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Sohnohlor's • (\Mirso ' In vorv .-(AtlsfActorv -uul viry niploto. And AiUy Hustains tho n'jmtatlon tho author liA« lona iv\».*»\v*<>d. Aj« A »«cct\<,s(\il h^Aohor y\( Fronoh, In Kdlnhurgh." */ A Spealm^n Copy sent to PrlncApAls of Sohools. post froe. on rcoelpt of OJ. In stAinpa. by OUvor ivnl Boyd, BiUubuigh. Edinburgh: Outrb xjin novo. London: SurKix, MARsnAtu and Co. J J! w 1 \, 1/ 2 . 0'> /\/> L FIBST LATIN COURSE. l-'oiirtli I'Mitiori, j.iico I«. Od! botirul. A mw Him LATIN COUnSE; rompriBin, (iinmiimr nud Kx«rciso«, witli VnvnhnlnrlvH. Uy (Jkoik.b HoIiim.Im, KdiiiliiirKli. fhrit nnd cnrM- ifiil Ukoly to bo irid wi) Iiavo Kreiit li.lHf„l,.n„ll Smon. - " |»r ()ujlvl.ut hook U OTr«.p(|lm'lv well n.lnn.. I '■"llyKr, pit'llHUIHl 111 n>('ol Ah«r,Uen Daily Frrc /V,'M.~"Tho book in Jimt tho nor* nf nnn ♦», . wo buvo oftmj wlHhed for to put int. tlin l.u.ffiof ,;,",„",; ''"^*^^' ortliHt Bhould ruthor \w miurvod for tho8o lirLr nrll "CKlnner, moro flttod to b., bookH of r.f.renc„ u/a.To Z , XolcT l\lZ •|,« y/tw CloM^oi supplies aufficient wcn-Jt for a year, leithout tJui ticcesaity (fusing any ot/ier Latin Book. A Bpeoimen Copy Bent to PrlnolpalB of Bohoois, post ftee. on rooelpt of 9a. In stamps, by OUver and Boyd. Edlnb^gh AI CAl AI ELK ill: NTS OF ASTRONOMY; ADAPTED FOE USE IN SCHOOLS AND PRIVATE STUDY. I^i' HUGO KEID, LATH I-INCn-aL Of DA..M0II8IK OM.KCE, IIAUVAX, H.8. Illustrator bg ^nk-m (Bmnhbp on Wioo)i. Fourth Edition, CAnEPUU.Y REVISED AND BKOUGll I DOWN TO THE PIIESKNT STATE OF ASTKONOMICAL SCIENCE, By Re\. ALEX. MACKAY, LL.D., FR.G.S., AUTHOR OF " MANUAL OF MODRRN OEOOnAl'Iiy," " FACTS AND 1>ATK«," ETC. EDINBURGH : OLIVER AND BOYD, TWEEDDALE COURT. LONDON: SIJIPKIN, MARSHALL, AND CO. PLAN OP THE SOLAR >LAN OP THE SOLAR SYSTEM. (As 6 2.0 4^ M I>RINTKI> BY OUVKH ANIi n PRRFACE TO TIIK FOUIlfll KDITION. A MONO tho many nblo i.ftn.|.l,.)okii of phyHicftI ncfcnco that Imva rocontly Apponrud, very few cnn bo c(»tiipftre.l xvitl. tlio work now rc-JMucl, citlu r In nutunOncM of plan, torMcntw of ntylo or occuracy of doHcriptiun * Since tho publication, however, of the third edition, c or- dinary progrcfn ImM been made in every department cf \»tro- aomy, and dlMcovcries effected vying in importance with .he brilliant nchiorom.nt*. of Newton, U. Place, and the el ' • Her- iwhel. In piirticular, tho great physical problem of the t go— the earth's mean distance from the ««/»— ha8 Leon well-nlgh definitely and satigfactorily sg^lved. KquaUy important hare lioen tho splendid disccvcri.^n reeulting from the researches of Kirchhoff and others in Hpeetrum analyHis; inasir uch an they lay open to UH, for tho first time, tho physieal constitution of the great central orb of our syjtem, and conclusively dem.mBtrato that tho sun, stars, earth, and all tho oth^^r niembcr« of tho planetary systeia, aro mainly composed of tho same identical materials; and they also throw special light on tho peculiar ccntlition of the m bulaj. Groat additions have been made to our knowledge of tho individual members of our systen.. T» e existonco of a planet, nearer the sun than Mercury, has been all but demonstrated' The planet Mars, at the form of whoso orbit the illur.trioui Keplor laboured A.r so many years— labours resulting in tho tliree famous " laws ol motion " for which that astronomer will be for ever distinguished— is now clearly shown to be enveloped in an atmosphere; to have his surface variegated with conti- ncnts, (KJeans, islands, and seas; and, in faet, to contain the chief requisites esseuUal to animal and vegetable life. The same researches, however, have also shown the great improba- bility of Mars sharing these characteristics with any other orb of the solar system; unless, indeed, we aro to except tlie inner satellites of Jupiter, Saturn, and the other larger * PnEFACE. l)Ianctfl, which, 80 far ft.s our |irc8ent knotvlcdgc extcnda, mny perhaps bo honioa of livuig beings. Jupiter and Saturn them- selves can no longer be regarded as habitable worlds, notwith- standing the eloquent pleadings of Sir David Brewster; but rather as expirimi suns, no longer, indeed, shining with all their wonted light, but still capable of yielding important supplies of heat to the tiny orbs that revolve more immediately around them. Since the publication of the last edition, moreover, we have made the acquaintdnce of many additional members of the great family of asteroids, or smaller planets, which fill up the void between Mars and Jupiter. The mysterious colossal rings of Saturn have at length been shown to consist of myriads of small opaque bodies, each moving independently, and in its own orbit, around the planet, but forming collectively a series of luminous streams, which, in all probability, have their analogues in those streams of meteors and falling stars through which our planet passes in October and November of each year. These, and many more of the results of recent astronomical research, are em- bodied in this new edition. At page 179 will be found elaborate tables, prepared by Professor C. Piazzi Smyth, Astronomer- Royal for Scotland, showing in detail all the more important facts hitherto established by astronomers relative to the sun, moon, and planets. ^ In preparing this new editirn, the Editor has freely availed himself of the various admirable expositions of Astronomv by Richard A. Proctor, B.A., including "The Sun— Ruler, Fire, Light, and Life of the Planetary System," " Other Worlds than Ours," "The Orbs Around Us," etc. i also of J. N. Lockyer's exquisite little volume, entitled " Elementary Astronomy ;" of G. F. Chambers's " Descriptive Astronomy," Oxford, 1867; " Popu^ Inr Astronomy," by Sir George B. Airy, Astronomer-Royal ; and of the new edition of the late Sir John Herschel's " Outlines of Astronomy," Longmans, 1871. A plan of the solar system, and a good index, have also been added ; and, altogether, it is hoped the vork will be found to be abreast of the present state of astronomical science. ALEX. MACKAY. EDixnuROir, fanitari/ 1874. CONTENTS. Introduction P^Pfl 7 TAKT I. The Sphere op tkl Heavens 1. Definitions. 2. Apparent Motion of thci'lleZ'onZNZh'^'7 ^ 8. General Definitions. 4. IIow to dpfin„ « T "?"* ^"^«- in the Heavens. 5. Noihern Itt'lttns ? z"o r"' ?r^^ stellations. 7. So,.them Constellations rEvteut"n??.Tr^ ^'"• visible at any Place. "* °^ "'^ Heavens TART II. Leading Phenomena of the Earth, Sun, and Moov .« Sect. I. Definitions ° Sect. II. Day and Night-ainKale-Seasons To Day and Night, 49. Climate, 64. Seasons,67. Sect. III. Trade- Winds and Tides Trade-Winds, 69. Tides, 71. ^^ Sect. IV. Divisions of Time.... Sect. V. Moon'H Phases, Eclipses, etc Moon's Pliases, 90. Eclipses and Occi.ltations 92 "'" Refraction, 99. Koflection, 102. Twilight, 103. ^^ 6 CONTENTS. PART III. Page The Solau System 105 Sect, I. Definitions lOG Sect. II. Forces acting throughout tl'o Solar System 114 Piojectil'i Force, 114, Attractive Force, 116, Sect. III. Orbitual Motions of the Tlanots, Satellites, and Comets 122 Sect. IV. Rotatory Motions and Forms of the Sun, Planets, and Satellites 130 Sect. V. General Facts relating to the Solar System 135 Sect. VI. Of the Sun, Planets, Satellites, and Comets 139 The Sun, 139. Vulcan, 14(5. Mercury, 147. Venus, 148. Tlio Earth, 150. The Moon 155. Mars, 15V. The Asteroids, 161. Jupiter, 163. Saturn, 168. Uranus, 172. Neptune, 173. General Illustrations, 176. Table of the Solar System, 179. Comets, ISO. Zodiacal Light, 183. Meteoi-ic Systems, 184. PART IV. Parallax, Abkuration, and Precession 188 Parallax, 188. Aberration, 192. Precession, 196. Nutation, 199. PART V. Proofs 201 1. The Earth is Kound, 201. 2. The Karth Kotates, 205. 3. The Earth and the other Planets Move Kound the Sun, 210. PART VT. The FiXED Stars 212 Their Proper Motion, 212. Distances, 214. Divisions of the Stars according to their Brightness, 216. Ordinary Fixed Stars, 218. Temporary Stars, 218. Variable Stars, 219. Binary Stars, 220. Nebulae, 221. Clusters of Stars, 222. PART VIT. Sketch of the History of Astronomy 224 lNi>EX 235 ELEMENTS OP ASTRONOMY. Introduction. 1. Astronomy is the science which treats of the heavenly bodies. 2. By the "heavenly bodies," we mean the Sun the Moon, the Earth, and the Stars. ' 3. The discoveries of astronomy have taught us to class the world which we inhabit among the heavenly bodies, having proved many resemblances between them. We now know that our earth is a star, althouo-h It does not appear to us to be one ; and that several ^of the stars are large, solid, opaque bodies like the earth under our feet. 4. The ancients would not admit any community of nature between the earth and the stars. This idea of tiie essentially opposite nature of the earth and the brilliant lunnnanes which shine in the sky, for a long tmie retarded the progress of astronomy. 5. Astronomy informs us of what is known regardin< the forms of the heavenly bodies, their magnitude, dis- tances, relative situations, apparent motions, real motions, physical constitution, and actions on each other. 6. The term Astronomy is derived from the Greek S 8 ELEMENTS OF ASTRONOMY. words AtfTjj^ (aster), a star, and No/ao; (nomos), a law. Its literal signification is, thorclore, the law of the stars, or order of the stars. 7. A knowledge of astronomy is to \)q acquired partly by the study of books, partly by observing the appearances of the heavenly bodies and the changes going on. amongst them. As the latter is very interesting in itself, as well as essential to a full understanding of tho phenomena of astronomy, and as it can easily be pur- sued from the beginning, this work will open with a description of the sphere of the heavens. PART I. THE SPHERE OF THE HEAVENS. 1. Definitions. 8. A Circle is a curved line, eveiy point of which is equidis- tant from a point within it, called the Centre. Considered with respect to the enclosed snriace, whicli it hoiuids, it is often called the Circumference. 9. A Sphere is a round body (or a round space), every point on the surface (or outside) of which \6 equidistant from a point withm called the Centre. 10. A Diameter of a circle, or of a sphere, is a straight line from any point in the circumference of the circle, or on the sur- iace of the sphere, passing through the centre to the opposite sivie. A Radius is that half of a diameter between the centre and the circumference of the circle, or surface of the sphere ; or a straight line from the centre to the circumference of the circle or surface of the sphere. 11. The Horizon or Sensible Horizon of a place is that circle all round where the earth and sky appear to meet. _ We cannot see the earth beyond it, nor the sky below it. It bounds or limits our view ; and takes its name from a Greek word having this signification. x_, A -ic ».v4«xv*A ii3 iKt pall 01 tiiu &A\ jiuai. uooYe ELEMENTS OF ASTRONOMY, 9 tho head of the observer : and it means the same whether we say that a heavenly body is in the zenith at < f ^T'. '''*: *^'''^ '^ '' ^^^''^«^ «' '/'«^ place. U. Rotation is the act of a body turn-'ng round on self, without moving out of its ola/e ; as wlien a top Bleeps in spinning. The body is t.en said to rotate^ The term is derived from the Latin verb rata, I whirl a'wheel .'""" "' ' ''""^"' ^'"^'^^^ ^'"^ ^^^^ "«»^ ^^'^i 14. When a body rotates, there is an iman-inarv s rmght line in it whieh keeps the same plae^-^every other par describing a circle -oand some point in tha^ Ime.^ This line is called the Axis, or Axis of Rota- 15. A body may have a motion of translation, that , be continually changing its place, at the same time that It has one of rotation; as the wheel of a carria-e m motion, or a ball rolling along the ground. But each motion may be considered separately 16. Apparent Motion is the apparent change of a body s position, arising from a change in the position of the observer, not from a real motion of the body It IS sometimes called relative motion. 17. Real Motion is when a body actually does mS! ^''''^""- ^' '' sometimes called aloluTe rJl^' ^P7?° ^«Y^"g ^^^^S ^ road in a carriage has real or absolute motion : while the change of position which he observes in the trees, houses, etc., is on y an apparent or relative motion of these objects. ^ 19. Motion is called Uniform, when^its rate remains the same, that is, when the moving bo V passes over equal spaces in equal times; Acceleratedrwhen the rate of motion is continually increasing • Re arded when the rate is continually diminishing'' ' retarded, a2 ^^ ELEMENTS OF ASTRONOMY, 2. Apparent Motion of the Heavens- North Pole. 20. When we turn our eyes towanla the nky, it appears to us to bo the conc.ivo or inner surface of a hollow sphere in the centre of which we arc placed. It IS convenient to regard it as such, and to luia-ino various lines drawn upon it, to enable us to define w'*h precision the positions of the heavenly bodies. Thia hollow sphere wo shall call "the heavens." 21. The heavens appear to be in continual motion from east to west around us, carrying the sun, moon, and stars along with them : for, if we observe the posi- tion ol any heavenly body, in respect to the earth, at *\"^,/^"";' ""'^ ^''^^ ^'''' ^^ •'^o''^"^ i" a» hour or two, wo shall hnd it to the west of its former position. 22. Also, we shall find that there is a moVement of the whole heavens, not merely of one body, as the sun or any bright star we may watch ; for, 1. We find the westward movement in every one whose course wo watch, and, 2. The different celestial objects preserve the same positions in relation to each other, showincr that they all move together. Some ancient astrono° mers, who believed that this was a real motion of the heavens, were perplexed how to explain the various bodies preserving the same relative positions in this great westerly movement, and imagined that they were all immovably connected to each other by being em- bedded, like jewels when set, in a crijstal sphere, which performed the revolution, and carried sun, moon, and stars along with it. 23. The heavens are found to make one complete revolution in 24 hours (correctly, 23 hours, 56 minutes, 4-09 seconds). This is known by noting carefully the position of a star in reference to any fixed Icrrestrial object, and observing the time tliat elapses before it again comes into the same position. ELEMENTS OF ASTRONOMY. H 24. But this is only an apparent motion: the real motK.n winch causes it, is the rotation of the earth from west to east m the same time. This is proved by a variety of reasons, which will he alluded to snbse- qnently; but tvvo thin.-s may bo stated at present, wh.cM wdl satisfy us that the apparent revolution of tlie sky mai/ ho caused by a real motion of the earth. 1. I> e may he in motion without perceiving if, as in tho cabin of a^ ship, or of a canal boat, or in a railway train, movm- gently, when we may be carried a con- siderable way without knowing that we have moved at all. We do not perceive motion when it is uniform so hat there are no jarrings or joltings, and when the bodies around us are moving at the same rate, so that we retain the same relative position to them. 2. We knoio also that our motion maj/ cause bodies to appear to move wheh are really standing still ; as, when we are appear to fl, quickly past us in a direction opposite to tlij't^in which we ourselves are moving. 25. When the motions of the sta'is are observed they all seem to move together from the east side of the horizon towards the west. Some rise very far south, ascend but a little way above the horizon, and set far south on the west side of the horizon : some rise in the cast ascen.l very high in the sky, and after de- scribing a large curve in tht. heavens, set in the west • others rise and set north of due east and west: others o not set at all, but describe complete circles above ih^ horizon round one point : others describe smaller VP^I? I'/r^'- '"""'^ *^^'^* P^^"*5 ^"^^ «^^ stars IJ ?I *^''^* "^""'"'i ''^W^^'^'"' t^ i'^^^ff^^ ^y the naked eye, not to inove at all. 26. That point is the North Pole of the Heavens v!Z'' 'Vlf'"l ''' P?^"l ^^PP^'^^" *^ '^ i" the southern wg'i'^.ft'nf;^' v^"^ " '^' 'T -*^"- ^^^^^ '' *^-^ vw.j ii\, ,,Oxti} ol tuu equator, and whicli is the centre 12 LLEMENT8 OF AS-JRONOMV. ronnd winch the j..onthcrn stars appear to move daily. Iheso two points are the extreinitieH of tlie imaginary hue or axin, ahout whicli the heavens appear to rotate daily. 11,0, are vertical at tlie poles of the earth, and in the horizon at its equator. 27. x\l any place on the eartii's surface, the pole of the heavens, visible there, always appears in the same position in relation to fixed olijeets at that place, while every other point in the sky is continually chanLnn- Its position in relation to them. 28. The poles of the heavens may also be defined as the 2 J. I here is a pretty bright star very near the north pole of the heavi-ns, called the North Polar Star winch may be easily found out. 30. Tiie ancients had the starry heavens mapped out into constellations, each consisting of a collection ot acjjoining stars, separated from th.e others by an imaginary line, and included under one name, expres- sive of some figure which the leading stars in the con- stellation were sui>posed to resemble. 31. The stars in each constellation are named by the letters of the Greek alphabet,— the brightest being termed a (alpha) ; the next brightest /3 (beta), and so on. When there are more stars in a constellation than there ai^ Greek letters, the others are denoted by num- bers. The leading stars in each constellation have usually some name applied to each, as Dubhe, Capellr Vega, Arcturus, Aldebaran. ' 32. At the left side of Fig. 1, may be observed a cluster ot stars disposed within the figure of a small bear, and separated by a line from the adjoining stars. 1 he stars within that line form a constellation^ termed Ursa Minor, or the Little Bear. In the same hgure are seen parts of other constellations— the Great Bear (Lisa Major), the Dragon (Draco), the hand of Bootes, and the feet of Cepheus. ELKMKNTS OF AHTKONOAIY. 13 33. The north pole-star is the Lri^'htest star in tho coiistcllution r.ittlo Hear, at tho tip of itH tail. It is marked V H in the fi^nirc. It is easily found out by means of the well-known seven bri^dit stars commonly FlK. I. called the Bear, the Plough, Charles's Wain, the Butcher's Cleaver. These stars are represented in Fig. 1, towards the lower part of the right side. If, wnen these stars are in any pobltlou. a straight line be imagined through 11 BLEMENTS OF A8TK0N0MY. tbo two (6 un.l a) furthest from the tuil, niul i.ro.lii( ,.1 inad,roctH.n/n.. the limbs of the uni.nal i « will pass cl,.so to the north ,H,hir star. Those two Htarn an- hcnee culled "the l><,inters."-Tle sunll circle " marked I> near the pole-star, nhows L trio p(M ion of the north ^.^le <,f the heavens. At one time th.-y are Reen betwe, ., the pole-star and '^^tte zenith" ' "' ^'''"" ''"""^' ''-'' ^'^'"'^ "-"^^ 35. If the directum of north be known, the pole- ftar may easily be found. Looking north, n Hrita m ; w.ll be .3en a little higher than Indf- vay b wee n the honzon iind the zenith.-The height ot" the ,,oh above the horizon is always the same numl.r of dc™ 's etc as the latitude of the place; and as Hrit ah ex-' tends from about bif to GO' N. lat., the North l>ohr Mar Will in that country be from 5(r to GO^ above the ^^'of V."''^^"^: ^*^ '^'' ^'^^''^' ^'*' t'le place. 36. Jhe hrst thing to be d,me, in studyin- the heavens is to know the North Polar Star, whuh n y be readily found out by the methods described, llavinfr xound It, let some convenient fixed staticm be takeiP such that when at that station the polar star appear^ n the same strai^d.t line ^vith the eye and some pmn.i- nent object, as the top of a steeple, or tree, or the cn^rner ot a house. We shall then find, that at aU t nies of the n.ght, and at all times of the year, tlmt star wdl always be m the very same position in relation to our station and the object, and that every other heaverJy body will appear to describe a daily circle rouno it. Ihosc that are near it will describe small circles near it, and, unless by very close observation, will not appear to have moved at all ; while each will describe a greater circle the farther it is from the p(,lar Btar ; and the motion of those at a considerable distauce Pill ELKMENT8 OP A8TUONOMV. Ifi fmni it will bo m ^nout, tlmt wo inny ol.sorvc them to change tiioir [Hmluni in n-lution t.. m.y (ixcl ol.iVct on tho earth (we remaining' still in the same place)" in the course ot five or ten minui.H. 37. The pole-star and constellation fircat Hear boini: known, the next thi.ig to be done m to louk for the ntani ot the constellation Cassiopeia, an.l the very brijrht Htars CapeUa and Vega. These stars never sink below the horizon m liritain, so that they may almost alwava be seen on clear ni-hts; and they are very distinct and pronnnent, so that by their aid the other heavenly bodies can easily be found out. See Fig. 2. Fig. 2, CyynvS * * * CnstUpcia ** *** * • * * fey-. ^ ^ ^ * ^ * ■T- Crea.tSeaf Ca,p«l/n 38. A line drawn from about i\\G middle of the tail of the Great, I?eai throu^rh the pole-star, and cont'nued nearly as tar on the other side of that star, will tcr- mmate in the constellation Cassiopeia, or Lady in her (hair. The prominent stars in this constellation are -»- ni nutxi^/^i, a:i<.i iiiiuiij^ed so as to make u li'nire 16 ■LEMIMTf or ASTROXOHr. ■omowlmt like tho letter W, hut Htra^jjlin^, and with ono liinl) of tho \V Hliortcr than the other. ('iiHMioiM'irt IH ono of tho cotiHtellrttiofiH in tlint hn.ml wlntinh belt extcndinjjf acroHn tho Hky, cilh-d ••The M'lky Way." 3D. A Htrai;y do not twi.ikle as the other stars doj and they chan-e their positions in the sky, always however rem-ining near that circle or belt of the heavens through which the sun and moon run their conrscM. There are five planets y».siblc to the nakenr1inn= +i,„ j^l. . ficent object in creation: '' ~ '"' ^"'^ "'■"^"'- IH ELEMENTS OF ASTRONOMY 3. General Definitions.* 47 A plane superficies, plane surface, or, as It 13 s lorly ('xi,resse(l, a plane, is a surface of such a nature, tliat It a strai^rht hne be drawn between any two points in It, every point in the straiglit line shall touch the surface, wnl?" „^J.''?r'' '" ^;»"V"''" language, is cnlled ajlat surface. A Znl'C ,7.',= '-';"'"'I^ '^'1 table a unn.y, in whatever positi.m it n av be held, furnish exanu.lcs of a plane surface. Its nature will be at once understood Lv cndeaviuring to apply the above defnution to any curved surfi-e, as a sphere: thJ sfra Sit iin^ between two pon.ts will pass below thi curved surface 49. When two plane surfaces, on bein^ pvoduced so as to meet would lorm one plane, the?/ are said to be in trie same plane. h\ Fig. 3, the planes m A D n, K B C L, are in the same plane, as, on being produced, they form one I)lane, m B C n. 50. 'J'wo tables, of the same height above the floor, and n perfectly horizontal, are in the same plane. 51. When two planes, on being produced so as" to mec, wonid cross each other, and then diverge, they are sa^lto be rnclmed to each other, or, to cut each other. In lug. 3, the planes E K L H, A K L D, are in- clined to each other. The two plnnes in Fig. 4 are also inclined to each other. See also Fig. 5, in which a number of planes arc shown inclined to each other. 52. Planes which are Fig. 4. ELEMENTS OF ASTRONOMV. 19 every wliere at tlic same distance, are said to he parallel. In Fig. 5, the planes Bbc C, And U, are parallel ; also the [danes Bba A, C cdD. The opposite walls of a room are parallel, also the floor and ceiling. 53. If two planes cut each other, the line where they meet is a. straight line ; as K L, Fig. 3, E e, Fi"-. 4, or any of the straight lines in Fig. 5. 54. We speak of the plane of any figure, though the interior of it be not filled up, if it be one every point of which would touch a plane surface when laid upon it • as a triangle, a square, a circle, an ellipse. Such a figure is termed a plane figure. Thus, we speak of the plane of the path of a planet, meaning the imaginary plane surface which would touch every point of the planet's course : and we may imagine it to be extended on any side far beyond the actual path of the planet. It is essential for the student of astronomy to understand what is meant by "the i)l;ine of a figure." 55. An Angle is the opening between two straight lines, which meet, but are not in the some strai.o-ht line. In Fig. 6, the opening between the ^ c y; lines A B and C B is an angle, termed the angle B, or the angle ABC: the letter at the point where the lines meet is placed in the middle. 6Q. A Right Angle is the angle formed when one straight line stands upon another in such a manner that the angles on each side are equal to one another. These angles are termed the adjacent angles. In Fig. 7, A B C and A B D are right angles, for they are equal to each other. 20 KVKMENTS OF ASTKONOMV. said to bo perpendicular or ■A- at right angles to the other. I In Fig. 7, A B is prrpon- ' dicular to C 1) :~also D B and C B are, cacli of them, perpendicular to A B. c- 58. A straight line is said to be perpendicular to a plane, when it is perpendioular to every straight lino drawn on that plane which it meets. 59. An Obtuse Angle is one which is greater, or has a AvMor aTr\ rcut/'A";:,;"^'^- ^". .*>. ^'^ ^ ^'^ is an obtt: an^ic. An Acute Angle is one which s ess, or 1ms a narrnwpr opening, than alright angle. In Fig. 6, A B'c\:a™cuto 60. The rnethjd of comparing angles exactly, with resnect to their magiutiule, is described in Par. 75, page 22 ^ . 61. The Inclination of a Straight line to a Plane IS the smallest angle which the line makes with any straight lines drawn on the plane. ^ 62. The IncUnation of a Plane to a Plane is the acute angle contained by two straight lines, one in each plane drawn from any point in the straight line 63. Two lines which are everywhere at the same S:i finer' '^ '' ^''''''' '^ ^^^^ «^^-' - 64. Planes or lines which are parallel to the pl«ne of the horizon, are caHed Horizontal; as the surface cin:ta.^^^^^ '''' - ^-« -^ ^^^^ p-p-?; 65. Any straight line or plane that is perrondicular to the plane of the horizon, is said to be Veriicai L a plumb-line (a cord with a weight at its end freely suspended), or the walls of buildings. ^ 66. When the sun is right over head at any place, :lements of astronomy. 21 l.is rays fuli upon it so as to Lo i)eri)endicular to the plane of its horizon ; that is, vertically. He is then said to be vertical at that place. 67. A Circle has been nheady defined in Par. 8. In Fig. 8, C is the centre, »\nd the curved lino A B D E H O, the circumference of the circle; C A is a radius; C B and C D are also radii. A D is a diameter. 68. It follows from the definition of a circle (8.) that all radii of the same circle are equal in length, 69. The diameter is double the radius, and it divides the circle into two equal parts. Ffp. 8. 70 An Arc of a circle is any portion of the circumference, n Iig. 8, D E, E H, H 0, B E, E 0, « I A B H 0. are arcs Oi the circle 71. A Semicircle is the part cut off by the diameter, or half the area of the circle. In Fig. 8, A B D A and A H D A are semicircles. A Quadrant is the half of a semicircle. In Fig. 8, A B C A and D B C D are quadrants. 72. The terms semicircle and quadrant are sometimes applied to the portions of the circumference which bound them, as well as to the area enclosed. In this case, the semicircle is one-half, the quadrant one-fourth of the circumference. 73. The magnitude of an arc of a circle is described by stating what proportion of the whole circumference It forms. For this purpose, the circumference of a circle, wliatever its magnitude may be, is supposed to be divided into 360 equal parts, called degrees, and marked °. To express still smaller parts, each degree IS divided into 60 c^timl nnrfo n^^^..A .v,,\,,.^.» _^j Bqual part s, called minutes, and i-aia-eu , auu. cuni iiiinuLu la auuuiviaed into bU equal 22 ELEMENTS OP ASTilONOMY. part^, tornied seconds, and marked - Tlins, an arc of thirty - nine de-recs, forty minutes, and thirty -ono seconds, is shortly expressed, 31)'' 40' 31" 74. A semicircle is an arc of 180 degrees; a quadrant an are of !K) deirrecs. 75. An Angle is measured by makin- its sides radii of a circle, the angular point being the centre, and taking the lengtli of the arc on which it stands, in de- grees, minutes, and seconds. The arc on which the angle stands is the portion of the circumference be- tween the extremities of its sides or radii. In Fiff 8 the angles ACE and D C E are measured by the number of degrees in the respective arcs A H E and ^''Vr'V,'''^',' ^^'"^y stand,— the angle A C E by the arc A n E, the angle D C E by the arc D E. We thus speak of an angle, as of so many degrees and minutes in magnitude. The angle BCD, whoso arc H L) IS a quadrant or fourth-part of the circumference, is therefore an angle of 00 di rees. The angle D C E an acute angle must be considerably less, ab ut 60 degrees or 60°— the angle A C E, about 120^ The arc on which an angle stands is said to subtend that angle. 76. An angl^e of 90° is a right angle „, is less than 90° ; an obtuse, angle greater than 90°. 77. The length of tlie radii, or magnitude of the circle, makes no difference in the size of the angle, for the arc on which the irr:-^^' 'T^' ^'"/ ^^^'^>^^ ^'^''^^^'^^ ^"'"^ proportfon to t e vhole circuniference however dificrent ihat circumference may be, or whatever the length of the radius. ^ 78. The sphere has been defined in Par. 9 The a(\joining figure will illustrate the nature of those lines which -re imagined in or on a sphere with the view of defining the relations of the different parts. In Fio- 9, straight lines from E to Q, from P to^, i from Z to N, would be diameters. 79 A Great Circle of a sphere is a circle drawn upon its surface, whos-^ plane passes through the centre ELEMENTS OF ASTRONOMY. 23 of the sphere, "^n Fip^. 9, P f p r, the dotted lino, Z A V N m, E f ' H -V. rf , and tlio outer circle, are g-reat circ! -i.' 80. All grout circles of a si)here are equal to each other; cross each other twice, divide each other into two equal semicircles, and divide the surface of the sphere into two equal parts called Hemispheres. In Fig. 9, each of the great circles P T p, Q « T E, Fig. 9. divide each other into two equal parts or semicircles , the former into T P ^Os and ^ p r^^ the latter into ai Q T and T E ^. 81. A Small Circle of a sphere is a circle drawn upon its surface, whose plane does not cut the centre of the sphere. In Fig. 9, Z 6? T, A a H, N v R, are * This character, j, may be read, Aries— this mark, ^ct, Libra. 24 ):lf,mrnts of astronomy. small circles. Or, a sniiiU circle of u sphere divides its surt'ace into two unequal parts. 82. Distances on a splierc, and the Lreadth or length of figures on its surface, are expressed in degrees of some of the circles drawn on its surface. 83. Wiien a sphere revolves, like a top Fpinning, this is termed rotation on its axis. The Axis ab(.'Ut which it rotates is usually a diameter: and the ex- tremities of the axis are termed Poles of the sphere. 84. The extremities of a diameter at right angles to the plane of a great circle are sometimes termed the Poles of that great circle. In Fig. 9, P, p are the poles of the great circle E T e Q ; Z, N, the poles of the great circle 11 T sO.. 85. The poles of a great circle are each of them 90" distant from that circle. That is, if a great circle be drawn through the poles of any great circle, cutting the latter, the part of the former between each pole and • the second great circle will be 90°, or l-4th of the whole circumference. In Fig. 9, the arcs P a e, P cZ '"i"' , between the great circle E T Q and its pole P, are arcs of 90° each. 86. It is impossible to represent a sphere accurately on a flat surface. In Fig. 9, the outer circle is the only one wliich retains its proper form — the others appear as ovals. But each of these should represent a true circle (8). 4. How to define the Positions of Objects in the Heavens. 87. It is necessary, for astronomical purposes, to be f.ble to define the exact position of the stars in the heavens. This is done by taking certain fixed points or lines, and marking the distance of each star from these points or lines. 88. For this purpose, the surface of the heavens is ELEMENTS OF ASTRONOMY. 25 ro^rrarfled as it appears to us, as a concave sphere and an infinite number of lines, crossing each other' are supposed to be drawn upon it. Thes? lines are di;ided jnto degrees, numbered from certain fix "d points td by observing the position of a star on these 1 'n , ^vh "re two of them cross each other, its situation can bo de Fi* To Th» fi , V '■.''P^o^^'"'"! I'y N and S in «f ?;,: 1^ '" *"■' • ^' '^ *-''™ed the Nortliem Pole the He^t^.If ''.'^ ""°"'^' ^' '^^ Southern Pole Jf I'a^ 26 ^ "^ '"■'""'-'■'•''' "' described in hJ'irJn o'J^'lt 'T' "fs^^t cireles is supposed to teles Tlwl ''''"'■"'*" P"''''"S thresh the two lelcs Ihese are represented in Fig. 10 by N e 8 ;!;",-, -f ™- ^'"'^« "" t"™*^"! Honr-Circles o? S aTs se^ "• ^""^ ^^"^^ "^ "- ™'- "tTi 91. A great circle round the heavens at ennil ^ic anees fton, each pole, is termed The EquUocS It EQin k" if r'^' "J"^ '^ ^^P™-"'^-! I'y 'he line ;, "P-^' "'g"*. because when the sun is on that fine here IS equal day and night all over the world Tw' IS on March 20 and September 23! ' ^^" Ihe LSs eTif""""' Z "'%"'"' ^'>''='' "'^ ?'"»<= of lue eaitn s equator would make round the "th of the oqm- iKK-tial. These circles are terme.l Parallels of De- clination. , , t • i i • * 94 All these circles are RUi)pose(l to he (hvi.led into decrees, mhmtes, and seconds, as ck-serihed ui I ar 16. 95 In any hour-circle there will he arcs of 90 de- rrrces hctween the points where it crosses the equi- noctial and either pole, and these arcs will be crossed hy every parallel on the same side of the equinoctial. Fig. 10. 61. Z ','ft 7:> n Accordhiglv, each parallel is named hy its distance north or south from the equinoctial, measured by the number of degrees along an liour-cuxle winch i i^^ distant from the equinoctial. Thus, from E by Z to IN is 90° of the hour-circle N E S Q. The first pamllel s lown north of E Q crosses N E S Q at 15° from E Q ; that parallel (15 d 15) is therefore 15° north ; its dis- ELEMENTS OF ASTRONOMY. £7 taneo nortli of E Q is tcrnioa its Nor*^ DecHnafinn I' « ,^, r r p, hour-clrcloH. In that CilLo U ' '"""^"'^ ' ' north .Inclination of a; the arc r T t n nL ^l"-^ * -^ '« *'=" K n, the 8outh declinatiol, ofk ' " "''"'' declination of J; t^es^eros.sitinspH;!^lS^^ I)omt of h,o sin^,, Aries: or the Vernal or Sprinff Equi f,-., 1 " ?•• ■'^'^'^''*^ hour-circle crosses the eouino/ t al, and each is named according to the de^^ree Zto St Asc^^^^^^^ '\^'\^^^ ^V'^^ox is termed its xvi^at Ascension. 1 ^s, the honr-c rcle N r S Fio- in crossmg the equinoctial at 45° east from tVn' ^' ™ position, as ever, paralldto^s' ::^;Z^ ^^'^''<^n^,!^al^?rq\^^ Ho. of the from . to a will ll th?dtlin!tTon t" h'o? t^ no'^^' '%''•'' right ascension will be the decrees from r rn ^iT^f ' ^"'^ ^*^'' Q, to e, r being the vernal en uhioVrJ- ^ "^^.^^^^ E^ =^ , and from which the'degrees" c rTkS " CfJI^ ^ tSf'^t' 18 in right ascension 30°, nortl. dr-linatu ^n?* Ik' ^'^''.P?*"* « n.,/.^ ascension 315^ nortli declinationll"; ami so on.^"'"' ^ '° ^ 100. R. A. is the contraption used for rio-bf „o S'on; D. N. declination nnrfb n q "f V^^^^"' south. ' " * ^'" ^' "<^ciuiation 38 KLKMKNTS OF ASTRONOMY. 101. The (listanct'H from the vornal equinox aro Ronu'timc'8 reckoned in hours, each hour consisting of IT) dej,'rees, and beinj,' divided into 60 minutes. In Fi^'. 10, above the line E Q, the degrees aro marked alternately in hours and degrees ; thus, commencing at the equinox, we have first 15", next II hours (30°), then 45°, then IV hours (GO"), 75°, VI hours (90°), etc. To briiii? time to dej^'rees, v/c must multiply by 15. Thus, 10"- 3"'- = 150° 45'. 102. The degrees of right ascension are reckoned eastward from the eciuinox, all the v'ay round from 0° to 300° : that is, in the direction from the head towards the tail of the Great Bear, when that constel- Iniion is hetweeri the pole-star and the horizon, 103. The places of the Bun and planets are expressed in the almanacs by stating their right ascension and decliiuition. 104. Observations of the sun have shown that he appears to move round a great circle of the heavens in a year. This ^-reat circle is called the Ecliptic; as eclipses take placj only when the moon also is upon that line. The ecliptic is represented by the line a o in Fig. 10, and S P in Figs. 11 and 12. The points where it crosses the equinoctial are called the equinoc- tial points or equinoxes ; the first point of Aries, T, where they cross in spring ; the first point of Libra, H, where they cross in autumn. 105. The plane of the ecliptic makes an angle of 23i° with the i)lane of the equinoctial ; so that the far- thest north point of the ecliptic is only 66^°, while the farthest south point is 113^° (90° + 23f ) from the north pole of the heavens. 106. The sun is in tlie north or highest point of the ecliptic on o le 21, and he is then vertical at the tropic of Cancer :— he is in the south or lowest point on December 21, and is then vertical at the tropic of Capricorn. When he crosses the equiuucLlal ELEMENTS OP Ai^TRONOMY. 29 (March 20 and ScptcmbcT 23) bo e«iiuit()r is vertical at tho in Ju !ll.''-i' ••"?["! r' "f.",'" ™'il"i^. 'vhor.. ,1,.. „„„ in a »tN iH in that part of tho h bright star called Capella tho Great Hoar, but nt polo. 8co Fig. 12 cavt'iiH a l-'ttic Kouth of which lit'H to tho west of a greater tlistanco from tiie north heavens must move 15 cle^rees u,,n \n ™ o' T " oJ^^•/^''^^f\Ml^c is divi E 4) P •BU«!S lu.niini)^ ^ p s cl ^^ 4 8 i J3 B O o n .2 I 03 P4 u o u to CO s o ■«-i 3 e o u •c O c« e^i eo '^' c« O Ci C^ CI CI C-l CI CI »- •^ r* "^ 43 ca •flUJpUMSV •auivuooHoa •ilujpuaoBv 1 .3 c« & •3 ^ 113. The signs of the zodiac in which the sun appears when he is north of tlie equinoctial, are callecl the nor- tJicrn sigyis ; those in which he is when south of the equinoctial, southern signs ; those in which he is i)assing in a northerly direction are called ascending ; those in which he is going south, descending. c4 > 4 -a r- KLKMKNT3 Of AiTUONOMY. 111. The terms lori^'itiido nnd lutilii.lo ftro uIbo ployed for tho liouvons— l,iit with r.-lerci.co to i. rr 7>//r ami its poles (85). Tims, tho iatitud, of cidt'stial body va its distance 31 cm- ('( IlDt \c nortli or south from th \tH lont/iUu/e is its distuiico (•u^t of the Imlt- I circle troin tiio north to the sonth p.do of tho ecHptio «^. passui- throu;,'h tht- lirst point of Aries. Tho north pole ot the eoIii)tic is in the constellation Draco, ^U" *rom tho north polo of tho heavens, and in U. A. 27(P Ihe n )rth polo of tho heavens moves so as to describo n circl,. ronnd tho pole of the ecliptic in 2r>,898 vears. J he movement thus made is too sli-ht t<» be apparent in a lifetime; but in time t!ie north pr) is well known. Its seven brightest 3tars are in the body and tail o^the hf Fi; f r'f ' r^ ^^ ^'"' constellation is shown in i^ ig. 1. Its brightest star, one of the pointers marked a in Fig. I, and termed Dubhe, is in K. A lO'^- 54-, or about 163°; and D. N. 62° 32^ The star at the tip of the tail, called Benetnasch, is in R. 1 13h. 4im.