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HOLDEN, M.A. DtBECTOR OF TUB WASIIBUHN OBaSRVATOBT h^ \v: s^ V-, N-.V- ^--^. -i ^^^ '.>•-. NEW YORK HENEY HOLT AND COMPANY i,jim«M- fl CopyriKht, 18M BY Hbmrv Holt & C!a / PREFACE. The present treatise i« a condensed edition of the AHronomy of J Lerican Science Series. The boolc bus not been shortened by eavtg out anything that ^vas essential, but by omitt.ng son.e of the ZZ of practical astronomy, thus giving to the descni,tive por- tions a greater relative extension. The most marked feature of this condensation .8 perhape. the om^ln of most of the mathematical formula of the ^^^^-^^^^ The present work requires for i»s understanding only a ^a- acquain ance with the principles of algebra and geometry and a slight knowlX of elementary physics. The space which has been gained irtU e^issionshas Ln utilized in giving a fuller discuss.on oj L more elementary parts of the subject, and m treatmg the funda- mental principles from various points of view. A familiar and secure knowledge of these « essential to the studerrealprogress. The ^"" '-'" ^f ^-^ J!:: uUde a referencebook to a student who has studied it and put it aside. Is in the larger work, the matter is given in two sizes of typ. It .in be found that the larger type contains a course P^cfcally com- iLt itself, and that the matter of the smaller type is chiefly e^ plana^ry of the former. It is highly desirable, however, that U^ Cks^Ld he rea. as a whole, while the -tual class^wo'k may be confined to the subjects treated in the larger type '« ^^« ^J^* " pressed for time. A celestial globe, and a set of B^«-^;;'' f ""^^ L's " New Star-Atlas" is as good as any), will be ^o^^^ t° b« °' L in connection with the study ; and if the class has access to a sm^l LTescope. even, much can be learned in this way. ^ ™- «^- glass wUl suffice to give a correct notion of the genera features of fhe moon's surface, and a very small telescope, if properly used, will do the same for the larger planets. f ~,.iaaii5a£p2iass- ':'':■ "^'IwtSS&B^MIHMML^ CONTENTS. PABT I. INTRODUCTION. PAOB and Abbreviations CHAPTER I. ,1 njmfln»lonB— The Celestial 8pbere-Tbe Tl.e Eartb's Shape and Dlmen'S-Diunial Motion in Different Horizon-The D'"™"^**"^!'"" the Terrestrial and Celestial Latitudes-Correspondence of the lerresw ^^ Spheres CHAPTER n. ««r Ti-ARTH TO Tffls HKAVBi»-(Cbn«inu«D. RBIjATIOH or THK KAUTH T" »•»" lr«t3rminatlon of Latltade^-P»«»>«- • CHAPTER HI- AOTROSomcAL IsmBtmmrni. „ ^«— .tia mocks— The Transit Instm- —The Nautical Almanac COXTKNTS. CHAPTER IV. MonoNB OK TiiK Earth. PAOI Ancient Ideaa of tlio Ploncts— Anniml Kcvoliition of the Earth —The Sun's Apparent Pulh— Obliqnily of tbo Ecliptic— The Seasons— Celestial Latitude and Longitude gi CHAPTER V. Tub Planetary Motions. Apparent and Real Motions of the Planets— The Copcrnlcan System of the World— Kepler's Laws of Planetary Motion . . 96 CHAPTER VL Universal Oravitatioit. Newton's Laws of Motion— Gravitation in tlie Heiivcns— Mutual Action of the Planets- Remarks on the Theory of Oravi- tation 118 CHAPTER VH. The Motions and Attraction of the Moon. The Moon's Motions and Phases— The Tides— Effect of the Tides upon the Eartli's Rotation 123 CHAPTER VIIL Eclipses of the Sun and Moon. The Earth's Shadow-Eclipses of the Moon-Ecllpscs of the Sun— The Recurrence of Eclipses 129 CHAPTER IX. The Earth. Mass and Density of the Earth- Laws of Terrestrial Gnivitation— Figure and Magnitude of the Earth— Geodetic Surveys- Motions of the Earth's Axis, or Precession of the Equinoxes —Sidereal and Equinocthil Year— The Causes of Precession 143 tl ..- tlie Earth Ecliptic— PAom 81 npcrnican Motion.. 90 —Mutual of Qravi- 118 ON. t of the 123 ) of the 129 tation — irveys — |Uinoxc8 ecession 143 COMHNrS. CHAPTER X. Cblkbtiai. Mbabubbme«t» or Ma« and Distance. ▼tt rAOS m.- n«l,.«ilal Scale of MeaBurcment-Mcasurcs of the Solar and ^'^ S„« irX-Mcthod. of Determining the Solar Parallax -Relative Masses of the Sun and PlaneU »«» CHAPTER XI. The Refbaction and Abbrbation of Light ; Twilight. A.™o«nherlc Rcfractlon-Qunntlty and Effects of Refractlon- ""'Twlllit-A^ratlon and the Motion of Llght-Dl««,very ^^ and EffecU of Aberration CHAPTER XII. CUBONOLOGT. .Ions of the Day-Equation of Time PART II. THE SOLAR SYSTEM IN DETAIL. CHAPTER I. &rRCCTlTBB or THE SOLAB STBTBM. Planets-Asterolds-Comets-Planetary Aspects-Tables of th. ^^ Elements of the Solar System CHAPTER II. The Sun. 1 a..mn.arv-The Photosphere-Light and Heat from °*"t S^^ JSTmount 0? Heat EmmedJ^^e Sun- ^lar Temperature-SunSpots and ^"cu'*--?^ .^^ «d Ba.»to%ature of Sun-Spots-Number and Periodic Uv oisSar 8pot»-The Sun's Chromosphere and Corona -VaL^^Nat^reof the Prominen«*-The Coron.^ Spec- truTsource. of the Sun's Heat-Theone. of th. Sun. ^ Constitution Vlii COtiTKNTS. CHAPTKU MI. Thk InPKHIDH Pl.AIIRTg. Motions and A«pecl8-Atni«H,,hero nnU Rotation of Merr.irv-"*" Atmosphcro uiul lU.Utlon of Vemis-TrunHlts of Mercury and Vcuug-8u|ip<)8cd Intrttmerciirlal PlaneU 321 CHAPTER IV. TlIK Mo<»N, Character of the M^n's Surface- Lunar Almoapherc-Light and Heat of the Moou-Ia tlicrc any Change on the Surface oftheMooD? CHAPTER V. The Pi,ankt Mars. DeBcrlplion of the Planet -Rotation- Surface -Sntelliles of **"" 233 CHAPTER VI. Tub Minor Planets The Number of Small Planets-Thelr Magnitudes-Forms of their Orbits— Origin -«. CHAPTER VII. Jupiter and nis Satellitbb. The Planet Jupiter-Satellites of Jupiter 240 CHAPTER VIII Saturn and rib Stbtbv. Oener.1 Descrlption-The Rings of Saturn-Satellites of Saturn 240 CHAPTER IX. Thb Planet IJRANua Discotery— Si»»flllitc8 ^^ ■ m ximmi Wercury— r Mercury aai re— Light u Surface •••••• I elliles of 233 'orms of 240 f Saturn 246 858 vom'KNra. *■ CIUPTBU X. TlIK Pl-ANBT NKPTUNE. ,aM ,....„„...,U.„......nU.«.M.n„-D,„.v.r,_.uB.