° 6' South. 21, " 0" 2'MO-; " 0° 17' North. C «•" 19" ; " 0° 41' North. Fig. 44. — the bun crossing the EquATon. If we lay these positions down on a chart, we sball find them to be as in Fig. 44, the centre of the sun beiiii,' south of the equator in the first two positions, and nortli of it in the last two. Joining the successive positions In' a line, we shall have a small portion of the apparent patli of the sun on the celestial sphere, or, in other words, a small part of the ecliptic. It is clear from the observations and the figure that tlie sun crossed the equator between six and seven o'clock on the afternoon of March 20tli, and therefore that the equa- tor and ecliptic intersect at the point where the sun was at that hour. This point is called the vernal equinox, the C- iind it will bt rc'sponc of 45. scale. tlie gD will rea floclinat I'his pc figure t'quinox iner sol Jiseensioi its declia The inclines it again TIW SUN' a APPAHKNT PATH. 103 while the second first word indicating the season, e.\])re88e8 the e(iuahty of the niglits and days which occurs when the sun is on tlie e(iuator. It will be renienibered that this luj^ninox is the point from wliiuh rijjrht ascensions are counted in the heavens in the same way that lonjjitudes on the earth are (M»unted from Greenwich or "Washington. The sidereal clock is therefore so set that the hands shall read hours minutes seconds at the moment when the vernal equi- nox crosses the meridian. Continuing our observations «)f the sun's apparent course for hix months from March 20th till September 23d, wo should | find it to be as in Fig. 45. It ^ will be seen that Fig. 44 cor- ^ responds to the right-hand end ^ of 45, but is on a much larger ^ scale. The sun, moving along % the great circle of the ecliptic, I will i-cach its greatest northern d(>c'lination about June 21st. This point is indicated on the figure as 90° from the vernal e(p]inox, and is called the sum- mer solstice. The sun's right ascension is then six hours, and its declination 23^° north. The course of the sun now inclines toward the south, and it again crosses the equator about September 22d at 104 ASTRONOMY. ^^^Ws a point diainetrically opposite the vernal equinox. In virtue of the theorem of spherical trigonometry that all great circles intersect each other in two opposite points, the ecliptic and equator intersect at the two opposite equi- noxes. The equinox which the sun crosses on September 22d is called the autumnal equinox. During the six months from September to March the sun's course is a counterpart of that from March to Sep- tember, except that it lies south of the equator. It at- tains its greatest south declination about December 22d, in right ascension 18 hours, and south declination 23^°. This point is called the vnnter solstice. It then begins to incline its course toward the north, reaching the vernal equinox again on March 20th, 1880. The two equinoxes and the two solstices may be re- garded as the four cardinal points of the sun's apparent annual circuit around the heavens. Its passage througli these points is determined by measuring its altitude or declination from day to day witli a meridian circle. Since in our latitude greater altitudes correspond to greater declinations, it follows tliat the summer solstice occurs on the day when the altitude of the sun is greatest, and the winter solstice on that when it is least. Tlie mean of these altitudes is that of the equator, and may therefore be found by subtracting the latitude of the place from 90°. The time when the sun reaches this altitude going north marks the vernal equinox, and that when it reaches it going south marks the autumnal equinox. These passages of the sun through the cardinal points have been the subjects of astronomical observation from the earliest ages on account of their relations to the change of the seasons. An ingenious method of finding the time when the sun reached the equinoxes was used by the as- tronomers of Alexandria about the beginning of our era. In the great Alexandrian Museum, a large ring or wheel was set up parallel to the plane of the equator — in other words, it was so fixed that a star at the pole would shin& THE ZODIAC. 105 perpendicularly on the wheel. Evidently its plane if extended must have passed through the east and west points of the horizon, while its inclination to the vertical was equal to the latitude of the place, which was not far from 30°. When the sun reached the equator going north or south, and shone upon this wheel, its lower edge would be exactly covered by the shadow of the upper edge ; whereas in any other position the sun would shine upon the lower inner edge. Thus the time at which the sun reached the equinox could be determined, at least to a fraction of a day. By the more exact methods of modern times, it can be determined within less than a minute. It will be seen that this method of determining the an- nual apparent course of the sun by its declination or alti- tude is entirely independent of its relation to the fixed Kcars ; and it could be equally well applied if no stars were ever visible. Thsre are, therefore, two entirely dis- tinct ways of finding when the sun or the earth has com- pleted its apparent circuit around the celestial sphere ; the one by the transit instrument and sidereal clock, which show when the sun returns to the same position among the stars, the other by the measurement of altitude, which shows when it returns to the same equinox. By the for- mer method, already described, we conclude that it has completed an aimual circuit when it returns to the same star ; by the latter when it returns to the same equinox. These two methods will give slightly different results for the length of the year, for a reason to bo hereafter described. The Zodiac and its Divisions. — The zodiac is a belt in the heavens, commonly considered as extending some 8* on each side of the ecliptic, and therefore about 16° wide. The planets known to the ancients are always seen within this belt. At a very early day the zodiac was mapped out into twelve signs known as the signs of the zodiac^ the names of which have been handed down to the present time. Eacli of these signs was supposed to be the seat of 106 ASTRONOMY. a constellation after which it was called. Commencing at the vernal equinox, the first thirty degrees through which the sun passed, or the region among the stars in which it was found during the month following, was called the sign Aries. The next thirty degrees was called Taurus. The names of all the twelve signs in their proper order, with the approximate time of the sun's en- tering upon each, are as follow : Aries ^ the Ram, Taurus^ the Bull, Gemini,, the Twins, Cancer, the Crab, Leo, the Lion, Virgo, the Virgin, Libra, the Balance, Scorpkts, the Scorpion, Sagittarius, tlie Archer, Capricornus, the Goat, Aquarius, the Water-bearer, Pisces, the Fishes, March 20. April 20. May 20. June 21. July 22. August 22. September 22. October 23. November 23. December 21. January 20. February 19. Each of these signs coincides roughly with a constella- tion in the 'leavens ; and thus there re twelve constella- tions called by the names of these signs, but the signs and tht constellationo no longer correspond. Although the sun now crosses the equator and enters the sign Aries on the 20th of March, he does not reach the constellation Aries until nearly a month later. This arises from the preces- sion of the equinoxes, to be explained hereafter. § 4. OBLIQUITY OP THE ECLIPTIC. We have already stated that when the sun is at the euminer solstice, it is about 23^° north of the equator, and when at the winter solstice, about 23^° south. This shows that the ecliptic and equator make an angle of about 23^° with each other. This angle is called m OBLIQUITY OF THE ECLIPTIG. 107 wm the obliquity of the ecliptic, and its determination is very simple. It is only necessary to find by repeated observation the sun's greatest north declination at the summer solstice, and its greatest south declination at the winter solstice. Either of these declinations, which must be equal if the observations are accurately made, will give the obliquity of the ecliptic. It has been con- tinually diminiphing from the earliest ages at a rate of about half a second a year, or, more exactly, about forty- seven seconds in a century. This diminution is duo to the gravitating forces of the planets, and will continue for several thousand years to come. It will not, however, go on indefinitely, but the obliquity will only oscillate be- tween comparatively narrow limits. The relation of the obliquity of the ecliptic to the sea- sons is quite obvious. When the sun is north of the equa- tor, it culminates at a higher altitude in the northern -hem- isphere, and more than half of its apparent diurnal course is above the horizon, as explained in the chapter on the celestial sphere. Hence we have the heats of summer. In the southern hemisphere, of course, the case is re- versed : when the sun is in north declination, less than half of his diurnal course is above the horizon in that hem- isphere. Therefore this situation of the sun corresponds to summer in the northern hemisphere, and winter in the southern one. In exactly the same way, when the sun is far south of the equator, the days are shorter in the north- ern hemisphere and longer in the southern hemisphere. It is therefore winter in the former and summer in the latter. If the equator and the ecliptic coincided — that is, if the sun moved along the equator — there would be no such thing as a difference of seasons, because the sun would always rise exactly in the east and set exactly in the west, and always culminate at the same altitude. The days would always be twelve hours long the world over. This is the case with the planet Jupiter. In the preceding paragraphs, we have explained the 108 ASTRONOMY. apparent annual circuit of the sun relative to the equator^ and shown how the seasons depend upon this circuit. In order that the student may clearly grasp the entire subject, it is necessary to show the relation of these apparent move- ments to the actual movement of the earth around the sun. To understand the relation of the equator to the eclip- tic, we muoo remember that the celestial pole and tlie celestial equator have really no reference wliatever to the lieavens, but depend soKly on the direction of the earth's axis of rotation. The pole of the heavens is nothing more than that point of the celestial sphere toward which the earth's axis points. If the direction of this axis changes, the position of the celestial pole among the stai-s will change also ; though to an observer on the earth, unconscious of the change, it would seem as if the starry sphere moved while the pole remained at rest. Agam, the celestial equator being merely the great circle in which the plane of the earth's equator, extended out to infinity in every direction, cuts the celestial sr>here, any change iu the direction of the pole of the earth necessarily changes the position of the equator among the stars. Now the positions of the celestial pole and the celestial equator among the stars seem to remain unchanged throughout the year. (There is, indeed, a minute change, but it does not affect our present reasoning.) This shows that, as the earth revolves around the sun, its axis is constantly directed toward nearly the same point of the celestial sphere. § 5. THE SEASONS. The conclusions to which we are thus led respecting the real revolution of the earth are shown in Fig. 4^5. Here S represents the sun, with the orbit of the earth surrounding it, but viewed nearly edgeways so as to be much foreshortened. A B C D are the four cardinal positions of the earth which correspond to the cardinal ;:ii IHE SEASONS. 109 points of the apparent path of the sun already described. In each figure of tlie earth JVS is the axis, iV being its north and iS its south pole. Since this axis points in the Fig. 46. — causes of the seasons. same direction relative to the stars during an entire year, it follows that the different lines JV S are all parallel. Again, since the equator does not coincide with the ecliptic, tliese lines are not perpendicular to the ecliptic, but arc inclined from this perpendicular by 23^°. Now, consider the earth as at vl ; here it is seen that the sun shines more on the southern hemisphere than on the northern ; a region of 23^° around the north pole is in darkness, while in the corresponding region around the south pole the sun shines all day. The five circles at right angles to the earth's axis are the parallels of latitude around wliich each region on the surface of the earth is carried by the diurnal rotation of the latter on its axis. It will be seen that in the northern hemisphere less than half of these are illuminated by the sun, and in the southern hemisphere more than half. This corresponds to our winter solstice. When the earth reaches B, its axis ^VaS' is at right an- gles to the line drawn to the sun, so that the latter shines perpendicularly on the equator, the plane of which passes through it. The diurnal circles on the earth are one half 110 ASTRONOMY. ■ \ illuminated and one half in darkness. This position cor- responds to the vernal equinox. At C the case is exactly the reverse of that at A, the sun shining more on the northern hemisphere than on the southern one. North of the equator more tlian half the diurnal circles are in the illuminated hemisphere, and south of it less. Here then we have winter in the southern and summer in the northern hemisphere. The sun is ahove a region 23^° north of the equator, so that this position cor- responds to our summer solstice. At D the earth's axis is once more at right angles to a line drawn to the sun. The latter therefore shines upon the equator, and we have the autumnal equinox. In whatever position we suppose the earth, the line SJ^T, continued indefinitely, meets the celestial spliere at its north pole, while the middle or equatorial circle of the earth, continued indefinitely in every direction, marks out the celestial equator in the heavens. At first sight it might seem that, owing to the motion of the earth through so vast a circuit, the positions of the celestial pole and equa- tor must change in consequence of this motion. We miglit say that, in reality, the pole of the earth describes a circle in the celestial sphere of the same size as the earth's orbit. But this sphere being infinitely distant, the circle thus de- scribed appears to us as a point, and thus the pole of the heavens seems to preserve its position among the stars through the whole course of the year. Again, we may suppose the equator to have a sliglit annual motion among the stars from the same cause. But for the same reason this motion is nothing when seen from the eartli. On tlie other hand, the slightest change in the direction of the axis S ^ will change the apparent position of the polo among the stars by an angle equal to that change of direc- tion. We may thus consider the position of the celestial pole as independent of the position of the earth in its orbit, and dependent entirely on the direction in which the axis of the earth points. § 6. CELESTIAL LATITUDE AND LONGITUDE 111 If this axis were perpendicular to the plane of the eclip- tic, it is evident that the sun would always lie in the plane of the equator, and there would be no change of seasons except such slight ones as might result from the small differences in the distance of the earth at different seasons. § 6. CELESTIAL LATITUDE AND LONGITUDE. Besides the circles of reference described in the first chapter, still another system is used in which the ecliptic is taken as the fundamental plane. Since the motion of the earth around the sun takes place, by definition, in the plane of the ecliptic, and the motions of tlie planets very near that plane, it is frequently more convenient to refer the positions of the planets to the plane of the ecliptic than to tliat of the equator. The co-ordinates of a heavenly body thus referred are called its celestial latitude and longitude. To show the relation of these co-ordinates to right ascension and declination, we give a figure showing both co-ordinates at the same time, as marked on the celestial sphere. This figure is supposed to be the celes- tial sphere, having the solar system in its centre. The direction P ^ is that of the axis of the earth ; /«/is the ecliptic, or the great circle in which the plane of the earth's orbit intersects the celestial sphere. The point in which these two circles cross is marked O"", and is the ver- nal equinox. From this the right ascension and the longi- tude are counted, increasing from west toward east. The horizontal and vertical circles show how right ascen- sion and declination are counted in the manner described in Chapter I. As the right ascension is counted all the way around the equator from O** to 24"', so longitude is counted along the ecliptic from the point 0'', or the vernal equinox, toward Jm. degrees. The whole circuit measuring 360°, this distance will carry us all the way round. Thus if a body lies in the ecliptic, its longitude is simply the number of degrees from the vernal equinox to its position, meas- ured in the direction from /toward t/(from west to east). 112 ASTRONOM^^. If it is not in the ecliptic, but at, say, the point B, we let fall a perpendicular BJ from the body upo/i the ecliptic. The length of this perpendicular, measured in degrees, is called the latitude of the body, which may be north or south, while the distance of the foot of the per- pendicular from the vernal equinox is called its longitude. In astronomy it is usual to represent the positions of the bodies of the solar system, relatively to the sun, by their longitudes and latitudes, because in the ecliptic we have a FlO. 47.— CIRCLES OP THE SPHERE. plane more nearly fixed than that of the equator. On the other hand, it is more convenient to represent the position of all the heavenly bodies as seen from the earth by their right ascensions and declinations, because we cannot meas- ure their longitudes and latitudes directly, but can only observe right ascension and declination. If we wish to determine the longitude and latitude of a body as seen from the centre of the earth, we have to first find its right ascension and declination by observation, and then change these quantities to longitude and latitude by trigonometri- cal fonnulje. CHAPTER IV. THE PLANETARY MOTIONS. % 1. AFPABENT AND BEAL MOTIONS OF THE PLANETS. Deflnitions. — The solar system, as wc now know it, com- prises so vast a number of bodies of various orders of mag- nitude and distance, and subjected to so many seemingly complex motions, that we must consider its parts sepa- rately. Our attention will therefore, in the present chap- ter, be particularly directed to the motions of the great planets, which we may consider as forming, in some sort, the fundamental bodies of the system. These bodies may, with respect to their apparent motions, be divided into three classes. Speaking, for the present, of tlie 8un as a planet, the first class comprises the sun and moon. We have seen that if, upon a star chart, wc mark down the positions of the sun day by day, they will all fall into a regular circle which marks out the ecliptic. The monthly course of the moon is found to be of the same nature, although its motion is by no means unifonn in a month, yet it is always toward the east, and always along or very near a certain great circle. The second class comprises Ventts and Mercury. The peculiarity exhibited by the apparent motion of these bodies is, that it is an oscillating one on each side of the sun. If we watch for the appearance of one of these planets after sunset from evening to evening, we shall find 114 ASTRONOMY. it to appear above tlic western horizon. Night after night it will be farther and farther from the sun until it attains a certain maximum distance ; then it will appear to return to the sun again, and for a while to be lost in its rays. A few days later it will reappear to the west of the sun, and thereafter be visible in the eastern horizon before sunrise. In the case of Mercury^ the time recpiired for one complete oscillation back and forth is about four months ; and in the case of Venus more than a year and a half. The third class comprises Mars, Jupiter, and Saturn as well as a great number of planets not visible to the naked eye. The general or average motion of these planets is toward the east, a complete revolution in the celestial sphere being performed in times rf»iia:ing from two years in the case of Mars to 164 years in that of Neptune. But, instead of moving uniformly forward, they seem to liave a swinging motion ; first, they move forward or toward the east through a pretty long arc, then backward or westward through a short one, then forward through a longer one, etc. It is only by the excess of the longer arcs over the shorter ones that the circuit of the heavens is made. The general motion of . the sun, moon, and planets among the stars being toward the east, the motion in this direction is called direct / whereas the occasional short motions toward the west are called retrograde. During the periods between direct and retrograde motion, the planets will for a sliort time appear stationary. The planets Vetuis and Mercury are said to be at great- est elongation when at their greatest angular distance from the sun. The elongation which occurs with the planet east of the sun, and therefore visible in the western hori- zon after sunset, is called the eastern elongation, the other the western one. A planet is said to be in conjunction with the sun when it is in the same direction, or when, as it seems to pass by AliRANaRMKNT OF TIIK PLANETS. 115 tlio sun, it approaches nearest to it. It is said to be in oppoHitlon to the sun when exactly in the opposite direc- tion — rising when the sun sets, and viae versa. If, when a pUinet is in conjunction, it is between the earth and tlie sun, the conjunction is said to be an inferior one ; if be- yond the sun, it is said to be suj)erlor. Arrangements and Motions of the Planets. — "Wc now know that the sun is the real centre of the solar system, and that the planets proper all revolve around it Jia the centre of motion. The order of the five innermost large planets, or the relative positions of their orbits, are shown ill Fig. 48. These orbits are all nearly, but not exactly^ vtc ;-Wv-k i/'V% ^> Pig. 48. — orbits of the planets. in the same plane. The planets Mercury and Vemia wliich, as seen from the earth, never appear to recede very fur from the sun, are in reality those which revolve inside 116 ASTHONOMY. the orbit of the cartli. The plaiietH of tlic tliird class, whieli perform their (Mi'cuils at all distances from the huh, are what we now call the superior planets, and arc more distant from the sun than the earth is. Of these, the or- bits of 3/a/'.H, jNjf!tt'/\ and a swarm of telescopic planets are shown in the figure ; next outside of Ju^titer comes /Saturn, the farthest planet readily visible to the naked eye, and then Uranus and j\'<'j4u7i(', teloscoj)ic planets. On the scale of Fig. 48 the orbit of Neptune would hi' more than two feet in diameter. Finally, the moon is a small planet revolving around the earth as its centre, and Carried with the latter as it moves around the sun. Inferior jdanets are those whose orbits lie inside that of the earth, as Merc}iry and VenuH. Superior planetn are those whose orbits lie outside that of the earth, as Jlars, Juptter, Saturn, etc. The farther a planet is situated from the sun, the slowor is its orbital motion. Therefore, as we go from the sun, the periods of revolution are longer, for the double reason that the planet has a larger orbit to describe and moves more slowly in its orbit. It is to this slower motion of tlio outer planets that the occasional ap])arent retrograde motion of the planets is due, as may be seen by studying Fig. 40. We first remark that the apparent direction of a planet, as seen from the earth, is determined by the line joiniiii,' the earth and planet. Supposing this line to be continucMJ onward to infinity, so as to intersect the celestial sphere, the apparent motion of the planet will be defined by tlie motion of the point in which the line intersects the sphere. If this motion is toward the east, it will be direct ; if toward the west, retrograde. Let us first take the case of an inferior planet. Sup- pose II I K L M N to be successive positions of the earth in its orbit, and A B C D E F to be corresponding posi- tions of Yenns or Mercury. It must be remembered that when we speak of east and west in this connection, we flo not mean an absolute direction in space, but a direction I, APPAHENT MOTIONS OF TllK PLAM-ns. ii: .around tlie splicro. In tlie fignrc we aru supposed to look down upon tlie planetary orhits from the north, and a direction west Ih, then, that in which the hands of a watch move, while east ib in the opposite direction. When tho earth is at 7/ the planet is seen at A. The line 7/ vl being supposed tangent to the orbit of the planet, it is evident from geometrical considerations that this is tho greatest angle which the planet can ever make with the sun as seen from the earth. This, therefore, corresponds to the greatest eastern elongation. Fig. 49. When the earth has reached /the planet is at B^ and is therefore near the direction IB. The line has turned in a direction opposite that of the hands of a watch, and cuts tlio celestial sphere at a point farther east than the line II A did. Hence the motion of the planet during this period has been direct ; but the direction of the sun hav- ing changed also in consequence of the advance of the eiirth, the angular distance between the sun and the planet is less than before. While the earth is passing from / to /i", the planet 118 ASTRONOMY. passes from B to C. The distance B C exceeds I K^ be« cause the planet moves faster tlian the earth. The line joining the earth and planet, therefore, cuts the celestial sphere at a point farther west than it did before, and therefore the direction of the apparent motion is retro- grade. At C the planet is in inferior conjunction. The retrograde motion still continues until the earth reaches Z, and the planet D^ when it becomes stationary. After- ward it is direct until the two bodies again come into the relative positions IB. Let us next suppose that the inner orbit A B CD EF represents that of the earth, and the outer one that of a superior planet. Mars for instance. We may consider O Q PB tthe the celestial sphere, only it should be infi- nitely distant. While the earth is moving from Ato B the planet moves from II to /. This motion is direct, the di- rection O Q P B being from wes^ to east. While the earth is moving from B to B, the planet is moving from / to B ; the former motion being the more rapid, the earth now passes by the planet as it were, and the line conjoin- ing them turns in the same direction ae the hands of a watch. Therefore, during this time the planet seems to describe the arc P Qin the celestial sphere in the direction opposite to its actual orbital motion. The lines Z B and M E are supposed to be parallel. The planet is then really stationary, even though as drawn it would seem to have a forward motion, owing to the distance of these two hues, yet, on the infinite sphere, this distance appears as a point. From the point M the motion is direct until the two bodies once more reach the relative positions B I. When the planet is at K and the earth at 0^ the former is in opposition. Hence the retrograde motion of the supe- rior planets always takes place near opposition. Theory of 2picycles. — The ancient astronomers repre- sented this oscillating motion of the planets in a way which was in a certain sense correct. The only error they mad& was, in attributing the oscillation to a motion of the planet APPARENT MOTIONS OF THE PLANETS. 119 instead of a motion of the earth around the sun, which really causes it. But their theory was, notwithstanding, the means of leading Copernicus and others to the ^♦'^rcep- tion of the true nature of tlie motion. We allude to the celebrated theory of epicycles, by which the planetary motions were always represented before the time of Coper- nicus. Complicated though these motions were, it was seen by the ancient astronomers that they could be repre- sented by a Gf mbination of two motions. First, a small circle or epicycle was supposed to move around the earth with a regular, though not uniform, forward motion, and then the planet was supposed to move around the circum- ference of this circle. The relation of this theory to the true one was this. The regular forward motion of the epicycle rnpresents the real motion ^f the planet around the sun, while the motion of the planet around the cir- cumference of the epicycle is an apparent one arising from the revolution of the earth around the sun. To ex- plain this we must understand some of the laws of relative motion. It is familiarly known that if an observer in unconscious motion looks upon an object at rest, the object will ap- pear to him to move in a direction opposite that in which he moves. As a result of this law, if the observer is unconsciously describing a circle, an object at rest will appear to him to describe a circle of equal size. This is shown by the following figure. Let S represent the sun, and A B CD EF the orbit of the earth. Let us suppose tlie observer on the earth carried around in tMs orbit, but imagining himself at rest at 8^ the centre of motion. Suppose he keeps observing the direction and distance of the planet P^ which for the present we suppose to be at rest, since it is only the apparent motion that we shall have to consider. When the observer is at A he really sees the pLnet in a direction and distance A P, but imagining himself at 8 he thinks he seee the planet at the point a delermined by drawing a line Sa parallel and 120 ASTliOI'OMT. equal to A P. As lie passes from A to B the planet will seem to Mm to move in the opposite direction from a to 5, the point h being deter- mined by drawing Sh equal and parallel to B P. As he recedes from the planet through the arc B C D^ the planet secnis to re- cede from him through hed'^ and while he moves from left to right through 1) E the planet seems to move from right to left through de. Finally, as ho ap- proaches the planet through the arc EPA the planet seems to approach him through e f a, and when he returns to ^1 tho planet will appear at a, as in tL' beginning. Thus the planet, though really at rest, will seem to him to move over the circle ahcdef corresponding to that in which the observer himself is carried around the sun. The planet being really in motion, it is evident that the combined eifect of the real motion of the planet and the apparent motion around the circle « J c''"■ >«'■> Fig. 51. — law of areas. In the time of Kepler the means of measuring the sun's angular diameter were so imperfect that the preced- ing method of determining the path of the earth around the sun could not be applied. It was by a study of the motions of the planet Mars, as observed by Tycho Bra he, that Kepler was led to his celebrated laws of planetary ixiotion. He found that no possible motion of Mai's in a truly circular orbit, however eccentric, would represent the observations. After long and laborious calculations, and the trial and rejection of a great number of hypotheses, he was led to the conclusion that the planet Mars moved in an ellipse, having the sun in one focus. As the analo- gies of nature led to the inference that all the planets, the earth included, moved in curves of the same class, and according to the same law, he was led to enunciate the first two of his celebrated laws of planetary motion, which were as follow : * More exactly if we considei* the arc PP\ as a straight line, the area of the triangle PPi SviWX be equal to \8P-x SPi x sin angle S. But in considering only very small angles we may suppose 8P= SPi and the sine of the angle S equal to the angle itself. This supposition will give the area mentioned above. sun. KEPLER'S LAWS. 135 I. Each planet moves around the sun in an ellipse, hav- ing the sun in one of its foci. II. The radius vector joining each planet with the sun, moves over equal areas in equal times. To these he afterward added anotlier showing the rela- tion between the times of revolution of the separate planets. III. The square of the time of revolution of each flanet is proportional to the cube of its mean distance from the sun. These three laws comprise a complete theory of plan- etary motion, so far as the main features of the motion are concerned. There arc, indeed, small variations from these laws of Kepler, hut the laws are so nearly correct tliat they are always employed by astronomers as the basis of their theories. Mathematical Theory of the Elliptic Motion. — The laws of Kepler lead to problems of such mathematical elegance that we give a brief synopsis of the most impor- tant elements of the theory. A knowledge of the ele- ments of analytic geometry is necessary to understand it. Let us put : a, the semi-major axis of the ellipse in which the planet moves. In the figure, if G is the centre of the el- lipse, and S the focus in which the sun is situated, then a=. A C ■= C t. f, the eccentricity of the ellipse = C_S a TT, the longitude of the perilielion, rep- resented by the angle n S E, E being the direction of the vernal equinox from •which longitudes are counted. tt, the mean angular motion of the planet round the sun in a unit of time. The actual motion being variable, the mean motion is found by dividing the circumference = 360° by the time of revolution. T, the time of revolution. r, the distance of the planet from the sun, or its radius vector, «i variable quantity. I. The first remark we have to make is that the ellipticities of tha Fio. 53. 126 A8TR0N0M7. planetary orbits — that is, the proportions in which the orbits are flat- tened — is much less than their eccentricities. By the properties of the ellipse we have : 8 B = semi-major axis = a, BC=s semi-minor axis = a Vl — «?', or, B = a{l — ^ e") nearly, when e is very small. The most eccentric of the orbits of the eight major planets is that of Mercury, for which e = 0.2. Hence for Mercury 50 = «(i-A) very nearly, so that flattening of the orbit is only about ^ or .03 of the major axis. The next most eccentric orbit is that of Mars for which e = .093 ; B C = a (1 — .0043), so that the flattening of the orbit is only about ^^. We see from this that the hypothesis of the eccentric circle makes a very close approximation to the true form of the planetary orbits. It is only necessary to suppose the sun removed from the centre of the orbit by a quantity equal to the product of the eccentricity into the radius of the orbit to have a nearly true representation of the orbit and of the position of the sun. II. The least distance of the planet from the sun is /Sn = a(l — «), and the greatest distance is AS = a{\ + e). III. The angular velocity ot the planet around the sun at any point of the orbit, which we may call S, is, by the second law of Kepler : S = —^j ft C bein^ a constant to be determined. To determine it we remark that 8 IS the angle through which the planet moves in a unit of time. If we suppose this unit to be very small, the quantity S r' is double the area of the very small triangle swept over by the radius vector during such unit. This area is called the areolar velocity of the planet, and is a constant, by Kepler's second law. Therefore, in the last equation, C = 8 r^ represents the double of the areolar velocity of the planet. When the planet completes an entire revo- lution, the radius vector has swept over the whole area of the ellipse which is tt a' V 1 — e'.* The time required to do this be- * In this formula ir represents the ratio of the circumference of the circle to its diameter. and IV. — ,- is a c or ^ KEPLER' fi LAWS Vll ing called ST, the area swept over with the areolar velocity i C i* also \Q T. Therefore \CT-iia} V\ — «» ; V = s; • The quantity 2 it here represents 360*, or the whole circumterence, which, being divided by T, the time of dencribing it will give the mean angular velocity of the planet around the sua which we have called ». Therefore n = 2c and 7" = a*nVl —e\ This value of C being substituted in the expresAion for 8, wc o= I, • have IV. By Kepler's third law T* is proportioned to a* ; that is, — i- is a constant for all the planets. The numerical value of this constant will depend upon the quantities which we adopt as the units of time and distance. If we take the year as the unit of time and the mean distance of the earth from the sun as that of distance, T and a for the earth will both be unity, and the ratio — r will there- fore be unify for all the planets. Therefore a*= T*; a= T*. Therefore if we square the period of revolution of any planet in years, and extract the cube root of the square, we shall have its mean, distance from the sun in units of the carta's distance. It is thus that the mean distances of the planets are determined in practice, because, by a long series of observations, the times of revolution of the planets have been dctcnnined with very great pre- cision. V. To find the position of a planet we must know the epoch at which it passed its perihelion, or some equivalent quantity. To find its position at any other time let r be the time which has elapsed since passing the perihelion. Then, by the law of areas, if P be the position of the planet at this time we shall have Area of sector P. 9 ir Area of whole ellii>8c T f (1). 128 ASTRONOMY. Tike times r and 2' being botli given, the problem is reduced to that of cutting a given area of the ellipse by a line drawn from the focus to some point of its circumference to be found. This is kaown as Kki'leu'h problem, and may be solved by analytic geom- Fio. 63. etrv as follows : Let A Bhe the major axis of the ellipse, P the position of tlio planet, and 8 that of the focus in which the sun is situated. On .1 B as a diameter describe a circle, and through P draw the right line P' P D perpendicular to A B. The area of the elliptic sector S PB, over which the radius vector of the planet iuis swept since the planet passed the periiielion at B, is equal to the sector V P B minus the triangle C P 8. Since an ellipse is formed from a circU? by shortening all the ordinates in the same ratio (namely, the ratio of tiie minor axis h to the major axis rt), it follows that tiie elliptic sector CPB may be formed from the circtilar sector C l" B by shortening all the ordinates in the ratio of D P to D i-", or of a to h. Hence, Area CPB : area C P' B = b : a. But area C P' B = angle P' C B x i a", taking the unit radius as the unit of angular measure. Hence, putting u for the angle P* C B v/e have Area CPB = - area CP'B = lahu (2). Again, the area of the triangle CP Sh equal to ^ base C S x al- titude Pi). Also PD = - P'D, and P' i) = CP' sin m = asinw. a ' Wherefore, P D = h sin u (8). KKPLERS LA\y8. 129 By the first principles of conic sections, C 8, tlie base of the triangle, is equal to a e. Hence Area CPS =: ^ahesinu, and, fiom (2j and (4), Area SP B = ^ah{u — es\nv). (4) SiibHtitutiug in equation (1) this value of the sector area, anu jr tf 6 for the area of the ellipse, we have «r. u — esin u T 2n ~ 7" w — ^ sin « = 2 TT — . T From this equation the unknown angle u is to be found. The c(iuation being a transcendental one, this cannot be done directly, but it may be rapidly done by successive approximation, or the value of It may be developed in un infinite scries. Next we wish to express thejjositionof the planet, which is given by its radi ss vector S P and the angle B 8 P which this radius vector makes with the major axis of the orbit. Let us put r, the radius vector SP, J\ the angle B SP, called the tnie anomaly. Then rsin/= PD — halnu (Eciuation 3), rcosf=SI)z= CD— C3= P' co^u — ae =a (cos m — e), from which r and /can both be determined. By taking the square root of the sums of the squares, they give, by suitable reduction and putting &" = a" (1 — e'), r= a{l — e cos «}, and, by dividing the first by the second, ftsintt tan/ = vr^ e' sin u a (cos u — e) cosw Putting, as before, n for the longitude of the perihelion, the true longitude of the planet in its orbit will be/ + ir. YI. To find the position of the planet relatively to the ecliptic, i# t. t'". 130 ASTHONOMT. the inclination of tlic orbit to the ecliptic has to be talccn Into ac- count. The orbits of tlie several large planets do not lie in the BUine plune, but tire inclined to each other, and to the ecliptic, by various small angles. A table giving the values of these angles will be given hereafter, from which it will be seen that the orbit of Mercury has the greatest inclination, amounting to 7°, and that of Uranus the least, being only 46'. The reduction of the position of the planet to the ecliptic is a problem of spherical trigouumctry, the solution of which need not ue discussed nere. CHAPTER V. UNIVERSAL GRAVITATION. g 1. NEWTON'S LAWS OP MOTION. The establishment of the theory of universal jfravitation furnishes one of the best examples of scientific method wliich is to be found. We shall describe its leading features, less for the purpose of making known to the reader the technical nature of the process than for illus- trating the true theory of scientific investigation, and showing that such investigation has for its object the dis- co-ery of what we may call generalized facts. The real test of progress is found in our constantly increased a])ility to foresee either the course of nature or the effects of any accidental or artificial combination of causes. So long as prediction is not possible, the desires of the inves- tigator remain unsatisfied. When certainty of prediction is once attained, and the laws on which the prediction is founded are stated in their simplest form, the work of science is complete. , The whole process of scientific generalization consists in grouping facts, new and old, under such general laws that they are seen to be the result of those laws, combined with those relations in space and time which we may suppose to exist among the material objects investigated. It is essen- tial to such generalization that a single law shall suffice for grouping and predicting several distinct facts. A law invented simply to account for an isolated fact, however •VJ^jti*^ 182 ASTRONOMY. lii^ general, cannot be regarded in science as a law of nature. It may, indeed, be true, but its truth cannot be proved until it is shown that several distinct facts can be accounted for by it better than by any other law. The reader will call to mind the old fable which represented the earth as supported on the back of a tortoise, but totally forgot that the support of the tortoise needed to be accounted for as much as that of the earth. To the pre-Newtonian astronomers, the phenomena of the geometrical laws of pianetary motion, which we have just described, formed a group of facts having no connection with any thing on the earth. The epicycles of I' .tTARciius and Ptolemy w^ere a truly scientific conception, in that they explained the seemingly erratic motions of the planets by a single simple law. In the heliocentric theory of Coper- nicus this law was still further simplified by dispensing in great part with the epicycle, and replacing the latter by a motion of the earth around the sun, of the same nature with the motions of the planets. But Copernicus had no way of accounting for, or oven of describing with rigor- ous accuracy, the small deviations in the motions of tlie planets around the sun. In this respect he made no real ad^'ance upon the ideas of the ancients. Kepler, in his discoveries, made a great advance in representing the motions of all the planets by a single set of simple and easily understood geometrical laws. Had the planets followed his laws exactly, the theory of planetary motion would have been substantially complete. Still, further progress was desired for two reasons. In the first place, the laws of Kepler did not perfectly represent all the planetary motions. When ob- servations of the greatest accuracy were made, it was found that the planets deviated by small amounts from the ellipse of Kepler. Some small emendations to the motions com- puted on the elliptic theory were t^ierefore necessary. Tiad this requirement been fulfilled, still another stcj) would have been desirable — namely, that of connecting tliu LA WS OF MOrWN. 133 motions of the planets with motion upon the earth, and reducing tliem to the same laws. Notwithstanding the great step which Kkpler made in descnbing the celestial motions, he v .iveiled none of tlic great mystery in which they were euslirouded. This mys- tery was then, to all appearance, impenetrable, beciiuse not the slightest likeness could be perceived between the celestial motions and motions on the surface of the earth. The difficulty was recognized by the older philosophers in the division of motions into "forced" and "natural." Tlie latter, they conceived, went on perpetually from the very nature of things, while the fonner always tended to cease. So when Km*lkr said that observation showed the law of planetary motion to be that around the c''"cum- ference of ai ellipse, as asserted in his law, he said all that it seemed possible to learn, supposinji^ the statement per- fectly exact. And it was all that couM l)e learned from the mere study of tlie planetary motions. In order to connect these motions with those on the eaitli, tlio next step was to fitiidv the laws of force and motion bere around us. Sin- gular though it \nay appear, the ideas of the ancients on tins subject were far more erroneous than their concep- tions of the motions of the planets. We might almost say that before the time of Galilko scarcely f. single correct idea of the laws of motion was generally entertained by men of learning. There were, indeed, one or two who in this respect were far ahead of their age. Lf.onardo da Vinci, the celebrated painter, wa: noted in this respect. Puit the correct ideas entertained by him did not seem to make any headway in the world until the early part of the seventeenth century. Among those wl. >, before the time of Newton, prepared the way for the theory in question, Galileo, Huyghens, and IIooks are entitled to especial mention. As, however, we cannot develop the history of this subject, we must pass at once to the gen- eral laws of motion laid down by Newton. These were three in number. nkn 134 ASTRONOMt. Law First : Every hody preserves its state of rest or oj uniform mofion in a right line^ unless it is compelled to change that state hyfoi'ces impressed thereon. It was formerly supposed that a body acted on by no force tended to come to rest. Here lay one of the great- est difficulties which the predecessors of .Newton found, in accounting for the motion of the planets. The idea that the sun in some way caused these motions was enter- tained from tiie earliest times. Even Ptolemv had a vague idea of a force which was always directed toward the centre of the earth, or, which was to him the same thing, toward the centre of the universe, and which not only caused heavy bodies to fall, but bound the whole uni- verse together. Kepler, again, distinctly affirms the ex- istence of a gravitating force by which the sun acts on the planets ; but he supposed that the sun nmst also exercise an impulsive forward force to keep the planets in motion. The reason of this incorrect idea was, of course, that all bodies in motion on the surface of the earth had practically come to rest. But what was not clearly seen before the time of N ewton, or at least before Galh^eo, was, that this arose from the inevitable resisting forces which act upon all moving bodies around us. Law Second : The alteration of motion is ever propor- tional to the .iioving force impressed, and is made in thd direction of the right line in which that force acts. The first law might be considered as a particular case of this second one arising when the force is supposed to van- ish. The accuracy of both laws can be proved only by very carefully conducted experiments. They are now considered as mathematically proved. Law Third : To every action there is always opposed an equal reaction / or the mutual actions of two bodies upon each other are always equal, and in opposite directions. That is, if a body A acts in any way upon a body B, B will exert a force exactly equal on A iu the opposite direction. force wi Bun, ha^ GRAVITATION OF THE PLANETS. 135 These laws once established, it became possible to calcu- late the motion of any body or system of bodies when once the forces which act on them were known, and, vice versa^ to define what forces were requisite to produce any given motion. The question which presented itself to the mind of I^ EWTON and his contemporaries was this : Under what law qf force will planets move round the sun in accord- ance loith Kepler's la/wa f The laws of central forces had been discovered by Huy- GHEN8 some time before Newton commerced his re- searches, and there was one result of them which, taken in connection with Kepler's third law of motion, was so obvious that no mathematician could have had much diffi- culty in perceiving it. Supposing a body to move around in a circle, and putting i? the radius of the circle, T the period of revolution, Huyghens shewed that the centrifugal force of the body, or, which is tbo . uire thing, the attract- ive force toward the centre which would keep it in the circle, was proportional to 77^. But by Kepler's third law T* is proportional to R". Therefore this centripetal force is proportional to -7^, that is, to -^. Thus it fol- lowed immediately from Kepler's thi law, that the central force which would keep the planets in their or- bits was inversely as the square of the distance from the sun, supposing each orbit to be circular. The first la\' of motion once completely understood, it was evident that the planet needed no force impelling it forward to keep up its motion, but that, once started, it would keep on forever. The next step was to solve the problem, what law of force will make a planet describe an ellipse around the Bun, having the latter in one of its foci ? Or, supposing a planet to move round the sun, the latter attracting it with a force inversely as the square of the distance ; what will be the form of the orbit of the planet if it is not cir* k 136 ASTRONOMY. cular ? A solution of either of these problems was beyond the power of mathematicians before the time of x^I ewtoxX ; and it thus remained uncertain whether the planets mov- ing under the influence of the sun's gravitation would or would not describe ellipses. Unable, at first, to reach a satisfactory solution, Np:wton attacked the problem in another direction, starting from the gravitation, not of the sun, but of the earth, as explained in the following section. § 2. GRAVITATION ES" THE HEAVENS. The reader is probably familiar with the story of New- ton and the ^^nlling apple. Although it has no authorita- tive foundation, it is strikingly illustrative of the method by which Xewton first reached a solution of the problem. The course of reasoning by which he ascended from grav- itation on the earth to the celestial motions was as follows : We see that there is a force acting all over the earth by which all bodies are drawn toward its centre. This force is familiar to every one from his infancy, and is properly called gravitation. It extends without sensible diminution to the tops not only of the highest buildings, but of the highest mountains. ITow .much higher does it extend ? Why should it not extend to the moon ? If it docs, the moon would tend to drop tow^ard the earth, just as a stono thrown from the hand drops. As the moon moves round the earth in her monthly course, there must be some force drawing her toward the eartli ; else, by the first law of motion, she would fly entirely away in a straight line. Why should not the force which makes the apple fall be the same force which keeps her in her orbit ? To answer this question, it was not only necessary to calculate the intensity of the force which would keep the moon herself in her orbit, but to compare it with the intensity of gravity at tlie earth's surface. It had long been known that the distance of the moon waa about sixty radii of the earth. If thi* GRAVITATION OF THE PLAiy'ETS. 137 force diminished as the inverse square of the distance, then, at the moon, it would be only ^^Vir ^^ great as at the surface of the earth. On the earth a body falls six- teen feet in a second. If, then, the theory of gravitation were correct, the moon ought to fall toward the earth suVir ^^ *^'^ amount, or about -^^ of an meh in a second. The moon being in motion, if we imagine it moving in a straight line at the beginning of any second, it ought to be drawn away from that line -j\ of an inch at the end of the second. When the calculation was made with the t'ori'ect distance of the moon, it was found to agree ex- a(^tly with this result of theory. Thus it was shown that the force which holds the moon in her orbit is the same which makes the stone fall, only diminished as the inverse square of the distance from the centre of the earth.* As it appeared that the central forces, both toward the sun and toward the earth, varied inversely as the squares of the distances, ^Newton proceeded to attack the mathe- matical problems involved in a more systematic way than any of his predecessoi-s had done. Kkpler's second law showed that the line drawn from the planet to the sun will describe equal areas in equal times. Newton showed that this could not be true, unless the force which lield the planet was directed toward the sun. AVe have already stated that the third law showed that the force was in- versely as the square of the distance, and thus agreed ex- actly with the theory of gravitation. It only remained to * It is a remarkable fact in tlie liistory of science tliat Newton would have reached this result twenty years sooner than he did, had lie not been misled by adopting an erroneous value of (he earth's diame- ter. His first attempt to compute the earth's gravitation at the distance of the moon was made in 1065, when he was only twenty-three yeais of iige. At that time he supposed that a degree on the earth's surface was sixty statute miles, and was in consequence led to erroneous results by supposing the earth to be smaller and the moon nearer than they really were. He theretore did not make public his ideas ; but twenty years later he learned from the measures of Pica no in France what the true diameter of the earth was, when he repeated his calculation with entire success. 138 ASTRO^rOMY. consider the rer.ults of the first law, that of the elliptic motion. After long and laborious efforts, Newton was enabled to demonstrate rigorously that this law also re- sulted from the law of the inverse square, and could result from no other. Thus all mystery disappeared from the celestial motions ; and planets were shown to be simply heavy bodies moving according to the same laws that were acting here around us, only under very different circum- stances. All three of Keplek's laws were embraced in the single law^ of gravitation toward the sun. The sun attracts the planets as the earth attracts bodies here around us. Mutual Action of the Planets. —It remained to extend and prove the theory by considei-iiig the attractions of the planets themselves. By Newton's third law of motion, each planet must attract the sun with a force equal to that which the sun exerts upon the planet. The moon also must attract the earth as much as the earth attracts the moon. Such being the case, it must be highly probable that the planets attract each other. If so, Kepler's laws can only be an approximation to the truth. The sun, being immensely more massive than any of the planets, overpowers their attraction upon each other, and makes the law of elliptic motion very nearly true. But still the comparatively small attraction of the planets must cause some deviations. Now, deviations from tlie pure elliptic motion were known to exist in the case of several of the planets, notably in that of the moon, which, if gravitation were universal, must move under the influence of the com- bined attraction of the earth and of the sun. Newton, therefore, attacked the complicated problem of the deter- mination of the motion of the moon under the combined action of these two forces. He showed in a general way that its deviations would be of the same nature as those shown by observation. But the complete solution of tlie problem, which required the answer to be expressed in numbers, was beyond his power. ATTRACTION OF ORAVITATION. 139 .o, id Gravitation Resides in each Particle of Matter. — Still another question arose. "Were these mutually attractive forces resident in the centres of the several bodies attracted, or in each particle of the matter composing them ? New- ton showed that the latter must be the case, because the smallest bodies, as well as the largest, tended to fall toward the earth, thus showing an equal gravitation in every separate part. The question then arose : what would be the action of the earth upon a body if the body was attracted — not toward the centre of the earth alone, but toward every particle of matter in the earth ? It was shown by a quite simple mathematical demonstra- tion that if a planet were on the surface of the earth or outside of it, it would be attracted with the same force as if the whole mass of the earth were concentrated in its centre. Putting together the various results thus arrived at, Newton was able to formulate his great law of uni- versal gravitation in these comprehensive words : " Every particle of matter in the universe attracts every other particle with a force directly as the masses of the two particles, and inversely as the square of the distance which separates them.'''' To show the nature of the attractive forces among these various particles, let us represent by m and m' the masses of two attracting bodies. We may conceive the body m to be composed of m particles, and the other body to be composed of m' particles. Let us conceive that each particle of the one body attracts each particle of the Then every particle of m will be other with a force -„ r attracted by each of the m' particles of the other, and therefore the tot il attractive force on each of these m par- m tides will be — ^. Each of the m particles being equally subject to this attraction, the total attractive force between When a given force acta tlie two bodies will be mm. 140 ASTJiOJ/OM7. upon a body, it will produce less motion the larger the- body is, the accelerating force being proportional to the total attracting force divided by the mass of the body moved. Therefore the accelerating force which acts on the body 7n\ and which determines the amount of motion, will fn be —J ; and conversely the accelerating force acting on the /' ro' body m will be represented by the fraction — ^. § 3. FBOELEMS OF GRAVITATION. The problem solved by Newton, considered in its great- est generality, was this : Two bodies of which the masses are given are projected into space, in certain directions, and with certain velocities. What will be their motion under the influence of their mutual gravitation ? If their rela- tive motion does not exceed a certain definite amount, they will each revolve around their common centre of gravity in an ellipse, as in the case of planetary motions. If, how- ever, the relative velocity exceeds a certain limit, the two bodies will separate forever, each describing around the common centre of gravity a curve having infinite branches. These curves are found to be parabolas in the case where the velocity is exactly at the limit, and hyperbolas when the velocity exceeds it. Whatever curves may be de- scribed, the common centre of gravity of the two bodies will be in the focus of the curve. Thus, when restricted to two bodies, the problem admits of a perfectly rigorous mathematical solution. Having succeeded in solving the problem of planetary motion for the case of two bodies, Newton and hie con- temporaries very naturally desired to effect a similar solu- tion for the case of three bodies. The problem of motion in our solar system is that of the mutual action of a great number of bodies ; and having succeeded in the case of two bodies, it was necessary next to try that of three PROIiLKMS OF QHAVirATION. 141 Thus arose the celebrated problem of three bodies. It is found thai no rigorous and geneml solution of this problem. is possible. The curves descrilied by the several bodies, would, in general, be so complex aft to defy mathematical definition. But in the special case of motions in the solar system, the problem admits of l>cingwjlved by approxima- tion with any required degree of a<;curacy. Tlie princi- ples involved in this system of approximation may be com- pared to those involved in extracting the square root of any number which is not an exact s^|uare ; 2 for instance. The square root of 2 cannot l>e exactly expressed either by a decimal or vulgar fraction ; but by increasing the number of figures it can be expressed to any required limit of approximation. Thus, the vulgar fractions 3, ij, i^t.^ etc., are fractions which approach more and more to the required quantity ; and by using larger numbers the errors of such fraction may be made as small as we please. So, in using decimals, we diminish the error ten times for eve- ry decimal we add, but never reduce it to zero. A process of the same nature, but immensely more complicated, has to be used in computing the motions of the planets from their nmtual gravitation. The jKwsibility of such an ap- proximation arises from the fact that the planetary orbits are nearly circular, and that their masses are very small compared with that of the sun. The first approximation is that of motion in an ellipse. In this way the motion of a planet through several revolutions can nearly always be predicted within a small fraction of a degree, though it may wander widely in the course of centuries. Then sup- pose each planet to move in a known ellipse ; their mutual attraction at each point of their respective orbits can be expressed by algebraic formulae. In constructing these formulsB, the orbits are first supposed to be circular ; and afterward account is taken by several successive steps of the eccentricity. Having thus found approximately their action on each other, the deviations from the pure elliptic motion produced by this action may be approximately cal- Ml' jS! OT 1^ III 14^ ASTRONOMY. culated. This being done, the motions will be more exact- ly determined, and the mutual action can bo more exactly calculated. Thus, the process can be carried on step by step to any degree of precision ; but an enormous amount of calculation is necessary to satisfy the requirements of modern times with respect to precision.* As a general rule, every successive step in the approximation is nmch more laborious than all the preceding ones. To understand the principle of astronomical investiga- tion into the motion of the planets, the distinction be- tween observed and theoretical motions must be borne in mind. When the astronomer with his meridian circle de- termines the position of a planet on the celestial sphere, that position is an observed one. When he calculates it, for the same instant, from theory, or from tables founded on the theory, the result will be a calculated or theoretical position. The two arc to be regarded as separate, no mat- ter if they should bti exactly the same in rejdity, because they have an entirely different origin. But it must be re- membered that no position can be calculated from theory alone independent of observation, because all sound theory requires some data to start with, which observation alone can furnish. In the case of planetary motions, these data are the elements of the planetary orbit already described, or, which amounts to the same tiling, the velocity and di- rection of the motion of the planet as well as its mass at some given time. If these quantities were once given with mathematical precision, it would be possible, from the theory of gravitation alone, without recourse to observa- tion, to predict the motions of the planets day by day and generation after generation with any required degree of precision, always supposing that they are subjected to no influence except their mutual gravitation according to the law of Newton. But it is impossible to determine the elements or the velocities without recourse to observation ; * In the works of the great mathematicians on this subject, algebraic- formulee extending through many pages are sometimes given. riiOBLEMS OF OllAVJTATIOS. 148 nnd however correctly they may seeiningly be determined for the time being, subsequent observations always show tliem to have been more or less in error. The reader must understand that no astronouiieal observation can 1)0 mathematically exact. Both the instruments and the (>l)server are subjected to influences which prevent more than an approximation being attained from any one observation. Tlie great art of the astronomer consists in so treating and combining his observations as to eliminate their errors, and give a result as near the truth as possible. When, by thus combining his observations, the astrono- mer has obtained the elements of the planet's motion which lie considers to be near the truth, he calculates from them a series of positions of the planet from day to day in the future, to be compared with subsequent observations. If lie desires his work to be more permanent in its nature, he may construct tables by which the position can be de- tennined at any future time. Having thus a series of the- oretical or calculated . places of the planet, he, or others, will compare his predictions with observation, and from the differences deduce corrections to his elements. We may say in a rough way that if a planet has been obser\'ed through a certtiin number of years, it is possible to calculate its place for an equal number of years in advance with some approach to precision. Accurate observations are con?monly supposed to commence with Bradley, Astron- omer Royal of England in 1750. A century and a quarter having elapsed since that time, it is now possible to con- stract tables of the planets, which we may expect to be tolerably accurate, until the year 2000. But this is a possibility rather than a reality. The amount of calcu- lation required for such work is so immense as to be en- tirely beyond the power of any one person, and hence it is only when a mathematician is able to command the ser- vices of others, or when several mathematicians in some way combine for an object, that the best astronomical tables can hereafter be constructed. 144 ASTTiONOM-y. 8 4. BESXTLTS OP GKAVTTATION. From wliat wo have said, it will l)o seen that the problem of the motions of the planets under the inHuence of grav- itation has called forth all the skill of the mathematicians who have attacketl it. They actually find themselves able to reach a solution, which, so far as the mathematics of the subject are concerned, may be true for many ccTitunes. but not a solution which shall be tnie for all time. Among those who have brought the solution so near to perfec- tion, La. Vlxce is entitled to the lirst rank, although there are others, especially La. Guanoe, who are fully worthy to be named along with him. It will be of interest to state the general results reached by these and other mathema- ticians. Wo call to mind that but for the attraction of the planets upon each other, every planet would move around the sun in an invariable ellipse, according to Keplku's laws. The deviations from this eUiptic motion produced by their mutual attraction are csiHed j!)eriurhatio)is. When they were investigated, it was found that they were of two classes, which were denominated respectively pei'lodic perturbations and secular variations. The periodic perturbatiorts consist of oscillations depend- ent uj)OM the mutual positions of tlie planets, and there- fore of comparatively short period. Whenever, after a number of revolutions, two planets return to the same position in their orbits, the periodic perturbations are of the same amount so far as these two planets are concerned. They may therefore be algebraically expressed as depend- ent upon the longitude of the two planets, the disturbing one and the disturbed one. For instance, the perturba- tions of the earth produced by the action of Mercury depend on the longitude of the earth and on that of Mer- cury. Those produced by the attraction of Venus de- pend upon the longitude of the earth and on that of VenuSy and so on. RESULTS OF GRAVITATION 145 Tlic HroulnrpeHurbations, or Rcciilar variatioriH as they nre coininonly called, consist of slow clmnges in the forms and positions of the several orbits. It is found that the ponhelia of all the orbits arc slowly changing their ap- parent directions from the sun ; that the eccentricities of M»ine are increasing and of otliors diminishing ; and that the positions of the orbits are also '.^hanging. One of the first (juestions which arose in reference to these eecular variations was, will they go on indefinitely i If tliey should, they would evidently end in the subversion of the solar system and the destruction of all life upon the earth. The orbits of the earth and planets would, in the course of ages, become so eccentric, that, ai)proaching near the sun at one time and receding far away from it at another, the variations of temperature would be destruc- tive to life. This problem was tii-st solved by La Gkanoe. lie showed that the changes could not go on forever, but that each eccentricity would always be confined between two quite narrow limits. His results may be expressed by a very simple geometrical construction. Let S repre- sent the sun situated in the focus of the ellipse in which Pro. 54. the planet moves, and let C be the centre of the ellipse. Let a straight line SB emanate from the sun to B^ another line pass from B to Z), and so on ; the number of these lines being equal to that of the planets, and the last one terminating in C, the centre of the ellipse. Then the line S B will be moving around the sun with a very slow motion ; B D will move around B with a slow motion somewhat different, and so each one will revolve in the 146 ASTRONOMF. mr. 'M same manner until we reach the line which carries on its end the centre of the ellipse. Tliese motions are so slow that some of them require tens of thousaiuls. and others hundreds of thousands of years to perform the revolution. By the combined motion of them all, the centre of the ellipse doocribes a somewhat irregular curve. It is evi dent, however, that the distance of the centre from the sun can never be greater than the sum of these revolving lines. Now this distance shows the eccentricity of the ellipse, which is equal to half the diflEerence between the greatest and least distances of the planet from the sun. The perihelion being in the direction C S, on the opposite side of the sun from C, it i^ evident that the motion of G will carry the perihelion with it. It is found in this way that the eccentricity of the earth's orbit has been diminishing for about eighteen thousand years, and will continne to diminish for twenty-five thousand years to come, when it will be more nearly circular than any orbit of our system now is. But before becoming quite circu- lar, the eccentricity will begin to increase again, and so go OR oscillating indefinitely. Secular Acceleration of the Moon. — Another remark- able result reached by mathematical research is that of tlie acceleration of the moon's motion. More than a centurv ago it was found, by comparing the ancient and modern observations of the moon, that the latter moved around the earth at a slightly greater rate than she did in ancient times. The existence of this acceleration was a source of great perplexity to La Grange and La Place, because they thought that they had demonstrated mathematically thai; the attraction could not have accelerated or retarded the mean motJon of the moon. But on continuing his in- vestigation. La Place found tltat there was one causd \thich ho omitted to take acc« nt of — namely, the secular diminution in the eccentricity of the earth's orbit, of which we have just spoken. He found that this change in the eccentricity would slightly alter the action of the longer. ACCELERATION OP THE MOON. 147 ISO ar lof m sun upon the moon, and that this alteration of action would be such that so long as the eccentricity grew smaller, the motion of the moon would continue to be ac- celerated. Computing the moon's acceleration, he found it to be equal to ten seconds into the square of the number of centuries, the l?w being the same as that for the motion of a falling body. That is, while in one century she would be ten seconds ahead of the place she would have occupied had her mean motion been uniform, she would, in two centuries, be forty seconds ahead, in three centuries ninety seconds, and so on ; and during the two thousand years, which have elapsed since the observations of Hipparchus,. the acceleration would be more than a degree. It has re- cently been found that La Place's calculation was not com- plete, and that with the more exact methods of recent times the '.eal acceleration computed from the theory of gravita- tio.i is only about six seconds. The observations of ancient eclipses, however, compared with our modern tables, show an acceleration greater than this ; but owing to the rude and doubtful character of nearly all the ancient data, there is some doubc about the exact amount. From the most celelirated total eclipses of the sun, an acceleration of about twelve seconds is deduced, while the observations of Ptolemy and the Arabian astronomers indicate only eight or nine seconds. There is thus an appar. nt disci 'jpancy between theory and observation, the latter giving a larger value to the acceleration. This difference is now accounted for by supposing that the motion of the earth on its axis is retarded — that is, that the day is gnwlually growing longer. From the modem theory of friction, it is found that the motion of the ocean under the influence of the moon's attraction which causes the tides, must be accom- panied with some friction, and that this friction must re- tard the earth's rotation. There is, however, no way of determining the amount of this retardation unless we JiKsume that it causes the observed discrepancy between the theoretical and observed accelerations of the moon. :'"» 148 ASTUOlfOMr. How this effect is produced will be seen by reflecting that if the day is continually growing longer without our know- ing it, our observations of the moon, which we may suppose to be made at noon, for example, will be constantly made a little later, because the interval from one noon to another will be continually growing a little longer. The moon con- tinually moving forwai*d, the observation will place her fur- ther and further ahead than she would have been observed had there been no retai-dation of the time of noon. If in the coui*se of ages our noon-dials get to be an hour too late, we f>hould find the moon ahead of her calculated place by one hour's motion, or about a degree. The present theory of acceleration is, therefore, that the moon is really accelerated about six seconds in a century, and that the motion of the earth on fis axis is gradually diminishing at such a rate as to produce an apparent additional ac- celeration which may range from two to six seconds. iii'* H § 5. REMABES ON THE THEORY OF GRAVITA- TION. The real nature of the great discovery of Newton is so frequently misunderstood that a little attention may l>e given to its elucidation. Gravitation is frequently spoken of a.s if it were a theory of Newton's, and very generally rcccived by astronomers, but still liable to be ultimately rejected as a great many other theories have been. Not infrequently ]^eople of greater or less intelligence are found making great efforts to prove it erroneor^s. Eveiv prominent scientific institution in the world frequently receives essays having this object in view. Inow, the fiut is that Newton did not discover any new force, but oiily showed that the motions of the heavens could be accounted for by a force which we all know to exist. Gravitation (Latin gravitna — weight, heaviness) is, properly speakin;;, the force which makes all bodies hero at the surface of tlio earth tend to fall downward j and if any one wishes to 'i REALITT OF GRAVITATION. 