^ or ai^Q^^ 205°; I). N. 50° 7' 120 Upon the other side of the Little Bear, but nearer to it, is an irregular cluster, which have been thrown into a male figure called Cepheus, the feet of which are seen in Fig. 1. f , me leer ot 121. The constellation Cassioneia. nr l.^^^r\^ i,pr Chair, and the stars Capella and Vega7have been already B 2 i |H ELEMENTS OF ASTRONOMY. desc; ibod. Capella is in "R. A. 5^- 5'"-, or about 7G° ; D. N. 45° 50'. This is the brif,'litest and most northt'in of the leading: staio in the constelhition Auriga, or tlic Charioteer. The principal stars in this constellation, along with one of Taurus, form an elongated six-sided figure, stretching from north to south, and very well marked. Sec Fig. 12. Capella does not set in Great Ikitain. 122. I'etwcen Capella and Cassiopeia, but further south, is the constellation Perseus. Three of its leading stars form a gentle curve. Tt is shown in Fig. 2, par. 37. The star above the letters vs in Perseus, is Algol, a remarkable star, to be described al'i orwards. 123. A straight line from the pole-star, in the direction nearly opposite to the line cutting Capella, leads to another very bright star, Vega, the principal star in the constellation Lyra. Vega is in li. A. 18''- 31'"-, or about 277° ; and D. N. 38° 38'. This star docs not set north of liondon, just skirting the horizon. 124. East of Vega, in E. A. from 20»i- to 2^'-, and D. N. about 33° to 45°, a^e seen four bright stars, three nearly in a line, and one above the middle of the three : these are the principal stars in the constellation Cygnus, or Swan, which lies in the Milky Way, They are shown in Fig. 2. 125. A straight line from the pole-star, passing near the star in the tip of the tail of the Great Bear, and twice the distance of the tail from the pole-star, cuts Arcturus, a very bright star, of a distinct reddish colour, the principal star in the constellation Bootes, or the Huntsman. Arcturus is in R. A. 14^^- S""-, or about 212°; and D.N. 19° 56'. 126. A straight line south from Cassiopeia, and nearly at right angles to the line joining Cassiopeia and the Swan, will pass near a large square of four stars; the furthest north and brightest of which is is Alpherat, the principal star in the constellation ELEMENTS OF ASTRONOMY. 35 Andromeda; while the other three of the square are part of the constellation Pegasus. The star Alj.iierut i« in K. A. Oi'- O'"- 47«-, about 0°, that is, on the hour- circle crossnig the equinox; D. N. 28° 1(/. It is on the eye of Andromeda, which constellation stretches eastward across the heavens towards I'erseus, from Alpiierat. ' ^ 127. This prominent square, with several other prin- cipal stars near it, are represented in Fig-. 11 The constellations Aquarius, Pisces, and Arios of the zodiac are seen extending along the ecliptic, S P. At the south-east (left) are seen several stars of the great constellation Cetus. In a line with the two most westerly stars of the square, a and /3 of Pegasus, but far south the brig]:^ star Fomalhaut may be seen It IS in II. A. 342° 15' ; D. S. 30° 23^ 128. In ancient times, when names were inven to the signs and constellations, the ecliptic and equinoctial crossed each other about 30° further east than now— that IS, nearly where the sign of Taurus ( » ) is seen on the ecleptic in the figure. Then the 30° east of that point were in the constellation Aries, and these 30 were from their position termed the sign Aries. But now the equinoctial has receded back or west along the ecliptic, and the old names for both signs and constel- lations being retained, they do not correspond. The sign Aries is in the constellation Pisces ; the sign Pisces in the constellation Aquarius, and so on. 129. The brightest star in the constellation Cassio- peia has nearly the same R. A. as Alpherat; or rather between 0^- and P- eastward. Between Arcturus and Vega, but considerably nearer Arcturus, is a half-circle of stars, ten.ied Corona Borealis. TT.^rpli'li"''^ Ti ""'* ""^ ^°T^ ^^'^ *^^ ^'""^^ constellation Hercules. Ihere are four stars forming a sort of diamond or lozenge in Fig, 2, near Veo-a. The thr- o nearest to the pole-star belong to thS constellation 36 ELEMENTS OF ASTRONOMY. Drac(. the stars in wliich form a curve between tlie Great and Little Bears, and between the latter and Hercules. The other is in the foot of Hercules. 6. Zodiacal Constellations. 131. These are twelve in number, and encircle the heavens like a bek. They are named Aries, the Ram ; Taurus, the Bull; Gemini, the Twins; Cancer, the Crab ; Leo, the Lion ; Virgo, the Virj^in ; Libra, the Balance ; Scorpio, the Scorpion ; Sagittarius, the Archer ; Capricomus, the Goat ; Aquarius, tlie Water- man ; Pisces, the Fishes. The constellations of the zodiac do not rise high above nor sink far below the horizon in Great "Britain. 132. The sun, moon, and principal planets, are always found in some of the constellations of the zodiac. J33. The brightest star in Aries is in R. A. 1^- 58"™-, about 29° , D. N. 22° 45'. See Fig. U. 134. Aldebaran, the brightest 3tar in Taurus, is in R. A. 4»i- 27'»-, about 67°; and D. N. 16° 12'. The Pleiades, or seven stars of Taurus, are in R. A. about 54° 30', and D. N. 23° 38'. See Fig. 12. 135. Castor and Pollux, the brightest stars in Gemini, are very near each other; Castor, in R. A. 7h. 25">-, or about 111°; and D. N. 32° 12'; Pollux, in R. A. 7h. 36'"-, or about 114°; and D. N. 28° 22'. See Fig 12. 136. There arc no very prominent stars in the con- stellation Cancer. ■ 137. Kegulus, the principal star in Leo, is on the ecliptic in R. A. 10^>-, about 150°; D. N. 12° 41'. The leading stars in this constellation form a figure like a sickle, of which Regulus is the handle. This great constellation is nearly due south of the Great Bear. 138. Spica, the brightest star in Virgo, is in R. A. 1.3i»- 17"i-, or about 199°; and D. S. (declination south) 10° 23'. It is a very little south of the ecliptic. I ELEMENTS OF ASTRONOMY. 87 13D. The constellations Libra, Scorpio, Sagittarius, are seldom seen in Great Britain. 7. Southern Constellations. 140. The only southern constellations of interest that are frcvpiently visible in Great Britain are, Orion, Canis Minor, and Canis Major : these constellations lie due south of Capella and Gemini, and are very prominent in the heavens during our winter. 141. Orion is a large well-marked figure, a little east of due^south from Capella. It is in the form o." a four-sided i"gure, considerably elongated from north to south. In the middle are three stars, lying in a south- east and north-west direction, usually termed Orion's Belt. Betelgeux, the brightest star in Orion, is in the north-east angle. It is of a distinct reddish colour. It is in R. A. 5h- 47i"-, about 88°; in D. N. 7° 22'. 142. Sirius, in the constellation Canis Major, the Greater Dog, and the brightest of the fixed stars, is south-east from Orion, in R. A. 6^- 38™-, about 100° • and D. S. 16° 31'. ' 143. Procyo^;, a star of the first magnitu.le, in the constellation Canis Minor, or Lesser Dog, is nearly due south from the Twins, and due east of Betelgeux Its R. A. is 71^- 31™-, about 113°; its D. N. 5° 35'. 144. These stars and constellations are represented in the fol lowing figure (12). At the upper part or north is seen the constellation Auriga or Charioteer with the bright star Capella, also shown in Fig. 2. At the east we observe Gemini, Orion below, Taurus at the right' with the clusters, Pleiades in the shoulder, and Hyades in the head. At the south-east is bjen the very bright star Sirius, a of the constellation Canis Major; and north-east of ISirius, Procyon, a of the Lesser Dog, and another prominent star jS near it. At tlie left toe of Castor, the more northern of the Twins, is the first point 38 ELEMENTS or ASTRONOMV. fl-' 12. ^^^-==*^%*f,\j 1 I ^... r^' ) of tlie sign Cancer, where the sun is on June 21, being his greatest distance north from the equinoctial. This is the summer Solstice. l-i5. It will be observed that Sirius, Orion's Belt, the llyades with Aldebaran (a), and Pleiades, are ELEMENTS OP ASTRONOMY. 39 kP ^ nearly in one lino; ami that Orion is nearly duo south of Capc'lhi. 1 ho hinbs at the north-west corner of the fi^Mire are those of Terseus, the leading, stars in whoso body are shown in l\r, 2. Celow Orion is seen the conste ation Lepus or Hare, and at the right the great constellation Eridanus. Between Dec. S. 5G° and G2» ;t.Hl K. A mr and 190°, there is a brilliant constella- tion, well known m southern latitudes as the Southern Cross, once (about 4000 years sincej visible in the south of liritain, now lost to our view by Precession 14G. The Milky Way, another prominent object" in the heavens, lies between Procyon and Sirius, passes north-west between Gemini and Orion, then throucrh Auriga, south-west of Capella ; then passes through several minor constellations and Cassio])eia, and south- west, splitting into two divisions, south of the constel- lation Cygnus or the Swan, not far from Vega. 8. Extent of the Heavens visible at any Place. 147. With respect to the extent of the heavens visible at any place, the celestial sphere may be divided into three portions :--l. That part which never sets at the place {i.e., never sinks below the horizon), and the stai-s in which are always visible on clear ni-hts ^. Ihat part which is only occasionably visible bein^ sometimes above, sometimes below, the horizon of the place. 3. That part which is always b'.dow the horizon ot the place, and therefore can never be seen from thit place. '*■*' 148. The Celestial Meridian of any place on earth means the Hour-circle which passes through the zenith ot the place. Ihe distance from the zenith to the hori zon along that circle will be 90°. 149. At any place, the height of the pole of the heavens above the horizon (called the elemfinn of^in pole) IS always the same number of degrees, minutes" 40 ELEMENTS Or ASTHONOMV. etc., as the latitude of the place. Tliat is, if wo measure tlie number of defz^recs, etc., alou^ the celestial meridian of r place from tlio horizon to the pole, there will be exactly as many as in the latitude of the place. The N. latitude of London is 51° 80', and there the north pole (or north polar star, which is close to the pole) is 5V 30' above the horizon. At Edinburgh, the elevation of the pole is 55" 57', for that city is in N. L. 55° 57'. 150. The distance in degrees, etc., of the zenith of a place from the equinoctial is the same as the elevation of the pole, or latitude of the place. 151. The distance of the zenith from the pole (called the zenith distance of the pole) is equal to the difference between the elevation of the pole and 90° ; at London, 38° 30' ; at Edinburgh, 34° 3'. And this is equal also to the elevation of the equinoctial above the horizon on one side, or its dejtression below the horizon on the other side of the heavens. 152. Thus, at London, the terrestrial latitude, eleva- tion of the pole, and zenith distance of the equinoctial, are each 51° 30'. The zenith distance of the pole, elevation of the equinoctial above the horizon, and its depression below the horizon, are each 38° 30'. 153. That i)art of the heavens between the pole and a parallel of declination the same distance from the pole as its elevation at the place, nevet^ sets. Thus, at London, the stars 51° 30' all round from the north pole can always be seen on a clear night. A parallel 51° 30' from the pole is 38° 30' from the equinoctial, that is, about 38° 1). N. If we look for that parallel on a map of the stars, we ':nall find north of it all the stars wUch may be seen at London. — Or, it may be said, that the stars at a less distrjice from the pole than the degrees in the latitude of the place, or than the north point of the horizon, never set. 154. A like part of the heavens around the opposite ELEMENTS OF ASTRONOMY. 41 p lo never rtses. Thus, at I.ondon, the stars 51" 30' all romul from the south pole are .ever seen or all those beyond 38° 30' D. S. ' ' holt^t J^'^^""'^ ""{ ^^'' '^y ^^"""^'"^ ^J'« intermediate bolt IS sometimes above, sometimes below ^he horizon of the place. That belt extends as many eVees o" t lat line above the horizon. Thus, at London th« «^ars in the belt of sky from 38° 30' D. N to 38° 30' tto; tl^'^'Tf ^^° +)' ^^^' '^^''^'^ ^bove, some, times below the horizon. ' %ife^*-^^"' ""'" ^' understood from the following Fig. 13 the' eirth 1 f." T"" "'■"'"• '"^ ""^ °'''1'"« '•^P'-^^ont t,,L f T / observer on its surface, about the lati- " •' ^'^^'^'-'^n j then Z will be iiis zenith. Let 43 ELEMENTS OP ASTRONOMY. N bo tl)(5 nortli polo of the Ijoavcns, S the south polo, ftiid let K Q rojtruHent iho, [)l!ino of the efpiiuoclial ; the imrt where it erosscH the cartli (e q) will represent the e.'irth'H etpiator. From K to N will be 90^ and from Q to N also [Hf. From S to E and to Q will be the sutne nund)er of depfrees, niakiii'^' IM'Af all round. 158. The dotted Tum! a o will be the sensible hon'zon of the observer at n ; the points a and o being the parts of the sky below whieh ho could not see tho heavens for the earth interposing. Let II K be a plane par- allel to that of the sensible horizon, but passing through the centre of the earth. It is i)lain th.it, if the inner circle representing tlie earth were smaller, the place of the observer, Wj^and also tho line a o, would be propor- tionably nearer to II K; and that if the space in tho figure occupied by the earth wore reduced to a mere ponit, tho lines (or [)lanes) a o and II R would coalesce. Now this is actually the case with respect to tho horizon of any [)lace on the earth and tho starry hcavena. Tho distance from the earth's surfMco to its centre is as nothing^ — a more point — in relation to tho distances of tho stars; and hence, in relation to them there is no practical dilTf'erenco between tho sensib' ' horizon a o, and a plane parallel to it passing through tho earth's centre, which is called the Rational Hori- zon, and represented by the line H U in the figure. We may therefore reason with respect to tho starry heavens and tho positions of the earth in relation to them, as if tho observer at n were at the earth's centre 0, and the distances a H, o R in the sky, and n reduced to nothing. 159. H and R being tho points whore the horizon meets the sky, the distances from Z to H and to R, will bo 90° each. 160. From Z to R being 90°, and from E to N 90°, taking away tho arc Z N, which is a part of each, there will remain the arc N R, the elevation of the pole, CtBIIENTS OP ASTRONOMY. 43 equal to tbo arc Z E, the zenith distanro of the eoui- rjoctijil; w'ich i^ in manifost in the 8ani(3 mi in I. er of de^frces in tho Cflcslinl nioridlan as n e on the terrestrial meridian, tvhich is the. latitude of n. IGl. Since 1[ PC, EN, and N Q are 90' each, by t-^ -111^ EZ from each of tlio first two, and tho eniiul a.c .i W from the last, there remain E H, the elevation of tho equinoctial above tiio horizon, Z N, the zenith distanco of the i)ole, and U Q, tho depression of tho equinoctial below tho horizon, all equal to each other, nnd equal to the diirerence between tho elevation of the pole and 90°. 1G2. Now, in considering tho apparent daily rotation ot tho sphere of tho heavens, so far as relates to the remote fixed stars, we may re<(ard the observer at n as It ho were at 0, and nis hor/'on H R as shutting out from his view all below tho lino H K. Also, tho points N and S, the poles of the heavens, maintaiii the same places. Hence, in rotating, all the stars from N by o, R, Q, and h, to S, will in 12 hours have come to like distances from N and S on the other side of these points along the lino N Z E « II S ; and stars on tho latter line will be on the opposite line from N by Q to Z. 1G3. A star at r (the same distance from N as R) will in 12 hours be at R, just on the horizon ; stars nt K will have been elevated to r; and a]I north of these points will have continued above the horizon lurino- the whole rotation j that is, always to ihe observer at tiie place n. 164. The stars from R by Q to h will in 12 hours come to the position r E II, any star i.t h just appear- ing upon the horizon at H ; and the stars from r to H then sink below the horizon, as from R to h. 165 The stars, from A by S to H, in the'rotation of tbe^ celestial sphere, evidently cannot rise above the horizon at all. They are never seen at tlu latitude of n. 166. It mav easilv be sli ow «x tiJUL the i ._._ CI 11 Q aiUH (O XI, D il '» 44 ELEMENTS OP ASTRONOMY. nro each eqiml to E Z or N R ; and that the nrc Q h is t'ciuul tocftcli of tho arcH K If, Q H, or Z N. 1 67. ThuH, at the latitude of n, the part of t.ie heavens from r by N to H, never HetH; tho part from U to /i, or r to H, iH Hoiiietimes above, HomctimeH below the horizon • the part from H by 8 to A, is never above the horizon.' 1G8. At Londo!!, Vega just skirts the horizon when at tho lowest point of its daily course; and Capella, in the opposte (piarter of the heavens, at its lowest point IS alK)ut 7° above tho horizon; so that these two very bri^rht stars are almost always visible in Great Britain at about from 50° to 45° from the north polar star. ' 109. The motion of the earth round the sun, by which wo undergo a change of place to the extent of no less than 184 millions of miles, makes no sensible diflereneo .i tho relative positions of tho earth and fixed stars. Ihat enormous distance is but a mere point in com- parison with the distance of the stars. At all times of thv) year, the polo of tho heavens is in the same relative position to every place upon earth. 170. It will be observed, that though tho stars in their daily rotations preserve the same relative positions at ench place, they arrive at these positions at dillerent times of the day ; so that stars which are abovo the horizon during night at one season, an; below the horizon during night, and cannot bo seen at another season. This arises from the time of one complete daily rotation of the starry sphere being a little different from the time occupied by the sun in his apparent daily revolution round the earth, which is called a solar day and by which tho periods of night and day, and our divisions of time, are regulated. 171. Upon considering the relations of the various parts of the earth's surface to the starrv 8»)hcre during the apparent daily rotation of the latter,* it will be found that at the poles, only one and the same half of the btarry heavens will be above the horizon during the 24 ElBMENTS or A8TimKOMY. 45 J,onr«-tl)at bcmiNphcro north or 8ou*h of tho oquinoctinl- jUHl thatut the equator, the Hpectntor will Imve a\mve hi8 horizon in tho course of 24 hours tho whole of the sphere or the l.ouvon£-tho poles of the heavens being in his horizon. T he whole of the 8tarH are hroudit muler h.e view witnin the night of 12 hours; one-half at ho beginning of that period, whilo the opposite half will be above his horiz.)n at tho end of that time. There alone man may enjoy, during the ' ht of 12 hours, tho magnificent spectacle of tho whole u tho sphere of the heavens. '^ 46 ELEMENTS OF ASTRONOMY. PAUT II. LEADING PHENOMENA OF THE EARTH, SUN, AND MOON. SECTION I. 1. Definitions. 172. The Poles are the extremities of the earth's axis (83). 173. The Equator is an imaginaiy great circle round the earth, equidistant from the poles. 174. Parallels of Li\titude are small circles round the earth, parallel to the equator. A parallel is called the parallel of any place through which it passes. is the circle which each place describes by the earth's dail_\ station. 175. Meridian" Circles arc sr»;at circles round the earth, pass- ing through both p des. Each cuts the equator and every parallel twice, and divides each of them into two equal semi- Circles. 176. A Meridian is that half of a meridian circle hetween the poles. It is called the meridian of any place through which it passes. A meridian is so called from the Latin word meruhcs, midda) ; because it is midday at a place when the sun is on its meridian. , 177. The sun is said to be on the meridian of a place when he is in the plane of its meridian above the horizon ; that is, at the greatest elevation in the sky, which he reaches at that place at that time in his apparent d?ily motion. 178. The meridian continuous with or opposite to the meri- dian of a place, is called the opposite, or inferior, or lower meri- dian of that place. It is the other half of the meridian circio passing through the place. 179. Those, who live on the same meridian have midday at the same moment, midnight at the same moment, and their time corresponds. ^ . ,. . xi 180. Thus, the earth is divided by imaginary lines ni the same manner as the sky ; but the names applied to them are different. 1 ( 1 ( t f c t t i n I ELEMENTS OF ASTRONOMY. 47 The following table shows the Heavens. Poles. Equinoctial. Pamllels of Declination, llour-circles. Declination. Kight Ascension, lluur-circle through first point of Aries. corresponding terms : — Earth. Poles. Equator. Parallels of Latitude. Meridian-circles. Latitude. Longitude. Meridian of Greenwich. 181. The same fi^^jj, ^jji ggj^g ^^^ illustration. Let Fi? lU, page 26, be now viewed as a representation of the earth JN and b will be the north and south poles; E Q the equator- all the lines from N to S meridians; the curved lines crossing latiUuir'' *"* equator, as a b, k o, are parallels of 182. latitude is the distance of a place rorth or south from tlie equator. It is measured in degrees, minutes, etc., along the meru ban of the place— the line going north and south through the place—and is marked on the parallels at the sides of the map. In I ig. 10, the line c II is the N. latitude of C. 183. Longitude is the distance of a place cast or west of some agreed-on meridian, as that of Greenwich for the 13ritish, of Paris lor tlie brmch, etc. Longitude is measured in degrees, minutes, etc, along the parallel of the place-the line going due east and west from a place. It is marked on the meridians where thev cross the equator, or at the top and bottom of the map Thus m l■' "-"l «'«= d'^y and the night will tl.i'f, n '"■'"' r '" '"' ''''"" '""'"Stood by referring to tiark and dlu.nnied jmrts when tho sun is on the tronio of-0«„eer. Let A N K S represent the earth, Nt'ho he r,Vht 'thf' ' "'T\'"' 4' "" « » --Wian, S a tlie right, the sun, rf A o the part of the e^rth lot pole C „ ,1 ,^'; "^"%T'"' '^° ^»' fr"-" ">« north to, ' It wM ll '"^"^ ^''?'"' ^^° ^«' f™"' "'0 equa- tor. It will be seen from the position of the sun that Flf. IS. tte north pole is turned towards it, and the south pole A I hZr,t n,=^-"^ r'"'' '" "^^olving, will take twelve fil tZdi^TT^r'r ""' '•"'o "f N S to the other, as again and the middle of each twelve hours will be where the point crosses N S. Now, the earth revolvin ' about a line from N to S, it will be at once evident that I . 1 C tv" ow-''.'"'- °"' "^ ""^ ™"'^ "y^- ""<• ftere- i.,ie ..avc vOiistauD any; tliat any point from d e to 54 ELEMENTS OP ASTRONOMY. A E the equator, will bo more than half tho period of rotation without the terminator ; that it will bo a less proportion of its course without the terminator, us it is further south from d e ; that any point in A E will s{)end half its course within, and half without the ter- minator, as that circle cuts A E, the circle in which such a point revolves, exactly in the middle. 209. The point Z, for instance, revolving in 12 hours from / to /j, will have h for its midday or noon, when nearest to the sun ; tho point A', where the circle I h cuts the terminator, for sunrise ; and I for midnight. As the period from sunrise to noon (from k io h) is longer than that from midnight to sunrise {I to k), so likewise the time from noon to sunset is longer than that from sunset to midnight : — and the whole day of that point will be longer than its night. Short Day in the Northern Hemisphere. 210. On the 22d of December, the sun is perpendic- ular to the south tropic (tropic of Capricorn), which is 23° 2W south of the equator, or 1 i3" 28' (23° 28' + 90°) from the north pole. Accordingly, the sun will tlieu be 90° from the arctic circle, and the terminator will be 23° 28' on this side of the north pole. In revolving, therefore, that pole, and all within the arctic circle (the parts around it for a distance of 23° 28' north), will wave continual night, for they will never cross the terminator, but just skirt it in their revolution. The sun will not rise there. The parts further south, from 66° 32' to the equator, will describe more than half their daily circle on the dark side of the terminator, and have longer night than day. And the proportion on the dark side of the terminator will diminish as the place is further south, till, at the equator, an equal portion of the time of rotation will be spent on each side of the terminator, and the dav and the niirht will be cnual. i EI.EMKNTS OF ASTRONOMY. 55 • ?/^r '^1'" *''"''''' "^ Capricorn, latitude 2.'^ 28' south IS the urthcHt Houth parallel at which the sun }>econ es ver ncal. At places farther south, he never reaches to /enith — never appears perpendicuUir — and appears lower as the ph-iee is farther south. ^^ 212. This vyill be better understood by reference to tlie ad,<„nn,g hgure ; which illustrates tlu) relation of Fig. 16. the dark and illun.ined parts when the sun is on the ropic of Capricorn. The same letters indicate t le arts as in the former figure (page 53), excepting those utthe terminator, w])ich is now from e to n., complete y enveloping in the shade the north pole and the loZZ around i for 23° 28' south. Within the arctic circle lere will be continual night. From that paral to the equator A E, any point, in its daily rotation, will pass from midday to the terminator before it has gone through half ot Its circle, and will therefore have onger night than day. It will be enveloped in the dLk ImTf sooner after noon, and have longer night, in ^rinor io as It IS nearer to the pole. And as the tWmfnaTor I" stili cuts the equator in two equal parts, there w^Il be point /'r "^' r^'"' f ^ /^" ^^'"''^- ^^1-MhV ame -ii-i.n„ior, 1,. a^uTv uuiii six nours, and to be less than £6 ELEMENTS OP A8TR0N0MV II Hix lioura in revolvinjj from k to A, its middny. From midday to Runso twill also bo less thuii nix hours ; and its whole ni'^'ht must be greater than its day. 213. Thus, the noithern homiH[)here, with respect to the «lurk part of the earth's surface, is placed on Decem- ber 22 (in Fi^. !(>) in exactly the same position for- merly illustratotl with respect to the illumined part. State of the Southern Hemisphere. 214. As already mentioned, the two hemispheres aro always in exactly opposite conditions in regard to day and ui;j:ht, except at the time of the cipiinoxes. This is at once seen by inspection of Fi^nires 15 and 1(5. When the sun is on the north tropic (Fig. !'>), and Iho north polo is entirely in the illiiinined part, the south pole is entirely in the shade. When the snn is on tho south tropic (Fig. Ifi), the north pole is out of the reach of his rays, and tho south pole is never out of them, etc. At tlie e(|uinoxes, when the sun is vertical at the equator, and tho terminator passes through both poles, each hemisphere is situated in tho same position with respect to the sun's rays, and they are therefore in similar conditions as to day and U'ght. Equal Day and Night over all the Earth. 215. At the c(pilnoxes, tho sun is vertical at tho equator, or appears in the zenith there, ayid the termi- nator^ always 90° distant from the parallel at which the sun is vertical, passes through both poles ; and its plane passes thiough the earth's axis. Then, there is equal day and night over all the earth ; for the terminator will cut every parallel equally, and every part will spend half of its rotation without and half within the terminator. 216. This is illustrated by the following figure, whicli exhibits tho state of the world with respect to dav and I , I , 1 ILEMENT8 OP ASTRONOMY. 67 night when tho mn is or. tlic cquntor. The biiu la soct, |.crpc.,Khcuhtr to the earth ut the equator, the e „ nnt wlucli the sun 18 vertical. * FIf. 17. ^K- 9 c1..k iJtlf N r"s^ '' '\ '- '"^^'"^ '^^'-^^ '-^ P«'"t in the noon h, vvill cross tho terminator at /L- exactly half way 8.imc w 1 take place m passm^^ from h back to I; and ti.e ni^ht and day must therefore bo equal on every part ot the earth's surface. ^ ^ 218. At the poles at this period the sun will appear p move round the horizon ; and, as he thus nei her rises nor sets, there will be continual day there 1 or ltV:7 ""'W' ''^^-'- -fraction and ^^.flection 'nZ long he day, there will be continual day there even though he be actually a little below the horizon. ' Of the Change in the Length of the Day. iJl^\ ^- "^ '^'''"^' ""^ *^^' ^^""Sth of the day occurs in he following manner :-When it is said that the sun invl%f"\ '■ '' '"^ r^'^^"^^' ^' i« meant t at he 290 wT ''.1^ ^''*^'-"^ '" ^*' '' ''' ^^^"^ ^^''tical to it. -_-, 1.. ... a. tliu laitbctii north paiuilei which he reaches c 2 li 53 ELEMKNT8 OF ASTRONOMY. (Fig. 16), and from that trav.'ln south from n to E ar.y this, tjjo termi'intor Hh)wly wht'cls round from do (Fiij. 15) to N 8 (Fig. 17), atid then onwards in the same direction till it reaches e m (Fig. IG). This brings more and more of the northern hemisphere into the hhadc, so tlint each piirt in revolving is more of 'ts time on the dark side of the terminator, and its day be- C\*mes sliorter till the terminator comes to e m. Thero the sun ceaees its motion south, and begins to retrace his steps from p by E to n, which causes the ternjinator also to retrace its course, and move back from c m by N S to s towards the sun. As the earth proceeds onwar it gradually gets into the position which it occupied at first. 237. This will be better illustrated by the following figure. Let the twelve circles represent the earth in A Fijj. 18. tTT,l»lxrp rl 'flV.r.rt'J-'f ■•-.T.io. r^f^i^ -«,,,.'--^ V-" ' Jl- T et 62 ELKMENTS OF ASTRONOMY. I the lino n s represent the axis of the eartli or a meridian lino, n beinn; the north pole, s tht sontii polo. The strai^'ht edge of the shaded part will represent the termi- nator, or the plane of the -minator, seen always perpen- dicuJar to the sun's rays, hut varying its position with respeet to the axisns, which points in all the positions in tue same direction. At tlie top is seen the position on Decemher 22, the north pole within the dark half, and turned from the sun, the south polo in the illumined halt, and leaning towards the sun. At the left and right, the positions on March 20 and September 23 arc represented, the terminator passing through the north and south poles, coinciding with a meridian line, and the axis lying sideways towards the sun, so that each pole IS equally under the sun's influence. At the bot- tom IS seen the position on June 21, the north pole in the sun s rays ; the south pole in the shade.* 238. The following figure will also illustrate the state of the dhlcrcnt parts of the earth at difRrent seasons in regard to light and shade. The terminator is distinctly seen, the gently curved line between the dark and light parts. The north pole is shown at the upper part m each of the four positions, with all tlie meridian lines radiating fro.n it. At the top it is seen entirely enveloped in darkness, and so tliat the earth's rotation about its axis does not bring it all out of the shade. At the sides the terminator is seen passing through both poles, the axis lyinj? sideways towards the sun. At the bottonf. the north pole and regions around it are seen entirely in the illumined part, havin- continual day. J he upper position represents December 22! the lower June 21, the solstices; ~ih^ two sides, March 20 and fceptember 2;], the equinoxes. ' 239. Tho date at each position in Fig. 18 shows the period when the earth gets into each position ; and the accompanying character is the astronomical mark for nvi«1r?H I ? . • ^'l^^ °^M^'' prece.hns fi.^'ure, nrnl of tlio inclination of the HMs to the te nnin.i or, will convey a precise idea of tlie various cl.an-es J I.e h^n.re .s irregular as a dra>viug, being a mixture of plan, sc^H, , an'i persp<.ct.ve but gives a c ear view of the cflTect of the ear h's notion romd tiie suii, on the relation ot the terminator to the diffcreul henu"iheres ELKMKNTS OF AHTKONOMY. 63 tlie sign, OT part of tlie zodiac in which the sun appears at the time of tl)c earth entering into each position. Of course, the earth, as seen from tlie sun, wouhl appear iu the opposite sign. Fig. 13. ^^ 240. Thus, the effect of the earth's motion round the sun is to make the latter appear to oscillate backwards and forwards between the highest and lowest positions, shown in Figs. 15 and 16— that is, from being perpen- dicular to the tropic of Capricorn, c p, 23° 28' south ot the equator, on December 22,— to being perpendicular to the tropic of Cancer Cn, 23° 28' north of the equator, 1 64 ELEMENTS OF A3TnONOMY. i on June 21, crossing the oqnator twice during these osculations, at March 20 and September 23.* 241. The sun is about 7 days, 16 hours longer in the northern than in the southern half of the ecliptic ; being about 187 days in the northern signs, 179 davs among the southern signs. *' 242. The following table shows the length of the longest days in different latitudes, from the equator to the poles : — 0° 0' (E( 16 44 30 48 41 24 49 2 54 31 58 27 61 19 63 23 64 50 Hours. Hours . 12 65" 48' . 22 . 13 66 21 . 23 . 1A 66 32 . 24 . 15 Months . 16 67 23 1 . 17 69 51 . 2 . 18 73 40 . 3 . 19 78 11 . 4 . 20 84 5 . 5 . 21 90 (Pole) . 6 2. Climate. 243. The Climate of a place signifies the prevailing character of the weather at that place ; that is, the temperature, moisture, atmospheric pressijre, winds, electric condition of the air, etc. These, as is well known, are very different at different places. 244. The leading circumstances which determine the character of the climate are,— 1. The latitude of the place ; that is, its distance from the equator : 2. The height of the place above the level of the sea : 3. Its position with respect to large tracts of land and water : 4. Oceanic currents: 5. The character of the prevailing winds.— -Only the first of these can be regarded as aa astronomical cause ; and it alone requires consideration in this work. \ From o to o, Fig. 10, page 2G ; and then back from o to i ELEMENTS OF ASTRONOMY. 65 245. The climate is wvrmost about the equator, and becomes gradually colder as tlic place is fartlier north or south from the equator, that is, as the latitude increases. 246. This rule is only true generally^ and of largo changes in latitude. Considerable deviations from it are produced by the other causes. 247. The position of the different latitudes, in respect to the sun's rays, is the cause of these differences in climate. 248. The heat at any place is in proportion to the number of the sun's rays which fall upon it ; and the number of rays which it receives (other things being equal) depends upon the direction in which they fall. Any surface receives more rays tb*^ more perpendicu- larly they strike upon it, and less, in proportion as the rays fall more obliquely ; that is, as the angle they form with it is further from a right angle. 249. This may be illustrated by the following figure. Let R and R^ be rays proceeding in the direction from S towards T, and falling upon the equal surfaces A B, A C, A D, A E, A F, etc., all lying in different direc- tions. It is plain that more rays fall upon tlie surface A B, which is perpendicular to the direction of the rays, than on any other; that A C, which is nearest to the perpendicular, receives more than A D, A D more tiian A E, and so on ; more rays being received in GG ELEMENTS OF ASTHONOMY. })roportion as the surfuce is nearer to being pcrpeu- tlicular to ll'.e mys. 250. As the Klin osoillatos between the tropics, con- tinually vei tieal to some parallel in the torrid zone, liis rays always fall [jerpendicularly at some parallel between the tropics, and less so as the parallel is further north of the north tropic, or south of the south tropic. Accordingly, more rays are received in a given space at the torrid 2one, than in an equal space north or south ; so that the temperature is always higher there than anywhere else. And as fewer rays are received in proportion as the place is further to the north or south, the heat must diminish in these directions. 251. This is illustrated by the following figure. Let S represent the sun, E the earth's equator, c, d the Fig. 21. tropics, «, h the polar circles, N the n.irth pole. It is seen that the earth's surface at the equator is perpen- dicular to the sun's rays, the zone between the tropics more nearly perpendicular to the sun's rays than any parts north or south, while all the other parts are much inclined ; that they are more inclined as they are furAer from the equator, the rays towards the poles only skirting the ground. 252. The air absorbs part of the sun's rays, — little in the upper strata, but a considerable portion in the dense lower strata loaded with vapour. Hence, from this ELEMENTS OF ASTRONOMV 67 cause also, loss of the sun's rays strike upon a place in proportion to the quantity of atniosphero t]irou«,^h which they pass, and in proportion to the density of that atmosphere. Perpondicular rays pass throu^di least of the air before coming to ihe ground. Oblique rays not only pass throng i more air, but tiirough a larger pro- portion of the dense parts, so that a much greater por- tion is absorbed before tlu>y strike the soil. 253 Th(^ diminution of the mean temperature in passing from the equator to the poles, so far as this is regulated by the solar influcii ;, la in proportion to the square of the cosine of the latitude. The change is, therefore, slight from the equator towards either tropic, greatest about lat. 46", and slight from the polar circles to the poles. 3. The Seasons. 254. Tliat regular alternation of different kinds of weather which takes place at any place during the year is termed change in season. 255. The same causes which give rise to the change in the length of the day and to diflerences in climate, produce the change in the seasons. The sun imparts more heat in proportion ; 1. as he is higher above the horizon of a place, and his rays fall more perpendicu- larly ; 2. as he is longer in the day above the horizon of a place. In the northern hemisphere, the sun rises higher and ^ remains longer above the liorizon, from IVIarch to September : we have warm weather, or summer, then. From September to March the sun's rays fall in a more slanting direction, and he is a shorter time daily above the horizon : there is cold weather,^ or winter, then, in the northern hemisphere. 256. The southern hemisphere is in exactly the reverse state then — summer during our winter, winter during our summer. 257. This is illustrated by Figs. 15 and 16. In I ig. 15 the sun's rays fall more perpendicularly on the 68 ELEMENTS OF AbTKONOMY. northern humiaplifirp, and sljintingly on tlio Routbern hcmiRphero. In Fi^. IG the reverse is seen. In Fig. 17 and Fifjf. 21, the relative position of the snn and earth at the eqninoxt'S is shown — the snn vertical at the eqnator, the rays more and more slanting as the place is further north or south. 