«>U..». CHAPTEU XI. The Phtmcm. Co«otitution of the Planets . v,.nns-'rhc Eurlli and MarB-Jupiltr uiul Salun. Mercury mi" Vcnu»— • n^ ^" 201 — UVanui and Ncplune CHAPTER XII. Meteors. CHAPTER XIII. COMBTB. The BesUUng Medium PART III. 286 INTRODUCTION CHAPTER I. COHBTEI.1.ATIOSB. UieBtar*.... " CHAPTER II. Variable and Tempobabt Stabb. gtarsIteguMy Varlnble-Temporary or New 8uts ^ r««i,T^,„r.,,, . .n. » KL^!,!^a{iJUlMd Ki nM«««iyM< MNi iH wnuriii RBHBHHHHfckt X CONTENTS CHAPTER in. Multiple Stars. PAOB Character of Double and Multiple Stars— Binary Systems 801 CHAPTER IV. NBBULiG AND CLUSTERS Discovery of Nebulae— Classiftcntion of Nebulae— Clusters— Star Clusters— Spectra of Nebulae, Clusters, and Fixed Stars— Motion of Stars in the Line of Sight 804 CHAPTER V. Motions and Distances op the Stars. Proper Motions— Proper Motion of the Sun— Distances of the Fixed Stars 313 CHAPTER VI. Construction op the Heavens Star-gauging- The Milky Way 818 CHAPTER VII. CoSMOaONT. Laplace's Nebular HypoihcsiH— Oeneral Conclusions 828 INDEX aaa PAOB ms 801 ASTRONOMY. ere— Star ] Stars— 804 ;s of the 813 818 INTRODUCTION. Artronomy Deflnei-Astronomy {a" a llw) is the science which has to do with he Lavenly bodies, their ar>l>earanceB, their natur., and the laws governing their real and their apparent motions Tn'woaching the study of this the oldest of th. sciences 'depending upon observation, it must be homo m n,iad that its progress is most intimately <>onn^^ ^^^ It of the race, it having always been the basis of ge<^- raphy and navigation, and the soul of chronology. Some 71 chief advances and discoveries in ab^ract -the. „,atics have been made in its serv.oe, and the method both of observation and analysis once peculiar to its prac- Uce now furnish the firm bases upon which rest that great group of exact sciences which we call Physics. ^ It is more important to the student that he should be- come penetrated with the spirit of the methods of .^tron- omy tlan that he should recollect its minut.« ; and it s most important that the knowledge which he ""^y «^° from this or other books should bo referred by him to ite true sources. For example, it will often be necessary to sSTf certain planes or circles, the ecliptic, the equa- tTtbe meridian! etc.. and of the relation of the appa- ABTRONOMT. rent positions of stars and planets to them; but his labor will be useless if it has not succeeded in giving him a pre- cise notion of these circles and planes as they exist in the sky, and not merely in the figures of his text-book. Above all, the study of this science, in which not a single step could have been taken without careful and painstaking observation of the heavens, should lead its student himself to attentively regard the phenomena daily and hourly pre- ■ented to him by vhe heavens. Does the sun set daily in the same point of the horizon? Does a change of his own station affect this and <4her aspects of the sky? At what time doe« the fuU moon rii»? Which way are the horns of the young moon pointed? These and a thonsand other questions are «lroM|y vaamvnA by the obsarvant eyes of the ancients, who disooverad not only the existence, but the motion*, of the vari<»i plna»t^ and gave special names to no less than lonrscoie ^an. The modem pupil is more richly eqaipped fwr observation than the ancient philoaopher. |f one oonW hav» pnt % mere opera.gUw8 in the hands of HiPVABoaire the world need not have waited two thonsand years to know the natnra of that early mystery, the Milky Way. nor wonW it have required a Oaliwo to discover the phases of Fmmm and the spots on the sun. Astronomy furnishes the principles and the methods by monna ol which thousands of ships are navigated vith lafety and oertainiy from port to port; Iff wWA thn dimenaiona of the earth itself are fixed with higH praoinoB} by which the distances of the sun, the pknetf, and the hri(^ter stare are measured nnd detemined. The letaila of these methods cannot he given in iA eWmwIniy wofk ; hnt the genrnd prinoiplea and even the apiritol tk« )at his labor I him a pre' exist in the ook. Above a single step painstaking ident himself I hourly pre- the horizon? lis and <^her til moon rise? >on pointedf acljaniiraiied isooTerad not ri west of Washington. In the figure, suppose Ftohe west of the first meridian. All the phKses on the straight line PQ have a longitude of 15° or 1 hour; all on the curve Pi'^Q have a longitude of 75° or 6 hours; and so on. The difference of longitude of any two placee on the earth it the angular distance between the terrestrial tneridiane passing through the two places* Thus Washington is 77° west of Greenwich, and Sydney is 209° west of Greenwich. Hence Sydney is 132° west of Washington, and this in the difference of longitude of the two places. 4L 1 (ainally ney is 209° ■s. In this degrees, or )60 divided ue either in nwioh, and we choose. ortoWash- and Oreen- t meridian, ragitude of k longitude m iht earth meridiatu tnd Sydney Si' west of tade of the SYMBOLS AND ABBREVIATIONS naMB 0» THB PLAimW, wto. ® or Tlie Sun. The Moon. Mercury. Venus. The Earth. 6 V Man. Jupiter. Saturn. Uranus. Neptune. The asteroids are distinguished by a circle enclosing a number, which number Indicates the order o( dlscoTery, or by their names, or by both, as @) ; HeeaU, noiiB or TBa kodiao. Spring ■igns, (1. T « U. « •• /a n Aries. Taurus. '. 8. n Qemtni. (4. O Canoer. Summers J ft Leo. •*«°* (e.iBl Virgo. ( 1. Autumn \ g signs. J j' Wlnter^^ ■ £k Libra. HI Scorplus. f Saf^ttarius. ^ Cnpricomus. a Aquarius. H Pisces. The Greek alphabet Ishere inserted to aid those who are not already familiar with It in reading the parts of the teit in which ito lettera occur: UttMS. A a Bfi rr J 8 E e ZC Ht, e » /« AX Kames. Alpha BeU Oamma Delta Epsilon Zeta Eta Theto Iota Kappa Lambda Mu LrttoiSL N V Si Oo n nit pp sat Tr T V 9 9» XX am Ka Na Xi Omleron PI Bho Sigma Tau Uprilon Phi Chi Psl Omega mmuM'* 19 ABTRONOMT. THE METRIC SYSTEM. The metric nyatem of wcightt nnd meniurea being employed In thii volume, the following reliillon» between the unlu of tliin iiyitcm most uited and thoee of our ordinary one will be fountl convenient for reference : MKAaURKB or LRMOTH. 