140 I'V let llv »>(! 10 Ito subvert the theory of gravitation, he must begin by prov- ing that this force does not exist. This no one would think of doing. What Newton did was to show that this force, which, before his time, had been recognized only as acting on the surface of the earth, really extended to the heavens, and that it resided not only in the earth itself, but in the heavenly bodies also, and in each particle of matter, however situated. To put the matter in a terse form, what Newton discovered was not gra/vitatiouy but the universality of gravitation. It may be inquired, is the induction which supposes gravitation univereal so complete as to be entirely beyond doubt ? We reply that within the solar system it certainly is. The laws of motion as established by observation and expeiiment at the surface of the earth must be considered as mathematically certain. Now, it is an observed fact that the planets in their motions deviate from straight lines in a certain way. By the first law of motion, such deviation can be produced only by a force ; and the direc- tion and intensity of this force admit of being calculated onee that the motion is determined. When thus calculated, it is found to be exactly represented by one great force constantly directed toward the sun, and smaller subsidiary forces directed toward the several planets. Therefore, no fact in nature is more finnly established than is that of univei'sal gravitation, as laid down by Newton, at least within the solar system. We shall find, in describing double stars, that gravita- tion is also found to act between the components of a great nniuber cf such stars. It is certain, therefore, that at least some stars gravitate toward each other, as the bodies of the solar system do ; but the distance which separates most of the stars from each other and from our sun is so immense that no evidence of gravitation between them has yet been given by observation. Still, that they do gravitate according to Newton's law can hardly be seri- ously doubted by any one who understands the subject. '^\ ^IN It i ■ 'If* 150 A8TR0N0MT. The reader may now be supposed to see the absurdity of supposing that the theory of gravitation can ever be sub- verted. It is not, however, absurd to suppose tliat it may yet be shown to be the result of some more general law. Attempts to do this are made from time to time by men of a philosopliic spirit ; but thus far no theory of the sub- ject having the slightest probability in its favor has been propounded. Perhaps one of the most celebrated of these theories is that of George Lewis Le Sage, a Swiss physicist of the last century. He suppored an infinite number of ultra- mundane corpuscles, of transcendent minuteness and veloc- ity, traversing space in straight lines in all directions. A single body placed in the midst of such an ocean of mov- ing corpuscles would remain at rest, since it would be equal- ly impelled in every direction. But two bodies would ad- vance toward each other, because each of tliem would screen the other from tliese corpuscles moving in the straight line joining their centres, and there would be a slight excess of corpuscles acting on that side of eacli body which was turned away from the other.* One of the commonest conceptions to account for grav- itation is that of a fluid, or ether, extending through alt space, which is supposed to be animated by certain vibra- tions, and forms a vehicle, as it were, for the transmission of gravitation. This and all other theories of the kind are subject to the fatal objection of proposing coinplicated systems to account for the most simple and elementary facts. If, indeed, such systems were otherwise knov n to exist, and if it could be shown that they really would produce the effect of gravitation, they would be entitled to reception. But since they have been imagined only to account for gravitation itself, and since there is no proof of their existence except that of accounting for it, they * Reference may be made to an article on the kinetic tlicories of gravi'Atioa by William B. Taylor, in the Smithsonian Report for 1876. It to e< CAUSE OF ORAVITATION. in are not entitled to any weight wliatever. In the present state of science, we are justified in regarding gravitation as an ultimate principle of matter, incapable of alteration by any transformation to which matter can oe subjected. The most careful experiments show that no chemical pro- cess to which matter can be subjected either increases or diminishes its gravitating principles in the slightest degree. We cannot therefore see how this principle can ever be referred to any more general cause. ^•i ley of for CHAPTER VI. THE MOTIONS AND ATTRACTION OF THE MOON. Each of tlie planets, except Me7'cury and Veniis, is at- tended by one or more satellites, or moons as they are some- times familiarly called. These objects revolve around their several planets in nearly circular orbits, accompanying them in their revolutions around the sun. Their distances from their planets are very small compared with the distances of the latter from each other and from the sun. Their magnitudes also are very small compared with those of the planets around which they revolve. Where there are several satellites revolving around a planet, the whole of these bodies forms a small system similar to the solar sys- tem in arrangement. Considering each system by itself, the satellites revolve around tiieir central planets or " primaries," in nearly circular orbits, much as the planets re vol ve around the sun. But each system is carried around the sun without any serious derangement of the motion of its several bodies among themselves. Our earth has a single satellite accompanying it in this way, the familiar moon. It revolves around the earth in a little less than a month. The nature, causes and con- sequences of this motion form the subject of the present chapter. g 1. THE MOON'S MOTIONS AND PHASES. That the moon performs a monthly circuit in the lioav- ens is a fact with which we are all familiar from child- hood. At certain times we see her newly emerged from MOTION OF THE MOON. 153 tlie snn's rays in the western twilight, and then we call lier the new moon. On each succeeding evening, we see her further to the cast, so that in two weeks she is oppo- nite the suti, rising in the east as he sets in the west. Continuing her course two wecVs more, she has approached tlie sun on the other side, or from the west, and is once more lost in his rays. At the end of twenty-nine or thirty (lays, we see her again emerging as new moon, and her cir- cuit is complete. It is, however, to be remembered that the sun has been apparently moving toward the east among the stars during the whole month, so that during the interval from one new moon to the next the moon has to make a complete circuit relatively to the stars, and move forward some 3(»" further to overtake the sun. The revolution of the moon among the stars is performed in about 27i days,* so that if we observe when the moon is very near some star, we shall find her in the same position relative to the star at the end of this interval. The motion of the moon in this circuit differs from the apparent motions of the planets in being always forward. We have seen that the planets, though, on the whole, mov- ing directly, or toward the east, are affected with an ap- parent retrograde motion at certain intervals, owing to the motion of the earth around the sun. But the earth is the real centre of the moon's motion, and carries the moon along with it in its annual revolution around the sun. To form a correct idea of the real motion of these three bodies, we must imagine the earth performing its circuit around the sun in one year, and carrying with it the moon, which makes a revolution around it in 27 days, at a distance only about j^ that of the sun. In Fig. 55 suppose S to represent the sun, the large circle to represent the orbit of the earth around it, E to be some position of the earth, and the dotted circle to rep- tesent the orbit of the moon around the earth. We must ♦ More exactly, 27-32166''. 154 ASTRONOMY, Pig. 55. Imagine the latter to carry this circle with it in its an- nual course around the sun. Suppose that when the earth is at E the moon is at M. Then if the earth move to J?, in 27j^ days, the moon will have made a complete revohitiou relative to tlie stai*s — that is, it will ha at J/„ the line E^ J/, being par- allel to EM. But new moon will not have arrived again because the sun is not in the same direction as be- fore. The moon nnist move through the additional arc J/, EM.^, and a little more, owing to the continual ad- vance of the earth, before it will again be new moon. Phases of the Moon. — The moon being a non-luminous body sliines only by retlecting the light falling on her from some other body. The principal source of light is the sun. Since the moon is spherical in shape, the sun can illuminate one half her surface. The appearance of the moon varies according' to the amount of lier illumi- nated hemisphere which is turned toward the earth, as can be seen by studying Fig. 56. Here the central globe is the earth ; the circle around it represents the orbit of the moon. The rays of the sun fall on both earth and moon from the right, the distance of the sun being, on tiio Bcale of the figure, some 30 feet. Eight positions of the moon are shown around the orbit at J., E^ C^ etc., and the right-hand hemisphere of the moon is illuminated in each position. Outside these eight positions are eiglit others showing how the moon looks as seen from the earth in each position. At A it is "new moon," the moon being nearly between the earth and the sun. Its dark hemisphere \ PIIASKH OF TliK MOOS, 155 is then turned toward the earth, ho tlmt it is entirely invisible. At E the ol)server on the earth Kces about a fourth of the illuininjitod IjoniLspherc, which looks like a crescent, ns shown in the outside figure. In this position a <:fieat deal of light is reflected from the earth to the moon, ren- dering the dark part of the latter visible by a gray light Fio. 50. This appearance is sometimes called the " old moon in the new moon's arms.'* At 6' the moon is said to be in her "first quarter," and one half her illuminated hemiHpliere is visible. At G three fourths of the illuminated hemisphere is visible, and at B the whole of it. The latter position, when the moon is opposite the sun, is T--'"-^Un^ky = SPx J'E\* 0+^) = 5P(l-2:^+etc.), the last equation being obtained by the binomial theorem. But PE the fraction -^rp is so small, being less than f^, that its powers above the first will be small enough to be neglected. So we shall have for the required line, SP-2EP. If, therefore, we take the point A so that P A shall be equal to 3 EP, the attraction of the sun upon the earth will on the same scale be represented by the line A S. The disturbing force which we seek is represented by the difference between the attraction of the sun upon the earth and that of the same body upon the moon. If then we suppose the force .4 aS to be applied to the moon in the opposite direction, the resultant of the two forces M S and S A will repre- sent the disturbing force required. By the law of the composition of forces, this resultant is represented by the line MA. We are thus enabled to construct this force in a very simple man- ner, when the moon is in any given position. When the moon is at N, the line N A will be equal to 2 EM; the disturbing force will therefore be represented by twice the distance of the moon. On the other hand, when the moon is at Q the three points E iV, and A will all coinoide. Hence the disturbing force which tends to bring the moon toward the earth will be represented by the line Q E ; hence the force which tends to draw the moon away from tiie earth at new and full moon is twice as great as that which draws MOON'S NODKS. 150 the bodies together at the quarters. Consequently, upon tlic tendency of the sun's attraction is to diminish the al the earth upon the moon. the whole, attraction of % 3. MOTION OF THE MOON'S NODES. Among the changes wliicli the sun's attraction produces in the moon's orbit, that which interests us mort is the constant variation in the plane of the orbit. This plane is indicated by .he path which the moon seems to describe in its circuit around the celestial sphere. Simple naked eye estimates of the moon's position, continued during a iiionth, would show that her path was always quite near the ecliptic, because it would be evident to the eye that, like the sun, she was much farther north while passing from the vernal to the autumnal equinox than while de- scribing the other half of her circuit from the autumnal to the vernal equinox. It would be seen that, like the sun, she was farthest north in about six hours of right as- cension, and farthest south when in about eighteen liours of right ascension. To map out the path with greater precision, we have to observe the position of the moon from night to night with a meridian circle. We thus lay down lier course among the stars in the same manner that we have formerly shown it possible to lay down the sun's path, or the ecliptic. It is thus found that the path of the moon may be considered as a great circle, making an angle of 5° with the ecliptic, and crossing the ecliptic at this small angle at two oppo- site points of the heavens. These points are called the moon's nodes. The point at which she passes from the south to the north of the ecliptic is called tlie ascending node ; that in which she passes from the north to the south is the descending node. To illustrate the motion of the moon near the node, the dotted line a a may be taken as showing the path of the moon, while the circles show her position at successive intervals of one hour as she is ap- proaching her ascending node. Position number 9 is exactly '1 Wf 160 ASTRONOMY, at the node. If we continue following lier course in this way for a week, wo should find that she had moved about 90°, and attained her greatest north lati- tude at 5° from the ecliptic. At the end of another week, we should iind that she had returned to the ecliptic and crossed it Jit her descending node. At the end of the third week very nearly, we should find tiiat she had made three fourths the circuit of the heavens, and was now in her greatest south latitude, being 5° south of the ecliptic. At the end of six or seven days more, we should again find her crossing tlio ecliptic at her ascend- ing node as before. We may thus conceive of four cardinal points of the moon's orbit, OO"^ apart, nnirked by tlu! two nodes and the two points of greatest nortli and scath latitude. Motion of the Nodes. — A remarkable p^'op- crty MOON'S NODES. 161 crty of these jioints is that they are not fixed, but are con- Btimtly moving.';. The general motion is a little irregular, but, leaving out small irreguhirities, it is constantly toward the west. Thus I'eturning to our watch of the course of tlie ni(>on, we should find that, at her next return to tlio ascending node, slie wcviM not describe the lino aa m before, but the line hh about one fourth of a diame':er \\o\'i\\ of it. She would tlierefore reach the ecliptic more than 1^° west of the preceding point of crossing, and her other cardinal points would be found 1^° farther west as t^lio went around. On her next return she wouKl describe the line c c^ then the line (hJ^ etc., indefinitely, each line being farther toward tlie vest. Tiic figure shows the patlis in five coMsecutive returns to the node. A lapse of nine years will bring the descending node aroiuul to the j>lace which was before occupied by the ;iseending node, and thus we shall have the moon crossing at a small inclination toward the south, as shown in the liijure. A complete revolution of the nodes takes place in IS '6 vears. After the lapse of this period, the motion is re- l)e.t(ed in the same manner. One consequence of this motion is that the moon, after liaving a node, reaches the same node again sooner than (sjie completes her true circuit in the heavens. How mueh sooner is readily computed from the fsict that the retro- j>ra(lo motion of the node amounts to 1° 2<>' 81" during the ]K'i'iod that the moon is returning to it. It takes the moon alK)Ut two boui-s and a half (more exactly 0''.l()t)44) to .iiove through this distance r, conse(|Ucntly, coniparing MMtli the sidereal period already given, we find that the return of the moon to her node takes place in 27''.321P><) - ()''. 10944 = 27''. 21222. This time will be important to us in considering the recurrence of eclipses. In Fig. 51) is illustrated the effect of these changes in the position of the moon's orbit upon her motion rela* m 162 ASTRONOMY. 1 tive to the equator. E here represents tho vprna! and A the autiunnal equinox, situated 180° apart. In Marcli, 1876, tlie moon's ascending node cor« responded witli the vernal equi- nox, and her descending node with the autumnal one. Conse- quently she was 5° north of the ecliptic when in six hours of right ascension or near the mid- dle of the figure. Since tho ecliptic is 2;^i° north of the equator at this point, the moon at- tained a maximum declination of 284° ; she therefore passed nearer the zenith when in six hour* of right asccnsiini than at an)' other time during the eighteen years' period. In the language of the almanac, " the moon ran hif^h." Of course when at her greatest distance south of the equator, in the other half of her orbit, she attained a correspond- ing south declination, and cul- minated at a lower altitude than she ha of tho moon from the equator vill be nearly equal to that of the sun. PERIGEE OF THE MOON. 163 g 4. MOTION OF THE PERIGEE. If the siin exerted no disturbing force on tlie moon, the latter would move round the earth in an elHp^3 according to Kepler's laws. But the difference of the sun's attrac- tion on the earth and on the moon, though only a small fraction of the earth's attmctive force on the moon, is yet 80 great as to produce deviations from the elliptic motion very much greatvir than occur in the motions of the planets. It also produces rapid changes in the elliptic orbit. The most remarkable of these changes are the progressive motion of the nodes just described and a corresponding motion of the perigee. Referring to Fig. 52, which illus- trated the elliptic orbit of a planet, let us suppose it to represent the orbit of the moon. S will then represent the earth instead of the sun, and n will be the \\\\\i\v per- igee, or the point of the orbit nearest the '^arth. But, instead of remaining nea»*ly fixed, as do the orbit§ of the planets, the lunar orbit itself may be considered as making 11 revolution round th?) earth in about nine yeai-s, in the Bame direction as the moon itself. Hence if we note the longitude of the moon's perigee at any time, and again two or three yeai*s later, we shall find the two positions quite different. If we wait four yeai*s and a half, we shall lind the perigee in directly the opposite point of the lieavens. The eccentricity of the moon's orbit is about 0.055, and in consequence the moon is about (5° ahead of its mean jtlace when \)(f past the perigee, and about the same dis- tance behind when half way from apogee to perigee. The disturbing action of the sun produces a great num- hcr of other inecpudities, of which the largest are the ti'irfion and the variation. The former is more than a il( j;roe, and the latter not much less. The formulie by ^vhi(•il t'ley are expressed belong to Celestial Mechanics, and tlio reader who desires to study them is referred to Works on that subject. 164 ASTRONOMY, § 6. ROTATION OF THE MOON. The moon rotates on her axis in tlie same time and in the same direction in which slie revolves around tlie earth. In consequence slie always presents very nearly the same face to the earth.* There is indeed a small oscillation called the lihration of the moon, arising from the fact tliat her rotation on her axis is uniform, while her revolution around the earth is not Tmiform. In consequence of this we sometimes see a little of her farther hemisphere first on one side and then on the other, but the greater part of this hemispliero is forever hidden from huniuu 8>gl»t. ^ ^ . The axis of rotation of the moon is inclined to tlio \ ecliptic about 1° 21>'. It is remarkable that this axis changes its direction in a way corresponding exactly to the motion of the nodes of the moon's orbit. Let us sup- pose a line passing through the centre of the earth per- pendicular to the plane of the moon's orbit. In conso- quence of the inclination of the orbit to the eclipti*', tin's line will point 5° from the pole of the ecliptic. Then, suppose another line parallel to the moon's axis oi rota- tion. This line will intOrsect the celestial sphere 1° 2'.)' from the pole of the ecliptic, and on the opposite si'le from the pole of the moon's orbit, so that it will be (!.r from the latter. As one j)ole revolves around the pole of the ecliptic in 18.6 years, the other will do the same, always keeping the same position relative to the tirst. * This conclusion Is often a pom animrum to some 'vho conceive that, if the same face of the moon is always presented to the eiirtii, slie cannot rotate at all. Tlie diJHcully arises from a niisunderstaudinu; of the difference between a iv'-t've and an absolute rotation. It is triiu that slie does not rotate relativeiv to tlie line drawn from the earth to her centre, bnt slie mtist rotate relative to a tixed line, or a line dniwu to a (ixed star. THE TIDES. 105 § 6. THE TIDES. The ebb and flow of the tides are produced by the un- equal attraction of the sun and moon on different parts of the earth, arising from the fact that, owing to the magni- tude of the earth, some parts of it are nearer these attracting bodies than othei-s, and arc therefore more strongly at- tracted. To understand the nature of tlie tide- producing force, we muht recall tlie principle of mechanics already cited, that if two neighboring bodies sire acted on by equal and parallel acceicating forces, their motion rel- ative to each otlier will not be altered, because both will move equally under the influence of the forces. When the forces are slightly different, either in magnitude or direction or both, the relative motion of the two bodies will depend on this difference alone. Since the sun and moon attract those parts of the earth which are nearest them more powerfully than those which are remote, there arises an inequality which j^roduces a motion in the watei*8 of the ocean. As the earth revolves on its axis, different parts of it are brought in succession under the moon. Thus a motion is produced in the ocean, which goes through its rise and fall according to the apparent position of the moon. This is called the tidal wave. The tide-producing force of the sun and moon is so nearly like the disturbing force of the sun upon the motion of the moon around the earth tluit nearly the same explanation will apply to both. Let us tliea refer again to Fig. 57, and suppo.se E to represent the centre of the earth, the circle F Q N its circumference, M a par- ticle of water on the earth's surface, and S either the sun or the moon. The entire earth being rigid, each part of it will move under the iiiHuence of the moon's attraction as if the whole were concen- trated at its centre. But the attraction of the moon upon the particle M, being different from its mean attraction on tlio curtli, will tend to make it move differently from the earth. The force which causes this diffe<-ence of motion, as already explained, will be repre- sented by the line MA. It is true that this same disturbing force is acting upou that portion of the solid ear^^^h at Jf as well us upon the Water. But the earth cannot yield on account of its rigidity ; the ri' 106 ASTRONOMY. water therefore tends to flow nlong the earth's surface from 3/ toward N. There is therefore a residual force tending to make tiie water higher at N than at M. If we suppose the particle M to be near F, then tlie point A will be to the left of F. The water will therefore be drawn in an oppo- site direction or toward F. There will therefore also be a force tending to make the water accumulate around F. As the disturb- ing force of the sun tends to cause the earth and moon to separate both at new and full moon, so the tidal force of the sun iind moon upon the earth tends to make the waters accumulate both at M and /'. More exactly, the force in question tends to draw the earth out into the form of a prolate ellipsoid, having its longest axis in the direction of the attracting body. As the earth rotates on its axis, each particle of the ocean is, in the course of a day, brought in to the four jiositions JV Q F Jt, or into some positions corresponding to these. Thus, the tide-producing force changes back and forth twice in the course of a lunar day. (By a lunar day we mean the interval between two successive passages of the moon across the meridian, which is, on the average, about 24*" 48"*.) If the waters could yield immediately to this force, we should always have high tide at F and N and low tides at Q and Ji. But there are two causes which prevent this. 1. Owing to the inertia of the water, the force must act some time before the full amount of motion is produced, and this motion, once attained, will continue after the force has ceased to act. Again, the waters will continue to accumulate as Icng as there in any motion in the required direction. The result of this would be high tides at Q and B and low tides at F and iV, if the ocean covered the earth and were perfectly free to move. That is, higli tides would then be six hours after the moon crossed the meridian. 2. The principal cause, however, which interferes with the regularity of the motion is the obstruction of islands and continents to the free motion of the water. These deflect the tidal wave from its course in so many different ways, that it is hardly possible to trace the relation between the attraction of the moon and the mo- tion of the tide ; the time of high and low tide must therefore he found by observing at each iK>int along the coast. By comparing these times througfi a series of years, a very accurate idea of the motion of the tidal wave can be obtained. Such observations have been made over our Atlantic and Pacific coasts by the Coast Survey and over most of the coasts of Europe, by the countries occupying them. Unfortunately the tides cannot be observed away from the land, and hence little is known of the course of the tidal wave over llu> ocean. Wc Imve i*oinarked that botli tlio siiii anil moon cxurt a tide-producing foreo. Tluit of tlio sun is about ^\ of tliiit of the moon. At now and full moon the two foreoi ur« united, and the actual force is equal to their sum. At THE TWE8. 167 iirst and last quarter, when the two bodies arc 90** apart, they act in opposite directions, the sun tending to produce a liigh tide where the moon tends to produce a h)W one, and mce versa. The result of this is that near the time of iit'W and full moon we have what are known as the spring tides, and near the quarters what are called neap tides. It the tides were always ]>roportional to the force which pro- duces them, the spring tides would be highest at full moon, but the tidal wave tends to go on for some time after the force which produces it ceases. Hence the high- est spring tides are not reached until two or three days after new and full moon. Again, owing to the effect of fric- tion, the neap tides contimie to be less and less for two or three days after the ^rst and last quarters, when the grad- ually incireasing force again has time to make itself felt. The theory of the tides offers very complicated prob- lems, which have taxed the powers of mathematicians for several generations. These problems are in their elements less simple than those presented by the motions of the planets, owing to the number of disturbing circumstances which enter into them. The various depths of the ocean at different points, the friction of the water, its momen- tum when it is once in motion, the effect of the coast-lines, have all to be taken into account. These quantities are 60 far from being exactly known that the tlieory of the tides can be expressed only by some general principles wliich do not suffice to enable us to predict them for any given place. From observation, however, it is easy to constnict tables showing exactly what tides correspond to given positions of the sun and moon at any port where the ohservations are made. With such tables the ebb and flow ini! |ir(idi' B' T, each tangent to the sun and the earth. The two bodies being supposed spherical, these lines will be the intersections of a cone with the plane of the paper, and may be taken to repre- sent that cone. It is evident that the cone B V B' will be the outline of the shadow of the earth, and that witliiii this cone no direct sunlight can penetrate. It is therefore called the earth's shadow cone. Let us also draw the lines D' B P and D B' P' to re[>- resent the other cone tangent to the sun and earth. It i» TUK EARTirS HIIADOW. 169 tlien evident tliat within the n-^ion V B P aui} V B' P' the light of the BUii will be partially but not entirely cut off. Fig. 00.— form op hhadow. Dimermiona of S/iadow. —Let uh invcfftii^ate the (li»tancc E Ffrom tlu! centre V E liaiK Hence, of tiie eiirtli to tlie vert<'X of the shadow. The triangles K «S i> are similar, having a right angle at Ji and at I). VEi KD = VS.8D= ES'.{SD- E li). So if we put l=V E, the length of the shallow measured from the eentre of the earth. r = ES, the radius vector of the earth. Ji = S J), the radius of the sun, p=r. E Ji, tlie radius of the earth. fi, the angular semi-diameter of the Kun as seen from the earth, n, the horizontal parallax of the Kun, we have 1= VE=^ ES X ED rp SD-EJi Ji-p Kut by the theory of parullaxen (Chapter I., % 1), p = r sin T R = r»\n 8 Hence, ?= . / . ■ sm H—nm r The mean value of the sun's an^^ular Hemi-diameter, from which the real value never differs by more than the sixtieth part, is found by observations to be about 16' 0' = 960', while the mean value of n k ASTRONOMY. M j» about 8' -8. We find sin k.. /; '/ Photagriiphic Sdehces Corporatiori d L17 V 4 ^ ,v N> r^ <^ 23 WEST MAIN STRKT WEBSTER, N.Y. )4S80 (716) 873-4503 4^ '^ Z ^ 172 ASTRONOMY. ring would appear red, owing to the absorption of the blue and green rays by the earth's atmosphere, just as the sun seems red when setting. The moon may remain enveloped in the shadow of the earth during a period ranging from a few minutes to nearly two hours, according to the distance at which she passes from the axis of the shadow and the velocity of her angu- lar motion. When she leaves the shadow, the phases which we have described occur in reverse order. It very often happens that the moon passes through the penumbra of the earth without touching the shadow at all. No notice Ig taken of these passages in our almanacs, be- cause, as already stated, the diminution of light is scarcely perceptible unless the moon at least grazes the edge of the shadow. ! I i| 1 § 3. ECLIPSES OF THE SUN. In Fig. 60 we may suppose B E B' to represent the moon as well as the earth. The geometrical theory of the shadow will remain the same, though the length of the shadow will be much less. "VVe may regard the mean semi- diameter of the sun as seen from tt)e moon, and its mean distance, as being the same for the moon as for the earth. Therefore, in the formula which gives the length of the moon's shadow, S may retain the same value, while p and n must be diminished in the ratio of the moon's radius to that of the earth. The denominator, sin S — sin n^ will be but slightly altered. The radius of the moon is about 1 730 kilometres. Multiplying this by 217, as before, we find the mean length of the moon's shadow to be 377,000 kilometres. This is nearly equal to the distance of the moon from the earth when she is in conjunction with the sun. We therefore conclude that when the moon passes between the earth and the sun, the former will be verv near the vertex F^of the shadow. As a matter of fact, an observer on the earth's surface will sometimes pass i! ■&vn'm% THE MOON'S SHADOW. 17S through the region C VC, and sometimes on the other side of F. Now, in Fig. 60, still supposing B E B' to he the moon, let us draw the lines D B' P' and D' B P tan- gent to bothtlie moon and the sun, but crossing each other between these bodies at h. It is evident that outside the space P B B' P' an observer will see the whole sun, no part of the moon being projected upon it ; while within this space the sun will be more or less obscured. The whole obscured space may be divided into three regions, in each of which the character of the phenomenon is differ- ent from what it is in the othei*s. Firstly, we have the region B VB' forming the shadow cone proper. Here the sunlight is entirely cut oS by the moon, and darkness is therefore complete, except so far as light may enter by refraction or reflection. To an obser*'er at V the moon would exactly cover the sun, the two bodies being apparently tangent to each other all around. Secondly, we have the conical region to the right of V between the lines B Fand B' V continued. In this region the moon is seen wholly projected upon the sun, the visible portion of the latter presenting the form of a ring of light around the moon. This ring of light will be wider in proportion to the apparent diameter of the sun, the farther out we go, because the moon wnll appear smaller than the sun, and its angular diameter will dimin- ish in a more rapid ratio than that of the sun. Thi& region is that of annular eclipse, because the sun will pre- sent the appearance of an annulus or ring of light around the moon. Thirdly, we have the region P B V and P' B' V, which we notice is connected, extending around the interior cone. An observer here would see the moon partly projected upon the sun, and therefore a certain part of the sun's light would be cut off. Along the inner boundary B V and B' V the obscuration of the sun will be complete, but the amount of sunlight will gradually increase out in 174 ASTRONUMF. the outer boundary B P B' P\ where the whole sun Is visible. Tliis region of partial obscuration is called the pcnumhra. To show more clearly the phenomena of solar eclipse, we present another ligure representing the penumbra of Fig. fll. — ^FIGURE OF SHADOW FOR ANNTTIiAR ECIilFSB. the moon throw^n upon the earth.* The outer of the two circles S represents the limb of the sun. The exterior tan- gents which mark the l)0undary of the shadow cross each other at V before reaching the earth. The earth being a little beyond the vertex of the shadow, there can be no total eclipse. In this case -an observer in the penumbral region, C O or D O, will see the moon partly projected on the sun, while if he chance to be situated at O he will see an annular eclipse. To show how this is, we draw dotted lines from tangent to the moon. The angle between these lines represents the apparent diameter of the moon as seen from the earth. Continuing them to the sun, they show the apparent diameter of the moon as projected upon the Bun. It will be seen that in the case supposed, when * It will be noted that all the tigures of eclipses are necessarily drawn Very much out of proportion. Really the stin is 400 times the distance of the moon, which again is 60 times the radius of the earth. But it would be entirely impossible to draw a figure of this proi)ortion ; we are therefore obliged to represent the earth as larger than the sun, ana the moou as nearly half way between the earth and sun. ECLIPSES OF THE SUN. 17ft the vertex of the shadow is between the earth and moon, the latter will necessarily appear smaller than the sun, and the observer will see a portion of the solar disk on all sides of the moon, as shown in Fig. 62. If the moon were a little nearer the earth than it is rep- resented in the figure, its shadow would reach the earth Fig. 62. — dark body of moon projected on sun dubino an annular eclipse. in the neighborhood of O. We should then have a total eclipse at each point of the earth on which it fell. It will be seen, however, that a total or annular eclipse of the sun is visible only on a very small portion of the earth's sur- face, because the distance of the moon changes so little that the earth can never be far from the vertex F'of the shadow. As the moon moves around Me earth from west to east, its shadow, whether the eclipse be total or annu- lar, moves in the same direction. Tho diameter of the shadow at the surface li the earth ranges from zero to 150 miles. It therefore sweeps along a belt of the earth's sur- face of that breadth, in the same direction in which the earth is rotating. The velocity of the moon relative tc the earth being 3400 kilometres per hour, the shadow would pass along with this velocity if the earth did not ro- tate, but owing to the earth's rotation the velocity relative 176 ASTRONOMY. to points on its surface may range from 2000 to 3400 kilometres (1200 to 2100 miles). The reader will readily understand that in order to see a total eclipse an observer must station himself before- hand at some point of the earth's surface over which the shadow is to pass. These points are generally calculated some years in advance, in the astronomical ephemerides, with as much precision as the tables of the celestial mo- tions admit of. It will be seen that a partial eclipse of the sun may be visible from a nmch larger ])ortion of the earth's surface than a total or annular one. The space CD (Fig. 61) over wliich the penumbra extends is generally of about one half the diameter of the earth. Roughly speaking, a partial eclipse of the sun may sweep over a portion of the earth's surface ranging from zero to perhaps one fifth or one sixth of the whole. There are really more eclipses of the sun than of the moon. A year never passes without at least two of the former, and sometimes five or six, while there are rarely more than two eclipses of the moon, and in many years none at all. But at any one place more eclipses of the moon will be seen than of the sun. The reason of this is that an eclipse of the moon is visible over the entire hemi- sphere of the earth on which the moon is shining, and as it lasts several hours, observers wlio are not in this hemi- sphere at the beginning of the eclipse may, by the earth's ro- tation, be brought into it before it ends. Thus the eclipse will be seen over more than half the earth's surface. But, as we have just seen, each eclipse of the sun can be seen over only so small a fraction of the earth's surface as to more than compensate for tiie greater absolute frequency of solar eclipses. It will be seen that in order to have either a total or an- nular eclipse visible upon the earth, the line joining the centres of the sun and moon, being continued, must strike the earth. To an observer on this line, the centres RECURRENCE OF EGLIP8BS. 177 of the two bodies will seem to coincide. An eclipse in which this occurs is called a central one, vhether it he total or annular. The accompanying figure will perhaps aid in giving a clear idea of the phenomena of eclipses of both sun and moon. »s::ii^-ci:r>i— !n=>-— 1.--"--. J—- -. "■ " " ■ "'" ■'-^: -i'Ss> '- j£^ ^mHir^'^ Fig. 63. — comparison of shadow and penumbra op earth and moon. a 18 the position of the moon durino a solar, b dur- ing a lunar eclipse. § 4. THE BECTntBEITCE OF ECLIPSES. If the orbit of the moon around the earth v/ere in or near the same plane with that of the latter around the sun — that is, in or near the plane of the ecliptic — it will be readily seen that there would be an eclipse of the sun at every new moon, and an eclipse of the moon at every full moon. But owing to the inchnation of the moon's orbit, described in the last chapter, the shadow and penumbra of the moon commonly pass above or below the earth at the time of new moon, while the moon, at her full, commonly passes above or below the shadow of the earth. It is only when at the moment of new or full moon the moon is near its node that an eclipse can occur. The question now arises, how near must the moon be to its node in order that an eclipse may occur ? It is found by a trigonometrical computation that if, at the moment of new moon, the moon is more than 18° '6 from it node, no eclipse of the sun is possible, while if it is lesj than 13° 'Y an eclipse is certain. Between these limits an ecHpse may ocur or fail according to the respective dis- tances of the sun and moon from the earth. Half way be- tween these limits, or say 16° from the node, it is an even m. 178 ASTRONOMY. chance that an eclipse will occur ; toward the lower limit (13° • 7) the chances increase to certainty ; toward the upper one (18° -6) they diminish to zero. The correspond- ing limits for an eclipse of the moon are 9° and 12^° — that is, if at the moment of full moon the distance of the moon from her node is greater than 12^° no eclipse can occur, while if the distance is less than 9° an eclipse is cer- tain. We may put the mean limit at 11°. Since, in the long run, new and full moon will occur equally at all dis- tances from the node, there will be, on the average, sixteen eclipses of the sun to eleven of the moon, or nearly fifty per cent more. Fig. 64.— ninstrating lanar eclipse at different distances from the node. The darlc * circles are the earth's shadow, the centre of which ia aiways in the ecliptic A B. The moon's orbit is represented by CD. At O the eclipse is central and total, at F it is partial, and at E there is barely an eclipse. As an illustration of these computations, let us investigate the lim- its within which a central eclipse of the sun, total or annular, can occur. To allow of such an eclipse, it is evident, from an inspec- tion of Fig. 61 or 63 that the actual distance of the moon from the plane of the ecliptic must be less than the earth's radius, because the line joining the centres of the sun and earth always lies in this plane. This distailce must, therefore, be less than 6370 kilo- metres. The mean distance of the moon being 884,000 kilometres, the sine of the latitude at this limit is ^fH^, and the latitude itself is 57'. The formula for the latitude is, by spherical trigonometry, sin latitude = sin « sin u, t being the inclination of the moon's orbit (5° 8'), and ti the distance of the moon from the node. The value of sin i is not far from i\, while, in a rough calculation, we may suppose the comparatively small angles u and the latitude to be the same as their sines. We may, therefore, suppose M = 11 latitude » 10^'. REUURUENCE OF ECLIPSES. 179 We therefore conclude that if, ftt the moment of now moon, the distance of the moon from the node is less tliim lOi there will be a central eclipse of the sun, and if greater than this there will not be such an eclipse. The eclipse limit may range half a degree or more on each side of this mean value, owing to the varying distance of the moon from the earth. Inside of 10 a central eclipse may be re- garded as certain, and outside of IV as impossible. If the direction of the moon's nodes from the centre of the eartli were invariable, eclipses could occur only at the two opposite months of the year when tlie sun had nearly the same longitude as one node. For instance, if the lon- gitudes of the two opposite nodes were respectively 54" and 234°, then, since the sun must be within 12° of the node to allow of an eclipse of the moon, its longitude would have to be either between 42° and 00°, or between 222° and 246°. But the sun is within the first of these re- gions only in the month of May, and within the second only during the month of November. Hence lunar eclipses could then occur only during the months of May and No- vember, and the same would hold true of central eclipses of the sun. Small partial eclipses of the latter might be seen occasionally a day or two from the beginnings or ends of the above months, but they would be very small and quite rare. Now, the nodes of the moon's orbit were act- ually in the above directions in the year 1873. Hence during that year eclipses occurred only in May and No- vember. We may call the '^ months the seasons of eclipses for 1873. But it was explained in the last chapter that there is a retro^ ade motion of the moon's nodes amounting to 19^° in a year. The nodes thus move back to meet the sun in its annual revolution, and this meeting occurs about 20 days earlier every year than it did the year before. The re- sult is that the season of eclipses is constantly shifting, so that each season ranges throughout the whole year in 1 8 • 6 years. For instance, the season corresponding to that of November, 1873, had moved back to July and August in m 180 A8TR0N0MT. 1878, and will occur in May, 1882, while that of May, 1873, will be shifting back to November in 1882. It may be interesting to illustrate this by giving the days in which tlie sun is in conjunction with the nodes of the moon's orbit during several years. Ascending Node. 1879. January 24. 1880. January 6. 1880. December 18. 1881. November 30. 1882. November 12. 1883. October 25. 1884. October 8. Descending Nod*. 1879. July 17. 1880. June 27. 1881. June 8. 1882. May 20. 1883. May 1. 1884. April 12. 1885. March 25. During these years, eclipses of the moon can occur only within 11 or 12 days of these dates, and ecHpses of the sun only within 15 or 16 days. In consequence of the motion of the moon's node, three varying angles come into play in considering the occur- rence of an eclipse, the longitude of the node, that of tlie sun, and that of the moon. We may, however, simplify the matter by referring the directions of the sun and moon, not to any lixed tine, but to the node — that is, wo may count the longitudes of these bodies from the nodo instead of from the vernal equinox. We have seen in tlio last chapter that one revolution of the moon relatively to the node is accomplished, on the average, in 27-21222 days. If we calculate the time required for the sun to re- turn to the node, we shall find it to be 346 • 6201 days. Now, let us suppose the sun and moon to start out together from a node. At the end of 346 • 6201 days the sun, having apparently performed nearly an entire rev- olution around the celestial sphere, will again be at the same node, which has moved back to meet it. But the moon will not be there. It will, during the interval, have passed the node 12 times, and the 13th passage will not occur for a week. The same thing will be true for RECURRENCE OF ECLIPSES. 181 18 successive returns of the sun to the node ; we shall not find the moon there at the same time with the sun ; slie will always have passed a little sooner or a little later, liut at the 19th return of the sun and the 2rt2d of the moon, the two bodies will be in conjunction within half a degree of the node. "We find from the preceding periods that 242 returns of the moon to the node require 6585 '357 days. 19 u (( sun u (( u 6585-780 (( The two bodies will therefore pass the node within 10 liours of each other. This conjunction of the sun and moon will be the 223d new moon after that from which we started. Now, one lunation (that is, the interval between two consecutive new moons) is, in the mean, 29-530588 days ; 223 lunations therefore require 6585-32 days. The new moon, therefore, occurs a little before the bodies reach the node, the distance from the latter being that over which the moon moves in 0** • 036, or the sun in 0'*.459. We readily find this distance to be 28' of arc, somewhat less than the apparent diameter of either body. This would be the smallest distance from either node at which any new moon would occur during the whole period. The next nearest approaches would have occurred at the 35th and 47th lunations respectively. The 35tli new moon would have occurred about 6° before the two bodies arrived at the node from which we started, and the 47th about 1^° past the opposite node. No other new moon would occur so near a node before the 223d one, which, as we have just seen, would occur 0° 28' west of the node. This period of 223 new moons, or 18 years 11 days, was called the Saroa by the ancient astron- omers. It will be seen that in the preceding calculations we have assumed the sun and moon to move uniformly, so that the successive new moon's occurred at equal intervals of ^-9 • 530588 days, and at equal angular distances around the ecliptic, i. fact, however, the month* ly inequalities in the motion of the moon cause deviations from her 183 ASTRONOMY. mean motion which amount to six degrees in either direction, while the annuitl ine(|uulity in tiie motion of tlie sun in longitude is nearly two de;,Tce8. (-'onseciucntly, our conclusions respecting the point tit which new moon occurs may be astray by eiglit degrees, owing to these ine<|ualities. IJut there is a remarkable feature connected with the Saroa which greatly reduces these inecjualities. It is that this period of 0585^ days corresponds very nearly to an integral inimber of revolutions both of the earth round the sun, and of the hinar perigee around the earih. Hence the inequalities both of the moon and of the sun will be nearly the same at the beginning and the end of a Saros. In fact, (jri*^')J days is about 18 years and 11 days, in whicih time the earth will have made 18 revolutions, and about 11° on the 19th revolution. The longitude of the sun will therefore be about 11° greater than at the beginning of the period. Again, in the same period the moon's perigee will have made two revolutions, and will have advanced 13 ' 38' on the third revolution. The sun and moon being 11° further advanced in longitude, the conjunction will fall at the samo listance from the lunar |)erigee within two or three degrees. Wivnout going through the details of the calcula- tion, v.'« may say as the residt of this remarkable coincidence that the time of the 223d lunation will not generally be accelerated or retarded more than half an hour, though those of the intermediate lunations will sometimes deviate more than half a day. Also tlutt the distance west of the node at which the new moon occurs will not generally differ from its mean value, 28' by more than 20'. In the preceding explanation, we have supposed the sun and moon to start out togetlier from one of the nodes of the moon's orbit. It is" evident, however, that we miglit have supposed them to start from any given distance east or west of the node, and should then at the end of the 223d lunation find them together again at nearly that distance from the node. For instance, on the 5th day of May, 1864, at seven o'clock in the evening, Washington time, new moon occurred with the sun and moon 2° 25' west of the descending node of the moon's orbit. Counting for- ward 223 lunations, we arrive at the 16th day of May, 1882, when we find the new moon to occur 3° 20' west of the same node. Since the character of the eclipse dependij principally upon the relative position of the sun, the moon, and the node, the result to which we are led may be stated as follows : Let us note the time of the middle of any eclipse. I RECURliKNVE OF ECL/PSKS. 183 whether of the sun or of the iiiooii. Tlieii lot us go for- wiird C5S5 days, 7 hours, 42 nnnutes, uud wu shall find another eclipse very similar to the first, lieduced to yeare, the interval will be 18 years and 10 or 11 days, according jis a 29th day of February intervenes four or five times tliiring the interval. This being true of every eclipse, it follows that if we record all the eclij)ses which occur dur- ing a period of IS years, we shall iind a new set to begin over again. If the period were an integral number of (lays, each eclipse of the new set would be visible in the .same regions of the earth as the old one, but rince there is u fraction of nearly 8 hours o\" the round number of days, the earth will be one third ' f a revolution further advanced before any eclipse of tlie new set begins. Each c(;Iip8e of tlie new set will therefore occur about one third of the way round the world, or 12<>^ in longitude west of the region in which the old one occurred. The recur- rence will not take place near the same region until the end of three periods, or 5-t years ; and then, since there is a slight deviation in the series, owing to each new or full moon occurring a little further west from the node, the fourth eclipse, though near the same region, will r.ot necessarily be similar in all its particulars. For examj)le, if it be a total eclipse of tlie sun, the path of the shadow may be a thousand miles distant from the path of 54 years })reviou8ly. As a recent example of the Saros, we may cite some total eclipses of the sun well known in recent times ; for instance : 1842, July 8th, l"* a.m., total eclipse observed in Europe ; 1860, July 18th, 9** a.m., total eclipse in America and Spain ; 1878, July 29th, 4" p.m., one visible in Texas, Col- orado, and on the coast of Alaska. A yet more remarkable series of total eclipses of the !!!: 184 ASTRONOMY. sun are those of the years 1850, 1868, 1886, etc., the dates and regions being : 1850, August 7th, 4*' p.m., in the Pacific Ocean ; 1868, August 17th, 12'' p.m., in India ; 1886, August 29th, 8'' a.m., in the Central Atlantic Ocean and Southern Africa ; 1904, September 9th, noon, in South America. This series is remarkable for the long duration of total- ity, amounting to some six minutes. Let us now consider a series of eclipses recurring at reg- ular intervals of 18 years and 11 days. Since every suc- cessive recurrence of such an eclipse throws the conjunc- tion 28' further toward the west of the node, the conjunc- tion must, in process of time, take place so far back from the node that no eclipse will occur, and the series will end. For the same reason there must be a commencement to the series, the first eclipse being east of the node. A new eclipse thus entering will at firet be a very small one, but will be larger at every recurrence in each Saros. If it is an eclipse of the moon, it will be total from its 13th until its 36th recurrence. There will then be about 13 partial eclipses, each of which will be smaller than the last, when they will fail entirely, the conjunction taking place so far from the node that the moon does not touch the earth's shadow. The whole interval of time over which a series of lunar eclipses thus extend will be about 48 periods, or 865 years. When a series of solar eclipses begins, the penumbra of the firet will just graze the earth not far from one of the poles. There will then be, on the average, 11 or 12 partial eclipses of the sun, each larger than the preceding one, occurring at regular intervals of one Saros. Then the central line, whether it be that of a total or annular eclipse, will begin to touch the earth, and we shall have a series of 40 or 50 central eclipses. The central line will 'strike near one pole in the first part of the series ; in the equatorial regions about the middle of the series, and will VUARACTERS OF ECLIPSES. 186 in, leave the earth by the other pole at the end. Ton or twelve piirtial eclipses will follow, and this particular se- ries will cease. The whole nainber in the series will aver- age between 60 and 70, occupying a few centuries over a thousand years. § 5. OHARAOTERS OF EOLIPSBS. We have seen that the possibility of a total eclipse of the sun arises from the occasional very slight excess of the apparent ani^ular diameter of the moon over that of the sun. This excess is so slight that such an eclipse can never last more than a few minutes. It may be of interest to point out the circumstances wliicli favor a long duration of totality. These are : (1) That the moon should be as near as possible to tlie earth, or, technically speaking, in perigee, because its angular diameter as seen from the earth will then be greatest. (2) That the sun should be near its greatest distance from the earth, or in apogee, because then its angular diameter will be the least. It is now in this position about the end of June ; hence the most favorable time for a total eclipse of very long duration is in the summer months. Since the moon must be in perigee and also between the earth and sun. it follows that the longitude of the perigee must be nearly that of the sun. The longitude of the sun at the end of June being 100°, this is the most favorable longi- tude of the moon's perigee. (3) The moon must be very near the node in order that the cen- tre of the shadow may fall near the e(iuator. The reason of this con- dition is, that the duration of a total eclipse may be considerably increased by the rotation of the earth on its axis. We have seen that the shadow sweeps over the earth from west toward east with a velocity of about 3400 kilometres per hour. Since tlie earth rotates in the same direction, the velocity relative to the observer on the earth's surface will be diminished by a quantity depending on this velocity of rotation, and therefore greater, the greater the velocity. The velocity of rotation is greatest at the earth's equator, where it amounts to 1660 kilometres per hour, or nearly half the velocity of the moon's shadow. Hence the d"-'-*.ion of a total eclipse may, with- in the tropics, be nearly doubled jy the earth's rotation. When all the favorable circumstances combine in the way we have just de- scribed, the duration of a total eclipse within the tropics will be about seven minutes and a half. In our latitude the maximum du- ration will be somewhat less, or not far from six minutes, but it is only on very rare occasions, hardly once in many centuries, that all these favorable conditions can be expected to concur. Of late years, solar eclipses have derived an increased in- terest from the fact that during the few minutes which 186 ASTRONOMY. itfii they last they afford uni(jue opportunities for investigating the matter which lies in the immediate neighborhood of the sun. Under ordinary circumstances, this matter is rendered entirely invisible by the effulgence of the solar rays which illuminate our atmosphere ; but when a body so distant as the moon is interposed between tlie obr.erver and the sun, the rays of the latter are cut off from a region a hui'.dred miles or more in extent. Thus an amount of darkness in the air is secured which is impossible under any other circumstances when the sun is far above 1;he horizon. Still this darkness is by no means complete, because the sunlight is reflected from the region on which the ran is shining. An idea of the amount of darkness may be gained by considering that the face of a watch can be read during an eclipse if the observer is careful to shade his eyes from the direct sunlight during the few minutes be- fore the sun is entirely covered ; that stars of the first magnitude can be seen if one knows where to look for them ; and that all the prominent features of the land- scape remain jjlainly visible. An account of the investi- gations made during solar eclipses belongs to the physical constitution of the sun, and will therefore be given in a subsequent chapter. Occultation of Stars by the Moon. — A phenomenon which, geometrically considered, is analogous to an eclipse of the sun is the occultation of a star by the moon. Since all the bodies of the solar system are nearer than the fixed stars, it is evident that they must from time to time pass between us and the stars. The planets are, however, 80 small that such a passage is of very rare occurrence, and when it does happen the star is generally so faint that it is rendered invisible by the superior light of the planet before the latter touches it. There are not more than one or two instances recorded in astronomy of a well- authenticated observation of an actual occultation of a star by the opaque body of a planet, although there are several cases in which a planet has been known to pass over a star. ! ; OCCULTATION OF STABS. 187 But the moon is so large and her angular motion so rapid, that she passes over some star visible to the naked eye every iew days. Such phenomena are tenned occultations of stars hy the moon. It must not, however, be supposed that they can be observed by the naked eye. In general, tlie moon is so bright that only stars of the iirst magnitude can be seen in actual contact with her limb, and even then tlie contact must be with the unilluminated limb. But with the aid of a telescope, and the predictions given in the Ephemeris, two or three of these occultations can be observed during nearly every lunation. 1 . ;1 CHAPTER VIIL THE EAETH. Our object in the present chapter is to trace the effects of terrestrial gravitation and to study the changes to which it is subject in various places. Since every part of the earth attracts every other part as well as every object upon its surface, it follows that the earth and all the objects that we consider terrestrial form a sort of system by themselves, the parts of which are firmly bound together by their mutual attraction. This attrac- tion is so strong that it is found impossible to project any object from the surface of the earth into the celestial spaces. Every particle of matter now belonging to the earth must, so far as we can see, remain upon it forever. § 1. MASS AND DENSITY OF THE EARTH. We begin by some definitions and some principles re- specting attraction, masses, weight, etc. The mass of a body may be defined as the quantity of matter which it contains. There are two ways to measure this quantity of mat- ter : (1) By the attraction or weight of the body — this weight being, in fact, the mutual force of attraction be- tween the body and the earth ; (2) By the inertia of the body, or the amount of force which we must apply to it in order to make it move with a definite velocity. Mathe- matically, there is no reason why these two methods should give the same result, but by experiment it is found that MASS OF THE EARTH. 189 the attraction of all bodies is proportional to their inertia. In other words, all bodies, whatever their chemical consti- tution, fall exactly the same number of feet in one second under the influence of gravity, supposing them in a vacu- um and at the same place on the earth's surface. Although the mass of a body is most conveniently determined by its weight, yet mass and weight must not be confounded. The weight of a body is the apparent force with which it is attracted toward the centre of the earth. As we shall see hereafter, this force is not the same in all parts of the earth, nor at different heights above the earth's sur- face. It is therefore a variable quantity, dej)ending rpon the position of the body, while the mass of the body is re- garded as something inherent in it, which remains constant wherever the body may be taken, even if it is carried through the celestial spaces, where its weight would be reduced to ahnost nothing. The unit of mass which we may adopt is arbitrary ; in fact, in different cases different units will be more con- venient. Generally the most convenient unit is the weight of a body at some fixed place on the earth's surface — the city of Washington, for example. Suppose we take such a portion of the earth as will weigh on« kilogram in Wash- ington, we may then consider the mass of that particular lot of earth or rock as a kilogram, no matter to what part of the universe we take it. Suppose also that we could bring all the matter composing the earth to the city of Washington, one kilogram at a time, for the purpose of weighing it, returning each kilogram to its place in the carta immediately after weighing, so that there should be no disturbance of the earth itself. The sum total of the weights thus found would be the mass of the earth, and would be a perfectly definite quantity, admitting of being expressed in kilograms or pounds. We can readily cal- culate the mass of a volume of water equal to that of the earth because we know the magnitude of the earth in litres, and the mass of one litre of water. Dividing this 190 ASTRONOMY, into the mass of the earth, supposing ourselves able to de- termine this mass, and we shall have tlie specilic gravity, or what is more properly called the density of the earth. Wliat we have supposed for the earth we may imagine for any heavenly body — namely, that it is brought to tlie city of Washington in small pieces, and there weighed one piece at a time. Thus the total mass of the earth or a ny heavenly body is a perfectly defined and determined quantity. It may be remarked in this connection that our units of weight, the pound, the kilogram, etc., are practically units of mass rather than of weight. If we should weigh out a pound of tea in the latitude of Washington, and then take it to the equator, it would really be less heavy at thq equator than in Washington ; but if we take a pound weight with us, that also would be lighter at the equator, so that the two would still balance each other, and the tea would be still considered as weighing one pound. Since things are actually weighed in this way by weights which weigh one unit at some definite place, say Washingt^ \, and which are carried all over the world without being changed, it follows that a body which has any given weight in one place will, as measured in this way, have the same apparent weight in any other place, although its real weight will vary. But if a sjjring balance or any other instrument for determiruig actual weights were adopted,, then we should find that the weight of the same body varied as we took it from one part of the earth to another. Since, however, we do not use this sort of an instrument in weighing, but pieces of metal which are carried about without change, it follows that what we call units of weight are properi^ units of mass. Density of the Earth. — We see that all bodies around us tend to fall toward the centre of the earth. According to the law of gravitation, this tendency is not simply a single force directed toward the centre of the earth, but is the resultant of an infinity of separate forces arising from MASS OF THE EARTH. 191 tlie attractions of all the separate parts wliicli compose the earth. The question may arise, how do we know that each particle of the earth attracts a stone which falls, and that the whole attraction does not reside in the centre ? The proofs of this are numerous, and consist rather in the exactitude Avitli which the theory represents a ^reat uuiss of disconnected phenomena than in any one principle ad- mitting of demonstration. Perhaps, however, the most conclusive proof is found in the ohserved fact that masses of matter at the surface of the earth do really attract each other as required by the law of Nkwton. It is found, for example, that isolated mountains attract a plumb-line in their neighborhood. The celebrated experiment of Cav- endish was devised for the purpose of measuring the at- traction of globes of lead. The object of measuring this attraction, however, was not to jirove that gravitation re- sided in the smallest masses of matter, because there was no doubt of that, but to determine the mean density of the earth, from which its total mass may be derived by simply multiplying the density by the volume. It is noteworthy that though astronomy affords us the means of determining with great precision the relative masses of the earth, the moon, and all the planets, it does not enable us to determine the absolute mass of any hea- venly body in units of the weights we use on the earth. We know, for instance, from astronomical research, that the sun has about 328,000 times the mass of the earth, and the moo/* only -^ of this mass, but to know the abso- lute mass of either of them we must know how many kilograms of matter the earth contains. To determine this, we must know the mean density of the earth, and this is something about which direct observation can give us no information, because we cannot penetrate more than an insignificant distance into the earth's interior. The only way to determine the density of the earth is to find how much matter it must contain in order to attract bodies on its surface with a force equal to their observed weight — 192 ASTRONOMY. that is, with sucli intensity that at the equator a body shall fall nearlv five metres in one second. To find this we must know the relation between the mass of a body and its attractive force. This relation can be found only by measuring the attraction of a body of known mass. An attempt to do this was made by Maskklyne, Astronomer Royal of England, toward the close of the last century, the attracting object he selected being Mount Schehallien in Scotland. The specific gravity of the rocks composing this mountain was well enough known to give at least an approximate result. The density of the earth thus found was 4' 71. That is, the earth has 4.71 times the mass of an equal volume of water. This result is, however, un- certain, owing to the necessary uncertainty respecting the density of the mountain and the rocks below it. The Cavendish experiment for determining the attrac- tion of a pair of massive balls ailords a much more perfect method of determining this important element. The most careful experiments by this method were made by Baily of England about the year 1845. The essential parts of the apparatus which he used are as follows : A long narrow table Tbearstwo massive spheres of lead W ir, one at each end. This table admits of being turned around on a pivot in a horizontal direction. Above it is suspended a balance — that is, a very light deal rod e with a weight at each end suspended horizontally by a fine silver wire or fib^e of silk FE. The weights to be attracted are attached to each end of the deal rod. The right-hand one is visible, while the other is hidden be- hind the left-lmnd weight W. In this position it will be seen that the attraction of the weights IF tends to turn the balance in a direction opposite that of the hands of a watch. The fact is, the balance begins to turn in this di- rection, and being carried by its own momentum beyond the point of equilibrium, comes to rest by a twist of the thread. It is then carried part of the way back to its original position, and thus makes several vibrations which DENSITY OF THE EARTH. 193 require several minutes. At length it comes to rest in a position somewhat different from its original one. This position and the times of vibration are all carefully noted. Then the table T is turned nearly end for end, so that one weight W shall be between the observer and the right- hand ball, while the other weight is beyond the left-hand ball, and the observation is repeated. A series of ol)serva- tions made in this way include attractions in alternate di- to Fig. 65. rections, giving a result from which accidental errors will be very nearly eliminated. A third method of determining the density of the earth is founded on observations of the change in the intensity of gravity as we descend below the surface into deep niines. The principles on which this method rests will be explained presently. The most careful application of it was made by Professor Aiby in the Harton Colliery, Eng- WHI 194 ASTRONOMY. land. The results of this and the other methods are as follows : Cavkndish and IIurroN, from the attraction of balls. 