258. It is evident that if the axis of the earth wero perpendicular to the plane of its orbit, each parallel would always be turned in the same degree towards the sun, and we would therefore have no chamje in its seasons. It is the inclination of the axis that causes the same parallel to lie differently towards the sun in different parts of the orbit. Hence, in a phinet such as Jupiter or the moon, where the axis is perpendicular to the plane of the orbit, there can be no change in seasons; while in Venus, where the axis is very much inclined, the change is very great, — so great that a marked difference prevails between the state of the equatorial regions at the equinoxes and solstices. From this, the equatorial regions have two winters at the solstices, and two summers at the equinoxes. The same prevails on the earth in a slight degree — but it is very marked at Venus, from her tropics being so far from ner equator. 259. The sun being nearer to the earth in our winter than in our summer, it might be supposed that the weather should be warmer over all the world then. But thi3 makes no di*^.rence ; for, as much heat is lost by our more rapid motion in winter as is gained by our greater proximity to the sun then ; and in summer, while there is less heat from our greater distance, this is compensated for by our slower motion. 260. The warmest part of the season is not when the sun is highest and longest above the horizon; nor the coldest, when the sua is h)west and the day shortest — but some weeks after these periods. The reasons of this are, that the heat must increase, so long as the earth receives more heat during the day than it parts with during the niglit ; and this is tlie case for a considerable time after the longest day : and that the tempera- FLEMENTS OP ASTRONOMY. 69 turc muHt (h'creaac, m long an mor ^ heat is lost during tlio niglit tlian iH gained during tlio day; which goes on for nevcral weeks after the shortest day. 2G1. In like manner, the warmest part of the day is not at noon, when the sun in highest, and his rays fall most perpen- dicularly, but some little time after, about* 2 p.m. The reason is, that till that period the heat received is greater than what is lost,* so that the temperature must rise till that time, although less new heat is received then than at not'n\n two wiccessivo floods \h 12 hours 19 nimutcs V ind ut full moon ; 12 ho\iTn 30 minutes «.t the qnurtt 270. Thtif 'uring every 24 hours and 50 minutes there is I ] .iter tvv.ce and low water twice nt every olaee, and tlie flood ia al)u..i threi-(iuurt(!rH of an hour atcr every day Iler.ce, therefore, as tlie earth turns halt round m that time, 12 hours, there muKt be hiirh water at the opponite parts of the earUi's surface at the same time— that is, at the two pl-iees having the same m.iruiia!. circle (or on the opposite meridians, reckoned hy tlieir nii.nbers). 277. (2.) The height of high water, as well as that ot low water, varies* very considerably, but regularly But, when the tide risos highest, it falls lowest, ami when It rises least, falls least. At Plymouth, there is sometimes a difference of 21 feet between high and low water; sometimes only 12 feet. 278. The highest or sprmg^iide occurs once every fortnight, and is usually about the third or fourth high tide after new moon, and the third after full moon —about a day and a half to two days and a half after these periods. 279. The lowest tide,* or neap-tide, also occurs once every fortnight, being the third or fourth high ti(1e after the moon is in her quarters-from about a day and a hall to two days and a half after these periods. 280. The tides gradually decrease from about new moon to the first quarter, increase from tlie first quarter to lull moon, decrease from full moon to the third (,uar- ter, and again increase from the third quarter to new moon. • ?^^*i ^?''. "^^^^^^ ^^ ^^^*' ^ monthly period of change m tlie height of the tides: the highest spring-tide is that which occurs when the moon is \n perigee (nearest * Thftt is, when tUo water falls least and rises Ic ast. 'iki- U 74 ELF.MENTS OF ASTIIONOMY. to the earth) ; and the next spnn-.tidc ih the smnnest, occurrin- when the moon is in apogee (iarthest from the eartli). Tlie force of the moon's attraction l)em.£f the main cause of the tides, it is to be expected that they will vary somewhat as her dintance vanes. 28'> 4 ) The height of the tides is also aftected l)> the foilowin- causes: the san's distance ;* the ele- vation of the sun and moon; the latitude of the place; the local circumstances, such as banks in the ocean, and the form and elevati(m of the shores, channels, cur- rents of rivers, winds, etc. High Water at the Part nearest to the Moon. 283. The chief cause of the phenoruena of the tides is the /ore. of the moon's attraction. The waters under the moon (/. e, at the place where the moon is on the meridian) are attracted towards her, while the waters at the side^, where the moon appears in the horizon, are also drawn towards that part, forming high water there. As, by the earth's rotatiim and moon s motion, the moon comes on the meridian of each place once in 24 hours 50 minutes, there N.ill be high water every- where once in every period of 24 hours 50 minutes 284. The period of high water will not be exactly when the moon is on the meridian and her action strongest ; for, the impetus the waters ^^^^ received, and the continuance of the moon's action (still strong, thouo-h decreasing), cause them to continue rising lor some°time after. ^The period of high water, therefore, is usually (local causes being disregardedj Irom two to fiiree hours after the moon is on the meridian. At new moon, the sun and moon cross the meridian together, at noon. At fall moon she crosses the meridian at !lSt Idea abolu the cciuator -the least within the polar circles. \ ELEMENTS OP ASTRONOMY. 75 niillest, ^t from ed tliiit cteil by he ek- i place ; I ocean, els, cur- Moon. he tides rs under 5 on the e waters horizon, jh water J mc>tion, ; once in sr every- Qutes } exactly 3r action received, 11 strong, rising lor therefore, )m two to , At new together, eridian at 1 liemisphere, lighest in the s. \ midnight — when in her quarters, at G o'clock, a.m. or P.M. ' Low Water where the Moon is in the Horizon. 2S5. As the moon tends to draw the waters in straight hnes towards her, she will evidently draw off the sur- lace, or depress the waters on which she acts sideways; i.e., those parts at which she appears in the horizon, 90° on each side from the meridian she is on ; this will cause low vmter at these two places once every 12 hours 25 minutes. High Water at the Part farthest from the Moon. 286. As the moon attracts the earth, as well af the loose waters on its surface, she will tend to draw the earth from the waters which are on the side of the earth most distant from the moon. As she attracts the earth more forcibly, being nearer, thj^n those distant waters, she will dra?,' the earth further towards her than those waters. This will cause the earth to recede from under these waters, which causes them to rise relatively to the land at those parts, and thus there is high water there also. As the moon come.s into this position every 24 hours 50 minutes, there will be high 'vater at the part farthest from the moon once in every period of 24 hours 50 minutes. 287. This accounts for the two tides daily; each part, by the earth's daily rotation, being brought once near to and once remote from the moon during each 24 hours 50 minutes. 288. The following diagram will illustrate the action of the moon upon the waters. \li 76 ELEMENTS OP ASTRONOMY, Fig. 22. Let A B C D E F represent the earth, M the moon, C the pomt nearest to the moon, F the meridian far- thest from the moon, A and E the points at which the moon appears in the horizon, 90° east and west from C and F ; then there will be high water at C and F ; low water at A and E. 289. The moon's attractive force at C evidently tends to raise the waters towards c, and to draw them from A to B, E to D, and from B and D towards c ; as shown by the arrows in Fig. 22. Also, as the moon's force draws the earth from F with more force than it draws the waters at F, the earth must recede from these loose waters and cause them to be proportionally elevated. Hence, there is high water at C, where the moon is on the meridian, and also at the opposite meri- dian F. 290. But the moon's action evidently draws the waters from. A and E, and tends to make thorn low at these points : while these waters tend also to rush towards F, where, from the earth's recession, the waters are lighter. These two causes depress the waters at A and E, and there is therefore low water there. 291. The action will be readily understood, if we reflect du the simple law of the diminution of the force of attraction as the distance increases; and boar in mind that the earth is less \, ELEMENTS OF ASTRONOMY. 77 attracted by the moon tlmn the waters near hor, but more ♦^an tlio waters more remote. Sun's Action upon the Tides. 292. The sun also by his action influences the waters of the ocean, and is the main cause of those regular changes in the height of the tides which are everywhere observed. 293. His action raises the tides higher than usual when It unites with that of the moon,— renders them lower when his action is opposed to that of the moon At new moon and full moon, the action of the sun and moon coincide. At the quarters, they are opposed in their action. Therefore there are spring-tides at new and full moon, neap-tides at the quarters. _ 294. This will be readily understood from the follow- ing figures. Fig. 23. If S represent the sun, m the moon, and /A c E the earth, then, as the sun and moon act in the same man- ner a^ -: the same direction, it is evident that ti^• ettect upou the waters will be increased, or there Wiil be aspnng.tide at c and/ and very low water at A and /' ..^^^ ^'^^ ""^^ ""^^^ *^"^ *^ ^^^s« c and/ to depre:- V^;l^oA ?i"* '^*^^ '^''''^ ^"^ ^" ^"^ of ^er quarters, as in i? ig. ^4, then they act in opposition to each other. The sun tends to draw the waters towards n from A ,ind E • and thus prevents the tide at A and E from being so 5 .J 78 ELEMENTS OF ASTRONOMY. i ii hi^h, and that at c from bcini^ so low, — or forms neap- tides. The moon tends to raise A and E, to depress c and/— the sun exactly the reverse. 296. The ratio of the sun's action on the tides to that of the moon is as 38 to 100, while the ratio of spring-tides to neap-tides is as 138 to 62. 297. 'Y\\Q Baltic Sea has no perceptible videri ; and that in the Mediterranean Sea is very slight. These seas have no tides in themselves, because, being of comparatively small extent, the moon's action is equal at every part , and they do not receive the influence of the Atlantic tide, because their entrances art- narrow, and do not lie in the direction of the curreni produced by that great tidal wave. SECTION IV. Dh ions of Time. 298. The leading divisions of time are, the Day, \ tLEMKNTS OF ASTUONOMY, 79 the Month, and the Year.* Tlio civil standiinl, In tho reckoning of time, is the Mean Solar Day of twenty- four hours ; that is, the mean or average time which the earth takes in revolvin , from the moment when tho sun is on the meridian of a place till he returns to that meridian again. The most perfect measure of time is the sidereal day, or the time which the earth takes in revolving from the moment when any star is on the meridian of a place till it returns to the same meridian. 1. The Day. 299. There are four different kinds of days. 1. The sidereal day. 2. The solar day. 3. The mean solar day, 4. The lunar day. 1. Sidereal Day. 300. The sidereal day is the true time of one com- plete rotation of the earth on its axis, — and its length is 23 hours, 56 minutes, 4*09 seconds. It is called " Kidercal " from sidus, a star, because it is determined by the interval between the two successive appulses ot any star to the same meridian. 301. The true time of the earth's rotation on its axis is judged of from the return of a star to the meri- dian, because the distance from the earth to the fixed stars is so great, that its position in the most distant parts of its orbit may he considered always the same with respect to any fixed star. Hence, in reference to the fixed stars, the earth may be looked on as not moving round the sun at all, but ever remaining in the same spot, rotating at a uniform rate upon its axis, and therefore ever returning to any star in the same time. 2. Solar Day. 302. The soltir day is the time from the sun's being on the meridian of a place till he returns to that meri- 80 ELEMENTS OF ASTRONOMY. i it I dian, — in other words, the intcrvul "between two suc- cessive apijulses of the sun to the s.aine meridian. 303. The solar day is lon^ifei than tlie sidereal day, and its duration is different at different periods of the year. 304. The solar day is longer than the sidereal day, because, while the earth's motion onwards in its orbit makes no sensible change in its position in relation to the fixed starsj it makes a material difference in its position in relation to the sun. This affects the solar day in the following manner : After the earth has made one com- plete turn on its axis, and brought any meridian on which the sua and any star were at the commencement of that rotation to the same star, that meridian loill not have reached the sun at the close of the rotation ; for, the earth has during that period moved onward in its orbit and, having in a manner moved past the sun, must turn further round than the complete rotation to bring that meridian to the sun again. Fig. 25. 1 2 3 305. This may be illustrated by the above figure. I ELEMENTS OP ASTRONOMY. 81 Let S represent the sun, E A F, a section of the earth through the equator, A the meridian on which the sun is at any given time. If the earth revolve on its axis in the direction F A E, as indicated by the arrows, and move in its orbit from 1 to 2 in the time in which it turns on its axis, it will have moved to 2 when the point A or A' has returned to the same star; but as it has moved so as to place the sun in a manner behind its new position, it will not have brought that point to the sun, but require to move round to a before that meridian comes again to tho sun. Hence, the solar day is longer than the sidereal day by the time the point A' takes in revolving from A' to a. 306. The length of the solar day is different at different periods of the year from two causes : — 1. The inequality in the rate of the earth's motion round the sun ; — 2. The inclination of the earth's u is to tho plane of its orbit. 307. As the earth does not alv.dys move at the same rate round the sun, it will, at different times, have moved different distances during one rotation, and therefore the excess over the complete rotation neces- sary to bring a point back to the sun will be more at certain times than at others. 308. Thus, if the earth, instead of moving from 1 to 2 (Fig. 25), during one rotation, had moved from 1 to 3, the point A, or A", at the end of the rotation, would be still further from the sun, and have to move further besides the complete rotation to bring A to have the sun on its meridian — namely to a\ 309. Perhaps the best illustration of the difference between the solar and sidereal days is afforded by the motion of the hands of a watch or clock. If both hands be at twelve o'clock, and set out together from that point, the long or minute hand, when it has made a complete revolution, will have returned again to 12 o'clock, but will not have reached the hour hand, because it also has been moving, though more slowly, in the same direction; and the long hand will have to go more ihau the complete circle before it overtakes the short hand. Now, the long hand resembles any terrestrial meridian, the short hand — c\ 82 ELEMENTS OF A8TKUN0MY. the «un, and the dial-plato and figures the «ta>-ry Rpl.cro tt d Btars If the hour haud he HuppoHid to move at different DiteJi in different parts of its circuit, the rninuto hand must take different periods to come up to it. 310. The inclination of the earth's axis to the plane of its orhit affects the Icn^Hh of the day by causing the earth to move in a plane inclined to that of its equa- tor ; that is, inclined to the direction of the earth 8 rotatory motion, which is parallel to its eopiator. ^ ^ 311 This will he best explained by the supposition that (as it reallv appears) the sun moves round the earth in the ecliptic, while the earth turns daily on its axis- and that while the real sun moves in the ecliptic, another, which marks uniform time, moves in the equi- noctial. With these suppositions, and the aid ot tlie following figure, the inequality caused by the sun being Fig. 26. in the ecliptic may be comprehended. Let the figure \. KI.KMENTS OF ASTRONOMY. 83 represent the sphere of the heavens,* Ten the ('(liiinoctial, and T ^ JQ. the ecliptic. Let the real sun be supposed to move from T hy o' &' c' lY ef S\, g h I m, roturnin<]f to T in th<' year, wliile the other, startin** nt the same time from T, moves along the equinoctial by a 6 c O .V w '!^ A 1.0 I.I us m m £ 1^ 1^ 12.2 20 1.8 1-25 1.4 1.6 ^ . 6" ► ^^ <^ /a /: >^ Photographic Sciences Corporation 33 WEST MAtN STREET WEBSTER, N.V. 14S80 (716) 872-4503 <. f •X 86 ELKMENTS OP ASTRONOMY. sun, — frona about the time of the solstices, the clock is before the sun. The days vary so much, that sometimes apparent noon is 16^"'- before mean noon, — sometimes 14j^™- after mean noon. 322. Althoup;h the sidoroal day never varies, it cannot be adopted as the standard of time for ordinary occasions of life; because it would not conform with those natural divisions into day and night (periods of sunshine and periods of darkness) from which, for the sike of convenience, our arrangement of time cannot depart far. As the stars always come to the meri- dian at tlie same successive intervals, and the sun does not, — if the hours were regulated by the sidereal day, the same hour would now be at sunrise, now at noon, now at sunset, continually changing its relation to tl.o occurrence of those changes of the day and night, by which it Is most convenient to divide our time. 4. Lunar Day. 323. The lunar flay is the interval between two suc- cessive appulses of the moon to the same meridian. This is different from the true day, as the moon has a motion throug'h the heavens, so that the earth has to make more than a compl(;te rotation before she brings any meridian again round to the moon. As the moon moves daily about 13° through the sky, to overtake which the earth requires about 50 minutes, this time must be added to the common day to constitute a lunar day ; which is theaefore 24'i' 50"'- in duration. 2. The Month. 324. The month is of three kinds, — the sidereal^ or periodical months of 27 days, 7 hours, 43 minutes ; the si/nodical, or lunar month, of 29 days, 12 hours, 44 minutes, being the interval from one new moon to the next (335) ; and the calendar, or common month, January, February, March, etc., 31 or 30 days, except- ing February, which is 28 or 29 days. In each year there are 12 common or calendar months; a little less 1 \ ELBMENTS OF ASTRONOMY. 87 i than 12J synodical raonlbs; and a little less than ISA sidereal months. 3. Tho Year. 325. The year is of five kinds, — 1. The equinoctial, or tropical year;— 2. The sidereal year;— 3. The anomalistic year;— 4. The common year, of 365 days ;— 5. The leap year, of 3G6 days. 1. The Tropical Year. 326. The period of time adopted for the astronomical year is ;he interval between two returns of the sun to the same equinox; called, therefore, the equinoctial year. Us duration is 365 days, 5 hours, 48 minutes, and 49"7 seconds. 327. The calendar or common year contains 365 days. The odd hours, S''- 48'n- 49-7''-, would soon accumulate to a serious amount of error : and, by a chfinge of about a day in four years, would gradually throw the seasons forward, so as to arrive later each year, till they would no longer occur at the same months as at present; and this change would be continually going on, the fixed relation between the months and the seasons being destroyed. To prevent this inconvenience, the odd hours are disposed of as follows : They amount to nearly a quarter of a day, and are allowed to accumu- late till every fourth year^ when they amount to a day, and are got rid of by making that year one day longer, or 366 days. That additional day is added in February, which has then 29 days : and that year is called leap year, or bissextile. This and other important improve- ments were introduced by Julius Caesar, according to the plans of the astronomer Sosigenes. 328. But the excess of the tropical year over 365 days is not quite a quarter of a day, being 1 1 minutes !0 seconds less; hence one day every four years is too much to add, and causes an excess of one day in about 88 ELEMENTS Ok' A8TU0N0MY. m. i 135 years. This iii compensated for, within a very trifling quiintity, bi/ making every hundredth year a common year, except the fourth, which is to be a leap year. Thus in every four hundred years (3 limes 135 = 405), three years, which wo\..d otherwise be leap years, have only 365 days, which takes off the excess of the day added in each leap year over four times 5h. 48m. 49-78. The remaining error amounts only to one day of excess in 3866 years. The principle of arrangement may be thus shortly stated. Every common year which leaves no remainder when divided by 4 (as the year 1872), and every hun- dredth year (years ending in 00), which leaves no remainder when divided by 400 (as the year 2000), are leap years, having 366 days. All the others are years of 365 days. Thus, 1600, 2000, 2400, ure leap years; but 1700, 1800, 1900, 2100, 2200, 2300 are ordinary years. 329. This arrangement was introduced by Pope Gregory XVI. in 1582, and has been adopted in all civilized countries, except Russia. It was introduced into Great Britain in 1752,— being termed the new style. The error had then accumulated to 11 days, and was rectified by advancing the days of the month 11 days : the 3d of September to be the 14tli. The differ- ence between the new and old styles now amounts to 12 days. 2. The Sidereal Year. 330. The true time of the earth's revolution in its orbit, is the period of its return to the same star. After the sun has returned to the same equinox, as that has receded 50*1" (by the precession of the equinoxes, — which see), he has still 50*1'' of his orbit to complete the real revolution, which requires 20™- 19-9«- of time, which must therefore be added to the tropical year to ELEMENTS OF ASTttONOMY. 89 5 are leap ' are make the sidereal year. The duration of the latter is therefore, 365'>- G*'- 9°" 9-6«- 3. The AnomaUatio Year. 331. The line of the earth's aphelion and perihelion —that is, the longer axis of the orbit— undergoes a gradual change, which shifts the perihelion ll"-8 annually. The earth, therefore, must describe this small arc in addition to its real revolution to bring it round to the perihelion again. It requires 4">- 39-78- to complete this small arc, and therefore the anomalistic year— as the time required to bring the earth to the same relative position to the major axis of its orbit is called— is 4'"- 39-7«- more than the sidereal year, cr 'SarA 6h- IS™- 49 3«- 332. The following table exhibits the leading divi- sions of time : — Standards of Time. Hours. Mirutes. Seconds. Rotation of earth on axis ... 23 56 Vibration of pendulum 3913 inches long at the lat. of London, 51° 30' N. . Civil day, 86400 of the above seconds (divided into 24 hours of 3600 such seconds each ; and each nour divided into 60 minutes, composed of 60 such seconds) 24 4-09 Days. Sidereal day (as above) Solar day, more or less than . Mean solar day (civil day) . Lunar day Months. Sidereal month , Lunar month Calendar month, 31, 30, 29, or 28 days. 23 56 409 24 24 24 60 Days. Hours. Minutes 27 7 43 29 12 44 90 LLtMliNTS OF ASTHONOMy. Years. I Hidcrral ycir Equinoctial year Calendar year Leap year , Days. lIoiirH. I klinutu H. SfCH. 365 9 (♦ 3r,.5 5 48 4'J 365 306 * SECTION V. MOON'S PHASES.— ECLIPSES, ETC. 1. The Moon's Phases, 333. The changes in tlie moon's appearance, from a small illumined crescent to tliat of a full enlightened orb, and from that to a crescent again till she disappears ^entirely, are termed phases. 334. The moon's phases are owing to the following causes. She is a dark body in herself, and shines only by reflecting the sun's light; so that only ony half of her surface — that which is next the sun — is illumined at a time: and the only parts that can be seen are those parts of the illumined half which are turned toWt,.ds the observer. But, owing to the moon's motion round the earth, different amounts of the bright half are turned towards the earth at different times, so that she appeal of every different magnitude, from full moon till she disappears altogether. 335. The following figure will illustrate the moon's phases, and also those of Mercury and Venus. Let S represent the sun, E the earth, and A, B, C, D, F, G, H, K, in the inner circle, the moon, revolving round the earth in the direction of the order in which the letters have just been named. Then at A, when the sun and moon are in conjunction, the unenlightened half of the moon is turned towards the earth, as shown at A' in the outer circle, and the moon is not seen ; or, it is new moon ; or, as sometimes expressed, the moon \ I ELKMENTS OK ASTICONUMV. Ui changes. At B, as is scon by the points wlioro the inner circle cits tlic inooji, a small part of the enlight- Fig. 29, © moon ened side comes into view to the earth ; but the greater part of the side turned towards the earth is dark, and the moon appears an illumined crescent, as shown at 13 , in the outer circle. At C, half of the enlightened part iS turned towards the earth, the moon appears like a semicircle, as at C in the outer circle. At F, the enlightened side is turned towards the earth, and the moon appears full, as at F', being then in opposition. As she continues her course, she gradually presents less and less of her bright side to the earth, successively appearing as at G', H', K', in the out r circle, until she again comes into conjunction, and entirely dis- appears. By tracing the figure, the phases will be 93 f.li:mi:nt8 of astronomy. 11! roftdily tindcrstoofl. The inner circle sliows the illu- mined and dark parts — the outer circle the appearnnro presented to tlio earth. 336. When the moon is in conjunction or opposition fas at A and F, Fig. 28), she is said to he in her Syzigies — when midway between these points (as at C and II, Fig. 28), in her ftuadratr'^es (or quarters). The points in her course between the syzigies and quadratures are called Octants. 337. The earth appears to the moon as she does to us, but of about tliirtoen times the size, and affords her a very considerable degree of light. The light which the earth yields the moon renders the dark parts of l". i latter faintly visible, a little before and after new moou. At these periods the moon's light, as it appears at he earth, is weakest, and the illumined half of the eaitii most fully turned towards her. See A, K, and D, Fl,(. 28. This enlightens the dark part of the moon, and this light reflected back to us, renders these dark parts visible with a dull, grayish light — forming tho appear- ance popularly termed *' the old moon in the new moon's arms.' Eclipses and Occultations. 338. When the sun or moon is, in whole or in part, obscured by a shadow which gradually comes over the disc and then glides off, this phenomenon is termed an eclipse. Eclij)ses arc of two kinds — eclipses of the sun and eclipses of the moon. 339. When any fixed star or planet is obscured by the moon, or a planet passing between it and the earth, this phenomenon is termed an "occultation." 340. Eclipses occur only when the moon is in or near to her nodes (that is, when she is crossing the plane of the ecliptic) ; because then only the moon, earth, and Bun can be in the same straight line, or so nearly so that ^ part of one can obscure part of another. They also ELEMENTS OP ASTRONOMY. 93 occur only at new and at A.ll moon ; that is, when the moon iH in conjunction or in opjwsition. 1. Eclipse of the Moon. 341. An eclipse of the moon is caused by the inter- position of the earth between the sun and moon, so that the earth prevents the moon from receiving the sun's light, and she is therefore obscured. 342 Hence, an eclipse of the moon takes place only when she is in opposition. ^ 343. The following figure will illustrate an eclii)so ot the moon. ^ Fig. 29. Let A S. B represent the surface of the sun, H the earth, m th cmoon, dnip the moon's orbit. Then, the sun's rayp from A and B, skirting the earth at H and will project a conical shadow H C 0, within any part of which no rays will be received from the sun. But the parts A and B of the sun also send rays cross- ing in K, A a, and B U b ; and between the' line of these rays, and the perfectly dark cone H C 0, any object will receive part, but not be illumined by the whole of the sun's rays, part being cut off by the inter- posed earth. Thus, at n, no rays from the sun's surface between S and B will be received, and therefore a leso perfect light will be shed at n. 94 ELEMENTS OF ASTRONOMY. 844. Tlio perfectly dark rnnce 11 C 0, is called tl)0 umbra or sluulo ; tlu^ surroniKllrvc^ parts 6 H (!, a (', the penumbra or " aiiuostshado " (/)^'nf, almost; umbra^ Bliade). Ml t r 11 345, Now, when tho moon is at d hIjo will be fally illuminated, receivinj; rays from the whole of tho sun's surface A S B; but whenever she enters the penumbra, by crossing tho line b H, the earth will cut off a por- ti cttiiBo ail int!?™l«"whl!l"i ""'"r" ''" '•«^'" »' <="t»in rcK,.lar Sun eclipsed, Moon eclipsed, Moon (( 1828. April 1 J. Oct. i). 1829. Mftr. 20. Aj.ril 3. iscpt. 13. Sept. 28. Sun eclipsed, Moon eclipHed, Moon Sun 1846. April 2.5. Oct 20. 1847. Mar. 81. April l.^i. ^ept 24. «- -t. 9. 98 Full Moon, Nuw ... Full ... Now ... Full ... Now ... Full ... etc. ELEMENT? O" ASTRONOMY 1828. January 2. January 17. Fcbn.ary 1. February 15. March 1 . March 15. March 31. etc. 1847. .January 1. January 17. January 31. February 15. March 2. March 16. March 31. etc." A. De Mouoan, in Companion to the Almanac for 1847. 357. A remarkable plienomenon, hitherto unex- plained, was seen during the total eclipse of the sun on the 8th of July 1842. " The moon was like a black patch on the sky, surrounded by a faint whitish light about the eighth of the moon's diameter in breadth, in which three red flames appeared in form like the teeth of a saw."— ifrs Somerville. SECTION VI. Influence of the Atmosphere on Astronomical Phenoroena. 358. The heavenly bodies are rendered visible to us by rays of light which emanate from them and pro- duce impressions of their forms on the eyes of the observer. These rays are somewhat modified in their course before they reach us by passing through the atmosphere. 359. The atmosphere is an aerial fluid, which surrounds the earth on every side. It extends above the surface to a height* of about fortj-five or fifty miles. it is heavy and dense m tlie lower regions, but becomes gradually 1; ^'hter^ and more rare or expanded as it is higher up ; as represented m l^ig. 66, where the particles are shown densely crowded b-low, becom- inff moie open as they are iunucr irom v^v- ^^i..,?.,.. -_ '*",. I, figure the extent ot the atmosphere in relation to the size ot the \ * ELEMF.NTS OF ASTRONOMY. 99 fru V^ greatly exapprerated. I he depth of the atmosphere 18 about one hundredth of the distance from the surface of the earth to the centre. 360. The atmosphcro is concerned in astronom- ical phenomena by its power of refracting and reflecting the rays of F itf. rw. '•,'>>■;(! •ht. 36 ] . Refraction is tliat " ■••••■/■^: :!::-•?• ••::■• ' bending of the rays of light which takes place when they pass obliquely from ?ro n atT ''r't'' '' ' ^^/ohght pal obl'ueT^ s ace to onV7 ''' f""^ ""'''' *« ^^^' fi-om surrounding densifio. If f ""'P^^^^^' ^' between strata of different densities of the same medium, it does not continue in les^ inTo '''7^'}}^^ -^ before, but is bent, more or Is ; '""^Z' \'\^'^^'^oUon, which it preserves'so long ir.f 4"^'" '" *^^ ^""''^ medium. T oi r ^'^'■'^^*^^" ^s illustrated by the following figure, i^ct L D represent a ray of light passing at D from a rare into a dense medium, to the surface of which it is not perpendicular. It will not continue in the direction of C D, but will be bent into the direction D E. If the ray had come from the tZS';?D i? '^t'^'r ^ ^' ^^*^^^"^ *be rare medium at D, it would be bent into the direction D C. Fig. 34. s-3 i" reicreuce to that influence, as air to light <^o is trariiiniitted is called "t 100 ELEMENTS OP ASTRONOMY. I i It^ ^i I Let the line G D F be perpendicular to ilio surface betwf^«n the two media; then, it will be evident from the figure that the following is the rule of refraction : " When the ray passes into a denser medium, it k refracted so as to be nearer to the perpendicular than before ; when it passes into a rarer medium, it is re- fracted so as to pursue its course further from the per- pendicular than before." 363. If the ray entered perpendicularly, as in the direction G D or F D, it would not be refracted, but would continue in the same course, G D F, or FDG. 364. Owing to Refraction, no heavenly body is seen in its true place unless it be in the zenith. Every- where else, refraction causes bodies to appear to be higher above the horizon than they really are. 365. This takes place in the following manner: When a ray of light enters the atmosphere obliquely, it is bent down towards the surface of t) a earth, and as it approaches the ground, it becomes more and more bent in passing from the rarer strata above to the denser medium below. Now the object from which the ray comes appears in the direction which the ray has at the moment when it strikes the eye. Accordingly, as refraction in a denser medium bends the ray towards the perpendicular direction, the object will be seen in a direction more perpendicular to the surface than its real one— that is, nearer the zenith, or more elevated above the horizon than it should be. 366. Refraction is very slight on the first ray entering the atmosphere, owing to the extreme tenuity of the air in the upper regions; but gradually increases as the ray approaches^ the earth, the strata of air becoming more and more dense. It is affected by the air's temperature and pressure, which must be taken into account by the astronomer. 367. As the rays from a celestial object in the zenith enter the atmosphere perpendicularly, there can be no ELEMENTS OF ASTRONOMY. 101 refraction of its rays, and it will bo seen in its true place But, from every other position, the rays will enter the atmosphere obliquely, be refracted, and there- tore represent it tor elevated. 368. The following figure illustrates atmospheric ra- traction. Let o represent any point on the earth's Fig. 36. surface, and A any star or heavenly body. It is seen at o by means of rays of light from it which reach he more den.7 Z. "^u'i ^ ^^' ^^^' ^' ^^' ^^' ^^'^^^^ more dense, to v o, which is the direction they have on ftwefe tth"'r- /-T^-^ly^ the star I s'n ns but aTT ' ''"' ""^''^ represents it not at A, Lt:^!?lril^-? '-^-od the obji^t visible al o had 1" " '•-' ^-"«^""", VIZ., A ii, is refracted down to e. ^ 11 102 el^:ment8 or astronomy. 370. Refraction increases as the object is nearer tlio horizon, as the rays then pass through more of the dense strata of air. At the zenth it is 0° 0' 0". At 45° ahovo the horizon it elevates the apparent ahove the true position of a celestial object about V — more correctly ST''. At the horizon it elevates the object so much as 33', or about half a (Jegree — that is, about as much as the sun's apparent diameter. 371. Refraction, by elevating the position of celestial objects, brings into view bodies actually below the hori- zon, and which, therefore, could not otherwise be seen. Thus, in Fig. 35, the body S, which is below the hori- zon H o of a spectator at o, and would therefore be invisible to him, is brought into view and made to appear above his horizon at s. 372. Thus, refraction raises the sun above the horizon at both suncet and sunrise, and by causing him to rise earlier and set later than he otherwise would, lengthens the day. As refraction at the horizon is 33', and the sun's diametpr is about 32', the sun will have sunk below the horizon when his lower margin appears to us resting on it, just about to dip beneath it. ?73. Refraction also distorts the figures of the sun and moon T/hen they are near the horizon, rendering them of an oval form, and flattened at the lower part. This is caused by the very rapid increase of refraction near the horizon, so that the lower margins of these orbs are much more elevated than the upper, which shortens the perpendicular diameter, and gives the figure a somewhat oval shape. 374. The Reflection of light signifies the bounding off of rays of light from bodies on which they strike ; this takes place in the same manner in which a ball rebounds from any hard surface on which it is thrown, or in which sound and beat are reflected. 375. The atmosphere reflects and disperses in all directions the rays which it receives from the sun. Were there no atmosphere, those bodies only would ELEMENTS OF ASTRONOMY. 103 be visible to us which are in 'he direct rays of the sun, and thus receive light, whic they would transmit to us and render us sensible of their presence. But, by the reflective power of the atmosphere, bodies have light thrown upon them, though out of the direct course of the sun's rays ; and thus, as tL°) atmojphere is every- where present^ they receive light in whatever positioUj which they in turn reflect to us, and thus render them- selves visible. Twilight. 376. Twilight is the faint and gradually diminishing light which we enjoy for a considerable time after the sun has fdrly sunk below the horizon ; and we are indebted for twilight to the reflective power of the air. Those portions of air which are a little nearer to the sun than any place at which the sun has just set, will reflect down to that p»lace (as well as to the parts which have had the sun still longer below the horizon) a part of the light which they receive ; accordingly that place will, for a little after sunset, receive an inferior degree of light reflected from the air — or twilight. And, as it will receive reflected light from a less body of air as the sun sinks lower below the horizon of a place, its twilight will diminish gradually till total darkness supervenes. 