1 kilometre = 1000 metres = 0-63187 mile. 1 metre = tbe unit = 89 -870 inciiei. 1 millimetre = xin »' » met™ = 0-08987 incb. MBAtUBEa or WRIOBT. 1 kilofnvmme = 1000 grammea = 2- 2049 pnunda- 1 gramme = the unit = 10-482 grains. The following rough approximations may be memorised *. The kilometi« U a little more than ^, of a mile, but less than | of a mile. The mile is 1 A kilometres. The kilogramme is 2| pounds. The pound is less than iialf a kilogramme. One metre is 8-8 feet. One metre la 80 -4 inches. ' ' 1 . . ■' ii.i-!' -. ' V- i j^iA 4 y\ Pinploycil li. tf tliiH nyitctn unvenient for ile. lea. ich. jnda. DS. led -. lesR than | of CHAPTER I. THE UBLATION OF THE EAUTH TO THE HBAVBNa THX EAiTrfs Sham amd Dimmoii. The earth ii a globe whoM dimeMions are gigantic when compared with our ordinary and daily ideas of size. lt> shape is nearly a sphere, as has been abuuduntly proved by the accurate geodetic surveys which have been made by various nations. Of its size we may get a rough idea by remembering tliat at the present time it requires about three months to travel completely around it. To these familiar facts we may add two propositions which are fundamental in astronomy. I The earth w compMely isolated in space. The most obvious proof of this is that men have visited nearly every part of the earth's surface without finding anything to the contrary. .. II The earth is one of a vast number of globular bodies, familiarly known as stars and planets, moving according to certain laws and separated by distances so immense that the magnitudes of the bodies themselves are insignificant tn comparison to these distances. The first conception which the student of astronomy has to form is that of living on the surface of a spherical earth which, although it seems of immenie die to him, is really but a point in comparison -.-,i:^mm!3»^'.m't'*'!*n^'«-y- '■•■* ur :u';.i 14 ASTRONOMY. !i !"i If m with the distances which separate him from the stars which he nightly sees in the sky. The Celestial Sphebs. When we look at a star at night we seem to see it set against the dark surface of a hollow sphere in whose centre we are. All the stars seem to be at the same distance from us. When we stop to consider, we see that it is quite possible that some one of the many stars visible may be nearer than some other, but as we have no immediate method of knowing which of two stars is the nearer, we are driven to speak of their apparent positions just as if they were bright points studded over the inner surface of a large hollow globe, and all at the same distance from us. The radius of this globe is unknown. We do not, however, think of any of the stars as beyond the surface and shining through it. We therefore suppose the radius of the sphere to be equal to or greater than the distance of the remotest star. Students generally fail at the outset to realize two very important facts in relation to the celestial sphere. First, that for all ''-e purposes of our present knowledge the relative positions of the stars on its surface do not vary. Maps were made of these positions centuries ago which are as correct now as old maps of portions of the earth. The motions of the earth present different portions of the celes- tial sphere to our observation at different times, and one who has not thought at all of the subject might by that fact be led to suppose that changes are taking place in the relative positions of the stars themselves. Most people, however, know that they can find the same groups of stars . iss^' :'''^#B-'■ le stars which to see it set I whose centre ance from us. quite possible lay be nearer idiate method we are driven , if they were ice of a large rom UB. The not, however, B surface and the radius of he distance of )alize two very jphere. First, knowledge the B do not vary, ago which are le earth. The ns of the celes- times, and one might by that Dg place in the Most people, gronps of stars RELATION OF THE EAltTH TO THE HEAVENS. 15 -"constellations," as they are called-in different direc tions from the observer's location on the earth, n.ght after night; the difference in the directions being due to he eartli's motions. Reflection on the foregoing will help he student to realize the second imporUnt fact alluded to m the besinning of this paragraph-that for most practical pur- poses of astronomy the earth may be regarded as a pomt Fia. 4. in the centre of a hollow globe whose inside surfaw. w spotted over with the stars, that hollow globe corresponding tothe celestial sphere. In fact ingenious instruments to illnstrate some of the truths of astronomy have been made of Urge globes of glass or other transparent substanoe., with the stars painted in their unvarying positiont on the 16 ABTRONOMT. inside surface, and the earth snspended at the centre by supports rendered as nearly invisible as possible. Suppose an observer at the point in the figure. If he sees a star at the point Q it is clear that the real star may be anywhere in space on the line OQ, as at q for example, and still appear to be at Q. Again, stars which appear to be at the points P, 'V, U, T, S, R, may in fact be anywhere on the lines OP, V, OU, OT,OS,OR. Thus, if there were three stars along the line T, they would all be projected at the point T of the celestial sphere, and would api>ear as one star. The celestial sphere is the surf me upon which we im- agine the stars to be projected. The projection of a body upon the celestial sphere is the point in which this body appears to bo, when seen from the earth. This point is also called the apparent