5-32 Rkicmi, " *' " ' 5-58 Baily, '' " "■ s-tm Maskelyne, from the attraction of Schehallien 4-71 AiKY, from gravity in the Ilarton Colliery 6.5») Of these different results, that of Baily is probably the best, and tlie most probable mean density of the earth is about 5^ times that of water. This is more than double the mean speciiic gravity of the materials which compose the surface of the earth ; it follows, therefore, that the in- ner portions of the earth are much more dense than its outer portions. § 2. LAWS OF TEBBESTBIAL GRAVITATION. The earth being very nearly spherical, certain theorems respecting the attraction of spheres may be applied to it. The fundamental theorems may be regarded as those which give the attraction of a spherical shell of matter. The demonstration of the'se theorems requires the use of the Integral Calculus, and will be omitted here, only the conditions and the results being stated. Let us then im- agine a hollow shell of matter, of which the internal and external surfaces are both spheres, attracting any other masses of matter, a small particle we may suppose. This particle will be attracted by every particle of the shell with a force inversely as the square of its distance from it. The total attraction of the shell will be the resultant of this infinity of separate attractive forces. Determining this resultant by the Integral Calculus, it J ? found that : Theorem I. — If the particle he outside the shell, it will he attracted as if the whole mass of the shell were con- centrated in its centre. Theorem II. — If tJie particle he inside the sJiell, the op- ATTRAUriON OF ^PIIKHES. 195 iwalte attractions in every direction vrlll neutralise each other^ no matter whereabouts in the interior the particle may be, and the resultant attraction of the shell ivill there- fore be zerc. To apply tliis to the attraction of a solid s])liorc', let us first 8U])poso a body either outside the sphere or on its sur- face. If we conceive tl;o sphere as made uj) of a great number of spherical shells, the attracted point will be ex- ternal to all of thenj. Since each shell attracts as if its whole mass were in the centre, it follows that the whole sphere at- tracts a body upon the outside of its surface as if its entire mass were concentrated at its centre. Let us now suppose the attract- ed particle inside the sphere, as at P, Fig. 6G, and imagine a splierical surface 1* Q concentric with the sphere and passing through the attracted j)article. ^®* ^®* All that jjortion of the sphere lying outside this spherical surface will be a spherical shell having the particle inside of it, and will therefore exert no attraction wliatever on the particle. That portion inside the surface will con- stitute a sphere with the jjarticle on its surface, and will therefore attract as if all this portion were concentrated in the centre. To find what this attraction will be, let us first suppose the whole sphere of equal density. Let us put a, the radius of the entire sphere. /*, the distance P C of the particle from the centre. The total volume of matter inside the sphere P Q will then be, by geometry, o ^rr*. Dividing by the square of tlie distance /•, we see that the attraction will be repre- sented by 4 3 - TTT*; 196 ASTIiONOMT. tliat 18, inside the sphere the attraction will bo directly as the distance of the particle from the centre. If the par- ticle is at the surface we have r = <<, and the attraction is 4 Outside the surface the whole volume of the sphere -^ ^ a' will attract the particle, and the attraction will be 4 a' 3 r li we put r = a\n this formula, wo shall have the same result as before for the surface attraction. Let us next suppose that the density of the sphere va- ries from its centre to its surface, but in such a way as to be equal at equal distances from the centre. We may then conceive of it as formed of an infinity of concentric Bpherical shells, each homogeneous in density, but not of the same density with the others. Theorems I. and II. will then still apply, but their result will not be the samo as in the case of a homogeneous sphere for a particle in- side the sphere. Referring to Fig. 06, let us put 7), the mean density of the shell outside the particle P- D\ the mean density of the portion P Q inside of P. We shall then have : 4 Volume of the shell, 5-'t(«' — r*). o 4 Volume of the inner sphere, -- re r*, o 4 Mass of the shell = vol. x /> = o- ;r 2> (a* — /•*). 4 Mass of the inner sphere = vol. x Z>' = „- tt i>' y*. Mass of whole sphere = sum of masses of shell and inner sphere = | tt ^i> a' + (i>' - D) /•'). ATTItAVTION OF SPIIKRES. 197 Attraction of the whole sphere upon a point at its anr .ce = *^^=l.(i,«.(Z)'-i,)il). Attraction of tlie inner spliero npoii a point at Mass 4 If, as in the case of the earth, the density contimially in- creases toward the centre, the vahie of D' will increase also as r diminishes, so that pjravity will diminish less rapidly than in the case of a honiogeneons 8})here, and may, in fact, actually increase. To show tiiis, let us sub- tract the attraction at P from that at the surface. The difference will give : Diminution at P = |- tt (/> a + (2>' - 2>) ^ - 2)' /•) . Now, let us suppose r a very little less than a, and put d will then be the depth of the particle below the surface. Cubing this value of /•, neglecting the higher powers of - ^D')d. We see that if 3Z> < 2Z)', that is, if the density at the eurface is less than | of the mean density of the whole in- ner mass, this quantity will become negative, showing that the force of gravity will be less at the surface than at a small depth in the interior. But it must ultimately diminish, because it is necessarily zero at the centre. It was on this principle that Professor Airy determined the density of the earth by comparing the vibrations 198 ASTRONOMY. of a pendulum at the bottom of tlie Harton Colliery, aiid at the surface of the earth in tlie neighborhood. At the bottom of the mine the pendulum gained about 2* -5 per day, showing the force of gravity to be greater than at tlie surface. § 3. PIGUBE AND MAGNITUDE OF THE EABTH. If the earth were fluid and did not rotate on its axis, it would assume the form of a perfect sphere. The opinion is entertained that the earth was once in a molten state, and that this is the origin of its present nearly spherical form. If we give such a sphere a rotation upon its axis, the centrifugal force at the equator acts in a direction op- posed to gravity, and thus tends to enlarge the circle of the equator. It is found by mathematical analysis that the form of such a revolving fluid sphere, supposing it to be perfectly homogeneous, will be an oblate ellipsoid — that is, all the meridians will be equal and similar ellipses, hav- ing their major axes in the equator of the sphere and their minor axes coincident with the axis of rotation. Our earth, however, is not wholly fluid, and the solidity of its conti- nents prevents its assuming the form it would take if the ocean covered its entire surface. When we speak of the lig- ure of the earth hereafter, we mean, not the outline of the solid and liquid portions respectively, but the flgure which it would assume if its entire surface were an ocean. Let us imagine canals dug down to the ocean level in every direc- tion through the continents, and the water of the ocean to be admitted into them. Then the curved surface touch- ing the water in all these canals, and coincident with tho surface of the ocean, is that of the ideal earth considered by astronomers. By the figure of the earth is meant the figure of this liquid surface, without reference to the in- equalities of the solid surface. We cannot say that this ideal earth is a perfect ellipsoid, because we know that the interior is not homogeneous, \'\ MEAiiUREMENT OF THE EARTH. 199 but all the geodetic measures heretofore made are so nearly represented by the liypothesis of an ellipsoid that the lat- ter is considered as a very close approximation to the true liirure. The deviations hitherto noticed are of so irreuru- lar a character that they have not yet been reduced to any certain law. The largest which have been observed seem to be due to the attraction of mountains, or to inequalities of density beneath the surface. Method of Triangiilatioii. — Since it is practically im- possible to measure around or through the earth, the mag- nitude as well as the form of our planet has to be found by combining measurements on its surface with astronom- ical observations. Even a measurement on the earth's surface made in the usual way of surveyors would be im- ])racticable, owing to the intervention of mountains, rivers, forests, and other natural obstacles. The method of tri- anjjulation is therefore universally adopted for measure- iiieuls extending over largo areas. A triangulation is ex- ecuted in the following way : Two points, a and b, a few Fig. 67,— a part of the fkench triangulation nbab vkbsb. miles apart, are selected as the extremities of a base-line. Tliey nmst be so chosen that their distance apart, can be accurately measured by rods ; the intervening ground should therefore be as level and free from obstruction as possible. One or more elevated points, EF, etc., must be visible from one or both ends of the base-line. By 200 ASTRONOMY. means of a theodolite and by observation of the pole-star, the directions of these points relative to the meridian are accurately observed from each end of the l)ase, as is also the direction a b of the base-line itself. Suppose F to be a point visible from each end of the base, then in tl:-^ triangle abFwQ have the length a h determined by actual measurement, and the angles at a and h determined by ob- servations. With these data the lengths of the sides a F and J 7^ are determined by a simple trigonometrical com- putation. The observer then transports liis instruments to F^ and determines in succession the direction of the elevated points or hills D E G IIJ^ etc. He next goes in succes- sion to each of these hills, and determines the direction of all the others whicli are visible from it. Thus a network of triangles is formed, of which all the angles are observed with the theodolite, while the sides are successively calcu- lated trigonometrically from the first base. For instance, we have just shown how the side aF is calculated ; this forms a base for the triangle EFa^ the two remaining sides of which are computed. The side EF forms the base of the triangle G J F^ the sides of which are calcu- lated, etc. In this operation more angles are observed then are theoretically necessary to calculate the triangles. This surplus of data serves to insure the detection of any errors in the measures, and to test their accuracy by the agreement of tlieir results. Accumulating errors are fur- ther guarded against by measuring additional sides from time to time as opportunity offers. Chains of triangles have thus been measured in Hussia from the Danube to the Arctic Ocean, in England and France from the Hebrides to Algiers, in this country down nearly our entire Atlantic coast and along the great lakes, and through shorter distances in many other countries. An east and west line is now being run by the Coast Sur- \ ey from the Atlantic to the Pacific Ocean. Indeed it may be expected that a network of triangles will be grad- MAGNITUDE OF THE EARTH. 301 ually extended over the surface of every civili'^ed country, in order to construct perfect maps of it. Suppose tliat we take two stations situated north and south of eacli other, determine the latitude of each, and measure the distance between them. It is evident that by dividing the distance in kilometres by the difference of la*^^itude in degrees, we shall have the length of one degree of latitude. Then if the earth were a sphere, we should at once have its circumference by multiplying the length of one degree by 3G0. It is thus found, in a rough way, that the length of a degree is a little more than 111 kilo- metres, or between 09 and TO English statute miles. Its circumference is therefore about 40,000 kilometres, and its diameter between 12,000 and 13,000.* Owing to the ellipticity of the earth, the lengtl of one degree varies with the latitude and the direction in which it is measured. The next step in the order of accuracy is to find the magnitude and the form of the earth from measures of long arcs of latitude (and sometimes of longi- tude) made in different regions, especially near the equa- tor and in high latitudes. But we shall still find that dif- ferent combinations of measures give slightly different re- sults, both for the magnitude and the ellipticity, owing to the irregularities in the direction of attraction which we liave already described. The problem is therefore to find what ellipsoid will satisfy the measures with the least sum total of error. New and more accurate solutions will be reached from time to time as geodetic measures are extend- ed over a wider area. The following are among the most recent results hitherto reached : Listing of Gottingen in 1878 found the earth's polar semidiameter,6355 • 270 kilO' * When the metric system was originally designed by the French, it was intended that tlie kilometre should be T^ioTj of the distance from the pole of the earth to the equator. This would make a degree of the meridian equal, on the average, to lllj kilometres. But, owing to the practical difficulties of measuring a meridian of the earth, tlie corre- Bpondence with the metre actually adopted is not exact. 203 ABTRONOMY. metres ; earth's equatorial semidiameter, 6377 • 377 kilo- metres ; earth's compression, -gj^Tg of the equatorial di- ameter ; earth's eccentricity of meridian, 0-08319. An- other result is that of Captain Clarke of England, who found : Polar semidiameter, 6356-456 * kilometres ; equa- torial semidiameter, 6378-191 kilometres. It was once supposed that the measures were slightly bet- ter represented by supposing the earth to be an ellipsoid with three .mequal axes, the equator itself being an eUipse of which the longest diameter was 500 metres, or about one third of a laile, longer than the shortest. This result was probably dut to irregularities of gravity in those parts of the continents over which the geodetic measures have extended and is now abandoned. Geographic and Geocentric Latitudes. — An obvious re- sult of the ellipticity of the earth is that the plumb-line does not point toward the earth's centre. Let Fig. 68 represent a meridional section of the earth, iT/S' being the axis of rotation, EQ the plane of the equator, and the position of the observer. The line H i?, tangent to the * Captain Clarke's results are given in feet, the polar radius being 20,854,895 feet. In changing to metres, the logarithm of the factor has been taken as 0.4840071. * i\' FORCE OF GRAVITY. 203 earth at 0, will then represent the horizon of the observer, while the line Z-N\ perpendicular to 11 JR., and therefore normal to the earth at 0, will be vertical as determined by the plumb-line. The angle N' Q, or Z O Q\ which the observer's zenith makes with the equator, will then be liis astronomical or geographical latitude. This is the lat- itude which in practice we nearly always have to use, be- cause we are obliged to determine latitude by astronomical observation, and not by measurement from the equator. We cannot determine the direction of the tnie centre C oi the earth by direct observation of any kind, but only that of the plumb-line, or of the perpendicular to a fluid sur- face. Z O Q' \& therefore the astronomical latitude. If, however, we conceive the lire C O2 drawn from the cen- tre of the earth through 0-^ 3 will be the observer's geo- centric zenith, while the angle O G Q will be his geocen- tric latitude. It will be observed that it is the geocentric and not the geographic latitude which gives the true posi- tion of the observer relative to the earth's centre. The diiference between the two latitudes is the anjjle CON* ox Z z\ this is called the angle of the vertical. It is zero at the poles and at the equator, because here the normals pass through the centre of the ellipse, and it attains its maximum of 11' 30" at latitude 45°. It will be seen that the geocentric latitude is always less than the geographic. In north latitudes the geocentric zenith is south of the ap- parent zenith and in southern latitudes north of it, being nearer the equator in each case. \', § 4. CHANGE OP GRAVITY WITH THE LATI- TUDE. If the earth were a honiugeneous sphere, and did not rotate on its axis, the intensity of gravity would be the same over its entire surface. There is a slight variation from two causes, namely, (1) The elliptic form of our globe, and (2) the centrifugal force gene- rated by its rotation on its axis. Strictly speaking, the latter ia not a change in the real force of gravity, or of the earth's attrac- tion, but only an apparent force of another kind acting in oppo- sition to gravity. 204 ASTRONOMY. Hi The intensity of gravity is measured by the velocity which a heavy body in a vacuum will acquire in a unit of time, say one second. Either 10 metres or ;i2 feet may be regarded as a rough approxima- tion to its value. There are, however, so many practical difficul- ties in the way of measuring with precision the distance a body falls in one second, that the force of giiivity is, in practice, deter- mined indirectly by finding the length of the second's pendulum. It is shown in mechanics that if a pendulum of length L vibrates in a time T, a heavy body will in this time T fall through the space n' L, it being the ratio of the circumference of a circle to its Therefore, to find the length of the diameter. (7r=3- 14159 . . . 7r'=9- 869604.) force of gravity we have only to determine the second's pendulum, and multiply it by this factor. The determination of the mean attractive force of the earth is important in order that we may compute its action on the moon and other heavenly bodies, while the variations of this attraction afford us data for judging of the variations of density in the earth's interior. Scientific expeditions have therefore taken pains to determine the length of the second's pendulum at numerous points on the globe. To do this, it is not necessary that they should actually measure the length of the pendulum at all the places they visit. They have only to carry some one pendulum of a very solid construction to each point of observation, and observe how many vibrations it makes in a day. They know that the force of gravity is proportional to the square of the number of vibrations. Before and after the voyage, they co\mt the vibrations at some standard point — London for instance. Thus, by simply squaring the number of vibrations and comparing the squares, they have the ratio which gravity at various points of the earth's surface bears to gravity at London. It is then only necessary to determine the absolute intensity of gravity at London to infer it at all the other points for which the ratio is known. From a great number of observations of this kind, it is found that the length of the second's pendulum in latitude ^ may be nearly represented by the equation, i = 0-" • 99099 (1 + • 00520 sin' ^). From this, the force of gravity is found by multiplying by jr» = 9-8696, giving the result : <7' = 9-" • 7807 (1 + . 00520 sin« ^). These formulae show that the apparent force of gravity increases by a little more than -^^ of its whole amount from the equator to the poles. We can readily calculate how much of the diminution at the equator is due to the centrifugal force of the earth's rotation. By the formulae of mechanics, the centrifugal force is given by the equation, J 7Ta~» TERRESTRIAL ORAVITT. 205 by T being the time of one revolution, and r the radius of the circle of rotation. Supposing the earth a sphere, which will cause no important error in our present calculation, the distance of a point on the earth's surface in latitude from the axis of rotation of the earth is, r = a cos <&, a being the earth's radius, therefore The centrifugal force in latitude ^ is - Alt' a cos 9 But this force does not act in the direction normal to the earth's surface, but perpendicular to the axis of the earth, which direction makes the angle <^ with the normal. We may therefore resolve the force into two components, one, / sin 0, along the earth's surface toward the equator, the other,/ cos ^, downward toward its centre. The first component makes the earth au oblate ellipsoid, as already shown, while the second acts in opposition to gravity. The cen- trifugal force, therefore, diminishes gravity by the amount, . 4 tt" « cos" /cos = ^^ 1. r, the sidereal day, is 86,164 seconds of mean time, while a, for the equator, is 6,377,377 metres. Substituting in this expression, the centrifugal force becomes /cos?> = O-"- 03391 cos" = 0"- 08891 (1 — sin".^), or at the equator a little more than g^ the force of gravity. The expression for the apparent force of gravity given by observation, which we have already found, may be put in the form, g' =9'". 7807 + 0". 05087 sin" 0. This is the true force of gravity diminished by the centrifugal force ; therefore, to find that true force we must add the centri* fugal force to it, giving the result : ^ = O™. 8146 + 0"- 01696 sin' = 9».8146 (1 + 0-001728 sin' ^), for the real attraction of the spheroidal earth upon a body on its surface in latitude 0. It will be interesting to compare this result with the attraction of a spheroid having the same ellipticity as the earth. It is found by integration that if e, supposed small, be the eccentricity of a homogeneous oblate ellipsoid, and go its attraction upon a body on its equator, its attraction at latitude f will be given by the equation, i^ = ^0 (1 + IIj- 8inV> 20G ASTRONOMY. iiiiii In the case of the earth, e — 00817 ; -^e' =0000667 ; so that the expression for gravity would be, gr = gfo (1 + 0- 000667 sin'^). We see that the factor of sin' 0, which expresses the ratio in which gravity at tlie poles exceeds that at the eqiiator, has less than half the value (-001780), which we have found from observation. This difference arises from the fact that the earth is not homogene- ous, but increases in density from the surface toward the centre. To see how this result follows, let us first inquire how the earth would attract bodies where its surface now is if its whole mass were concentrated in its centre. The distance of the equator from the centre is to that of the poles from the centre as 1 to V\ — e". Therefore, in the case supposed, attraction at the equator would be to attraction at the poles as 1 — e' to 1, The ratio of in- crease of attraction at the poles is therefore in this extreme case about ten times what it is for the homogeneous ellipsoid. We con- clude, therefore, that the more nearly the earth approaches this extreme case — that is, the more it increases in density toward the centre — the greater will be the dillerence of attraction at the poles and the equator. i giait mm; vm § 5. MOTION OP THE EARTH'S AXIS, OR PRE- CESSION OP THE EQUINOXES. Sidereal and Equinoctial Year. — In describing the ap- parent motion of the sun, two ways were shown of find- ing the time of its apparent revolution around tlie sj^here — in other words, of fixing the length of a year. One of these methods consists in finding the interval between suc- cessive passages through the equinoxes, or, whicli is the same thing, across the plane of the equator, and the other by finding wlien it returns to the same position among the stars. Two thousand years ago, Hipparchus found, by comparing his own observations with those made two centuries before by Timocharis, that these two methods of fixing the length of the year did not give the same result. It had previously been considered that the length of a year was about 365^ days, and in attempting to correct this period by comparing his observed times of the sun's passing the equinox with those of Timocharis, Hippar- chus found that it required a diminution of seven or eight LENGTH OF THE YEAR. 207 minutes. He therefore concluded that the tnie length of the equinoctial year was 365 days, 5 hours, and about 53 minutes. When, however, he considered the return, not to the equinox, bnt to the same position relative to the bright star Spica Virginis, he found that it took some minutes more than 365J days to complete the revolution. Thus there are two years to be distinguished, the ti'opical or equinoctial year and the sidereal year. The first is measured by the time of the earth's return to the equinox ; the second by its return to the same position relative to the stars. Ahhough the sidereal year is the correct astronom- ical period of one revolution of the earth around the sun, yet the equinoctial year is the one to be used in civil life, because it is upon that year that the change of seasons depends. Modem determinations show the respective lengths of the two years to be : Sidereal year, SGS'^ e^* 9" 9» = 365". 25636. Equinoctial year, 365'^ 5'' 48'" 46" = 365''. 24220. It is evident from this difference between the two years that the position of the equinox among the stars must be changing, and must move toward the west, because the equinoctial year is the shorter. This motion is called the precession of the equinoxes, and amounts to about 50" per year. The equinox being simply the point in which the equator and the ecliptic intersect, it is evident that it can change only through a change in one or both of these circles. Hipparchus found that the change was in the equator, and not in the ecliptic, because the declinations of the stars changed, while their latitudes did not.* Since * To describe the theory of the ancient astronomers with perfect correctness, we ought to say that they considered the planes both of the equator and ecliptic to be invariable and the motion of precession to be due to a slow revolution of the whole celestial sphere around the pole of the ecliptic as an axis. This would produce a change in the position of the stars relative to the equator, but not relative to the ecliptic. iJOS ASTRONOMY. the equator is defined as a circle everywhere 90° distant from tlie pole, and since it is moving among the starB, it follows that the pole must also be moving among the stfu-s. But the pole is nothing more than the point in which the earth's axis of rotation intersects the celestial sphere : it must he remembered too that the position of this pole in the celestial sphere depends solely upon the directimi of the earth's axis, and is not changed by the motion of the earth around the sun, because the sphere is considered to be of infinite radius. Hence precession shows that the direction of the earth's axis is continually changing. Careful observations from the time of IIiiM'AKtnus until now show that the change in question consists in a slow revolution of the pole o'^ the earth around the pole of the ecliptic as projected on the celestial sphere. The rate of motion is such that the revolution will be completed in between 25,000 and 20,000 years. At the end of this period the equinox and solstices will have made a com- plete revolution in the heavens. The nature of this motion will be seen more clearly by referring to Fig. 46, p. 109. We have there represented the earth in four positions during its annual revolution. We have represented the axis as inclining to the right in efvch of these positions, and have de- scribed it as remaining parallel to itself during an entire revolution. The phenomena of precession show that this is not absolutely true, but that, in reality, the direction of the axis is slowly changing. This change is such that, after the lapse of some 6400 years, the north pole of the earth, as represented in the figure, will not in- cline to the right, but toward the observer, the amount of the in- clination remaining nearly the same. The result will evidently be a shifting of the seasons. At D we shall have the winter solstice, because the north pole will be inclined toward the observer and therefore from the sun, while at A we shall have the vernal equinox instead of the winter solstice, and so on. In 6400 years more the north pole will be inclined toward the left, and the seasons will be reversed. Another interval of the same length, and the north pole will be inclined from the observer, the seasons being shifted through another quadrant. Finally, at the end of about 25,800 years, the axis will have resumed its original direction. Precession thus arises from a motion of the earth alone, and not of the heavenly bodies. Although the direction of the earth's axis changes, yet the position of this axis relative to the crust of the PRECESSION. 209 earth remains invariable. Some have supposed that precession would result in a change in the position of the north pole on the surface of tlie earth, so that the northern regions would be covered by the ocean as a result of the different direction in which the ocean would be carried bj' the centrifugal force of the earth's rota- tion. This, however, is a mistake. It has been shown by a mathe- matical investigation that the position of the poles, and therefore of the equator, on the surface of the earth, cannot change except from some variation in the arrangement of the earth's interior. Scientific investigation has yet shown nothing to indicate any prob- ability of such a change. The motion of precession is not uniform, but is subject to several inequalities which are called Nutation. These can best be under- stood in connection with the forces which produce precession. Cause of Precession, etc. — Sir Isaac Newton showed that pre- cession was due to an inequality in the attraction of the sun and moon produced by the spheroidal figure of the earth. If the earth were a perfect homogeneous sphere, the direction of its axis would Fig. 69. bever change in consequence of the attraction of another body. But the excess of matter around the equatorial regions of the earth is attracted by the sun and moon in such a way as to cause a turn- ing force which tends to change the direction of the axis of rota- tion. To show the mode of action of this force, let us consider the earth as a sphere encircled by a large ring of matter extending uround its equator, as in Fig. 69. Suppose a distant attracting body situated in the direction (7 c, so that the lines in which the parts of the ring are attracted are Aa, Bb, Cc, etc., which will be nearly parallel. The attractive force will gradually diminish from A to B, owing to the greater distance of the latter from the attracting body. Let us put : r, the distance of the centre C from the attracting body, P, the radius A G = B C of the equatorial ring, multiplied by the cosine of the angle ^ C c, so that the distance of A from the attract- ing centre is r—p, and that oi Bisr + p. m, the mass of the attracting body ; 210 ASTIiONOMT. The accelerative attraction exerted at the three points A^ C, B will then be m ;:3 > m The radius p being very small compared witli r, we may develop tiio denominators of the first and tliird fractions in powers of ^- by the binomial theorem, and neglect all powers after the first. The attractions will then be approximately : m 2m p m m 2mp imp, m The forces — -— will be very small compared with -^ on account of the smallness of p. • m The principal force — will cause all parts of the body to full equally toward the attracting centre, and will therefore cause no rotation in the body and IjO cha^i^e in the direction of the axis NS. Supposing the body to revolve around the centre in an orbit, we may conceive this attraction to be counterbalanced by the so-called centrifugal force.* Subtracting this uniform principal force, there is left a force — ^ acting on A in the direction A a, and an equal force acting on B in the opposite direction b B. It is evident that these two forces tend to make the earth rotate around an axis passing through C in such a direction as to make the line C A m coincide with C c , and that, if no cause modified the action of these forces, the earth would os- cillate back and forth on that axis. • We may here mention a very common misapprehension respecting what is sometimes called centrifugal force, and is supposed to be a force tending to make a body fly away from the centre. It is some- times said that the body will lly from the centre when the centrifugal force exceeds th(; centripetal, and toward it in the opposite case. This is a mistake, such a force ns this having no existence. The so-called centrifugal force \s not properly a centrifugal force at all, but only tb(! reaction of the whirling body against the centripetal force, which, by the third law of motion, is equal and opposite to that force. When a stone is whirled in a sling the tension on the string is simply the force neces- sary to make the stone constantly deviate from the straight line in which it tends to move, and is the same as the resistance which the stone offers to this deviation in consequence of its inertia. So, in the case of the planets, the centrifugal force is only the resistance offered by the inertia of the planet to the sun's attraction. If the sling should break, or if the sun should cease to attract the planet, the centripetal and centrifugal forces would both cease instantly, and the stone or planet would, in accordance with the first law of motion, fly forward in the straight line in which it was moving at the moment. But a mr "wn axis, (■.iiiscs II ve liicular line Nutatio iiiitioii of t time of the tlie sun, un( Itrcccssional Tills force iiiaxinnim ai |)i('f'cssion ) One of thci Iteciiuse the Again, we till' equator SiiK'f the amount of | «i|iial to one i'M'<|iiaIitics i Changes the Stars.- gular distaiK flianye in tlic •'(' tile fixed IVoiii tlie posi of tills eqiiUK the right ascc he rcprcsente ill its plane, that section (see Fig. 45, the figure), w sioii, is inovin it is evident toward the rij tliat the ainou * The reason f n ,1 and B a A'S'. Suppose, Ward impulse. fiid of twelve motion now ten ^^has tiiesame l "f the iuclinatio that the effect o hours before. every impulse m ot tlie axis iV aS, Tills same la child's top, eacli 'ty tends to mak NUTATION. 211 But (I modifying; rnusf is found in tlic rotntinn of the earth on its own axis, whicii prevents any clinnge in the anjxlc 7n (' c , hnt (•!Hises a very slow rc'vointion of tlse axis N S nronnd tl>c perpen- (licuhir line V h\ which motion is that of precession.* Nutation. — It will be seen that, under the influence of the fjniv- iliition of the sun and moon, precession cannot be uniform. At tha time of the e;}i°. Hence the ]irecession ])roduced by the sun takes ))lace bv semi-aniniul steps. OiK! of these steps, however, is a little longer tlian the other, l)eeause the earth is nearer the sun in December tiian in June. Afjain, we have seen that the inclination of tlie moon's orbit to tlie equator ran*/7«n)y the diurnal rotatitm around N8. Suppose, for example, that A receives a d<»wnvvar(land /?an up- ward impulse, so that they begin to move in tliest; directions. At the vnd of twelve hours A has moved around to /?, so that its downward motion now tends to m(n*ease the angle m C c. and the upward motion of //has the same effect. If we suppose a series of inipulses, udiminutioa of the inclination will be produced during the irst 13 hours, but after that the effect of each impulse will be counteriialanced by that of 12 hours before, so that no further diminution will take place ; but every impulse will produce a sudden permanent change in the direction of tiie axisA^iS, the end N moving toward and aS' from the observer. This same law of rotation is exemplified in the gyroscope and the child's top, each of wliich are kept erect by the rotation, though gruv ity tends to make them fall. , f*\#. . n2 A8TR0K0MT On the equator, 20" cot u ; On the ecliptic, 20" cosec u ; M being the obliquity of the ecliptic (23' 27|'). In consequence, the right ascensions of stars near the equator are constantly increas- ing by about 46" of arc, or 3».07 of time annually. Away from the equator the increase will vary in amount, because, owing to the motion of the pole of the earth, the point in which the equator is intersected by the great circle passing through the pole and the star will vary as well as the equinox, it being remembered that the right ascension of the star is the distance of this point of intersec- tion from the equinox. The adept in spherical trigonometry will find it an improving exercise to work out the formulse for the annual change in the right ascension and declination of the stars, arising from the motion of the equator, and consequently of the equinox. He will find the result to be as follows : Put n, the annual angular motion of the equator (20" • 06), w, its obliquity (23" 27' -5), a 6, the right ascension and declination of the star ; Then we shall find : Annual change in R. A. = n cot w -i- n sin it tan 6, Annual change in T>ec. = n cos a. CHAPTER IX. CELESTIAL MEASUREMENTS OF MASS AND DISTANCE. § 1. THE CELESTIAL SCALE OF MEASUBEMENT. The units of length and mass employed by astronomers are necessarily different from those used in daily life. For instance, the distances and magnitudes of the heavenly bodies are never reckoned in miles or other terrestrial jiieasures for astronomical purposes ; when so expressed it is only for the purpose of making the subject clearer to the general reader. The units of weight or mass are also, of necessitv, astronomical and not terrestrial. The mass of a body may be expressed in terms of that of the sun or of the earth, but never in kilograms or tons, unless in popular language. There are two reasons for this course. One is that in most cases celestial distances have first to be determined in terms of some celestial unit — the earth's distance from the sun, for instance — and it is more con- venient to retain this unit than to adopt a new one. The other is that the values of celesllal distances in terms of ordinary terrestrial units are for the most part extremely uncertain, while the corresponding values in astronomical units are known with great accuracy. An extreme instance of this is afforded by the dimen- sions of the solar system. By a long and continued series of astronomical observations, investigated by means of Kepler's laws and the theory of gravitation, it is possible to determine the forms of the planetary orbits, their positions, and their dimensions in terms of the ou-th's 214 ASTBONOMY. mean distance from the sun as the unit of measure, witli great precision. It will be remembered that Kepleu's third law enables us to determine the mean distance of a planet from the sun when we know its period of revolu- tion. Now, all the major planets, as far out as Saturn, have been observed through so many revolutions that their periodic times can be detennined with great exactness — in fact within a fraction of a millionth part of their whole amount. The more recently discovered planets, Uranus and Neptune, will, in the course of time, have their periods determined with equal precision. Then, if we square the periods expressed in years jMid decimals of a year, and extract the cube root of this square, we have the mean distance of the planet with the same oruer of pre- cision. This distance is to be corrected 'i\e impracticable to make simultaneous observations at distant stations, and as the planet is continually in motion, the problem is a much more complex one than that of simply solving a triangle. The actual solution is effected hy a process which is algebraic rather than geometrical, but we may briefly describe the geometrical nature of the problem. Considering the problem as a geometrical one, it is evi- dent that, owing to the parallax of Venus being nearly four times as great as that of the sun, its path across the sun's disk will be different when viewed from different points of the earth's surface. Tlie further south we go, the further north the planet will seem to be on the sun's disk. The change will be determined by the difference between the parallax of Yemis and that of the sun, and this makes the geometrical explanation less simple than in the case of a determination into which only one parallax enters. It will be sufficient if the reader sees that when we know the relation between the two parallaxes — when, for instance, we know that the parallax of Yenus is 3-T8 times that of the sun — the observed displacement of Yenus on the sun's disk will give us both parallaxes. The " relative paral- lax,"^ it is called, will be 2-78 times the sun's parallax, and it is on this alone that the displacement depends. The algebraic process, -which is that actually employed in the solution of astronomical problems of this class, is as follows : Each observer is supposed to know his longitude and lati- tude, and to have made one or more observations of the angular distance of the centre of the planet from the centre of the sun. To woik up the observations, the investigator must have an ejjhetneria of Venus and of the sun — that is, a table giving the right ascension and declinationrof each body from hour to hour as calculated from ihe best astronomical data. The ephemeris can never be considered absolutely correct, but its error may be as- sumed as constant for an entire day or more. By means of it, the right ascension and declination of the planet and of the sun, as seen from the centre of the earth, may be computed at any time. It is shown in works on spherical astronomy how, when the right 218 ASTBONOMT. ascensions, declinations, and parallaxes of Vemis and the sun are given for ;i definite moment, the distance of their centres, as seen from a given point on the surface of the earth, may be computed. Referring to such works for the complete demonstration of the re- quired formulae, we shall tiive the approximate results in such a way as to show the principle involved. Let us put: a, 6, p, the geocentric right ascension and declination of Ventis, as given in the ephemoris for the moment of observation, and its dis- tance from the earth's centre, a', <5', p', the same quantities for the sun, TT, the sun's equatorial horizontal parallax at distance unity. //, the hour angle of the sun, as seen from the place at the mo- ment of observiition. 9', the geocentric latitude of the observer. r, the e irth's radius at the point of observation ; that is, the dis- tance of the observer from the earth's centre, the equatorial radius being taken as unity. The paridli.x is so small that we may regard it as equal to its sine. If we put : TT,, the eijuatorial horizontal parallax of Venus at its actual dis- tance, /' ; jr'i, the same for the sun. Then, because the parallaxes are inversely as the distances of the bodies : ^ - '^ ' ■^ (1) Ti = — ; jr'i = _ . w P P If wo put : JD, the angular distance of the centres of Venus and the sun, as seen from tht^ earth's centre, D will be the hypothenuse of a nearly right-angled spherical triangje, of which the north and south side will be the difference of declination ; and the east and west side the difference of right ascension, multiplied by the cosine of the decli- nation. We sliall, therefore, have approximately : i)« = (d — J')2 + (a — a'f cos.« 6'. (2) This value of D being very near the truth, it is supposed that the effect of small corrections to a, a\ d and (5' may be treated as differ- entials, and obtained by differentiation. Differentiating the abovo expression, and dividing by 2, we have : BdD = (fJ-tJ) {d6 — dfi') -f (a - a') cos.« d' {da — da') or. rf-fJ' a dD = [dS — d6')-t — D •COS.' i' {da — da'). (3^ Because the observer is at the earth's surface the apparent direc- tion of the two bodies, and hence the values of a, a , 6 and d', will be changed by parallax. If we suppose the differentials, da, d6, etc., to repi esent the changes due to parallax, it is shown in spherical as tronomy that they may be computed by the formuloe : TliANSITS OF VENUS. 319 da = r COS. <&' sec. J sin. // X ""i, da = r COS. are also known, if we substitu'e the values of tti, and tt'i, from the equations (1), tt, the mean paralliu of the sun itself, will be the only unknown quantity left. So if we put, for brevity, a = a = r COS. ¥ sec. (5 sin. H P r cos. 9 sec. J' sin. H b = r cos. ' sin. J cos, // — r sin. ' sin. <5' cos. // — r sin. ^' cos. 6' P (5) we have, for the effect of parallax, da = a-T ; da' = air ; dS = bir ; d6' = b'jT. (6) If there were no parallax, and if the values of the right ascension and declination given in the ephemeris were perfectly correct, the values o( D computed from (2) would be those given by a correct measurement from any point of the earth's surface. Suppose that the observer on measuring the value of D, finds it different from that calculated. Assuming his measure to be correct, he must as- sume the difference to be duo to two causes : Firstly, parallax ; Secondly, errors in the values of a and (J given in the ephemeris. For the effect of parallax we substitute in (3) the values of da, etc., in (6). We thus have: { d-6' a~a' cos.' rf' (a — a) r ir. (7) In this equation all the quantities in the second member ex- cept TT are supposed to be known, and we may represent the co- efficient of TT by the single symbol c, putting: dD = C1T (8) To consider the effect of the second cause we must suppose rfrf, rf(5'. da and da' in (3) to be replaced by f5f5 <5rf', <5a and Aa\ which we put for the unknown corrections to the positions in the ephemeris. If we put, for brevity, 380 ASTRONOMY. y = (5(5 — 66' ; 6 - (!' = w ; a? = (5a — 6a' a — a D D — COS.* 6' = n we shall have dD — my + nx. (9) The true value of D is given by adding the two values of dD in (8) and (9) to the value of D computed from (2). Hence, this true value of i> is D + my + fix -h en, (10) in which 2), «i, n and c are all calculated numbers, and a-, y and n are unknown. Now, suppose that, at this same moment, the observer has meas- sured the distance of the centres of the two l)odies and found it to be D'. This being supposed true, must be equal to (10), that is, we must have X) 4- my + ?ix + CTT = D' ; or, by transposing, viy + nx + en = D' — D. Thus, for every observation of distance, we have an equation of condition between the three unknown quantities y, x and tt. The solution of these equations gives the value of a;, y and tt, the un- known quantities required. Measurements of the Parallax of Mars. — This parallax may be determined from observations in two ways. In that usually adopted tliere are two observers or sets of observers, one in the northern and the other in the southern hemisphere, each of whom determines the declination of the planet from day to day at the moment of transit over his meridian. These declinations will be different by the whole amount of parallactic difference between tlie two stations, or by the angle *S' PS" in Fig. 18, p. 49. Tlie observa- tions are continued through the period when Mars is nearest the earth, generally about a couple of months. Any opposition of the planet may be chosen for this purpose, but the most favorable ones are tho«e when the planet is nearest its perihelion. Should the planet be exactly at its perihelion at the time of opposition, its distance from the earth would be only about 0-37, while at aphelion it would be 0-68. This great difference is owing to the considerable eccen- tricity of the orbit of Mars, as can be seen by studying Fig. 48, p. 115, which gives a plan of most of the orbits of the larger planets. The favorable oppositions occur at intervals of 15 or 17 years. One was that of 1862, which gave almost the first conclusive evidence that the old parallax of the sun found by Encke was too small. This parallax was 8""577, and the corresponding distance of the sun was 95 J millions of miles. The observations of 1862 seemed to show that this parallax must be increased by about one thirtieth part, and the distance diminished in about the same ratio. But the most recent results make it probable that the change should not be quite so great as this. \ PARALLAX OF MARS. 99 21 \ Parallax of Mars in Bight Ascension.— Another mothod of measuring the parallax of Mnrn is founded on principles entirely different from those we have hitherto eonside ed. In the latter, observations have to be made by two observers in opposite hemi- spheres of the earth. But an observer at any point on the earth's surface is carried around on a circle of latitude every day by the diurnal motion of tlve earth. In consequence of this motion, there must be a corresponding apparent motion of each of the planets in an opposite direction. In other words, the parallax of the planet must be different at different times of the day. This diurnal change in the direction of the planet admits of being measured in the following way : The effect of parallax is always to make a heavenly body appear nearer the fiorkoii than it would appear as seen from the centre of the earth. This will be obvious if we reflect that an observer moving rapidly from the centre of the earth to its circumference, and keeping his eye fixed upon a planet, would see the planet appear to move in an opposite direction — that is, down- ward relative to the point of the earth's surface which he aimed at. Hence a planet rising in the east will rise later in consequence of parallax, and will set earlier. Of course the rising and setting cannot be observed with sufficient accuracy for the ))urpose of parallax, but, since a fixed star has no parallax, the jtosition of the planet relative to the stars in its neighborhood will change during the interval between the rising and setting of the planet. The observer therefore determines the positpn of Mars relat.ve to the stars surrounding him shortly after he rises and a'^ain shortly before he sets. The observations are repeated right after night as often as possible. Between each pair of eas'. and west observations the planet will of course change its position among the stars in consequence of the orbital motions of the earth and planet, but these motions can be calculated and allowed for, and the changes still outstanding will then be due to parallax. The most favorable regions for an observer to determine the par- allax in this way are those near the earth's equator, because he is there carried around on the largest circle. If he is nearer the ijoles than the equator, the circle will be so small that the parallax will l)e hardly worth determining, while at the poles there will be no par- iillactic change at all of the kind just described. Applications of this method have not been very numerous, although it was suggested by Flamsteed nearly two centuries ago. The latest and most successful trial of it was made by Mr. D avid G n,L of England during the opposition of Ma7's in 1877 above described. The point of observation chosen by him was the isUnd of Ascen- sion, west of Africa and near the equator. His meas-ires indicate a considerable reduction in the recently received values of the solar parallax, and an increase in the distance of the sun,, making the latter come somewhat nearer to the old value. Acouraoy of the Determinations of Solar Parallax. The parallax of Mars at opposition is rarely more than 2^2 ASTRONOMY. 20", and the relative parallax of Venus and the sun at the time of the transit is less than 24". These quantities are so small as to almost ehide very precise measurement ; it is hardly possihle hy any one set of measures of i)arallax to determine the latter without an uncertainty of ^f^j of its M'hole amomit. In the distance of the sun this corre- sponds to an uncertainty of nearly half a million of miles. Astronomers have therefore sought for other methods of determining the sun's dist.ance. Although some of these may be a little more certain than measures of parallax, there is none by which the distance of the sun can be determined with any approximation to the accuracy which character- izes other celestial measures. Other Methods of Determining Solar Parallax. — A very interesting and probably the most accurate method of measuring the sun's distance is by using light as a mes- senger between the sun and the earth. We shall hereafter sec, in the chapter on aberration, that the time required for light to pass fronj the sun to the earth is known with con- siderable exactness, being very ne. .ly 408 seconds. If then we can determine experimentally how many miles or kilometres light moves in a second, we shall at once have the distance of the sun by multiplying that quantity by 408. But the velocity of light is about 300,000 kilometres per second. This distance would reach about eight times around the earth. It is rarely possible that two points on the earth's surface more than a hundred kilometres apart are visible from each other, and distinct vision at distances of more than twenty kilometres is rare. Hence to deter- mine experimentally the time required for light to pass between two terrestrial stations requires the measurement of an interval of time, which even under the most favorable cases can be only a fraction of a thousandth of a second. Methods of doing it, however, have been devised and ex- ecuted by the French physicists, Fizeau, Foucault, and CoRNU, and quite recently by Ensign Michelson at the U. S. Naval Academy, Annapolis. From the experiments SOL All PAHA LL AX. 223 If of the latter, which arc probably the most accurate, the velocity of light would seeiu to be about 21>i^*.>00 kiloiue- tres per second. Multiplying this by 45>8, we obtain l-iU,- 3r)0,(K)0 kilometres for the distance of tiie sun. The time required for light to pass from the sun to the earth is still uncertain by nearly a second, ])ut this value t>f the sini's distance is jjrobably the best yet obtained. The corre- sponding vahie of the sun's i)arallax is 8"vSl. Vet other methods of tleteniiining the sun's distance are given by the theory of gravitation. The best known of these depends upon the determination of the parallactic inequality of the moon. It is found by matliematical in- vestigation that the motion of the moon is sul)jccted to several inequalities, having the sun's horizontal i)arallax as a factor. In consequence of the largest of these in- equalities, the moon is about two minutes behind its mean place near the first quarter, and as far in advance at the last quarter. If the position of the moon could be deter- mined by observation with the same exactness that the po- sition of a star or planet can, this would probably alTord tlie most accurate method of determining the solar par- allax. But an observation of the moon has to be made, not upon its centre, but upon its lind) or circumference. Only the lind) nearest the sun is visible, the other one being unilluminated, and thus the illuminated limb on M'liich the observation is to be made is different at the first and third quarter. These conditions induce an uncertain- ty in" the comparison of observations made at the two quarters which cannot be entirely overcome, and therefore leave a doubt respecting the correctness of the result. Brief History of Determinations of the Solar Parallax. — The distance of the sun must at all t' \es have been one of the most interesting scientific problems presented to the human mind. The first known attempt to effect a solu- tion of the problem was made by Aristarchus, who flour- ished in the third century before Christ. It was founded on the principle that the time of the moon's first quarter 324 ASTRONOMY. will vary with the ratio between the distance of the mooji and sun, wliich may be shown as follows. In Fig. 7o let y^' represent the earth, M the moon, and A' the sun. Since the sun always illuminates one half of the lunar globe, it is evident that when one half of the moon's disk .ippears illuminated, the triangle E M S must be right- ngled at JJ/". The angle J/ iiW can be determined by measurement, being equal to the angular distance between the sun and the moon. Having two of the angles, the third can be determined, because the sum of the three must make two right angles. Thence we shall have tin- ratio between E M^ the distance of the moon, and ii\S', the distance of tho sun, by a trigonometricul computation. •Pig. 70. Then knowing the distance of the moon, which can be determined with comparative ease, we have the distance of thj sun by multiplying by this ratio. Aristarciius con- cluded, from his supposed measures, that the angle M ES was three degrees less than a right angle. We should then have ^r^7 = sin 3° = y^^ very nearly. It would follow from this that the snn was 19 times the distance of the moon. We now know that this result is entirely wrong, and that it is impossible to determine the time when the moon is exactly half illuminated with any ap- proach to the accuracy necessary in the solution of the problem. In fact, the greatest angular distance of the SOLAIi PA HALL AX. 225 earth and moon, Jis scon from the sun — tliat if», tlio anglo JCSM — is only about ono (juaiter the anji^uhir diameter of the moou m seen from the earth. Tlie second attempt to determine the (hstance of tlio mn is mentioned hy Ptolkmv, thou tronomical purposes, where only till' relative masses of the several ^jlanets are required. In estimat- injf the masses of the individual planets, that of the sun is generally t'lkcn as a unit. The planetary masses will then all be very small fractions. Masses of the Earth and Sun — We shall first consider the niuss of the earth because it is connected by a very curious relation \vitli the parallax of the sun. Knowing the latter, we can determine 1/ fii i 228 ASTRONOMY. the mass oi the sun relative to the earth, which is the same thing as determining the astronomical mass of the earth, that of the sun being unity. This may be clearly seen by reflecting that when we know the radius of the earth's 'jrbit we can determine how far the earth moves aside from a strai »ht line in one second in consequence of the attraction of the sun. This motion measures the attractive force of the sun at the distance of the earth. Comparing it with the attractive force of the earth, and making allowance for the difference of distances from centres of the two bodies, we deter- mine the ratio between their masses. The calculation in question is made in the most simple and ele- mentary manner as follows. Let us put : TT, the ratio of the circumference of a circle to its diameter (rr = 3-14159...) r, the mean radius of the earth, or the radius of a sphere having the same volume as the earth. a, the mean distance of the earth from the sun. g, the force of gravity on the earth's surface at a point where the radius is r — that is, the distance which a body will fall in one second. g', the sun's attractive force at the distance a. T, the number of seconds in a sidereal year. M, the mass of the sun. m, the mass of the earth. P, the sun's mean horizontal parallax. The force of gravity of the sun, g', may be considered as equal to the so-called centrifugal force of the earth, or to the distance which the earth falls toward the sun in one second. By the formula for centrifugal force given in Chapter VIII., p. 204, wo have. g' 4 TT* a and by the law of gravitation. whence and M _ 4 tt' a a* ~ T* M = in* a* We have, in the same way, for the earth, whence m m = gr\ !f,)l MASS OF THE SUN. 229 ele- Tberefore, for the ratio of the masses of the earth and sun, we have t 4 1 («). M m 4 tt" a' 4 jt' r a* By the formulae for parallax in Chapter I., § C, we have: 1 a' Therefore ' r' sin»P M 4 7r« r 1 m T' sin'-P (J). The quantities T, rand g may be regarded as all known with great exactness. We see that the mass of the earth, that of the sun being unity, is proportional to the cube of the solar parallax. From data already given, we have ; T= 365 days, 6 hours, 9"' 9»; in seconds, T=U 558 149, Mean radius of the earth in metres,* . . r = 6 '570 008, Force of gravity in n. -^tres, . . . . g= 9*8202, while log t' = 1 -SOeS* . C ibstituting these numbers in the formulie, it may be put in the form, ?- = [7-58984] sin* P,t M where the quantity in brackets is the logarithm of the factor. It will be convenient to make two chiuiges in the parallax P. This angle is so exceedingly small that wc may regard it as equal to its sine. To express it in seconds ve must multiply it by the number of seconds in the unit radius— it is, by SOOStiS". This will make ./'(in seconds) =206265 "sin P. ;,^aiti. the standard to which |>ar- allaxes are referred is always the earth's equatorial radius, whi-li is greater than r by about jj^j^j of its whole luuount. So, if we put P* for the equatorial horizontal parallax, expressed in seconds, we shall have, P" = (1 + ^g) 306265' sin P= [5-31492] siu P, whence, for sin P in terms of P\ r>» sin P = _ [5.31492J * The mean radius of the earth is not the mean of tli polar and equatorial radii, but one third the sum of tlie polar radius and twice the equatorial one, because we can draw three such radii, each mak« iug a right angle with the other two. f A number enclosed in brackets is frequently used to signify the logarithm of a coefficient or divisor to be used. ■ n i;if^^ 230 ASTRONOMY. If we substitute this value in the expression for the quotient of the masses, it may be put into either of the forms : M _ [8-35493) P" = [2-78498] C~)l The first formula gives the ratio of the masses when the solar par- allax is known ; the second, the parallax when the ratio of the masses is known. The following table shows, for different values of the solar parallax, the corresponding ratio of the masses, and distance of the sun in terrestrial measures : in Distance of the Sun. Solar Pauallax. In equatoria! radii of the earth. In millions of miles. In millions of kilomttres. 8'. 75 8'. 76 6' -77 8" -78 8" -79 8' -80 8' -81 8" -82 8" -83 8' -84 8' -85 337992 33(;!-.35 335684 334538 3^3398 332262 331133 330007 328887 327773 326664 23573 23546 23519 23492 23466 23439 23413 23386 23360 23333 ■ 23307 93-421 93-314 93-208 93-102 92-996 92-890 92-785 92-680 92-575 92-470 92-366 150-343 150-172 150-001 149-830 149-660 149-490 149-330 149-151 148-982 148-814 148-646 We have said that the solar parallax is probably contained between the limits 8". 79 and 8. 83. It is certainly hardly more than one or two hundredths of a second without them. So, if we wish to expres.s the constants relating to the sun in round numbers, we may say that— Its muss is 330,000 times that of the earth. Its (Jitttttnce in miles is 93 millions, or perhaps a little le . Its distance in kilometres is probably between 149 and 150 mil- lions. Density of the Sun. — A remarkable result of the precedini; investigation is that the density of the sun, relative to that of the earth, can be determined independently of the mass or distance of the sun by measuring its apparent angular diameter, and the force of gravity at the earth's surface. Let us put />, the density of the sun. d, that of the earth. «, the sun's angular semi-di»meter, as seen from the earth. Then, continuing the notation ah' idy given, we shall have: II ' . •..■■M\ MASS OF THE SUK 231 Linear radius of the sun = a sin s. Volume of the sun = — a'sin'« 3 (from the formula for the volume of a sphere). 4ir Mass of the sun, M ~ -^ a' J) sin* a. 47r Mass of the earth, wi = -— r*d. Substituting these values of M and m in the equation (a), and dividing out the common factors, it will become I) 4:Tr^r from which we find, for the ratio of the density of the earth to that of the sun, d gT' . . D 4 JT^r sm° «. This equation solves the problem. But the solution may be trans- formed in expression. We know from the law of failing bodies that a heavy body will, in the time t, fall through the distance ^ g t^. Hence the factor g 2" is double the distance which a body would fall in a sidereal year, if the force of gravity could act upon it continu- ously with the same intensity as at the surface of the earth. Hence gT' n , will be the number of radii of the earth through which the body will fall in a sidereal year. If we put F for this number, the preceding equation will become, rf Fs\n*8 We therefore 'nave this rule for finding the density of the earth relative to that of the sun : Find how mani/ radii of the earth a heavy body would fall through in a sidereal yjar in virtue of the force of gravity at the earth* a sur- face. Multiply thia number by the cube of the sine of the sun''s angular Herni-diameter, as seen from the earth, and divide by the numerical factor 2 jt' = 19-7392. The quotient will he the ratio of the density of the earth to that of the sun. From the numerical data already given, we find : Density of earth, that of sun being unity. ^ = 8-9208. 4 ■■ ~ If ■'■• ■ui lU 111 233 ASTRONOMY. Density of the sun, that of the earth being unity, d = 0-25506. These relations do not give us the actual density of either body. We have said that the mean density of the cartii is about 5f, that of water being unity. The sun is therefore about 40 or 50 per cent denser than water. Masses of the Planets.— If we knew how far a body would fall in one second at the surface of any other planet than the earth, we could determine its mass in much the same way as we have de- termined that of the earth. Now if the planet has a satellite re- volving around it, we can make this determination — not indeed directly on the surface of the planet, but at the distance of the sat- ellite, which will equally give us the required datum. Indeed by observing the periodic time of a satellite, and the angle subtended by the major axis of its orbit around the planet, we have a more direct datum for determining the mass of the planet than we actually have for determining that of the earth. (Of course we here refer to the masses of the planets relative to that of the sun as unity.) In fact could an astronomer only station himself on the planet Venus and make a series of observations of the angular distance of the moon from the earth, he could determine the mass of the earth, and thence the solar parallax, with far greater precision than we are like- ly to know it for centuries to come. Let us again consider the equation for M found on page 228 : M = 4 7r'o« Here a and T may mean the mean distance and periodic time of any planet, the quotient -^.^ being a constant by Kepler's third law. In the same equation we may suppose a the mean distance of a satellite from its primary, and T its time of revolution, and if will then represent the mass of the planet. We shall have therefore for the mass of the planet, m = 47r«a'» 7" a a' being the mean distance of the satellite from the planet, and T^ its time of revolution. Therefore, for the mass of the planet rel ative to that of the sun we have : m M a' a*r «» Let us suppose a to be the mean distance of the planet from the sun, in which case T must represent its time of revolution. Then, if we put « for the angle subtended by the radius of the orbit of the MASSES OF THE PLANETS. 233 satellite, as seen from the sun, we shall have, assuming the orbit to be seen edgewise. sm8 = a' a If the orbit is seen in a direction perpendicular to its plane, we should have to put tang s for sin s in this formula, but the angle » is so small that the sine and tangent are almost the same. If we put T for the ratio of the time of revolution of the planet to that o' the satellite, it will be equivalent to supposing The equation for the mass of the planet will then become -jj: = t' sin' «, which is the simplest form of the usual formula for deducing the mass of a planet from the motion of its satellite. It is true that we cannot observe « directly, since we cannot place ourselves on the sun, but if we observe the angle » from the earth we can always reduce it to the sun, because we know the proportion between the distances of the planet from the earth and from the sun. All the large planets outside the earth have satellites ; we can therefore determine their masses in this simple way. The earth having also a satellite, its mass could be determined in the same way but for the circumstance already mentioned that we cannot determine the distance of the moon in planetary units, as we can the distance of the satellites of tlie other planets from their pri- maries. The planets Mercury and Venus have no satellites. It is therefore necessary to determine their masses by their influence in altering the ellipdc motions of the other planets round the sun. The altera- tions thus produced are for the most part so small that their deter- mination is a practical problem of some difficulty. Thus the action of Mercury on the neighboring planet Venus rarely changes the po- sition of the latter by more than one or two seconds of arc, unless we compare observations more than a century apart. But regular and accurate observations of Vemm were rarely made until after the beginning of this century. The mass of Venus is best determined by the influence of the planet in changing the position of the plane of the earth's orbit. Altogether, the determination of the masses of Mercury and Venus presents one of the most complicated prob- 1 jms with which the mathematical astronomer has to deal. 11 I 1^141 CHAPTER X. THE REFRACTION AND ABERRATION OF LIGHT. § 1. ATMOSPHERIC REFRACTION. WiiKN we refer to the place of a planet or star, we usually mean its true place — i.e.^ its direction from an observer situated at the centre of the earth, consid- ered as a geometrical point. We have shown in the sec- tion on parallax how observations which are necessarily taken at the surface of the earth are reduced to what they would have been if the observer were situated at the earth's centre. In this, however, we liave supposed the star to appear to be projected on the celestial sphere in the prolongation of the line joining the observer and the star. The ray from the star is considered as if it suffered no deflection in passing through the stellar spaces and tlirough the earth's atmosphere. But from the principles of physics, we know that such a luminous ray passing from an empty space (as the stellar spaces are), and through an atmosphere, must suffer a refraction, as every ray of light is known to do in passing from a rare into a denser medium. As we see the star in the direction which its light beam has when it enters the eye — that is, as we pro- ject the star on the celestial sphere by prolonging this light beam backward into space — there must be an appar- ent displacement of the star from refraction, and it is this which we are to consider. "We may recall a few definitions from physics. Tlie ray which leaves the star and impinges on the outer sur- REFRACTION. 235 e 111 the 2red I'oin li an \m pr( face of the earth's atmosphere is called the incident ray ; after its defle(^tion by the atiiiospliere it is called the re- fracted ray. Tiie difference between these directions is called the afitronnmical refraction. If a normal is drawn (perpendicular) to the surface of the refractiuii^ niediuni at tlie point where the incident ray meets it, the acute an«;le between the incident ray and the normal is called the angle of incidence, and the acute anj^le between the nor- mal and the refracted ray is called the angle of refraction. The refraction itself is the difference of these angles. The normal and both incident and refracted rays are in the same vertical plane. In Fig. 71 S A is the ray incident upon the surface B A oi the re- fracting medium B' B A N^ A C \% the refracted ray, M N tlie normal, SAM and CAN tlie angles of incidence and re- fraction respectively. Produce C A backward in the direction A S' : -6" JV S' is the refraction. An observer at C will see the star S as if it were at S'. A S' is the apparent direction of the ray from the star ^S", and xV is the aj)j)arent place of the star as affected by refrac- tion. This supposes tlie space above B B' in the figure to be entirely empty space, and the earth's atmosphere, equally dense throughout, to fill the space below B B'. In fact, how- ever, the earth's atmosphere is most dense at the surface of the earth, and gradually diminishes in density to its exterior boundary. Therefore, if we wish to represent the facts as they are, we must suppose the atmosphere to be dividtid into a great number of parallel layers of air, and by as- suming an infinite number of these we may al^o assume that throughout each of them the air is equally dense. Hence the preceding figure will only represent the refraction at FIG. 71. — HEFRACTION. 230 ASTRONOMY. ^, ft a single one of these layers. It follows from this that the patli of a ray of light through the atmosphere is not a straight line like A C\ but a curve. We may suppose this curve to be represented in Fig. 72, where the num- ber of layers has been taken very small to avoid confusing the drawing. Let C be the centre and A a point of the surface of the earth ; let S be a star, and Sen. ray from the star which is refracted at the various layei^s into which we sup- pose the atmosphere to be divided, and which tinally no. 72.— REFRACTION OF LAYERS OF AIR. enters the f;ye of an observer at J. in the apparent direc* tion A S'. He M'ill then see the star in the direction aS" instead of that of S, and S A S\ the i-efraction, will throw the star nearer to the zenith Z. The angle S' A Z\s, the apparent zenith distance of S ; the true zenith distance of S \% ZA S, and this may he assumed to coincide with Se., as for all heavenly bodies except the moon it practically does. The line Se pro- longed will meet the line A Z\n o. point above -4, sup- pose at h'. m REFRACTION. 