377, This is illustrated by the lower part of the above figure, 35. Let the sun, P, be on the horizon of the place m, having completely set to n and t. These places, n and <, would be completely dark were there no atmosphere. But though the sun is far below the hori- zon of ^, it will receive a small portion of light reflected from the upper air at k, and from all the air higher than the shaded p'vrt and beyond the line k t. The earth at n, not so far out of the sun's rays, will receive reflected light from a much larger portion of the atmosphere, viz., from b, lower down, and from all the air without the shaded part and beyond thrj line 6 n. Hi 104 ELEMENTS OF ASTHONOMY. ■\ 378. Twilight continues wLilc the sun is less than 18° below the horizon. Hence, some parts of the earth have continual twilight at certain periods of the year, as at London, from May 22 to July 21. The real, or astronomical twilight, is of much longer duration than what is popularly regarded as twilight; for it com- mences immediately after the sun is below the horizon, when there is still good daylight, and continues for some time after it is apparently dark. There is long twilight around the polos, which illumines these desolate regions when the day is short, or the sun below the horizon for days or months together. 379. There is shorter twilight the nearer the place is to the equator — there the astronomical twilight con- tinues for about 1 hour 12 minutes. The rapid rotation of the parts about the equator, and the great distance from the axis, bring very soon a considerable convexity between the sun and the spectator, so that the period of reflection is cut short. Hence the diminishing duration of twilight as we approach the equator, where it is often said that there is no twilight. This is incorrect ; the twilight is merely very short. 380. The daivn, or light before the sun has actually risen above the horizon, is due to the same cause and subject to the same general rules as the twilight in the evening. Owing to the ditferent condition of the atmos- phere as to vapours, which abound after sunset, twilight is a little longer than dawn. ELEMENTS OP ASTRONOMY, 105 PART III. THE SOLAR SYSTEAf. 381. The solar system (or our system) consists of certain of the heavenly bodies, which are connected with the sun, and form a system by themselves, apart from the others. Tlie word " solar " is derived from " Sol," the Latin word for " the Sun." 382. The solar system is composed of the Sun, the Planets with their Satellites, the Comets, Aerolites (or meteoric asteroids), and, probably, a thin fluid or Ether occupying the intermediate spaces, and spreading out into space far beyond the limits of our system. 383. The Planets are those stars which do not* remain in one spot, but are found to change their posi- tions in the heavens. They are therefore termed planets, from the Greek word wXavi^Trie, signifying a wanderer. They are so named in contradistinction to the fixed stars, which preserve their relative positions comparatively unchanged. Five are visible to the naked eye.— See par. 45. The earth also is a planet, and must appear as a star to. those who live on the neighbouring planets, as Venus and Mars. A Comet is a kind of irregular and less substantial planet. 384. The connexion between these bodies is this: The planets and comets revolve round the sun, receive light and heat from him, and are preserved, mainly by his action, in their proper paths around him. The Satellites are lesser or secondary planets, which revolve round some of the larger planets, are carried with them round the sun, and also receive light and heat from that luminary. The moon is a satellite to the earib, 385. The heavenly bodies which compose the solar E 2 lOG ELEMENTS OP A8TK0NOMY. Bystcm have each two principal motions, ono round tlio sun, tormcd its revolution or orbitual motim ; anotlior, turninf? on itst'lf, round an ima«,Mnary lino called the axis, paKsin/^ throu^di it, termed its rotation. Some, as the earth, have other motions; see Precession. In addition to these, the sun himself, with all the planets in his train, is rapidly advancing throu^'h space. — Sco pars. 502 and 707. SECTION I. Definitions. 386. An Ellipse, or Oval, is a curved line, such, that the sum of two straight lines, drawn from two points within to any i)oint in the curve, shall always be the same. These two points are termed the Foci of 'the ellipse. Fi^. 36 represents an ellipse. F and E are its foci, and if G, K, L, be any points in its circumference, then G F and G E together will be of the same length as K F and K E together, or L F and L E together. 387. An ellipse may easily bo drawn in the foUowinpf man- ner : — Fix two pins iu tlio paper at the points selected for the foci, as at F and E; and pass a thread having its ends tied togetlier (an endless thread) round them ; the thread being longer or shorter, according to the size and form of ellipse desired. Then stretch the tlircad out by the pencil, giving the thread the form F G E F. or F K E F, as may bo, and then carry the pencil round the fi>cx, pressing it gently but firmly on the paper, and keeping the thread equally stretched till the pencil has completed its circuit. The pencil will then have loiiued &i> oval or eiiipse upon the paper. elkmi;nt8 of astronomy. 107 388. The eltipite in ono of tho nffun-s called rnnlc »e tmni,, formed by tho section or cutting of a c.no by a idano. If tho plane cut the cono parallel t» the bane, tho section will Imj a oircle: oblu/udf/ throiujh both aiden, the Huction will Jh! an ellipM parallel to the aide, tho section will bo a parabola; Hud when tho cutting piano maken a greater amjle with the ba«e than the side of the cone, tho section is a hyperbola. If tho plane pass through tho vertex, tho section will bo a triangle. ^ 389. The Major Axis of an cllipso is the Rtruight line druwn throui^'h tho foci, and terminated both ways by tho circiimfen-ncc, as A 0. T\ Middle point of this line, C, in the Centre of tho clHj^se. The minor axis of the ellipse is tiie Htrai«,dit line through iht centre at right angles to the Major Axis, as J5 D. 390. A Tangent (or touciiing line) to a curve is a straight line which touches the curve, and being pro- duced both ways, does not cut it, that is, does not go mto it. In Fig. 8, D K and P H Q are tangents. (A tangent of a circle is at riglit angles to the diameter drawn through tho point of contact.— There may bo tangents^to other curve lines as well as to circles.) 391. The path or course in which any of the heavenly bodies moves is termed its orbit; from the Latin orbita. The orbits of the planets, satellites, and many of tho comets, are ellipses, the sun, or planet round which a satellite revolves, being in one of tho foci ; as at S ir. Fig. 37 below. 392. Tiie Linear Eccentricity (from ex, out of, and centrum, the centre) of a planet's orbit is the distance from the centre of the ellipse in which it revolves to the body round which it revolves. fn the adjoining figure, if A B i) l<] represent tho orbit of a planet or satelJite, if C I Fig. 37. U\J ibS lOS BLEMENTB OF ABlRONOMY. i centre, and S the sun for primary planet), tlien tho dhtanco C S will bo the linear eccentricity. 393. The eccentrldUj in moro usunUy taken to nicnn tlio pro- portion which the lineal eccentricity bears to tlie Hoini-uxii* major, t.*-., the proportion of C 8 to A C. 'I'liuH, if C 8 were \ of A C, wo should say that the eccentricity Ih \ or 'jr). 391. As the minor axis (B E, Fi«,'. 37) of nn oUipso increases, or the mtijor axis decreases, the foci (S and V) draw nearer to the centre and to each other; the eccen- tricity (C S or C F) lessens ; and the figure approaches to that of the circle. When the major and minor axc8 are equal, the foci and centre coincide, and the figure is Ok circle. 39.*). In the case of the planets and Batellites the two axes are nearly equal, the eccentricity Is small, and the orbits, therefore, are nearly circular. In the orbits of the comets, the minor axis is considerably less than the major axis, the eccentricity great, and the ellipse elongated. 396. A planet's greatest distance from the sun is when it is at the extremity of the major a.ds farthest from that luminary — its least distance when at the other end, that nearest the sun. And the difference between the least and greatest distances will be twice the eccen- tricity. In Fig. 37 above, if S represent the sun, a planet is farther from the sun at D than at A by S F, i.e., C S and C F, or twice the eccentricity. The mean distance of the planet from the sun is the half of the major axis, or, the semi-axis major, as C A or C D. Observe the sun, S, is not in the centre of the ellipse. 397. These two points in a planet's orbit, where it is at its greatest and' least distances from the sun, are termed its Apsides, from the Greek word a-^ig (apsis), the curvature or bend of an arch. The point fur^V.est from the sun (D, Fig. 37) is termed the Aphelion: the point nearest the sun, Perihelion (A, Fig. 37) -.—from ,1 r^..-.i_ l„ .^^ .-- /l-.r.1i<\trtH are on tho fiune meridian *uoy nro mu\ to bo in oonjunotion ; when on the oppoHite nifridiiiuH, thoy are suid to be in opposition. 405. For cxainple, wlien a snpciior planet, aa Mars, Ib on the same meridian aa the Hun, the mu being between tho earth and the planet, which ap- pears in tho «anio part of tho iiettvens &h the sun, and on the Banie celestial meridian, the sun and planet are said to be in con- junction. Thus, in Fig. 39, if E be tho earth, and a Mars, ihe sun and Mars would bo said to be in conjunction. When the earth is between the sun and planet, so that tiiey appear on tho opposite parts of tho heavens, that planet and the sun are said to be in op- position, as at b in tho same figure. 400. In tho case of the inferior planets, when the planet is between tho earth and sun, it is said to bo in infc ior*- conjunction; when the fiun is be- tweon tho earth and planet, it is said to bo in superior conjunc- tion fn I'ig. 40, if E bo the ea' .. '"d '., b, different positions of an inferior planet, it is in hi- ferior conjunction at 6, hi superior conjunction at a. 407. Hence, when a planet is in conjunction, it rises and sets about the same time as tho sun. When it is in opposition, it sets when the sun rlKPS. nnd risPR vvlion ihn snn atita Fig. 40. fl ■t'ifENTS OF AgTIlONnMY. ni t * t 408. Tlio disc of u liiuvoiily b A H Ih less than 1) A C, A H being greater than A C, and A U evidently lies nearer to A B than to A C. A single force which produces the same effect as two or more other forces is called their resultant. 420. Centre of Gravity,— There is a certain point in every body which bears such a relation to it, that the same effects would ensue from its gravity (weight) if a single force, equal to its weight ancl in tlie same direc- tion (vertically downwards), acted upon the bod)' at that point, the rest of it being then sup{)oscd to be without weight. Such a point in a body is called its centre of gravity. It is in the middle of a straight rod or bar, in the centre of a circular plate of any mate- rial, and in the centre of a sphere or spheroid, suppos- ing these to be of uniform density at every part. As any number of forces acting on a body may be replaced by a single force called their resultant^ so a body may be considered as an assemblage of separate particles rigidly connected, the gravity or weight of each particle is a force acting upon it, and the centre of gravity of the body is the point through which, in whatever posi- tion^ it might be placed, the resultant of the forces of all its separate particles would pass. Hence, all the parts exactly balance each other about that point. 421. Two or more bodies taken together may have a common centre of gravity. The centre of gravity of two bodies is found by joining their centres of gravity, and dividing the joining line so that the weight of the first is to the weight of the second, as the distance of the centre of gravity of the second from the point of division of the joining line, is to the distance of the i 'il» t \i I ( ! M II II 114 ELEMENTS OF ASTRONOMY. centre of gravity of the first from that point. Then, by ' simihir method, the centre common to that centre of ^^ravity, and the centre of gravity of a third body may be found, and so on. SECTION II. Forces Acting Throughout the Solar System. 422. The heavenly bodies are found to move in curved lines: they must, therefore, be acted upon by more than one force. (410.) 423. The orbitual moiions of the planets, satellites, and comets, are caused by the concurrent action of at least two forces ; — irst, A projectile, tangential, or centrifugal force; second^ An attractive, central, or centripetal force. 1. Projectile Force. 424. Any body thrown or projected forward, is called a projectile^ as a stone from the hand or a sling, an arrow, a musket or cannon ball ; and any force which tends to impel a body in such a manner, is called a projectile force. It is considered that, at some time, the planets, satellites, and comets must have received some such impulse, vvhich set them ^'n motion, and which, combined with the attractive force, preserves them in motioi in that course which they now pursue. 425. As, by the inertia of matter, a body tends to continue in the state in which it is, whether that be one of rest or of motion, the heavenly bodies do not require new impulses to preserve their motion. That motion, once imparted, continues uninter- ruptedly till it is weakened or destroyed by the oppusinj^ action of some other force. — " The force by which the body is projected ELEMENTS OP ASTRONOMY. 115 II- 18 one which we suppose to ho necessary at some past timo to account for the planet's motion, but which acts no more. The Elanets are in motion, and it is of no consequence to our inquiry ow they received this motion; but it is convenient, for the pur- poses of'calculation. to suppose that at some time they received an impulse of the same kind as that which a stone receives when thrown from the hand ; and this is the whole meaning of the term 'projectile force.' " — Gravitation, by Amy. 426. The projectile force, acting alone, would throw the revolving body out of its orbit, and cause it to move on for ever in a straight line. The direction of this line would be a tangent (see par. 390, and Fig. 8, p. 21) to the orbit at that point where the attractive force ceased and the projectile force alone acted on the body : or, would bo in the direction which the planet had at the moment of quitting the orbit. 427. Thus, in the adjoining figure, let the circle A B C D represent the course of a body moving round in the direction from A towards B, B towards C, and so on, and at the same time drawn by a central force towards F. If, when at A, the central force were to cease, the projectile force would cause the body to break off from its course and proceed on in the straight line A G, v/hich would be a tangent to the circle at A. At B, C, or D were the projectile force alone acting, the body would proceed in the lines drawn from t' ese points in the figure. And in the whole course of Its revolution, the body has a tendency to break off" in this man- ner — in a tangent to the curve at the point where it is when the central force ceases. 428. This force, therefore, is termed projectile^ as it tends to throw the body out of its orbit, and resembles the force with which any projectile is impelled from the surface of the earth. It is termed tangential, as it tends to throw the body off in a tangential direction , and centrifugal, as it tends to impel it from the centre round which it has been revolvinsr. 42y. The Gxistence of the projectile force is iaiferred from the \i 116 ELEMENTS OF A8T110N0MY, orbitiial motions of tho plnncts; but no pnrticularB nn to Un Hourco or nature have been nHccrtainod. It lias bocu caleulatod that if tho earth received its motions of rotation and round the sun from a ninglo impulse, that impulse must have passer through a point alK)Ut twenty-five miles from its centre. An impulse through tiio centre of gravity of a sphere would cause it to move forwards in a straight line — through any other point, tho impulse would cause both rotation and motion in space. 430. This cciitrifu«^al force, or tendency of a revolv- ing body to fly off from tlie circle in which it moves, in the tangential direction, is well illustrated by the pro- jection of the mild which adheres to a carriage wheel, — by tho water being thrown out of a mop when it is rapidly whirled, — by the necessity which compels the eipiestrian galloping in a circular arena to lean inwards when the speed is great, to ovtirconie the tendency of his rapid motion to throw him outwards, — in the manu- facture ot crown or window glass, in wliich a knob of glass is made to become a bowl of many forms, gradu- ally spreading out, until it suddenly expands ''nto a broad flat sheet, — in a railway train running off the rails at a curve when the speed is not slackened, — and very strikingly, in the centrifugal railway. 2. Attractive Force. 431. This is the force exerted by the central body, on a planet, comet, or satellite revolving round it, by which the latter is preserved in its orbit, and prevented receding from the centre into free space, as it otherwise would do from the action of the projectile force. 432. This power is termed attractive^ as it tends to draw the planets towards the sun, and bodies genera^y towards each other, etc. ; central or centripetal (centre- seeking), as it urges them towards the centre round which they rr-volve; and radial^ as it acts in the direc- tion of the .ins. 433. The attractive force, acting alone, would draw the revolving bodies inwards from their brbits in tho ELEMENTS OP ASTRONOMY. 117 (lircction of tlio rad'uia, and procipitato tlio planots and comets on tlio surfaco of the 8un, and satellites en the primary planet round which they revolve. Thus, if A, Fi^'. 42, be a body revolvin^^ in the orbit A B C D, and the projectile force were suspended at A, the planet would move to the central body in the direc- tion A F. 434. It WftB dcmonatratod by Sn* Isaac Newton that a particle of matter placed on the outer wurfaco of a hollow sphere in attracted by it in the same manner as if the whole niattor of the hollow sphere were collected into one particle in its centre. As a solid sphere may bo rej^ardedas made npof an infinite numhc^r of concentric hollow spheres, of uach of which the ahove would be true; the same must bo the case with the solid sphere: it must attract a particle at its surface in the same manner as if its whole nmss wore in its centre. The heavenly hodies are bo nearly spheres, and so distant, that they act upon each other as if each were gathered into one very dense particle at its centre of gravity, possessing the aggregate force of the mass. And the true centre of the planetary motions is not the sun's centre, hut the centre of gravity of the solar system (421). This point, however, owing to the enormous mass of the sun comi)ared with that of all the planets, etc., is only twenty-five miics distant from his actual centre. In like manner, the earth and moon movo round their common centre of gravity, and that is to bo regarded as the point which is attracted by and moves round the sun. 435. Thefofxe of attraction is measured by the space through which it draws a body in one second of time after the body ij set at liberty. If the attractive force be great, it will cause the body to move thiough a greater space than a smaller attractive force would do ; and this is the best measure of gravity, as it applies equally to all bodies, irrespective of their size or density. For, it has been found (first by the celebrated experi- ments of Galileo) that, disregarding the resistance of the air, large and small bodies, dense and light bodies, f;ill through the same space in the same time. And if the planets, satellites, and comets were at equal distances from the sun, and left solely to his action, they would all reach his surface in the same time. The force of the 113 r.r.EMRNTS OF ASTRONOMY. II earth 'h attraction, or force of pfravity, is such as to cause a body witliiti any moderate distance of the earth's sur- face to fall IG feet (correctly, IGi'.r feet) in a second, im- I)arting to it at the end of the second a velocity of 32 feet per second, and continuinp; its action at the same rate ; while the effect of the j)revi()us inij)ulse8 remain, and thus the rate of descnit becomes rapidly accelerated. The pendulum, when drawn out of the vertical line and left to itself, is, in a manner, a falling body; and the time in which it descends affords a measure of the earth's attraction— the force which causes its oscillation (a descent and ascent). 436. The attractive force prevailing through the solar system seems to be the same as that well-known power, distinguished on our i)lanet as the force of gravity, which causes bodies to fall to the ground when l«ft unsupported in the air, and which makes them exert on bodies beneath them the pressure which we term weight. Newton first showed that the force which retains the moon in her orbit is the same which causes heavy bodies to fall to the ground. The sun in like manner attracts the planets and comets ; the moon in her turn attracts the earth, and thus moves the waters ; and each body is the source of an attractive energy spreading through space, and more or less acting on every other. 437. When spoken of with respect to its action throughout the solar system, it is termed attraction of gra"itation, or, simply, gravitation. 438. Three things may bo noted with respect to gravitation. 1. That it acts in all directions, spread- ing its influence out from a body like rays of light from a luminous object. 2. That its force is in direct* pro- portion to the quantity of matter {i. e., to the mass) in the attracting body. 3. That its force is in inverse* proportion to the square of the distance. * When one thing alters in a certain way in the same proportion in ELEMENTS OP ASTRONOMY. 119 439. Tliat prmvitation nets in all (Urcctions is shown l)y a plmnmet Busponded near tlie top of a lii^'li preci- pice loaning towards the rock, — hy bodioH tending towardB the earth on every side,— hy the action of iho moon in raising the waters of the ocean, and forming the tides, — by tlio mutnal action of the sun, planets, and satellites,— -and by Mr Cavendish's celebrated ex- periments, in which small leaden balls were supported on the ends of a rod which was suspended at tlio middle by a slender wire ; and when large leaden balls were brought near to them, it was found that the wire was immediately twisted by the motion of the balls. 440. Oil tho eartli'8 surface gravitation acts in one predomi- nating direction— namely, towards tho centre of tlio earth- giving bodies that strong nnd invariable tendency downwards called Gravity. This is not owing to any difference in nature between the mass of tho earth and bodies upon it— but to tho cncu instance of that mass being so very great compared with that of any body on its surface, that all lotcral attractions aro overpowered by the overwhelming force of the immense mass under our feet. Also, lateral attractions neutralize each other, while the force of the earth's attraction is not neutralized by any opposite force equally near. 4^1. That the force of gravitation is in inverse pro- portion to the square of the distance, is a mathematical deduction from the elliptic form of the orbits of the planets, with the mn in one focus ; following, there- fore, from the second law of Kepler (see par. 454). 442. That gravitation has force in inverse proportion to the square of the distance, signifies, that tho attraction of one body for another, when placed at dillerent dis- tances (other things remaining tlie same), is as much greater as the square of the distance is less, and as which another alters in the same way, this is torrnod direct proportion IhuB, in tlie above instance, if the quantity of mutter diminish>s, the force ot attraction diminishes as much. When one thinK alters in a certain way in tho same proportion in which another altcrn in the opposite way this ia invarse proportion. Thus, in tlie above instance, if the square of the dis- tance between two bodii-.s dtnii/iis/ii».T, thn forpo rtf ntfronti,,,, »>,.* iU , tucreases as much as the square of tho dibtance has diminished. L^i , JK : 120 ELKMENT8 OF AbTKONOMY. n I ■ much less as the eqiuiro of the distatico is greater. This is iihistrated by the following table, wlicrc the first two columns reprcKont diftcront clibtanct'H,— tho next two, the proportionate forces of attraction at these distances, in sciuares, — and the last two, the value of these squares expressed in numbers. Attraction Attract lot? at 1 is to at 2 as 2*^ l^ as 4 : 1 Ji • ... O 2-' ... 25 : 4 m •*. ... X ... 1^ 2'J ... 1 . 4 •«• ... i ... X' 3^ ... 49 : 9 Thus, if a body be first at a distance of 1, and then of 2 from another bjdy, the proportionate forces of attraction exerted by it on the latter body will be 1 at the distance of 2, 4 at the distance of 1. If they be at distances of 3 and 7, the attraction at 3 will be 49, while that at 7 will be 9. 443. The diminution in the above proportion of an influence radiating from a central point, may bo iUustratod by the follow- ing figure. Let G represent any luminous body, A \\ C D, Fig. 43. and E F, boards at the same successive distances as A B from G, A B being at 1, C D at 2, E F at 3. The same quantity of light which spreads over A B will, at C D, innce the distance, spread over /bwr times the surface ; at E F, ilirice, the distance, spread over nine times the surface. But the same amount of light, when diffused over four times the space, will only have oue-fouTtli the intensity — over ■^me times the space, one-ninth of the intensity. Hence tiie light at 1 i» to that at 3 as 3^ : 1^, as 9 : 1, or as 1 : i ;— that is, inversely as the squares of the distances. ELEMENTS OP ASTRONOMY. 121 444. It IS known tlmt tins universally diffused power extend^ to the utmost limits cf the solar system. We have reason to believe, from the phenomena of binary stars, that it also prevails among the fixed stars. And there 18 reason to suppose, that its various forms, as exhibited on our globe,-gravity, cohesion, chemical attraction, electric and magnetic attraction,— are merely varieties of one fundamental power. 445. Few things are more striking than that invisihle and S foT' '"""^T" ^'^•^^ «ubHiHtsl.etween the epa a e par eacn other— acting with such enormous power, and at such itn- thosunhfnllT ";•'" '*'« ««"tral force Vhich, Bpreading from ^1Z« of th""'"-'"?"' ^r'^ir' ^^'^ P'°"«*« '" t»'^''r 'orbits, at distances of thousands ot millions of miles, and perhaps pre- in'SZf ?* jn their proper positions, at distanc^JsSu^^^^^ m millions of millions of miles-exhibited also between the plan- clot« °^^* •'^'"^."'''°" ^^'^^ P^'^"«« °" ^^^'h other or oHho comets-drawmg a stone or drop of rain to the ground-causing the ram or dew drops to form into globules like tuns and planet! hBtr«'"in^'"^l^^ ^''° r''''^'' ^^ ^r'^" t« each other with i nlod^f^rn rf? '' • ^^''. '^ *r '"■* '""'• prodigious strains-aiding m producing the singular phenomena of electricity and matmet- r«";:f?h' ^T^' '" ''' ^''r l^'^^^^^" dlfferentUies g^lnl S J5' phenomena of chemistry, and creating the irinlmer? eviry slde.'"''"'"'''''^'"^ combinations which surround us on ♦l,A InV^* ''f ^^^" inferred from astronomical phenomena, that lvTsZfj'ST''7- '' V'^''' instantaneous%r that its'velo- c ty IS at le„st// nf tho rhnricres in Dosition of the planets, satellites, and comets, and by computation I \ ELRMKNTP OV AHTKONOMV. 12.1 from tluar (.bsema i ov<.ment«, it lm« been ascertaind orbL ♦{ "T ^^^"«*'^?^'y '^'"l '"K"larly in certain satelliteH roun.i some plur.ot. And tlieno niotionn aro expiaiiuMi by the supposition of a prcyectile mvulse orifrumily imparted to each body, and a central or at- tractive force continually acting on it. 451. Suppose that a body is projected in a direction transverse to, or crossing the direction in which tho force ot attraction draws it, how will it move ? J. ♦!!..» T'^'P'r* instAuco of this motloa that -ve can Imneine in the inotum of a stoi.o when it Ih thrown from the hand w u hor,^„ntal (hrcction, or ir» a directio,, nearly .or ionta We all know that the Htonc «cM.n falls to the ground ; amlif wo o^,- Bcrve .t8 n.otion with tluj least ftttentio„,^e «", ha t d<^H no move iu a HtraiK'ht lino It I^KinH to „ ovc Tn tl e d irec LnTn winch .t .s thrown; b„t this direction iH speedily chanK^^^^^^ ft .Tlkrthe ::.o un'i'''" '?'--'"""y/"d.c--tal.tly, Ld the «tono' S^A fi *^ •"•'' TV""^ .*' ''"** ♦''"" '" a direction much in- chncd to tlie onguial direction. The most powerful eflrot that wo can nmko. even when we uhc artidcial meannVaJ in pnduc forp «. n r^yfr'"^ falling at last. This experiment, there- if a'lx^dv 'aP .^nl '' n "y!"f' '^tcly to judge w'hat will heco,.to 01 a body ^ap a planet) which is put in motion at a creat dis- ancofrorn another body, which' attracts it (as the S- Im It w. 1 assist „H much in judging generally what is en" nature ^fersrr^S.'" ^^^::t^^^ ^~^- th;'b^^:;:£^L ,,,;S'-»-t«re of the motion is this: path, of which the first part has the same direction as the line in which it is projected. Tho circumstances of the motion of a strjne may be calculated with the utmost accuracy from tho following ru'e, called the second law of motion the accuracy of which has been established by many simple experiments, and n^any inferences from compli- cated motion ^. If A V;.^ AA :^^\^. ' ■ e - Fig. 44. 194 rXEMKMTi or A8TR0NCMY. If wo wliih to know whor.? tho ntom will Iw at tl«o on.l of tnr nirticulfir turn (Mupp'»H«, for luHtuicc, tliro.o nocomlii), and If tho vol.Kjitv with whii^h It W.IH thrown wouia, In throe •econ.N, hare oarruHl it to H, nupiMHinR gravity not to havo ftctoil on 't' and if f^rAvUy would have inadn it frtll from A tot.,. *upp,)^inK it to hiivc JMJon n»«r«ly droppctl from th" hand ; then, at tho on.l of thrco second**. t!u! «U)no i-m'.ly wdl ho at tho p/, which differont point* can Imj determined in the aamo way for differont initants of time."— .4 tr^/ on (huinlution. 452. In giviii{? tho planets tlieir orbitual motions, those two forces act on tlio prujciple of the composition of motion (par. -117). Any curved lino maybe con- sidored as made up of a iminler of infinitely Hmall straiglit lines, which will be tho diagonals of a series of parallelograms, whoso sides will bo lines m the directions of tho projectile and attractive forces at each point, and of lengths proportionate to tho intensities of these forces. As the directions of the tangent and radius change at every step, the body enters every moment upon a new diagonal, the series of which will form the curve which it describes. 4.'}3. " It is demonstrated that if a body (a planet^, for instance) is by sor o torce projected from A, Fig. 45, m the direction A B, and if the at- traction of the sun, situated at S, begins immediately to act on it, and continues to act on it accord- ing to the law we have mentioned (that is, being inversely propor- tional to the square of its distance from S, and always directed to S) ; and if no other force whatever but this attraction acts upon the body ; then the body will mov in one of the following curves — a circle, an ^llittco o nnrjiVinln.. or ft hvDHrholft. •-•"i J •- i < -- " ■-.• t -- " -=--- " In every case the curve will, at the point A, have K BLtirani or astkonouy. Im 125 the wimp direction ns Iho lino A II ; or (to tine the lan- gnagu of niftthointtticians) A H will be u tungent to tlio curve at A. ^ "The curve cannot be a circle unless the line A B w iwrpendiculur to S A, and, moreover, unlcsii the velocity with which the planet in projec^-d i» neither greater nor Ichh than one particular velocity determined by the k-n^'th of 8 A and the nuihH of the IxKly S. If it diflcFH little from this particular velocity (either greater or less), the body will move in an eliipHo; but if It is much greater, the botly will move in a parabola or hyperbola. ^ •* If A B is oblique to S A, afid the velocity of pro- jection is small, the body will move in an ellipHr ; but if the velocity is great, it may move in a parabola or hyperbola, >>ut not in a circle. " If the body describcH a circle, the sun is the centre of the circle. " If the body dcRcribeR an rllipse, the sun is not in the centre of the ellipse, but in one focus."— ^/ry. 454. The following general laws, developed by Kepler, are found to prevail tliroiighout the solar system : — I. The planets move round the sun in such a manner that the Ik.? drawn from a planet to the sun passes over areas proportional to the times of the motions. II. Each planet descr'hes an ellipse, having the sun in one of the foci. III. The squares of the periodic times* of the planets nre in the same proportion as the cubes of their mean distances from the sun. 455. The first of Kepler's Laws is shortly expressed as follows : — " The radius vector of a planet describes areas proportional to the times." 456. This will be illustrated by the following figure. tlon^u i'^'orbit:^""'''' ^'"'^ "^^"P^'^^ ■»>• -"3^ '^> i" conipieting one revoliT. 126 liLEMENTS OF ASTUONOAIY. The radius vector of a planet is an iniai^'inary straight lino passing from tlio sun to the planet, supposed to emain fixed at the formor, but to follow the planet m its course round that orb, expanding or contracting according as the planet is further from or nearer to the Bun. Fig. 46. 457. In the above figure let S be the sun, and A, E, G, H, a, e, successive positions of a planet ; then S A, S E, S G, S H, i- , S e, will be the radius vector in these several positions. Now, let it be supp^aed that the planet moves from A to E, in the same time in which it moves from a to e : it would then be found that the radius vector, in passing from S A to S E, has tra- versed the same extent of space as in passing from S a to Se; that is, that the shaded area S A E is equal to the shaded area S ae; or, as expressed above, that the area S A E bears the same proportion to the area Sac, as the time of the motion from A to E does to the time of the motion between a and e; i.e., that the areas are proportional to the times — (equal in the instance just given, since the times were supposed equal). 458. Conversely, if the area S E G be equal to ft a TT iho Tilunet will move from E to G i the ?a ?5 \ ELEMENTS OF ASTRONOMY. 127 in tho sarno time .is from G to H. And any area, S G H, will bear tho same proportion to any other area, S 11 K, as the time in [)assin^ from G to H docs to the time in passing from H to K. 459. Hence, then, a planet does not move round the Bnn at a uniform rate ; its motion is at one time acceler- ated, at another retarded. 4G0, For, as the planet is at different distances from the sun, and its radius vector describes equal areas in equal times, any area, when the planet is near the sun, must be broader than an equal area when the planet is remote : tho part of the orbit which bounds the broad area must be longer than that which bounds the narrow one ; find as they are both described in tlio same time, the planet must move faster in that nearest the sun. 461. The velocity of a planet is least when furthest from the sun, becomes accelerated as it comes nearer, is at its highest when the planet is nearest to the sun, and becomes retarded as its distance from the sun increases. 462. The velocity of a planet in different parts of its orbit is in inverse proportion to the square of its distance from tho sun. 463. From this law, that the areas described by the radius vector are proportional to the times, tho conclu- sion was drawn by Newton that the powers by wh'ch the tangential force of the planets is neutralized is directed towards the sun. 464. The second of Kepler's Laws is, that " the orbits of the planets are ellipses, with the sun in one focus." 465. The planets and comets do not fall to the sun when they approach nearer to him, as might be ex- pected, because the tangential force becomes stronger at the same time ; and they do not fly from the sun alto- gether when they recede from him, because while they recede from him the tangential force at the same time diminishes in energy. 466. That this is the case will be illustrated by the folic wing figure. Let this figure represent the orbit uf P 128 ELEMKNTS OF A8TU0N0MY. 1 !i IB I ^ a planet, A ; S being the sun. Let the phanet be in its aphelion at A. It is there under the influence of tho attractive and pro- jectile forces, whoso united operation brings it to B. Be- ing there nearer to the sun, it is more powerfully attracted and drawn still nearer to him ; and, as the at- tractive and projectile forces are operating ? V arly in the same \ direction^ the velo- city is increased, the planet proceeding from B to C, a greater distance, in the same time in which it passed over the short- er distance from A to B. At C, being nearer than at B, the attractive energy is further increased, and as this still concurs in direction with the tangential force, the velocity is augmented. This goes on till it comes to its perihelion at E, where its velocity is greatest. The great projectile force thus acquired prevents it going still nearer, overcomes the incrvrased attractive force, and causes it, at E, to begin to increase its dis- tance, which it does, step ^ step, from E towards A, in the reverse order to that by which it had lessened its distance. The attractive force decreases rapidly as the distance increases; but the projectile force also diminishes, as the sun's attraction is now acting nearly directly against the projectile force^ and it thus lessens its impetus at every step. By this, in progressing from E to Fj Gj H, the projectile force is so much ELEMRNT3 OF ASTKONOMY. 129 •;"t weakened that the attraction of the sun overcomes it 111 turn, and bends the phinet's course towards A, where, when it arrives, the same series of action? com- mence again. 467. That the attractive and projectile forces act mostly to- gether as the planet passes from its aphelion to perihelion, and mostly of/ainst each other when it is proceeding trom perihelion to aphelion, is shown hy the directions of the arrows. 468. Were the planets, satellites, and comets under the influence only of their own projectile force, and the attractive force of the central body round which each revolves, they would obey strictly the laws which have just been developed, of motion in ellipses with their radii vectores describing areas proportional to the times. But each is a source of attractive force which more or less influences every other one, and causes disturb-^nces and irregularities ir^ their movements, by which tht^ deviate, often considerably, from truly elliptical orbits. These disturbing forces render the motions of the heavenly bodies exceedingly complicated. The deviation of the planet Uranus from his calculated course led astrono- mers to suspect some disturbing force, previously un- known ; which idea, followed out, led to the great discovery of the planet Neptune, the body whose action on Uranus caused the irregularities in the movements of the latter. 469. The third law of Kepler establishes a relation between the distances of the planets from the sun and the periods in which they complete their revolutions round him— namely, that " the squares* of the periods are proportional to the cubes* of the distances." 