position of the body. Thus to an observer at 0, T is the apparent position of any of the stars whose true positions are t, t, t. Hence it follows that positions on the celestial sphere re- present the directions of the heavenly bodies from the ob- server, but have no necessary relation to their distances. If the observer changes his position, the apparent posi- tions lof the stars will also change. We need some method of describing the apparent posi- tions of stars oh the celestial sphere; to do this we im- jigine a number of great circles to be drawn on its surface, and to these circles we refer the apparent positions of the stars. A consideration of Fig. 2 will show the correctness of the following propositions, which it is necessary should be clearly understood : L Every straight line through the observer, when pro- M the centre by >le. figure. If he real star may for example, uts P, 'V, U, icaOP, or, CO stars along he point T of star. which we im- l sphere is the en seen from Trent position I the apparent ons are /, /, t. Hal Hphere re- from the oh' distances. ipparent posi* apparent posi- o this we im- on its rarface, ositionB of the correctness of sary should be rer, when pro- BELATION OF THE EAJiTU TO THE HEAVENS. 17 duced indefinitely, intersects the celestial sphere in two opposite points. II. Every plane through the observer intersects the sphere in a great circle. III. For every such plane there is one lino through the observer's position which intersects the plane at light angles. This lino meets the sphere at tho poles of the gi-eat circle which is cut from the sphere by the plane. Example: PP',Fig. 2, is a line through perpendicular to the plane ^ 5. P, P' are the poles of ^ -R IV. Every line through the centre has one plane perpen- dicular to it, which plane cuts the sphere in a great circle whose poles are the intersection of tho line with the sphere. t, v /i Example: The line QQ'hfiBone plane ^i? through O perpendicular to it, and only this one. The Hobi^. A hvel plane touching the spherical earth at the point where an observer stands is called the horizon of that This plane cnts the celestial sphere in a great circle, which is called the celestial horizon. The celestial horizon is therefore the boundary between the visible and the in- visible hemispheres to that observer. The Vertical Line.— The vertical line of any observer w the direction of a plumb-line where he stands. This line is perpendicular to his horizon. It intersects the celestnd sphere in two points, called the zenith and the nadtr of that observer. , . j • i The zenith of an observer is the point where hts vertical line cuts the celestiitl sphere abovf Ms Aw?. m I 18 AarRONO^r. The nadir of an observer is the point where his vertical line cuts the celestial sphere below his feet. The zenith and nadir are the poles of the horizon. Vertical Planei and Cirolei.— A vertical plane with re- spect to any observer is a plane which contains his vertical line. It must pass through his zenith and nadir and must be perpendicular to his horizon. A vertical plane cuts the celestial sphere in a verticai circle. As soon as we imagine an observer to be at any point on ^ the earth's surface his horizon is at once fixed; his zenith and nadir are also fixed. From his zenith nidiate a number of vertical circles which cut the celestial horizon perpendicu- larly, and unile again at his nadir. This is a system of lines and circles which every person carries about with him, as it were, and which may eerve him for lines to which to refer the apparent position of every etar which he Some one of these vertical circles will pass through any and every star visible to this observer. ri« altitude of a heavenly body is its eUvation dbtm the plane of the horizon measured on a vertical circle through the star. The zenith distance of a star is its angular d%slancefrom the zenith measured on a vertical circle. In the figure, ZS'w the zenith distance (5) of S, and H8{a) is its altitude. ZSUiimto of » great oirde; ■^s^igti00eisBSi ^mmmMmtwNaiHtim .'.Itjit'^l' J his vertical rizun. ine with re- his vertical lir and must a a vertical my point on ) bis horizon ; his zenith fixed. From e a number rhich cut tbo perpcudicu- again at his a system of which every about with 1 for lines to star which he through any tion above the circle through dietaneefrom {Z) of 8, and k great oirdei BELATION OF TUB EABTH TO THE UEAVBN8. 19 the vertical circle through the star. ZSH = a + Z = 90°, and 5 = 90° - a or o = 90° - Z. The altitude of a star in the zenith is 90°; half way from the zenith to the horizon it is 45°; in the horizon it is 0°. Theatimuth of a star is tlte angular distance from the point where the vertical circle through it meets the horizon, to the north {or south) point of the horizon. In the figure, NHxn the azimuth of S. The azimuth of a star in the east or west is 90°. The prime vertical of an observer is that one of his verti- cal circles which passes through his east and west points. Coordinates of a 8Ur.