237 Law of Refraction. — A consideration of the pliysicnl condi- tions involved liiis led to the following form for thu refraction ia zenith distance (A i), (A0 = ^'ltan(;'-8(AC)), in which C is the apparent zenith distance of the star, and A is a constant to be determined by observation. A is found to be about 57", 80 that we may write (A (,') = 57" tan ^' approximately. Tins expression gives what is called the mean refraction — that is, the refraction corresponding to a mean stale of the barometer and thermometer. It is clear that changes in the temperature and pres- sure will affect the density of the air, and hence its refractive power. The tables of the mean refraction nuide by liKssKii, based on a more accurate formula than the one above, are now usually used, and these are accompanied by auxiliary tables giving the small corrections for the stat(; of the meteorological instruments. Let us consider some of the consequences of refraction, and for our purpose we may take the formula (AQ=:57' tan C, as it very nearly represents the facts. At C' = (A f) = 0, or at the apparent zenith there is no refraction. This we should have antici- pated as the incident ray is itself normal to the refracting surface. The following extract from a refraction table gives the amount of refraction at various zenith distances : f (AC) C (AC) 0° 0' 0' 70° 2' 39' 10° 0' 10' 80° 5' 20' 20° 0' 33' 85° 10' 0' 45° C 58' 88° 18' 0' 50° 1' 09' 89° 21' 25' 60° 1' 40' 90° 34' 30* Quantity and Efibcts of Refraction. — At 45° the refrac- tion is about 1', and at 90° it is 84' 30"— that is, bodies at the zenith distances of 45° and 90° appear elevated above tlieir true places by 1' and 34|^' respectively. If the sun has just risen — that is, if its lower limb is just in apparent contact with the horizon, it is, in fact, entirely below the true horizon, for the refraction (35') has elevated its cen- tre by more than its whole apparent diameter (32'). The moon is full when it is exactly opposite the sun, and therefore were there no atmosphere, moon-rise of a full moon and sunset would be simultaneous. In fact, 238 AlSTIiONOMT. both l)0(Hc8 bcinn^ inlevated by rGfmptio.i, wo rco the full iMooii risi'M before the tjiiii lius Het. On April liutli, 1837, the full moon roHO eclipHed boforc the sun had set. Wo 800 from tho table that tho refraction varies com- paratively little between 0° and <')0° of ze»iith distance, but that beyond 80° or 85" its variation is seconds. The cir- cnniference of the orbit being found by multiplying its diameter by 3-1416, we thus lind that, on the supposition we have made, light would move around the circumfer- ence of the earth's orbit in 52 minutes and 8 seconds-. But the earth makes this same circuit in SHS^ days, and the ratio of these two quantities is 10090. The maxinuim displacement of the star by aberration will therefore be the angle of which the tangent is j^ji^^, and this angle we find by trigonometrical calculation to bo 20". 44. This calculation presupposes that we know how long light requires to como from the sun. This is not known with great accuracy owing to the unavoidable errors with which the observations of Jupiter^s satellites are affected. It is therefore more usual to revei-se the process and de- termine the displacement of the stars by direct observa- tion, and then, by a calculation the reverse of that we have just made, to determine the time required by light to reach us Irom the sun. Many painstaking determiua- 244 ASTRONOMY. tions of tills qua itity liavc been made since the time of Bradley, ana as the result of them we may say that the value of the " constant of aJferraiion,^'' as it is called, is certainly between 20". 4 and 20". 5 ; the chances are that it does not deviate from 20". 44: by more than two or three hundredths of a second. It will be noticed that by dctenniuinij^ the constant of aberration, or by observing the eclipses of the satellites of Jujtitci', Me may infer the time reijuired for light to pass from the sun to the earth. But v/e cannot thus determine the velocitv of liijht anless we know how far the sun is. The connection between this velocity and the distance of the sun is such that knowing one we can infer the other. Let us assume, for instance, that the time required for light to reach us from the sun is 408 seconds, a time which is probably accurate within a single second. Then know- ing the distance of the sun, we may obtain the velocity of light by dividing it by 498. But, on the other hand, if we can determine how many miles light moves in a second, we can thence infer the distance of the sun by nmltiplying it by the same factor. During the last century the distance of the sun was found to be certainly between 00 and 100 millions of miles. It \va8 therefore correctly concluded that the velocity of light was something less than 200,000 miles per second, and probably between 180,000 and 200,000. This velocity h.is since b( m determined more exactly by the direct measurements at the surface of the earth already mentioned CHAPTER XI. CHRONOLOGY. 3 1. ASTRONOMICAI, MEASURES OP TIME. Thk most intimate relation of astronomy to the daily life of mankind has always arisen from its affordin<; tlie only reliable and aeeurate measure of lonj; intervals of tinie. The fundamental units of time in all ages have heen the day, the month, and the year, the lii^st being measured by the revolution of the earth on its axis, the second, prim- itively, by that of the moon around tlie earth, and the third by that of the earth round the sim. Had the natural month consisted of an exact entire mimber of days, and the year of an exact entire number of months, there would have been no history of the calendar to write. There being no such exact relations, iimumerable devices have been tried for smoothing off the difficulties thus arising, tlie mere description of which would fill a volume. AVe shall en- deavor to give the reader an idea of the general character of these devices, including those from which our own cal- endar originated, without wearying him by tlie introduc- tion of tedious details. Of the three units of time just mentioned, the most nat- lu'al and striking is the shortest — namely, the day. Mark- ing as it does the regular alternations of wakefulness and rest for both man and animals, no {istronomical observa- tions were necessary to its recognition. It is so nearly uniform in length that the most reiined astronomical obser- vationa of modern times have never certainly indicated 246 ASTRONOMY. any change. Tliis uniformity, and its entire freedom from all ambiguity of meaning, have always made the day a common fundamental unit of astronomers. Except for the inconvenience of keeping count of the great immbur of days between remote epodis, no greati^r unit would ever have been necessary, and we might all date our let- ters by the number of days after Cniiisr, or after a suj)- posed epoch of creation. The ditticulty of remembering great numbers is sueli that a longer unit is absolutely necessary, even in keoi)ing the reckoning of time for a single generation. Such a unit is the year. The regular changes of seasons in all e.\- tra-trojiical latitudes renders this unit second only to the day in tlie prominence with which it must have struck the minds of primitive man. These changes are, however, so slow and ill-nuirked in their progress, that it would have been scarcely possible to make an accurate determination of the length of the year from the observation of the sea- sons. Here astronomical observations came to the aid of our progenitors, and, before the beginning of extant his- tory, it M'as known that the alternation of seasons was due to the varying declination of the sun, as the latter seemed to perform its annual- course among the stars in the " oblique circle" or ecliptic. The common people, who did not understand the theory of the sun's motion, knew that certain seasons were marked by the position of certain bright stars relatively to the sun — that is, by those stars rising or setting in the morning or evening twilight. Thus arose two methods of measuring the length of the year — the one by the time when the sun crossed the equi- noxes or solstices, the other Avhen it seemc d to pass a cer- tain point among the stars. As we have already explain- ed, these years were slightly different, owing to the pre- cession of the equinoxes, the first or equinoctial year being a little less and the second or sidereal year a little greater than 365|^ days. The number of days in a year is too great to admit of CURONOLOQY. Ul their being easily remembered witlioiit any break ; an in- termediate period is therefore necessary. Such a period is mejisnred by the revolution of the moon around the earth, or, more exactly, by the recurrence of new moon, which takes ])la! ^', on the average, at the end of nearly 29^ days. The nearest round number to this is 30 days, and 12 periods of JJO days each oidy lack 5^ days of being a year. It has therefore been common to consider a vear as made up of 12 months, the lack of exact correspondence being filled by various alterations of the length of the month or of the year, or by adding surplus days to each vear. The true lengths of the day, the month, and the year having no common divisor, a difficulty arises in attempting to make months or days into yeare, or days into months, owing to the fractions which will always be left over. At the same time, some rule bearing on the subject is necessary in order that people may be able to remember the year, month, and day. Such rules are found by choosing some ■i'yde or period which is very nearly an exact number of two units, of months and of days for example, and by di- viding this cycle up as evenly as possible. The principle on which this is done can be seen at once by an example, for which we shall choose the lunar month. The true length of this month is 29-53()5'-' days. AVe see that two of these months is only a littL over 50 days ; so, if Ave take a cycle of 50 days, and idays, it wats common in the use of the pure lunar month to have months of 2!> and ;i< > days alternately. This supposed period, however, as just shown, will fall sliort by a day in about 2^ years. This de- tect was remedied by introducing cycles containing rather more months of 30 than of 29 days, the small excess of long months being spread uniformly through the cycle. Thus the Cxreeks had a cycle of 285 months (to be soon described more fully), of which 125 were full or long months, and 110 were short or deticient ones. We see tliat the length of this cycle was 01)40 days '125 x ;'.0 f 110x29), whereas the length of 235 true lunar months is 235 X 29 • 53058 = C939 • {)>^ii days. The cycle was there- fore too long by less than one third of a day, and the error of count M'ould amount to only one day in more than 70 years. The Mohannnedans, again, took a cycle of 300 months, which they divided into 109 short and 101 long ones. The length of this cycle was 10031 days, while the true length of 300 lunar months is 10031.012 days. The count would therefore not be a day in error until the eiul of about 80 cycles, or nearly 23 centuries. This month there- fore follows the moon closely enough for all practical pur- poses. Months other than Lunar. — The complications of the system just described, and the consy(pient ditWculty of making the calendar month represent the course of the moon, {ire so great that the pure lunar month was gen- erally abandoned, except among people whose religion re- ([uired important ceremonies at the time of new moon. In cases of such abandonment, the year has been usually •livided into 12 months of slightly different lengths. The ancient Egyptians, however, had 12 months of 30 days each, to which they added 5 supplementary days at the close of each year. 350 ASTH0NOM7. Kinds of Year. — As we find two different sjBteins of montlis to have heen used, fto we may divide the calendar years into three chisscR — namely : (1.) The lunar year, t> lunar months, 5 of the years having 12 months each, and ;{ of them 13 months each. Such a period woidd comprise '2!>2.'?i days, so that tlie a\crage length of the year would be 3(55 days 10^ horn's. This is too groat l>y about 4 hotirs 42 mimites. This very plan was proposed in ancient (treeee, but it was superseded by tlie discovery of the Metonio Cifdc^ whieli figures in our church calendar to this day. A luni-solar year of this general character was also used by the Jews. The Metonio Cycle. — The j)rcliminary considerations we have set forth will now enable us to undei'stand the origin (if our own calendar. We begin with the Metonic ('yclo of the ancient Greeks, which still regulates some religious festivals, although it has disapjieared froiii our civil reck- oning of time. The necessity of employing lunar months caused the Greeks great ditliculty in regulating their <'al- cndar so as to accord with their rules for religious feasts, until a solution of the j)roblem was found by ]\li;r<)\, about 4.'5.'5 H.c. The great discovery of ]\Ikto\ was that a period or cycle of 01)40 days could he divided u]) into 23.") lunar months, and also into 19 solar years. Of .liese months, 125 were to be of 30 days each, and 110 of 29 days each, which would, in all, make up the required f)940 days. To we how nearly this rule represents the actual motions of the sun and moon, we remark that : Days. 235 lunations require C939 19 Julian yeare '' 6939 19 true solar years require 6939 We see that though the cycle of 0940 days is a few hours too long, yet, if we take 235 true lunar months, we tiud Iloiirx. Mln. 10 31 18 14 27 §m 252 ASTUoyOM I. their wliolc duratioii tol)o ii little less lliiiii ll> Julian J(!!ii"h of 3(5.")] (lays t-at'li, and a little nioru than !'.> true s(tlar yi-ars. Tliu' prohloni now was to take tlu'si" li;».'> nioiitliK and vi-ars, <»f whidi liishoidd have 12 nioiiths each, and 7 should havo V.\ niontlis each. Tlu' lon^ ycai's, or those of V.\ months, wcj'i; prohahly those (*orrc's])ondiii^ to the innn!)ers .'5, ;">, S, 11, !:', HI, and IJ), while the first, Kecond, fourth, sixth, etc., were short years. In general, the months had 2'.) and 150 days alternately, hut it was necessary to suhstitnte a loiij^ month for a shoi't one every two or three years, so that in the cycle there should he 12.") loni; an from the year. It is employed in om* church calendar for lind- iuij the time oi Easter Simdav. Period of Callypus. — We have seen that the cycle of Ci)4-0 days is Ji few hours too lon^ either for 235 lunar months or for 11) solar years. Cvi-i.vi'is therefore sou years. These years would then he Julian years, while the recur- rence of new moon would only he six hours in error at tlu; end of the 7(» years. Had he taken a dav from evei\ third cycle, and fi'om some year and month of that cycle, lie would have heen yet nearer the truth. The Mohammedan Calendar. — Among the most remark - ahle calendai*s which liave remained in use to the present time is that of the Mohammedans. The year is composed THE Mo//A}f}rf':nAy calendar. of 12 liiimi* iiiontlis, and tluTufoiv, as aliva days. The fraction of a day heing jt far from one third, a three-yenr cycle;, comprising two veal's of 1^54 and 10 years, so that this system is accurate enough for all practical purposes. The common Mohammedan year of 854 days is composed of months containing alternately 30 and 2*.) days, the first having 30 and the last 21). In the years of 355 days the alter- nation is the same, except that one day is added to the last month of the year. The old custom was to take for the first day of the month that follow'ing the evening on which the new moon could first he seen in the west. It is said that hefore the exact arrangement of the Mohammedan calendar had heen completed, the rule was that the visihility of the crescent moon should bo certified hy the testimony of two wit- nesses. The time of new moon given in our modern almanacs is that when the moon passes nearly between us and the sun, and is therefore entirelv invisible. The moon is generally one or two days old before it can be seen in the evening, and, in consecpience, the lunar month of the Mo- hammedans and of othei's conmiences about two days after the actual almanac time of new moon. •t l1 254 ASTllONOMT. The civil calendar now in use tlironjijuont Cliristerulom had its origin among tlie Konians, and its foundation vvas laid l>y Julius C>:8ar. Before his time. Home can hardly he said to have had a elironological system, tlie length of tlie year not heing prescrihed hy any invariable rule, and be- ing therefore changed from time to time to suit the caprice or to compass the ends of the rulers. Instances of this tampering disposition are familiar to the historical student. It is said, for instance, tJiat the Gauls having to ])ay a certain monthly tribute to the Komans, one of the govern- ors ordered the year to be divided into 14 montlis, in order that the pay days might recur more fre(|nently. To remedy this, CiiSAR called in the aid of Sosioenks, an as- tronomer of the Alexandrian scho(»l, and by them it was arranged that the year should consist of 3(>5 days, with the addition of one day to every fourth year. The old lloniiin months were afterward adjusted to the Julian year in such a M'ay as to give rise to the somewhat irregular arrangemeiit of months which we now have. Old and New Styles. — The mean length of the Julian year is 'M\i^\ days, about 11^ minutes greater than that of the true equinoctial year, which measures the recurrenco of tlie seasons. This difference is of little practical im- portance, as it only amounts to a week in a thousand years, and a change of this amoutit in that period is produ(^t;ve of no inconvenience. But, desirous to have tlie year as correct fis possible, two changes were introduced into tin; calendar by Pope Gkixjohy XIII. with this object. They were as follows : 1. The day following October 4, 1582, wascalled tlic 15th instead of the 5th, thus advancing the count 10 days. 2. The closing year of each century, UIOO, 1700, etc., instead of being always a leap year, as in the .luliaii calendar, is such only w);en the namber of tlu century is divisible by 4. Thus while 1()«)0 remained a leap year, as before, 1700, 1800, and 11)00 were to oe common years. This change in the calendar was speedily adopted by all TIIK CALENDAR. ')r. r)5 h1 tliii (lays. ', etc., Julian ury is LMir, as •ars. by all OatlioHc coiiiitrios, and more slowly hy Protestant ones, Enjjfland holding out until 1752. In Russia it has never been adopted at all, the Julian calendar beint was not universal 'intil comj)ara- lively recent times. I Miring the iirst sixteen centuries of tl:3 Julian calcmlar there was such an absence of definite rules on this subject, and such a variety of practice on the ])art of dilferent j)owers. that the simple enumeration of the times chosen by vai'ious govcrmncnts and pontiiTs for the commencement of the vc^ar would make a tedioun (•hapter. The most common times of connntMicing' woiv, perhaps, March 1st and INFarch 22(1, the latrer being the time of the vernal efpiinox. I>ut January 1st gradually made its wav, and became universal after its adoi)tion bv England in 1752. Solar Cycle and Dominical Letter.— In our church cal- endars .January 1st is marked by the letter A, .January 2d by li, and so on to (r, when the seven lettei-s begin over again, and are repeated through the year in the same order. Each letter there indicates the same day of the week throughout each separate year, A indicatiiig tin* day on which January 1st falls, J} the day following, and so on. An exception occurs in leap years, when l'\'bruary 2i>th and March 1st are marked by the sanu' letter, so that a change (khmu's at the bi-gimiing of ^farcli. The letter corresponding to Sunday on this sclienu; is called the /)(>• //n'nicnl or Sunday letter, and, wlieii we once know what letter it Is, all tlie Sundays of the year an; indicated by that letter, and heiu^e all the other days of the week bv tlieir letters. In leap yeai-s there will be two Dominical *t' ' ■ M ^^i ^5G ASTRONOMY. letters, that for tlit (ast ten montlis of the year l)eing the oiu" next ])rec'e(ling the letter for January and February. In tlie Julian calendar the Donunieal letter must always recur at the end of 2S yeai'8 (besides three recurrences at -.:ie<|ual intervals in the mean time). This ])eriod is called the tiohir <'>/<'f<'^ and determines the days of the week on ■which the days of the month fall and a remainder of ;>, showing that, had every fourth yi'ar in the interval been a lea[) year, there were either .'{<» or 157 leaj) years. As a Februarv 2'.»th followed onlv a week after the date, the nuiidter must be .'17 ;* but as ISdO was dropped fntiii the list of leap yeai^s, the number was really only ;'»<•. Then 147 + v{<) = 188 days advanced in the week. Di- viding by 7, because the sanu3 day of the wetd; recurs after seven days, we find a remainder of I. So Februaiy 22(1, lS7i>, is one day further advanced than was Februarv 22(1, 17'">2; so the former being Saturday, WAsniN(.in\ was born on I'riduy. * Perliai)s the most convenient way of dcoidini; wlit-tlier tlic n'maiiidcr doi!s or dot's not indicate an additional leaj) jear iHtosuiUract it frointlu! last dale, and s('(! wlictluT a February 2!)th tlien intcrvent's. Se.Ittr.K I- Juj? ;} years from Fel)niary 'i'Jd. iHT'.t, we liave Fehriiary 2'2d, \>^'>^'u and u 2!>tii occurs between tlie two dales, only u w«.'ek alter the lirst. Dirrs/oy OF riii'j day 257 linnindtr rroinilii' i; 3. DIVISION OP THE DAY. The division of tlie day into lionrs was, in ancient nnd niedia^Nal tinu's, ('tTecti'd in awiiv vorv ditYeivnt from that wiiic'li wo practice. >VrtiHciaI time-keepers not l»ein»^ in •general nse, the two fiuKhimental moments were sunrise and sunset, whicli marked tlie day as tinctivo division of the astronomical dav than that MM I w 'laii 258 ASTliOKOMY. I wliicli we employ, and led luiturally to considering the doi/ and the niyht as two distinct periods, each to be di- vided into 12 lioure. So long as temporary hours were nsed, the beginning of the day and the beginning of tlie night, or, as we shonld call it, six o'clock in tiie morning and six o'clock in the evening, were marked by the rising and setting of the sun ; but when ecpiinoctial hours were introduced, neither sun- rise nor sunset could bv taken to count from, because both varied too nnicii i;i tl^e course of the year. It therefore became customary tc count from noon, or the time at which the sun passed the meridian. The old custom of dividing the day and the night ea(!li into 12 parts was con- tinued, the first 12 being reckoned from midnight to noon, and the second from noon to midnight. The day ■was made to commence at midnight rather than at nijon for obvious reas(»n8 of convenience, altliough noon was of coui'se the jH)int ut which the time hud to be determined. Equation of Time. — To any one who studied tlie annuiil motion of the nun, it must have been (piite evident tliut the intervals between its successiv, passages over the meridian, or ])etween one noon and he next, could not be the same throughout the year, because the apparent motion of the sun in right ascension is not constant. It will be renu)nd)ered that the apparent revolution of the starry sphere, or, which is the same thing, the diunial revolution of the earth upon its axis, may be regarcKil as absolutely constant for all practical purposes. This rev- olution is measured around in right ascension as exi»laine(l in the opening chapter of this work. If the sun increased its right ascension by the same amount every day, it woiiM pass the meridian .'5'" 5(5' later every day, as measured l»_v sidereal time, and hence the intervals betwecji successive jjassagc; vvould be e(|ual. J^ut the motion of the sun in riglit ascensio!! is unequul from two causes : (1) the mi- e<{' ; the actual motion therefore varies frouj 3'" 48" to 4" 4". The effect of the obliquity of the ecliptic is still greater. When the sun is near the equinox, its nu^ticm along the ecliptic makes an angle of 23^° with the j)arallels of dec- lination. Since its motion in right ascension is reckoned along the parallel of declination, we see that it is e(pial to the motion in longitude multiplied by the cosine of 2^^if. This cosine is less than unity by about 0.08 ; therefore at the times of the equinox the mean motion is diminished by this fraction, or by 20 seconds. Therefore the days ai'c then 20 seconds shorter than they would be were there no obliquity. At the solstices the o|)po8ite effect is ])ro- duced. Here the different meridians of right ascension are nearer together than they are at the eipuitor in the proportion of the cosine of 234° to unity ; therefore, when the sun moves through one degree along the ecliptic, it changes its right ascension by 1-08° ; here, therefore, the days are about 19 seconds longer than they vnjuld be if the obliquity of the ecliptic was zero. We thus have to reco*jnizo two sliijhtlv difftMTiit l- iiids of days : sohw days and m('((n days. A solar day is the interval of time between two sncccsKive transits of tlic -^im over the same meridian, while a mean day is the mean of all the solar days in v year. If we had two clocks, the Olio going with perfect uniformity, but regulated ,so ajs to ^■^H III f 260 ASrilONOMY. keep as near the sun as possible, and the other changing its rate so as to always follow the sun, the latter would gain or lose on the former by amounts sometimes rising to 'I'l seconds in a day. The accumulation of these variations through a period of several months would lead to such deviations that the sun-dock Mould be 14 minutes slower than the other during the first half of February, and Hi minutes faster during the iirst week in November. The time-keepers formerly used were so imperfect that these inequalities in the solar day were nearly lost in the neces- sary irregularities of the rate of the clock. All clocks wei'o therefore set by the sun as often as was fV>und neces- sary or convenient. But during the last century it w;is found by astronomers that the use of units of tinie vary- ing in this way led to much inconvenience ; they thciv- fore substituted vuuoi time for solar or aitpai'ent time. Mean time is so measured that the hours and days shiill always be of the same length, and shall, on the average, be as nnich behind the sun as ahead of it. We nuiy imagint; a fictitious or mean sun moving along the equator at the rate of 3"' 50' in right ascension every day. A[ean time will then be measured by the passage of this fictitious sun across the meridian. Apparent time was used in ordinary life aftei' it was given up by astronomers, because it was very easy to set a clock from time to time as the sun passed a noon-mark. But when the clock was so far im- proved that it kept much better time than the sun did, it was found troublesome to keep putting it backward and forward, so as to agree with the sun. Thus mean time was gradually introduced for all the purposes of oruinaiv life except in very remote country districts, whi're the farmers ma,v llnd It more troublesome to allow for alt eijiia tion of time than to set their clocks by the siin every few days. The common household almanac slKtidd give tho equa- tion of time, or the mean time at which tiie sun passes tlit' meridian, on each day of the year. Then, if any one wishes IMP no VINO TUB CALENDAR. 2G1 to pet Ills clock, ho knows tlie inoment of the sun passing tlie moridiiin, or bein<^ at some noon-mark, and sets his time-piece accordinj^ly. For all pur|)oses where accurate time is re«|uired, recourse must he hail to iistronomical oh- servation. It is now custoniary to send time-si<^nals every day at noon, or some other liour agreed upon, from obser- vatories ahmg tlie principal lines of telci^raph. Thus at tlie present time the moment of Washin«;ton noon is sig- nailed to New York, and over the jjrincipal lines of rail- way to the South and "West. Each pers«m within reach of a telegraph-otlicecan then determine his local time hy cor- relating these signals for the dilference of lojigitude. i; 4. REMARKS ON IMPROVING THE CALENDAR. It is an interesting (pu'stion whether our calendar, thia jtroduct of the growth of ages, which wc have so rapidly (lescril)e(l, would admit of decided improvement if wo were free to make a new one with the improvtid materials (•1 iiKxlcrn science. This (juestion is not to he hastily an- swcihm' in the atHrmative. Two small improvements are uiidouhtedly practicable: (1) a more regular division of the 'MMS days in common years and .SI in leap years. When we consider niore radical changes than this, ue iinil advaiitajjes set off by disadvantajjres. For in- stance, it woidd on some accounts be very convenient to ilividi! the year into l.'{ nionths of 4 weeks each, the last month having one or two extra days. The numths would tlien begin on the same day of the week through each vt'iir, and would admit of a nnich more convenient subdi- 1'^ 202 AS'IRONOMY. vision into luilvosand quarters tlian they do now. But tlie year would not admit of sueli a subdivision witliout divid- ing the niontlis also, and it is possible that this inconven- ience would balance tlie conveniences of the plan. An actual attetnpt in modern times to form an entirely new calendar is of sutHcient liistoric interest to be men- tioned in this connection. We refer to the so-called Itepub- lican Calendar of revolutionary France. The year some- times had 3(>5 and sometimes 3(50 days, but instead of having the leap years at delined intervals, one was inserted whenever it might be necess/iry to make the autumnal equinox full on the first day of the year. The division of the year was effected after the plan of the ancient Egyp- tians, there being 12 months of 30 days each, followed by 5 or 6 supplementary days to complete the year, which were kept as feast-days.* The sixth day of course occur- red only in the leap years, or Franeiads as they were call- ed. It was called the Day of the Revolution, and was set apart for a quadrennial oath to renuiin free or die. No attempt was made to fit the new calendar to the old one, or to render the change natural or convenient. The year began with the autumnal equinox, or Septend)er 2lM of the Gregorian calendar ; entirely new names were given to the months ; the week was abolished, and in lieu of it the month was divided into three decaf con- iponcnts f^ 6. THE ASTRONOMICAL EPHEMERIS, OB NAU- TICAIi ALMANAC. The Astronomical EpJtemer'tH, or, as it is more c'o!n- monly culled, the JVautiiuil Alm,anat% is a work in whicii celestial phenomena and the jmsitions of the heavenly bodies are computed in advance. 'V\\v need of such a work must have been felt by navigators and astronomers from the time that astronomical i)redictions became sntficiently accurate to enable them to determine their position on the surface of the earth. Attii'st worksof this (rlass were pre- pared and published by iinlividual astronomers who had the taste and leisure for this kind of labor. MAXFUKor, ■of Bonn, published KpJwtiieriih's in two volumes, which gave the principal aspects of the heavens, the positions of the stars, planets, etc., from 1715 until 1725. This work included maps of the civilized world, showing the j)ath8 of tlie principal eclipses during this interval. The usefulness of such a work, especially to the naviga- tor, depends npon its regular appearance on a uniform plan and upon the fulness and accuracy of its data ; it was there- fore necessary that its issue should be taken up as a gov- ermnent work. Of works of this class still issued the earliest was the CotuuilNmiwe dcs TeinpH of France, the th'st volume of which wsus publislied by Picaud in 1070, and which has been continued without interruption until the present time. The publication of the British Nautical Almanac was commenced in the year 1707 on the repre- sentations of the Astronomer Royal showing that such a work would enable the navigator to determine his longi- tude within one degree by observations of the moon. An astronomical or nautical almanac is nowi)ublished annually l>y each of the governments of Germany, Spain, Portugal, France, Great Britain, and the United States. They have liiadually increjised in size and extent with the advancing wants of the astronomer until those of Great Britain and this country have become octavo volumes of between 600 204 ASTHONOMY. m and fiOO pajfcs. These two nro piiMislicd tljreo years or more liut'orehuinl, ill order that ija\ipitt>rs guiiii^ on loti^ voyaires may supply theini^elves in atlvan(;e. Tiie Aine.'}- eon Kplitiiii i'Ih and Nanthnl AhiiamK' lias been re^nhir- ly puhlisiied since 1855, tlie iir^t vohnne heini^ for that year. It is such a degree of perfection that an astronomer, armed with a naii- ti(!al almanac, a chronometer regulated to (freenwi(rh or Washington time, u catalogue of stars, and the necessary instruments of observation, can determine his position at any point on the earth's surface within a hundred yards by a single night's observations. If his chron()meter is not so regulated, lie can still determine his latitude, but not Ids longitude, lie could, however, obtain a rough iiter'H siitdlitcs ttiid misccliimcouH phciioincim. To f?ivc' tlic reader ii still further idea of tlie Epltcmcrin, w« pro- sent a small portion of onu of its pages for the year 1882 : FkHUUAUY, IHSa— at (JllKK.NWK II MkaN NtM)N. Diiv of tllcl wi-ck. V J3 . "Si "35 >.2 TiiK Sin'h Ki|iiiiiiun (•rtiiiic to Sldrrniilinie Apparent rlKhi ii»f»'ii- bloll. Diir. lor 1 huiir. Appnront do- l-Illiiklloli. Ditr. fori hour. • 43 -.57 44-;w -|4I-!«I 45 (i!t 40-30 f-17 ft3 17 (MI 48-28 48-88 411-47 50-(« 4. 50 -.50 51-12 51.(» K>2U 52-02 53-07 btt ttiili- Iriicioil 1 *" from MiciiM ig liiuc. , 'p^ 1 or rlKlit HH. ••••iiHioii of iiu'uu ttiiii. W..1. Tliiir. l-ri«l. Sftt. Sim. .Moil. TllrH. W.'d. Thiir. Krid. Silt. Siiii. Mon. 'I'lll-H. WimI. TImr. Frill. Sul. 1 2 3 4 5 7 H U 10 II U 14 15 10 IT 18 11. M. f. 21 13 (M 21 4 10 81 21 8 l!»-82 21 19 31 -im 21 1(1 2.3-3.1 21 20 23-88 21 21 23 (W 21 28 •.«(«• at 3-4 ao Tit 21 8(1 18-21 21 -10 14-8N 21 41 10-80 21 48 n-!IS 21 .5^J 013 21 55 6110 21 .5i> .17-17 82 3 .Hit -47 'ii 7 31 07 ». 10- 175 10-141 10- 107 10 073 I0-U4O 10-007 (174 \» nil tl-iNItt i»-877 '.1-810 '.1 815 n 781 !•■ 7.5.3 U-7-2:j 1) (HI3 1I-(H^ U-IKU / • H 17 3 22-4 1(1 45 5-4 10 27 :io-ii 1(1 !> .H!l-a 15 51 .30-8 15 33 01 15 14 25-4 14 Tm 211-1 14 30 17-7 M l(i BIO 13 .57 11 a 13 .'17 1(1 -1» 13 IT fl-1 la .5(i 48 -:i 12 30 14 -U \'i 15 20 3 11 51 .'12-1 11 .3.) 2.3 M. d. 13 51 ,'tl 13 t«:^l^ 14 5 111 It 10 01 14 15 41 It lU 40 It 22 (Ml It 25(11 It 20(15 It 27 51 II •27(11 14 20 ini 14 25 (W 14 •A') -.52 14 20-70 It 17-15 11 12 90 14 7-'.»4 0-318 0.-28I 0-2.5(1 210 IK-I 1.50 0-117 (K« (1,52 0-(fJII 0011 ()-(H2 073 O-Kkl 1.I4 0-1(14 0-11)1 0-2^ja 1 II. M. H. •JO 40 21 70 •20 .50 18 20 •20 r>l 14 81 •JO 58 11-37 21 2 7 IfJ 21 (i 4 48 21 10 1 OS 21 13 .57 .59 21 IT .51 It 21 21 .'lO TO ai a5 4T -25 21 29 43 81 •21 .3:1 40 .'15 21 3T ;»1 91 21 41 .'13 4b ai 15 an- 09 21 49 •J(1-.5T 21 5.3 23-13 Of the same general nature with tlu; Kpliemeris are catalogues of tlie fi.ved stars. The object of such a catalogue is to give i\w right !i>*('eiision and declination of a number of stars for some epoch, tho liiginning of tho year IH7.") for instance, with the data by which the jKtsition of a star can be found at any other epocih. Such cata- Inifues are, however, imperfect owing to the constant small changes in the positions of the stars and the errors and imperfections of tho cliler observations. In conseipietico of these iniperfections, a consid- erable part of the work of tho astronomer engaged in accurate de- .i.>inations of geographical position.s consist in Hnding the luost ill ' 'i; ato pu-sitious of thu stars which ho mukca use cf. IMAGE EVALUATION TEST TARGET {MT-3) // L 4i 7a 1.0 I.I 11.25 |iO "l^™ 1^ 1^ IIM 12.2 44 U 11.6 i? / Sciences Corporation •ss \ <^ ?>.^ ^ 23 WEST MAIN STREET WEBSTER, N.Y. 14S80 (716) 872-4503 '^j^'^ ^ tl n PART II. THE SOLAR SYSTEM IN DETAIL CHAPTER I. STRUCTURE OF THE SOLAR SYSTEM. The solar system, as it is known to us through the dis- coveries of Copernicus, Kepler, Newton and their suc- cessors, consists of the sun as a central body, around which revolve the major and minor planets, witli their satellites, a few periodic comets, and an unknown number of meteor swarms. These are permanent members of the system. At times other comets appear, and move usually in par- abolas through the system, around the sun, and away from it into space again, thus visiting the system without be- ing permanent members of it. The bodies of the system may be classified as follows : 1. Thecentralbody— the Sun. 2. The four inner planets — Mercury^ Vernis, the ^arth, 3Iars. 3. A group of small planets, sometimes called Asteroids, revolving outside of the orbit of Mars. 4. A group of four outer planets — Jupiter^ Saturn, Uranus, and Neptune. 5. The satellites, or secondary bodies, revolving about the planets, their primaries. G. A number of comets and meteor swarms revolving in very eccentric orbits about the Sun. 268 ASTRONOMY. The eight planets of Groups 2 and 4 are sometimes classed together as the major planets, to distinguish them from tlie two hundred or more ininor planets of Group 3. The formal definitions of the various classes, laid down by Sir William Hekschel in 1802, are worthy of repe- tition : Planets are celestial bodies of a certain very consider- able size. They move in not very eccentric ellipses about tho sun. The planes of their orbits do not deviate many degrees from the piano of the earth's orbit. Their motion about the sun is direct. They may have satellites or rings. They have atmospheres of considerable extent, which, however, bear hardly any sensible proportion to their diametere. Their orbits are at certain considerable distances from each otlier. Asteroids, now more generally known as small or minor planets, are celestial bodies which move about ihe sun in orbits, either of little or of considerable eccen- tricity, the planes of which orbits may be inclined to the ecliptic in any angle whatsoever. They may or may not have considerable atmospheres. Comets are celestial bodies, generally of a very £ aall mass, though how far this may be limited is yet un- known. They move in very eccentric ellipses or in parabolic arcs about the sun. The planes of their motion admit of the greatest variety m their situation. The direction of their motion is also totally undeter- mined. They have atmospheres of very great extent, which show themselves in various forms as tails, coma, haziness, etc. MAGNITUDES OF THE PLANETS. 2G9 Relative Sizes of the Planets.— The comiiaratlve sizes of the major planets, as thej would appear to an observer situated at an equal distance from all of them, is given in the following figure. Fig. 74.— rela nrs sizes of the planets. The relative apparent magnitudes of the sun, as seen from the various planets, is shown in the next figure. Flora and Mnemosyne are two of the asteroids. A curious relation between the distances of the planets, known as Body's law, deserves mention. If to the num- bers, 0, 3, 6, 12, 24, 48, 90, 192, 384, 270 ASTRONOMY, €ach of wliicli (the second excepte,o(X),aoo Mu.SBCS. 200 < The mass of Mercury is less tlmn the mass ) of Mars : j The sum of masses of Mercury and Mars ) is less than the mass of Venus : J Mercury + Mars + Venus < Earth : Mercury + Mara + Venus + Earth < Ura- \ nus : ) Mercury + Mars + Venus + Earth + lira- ) nus < Neptune : y Mercury + Mars + Venus + Earth + Ura- ) nus + Neptune < Saturn : J Mercury + Mara + Venus + Earth + Ura- nus + Neptune + Saturn < Jupiter : Combined mass of all the planets is less/ ^ o^i p'to ^ ■• aaa tl.Hn tlmt of tlw, Snn • • \ 1.341,672 < 1,000; 324 \ 524 < 2,353 2,877 < 3,0G0 5,937 < 44,250 50,187 < 51,600 101,787 < 285,580 387,307 < 954,305 \ 1.000,000 The total mass of the small planets, like their number, is unknown, but it is probably less than one thousandth that of our earth, and would hardlj increase the sum total of the above masses of the solar system by more than one or two units. The sun's mass is thus over 700 times that of all the other bodies, and hence the fact of its central position in the solar system is explained. In fact, the centre of gravity oi the whole solar system is very little outside the body of the sun, and will l3e inside of it when Jupiter and Saturn are in opposite directions from it. Planetary Aspects. — The motions of the planets about the sun have been explained in Chapter IV. From what is there said it appears that the best time to see one of the PL A XKTA li y A SP KCTS. lan- 834 2,353 3,0G0 44,250 51,600 285.580 954,305 1,000,000 liber, mclth total 111 one that ientval t, the little when lit. about hilt outer planets M- ill ho when it is in ()])])(>siti(U) — that is, when its geocentric lonu'itude or its \\ SIS £e it ^ CO 00 ^S o» J_ 0) ■ -33 CO to ■^ cs s o OI 00 CO eo to (TJ 1-1 »^ f^ 1-1 Ol ^ •»>< . i-H t-t^ 00 52 © «o ©© o> © I-l tom •c iC^ 1— t CO . eo coco OS OS ss © Tj. TJI © ■f aci rH »H (?* s? ©> -« o © (3S© «o CO •S ^ CO OJ M CO ;o oS© r^ 00 2-1 ICO o 1— ( lO eo TH 6flO,< -§5 mos CO o ©© I" l> 3 5 i-» »-i (?l o (TJOi 1^ . w 1(0 1(3 00 00 07W CO © e ^ I- I- ■* © 1-H •^ t- CO ¥-4 *^ TH a r-l sss * eo So» s s •c .a t^ ^^ w 1— 1 ^^ i § ncli Ecli ^ o COM vrf 00 © © to © OOJ o 1— ( CIOJ ■^ ■v *-4 ' t— coco 1-H 1-1 OJOJ © TH ^ g QO ■«»<» •^ s to OJ lOQO t' TH eo i^ i^ ^ CO § (i© 00 CO = 3 »— ( w^ iO urio ■<»< TH ■&oJ «. t' t-t- 1-^ ^■ t- ■»»< ©CO ^ © Lon Peri OJOl OJOl »H KO •S CTiN ss ss 1-1 T-l sg g ^ 1— < 1—1 CO TH GO w^ >-^ ©e eo , 6 l> eo-H 1-l(^ ^ © 00© O) CO •C*-w eo« <-i 1-H oil- © ^ •S o-^ ^» t^i^ o tn ©© ^ Oi Eccen Orb CD QQ 00 t- 1- c» a Od 8 oj ii eoto CO So § to© • © i 1 «/ CP •*# •M • H» 1-1 —1 o * •^ i s S ^ : 1 tH ^ o8 • 5g » 5 1-1 (^^ 30 CJ ■<1' £2 is 00 1 §?00 OJO> 1-^ 1 s 1 a J^ eo t-e> ©c > lO °? *?"? TH •<•» o ©6 1-t »- < y-t lO ©© O) O 1-H CO , »o ©© ~§^^ t CO t- 00 — S £. OT 00tJ< 1—1 © §§ t- c^ O CJO (MO © ^^ © CO « COCO <3p © ©OJ £- QO S:^ o T-t 1-H l>t^ © CO ©© ^ t ■^ •* l>t- » JO W5 ©© ^ 1^ © oo ©c- (^ (W 00 »-( eo?o ou: © s CO CO to t> 00 © © ©s: CT 1"^ TH CO »— 1-< 0»(N ^ T-( ut) 0?CJ 1— ^ • • — r^-- ^ • — Y~ • ; aj • >> . 1 I . • d H u • • u " EO a 3 g > • 1 1^ 'a. 1 3 C d a ELEMENTS OF THE PLANETS. m B o Is loo 11^^ S VOT i°Mi- = o> '"^x^ X' s 'Es-r II O ta © o « ss s ^ ^ Oi w^ oo ^ Oi Oi r^ r-> ffl 00 ui ^ CO o> 00 t- Oi -f 00 S-< OS 2 ^ S r- «S SS 8 ^ 3 2 © 1—1 M r-i <0 o •933 ^ & u> tn S3 P (3 II 1" O 05 1^ CO o op O CO « oi B S - S '^ a « 2 & & O 1-1 O »H J> ^ S 00 5 T-t TH o o 2435 1-1 1 t « © s ;? §8 f-1 f H l-H T-H _ 4> 0/ £.= — a a H 0> O 00 '-t OS 50 ^ '-I OS CO o:> C) 8 00 (N l» x> © 1-1 t- CO © GO O © C) Ci t-H f- ""T * © «o t^ t^ « 00 00 CJ «o g CO (S © © • © CO QO © © IC © CO c* OS CO CO © t- Ed's es 3 » *> 2© © © © © OJ, ^ J. ^ J, © 01 Ki CO V5 CO 00 00 00 © © o © CJ -H 00 00 00 i ^ a 1= 10 10 t i. S go ^ 3 QD S k « a >> a t3 ^ (N OS © 1— < CO 00 a 3 a >5 CHAPTER 11. THE StJN. § 1. GENEBAL SUMMABY. To the student of the present time, armed with the powerful means of research devised by modern science, the sun presents phenomena of a very varied and complex character. To enable the nature of these phenomena to be clearly understood, we preface our account of the physical constitution of the sun by a brief summary of the main features seen in connection with that body. Photosphere. — To the simple vision the sun presents the aspect of a brilliant sphere. The visible shining sur- face of this sphere is called the photosphere^ to distinguish it from the body of the sun as a whole. The apparently flat surface presented by a view of the photosphere is called the sun's disk. Spots. — When the photosphere is examined with a tele- scope, small dark patches of varied and irregular outlino are frequently found upon it. These are called the solar spots. Botation. — When the spots are observed from day to day, they are found to move over the sun's disk in such a way as to show that the sun rotates on its axis in a period of 25 or 26 days. The sun, therefore, has «a?/«, poles, and equator, like the earth, the axis being the line around which it rotates. Faoiilse. — Groups of minute specks brighter than tlio general surface of the sun are often seen in the neighbor- hood of spots or elsewhere. They are iidWa^faculiB. FEATURES OF THE SUN. 379 Chromosphere, or Sierra. — The solar photosphere is covered by a layer of glowing vapors and gases of very ir- regular depth. At the bottom lie the vapors of many metals, iron, etc., voIatiHzed by the fervent heat which reigns there, while the upper portions are composed prin- cipally of hydrogen gas. This vaporous atmosphere is commonly called the chromosphere, sometimes the sierra. It is entirely invisible to direct vision, whether with the telescope or naked eye, except for a few seconds about the beginning or end of a total eclipse, but it may be seen on any clear day through the spectroscope. Prominences, Protuberances, or Red Flames. — The gases of the chromosphere are frequently thrown np in irregular masses to vast heights above the photosphere, it may be 50,000, 100,000, or even 200,000 kilometres. Like fhe chromosphere, these masses have to be studied with the spectroscope, and can never be directly seen ex- cept when the sunlight is cut off by the intervention of the moon during a total eclipse. They are then seen as rose- colored flames, or piles of bright red clouds of irregular and fantastic shapes. They are now usually called ' ' prom- inences" by the EngHsh, and " protuberances" by French writers. Corona. — During total eclipses the sun is seen to be en- veloped by a mass of soft white light, much fainter than the chromosphere, and extending out on all sides far be- yond the highest prominences. It is brightest around the edge of the sun, and fades off toward its outer boundary, by insensible gradations. Tl ^^ halo of light is called the corona, and is a very striking object during a total eclipse. § 2. THE PHOTOSPHERE. Aspect and Structure of the Photosphere. — The disk of the sun is circular in shape, no matter what side of the sun's globe is turned toward us, whence it follows that the Bun itself is a sphere. The aspect of the disk, when Ml 380 ASTRONOMY. viewed with the iialhotograpli of tlie appearances described, which is enhirgeil threefold. Photographs less than four inches in diameter cannot satisfactorily show such details. As the granulations of the solar surface are, in general, not greatly larger than 1" or 2", the photo- graj)liie irradiation, whicii is sometimes 30" or more, may completely obscure their characteristics. This difficulty M. .Jvnssen has over- come by enlarging the innige and shortening the time of expos- ure. In this way th,; irradiation is diminished, because as the di- ameters increase, the linear dimensions of the details are increased, and " the imperfections of the sensitive plate have less relative im- portance." |: THE SUN'S PHOTOSPHERE. m Again, M. Janssen has noted tliat in sliort exposures the jjhotO" graphic spectrum is almost monochromatic. In this way it differs {greatly from the visible spectrum, and to the advantage of the former for tliis special purpose. The diameter of the solar photograms have since 1874 been successively increased to 13, I;"), 20, and 80 centimetres. The exposure is made c(]ual all •over the surface. In summer this exposure for the largest photo- ks over- I expos- Ithedi- Ireased, live im- Fro. 77. — RETTCULATKD ATinANOEMENT OF THE PHOTOSPnEUE. grams is less than O'OOOr). The development of such pictures is very slow. These photograms, on examination, show that the solar surface is covered with a line granulation. The forms and the dimensions of the elementary surfaces are very various. They vary in size from 0"-3 or 0"-4 to 3' or 4" (200 to 3000 kilometres). Their forms 283 ASTRONOMY. are generally circles or ellipses, but these curves are sometimes greatly altered. This granulation is apparently spread equally all over the disk. The brilliancy of the points is very variable, and they appear to be situated at different depths below the photo- sphere : the most luminous particles, those to which the solar light is chiefly due, occupy only a small fraction of the solar surface. The most remarkable feature, however, is "the reticulated ar- rangement of the parts of the photosphere." "The photogrums show tliat the constitution of the photosphere is not imiform throughout, but that it is divided in a series of regions more or less distant from each other, and having each a special constitution. These regions have, in general, rounded contours, but these are often almost rectilinear, thus forming polygons. The dimensions of these figures are very variable ; some are even V in diameter (over 25,000 miles)." "Between these figures the grains are sharply defined, but in their interior they ar j almost effaced and run together as if by some force." These phenomena can be best understood by a reference to the figure of M. Janssen (p. 281). Light and Heat from the Photosphere. — The photo- sp7ie7'e is not equally bright all over the apparent disk. This is at once evident to the eye in observing the sun with a telescope. The centre of the disk is most brilliant, and the edges or limbs are shaded off so as to forcibly suggest the idea of an absorptive atmosphere, which, in fact, is the cause of this appearance. Such absorption occurs not only for the rays by which we see the sun, the so-called msual rays, but for those which have the most powerful effect in decomposing the salts of silver, the so-called chemical rays^ by which the ordinary photograph is taken. The amount of heat received from different portions of the sun's disk is also variable, according to the part of the apparent disk examined. This is what we should ex- pect. That is, if the intensity of any one of these radiations (as felt at the earth) varies from centre to circumference, that of every other should also vary, since they are all modifications of the same primitive motion of the sun's constituent particles. But the constitution of the sun's atmosphere is such that the law of variation for the three classes is different. The intensity of the radiation in the sun itself and inside of the absorptive atmosphere is prob- SOLAR RADIATION. 283 tlie three the )rob- ably nearly constant. The ray wliich leaves the centre of the sun's disk in passing to th ". earth, passes througli the smallest possible thickness of the solar atmosphere, while the rays from points of the sun's body wliich appear to us near the limbs pass, on the contrary, through the maxi- mum thickness of atmosphere, and are thus longest sub- jected to its absorptive action. This is jjlainly a rational explanation, since the part of the sun which is seen by us as the limb varies witli tlie position of the earth in its orbit and with the position of the sun's surface in its rotation, and has itself no physical peculiarity. The various absorptions of different classes of rays correspond to this supj)osition, the more refrangi- ble rajs suffering most absorption, as they must do, being composed of waves of shorter wave length. The following table gives the observed ratios of the amount of heat, light, and chemical action a' the centre of the sun and at various distances from the centre toward the limb. The first column of the table gives the apparent distances from the centre of the disk, the sun's radius being 1"00, The second column gives the percentage of heat-rays received by an observer on the earth from points at these various distances. That is, for every 100 heat- rays reaching the earth from the sun's centre, 95 reach us from a point half way from the centre to the limb, and so on. Analogous data are given for the light-ray. :'nd the chemical rays. The data in regard to heat are due to Professor Langley ; those in regard to light and chemical action to Professor Pickeklng and Dr. Vogel respectively. Distance frou Centkb. Heut Rays. Light Rays. Chemical Rays. 000 100 99 95 86 • • » • • • • - 62 50 .... 100 97 91 79 69 55 • • • • '37' 100 98 90 66 48 25 23 18 13 0-35 0-50 0-75 0-85 , 0-95 0-91) 0-98 100 For two equal apparent surfaces, A near the sun's centre and B uear the limb, we may say that the rays from the two surfaces when ^84 ASTRONOMY. received at the earth have approximately the following relative eflfects : A has twice as much effect on a thermometer as li (heat); A has three times as mucii illuminating effect as B (light); A has seven times as much effect in decomposing the photo- graphic salts of silver as B (actinic effect). It is to be carefully borne in mind that the above numbers refer to variations of the sun's rays received from different equal surfaces A and i?, in. their effect «/w/i certain arbitrary terredrial standurdu of measure. If, for example, the decomposition of other salts than those employed for ordinary photographic work be taken as stand- ards, then the numbers will be altered, and so on. We are simply measuring the ])ower of solar rays selected froni different parts of the sun's apparent disk, and hence exposed to different conditions of absori)tion in his atmosphere, to do work of a certain selected kind, as to raise the temperature of a thermometer, to affect the human retina, or to decompose certain salts of silver. In this the absorption of the earth's atmosphere is rendered con- stant for each kind of experiment. This atmosjihere has, however, a very strong absor])tive effect. We know that we can look at tlie setting or rising sun, which sends its light rays through great depths of the earth's atmosphere, but not upon the ^^un at noon- day. The temperature is lower at :unrise or at sunset than at noon, and the absor])tion of chemical rays is so marked that a photograjjli of the solar spectrum which can be taken in three seconds at noon requires six hundred seconds about sunset — that is, two hund'^ed times as long (Duapeu). Amount of Heat Emitted by the Sun. — Owing to the absorption of the solar atmosphere, it follows that we re- <;eive only a portion — perhaps a very small portion — of the rays emitted by the sun's photosphere. If the sun had no absorptive atmosphere, it would seem to us hotter, brighter, and more blue in color. Exact notions as to how great this absorption is are hard to gain, but it may be said roughly that the best authori- ties agree that although it is quite possible that the sun's atmosphere absorbs half the emitted rays, it probably do(,'s not absorb four fifths of t. m. It is a curious, and as yet we believe unexplained fact, that the absorption of the solar atmosphere does not affect the darkness of the Fraunhofer lines. They seem equally black at the centre and edge of the sun.* The amount * Prof. Young has spoken of a slight observable difference. HEAT OF THE SUJfT. 285 lative photo- 's refer urfacea ardii of ts than ! stand- simply parts of iditions selected tect the red con- lowevev, ik at tlie r\\ great at noon- at noon, otograph 3 at noon hund'-';d to the we ve- lou — ^jf lid seem ire hard tuithori- je sun's Ijly does led fact, )t afEect equally 1 ainoiint ence. of tin's absorption is a practical question to us on the earth. So long as the central body of the sun continues to emit the same quantity of rays, it is plain tiiat the thickness of the solar atmosphere determines the number of such rsiys reaching the earth. If in former times this atmosphere was much thicker, then less heat would have reached the earth. Professor Laxglky suggests that the glacial epoch may be explained in this way. If the central body of the sun has likewise had different emissive ])o\vers at different times, this again would produce a variation in the tempera- ture of the earth. Amount of Heat Badiated. — There is at present no way of determining accurately either the absolute amount of heat emitted from the central body or the amount of this heat stopped by the solar atmosphere itself. All that can be done is to measure (and that only roughly) tlic amount of heat really received by the earth, without attempting to define accurately the circumstances which this radiation has undergone before reaching the earth. The difficulties in the way of determining how much heat reaches the earth in any definite time, as a year, are twofold. First, we nnist be able to distinguish l)et\veeu the lieat as received by a thermometric ajjparatus from the sun itself and that from external objects, as our own atmosphere, adjacent buildings, etc.; and, second, we must be able to allow for the absorjition of the earth's iitmosphere. PouiLLET has experimented upon this question, making allowance for the time that the sun is below the horizon of any place, and for the fact that the solar rays do not in general strike perpendicularly but obliquely upon any given part of the earth's surface. Ilis conclusions may be stated as follows : if our own atmosphere were re- moved, the solar rays would have energy enough to melt a layer of ice 9 centimetres thick over the whole earth iiaih/, or a layer of about 32 metres thick in a year. Of the total amount of heat radiated by the sun, the 286 ASTliOJfiOAfr. earth receives hut an insignificant share. The sun is capable of heating the entire surface of a sphere Avliose ra- dius is tlie earth's mean distance to tlie same degree that the eartli is now lieated. The surface of such a spliere is 2,170,000,000 times greater than the nnguhir dimensions of the earth as seen from tlie sun, and hence tlie earth re- ceives less than one two hillionth part of the solar radia- tion. Tlie rest of the soliir rays are, it is generally believed, lost in space, so far as the human race is concerned. It is found, from direct measures, that a sun-spot gives less heat, area for area, than tlie unspotted photosphere, and it is an interest- ing question how mucli the climate of the earth can be affected by this ditlerence. Professor Lanoley, of Pittsburgh, has made measurements of the direct effect of sun-spots on terrestrial temperature. The observa- tions consisted in measuring the relative amounts of umbral, penum- bral, and photospheric radiation. The relative umbral, penumbral, and photospheric areas were deduced from the Kew observations of spots ; and from a consideration of these data, and confining the question strictly to changes of terrestrial temperature due to tliis cause alone, Lanoley deduces the result that " sun-spots do ex- ercise a direct effect on terrestrial temperature by decreasing tin* mean temperature of the earth at their msiximum." This change is, however, very small, as "it is represanted by a change in the mean temperature of our globe in ehjven years not greater than 05° C, and not less than 0-3° C." It is not intended to show that the earth is, on the whole,, cooler in maximum sun-spot years, but that, as far as this cause goes, it tends to make the earth cooler by this minute amount. What other causes may co-exist with the maximum spot-frequency are not considered. Solar Temperature. — From the amount of heat actually radiated by the sim, attempts have been made todetennino the actual temperature of the solar surface. The esti- mates reached by various authorities differ widely, as the laws which govern the absorption within the solar en- velope are almost unknown. Some such law of absorp- tion has to be supposed in any such investigation, and the estimates have differed widely according to the adapted law. Secchi estimates this temperature as about 6,100,000° C. Other estimates are far lower, but, according to all sound SPOTS ON THE SUN. 287 philosophy, thd temperature must far exceed any ter- restrial temperature. There can be no doubt that if the temperature of the earth's surface were suddenly raised to that of the sun, no single chemical element would remain in its present condition. The most refractory materials would be at once volatilized. We may coaoeatrato tlio I'leivt received upon several square feet nd examine its effects. If a lens three feet in diameter be used, the most refractory materials, as tire-clay, plaliiium, the dia- mond, are at once melted or volatilized. The effect of the lens is plainly the same as if the earth were brought closer to the sun, in the ratio of the diameter of the focal image to that of the lens. In the case of the lens of three feet, allowing for the absorption, etc., this distance is yet greater than that of the moon from the earth, so that it appears that any comet or planet so close ?'s this to the sun, if composed of materials similar to those in the earth, must be vaporized. If we calculate at what rate the temperati.ie of the sun would be lowered annuidly l)y the radiiition from its (surface, we shall tind it to be l}^' Centigiade yearly if its specific lu^at is that of water, and between 3° and 6' per annum if its specific heat is the same as that of the various constituents of the enrth itself. It would there- fore cool down in a few thousand years by an appreciable amount. )00° c. sound § 3. SUN-SPOTS AND PACULiB. A very cursory examination of the sun's disk with a small telescope will generally sliowone or more dark spots upon the photosphere. Tliese are of various sizes, from minute black dots 1" or 2" in diameter (1000 kilometres or less) to large spots several minutes of arc in extent. Solar spots generally have a dark central micleus or urribra^ surrounded by a border or penumbra of grayish tint, intermediate in sir de between the central blackness and the bright photosphere. By increasing the power of the telescope, the spots are seen to be of very complex forms. The umbra is often extremely irregular in shape, 288 ASTRONOMY. , and is sometimes crossed by bri(l^vi^f//i/>/v« is composed of lilaments of brighter and dari2.... 09 ia53 09 1854 1855 , 1856 1857 81 41 98 95 1858 41 1859 •87 1860 05 1861 17 1862 59 1863 •84 1864 ■ 02 1865 8 14 1866 7 '65 1867 . . . .. 709 1868 8-15 294 ASTRONOMY. The periodicity of the spots is evident from the table. It will appear in a more striking way from the following summary : From 1838 to 1831, sun without spots on only. In 1883, " " " From 1836 to 1840, " In 1843, From 1847 to 1851, " In 185G, From 1858 to 1861, " In 1867, 1 day. 139 days. 3 " 147 " 3 " 193 " no day. 195 days. Every 11 years there is a minimum number of spots, and about 5 years after each minimum there is a maxi- mum. If instead of merely counting the number of spots, measurements are made on solar photograms, as they are called, of the extent of spotted area^ the period comes out with greater distinctness. This periodicity of the area of the solar spots appears to be connected with mag- netic phenomena on the earth's surface, and with the num- ber of auroras visible. It has been supposed to be con- nected also with variations of temperature, of rainfall, and with other meteorological phenomena such as the mon- soons of the Indian Ocean, etc. The cause of this period- icity is as yet unknown. Carrington, De la Rue, LoEWY, and Stewart have given reasons which go to show that there is a connection between the spotted area and the configurations of the planets, particularly of Jujnter, Venus, and Mercury. Z()llner says that the cause lies -within the sun itself, and assimilates it to the periodic action of a geyser, which seems to be ^ priori probable. Since, however, the periodic variations of the spots cor- respond to the magnetic variation, as exhibited in the last column of the table of Scuwabe's results, it appears that there may be some connection of an unknown nature l>etween the sun and the earth at least. But at present wo can only state our limited knowledge and wait for further information. ^ii PERIODICITT OF SUN-SPOTS. 295 Dr. Wolf (Director of the Zurich Observatory) has col- lected all the available observations of the solar spots, and it is found that since 1610 we have a tolerably complete record of these appearances. The number and character of the spots are now noted every day by observers in many quarters of the civilized world. This long series of obser- vations has served as a basis to determine each epoch of maximum and minimum wliich has occurred since 1010, and from thence to detcmine the length of each single pariod. The following table gives Dr. Wolf's results : Table giving the Times of Maximum and Minimum Sun-Spot FUEQUENCY, ACC'OKDING TO WOLF. First S -iries. Second Series*. Minima. Diflf. Maxima. Diff. Minima. Diff. Maxima. Diff. A.D. lGlO-8 1615-5 1745-0 1750-3 8-3 10-5 10-2 11-3 1619-0 1626-0 1755.2 1761-5 15-0 13-5 113 8-3 1634 1639-5 1766-5 1769-'; 11-0 9-5 9-0 8-7 1645 1649-0 1775-5 1778-4 10-0 11-0 9-3 9-7 1655-0 1660 1784-7 1788-1 11-0 150 13-6 16-1 1666 1675-0 1798-3 1804-2 13-5 10-0 12-3 13-3 1679 -S 1685-0 1810-6 1816-4 10-0 8-0 13-7 13-5 1689-5 1693-0 1833-3 1839-9 8-5 13-5 10-6 7-3 1698-0 1705-5 1833-9 1837-2 14-0 13-7 9 6 10-9 1713-0 1718-3 1843-5 1848-1 11-5 9-3 12-5 13-0 1723-5 1737-5 1856-0 1860-1 10-5 11-3 11-2 10-5 1734-0 1738-7 1867-3 1870-1 11-20±2.11 years. ll-20±2 • 06 ys. 1 11-11±1- )4 ys. 10-94 ±3 -53 VB, ±0-64 ±C 1-03 1 ±0- 47 ±( )-76 296 ASTRONOMY. From the first series of earlier observations, the period comes out from observed minima, 11-20 years, with a variation of two years ; from observed maxima the period is 11 • 20 years, with variation of i;liree years — that is, this series shows the period to vary between 13 • 3 and 9 • 1 y?ars. If we suppose these errors to arise only from errors of observation, and not to be real changes of tiie period itself, the 7nea^ period is 11-20 ± 0-64. The results iVora the second series are also given at the foot of the table. From a combination of the two, it follows that the m^t-an period is 11-111 ± 0-307 years, with an oscillation of ± 2-030 years. These results are formulated by Dr. Wolf as follows : The frequency of solar spots has continued to change periodically since their discovery in 1010 ; the mean length of the period is 11^ years, and the separate periods may differ from this mean period by as much as 2-03 years. A general relation between the frequency of the spots and +he variation of the magnetic needle is shown by the numbers which have been given in the table of Schwabe's results. This relation has been most closely studied by Wolf. He denotes by g the number of groups of spots, seen on any day on the sun, counting each isolated spot as a group ; by/ is denoted the number of spots in each group (fy is then proportional to the spotted area) ; by A? a coefficient depending upon the size of the telescope used for obser- vation, and by r the daily relative number so called ; then he sup. poses r = kif+10-g). From the daily relative numbers are formed the mean monthly and the mean annual relative numbers i'. Then, according to Wolf, if v is the mean annual variation of the magnetic needle at any place, two constants for that place, a and /?, can be found, so that the following formula is true for all years : V = a + ^-r. Thus for Munich the foimula becomes, and for Prague, V = C'-27 + 0'.051 n V = 5'«80 4- 0'-045 r, and so on. ■ f^ TOTAL ECLIPSES OF THE SUJ^T. 297 Yeah. Munich. Prague. Observed. 12-27 11-70 10-96 9-13 Computed. A Observed. Computed. a 1870 1871 1872 1873 13-77 11-56 1113 9-54 -0-50 + 0-14 -017 -0-42 11-41 11-60 10-70 9-05 12-10 10-89 10-46 8-87 -0-69 + 0-71 + 0-24 + 0-18 The above comparison bears out the conclusion that the magnetic variations are subjected to the same perturba- tions as the development of the solar spots, and it may be said that the changes in the frequency of solar spots and the like changes of magnetic variations show that these two phenomena are dependent the one on the other, or rather upon the same cosmical cause. What this cause is remains as yet unknown. ^ 4. THE SUN'S CHBOMOSFHERE AND CORONA. Phenomena of Total Eclipses. — The beginning of a total solar eclipse is an insignificant phenomenon. It is marked simply by the small black notch made in the lu- minous disk of the sun by the advancing edge or limb of the moon. This always occurs on the western half of the sun, as the moon moves from west to east in its orbit. An hour or more must elapse before the moon has advanced sufficiently far in its orbit to cover the sun's disk. During this +ime the disk of the sun is gradually hidden until it becomes a thin crescent. To the general spectator there is little to notice during the first two thirds of this period from the beginning of the eclipse, unless it be perhaps the altered shapes of the images formed by small holes or apertures. Under ordinary circumstances, the image of the sun, made by the solar rays which pass through a small hole— in a card, for example— are circular in shape, like the •shape of the sun itself. When the sun is crescent, the i»ip"ip iil i 298 ASTRONOMY. image of the sun formed by such rays is also crescent^ and, under favorable circumstances, as in a thick forest where the interstices of the leaves allow such images to be formed, the effect is quite striking. The reason for this phenomenon is obvious. The actual amount of the sun's light may be diminished to two thirds or three fourths of its ordinary amount with- out its being strikingly perceptible to the eye. What is first noticed is the change which takes place in the color of the surrounding landscape, which begins to wear a mid- dy aspect. This grows more and more pronounced, and gives to the adjacent country that weird effect which lend& so much to the impressiveness of a total eclipse. The rea- son for the change of color is simple. We have already said that the sun's atmosphere absorbs a large proportion of the bluer rays, and as this absorption is dependent on the thickness of the solar atmosphere through which the rays must pass, it is plain that just before the sun is total- ly covered the rays by which we see it will be redder than ordinary sunlight, as they are those which come from points near the sun's limb, where they have to pass through the greatest thickness of the sun's atmosphere. The color of the liglit beconies more and more lurid up to the moment when ihe sun has nearly disappeared. If the spectator is upon the top of a high mountain, he can then begin to see the moon's shadow rushing toward him at the rate of a mile in about two seconds. Just as the shadow reaches him there is a sudden increase of darkness — the brighter stars begin to shine in the dark lurid sky, the thin crescent of the sun breaks up into small points or dots of light, which suddenly disappear, and the moon it- self, an intensely black ball, appears to hang isolated in the heavens. An instant afterward, the corona is seen surrounding the black disk of the moon with a soft effulgence quite differ- ent from any other light known to us. Near the moon's limb it is intensely bright, and to the naked eye uniform TOTAL ECLIPSES OF THE SUN. 29» 111 structure ; 5' or 10' from the limb tliis inner corona has a boundary more or less defined, and from this extend streamers and wings of fainter and more nebulous light. These are of various shapes, sizes, and brilliancy. No two solar eclipses yet observed have been alike in this re- spect. These wings seem to vary from time to time, though at nearly every eclipse the same phenomena are described by observers situated at different jjoints along the line of totality. That is, these appearances, though changeable, do not change in the time the moon's shadow requires to pass from Vancouver's Island to Texas, for example, which is some fifty minutes. Superposed upon these wings may be seen (sometimes with the naked eye) the red flames or protuberances which were first discovered during a solar eclipse. These need not be more closely described here, as they can now be studied at any time by aid of the spectroscope. The total phase lasts for a few minutes (never more than six or seven), and during this time, as the eye becomes more and more accustomed to the faint light, the outer corona is seen to stretch further and further away from the sun's limb. At the eclipse of 1878, July 20th, it was seen by Professor Langley, and by one of the writers, to extend more than 6° (about 9,000,000 miles) from the sun's limb. Just before the end of the total phase there is a sudden increase of the brightness of the sky, due to the increased, illumination of the earth's atmosphere near the observer, and in a moment more the sim's rays are again visible, seemingly as bright as ever. From the end of totality till the last contact the phenomena of the first half of the eclipse are repeated in invei-se order. Telescopic Aspect of the Corona. — Such are the ap- pearances to the naked eye. The corona, as seen through a telescope, is, however, of a very complicated structure. The inner corona is usually composed of bright striae or fil- aments separated by darker bands, and some of these lat- 300 ASTRONOMY. ter are sometimes seen to be almost totally black. The appearances are extremely irregular, but they are often as if the inner corona were made up of brushes of light on a darker background. The direction of these brushes is often radial to the sun, especially about the poles, but where the outer corona joins on to the inner these brushes are sometimes bent over so as to join, as it were, the boundaries of the outer light. The great difficulties in the way of studying the corona have been due to the short time at the disposal of the ob- server, and to the great differences which even the best draughtsmen will nuike in their rapid sketches of so com- plicated a phenomenon. The figure of the inner corona on the next page is a copy of one of the best drawings made of the eclipse of 1860, and is inserted chiefly to show the nature of the only drawings possible in the limited time. The numbers refer to the red prominences around the limb . The radial structure of the corona and its different exten- sion and nature at different points are also indicated in the drawing. The figure on page 302, is aoopy of a crayon drawing made in 1878. The best evidence which we can gain of tlie details of tlie corona comes, however, from a series of photographs taken during the whole of totality. A photograph with a short exposure gives the details of the inner corona well, but is not affected by the fainter outlying parts. One of longer exposure shows details further away from the sun's limb, while those near it are lost in a glare of light, being over-exposed, and so on. In this way a series of photographs gives us the means of building up, as it were, the whole corona from its brightest parts near the sun's limb out to the faintest por- tions which will impress themselves on a photographic plate. The corona and red prominences are solar appendages. It was formerly doubtful whether the corona was an atmosphere belonging to the sun or to the moon. At the eclipse of 1860 it was proved by measurements that the red prominences belonged to the sun and not to the moon, since the moon gradually covered them by its motion, they remaining attached to the sun. The corona has also since been shown to be a solar appendage. TOTAL ECLIPSES OF THE SUN. 801 The eclipse of 1851 was total in Sweden and neigh- boring parts, and was very carefully observed. Similar prominences were seen about the sun's limb, and one of 80 bizarre a form as to show that it could by no possibility i Fig. 82. — dkawinq op the conoxA made durino the eclipse of AUGUST 7, 1869. be a mountain or solid mass, since if such had been the case it would inevitably have overturned. It was there- fore a gaseous or cloud-like appendage belonging to the it 302 ASTJtONOMY. Fig. 83. — bun's corona ddking tue eclipse of julv 29, 1878. rilE SUN'S PUOMIXENVES. 