470. That is, the square of the number of days any The square of a number is tlie number produced by mnltiplyinp the number by itself: the cube of a number is the product obtained by multi- plyinff it twice bv itself. Thus. 9 is the Rfinarp nf a 97 tha /.i.Ko of 3- a the square of ii, 8 the cube of 2 ; 25 the square of 5, 125 tlie cube of 5.' ' "* F 2 11 ELEMENTS OP ASTRONOMY. planet takes to go once round the sun, bears the same proportion to the square of the number of days any other planet tp-kes to complete its revolution round the sun, ks the cube of the distance of the first planet from the sun b'^ars to the cube of the distance of the second planet from the sun. 471. Or, in the case of Venus and the earth, cube of cube 0/ : 66-6 : 92 Bqnare of 224-7 sqtiare of 365-25 The first number expresses the number of days occupied by Venus fn her revohition round the sun ; the second the number of days the earth takes to go round the sun; the ^ird number Z the distance of Venus from the sun, expressed m milhons of miles ; the fourth, the distance of the earth from the sua m niillions of miles. SECTION IV. Rotatory Motions and Forms of the Sun, Planets, and Satellites. 472 The sun, planets, and satellites, rotate, or turn ^ipon themselves, in regular periods. The time in which this rotation is completed is called the day ot the revolving body ; the imaginary line about jliich it turns the axis ; and the two extremities of this line, the poles. They are known to have this rotatory motion by the motion of spots upon tbeir discs ; and, by observing the tiiue a spot takes to move through aiiv arc, the time of a complete rotation is ascertained. This motion goes on simultaneously with their motion in ' space, iust as the wheel of a carriage, or a ball in rolling along the ground, rotates while movmg on- ^ItS The sun and planets are of a globular form, but not perfect spheres. They are oblate spneroius \ ELEMENTS OF ASTRONOMY. 131 (413). The flattening is at the poles, or opposite ex- tremities of the axis, and is somotinies termed the " polar compression. " This f\k. 4s. flattening is most remarkable iu Jupiter, in which it is so great as to give to that planet a distinctly oval shape. The spheroidal form is shown, con- siderably exaggerated as re- gards the r>un and planets, in the adjoining figure, where N and S are the poles, and E Q the equatorial diameter. 474. The spheroidal form of the sun and planets is most probably canned by their rotatory motion ; which has a tendency to produce a flattening at the poles and bulging out at the equatorial regions, even though they had. at first been formed perfectly spherical : and their having this form affords a presumption in favour of their having: a iotatorv motion. A fluid mass of uni- form density, the particles of which mutually attract each other, will take the form of a sphere if at rest, but will become spheroidal if it rotates. 475. That the earth is of a spheroidal form is proved bv two cirouiiiStances ; the slower vibration of the pen- dulum as the place is nearer the equator, and the in- crease in length of the degree of latitude af the place is farther from the equator. 476. The rapidity of descent of a falling body is the measure of the force of gravity : the pendulum is such a body ; and as it moves {i. e., falls) more slowly the nearer it is to the equator, we infer that the force of gravity diminishes towards the equator; and as the diminution in the rate of movement of the pendulum is greater than can be accounted for by other causes (heat and centrifugal force), part is attributed to the Bpheroidal formj which must lessen the force of gravity f- ■ 132 ELEMENTS OF ASTRONOMY. fl I 1 :'' of the parts near the equator, hy phicing them at a greater distance from the centre.* 477. But the spheroidal form of our eartli is still more clearly proved by the length of the degree of lat- itude, which is not everywhere the same, but increases slightly towards the poles. Our means of measuring the length of a degree of latitude consist in measuring a degree of an hour-circle in the starry sphere, and finding the distance we must go north or south on the earth, to cause any star to rise or sink one degree in the heavens. It is found that a greater distance is required to effect this the nearer wo are to the poles ; this is exactly what would take place on a spheroid ; and the degree of difference affords a means of estimat- ing the degree of spheroidicity. This may be illus- trated by the adjoin- ing figure. Let P Q represent the earth's surface from onr pole to the equator, and p q the corresponding arc of the heavens, p being the pole of the heavens and q the equinoctial, 90° dis- tant from the pole. Let the arc p q ha divided by the points 1,2,3,4,5 into six ^ equal arcs, -"^^"^^ Fig. 49. may represent degrees of declination (being in fact arcs of 15° each). Then, the places on the earth at which these points (1,2, 3, 4, 5) are vertical, would be the corresponding degrees of latitu de on the earth. But it • As mentioned in par. 414, the pendulum vibrates more slowly as It is lonecr. Now, heat expands or lengthens a pendulum rod; so that, ftora , ." 1 - - J-1-- ~,.,ot »Y,n„n Tnni-n cinwlv in tlip. wiirm rn "iiiiia tbis caubu aiouc, £1 ^iciiuuniui mi.~. TT.n ,. - .<,- of the torrid zone than in higher latitudes. ELEMENTS OF ASTRONOMY. 133 IS evident from the fignro, in which the lines a 1, J 2, c 3, rf 4, etc., are perpendicular to the earth's surface, that the distance l)etvveen the two adjoining points in- creases as we pass from the equator to the poles ; or that a degree of latitude is longer in proportion as the distance from the equator increases. Thus, one degree of latitude is not exactly one 360th part of a meridian circle. If the earth were a true sphere, arcs in the celestial meridian would correspond with arcs of like number of degrees in the terrestrial meridian ; that is, to refer to the above figure, straigiit lines from the earth's centre, C, to the points q, 1,2, 3, 4, 5, 6, in the heavens would divide the arc P Q on the earth into six parts exactly equal to each other ; and these points in the heavens would be vertical at the points where these lines would cut the earth's surface. 478. In consequence of the rotatory motion, the parts at a distance from the axis have a considerable centri- fugal force, or tendency to fly off in the tangential direction, and they would do so if they were not held together by a firm attractive force ; or if the centrifugal force were sufficiently strong. And they have the greater tendency to fly off, the nearer they are to the equator, for the parts at the surface of a rotating body move with different degrees of rapidity, and conse- quently different degrees of force. The polar points do not move out of their places, but simply turn round during the whole rotation ; and each point describes a larger circle of rotation as it is nearer to the equator. Thus, while a person at the equator is carried 24,897 miles by rotation in the 24 hours, one tit London moves only 15,500 miles; at the arctic circle, about 10,000 miles in the same time. But, by the planet's attraction, the parts have also a tendency towards the centre, in the direction of the radius ; and as the tendency to fly off acts in some degree against the tendency to the centre, it neutralizes a part of that tendency, and thuB i Ml 131 ELEMENTS OF ASTRONOMY. diminishes the gravitating' force sensibly where the centrifugal force is great; that is, in ti»o equatorial regions. .11 479. As the centrifugal force of a rotating boMy thus lessens gravity towards the eciuatorial regions, the parts there are urged outwards by this centrifugal force, until an equilibrium is induced by the increased quantity of matter between the centre and the equa- torial regions. 480 Ry thcso forccH it is at onco evident that in a rolatinj? body tho crcatcr centrifugal force in the equatorial regions would cauMO a bulging out of these regions, if in th" fluid state. IJut even were a planet, «uch m the earth, with large portions of its surface covered with water, mainly in the solid state ana perfectly spherical at first, a rotatory motion would cause a polar co.npressi.m. For, the parts at the surface m the liamd form would be thrown towards the etiuatorial nigions, and heaped up there, while the polar regions would bo left dry. Again, as tho parts at the surface are elevated by volcanic heat, and tluis to a certain extent movable, and the earth is continually worn dovyu by the action of disintegrating agents, dilTused through the waters and thus rendered loose and movable, subsiding after- wards and filling up the lower parts of tho deep seas,— the ex- cess of land near the poles might be in time reinoved, spread out over the equatorial regions, and thus an equal distribution of land and sea might take place over the whole. 481. In the case of the earth it is probable, from geological considerations, that the spheroidal form was assumed while it was mainly or entirely in the fluid state; the opinion being held that the eaHh was atone time wholly, and that it is still partially, in a molten, fluid state. n 1 i i 482. Next, the spheroidal form of the planet also lessens the force of gravity about the equatorial regions ; the parts there being further from the centre. Hence, even though the planet did not rotate, if it had the spheroidal form, the force of gravity would be somewhat greater at the flattened than at the projecting parts. Thus, directlfj^ by giving the great centrifugal ibrce to \ ELEMENTS OP ASTUONOMY. 135 tlie parts in tlio equatorial ro^ons; and indiredly^ in causing the spheroidal form, tlic rotatory motion is the Bource of the diflerences of the force of gravity ut dif- ferent latitudes. 483. Accordinfjiy, it is actually found that a body weighs less, or produces less downward pressure, in proportion as it is nearer to the earth's equator ; that its gravity increases as we approach either pole. This difference in the force of gravity at the poles and middle regions cannot be manifested by a c(mjmon balance, as the weights used would bo as much affected as tlie body to be weiglicd. But it is at once detected by a spring balance, or by the pendulum. The spring is less stretched by the same body in proportion as the distance from the pole is greater: and the pendulum vibrates slower. Both of these circumstances indicate a diminu- tion in the force of gravity. For particulars, see the description of the eai'th in ISect. VI. SECTION V. General Facts relating to the Solar System. '?4. The solar system, as presently known to astro- nomers, consists of IGO distinct bodies, viz., the Sun; 9 large planets revolving around him in nearly circular orbits ; 132 asteroids, or small planetary bodies, between the orbits of Mars and Jupiter; 18 moons or satellites, one of which belongs to the earth, and all the others to the four most distant planets; together with a host of comets and countless myriads of meteorites. The large planets, in the order of their distance from the sun, are: — Vulcan (whose existence is somewhat doubt- ful), Mercury, Venus, the Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. The asteroids have all been discovered during the present century, the first of them (Ceres) huviiig been detected on Junuaiy 130 ELEMENTS OP ASTUONOMY. 1, 1801 (roo par. r>71). Owinj? to its proximity to 1 (r. 1, V tlio Hun, Vulcuii ia never seen by the nsiked cyo, and Mercury very soldom, nor can Uranus or Neptune, o\vin«? to their vast distance from tlie sun and earth, while the asteroids are invisible on account of the small- ness of their dimensions. Hence, with the exception of Mercury, all these bodies were wholly unkno ^ .: to the ancients. 485. All the p'.mets move round the sun in the same direction as the carih— west by south to east ,- and their rotations on their axis are in the same direction— /row west to east, 486. La Place calculated that the probaT)ility is as four millions to one that all the motions of the planets, both of rotation and revolution, were imparted at tho same time by on-j original cause, common to them all. 487. The [)lanes of the orbits of the principal planets are not much inclined to that of the earth's orbit ; but all are inclined to it a little, so that one half of a planet's course lies north of the plane of the ecliptic— the other half south of it. From the orbits of the leadin^-j planets being a little above or below the plane of the ecliptic, they°always appear i.:ar the ecliptic. Few lie beyond the zodiac. 488. If a spectator were to view the solar system from a point on the north side of the planes of their orbits, the planets and satellites would appear to move in a direction opposite to that of the hands of a watch, as in Fig. 47 and Fig. 18 ; and this is the manner in which the courses of the planets, etc., are usually repre- sented in diagrams. 489. From the earth, as well as each of the planets, being in motion round the sun, the planets appear at times to be actually stationary in the heavens, or even to move back, i.e., in a retrograde direction. But these apparent irregularities can be explained and calculated : the real motion of all is from west to east. The reUo- I.I.HMENT8 or ASTRONOMY. 137 * Fig. 60. grade niovoinont of a planet may 1)0 undiTstcMHl from the nfljoinin^^ ri«;uro. If a planet, moving in the orbit ro- t)resente(l in tho ower curve, move through tho dis- tances between the anocessive numbers in tho same lime as the planet in tho up- per curve moves between the cor- responding' num- bers, both starting together from tho positions num- bered 1, then tho planet in the upper curve will appear to those who view it from tho other planet to move from I to 2 in the sky — represented by the dotted line at the top; then from 2 to 3, a retrograde movement; then froir. 3 to 4, also retrograde; and then will resume its original direction, and pass ftom 4 to 5. 490. Though the planets appear as mere points to the naked eye, they present discs of considerable breadth when viewed through telescope, wen of very moderate magnifying power. 491. This affords a very striking illustration of the remote- ness of t- fixed RtArs: an ordinary telescope magnifies a planet .^ 138 ELEMENT! OY ABTUONOMY. into a tK'.rccptil.lo i\Uc, or br«R03. The sun has two apparent motions^ one daily, through the sky, giving rise to the alternations of night and day; another yearly through the constellations of the zodiac, causing its different degrees of elevation above the horizon at different periods of the year. These apparent motions of the sun are caused, the first by the rotation of the earth on its axis, the latter by the earth's annual revolution round the sun. 504. The sun is considered to be opaque in its body, but to be surrounded by a highly luminous atmosphere, from which emanate the rays that cause light and heat when they strike upon bodies. 505. Viewed through a telescope, the sun presents a somewhat mottled appearance, with minute shady spots scattered through the luminous matter. Large dark spots, which are not permanent, and which change both in size and form, are se:n upon its surface. These are termed maculae : they consist of a dark or black part in the centre, called nucleus, with a surrounding part not so dark, termed penumbra. In the vicinity of the spot, brilliant and highly luminous strej^.ks are seen ; ^^r|g« 1 to 142 ELEMENTS OF ASTRONOMY. Ill II 506. The maculae are found only about tlie equa- torial regions of the sun. Their magnitude is very various — from a few hundreds to upwards of 45,000 miles. A circle of 461 miles in diameter, corresponding to a single second of angular measure on the sun's disc, is the least space which can be distinctly discerned on the sun as a visible area. " Herr Schwabe, of Dessau, has very recently made a most interesting discovery regarding these sun-spots, viz., that ihey increase and decrease in frequency periodically. He has shown that in the course of about ten uiid a half years they pass through a complete cycle of changes. They become grfidually more and more humerous up to a certain maximum, and then as gradually diminish. At length tluo sun becomes not only clear of spots, but a certain well-marked darkening around the border of his disc disappears altogether for a brief season. At this time the sun presents a perfectly uniform disc. Then gradu- ally the spots return, become more and more numerous, and so the cycle of changes is run through again. There seems every reason for believing that these periodic changes are due to the influence of the planets, especi- ally of Jupiter, upon the solar photosphere ; though in what way that influence is exerted is not at present perfectly clear. Some have thought that the mere attraction of the planets tends to yn'oduce tides of some sort in the solar envelopes. Another equally interesting discovery is closely allied to that now mentioned. It appears that the periodic changes in the solar spots are associated with the periodic changes in the character of the earth's magnetism. The sun-spots vary in frequency within a period of ten and a half yeai-s, and the mag- netic diurnal vibrations vary within a period of the same duration. They agree most perfectly, not merely in length, but maximum for maximum and minimum for minimum. When the sun-spots are most numerous, then the daily vibration of the magnet is most extensive, ELEMENTS OP ASTRONOMY. 143 while, when the sun's disc is clear of spots, the needle vibrates over its smallest diurnal arc. In short, such is the bond of sympathy between the earth and the sun, that no disturbance can affect the solar photosphere without affecting the earth, and doubtless all the other planets, in a greater or less degree." — Other Worlds than Ours, p. 26, et seq. 507. It is but very recently that astronomers arrived at any definite knowledge of the physical constitution of the Sun, and this knowledge has resulted form a skilfully contrived instrument called the Spectroscope. Sir Isaac Newton showed that if a pencil o^' solar light be introduced into a dark room through a small round aperture in the window-shutter, and be then made to pass through a glass prism with its refracting angle downward, an oblong rainbow-coloured picture of the sun, called the solar spectrum, will be formed on the opposite wall, or on a white vertical screen placed in a line with the glass prism and the aperture. The prism has analyzed or decomposed the pencil of colourless light, and portrayed its seven constituent colours (vio- let, indigo, blue, green, yellow, orange, red), according to their various degrees of refrangibility, on the wall or screen. By employing another prism he re-combined these seven coloured rays, and reproduced the clear, transparent, solar ray ; but here his beautiful discovery ended. In 1802, Wollaston discovered that there were dark lines crossing the spectrum in different places. Subsequently, a celebrated German optician, named Fraunhofer, mapped down the principal of these lines with great exactitude. He also discovered similar lines in the spectra of the stars. Such lines are now known as the Fraunhofer lines, and they have led to the most brilliant discoveries of modern times. Kirchhoif, an- other celebrated German, has greatly distinguished himself by aflfording a satisfactory explanation of the d--l_ i: I-:!- cj-.I-cc T>,^^er-.■,^ Cf^.^To^.^- T ^^I'.T/^., Uik iilit'H ; WililC QLUr..Cb, OJllliUlil i^lcvvail, xjv^r.yti, M \0. 144 ELEMENTS OF ASTRONOMY. Frankland, and others, in our own country, have power- fully contributed still further to develop the woudertul science of spectroscopy. " They examined the spectra of the light from incandescent substances (white-hot metals and the like), and found that in these spectra there are no dark lines. They examined the spectra of the light from the stars, and found that these spectra are crossed by dark lines resembling those m the solar spectrum, but differenthj arranged. They next tried the spectra of glowing vapours, and they obtained a perplexing result: instead of a number of dark lines across a rainbow-tinted streak, they found bright lines of various colour; some gases gave a few such lines, others many, some only one or two. Then they tried the spectrum of the electric spark, and they found hero also a series of bright lines, but not always the same series— the spectrum varied according to the substances between which the spark was taken, and the medium through which it passed. Lastly, they found that the light from an incandescent solid or liquid, when shimng thr(»igh various vapours, no longer gives a spectrum without dark lines, but that the dark lines which then appear vary in position, according to the nature of the vapour through which the light has passed. Here were a number of strange facts, seemingly too discor- dant to admit of being interpreted. One discovery only was wanting to bring them all into unison. In l»5y, Kirchhoff, while engaged in observing the solar spec- trum, lighted on the discovery that a certain double dark line, which had already been found to correspond exactly in position with the double bright line forming the spectrum of the glowing vapour of sodium, was intensified when the light of the sun was allowed to pass through that vapour. This at once suggested the idea that the presence of this dark line (or rather, pair of linfia^ in the spectrum of the sun is due to the exist- ence of the vapour of sodium in the solar atmosphere, t ELEMENTS OF ASTRONOMY. 145 was and that this vapour has the power of ahsorhing the same order of light-waves as it emits. It would of course follow from this, that the other dark lines in the solar spectrnm are due to the presence of other absor- bent vapours in its atmosphere." — Other Worlds than Ours. 508. It is now found that besides sodium (first dis- covered), the sun's atmosphere contains the vapours of iron, magnesium, barium, copper, zinc, calcium, chro- mium, nickel, titanium, and probably gold, together with the non-metallic element hydrogen, which is largely present. As yet it has not been proved that gold, sil- ver, mercury, tin, lead, arsenic, antimony, or aluminium exist in the sun, though it by no means follows that these, and indeed all the sixty-five elements which are known to exist in our planet, are really absent. 509. Now, if the vapours of these metallic bodies exist in such marked quantity in the sOlar atmosphere, such vapours must arise from molten oceans of these substances covering the sun's surface. This will enable us to form some idea, however inadequate, of the intense heat characterizing the great central luminary. Indeed, it has been calculated that the heat thrown out by every square yard of the sun's surface is as great as that which would be produced by burning six tons of coals on it each ^lour. Now, the surface of the sun amounts to about 2 4,000,000,000 square miles, and there are 3,097,600 square yards in each square mile. Then, with regard to its brightness. Sir John Herschel has found that the sun's light exceeds in brilliancy the brightest light we can form, viz., the lime-light (pro- duced by a flame of oxygen and hydrogen playing on a ball of lime made intensely hot), at least 146 times. Now, as the earth is so far away from the sun, and is, moreover, so very small as compared with the sun's volume, it is clear that we receive but a very small portion of the total amount of light and heat which ho 116 ELEMENTS OF ASTIlONOMY. is constantly radiatin-. If wo suppose al the I gl t and heat which the sun discharges to be divided into 227 million parts, our earth only receives orie of them. 510 As to the transmission of light and heat from the sun to the earth and the other planetary worlds, two leading theories have prevailed. Sir I^'-^^^ NewV^J lield that the sun is constantly discharging from his surface inconceivable multitudes of extrenriely mmuto luminiferous particles of matter capable ot producmg, when they strike against bodies, the well-known pheno- mena of light and heat; but this theory, besides the improbability of a continual loss of substance without any diminution cf brilliancy, is not considered to expLam satisfactorily the phenomena of light and heat Tne opinion now most generally entertained is, that light and heat are to be attributed to vibrations or undulations in a thin fluid called ether diffused throughout space a lluid supposed to be excited by the presence of luminous and hot bodies into unduhiticms capable of causing impressions of light and heat on bodies which they meet that the sun causes these undulations in this ethereal fluid, which being propagated through space in waves, cause heat and light on the surface of the planets. The Planet Vulcan. 511 The existence of this planet is somewhat doubt- ful, mainly owing to conflicting evidence _ Its supposed discovery was made on 26th March 1859, by M. Les- cXultf a French physician, who o^-^-f^^^/^c dark object, like a planet, crossmg the sun s disc Having given publicity to his discovery, Lev^^"^;"'/^^^ ominent astronomer, hastened to the residence of M. I escarbault, whom he very closely interrogated retrard- ingTl the alleged facts. The result was that Leverrier l"i,... .pvfpr..tlv satisfied that an intra-Mercurialplanet ad beenVeally'observed. On the other hand, M. Liais ELEMENTS OF ASTRONOMY. 147 asserts that he was watching the sun in Brazil at the very time when Lescarbault professes to have seen the dark object crossing the sun's disc, and that he is per- fectly certain nothing of the kind was visible. Still, this is merely negative evidence, and it does not demon- strate the non-existence of the planet. On 20th March 1862, Mr Lummis, of Manchester, while examining the sun's disc, between the hours of eight and nine a.m., was struck by the appearance of a spot possessed of a rapid proper motion, and of circular form. After fol- lowing it for about twenty minutes, he was unfortu- nately called away to other duties ; but he has no doubt upon the subject. As the results of Mr Lunimis's observations, it is calculated thai Vulcan is 13,082,000 miles distant from the sun ; that his periodic time of revolution is 19-70 days; his velocity in orbit per hour, 174,000 miles ; and his polar diameter 785 miles. ■^,: The Planet Mercury, 5 512. With the exception of Vulcan, this is the nearest of all the planets to the sun, so fur as is yet known. His mean distance from the sun is about thirty-six millions of miles (35,649,000). His orbit is rather more elongated than is usual among the planets, his eccentricity (par. 393) being more than a fifth of his mean distance from the sun. He will thus be at one time 2-5ths of his mean solar distance nearer to the sun than at another. 513. Mercury is the smallest of the planets, excepting Vulcan and the asteroids. His diameter is a little less than 3000 miles — correctly, 2962 miles. Mercury rotates upon his axis in 24 hours, 5 minutes, and a few seconds. He completes his course round the sun in nearly 88 days — correctly, 87 days, 23 hours, 15 minutes; moving in his orbit at the amazing rate of 105,330 miles in an hour, or 29|^ miles per second. 148 ELEMF.NT8 OF ASTRONOMY. 614. The orbit of Mercury is inclined about seven dep^rees to that of the earth : that is, there is an anp^le of 7° at the intersection of the planes of their orbits (62). 515. This planet can be seen by the naked eye but very seldom, and only for a short time. Being so near to the sun, he is always in that part of the sky close around the sun, and his inferior light is lost amid the sun's rays. He nev.r departs above 29° from the sun, and when ho is visible, can only be seen for a httle before sunrise and a little after sunset. 516 Mercury occasionally passes directly between the earth andfiun; appearing then as a black spot traversing the sun s Burfaco. This is tcnned a transit of Mercury over the sunt iligc. 517. Mercury, as seen through a telescope, does not always appear of the same size and form. He has phases, like the moon, being sometimes horned like the new moon, sometimes full like the full moon. The cause of these changes is this:— We can see only that part which is illuniinated by the sun ; and as different ouniititios of thnt part are turned towards us succes- Bively, we see different amounts of the illuminated halt at ditferent times. 518. At Mercury, the sun will present a diameter about two and a half times greater than at the earth. And he will receive nearly seven times as much of the influence which, emanating from the sun, gives rise to the phenomena of heat and light. The Planet Venus, $ 519. This planet is the third in order from the sun— her orbit lying between those of Mercury and the earth. Her mean distance from the sun is a little less than sixty-seven millions of miles (66,614,000), Her dis- tance from the sun does not vary much, her eccen- +nr.;tv "hfMnP- onlv l-147th of her mean distance from tv h the sun. I ELEMENTS OF ASTRONOMY. 149 520. The polar diameter of Venus is about 7510 miles. »She is very little less than tiio earth, the polar diameter of the latter being only 389 miles more. Venus rotates upon her axis in 23 hours, 21 minutes; and completes her course round the sun in 224 days, 16 hours, and 49 minutes: — moving at the rate of 77,050 miles per hour. 521. The orbit of Venus is inclined about three de- grees, twenty-three minutes to the ecliptic (3° 23') : so that the plane of tlie earth's orbit and that of this planet are nearly coincident. 522. Venus is visible frequently. She is the most bcf'iutiful of the planets (whence her name), and, being near to us, she appears as bright and large as Jupiter, although that planet exceeds her very much in magni- tude. Venus is seen only about the times of sunriso and sunset ; but is visible for a mucli longer time before sunrise and after sunset than Mercury, departing much further from the sun than that planet can do, — namely, to a distance of forty-seven degrees (47°) from that luminary. When seen before fcunrise, Venus is well known as Phosphorus, Lucifer, or the morning star; when she appears after sunset, she is termed Hesperus, Vesi^er, or the evening star. 523. The transit of Venus over the ami's disc is a rare occurrence, for the same reasons assigned above for the rare occurrence of the transit of Mercury. The transit of Venus takes place alternately at intervals of 8, 122, 8, 105, 8, 122, etc. years. The last was in 1769, the next will be in 1874, and there will be another in 1882. — This phenomenon is of great use in practical astronomy: — it has been taken fmvantage of to aid us in determining exactly the sun's distance. 524. Venus exhibits phases, as Mercury and the moon do, and for similar reasons. She appears to us of very different degrees of magnitude and brilliancy ; being only 25,479,000 miles distant when nearest to us, and then receding till she is about six times that distance from the earth (see Fig. 61). ■i i m' 150 ELEMENTS OP A8TUONOMY. 525; At Venus, the dianieter of the sun appears about one third greater tlian at the eartli; anti liis anparent Burfaco dimensions, on which, of course, his heating and illuminating powers depend, are greater in the pro- portion of sixteen to nine. 526. The axis of this planet leans very much towards the plane of her orbit, forming with it an angle of only 15 degrees; that is, inclining 75 degrees from the per- pendicular. Her tropics are therefore ordy 15 degrees from her poles, and her polar circles only 15 degrees from her equator. This gives rise to some striking peculiarities in the constitution of Venus; namely, that there is much greater diversity of seasons than prevails on the earth,— that the days are much longer where it is summer, and much shorter where it is win- ter, — that a larger proportion of the regions about the poles have day or night for several rotations, — and that the middle or equatorial regions have two summers and two winters in each of her years. 527. This planet is believed to be surrounded by an atmosphere : and it has been conjectured that she may have a satellite, though that idea is now discredited. The Planet Earth [Tellus\ © 528. The next planet aftor Venus, in order from the sun, is that which we inhabit ; having its orbit situated between those of Venus and Mars. 529. The mean distance of the earth from the sun is about ninety-two millions of miles (92,093,000). Her eccentricity is about A, or 0-0167918. The least dis- tance of the earth from the sun is about ninety and a half millions (90,562,000) miles ; the greatest distance about ninety-three and a half millions (93,624,00 ) miles. The earth is in its aphelion on the 1st of July ; in its perihelion on the 31st of December. The sun, therefore, appears larger on December 31 than on July 1 , in the proportion of 32 J to 31 4. ELEMENTS UF A8TUONOMY. 151 fiSO. If tho mean dintancc of the cnrth from the mm bu 1-00000, iu diHtauco on July I is 101679; on December 31, 0*98321. 631. Tho mean diamoter of tho earth is 7912 niileg; tho shorter or palar diameter is 7899 miles ; the longer or e-j-'alorial diameter, 7925 miles. Tho diflference betw( n the polar and equiitorial diameters is therefore 26 miles. The ecjuator, or circtimference of tho earth at the widest part, is 2 1,907 miles in len^Hh,*— ahoiit 2,'),000 miles. A degree of longitudo at the equator is 305,144 feet, or 09 British miles and 824 feet. 632. Tho earth's surface is marked by lines in tho same manner as the spliero of the heavens. — See Parallels, Meridians, Latitude, Longitude, in the Urtii section of Part III. 633. From the Bphcroidal form of the earth, tho (IcgrecB of Irttitude arc not all of tho Raino maKnitiulo, hut incnsaMe from tho cnuator towardfl either pole. Tho following table ahows tho Icnpjth at every 30° of latitude : — Latitude. 0° (Kquator^ . . * i 80^ GO" 90° (Poles) .... Degrees of longitude, of course, graduall. greatest, at the equator, to nothing at the poles. The following tibles represent the length of a degree of longitude at every b" latitude, and at four leading latitudes :— iv ( LenRth of degree in JlnKllHli ttt't. 302,734 . 3(i3,»;4l 365,454 . 306,361 [liminish from their Liitittiilo. 0" h" 10" 15° 20» 25° 80° 35" 4u° 45° £n,{liHh miles. Latitude. 69-07 68-81 67-95 60-65 64-84 6253 59-75 6651 52-81 48-78 50° 55° 60° 65° 70° 75° 80° 85° 90° English miles. . 44-35 39-58 . 34-53 2915 . 23-60 17-86 . 11-98 6-00 . ' 'I'lic circumference of a circle Is obtained by multii»lyinj,' its diameter byJUioi). ^ I.V2 ELEMKNTS OP ASTRONOMY. 2.1" 28' (Cancer) nearly 63 miltm. 6r32'(Lotul..n) — 43 ^ 55'57'(K.lmburgli) . . . . — 8H§ -- 66" 32' (Arctic Circle) . . . . — 28 — 534. Tho enrth turiiH upon Uh axis in 23 hotirH, 50 minutoB, 4'09 Hoconds. This Ih a truo or tidere&l day (300). 535, Tho equatorial parts of tho oarth'Hclrcumferonco rorolve ftt the rate of 17'3 milcH per mimite, or 1038 miles an hour. 586. Tlio interval between two successive apj/ulses of tho 8itn to the meridian of a place is termed a lolar day; that is, the time from the sun being on the meridian of a place till tho earth's rotation brings it round again to the sun. 537. The earth completes her revolution round tho sun in 3(15 days, 5 hours, 48 minutes, 49*7 seconds; which period is termed a tropical year. The earth's orbit is 578,000,000 miles in length; and her daily motion in her orbit 1,572,892 miles, or 65,533 miles an hour ; that is, at the mean rate of 18^ miles in a sec- ond, or 1092 miles every minute. 638. The auhrcal year (see Procession of tho Equinoxes) is longer than tlie tropical year by 20 minutes, 199 seconds ; being 805 days, G hours, 9 minutes, 9't) seconds. 5^9. The mean diameter of the sun, as seen from-^the ea*th, is about half a degree, or thirty-two minutes (82'). Its apparent diameter on the Ist of July, when furthest from us, is 31' 32" —on the 31st Decemb r, when nearest to us, 32' 36". 640. That is, supposing a great circle of the heavens to bo divided into 360 equal parts, the sun's diameter would be equal in length to one-half of one of these parts or degrees. 641. The mean daily motion of the earth is 59' 8"33"; mo- tion on 31st December, 1° 1' 9'9"; on Ist July, 57' 11*5". Tho mean velocity being I'OOOOO, the velocity on 3l8t December Is 1'03386; on Ist July, 0-96671. 542. The axis of tho earth is considerably inclined to the plane of its orbit. It makes an angle of 66° 32' 36" with the ecliptic, thus leaning 23° 27' 24" from the pcfpcudiculuf to tiiC orbit. IIcncG arise the ebangcs ■LBMENTS or ASTRONOMY. 153 in tho seasons und in tho longth of tho day. — SetSea- sons. 643. ITenco, tho trnpien, roprpm-ntlnpf tho furtho«t north «in«l Bnuth parnlloU nt which the «un i« vcrticnl, an^ 2W- 1' 24" fr«)m h«r eqimtor; and her arctic circlet, the paralloU within which tho dun doe* not net or risu for r rX rotationn, are 23" 27' 24" from her \w\ca. Tho extent of I .o inclination nmy Iks ■een in Vig. 10, pnge 20. L at least five and a half times that of distilled watCi ,.1 the temperature of 68° Fahr. The famous Schehallitii experiment, conducted by Maskelyne in I'l 74, indicated a density of only 4-713. By certahi pendulum experi- ments, conducted on Alont Cenis by Carlini, at a mnch later date, the mean density is 4950. In 1793. the celebrated Mr Henry Cavendish, by an ingeniously executed experiment, arrived at a result of 5 "480. More recently, the late F. Daily carefully repeated the Cavendish experiment with consummate skill and patience, and obtained as his result 5-GGO. The present Astronomc-Royal (Mr Airy) has also con- ducted au elaborate pendulum experiment, m the g2 154 ELEMENTS OF ASTRONOMY. Ilarton coal-pit, near South Shields, by which he estimates the density of the earth as 6 "565, a result which we have no doubt the progress of science will show to be greatly too large. The accomplished author of " Life and Work at the Great Pyramid in 1865," conclusively shows that the architect of that stupendous structure kn3w the specific gravity of our planet upwards of 4000 years ago, and gave it as 5*7 times that of pure water at 68° Fahr.* Seeing that all the other ph) sical revelations treasured up in that pro- foundly mysterious pile have been found to be in exact harmony with the latest results of modern science, we entertain very little doubt that tlie specific gravity which it assigns to the earth will be found altogether reliable. The immortal Newton predicted, some two hundred years ago, that the density of the earth would be found to lie between five and six times that of water. 546 Experiment shows that the f^ ace of gravity at the earth's surface causes a body to fall 16-rV f«et in the first second, three times that amount in the next second^ Jive times 16t*t in the third second, etc. The force of gravity at the earth's equator is diminished about l-289th by centrifugal force: from this cause alono, therefore, a body will weigh 1 -289th less than at the poles. From the spheroidal form of the earth, the force of gravity is l-590th less at tbe equator than at the poles. The total difference in cbe force of gravity at the poles and equator is equal to the sum of these quantities, or 1-1 94th, for ^i^ and -^io make ^K- Accordingly, a body which weighs any given quantity at the poles, as indicated by a spring balance, m.ust be increased in weight by 1- 194th ^jart, to produce the same effect on the spring at the equator.-j- • See Life and Work at the Great Pyramid in 1866, by C. Piazzi Smyth.. Astronomer-Royal for Scotland (Edinburgh, Edmonston and Douglas). t The increase of the force of gravity from the equator towaicds either polo is in the proportion of the sq-iare oj the suie of the latitude'. I I ELEMENTS OP ASTRONOMY. 