— The apparent position of a heav- enly body is completely fixed by means of its altitude and azimuth. If we know the altitude and azimuth of a star we can point to it. If, for example, its azimuth is 20' from north towards the west and if its altitude is 30°," we can point to the star by measuring an angle of 20° from the north point towards the west, which will fix the foot of a vertical circle through the star. The star itself will bo on the vertical circle, 30° above the horizon. This point, and this alone, will correspond to the posi- tion of the star as determined by its altitude and azimuth. Numbers {or quantities) which exactly define the position of a body are called its co-ordinates. Hence altitude and azimuth form a pair of co-ordinates which fix the apparout position of a star on the celestial sphere. It must be remembered that these two co-ordinates give only the position of ihe projection of the star on the celes- tial sphere, and give no knowledge of its distance from the obserTor, The body may be any where o* thQ Une defined l|^!3iW9WB(IIB™M«BWiiBSpSS^B^^W MiHBUfi w ^ ASTRONOMY. by the position on the celestial sphere and the place of the If we also know the distance of the star from the ohaer- ver, we know every possible fact as to its place in space. Thus, three co-ordinates suffice to fix the absolute position of a body in space; two co-ordinates suffice to determine its apparent position on the celestial sphere. These propositions suppose the place of the observer to be fixed, since the altitude and azimuth refer to an obser- ver in some one definite position. If the observer should change his place, the star remaining fixed, the apparent position of the star on the celestial sphere would change to him owing to his own motion. The numbers which ex- presi this apparent position-the altitude and azimuth of the star— would also change. But wherever the observer is, if he has these two co- ordinates for a star, the apparent place of the star is fixed for him. . , . . J The Horiioii.— Since the earth is spherical m form, and the horizon is a plane touching this sphere, every different place must have a different horizon. Wherever an observer goes on the earth's surface he carries an horizon, a zenith^ and a nadir with him, and a set of vertical circles to which he can refer the positions of all the stars he sees. If he stays at a fixed point on the earth's surface his horizon is always fixed with relation to his vertical line. But Oje earth on which he stands is turning round its axis, and hw horizon being tangent to the earth is moving ako, and the vertical line moves with it The stars stay in the B«ne abM- lute places from year to year. The earth on which ^ observer stands is turning round from west to east His horiisonia thus brought successively to the east of the varioug m >lace of the a the ohser- in space. ute position etermine itt I observer to to an obser- »rver should he apparent Id change to irs which ex- l azimuth of bese two co- I star is fixed in form, and rery different r an obserrer on, a zenith, cles to which ) sees. If he lis horizon is ne. But the axis, and his also, and the he seme abio- on which the to east Hit ;of theT»rioa« RELATION OF THE EARTH TO THE HEAVENS. 21 stars, which thus appear to rise higher and higher above it. The earth continues its motion, and the plane of his ho- rizon finally approaches the same stars from the west and they set below it, only to repeat this phenomenon with every rotation of the earth. The horizon appears to each observer to be the stable thing, and the motion is referred to the stars. As a matter of fact it is the stars that stand still and the horizon which moves below them, causing them to appear to rise, and then above them, causing them to appear to set. tmt DiDBVix Mono*. The diurnal motion is that apparent motion of the sun, . moon, and stars from east to west in consequence of which they rise and set. We call it the diurnal motion because it repeats itself from day to day. The diurnal motion is caused by a daily rotation of the earth on an axis passing through its centre called the axis of the earth. This axis intersects the earth's surface in two opposite points called the north and south poles of the earth. If the earth's axis be prolonged in both directions, it meets the celestial sphere in two points which are called the poles of the celestial sphere or the celestial poles. The north celes- tial pole corresponds to the north end of the earth's axis; the south celestial pole to the south end. The plane of the equa )or is that plane which passes through the earth's centre perpendicular to its axis. This phme intersects the earth's surface in a great circle of the earth's sphere which is called the earth's equator {eq in Fig. 6). , .-i:.."^4i'';i«*Hi^ j^;-..E."-IiS ■a^ M^ m m g2 ASTltONOMY. This piano intersects the celestial sphere in a great circle of this sphere which is called the celestial equator or equi- noctial (EQ in Fig. C). , * --« ^^^a The celestial equator is everywhere half way between the two celestial poles and thus 90'' from each. The celestial poles are thus the poles of the celestial equator. Apparent Diurnal Motion of the Celeitial Bphere-The fl4.& Observer on the earth is nnconsoious of its rotation, and the celestial sphere appears to him to revolve from east to west around the earth, while the earth appears to remain at rest. The case is much the same as if he was on a steamer which is turning round, and as if he saw the bar- bor-shores, the ships, and the houses apparently turning m an opposite dirwtiofli great circle lor or equi- letween the 'he celestial (here.— The rotation, and from east to an to remain he was on a 9 saw the har- tly tnrning in BBLATION OF TUB EARTH TO TUB UBAVEN8. 23 So far as appea. ea are concerned, it is (inite the same thing whether we conceive the earth to be at rest and the heatens to turn about it, or whether we conceive the stars to remain at rest and the earth to move on its axis. We can explain all the phenomena of the diurnal motion in either way. We must, however, remember that it really is the earth which turns on its axis and successively presents to the observer different parts of the celestial sphere. The parts to his east are just coming into view (rising above his horizon). The parts to his west are about to disappear, (setting below his horizon). Since the diurnal motion is an apparent rotation of the celestial sphere about a fixed axis, it follows that there must be two points of this sphere that remain at rest; namely, the two celestial poles. Moreover, since the celes- tial poles are opposite points, .one pole must be above the horizon and therefore a visible point of this sphore, and the other pole must be below the horizon and therefore in- visible. . „ ,, The celestial pole visible to observers in the northern hemisphere is the north pole. To locate its place in the sky let the student look at the northern sky on any dear evening. . , . He will see the stars somewhat as they are represented in the figure. , .