303 sun. There ■\vert' otlicrs of various mikI pfrliiips viir^'inj^ 81ki})0s, aiul the Imses of these were connected hy a h)W l)iUKl of serrated ro8o-coh>re(l Hy more astronomers than any preceding eclii)se. Two American astronomers, Professor YoiiN(», of Dartmouth College, and Professor IIakknksh, of the Naval Observatory, especially observed the spec- tr\im of the corona. This spectrum was foimd to consist of one faint greenish line crossing a faint continuous spectrum. The place of this line in the maps of the solar spectrum published by KiuciiiioKF was occupied by a line v/hich he had uttril)Uted to the iron spectrum, and which liad been numbered 1474 in his list, so that it is now spoken of as 1474 K. This line is probably due to some gas which must be present in large and ])ossibly variable quantities in the corona, and which is not known to us on the earth, in this form at least. It is probably a gas even lighter thtm hydro- gen, as the existence of this line has bctn traced 10' or 20' from the sun's limb nearly all around the disk. In the eclipse of July 29th, 1878, which was total in Colorado and Texas, the continuous spectrum of the corona was found to bo crossed by the dark lines of the solar spectrum, showing that the coronal light was composed in part of reflected sunlight. § 6. SOURCES OP THE SUN'S HEAT. Theories of the Stin's Constitution. — No considerable fraction of the heat radiated from the sun returns to it from the celestial spaces, since if it did the earth would intercept some of the returning rays, and the temperature of night would be more like that of noonday. But we know the sun is daily radiating into space 2,170,000,000 times as much heat as is daily received by the earth, and it follows that unless the supply of heat is infinite (which v/e cannot believe), this enormous daily radiation must in time exhaust the supply. When the supply is exhausted, or even seriously trenched upon, the result to the inhab- itants of the earth will be fatal. A slow diminution of im 306 ASTRONOMY. the daily supply of heat would produce a slow change of <;limates from hotter toward colder. The serious results of a fall of 50° in the mean annual temperature of the «arth will be evident when we remember that such a fall would change the climate of France to that of Spitzber- gen. The temperature of the sun cannot be kept up by the mere combustion of its materials. If the sun were solid carbon, and if a constant and adequate supply of oxygen were also present, it has been shown that, at the present rate of radiation, the heat arising from the com- bustion of the mass would not last more than 5000 years. An explanation of the solar heat and light has been fi'iggested, which depends upon the fact that great amounts of Jieat and light are produced by the collision of two rapidly moving heavy bodies, or even by the passage of & heavy body like a meteorite through the earth's atmos- phere. In fact, if we had a certain mass available with which to produce heat in the sun, and if this mass were of the best possible materials to produce heat by burning, it can be shown that, by burning it at the surface of the €un, we should produce vastly less heat than if we simply allowed it to fall into the sun. In the last case, if it fell from the earth's distance, it would give 6000 times more heat than by its burning. The least velocity with which a body from space could fall upon the sun'' surface is in the neigliborhood of 280 miles in a second of time, and the velocity may be as great as 350 miles. From these facts, the meteoric theory of solar heat oris:inated. It is in effect that the heat of the sun is kept up by the impact of meteors upon its surface. No doubt immense numbers of iueteorites fall into the sun daily and hourly, and u: each one of them a certain considerable portion of heat is due. It is found that, to account for the present amount of radiation, meteorites equal in mass to the whole earth would have to fall into the sun every century. It is extremely improbable that a Tiiass one tenth as large as this is added to the sun in this SUPPLY OF SOLAR HEAT. 307 way per century, if for no other reason because the earth itself and every planet would receive ■*^ar more than its present share of meteorites, and would itself become quite hot from this cause alone. There is still another way of accounting for the sun's constant supply of energy, and this has the advantage of appealing to no cause outside of the sun itself in the eX' pianation. It is by supposing the heat, light, etc. , to be generated by a constant and gradual contraction of the dimensions of the solar sphere. As the globe cools by radiation into space, it must contract. In so contracting its ultimate constituent parts are dra\\n nearer together })y their mutual attraction, wherebv a form of enerijv is do- velopcd M'liich can be ti»nsfonued into lieat, light, elec- tricity, or other physical forces. This theory is in complete a&reement with the known laws of force. It also admits of precise comparison with facts, since the laws of heat enablj us, from the known amount of heat radiated, to infer the exact amount of con- traction in inches which the linear dimensions of the sun uiust undergo in order that this supply of heat may be kept unclianged, as it is practically found to be. With the present size of the sun, it is found tlnit it is only necessary to sujipose that its diameter is diminishing at the rate of about 220 feet per year, or 4 miles per century, in order that the supply of heat radiated shall be constant. It is plain that such a change as this may be caking place, since we possess no instrument , sufficiently delicate to have detected a chano-e of even ten times this amount since the invention of the telescope. It nuiy seem a paradoxical conclusion that the cooling of a body may cause it to become hotter. This indeed is true only when we suppose the interior to be gaseous, and not solid or liquid. It is, however, jjroved by theory tiiat this law holds for gaseous masses. , If a spherical nmss of gas be condensed to one lialf the primitive diameter, the central attraction upon any part of its mass willt;' in 308 ASTR('NOMT. creased fourfold, while tlie surface subjected to this attraction will be reduced to one fourth. Hence the pressure per unit of surface will be augmented sixteen times, whil«> the density will be increased but eight times. If the elastic and the gravitating forces were in equilibrium in the original condition of the mass, the temperature must be doubled in order tiiat they may still be in equilibrium when the diameter is reduced to one half. If, however, the primitive body is originally solid or liquid, or if, in the course of time, it becomes so, then this law ceases to hold, and radiation of heat produces a lowering of the temperature of the body, which progressively continues until it is finally reduced to the temperature of surrounding space. We cannot say whetliertlie sun lias yet begun to liquefy in liis interior parts, and hence it is impossible to predict at present tlie duration of liis constant radiation. Theory bhovvs us that after about 5,000,000 years, the sun radiating heat as at present, and still remaining gaseo is. I'^ be re- duced to one half of its present volume, x., souit' prob- able that somewhere about this time the solidification will have begun, and it is roughly esiimated, from this line of argument, that the present conditions of Jieat radi- ation cannot last greatly over 10,000,000 years. The future of the sun (and hence of the earth) cannot, as r/e see, be traced with great exactitude. The past can be more closely followed if we assume (which is tolerably safej that the sun up to the present has been a gaseous, and not a solid or liquid mass. Four hundred years ago, then, the sun was about 16 miles greater in diamet'r than now ; and if we suppose this process of contt <•- tion to have regularly gone on at the same rate ^..u imcertain supposition), we can fix a date when the 'ij' filled any given space, out even o the orbit of JV^ej)- tune — that is, to the time wlien the solar system insisted of but one body, and that a gaseous or nebu.v. one. It will subsequently be seen that the ideas here reached dimsteriori have a striking analogy to the a priori ideas of Kant and La Plac^k. It is not tobeHaken for granted, however, tli' the amount of heat to be derived from the contraction '><^ the AOE OF TUE SUN. 309 sun's dimensions is infinite, nc matter how large the prim- itive dimensions may have been. A body falling from any distance to the snn can only have a certain finite veloc- ity depending on this distance and the mass of the sun itself, which, even if the fall be from an infinite distance, cpnnot exceed, for the snn, 350 miles per second. In the same way the amount of heat generated by the con- traction of the sun's volume from any size to any other is finite, and not infinite. It has been shown that if the sun has always been radiating heat at its present rate, and if it had originally ^filled all space, it has required 18,000,000 years to contract to its present volume. In other words, assuming the pres- ent rate of radiation, and taking the most favorable case, the age of Ihe sun does not exceed 18,000,000 years. The earth, is of course, less aged. The supposition lying at the base of this estimate is that the radiation of th ^ sun has been constant throughout the whole period. This is quite imlikely, Jind any changes in this datum affect greatly the final number of years which we l.avc assigned. While this number may be greatly in error, yet the }ncthod of obtaining it seems, in the present state of science, to be satisfactory, and the main conclusion remain? that the past of the sun is finite, and that in all probability its future is a limited one. The exact number of centuries that it is to last are of no moment even wore the data at hand to ob- tain them : the essential point is, that, so far as we can see, the fcim, and incidentally the solar system, lias a finite past and a limited future, "ind that, like other natural ob- jects, it passes through its regular stages of birth, vigor, decay, and death, in one order of progress. CHAPTER III. U: THE INFERIOR PLxiNETS. § 1. MOTIONS AND ASPECTS. IE inferior planets are tliose whose orbits lie between tlu sun and the orbit of the earth. Commencing with the more distant ones, they com23rise Venus, Mercury, and, in the opinion of some astronomers, a planet called Yulcaiiy or a gronj) of planets, inside the orbit of Mercury. The planets Mercury 'a\\(S. T'6'm'.6' have so much in connnon that a large part of what we have to say of one can be applied to the other witli but little modification. The real and apparent motions of these planets have already been briefly described in Part I., Chapter lY. It will be remembered that, in accordance with Kkpler's third law, tlieir periods of revolution around the sun are less than that of the earth. Consequently they overtake the latter between successive i ferior conjunctions. The interval between these conjunctions is about four months in the case of 2[ercury, and between nineteen and twentv months in that of Yerius. At the end of this period each rej'Jeats the same series of motions relative to the sun. What these motions are can be readily seen by studying Fig. Si. In the first place, suppose the earth, at any point, E, of its orbit, and if we draw a line, EL or EM, from E, tangent to the orbit of either of these planets, it is evident that the angle which this line makes with that drawn to the sun is the greatest elongation of the planet froju the sun. The orbits being ecc>',ntric, this ASPECTS OF MERCURY AND VENUS. 311 four and this ve to 11 by iirtli, EL tliese uakes on of this elongation varies witli t)ie position of the eartli. In the case of Mercury it ranges from 16° to 29°, while in tlie case of VenuSy the orbit of which is nearly circnlar, it varies very little from 45°. These planets, therefore, seem to have an oscillating motion, first swinging toward the east of the sun, and then toward the west of it, as already explained in Part I., Chapter lY. Since, owing to the anmial revo- lution of the earth, the Bun has a constant east- ward motion among the stars, these planets must have, on the whole, a correspop ling though intermittent motion in the same direction. Therefore the ancient astronomers supposed their period of revolution to be one year, the same as that of the sun. If, again, we draw a line ESC irom. the earth through the sun, it is evident that the first point /, in which tliis line cuts the orbit of the planet, or the point of inferior conjunction, will (leaving eccentricity out of the question") be the least distance of the planet from the earth, while the second point C, or the point of superior conjunction, on the op- posite side of the sun, will be Fig. 84. the greatest distance. Owing to > the difference of these distances, the apparent magnitude of these planets, as seen from the earth, is subject to great variations. Fig. 85 shows these variations in the case of MercAiry., A representing its apparent magnitude when at its greatest •distance, B when at its mean distance, and C when at its Fig. 85.— apparent magni- tudes OF THE DISK OP MEUCUUY. 312 ASTRONOMY. m least distanro. In tlie case of Yeiius (Fig. 86) the laria* tions are much greater tliaii in that of Mercury, the great- est distance, 1-72, being more than six times the least distance, which is only • 28. Tlie variations of apparent magnitude are therefore great in the same proportion. In thus representing the apparent angular magnitude of these planets, we suppose their whole disks to be visible, as they would be if they shone by their own light. But since they can be seen only by the reflected light of the sun, only those portions of the disk can be seen which are at the same time visible from the sun and from the earth. A very little consideration will show that the proportion of the disk which can be seen constantly diminishes as tha planet approaches the earth, and looks larger. Pig. 86. — ^apparent magnitudes op disk op venus. "When the planet is at its greatest distance, or in superior conjunction (6', Fig. 8-4), its whole illuminated hemisphere can be seen from the earth. As it moves around and ap- proaches the earth, the illuminated hemisphere is gradually turned from us. At the point of greatest elongation, M or Z, one half the hemisphere is visible, and tlie planet has the form of the moon at first or second quarter. As it approaches inferior conjunction, the apparent visible disk assumes the form of a crescent, which becomes thinner and thinner as the planet approaches the sun. Fig. 87 shows the apparent disk of Mercury at various times during its synodic revolution. The planet will ap- pear brightest when this disk has the greatest surface. ASPECTS OF MERCURY AND VENUS. 313 lOUS ap- ace» This occurs about lialf way between greatest elongation tnd inferior conjunction. In consequence of the clianges in the brilhancy of these phinets produced by the variations of distance, and those produced by tlie variations in tlie proportion of ilhnninated disk visible from the earth, partially compensating each other, their actual brilliancy is not subject to such great variations as might have been expected. As a general rule, Mercury shiiies with a light exceeding that of a star of the first magnitude. But owing to its proximity to the sun, it can never be seen by the naked eye except in tlie west a short time after sunset, and in the east a little be- fore sumise. It is then of necessity near the horizon, and Tig. 87. — appearance of mercup.y at different points op its ORBIT. therefore does not seem so bright as if it were at a greater altitude. In our latitudes we might almost say that it is never visible except in the morning or evening twiliglit. In higher latitudes, or in regions where the air is less transparent, it is scarcely ever visible without a telescope. It is said that Copernicus died without ever obtaining a view of the planet Mercury. On the other hand, the planet Yeans is, next to the sun and moon, the most brilliant object in the heavens. It is BO much brighter than any fixed star that there can seldom be any ditiiculty in identifying it. The unpractised ob- server might under some circumstances fin . From ofractivo u that of 10 its ca- ,'ortliy of NUS. Diirtli and tlio plic- 3(1 around ilent that ion. But I ecliptic, cion takes a transit, til, must — that is, 7'y at the iscending ly 7th and within a within a hs is now lof th« orbit ] interesting iwhichin- lay occur, be found that from |l>r Mercury to be only TRANSITS Of MKHCUliY. 311) about 250^, and therefore that of the nscendiiifj node is 7<>°. The earth has these longitudes on .lune Oth and De- cember 7th of each vear. Transits of Viniis can there- fore occur only within two or three days of these times. Recurrence of Transits of Mercury.— Tlio transits of Mer- curu and Viiiiih rt'cur in cyclos wiiirh ri'scnible tlic fij^htct'ii- yi'ar cycle of eclipses, but in wiiich the precision of the recurrence IS less striking. From the mean motions of Mfrcunj and the earth already given, we find that the mean synodic period of Merninj is, in (U'cimals of a .lulian year, 0>-;jn2.')0. Tlirec sjniodic periods are tricrefore some eighteen days less than a year. If, then, we suppose nn inferior conjunction of Meri'ury to occur exactly at a node, the third conjunction following will take i)lace about eighteen daja before tlie earth again reaches the node, and therefore about 18" from the node, since the earth moves nearly 1° in a dav. This is far outside the limit of a transit ; we must, therefore, wait until another conjunction occurs near the same place. To find when this will be, the successive vulgar fractions which converge toward the value of the above period may be found by the method of con- tinued fractions. The first six of t' ise fractions are: T "nr ¥T if lo-r 4 i4y Here the denominators are numbers of synodic periods, while tho numerators are the apjH'oxmiate corresponding number of years. By actual nuiltiplication we find : 3 Periods := 0>-9517 sun, and the ciiole diawn around it the orbit of the earth. FlO. 88. — CON.TTJNCTION8 OF VENUS. TRANSITS OF VENUS. 3a I insits of nto May jvember nsits are mn, and May tran- !e as nu- re sliglitly or the en- ■f series, it ^ears after very near thin a few probably 1911. centuries xact than motion of in motion jrds, Veiiug •ound the time thut ilutions— During 5 inferior cause the ions more [uently, if in inferior . shall, at 'e another ftfth in the same It will, ime tinii! the same represent ihe earth. Suppose also that at the moment of the infen conjunction of Venus, we draw a straight line S 1 through F<»;, ,, ^ lo the earth at 1. We shall then havp to wa.t about 1^ years f- -r other inferior con- junction, during which *^,me the earth will have made one revolu- tion and ^ of another, id Venus 2^ revolutiong. The straiirht line drawn through tiie point of inferior conjunction will then be S 2. The third conjunction will in the same way take place in the posi- tion S 3, which is 1-^ revolutions further advanced ; the fourth in the position S 4, and the fifth in the ])osition -S'5. If the corre- spondence of the motions were exact, the sixth conjunction, at the end of 8 years (5 x 1^ = 8), would again take place in the original position S 1, and all subsequent ones would follow in the same order. All inferior conjunctions would then take place at one of these five points, and no transit would ever be possible unless one of these points should chance to be very near the line of nodes. In fact, however, the correspondence is not perfectly exact, but, at tl.e end of 8 years, the sixth conjunction will take place not «xactly along the line of iiccouiiting for this iin on in accordance with well-established lawn, i vcept iiy supposing matter of some sort to be revolving around tlie sun in the supposed posi- tion. At the same time it is always possible that the effect may be produced by somo unknown cause.* (2) Astronomical records contain upward of twenty instances in which dark bodies have been supposed to be -con in transit across the disk of the sun. If we suppose these ol crvatioiis to be all perfectly correct, the existence of a great number of considerable planets within the orbit of Mercury would be placed beyond doubt. But a critical analysis shows that these observations, cons' red as a class, are not entitled to the slightest credence. In tli irst place, * An electro-dynamic theory of attraction has been within (he past twenty years suggested by several German physicists, which involves a small variation from the ordinary theory of gravitation. It has been shown that, by supposing this theorv true, the motion of the perihelion Cii Mercury could be accounted for by the attraction of the sun. 324 ASTRONOMY. ■«- scarcely any of them were made by experienced observers with powerful instruments. It is very easy for an unpractised observer to mistake a round solar snot for a planet in transit. It may there- fore be supposed that in many cases the observer saw nothing but a spot on the sun. In fact, the very last instance of the kind on record was an observation by Webeu at Peckeloh, on April 4th, 1876. He published an account of his observation, which he sup- posed was that of a planet, but when the publication reached other observers, who had been examining the sun at the same time, it was shown conclusively that what he saw was nothing more than an unusually round solar spot. Again, in most of the cases referred to, the object seen was described as of such magnitude that it could not fail to have been noticed during total eclipses if it had any real existence. It is also to be noted that if such planets ex- isted they would freqiiently pass over the disk of the sim. Dur- iiifj the past fifty years tiie sun has been observed almost every day with the greatest assiduity by eminent observers, armed with p >\verful instruments, who have made the study of the sun's sur- face and spots the principal work of their lives. None of these observers has ever recorded the transit of an unknown planet. This evidence, though negative in form, is, under the circumstances, con- clusive against the existence of such a planet of such magnitude as to be visible in transit with ordinary instruments (3) The observations of Professor Watson during the total eclipse above mentioned seem to afford the strongest evidence yet obtained in favor of the real existence of the planet. His mode of proceeding was briefly this : Sweeping to the west of the sun during the eclipse, he saw two objects in positions where, suppos- ing the pointing of his telescope accurately known, no fixed star existed. There is, however, a pair of known stars, one of which is about a degree distant from one of the unknown objects, and the other about the same distance and direction from the second. It is considered by some ihat Professor Watson's supposed planets may have been this pair of stars. Still, if Professor Wai son's planets were capable of producing the motion of the perihelion of Mercury already' referred to, we should regard their existence as placed beyond reasonable doubt. But his observations and the theoretical results of Lk Veruieh do not in any manner strengthen each other, because, if we suppose the observed perturbations in the orbit of Mermrif to be due to planets so small as thoae r n by Watson, tlie nunil)or of these planets must be many thousands. Now, it is very n8 ap- otherft [alleys. Ind re- names. |w that Irch, it has become more and more evident that tlie surface of the moon is totally unlike that of our earth. There are no oceans, seas, rivers, air, clouds, or vapor. We can hardly suppose that animal or vegetable life exists under such circumstances, the fundamental conditions of such ex- istence on our earth being entirely wanting. We might almost as well suppose a piece of granite or lava to be the abode of life as the surface of the moon to be such. Before proceeding with a description of the lunar sur- face, as made known to us by the telescopes of the present time, it will be well to give some estimates of the visi- bility of objects on the moon by means of our instruments. Speaking in a rough way, we may say that the length of one mile on the moon would, as seen from tiie earth, sub- tend an angle of 1" of arc. More exactly, the angle sub- tended would range between 0"-8 and ()"•{), according to the varying distance of the moon. In order that an ob- ject nuiy be plaiidy visible to the naked (iyo, it nnist sub- tend an angle of nearly 1'. Consequently, a magnifying power of GO is required to render a round object one mile in diameter on the surface of the moon plainly visible. Starting from this fact, we may readily form the follow- ing table, showing the diametei*s of the smallest objects that can be seen with different magnifying powers, alw^ays assuming that vision with these powers is perfect : Power 60 ; diameter of object 1 mile. Power 150 ; diameter 2000 feet. Power 500 ; diameter GOO feet. Power 1000 ; diameter 300 feet. Power 2000 ; diameter 150 feet. If telescopic power could be increased indefinitely, there would of coarse be no limit to the minuteness of an ob- ject visible on the moon's surface. But the necessary imperfections of all telescopes are such that only in extra- ordinary cases can any thing be gained by increasing the 328 ASTIiOJiOMY. magnifying power beyond 1000. The inlluenee of warm and cold currents in our atniosj^liero is such as will for- ever prevent the advantageous use of high magnifying powers. After a certain limit wo see nothing more by increasing the power, vision becoming indistinct in pro- portion as the power is increiused. It may be doubted whether the moon was ever seen through a telescope to so good advantage as she would be seen with a magnifying power of 500, unaccompanied by any drawback from at- mospheric vibrations or imperfection of the telescope. In other words, it is hardly likely that an object less than (500 feet in extent can ever be seen on the moon bv any telescope whatever, unless it becomes possible to mount the instrument above the atmos])her(; *»f the earth. It is there- fore only the great features on the surface of the moon, and not the minute ones, which can be made out with the telescope. Character of the Moon's Surface. — The most striking point of difference between the earth and moon is seen in the total absence from the latter of any thing that looks like an undulating surface. Ko formations similar to our valleys and mountain-chains have been detected. The lowest surface of the moon which can be seen with the telescope appears to be nearly smooth and Hat, or, to epeak more exactly, spherical (because the moon is a sphere). This surface has different shades of color in different regions. Some portions are of a bright, silvery tint, while others have a dark gray appearance. These dif- ferences of tint seem to arise from differences of material. Upon this surface as a foundation are built numerous formations of various sizes, but all of a very simple char- acter. Their general form can be made out by the aid of Fig. 89, and their dimensions by the scale of miles at the bottom of it. The largest and most prominent features are known as craters. They have a typical form consisting of a round or oval rugged wall rising from the plane in the maimer of a circular fortification. These THE MOON'S SURFACE. 3",>9 walls are t'iV(|iu;i.tl_v from three to six thuiisaiul inetrt's in height, very rough uiid broken. In tlieir interior we see Fig. 89. — lunar landscape {Mare Crmum). (From a pbotoKraph taken at the Ijiok Observatory.) the plane surface of the moon already doscrihed. It is, however, generally covered with fragments or broken up 3*) ASTJtONOM r. It by small inequalities so as not to be easily made out. In the centre of the craters we frequently find a conical for- mation rising up to a considerable height, and much larger than the ine(|ualities just described. In the craters we have a vague resemblance to volcanic formations upon the earth, the principal difi'erence being that their niagnitude is very much greater than any thing known here. The diameter of the larger ones ranges from 50 to 2i)0 kilo- metres, while the snudlest are so minute as to be hardly visilde with the telesco[)e. When the moon is oidy a few days old, the sun's rays strike very obliquely upon the lunar mountains, and they cast long shadows. From the known j)osition of the sun, moon, and earth, and from the measured length of these shadows, the heights of the mountains can be calculated. It is thi;s found tliat some of the mountains near the south pole rise to a height of 8000 or 9000 metres (from 25,000 to 80,(t0(» feet) above the general surface of the moon. Heights of from 3000 to 7* ►00 metres are very conunon over almost the whole lunar surface. Kext to the so-called craters visible on the lunar disk, the most curious features are certain long bright streaks, which the Germans ca'll ri/f-f or furrows. These extend in long radiations over certain of the craters, aiul have the appearance of cracks in the lunar surface which have been subsequently filled by a l)rilliant white material. Na- SMYTH and Cakpkntku have described some experiments designed to produce this appearance artificially. They took hollow glass globes, filled them with water, and heat- ed them until the surface was cracked. The cracks gen- erated at the weakest point of the surface radiate from the point in a manner strikingly similar in appearance to the rills on the moon. It would, however, 1 e premature to conclude that the latter were actually produced in this way. The question of the origin of the lunar features has a theories of terrestri rn)g geology upon wmtm LIGHT AND UEA T OF THE MOON. 331 ■ disk, reuks, jxtend ve the boon Na- ments Thev lieat- gen- m tlie to the re to n this has a upon various (jucHtions respecting tlie past liistory of the moon itself. It has been eonsidered in this aspect by various geologists. Lunar Atmosphere. — The question whether the moon lias ail atmospliere has been much discussed. The only conclusion which luis yet l)een reached is that no j)()sitive evidence of an atmosphere liiis ever heeii ohtained, and that if one exists it is certainly several hundred times rarer than the atmosphere ot" our earth. The most delicate method of detecting one is to determine whether it will refra(rt the light of a ; tiir seen through it. As the moon advances in her monthly course anmnd the earth, she fre(piently appenrs to pass over bright stars. These phe- nomena are called ocrnltnt'tohx. Just before the limb of the moon api)ears to reach the star, the latter will be seen through the moon's atmosphere, if there is one, and will be disi)laced in a direction from the moon's centre. Jhit the most careful observations have failed to show the slightest evidence of any such (lis[»la(^ement. Hence the most delicate test for a lunar atmosphere gives no evi- dence whatever that it exists. The spectra of stars when about to be occulted have also been examined in order to see whether any ahsor])tion lines which might be })roduced by the lunar atmosphere became visible. The evidence in this direction has also been negative. Moreover, the sj)ectrum of the moon itself does not seem to differ in the slightest from that of the sun. We conclude therefore tliar if there is a lunar at- mos])here, it is too rare to exert any sensible absorption upon the rnys of light. Light and Heat of the Moon. — ^^Fany attempts have been made to measure the ratio of the light of the full moon and that of the sun. The results have been very discordant, but all have agreed in showing that the sun emits several hundred thousand times as much light as the full moon. The last and most careful determination is m ^ Xi-i AUTRONOMY. that of Z('»iJ-NKR, who ilnjH the sun to bo r>18,()(M) tiiiioH as bright as tlie full moon. The moon must reflect the heat as well as the lij^ht of the 8UJ1, and inut:t also radiate a small amount of its own heat. JJut the quantities thus retleetedand radiated are so minute that they have defied detection except with the most delicate instruments of research now known. By col- lecting the moon's rays in the focus of om^ of his large re- flecting telescopes, Lord Hosse was able to show that a certain amount of heat is actually received from the moon, and that this amount varies with the moon's phase, as it should do. He also sought to learn how mudi of the moon's heat was reflected and how much radiated. This he did by ascertaining its capacity for passing through glass. It is well known tc students of physics that a very much larger portion of the heat radiated by the sun or other extremely hot bodies will pass through glass than of heat radiated by a cooler body. Experiments show that about 80 per cent of the sun's heat will pass through ordinary optical glass. If the heat of the mu.>n were entirely reflected sun heat, it wonld possess the s:.;no property, and the same proportion would pass through gUiss. But the experiments of Lord Eossk have shown that instead of 80 percent, only 12percent])assed through the glass. As a general result of all his researches, it may be supposed that about six sevenths of the heat given out by the moon is radiated and one seventh reflected. Is there any change on the surface of the Moonp — When the surface of the moon was first found to be cov- ered by craters having the aj>pearance of volcanoes at the surface of the earth, it was very naturally thought that these supposed volcanoes might be still in activity, and ex- hibit themselves to our telescopes by their flames. Sir William Herschkl supposed that he saw several such vol- canoes, and, on his authority, they were long believed to exist. Subsequent observations have shown that this was a mistaken opinion, though a very natural one under the CHANG KS ON TllK MOON. 8b8 sllOAVll circumstances. If we look at tlie moon with a telescope wlien she is three or four days old, we shall see the darker portion of her sviTace, which is not reached hy the sun's rays, to be faintly illuminated by light reHected from the earth. This appearance may always be seen at the right time with the naked tye. If the telescope has an aperture of live inches or upward, and the magnifying power does not exceed ten to the inchy we shall generally sec one or njore spots on this dark hemisphere of the moon so much brighter than the rest of the surface that they may well BUggest the idea of being self-luminous. It is, however, known that these are oidy spots possessing the power of reflecting back an unusually large portion of the earth's light. Not the slightest sound evidence of any incandes- cent eruption at the moon's surface has ever been found. Several 'nstances of supposed changes on the moon's surface hiive been described in recent times. A few years ago a spot known as Linnaeus, near the centre of the inoon'b visible disk, was found to present an appearance entirely different from its represcTitation on the map of Beer and Maedler, nuide loicy years before. More recently Klein, of Cologne, supposed himself to have dis- covered a yet more decided change in another feature of the moon's surface. The question whether these changes are proven is one on which the opinions of astronomers differ. The dithcul- ty of reaching a certain conclusion arises from the fact that each feature necessarily varies in appearance, owing to the different ways in which the sun's light falls upon it. Sometimes the changes are very difficult to account for, even when it is certa'a that they do not arise from any change on the moon itself. Hence while some regard the apparent changes as real, others regard them as due onljr to differences in the mode of illuminutiou. I I CHAPTER V. THE PLANET MARS. § 1. DESCRIPTION OP THE PLANET. Mars is tlio next planet beyond tlie earth in tlie order of distance from tlie sun, being about iialf as far again as the earth. It has a decided red color, by which it may be readily distinguished from all the other planets. Owing to the considerable eccentricity of its orbit, its distance, both from the sun and from the earth, varies in a larger proportion than does that of the other outer planets. At tlio most favorable oppositions, its distance from the earth is about 0-38 of vhe astroviomical unit, or, in round nund)ers, fw, 000, 000 kilometres (35,000,000 of miles). This is greater than the least distance of VenuH^ hnt v/e can nijvertheless obtain a better view of Mars under thess circumstances than of Venus, because when the latter is nearest to us its dark hemisphere is turned toward us, while in the case of Mars and of the outer planets the lvemisi)here turned toward us at oppoelticn is fully illu- minated by the sun. The period of revolution of Ma'^s around the sun is a little less than two years, or, more exactly, 087 days. The snccessive oppositions occur at intervals of two years and one or two moi'lie., the earth having made during this interval a little ^nore than two revolutions around the sun, and the planet Mars a little more than one. The dat(!s of several past and future oppositions are shown in the following table : i OPPOSITIONS OF MARS. 1871 March 20th. 1873 April 27th. 1875 June 20th. 1877 September 5th. 1879 November 12th. 1881 December 26th. 1884 January Slst. 1886 March 6th. 335 3 order irain as it may planets, •bit, its ies in a planets, rom the round miles), but v/e r thess atter is |ard us, ets the lly ilUi- liin is a . The ars and ng this he sun, e dates in the Owing to the unequal motion of the planet, arising from the eccentricity of its orbit, the intervals between suc- cessive oppositions vary from two years and one month to two years and two and a half months. About August 2Gth of each year the earth is in the same direction from the sun as the perihelion of the orbit of Mars. Hence if an opposition occurs about that time, Mars will be very near its perihelion, and at the least possible distance from the earth. At the opposite season of the year, !:oar the end of February, the earth is on the line drawn from the sun to the aphelion of the orbit Mars. The least favorable oppositions are therefore those which occur in February. The distance of Mars i» then about • 65 of the astronomical unit. The favorable oppositions occur at intervals of 15 or 17 years, the penod being that required for the successive increments of one or two months between the times of the year at which successive oppositions occur to make up an entire year. This will be readily seen from the preceding table of the times of opposition, which shows how the op- positions ranged through the entire ye.ar between 1871 and 1886. The opposition of 1877 was remarkably fa- vorable. The next most favorable opposition will occur in 1892. Mars necessarily exhibits phases, buL they are not so well marked as in the case of Vcnus^ because the hemi- sphere which it presents to the observer on the earth is always more than half illuminated. The greatest phase 330 ASTRONOMY. i- -i i< occurs when its direction is 90^^ from that of tlie sun, and even t!ien six sevenths of its disk is ilhiniinuted, like that of the moon, three days before or after full moon. The phases of Mars were observed by Galileo in 1010, who, however, could not describe them with entire certainty. Botatiou of Mars. — The early telesco]MC observers noticed that the disk of Mars did not appear uniform in color and brightness, but had a variegated aspect. In 1606 the celebrated Dr. IIohkrt IIookk found that tlio markings on 2Iars were permanent and moved around in such a way as to show that tlie ])lanet revolved on its axis. The markings given in his drawing can be traced at the present day, and are made use of to determine the exact period of rotation of the planet. Drawings made by IluYOHEXs about the same time have been used in the sanu^ way. So well is tlie rotation fixed by them that the astronomer can now determine the exact number of times the planet has rotated on its axis since these old drawings were made. The period lias been found by Mr. Puoctob to be 21'' .'57'" 22* -7, a result which appears certain to one or two tenths of a second. It is therefore less than an hour greater than the period of rotation of the earth. Surface of Mars. — The most interesting result of these markings v\\ Mars is the probability that its surface is di- versilied by land and water, covered by an atmosphere, and altogether very similar to the surface of the earth. Some ]>()rtions of the surface are of a decided red color, and thus give rise to the well-known fiery aspect of the planet. Other i)arts are of a greenish hue, and are there- fore supposed to be seas. The most striking features are two brilliant white regions, one lying around each pole of the planet. It has been suj)pose(l that this ai)pearance is due to immense masses of snow and ice surrounding the poles. If this weres(», it would indicate that the processes of evap- oration, cloud formation, and condensation of vapor into rain and snow go on at the surface of Mars as at the sur- face ui the earth. A certain amount of color is given to ■Maw ASPECT OF MASS. 337 in, and M that , Tho ), wlio, inty. •servers orin in ct. In [lat tlio Hind in its axis. at the e exact lade by in the that the of times irawings ?KOCT<)K 1 to one than an th. 3f these ce is di- jsphere, i earth, color, of the o there- ircs are le of the G 18 due le poles, of evap- por into the sur- iven to this theory by supposed changes in the magnitude of these ice-caps. But tlie ])roblem of cstablisliing such changes is one of extreme ditticiilty. The only way in which an adequate idea of tliis dithculty can be formed is by the reader himself looking at JIars through a telescope. If he will then note how hard it is to make out the different shades of light and darkness on the planet, and Pia. 90.— TET.Esroptc view of mars. how they must vary in aspect under different conditions of clearness ii» our own iitmosphere, he will readily per- ceive that much evidence is necessary to cstal)lish great changes. All we can say, therefore, is that the formation of tho ice-caps in winter and their melting in summer has some evidence in its favor, but is not yet completely proven. i •'^^p 338 ASTRONoyrr. § 2. SATELLITES OF MABS. Until the year 1877, Mars was supposed to have no sat- ellites, none having ever been seen in the most powerful telescopes. But in August of that year, Professor Hall, of the Naval Observatoiy, instituted a systematic search with the great equatoi'iiil, which resulted in tlie discovery of two such objects. We have already described the op- position of 1877 as an extremely favorable one ; otherwise it would have been hardly possible to detect these bodies. They had never before been seen, partly on account of their extreme minuteness, which rendered them invisible except with powerful instruments and at the most favor- able times, and partly on account of the fact, already al- hidedto, that the favorable oppositions occur only at inter- vals of 15 or 17 years. There are only a few weeks dur- ing each of these intervals when it is practicable to distin- guish them. These satellites are by far the smallest celestial bodies known. It is of course impossible to measure their diam- eters, as they appear in the telescope only as points of light. A very careful estimate of the amount of light which they reflect was made by Professor E. C. Pickkr- ING, Director of the Harvard College Observatory, who calculated how large they ought to be to reflect this light. He thus found that the outer satellite was probably about six miles and the inner one about seven miles in diameter, supposing them to reflect the solar rays precisely as Mars does. The outer one was seen with the telescope at a dis- tance from the earth of 7,000,000 times this diameter. The proportion would be that of a ball two inches in di- ameter viewed at a distance equal to that between the cities of Boston and New York. Such a feat of telescopic seeing is well fitted to give an idea of the power of modern optical instruments. Professor Hall found that the outer satellite, which he called De'unos^ revolves around the planet in 30'' 10'", SATELLITES OF MA US. 3a{» no sat- werfiil Hall, search scovery the op- iierwise bodies. Jllllt of 11 visible favor- iady al- it inter- ks dur- t distiii- bodies r diam- )ints of )f hght ICKKR- y, who is hght. about fimeter, Mars a dis- imeter. \% in di- ;en the [escopic Inodem and tlie inner one, calk'd PhoJio^^ in 7'' 38'". Tlie hitter is only 5800 niik's iVuni the centre ot" JA?/v, and less than 4000 miles from its surface. \. would therefore be almost possible with one of our telescopes on the surface of Mars to see an object the size of a large animal on the .satellite. This short distance and rapid revolution make the imuM- satellite of 31,(MI0,00() kilometres (4S(>,000,- 000 miles). His diameter is 140,000 kilometres, corre- sponding? to a mean apparent diameter, as seen from the sun of 36" -5. His linear diameter is about -j^, his surface is j-^jj, and liis volume yxsV^ ^''''*' ^^ ^^'^ ^"'^- ^^'^ mass is Ysj-g, and his density is tlius nearly the same as the sun's — viz., 0-24 of the earth's. He rotates on his axis in 1)'' 55'" 20% He is attended by four satellites, which were discovei'ed hy Galileo on January 7th, KUO. He named them in lionor of the Mkdk^is, the Mcdleean stdra. These satellites were independently discovered on January lOth, KUO, by Haruiot, of England, who observed them through several subsequent years. SnioN Makius also appears to have early observed them, and the honor of their discovery is claimed for him. They are now known as Satellites I, II, III, and IV, I being the nearest. The surface of Jupiter has been carefully studied with the telescopic, particularly within the past 20 years. Al- though further from us than Jfars, the details of his disk 'ire much easier to recognize. The most characteristio features are given in the drawings appended. These feat- ures are, fratly^ the dark bands of the equatorial regions, and, seeondlyy the cloud-like forms spread over nearly the whole surface. At the limb all these details become indis- 1 344 ASTli(L\OMy. tiiu't, aiul finiilly vaiiisli, thus iruiicatini; a highly aLsorptive Jitiiiospheiv. The ligiit froin the ceiitrL' of the disk is twice us bright as that fnuii the ])oIes (AK.\(a»). The h.mds can he seen with iiistniiiierits no more powerful than those- used hy (i.vMi.Ko, yi't lie iiiak«'.s uo irientiou of theui, al- though they were st en hy Zrccni, Fontana, ami others he- fore 1 »!;{;}. ill voiiKNs (1 <)."»'.>) u which we must look witli some distrust, as since lOdtt they have constantly been seen darker than the rest of the ])lanet. The color of the bands isfr'<|uently described as a brick- ied, but one of the authors has nuide careful studies in FlO. 01.— TELESCOPIC VIEW OF JUPITEn AND HIS 8ATRLLITE8. color of this ])lanet, and linds the prevailing tint to bo a salmon color, exactly similar to the color of JA/r.v. The position of the bands varies in latitude, and the shapes of the limiting curves also (diange from day to day ; but in the main they renuiin as ])ermam'nt features of the region to which they belonic. Two such bands are usuallv vis- ible, but often more are seen. For example, Cassixi (109(», Decend)er KUh) saw six j)arallel bands extending completely around the planet. IIi:i4senKr., in the year 1708, attributed the aspects of the bands to zones of the planet's atmosphere more traiKpiil and less filled with clouds than the remaining j)ortions, so as to permit the ASPECT OF JVl'llHli. 345 rorigliti'r tint to these hitter. The eolur of X\\v hands seems to vary from time to time, and tiieir iMirderniii; lines sometimes alter with such rapidity as to show that tliese l)()rderrt are formed ITS SHADOW SKKN ON IT. brilliant circular white masses, hut oftenerthey are similar in form to a series of white cunmlous chmds such as are frequently seen piled up near the li(»ri7,on on a summer's day. The hands themselves seem freuds luive often u motion of their own, which is also evident from otiier con* Bi(U'ratit>ns. The foUowin^ results of observation of spots situated ill various regions of the planet will illustrate this : C'AssiNr 1005. Hkkhiiiki 177H, 1Ie»s( iiKi, 17TU, SciIHOKTKlt 178.'), Hekii & Madm.u iH;jr), Airy... is:!.!, SciiMiuT 180:^, rotation time = h. m. I. 9 50 00 y 55 40 50 48 S) 50 50 9 55 20 9 55 21 9 55 30 § 2. THE SATELLITES OP JUPITEK. Motions of the Satellites. — The four satellites movo about Ji(j/!f>'/' from west to east in nearly circular orbits. When one of these satellites passes between the sun and Jupiter^ it casts a shadow uj)on J \i inter'' s iXxAs. (see Fig. t>2) precisely as the shadow of our moon is thrown Ui)on the earth in a solar eclii)se. If the satellite j)asses through Juptler^H own shadow in its revolution, an eclipse of this satellite takes place. If it jiasses between the earth and Jupltt'i'^ it is projected upon Jiq)lter''s disk, and we have a transit ; if Jup'drr is between the earth and the satellite, an occultation of the latter occurs. All these phenomena can be seen from the earth with a common telescope, and the times of observation are all found predicted in the Nautical Alnia)ia<\ In this way we are sure that the black s]>ots which we see moving across the disk of Jupiter are really the shadows of the satellites themselves, aiul not})he- nomena to be otherwise explained. These shadows being seen black upon Jupiter'' n surface, show tliat this planet shines by reflecting the light of the sun. I rough of this i-th Jind hiive a itc'llite, loniena 10, and ill the black tcr are ot phe- heing planet HATHI.LITHS OF JUniTKR. 347 ToloBcopio Appoaranco of tho Satollitcs. — Frulor ordi- nary circiiinstaiici'H, the sattllitos oi Jn^t'it*!' arc soon to liavo (linkH— tliat is, not to ho niero points of ligiit. I'n- der very favorahlo coiulitioms, inurkings have Iktoii seen on these disi\H, and it is very onrious that tiie anoniahms appearances gi von in Fig. !>;{ (i)y I*r. II.\stin({s) have been soen at various times by other good ()hsi>rvers, as Skcchi, JJawks, ami RuTiiKKFLiti). Satellite 111, which is niiieh the largest, has decided markings on its face ; IV some- times ai)pears, iw in the ligure, to have its circular outlino C •• HI IV I FlO. 93. — TELESCOPIC AlTEAltANCE OF JIJPITEU'S SATELLITES. cut off by right lines, and satellite I sometimes appears gibbous. The opportunities for observing these appear- ances are so rare that nothing is known beyond the hare fact of their existence, and no plausil)le exphmation of the ligure shown in IV has been given. Phenomena of the Satellites. — The plienoinemv of tlie satel- litt's are illustrated in Fig. 1)4. Here .S represents the sun, ^1 T tlie orl)it of tiie eartli (tiie earth itself beinj^ at 7'), the outer circle the orbit of Jupiter, anil the four small circles upon the latter four dillerent positions of the orbit of a satellite. In the centre of each of the satellite orbits will be seen u small white circle dcsiffiied to rej)resent the planet Jupiter itself. The dotted lines drawn from each edge of the sun to tlie corresponding edges of the planet and continued until they meet in a point show the outlines of the shadow of Jupiter. liCt us Jirst consider the position of Jupiter marked ,7 to the left of the figure, it being then in opposition to the sun. The observer on the earth at T could not then see an object anywhere in tho shadow of Jupiter because the latter is entirely behind the planet. Hence, as the satellite moves around, he will see it disap|)ear behind the rigiit-hand limb of the planet and reappear from the left-hand limb. Such a phenomenon is called an occultation, and is desig- nated as disappearance or reappearance, according to the ])liase. It may be renr.arked, iiowever, that the inclination of the outer satellite to the orbit of Jujnter is so great that it sometimes passes fii 348 ASTliOXOMY. entirely above or below the planet, and therefore is not oeculteci iit all. Let us next (consider Ju)>ifer in the position J'' near the bottom of the figure, the shadow, as before, pointing Intni the planet directh away from the suu. If the shadow were a visible object, the ob- server on the earth at 7'c(nild see it projected out on the right of the planet, because he is not in the line between Ju/iitcr and the siui. Hence as a satellite nwves around and enters the shadow, he will see it disappear from sight, owing to the sunlight being cut otT ; this Fro. 94.— pnK>'OMKNA of jtrrtTEH's batkt-mtes. Is oallcrl an ecU/ise tfiKopprnranre. If the satellite is one of the two outer ones, he will l)e able to see it reappear again after it comes out of the shadow before it is occulted behind the planet. Soon afterward the occidtation vid occur, and it will afterward reappear on the left. In the case of the inner or first satellite, how- ever, the point of emergence from the shadow is hidden behind the planet. consecpiently the observer, after it once disn].pears in the shad- ow, will not see it reappear until it emerges from behind the planet. If the planet is iu the position J', the satellite will be occulted SATELLITES OF jupithh. 340 Iho two conit's tcrwanl how- lind the V* shapfarances are, for convenience, represented in the figure? as corresponding to dilTerent positions of Jupittr in his orbit, the earth having the sanu' position in all ; biit since Jupiter revolves around the sun only once in twelve years, the changes of relative ])osition really c ifspond to dilTerent jiositions of the earth in its orbit during the coiirse «)f the year. The satellites com|)letely diaiippear from t'-lescopic view when they t'nter tlui shadow of the planet. This seems to show that neither planet nor satellite is self-luminctus to any great extent. If the satellite were self-lumino\is, it would be seen by its own light, and if the planet were luminous the satellite might be seen by the re- flected light of tl."' jdanet. The motions of these objects are conne'-ted by two curious and important relr.tions tliscovered by L.v I'i.ack, and expressed as UA- lows: I. Thf mi (III }ii()fi(>:i of' the JjikI xatiVitc tulilnl to ti'in' tfw mean motion of the third is ixdctli/ eqinil to thne times the menii motion of the seeoiiil. II. Jf' to the menu loniiitiufe of the ihxt Kitilliie ire mhl tirirr the ineiiu loiKjitudi of thi thin/, ninl fnilitinrf thue times the iiunn fomjitmle of theseroiid, thi iti^p'en nee is ofirat/s INO . The first of these relations is sliown in the following tabic of the mvun daily motions of the (satellites: Satellite I in one day moves 208 "^HOO II " " IIU •;n48 III " •' 50 .;Ji77 IV " " ',M -5711 Motion of Sat. '.lit.' 1 2o:{ 4800 ..wice that of Sntt llitr 111 100 O;?.")-! Slim ;i04 -1244 Three times motion of Sattllitc II iU)4 -1244 Observations sliowed that this condition was fulfilled as exactly as possible, but the discovery of L.v Pi.AtK consisted in showing that if the approximate <'oiii(idence of the mean motions was once »'s- tablished, thi-y co

gous to that of the moon, which always ])rcacnts the same face t(» us and which always will since the rela- tion being unee uiipruxinmtcly true, it will become cxact untl ever remain so. r — .'v,y.^!^!— ' ' 350 ASrnONOMY. The discovery of the i^^raduiil propagation o* light by means of these satellites has already been deseribed, r^nd it has also been ex- plained that they are of use in the rough vletermination of longi- tudes. To facilitat(i their observation, the Naiiticai Almanac gives complete ephemerides of their phenomena. A specimen of a por- tion of such an ephcnieris for 1H05, March 7th, 8th, and 9th, is added. The times an* Washington mean times. The letter >r in- dicates that the phenomenon is visible i:i Washington. 1866— Maiich. (/. h. m. 8 Eclipse Disapp. 18 27 88-5 Occult. Rcapp. 7 21 56 III. Sli.tdow Ingresfl 8 7 27 III. Shadow Egrexs 8 9 58 III. Transit In^rrt-sa 8 13 31 11. Kclipse Disapp. 8 13 1 23.7 III. Transit Kgr»-H8 w. 8 15 6 II. Eclipee Hen pp. w 8 15 24 IM II. Occult. l)isap|i. w. 8 15 27 Shadow IiigrcMS w. 8 15 43 Transit 1 Illness w. 8 16 58 Siiadow Egress 8 17 57 II'. Occult. Kt'Hpp. 8 17 59 Transit Ejjrcss 8 19 13 Kclipse DisHjip. U 13 T^Tr 59.4 Occult. lleapp. w. 9 16 2r» Suppos«! an observer near New York City to have determined his local time accurately. This is abour 13'" faster than Washington time. On 1865, March 8th, he woidd look for the reappearance of II at about 15'' 34'" of his local time. Suppose he observed \t, at 15'' 36"' 22" -7 of his time : then his m"ridian is 12"" ll'-6 cast of Washington. The dilHculty of observing these eclipses with accuracy, aiul the fact that the aperture of the telescope employed has an important etfect on th<' appearances seen, have kept this method from it wide utility, which it at lirst seemed to ))romise. The apparent dianu'tcrs of these satellites have been measured by Stuuvk, Skcciii, and others, and the best results are : I. 1 "0: II. •!>; Ill, l"-5: IV, l"-3. Their masses {Jif/iifri =\) are : 1, OdOdOlT ; II, 00(1023; III, 000088; IV, 0-000043. The third satellite is thus the largest, and it lias about the den- sity of the ])lanet. The true diameters vary from 2200 to 3700 miles. The vctlumcr of 11 is about that of our moon ; III is probably about one eighth the sivx of our earth. Variations in the lit^ht of these bodies have constantly been noticed which have been supposed to be due to the fact that they turned on their axes once in a revolution, and thus |)resented various faces to us. The recent accurate ])hot()inetric measures of Enciki- MANN show that this hypothesis will not account for all the changes observed, some of whicli appear to be quite sudden. Rnns of L'en ex- longi- ,c gives a por- 9th, is r Win- ' 88-5 J r i 1 1 23-7 15 4 IM 7 3 8 7 »g 3 r)9.4 jr» inea his jingtou iince of rvcd it, ' 11"0 (SOS with m ployed ept thia inise. ured by the don- to ;{7()0 probftbly ly been hut thoy 1 variovis Enoki- ohiinges SATELLITES OF JUPITER. 351 3 O H O CHAPTER YiiL I i 1 fii SATUnX AND ITS SYSTEM § 1. GENEBAL DESCRIPTION. Sahirn is tlie most distant of the major planets known to the ancients. It revolves around tlie sun in 29^ years, at a mean distance of about 1,400,000,000 kilometres (882,000,000 miles). The angular diameter of the ball of the planet is about l«r'.2, corresponding to a true diam- eter of about 1 I0,00(i kilometres (7<>,.500 miles). Its diam- eter is therefore nearly nine times and its volume about 700 times that of the earth. It is remarV:il)lo for its small density, which, so far as known, is k>s than that of any other heaveidy body, and even less tnaii that of water. Consequently, it cannot be composed of rocks, like those which form our earth. It revolves on its axis, according to the recent observations of Professor IIai.t,, in lO'' 14'" 24% or less than half a day. Saturn is ])erhaj)s the most remarkable planet in the so- lar system, being itself the centre of a system «)f its own, altogether uidike any thing else m the heavens. Its most noteworthy feature is seen in a pair of rings which sur- round it at a considerable distance from the planet itself. Outside v)f these rings revolve no less than eight satellites, or twice the greatest Jiumber kiu)wn to surround any other ])lanet. ^hi} planet, rings, and satellites are alto- getlier called the Sdlurnian ,<>5 it was found by Ball, of England, that what IliiY(MiKN8 had seen as a single ring was really two. A division extended all the way around uear the outer edge. This division is shown in the figures. In 1850 the Messi-s. Bond, of Cambridge, found that there was a third ring, of a dusky and luibulous aspect, inside the other two, or rather attached to the inner edge of the inner ring. It is tlierefore known as JiomVs dusky ring. It had not been before fully descril)cd owing to its dark- ness of color, which made it aditiicult object to see except with a good telescope. It is not separated from the bright ring, but seems as if attached to it. The latter shades off toward its inner edge, which merges gradually into the dusky ring so as to make it difficult to decide precisely where it ends and tlio t^usky ring begins. The latte»* ex- tends about one half wuy from the inner edge of the bright 1 ing to the ball of the })lanet. Aspect of the Bings. — As Safurn revolves around the sun, the plane of the rings remains parallel to itself. Thar is, if we consider a straight line passing through tiie centre of the planet, perpendicular to the plane of the ring, a^ the axis of the latter, this axis will always point in the siime direction. In tiiis respect, the motion is similar t(* Biisible t until ;bmted Biiiark- the tri- logo- [innnnn read — lerente, le ring, lat what wo. A 3r edge. lat there ;, inside e of the 'If ring. ts dark- except e bright ades off iito the )rocisely tte>* ex- of the mnd the That le centre ring a> in the iiiihir to liIN(JtS OF HA TURN. 3o7 that of tlie earth around tlie sun. Tiio ring of Saturn is incHned about 27° to the plane of its orbit. Conse- quently, as the ])lanet revolves anmnd the sun, there is a change in the direction in which the sun shines upon it similar to that which produces the change of seasons upon the earth, as shown in Fig. 4(}, l)age 109. The corresponding changes for Saturn arc shown in Fig. 97. During each revolution of Saturn the plane FlO. 97.— DIKFERKNT ASPECTS OF THE RINO OF SATURN AS SEEIT FKOM THE EARTH. of the ring passes tlmmgli the sun twice. This occurred in the years 18(12 and 1S78, at two opi)ositc \m>\\\{<, of the orhit, as shown in the Hgurc. At two otlicr points, mid- way between these, the sun shines ujx)!! the plane of the ring at its greatest iiiclination, about 27^ Since the earth is little more than one tenth as far from the sun as Sat- urn is, an observer always sees Saturn nearly, but not '^^uite, as if lie were upon the sun. Hence at certain timea 358 AsruONOMY. tlio rings of Saturn aro Keen edgeways, wliilo at other times they are at an inclination of 27", tiie as])ect depend- ing upon the position of the [)hinet in its orhit. The fol- lowing are the times of some of the ])hases : l!S7H, Fehruary 7th.— The edge of the ring was turned toward the sun. It eould then he seen only as a thin line of light. 1885. — The planet having moved forward UO*^, the south side of the rings may he seen at an inclination of 27°. 181)1, Decend)er. — The planet having moved 1)0° fur- ther, the edge of the ring is again turned toward the sun. 1890. — The north side of the ring is inclined toward the sun, and is seen at its greatest inclination. The rings are extremely thin in proportion to their ex- tent. Ilings cut out of a large newspaper would have much ihe same proportions as those of ISaturn. (.'onsequently, when their edges are turned toward the earth, they appear as a thin line of light, which can be seen only with power- ful telescopes. With such telescopes, the ])lanet appears as if it Mere pierced through by a piece of very tine wire, the ends of which project on each side more than the diam- eter of the planet. It has frequently been remarked thu^ this appearance is seen on one side of the planet, when no trace of the ring can be seen on the other. There is sometimes a })eriod of a few weeks during which the plane of the ring, extended outward, passes be- tween the sun and the earth. Tluit is, the sun shines on one side of the ring, while the other or dark side is turned toward the eartli. In this case, it seems to be established that only the edge of the ring is visible. If this be so, the substance of the rings cannot be transparent to the Bun's rays, else it would be seen by the light which passes through it. Possible Changes in the Rings.— In 1851 Otto Struve pro- pounded rt noteworthy theory of clitmges going on in the rings of SfUurn. From all the descriptions, figures, and mensures given by the older astronomers, it appeared that two Imndred years ago tho ;;/A7;.s' 0/.' sATuny. n.-io lurmg ses be • lues on turned hlished J be so, Ito the passes I'E pro- rings of ^ven by igo tho spiicc botwccn the nlaiict imtl tho inner ring wns nt U'list <'«|uul to the (Miiiil)!^'^ Itrnidtli of tlic two rings. At present this distancu is hss than one half nf this Itreadth. Ilenee Stiii \ k (((ncliitleil tliat tiie inner ring was widening on tiie inside, so that ilsed;.;e had lieen approaching the piain-t at tin- rale of al)ont 1 •;{ in a centiiry. Tin; 8pa(;e hetween the planet and the inner edge of the bright' ring is now about 4\ so that if Sthivk'h theory were true, the inner eilgu of tlie ring would actnidly reach the jtl'anet about the year 'J',M»(>. Notwithstaiuliiig the amount of evidence which Srnrvi: cited in favor of his theory, aslrononu-rs generally are incredulous respecting tho reality of so extraordinary a change. The measures neces>ary to settle the (|uestion art; sodiilicidt and the changi- is so slow that some tinu' nnist elapse before the theory can be eslabli>hed, even if it is true. Thu measures of I\\isi;it render this doubt ful. Shadow of Planet and Ring. Witii any good telescope it U easy to observe both tin- shadow of the ring upon thi' bi.il of Suhirn ami that of the ball upon the ring. The form which the shadows l)rt'.sont often appears dilferent from that which the >ha(i,)w ought to have according to the geometrical conditions. These dilTeiences ])robablv arise from irradiation and other optical illusions. Constitutionof the Rings of Saturn.- 'I'lie nature of these objects has been a sidiject both ol wonder ami of investigation by mathenniticians and astronomers ever since they were disco\ered. They were at first supposed to l»e solid bodies ; indeed, from their a])pearance it was dilHcnlt to conceive of them as anything else. The (piestion then arose : What keeps them from falling on tlio ])lanet 'i It wiis shown by La I*i.a< k that a liomogeiieous anip- ])osed that such a support might be furnished by the satellites. This view has also been abandoned. It is now established beyond reasonal)Ie doubt that tlu' rings do not form a continuous mass, but are really a countless nuiltitude of SI ;i!l separate particles, each of which revolves on its own account. 'I'Ik -t' satellites are individually far too small to be seen in any tele- seo|)(;, but so numerous that wIhii vu-wed from the distance of tho t'urtii they appear us a eontimious muss, like ])articles of dust float- FMAGE EVALUATION TEST TARGET (MT-3) fe {< v. 1.0 I.I 11.25 t^ |5o — m^ \*o 12.0 JA 111116 HiotDgmphic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14SS0 (716) 872-4503 iV :1>^ :\ \ rv 6^ 300 ASTRONOMY. ing in a sunbeam. This tlieory was first propounded by CassixIj of Paris, in 1715. It had been forgotten for a century or more, when it vfas revived by Professor Clekk Maxwell in 1856. The latter published a ])rofound mathematical discussion of the whole question, in which he shows that this hypothesis and this alone would account for the appearances presented by the rings. Kaiseu's measures of the dimensions of the Saturniau system are : BALL OF SATUUN. Equatorial diameter 17-"274 Polar " 15-"31)2 KINGS. Major axis of outer ring 39* '471 " " " the great division 34- 227 " " " the inner edge of ring 27*"8.'59 Width of the ring 5-806 Dark space between ball and ring 5*"293 § 3. SATELLITES OP SATURN. Outside the rings of Saturn revolve its eight satellites, the order ami discovery of which are shown in the following table : No. NA.ME. Distance from Planut. Discoverer. Date of Discovery. 1 2 8 4 5 6 7 8 Mimas. Enceladus. Tetliys. Dioiie. Rliea. Titan. Hyperion. Japetusb 3-3 4-3 5-3 6-8 9-5 20-7 26-8 64-4 Herachel. Herscliel. Cassiui. Cassini. Cassini. Huygheus. Bond. Cassini. 1789, September 17. 1789, August 28. 1684, March. 1684, March. 1672, December 23. 1655, March 25. 1848, September 16. 1671, October. The distances fronv the planet are given in radii of the latter. The satellites Mimas and Hyperion are visible only in the most powerful telescopes. The brightest of all is Titan^ which can be seen in a telescope of the small- est ordinary size. Japetus has tlie remarkable peculiarity SATELLITES OF SATURN. 301 of appearing nearly as bright as Tltmi when seen west of the pUinet, and so faint as to he visible only in large tel- escopes when on tlu other side. This appearance is ex- plained by supposing that, like our moon, it always pre- sents the same face to the planet, and that one side of it is black and the other side white. When west of the planet, the bright side is turned toward the earth and the satellite is visible. On the other side of the planet, the dark side is turned toward us, and it is nearly invisible. Most of the remaining live satellites can be ordinarily seen with tele- sf ^pes of moderate power. The elements of ail the satellites are shown in the fol- lowing table : Satellite. Mimas j Enceladiis. I Tetliys.... Diane Rliea 'titan Hyperion., Japetus. . . Muan Dally Motiuii. 381-953 262- 721 190-69773 131-534930 79-690216 22-577033 16-914 4-538036 Mean Distance from Saturn. 42-70 54.60 76-12 176-75 214-22 514-64 Loniritude of Peri-Sat. V ? •? 1 257.18 40-00 351-25 Eccen- tricity. ? ■0286 •125 -0282 Inclina- ^Longitude tion to of Ecliptic. Node 28 00 28 00 28 10 28 10 28 11 27 34 28 00 18 44 168 00 168 00 167 38 167 38 166 34 167 56 168 00 142 53 CHAPTER IX. THE PLANET URANUS. ZTranjo^ was discovered oil Mareli IStli, 17S1, by Sir William irKusciiKL (then an amatiMir observer) witli a ten-foot retleetor made bv bimselt". Wa was exaniiuiiiy; ii ])oi'tiou of the sky near II (frininoruin, wlieii one of the stars in tlie field of view attracted his notice by its pecu- liar appearance. On fnrther scrutiny, it proved to haveu planetary disk, and a motion of over 2" per lionr. II eu- sciiKL at first supposed it to be a comet in a distant part of its orl)it, and under this impression parabolic orbits M'ere computed for it by various mathematicians. None of these, however, satisfied subsecpient observatioih ^ and it was finally announced by Lexkll and La Plack that the new body was a planet revolving in a nearly circuhir orbit. We can -scarcely comprehend now the enthusiasm with wluch this discovery was received. No new l)ody (save comets) had been added to the solar system since the discoverv of the third satellite of iS'<'/?'?^yv«. inl(>84. ' and all the major })lanets of the heavens had been known for thousands of vears, IIkusciill suggested, as a name for the i)lanet, Geor- glum Sid us, and even after 1800 it was known in the Eng- lish Ntuitleal Almanac as the Georo-ian Planet. Lalande suggested Tlo'nchel as its designation, but this was judged too personal, and finally the name Uranus was adopted. Its symbol was for a, time written J^I, in recognition of tho name proposed by Lalande. Uranus revolves about the sun in 84 years. Its appar- ent diameter us seen from tha earth varies little, being THE PLANET URANUS. 3d5 LUOWll Geor- Eng- Ilandk ludgcd ppted. lot' tho tvppar- buing about 3* '9. Its tme ("liametor is about 50,000 kilometres, and its figure is, so far as we yet know, exactly spherical. In i^liysical a2:)pearance it is a small greenish disk with- out markings. It is possible that the centre of the disk is sliglitly brighter than the edges. At its nearest approach to the earth, it shines as a star of the sixth magnitude, and is just visible to an acute eye when the attention is directed to its place. In small telescopes with low pow- ers, its appearance is not markedly different from that of stars of about its own brilliancy. It is customary to speak of IIehscukl's discovery of Uranua as an accident ; but this is not entirely just, as all conditions for the detection of such an object, if it ex- isted, were fuliilled. At the same time the early identifi- cation of it as r >lanet was more easy than it would have been eleven days earlier, when, as Akago points out, the planet was stationary. Sir AViLLiAM IIkuscukl suspected that Uranus was ac- companied by six satellites. Of the cxistenc(i of two of these satellites there has never been an}'' doul)t, as they were steadily observed by IIkrscukl from 1787 until 1810, and by iSir Jonx IIku- 6CHi;r. durino- the years 1828 lO 18J>2, as avcU as bv other later observers. Xone of the other four satellites de- scribed by IIeuscukl have ever been seen by other ob- servers, and he was undoubtedly mistaken in supposing them to exist. Two additional ones ^ 'fM-c discovered by Lasskll in 1817, and are, with the satellite of J/t- ed to avoid confusion : 1)AV9. I, Arid Period r^ 2 • 52038;} II, Umhr'id " = 4.144181 III, 7yV.?;i/V, IIerschel's (II.) " = 8.705807 lY, Oheron, II euscuel's (IV. ) " = 13 • 4632G9 3G4 ASTliO^'^OMY. It is an interesting question whether the observations wliich lli:usciiKL assigned to liis supposit^ious satellite 1 may not be composed of observations sometimes of Artel, sometimes of Umhriel. In fact, out of nine supposed observations of I, one ciise alone was noted by IIeksciiel in wliich his }30sitions were entirely trustworthy, and on this night Umhriel was in the position of his supposed satellite I. It is likely ^:hat Ariel varies in brightness on different sides of the phmet, and the same phenomenon has also been suspected for Tltaiiia. The most remarkable feature of tlie satellites of Uranus is tliat their orbits are nearly perpendicular to the ecliptic instead of having a small inclination to that plane, like those of all the orbits of both planets and satellites previously known. To form a correct idea of the position of the orbits, we must imagine them tipped over until their north pole is nearly 8° below the ecliptic, instead of 1)0" above it. The pole of the orbit which should be considered as the north one is that from which, if an observer look down upon a re- volving body, the latter would seem to turn in a direction opposite that of the hands of a watch. When the orbit is tipped over more than a right angle, the motion from a point in the direction of the north pole of the ecliptic will seem to be the reverse of this ; it is therefore sometimes considered to be retrograde. This term is fre- quently applied to the motion of the satellites of Uranus, but is rather misleading, since the motion, being nearly perpendicular to the ecliptic, is not exactly expressed by the term. The four satellites move in the same plane, so far as the most re- fined observations have ever shown. This ifact render.