155 I 647. The earth is found, in every part where it has vet been tried, to become sensibly and regularly warmer in propm-tion as the distance below the surface is greater — the temperature increasing about one degree Fahrenheit for every de-cent of 55 o^fnAo i^a'culating at this rate of increase, a temperature of J400 l-ahr. would be reached at a depth of twenty-five miles sufficient to keep in fusion such rocks as basalt, greenstone, and r''S7.7 ' at a depth of thirty-six miles, the temperature would be 3272 sufficient to melt iron ; and at a depth of fifty-four miles, a heat of 4892° would prevail— a temperature at which ail known substances would pass into the liquid or molten form 1 he phenomena of hot springs, volcanoes, and earthquakes! attord other and independent evidence of the intense heat pre- vailing m the interior of our planet, t rom an apparent coiiicU dence between the positions of the moon in relation to the earth and the penods at which many earthquakes have occurred, it has been conjectured by M. Perrey of Dijon, that earthquakes may be caused by the attraction exercised b^ the moon on the fluid mass m the interior of the earth. The Moon (Luna), j 548. The moon is a satellite or secondary planet to the earth, round which it revolves, and with which it is carried annually round the sun. 549. The mean distance of the moon from the earth is about two hundred and forty thousand miles (238,793) or 60-2734 times ^ le equatorial radius of the earth! Her distance from he earth does not varv much. Her eccentricity is about l-20th of her mean" distance from the earth, or about 13,000 miles. ^v^^^v'^'^^® ®*'*^'^ ^'" appear at the moon about 13 times larger than the moon does to the earth, and supply that satellite with a proportionately more brilliant light than she affords to us. 551. The diameter of the moon is 2158 miles, a little more than l-4th of that of the earth. The bulk of the moon is about ^^Vth of „hat of our earth, or as -02012 to 1 : her mass is about ^V (-0125) of tha of the earth • her density 0-6'', that of the earth being 1. ' 552. The moon performs her revolution round the earth in 29 days, 12 hours, 44 mmutes. This is the :i 156 ELEMENTS OF ASTRONOMY. period from one new moon to the next, — from the time of the moon being in conjunction with the sun till she comet to the the same position again, — and it is termed a lunar month, a si/nodical month, or her si/nodical revolution. She moves in her orbit at the rate of 2-3d8 of a mile each second, 37*9 miles in a minute, or 2277 miles per hour. 553. The period of the moon's rotation on her axis is the same as that of her revolution round the earth (see 554) ; and this is the reason why she always pre- sents the same side to the earth. And that side is never totally dark, having one fortnight of sunlight, and being illuminated by the earth the other fortnight. The other side has alternately a fortnight of sunlight and a fortnight of darkness. So far as yet ascertained, all the other satellites belonging to our system follow the same law — that is, they rotate on their axes in the same time as they revolve i: round their primaries. 554. Viewed, not with respect to the sun, but to the stars, the moon is found to return to the same star in 27 days, 7 hours, 43 minutes. This is termed a sidereal or periodical month; and is the true period of the moon's revolution round the earth and on her axis. 555. The plane of the moon's orbit forms an angle of 5° 8' 40'' with the plane of the earth's orbit ; so that the two orbits are not very far from being in the same plane. The moon's axis scarcely 1 ans towards the earth's orbit, forming an angle of 88° 30' with the plane of the ecliptic, — or leaning only 1° 30' to the ecliptic. Being so nearly perpendicular to the plaae of the ecliptic— the path in which the moon moves round the sun — the moon can have little or no change in her seasons, or in the length of her day. 556. When the moon is viewed by a telescope, its surface appears irregularly illuminated, with dark and bright parts, now considered to be mountains and valleys; the former very high in proportion to the ELEMENTS OP ASTRONOMY. 157 I magnitude of the moon, some being about five mile . in height above the general level of the moon's suriace. These mountains have much of a volcanic aspect, with craters of great breadth — some upwards of 100 miles. It was at one time supposed that the darker spots were seas or lakes ; but it is now believed that there is no water on the surface of thj moon. These mountains have been measured, as to altitude, and names have been assigned to them, taken from the names of cele- brated astronomers and other philosophers: as Plato, Tycho, Newton, Flamsteed, Herschel, Huyghens. There is no appearance of clouds, or any indications of an atmosphere on the moon. When the moon presents less than her full enlightened surface to us, the edge next the sun, which is fully illuminated, appears smooth and rounded, while the other appears rough and broken — probably from the hills being enlightened by the sun's rays, while the low grounds are dark. The same side is always turned towards us ; but from her motion in her orbit not being uniform, we sometimes see a little of her surface beyond that half on each- side; and, from her axis being inclined to the plane of her orbit, we see at times a little beyond her poles. ^ These shift- ings of the face next us are termed llbrations. The Planet Mars, ^ 557. Mars is the next planet beycmd the eaith, the orbit of this planet lying between those of the earth and Flora, or that Minor Planet which is nearest the sun. It is the first of the superior planets. 558. The mean distance of Mars from the sun is one hundred and forty millions three hundred thousand miles (140,322,000). His distance from the sun varies con-^ siderably ; his eccentricity is a little less than 1-lOth of }i\a TYic.Q.n flistance from that luminary. 559. The diameter of the sun, seen from Mars, is to m I J-- 1 573. Their eccentricities are consideruLle, and they are remarkable for the great angle which the planes of their orbits form with the ecliptic, the inclinations being as follows -.—Vesta, 7° T 50" ; Juno, 13° V 9"; Ceres, 10° 36'; Ilebe, 14° 47'; Pallas, 34° 4.Y. See Fig. 52, in which their great departure from tiie plane of the ecliptic is shown. From their orbits being so much out of the plane of the ecliptic they are seldom seen in the zodiac, being generally above or below it, while all the other planets constantly appear in that zone of the heavens. Hence, these planets are sometimes termed ultra- zodiacal^ i.e.j out of or beyond the zodiac. 574. The asteroids present several peculiarities, in •which they differ considerably from the other planets. They are extremely small, while, generally speaking, the planets rather increase in size as they are more distant from the sun. They are comparatively near to each other, whereas a very diflferent law prevails with respect to the other planets. The distance between two planets increaics in a very high proportion as they are further from the sun, as follows : — Mercury, 36 ; Venus, 67; Earth, 92; Mars, 140; Asteroids, 259; Jupit'jr, 479; Saturn, 878; Uranus, 1766; Neptune, 2766. Also, their orbits are very far out of the plane of the ecliptic, whereas the orbits of the other planets are nearly coincident with that plane. The orbits of Venus, Mars, Jupiter, Saturn, Uranus, form angles with the plane of the ecliptic of from 3° 23' to 0° 46', and Mercury of 7° ; but the angles which several of the asteroids form with that plane are 5°, 7°, 10°, 13°, 14°, and 34°.— See Fig. 52. 575. The following singular relation has been observed regard- ing the distances of the planets, and it led to the conjecture of the existence of another planet between Mars and Jupiter, before the discovery of the asteroids. If the numbers 0, 3, 6, V?.. 24, 48, 96, 192, be taken, and the number 4 added to each, the sum will express the proportionate distances of th© planets in order from the sun : ».e ELEMENTS OP ASTRONOMY. 1C3 8 6 18 24 48 98 192 + = 4, Distance of Mercury = 7, •(• > enuM, = 10, ••• Earth. = 16, ••• Mars. = 28, ••1 = 62, ••t Jupiter. = 100, ••« Huturn. added afterward »t 4 = 196, • • • Uranus. A void being observed between the numbers 10 and 52, Pro- fessor Hodo conjectured that a planet filling up the vacant number might exist, which was confirmed by the discovery of the asteroids, in the situation in the solar system indicated by the vacant place. This law has failed, however, in the case of Neptune. 576. Those peculiarities led to the singular conjecture, that these planets originally formed one planet ; that that planet has been ruptured by some great convulsion, which has divided the one into a number of separate parts, and thrown the fragments out of the former orbit into orbits deviating considerably from the general order. But this is a mere speculation at present, though strengthened by the ascertained intersection of many of their orbits ; as, if a planet were so ruptured, the fragments would return periodically to the spot where the explosion had taken place. The Planet Jupiter, 7f 577. Jupiter is the next planet beyond the asteroids, his orbit lying between them and Saturn. He is the largest of the planets, and, though so remote from the earth, owing to his great magnitude often appears as bright and large as Venus. 578. The mean distance of Jupiter from the sun is about four hundred and seventy-nine millions of miles (479,141,098). His distance from the sun does not vary much, his eccentricity being less than l-20th of his mean distance. 579. The sun's diameter as seen from Jupiter is only l-5th of its apparent magnitude at the earth. — cor- rectly, as 6 to 32. The relative proportion of the sun's influence at Jupiter and at the earth is as 1 to 27^ (as 1C4 ELEMENTS OP A8TR0N0MV. 1 92' : 479^). Gravity at Ins surface is about 2 J timci. as great as on our earth's; bo that such creatures as exist around us would find their weight much more than doubled if they were removed to Jupiter. 580. The diameter of Jupiter is eighty-eight thousand miles (88,400), more than eleven times that of the earth. This is the equatorial diameter. Ho is about 1387 times larger than the earth. The polar or shorter diameter of Jupiter is about l-18th, or 5000 miles, less than tho equatorial diameter ; or, as 83 to 88. Tho great differ- ence between the polar and equatorial diameters of this planet is attributed to the very great centrifugal force generated by his rapid rotation on his axis. When viewed through a telescope, Jupiter appears of a dis- tinctly oval shape, from the extreme polar flattening. 581. Jupiter turns on his axis in a little less than 10 hours, — correctly, 9 hours, 55 minutes, 28 seconds. His equatorial parts, therefore, revolve at the amazing rate of 7*5 miles in a second, or 453 miles per minute. 582. Jupiter completes his revolution round the sun in 4332 J days, nearly 12 of our years (more correctly, 11 years 314 days) : — moving in his orbit at tlie rate of 8 miles in a second, 480 miles in a minute, or 28,744 miles per hour. 583. The planes of tlie orbits of Jupiter and the earth are nearly coincident, the angle between them being only 1° 18' 61". 584. The axis of Jupiter does not lean more than 3° 4' towards the plane of its orbit, being nearly perpen- dicular to that plane. From this, Jupiter can have little or no variety in his seasons, and little or no change in the length of the day. This planet, there- fore, will have a perpetual winter around his poles, and continual summer in his equatorial regions; and the weather c mparatively uniform. 585. The density or specific gravity of Jupiter, in common with all the remoter orbs of our sysLem, is Ij timcb tares m ch more bousand le cnrth. 87 times liameter ban tho it (liffcr- '8 of tbis ;al force When f a dis- ening. than 10 seconds, imazing minute, the sun orrectly, the rate r 28,744 earth are °18'61". )re than perpen- an have e or no t, there - )les, and and the piter, in ^sLem, is ILBMENTS OF ASTRONOMY. 16! I very small as compared with the density of tlio oarth, and of all tho planets revolving inside of Jupiter's orbit. Thus, regarding tho density of our planet as unity, and that of Mercury, Venus, and Mars as respectively 1-24, '92, and -96, wo find the density of Jupiter as only -22, of Saturn -12, of Uranus -18, and of Neptune •17. Be it now remembered that the density of tho sun is '25, or a very little more than the density of Jupiter. Wo cannot regard this vast difference of density be- tween tho superior and inferior members of the solar system as arising from any great diflerenco in tho nature of their constituent materials, for tho spectro- scope has conclusively shown that all the members of the system are in this respect identical with the great central orb. In all probability tho cause of the great difference will be found, not in their constituents, but in their condition with respect to their internal heat. Doubtless all tho planets had at one time the same temperature as tho sun, and were real stars, shining with intrinsic splendour. In the course of ages the smaller planets have gradually cooled down, lost their luminosity, but increased in density. The existence of volcanoes, boiling springs, and increase of temperature as we descend beneath the surface, afford ample evi- dence that the only member of the solar system which we can fully examine, once possessed a much higher temperature than now ; while there appears no reason why the other worlds, which in other respects so closely resemble it, should not resemble it in this also. Jupiter and the other more distant planets have, in like man- ner, cooled down, but owing to their vastly greater dimensions the progress has been much less rapid, and accordingly their density continues pretty closely to correspond with that of the great central orb. They have not wholly lost their luminosity even, for Jupiter and Saturn exhibit several phenomena which can be accounted for only on the supposition that they are still I 4 IGG EI.EMKNTS OF A8TR0NOMV. faintly flowing* The larper plnnots, therefore, of ur syBtem cannot, by r. 'ly poHHibility, Im) inhabited hy • v- inpf creatiircH, thoiigi it seems not unlikely that t' SAtcllites may. Satellites of Jupiter. 586. This planet is attended by four BatellitcH or moons, named, respectively, To, Europa, (lanymedo, and (.allisto. These cannot bo scon by the naked eye, and hence they were not known till after the invention of the telescope. In IGIO, within a very siiort timo after the discovery of tiiis powerful instrument of as- tronomical observation, the satellites of Jupiter were discovered by Oalileo. 587. The distance wom Jupiter of luH noaroHt Batclllte is 267 .UUO miles ; its diameter is 2252 miles ; and it revolves round its primary planet in 1 day, 18 hours. 27 minutes. The distance from the planet of t' e next satellite is 42.''»,000 miles; its diameter is 2099 miles; audi', co npletes its revolution round Jupiter in .3 days, 13 hours, 14 minutes. Jupiter's third satel- lite is at a distance of 678,000 miles ; its diameter is 3436 miles ; and it revolves round Jupiter in 7 ''"y." 3 hours, and 43 minutes. TliJ fourth and most remote of oupiter's satellites is distant from him 1,192,000 miles;— its diameter is 2929 miles;— and it occupies 16 days, 16 hours, 32 minutes in its revolution round Jupiter. The satellites of this nhinet are rather larger in gene- ral than our moon. 588. Jupiter's satellites re\olveroun«i him /rom west to east, as the moon does rcund the earth, and the planets round the sun. Tho pi^ruds of rotation on their axis are the same as their })criod8 of revolution round taeir primary planet ;— obeying, in this respect, the same law as our satellite, the il on. 589. When the body of Jupiter interposes between * " We are Unis led to the conclusion that Jupiter Ih still a glowing mass fluid probably tlironghout, still bubblinf? and Heething with the intensity of the primeval tiros, sending up continually enormous inaases of cloud to be gathered Into bands under the influence of tlit< swift rotntiuu giant planet."— Cy the attrac- tion of the planet." * * Lockycr's Elementary Lessons in Astronomy, p. 117. ELEMENTS OP ASTRONOMY. 171 Satellites of Saturn. ^ 603. This planet is accompanied by no less than eight satellites. "" \e six which aro nearest to the planet have their orbits nearly in the same plane as the ring. The satellites of Saturn are supposed to revolve on their axes in the same periods in which they com- plete their revolutions round the planet: which has been ascertained of the eighth. They are believed to vary in size from 500 to 3300 miles in diameter. "The eight satellites, taken in their order from the planet, cover spaces on the Saturnian heavens which bear to the space covered by our moon the resr>ertive proportions of 2, 1, U, f, |, I ^i^, ^^^. In all, then, they cover an area about six limes that of our moon. But as, owing to their great distance from the sun, they are illumined by only t^^ c^ the light which illuminates our moon, they can only send back to the planet about rVth part of the light we receive from the full moon, even if it were possible for them tc ')e all full at once." — Other Worlds than Ours. 604. The first satellite is at a distance of about 120,000 miles from Saturn, and revolves round it in 22 hours, 37 min- utes : — the spcond is about 155,000 iniles from the planet, and completes its revrolution in 1 day, 8 hours, 52 minutes :— the third is about 191,000 miles frv,m Saturn, and Its period is 1 day, 21 hours, 18 minutes: — the distance of the fourth is about 246,000 miles ; its period 2 dp ys, 17 hours, 41 minutes .-—the jftfth is about 343,000 miles from Saturn, and revolves round him in 4 days, 12 hours, 25 minute's: — the sixth is about 796,000 miles from the planet, and resolves round him in 15 days. 22 hours, 41 minutes : — the di"* mce of the seventh is about 1,007,000 miles, and its "^nou 21 days, 7 hours - :he eighth is about 2,314,000 mile^ , ,ai Saturn; and its period, 79 days, 7 hours, 55 m'nutes. 605. The satelUtes of Saturn were discovered by Huyghens, Cassini, Herschel, Lassel, and Bond;— one by Huyghens in 1 655,— four by Cassini m , 6V1 and subsequent years, — two by Sir W. Herschel m 1 <"89, — and one (the seventh) in 1848, on the same day, by Lassel in Liverpool, and Bond in Cambridge, United States. The satellites of Saturn have received the names Mimas, Enoeladus, Tethys, Dione, Rhea, Titan, Hyperion, -Japetus. „i I 172 ii.i: ELEMENTS OF ASTRONOMY. The Planet Uranus, I^I 606. Though Uranus is of considerable magnitude, it is rarely and with difficulty seen by the naked eye, owing to its great distance. This planet was discovered by the celebrated astronomer Sir William Herschel, on the 13th of March 1781. It was called by him "Georgium Sidus," in honour of George III., and by some astronomers, "Herschel," in honour of the dis- coverer. The name Uranus, however, from one of the characters in the ancient mythology, is preferred, as being more in harmony with the appellations of the other planets. 607. The mean distance of Uranus from the sun is seventeen hundred and sixty-six millions of miles (1,766,565,000), a little more than IS times the dis- tance of the earth from the sun. The listance of Uranus from the sun does not vary much, Ins eccen- tricity being less than l-20th of his mean distance. 608. The sun's diameter appears at Uranus of l-19th his apparent magnitude at the earth, or as If to 32 : and the proportion of the sun's influence enjoyed by this planet is only l-368th ot that experienced at the earth: as 92^ to*J766^ 609. The polar diameter of this planet is 29,722 miles; his equatorial diameter, 33,024 miles; his volume, 72 times that of the earth ; but his density is so small (-18) that his weig^st or mass is only 12-64: times that of our planet, and the force of gravity at his surface only ^'^tb greater f.han at the earth's. 610. Uranus completes his revolution round the sun in 30,686 days, about 84 years ; — moving in his orbit at the rate of 4 miles in a second, or 14,963 miles per hour. 611. The plane of the orbit of Uranus is more nearly coinci- dent with that of the ecliptic than in the case of any other planet, the angle between them being only 0° 46' 28*4". The inclination of the planet's equator to the plane of his orbit is ELEMENTS OF ASTRONOMY. 173 believed to bo ftljout 7G°. From this, it follows that tli'i Uranian sun, which has an ajjparent magnitude of only i,4flth part his size as seen from the earth, has a range of about 70° on either side of the celestial equator, and that he will continue 23j of our years above the horizon, while in winter ho will continue for the same period of time under the horizon. These facts have a most important bearing on the question of the habita- bility of the planet. It seems certain that none of the animals or plants with which we are acquainted could possibly live either on Uran-is or Neptune. Indeed, it is far more probable that, like Jupiter and iSaturn, these planets perform the part of suns to the systems of satellites which respectively revolve around them, aflbrding to the latter a large amount of heat, to- gether with, possibly, an appreciable amount of light also (585). Satellites of Uranus. 612. This planet is known to be attended by at least four satellites, known as Ariel, Umbriel, Titania, and Oberon. The latter two were discovered by Sir W. Herschel in 1787. Umbriel was discovered by Otto Struve in 1S47, and Ariel in the same year by Lassel of Liverpool, Ariel, the nearest to the planet, IS 123,000 miles distant; Umbriel, 171,000; Titania, 281,000; and Oberon, 376,000 miles. The first revolves round his primary in .' days 12 hours, and the last in 18 days 11 hours. Hitherto their magnitudes have not been determined. 613. These satellites present some remarkable pecu- liarities and departures from the usual order in the solar system. The planes of their orbits are nearly perpen- dicular to the plane of Uranus's orbit, forming an angle of 78° 58' with the plane of the ecliptic (which is nearly the plane of Uranus's orbit) ; and they do not move in the same direction which prevails everywhere else in the solar system, viz., from west to east; but in a retro- grade direction, 2.e., from east to west. The Planet Neptune, 614. This recently-discovered planet is the most distant member of the planetary system, so far as we know at present. Neptune is a planet of considerable magnitude, being 36,620 miles in diameter; and he revolves round the sun in about 164*6 years (60126'7 174 ELEMENTS OP ASTRONOMY. days), at a mean distance of 2766 millions of miles. Tlic incliii'ition of his orbit to the ecliptic is V 47'; and one satellite has been observed near him, which revolves round him in 5^- 21"™-, at a distance of about 220,000 miles. It is probable, however, from the analogy of Jupiter, Saturn, and Uranus, that he has a greater number of moons attendant upon him. G15. Neptune was discovered in an interesting and very remarkable manner. In the year 1846, his exist- ence and position were predicted simultaneously by two astronomers, M. Leverrier of Paris, and Mr Adams of Cambridge. On the 23d of September in that year, "a day," says Sir John Herschel, " for ever memorable in the annals of Astronomy," Dr Galle, of the Royal Observatory at Berlin, received a letter from M. Leverrier, requesting him to look for the predicted planet about the place in which he had calculated it should be found. Dr Galle did so on that very night, and found the new planet within one degree of the place assigned to it by M. Leverrier. Next night it was found to have moved from its place, and repeated subsequent observations have fully confirmed the exist- ence of this new planet, and enabled its orbit, period, and distance to be laid down correctly. 616. As already mentioned, the mutual actions of the planets on each other cause disturbances in their movements ; that is, deviations from the course which each would pursue if influenced only by the sun's attractive force and its own projectile energy. As might be expected, these disturbing forces produce consider- able effects among the more remote planets where the sun's in- fluence is comparatively weak. Soon after the discoverer of Uranus in 1781, it was found, on searching the astronomical records, that he had been seen often by previous astronomers, once so far back as 1 690, though not even conjectured to be a planet. But it was observed, on calculating what his position should have been at former times, to judge from the ascertained elements of his orbit, that, making every allowance for disturb- ances by known planets, the recorded positions were far from coinciding with those assigned by computation. Moreover, his actual course after discovery did not coincide with the theory ELEMENTS OP ASTRONOMY. 175 deduced fiom tho elomcnta of his orliit as found by the first ob- nervations. Up to 1830-1, his real position was continually in advance of his computed position; about that time they corre- sponded, subsequently he fell behind his calculated positions. The true cause, the disturbing influence of a more remote planet, h.'xd been conjectured by several astronomers. Simultaneously, Leverrier and Adams, from the observed deviations, deduced the mass of the previously unknown disturbing body ; and assigned its position within 3° of each other's calculations. I i 17G ELEMENTS OP ASTUONOMV, General Illustrations of the Solar System. Havinpf now concluded m account of the pInnetH in detail, wo Bhall endeavour to illuHtrato tJioin as parts of one great PVHtom, and give some idoa of thoir relative niagnitudcH, diH- tance«, etc. 617. "Chooflo any well-levelled field or bowling-grncn. On it place a globe, two feet in diameter; tliis will represent the Bun; Mercury will be represented by a grain of mustard seed, on tbo circumference of a circle 1(51 feet in diameter for its orbi* ; Venus, a pea, on a circle 284 fe(!t in diameter ; the Earth, also a pea on a circle of 430 feet; Mars, a rather large pin's head, on a circle of <)5t feet; Jjino, Ceres, Vesta, and I^illas. grains of sand, in orbits of from 1000 to 1200 feet ; Jupiter, a moderate-sized orange, in a circle nearly half a mile across ; Saturn, a small ()rangc, on a circle of four-fifths of a njile ; Uranus, a full-sized cherry, or small j)lum, upon the circum- ference of a circle more than a mile and a half; and Neptune, a good-sized plum, on a circle about two miles and a half in diameter. As to getting correct notions on this subject by drawing circles on paper, or, still worse, from those very childish toys called orreries, it is out of the question. To imitate the motions of tlu! jilnriets, in the above-mentioned orbits. Mercury must de 'M'ibo its own diameter in 41 seconds; Venus, in 4'"14»-; :he Karth, in 7 minutes ; Mars, in 4'"- 4S''- ; Jupiter, in 2^- SG-"-; Saturn, in S^- la-"-; Uranus, in 2^- IG'"-; and Nep- tune, in Sh- .3U'n- "Sir John Ilc.rfichel. To this it may be added, that owing to the inclinations of their orbits to the plane of the ecliptic, the objects representing the planets, in the above illustration, ought to be some a little above, some a little below the level of the ground, and some just on it, or with one half above, the other half below the surface of the ground— the planet being then in its nodes. The greatest elevations above or deptha below the f/round attained in the above example would be, 10 feet for Mercury ; 8 feet for Venus; 10 feet for Mars; 128 feet for Hebe (14" 47'); 284 feet for Pallas (34° 37') ; 23 feet for Jupiter ; 87 feet for Saturn ; 52 feet for Uranus; and 183 feet for Neptune. Thus, all the planets, excepting Juno, Hebe, and Pallas, would circulate near the level of the ground; 87 and 183 feet, the greatest distances of Saturn and Neptune from the level of the ground, being little in comparison with their distances from the sun — two-fifths of a mile, and a mile and a quarter. 618. The following woodcut (Fig. 52) will give an idea of several important particulars regarding the planets. The white line at the right (looking at the figure in the way in which the book is held for reading) is intended to represent the sun's radius ELEMENTS OF ASTRONOMY. 177 nilc ; or «emi(1i*nnictor ; nnd the fif^iirofi next it, roprcBent tlio mftgni- tudcs of the planets, in proper pruportinn to tlio bum'k sciiii- Fi'. .-. I 1. I diameter and to each other, in the tbllowinoj order: Saturn, Jupiter, Uranus, the Earth, Venus, Mars, Mercury, Neptune, with their signs. The circular outlines in the middle of th'/ H '^ ^^: 178 BLEUENTa OF ASTRONOMY. fijruro n-prt'scmt tlic reliitivo magnitude* of tlio cnrtli nnd tTHt<»n. The lin.!H luul charurtcrH at tho lefi «ii. ni. • •• ... I7,6aj 25 7 48 ... 18,0fl2,00O 1970 174,000 ... •» t 85,649,000 87ii7 105,3;JO 1 5 6m] 6fl,614,0(Xt 22470 77,050 23 21 1932 t)2,093,(X)(» 305-25 65,633 1 I'OOO 140,322,0()0 686 9H 63,000 1 •' 37 •436 259,00<),(X)0 1,884-7 1 39,882 ... •130 479,141,098 i,33•i■(i^^ 28,744 9 65 •030 878,461,000 10,759-30 21,221 10 2U •on 1,766,565,000 30,686-82 14,96.1 9 30 •003 2,766,133,000 60,126-71 11,958 ... -001 No. of Mooni, 1 4 8 4 1 Name of Iludy, SUW Vulc^vn Mercury Venus Earth Mars The Asteroids Jupiter Saturn Uranus Neptune Moon 852,38(1 785? 2,902 7,510 7,809 4,030 670' 83,151 64,714 29,722 36,620 2,ir)S 862,584 786 y 2,9G2 7,510 7,925 4,920 670' 88,400 71,904 33,024 .W.fi'JO Volume or tizc. Earth = 1. Mau or Welghl, Eartb = 1. I 1,245,130 000 •052 •861 1-000 •139 1,387-431 746-898 72-369 98-664 •021 314,760000 •070 •790 l-OOO •120 300-860 90-030 ] 2-640 16-760 -01:( ^fell I u •25 1-24 -92 1-00 -9(i •12 •18 •17 •6.'! t 27- 2 1-15 -91 1-00 •60 245 1-09 1-05 1-20 •17 Inclina- tion of Plain't'i Kqiiator to |ilnn« of Uibil. 0° O'O* 49 58 23 27 24 28 61 3 4 26 49 C 76 26? C Pallas, the largest of them. IMAGE EVALUATION TEST TARGET (MT-3) /. // / /. ^ ^ 1.0 I.I 1.25 ItilM |2.5 ui liil 2.0 1.4 1.6 V] ■% v^*.^ '%.^ ""^ J*" '^ HiotDgraphic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 :« .^fc* ^ c.^ ^ k ^ 130 ELEMENTS OP ASTRONOMY. Comets. 620. The comets are those stars which appear at times in various parts of the heavens, describing an apparently irregular course when compared with the plan- ets ; approaching very near to the sun, and again reced- ing to a great distance from him and disappearing. 621. Comets appear under very various aspects. Usually, there is a brilliant luminous point called the nu- cleus ; and a more diffuse light surrounding the nucleus, called the coma or hair. These two constitute the head; and there is oiten present, thor.gh not always, a long luminous appendage, called the tail. The tail is generally turned in a direction from the sun : and frequently is bifurcated, that is, divides into two branches, sometimes into more. Occasionally it is bent into a gentle curve. Some conicts have several tails, that is, streams of light diverging from them ; and many small comets are without any such appendage. _ 622. The comets are considered to be masses of highly-heated, self-luminous vaporous matter, or solid nuclei surrounded by much gaseous matter, revolving round the sun in very elongated ellipses, so that at one time they are very near the earth and sun, and at an- other time very remote from these orbs. But the exist- ence of a solid nucleus is by no means established. 623. The tails of the comets vary considerably in magnitude. The tail is often scarcely perceptible at first, enlarges as the comet approaches to the sun, is most developed just after it has passed its perihelion ; and gradually diminishes as the distance from the sun increases, and the influence of that body lessens. The tails of some comets have been estimated at upwards of 100 millions of miles in length— that of the comet of 1843 at^ 200 millions of miles. Some have had the extremities of their tails in the zenith, while they them- selves were in the horizon. From the above phenomena, ELEMENTS OP ASTRONOMY. 181 it has been conjectured that the tail of a comet is formed of matter ejected from its body by the sun's heat. 624. The comets revolve in extremely eccentric orbits. The groat comet of 1680 was calculated to have approached within about 150,000 miles of the sun, — about ono-sixiii of his diameter. 625. The periods in which several of the comets revolve round the sun have been computed, and the correctness of the calculation proved by the return of the comet several times. A very bright comet was recorded to have been seen in the years 1531 and 1607. In 1682, a comet appeared, which was observed by the celebrated astronomer Halley, and calculated by him to be the same which had been seen in 1531 and 1607 (and which might be traced back to the year 11 b.c, and is supposed identical with the comets of 1305 and 1456). He accordingly predicted its return in about 1758, computing it to have a period of between seventy- five and seventy-s'x years. It did appear, to the greac delight of the astronomical world, in 1759, nearly about the assigned period ; its delay being caused, as pre- dicted by Halley and correctly calculated by Clairault, by the action of Jupiter and Saturn upon it. This comet again, in 1835, returned at the calculated time (28,105 days), and followed very nearly the course among the stars predicted for it. It remained visible, by the aid of the telescope, from August 1835 to May 1836 ; and was very bright when crossing among the stars of the Great Bear. In 1682, the tail of this comet stretched over a space of 30°. It is expected again about the year 1910. The great comet of 1680 has been conjectured to be identical with the comets of 43 B.C., 575 A.D., and 1105 a.d., having a period of about 575 years. A brilliant comet with a very long tail, which appeared in the year 1 264, is supposed to have been the same which was seen in 1556. If so, it must have a period of about 300 years ; while the great comet 182 RLEMENTS OP ASTRONOMY. -of 1811 is supposed to have a period of about 3000 years. 62G. The comet of Biela performs its revolution in the short period of 6J years (2413 days). It does not pass much beyond the orbit of Jupiter. The c. bit of this comet crosses that of the earth, and we were within a month of encountering it in the year ] 832. -A re- markable phenomenon recently took place in this comet. Shortly after its second last appearance, between November 1845 and January 1846, it separated into two distinct comets, each with a nucleus and a short tail, which moved on together, as if independent, and still continued separate when the comet had run through one complete revolution in its orbit, and re- appeared in 1852. The distance between the nuclei had then considerably increased. 627. A comet, with a period of about 7} years, was discovered in 1843 by M. Faye. The comet of Encke has a still shorter period, 3 J years, or 1210 days. There are two other comets, De Vice's and Brorsen's, whose periods have been calculated — 1993 and 2042 days. G28. The comet of Encke has led to some singular specu- lations regarding the existence of a fluid called the eiher, sup- posed to be spread out through space. Its period of revolution round the sun is found to be diminishing. This is attributed to a resistance opposed to its progress by some material fluid through which it passes, which weakens its centrifugal force, gives the sun's attractive force greater proportionate power, enables that body to draw it into a smaller orbit, in which it moves more rapidly, and therefore runs through its course iu a shorter time. 629. Some comets have been so exceedingly bright as to be visible in daylight. This was the case with the great comets of 43 u.c, 1402, 1532, and 1843, A.D. 630. The number of comets which circulate in the Bolar system is supposed to be very great, — perhaps ELEMENTS OF ASTRONOMY. 183 thousands. Some 800 have been recorded ; and it is believed that the proportion, of comets whicli are visi- ble to us must be greatly under the number which really exist. 631. Comets appear in all parts of the heavens, move in all directions, and with very different degrees of velocity. They are not, like the principal planets, confined to the zodiacal belt. 632. Comets are considered to be mostly, if not entirely, in the aerial state, for the following reasons. The stars, even those of very small magnitude, can be seen through their substance. They have been found to cause no sensible derangement in the motions of the satellites of Jupiter near to which they have passed, while they themselves have been considerably influenced and divci A from their course by the latter — indica- tions that their mass is small, and therefore, as their bulk is considerable, that they are in the aerial state. Also, they present no phases^ which seems to show that light is reflected from every part of the comet, and hence, that the sun's light penetrates their substance, which indicates an aerial state. 633. In ancient times, comets were supposed to resemble planets, and, like them, to go through certain revolutions in regular periods. But from the commencement of the Christian, era to the time of Tyoho Brahe, they were generally regarded by astronomers merely as meteors, existing in the atmosphere. He found that their distances were beyond that of the moon ; and the idea that comets are at considerable distances, and re- volve round the sun in regular periods, was confirmed by Kep- ler, Hevelius, Dorfel, Newton, Halley, and others. The Zodiacal Light. 634. This is a faint luminosity in the sky, visible in the west, immediately after twilight in spring ; and in the east, towards the close of autumn, just before sun- rise. It is very distinct in tropical regions, and is par- ticularly descriJbcd by Humboldt, who speaks of " the J 184 ELEMENTS OP ABTRONOMV. mud radiance with which the zodiacal light, shooting pyramidally upwards, illuraineb a part of the uniform length of tropical nights." He states that in his voy- age from Spain to South America, " the strength of the light — it might almost be called illumination — increased surprisingly the more I approached the equa- tor in South America and the South Sea. In the continually dry, clear air of Cumana, in the grass steppes of Caraccjts, upon the elevated plains of Quito and the Mexican seas, especially at heights from eight to twelve thousand feet, the brightness sometimes ex- ceeded that of the most beautiful sparks of the Milky Way." — Cosmos, vol. iv. It has been supposed to be a vast nebulous ring revolving between the orbits of Venus and Mars ; but, within the last few years, some curious particulars have transpired, which would seem to show that that theory must now be abandoned. In 1855, the Rev. G. Jones, chaplain of the U. S. steam-frigate " Mississippi," narrates the following : " I was fortunate enough to be twice near the latitude of 23" 28' N., when the sun was at the opposite solstice, in which position the observer has the ecliptic at midnight at right angles with his horizon, and bearing east and west. There I had the extraordinary spectacle of the zodiacal light simultaneously ?>*^ both east and west horizons, from 11 to 1 o'clock, i . several nights in succession. It seems to me that this can be explained only on the supposition that the zodiacal light is a nebulous ring having the earth for its centre, and lying within the orbit of the moon." * The Meteoric Systems. 