„ . In fact Fig. T. shows the stars as they will appear to an observer in the month of August in the early hours of the evening. But theconfigurations of the stars can be recognized at any other time. The first star to be identified is PoUria, or the Pole Star. It may be found by means of the Pointers, two stars in the constelUtion Ursa Major, famiHarly known as the Great wmm i iHl i .i m^'t mmmm II 94 AarsoNOMT. Dipper. The Btraight line throngli these Btors, as shown in the figure, posses near Polaris. Polaris is U degrees from the true pole. There is no star exactly at the pole itself. The altitude of the pole-star above the horizon of any place is equal to the latitude of the place, as will be shown rm. T. hereafter. Hence in most parts of the United States the north pole is from 30° to 45° above the horizon. In Eng- land it is 61°, in Norway 80°. I%e north-polar distance of a star is its angular distanet from the north celestial pole. kwsMb nSlATtOlr OF THK SAltrH To /f n/SAl'^m 9| as shown i degreei the pole on of any be shown States the . In Eng- !0r di»tanc» The following laws of the diurM*! aotioii wil now be clear: I. Every »tar in th» heavens appears to describe a circle tttound the pole as a centre in consequence of (he diurnal motion. II. The greater tin star's north-polar distance the larger is the circle. III. All the stars describe their diurnal orbits in the $ame interval of time, which is the time required for th$ earth to turn once on its axis. The circle which a star appears to describe in the sky in consequence of the diurnal motion of the earth is called the diurnal orbit of that star. These laws can be proved by obsei-yation. Tlw student can satisfy himself of their correctness in any clear i^ight. If the star's north-polar distance is less than the altitude of the pole, the circle which the star describes will not meet the horizon at all, and the star will therefore neither rise nor set, but will simply perform an apparent diurnal rcTolution round the pole. Such stars are shown in the figure. The apparent diurnal motion of the stars ii in the direction shown by the arrows in the cut. Below the pole the stars appear to more from left to right, west to east ; abore the pole they appear to moye from east to west. The circle within which the stars neither rise nor set is called the eireU of perpetual apparition. The radius of this circle is equal to the altitude of the i)ple above the iMrison, or to the north pohir distance of tihe north point of the horison. ,.^ As a lesnlt of this apparent motion each ii\diTidnal con- gtetfvtion dumges its configuration with r^jgpect to the I mmittiiiSSiim 91 ABTRomMT. horizon. That part of the comtellation which in highett when the group i« above the pole becomes lowwt when it Is below the pole. This i> shown in the figure, which represents a supposed constellatioa at diflercMt times of the night as it revolves round t\\e pole. The culmination of a star occurs when it is at its highest point above the hori- lon. The jwint of culmination is midway between the points of rising and setting. If the polar distance of a star exceeds the altitude of the Fia. a pole, the star will dip below the horizon for a i'Wt of its diurnal orbit, and the greater the polar distance of the star thd longer it will be below the horizon. A star whose polar distance is 90" lies on the celestial equators and one half of its diurnal orbit is above and one half below the horizon. ' The fan is in the celestial equator about March Slst and September 21st of each yoai, ao that at th^ times the ^Ama in higheit at when it ire, which mes of the nation of a 9 the hori- )tween the bude of the I ^>Art of its Bnce of the the celeitial I above and rch Slit and e timed the RMLATWlf OP TUS KAHTH TO THK ttKAVBSB. 97 dayi and night, are of equal length. Thii ii why the celortial equator waa formerly called the equinoctial. Looking further wuth at the celestial sphere, we ihall gee Btani which rise a little to the ea«t of the south point of the horizon and set a little to the west of this point, being above the horizon but a short time. The south pole is as far below the horizon of any place as the north pole is above it. Hence stars near the south pole never rise in uur latitudes. The circle within which stars never nae is called the circle of perpetual occultation. It is clear that the positions of the circles of perpetual apparition and occultation depend upon the \ --tion of the observer upon the earth, and hence that they will change their positions (is the obse» fer changes his. By going to Florida we may see groups of stars which are not visible in the latitude of New York. The Meridian.— The pJane of the meridian of an observer is that otte of his vertical planes which contains the earth's »:- >. Being a vertical plane it must contain the senith an nadir of the observer; as it contains the earth's axis it must contain the north and s.