- it highly probable that the planet Uranus revolves on its axis in the same plane with the orbits of the satellites, and is therefore an oblate spheroid like the earth. This conclusion is founded on the consid- eration that if the planes of the satellites were not kept together by some cause, they would gradually deviate from each other owing to the attractive force of the sun upon the planet. The different satel- lites would deviate by different amounts, and it would be extremely improbable that all the orbits would at any time be found in the same plane. Since we see them in the same plane, we conclu:ie that some force keeps them there, and the oblateness of the planet would cause such a force. CHAPTER X. THE TLANET XEPTUXE. After the planet Uranus liad been oLserved for some thirty years, tables of its motion were prepared by BouViMti). lie had as data available for this purpose not only the observations sinee ITSl, but also observations made by Le Moxnier, Flamstekd, and others, extending back as far as 1095, in M'hieh the planet Mas observed for a fixed star and so recorded in their books. As one of the chief difficulties in the way of obtainin<^ a theory of the planet's motion was the short period of time during which it had been regularly observed, it was to be suj)- poGcd that these ancient observations would materially aid in obtaining exact accordance between the theory and ob- Bervation. But it was found that, after allowing for all perturbations produced by the known j)lanets, the ancient and modern observations, though imdoubtedly referring to the same object, were yet not to be reconciled with each other, but differed systematically. Bouvakd was forced to omit the older observations in his tables, which were published in 1820, and to found his theory upon the modern observations alone. By so doing, he obtained a good agreement between theory and the observations of the few years immediately succeeding 1820. BouvARD seems to have fonnulated the idea that a possi- ble cause for the discrepancies noted might be the exist- ence of an unknown planet, but the meagre aata at his disposal forced him to leave the subject untouched. In 1830 it was found that the tables which reprebented the aoc AaTRONOMT. motion of tlie planet well in 1820-25 were 20* in error, in 1840 the error was liO", and in 1845 it was over 120". Tiiese progressive and systematic changes attracted tlio attention of astronomers to tiie snbject of the theory of the nujtion of Uranus. Tlie actual discrepancy (^I2va, prosecuted a search for a new ]>lanet ah)iig with his double star obser- vations ; ]^)r.ssKL, at Koenigsberg, set a student of his own, Fleming, at a new comparison of observation with theo- ry, in order to furnish data for a new determination ; AuAGo, then Director of the 01)servatory at l*aris, sug- gested this subject in 1845 as an interesting held of re- search to Le Vkuhiek, then a rising mathematician and astronomer. ]\[r. ,\. C. Ai)a:\[s, a student in Cam- bridge University, England, had become aware of the problems presented by the anomalies in the motion of Uranus^ and had attacked this question as early as 1843. In October, 1845, Adams -connnunicated to the Astrono- mer Ro3'al of JMigland elements of a new planet so situated as to produce the perturbations of the motion of Unuius which had actually been observed. Such a prediction from an entirely unknown student, as AoA^ts then w^as, did not carry entire conviction M'ith it. A series of acci- dents prevented the unknown planet being looked for by one of the largest telescopes in England, and so tlie mat- ter apparently dropped. It may he noted, however, that we now know Adams' elements of the new planet to have been so near the trntli that if it had been really looked for by the powei'ful telesco])e wdiich afterward discovered its satellite, it could scarcely have failed of detection. Bessei/ s pupil Fleming died before his work was done, and Bessel's researches were temporarily brought to DISCOVERY OF NEl^TUNE. 3Gr ;ion of IS-HJ. roiio- tiiated ilCCl- for l)y iiiiit- '1', that o luivo xl for irod its done, [rlit to an end. Stkuve's search \vas uiisuccossful. Only J.h Vkukiku continued his investigations, and in tiio most thorough mauner. Ifo first counnited anew the pertur- bations of Uniims j)rodueey an unkno'Nvn ])lanet, it could not he between Sdturii and (Tr((?iihs^ or else Sutiit'n would have been more atit'ected than Avas tiic case. The new planet was outside of ZTramis if it existed at all, and as a rough guide JJodk's law was invoked, which indicated a distance about twice that of Uratms. In the Bumincr of 1S4(!, Lk Ykukikk obtained complete elements of a new planet, which would account for the observed irregularities in the motion of Unmus, and these were published in France. They were very similar to those of Adams, M'hich had been communicated to Professor Cual- Lis, the Director of the Observatory of Candjridge. A search was immediately begun by Cuallis for such an oT>ject, and as no star-maps Avere at haiul for this region of the sky, he began mapping the surrounding stars. In so doing the new planet was actually observed, both on August 4th and 12tli, 1840, but the observations remain- ing unreduced, and so the planetary nature of the object was not recognized. In September of the same year, Le Verrter wrote to Dr. Galle, then Assistant at the Observatoiy of Berlin, asking him to search for the new planet, and directing him to the place where it shoidd be found. By the aid of an excellent star chart of this region, which had just been completed by Dr. Bkemiker, the planet was found September 23d, 1840. The strict rights of discovery lay with Le Yerrier, but the common consent of mankind has always credited Adams with an equal share in the honor attached to this most brilliant achievement. Indeed, it was only by the most unfortunate succession of accidents that the discovery 368 ASTItONOMT. mm did not attacli to Adams' researclies. One thing must in fairness be said, and tliat is that the results of Le Ver- KiEK, wliicli were reached after a most tliorough investi- gation of the wiiole ground, were announced with an en- tire confidence, wliicli, perliaps, was lacking in the other ease. This brilliant discovery created more enthusiasm than even the discovery of Uranus^ as it was by an exercise of far higher (qualities that it was achieved. It appeared to savor of the marvellous that a mathematician could sajr Fig. 98. to a working astronomer that by pointing his telescope to a certain small area, within it should be found a new major planet. Yet so it wjis. The general nature of the disturbing force which re- vealed the new planet may be seen by Fig. 98, which shows the orbits of the two planets, and their respective m.otions between 1781 and 1840. Tiie inner orbit is that of Cfranus, the outer one that of Neptune. The arrows passing from the former to the latter show the directions of the attractive force of Nejjtune. It will be seen that SATELLITE OF NEPTUNE. 369 ;ope to a new the two planets were in conjunction in the year 1H22. Since that time Uranus has, by its more rapid motion, passed more tlian 1)0° beyond Nejdune, and will eoiitinue to increase its distance from the latter until the begin- ning of the next cen.tury. Our knowledge regarding Neptune is mostly confined to a few numbers rejjresenting the elements of its motion. Its mean distance is more than 4,000,(>00,()00 kilometres (2,775,000,000 miles) ; its periodic time is 1()4.78 years ; its apparent diameter is 2"' G seconds, corresponding to a true diameter of 55,000 kilometres. Gravity at its surface is about nine tenths of the corresponding 'e 'restrial surface gravity. Of its rotation and j)hysical condition nothing is known. Its color is a pale gieenish blue. It is atteiul- ed by one satellite, the elements of whose orbit are given herewith. It was discovered by Mr. Lasskll, of Eng- land, in 1S47. It is about as faint as the two outer satel- lites of Uranus^ and requires a telescope of twelve inches aperture or upward to be well seen. Elements op the Satelmte op Neptune, fkom Washington Obseuvations. Mean Daily Motion 61° •256:9 Periodic Time S-i-STeOO Distance (lojr. ^ = 1.47814) 16'-275 Inclination of Oil>it to Eciliptio 145° 7' Longitude of Node (1850) 184° 30' Increase in 100 Yea-B 1° 24' The great inclination of the orbit showa thiit it Is turned nearl;^ upside down ; the direction of motion is therefore retrogade. CHAPTER XI. THE PHYSICAL CONSTITUTIOX OF THE PLAiNETS. It is remarkiiblo tliiit the eight large pliuictM of the solar Bystem, considered with respect to tlieir physical constitu- tion as revealed by the telescope and the si)octro8oope, may be divided into four pairs, the ^^lanets of each pair having a great similarity, and being quite different from the adjoining pair. Among the most complete and sys- tematic studies of the spectra of all the planets are those made by Mr. IIuggins, of London, and Dr. Vogel, of Berlin. In what we have to say of the results of spectro- scopy, we shall depend entirely upon the reports of theso observers. Mercury and Venu8. — Passing outward from the sun the first pair we encounter will be Mercury and Venus. The most remarkable feature of these two planets is a neg- ative rather than a positive one, being the entire absence of anv certain evidence of change on their surfaces. AVe have already shown that Ve7ius has a considerable atmos- phere, while there is no evidence of any such atmosphere around Mercury. They have therefore not been proved alike in this respect, yet, on the other hand, they have not been proved different. In every other respect than this, the similarity appears perfect. No permanent markings have ever been certainly seen on the disk of either. If, as is possible, the atmosphere of both planets is filled with clouds and vapor, no change, nu openings, and no for- PHYSICAL CONSTITUTIOX dF TUK PLANETS. '^1\ neg- Isonco Itmos- nliere •oved Q not this, |king8 If, witb for- matnHis among tlieso cloud masses aro visiMu from tlio earth. Wljunexer either of these planets is in a certain position relative to the earth and the sun, it seemingly presents the same appearance, and not tlie sliglitest change occiirs in tliat a])pearance from the rotation of tho planet on its axis, which every anal(»gy oi the solar sys- tem leads us to helieve nnist take place. When studied with the spectroscope, the spectra of Mercury and Ycrius do not diifer strikingly from that of the sun. This would seem to indicate that the atmos- pheres ol" these nlanets do not exert any decided ahsorption upon the rays «. . light which pass through them ; or, at least, they ahsorb oidy the same ra;' which are absorbed by the atmosphere of the sun and by tliat of the earth. The one point of difference which Pr. Yocjii. brings out is, tliat the lines of the spectrum iirodi.ccd by the absorp- tion of our own atmosphere aj)pear da vkcr in the spectrum of Venus. If this were so, it would indicate that the at- mosphere of Venus is simiUir in constitution to tliat of our earth, because it absorbs the same rays. But the means of measuring the darkness of the lines are as yet so imjjerfect that it is impossible to speak with certainty on a point like this. Dr. Yooel tiiinks that the light from Venus is for the most part retleeted from clouds in the higher region of the planet's atmofiphere, and there- fore reaches ns without passing through a great dejDth of that atmosphere. The Earth and Mars. — These planets are distinguished from all the othei*s in that their visible surfaces are marked by permanent features, which show them to be solid, and which can be seen from the other heavenly bodies. It is true that we cannot study the earth from any other body, but we can form a very correct idea how it would look if Been in this way (from the moon, for instance). Wherever the atmosphere was clear, the outlines of the continents and oceans would be visible, while they would be invisible where the air was cloudy. 373 ASTRONOMY. Now, so far as we can judge from observations raade at 80 great a distance, never nmcli less than forty mil- lions of miles, the planet Mars presents to our tele- scopes very much the same general appearance that the earth would if observed from an equally great distance. The only exception is that the visible surface of Mars is seemingly much less obscured by clouds than that of the earth would be. In other words, that planet has a more sunny sky than oui-s. It is, of course, impossible to say what conditions we might find could we take a much closer view of Mars : all we can assert is, that so far as we can judge from this distance, its surface is like that of the earth. This supposed similarity is strengthened by the spectro- scopic observations. The lines of the spectrum due to aqueous vapor in our atmosphere are found by Dr. Yogel to be so much stronger in Mars as to indicate an absorp- tion by such vapor in its atmosphere. Dr. IIuggins had previously made a more decisive observation, having found a well-marked line to which there is no correspona- ing strong line in the solar spectrum. This would indi- cate that the atmosphere of Mars contains some element not found in our own, but the observations are too diffi- cult to allow of any well-established theory being yet built upon them. Jupiter and Saturn. — The next pair of planets are Jupiter and Saturn. Their peculiarity is that no solid crust or surface is visible from without. In this respect they differ from the earth and Mars^ and resemble Mer- cury and Venus. But they differ from the latter in the very important point that constant changes can be seen going on at their surfaces. The nature of these changes has been discussed so fully in treating of these planets in- dividually, that we need not go into it more fully at pres- ent. It is sufficient to say that the preponderance of evi- dence is in favor of the view that these planets Iiave no Bolid crusts whatever, but consist of masses of molten PHYSICAL CONSTITUTION OF THE PLANETS 373 are solid jspect \Met'- |n the seen mges Its in- Ipres- evi- |e no lolten matter, surrounded by envelopes of vapor constantly rising from the interior. The view that the greater part of the apparent volimae of these planets is made of a seething mass of vapor is f mther strengthened by their very small specilic gravity. This can be accounted for by supposing that the liquid interior is nothing more than a comparatively small central core, and that the greater part of the bulk of each planet is composed of vapor of small density. That the visible surfaces of Jivpiter and Saturn are cov- ered by some kind of an atmosphere follows not only from the motion of the cloud forms seen there, but from the spectroscopic observations of Huggins in 1804. He found visible absorption-bands near the red end of the spectrum of each of these planets. Yogel found a com- plete similarity between the spectra of the two planets, 'he most marked feature being a dark band in the red. What is worthy of remark, though not at all surprising, is that this band is not found in the spectrum of Saturn's rings. This is what we should exijcct, as it is hardly pos- sible that these rings should have any atmosphere, owing to their very small mass. An atmosphere on bodies of so slight an attractive power would expand away by its own elasticity and be all attracted around the planet. Uranus and Neptune. — These planets have a strikingly similar aspect when seen through a telescoije. They differ from Jupiter and Saturn in that no changes or va- riations of color or aspect can be made out upon their sur- faces ; and from the earth and ^dars in the absence of any permanent features. Telescopically, therefore, we might classify them with Mercury and Venus, but the spectro- scope reveals a constitution entirely different from that of any other planets. The most marked features of their spectra are very dark Dands, evidently produced by the absorption of dense atmospheres. Owing to the extreme faintness of the light which reaches us from these distant bodies, the regular lines of the solar spectrum are entirely I 374 ASTRONOMY. v. invisible in their spectra, yet these dark hands which are peculiar to them have been seen by Huggins, Secchi, VoGEL, and perhaps others. Tliis classification of the eight planets into pairs is ren- dered yet more striking by the fact that it applies to what we have been uble to discover respecting the rota- tions of these bodies. The rotation of the inner pair, Mercury and Venus^ haa eluded detection, notwith- standing their comparative proximity to us. The next pair, the earth and Mars^ have perfectly definite times of rotation, because their outer surfaces consist of solid crusts, every jiart of which must rotate in the same time. The next pair, Jupiter and ■Saturn, have well-establislied times of rotation, but these times are not perfectly defi- nite, because the surfaces of these planets are not solid, and different portions of their mass may rotate in slightly different times. Jupiter and Fig. 99.-8PECTBUM op ckanus. Saturn have also in common a very rapid rate of rotation. Finally, the outer pair, Ura- nus and Neptune, seem to be surrounded by atmospheres of such density that no evidence of rotation can be gathered. Thus it seems that of the eight planets, only the central four have yet certainly indicated a rotation on their axos* « — 1 s — S5 — •Q ft — 8 — a — m ■ — q M s — at ?- « BtKiaai:^ -R, ? - 5 — ■ — tt Ires of tered. tral 3n axes- CHAPTER Xn. METEORS. % 1. PHENOMENA AND CAUSES OP METEORS. During the present century, evidence has been collected that countless masses of matter, far too small to he seen M'^ith the most powerful telescopes, are moving through the planetary spaces. This evidence is afforded by the phonomena of " aerolites, " " meteors," and " shooting otars." Although these several phenomena have been ob- served and noted from time to time since the earliest his- toric era, it is only recently that a complete explanation has been reached. Aerolites. — Reports of the falling of large masses of etone or iron to the earth have been familiar to antiqua- rian students for many centuries. Arago has collected several hundred of these reports. In one instance a monk was killed by the fall of one of these bodies. One or two other cases of death from this cause are supposed to have occurred. Notwithstanding the number of instances on record, aerolites fall at such wide intervals as to be ob- served by very few people, consequently doubt was fre- quently cast upon the correctness of the narratives. The problem where such a body could come from, or how it could get into the atmosphere to fall down again, formerly seemed so nearly incapable of solution that it required some credulity to admit the facts. Wlien the evidence became so strong as to be indisputable, theories of their origin began to be propounded. One theory quite fashion- 376 ASTRONOMY. able in the early part of this century was that they were thrown from volcanoes in the moon. This theory, though the subject of mathematical investigation by La Place and others, is now no longer thought of. The proof that aerolites did really fall to the ground first became conclusive by the fall being connected with other more familiar phenomena. Nearly every one who is at all observant of the heavens is familiar with holides, or lire-balls — brilliant objects having the appearance of rockets, which are occasionally seen moving with great ve- locity through the upper regions of the atmosphere. Scarcely a year passes in which such a body of extraordi- nary brilliancy is not seen. Generally these bodies, bright though they may be, vanish without leaving any trace, or making themselves evident to any sense but that of sight. But on rare occasions their appearance is followed at an interval of several minutes by loud explosions like the dis- charge of a battery of artillery. On still rarer occasions, masses of matter fall to the ground. It is now fully understood that the fall of these aerolites is always ac- companied by light and sound, though the light may be invisible in the daytime. When chemical analysis was applied to aerolites, they were proved to be of extramundane origin, because they contained chemical combinations not found in terrestrial substances. It is true that they contained no new chemi- cal elements, but only combination of the elements which are found on the earth. These combinations are now so familiar to mineralogists that they can distinguish an aerolite from a mineral of terrestrial origin by a careful examination. One of the largest components of these bodies is iron. Specimens having very nmch the appear- ance of great masses of iron are found in the National Museum at Washington. Meteors. — Although the meteors we have described are of dazzling brilliancy, yet they run by insensible grada- tions into phenomena, which any one can see on any clear W^ CAUSE OF METEORS. 377 night. The most brilliant meteoris of all are likely to be seen by one person only two )r three times in his life. Meteors having the appearance and brightness of a distant rocket may be seen several times a year by any one in the habit of walking out during the evening and watching the sky. Smaller ones occur more frequently ; and if a care- ful watch be kept, it will be found that several of the faintest class of all, familiarly known as shooting stars, can be seen on every clear night. "We can draw no distinction between the most brilliant meteor illuminating the whole sky, and perhaps making a noise like thunder, and the faintest shooting star, except one of degree. There seems to be every gradation between these extremes, so that all should be traced to some common cause. Cause of Meteors. — There is now no doubt that all these phenomena have a common origin, being due to the earth encountering innumerable sma'i bodies in its annual course around the sun. The great difficulty in connecting mete- ors with these invisible bodies arises from the brilliancy and rapid disappearance of the meteors. The question may be asked why do they burn with so great an evolu- tion of light on reaching our atmosphere ? To answer this question, we must have recourse to the n. ^ ihanical theory of heat. It is now known that heat is really a vibratory motion in the particles of solid bodies and a progressive motion in those of gases. By making this motion more rapid, we make the body warmer. By simply blowing air against any combustible body with sufficient velocity, it can be set on fire, and, if incombustible, the body will be made red-hot and finally melted. Experiments to deter- mine the degree of temperature thus produced have been made by Sir William Thomson, who finds that a veloci- ty of about 50 metres per second corresponds to a rise of temperature of one degree Centigrade. From this the temperature due to any velocity can be readily calculated on the principle that the increase of temperature is pro- portional to the "energy" of the particles, which again w 878 ASTRONOMY. is proportional to the square of the velocity. Hence a velocity of 500 metres per second would correspond to a rise of 100° above the actual temperature of the air, so that if the latter was at the freezing-point the body would be raised to the temperature of boiling water. A velocity of 1500 metres per second would produce a red heat. This velocity is, however, much higher than any that wo can produce artificially. The earth moves around the sun with a velocity of about 30,000 metres per second ; consequently if it met a body at rest the concussion between the latter and the at- mosphere would correspond to a temperature of more than 300,000°. This would instantly dissolve any known sub- stance. As the theory of this dissipation of a l)ody by moving with planetary velocity through the upj^er regions of our air is frequently misunderstood, it is necessary to explain two or three points in connection with it. (1.) It must be remembered that when we speak of these enormous temperatures, we are to consider them as potential^ not actual, temperatures. We do not mean that the body is actually raised to a temperature of 300,- 000°, but only that the air ,'icts upon it as if it were put into a furnace heated to this temperature — that is, it is rapidly destroyed by the intensity of the heat. (2.) This potential temperature is independent of the density of the medium, being the same in the rarest as in the densest atmosphere. But the actual effect on the body is not so great in a rare as in a dense atmosphere. Every one knows that he can hold his hand for some time in air at the temperature of boiling water. The rarer the air the higher the temperature the nand would bear without injury. In an atmosphere as rare as ours at the height of 50 miles, it is probable that the hand could be held for an indefinite period, though its temperature should be that of red-hot iron ; hence the meteor is not consumed so rap- idly as if it struck a dense atmosphere with planetary CAUSE OF METEORS. 379 velocity. In the latter ease it would probably disappear like a Hash of lightning. (3.) The amount of heat evolved is measured not by that which would result from the combustion of the body, but by the vis viva (energy of motion) which the body loses in the atmosphere. The student of physics knows that mo- tion, when lost, is changed into a definite amount of heat. If we calculate the amount of heat which is equiv- alent to the energy of motion of a pebble having a veloc- ity of 20 miles a second, we shall find it sufficient to raise about 1300 times the pebble's weight of water from the freezing to the boiling point. This is many times as nmch heat as could result from burning even the most combusti- ble body. (4.) The detonfition which sometimes accompanies tlie passage of very brilliant meteoi's is not caused by an ex- plosion of the meteor, but by the concussion produced by its rapid motion througli the atmosphere. This concus- sion is of much the same nature as that produced by a flash of liglitning. The air is suddenly condensed in front of the meteor, while a vacuum is left behind it. The invisible bodies wliich produce meteoi's in the way just described have been called ineteoroids. Meteoric phenomena depend very largely upon the nature of the ineteoroids, and the direction and velocity with Mliich they are moving relatively to the earth. With very rare exceptions, t]:f^y are so small and fusible as to be entirely dissipated in thb upper regions of the atmosphere. Even of those 60 hard and solid as to produce a brilliant light and the loudest detonation, only a small proportion reach the earth. It has sometimes happened that the meteoroid only grazes the atmosphere, passing horizontally through its higher strata for a great distance and continuing its course after leaving it. On rare occasions the body is so hard and massive as to reach the earth without being en- tirely consumed. The potential heat produced by its passage througli the atmosphere is then all expended in 380 ASTRONOMY. melting and destroying its outer layers, the inner nucleus remaining unchanged. When such a body first strikes the denser portion of the atmosphere, the resistance be- comes so great that the body is generally broken to pieces. Hence we very often lind not simply a single aerolite, but a small shower of them. Heights of Meteors. — Many observations have been made to determine the height at which meteors are seen. This is effected by two observei*s stationing themselves several miles apart and mapping out the courses of such meteors as they can observe. In order to be sure that the same meteor is seen from both stations, the time of each observation must be noted. In the case of very brilliant meteors, the path is often determined with considerable precision by the direction in which it is seen by accidental observers in various regions of the country over which it passes. The general result from numerous observations and in- vestigations of this kind is that the meteors and shooting stars commonly commence to be visible at a height of about 160 kilometres, or 100 statute miles. The separate results of course vary widely, but this is a rough mean of them. They are generally dissipated at about half this height, and therefore above the highest atmosphere which reflects the rays of the sun. From this it may be inferred that the earth's atmosphere rises to a height of at least 160 kilometres. This is a much greater height than it was formerly supposed to have. § 2. METEORIC SHOWEBS. As already stated, the phenomena of shooting stars may be seen by a careful observer on almost any clear night. In general, not more than three or four of them will be seen in an hour, and these will be so minute as hardly to attract notice. But they sometimes fall in such numbers as to present the appearance of a meteoric shower. On METEORIC SHOWERS. 381 rare occasions the shower has been so striking as to till the beholders with terror. The ancient and mediteval records contain many acconnts of these phenomena which have been brought to light through the researches of antiqua- rians. The following is quoted by Professor JMewton from an Arabic record : " In thfl year 599, on the last day of Moharrem, stars shot hither and thither, and flew against each other like a swarm of locusts ; this phenomenon lasted until daybreak ; people were thrown into consternation, and made supplication to the Most High : there was never the like seen except on the coming of the messenger of God, on whom be benediction and peace." It hais long been known that some showers of this class occur at an interval of about a third of a century. One was observed by Humboldt, on the Andes, on the night of November 12tli, 1799, lasting from two o'clock until daylight. A great shower was seen iu this country in 1833, and is well known to have struck the negroes of the Southern States with terror. The theory that the show- ers occur at intervals of 34 years was now propounded by Olbers, who predicted a return of the shower in 1867. This prediction was completely fulfilled, but instead of ap- pearing in the year 1867 only, it was first noticed in 1866. On the night of November 13th of that year a remarkable shower was seen in Europe, while on the corresponding night of the ye.ar following it was again seen in this coun- try, and, in fact, was repeated for two or three years, grad- ually dying away. The occurrence of a shower of meteors evidently shows that the earth encounters a swarm of meteoroids. The recurrence at the same time of the year, when the earth is in the same point of its orbit, shows that the earth meets the swarm at the same point in successive years. All the meteoroids of th' jwarm must of course be moving in the same direction, else they would soon be widely scat- tered. This motion is connected with the radiant jpoint^ a well-marked feature of a meteoric shower. 3&i ASTRONOMY. Badiant Point.— Suppose Unit, during ii mctcorir shower, wo mark the putu ot eacli meteor on a star map, as in the figure. If \\e continue the paths backward in a straiglit line, we shall find that they all meet near one and the same jxiint of the celestial sphere - that 13, tliey move as if they all radiated from this point. The Fig. 100. — kadiant point of meteoric bhoweb. latter is, therefore, called the radiant point. Tn the figure the lines do not all pass accurately through the same point. This is owing to the unavoidable errors made in marking out the path. It is found that the radiant point is always in the same position among the stars, wherever the observer may be situated, and that MtlTKORH AM) VOMKTh 383 lOWtT, Wo ro. U ^^^, •iiHl that splierc — int. The le lines owing osition d that it tloes not piirtiiko of tlio diurniil motion of the ciirtli — tliat U, us the stars a|)i)areiitly move toward tho west, tlie radumt point niovc!* with them. Tlio radiant point is duo to the fart that the meteoroida wlfuih strike the earth diirinj; u shower are all movinjf in the same direc- tion. If we suppose tl>e eartli to be at rest, and the actual motion of tlio meteoroids to he compounded witli an ima<;inary motion e(p>al and opposite to that of the earth, the motion of these imaj^- inary bodies will be the same as the actual relative motion of tho meteoroids seen from the earth. These relative motions will all be parallel ; hence when the bodies strike our atmosphere the paths described by them in their passaj^e will all be parallel straight lines. Now, by the principles of {geometry of the sphere, a .straij^ht line seen by an observer at any ])oint is jtrojected as a great circle of the celestial sj)here, of which tin; observer supposes himself to bo the centre. If we draw a line from the observer parallel to the paths of the meteors, the direction of that line will indicate a point of the sphere throuj^h which all the ])aths will seem to pass ; this will, therefore, be the radiant point in a meteoric shower. A sliji^htly dlllerent conception of the i)roblem may be formed l)y conceiving? the plane ])assing throujfh the observer and contain- ing the path of tin; meteor. Jt is evident that the diiTerent planes formed by the ])aradel meteor paths will all intersect each other in a line drawn from the observer |)arallel to this path. This line will then intersect the celestial sphere in the radiant point Orbits of Meteoric Showers. — From what has just been said, it will be seen that the position of the radiant point indicat^es the direction in which the meteoroids move relatively to the eanh. If we also knew the velocity with which they are really moving in space, we could make allowance for the motion of the earth, and thus determine the direction of their actual motion in space. It will be remembered that, as just explained, the apparent or rela- tive motion is made up of two components — the one the actual motion of the body, the other the motion of the earth taken in an opposite direction. We know the second of these compon(!nts already ; and if we know the velocity relative to the earth and the direction as given by the radiant point, we have given the resulttmt and one component in magnitude and direction. The computation of the other component is one of the simplest problems in kine- matics. Thus we shall have the actual direction and velocity of the meteoric swarm in space. Having this direction and velocity, the orbit of the swarm around the sun admits of being calculated. Kelations of Meteors and Comets. — The velocity of the meteoroids does not admit of heing determined from ob- eervation. One element necessary for determining the orbits of these bodies is, therefore, wanthig. In the case of the showers of 1799, 1833, and 1866, commonly called the November showers, this element is given by the time Il|! 384 AHTHOyOMT. of rovohitloii jinmiul tlio sun. Since the showers occur at intervals of about a tliird of a cuntury, it is highly i)rob- able this is the periodic time of the swarm around the sun. The periodic time being known, the velocity at any dis- tance from the sun admits of calculation from the theory of gravitation. Thus we have all the data f(jr determining the reid orbits of the group of meteors arounrl the sun. The calculations necessary for this ])urpose were made by Lk Vkukiku and other astronomers shortly after the great showtir of i860. The following was the orbit as given by Lio Vkukiku : Period of revolution 3!i- 25 years. Eccentri<;ity of <)rl)it • {)044. Least distiiiice from the sun 0-U8!)(). Incliniition of orl)it 1(15" 15)'. Lonfjitude of the node 51' 18'. Position of the periliclion (near the node). The pubhcation of this orbit brought to the attention of the workl an extraordinary coincidence which had never before been suspected. In December, 1805, a faint telescopic comet was discovered by Tempkl at Mar- seilles, and afterward by II. P. Turrr.E at the Naval Observatory, Washington. Its orbit was calculated by Dr. Oppolzek, of Vienna,, and his results were finally pub- lished on January 28th, 1867, in the Astronomlsche JSfaoh- rlcliten ; they were as follows : Period of revohition 33-18 years. Eccentricity of orbit • 9054. Least distance from the sun • 9765, Inclination of orbit 162° 42'. Longitude of the node 51° 26'. Longitude of the perihelion 42° 24'. The publication of the cometary orbit and that of the orbit of the meteoric group were made independently with- in a few days of each other by two astronomers, neither of whom had any knowledge of the work of the other. Comparing them, the result is evident. Ths swarms of meteoroids which cause the November showers move in the same orbit with Tempel-'s comet. THE AUGUST MhTKOIiS. 38D pub- Ti:mim:i/s comet passed its poriJiolioii in January, 180r>. The nioHt Ptriiri(! showers. Other Showers of Meteors- — Although the Xovember showers are the only ones so Iirilliant as to strike the ordi- nary eye, it has long been known that there are other nights of the year in which more shooting stars than usual are seen, and in which the large majoriry radiate from one point of the heavens. This shows conclusively that they arise from swarms of meteoroids moving together around the sun. August Meteors. — The best marked of these minor showers occurs about August Dth or loth of each year. The radiant point is in the constellation Perseus. By watching the eastern heavens toward midnight on the 9th or loth of August of any year, it will be seen that numer- ous meteors move from north-east toward south-west, hav ing often the distinctive characteristic of leaving a trail behind, which, however, vanishes in a few moments. As- suming their orbits to be parabolic, the elements were cal- culated by ScniAPAKELLi, of Milan, and, on comparing with the orbits of observed comets, it was fountl that these meteoroids moved in nearly the same orbit as the second comet of 1S62. The exact period of this comet is not known, although the orbit is certainly elliptic. Accord- ing to the best calculation, it is 121: years, but for reasons given in the next chapter, it nuiy be uncertain by ten years or more. There is one remarkable diflference between the August and the November meteors. The latter, as we have seen, appear for two IIM 386 ASTRONOMY. i'il or three consecutive years, and then are not seen again until about thirty years have elapsed. But the August meteors are seen every year. This shows that the stream of August meteoroids is endless, every part of the orbit being occupied by them, while in the case of the November ones they are gathered into a group. We may conclude from tliis tliat the November meteoroids have not been permanent members of our system. It is beyond all prob- ability that a group comprising countless millions of such bodies should all have tiie same time of revolution. Even if they had the same time in the beginning, the different actions of the planets on different parts of the group would make the times different. The result would be that, in the course of ages, those which had the most rapid motion would go further and further ahead of the others until they got half a revolution ahead of them, antt would finally overtake those having the slowest motion. The swiftest and slowest one would then be in the position of two race-horses running around a circular track for so long a time that the swiftest horse has made a complete run more than the slowest one and has over- taken him from behind. When this happens, the meteoroids will be scattered all around the orbit, and we shall have a shower in November of every year. The fact that has not yet happened shows that they have been revolving for only a limited length of time, probably only a very few thousand years. Although tlie total mass of these bodies is very small, yet their number is beyond all estimation. Professor Newton iias estimated that, taking the whole earth, about seven million shooting stars are encountered every twenty-four hours. This would make between two and three thousand million meteoroids which ar'; thus, as it were, destroyed every year. But the number which the earth can encounter in a year is only an insignificant fraction of the total number, even in the solar system. Ii may be interesting to calculate the ratio of the space swept over by the earth in the course of a year to the volume of the sphere surrounding the sun and extending out to the orbit of Neptune. We shall find this ratio to be only as one to about three millions of millions. If we measure by the number of meteoroids in a cubic mile, we might consider them very thinly scattered. There is, in fact, only a single meteor to several million cubic kilometres of space in the heavens. Yet the total number is immensely great, because a globe including the orbit of Neptune would Contain millions of millions of millions of millions of cubic kilometres.* If we reflect, in addition, that the meteoroids probably *The computations leading to this result maybe made in the fol- lowing manner : I. To find the cubical space mcept through by the earth in the course of a year. If we put tt for the ratio of the circumference of a circle to its diameter, and p for the radius of the earth, the surface of a plane section of the earth passing through its centre will be tt p'. Multiplying this by the circumference of the earth's orbit, we shall have the space re- quired, which we readily find to be more than 30,000 millions of millions of kilometres. Since, in sweeping through this space, the earth encounters about 2500 millions of meteoroids, it follows that THE ZODIACAL LIGHT. 387 weighbuca few grains each, we shall see how it is that they are en. tirely invisible even with jjowerful telescopes. The Zodiacal Light. — ^If we observe tlio western sky during the winter or spring months, about the end of the evening twilight, we shall see a stream of faint light, a little like the Milky Way, rising obliquely from tlie west, and directed along the ecliptic toward a point south-west from the zenith. This is called the zodiacal light. It may also be seen in the east before daylight in the morn- ing during the autumn months, and has sometimes been traced all the way across the heavens. Its origin is still involved in obscurity, but it seems probable that it arises from an extremely thin cloud either of meteoroids or of Bemi-gaseous matter like that composing the tail of a comet, spread all around the sun inside the earth's orbit. The researches of Professor A. W. "WRionr show that its spectrum is probably that of reflected sunlight, a result which gives color to the theory that it arises from a cloud of meteoroids revolving round the sun. there i3 only one meteoroid to more than ten millions of c ibic kil- ometres. II. To find the ratio of the sphere of spneewithin the orhit of Neptune to the space swept through by t?ie earth in a year. Let us put r for the dis- tance of the earth from the sun. Then the distance of Neptune may be taken as 30 r, and this will be the radius of the sphere. The cir- cumference of the earth's orbit will than be 2 7r r, and the space swept over will be 2 n^ rp*. The sphere of Neptuii^ will be J TT 30" ?•* = 36,000 ■K r\ nearly. The ratio of the two spaces will be 18.000 r> * p* — 6,000 -Y-, nearly. The ratio — la more than 23,000, showing the required ratio to be P about throe millions of millions. The total number of scattered mete oroide is thnrefore to be reckoned by millions of millions of millions. u CHAPTER XIII. COMETS. § 1. ASPECT OP COMETS. Comets are distinguishecl from the planets both by their aspects and tlieir motions. They come into view without anything to herald their approach, continue in sight for a few weeks or months, and then gradually vanish in the distance. They are commonly considered as composed of three parts, the nucleus, the coma (or hair), and the tail. The nucleus of a comet is, to the naked eye, a point of light resembling a star or planet. Viewed in a telescope, it generally has a small disk, but shades off so gradually that it is difficult to estimate its magnitude. In large comets, it is sometimes several hundred miles in diameter, but never approaches the size ( one of the larger planets. The nucleus is always surrounded by a mass of foggy light, whioh is called the coma. To the naked eye, the nucleus and coma together look like a star seen through a mass of thin fog, which surrounds it with a sort of halo. The coma is brightest near the nucleus, so that it is hardly possible to tell where the nucleus ends and where the coma begins. It shades off in every direction so gradually that no definite boundaries can be fixed to it. The nucleus and coma together are generally called the head of the comet. The tail of the comet is simply a continuation of the coma extending out to a great distance, and always di- rected away from the sun. It has the appearance of a stream o* milky light, which grows fainter and broader ASPECT OF COMETS. 389 ?gy If the rs di- of a Joader as it rccedSaa, f rom the head. Like the coma, it shades off 80 gradually thuit it is impossible to fix any boundarios to it. The length of the tail varies from 2^ or 3° to 90" or more. Generally the mcMre brilliant the head of the comet, the longer and brighter is the tail. It is also often brighter and more sharply defined at one edge than at the other. 7he above description applies to comets which can be plainly seen by the naked eye. After astronomers began to sweep the heavens carefully with telescopes, it was found that many comets came into sight which would entirely escape the unaided vision. These are called tel- escopio comets. Sometimes six or more of such comets i,iV discovered in a single year, while one of the brighter class may not be seen for ten years or more. FlO. 101. — TELESCOPIC COMET WITH- FlG. 102. — TELESCOPIC COMET OUT A NUCLEUS. WITH A NUCLEUS. When comets are studied with a telescope, it is found that they are subject to extraordinary changes of structurcy. To understand these changes, we must begin by saying that comets do not, like the planets, revolve around the sun in nearly circular orbits, but always in orbits so elongated that the comet is visible in only a very small part of its course. When one of these objects is first seen, it is gen« erally approaching the sun from the celestial spaces. At this time it is nearly always devoid of a tail, and some- times of a nucleus, presenting the aspect of a thin patch of cloudy light, which may or may not have a nucleus in 390 ASTUONOMY. its centre. As it approaches the sun, it is generally seen to grow brighter at some one point, and there a nncleus gradually forms, being, at first, so faint that it can scarcely be distingnished from the surrounding nebulosity. The latter is generally more extended in the direction of the sun. thus sometimes giving rise to the erroneous impres- sion of a tail turned toward the sun. Continuing the watch, the trun tail, if formed at all, is found to t)egin very gradually. A.t first so small and faint as to be almost invisible, it grows longer and brighter every day, as long as the comet continu<3s to approach the sun. § 2. THE VAPOROUS ENVELOPES. If a comet is very small, it may undergo no changes of aspect, except those just described. If it is an unusually bright one, the next object noticed by telescopic examina- tion will be a bow surrounding the nucleus on the side toward the sun. This bow will gradually rise up and spread out on all sides, finally assuming the form ol a semicircle having the nucleus in its centre, or, to speak with more precision, the. form of a parabola having the nucleus near its focus. The two ends of this parabola will extend out further and further so as to form a part of the tail, and finally be lost in it. Continuing the watch, other bows will be found to form around the nu- cleus, all slowly rising from it like clcuds of vapor. These distinct vaporous masses are called the envelopes : they shade off gradually into the coma so as to be with difficulty distinguished from it, and indeed may be con- sidered as part of it. The inner envelope is sometimes connected with the nucleus by one or more fan-shaped appendages, the centre of the fan being in the nucleus, and the envelope forming its round edge. This appear- ance is apparently caused by masses of vapor streaming up from that side of the nucleus nearest the sun, and grad- ually spreading around the comet on each side. The EI^ VELOPES OF COMETS. 391 illv seen , nucleus scarcely y. The 11 of the inipres- ling tlie to t)cgin le ahriost , as long anges of musually exaniina- the side up and )rni oi a to speak ving the parabola n a part uing the 1 the nu- vapor. nvelopes : be with ^ be con- onietimes m-shaped nucleus, 3 appear- 5t reaming and grad- ie. The form of a bow is not the real form of the envelopes, but only the apparent one in which we see tiiem projected against the background of the sky. Their true form is similar to that of a paraboloid of revolution, surrounding the nucleus on all sides, except that turned from the sun. It is, therefore, a surface and not a line. Perhai)s its form can be best imagined by supposing the sun to be directly above the comet, and a fountain, throwing a liquid hori- zontally on all sides, to be built upon that part of tlie comet which is uppermost. Such a fountain would throw its water in the form of a sheet, falling on all sides of the cometic nucleus, but not touching it. Two or three vapor surfaces of this kind are sometimes seen around the comet, the outer one enclosing each of the inner ones, but no two touching each other. Pig. 103.— formation op envelopes. To give a clear conception of the formation and motion of tho envelopes, we present two figures. The first of these shows the ap- pearance of the envelopes in four successive stages of their course, and may be regarded as sections of the real umbrella-shaped sur- faces which they form. In all these figures, the sun is supposed to be above the comet in the figure, and the tail of the comet to be directed downward. In a the sheet of vapor has just begun to rise. In & it is risen and expanded yet further. In c it has begun to move away and pass around the comet on all sides. Finally, in d this last motion has gone so far that the higher portions have nearly disappeared, the larger part of the matter having moved away toward the tail. Before the stage c is reached, a second envelope will commonly begin to rise as at a, so that two or three may be visible at the same time, enclosed within each' other. In the next figure th?^ actual motion of the matter compos* 393 ASTRONOMY. it ing the envelopes is shown by the courses of the several dotted lines. This motion, it will be seen, is not very unlike that of water thrown up from a fountain on the part of the nucleus nearest the sun and then falling down on all sides. The point in which the motion of the cometic matter differs from that of the fountain is that, instead of being thrown in continuous streams, the action is intermittent, the fountain throwing up successive sheets of matter instead of continuous streams. From the gradual expansion of these envelopes around the head of the comet and the continual formation of new ones in the im- mediate neighborhood of the nucleus, they would seem to be due to a process of evaporation going on from the surface of the latter. Each layer of vapor thus formed rises up and spreads out con- tinually until the part next the sun attains a certain maximum height. Then it gradually moves away from the sun, keeping its distance from the comet, at least until it passes the latter on every side, and continues onward to form the tail. Fig. 104. — formation op comet's tail. These phenomena were fully observed in the great comet of 1858, the observations of which were carefully collected by the late Professor Bond, of Cambridge. The envelopes of this comet were first noticed on September 20th, when the outer one was 16" above the nucleus and the inner one 3". The outer one disap- peared on September 30th at a height of about 1'. In the mean 'While, however, a third had appeared, the second having gradually expanded so as to take the place of the first. Seven successive envelopes in all were seen to rise from this comet, the last one com- mencing on October 20th, when all the others had been dissipated. The rate at which the envelopes ascended was generally from 50 to 60 kilometres per hour, the ordinary speed of a railway-train. The first ono rose to a height of about 30,000 kilometres, but it was finally dissipated. But the successive ones disappeared at a lower and lower elevation, the sixth being lost sight of at a height of about 10,000 kilometres. SPECTRA OF COMETS. 393 In the great comet of 1861, eleven envelopes were seen between July 2d, when portions uf three were in sight, and the 19th of the same month, a new one rising at regular intervals of every sec- ond day. Their evolution and dissipation were accomplished with much greater rapidity than in the case of the great comet of 1858, an envelope requiring but two or three days instead of two or three wc>(>.\cs to pass through all Ua phases. § 3. THE PHYSICAL CONSTITUTION OP COMETS. To tell exactly what a comet is, we should be able to show how all the phenomena it presents would follow from the properties of matter, as we learn them at the surface of the earth. This, however, no one has been able to do, many of the phenomena lieing such as we should not ex- pect from the known constitution of matter. All we can do, therefore, is to present the principal characteristics of comets, as shown by observation, and to explain what is wanting to reconcile these characteristics with the known properties of matter. In the first place, all comets which have been examined with the spectroscope show a spectrum composed, in part at least, of bright lines or bands. These lines have been supposed to be identified with those of carbon ; but although the similarity of aspect is very striking, the iden- tity cannot be regarded as proven. A B Fig. 105.— spectra op olefiant gas and of a comet. In the annexed figure the upper spectrum, A, is that of carbon taken in olefiant gas, and the lower one, B, that of a comet. These spectra interpreted in the usual way would indicate, firstly, that the comet is gaseous ; secondly, that the gases which compose it are so hot as to sliine by tlicir own light. But we cannot admit t i : ; i i i \i < ■ • ' 894 ASTRONOMY. these interpretations without bringing in some additional theory. A mass of gas surrounding so minute a body as the nucleus of a telescopic comet would expand into space by virtue of its own elasticity unless it were exceedingly rare. Moreover, if it were incandescent, it would speedily cool off so as to be no longer self- luminous. \ye must, therefore, propose some theory to accomit for the continuation of the luminosity through many centuries, such as electric activity or phosphorescence. But without further proof of action of these causes we cannot accept their reality. We are, therefore, imable to say with certainty how the light in the spectrum of comets which produces the bright lines has its origin. i In tlie last chapter it was shown that swarms of minute particles called meteoroids follow certain comets in their orhits. This is no doubt true of all comets. We can oidy regard these meteoroids as fragments or dehris of the comet. The latter has therefore been considered by Pro- fessor Newton as made up entirely of meteoroids or small detached masses of matter. These masses are so small and 80 numerous that they look like a cloud, and the light which they reflect to our eyes has the milky appearance peculiar to a comet. On this theory a telescopic comet ■which has no nucleus is simply a cloud of these minute bodies. The nucleus of the brighter comets may either be a more condensed mass of such bodies or it may be a solid or liquid body itself. If the reader has any difliculty in reconciling this theory of detached particles with the view already presented, that the envelopes from which the tail of the comet is formed consist of layers of vapor, he must remember that vaporous masses, such as clouds, fog, and smoke, are really composed of minute separate particles of water or carbon. Formation of the Comet's Tail. — The tail of the comet is not a permanent appendage, but is composed of the masses of vapor which we have already described as as- cending from the nucleus, and afterward moving away from the sun. The tail which we see on one evening is not absolutely the same we saw the evening before, a / MOTIONS OF COMETS. 395 lal theory, icleus of a f its own if it were )nger self- ;o account centuries, ut further ility. We fht in tlie its origin. I minute in their can only 9 of the by Pro- or small mall and he light pearanee c cojnet 1 minute ly either tiay be a 3 theory esented, omet is ber that ike. are vater or 3 comet of the as as- igaway 3ning is jfore, a portion of the latter having been dissipated, while new matter has taken its place, as with the stream of sn»oke from a steamship. The motion of the vaponms matter which forms the tail being always away from the sun, there seems to be a repulsive force exerted l)y the sun upon it. The form of the comet's tail, on the supposition that it is composed of matter thus driven away from the sun with a uniformly accelerated velocity, has been several times investigated, and found to represent the observed form of the tail so nearly as to leave little doubt of its correctness. We may, therefore, regard it as an observed fact that the vapor wiiich rises from the nucleus of tlio comet is repelled by the sun instead of lunng attracted toward it, as other masses of matter are. No adequate explanation of this repulsive force has ever been given. It has, indeed, been suggested that it is electrical in its character, but no one has yet proven experimentally that the attrac- tion exerted by the sun upon terrestrial bodies is influenced by their electrical state. If this were done, we should have a key to one of the most diflicult problems connected with the constitution of comets. As the case now stands, the repulsion of the sun upon the comet's tail is to be regarded as a well-ascertained and entirely isolated fact which has no known counterpart in any other observed fact of nature. In view of the difficulties we find in explaining the phenomena of comets by principles based upon our terrestrial chemistry and physics, the question will arise whether the matter which composes these bodies may not be of a constitution entirely different from that of any matter we are acquainted with at the earth's surface. If this were so, it would be impossible to give a complete explanation of comets until we know what forms matter might possibly assume different from those we find it to have assumed in our labora- tories. This is a question which we merely suggest without attempting to speculate upon it. It can be answered only by ex- perimental researches iu chemistry and physics. § 4. MOTIONS OP COMETS. Previous to the time of Newton, no certain knowledge respecting the actual motions of comets in the heavens had been acquired, except that they did not move around / 396 ASTRONOMY. the sun like the planets. "When Newton investigated the mathematical results of the theory of gravitation, he found that a body moving under the attraction of the sun might describe either of the three conic sections, the ellipse, par- abola, or hyperbola. Bodies moving in an ellipse, as the planets, would complete their orbits at regular intervals of time, according to laws already laid down. But if the body moved in a parabola or a hyporl)ola, it would never return to the sun after once passing it, but would move off Pig. 106.— elliptic and parabolic orbits. to infinity. It was, therefore, very natural to conclude that comets might be bodies which resemble the planets in moving under the sun's attraction, but which, instead of describing an ellipse in regular periods, like the planets, move in parabolic or hyperbolic orbits, and therefore only approach the sun a single time during their whole existence. This theory is now known to be essentially true for ORBITS ©> COMETS. 397 for most of the observed comets. A fetr are indeed found to be revolving around tbo sun in elliptic ofbits, which differ from those of the planets only in being much Hiore eccen- tric. But the greater number which liave been observed have receded from the sun in orbits which we are unftble to distinguish from parabolas, though it is possible they may be extremely elongated ellipses. Comets are there- fore divided with respect to their motions into two classes : (1) periodic comets^ which are known to move in elliptic orbits, and to return to the sun at fixed intervals ; and (2) parabolic comets, apparently moving in parabolas, never to return. The first discovery of the periodicity of a comet was made by Halley in connection with the great comet of 1682. Examining the records of observations, he found that a comet moving in nearly the same orbit with that of lf>82 had been seen in 1607, and still another in 1531. He was therefore led to the conclusion that these three comets were really one and the same object, returning to the sun at intervals of about 75 or 76 years. lie there- fore predicted that it would appear again about the year 1758. But such a prediction might be a year or more in eri'or, owing to the effect of the attraction of the planets upon the comet. In the mean time the methods of calcu- lating the attraction of the planets were so far improved that it became possible to make a more accurate predic- tion. As the year 1759 approached, the necessary com- putations were made by the great French geometer Clai- RAUT, who assigned April 13th, 1759, as the day on which the comet would pass its perihelion. This prediction was remarkably correct. The comet was first seen on Christmas-day, 1758, and passed its perihelion March 12th, 1759, only one month before the predicted time. The comet returned again in 1835, within three days of the moment predicted by De Pontecoulant, the most successful calculator. The next return will probably take ■' ' 398 ASrnONOMY. pliieo ill 1911 or 1012, the exact timo being Htill unknown, because tbe necesnary computations have not yet been made. We give a figure sliowing tlie position of tlio orbit of Ualley's comet relative to the orbits of tlie four outer planets. It attain- ed its greatest dis- tance from the sun, far beyond the or- bit of Neptune, about tlie year 1 873, and th en c o m- menced its return journey. Tlie fig- ure shows the prob- able position of the comet in 1874. It was then far be- yond the reach of the most powerful telescope, but its distance and direction admit of being calculated with so much precision that a telescope could be pointed at it at any required moment. We have already stated that great numbers of comets, too faint to be seen by the naked eye, are discovered by telescopes. A considerable number of these telescopic comets have been found to be periodic. In most cases, the period is many centuries in length, so that the comets have only been noticed at a single visit. Eight or nine, however, have been found to be of a period so short that they have been observed at two or more returns. We present a table of such of the periodic comets as have been actually observed at two or more returns. A immber of others are known to be periodic, but have been observed only on a single visit to our system. Fig. 107.— ORBrr op HAiiLEv's comet. V.' ! .'■A I nknoM'ii, yet been orbit of •ur outer It jittaiu- itest dis- 1 the 81111, I the or- Yeptune, ear 18 73, 1 COlll- 3 return Tlie tig. he prob- )ii of the 874. It far be- reacli of xjwerful >f being le could comets, 3red by lescopic 3t cases, comets ight or so short ns. mets as ns. A fG been ORBITS OF COM El S. 399 Tempe Hallev ^ •♦ \ 5" > 1 Faye's Brorsei S 3 f 7 a f t CO CO 00 •'I "» -^ 5C H- tJI ^ ^ ^ ^ O X Cp P CD CD Or •»» Cl JS i- !2l o < to CO £5 00 cc 2S 73 OS CO to 05 © t-» O H* O H* o OS 00 «i to Cn Cn Cn CI OS OO C^ Ol l-k I— © t2 S tS © © to «o Wi-'i-»lOi-»>-'i-». (&.i-'OSQ0^-tOC0» t-i|£kl-it-iVlOTt909 (;)^.<}.^Oi©tOtO or r3 •si 00 k-i t-k tS to 09 00 S © St 1^ OsS'sJOSCO-Jt.OtO© (^ ^^ tS i-^ 1-^ en © 9s to © Oft VI -' to -} o OS © M >A|^k_kCetot-')-'|~^ ^Z^otOOO&lOS© O H >i S o P5 w n H (3 <& 400 ASTRONOMY. I! ' > Theory of Cometary Orbits. — There is a |)roperty of all or- bits of bodies around the sun, an understanding of which will enable us to form a clear idea of some causes which affect the motion of comets. It may be expressed in the following tlieoreni : The mean distance of a body from the sun, or the major semi-axis of the ellipse in which it revolves, depends only upon the velocity of the body at a given distance from the sun, and may be found by the formula, a = u r 2 u — r V a » in which r is the distance from the sun, v the velocity with which the body is moving, and /i a constant proportional to the mass of the sun and depending on the units of time and length we adopt. To understand this formula, let us imagine ourselves in the celes- tial spaces, with no planets in our neighborhood. Suppose we have a great number of balls and shoot them out with the same velocity, buf in different directions, so that they will describe orbits around the sun. Then the bodies will all describe different orbits, owing to the different directions in which we threw them, but these orbits will all possess the remarkable property of having equal major axes, and therefore equal mean distances from the sun. Since, by Kefleu's third law, the periodic time depends only upon the mc-an distance, it follows that the bodies will liuve the same time of revolution around the sun. Consequently, if we wait patiently at the point of projection, they will all make a revolution in the same time, and will all come back again at the same moment, each one coming from a direction the opposite of tliat in which it was thrown. In the above formula the major axis is given by a fraction, having the expression 3 /x — r «" for its denominator ; it follows that if the 3 u squar« of the velocity is almost equal to — ^, the value of a will become very great, because the denominator of the fraction will be very small. If the velocity is such that 2 ft — r »" is zero, the mean distance will become infinite. Hence, in this case the body will fly off to an infinite distance from the sun and never return. Much less will it return if the velocity is still greater. Such a velocity will make the value of a algebraically negative and will correspond to the hyperbola. If we take one kilometre per second as the unit of velocity, and the mean distance of the earth from the sun as the unit of distance, the value of ft will be represented I y the number 875, so that the formula for a will be a = -^-- -. From this equation, we may 1750— rv" ^ ' •' calculate what velocity a body moving around the sun must have at any given distance r, in order that it may move in a parabolic orbit — that is, that the denominator of the fraction shall vanish. This condition will give »* = . At the distance of the earth ORIGIN OF COMETS. 401 from the sun wo have r = 1, so that, at thut distance, v will be the square root of 1750, or nearly 42 kilometres per second. The fur- ther we get out from the sun, the less it will i>e ; and we may remark, as an interesting theorem, that whenever Vui comet is at the dis- tance of one of the planetary orbits, its velocivy must be equal to that of the planet multiplied by the square rout of 2, or 1'414, etc. Hence, if the velocity of any planet were suddenly increased by a little more than -,*f of its amount, its orbit would be changed into a parabola, and it would fly away from the sun, never to return. It follows from all this that if the astronomer, by observing the '•jurse of a comet along its orbit, can determine its exact velocity from point to point, he can thence calculate its mean distance from the sun and its periodic time. But it is found that the velocity of a large majority of comets is so nearly equal to that required for motion in a parabola, that the difference eludes observation. It is hence concluded that most comets move nearly in parabolas, and will either never return at all or, at best, not until after the lapse of many centuries. a will earth § 5. ORIGIN OF COMETS. All that we know of comets seems to indicate that they did not originally belong to our c'vstem, but became mem- bers of it through tlie disturbing,- forces of the planets. From what was said in the last section, it will be seen that if a comet is moving in a parabolic orbit, and its velocity is diminished at any point by ever so small an amount, its orbit will be changed into an ellipse ; for in order that the orbit may be parabolic, the quantity 2 fi — r v" nmst remain exactly zero. But if we then diminish v by the smallest amount, this expression will become finite and positive, and a will no longer be infinite. Now, the attraction of a planet may have either of two opposite effects ; it may either incren-^'^ or diminish tl e velocity of the comet. Hence if the latter be moving in a parabolic orbit, the at- traction of a planet might either throw it out into a hyper- bolic orbit, so that it would never again return to the sun, but wander forever through the celestial spaces, or it might change its orbit into a more or less elongated ellipse. Suppose CD to represent a small portion of the orbit of the planet and A B ^ small portion of the orbit of a comet passing near it. Suppose also that the comet passes 402 ASTRONOMY. a little in front of the planet, and that the siinnltaneoiis positions of the two bodies are represented by the corre- sponding letters of the alphabet a, h, c, d, etc.; the shortest distance of the two bodies will be the line c iter, and approached so near it that it was impossible to determine on which side it passed. This approach, it wdll be remembered, could not be oV served, because the comet was entirely out of sight, but it was calculated with absolute certainty from the theory of the comet's motion. The attraction of Jupiter, therefore, threw it into some orbit so entirelv different that it has never been seen since. It is also highly probable that the comet had just been brought in l)y the attraction of Jupiter on the very revo- lution in which it was first observed. Its history is this : Approaching the sun from the stellar spaces, probably for the first time, it passed so near Jupiter in 1767 that its or- bit was changed to an ellipse of short period. It made two complete revolutions around the sun, and in 1779^ again met the planet near the same place it had met him before. The orbil was again altered so much that no tel- escope has found the comet since. No other case so re- markable as this has ever been noticed. Not only are new comets occasionally brought in from 404 ASTRONOMY. the stellar spaces, but old ones may, as it were, fade away and die. A case of this sort is afforded by Biela's comet, which has not been seen since 1852, and seems to have en- tirely disappeared from the heavens. Its history is so in structi VG that we present a brief synopsis of it. It was first -observed in 1772, again in 1805, and then a third time in 1826. It was not until this third apparition that its peri- odicity was recognized and its previous appearances iden- tified as those of the same body. The period of revolu- tion was found to be between six and seven years. It was 80 small as to be visible in ordinary telescopes only when the earth was near it, which would occur only at one re- *■ vr out of three or four. So it was not seen again until ii' : the end of 1845. Nothing remarkable was noticed in its appearance until January, 1840, when all were aston- ished to find it separated into two complete comets, one a little brighter than tlie other. The computation of Pro- fessor liuBBAKD makes the distance of the two bodies to have been 200,000 miles. The next observtjd return was that of 1852, when the two comets were again viewed, but far more widely separated, their distance having increased to about a mil- lion and a half of miles. Their brightness was so nearly equal that it was not possible to decide which should be considered the principal comet, nor to determine with certainty which one should be considered as identical with the comet seen during the previous apparition. Though carefully looked for at every subsequent return, neither comet has been seen since. In 1872, Mr. Pogson, of Madras, thought that he got a momentary view of the <3omet through an opening between the clouds on a stormy evening, but the position in which he supposed himself to observe it was so far from the calculated one that his obser- vation has not been accepted. Instead of the comet, however, we had a meteoric shower. The orbit of this comet almost intersects that of the earth. It was therefore to be expected that the latter, on passing REMARKABLE COMETS. 