635. Meteors have been noticed traversing the sky in all ages, and at all parts of the earth's surface. Many of them have been attended by the actual fall of * " Descriptive Astronomy," by G. F. Chambers. Oxford, 1867. ELEMENTS OF ASTRONOMY. 185 » ^Rome 8ul)«tanco or body, to which the names of aerolites and meteoric stones have been applied. When the body explodes into small fragments before reaching the earth, the fragments are termed fire-balls^ and some- times bolides ; and when the fragments are apparently consumed whilst traversing the upper regions of the atmosphere, they are known ns shooting-stars. Many ingenious theories have been devised to account for these remarkable phenomena. But it is now generally fiuppooed that they consist of small fragmentary masses, revolving in extremely eccentric orbits round the sun, some of which, coming within the sphere of the earth's attraction, are precipitated on its surface ; the intense heat and explosion being caused by the action of the atmosphere on bodies passing through it at a very high velocity. Other planets of the solar system, especial'/ the remoter ones, pass through similar rings of meteors, and, like the earth, attract multitudes of them to their surfaces ; while, doubtless, the sun himself, owing to his superior gravitating power, attracts inconceivable numbers of them, precipitating them with tremendous momentum on his own surface ; thus providing inex- haustible materials for maintaining his incessant light and heat, with which he vivifies and blesses our luiiverse. 636. Two remarkable circumstances in the history of shooting stars render it almost certain that they are of a planetary nature — their periodical recurrence at cer- tain times of the year, and their divergence from certain fixed points in the sky. A brilliant display of falling- stars has been observed in many years to occur between the 12th and 14th of November ; and a less numerous shower, very often about the 10th of August. The meteors of November appear to diverge from a star in the constellation Leo, — those of August from a star in the Camelopard, or the vicinity of Algol, in Perseus, whatever may be the elevation of these stars above the %^ . %' I JL ■■■ 186 ELEMENTS OF ASTRONOMY". horizon. " During tljc culobrated fall of Hbooting-stnrs, on the night bt'twecn the 12th and 13th of November 1833, the fire-balls and shooting-stars all (^'merged from one and the same quarter of the heavens, namely, in the vicinity of the star y in Leo, and did not deviate from this point although tlie star changed its apparent height and azimuth during the time of the observation. S..ch an independence of the earth's rotation shows that tho luminous body must have reached our atmosphere from without." — Cosmos. Astronomers have determined that the orbit of each member of tho November star- shower is an elongated ellipse, having its perihelion lying on the earth's orbit, and its aphelion beyond the orbit of Uranus ; that the time of revolution of each member of the ring is 33J years ; that the inclination to the earth's ecliptic is 17°; and that the motion is not direct, as in tho case of the planets, but retrograde. The August meteors, again, travel in a path so eccentric, that near the earth's orbit it is almost parabolic. Its period, like that of the comet of 1862, with which it seems closely associated, is 145 years; while its aphelion distance is about twice the distance of Neptune. 637. The periodical occurrence of meteors arises from their circulating round the sun in broken rings, in orbits near which tho eartn is at tho periods when the meteors are seen. There may be several planetary masses having the same orbit, follow- ing each other at certain intervfils, and crossing near the earth's orbit, so that they become visible at certain times, — " a stream of meteors in their progress of cir- culation round the sun." This supposition would also explain their appearance of diverging from one point in the heavens. 638. Upon an average, about seven shooting-stars of every description may be seen at any one spot every hour on clear nights. In the August shower of 1842, one observer saw 34 in ten minutes. In 1852, on the ELEMENTS OF ASTP.ONOMY. Ift7 10th of August, the writer saw 27 in h.ilf-an-hour. It has been roughly calcuhitod that tlio average number of meteors which traverse our atmosphere daily, and that are visible to the naked eye, does not fall short of 7,500,000. So far as observation has yet gone, these are divisible into 56 distinct grotips, pursuing their courses in 56 different orbits, and having as many radiant points in the celestial sphere. Having highly eccentric orbits, their velocities are very different in different parts of their paths. When in their perihelia, somfj of .licm travel at the rate of 200 miles per second, b' t.evr average velocity does not exceed 34 miles per .4 j'liJ, being nec^ily tvice the average velocity of the earf'a ii« bcr orbit. ShooLing-stars usually become vir'bie to the 7>aked eye at a height of 72 miles, and aga-ii diriapprar at a h^'if^ht of 52 miles. Some are cynriosed riodtly of netidlic iron always alloyed with nickel, and smaii quantities of other metals, as cobalt, coppev, tin, and chromium. In the main, they art composed of metallic iron and various compounds of silica, the iron forming in some cases as much as 95 per cent. Among the silicates may be mentioned olivine, a min ral found abundantly in volcanic rockf-', and augito. A hi I 188 LLEMENTS OF ASTRONOMY. PART IV. PARALLAX, ARKKRATIOX, AND PRECESSION. BIXTION I. Parallax. 639. The word Pamllnx is used in Astronomy in two senses ; a special and a general sense. In the special sense, parallax signifies the difference in tho fxltitudo of a celestial body as seen from a point on the surface of the earth and from the centre, if it could be seen from that place. This is sometimes termed the diurnal parallax, 640. This will be illustrated by the following figure (53) r Let the dotted circle A E B bo the earth ; p^ p\ and p"^ ai y heavenly bodies ; and the dotted arc at the right, G c', the imaginary surface of the heavens to which we refer the positions of celestial objects. Let E be the position of an observer on the earth's surface. Now, if the heavenly body p"^ be viewed from E, it will appear at e^ on the surface of the heavens, i.3 shown by the dotted line E p'^ e'^; but if viewed from C, the earth's centre, it would appear at c'^, as shown by the line C p^ c^. The difference of these two positions is the arc c^ c'^, which is therefore termed the parallax at E of the body p'^ ; or, instead of the arc c'^ e'\ the angle c^ p^ e'\ which the arc c^ e^ subtends, and which is of the same number of degrees (73-5), and may be called the parallax of p"^ at E. Or, the angle E p^ C, which is equal to the angle c^p"^ e^y may be called the parallax of/)' at E. The latter is what is usually stated as the parallax of the object. Thus the parallax of a celestial body is the angle at it formed by two straight lines, one drawn to it from the earth's centre, the other from the observer's position on the earth's surface. 1 ELEMENTS OF AflTRONOMY. 180 Fig. 5S. #0.*, * * # • VA*a. o Riirfuce, tlmn when W!cn from the centre. Thin iH evident, an c\ the |)OHitum of »• on seen from the centre, is nearer the zenith of E tlmn e\ its poHition m won from E. 642. Puralhix \h ulw.iyM groaleht wlit-n the bg lets than A »S'' B, and A ngle of paral- lax ig too small to be discernible ; the two lines from the street to the moon coalesce ; the distance between the two points of observation is a mere point compared with their distance from the moon; and we could not, with that distance as a basis, measure the moon's distance. The same may be observed of an object on earth. If an individual walk along a road for any given distance, and take some very remote object, such as the stars or a far-off tower or mountain, whereby to judge of the apparent motions of bodies between his line of motion and the fixed objects by which he judges of their apparent motions, he will find that these various bodies will have shifted their appa- rent position less and less according as they are further from him — that is, their parallax will be less. In proportion as they are more remote, he will find the angle at the body, formed by two straight lines drawr. to the two points of view, become less and less till it disappears find the two lines coalesce ; then there is no parallax, and ^'rt'iih. that basis nc means of measuring the distance of the object. SECTION n. Aberration. 653. Aberration is an apparent displacement of the true pORitiuii, arising from ceiesiiai bod lus irom theix KLEMENTa OP ASTRONOMY. 193 the motion of the earth in its orbit, and the time required by light to traverse space. 6o4. Every object is seen in the direction which the rays from it have when they strike the eye, if the eye he ^'t\x^ .. '^ ^^^ "^y^ ^^ ^^ "lotion, the direction in which the object is seen will be one compounded of the direction of the eye's motion and that of the rays fVom the object. The difference between the real direction aberration ''^ ^""^ ^^""^ '" '^^'''^ '* "'^P^'''^ '' '^'''"''^ ^^® 655. Let A, Fig. 54, be the position of an observer, and fe the position of a star. Let B be the situation of tlie earth, when that ray emanates from S, by which t^je star is seen at A,— the earth and ray coming to A at the same instant. Then, by the composition of motion, t^e star, when the earth comes to A, will appear at 5, in advance of its true position. The angle S A s is the aber- ration. As S A, which repre- sents the motion of light, is ^ ^ very great compared with B A |4 ^ or A C, which represents the earth's motion in the same time (as 185,000 to 18), the aberration is very small. 656. The aberration is great- est when (as in Fig. 54) the direction of the ray is perpen- Qicular to the direction of the earth's motion : in this position there is a displacement, by abberration, to the extent of 20-5'' (twenty seconds). It diminishes from this till the directions of the two motions are parallel, when it ceases altogether. There is also some aberration from the motion of the parts by the earth's rotation ; but this is insensible. 657. Had the earth been stationary at A, or had light come instantaneously from S to A, the star would appear in its true position at S. The'ph 194 ELEMENTS OF ASTRONOMY. :\ aberration is one of the most convincing proofs of tl»e earth's motion roun^l the sun ; and it confirms vory satisfactorily Roemer's discovery of the progressive motion of light, and also the rate of its »riotion as inferred from the eclipses of Jupiter's satellit-cs, and de- termined by M. Foucault in 1862 by a rotating mirror. 658. Aberration may bo illustrated by the manner in which drops of rain strike upon an individual, according as ho is in motion or at rest. If the drops fall perpendicularly, and he bo at rest, they will bo f5lt only on his head — that is, they iv'dl strike in the direction of their oion motion. But if he bo mov- ing quickly, they will strike upon his face, and appear to he coming in a slanting direction towards him, as if they fell from a point not only above him but in advance of him. It is evident that the direction in which they would appear to come must depend upon the real directions and comparative velocities of the two motions. 659. Or, if we conceive a ball to be let fall in the direction S A, Fig. 55, and to enter the tube S B, which has a motion Fig. 55. \ ... V in the direction B A sufficient to carry it to the position A s in the same time in whieh the ball would fall from S to A ; then the ball would, while passing from S to A, move in the axis of the tube (not touching the sides), and to an observer at the bottom of the tube would necessarily appear to hfive come from «, not from S, and to move in the direction s A, not S A. The ball ia analogous to the ray of light, the bottom of the tube ' ELEMENTS OP ASTRONOMY. 195 to the earth and the direction in which the ball appears to move to the directum m which the star is seen. ^ 660. Besides the aberration of the fixed stars, there 18 also an aberration of the planets and comets, arising from their motion. When a ray of light from a plant^ arrives at the earth, its direction does not show the true position oi the planet; as the latter has made a certain progress in its course smce that ray left it— and Its true position must be in advance of its apparent position. For the discovery of the aberration tVlwht and determination of its amount, science is indebted to the distinguished English astronomer Dr Bradley SECTION III. Precession of the Equinoxes— Nutation of the Earth's Axis. 661. Besides its rotation on its axis, the earth has two aihor TZZnIi t-^rf^-'^'"^''^" ^^^^^ parts wi?h^^faL'rtg except bvvP Tn 'f , ^'\ r'y '^"^' '^"^ ^'^ »«t discoverable except by ve./ caretul and long-continued observation. 1. Precession of the Equinoxes. n u^a' .V'^ ^'^^'.P^''' ''"*' *^'^ equinoctial in two points, called the equinoxes, during one revolution of the earth round the sun. But these two great circles cut each other in different points each year; that h ?he points (or stars) in the starry heavens where they inter-^ sec are different each year. This change in the posi- 663. The line of the equir. xe s moves backwards* 6ac-A«;a4: ^" """'' "' ''S^'"'*^ '^« ''"^''' «f »^« signs, retrograde or A. 196 ELEMENTS OP ASTRONOMY. Upon the ecliptic, tlisit is, from east to tvcsf, or in a direction contrary to the sun's apparent annual course through the ecliptic, which is from west to east; so tlutt each yi-ar the s\m crosses the equinoctial in a point west of that in which they last met. The amount of this retrocession is 50-21" yearly. 664. As the sun moves eastward through tie ecliptic, and the equinox moves westward, the sun vfiV. come sooner to the eqiiinox in each revolution, for they move round towards each other; hence the period of each e(piinox will come a little earlier evevy year ; from which the expression precession of the equinoxes is derived. Tlie time which the equinox precedes each year is 20'"- 20"* , that being the time in which the sun goes through an arc of 50*21''. 665. From this circumstance, the positions of the signs of the zodiac among the stars change regularly backwards (in the opposite direction to the sun's motion). The rate at which the equinox recedes is such, that it makes a complete revolution round the ecliptic in 25,898 years. This is equal to l'' in 71*6 years, or 30° (one sign) in about 2000 years. And accordingly it is found that the position of the equinox is now about 30° behind what it was 2000 years since : then, the signs and constellations of the same name were the same, — but each sign, which still retains the name it had then, is now in the preceding constellation. — See Par. 1 14. 6G6. From this recession of the equinox, the true year, or the period of the earth's return to the same star, is a little longer than the equinoctial or tropical year, which is the iuterval be- tween two returns to the same equinox. — See Par. 330. 667. This precession of the equinoxes is caused by a conical motion of the earth's axis^ by which, while the middle point remains fixed, the poles describe a small circle, as in the following figure. Let A a, B 6, C c, D rf, represent the earth's axis, being the middle point. It does not always remain in the ELEMENTS OF ASTRONOMY. 197 Fig. 66. ■# d' \a V same direction, pointing to ibe star a', — but shifts on its centre, passing from A a to B i, etc., the poles do- c ,-■' scribing tbe circles A B C 41 1), a 6 c c?, and tuccessively \ pointing to the stars a\ b\ *'■*- ^° c\ d\ Thus, each radius describes a cone — com- pleting it in the long period of 25,898 years. The ra- dius A describes the cone A B C D,— the radius a, the cone B ah c d. 668. The inotion of each ra- dius exactly resembles that of a top spinning. It is often observed, besides its rotatory inotion, to have a swinging motion, inclining to one side, then gradually shifting, and inclining as much all round, so that Its axis has a compound motion, turning like any revolving body, and at the same time describing a cone of which the apex IS at the ground. In this swinging motion, 'j always keeps the same inclination to the horizon, as the earth's axis does to the ecliptic. 669. From this, the pole of the heavens (the point in the heavens towards which the earth's pole is directed) describes a circle round the pole of the ecliptic ; this circle is always 23" 28' from that pole. 670. Hence the earth has not always the same star for its pole-star.* The precent pole-star is 1° 24' from the pole ; at the time of Hipparchus (about 140 b.c.) it was about 12° from the pole. It will be nearer to the • The brightest star near the pole of the heavens is the pole-star at the time. At present this star is Polaris in the constellation Ursa Minor At the time of the erection of the Great Pyramid (b.c. 2170), it was the' star ace i' tttia arm i/aios y^. i2a;, BiacKwooa «& jous, 1870. 198 ELEMENTS OP ASTRONOMY. pol(! still for a little, .and then will recede from it apain ; and in about 12,000 years the pole of the heavens will be on the opposite side of the pole of the ecliptic, 46° 56' from its present position, and very near Vega, the principal star in the constellation Lyra, which star will then servo for a pole-star. See Fig. 56, in which the axis is seen pointing successively to the diflercnt stars a', b\ c', cT in the sphere of the heavens. 671. But the angle of inclination of the axis to the ecliptic always remains unchanged ; so that the angl5 between the planes of the ecliptic and equinoctial still continues the same — 23° 28'. And the whole earth parta^'es of this motion, so that the axis and poles still bear the same relative j)osition to the other parts of ilie earth's surface ; the latitudes remain the same, and the waters are unaffected. 672. From this, then, the points where the ecliptic and equinoctial cut each other must be continually shifting. This will be illustrated by the following figure. Let P represent the pole of the ecliptic, the sphere representing the sphere of the heavens. Let B C be the ecliptic, and the small circle h h' h" the circle in the heavens marked out by the earth's pole round the pole of the ecliptic, and the points h hf h" on that circle different positions of the pole of the heavens. "When h is the pole, the equinoctial will be E r Q, intersecting the ecliptic in r. When h' is the pole, E' r Q' will be the equinoctial, cutting the ecliptic in r' — and when the pole is at A", tlie position of the equi- noctial will be E" r" Q", having r for the fequinox 673. The cause of this conical motion of the earth's axis is the action of the sun and moon upon the pro- tuberant matter at the earth's equator. As they move in the ecliptic, and the projecting matter at the equator is out of the plane of the ecliptic, their action tends to draw this towards the plane of the ecliptic and to make tho planes of tiic ecliptic and equator coiiicidc. But ELKMiiNTS OP ASTRONOMY. 199 the rotation of the earth on its axis prevents any change in the inclination of the equator and ecliptic ; Fig. 67. o and causes the earth to have tlic gyratory motion in its axis which gives rise to precession. 674. The amount of precession caused by the action of the sun is about 15*21''; that produced by the moon 35", or nearly as 2 to 5. 2. Nutation. G75. The circle which the earth's pole describes round the pole of the ecliptic is not a true circle, but waved or undulating, as represented in the adjacent figure. This oscillatory mo- tion of the pole backwards and for- wards is termed nutation, being a sort of nodding motion of the earth's axis. Fig. 68. u. 676. Nutation will be best understood bv supposing ■ i 200 KLRMENTS OP ASTRONOMY. the point rcprcsontinp; tlie mean place of the pole to describo the uniform circle round the pole of the ecliptic, while the real position of the pole describes a biiiall circle (or rather ellipse) round the mean place. 677. This small ellipse is completed in a little less than nineteen years, at a distance from the mean place of the pole of about 9"— the lonpfcr axis of the ellipse, which points towards the polo of the ecliptic, Leinff about 18-5^ ^ C78. Nutation is caused by the action of the mooii on the protuberant parts at the earth's equator, which, as tlie moon's orbit is inclined 5° 8' 40'' to the ecliptic, and its nodes complete their revolution round the ecliptic in eight<3en years seven months, causes ♦he above described motion, accompanying that of precession. ; ELEMENTS OP ASTRONOMY. 202 PART V. PROOFS. 679. Having now described the leading phenomena of the sphere of the heavens, of the earth, sun, and moon, and of the soiar wystem ; and having given tlio generally received explanations of these phenomena. •* yet remains to render some account of the reasons b^ which it is provfed that these are the correct explana- tions. There are three principal points to bo i)roved : that the earth is round; that it rotates; and that it moves round the sun. SECTION I. The Earth is Eound. 680. There is no scientific fact which can be estab- lished by a greater number of irresistible arguments than that the world we live on is round; and the greater number of these arguments are quite intelligible even to those who do not possess any mathematical knowledge. 681. (1.) Men have sailed round the world. 4 ship, starting from one place and sailing onwards, without ever turning back, merely moving a little to right or left to avoid running upon the land, has come back to the place from which it set out. This could only happen on a round body. It was first done by the e .pedition of Magellan (or Magalhaens) in the years 1.518-21 ; afterwards by Drake, Anson, Cooke, and by great numbers of navigators recently. ^ Magellan did not live to coiiipleto his voyage : lie vvas killed in the PLiiippino i2 202 ELEMENTS OP ASTRONOMY. ill Iwlftnds, and liiH Hlnps were broiiglit back by one of bis oflicers. Hut the 8trait8 of Mat^i'llati, at tliu Hoiith of tho American continent, and the Hingiilar ncbulw near the southern polo of tiie heavenH, called the Magellanic (^h)udH, will proHCi've to distant ages the nanie of the leader ot the first expedition that elreuninaviguted tho globe. It was found, on their return to Spain, that the navigators had lost une entire day during their long, circuitous voyage. Had they circumnavigated tho globe by sailing in tho oppoHite direction, tliey would have gained a day. No more striking proof of tho earth's rotundity could possibly be afTonlcd. GH2. It has also been well established that the world can bo sailed round in shorter time, the further south the voyage is performed — as in the South Atlantic Ocean, beyond Capes Horn and Agulhas — which shows that its circumference narrows as we pass from tho equator in a southerly direction ; and, though we can- not sail round the world in the northern hemisphere, on account of the land and state of the north seas, tho distance round can be very well ascertained by other means, and proves the same fact — the regular diminu- tion of the thickness, or of the circumference of the earth, as we pass north or south from the equator. 683. (2.) When a ship sails from us, the lower part, the broad massive hull, first disappears; the slender top-masts and rigging go last out cf view. And, if we look at it through a telescope, when it is too small and indistinct to be seen by the naked eye, we shall find that the highest parts of the masts are the last to dis- appear. Similarly, when a ship approaches, the upper parts come first into view. These things prove that the sea is not a flat plain, but that it bulges out between an observer and distant objects ; that is, that it is con- vex. As similar appearances are observed at every part of the wide ocean, and on land too, where we can got an extensive flat piece or olain, it followB that tiie ELKMKNTS OF AHTRONOMV. 203 world must bo ovurywhuro more . (4.) Ifwo iiduiit tho Bun •»nd moon to see from day to •• tho horizon, and disappears altogether if wo go south b'^yond that lino ; while new stars come into view foi every step wo take south, till at tho equator we commanci during one night a view of the whole of tho stars of the heavens. As wo can ascertain by simple measurements that the stars are at a very great distance from us, this regular change of elevation in any star as we pass north or south, and appearance of now stars and total disappearance of others, as we go soui.i, ulmw that wo avo moving along a surface that is more or less round from north to south. It is to be observed that the stars in sinking p^aI tben disappearing do not fade gradually in lustre, a? if vo were gral r.lly increasing our distance from th , i, \,at icmain equally bright to the last, showing that they are lost to our view from tho interposition of something opaque between the star and the observer. fi88. (fi.) In eclipses of the moon, the earth's shadow always has a circular edge, and none but a round body can give a circular shadow in whatever position it may bfi r»l np.pH. Wo know that eclit>sc'S of tho moon aro ELRMF.NT8 Ol' A*" lONOMY. 205 I CAUsod by the intorvontion of iho oartli Ijctwcon the nun and moon ; an, from tiino iinmctnorial, thewj phenom«iia have nevor tiiUen place except when the oarth, sun, and intMHi aro in one straight line — whc-n the ni'n and moon aro in exjictly oi)|)08ito parts of the sky ; that ut^ in op|K)sition. 689. (7.) The horizon, or oJJ^nf/, ai it is soiretinieH caUed, is always circular, from whatever point we take it; itrf extent is greater, and the angle l)ei,."een the ob-. server and ts opposite points less, the higbui the point from wiiich we view it ; and the dip of the horizon (the angle between a honzont.d line as given by m s[tirit level and a line from the spectator to the aetnal h i /, "u) 's greater, the greater our elevation. All these, .)b- fc^rved everywhere, givo certain indications of a surface more or Ichh round 690. (8.) Tile lessening duration of twilight, as wo pass towards tlio equator, gives distinct evidence of a spherical form in the earth, and of the variour parts at tlie surface being further from the axis of rotation the nearer they are to the e(piator — whether we regard the earth, or the heavens, as performing the daily rotation by which the phenomena of sunrise and sun.set are caused. SECTION II. The Earth Rotates. 691. That the world turns daily on an axis, from west to east, makm.^ a complete rotation in about 24 hours, is well established, by the following consider ations : — 692. (1.) The whole sphere of the heavens appears to rot^ite from east to v/est in 24 hours ; and we know 206 ELCMENT8 OF ASTRONOMY. that this apparent motion can be perfectly explained by a rotatory movement of the earth in the opposite di- rection in the same time. Thus, in the adjoining figure, let the circle A B „, «„ J , Fig. 60. a b, represent any parallel of latitude on the earth (the sign of the earth at A and of the sun in the centre being dis- ;'• : regarded) ; and let :■'.* it be supposed that •'•.' the earth rotates so -y. as to bring A to B, a the stary sphere B '• S A S remaining fixed. It is mani- fest that any one who was at A will, when at B, have come to a very different position as regards any object in the part oS.the starry sphere within his view, as B S. If he is not sensible of his motion, finding that any objects at B S are now in the position formerly occupied by those of A S, the former must have appeared to him to have moved from B S to A S, in a direction opposite to that in which he has moved,* and the whole starry sphere must appear to be moving round in the same direction. See par. 24, page 11. 693. (2.) The supposition of the daily revolution of the heavens is liable to this almost insuperable objection that, as the stars always, and the sun, moou, and plan- ets, for the most part, preserve the same reLtive positions to each other during this great movement, a * And opposite to tiiat shown by tlie arrow at the top of the figure, wLkli it) tLuru ilir u diil'urcut pur|ju»c, vlh will prjbuully be iicuii. ELEMENTS OP ASTRONOMY. 207 a vast number of bodies, some of them much larger than the earth, very distant from us, and far distant and de- tatched from each other, must have one circular motion in common, in the same direction, each completing its circle in the same time, and the circles described by all being perfectly parallel to each other ; an almost im- possible series of coincidences, and the extreme im- pobability of which led to the absurd theory of crystal spheres. (See par. 22, page 10). This simple and single act of the earth's rotation on its axis afibrds an easy and natural explanation of these otherwise extra- ordinary and unaccountable coincidences in rate and direction of motion in so many different bodies. 604. (3.) The slower oscillation of the pendulum as we pass to\vards the equator — this diminution of the force of gravity being more than can be accounted for by the increased length of the pendulum from warmth, and by the spheroidal form — affords a strong presump- tion in favour of a rotatory motion of the earth, which, by the great centrifugal force it would generate at the equatorial parts, must lessen the force of gravity. 69.'). (4.) The spheroidal form itself affords an argu- ment in favour of rotation, as we know that rotation tends to produce such a form, (5.) The analogy of the sun, moon, and planets, which are known by obser- vation to rotate, affords a presumption that the earth also, which resembles them in so many points, has this motion 696. (6.) The easterly direction acquired by the great currents of wind that are constantly rushing from the cold regions of the earth towards the heated parts on each side of the equator, afford a strong argument in favour of a rotatory motion of the earth from west to east, which, by the great velocity of the equatorial parts compared with that of parts at a distance from the equator, imparts this easterly direction to the north- ern and southern currents. See Trade-winds. f^ 208 ELEMENTS OF ASTRONOMY. 697. (7.^ A remarkable proof of the rotation of the earth from west to . ast is derived from the experiment of letting a pebble fall from the east side of the top of a very high tower; when it does not fall exactly at the bottom, as it would if it descended truly in the plumb line, but a little out from the bottom of the tower. This is inexplicable, except upon the supposition that the earth rotates; in which case, the pebble when at the top of the tower, being further from the axis of rotation than the bottom, moves in a larger circle, and therefore more rapidly, as the rotations of all the different parti are performed in the same time. Hence, while the pebble descends by the force of gravity, it also moves a little in advance of the lower parts of the tower by its greater velocity of rotation, and falls a ^ittle beyond the base. In short, it has a greater eastv/ard tendency than the bottom of the tower, and must therefore, in falling, take a position a little in advance of it. 698. (8.) A very clear and satisfactory proof of the earth's rotation is afforded by the celebrated pendulum experiment^ devised by M. Foucault. If a heavy body be suspended by a wire and made to vibrate (to oscillate backwards and forwards), its vibrations will taxe place in the same plane, even though the points from whi' h it is suspended have a slow rotatory motion imparted to them. M. Foucault's pendulum was sus- pended from the dome of the Pantheon in Paris, and a fine point at the bottom of the weight was made to leave a mark in sand at each swing. The murks suc- cessively made in the sand showed that the plane oi" oscillation varied with regard to the building. Here, then, was a proof that the building, and therefore the earth, moved. If, at the pole of the earth, such a pendulum were suspended and set in motion, and a circle divided into degrees were placed beneath it, as the earth rotates in 24 hours, while the pendulum con- tinues to vibrate in the same plane, the circle (attached pi ELEMENTS OP ASTRONOMY. 209 to the e.arth) would rotate, and bring the pendulum opposite to every successive degree till a complete revo- lution had been accomplished ;— and as tlio earth's motion is not sensible to us, it would appear as if the pendulum had been continually changing its piano of motion in the opposite direction, making a complete revolution and returning to the original plane in 24 hours (or rather 23»'- 5G'"- etc.). If made to vibrate in the plane of the meridian at other places, the same ap- pearances would be caused by the earth's rotation ; but the rate of apparent movement of the plane of vibraticm would gradually lessen as the place is nearer the equa- tor, at which it would cease, as the circle would there cease to have any motion of rotation, and have no motion except what would be common to itself and the pendulum. It has been computed that the apj)arent motion of the plane of vibration would be about 1 5° hourly at the pole, 12 7° at Aberdeen, 11'5° at Paris, 9-7° at New York, 1-8° at Ceylon, and 0° at the equator ; and as experiments made at many places coincide very closely with the calculated effects, we derive hence a very convincing proof that the earth rotates, — a means of ascertaining the period of its rotation (found to coin- cide as closely a^ can be expected with the time as ascertained by other methods)^ — and a means of ascer- taining also the latitude of the place. 699. That the earth is of a spheroidal form, and not a perfect sphere, is proved by the diminishing force of gravity towards the equator, by the diminution of the degree of latitude the nearer the place is to the equator, by analogy from the other planets, as Jupiter and Saturn, by the tendency of rotation to produce such a form, and by the phenomena of precession and nutation, in wliich we observe effects such as would arise from a protuberance towards the equator. Ii[' 4 210 ELEMENTS OF ASTRONOMY. 11' I!! N I SECTION III. The Earth and the other Planets move Round the Sun. 700. (1.) When tlic sun is observed from day to d;iy tlirouf^^liout the year, and his position in relation to tlio constellations watelicd, it is found that every 8()5 days ho makes a comi)lete tour of the heavens; that, setting out from the vicinity of any star, he moves to the east of it, daily increases his distance from it, till he is 180° from it in the opposite quarter of the heavens, then approaches towards it, and returns to the same position near it at the end of one year. This may be ascertained by ob!?erving his successive distances from any promi- nent star that is visible, or by observing from time to time what stars rise just before or set just after him, by which we can ascertain his position among the stars with tolerab] exactness. Now this apparent yearly motion of the un can be perfectly explained on the sup- position that lie sun is a fixed centre round wl ich the earth moves in the same direction in the same time. This will be understood by reference to Fig. 60. Let A re})resent the earth, moving in the ovhh A B a 6 in the direction indicated by the arrows, t'le sun being represented in the; centre of the figure. It is manifest, that if the earth move from A to B, the sun, seen from A in the position a s among the stars, will from B ap- pear at b s, and thus must appear to have moved from a s to b s through the starry heavens. As the earth passes from B eastwards, the sun must appear to pass westwards from b s ; and when the earth arrives at the opposite part of its orbit, a b, on the other side of the sun, the sun must be seen in +he opposite quarter of the heavens A S B S, and wL the earth moves in her orbit from a to 6, the sun appears to move among the stari:, from A S to B S. y.i ELEMENTS OF ASTRONOMY. 211 I 701. (2.) The theory of the fixity of tlio sun and ..-»nular motion of tlie eartli round that luminary is so Mch simpler, and avoids so m.'vny improhabilities, that it lias been adopted as the true one since about the times of Co[)ernicus and Galileo. It seems very unlikely that a large body like the sun should be revolving round one so much smaller, and is quite contrary to what we observe in the other paits of the solar system, as the lesser systems of Jupiter, Saturn, Uranus, and our own earth, with their attendant satellites. This improba- bility is greatly increased when we consider the number of large planets circulating round the sun as their undoubted centre, at vast distances from him. We cannot realize the idea cf so vast a system being depen- dent upon and revolving round our comparatively puny earth. Also the motions of the planets (particularly their retrograde movements) are infinitely complex and almost unintelligible on the theory of the earth's fixity as the centre of the universe ; while all their movements become plain, simple, and uniform on the other theory. 702. (3.) The other planets are known to move round the sun by observing their movements through the starry sphere, the different positions they occupy in respect to the earth and sun at different times, and par- ticularly in the cases of Mercury, Venus, and Mars, by the magnitude and position of the phases which they exhibit at different times. 703. (4.) The phenomenon of the aberration of light (653) affords the most convincing proof cf the earth's annual motion. 704. (5.) By the laws of mechanics, any force which would impart a motion of .otation to a body free to move, must also impart to it a motion of translation, which could then be stopped only by a force in an oppo- site direction through its centre of gravity ; from which there is necessarily a stronGf i^resumDtion in favour of an outward motion in any body rotating in free space. fell rrl 212 ELEMENTS OF ASTRONOMY. PART VI. THE FIXED STARS. 705. Those stars which preserve the same positions in relation to each other, without material change, are called " fixed stars." Such are the stars in the con- stellation "Great Bear," which appear to the "oldest inhabitant " to be clustered in the same form in which he saw them in his childhood. It is known from good records that form has not materially altered for hundreds of years. And we have reason to believe that the stars of the leading constellations appear to us now just as they did to the astronomers who flourished long before the Christian eia, and who arranged the stars in con- stellations, and gave them the names they still bear — names derived from the heroes and heroines of antiquity, and which have stamped on the heavens in indelible characters the heroic deeds and elegant fables of ancient times. 706. The fixed stars, however, are not absolutely fixed. Many of them do change their positions in rela- tion to each other. But this change, called their proper motion, is very slight; so much so that it must go on for thousands of years before it causes a change in posi- tion appreciable by 'he naked eye. The stars Sirius, Arcturus, and Aldebaran have moved southward, re- spectively, 37', 42', and 33', since the time of Hippar- chus — more than half a degree. The star 61 Cygni has been ascertained to have a proper motion to the extent of 5'3'' yearly, about a degree in 700 years; and some are believed to have a proper motion of so much as 7*7''' annually. 