>uth celestial poles. Different observers have different meridian planes, since they have different zeniths. The terrestrial meridian of an observer is the line in which the plane of his meridian intersects the surface of the earth. It is his north and south line. It follows that if several observers are due north and south of each other, they have the same terrestrial meridian. The celestial meridian of an obwsrver is the great circle cut from the celestial sphere by the phme of that observer's meridian. Persons on the same terrestrial meridian have the same celestial meridian. in 11 n \i) Sd AamoifbitT. Terrestrial meridianB are considered as l)eloDgiog to thd places through which they pass. For example, we speak of the meridian of Greenwich or of the meridian of Wash- ington, and hy this we mean the (terrestrial or celestial) meridian lines cut out by the meridian plane of the Boyal Observatory at Greenwich or the Naval Observatory at Washington. The Diubval Xotiom ni Jtawaaan "LktamoM. As we have seen, the celestial horizon of an observer wiU change its place on the celestial sphere as the observer travels fks. t. TM ^AmuUB. from place to place on the snrfiice of the earth. If he moves directly toward the north his zenith will approach the north pole; but as the zenith is not a visible point, the motion will be naturally attributed to the pde, which will seem to approach the point overhead. The new apparent position of the pole will change the aspect of the obBenfer'fl sky, as the higher the pole appears above the horiion tli9 teloDgiog to thd hmple, we spealc ridian of Wash- ial or celestial) ne of the Boyal Obserratory at LlTITUSIli m obseryer will observer travelB 9 earth. If he ill approach the iiUe point, the )de, which will ) new apparent f the obBenier'fl ihe horiion the nJSLATJ02f Of THU HABTlt TO TllS HEAVENS. 29 greater the circle of perpetual apparition, and therefore the greater the number of stars which never set. If the observer is at the north pole his zenith and the pole itself will coincide : half of the stars only will be vis- ible, and these will never rise or set, but appear to move around in circles parallel to the horizon. The hori-^on and the celestial equator will coincide. The meridian will be indeterminate since Zand P coincide; there will be no east and west line, and no direction but south. The sphere in this case is called a parallel sphere, (See Fig. 9.) Vm. M.— TnBraar If instead of travelling to the north the observer should go toward the equator, the north pole would seem to ap- proach his horison. When he reached the equator both poles wottld be in the horizon, one north and the other Mmtfa. All the stars in succession would then be visible, and W5h would be an equal time above and below the horiaon. (See Fig. 10.) The sphere in this case is called a right sphere, because the diurnal motion is at right angles to the horizon. If MMM IH, 80 ASTRONOMY. now the observer travels southward from the equator, the south pole will become elevated above his horizon, and in the southern hemisphere appearances will be reproduced which we have already described for the northern, except that the direction of the motion will, in one respect, be different. The heavenly bodies will still rise in the east and set in the west, but those near the equator will pass north of the zenith instead of south of it, as in our lati- tudes. The sun, instead of moving from left to right, there moves from right to left. The bounding line be- tween the two directions of motion is the equator, where the sun culminates north of the zenith from March till September, and south of it from September till March. If the observer travels west or east of his first station, his zenith will still remain at the same angular distance from the north pole as before, and as the phenomena caused by the earth's diurnal motion at any place depend only upon the altitude of the elevated pole at that place, these will not be changed except as to the times of their occurrence. A star which appears to pass through the zenith of his first station will also appear to pass through the zenith of the second (since each star remains at a con- stant angnhir distance from the pole), but hit«r ia time, since it has to pass through the zenith of every place be- tween the two stations. The horizons of the two stations will intercept different portions of the celestial sphere at any one instant, but the earth's rotation will present the same portions successively, and in the same order, at both. RELATION OF THE EARTH TO THE HEAVENS. 31 e equator, the irizon, and in w reproduced rthern, except ne respect, be se in the east lator will pass M in ourlati- left to right, nding line be- jqnator, where [)m March till bill March. B first station, gular distance lie phenomena f place depend ) at that place, times of their 8 through the pass through mains at a con- later in time, every place be- M two stations wtial sphere at rill present the order, at both. COBBlffOKDlirCB OF THE TMBMTEIAI AOT CBIMTUI 8FHEBE8. We have seen that the altitude of the pole above the horizon of any observer changes as the observer changes his place on the earth's surface. The exact relation of the altitude of the pole and the horizon of any ob^rver ,B expressed in the following Theorem: The altitude of m celestial pole above the horizon of an y place on the earth s surface is equal to the lati- tude of that place. Let i< be a place on the earth PEpQ, Pp being the earth's axis and EQ'\^ equator. Z is the zenith of the place, and HR its hori- zon. X C is the latitude of L according to ordinaiy geographical definitions; t.0.> it is the angular distance of L from the equator. Pro- __^_^_^ long OP indefinitely to P' '»»•"• and draw LP' parallel to it, P' and P' ate pomts on the celestial sphere infinitely distant from h. In fact they appear as me point since the dimension of the wth are vanishingly small compared vith the radius of the celestial sphere, which may be taktn as large as we please. We have then to prove that LOQ=P'LB. PO^ and ^i Fare right angles, and therefore equal. ZLP^ = ZOP' by construction. Hence ZLH- ZLP — POQ- ZOP',oT the latitude of the point L is meafr uwd by either of the equal angles LOQoxP'ltff* k[ -. +->*;J»iV.