405 fade away ^'s comet, 3 have en- rj is 80 in 't was first •d time in t its peri- ncea iden- )f revolu- s. It was )nly when at one re- Lgain until noticed in ere aston- lets, one a n of Pro- bodies to when the I'e widely out a mil- so nearly hould be nine with tical with it return, POGSON, w of the a stormy imself to lis obser- shower. he earth. 1 passing the orbit of the comet, would intersect the fragmentary metcoroids supposed to follow it, as explained in the last chapter. According to the calculated orbit of the comet, it crossed the point of intersection in September, 1872, while the earth passes the same point on November 27th of each year. It was therefore predicted that a meteoric shower would be seen on the night of November 27th, the radiant point of which would be in the constellation Andromeda. This prediction was completely verified, but the meteors were so faint tliat though they succeeded each other quite rapidly, they might not have been noticed by a casual observer. They all radiated from the predicted point with such exactness that the eye could detect no deviation what- ever. We thus have a third case in which meteoric showers are associated with the orbit of a comet. In this case, how- ever, the comet has been completely dissipated, and proba- bly has disappeared forever from telescopic vision, though it may be expected that from time to time its invisible fragments will form meteors in the earth's atmosphere. § 6. HEM ARK ABLE COMETS. It is familiarly known that bright comets were in former years objects of great terror, being supposed to presage the fall of empires, the death of monarchs, the approach of earthquakes, wars, pestilence, and every other calamity which could aftlict mankind. In showing the entire groundlessness of such fears, science has rendered one of its greatest benefits to mankind. In 1456, the comet known as Halley's, appearing when the Turks were making war on Christendom, caused such terror that Pope Calixttts ordered prayers to be offered in the churches for protection against it. This is supposed to be the origin of the popular myth that the Pope once issued a bull against the comet. The number of comets visible to the naked eye, so far as 406 ASTRONOMY. recorded, lias generally ranged from 20 to 40 in a cen- tury. Only a small portion of these, however, iiave been so bright as to excite universal notice. Comet of 1680. — One of the most remarkable of those brilliant comeU is that of 1680. It inspired bucli terror that a medal, of which we present a figure, was struck upon the Continent of Europe to quiet apprehension. A free translation of the inscription is : *' The star threatens evil things ; trust only ! God will turn them to good. ' ' What makes this comet especially remarkable in history is that Newton calculated its orbit, and showed that it moved around the sun in a conic section, in obedience to the law of gravitation. Pig. 109. — medal op the great comet of 1680. Great Comet of 1811. — Fig. 110 shows its general ap- pearance. It has a period of over 3000 years, and its aphelion distance is about 40,000,000,000 miles. Great Comet of 1843. — One of the most brilliant com- ets which have appeared during the present century was that of February, 1843. It was visible in full daylight close to the sun. Considerable terror was caused in some quarters, lest it might presage the end of the world, which had been predicted for that year by Miller. At perihelion it passed nearer the sun tlian any other body has ever been known to pass, the least distance being only about one fifth of the sun's semi-diameter. "With a very slight change of its original motion, it would have actuall;^ fallen into the sun. GREA T CO. VET OF 1858. 407 in a ccn- lave been 3 of these icli terror vas struck isioii. A threatens o good." in history ed that it ^dience to jneral ap- and its ant com- tury wa& dayhght in some e world, -ER. At ler body ling only h a very actuall;^ Great Comet of 1850. — Another rcmarhable comet for the length of time it remained visible was that of 1858, It is frequently called after the name of Donati, its first discoverer. 'No comet visiting our neighborhood in Fig. 110 —great comet op 1811. recent times has afforded so favorable an opportunity for studying its physical constitution. Some of the results of the observations made upon ithaTcilready been presented. l! ^ Fig. 111.— donati's comet of 1858. ENCKE'S COMET. 409 Its greatest brilliancy occurred about tlic beginning of October, when its tail was 40° in length and 1U° in breadth at its outer end. DoNATi's comet had not long been observed when it was found that its orbit was decidedly elliptical. After it disappeared, the observations were all carefully investigated by two mathematicians, Dr. Von Asten, of Gennany, and Mr. G. "W. Hill, of this country. The latter found a period of 1050 years, which is probably within a half a century of the truth. It is probable, therefore, that this comet appeared about the lirst century before the Chris- tian era, and will return again about the year 3800. Encke*s Comet and the Besisting Medium. — Of telescopic comets, that which has been most investigated by astrouomers is known as Encke's comet. Its period is between three and four years. Viewed with a telescope, it is not different in any respect from other telescopic comets, appearing simply as a mass of foggy light, somewhat brighter near one side. Under the most favorable circumstances, it is just visible to the naked eye. The circumstaiio-e which has lent most interest to this comet is that the observations which have been made upon it seem to indicate that it is gradu illy approaching the sun. Enckk attributed this change in its orbit to the existence in space of a resisting medium, so rare as to ha\ e no appreciable effect upon the motion of the planets, and to be felt only by bodies of extreme tenuity, like the telescopic comets. The approach of the comet to the sun is shown, not by direct obser- vation, but only by a gradual diminution of the period of revolu- tion. It will be n;any centuries before this period would hi so far diminished that the comet would actually touch the sun. If the change in the period of this comet were actually due to the cause which Encke supposed, then other faint comrts of the same kind ought to be subject to a similar influence. Put the in- vestigations which have been made in recent times on ^.hese bodies show no deviation of the kind. It might, therefore, be concluded that the change in the period of Encke's comet must be due to some other cause. There is, however, one circumstance which leaves us in doubt. Encke's comet passes nearer the sim than any other comet of short period which has been observed with sufli- cient care to decide the question. It may, therefore, be supposed that the resisting medium, whatever it may be, is densest near the sun, and does not extend out far enough for the other comets to meet it. The question is one very difficult to settle. The fact is that all comets exhibit slight anomalies in their motions which pre- vent us from deducing conclusions from them with the same cer- tainty that we should from those of the planets. * V |Ji f'f'J :^:i :i'^ 4' ilil PAET III. THE UNIVERSE AT LARGE. INTRODUCTION. In onr studies of the lieavenly bodies, we liave liitherto been occupied almost entirely with those of the solar sys- tem. Although this system comprises the bodies which are most important to us, yet they form only an insignifi- cant part of creation. Besides the earth on which we dwell, only seven of the bodies of the solar system are plainly visible to the naked eye, whereas it is well known that 200(> stars or more can be seen on any clear night. We now have to describe the visible universe in its largest extent, and in doing so shall, in imagination, step over the bounds in which we have liitherto confined ourselves and fly through the immensity of space. The material universe, as revealed by modern telescopic investigation, consists principally of shining bodies, many milhons in number, a few of the nearest and brightest of which are visible to the naked eye as stars. They extend out as far as the most powerful telescope can penetrate, and no one knows how much farther. Om sun is simply one of these stars, and does not, so far as we know, differ from its fellows in any essential characteristic. From the most careful estimates, it is rather less bright than the average of the nearer stars, and overpowers them by its brilliancy only because it is so much nearer to us. The distance of the stars from each other, and therefore 4 415 ASTIiOXOMr. from the nun, is iinmonsely greater than aii}' of the dis- taiicen which we liave hitlierto iiad to eonsider in tiie sohir system. Suppone, for iuntance, that a walker through tlio celestial sj)aceHeould start out from the sun, taking steps 3(KM> nn'les long, ore(|ual to the distance from Liverpool to New York, and making 120 steps a minute. This speed Avould carry him around the earth in ahout four seconds ; lie would M'alk from the sun to tlie earth in four hours, and in five days he would reach the orbit of y^'pttoie. Yet if lie should start for the nearest star, he would not reach it in a hundred years. Long hefore he got there, the whole orbit of Xcjjfnnc, supi)osing it a visible object, would have been reduced to a point, and have finally vanished from sight altogether. In fact, the nearest known star is about seven thousand times as far as the planet yoptam. If we supj)ose the orbit of this planet to bo represented by a chiUrs hoop, the nearest star would be three or four miles away. We have no reason to suppose that contiguous stars are, on the average, nearer than this, excep ' i sj^ecial cases M'here they are collected together in clus The total number of the stars is estimated by millions, and they are i)robably separated by these wide intervals. It follows that, in going from the sun to the nearest star, we would be siuiply taking one step in the universe. The most distant stars visible in great telescopes are probably several thousand times mere distant than the nearest one, and we do not know what may lie beyond. The point we wish principally to impress on the reader in this connection is that, although the stars and ]>lanets pre- sent to the naked eye so great a similarity in appearance, there is the greatest possible diversity in their distances and characters. The planets, though many millions of miles away, are comparatively near us, and form a little family by themselves, which is called the solar system. The fixed stars are at distances incomparably greater — the nearest star, as just stated, being thousands of times more distant than the farthest planet. The planets are, so far TIII'J UXlVEliSK AT LARGE. • the (lis- [ tlie Hohir ' tlirough king steps r'erpool to liis 8])eed seconds ; lOurs, and . Yet if t reach it :lie wliole Kuld have lied from r is about tanpear that there are in the whole celestial sphere about GOOO stare visible to an ordinarily good eye. Of these, however, we can never see more than a fraction at any one time, because one half of the sphere is always of necessity below the horizon. If we could see a star in the horizon as easily as in the zenith, one half of the whole number, or 3000, would he visible on any clear night. But stai-s near the horizon are seen through so great a thickness of atmosphere as greatly to obscure their light ; consequently only the brightest ones can there be seen. As CLASSES OF STAIiS. 415 SNS. eye, the 3ver tlie from an is a cer- 3llations. brighter of bril- barely ter stai'S le stan classes; '■ hirgely niiess of ch have le whole diuarily ore than iliere is Id see a If of the r night. great a r light ; 3en. As a result of this obscuration, it is not likely t\ *■ more than 2000 stars can ever be taken in at a sint'^ ^ .iew by any ordinary eye. About 2000 other sta > . re so near the South Pole that the; never rise in our latitudes. Hence out ol the 6000 supposed to be visible, only 4000 ever come within the range of our vision, unless we make a journey toward the equator. The Galaxy. — Another feature of the heavens, which is k^ss striking than the stars, but has been ivoticed from the earliest times, is the Galaxrj, or MUl'n \V, as well as the group of the Pleiades, or Seven Stars, and the constellation of Orion. Indeed, it would seem that all the earlier civilized nations, Egyptians, Chinese, Greeks, and Hindoos, had some arbitrary division of the surface of the heavens into irregular, and often fantastic shapes, which were distinguished by names. In early times, the names of heroes and animals were givf^n to the constellations, and these designations have come down to the present day. Each object was sup- posed to be painted on the surface of the heavens, and the stars were designated by their position upon some portion of the object. The ancient and medioBval astronomers would speak of ' ' the bright star in the left foot of Orion,^'' "the eyeof the J?mZ^," " the heart of theZ/ow," " the head of Perseus,'''' etc. These figures are still re- tained upon some star-charts, and are useful where it is desired to comjiare the older descriptions of the constella- tions with our modern maps. Otherwise tl ey have ceased to serve any purpose, and are not generally found on maps designed for astronomical uses. The Arabians, who used this clumsy way of designating stars, gave special names to a large number of the brighter ones. Some of these names are in common use at the present time, as Aldebaran, Fomalhaut, etc. A few other names of brigui: stars have come down from prehistoric times, that of Arcturua for instance : they are, how- ever, gradually falling out of use, a system of nomencla- ture introduced in modern times having been substituted. In 1654, Bayer, of Germany, mapped down the constel- lations upon charts, designating the brighter stars of each NAMIXG THE STARS. 4n 3 ev Jence icement of riglitest in r the name self. The our north- K and He [)ven Stars, I'ould seem s, Cliinese, ion of the sn fantastic imals were itions have :t was sup- ns, and the )nie portion istronomers Ift foot of the IJon^ ' ' re still re- tvhere it is 3 constella- lave ceased id on maps designating lie brighter liise at the few other [prehistoric are, how- nomencla- ibstituted. he constel- irs of each constellation by the lettei*s of the Greek alphabet. When this alphabet was exliausted, he introduced the letters of the Ronian alphabet. In general, the brightest star was designated by the first letter of the .alphabet a, the next by the following letter /3, etc. Although this is sometimes supposed to have been his rule, the Greek letter affords only an imperfect clue to tiie average magnitude of a star. In a great many of the constellations there are deviations from the order, the brightest star being 3; but where stars differ by an entire magnitude or more, the fainter ones nearly ahv.iys follow the brighter ones in alphabetical order. On this svsteni, a star is desii'iiated bv a certain Greek letter, followed by the genitive of the Latin name of the constelhition to which it belongs. For example, a Canis Majoi'ls, or, in English, a of the Great Dog, is the desig- nation of Sh'iuH^ the brightest star in the heavens. The seven stai*s of tlie Gt'ait /?^.v//' are called oc Ursw Jfcijo/'fs, (i Ursw JLtJo/'is, etc. ArduruH is a Boiltis. The reader will here see a resemblance to our wav of desii^nat- ing individuals by a Christian name followed by the family name. The Greek letters furnish the Christian names of the separate stars, while the name of the constellation is that ot the family. As there are only fifty letters in the two alphabets used by Bayeu, it will be seen that only the fifty brightest stars in each constellation could be desig- nated by this method. In most of the constellations the number thus cliosen is much less than fifty. When hy the aid of the telescope many more stars than these were laid down, some other method of denoting them became necessary. Flamsfkei), who oi)served be- fore and after 1700, prepared an extensive catalogue of stars, ill which those of each constellation were designated bv numbers in the order of ri<;ht ascension. These num- bers were entirely independent of the designations of Bayer — that is, he did not omit the Bayeu stars from his system of numbei-s, but numbered them as if they had 110 Greek letter. Hence those stars to which Bayer ap- 4^2 ASTRONOMY. r plied letters have two designations, the letter and the number. Flamsteed's numbera do not go much above 100 for any one constellation — I'aarus, the richest, having 131). When we consider the more numerous minute stars, no systematic method of naming them is possible. The star can be designated only by its position in the lieavens, or the imniber which it bears in some well known catalogue. § 4. DESCRIPTION OP THE CONSTELLATIONS. The aspect of the starry heavens is so j^leasing that nearly every intelligent person desires to possess some knowledge of the names and forms of the principal con- stellations. We therefore present a brief description of the more striking ones, illustrated by figures, so that the reader may be able to recognize them when lie sees them on a clear night. We begin with the constellations near the pf>le, because they can be seen on any clear night, while tlie southern ones can, for the most part, only be seen during certain seasons, or at certain hours of the night. The accompany- ing figure shows all the stars within 50° of the pole down to the fourth magnitude inclusive. The Roman numerals around the margin show the meridians of right ascension, one for every hour. In order to have the map represent the northern constellations exactly as they are, it must be hehl so that the hour of sidereal time at which the observer is looking at the heavens shall be at the top of the map Supposing the observer to look at nine o'clock in the even- ing, the months around the margin of the map show the regions near the zenith. He has tlierefore only to hold the map with the month upward and face the north, when he will have the northern heavens as they appear, except that the stars near the bottom of the map will be cut off by the horizon. The first constellation to be looked for is Ursa Major y TJIK CON STELLA TIONS. 4:i3 and the 5 100 for viiig 130. i stars, no The star iaveus, or catalogue. the Gfeat Bear, familiarly known as *' the Dipper." The two extreme stars in this constellation point toward the pole-star, as already explained in the opening chapter. Ursa 3lmor, sometimes called " the Little Dipper," is the constellation to which the pole-star belongs. Abou/" LTIONS. asing that ssess some icipal con- 3ription of ,0 that the ! sees them le, l)ecanse |e southern ng certain ccompany- ole down I numerals ascension, represent it must be le observer the map the even. show the ;o hold the when he ir, except I be cut off ha Major f ^'"'""lu/r,,nl(r/,; ""o// t'n.s.snjj»ciu Fm. 112— MAP OP THE NORTHERN CONSTELLATIONS. 15° from the pole, in right ascension XV. hours, is a star of the second magnitude, fi Ursw Minor is, sibout as bright as the pole-star. A curved row of three small stars lies between these two bright ones, and forms the handle of the supposed dipper. 4»4 ASTRONOMY. Cassiopeia^ or " the Lady in the Chair," is near hour 1 of riglit ascension, on the opposite side of the pole-star from Ursa Major^ and at nearly the same distance. Tlie six brigliter stare are supposed to bear a rude resem- blance to a chair. In mytliology, Cassiopeia was the queen of Cepheus^ and in tlie mytliological representation of the constellation she is seated in the chair from which she is issuing her edicts. In hour III of right ascension is situated the constella- tion Perseus^ about 10° further from the pole than Cas- slopela. The Milky Way passes througli these two con- stellations. Draco^ the Dragon, is formed principally of a long row of stars lying between Ursa Major and Ursa Minor. The head of the monster is formed of the northernmost three of four bright stars arranged at the corners of a lozenge between X y II and XVIII hours of right ascen- sion. Cepheiis is on the opposite side of Cassiopeia from. Perseus, lying in the Milky Way, about XXII hours of right ascension. It is not a brilliant constellation. Other constellations near the pole arc Camelopardalis^ Lyivx, and Lacerta (the Lizard), but they contain only small stars. In describing the southern constellations, we shall take four separate positions of the starr^y sphere corresponding respectively to VI hours, XII hours, XVIII houre, and houi-s of sidereal time or right ascension. These hours of course 0(!cur every day, but not always at con- venient times, because they vary with the time of the year, as explained in Chapter I., Part I. We shall lirst suppose the observer to view the heavens at VI lioure of sidereal time, which occurs on Decem- ber 21st about midnight, January 1st about 11.30 p.m., February 1st about 9.30 p.m., March Ist about 7.30- p. M. , and so on through the year, two houre earlier every month. In this position of the sphere, the Milky Way THE CONSTKLLA TIONS. 425 ir hour 1 pole-star distance. ) resera- lie queea on of the ich she ia ionstella- lian Cas- two con* f a long I Minor. henimost lers of a it ascen- eia from, hours of 1. mmlalis, ain only all take ponding I houi*s, These at con- of the heavens Decern- 50 P.M., mt 7.30 er every ky Way spans the heavens like an arch, resting on the horizon be- tween north and north-west on one side, and between south and south-east on the other. We shall first describe the constellations which lie in its course, beginning at the north. C'epheus is near tiie north-west horizon, and above it is Camiojpeia^ distinctly visible at an altitude nearly equal to that of the pole. Next is l^emeun^ just north- west of the zenith. Above l*ei'seus lies Aurhja, the Charioteer, which may be recognized by a bright star of the first magnitude called Capella (tlie Goat), now quite near the zenith. Auriga is represented as holding a goat in his arms, in the body of which the star is situated. About 10° east of Cajjella is the star li Aurig(JB of the second magnitude. Going further south, the Milky Way next passes between Tan r us and Gemini. Taurus^ the Bull, may be recognized by the Pleiades^ or " Seven Stars." lieally there are only six stars in the group clearly visible to ordi- nary eyes, and any eye strong enough to see seven will prob- ably see four others, or eleven in all. This group forms an interesting object of study with a small telescope, as sixty or eighty stare can then readily be seen. We therefore pre- sent a telescopic view of it, the six large stars being those visible to any ordinary eye, the five next in size those which can be seen by a re- markabl^"^ good eye, and the others those which require a telescope. East of the Pleia- des is the bright red star Aldebaran^ or " the Eye of the Bull." It lies in a group called the Ilyades, ar- ranged in the form of the letter V, and forming the face FlO. 113. — VIEW OF THE PI-EI- ADE8 AS SEEN IN AN INVEHT- INO TELESCOPE. 426 ASTRONOMY. of the Bull. In tlio niiMdU! of one of tlio ! '^s of tlio V will bo seen a beautiful pair of stars of tbo fonrtb nia«^ni- tude very close together. They are called H Tnurt. Oi'/nini, the Twins, lie east of the Milky Way, and may be recognized i>y the bright utars Cantor and Pollux^ which iio 20" or 30° south-east or south of the zenith. 'it I Pig. 114. — the constellation orion. They are about 5° apart, and Pollux, the southernmost one, is a little brighter than Castor. Orion, the most brilliant constellation in the heavens, is very near the meridian, lying south-east of Taurus and south-west of Gemijni. It may be readily recognized by the figure which we give. Four of its bright stars form 1 THE rONSTKLLA TIOXS. 427 ■)f the V li inagni- V^ay, and P(dlux, 3 zeuitli. ernmost leavens, rvs and ized by re form the cornorfl of a rectan«?le about I'l" lon sickle, of which Regulus is the handle. As the Lion was drawn among the old constellations, Reijulus formed hia heart, and was therefore called C(yr Leonis. The sickle forms his head, and his body and tail extend toward the horizon. The tail ends near the star Denehola, which is quit*^. near the horizon. Leo Minor lies to the north of Leo, and Sextans, the Sextant, south ov it, but neither contains any bright stars. Eridanus, the River Po, south-west of Orion,', Lepus, the Hare, south of Orion and west of Can is Major / Columha, the Dove, south of L^epus, are constellations in the south and south-west, which, however, have no strik- ing features. The constellations we have described are those seen at six hours of sidereal time. If the sky is observed at some other hour near this, we may find the sidereal time by the rule given in Chapter I., § 5, p. 30, and allow for the di- urnal motion during the interval. Appearance cf the Constellations, at 12 Hours Sidereal Time. — This hour occurs on April 1st at 11.80 r.M., on May 1st at 0.30 p.m., and on June 1st at 7.30 p.m. At this hour, Ursa Majtn- is near the zenith, and Cassi- opeia near or below the north horizon. The Milky Way is too near the horizon to be visible. Orion has set in the west, and there is no very conspicuous constellation in the south. Castor and Pollux are high u]) in the north-west, and Procyon is about an hour and a half above the horizon, a little to the "outh of west. All the constellations in the west and north-west have been previ- ously described, Leo being a little west of the meridian. Three zodiacal constellations have, however, risen, which we shall describe. Virgo, the Virgin, has a single bright star, Spica, about as bright as Regulus, now about or.e hour east of the meridian, and but little more than half way from the zenith to the horizon. Lihra^ the Balance, is south-east from YirgOf but haa uu conspicuous stars. ^4it 430 ASTRONOMY. Scof'j)iu3, the Scorpion, is just rising in the south-east, but is not yet high enougii to be well seen. Hydra is a very long constellation extending fronv Canis Minof in a south-east direction to the south hori- zon. Its brightest star is or ILjdra^ of the second magni- tude, 25° below liegidus. Corvus, the Crow, is south of Virgo, andmiiy be recog- nized l)y four or live stars of the second or third magni- tude, 15° south-west from Spica. Next, looking north of the zodiacal constellations, we see : Coma Berenices, the Hair of Berenice, now exactly on the meridian, and about 10° south of the zenith. It is a close irregular cluster of very small scars, unlike anything else in the iieavens. In ancient mythology, Berenice had vowed her hair to Yenus, but Jupiter carried it away from the temple in which it was deposited, and made it into a constellation. Bootes, the Bear-Keeper, is a large constellation east of Coma Berenices. It is marked hy uirctitrus, a bright but somewhat red star of the lirst magnitude, about 20"^ east of the zenith. Bootes is repre sented as holding two dogs in a leash. These dogs are called Canes Venatici, and are at the time supposed exactly in our ze- nith chasing Ursa Major around the pole. Corona Borealis, the North- ern Crown, lies next east of Bootes in the north-east It is a small but extremely beautiful constellation. Its principal stars are arranged in the form of a semicircular chaplet or crown. Appearance of the Constellations at 18 Hours of Side- real Time. — This hour occurs on July 1st at 11.30 p.m.., on August 1st at 9.30 p.m., and on September Ist at 7.30 P.M. Fig. 116. -CORONA BORE- ALIS. ith-east, g from th hori- . magni- e recog- inagni- lons, we cactly on It is a iiy thing nice had vay from it into a n east of •ight but 20^ east repre ogs in a called at the our ze- around North- east of It is eautiful le form >f Side- JO P.M.., at 7.30 TnE CONSTELLA TIONS. 431 In this position, the Milky Way seems once more to span the heavens like an arch, resting on the horizon iu the north-east and south-west. But yva do not see the same parts of it which were visible in the first position at six hours of right ascension. Cassiopeia is now in the north-east and Ursa Major has passed over to the west. Arcturus is two or tin ee hours above the western hori- zon. We shall commence, as in the first position of the sphere, by describing the constellations which lie along on the Milky Way, starting from Cassiopeia. Above Cassi- opeia we have Cepheus^ and then Lacerta, neither of which contains any striking stars. Cygnus, the Swan, may be recognized by four or five stars forming a cross directly in the centre of the I^ilky Way, and a short distance north-east from the zenith. The brightest of these stars, ex Cyyni, forms the northern end of the crobo, and is nearly of the fii-st magnitude. Lyra, the Harp, is a beautiful constellation south-west of Cyf/nvs, and nearly in the zenith. It contains the brilliant star Veya, or a ZyrcB, of the first mag- nitude, and of a bluish white color. South of Vega are four stars of the fourth magnitude, forming an oblique par- allelogram, by which the constellation can be read- ily recognized. East of Vega, and about as far £ -^ i.\ J. Fig. 117. — i-yua, the harp. from It as the nearest star of the parallelogram, is s Lynr, a very interesting object, because it is really composed of tw(> ntars oi the fourth magnitude, which can be seen separately by a very keen eye. The power to see this star double is one of the best tests of the acuteness of one's vision (see Fig. 1 22 1. ^mmm 432 ASTRONOMY. Afjuila, the Eagle, is the next striking constellation in the Milky Way. It is two hours east of the meridian, and ahoiit midway between the zenith and horizon. It is readily recognized by the bright star Altair or oe Aqtrilw, situated be- tween two smaller ones, the one of the third and the other of the fourth magnitude. The row of three stars lies in the centre of the IMilky Way. SiKjitta, the Arrow, is a very snuill constellation, formed of three stars innnediately north of PlO. 118.— AQUILA, DELPHI- Af/tti/a NU8.AND 8A01TTA. DelpMn»s, thc Dolphiu, is a striking little constellation north-east of Aquila, recog- nized 1)V four stai*s in the form of a lozenge. It is famil- iarly called "Job's Coffin." In this position of the celestial sphere three new zodia- cal constellations have arisen. Smrpiua, the Scorpion, already mentioned, now two Aours west of the meridian, and about 30° above the horizon, is quite a brilliant constellation. It contains An- iares, or ac Scorplly a red- dish star of nearly the first magnitude, aiid a long curv- ed row of stars west of it. S(i(j!tt by four e square 118. The lie meri- or four jrner of lie south standing st of the ther west it, about ueridian. ! STABS. i stars of lot go on brighter mid be a sent ones rs of the able that ould not 8th, 9th, ous labor will long uestion ; the sky 3U8 tele- imber of 1 to the tral por- zen stars have been found with the Washington 2G-inch refractor which were not seen with the Cambridge 15-inch, although the visible magnitude has been extended from 15"" •! to 16"' '3. If this is found to be tnie elsewhere, the conclusion may be ^^lat, after all, the stellar system can be experimentally shown to be of finite extent, and to contain only a finite number of stars. "We have already stated that in the whole sky an eye of avcrags power will see about 6000 stars. With a telescope this number is greatly increased, and the most powerful telescopes of modern times will probably show more than 60,000,000 stars. As no trustworthy estimate has ever been made, there is great uncertainty upon this point, and the actual number may range anywhere between 40,000,000 and 100,000,000. Of this number, not one out of twenty has ever been catalogued at all. The gradual increase in the number of stars laid down in various of the older catalogues is exhibited in the following table from CuAMBEKs's Descriptice Axtrunomy : Constella- tion, PloU'tnv. B.C. 130. Tycho liruhc. A.I). 1570. II<'vcliu». A.U. 1(500. Flainstecd. A.U. lUUO. B<)(li\ A.D. 1800. Aries Ursa Major.. Bootes Leo Virgo Taurus Orion 18 35 23 35 33 44 38 21 50 28 40 39 43 63 27 73 53 50 60 51 62 66 87 54 95 110 141 78 148 338 319 337 411 394 304 The most famous and extensive series of star observations arc noticed below. The uranometries of Bayer, Flamsteed, Aroei-andeu, Heis, and Gould give the lucid stars of one or both hemispheres laid down on maps. They are supplemented by the star catalogues of other observers, of which a great number has been published. These last were undertaken mainly for the determination of star positions, l«it they usually give as an auxiliary datum the magnitude of the star observed. When they are carried so far as to cover the heavens, they will afford valuable data" as to the distribution of stars throughout the sky. The most complete catalogue of stars yet constructed is the DurchmuHterunq dex Nordlichen Oextirnten Himmeh, the joint work of Aroblandkk and his assistants, KkCoer and Schonpeld. It embraces all the stars of the tirst nine magnitudofi from the North 43G ASTRONOMY N li i I h 1 1 > 1 !■ '! ^'? . i li, IM Pole to 2' of south declination. This work was begun in 1852, and at its completion a catalogue of the approximate places of no less than 314,1)20 stars, with a series of 8tar-mai)s, giving the aspect of the northern heavens for 1855, was jjublished for the use of astrono- mers. AiiGELANDEu's Original plan was to carry this Durchmmterung as far as 23" south, so that every star visible in a small comet-seeker of 2| inches aperture should l;e registered. His original plan was abandoned, but his former assistant and present successor at the observatory of Bonn, Dr. Scuonfeld, is now engaged in executing this important work. The Catalogue of Stars of the British Association for the Ad- vancement of Science contains 8377 stars in both hemispheres, and gives all the stars visible to the eye. It is well adapted to learn the unequal distribution of the lucid stars over the celestial sphere. The table on the opposite page is formed from its data. From this table it follows t'nat the southern sky has many more stars of the first seven magnitudes than the northern, and that the zones immediately north and south of the Equator, although greater in surface than any others of the same width in declination, are absolutely poorer in such stars. The meaning of the table will be much better understood by con- sulting the graphical representation of it on i)rtge 438, by Phoctor. On this chart are laid down all the stars of the British Association Catalogue (a dot for each star), and beside these the Milky Way is represented. The relative richness of the various zones can be at once seen, and perhaps the scale of the map will allow the student to trace also the zone of brighter stars (lst-3d magnitude), which is inclined to that of the Milky Way by a few degrees, and is approx- imately a great circle of the sphere. The distribution and number of the brighter stars (1st- 7th mag- nitude) can be well understood from this chart. In AiuJEi.ANDEii's Durchmusternng of the stars of the northern heavens, there are recorded as belonging to the northern hemi- sphere : 10 stars between the 1-0 magnitude and the 1 '9 magnitude. 87 « 09«osAi-*t^o»iu.ec'^tf>.cio)-^enoo-^e»it^H' + + o o + + o o i 14 i j^MMOiCOOSMWtStOOSi-'i-'OSCOtOi-'tOOSMrOtOtOtO + + +> ^*^ g i-'a>C»«)rf».<*»CS00O»H*QD-^Ol".t*>. eotOO>©QO*OeOCQi«kOSi-*i-'t3>-'K>MeotSi-*t5i-»i-'i-' n^^^^:^U^J,%frn^^'l^%^^^ttt^^ 1 1 3 ^fefeiSg!g2S;tg§^ggg§gSg;£2g5S^S3g 1 1 SSlggSSiS^Sgggl^gSS^I^^S^oSSJSS^iS 1 1 !> O o o O a a a > 3 t 8 d % lit,, i\l ■■■ \-Tr'~-' ' y ■n i BRIQIITNKSH OF THE STARS. 439 e that the brightness of an average star of the first magnitude is about 0"5 of that of a Lyrte. A star of tlie 2d uiagiiitude will shine with a light expressed by 0-5 xO'4=0'2(), and so on. The total brightness of 10 1st magnitude stars is 5-0 •• 37 2d •< II 74 " 132 3d M < « 22 I « 13,593 7th « (), ealleil T Corimm. It was first seen on the 12th (tf ^[ay, lS(U), and w;is then of the 2d ma;rnitnde. Its chanijes were followed bv vari- ous observers, and its m;ignitude found to diminish as follows : 18(i0. Mav n. 14. 15. 10. 17. m. 2-0 o.o ;j-o a- 5 4-0 4-5 1806. May 18. 19. 20. 21. 23. 33. no 70 7-5 8-0 By June 7th it liatl fallen to 0'"'0, and July Tth it waa 1)'"'5. Scumidt's observations of this star [T toronw)^ continued up to 18TT, show that, after falling from tho second to the seventh magnitude in nine days, its light diminished very gradually year after year down to nearly tlie tenth nnignitude, at wliich it has remained pretty con- stant for some years. 13ut during the whole })eriod there have been fluctuations of brightness at tolerably regular intervals of ninety-four days, though of successively de- crejising extent. After the first sudden fall, there seema to have been an increase of brilliaiu*y, which brought the star above tlie seventh magnitude again, in October, 1800, an increase of a full ma^jnitude ; but since that time VARIAIiLE STARS. 4-45 if such before isioii i» ^nition. 5 of de- tiirs ex- f error vention drawn throw- i;eneral. its tlieii l)y vari- iuish as no 6-5 7-0 7-5 8-0 it waa )in tliQ ts light ) nearly tv con- I there regular rely (le- Heema gilt the ctober, at time the changes have been much smaller, and are now but little more than a tenth of a magnitude. The color ot the star has been pale yellow thro'jghout the whole course of observations. The spectroscopic observations of tins star by IIiTdoixs and MiiJ.KU showed it to Imve a spectrum then absohitel} uniij'.jc. The report of tlieir observations says, "the spectrum of this ohjct-t is tw'ifohl, sho\vin<^ that the light \ty wlii(;h it shini's Ims cmiinated fn)!n two distinct sources. The principal spectrum is analogous to tiiat of the sun, and is formed of ligiit whicli was emitted by un incandescent solid or li»juid photosphere, and wiiich has suffered a partial absorption by passing through an atmosplicn; of vapors at a h)wer temperature than the photosphere. Superposed ovcrtius spectrum Is a second spc trum consisting of a few liri>//if lines ■which is duo to light whiv'h has emanated from intensely heated matter in the state of gas." In November, 1870, Dr. Schmidt discovered a new star in Ci/ff' niiH, whose telescopic histt)ry is similar to that given for 7' Curnnii'. When discovered it wiis of the 3d magnitude, and it fell rapidly below visibility to the naked eye. This new star in Ci/ifinin was observed by Cokni', Coi'Kt.AM), and VooKL, by means of the spectroscope ; amd from all the oliscrva- tions it is plain that the hydrogen lines, at first ])roinincnt, have gradually faded. With the decrease in their brilliancy, a line corresponding in position with the brightest of the lines of a nebu- la has strengtiiened. On December 8th, 1870, this last line v.as nuich fainter than F (hydrogen line in the solar spectrum), while on March 2d, 1877, F was very much the fainter of the two. At first it exhibited a continuous spectrum with lunmrous bright lines, but in the latter part of 1877 it emitted only nu*nochronnitic light, the spectrum consisting of a single bright line, correspond- ing in position to the characteristic line of gaseoii." nebuhe. The intermediate stages were characterized by a gradinil fading out, not only of the continuous spectriun, but also of the bright lineb which crossed it. From this fact, it is inferred that this star, which has now fallen to lO.'i magnitudt;, has actually become a plaiu'lary nebula, alTonling an instance of a remarkable reversal of the pro- cess imagined by L\ Placu in his nebular theory. § 3. THEORIES OP VARIABLE STARS. The theory of variable stars now generally accepted by investi- gators is founded on the following general conclusions : (1) That the only distinction whicJi can be made between the various classes of stars we have just described 's one of degree. Between stars as regular as Ah/ol, which goes through its pericnl in less than three days, r.ul the sudden blazing out of the star do ^«ii« '"■i •i 446 ASTIiOyOMT. scribed by Tvciio Buahr, there is every grntlntion of irregularity. The only distinction that run be drivwn between them is in the length of the period >»::J the extent and regularity of the changes. All sucli stars must, ..nerefore, for the present, bo inchided in the single class of variables. It W!is at one time supposed that newly createtl stars appeared from time to time, and that old ones sometimes disappeared from view. But it is now con^ide^ed that there is no well-established case either of the disappearance of an old star or the creation of a new one. The supposed cases of disai>pearance arose from cata- loguers accidentally recording stars in positions where none existed. Subse(|Uent astronomers finding no stars in the ])lace concluded that tlie star had van!"'»''d when in reality it had never existed. The view tliat temporary stars arc new creations is disproved by the rapidity with which they always fade away again. (2) That all stars may be to a greater or less extent variable ; only in a vast majority of cases the variations are so slight as to be impercej>tible to the eye. If our sun could be viewed froni the dis- tance of H star, or if we could actually measure the amount of light Aviiich it transmits to our eyes, there is little doubt that we should lind it to vary with the presence or absence of spots on its surface. "We are therefore led to the result that variability of light may be a common characteristic of stars, and if so we are to look for its cause in something common to all such (tbjects The spots on the sun may give \is a hint of the probable cause of the variations in the light of the stars. Tiie general analogies of the universe, and the observations with the s[>ectroscope, all lead us to the conclusion that the physical constitution of the ,an and stars is of the same general nature. As we see spots on t \e sun which vary in form, size and number from "ould take a suf- flcicntly close view of the faces of the stars we siiould probably see spots on a great number of 'them. In our sun the spots nevr cover more than a very small fraction of the surface ; but we have no reason to suppose that tliis would be the case with the stars. If the spots cover«'»i a large portion of the surface of the star, then th(!ir variatiunain number and extent woiild cause the star to vary in light. This view does hot, however, account for those cases in which the light of a star is suddenly increased in amount hundreds of times. But the spectroscopic observations of 2' Coroixe sIjow another analogy with operations going on in our sun. Mr. IIuooins's ob- servations, whicli we have already cited, seem to show that there was a sudden and extraordinary outburst of glowing hydrogen from the star, which by its own light, as well as by heating up the ■whole surface of the star, caused an increase in its brilliancy. Now, we have on a very small scale something of this same kind going on in our "'>t»i- The red flames which are seen during a total e(;lipse are causei; oy eruptionr, of hydrogen from tl;e interior of the s\m, and these eruptions are generally connected with the faculve or portions of the tuu's disk more brilliant than the rest of the photosphere. VAIUAHLE STARS. 4i7 lich tho times, another Ns's ob- iit there ydrogea \T up tho Tho general theory of variable stars which has now the most evidence in its favor is this : Tliese bodies are, from some <^onoral cause not fully understood, subject to eruptions of glowinj; liydro- gen gas from their interior, and to the formation of dark spots on their surfaces. These eruptions and forniations have in most cases a greater or less tendency to a reguhir period. In the case of our sun, the jjcriod is 11 years, but in the case of many of the stars it is much shorter. Ordinarily, as in the case of the .stm and of a large majority of the stars, the variations are too slight to affect the total quantity of light to any visible extent. But in the case of the variable stars this spot-producing jmvver and the liability to eruditions are very much greater tiian in the case of our sun, and thus we have changes of light which can be readily perceived by the eye. Some adclitional strengtii is given to this theory l)y the fact just nientioned, that .so large a jtroporMon of the variable stars are red. It is well known that glowing Ix.'lies emit a larger proportion of red rays and a smaller proportion of blue ones the cooler tiiey become. It is therefore proltable tl;ut tho red stars have the least heat. This being the case, it is more easy to produce spots on their surface ; and if their outside surface is so cool as to b(?come solid, the glowing hydrogen from the in- terior when it did burst through would do so with more power than if the surrounding shell were liipiid or gaseous. There is, however, one .star of which the variations may be due to an entirely different cause — .'uunely, Ahjol. The extreme regulnrity with which the light of this object fades away and disappears sug- gests the possibility that a dark body may be revolving around it, and partially eclipsing it at every revolution. The law of variation of its light is so different from that of the light of other variable stars as to suggest a different cause. !Most others are lu-ar their maximum for oniy a small part of their itcriod, while J/j/"/is at its maximum for nine tenths of it. Others are subject to nearly con- tinuous changes, while the light of Ahjol remains constant during nine tenths of its period. CHAPTER III. MULTIPLE STARS. § 1. CHABACTER OF DOUBLE AND MULTIPLE STABS. "When we examine the licavens with telescopes, we find many cases in wliicli two or more stHi*s are extremely close together, so as to form a pair, a triplet, or a group. It \& evident that there are two ways to account for this ap- pearance. 1. We may sui^pose that the stars happen to lie nearly in the sa/ne straight line from us, hut have no connection with each other. It is evident that in this case a ]xiir of stars might appear douhle, although the one was hundreds or thousands of times farther off than the otiier. It is, moreover, impossihle, from mere inspection, to determine which is the farther off. 2. AVe may suppose that the stars fire really as near together as they ai>pear, and are to he considered ;\s form- ing a connected pair or group. Couples of stars in the fiivt case are said to he optically dotihlt\ and are not generally classed hy astronomers as douhle stars. Stars which are considered as really douhle are those which are so near together that we are justified in coiisiflel'- ing tiiem as plivMU-ally connected. Such stars are said to be pht/sicif/ly double, and are generally designiited ua double sta/'s 8im])ly. Though it is itnpt^ssible by mere inRp«»ctlon to deuldo to which class a pair of stars should be cotisidered as belong ing, yet the calculus of prohiihilitics will enable us to do % I DOUBLE STARS. 449 TIPLE we find ly close . It is this up- 3 nearly iiiectioii ]>iiir of mid reds It is, tennino as near lis fonu- jticalhj luers as he those loiis'Kler- wiid to iiited ua |i!i!lde to 1 belong to do cide in a rough way M'hetiier it is likely that two stai's not pliysieally connected should appear so very close together as most of the double stai-s do. This question was first considered by the Kev. Jonx Michell, F.R.S., of Eng- land, who in 1777 published a i)aper on the subject in the Ph'doHophlcal TraimwilonK. He showed that if the lucid stare were equally distributed over the celestial sj)here, the chances were SO to 1 against any two being within three minutes of each other, and that the chances were 500,000 to 1 against the six visible stars of the J*h'!x being accidentallv associated as we see them. AVheii the mill- ions of telesc.pic stars are considered, there is a greater probiibility of such accidental juxtaposition. But the probal)ility of many such cases (K'curriiig is so extremely small that astronomers regard all the closest pairs j»>^ pliy- sieally connected. It is now known that of the (), or one out of every 0(>, has a companion within a distance of 30" of arc. This i)roportion is many times greater than could possibly 1)0 the result of (rhance. There are several cases of stars which appear double to the naked eye. Two of these we have already described — namely, 6 Tunrl and f Lyras. The latter is a nu)st curious and interesting object, from the fact that each of the two stars which compose it is itself doul)le. !No more striking idea of the power of the teles- cope can be formed than by pointing a powerful instrument upon this ol)ject. It will then be seen that this minute [)air of poir.*:s, capaldc of being distin- guished only by the most perfect eye, is really composed of two Pro. 122.— the QtrADRtrPLB pail's of stars wide apart, with a '*'^'^" * iah^k. group of smaller stars between and around them. The figure shows the appearance in a telescope of considerable power. 450 ASTRONOMY. Revolutions of Double Stars— Binary Systems.— Tlio most interesting (question suggested hy double stars is that of their relative motion. It is evident that if these bodies are endowed with the property of mutual gravita- tion, they must be revolving around each other, as the earth and planets revolve around the sun, else they would oe drawn together as a single star. With a view of detect- iiig this revolution, lustronomers measiire the j)o.sitwn- angle, and dldance of these (objects. The dldance of the FlO. 123.— MKA8TTREMKNT OF rOBmOTT-ANOLK. components of the double star is simply tlie ap])arent angle which separates them, jis seen by the observfci*. It is always expressed in seconds orfra(;tions of a second of arc. The aiKjle of position, or '' position-angle" as it is often called for brevity, is the angle which the line joining the two stars makes with the line drawn from the brightest star to the north pole. Tf the fainter star is directly north of the brighter one, this angle is zero ; if east, it is 0(1°; if south, .-Tho \ is that f these gnivita- , us the f woiikl f detect- rtf of the DOUBLE STARS. 40 1 )parent -r. It is Id of arc. is often Ininj; the litest star north of if south, it 18 180^ ; if west, it is 270^ This is ilhistrated hy the tigure, which is supposed to represent the field of view of an inverting telescoi)e pointed toward the south. Tlie arrow shows the direction of the apparent preceding. The two latter words refer to the und the other Sucli a pair is called a hiiiti/'i/ stur or l/nuinj fe re«,Mr(le(l as a universal property of matter. Colors of Double Stars.— There nre a few noteworthy stntistics in rt'jyard to the colors of the eoniponcnts of double stars whicli may be given. Among TM\ of the l)righter doiibh; stars, there are i}?.") pairs where each compon«!nt has the same color and intensity ; 101 pairs where the components luive same color, but ditlerent in- tensity ; 120 pairs of dilierent colors. Among those of the sam(! color, the vast majority were both white. Of the 470 stars of the same color, there wc^re 2l>ri pairs whose components were both white ; 118 pairs whose components were both yellow or both red ; (i:{ pairs whose cojnpoiu'iits were both bhiish. When the com- ponents are of different colors, the l)righter generally appears to nave a tinge of red or yellow ; the other of blue or green. These data indicate in part real physical laws. Tliiy also aro partly due to the physiological fact that the fainter a staris,tho more blue it will appear to the eye. Measures of Double Stars.— The first systematic mensures of the relative positions of the components of double stars were nuide by CiiKisTtAN Maykk, Director of the I)u(;id Observatory of Mann- heim, 1778, but it is to Srit Wim,ia.m Hkhsi ni:i. that we owe the ba- sis of our knowledge of this branch of sidereal astronomy. In 1780 HKHsciiKr. measured the relative situation of more than 400 doublu stars, and after repeating his measures some score of years later, he found in about 50 of the ])airs evidence of relative motion of the components. In this first survey he found 97 stars whose dis- tance was under 4", 103 between 4" and 8", 114 between 8" and 10', and l!J3 between 10' and 33'. Since Hkusciiei/s observations, the discoveries of Sir .John IIe'i- sciiEri, Sir .James Soutij, Dawes, and many others in P^ngland, oi W. Stkuvk, Otto Stuuve, Maui.eu, Secciu, DEMm)WSKi, Dit- NEH, in Europe, and of U. P. Bono, Ai.van Ci-auk, and S. W. BuKNiiAM, in the United States, have increased the number of known double stars to about 10,000. Besides the double stars, there aro also triple, quadruple, etc., stars. These are generically called multiple »tar». The most re- markable multiple star is the Trapezium, in the centre of the nebula of O/'itfH, commonly called Ononis, whose four stars are, without doubt, physically connected. The next combination beyond a multiple star ia a cluster of stars ; and beginning with clusters of 1' in diameter, such objects may be found up to 30' or more in diameter, every intermediate size being represented. These we shall consider shortly. § 2. ORBITS OF BINARY STARS. When it was established that many of the double stars were really revolving around each other, it became of great interest to determine the orbit and ascertain whether it was an ellipse, with DiyARY STARS. 453 univerenl ly stntistics j nchuhp. to certain circular or elliptic nebuhe which in his telescope presented disks like the planets. Spiral nehulm are those whose convo- lutions have a spiral shape. This class is qnite numer- ous. The different kinds of nebulaj and clusters will be better under- stood from the cuts and descriptions which follow than by formal definitions. It must be remembered that there is an almost infinite variety of such shapes. The figure by Sir Jv hnHerschel on the next page gives a good idea of a spiral or ring nebula. It has a central nucleus and a small and bright companion nebula near it. In a larger telescope than Herschel's its aspect is even more complicated. See also Fig. 128. ,1 \ 460 ASTRONOMY. The Omega or horaealioe nebula, so called from the resemblance of the brightest end of it to a Greek 0, or to a horse's iron shoe, is one of the most complex and remarkable of the nebulae visible in the northern hemisphere. It is particularly worthy of note, as there is some reason to believe that it has a proper motion. Cer- tain it is that the bright star which in the figure is at the left-hand upper corner of one of the squares, and on the left-hand (west) edge of the streak of nebulosity, was in the older drawings placed on the other side of this streak, or within the dark bay, thus mak ing it at least probable that either the star or the nebula has moved. Fig. 125.— sPTRATi nebula. The trijid nebula, so called on account of its three branches which meet near a central dark space, is a striking object, and was suspected by Sir JoriN Herschel to have a proper motion. Later observations seem to confirm this, and in particular the three bright stars on the left-hand edge of the right-hand (east) mass are now more deeply immersed in the nebula than they were observed to be by HEnscnEL (1833) and Mason, of Yale College (1837). In 1784, Sir William Herschel described them as " in the middle of the [dark] triangle." This description does not apply to their present situation. (Fig. 127). Pro. 12rt. — THK OMEOA Oil HORSESnOE KLBTTLA. 4C2 ASTRONOMT, g 3. STAB CLUSTERS. The most noterl of all the clusters is tlie ricimlcf, wliich have already been briefly described in connection with the constellation TnuruH. The averafje nuked eye can easily distinj^iiish six stars within it, but under favorable conditions ten, eleven, twelve, or FlO. 127.— THE TBIFID NEBULA. more stars can be counted. With the telescope, over a hundred stars are seen. A view of these is given in the map accompanying ihe description of the Pleiades, Fig. 118, p. 425. This group con- tains Tempel's variable nebula, so called because it has been sup- posed to be subject to variations of light. This is probably not 9 Variable nebula. NEBULJE AND CLUSTBRti. 463 The clusters represented in Figs. 139 and 130 are good examples of tlieir classes. Tlie first is globular and contains several thousand email stars. The central regions are densely packed with stars, and from tiiese radiate curved hairy-looking branches of a spiral form. The second is a cluster of about 200 stars, of magnitudes varying from the ninth to the thirteenth and fourtointh, in which the brighter stars are scattered in a somewhat unusual manner Pia. 138. — THE niNO nebula in lyra. over the telescopic field. This cluster is an excellent example of the " compressed " form so frequently exhibited. In clusters of this class the spectroscope shows that each of the individual stars is a true sun, shining by its native brightness. If we admit that a cluster is real — that is, that we have to do with a collection of stars physically connected — the globular clusC ; become important. It is a fact of observation that in general the stars composing such 464 ASTRONOMY. clusters are about of equal maj^nitude, and arc more condcnaed at the centre than at the ed^es. They are |)r».>l)al)ly subject to central powers or forces. This was seen by Sir William IIkuhciiel in 1 780. lie says : " Not only were round nebula? and clusters formed by central powers, but likewise every cluster of stars or nebula that shows a gradual condensation or increasing brightness toward a centre. This theory of central ]»ower is fully established «-n grounds of ob- servation which cannot be overturned. "Clusters can be fotmd of 10' diameter with a certain degree of compression and stars of a certain magnitude, and smaller clusters of 4', 3' or 2 in diameter, with smaller stars and greater compression, and so on through resolvable nebula; by imperceptlhle steps, to the smallest and faintest [and most distant] nebida-. Other dusters 129.— OLOBlllAB CLUSTER. PlO. 130.— COMPRESSED CLUSTER. Si ' ii r'' I there are, which lead to the belief that either they are more com- pressed 0. aie composed of laiger stars. Spheiical clusters aie probabl" not more ilifferent in size among themselves than different individuals of pliints of the same species. As it has been shown that the spherical liguie <»f n cluster of stars is owing to central powers, it follows that those clusters which, ceteris parihtts, are the most complete in this figure must have been the longest exjrosed to the action of these causes. " The maturity of a sidereal system may thus be judged from the disposition of the component parts. " Though we cannot see any individual nebula pass through all its stages of life, we can select particular ones m each peculiar stage," and thus obtain a single view of their entire course of de- velopment. i* P.'-tv NEliULJS. 405 g 4. SFECTBA OF NEBULiE AND CLUSTERS. In 1W04, fiv(! ypiirs after the invention of the spectroscope, Dr. HudoiNs, of London, commenced the exiuninution of the spectra of the nebnlie, and was led to the discovery tii:it while tlie spectra of stars were invariably continuous and crossed with dark lines similar to those of the solar spectrum, those of many nebuliu were tllnroiitinuoitu, showing these bodies to be composed of glowing gas. The figure shows the spectrum of one of the most famous planetary nebuhc. (II. iv. H7.) The gaseous nebuhe include nearly all the planetary nebulw, and very frequently have stellar-like condensa- tions in the centre. Singularly ('tiouKh, the most milky looking of any of the nebulte (that in And/onieda) gives a continuous spectrum, while the nebula of Orian, which fairly glistens with small stars, has a discontinuous CLUSTER. Fig. 131. — spectuum of a planet aky nebula. spectrum, showing it to be a true gas. Most of these stars are too faint to be separately examined with the spectro:-iCope, so that wo cannot say whcth'^r they have the same spectrum as the nebulae. The spectrum of most clusters is continuous, indicating that the individual stars are truly stellar in their nature. In a few cases, however, clusters are composed of a mixture of nebulosity (usually near their centre) and of stars, and the spectrum in such cases is compound in its nature, so as to indicate radiation both by gaseous and solid matter. § 6. DISTRIBUTION OP NEBULiB AND CLUSTERS ON THE SURFACE OF THE CELES- TIAL SPHERE. The following map (Fig. 132) by Mr. R. A. Proctok, gives at a glance the distribution of the nebulae on the celestial sphere with reference to the Milky Way, whose boundaries only are indicated. STAR.(JLUSTERS. 467 fTiVliI«r. • ^""^ nebula IS marked by a dot ; where the dots are IhTwrth^t .^,^V' •'h^'''° •""^' '"^ ^^'^"^*- ^ ^^«"^' examination shows that such rich regions are distant from the Galaxy, and it would appear that it is a general law that the nebula are distri- buted in greatest number around the two poles of the galactic circle, and that in a general way their number at any point of the sphere increases with their distance from this circle This was noticed by the elder Hekschei, who constructed a map simUarto the one given It is precisely the reverse of the law of apparent Zt^wV"' ''""" star-clusters. which in general lie inTn'ur i^w w CHAPTER V. SPECTRA OF FIXED STARS. 1. CHARACTERS OP STELLAR SPECTRA. Soon after the discovery of the spectroscope, Dr. Huggins and Professor W. A. Milleu applied this instrument to the examina- tion of stellar spectra, which were found to be, in the main, similar to the solar spectrum — i.e., composed of a continuous band of the prismatic colors, across which dark lines or bands were laid, the latter being fixed in jjosition. These results showed the fixed stars to resemble our own sun in general constitution, and to be com- posed of an incandescent nucleus surrounded by a gaseous and absorptive atmosphere of lower temperature. This atmosphere around many stars is different in constitution from that of the sun, as is shown by the different position and intensity of the various black lines and bands. The various stellar spectra have been classified by Secchi into four ti/pe.-*, distinguished from one another by marked differences in the position, character, and number of the dark lines. Type I is composed of tlie white stars, of which Sirins and Veffa are examples (the upper spectrum in the plate Fig. 133). The spec- trum of these stars is continuous, and is crossed by four dark lines, due to the presence of large quantities of hydrogen in the envelope. Sodium and magnesium lines are also seen, and others yet fainter. Type II is composed mainly of the yellow stars, like our own sun, Arcttinis, Capella, Aldebamn, and Pollu.v. The spectrum of the sun is shown in the second place in the plate. The vast ma- jority of the stars visible to the naked eye belong to this class. Type III (see the third and fourth spectra in the plate) is com- posed of the brighter reddish stars like a Orionis, Antarea, a HercuUs, etc. These spectra are much contracted toward the violet end, and are crossed by eight or more dark bands, these bands being them- selves resolvable into separate lines. These three types comprise nearly all the lucid stars, and it is not a little remarkable that the essential differences between the three classes were recognized by Sir William Herschel as early as 1798, and published in 1814. Of course his observations were made without a slit to his snectroscopic apparatus. ti ! , tilELLAR SPECTRA, 469 rBA. GGIN8 and I examina- ,in, similar »and of the B laid, the fixed stars ;o be com- iseous and itmosphere af the sun, the various KCCHi into lerences in s and Vega The spec- four dark drogen in seen, and our own )ectrum of vast ma- class. is com- a Herculis, t end, and eing them- 3) 8, and it is tween the sii as early tious were Ed OQ Pi OS "i F< ra CD a CO 00 470 ASTJiOXOMT. Type IV comprises the red stars, Avhich are mostly tc'lescoi>ic. The characteristic spectrum is shown in the last tigure of the plate. It is curiously banded with three bright spaces separated by darker ones. It is probable that the hotter a star is the more simple a spectrum it has ; for the briglitest, and therefore probably the hottest stars, such as Sirius, give spectra showing only very thick hydrogen lines and a few very thin metallic lines, while the cooler stars, such as our sun, are shown by their spectra to contain a much larger num- ber of metallic elements than stars of the type of Sirms, but no non-metallic elements (oxygen possibly excepted). The coolest stars give band-spectra characteristic of compounds of metallic with non-metallic elements, and of the non-metallic elements un- combiued. § 2. MOTION OF STARS IN THE LINE OP SIGHT. Spectroscopic observations of stars not only give information in regard to their chemical and physical constitution, but have been applied so as to determine ap{)roximately the velocity in kilometres per second with whieli the stars are ai^proaching to or receding from the earth along the line joining earth and star. The theory of such a determination is briefly as follows : In the solar spectrum we find a group of dark lines, as a, l, c, which always maintain their relative position. From laboratory experiments, we can show that the three bright lines of incandescent hydrogen (for example) have always the same relative position as the solar dark lines a, &, c. From tliis it is inferred that the solar dark lines are due to the presence of hydrogen in its absorptive atmosphere. Now, suppose that in a stellar spectrum we find three dark lines a'y b', c', whose relative position is exactly the same as that of the solar lines a, h, c. Not only is their relative position the same, but the characters of the lines themselves, so far as the fainter spectrum of the star will allow us to determine them, are also simi- lar — that is, a' and a, b' and b, c and e are alike as to thickness, blackness, nebulosity of edges, etc., etc. From this it is inferred that the star really contains in its atmosphere the substance whose existence has been shown in the sim. If we contrive an apparatus by which the stellar spectrum is seen in the lower half (say) of the eye-piece of the spectroscope, while the spectrum of hydrogen is seen just above it, we find in some cases this remarkable phenomenon. The three dark stellar lines, a', b\ c', instead of being exactly coincident with the three hydro- gen lines a, b, c, are seen to be all thrown to one side or the other by a like amount — that is, the whole group a\ h', c', while preserving its relative distances the same as those of the compari- son group a, b, c, is shifted toward either the violet or red end of the spectrum by a small yet measurable amount. Repeated experi' BTELLAR SPECTRA 471 merits by different Instruments and observers show always a shifting in the same direction and of like amount. The figure shows the shifting of the F line in the spectrum ot iHriun, compared with one tixed line of hydrogen. This displacement of the spectral lines is now ac- counted for by a motion of the star toward or from the earth. It is shown in Phy- sics that if the source of the light which gives the spectrum a', I', c is mov- ing away from the earth, tliis group will be shifted toward the red end of the spec- trum ; if toward the earth, then the whole group will be shifted toward the blue end. The amount of this shifting is a function of the velocity of recession or ap- proach, and this velocity in miles per second can be calculated from the meas- ured displacement. This has been dune for many stars by Dr. HtioGiNs, Dr. VoGEi., and Mr. Chuistie. Their lesuHs agree well, when the difficult nature of the research is considered. The rates of motion vary from insensible amounts to 100 kilometres per sec- ond ; and in some cases agree remarkably with the velocities com- puted from the proper motions and probable parallaxes. FlO. 134. — ^F-LTNE IN SPECTIIUM OK SIUIUS. CHAPTER VI. MOTIONS AND DISTANCES OF THE STARS. § 1. PBOPER MOTIONS. We have already stated that, to the unaided vision, the fixed stars appear to preserve the same relative position in the heavens through many centuries, so that if the" an- cient astronomers could again see them, they could hardly detect the slightest change in their arrangement. But the refined methods of modern astronomv, in which the power of the telescope is ajiplied to celestial measurement, have shown that there are slow changes in the positions of the brighter stars, consisting in a motion forward in a straight line and with uniform velocity. These motions are, for the most part, so slow that it would require thou- sands of years for the change of position to be percepti- ble to the unaided eye. They are called proper motions. As a general rule, the fainter the stars the smaller the proper mo- tions. For the most part, the proper motions of the telescopic stars are so minute that they have not been detected -except in a very few cases. This arises partly from the actual slowness of the mo- tion, and partly from the fact that the positions of these stars have not generally been well determined. It will be readily seen that, in order to detect the proper motion of a star, its position must be de- termined at periods separated by cc uderable intervals of time. Since the exact determinations of star positions have only been made since the year 1750, it follows that no proper motion can be detected unless it is large enough to become perceptible at the end of a century and a quarter. With very few exceptions, no accurate determination of the positions of telescopic stars was made until about the beginning of the present century. Consequently, we cannot yet pronounce upon the proper motions of these stars, aui MOTIONS OF THE STARS. 473 rAKS. can only say that, in general, they are too small to be cletectecT by the observations hitherto made. To this rule, that the smaller stars have no sensible proper mo- tions, there are a few very notable exceptions. The star Oroom- bridge 1830, is remarkable for having the greatest proper motion of any in the heavens, amounting to about 7 " in a year. It is only of the seventh magnitude. Next in the order of proper motion comes the double star 61 Cygni, which is about of the fifth magnitude. There are in all seven small stars, all of which have a larger proper motion than any of the first magnitude. But leaving out these ex- ceptional cases, the remaining stars show, on an average, a diminu- tion of proper motion with brightness. In general, the proper motions even of the brightest stars are only a fraction of a second in a year, so that thousands of years would be required for them to change their place in any striking degree, and hundreds of thousands to make a complete revolution around the heavens. !sion, the ^sition in : tlie an- Id hardly lit. But -hich the lUrenient, positions vard in a motions lire thou- Dercepti- niotions. iroper mo- copic stars in a very ■ the mo- stars have en that, in ust be de- of time, only been on can be at the end o accurate nade until uently, we staiiS, aui § 2. PROPER MOTION OP THE SUN. A very interesting result of tlie proper motions of the stars is that our sun, considered as a star, has a consider- able proper motion of its own. P»y observations on a star, we really determine, not the proper motion of the star it- self, but the relative proper motion of the observer and the star — that is, the difference of their motions. Since the earth with the observer on it is carried alouij with the sun in space, his proper motion is the same as that of the sun, so that what observation gives us is the difference between the proper motion of the star and that of the sun. There is no way to determine absolutely how much of the apparent proper motion is due to the real motion of the star and how n\\c\\ to the real motion of the sun. If, however, we find that, on the average, there is a large pre- ponderance of proper motions in one direction, Ave may conclude that there is a real motion of the sun in an op- posite direction. This conclusion is reasonable, since it is more likely that the average of a great mass of stars is at rest than that the sun, which is only a single star, should be. Now, observation shows that this is really the case, and that the great mass of stars appear to be moving from the direction of the constellation Hercules and toward 474 ASTRONOMY. that of the constellation Argus.* A numher of astrono- mers have investigated this motion witli a view of deter- mining the exact point in the heavens toward which the Bun is moving. Their results are shown in the following table : i '■'■'i Arjxelander O. Struve Lundalil , Galloway Madler Airy and Diinkiii Declinution, 28° 50' N. 36' N. 14° 26' N. 34' 23' N. 39° 54' N. 28° 58' N. It will be perceived that there is some discordance aris- ing from the diverse characters of tlio motions to be in- vestigated. Yet, if we lay these different points down on a map of the stars, we shall find that they all fall in the constellation Hercules. The amount of the motion is such that if the sun were viewed at right angles to the direction of motion from an average star of the first magnitude, it would appear to move about one third ai a second per year. § 3. DISTANCES OP THE FIXED STARS. The problem of the distance of the stars has always been one of the greatest interest on account of its involv- ing the question of the extent of the visible universe. The ancient astronomers supposed all the fixed stars to be situated at a short distance outside of the orbit of the planet Saturn, then the outerinost known planet. The idea was prevalent that Nature would not waste space by leaving a great region beyond Saturn entirely empty. When Copernicus announced the theory that the sun "was at rest and the earth in motion around it, the prob- lem of the distance of the stars acquired a new interest. * This was discovered by Sir William Hekschel in 1783. Il^: DISTANCES OF THE STABS. 