707. It was believed by Sir William Herschel, and il ELEMENTS OP ASTRONOMY. 213 are and has been confirraed by succeeding astronomers, that there was a tendency to an opening out or spreading of the stars in a particular region of the heavens, such as would bo caused by our approach towards that quarter of tlio lieavens, and a crowding together of the stars in the opposite part of the sky, such as would be caused by our receding from these stars. Hence has arisen the bold conjecture, otherwise not improbable, since every ana- logy is in favour of motions both of rotation and trans- lation in the heavenly bodies, that our sun has a proper motion through space, carrying all the planets, satellites, and comets along with it. It is supposed that +hi8 motion is towards the constellation Hercules (to a point in R. A. 261', N. P. D. 37°) ; and that it is at the rate of 422,000 miles (or nearly the sun's radius) daily, or 154,185,000 miles in a year. Speculations have even been entered into as to the centre round which our sun moves; oae astronomer (Miidler) having conjectured that that remarkable point is the star Alcyone, in the constellation Pleiades ; and this is now the general belief of astronomers. 708. All the stars usually seen in the heavens by the naked eye are fixed stars, excepting five, and an occasional comet.— See par. 45. They may be distin- guished from the planets and comets by their property of twinkling, that is, alternately expanding and con- tracting their rays. The planets shine with a steady equal light. 709. Until recently very little was known regarding the fixed stars. We could judge of their relative bright- ness, we could ascertain the direction and velocitv of their apparent daily motion round the earth, and any other motions they exhibit, and we could determine that they are at not less than a certain distance from us. But we did not know their actual magnitude, nor, except in the case of a few, their distance from the earth. 710. In the first place, all attempts to measure the d 214 ELEMENTS OP ASTRONOMY. 5 is distance of any of tlio fixed stars Imd fi'ilcd. None of them ffave any parallax with the loni^est known base- lino within onv reach — the radins of the earth's orbit, 92 millions of miles. In the year 1888, however, the parallax was nieasnred in the case of three of them. The parallax of a Centanri was ascertained by Profes- sor Henderson, at the Royal Observatory of the (^ape of Good Hope, to be 091 28" or about 4?ths of a second; that of Gl Cy<,'ni, by Professor liessel of Koni;,^sberg, to be 0'3483''; and that of a Lyra?, by Otto Struve, to be 0'2.>". The major diameter of the earth's orbit being about 185,000,000 miles, a parallax of owe second wifi give a distance of 20,000,000,000,000 (twenty billion) miles, which is, therefore, the i)robable distance of « Centauri from the sun — a distance so great that light, tiavelling at the rate of 185,000 miles per second, would require three and a half years to traverse it. The dis- tance of the star 61 Cygni, its parallax being only J of a aecond, will be thrice this number ; and of a Lyraj, four times twenty billi(ms. The distance of about twenty fixe 1 stars (including Sirius, Arcturus, Polaria, and Capella) is now approximately determined. 711. We have no certain knowledge of their size, for, even when viewed through the telescope, they present no disc or surface whose breadth can be measured. Even by the aid of this instrument they appear, as to the naked eye, brilliant shining points, only more bright and luminous. 712. The different maj^nitudes which the fixed stars present to us may arise from their different distances, different degrees of brightness, or from actual differences in magnitude : being, in most cases, ignorant of the two former, we have no sure dataVor judging of the latter. For the present we must be satisfied with approximate results. The star a Centauri is ascertained to be three times brigliter than our sun. "Sirius is mo'-c than four times brighter than a Centauri, but yet shows aa annual change of position among the stars of not more than one-fourth of that star's. It is therufurc suppoacd to bo four times farther away ELEMENTS OF ASTRONOMY. 215 from ns tlmn o rentftiiri ; aihI, did k emit no greater nmntmt of light, woi\l(l jippear tosliino with but ono-sixtceiith at' tiiat Htar*8 luHtro. r.tit «H in rciilit,, it is four times i\h bri;-'.it, the real amount of li^rht it omita must cxcuiod that of a Centauri no Ichs than Hixty-f(»ur times, and that of our sun no lesH than 192 times. So th.it, judged from tliis indicatidii alone, the diamet»!r of tViriu!* may ho lield to exceed that of our huu in the proportiosi of about 14 to 1— an estimate wliich assigns to Hiriusadiameter of nearly 12,000,000 miles, and a v«)lumo of 2688 times as lar^o as the sun's."— Proctor. 713. It has been calculated t'lat if any of the more remote stars which the telescope lirings into view bo equally bright with those near us, the light of such stars must have orcuuied more tlian 2000 vears in coining to us; and that the rays which render them visil)le to us do not indicate their existenco noWf but their existence 200(j years ago. 714. The fixed stars are supposed to be suns, having planets revolving round them, wliich they preserve in tlieir orbits, supply with light and heat, and thus render fit to be places of abode for living beings. 715. It is considered that they are independent systems, not subservient to our universe, muci. less to our earth ; because th' ^ shine from their own light, because, from their great dis- tance, their influence on the solar system must be very slight, and because it is improbable that bodies of the magnitude wh ch their distance shows the fixed stars to possess, are subsidiary to our comparatively small system. That the stars shine by their own inherent light, not by reflecting the sun's rays, is shown by their enormous distance from that luminary. 716. "The stars of our firmament, instead of being scattered in all directions indifferently through space, form a stratum, of which its thickness is small, in comparison with its length and breadth ; and in which the earth occupies a place somewhero about the middle of its thickness, and near the point where it subdivides into two principal lamina) inclined at a small angle to each other. For it is certain that, to an eye so situated, the apparent density of the stars, supposing them pretty equally scattered through the space they occupy, would be least in a direction of the vi al ray (as S A), perpendicular to the lamina, and greatest in that of its breadth, as S B, S C, S D; increasing rapidly in passing from one to the other direction, just as we setj a slight ^aze in the atmosphere thickening into a decided fog- bank near the horizon, by the rapid increase of the mere length 216 ELEMENTS OP ASTRONOMY. of the v\mn\ my. Snch Ir tho \iovr of tlu! rniiHtniction <.f tlio Blurry finmiuu'nt tnkiii by hir VVilliuin ll.iMchi!!, wliose |)<.w«r- ful tolcHcoiHis iltHt efllctcJ a complete a,ia\y»h of thin womlorful Fig. 61. fnno, nnd (lomonstrntcd the fact of its entirely consisting of 8tarn. N) crowded are tliey in Homo parts of it tlint, by countln-' tlio Btars in a single field of his telescope, he was led to conclude that r)0,()()0 had passed under his review in a zone two degrees In breadth, during a single hour's observation. In that part of the Milky Way which is situated in 10»» 30«»- H. A,, and between the 147th and ir)Oth degree of N. P. I)., upwards of nooO stars have been reckoned to exist in a square degree. The immenso dis- tances at which the remoter regions must bo situated will snfli- ciently account for the vast predominance of small mngnitudos which are observed in it."— *SVr John JJerschel. 717. The fixed stars are arranged according to four different principles:-—!. According to their brightness. 2. In constellations. — 3. According to tlieir situation in the heavens.— 4. According to their kind, so fur as that can be discovered. 1. Divisions of the Stars accordingr to their Brightness. 718. The fixed stars are divided, according to their brightness, into classes termed magnitudes. The bright- est are said to be of the first magnitude, the next in point of brightness of the second magnitude^ and so on down to the sixth magnitude, which are the faintest discernible by the naked eye. With powerful telescopes * *.e range is continued down to the sixteenth magnitude, ./here are about 20 stars reckoned of the first mao-ni- tUClO. Of th'^KP 11 nrn xricil'l" '"" Cl^r^..*- l>..:i..;_ o--^- - ELEMENTS OF ABTriONOMV. 217 tlio (log.8tnr, 18 the brightest of tbo itars of tl.o first magnitiide. There are about G5 of the secoiul uiUKi.i- nh ^^ i *^'" *'".''*^ magnitude, and, in ull, nearly uOOO have been registered, including the sixth magni- tude. It 18 only at the eciuator, however, that so luriro ft number can bo seen, for there only the spectator has th.^ opportunity of surveying the whole heaven without altering his jKhsitiou. At Alexandria the number of stars visib e to the naked eye is only 4638 ; at Paris 4140; and at Berlin, 3206. The whole number of stars already registered, including those of the seventh magnitude, IS about 18,000, but astronomers assert that the total number of stars visible through the best tele- scopes, uown to those of the fourteenth maifnitude ex- ceeds 20,000,000; while, by including those of' the hfteenth and sixteenth magnitude, the number may possibly amount to 500,000,000,000, or half a million of millions 1 719. Seldom above 1000 are visible at a time to the naked eye. Those of the fifth and sixth magnitudes may, on a clear night, be discerned without the aid of a telescope. The Milky Way is composed of innumerable stars, whose average brightness is about the eleventh magnitude, and whoso joint light is therefore separated only by very powerful telescopes. 720. Every increase in the powers of t' .cojmj brinM new stars .„to view; and as their distances are so groat, it is "SlI tha there may be mynads of stars so remote froA, our system tliat their light has never reached the earth, though they may have been created at the same period as our system ; while others, whose hglit still reaches us, may have been long since extin- guished. rhere is no reason to suppose that the boundaries of the sidereal system are within reach of even our most powerful telescopes. 1 he most remote of the stars which the best tele- scopes brmg into view may owe ...eir apparent minuteness, not to interior magnitude, but to immense (fistance; and, perhaps an observer at the furthest of these would find the same appear^ ance as wo do. star beyond star in countless myriads and at adequate conception. •' K 2\H r.l.P.MENT8 OV ASTRONOMY. 2. Arrangement of Fixed Stars in Oonstel- lations. 3. Aooordiuff to thoir Situation in the Heavens. These two iiK'tluxIs have been alroiwly described in onr ft' count of tlio sphere of the heavens, und need not be again discussed lierc. 4. Arrangremont of the Stars acoordingr to other Difibrences than their apparent Bright- ness or Situation. 721. f'onsidered with respect to other differences thar iheir situation or brightness, the fixed stars may bo divided into six kitids:— 1. Ordinary fixed stars; 2. Temporary stars; 3. Variablo stars; 4. Binary stars; 5. Nebuhe ; (}. Clusters of stars. 1. Ordinary Fixed Stars. 722. Tlieso are the stars which, eitlier lo the eye uv in tlie telescope, do not present any peculiar phenome- non, such as variation in lustre, motion, nebulous ap- pearance, or are not ag;,'re^ated wit)* any other stars in a distinctlv separate cluster. T'ls is the case with many >f Uio fixed stars. 2. Temporary Stars. 723. These are stars which have appeared for a limited time, and then dit-'ippeared. Many stars, given in old catalogues, are not to be seen now ; and on seve- ral occasions, in various parts of the heavens, new stars have suddenly come into view, anc^ disappeared at longer or shorter intervals, shining with various degrees of brilliancy during t!ieir short career. It is said that 't was the sudden appearance of a new an" bright star in the heavens, about 125 n.c, which led the illustrious ancic.-it (istronomcr Hipparchus to the idea of makinir ELEMRNTi OF ABTIloNoMV. 219 a CAtaloppifl of the stars, which ho did. Homo of thew;, which have appeared atditTcrcutperiotlM, arc conjectured to ho periodical in their viHitations, especially the stars of dA,\ 12GI, and l/iT'i, which a[)pearod in tho same rc^non of tiie lieavens, and have bi-ctn tiionglit to bo thfi ame star with a period of about 300 years. The star of 1572 appeared so ssidchMily that Tycho IJraho saw several people looking at it, attracted by its brilliancy, where he was curtain it was not prominent half-oii-hour previously. 2. inlciurr o 8. Variable Stars. 724. The variable stais present the singular phenomo- non of a change in their brightness ; they undergo a regula:- alternate increase and diminution in their lustre ; and several altogether dis»'ppear for a time. Tiiey are sometimes termed /;mo^/.'iu/. 725. Tho Bccond star, /9, in tho constellation Perseas, is a vaiiftblo star, tho phenomena of which arc visible to th'i nak"(t oyo. It is just on tho margin of tho Milky Way, on the side of it farthest from tho north polo-Htnr, and about tiie same d'stunco from tiiat star as Vega. It is in li. A. 45°, D. N. 40". It rnay be found by drawing a line from tJio polo-star in the direction of t!.o lottjrs Per, in Fig. 1, nago 13; and is siiown in Fig. 2, pago 15, ibovo tho word " PerseuH." It is called Algol, and usually apjXT.rs as a star of tho second magnitude!. It remains so for 2*'- 1 1"-, when it suddenly begins to diminish in bright- ness, and in about 3^ houra dwindles to a star of tho fourth magnitude. It then begins again to increasf and in 3A hours returns to its usual brilliancy, going through all its changes in 2'> •20»»; '^8 ■»• The star tj of the southern constellation Argus hasexhibite' very remarkable changes in lustre, from tho fourth to tho second m... :<'"aidc, then to the fourth, then to tho second again, and during the prcbcut century to tho first and second magnitudes alternately. 726. This singular and regular change in the bright- ness of Algol, is attributed to the revolution of jome body round it, sulliciently large to cut otT a portion of its bVht when inter nosed between the foi'tli and the i il:'%te 220 ELEMENTS OF ASTRONOMY. /«,i>''" star, tliongh not of sufficient maf^nitnde to eclipse the star altofjether: in other cases it may be caused by rotation, i he bo'^y having' a dark and bright side — or by revohition in an elliptic orbit with the longer axis nearly in a line with our position. 727. The foUowinjj are some of the leading variable stars visible in Great Britain. /3 (beta) of Perseus ; 5 (delta) of Ccpheus; /3 (beta) of Lyra, a little south from Vega; a (alpha) of Hercules ; o (omicron) of Cctus. These have periods varying from about 3 to 331 days, that of omicron of Cetus. The latter is one of those variable stars which disappear altogether for a time. It is called Mira, is a star of the second magnitude when at its brightest, in R. A. about 32° or 2»'- lO'"-, and D. S, between 3° and 4°. It is nearly due south of the leading stars in Aries: and is idiowi: in Fig. 11, page 32. It appears about 12 times every 11 years, and remains tolerably bright for up- wards of a fortnight. 4. Binary Stars. 728. Binary stars are those stars which, on examin- ation wills the aid of a powerful telescope, and obser- vation for a considerable time, are found to consist of two stars nearly equal in apparent magnitude, and hav- ing a revolution round each other, — " Sidereal systems, composed of two stars revolving out each other in regular orbits." 729. This great discovery was made by Sir William Herschel, towards the close of the last century. It was first publicly announced in papers read to the Royal Society of London in 1803 and 1804. 730. About 6000 binary stars have been discovered, and the periods of revolution of 700 of them have been determined. In Castor, which is a binary star, the revolution is completed in 252 years. In a binary star in Corona Borealis the orbit is completed in 43 years ; and therefore a complete period has in this instance been gone through since the discovery by Sir W. Herscheb The following are some of the most remark- able of the binary stai's : y (gamma) of the constellation ELEMENTS OF ASTRONOMY. 221 [)sc the mvA. by ide — or er axis bio stars lelta) of X (alpha) varying ! latter is er for a agnitude ind D. S, ing stars irs about k for up- jxamiii- i obser- )nsist of nd hav- ;y stems, )ther in Virgo (182 years); »j (eta) of Cassiopeia (181 yearsj; a Centaiiri (75 years) ; | Ursro Majoris (63 years) ; 7 (gamma) of Leo (1200 years); d (delta) of Cygnus (178 years). 731. The binary stars are often coloured, each being of a different hue ; and they usually exhibit those tints which are called complementary, as blue and yel- low — red and green. Triple, ?r>d even quadruple stars have been discovered, in which three or four stars are grouped together, forming one connected system. 7 32. The phenomena of periodical and binary stars seem to indicate that among the fixed stars there are the same general laws which prevail in our solar system ; for wherever we observe motion in an orbit, there we must infer the existence of some force analogous to that of universal gravitation. " No doubt," says Sir John Herschel, referring to the double star y Virginia, *' can remain as to the prevalence in this remote system of the Newtonian law of gravitation." 733. Stars of nearly equal magnitude, and placed close to each other, but in which no revolution has yet been detected, are termed double stars. Of these, there is a very great number. P[ y^illiam iry. It to the covered, ve been tar, the ary star \ years; instance Sir W. remark- ;ellation 5. Nebulae. 734. Nebulae are faintly luminous stars, different from either of the preceding varieties. The leading kinds are two: — (1.) Those which are resolved by powerful telescopes into a collection, or globular cluster^ of separate stars, densely crowded into one luminous mass in the centre, but becoming scattered and separate towards the border. These are regarded as systems of suns, — as a whole world of stars, separate from other systems ; the individuals of which are probably suns, at great distances from each other. 735. (2.) Another kind of nebulae, to which the term ^ 222 ELEMENTS OF ASTRONOMY. nebulg, is most usually applied, is that in which the star appears a thin cloudy mass, of that fleecy appearance observed in the tail of a comet. The latter nebulae, it wan at one time imagined, may be p^aseous matter in the process of formation into suns with their attendant plan- ets : but recent examination of nebula) presenting this character by more powerful telescopes, such as that of Lord Eosse, having entirely, or partly, resolved many of such nebuUe into numbers of separate si* rs, it has been presumed that they might all bo so resolved if we had telescopes of sufficient power. The nebulous theory of the formation of the sun, planets, and other stars and systems, has thus lost the support it derived from the apparently irresolvable nebula). But it still remains as an explanation of a possible mode of formation of the heavenly bodies, sanctioned formerly by die great names of Sir W. Herschel and La Place. 736. Tho nebuljB exhibit every variety of form, from the circular to that of an elongated ellipse ; such as the nebulae in the girdle of Andromeda, which is visible to the naked eye. Some are termed annular, from their ring-like form ; and others planetary, from their resemblance to planets in presenting discs; others are termed nebulous stars, appearing as bright stars sur- roundfii jy .i faint luminosity; and Lord Kosse's telescope has revealed anoiher class of a very remarkable character, termed spiral nebulce, from the spiral coils of luminous matter which they exhibit. The remarkable objects called the Magellanic Clouds, near tho southern pole of the heavens, are two rounded luminous spots, like a portion of the Milky Way; and are found to be resolved by the telescope into separate stars, globular clusters, and almost every variety of nebula). Their light is not great, and the lesser disappears in bright moonlight. 6. Clusters of Stars. 737. Where there is a number of stars gathered to- gether, apart from the others, and forming in a man- ner an isolated group, they are termed a cluster^ and are considered to belong to some system separate from the general body of the stars. The Milky Way, tho ELEMRNT8 OF ASTRONOMY. 223 Pleiades, Coma Berenices, the bright spot in Cancer called Prsesepe or ^ho Beehive, are examples of those clusters. 738. It thus appears that there are many descriptions of fixed stars, as they are called, and that no stars are truly fixed, but that movements and changes are going on amongst them, which in time must greatly alter the appearance of the heavens ; that the universe has no bounds that we can even fancy, and that wherever we know it, it is full of matter and of motion of every form and variety. There is no point in space that has not some body in it, or some influence })assing through it. There are no voids — no objects fixed and un- changing. Life, force, activity, and endless change pervade the boundless realms of creation. 9M ELEMENTS OF ASTRONOMY. PART VIL SKETCH OF THE HISTORY OF ASTRONOMY. 739. As the heavenly bodies are everywhere con- Bpicaoiis, and naturally attract the attention ; — as many of their relative changes of position are obvious, and must have been observed by even the rudest tribes ; and as the coincidence of these changes with important terrestrial phenomena could not escape observation ; Astronomy has been cultivated from the earliest ages, and is by far the oldest of the sciences. 740. The origin of this science cannot be distinctly traced to any one country or people. The earliest authentic records show that it was cultivated simultane- ously, and wiixi considerable success, by the four great nations of remote antiquity, the Chaldeans, Egyptians, Indians, and Chinese. The Egyptians and Chaldeans had divided the year into 365 days, observed the direct and retrograde motions of the planets, and that they were sometimes stationary, that the ecliptic was inclined to the equinoctial, and had the zodiac divided into twelve constellations ; * besides many other important astronomical phenomena. The Chaldeans are said to have been the first who divided the day into twelve hours ; and the Egyptians first used tiie period of seven days — the week. 741. From Egypt, which has been justly termed the "cradle of the arts and sciences," and fromChaldea, * Some of the ancient Oriental nations (Indians and Chinese) divided tho zodiac jiiti) 27 portions corresponding to the moon's daily progress, called tlie Houses or Mansions of the Moon, ELEMENTS OP ASTRONOMY. 225 a knowlcdg-o of astronomy passed into Greece. Among tho philosophers of that country, and of the famous school of Alexandria, founded in Egypt by Ptolemy, after the death of Alexander the Great, Astronomy was cultivated with much zeal, and enriched by num- bers of new observations, and important corrections of former observations. 742. Thales Is the first Grecian on record who seems to havo given a stimulus to astrenomy. lie is said to have predicted an eclipse of tho sun, to have understood the nature of eclipses, to have discovered the obliquity of tho ecliptic; and to have pointed out the Little Bear by which to steer as a ^uide to tho north, instead of the Great Pear. Ho lived about GOO b.c. Ho is said to have been of Phoenician extraction. Tho Phoenicians steered by the Little Bear. 743. The present view of the solav system was first promulgated by Pythagoras, a iiimous Grecian philo- sopher, who flourished about 500 years before the ommencemcnt of the Christian era; and taught by his disciple Philolaus. He supposed the sun to be in the centre, and the earth and planets to revolve round it ; and was persecuted for holding this opinion. 744. But this opinion was not generally entertained. It was confined to some of the learned, and was not confidently taught or firmly bplieved by them. The majority of the philosophers of those days, as well as the people, entertained the popular notion that the sun, moon, planets, and stars, revolve daily round the earth, supposed to be fixed. Though it is conjectured that the true system of the universe was known to some before Pythagoras, as Anaximander, it Las been always termed the Pythagorean System. 745. The progress of discovery and improvement in Astronomy, in ancient times, was greatly retarded by assumed fancies ret,arding the perfection and immuta- bility of the heavenly bodies ; the gross and corrupt nature of the earth, and the entirely opposite natures of K 2 I 220 ELEMENTS OP ASTRONOMY. the earth nnd the heavenly hodies ; the pLrfect nature of the circle ; the notion that the celestial bodies must move in circles, and that their motions must be uniform; and many other dop^mas which had the sanction of the great name of Aristotle. 746. Hipparchus, who has usually been regarded as the "Father of Astronomy," flourished about 140 n.c. He determined with greater accuracy the length of the year ; discovered the inequality in the rate of the sun's motion, which he explained by supposing the earth not in the centre of the sun's orbit ; observed the inequality in the length of the solar day ; discovered the preces- sion of the equinoxes;* drew up a catah)gue of the fixed stars, with their precise positions, and determined the positions of places on the earth's surface by their latitudes and longitudes. He is said to have been the inventor of spherical trigonometry. 747. Ptolemy of Alexandria, who flourished about 130 years after the commencement of the Christian era, being born in the year 69, is the next astronomer of note. He was the author of a work on astronomy, called " The Great System," which is still preserved, being known by the name of Almagest, which it received from the Arabians, in which the whole astronomical knowledge of the times is recorded. 748. Ptolemy upheld the popular system that the earth is a fixed centre, round which all the heavenly bodies revolve daily. He placed the stars, sun, moon, and planets in the following order of distance from the earth : — viz., Moon, Mercury, Venus, Sun, Mars, Jrpi- ter, Saturn, and, lastly, the si)here of the fixed stars. This was the Ptolemaic System, which so long held possession of public opinion. * But the precession of the equinoxes must have been known to the archi- tect of the Great Pyraiiiid, erected n.c. 2170. (See " Facts and Dates/' p. 131.) ELEMENTS OF ASTRONOMY. 227 Ptolemy nrgncd tlmt if tho cnrth moved round tlio Bun, tho IKjles of the heavens would not nlwaya remain tho Hnme, tluit tlio fixed stars would not preserve the same figures and relative distances,* tl .ct the earth, hy the greatness of its muss, would move faster than tho loose bodies on its surface, so that they Ptolemaic System. Fig. 62. would be left behind, and that the earth would soon move out of the heavens. He objected to the earth's rotatory motion, that if such were the case, clouds, birds, and bodies floating in the at- mosphere would be left behind. 749. The apparer.tly irregular and retrograde move- ments of the planets were explained by the theory of Epicycles: — namely, that the heavenly bodies revolve in small circles, the centres of which move in regular * Tlicse objections lind been removed by the suggestions of previous astronomers, that tlic earth's orbit miglit perhaps be a mure point iu coiu- "aribou with the distance of the stiirSi 228 ELEMENTS OF ASTRONOMY. orbits ronntl the earth. Thus, let E, in Fif^. C3, ho tho earth, and P any planet revolving round tho earth. It is supposed to revolve in a Biuall circle, P o 7, round a centre c, which af^ain revolves in the circle a m no round the centre E, tho earth. The small circle P ^, I in which the planet revolves, is called an epicyle, and the large circle round which it turns the deferent. This theory had been devised by Apollonius to explain the retrograde movements of the planets. 750. Ptolemy also entertained the eccentric hypothesis, namely, that the earth was not exactly the centre of the orbits of the sun and planets, by which the apparent inequality in the rate of the sun's motion was explained. He considered the earth to be spherical, and a mere point in comparison with the distance of the fixed stars. 751. It has been said that the ancient Egyptians at one period held the opinion that Venus and Mercury had the sun, and not the earth, Air the centre round which they revolve, i.o explain the constant vicinity of these planets to the sun. T> is was the ELEMENTS OF ASTRONOMY. Ber3^tian System. Fig. 64, 229 752. After the timo of Ptolemy, Astronomy made little progress for more than a thousand years. It was cultivated by the Arabs, who made some additions and corrections, and some improvements in trigonometry ; and through whose invasion of Spain it was introduced into Europe in the ..inth century. 753. In Europe, Astronomy made little progress till the restoration of the true system of the planets by Copernicus. This distinguished man was born at Thorn in Prussia in 1473. lie was professor of mathe- matics at Rome, but spent his latter days in his own country. In meditating upon the phenomena of As- tronomy, he found that the Ptolemaic system did not afford an adequate explanation of them, and that the Pythagorean system accoimted satisfactorily for all the changes and motions. He accordingly adopt-d it : and his views were published in a work called Astronomia luataurata, which was published only a few days 230 KLEMENT8 OP ASTRONOMY. :i, I before Ills (l(!utlj, which took place in 1543. His HyHtoui, culled the Copernican System, has now been fdlly established. 754. The next astronomer of note was Tychj Brahe, a D.ine, bom in 1540. He made many impor- tant corrections of previous observations, drew up a catalof,nie of the stars, discovered the refraction by tho air, and many imjjortant points in the motions of tho moon, and ascertained the comets not to be atmospherio phenomena, by showing' their .,'reat distance, etc. Ho devised a planetary system, in which the earth was placed in the centre, and tl.e sun and moon were con- jectured to have the earth for their centre of motion, while all the planets were supposed to have the sun for their centre. This, which has been called tho Tychonic System, Fig. 65 ^ .. was devised to accommodate better to astronomical pbe- *j ELEMF.NTS OP ABTUONOMY. 231 iiomona tho if)/ii(r. IWituralis I'rincipia Alnthrwatica. HeMitleH eHtuhlishin;,' AHtronomy on BciontiJic principles, he vXm mft«H, and many important a«MitionH liavo been made to our aHtrononiical know- Icd^n'. Tlio Asteroids liavo been discovorcd, 4 in th« onrly part of the century, and upwards of IW rticently ; Neptune lias boon added to the lint of known pbinetn, by L«verrier and Adams, in a manner that has aston- ishet. the worhl by the wonderful accuracy it has proved in aslronomical observaticns and calcuhitions. Num- berH of cometH have been observed, and tlufir periodic times calcuhited, ai. 1 tim phenomena of one of these has tended to coufj. • the idea of the existence of a uni- versal Ether dilVused tlirou^j^liout space. A second re- turn of the comet of Halley in ISaf)— the first comet whoso return was ^ jtlicted — luis confirmed his compu- tations, and those of his successors wlio liad calculated tl 3 operation of disturbing influences on its motions. The meteors that flash across the sky are beginning to take their place in the planetary system. 'J'he fixed starei, which so 'ong resisted all attempts to find their parailax, lave at last yielded to the perseverance of Henderson, Bessel, Struve, and others, and parallaxes have been found for many of these remote suns; ^o that we can now assign a definite distance for theni,^ which will be made the basis of further discoveries. Govern- ments, associations, and individuals have alike conspired to promote astronomical research. Sir Jolin Herschel visited and resided long in the sonth of Africa, for the purpose of exploring the southern skies ; and extended immensely our knowledge of these interesting regions of the heavens. The famous telescope of Lord Rosse has made its wonderful revelations. New catalogues of the stars have been prepared, and observatories founded. By these means a mass of observations has been accu- mulated, which must extend our knowledge of the most remote part;: of creation, and pave the way for new in- ductions and discoveries. -A niong very recent discover- ies there are two which rival the must bfilllc.nt of any 23J ELEMENTS OP ASTHONOMV. former time, viz. :—Jirst, the discovery of the earth's true distance from the sun ; and, second, the splendid invention of spectrum analysis, by which we have come to know tijat the materials of which the sun, planets, and stars ai'e composed do nr' differ in any respect from those which prevail in i e world which we inhabit. INDEX. Aberration, Algol, . Alphcrat, . Andromeda, Angle, Aphelion, Apogee, . Apsides, Arcturus, . Aries, . Ascension, Asteroids, rage . 192 34, 219 . 34 35 19,22 . 108 . 109 . 108 . 34 . 27, 29 . 27 . 161 Astronomy, History of, . 224 Atmosphere, Influence of, 98 Conjunction, Ccnstellations, Northern, Southern, Zodiacal, . Corona Borcalis, . Cygnus, . Page 110 . 33 37 . 36 35 . 34 Auriga, Axis, . 16, 34 9,24 Benetnasch, . 33 Bootes, . 34 Cancer, Capella, Capricorn, Cassiopeia, . Ccpheus, . . 29 . 15, 34, 44 . 29 . 15, 33 . 33 Cetus, . Circles, 35 . 8,21, 22 Arctic and Antarctic, 48 Hour, . . .25 Climate, ... 64 Comets. . . . 105, 180 Day, Sidereal and Solar, 79 Lunar, . . .86 Day and Night, . . 49 Equal over the Earth, 56 Change in the Length of, 57 Causes of Differences and Changes in, . 60 Declination, . . 27 Definitions, . 8-18, 46, 106 Diameter, ... 8 Disc, . . . .111 Draco, . . . .36 Dubhe, ... 33 Dragon, . . • .12 Earth, .... 150 Ax's, . .. . 152 Density, . • 153 Diameter, . . .151 Distance from Sun, 150 Form, . . 151, 201 Gravity, Force of, . 154 Kevolution, . 152, 210 notation on Axis, . 205 236 INDEX. Pngo Eccentricity, . . 107 Eclipses, . . . .92 Ecliptic, . . 28, 109 Ellipse, . . . .100 Equator, ... 40 Equinoctial, . . . 2f) Equinoxes. . . .50, 59 Precession of, . . 195 Vernal or Spring, . 27 Fomalhaut, ... 35 Force, . . . 112, 114 Attractive, . . 110 Gravity, . . .118 Heat, . . .121 Projectile, . . .114 FoiTii of Heavenly Bodies, 130 Gravity, Centre of, . .113 Heat, . . . 65, 121 Heavens, Sphere of the, . 8 Extent visible at any Place, ',) Hemisphero, . . 23 Northern, Long Day, 52 „ Short Day, 54 Southern, State of, .50 Hercules, ... 35 Horizon, .... 8 Sensible and Rational, 42 Horizontal, ... 20 Hour-Circlcs, , . .25 Inclination, . Jupiter, . Satellites, 20 . 163 166 Pnpfo Latitude, . . . 31, 47 Light, Velocity of, . 167 Zodiacal, . . .183 Linear Eccentricity, . 107 Longitude, . . 31, 47 Lyra, . . . . 16, 34 Mars, . . . .157 Mercury, .... 147 Meridian, ... 46 Celestial, . . . 39 Meteoric Systems, . 184 Milky Way, . . 39, 217 Month, ... 80 Moon, . . . .155 Diameter, . . 155 Distance from the Earth, . . .155 Eclipses and Occulta- tions of, . . .92 Octants of, . . 92 Orbit, . . .156 Penumbra, . , 94 Phases, . . .90 Quadratures, , . 92 Revolution, , . 155 Rotation, . , 156 Syzigies of, . 92 Umbra, . . 94 Motion, .... 9 Apparent, of the Heav- ens, ... 10 Composition of, . .113 Mean, . . . Ill Orbitual, of Planets, Satellites, and Com- ets, ... 122 Rotatory, . . .130 INDEX. 237 157 .147 46 . 39 184 39, 217 86 .165 155 he . 155 ta- . 92 92 . 156 94 . 90 92 . 155 156 92 94 . 9 av- 10 . 113 111 im- 122 .130 ■ ruRe I'ngo Ncbulro, t . . 22 1 Rotation, . • , . 9 Ncptuno, , , • . 173 Nodes, . . 109 Satellites, , , . 105 Nortli Polar Star, . 12-13 Saturn, . 168 North Polo, . 11 Satellites of, . 171 Nutation of Earth's A xis, 199 Seasons, . . . ' 49,67 Semicircle, . 21 Occultatioii, . Ill Shooting Stars, . 184 Opposition, . . 110 Signs, .... 29 Orbits, , . . . 107 Solstices, . . 29 Solar System, 105 Parallels, 20 General facts rclatin S of Declination, . . 26 to, . 135 of Latitude, , 6 General illustrations Parallax, . . 188 of, . 176 Pegasus, . . 35 Sphere, . . . 8,24 Pendulum, . Ill Spheroid, . , 111 Perigee, . 109 Stars, . 212 Perihelion, . 108 Binary, . 220 Perpendicular, 20 Brightness of, . .216 Perseus, . 31, 219 Fixed, . 218 Phases, . Ill Temporary, .218 Plane Figure, . . 19 Variable, 219 Planets, 17,105 Sun, .139 Inferior, . 109 Annular Eclipse of, 96 Superior, . 110 Atmosphere of, . . 145 Polar Regions, . . 48 Axis, 141 Poles, 21, 25, 40 Dial, . 83 Elevation of. . 39 Distance of, . 139 Zenith, Distance ! of, 40 Eclipse of, , . 94 Positions of Objects in the Facula), 141 Heavens, . 24 Macula}, , . . 141 Precession of Equinoxes, . 195 Magnitude, . 140 Physical constitution, 148 Radius, . 8 Rotation, . . 140 Vector, . . 12G Shape, . 139 Reflection, . • . 102 Spots, . 140 Refraction, . 99 i Tangent, . .. . 107 238 INDKX. Terminator, , Tides, Time, Divisions of, Standurds of, Transit, Tropics, . Twilight, . Uranus, . Satellites of, . Ursa Major, , Minor, . . Vega, Page 51,68 Venus, . . 71 Vertical, . 78 Vulcan, . 89 111 29,48 Winds, 103 . 172 . 173 . 12 12 15, 34, 44 Year, . rape 148 . 20 146 . 69 87 Zenith, .... 8 Zodiac, ... 29 Signs of, . . . 30 Constellations of, . 36 Zones, ... 48 THE END. -i" PRINTED BY OLIVER AND BOYD, EDINBUnOH. Page 148 . 20 146 . 69 87 . 8 29 . 30 36 48 f! r \.\ 'l WP ^ ^/ EDUCATIONAL WORKS PUBLiailBO BY OLIVER AND BOYD, EDINBURGH; BOLD ALBO BY SIMl'KIN, MARSHALL, AND CO., LONDON, A Specimen Copy of any Class-book will he sent to Principals of Schools, post free, on receipt of one-half the retail price in postiuje stamps. Applications to he addressed to Oliver at.d Buyd, Edinhuryh. EngliBh Beading, Grammar, eto. ArinBtrong'B Eng. Composition.... P. 7 Eiig. Etymology 7 Colville'B Standard Keading-Bookri. 4 Connon's EngliHh Grammar G First Spelling-Hook 6 Dalgleiuii's EngliHh Grammars 6 Gram. 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Carefully Revised, 6d. Dr Douglas's Progressive Geography. On a new plan, showing recent changes on the Continent and elsewhere, and em- bracing much Historical and other Information. 160 pages, Is. Carefully Revised. Athenaum.— "The information is copious, correct, well put, and adapted to the present state of knowledge." Dr Douglas's Text-Book of Geography, containing the Phtbical and Political Geography of all the Countries i the Globe. Systematically arranged. 2s. 6d. ; or with ten Coloured Maps, 38. Carefully Revised. Geography of the British Empire. By William Lawson, St Mark's College, Cnelsea. Carefully Revised. 38. Past I. Outlines of Mathematical and Physical Geography. II. Physical, Political, and Commercial Geography of the British Islands. III. Physical, Political, and Commercial Geography of the British Colonies. ^f,„ PotoiA lighu>n th$ labour 0/ both Uachtr and puvxl. 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