475 tstrono- [ deter- ich the llowing ition. ' N. 1' N. V N. V N. V N. V N. ice aris- be in- iown on 1 in the [1 is siicli lirection itude, it ►nd per always involv- liverse. b to be I planet lea was laving a Ihe snn prob- iterest. It was evident that if the earth described an annual orbit, then the stars wouhl appear in the course of a year to os- ciUate back and forth in corresponding orbits, unless they were so immensely distant that these oscillations were too small to be seen. Now, the apparent oscillation of Saturn produced in this way was described in Part I., and shown to amount to some 0° on each side of xhe mean position. These oscillations were, in fact, those which the ancients represented by the motion of the planet around a small epicycle. But no such oscillation liad ever been detected in a fixed star. This fact seemed to present an almost insuperable difficulty in the reception of the Copernican system. This was probably the reason why Tvcho J'kah?: was led to reject the system. Very naturally, therefore, as the instruments of observation were from time to time improved, this apparent annual oscillation of the stars was ardently st>ught for. When, about the year ITO-l, KoEMER thought he had detected it, lie published his ob- servations in a dissertation entitled ^^ Copernicus Trhmi- fhansy A similar attempt, made by Hookk of England, was entitled '''' An AtUmjpt to Pi'ove the Motion of the Earthy This problem is identical with that of the annual paral- lax of the fixed stars, which has been already described in the concluding section of our opening chapter. This parallax of a heavenly body is the angle which the mean distance of tlie earth from the sun subtends when seen from the body. The distance of the body from the sun is inversely as the parallax (nearly). Thus the mean distance of Saturn being 9.5, its annual parallax exceeds 6°, while that of Neptune^ which is three times as far, is about 2^. It was very evident, without telescopic observation, that the stars could not have a parallax of one half a degree. They must therefore be at least twelve times as far as Saturn if the Copernican system were true. "When the telescope was applied to measurement, a con- tinually increasing accuracy began to be gained by the 476 ASTRONOMY. improvement of the instruments. Yet for several jiijencra* tions the paraUax of tlie fixed Btars ehided measurement. Very often indeed did observers tiiink they liad detected a paraUax in some of the brigliter stars, but their succes- sors, on repeating tlieir measures witli better instruments, and investigating their metliods anew, found their con- chisions erroneous. Early in the present century it be- came certain that even the brighter stars had not, in gen- eral, a parallax as great as 1", and thus it became certain that they must lie at a greater distance than 200,000 timea that which separates the earth from the sun. Success in actually measuring the parallax of the stars was at leuiicth obtained almost simultaneouslv l)v two as- tronomers, Bessel of Kunigsberg, and Stkuvk of Dorp:it. Bessel selected for his star to be observed f»l Cf/t/ni, und commenced his observations on it in Auifust, 1S3T. Tlie result of two or three years of observation ^^'as that this star had a parallax of 0".85, or about one-third of a sec- ond. This would nuike its distance from the sun nearly 000,000 astronomical units. The reality of this paral- lax has been well established by subsefpient investigators, only it has been shown to be a little larger, and therefore the star a little nearer tlian Bessel supposed. The most probable parallax is now found to be 0".51, eorres2")onding to a distance of 400,000 radii of the earth's orbit. The star selected by S'rnnvE lor the measure of parallax was the bright one, a Lyrw. His observations were made between Novem- ber, 1835, and August, 1838. He tirst deduced a parallax of 0".35. Subsequent observers have reduced this parallax to " • 20, corre- sponding to a distance of about 1,000,000 astronomical units. Shortly after this, it was found by Henderson, of England, As- tronomer Royal for the Cape of Good Hope, that the star a Ce/itanri had a still larger parallax of about 1". This is the largest parallax now known in the case of any fixed star, so that a Centaur i is, be- yond all reasonable doubt, the nearest fixed s^ar. Yet its distance is more than 200,000 astronomical units, or thirty millio is of mill- ions of kilometres. Light, which passes from the sun to the earth in 8 minutes, would require 3^ years to reach us from a Centauri. Two methods of determining parallax have been applied in as- tronomy. The parallax found by one of these methods is known its absolute, that by the other as relative parallax. In determining the DISTANCES OF THE STAIiS. 4Tr absolute parallax, the observer finds the polar distance of the star as often as possible throu<^li a period of one or more years with a meridian circle, and then, by a discussion of all his observations, conchides what is tiie magnitude of the oscillation due to parallax. The ditttculty in applying this method is that the refraction of the air and the state of the instrument are subject to chanj^es arising from varying temperature, so that the observations are always un- certain by an amount which is important in such delicate work. In determining the relative jitiniflo.r, the astronomer selects two stars in the same field of view of his telescope, one of which is many times more distant than the other. It is ])ossiblc to judge with a high degree of probability which star is the more distant, from the magnitudes and proper motions of the two objects. It is assumed that a star which is either very bright or has a large pro- per motion is many times nearer to us than the extremely faint stars which may be nearly always seen around it. The effect of parallax will then be to change the apparent position of the bright star among the small stars around it in the course of a year. This change admits of being measured with great precision by the mi- crometer of the equatorial, and thus the relative parallax may bo determined. It is true that this relative parallax is really not the absolute par- allax of either body, but the difference of their parallaxes. So wo must necessarily suppose that the parallax of the smaller and more distant object is zero. It is by this method of relative i)arallax that the great majority of determinations have been made. The distances of tlie stars are sometimes expressed hy the time required for lii»;ht to pass from tliem to our sys- tem. Tlio velocity of hght is, it will he rememliered, about 300,000 kilometres per second, or such as to pasa from the «un to the earth in 8 minutes 18 seconds. The time required for light to reach the earth from some of the stars, of v/liicli the parallax has been measured, is as follows : Star. Years. Star. Years. ct Centnuri 3-5 6-7 63 6-9 9.4 10.5 11.9 131 16-7 17-9 70 Ophinchi t Urs(e MiijoHs Arcturus y Draconis 1830 Groombridge. Polaris. ......... 11) -1 61 Cygid 21,185 Lalando 6 Centaun fi CassiopeuB 84 Groombridge ... 21,258 Lalande 17,415 Oeltzen Sii'ius 24. 3 25-4 85-1 35-9 42-4 3077 Bradley 85 Pegad a Auriga a Draconia 46-1 64-5 70-1 (X LvrcB 129 1 CHAPTER VII. CONSTRUCTION OF THE HEAVENS. The visible universe, as revealed to us by the telescope, Is a collection of many millions of stars and of several thousand nebuloe. It is sometimes called the stellar or sidereal system, and sometimes, as already remarked, the stellar universe. The most far-reaching question with which astronomy has to deal is that of the form and mag- nitude of this system, and the arrangement of the stars which compose it. It was once supposed that the stars were arranged on the same general plan as the bodies of the solar system, being divided up into great numbers of groups or clus- ters, while all the stars of each group revolved in regular orbits round the centre of the group. All the groups were supposed to revolve around some great common centre, which was therefore the centre of the visible universe. But there is no proof that this view is correct. The only astronomer of the present century who held any such doctrine was Maedler. He thought that the centre of motion of all the stars was in the Pleiades, but no other astronomer shared his views. "We have already seen that a great many stars are collected into clusters, but there is no evidence that the stars of these clusters revolve in regular orbits, or that the clusters themselves have any regular motion around a common centre. Besides, the large majority of stars visible with the telescope do not appear to be grouped into clusters at all. BTRUVTURK OF TlIK llKAVKNa. 479 Tlie firet astronoTiior to inako a careful study of tho arran^'t'iiu'ut of tlio stars witli a view to learn the stnicturo of tlio heavens was Sir William IIi:KS("nKL. lie puhlished in tho I*hiloisop/iii' sliall therefore heijin with an account of IIi:K>^c:ni:L's methods Its. and resu IIi:ks(jiikl's method of study was founded (»n a mode of ohservation which he called tttxr-yatujiny. It consisted in pointin*^ a powerful telescope toward various parts of tho heavens and ascertaining by actnal count how thick tho stars were in each region. His 2(»-foot retlector was pro- vided with such an eye-piece that, in looking into it, he would see a ])()rtion of the heavens al)out 15' in diameter. A circle of this size on the celestial sphere lias about one (piarter the apparent surface of the sun, or of the full moon. On pointing the telescope in any direction, a greater or less munber of stars were nearly always visible. These were counted, and the direction in which the tele- scope pointed was noted. Gauges of this kind were made in all parts of the sky at which he could point his instru- ment, and the results were tabulated in the order of right ascension. The following is an extract from the gauges, and gives the average number of stars in each field at the points noted in right ascension and north polar distance : N. P. D. N. P. D. R.A. 92° to 94° R.A. 78° to 80» No. of Stars. No. of Stars. b. m. h. m. 15 10 9-4 11 6 3.1 15 22 10-6 12 31 3.4 15 47 10.6 12 44 4-6 16 8 12-1 12 49 8.9 16 25 13-6 18 5 3-8 16 87 18-6 14 30 3-6 480 ASTRONOMT. In this small table, it is plain that a different law of clustering or of distribution obtains in the two regions. Suoh differences are still more marked if we compare the extreme cases found by Hikschel, as E. A. = 19'' 41™, ]S[. P. D. = 74° 33', number of stars per field ; 588, and E. A. = 16" 10-", K. P. D., 113° 4', number of stars = 1 • 1 . The number of these stars in certain portions is very great. For example, in the Milky Way, near Orion,, six fields of view promiscuously taken gave 110, 00, 70, 00, 70, and 74 stars each, or a mean of 70 stars per field. The most vacant space in this neighborhood gave 60 stars. So tliat as Herschel's sweeps were iwo degrees wide in declination, in one hour (15°) there would pass through the field of his telescope 40,000 or more stars. In some of the sweeps this number was as great as 116,000 stars in a quarter of an hour. On applying this telescope to the Milky Way, IIer- scTiEL supposed at the time that it completely resolved the whole whitish appearance into small stars. This conclu- sion he siibsec[uently modified. He says : " It is very probable that- the great stratum called the Milky Way is that in wliich the sun is placed, though perhaps not in the very centre of its thickness. " We gather this from the appearance of the Galaxy, •which seems to encompass the ^vhole heavens, as it certainly must do if the sun is within it. For, suppose a number of stars arranged be- tween two parallel planes, indefinitely extended every way, but at a given considerable distance from each other, and calling this a sidereal stratum, an eye placed somewhere within it will see all the stars in the direction of the planes of the stratum projected into a great circle, which will appear lucid on account of the accumu- lation of the stars, while the rest of the heavens, at the sides, will only seem to be scattered over with constellations, more or less crowded, according to the distance of the planes, or number of stars contained in the thickness or sides of the stratum." Thus in Herscuel's figure an eye at aS within the stratum ah will see the stars in the direction of its length a h, or height c d, ■with all those in the intermediate situations, projected into the lucid circle A GBD, while those in the sides mv, nw, will be seen scattered over the remaining part of the heavens M VN W. STRUCTURE OF THE HEAVENS. 481 " If the eye were placed somewhere without the stratum, at no very great distance, the appearance of the stars within it would assume the form of one of the smaller circles of the sphere, which Fig. 135. — hebschel's theory of tub stellau system. would be more or less contracted according to the distance of the eye ; and if this distance were exceedingly increased, the whole stratum might at last be drawn together into a l"cid spot of any m 483 ASTRONOMY. shape, according to the length, breadth, and height of the stra- tum. "Suppose that a smaller stratum pq should branch out from the former in a certain direction, and that it also is contained between two parallel planes, so that the eye is contained within the great stratum somewhere before the separation, and not far from the place w^here the strata are still united. Then this second stratum will not be projected into a bright circle like the former, but it will be seen as a lucid branch proceeding from the first, and r'jturning into it again at a distance less than a semicircle. "In the figure the stars in the small stratum pq will be pro- jected into a bright arc P R R P, which, after its separation from the circle V B D, unites with it again at P. "If the bounding surfaces are not parallel planes, but irregularly curved surfaces, analogous appearances must result." The Milky Way, ar) we see it, presents tlie as})eet which has l)een just accounted for, iu its general appearance of a girdle around the heavens and in its bifurcation at a cer- tain point, and IIiiHscHEL's explanation of this appear- ance, as just given, has never been seriously (piestioned. One doubtful point remains: are the stars in Fig. 135 scattered all through the space /S' — a Jjt? <^? or are they near its bounding planes, or clustered in any way within this space so as to produce the same result to the eye as if uniformly disti'ibuted ? IIekschel assumed tliat they were nearly erpiably ar- ranged all Jirough the space in question. He only e.vam- ined one other arranijement — viz., that of a ring of stars surrounding the sun, aiul he pronounced against such an arrangement, for the leason that there is absolutely noth- ing in the size or brilliancy of the sun to cause us to sup- pose it to be the centre of such a gigantic system. No reason except its importance to us personally can be alleged fur such a supposition. By the assumptions of Fig. 135, each star will have its own appearance of a galaxy or milky way, which will vary according to the situation of the star. Such an explanation will account for the general appear- ances of the Milky Way and of the rest of the sky, sup- posing t'wB stars equally or nearly equally distributed in space. On this supposition, the system must be deeper STRUCTURE OF TEE HEAVENS. 483 where the stars appear more numerous. The same evi- dence can be strikingly presented in another way so as to include the results of the southern gauges of Sir John Herschel The Galaxy, or Milky AVay, being nearly a great circle of the sphere, we may compute the position of its north or south pole; and as the position of our own polar points can evidently have no relation to the stellar universe, we express the position of the gauges in galactic polar distance, north or south. By subtracting tliese polar distances from 90°, we shall liave the distance of each gauge from the central plane of the Galaxy itself, the stars near 90° of polar distance being within the Galaxy. The average number of stars per field of 15' for each zone of 15° of galactic polar distance has been tabulated by Struvb and Herscuel as follows: Zones of Galactic Average Number 1 1 Zones of Average Number North Polar of Stars per Galactic South Polar of Stars ptT Distance. Field of 15'. Distance. Field of 15'. 0=" to 15" 4-33 0° to 15° 605 15° to 30° 5-42 15° to 30° 6-62 30° to 45° 8-21 30° to 45° 9-08 45° to 60° 13 ()1 45° to 60° 13-49 60° to 75° 24 09 60° to 75° 26-29 75° to 90° 53-43 75° to 90° 59-06 This table clearly shows that the superficial distribution of stars from the first to the fifteenth magnitudes over the apparent celestial sphere is such that the vast majority of them are in that zone of 30° wide, which includes the Milky Way. Other independent researches havesho\\n that the fainter lucid stars, considered alone, are also dis- tributed in greater nmnber in this zone. Herschel endeavored, in his early memoirs, to find the physical explanation of this inequahty of distribution in the theory of the universe exemplified in Fig. 136, which was based on the funda mental assumption that, ou the whole, the stars were nearly equably distributed in space. 484 ASTRONOMY. If they were so distributed, then the number of stars visible in any gauge would show the thickness of the stellar system in the direction in which the telescope was pointed. At each pointing, the field of view of the instrument includes all the visible stars sit- uated within u cone, having its vertex at the observer's eye, and its base at the very limits of the system, the angle of the cone (at the eye) being 15' 4". Then the cubes of the perpendiculars let fall from the eye on the plane of the bases of the various visual cones are proportional to the solid contents of the cones themselves, or, as the ?*^3'.8 are supposed equally scattered within all the cones, the cube roots of the numbers of stars in each of the fields express the relative lengths of the perpendiculars. A section of the sidereal sys- tem along any great vircle can thus be constructed as in the figure, which is copied from i"''ER8CHEL. The solar system is supposed to be at the dot within the mass of stars. From this point Mnes are drawn along the directions in which the gauging tele8Cop3 was pointed. On these lines arc laid off lengths proportional to i he cube roots of the number of stars in each gauge. Pig. 136. — arrangement of the stars on the hypothesis op equable distribution. The irregular line joining the terminal points is approximately the bounding curve of the stellar system in the great circle chosen. Within this line the space is nearly uniformly filled with stars. Without it is empty space. A similar section can be constructed in any other great circle, and a combination of all such would give a representation of the shape of our stellar system. The more numer- ous and careful the observations, the more elaborate the represen- tation, and the 863 gauges of HEnsciiEii are sufficient to mark out with great precision the main features of the Milky Way, and even to indicate some of its chief irregularities. This figure may be compared with Fig. 135. On the fundamental assumption of Herschel (equable distribu- tion), no other conclusions can be drawn from his statistics but that drawn by him. This assumption he subsequently modified in some degree, and was led to regard his gauges as indicating not so much the depth of the system in any direction as the clustering power or tendency of the stars in those special regions. It is clear that if in any STRUCTURE OF THE HEAVENS. 485 OTHESIS OF given part of the sky, where, on the average, there are 10 stars (aay) to a field, we should find a certain small portion of 100 or more to a field, then, on Heusciiel's first hypothesis, rigorously in- terpreted, it would be necessary to suppose a spike-sliaped protu- berance directed from the earth in order to explain the increased number of stars. If many such places could be found, then the probability is great that this explanation is wrong. We should more rationally suppose some real inequality of star distribution here. It is, in fact, in just such details that the system of Her- sciiEii breaks down, and the careful examination which his system has received leads to the belief that it must be greatly modified to cover all the known facts, while it undoubtedly has, in the main, a strong basis. The stars are certainly not uniformly distributed, and any gen- eral theory of the sidereal system must take into account the varied tendency to aggregation in various parts of the sky. The curious convolutions of the Slilky Way, observed at various parts of its course, seem inconsistent with the idea of very great depth of this stratum, and Mr. Proctor has pointed out that the circular forms of the two " coal-sacks" oi the Southern Milky Way indicate that thej' are really globular, instead of being cylindric tunnels of great length, looking into space, with their axes directed toward the earth. If they are globular, then the depth of the Milky Way in their neighborhood cannot be greatly different from their diameters, which would indicate a much smaller depth than that assigned by Herschel, In 1817, Herschel published an important memoir on the same subject, in which his first method was largely modified, though not abandoned entirely. Its fundamental principle was stated by him as follows : " It is evident that we cannot mean to affirm that the stars of the fifth, sixth, and seventh magnitudes are really smaller than those of the first, second, or third, and that we must ascribe the cause of the difference in the apparent magnitudes of the stars to a differ- ence in their relative distances from us. On account of the great number of stars in each class, we must also allow that the stars of each succeeding magnitude, beginning with the first, are, one with another, further from us than those of the magnitude immediately preceding. The relative magnitudes give only relative distances, and can afford no information as to the real distances at which the stars are placed. " A standaru of reference for the arrangement of the stars may be had by comparing their distribution to a certain properly mod- ified equality of scattering. The equality which I propose does not require that the stars should be at equal distances from each other, nor is it necessary that all those of the same nominal magnitude should be equally distant from us." It consists of allotting a certain equal portion of space to every star, so that, on the whole, each equal portion of space within the stellar system contains an equal number of stars. 486 ASTJiOjyoMr. The space about each star can be considered spherical. 8up« pose such a sphere to surround our own sun, its radius will not differ greatly from the distance of the nearest fixed star, and this is taken as the unit of distance. Suppose a series of larger spheres, all drawn around our sun as a centre, and having the radii 3, 5, 7, 9, etc. The center ts of the spheres being as the cubes of their diameters, the first sphere will have 3x3 X 3 = 27 times the volume of the unit sphere, and will there- fore be large enough to contain 27 stars ; the second will have 125 times the volume, and will therefore con- tain 125 stars, and so with the successive spheres. The figure shows a section of portions of these spheres up to that with radius 11, Above the centre are given the various orders of stars which are situ- ated between the sev- eral spheres, while in the corresponding spaces below the cen- tre are given the num- ber of stars which the region is large enough to contain ; for in- stance, the sphere of radius 7 has room for 343 stars, but of this space 125 parts belong to the spheres inside of it : there is, there- fore, room for 218 stars between the spheres of radii 5 and 7. HersciieIi designates the several distances of these layers of stars as o'.ders ; the stars between spheres 1 and 3 are of the first order of distance, those between 3 and 5 of the second order, and so on. Comparing the room for stars between the several spheres with the number of stars of the several magnitudes, he found the result to be «s follows : Fig. 137. — ordebs of distance of btahs. i.iMt'ia.'gn'*rti--'V ■' 8TRUCTUBE OF THE UFA YENS. 487 ;al. Hup- \ will not y from the he nearest nd this is le unit of a series of leres, all nd our sun and having 5, 5, 7, 9 center ts of J being as 1 of their the first have 3x3 times the ' the unit 1 will there- rge enough I 27 stars; 1 will have the volume, leref ore con- tars, and so successive The figure section of of these p to that sll. Above are given [9 orders of ;h are situ- en the sev- bres, wliile rresponding )w the cen- len the num- iin ; for in- but of this •e is, there- ind7. le layers of if the first order, and iral spheres found the Order of Distance. Number of Stars there is Room for. Magnitude. Number of Stars of that Magnitude. 1 2 26 98 218 386 603 866 1,178 1,538 1 2 3 4 5 7 17 57 3 206 4 454 5 1,161 0,103 6,146 6 7 8 The result of this comparison is, that, if the order of magnitudes could indicate the distance of the stars, it would denote at first a gradual and afterward a very abrupt condensation of them. If, on the ordinary scale of magnitudes, we assume tiieldightncss of any star to be inversely proportional to the square of its dis- tance, it leads to a scale of distance different from that adopted by Hersciiel, so that a si.xth-magnitude star on the common scale would be about of the eighth order of distance according to this scheme — that is, we must remove a star of the first magnitude to eight times its actual distance to make it shine like a star of the sixth magnitude. On the scheme here laid down, Hersciiel subsequently assigned the order of distance of various objects, mostly star-clusters, and his estimates of these distances are still quoted. They rest on the fundamental hypothesis which has been explained, and the error in the assumption of equal brilliancy for all stars, affects these esti- mates. It is perhaps most probable that the hypothesis, of equal brilliancy for all stars is still more erroneous than the hypothesis of equal distribution, and it may well be that there is a very large range indeed in the actual dimensions and in the intrinsic brilliancy of stars at the same order of distance from us, so that the tenth- magnitude stars, for example, may be scattered throughout the spheres, which Hersciiel would assign to the seventh, eighth, ninth, tenth, eleventh, twelfth, and thirteenth magnitudes. Since the time of Hersciiel, one of the most eminent of the as- tronomers who have investigated this subject is Struve the elder, formerly director of the Pulkowa Observatory. His researches were founded mainly on the numbers of stars of the several magni- tudes found by Bessel in a zone thirty degrees wide extending all around the heavens, 15° on each side of the equator. With these he combined the gauges of Sir William Hersciiel. The hypothesis on which he based his theory was similar to that employed by Herschel in his later researches, in so far that he supposed the magnitude of the stars to furnish, on the average, a measure of their relative distances. Supposing, after Hersciiel, a number of concentric spheres to be drawn around the sun as a centre, the suc- cessive spaces between which corresponded to stars of the several 488 ASTEONOJfT. magnitudes, he found that the further out he went, the more the stars were condensed in and near the Milky Way. This conclusion may be drawn at once from the fact we have already mentioned, that the smaller the stars, the more they are condensed in the re- gion of the Galaxy. Stkuve found that if wo take only the stars plainly visible to the naked eye — that is, those down to the tifth magnitude — they are no thicker in the Milky Way tiian in other parts of the heavens. But those of the sixth magnitude are a little thicker in that region, those of the seventh yet thicker, and so on, the ineciuality of discribution becoming constantly greater as the telescopic power is increased. From all this, Stuuve concluded that the stellar system might be considered as composed of layers of stars of various densities, all parallel to the plane of the Wilky Way. The stars are thickest in and near the central layer, which he conceives to be spread out as a wide, thin sheet of stars. Our sun is situated near the middle of this hiyer. As we pass out of this layer, on either side we lind the stars constantly growing thinner and thinner, but we do not reach any distinct boundary. As, if we could rise in the atmosphere, we should find the air constantly growing thinner, but at so gradual a rate of progress that we could hardly say where it terminated ; so, on Stiiuve's view, would it be with the stellar system, if we could mount up in a direction perpendicular to the INIilky Way. Struve gives the following table of the thickness of the stars on each side of the principal ])iane, the unit of distance being that of the ex- treme distance to which Heuscuel's telescope could penetrate : Distance from Principal Plane. Density. Mean Distance betweon Neighbor- ing Siars. In the princi pal plane 1-0000 1-000 0-05 from principal plane 0-48568 1-272 0-10 0-33288 1-458 0-20 0-23895 1-611 0-30 0-17980 1-772 0-40 0-13021 1-973 0-50 0-08646 2-261 0-60 0-05510 2-628 0-70 0-03079 3-190 0-80 0-01414 4-131 0-866 0- 00532 5-729 This condensation of the stars near the central plane and the gradual thinning-out on each side of it are only designed to be the expression of the general or average distribution of those bodies. The probability is that even in the central plane the stars are many times as thick in some regions as in others, and that, as we leave the plane, the thinning-out would be found to proceed at very diflEerent rates in different regions. That there may be a gradual thinning-out JMM^li nuri -XT nuTK-ri STRUCTURE OF THE HEAVENS, 489 more the onclusioa entioned, in the re- tlic stars • the tilth I in other iidc are a icker, and greater as em might !nsitit's, all kest in and as a wide, lie of thia e iind the D not reach (sphere, we ) gradual a .nated ; so, if we could r. Struve n each side of the ex- netrate : Distance ;\\ Neiglibor- Siars. • 000 1-273 1-458 l-Gll ■ 772 1-973 2-261 2-628 3-190 4-131 5-729 je and the ■d to be the ose bodies. •s are many ./e leave the ry different hinning-out a V cannot be denied ; but Stuuve's attempt to form a table of it is open to the serious objection that, like Hersciiel, he supposed the diner- ences between tlie magnitudes of the stars to arise entirely from their different distances from us. Although where the scattering of the stars is nearly uniform, this supposition may not lead us into serious error, the ease will be entirely different where we have to deal with irregular masses of stars, and especially where our tele- scopes penetrate to the boundary of the stellar system. In the latter case we cannot possibly distinguish between small stars lying within the boundary and larger ones scattered outside of it, and Stuuve's gradual thinning-out of the stani may be entirely ac- counted for by great diversities in the absolute brightness of the stars. Distribution of Stars.— The brightness B of any star, as seen from the eiirtli, depei.ds upon its surface 8, the intensity of its light per unit of surface, i, and its distance D, so tliut its brightness can be expressed thus : for another star : B 8 -i B' ~ 8' ' i' B' and Now this ratio of the brightness /? 4- £' is the only fact we usually know with regurd to any two stars. D has Ijeeu determined for only a few stars, and for these it varies between 200,000 and 2,000,000 times the mean radius of the earth's orbit. 5 and i are not Ivuown for any star. There is, however, a probability that i does not vary greatly front star to star, as the great majority o\ stars are wliiie in color (only some 700 red stars, for instance, are known out of the 300,000 wliich have been carefully examined). Among 476 double sti'.rs of Stuuve's list 295 were white, 03 being bluish, only one fourth, or 118, being yellow or red. If 5 is of the rtth mag', its lifrht in terms of a first magnitude star \%6n — \ where 6 ■= 0-397, and if B' is of tiie mtli mag., its liofht is ,jnt— 1^ hoi\\ expressed in terms of the light of a first magnitude star as unity ((JO = 1). Therefore we may put B = 6'*~^, B' = d'""" ', and we have Jn-l = 6" /» S ■ i • B ~8' -i'-B' B In this general expression we seek the ratio -^, and we have it expressed in terms of four unknown quantities. We must therefore make some supposition in regard to these. I. ^f aU stars are of equal intrinsic bjilliancy and of equal size, tken 8i^ S' i\ and •'^ — " = a constant = 490 ASTRONOMY. whence the relative distance of any two stars would be known on this hypothenis. II. Or, suppone the stars to be uniformly diatributed in apace, or the star-density to be equal in all directions. From this we can also obtain some notions of the relative distances of stars. Call Di, Di, Da Dn the average distances of stars of the 1, 2, 8, »th nitignitudes. If K stars are situated within the sphere of radius 1, then the num> her of stars {Q„), situated within the sphere of radius !)„, is Qn = K' {Dn)*. since the cubic contents of spheres are as the cubes of their radii. Also Q„ , , = /iT (Dn _ ,)', whence 3 P., _ J Qn Dn-l ~ y Qn-l' If we knew Q„ and Q» - i, the number of stars contained in the spheres of radii Dn and Z>„ _ i, then lh^ ratio of Dn and Dn - i would be known. We cannot know Qn, Q„ - \, etc., directly, but we may suppose these quantities to be proportional to the numbers of stars of the «th and {n — l)tli magnitudes found in an enumeration of all tlie stars in tlio heavens of these ma^rnitudes, or, failing in these data, we may confine this enumeration to the northern hemisphere, where LiTTKOv has counted the nuinlier of stars of encli class in Argelan- DKR's jJurchmusterung. As we have seen (p. 430) whence Q, = 19,699 and Qe = 77,794, = /|:=i.58. D^ 'D, and this would lead us to infer that the stars of the 8th maprnitude were distributed inside of a sphere whose radius was about 1-6 times tliat of tlie corresponding sphere for the 7th magnitude stars provided that, 1st, tile stars in general are equally or about equally distributed, and, 2d, that on the whole tlie stars of the 8 .... w magnitudes are further away from us than those of the 7 (n — 1) magnitudes. We may have a kind of test of the truth of this hypothesis, and of the first employed, as follows : we had Dn _ l/~Qn bn-l y Qn-l' Qn Also from the first hypothesis the brightness B* of a star of the ntli magnitude in terms of a first magnitude star s 1 was If here, again, we suppose the distance of a first magnitude star to iw B 1 and of an nth magnitude star D», then wn on thia STRUCTURE OF THE UEAVENS. 491 n - 1 ^nsT \ va~J ' V V7~J • whence -^w _ 1 Comparing the exprenaion for ^f--., in the two cases, we Lave reMive intensity of varlou's'LsrJf 1^'^ "i ^"o"Tu "' tV'^ will be so far iin areuinent to slmw ti.af o « . ■ ' "~ "■^"' "'*'" this §, and §«, we Lave J'i'°^"«8«^8 l. and II. Taking the values of rf/ \_ Z' 19.699 \i ^"'^-K-lVfu) =0-40. S::n"at^ee^?;je^b"fytlTti^^^^ ''(.,) = 0-45. These, for 6, and show that (hnquS ^'^''«'^«"dem photometric values \Vd J ctTalnXraTto'trurac? ^^^tTe °'t ^^'^ ^ ""^^"^^"^^ -'^h a tude these distances a?er^* '*"' ^''°'" ^^^ *» ^^"^ n^agai- 1 to 1-9 magnitude . „„ 2 to 2-9 " 1-00 8 to 3-9 " 1'54 4 to 4-9 •« 2-36 6 to 5.9 " 3-64 6 to 6.9 " 5.59 7 to 7.9 " 8-61 8 to 8-9 «• 13.23 20-35 STS>r"*'^*'°" °' '^^ ^^^J^^'* '' -^^^^^^^7 that of Prof. Hugo CHAPTER VIII. COSMOGONY. m m A TnEORY of tliG operations by which the universe re- ceived its present form and arrangement is called Cosmog- ony. This subject does not treat of the origin of matter, but only with its transformations. Three systems of Cosmogony have prevailed among thinking men at different times. (1.) That the universe had no origin, but existed from eternity in the form in which we now see it. (2.) That it was created in its present shape in a moment, out of iwthing. (3.) That it came into its present form through an ar- rangement of materials which were before *' without form and void." The last seems to be the idea which has most prevailed among thinking men, and it receives many striking con- firmations from the scientific discoveries of modern times. The latter seem to show beyond all reasonable doubt that the universe could nor always have existed in its present form and under its present conditions ; that there was a time when the materials composing it were masses of glowing vapor, and that there will be a time when the present state of things will cease. The explanation of the processes through which this occurs is sometimes called the nebular hypothesis. It was first propounded by the philosophers SwEDENBORG, Kant, aud Laplace, and although since greatly modified in detail, the views of these men have in the main been retained until the present time. t- cosyroooNT. 403 Wo shall begin its consiilcratiou by a statement of tlio various facts which appear to show that the earth and planets, as Mell as the sun, were onco a fiery mass. The first of these facts is the gradiuil but uniform in- crease of temperature as we descend into the interior of the earth. Wlierever mines liavo been dug or wells sunk to a great depth, it is found that the temperature increases as Ave go downward at the rate of about one degree centi- grade to every 80 metres, or one degree Fahrenheit to every 50 feet. The rate differs in different places, but the general average is near this. The conclusion which we draw from this may not at first sight be obvious, because it may seem that the ejirth might always have shown this same increase of temperature. But there are several re- sults which a little thought will make clear, although their complete establishment requires the us^, of the higher mathenuitics. The first result is that the increase of temperature can- not be merely superficial, but must extend to a great depth, probably even to the centre of the earth. If it did not so extend, the heat would have all been lost long ages ago by conduction to the interior and by radiation from the surface. It is certain that the earth has not received any great supply of heat from outside since the earliest geological ages, because such an accession of heat at the earth's surface woidd have destroyed all life, and even melted all the rocks. Therefore, whatever heat there 13 in the interior of the earth must have been there from be- fore the commencement of life on the globe, and remained through all geological ages. The interior of the earth being hotter than its surface, and hotter than the space around it, must be losing heat. "We know by the most familiar observation that if any ob- ject is hot inside, the heat will work its way through to the surface by the process of conduction. Therefore, since the earth is a great deal hotter at the depth of 30 metres than it is at the surface, heat must be continually coming to the 4'J4 ASTRONOMY. surface. On reaching the surface, it must be radiated ofiE into space, else the surface would have long ago become as hot as the interior. Moreover, this loss of heat must have been going on since the beginning, or, at least, since a time when the surface was as hot as the interior. Thus, if we reckon backward in time, we tind that there must have been more and more heat in the earth the further back we go, so that we nmst finally reach back to a time when it was so hot as to be molten, and then again to a time when it was so hot as to be a mass of liery vapor. The second fact is that we find the sun to be cooling off like the earth, only at an incomparably more rapid rate. The sun is constantly radiating heat into space, and, so far AS we can ascertain, receiving none back again. A small portion of this heat reaches the earth, and on tlr's portion dejiends the existence of life and motion on tiie earth's sur- face. The quantity of heat which strikes the earth is only about "2 000000000 of that which the sun radiates. This fraction exjiresses the ratio of the ai:)parent surface of the earth, as seen from the sun, to that of the whole celestial sphere. Since the sun is losing heat at this rate, it must have had more heat 3'esterdiy than it has to-day ; more two days ago than it l;ad yesterday, and so on. Thus calculating back- ward, we find that the further we go back into time the hotter the sun must have been. Since we know that heat expands all bodies, it follows that the sun must have been larger in past ages than it is now, and we can trace back this increase in size without limit. Thus we are led to the conclusion that there must have been a time when the sun filled up the space now occupied by the planets, and must have been a very rare mass of glowing vapor. The plan- ets could not then have existed separately, but must have formed a part of this mass of vapor. The latter was there- fore the material out of which the solar system was formed. The same process may be continued into the future. COSMOGONY. 495 iiated oS > become eat must ast, since Thus, if iiust have her back ine when to a time ooling off ipid rate, nd, so far A small 's portion irth's sur- •th is only ;es. This ace of the } celestial have had days ago ^mg back- time the that heat lave been ace back ed to the n the sun and must he plan- lust have ras there- ;era was e future. Since the sun by its radiation is constantly losing heat, it must grow cooler and cooler as ages advance, and must finally radiate so little heat that life and motion can no longer exist on our globe. The third fact is that the revolutions of all the planets around the sun take place in the same direction and in nearly the same plane. We have here a similarity amongst the different bodies of the solar system, which must have had an adequate cause, and the only cause which has ever been assigned is found in the nebular hypothesis. This hypothesis supposes that the sun and planets were once a great mass of vapor, as large as the present solar system, revc^lving on its axis in the same plane in which the planets now revolve. The fourth fact is seen in the existence of ncbulie. We have already stated that the spectroscope shows these bodies to be masses of glowing vapor. We thus actually see nuit- ter in the celestial spaces under the very form in which the nebular hypothesis supposes the matter of our solar system to have once existed. Since these masses of vapor are bO hot as to radiate light and heat through tl?/^ immense distance which separates us from them, they must be grad- ually cooling off. TJiis cooling must at length reach a point when they will cease to be vaporous and condense into objects like stars and planets. We know that every star in the heavens radiates heat as our sun does. In the case of the brighter stars the heat radiated has been made sensible in the foci of '^^r telescopes by means of the thermo- multiplier. The general relation which we know to ex- ist between light and radiated heat shows that all the stars must, like the sun, be radiating heat into space. A fifth fact is afforded by the physical constitution of the plniiets Jupiter and Satimi. The telescoi>Ic examina- tion of these planets shows that changes on their surfaces, are constantly going on with a rapidity and violence to which nothing on the surface of our earth can compare. Such operations can be kept up only through the agency of 496 ASTRONOMY. heat or some equivalent form of energy. But at the dis. tance of Jupiter and Saturn the rays of the sun are entirely insufficient to produce changes so violent. We are there- fore led to infer that Jupiter and Saturn must be hot bodies, and must therefore be cooling off like the sun, stars and earth. We are thus led to the general conclusion that, so far as our knowledge extends, nearly all the bodies of the universe are hot, and are cooling off by radiating their heat into space. Before the discovery of the " conserva- tion of energy," it was not known that this radiation in- volved the waste of a something which is necessarily limited in supply. But it is now known that heat, motion, and other forms of force are to a certain extent convertible info each other, and admit cf being expressed as quanti Je;? f a general somethim^ which is called energij. We muy uo- fine the unit of energy in two or more ways : as the quan- tity which is required to raise a certain weiglit through a certain height at the surface of the earth, or to heat a given quantity of water to a certain temperature. However we express it, we know by the laws of matter that a given mass of matter can contain only a certain definite number of units of energy. When a mass of matter either gives oft' heat, or causes motion in other bodies, we know that its energy is being expended. Since the total quantity of energy which it contains is finite, the process of radiating heat must at length come to an end. It is sometimes supposed that this cooling off may be merely a temporary process, and that in time something may happen by whicii all the bodies of tin universe will receive back again the heat which they have lost. Th:3 i founded upon the general idea of a compensating process in nature. As a special example of its application, some have supposed that the planets may ultimately fall into the sun, and thus generate so much heat ps to reduce t)ie sun once more to vapor. All these theories are in direct opposition to the well-established laws of heat, and can be justified COSMOGONY 497 only by some generalization which shall be far wider than any that science has yet reached. Until we have such a generalization, every such theory founded upon or consist- ent with the laws of nature is a necessary failure. All the heat that could be generated by a fall of all the planets into the sun would not produce any change in its constitution, and would only last a few years. The idea that the heat radiated by the sun and stai*s may in some way be collected and returned to them by the mere operation of natural laws is equally untenable. It is a fundamental principle of tlie laws of heat that a warm body can never absorb more heat from a cool one than the latter absorbs from it, and that a body can never grow warm in a space cooler than itself. All differences of temperature tend to equalize themselves, and the only state of things to which the uni- verse cnnteud, under its present laws, is one in which all space and all the bodies contained in space are at a uniform temperature, and then all motion and change of tempera- ture, and hence the conditions of vitality, must cease. And then all such life as ours must cease also unless sustained by entirely new methods. The general result drawn from all these laws and facts is, that there was once a time when all the bodies of the universe formed either a single mass or a number of masses of fiery vapor, having slight motions in various parts, and different degrees of density in different regions. A grad- ual condensation around the centres of greatest density then went on in consequence of the cooling and the mutual at- traction of the parts, and thus aro-'.e a great number of nebulous masses. One of these masses formed the ma- terial out of which the sun and planets are supposed to havi been formed. It was probably at first nearly glob- ular, of nearly equal den?,ity throughout, and endowed with a very slow rotation in the direction in which the planets now move. As it cooled off, it grew smaller and smaller, and its velocity of rotation increased in rapidity by virtue of a well-Cbtablished law of mechanics, known as 498 ASTRONOMY. that of the conservation of areas. According to this law, whenever a system of particles of any kind whatever, which is rotating around an axis, changes its form or arrangement by virtue of the mutual attractions of its parts among them- Belves, the sum of all the areas described by each particle around the centre of rotation in any unit of time remains constant. This sum is called the areolar velocitij. If the diameter of tlie mass is reduced to one half, sup- posing it to remain spherical, the area of any j^lane section through its centre will be reduced to one fourth, because areas are proportional to the s(]uares ot" the diameters. In "vder that the areolar velocity may then l)e the same as bi j:' he mass nmst rotate four times as fast. The rotating ass we have described must have bad an axis around which it rotated, and therefore an equator defined as being everywhere 90° from this axis. In consequence of the increase in the velocity of rotation, the centrifugal force would also be increased as the mass grew smaller. This force varies as the radius of the circle described by tlie particle multiplied by the square of the angular velocity. Hence wlien the masses, being reduced to half the radius, rotate four times as fast, the centrifugal force at the equa- tor would be increased ^ X ^^ or eight times. The gravi- tation of the mass at the surface, being inverselj' as the square of the distance from the centre, or of the radius, would be increased four times. Therefore as the masses continue to contract, the centrifugal force increases at a more rapid rate than the central attraction. A time would therefore come when they would balance each other at the equator of the mass. The mass would then cease to con- tract at the equator, but at the poles there would be no centrifugal force, and the gravitation of the mass would grow stronger and stronger. In consequence the mass would at length assume the form of a lens or disk very thin in pro- portion to its extent. The denser portions of this lens would gradually be drawn toward the centre, and there more or less solidified by the process of cooling. A point COSMOGONY. 499 would at lengtli be reached, wlien solid particles would begin to be formed throughout the whole disk. These would gi-ad- ually condense around each other and form a single planet, or they might break up into small masses and form a group of planets. As the motion of rotation would not be altered by these processes of condensation, these planets would all be rotating around the central part of the mass, which is supposed to have condensed into the sun. It is supposed that at first these planetary masses, being very hot, were composed of a central mass of those sub- stances which condensed at a very high temperature, sur- rounded by the vaj)ors of those substances which were more volatile. We know, for instance, that it takes a much higher temperature to reduce lime and platinum to vapor than it does to reduce iron, zinc, or magnesium. There- fore, in the original planets, the limes and earths would condense first, while many other metals would still be in a state of vapor. The planetary masses would each be affected by a rotation increasing in rapidity as they grew smaller, and would at length form masses of melted metals and vapors in the same way as the larger mass out of which the sun and planets were formed. These masses would then condense into a planet, with satellites revolving around it, just as the original mass condensed into sun and planets. At first the planets would be so hot as to be in a molten condition, each of them probably shining like the sun. They would, however, slowly cool off by the radiation of heat from their surfaces. So long as they remained liquid, the surface, as fast as it grew cool, would sink into the in- terior on account of its greater specific gravity, and its place would be taken by hotter material rising from the interior to the surface, there to cool off in its turn. There would, in fact, be a motion something like that which occurs when a pot of cold water is set upon the lire to boil. Wlienever a mass of water at the bottom of the pot is heated, it rises to the surface, and the cool water moves V 500 ASTRONOMY. down to take its place. Thus, on the whole, so long as the planet remained liquid, it would cool off equally throughout its whole mass, owing to the constant motion from the centre to the circumference and back again. A time would at length arrive when many of the earths and metals would begin to solidify. At tirst the solid particles would be carried up and down with the liquid. A time would finally arrive when they would become so large and numerous, and the liquid part of the general mass become so viscid, that the motion would be obstructed. The planet would then begin to solidify. Two views have been entei*t.iined respecting the process of solidifica- tion. According to one view, the whole surface of the planet would solidify into a continuous crust, as ice forms over a pond in cold weather, w^hile the interior was still in a molten state. The interior liquid could then no longer come to the surface to cool off, and could lose no heat except what was conducted through this crust. Hence the subsequent cooling would be much slower, and the globe would long remain a mass of lava, covered over by a comparatively thin solid -crust like that on which we live. The other view is that, when the cooling attained a cer- tain stage, the central portion of the globe would be solidified by the enormous pressure of the superincumbent portions, while the exterior was still fluid, and that thus the solidification would take place from the centre out- ward. It is still an unsettled question whether the earth is now solid to its centre, or whether it is a great globe of molten matter with a comparatively thin crust. Astronomers and physicists incline to the former view ; geologists to the latter one. Whichever view may be correct, it appears -certain that there are great lakes of lava in the interior from which volcanoes are fed. It must be understood that the nebular hypothesis, as COSMOOONT. 5QJ ;^ ha™ explained it, is not a perfectly established scien t-hc theory, but only a philosophical Lcl„rnL,Z «nthew,dest study of nature, and pointed to by"„nv otherwise disconnected facts. The widest ^enemLS associated with itis that, so far as wc can seeflhe ™"e "o 1 no self-sustaining, but is a kind of organism wli ch hk! all other organisms we know of, must come to an end in consequence of those very laws of action wiicrkeeo I going. It must have had a beginning witi n » ? • tainty, but which cannot much exceed 20,000 000 and it « at;":r:he]r rat :„r" r' ^""^ ^'"'" '-o a^ an tneir neat, unless it is re-creatprl T^xr f].« action of foi.es of which we at present know notl^ " FINIS. tsa INDEX. jar This index is intended to point out the subjects treated in tlie work, and furtljer. to give references to the pages wl)ere technical terms are denned or explained. Aberration-constant, values of 244. Aberration of a lens (chromatic) 60. Aberration of a lens (spherical), 61. Aberration of light, 238. Absolute parallax of stars defined 476. Accelerating force defined, 140. Achro"iatic telescope described. 60. Ada^;s's work on perturbations of Uranus, 366. Adjustments of a transit instm ment are three ; for level, for collimation, and for azimuth, 77. Aerolites, 375. Amy's determination of the densi- ty of the earth, 193. Algol (variable star), 440. Altitude of a star defined, 25. Annular eclipses of the sun, 175. Autumnal equinox, 110. Apparent place of a star, 235. Apparent semi-diameter of a celes- tial body defined, 52. Apparent time, 260. Arago's catalogue of Aerolites 375. Arc converted into timo, 32. Argelander's Durchmusterunff. 435. ^ Argelander's uranometry, 435. Aristarchus determines tlie solar parallax, 223. Aristarchus maintains the rota- tion of the earth, 14. Artificial horizon used with sex- tant on shore, 95. Aspects of the planets, 272 Asten's, von, computation of orbit of Donati's comet, 409. Asteroids defined, 268. Asteroids, number of, 200 in 1879. 341. Asteroids, their magnitudes, 341. Astronomical instruments (in gen- eral), 53. Asironomical units of length and mass, 214. Astronomy (defined). 1. Atmosphere of the moon, 331. Atmospheres of the planets, m Mercury, Venus, etc. Axis of the celestial sphere de- fined, 23. Axis of the earth defined, 25. Azimuth error of a transit instru- ment, 77. Baily's determination of the den- sity of the earth. 193. 604 INDEX. Bayeh's uranometry (1054), 420. Beek and Maedleu's map of the mouu, 888. Bessel's parallax of 61 Cygui (1«37), 470. Bessel's work on the theory of Uranus, 800. Biela's comet, 404. , Binary stars, 450. Binary stars, their orbits, 453. Bode's catalogue of stars, 435. Bode's law stated, 209. Bond's discovery of the dusky ring of Saturn, 1850, 856. Bond's observations of Donati's comet. 892. Bond's theory of the constitution of Saturn's rings, 859. BouvAKu's tables of Uranus, 805. BuADLEY discovers aberration in 1729, 240. Bradley's method of eye and ear observations (1750), 79. Brightness of all the stars of each magnitude, 489. Calendar, can it be improved ? 201. Calendar of the French Republic. 202. Calendars, how formed, 248. Callypus, period of, 252. Cassegrainian (reflecting) telescope, 67. Cassini discovers four satellites of Saturn (1084-1671), 800. Cassini's value of the solar paral- lax, 9 "•5, 226. Catalogues of stars, general ac- count, 434. Catalogues of stars, their arrange- ment, 265. Cavendish, experiment for deter- mining the density of the earth, 193. Celestial mechanics defined, 8. Celestial sphere, 14, 41. Central eclipse of the sun, 177. Centre of gravity of the solar sys- tern, 272. Centrifugal force, a misnomei 210. Ciikistie's determination of mo- tion of stars in line of sight, 471. Chromatic aberration of a lens, 00. Chronograph used in transit ob- servations, 79. Chronology, 245. Chronometers, 70. Claihaut predicts the return of Ilalley's comet (1759), 897. Clakke's elements of the earth, 202. Clocks, 70. Clusters of stars are often formed by central powers, 404. Coal-sacks in the milky way, 415^ 485. Coma of a comet, 388. Comets defined, 208. Comets formerly inspired terror, 405-0. Comets, general accuu/t, 388. Comets' orbits, theory of, 400. Comets' tails, 388. Comets' tails, repulsive force, 395. Comets, their origin, 401. Comets,their physical constitution, 898. Comets, their spectra, 393. Conjunction (of a planet with the sun) defined, 114. Collimation of a transit instru- ment, 77. Conjugate foci of a lens defined, 65. Constellations, 414. Constellations, in particular, 423, et seq. Construction of the Heavens, 478. Co-ordinates of a star defined, 41. Copeland observes spectrum of new star of 1876, 445. CoKNu's observations of spectrum of new star of 1876, 445. INDEX. 605 CoHNU (letermlut's the velocity of liglit, 222. (/orrection of a clock defined, 72. Cosniical physics detlned, 'S. Cosmogony defined, 492. Corona, its spectrum, ;}05. Corona (the) is a solar appendage, 802. Craters of the moon, 328. Day, how subdivided into hours, etc., 257. Days, mean solar, and solar, 2.59. Declination of a star defined, 20. Dispersive power of glass defined, 01. Distance of the fixed stars, 41'", 474. Distribution of the stars, 489. Diurnal motion, 10. Diurnal paths of stars are circles 12. Domi ical letter, 255. DoNATi's comet (IH-W). 407. Double (and multij)le) stars, 448. Double stars, their colors, 452. Earth (the), a sphere, 9. Earth (the) general account of, 188. Earth (the) is a point in compari- son with the distance of the fixed stars, 17. Earth (the) is isolated in space, 10. Earth's annual revolution, 98. Earth's atmosphere at least 100 miles in height, 380. Earth's axis remains parallel to it- self during an annual revolution, 109, 110. Earth's density, 188, 190. Earth's dimensions, 201. Earth's internal heat, 493. Earth's mass, 188. Earth's mass with various values of solar parallax (table), 230. Earth's motion of rotation proba- bly not uniform, 148. Earths' (the) relation to the heav- ens, 9. Earth's rotation maintained hy AiiisTAiunus and TiMOciiARfn. and opposed by Ptolkmy, 14. Earth s surface is gradually cool- ing, 493. Eccentrics devised by thcf ancients to accoiuU for tlie irregularities of planetary inoliouH. 121. Eclipses of the moon, 170. Eclipses of tiie sun and moon. 108. Eclipses of the sun, explanation, 172. Eclipses of the sun, physical phe- nomena, 297. Eclipses, their recurrence, 177. Ecliptic defined, 100. Ecliptic limits, 178. Elements of the orbits of the ma- jor planets, 27(5. Elliptic motion of a planet, its mathematical theory, 125. Elongation (of a planet) defined, 114. Encke's comet, 409. Enckk's value of the solar paral- lax, 8'-857, 22(1. Engklm.vnn's photometric meas- ures of Jupiter's satellites, 350. Envelopes of a comet, 390. Epicycles, their theory, 119. Equation of time, 258. Equator (celestial) defined, 19, 24. Equatorial telescope, description of. 87. Equinoctial defined, 24. Equinoctial year, 207. Equino.xes, 104. Equinoxes ; how determined, 105. Evection, moon's 103. Eye-pieces of telescopes, U2. Eye (the naked) sees about 2000 stars, 411, 414. Fabritius observes solar spots (1611), 288. Figure of the earth, 193. FizEAU determines the velocity of light, 222. 606 INDEX Flamsteed's cntalogue of stars (1080). 421. Focal distance of a lens defined, (If). FoucACLT determines the velocity of light, 233. Futiireof the Holar»ystoni,;}09, 1)01. Gahixy, or milky way, 415. Gamijco observes soiarspots (1011), 3HH. Galileo's discovery of satellites of Jupiter (1010), 343. Galileo's resolution of the milky way (1010), 415. Oalle first observes Neptune (1H40), 307. Geodetic surveys, 199. Golden number, 353. Gould's uranometry, 435. Gravitation extends to the stars, 451, 450. Gravitation resides in each particle of n)atter, 139. Gravitation, terrestrial (its laws), 194. Gravity (on the earth) changes with ihe latitude, 303. Greek alphabet, 7. Gregorian calendar, 255. Gvi-DEN, hypothetical parallax of stars, 454. GvLDEN on the distribution of the stars, 489. Halley predicts the return of a comet (1083), 397. Halley 's comet, 398. Hall's discovery of satellites of Mars, 338. Hall's rotation-period of Saturn, 353. Haukness observes the spectrum of the corona (1809), 305. ITauptpunkte of an objective, 04. Hansen's value of the solar paral- lax, 8".93, 237. Heis's uranometry of the northern sky. 417. Helmiioltz's mnasurcB of the limits of naked eye vision, 4. Heusciiel (W.), first olocrves the spectra of stars (1798), 408. IlEUsciiEii (W.), dl.scovcTs two satellites of Saturn (1789), 300. Heuschel (W.), discovers two satellites of Uramis (1787). 303. nEKsciiEL (W.) discovers Uranus (1781), 303. Heuschel (W.) observes double stars (1780), 453. Hehsciiel's catalogues of nebu- la;, 457. Heuschel's star-gauges, 479. Heuschel (W.) states tiuit the .solar system is in motion (1783), 474. Heuschel'm (W.) views on the nature of ncbuiie, 4.'J8. Hkvelius'h (.'atalogue of stars,4.35. Hill's (G. W.) orbit of Donati's comet, 409. Hill's (G. W.) theory of cury, 333. Hooke's drawings of Mars (1000), 330. Horizon (celestial — sensible) of an observer defined, 23. HoiiHox's guess at the solar par- allax, 225. Hour angle of a star defined, 25. HuuHAUU's investigation of orbit of Biela's comet, 404. HuooiNs' determination of mo- tion of stars in line of sight, 471. Hugo ins first observes the spectra of nebulcB (1804), 405. HuoGiNs' observations of the spec- tra of the planets, 370, et seq. Hugo ins' and Millek's observa- tions of spectrum of new star of 1800, 445-0. HuGGiNs' and Miller's observa tions of stellar spectra, 408. HuYGiiENS discovers a satellite of Saturn (1055). 300. INDEX, 507 ;b of the iHif>n. 4. t ol>.s(.'rve» 7»8), \m. lovcrs two 781)), JJOO. :overs two 1787). ;{«;{. LTs Urauiis ves (l(ml)lo 3 of nelm- s, 479. 9 tliat the tion (178;{), wa on the J. if stiirs,435. )f Dounti'a J of lars (1006), iihlo) of an solar par- fined, 25. >u of orbit n of mo- sight, 471. the spectra af the spec- ), et seq. 's observa- aew star of s observa a. 408. satellite of HiiYoiiENS discovers laws of cen- tral forces, 135. HuYoiiENs discovers the neb- ula of Orion (1050), 457. IIuYoiiKNs' explanation of tho appearances of Saturn's rings (1055), ;J50. IIuyqiiicnb' guess at the solar par- allax, 320. HuYOiiENs' resolution of the milky way, 410. Inferior planets defined, 110. Intrantercurlal planets, 822. Janhsem first observes solar promi- nences in daylight, 304. Janssen's photographs of the sun, 281. Julian year, 250. Jupiter, general account, 343. Jupiter's rotation time, 340 Jupiter's satellites, 340. Jupiter's satellites, their elements, 351. Kant'8 nebular hypothesis, 4!)2. Kepleu's idea of tho milky way, 410. Kepler's laws enunciated, 125. Kepler's laws of planetary mo- tion, 122. Klein, photometric measures of Beta Lyra', 442. Lacaille's catalogues of nebula;, 457. Langley's measures of solar heat, 283. Langley's measures of tho heat from sun spots, 280. Laplace investigates the accelera- tion of the moon's motion, 146. Laplace's nebular hj'pothesis, 492. Laplace's investigation of the constitution of Saturn's rings, 'Sod. Laplace's relations between the mean motions of Jupiter's satel- lites, 349. Lassell discovers Neptune's sal- elllto (1847), 309. Laksell discovers two satellites of Uranus (1847), 303. Latitude (geocentric — geographic) of a place on the earth defiui-d, 203. Latitude of a point on the earth is measured by the elevation of tho pole, 21. Latitudes and longitudes (celes- tial) defined, 112. Latitudes (terrestrial), how deter- mined. 47, 48. Le Sage's tlieory of the cause of gravitation, 150. Level of a transit instrument, 77. Le Veuuieu computes the orbit of meteoric sliower, 384. Le Veiiuieii's researches on the theory of Mercury, 323. Le Veuiiiiii's work on perturba- tions of '^ranua, 300. Light-t ering power of an ob- ject glass, 50. Light-ratio (of stars) is about 2 5, 417. Line of collimation of a telescope, 69. Local time, 82. Lockyer's discovery of a spec- troscopic method, 304. Longitude of a place may bo ex- pressed in time, 33. Longitude of a place on the earth (how determined), 34, 37, 38, 41. Longitudes (celestial) defined, 112. Lucid stars defined, 415. Lunar phases, nodes, etc. iSee Moon's phases, nodes, etc. Maedler's theory of a central sun, 478. Magnifying power of an eye-piece, 55. Magnifying powers (of telescopes), which can be advantageously employed, 58. 508 INDEX. Magnitudes of tlic stars, 416. Major planets defined, 268. Mars, its surface, 336. Mars, physical description, 334. Mars, rotation, 886. Mtirs's satellites discovered by Hall (1877), 838. Mahius's claim to discovery of .Jupiter's satellites, 843. M'.SKELYNE determines tie den- sity of the earth, 193. Muss and density ox the sua and planets, 277. Mass of the sun in relation *.o masses of planets, 227. ]klasses of the planets, 232. Maxwell's theory of constitution of Saturn's rin^s, 300. Mayeu (C.) first observes double stars (1778), 452. Mean solar time defined, 28. Measurement of a degree on the earth's surface, 201. Mercury's atmosphere, 814. Mercury, its apparent motions, 310. Mercurv, its aspects and rotation, 318. ' Meridian (celestial) defined, 21, 25. Meridian circle, 83. Meridian line defined, 25. Meridians (terrestrial) defined, 21. Messier's catalogues of nebulae, 457. Metonic cycle, 251. Meteoric showers, 380. Meteoro showers, orbits, 383. Meteors and comets, their relation, 383. Meteors first visible about 100 miles above the surface of the earth, 380. Meteors, general account, 375. Meteors, their cause, 377. Metric equivalents, 8. MiCHAELsoN determines the ve- locity of light (1879), 223. Michell's researches on distrl. bution of stars (1777), 449. Micrometer (filar), description and use, 89. Milky way, 415. Milky way, its general shape ac- cording to Heuschel, 480. Minimum Visibile of telescopes (table), 419. Minor planets defined, 268. Minor planets, general account, .S40. Mira Ceti (variable star), 440. Mohammedan caK ..liar, 253. Months, different kinds, 249. Moon's atmosphere, 331. Moon craters, 329. Moon, general account, 326. Moon's light and heat, 331. Moon's light l-618,000th of the sun's, 332. Moon's motions and attraction, 152. Mo(m's nodes, motion of, 159. Moon's perigee, motion of, 103. Moon's phases, 154. Moon's rotation, 164. Moon's secular acceleration, 140. Moon's surface, does it change? 332, Moon's surface, its character, 828. Motion of stars iu the line of sight, 470. Mountains on the moon often 7000 metres high, 330. Nadir of an observer defined, 23. Nautical almanac described, 263. Nel)ula) and clusters, how distrib- uted, 465. NebulJB and clusters in general, 457. Nebula of Orion, the first telescopic nebuli- discovered (1656), 457. Nebulae, their spectra, 465. Nebular hypothesis stated, 497. Neptune, discovery of by Le Ver- liiER and ADAM3 (1846), 367. IXDEX. 609 looa often Neptune, general account, 30/5. Neptiin^^'s satellite, elements, 369. New star of 1876 lias apparently become a planetary nebula, 445. J e\v stars, 443. Newton (I.) calculates orbit of comet of 1680, 406. Newton (I.) Laws of Force, i:i4. Newton's (I.) investigation of comet orbits, S96, Newtonian (reflecting) teleucope, 60. Newton's (H. A.) researclit-a on meteors, 386. Newton's (H. A.) Ineory of cou- Btitutioo of comets, 394. Nucleus ot a comet, 388. Nucleus of a solar spot, 287. Nutation, 211. Objectives (matliematical theory), 03. Objectives or object glasses, 54. Obliqaity of the ecliptic, 100. Occultations of stars by the moon (r planets), 180, 331, Olbkhs's hypothesis of the origin of asteroids, 340, 342. Olbehs predicts the return of a meteoric shower, 381. Old style (in dates), 254. Opposition (of a planet to the sun) defined, 115, Oppositions of Mars, 335. Parallax (annual) defined, 50. Parallax (equatorial horizontal) de- fined, 52. Parallax (horizontal) defined, 50. Parallax (in general) defined, 50. Parallax of Mars, 220, 221, Parallax of the sun, 216. Parallax of the stars, general ac- count, 470. Parallel sphere defined, 20. Parallels of declination defined, 24. Peihce's theory of the constitu- tion of Saturn's rings, 350. Pendulums of astronomical clocks 71, Penumbra of the earth's or '"gi ^'!i shadow, 174. Perir ic comets, elements, 399. Perturbations defined, 144. Perturbations of comets by Jupi- ter, 403. Piiotomeler defined, 417. Photosphere of the sun, 279. PlAZZi discovers the first asteroid (1801), 340. PiCAKD publishes the Connaissance dcs 7'^'ws(1079). 203. PiCKEKiNo's measures of solar light, 283. Planets, their relative si/e exhib- ited, 209. Planetary nebulae defined, 459. Planets ; seven bodies so called by the ancients, 96. Planets, their iipparent and real mo'„lons, 113. Planets, tl.ieir physical constitu- tion, 370. Pleiades, map of, 425. Pleiades, these stars are physically connected, 449. Polar distance ot a star, 25. Poles of tV'^ celestial sphere de- fined, 14, 20, 24. Position angle defined, 90, 4')0. Pouillet's measures nf solar racti- ation, 285. Power of telescopes, its limit, 328. Practi(;al astronomy (defined), 2. Precession of the eciuinoxes, 206, 209. Prime vertica' of an observer do- fined, 25. Proldem of three bodies, 141. PuoCTOu's map of distribution of nebulae and clusters, 406. PuocTOU's rotation period of Mats, 330. Proper motions of stars, 472. Proper motion of the sun, 473. 510 INDEX. Ptolemy deteriuines the Eolar parallel, 225. Ptolemt's catalogue of Btars, 435. Ptolemy niaiatains the immova* hilUy of the eartli, 14. PvTHAciouAs' conception of crys- talline spheres for tiie planets, 96. Radiant point of meteors. 381. Rate of a clock defined, 73. Reading microscope, 81, 85. Red stars (variable stars often tetar 443. Theoretical astroiionu (defined), 8. Tides, 165. Time converted into arc, 33. TiMOCiiAuis maintains the rota- tion of the earth, 14. Total solar eclipses, description of, 297. Transit instrument, 74. Transit instrument, methods of observation, 78. Transits of Mercury and Venus 318. Transits of Venus, 216. Triangulation, 199. Tropical year, 207. Tvcno Bkaiie's catalogue of stan, 435. 512 INDEX. Ttcho Brahe observes new star of 1573, 443. Units of mass and length employed in astronomy, 213. fTniversal gravitation discovered by Newton, 149. Universal gravitation treated, 131. Universe (the) general account, 411. Uranus, general account, 303. Variable and temporary stars, gen- eral account, 440. Variable stars, 440. Variable stars, their periods, 442. Variable stars, theories of, 445. Variation, moon's, 163. Velocity of liglit, 344. Veaus's atmosphere, 317. Venus, its apparent motions, 310. Venus, its aspect and rotation, 315. Vernal equinox, 102, 110. Vernier, 82. Vogel's determination of motion of stars in line of sight, 471. Vogel's measures of solar actinic force, 283. Vogel's observations of Mer- cury's spectrum, 314. Vogel's observations of spectrum of new star of 1876, 445. Vogel's observations of the spec- tra of the planets, 370, et seq. Volcanoes on the moon supposed to exist by Herschel, 332. Vulcan, 333. Watson's supposed discovery of Vulcan, 323, 334. Wave and armature time, 40. Weight of a body defined, 189. Wilson's theory of sun-spots, 390. Winter solstice, 109. Wolf's researches on sun-spots, 295. Years, different kinds, 250. Young observes the spectrum of the corona (1869), 305. Zenith defined, 19, 23. Zenith telescope described, 90. Zenith telescope, method of observ- ing. 92, Zodiac, 105. Zoellner's estimate of relative brightness of sun and planets, 271. Zoellner's measure of the rela- tive brightness of sun and moon, 332. Zone observations, 80. if spectrum 145. f the spec« ), et seq. i supposed L, 332. scovery of \e, 40. 3d, 189. spots, 290. sun-spots, 250. ectrum of •ed, 90. of observ- f relative 1 planets. the rela- ind moon,