-'-i''WS^- •■^mr ' >- huj^ I ![ $H ABTRONOMT. If we denote the latitude by q> it follows that the N. P.D. (north-polar distance) of Z is 90° — g>. As an observer moves to various parts of the earth, his senith changes position with him. In every position the N.P.D. of his lenith is 90° — q>. If he is at the equator his ^ is 0° and his zenith is 90° from the north pole, which must there- fore be in his horizon. If he is at the north pole, q> — ■\- 90° and the N.P.D. of his zenith is 0°, or his zenith co- incides with the north pole. If he is at the sonth polo {tp= - 90°) the N.P.D. of his zenith is 90° - (- 90°) or 180°. That is, his zenith is 180° from the north pole, or it must coincide with the sonth pole ; and so in other oases. All this has just been shown (pages 38-30) in another way, but it is of the first importance that it should be not only dear but familiar to the student. When he sees any astronomical diagram in which the north pole and the hori- son are laid down he can at once tell for what latitude this diagram is constructed. The elevation of the pole above the horizon measures the latitude of the observer, to whose station this particular diagram applies. Change of the Position of the Zenith of an Obsermr by the Diiinal Motion.— In Fig. 12 suppose nesqia repre- sent the earth and NE 8 Q the celestial sphere. The earth, as we know, is rotating on the axis NS. We have now to inquire what are the real circumstances of this motion. The apparent phenomena have been previously described. Bemember that the vertical line of an observer is (practi- cally) that of a radius of the earth passing through his station. If the observer is at n his zenith is at N. As the earth revolves the zenith will revolve also. If the ob- server is in 45° north latitude, he is carried ronnd b^ the ■-, ■'■^■'^>$^-\^^^¥^/0^i'i^'''fi'<'4 i.i%-;L.'-;i-^i'M?i.% t the N.P.D. I an observer inith ohangei T.P.D. of his is 9» ifl 0° and , most there- pole, one point of e on the earth his terrestrial the earth and n the celestial L rotates on its ftl sphere in a that the- east loint being bo- th Z will move » celestial meri- id the point Z, sat circles join- intatiTes of the rent times dur- [^heyhave been ian at interrals ^n to represent daring a 8emi« RELATION OF TUB EARTH TO TUB UEAVEHS. 36 revolution of the earth. In this time Z moves from Z to L. In the next semi-revolution Z moves from L to Z, along the other half of the parallel ZL. In 24 hours the zenith Z of the observer has moved from Zto L and from L back to Z again. The celestial meridian has also swept across the heavens from the position N.P., Z, Q, S, S.P. through every intermediate position to N.P., L, E, 0, S.P., and from this last position back to N.P., Z, Q, S, S.P. The terrestrial meridian of the observer has been under it all the iime. This real revolution of the celestial meridian is incessantly repeated with every revolution of the earth. The sky is studded with stars all over the sphere. The celestial meridian of any place approaches these various stars from the west, passes them, and leaves them. This is the real state of things. Apparently the observer is fixed. His terrestrial and celestial meridians seem to him to be fixed, not only with reference to himself, as they are, but to be fixed in space. The stars appear to him to approach his celestial meridian from the east, to pass it, and to move away from it towards the west. When a star crosses the celestial meridian it is said to culminate. The passage of the star across the meridian is called the transit of that star. This phenomenon takes place successively for each observer on the earth. Suppose two observers, A and B, A being one hour (15°) east of B in longitude. This means that the angular distance of their terrestrial meridians is 15" (see page 10). From what we have just learned it follows that their celestial mesi- dians are also 16° apart When B's meridian is N.P., Z, Q, R, S.P., A's will be the first one (in the figure) beyond it; when B's meridian has moved to this first posi- tion, A's will be in the second, and so on, always 16* ,lf I w ASTRONOMY. (1 honr) in advance. A group of stars which has jnst como to A's meridian will not pass B's for 1 hoar. When they are on B's meridian they will bo 1 hour west of A's, and so on. Notice also that A's zenith is always 15" east of B's. The same stars will succeFsively rise, calminate, and set to each observer, but tlie phenomena will be presented to the eastern observer sooner than to the other. I ' »• « hag jnat cnmo Wht'ii they si of A's, and |ra 15" east of inate, and set presented to CHAPTER n. THE RELATION OP THE EARTH TO THE HEAVENS- {OonUnutd.) Tn CSUCTIAL Bphui. gygtemi of Oo-ordinatea— The great circles of the celestial sphere which pass through the two celestial poles are called hour-eirdea. Each hour-circle is the celestial meridian of some place on the earth. The honr-oirole of any partionlar star is that one which passes through the star at the time. As the earth revolves, different honr-droles, or celestial meridians, come to the star. In Fig. 18 l«t be the position of the earth in the centre of the celestial iphwe 2fZ 8D. Let Zbe the zenith of the ob- server at a given instant, and P, p^ the celestial poles. By definition PZSpnNP is his celestial meridian. (Each of these points hits a name; let the student give the names in order.) N8'\% the horizon of the observer at the instant chosen. PO JV^ is his latitude. If P is the north pole, he is in latitude 34° north. (See page 31.) EC WD is the celestial equator; J? and W are the east and west points. The earth is turning from WUtB. That is, the celestial meridian which at the instant chosen in the picture oontains P Zp was in the position P D Rp twelve bonrs earlier. gg ASTRONOMY. PV, PB, PV, PD lire parts of hour-circlos. If A is a sUir, 7' B is tho hour-circle of that star. As the eartli tiiriw P B turns with it, and directly P B will have moved away from A towards liio top of tho picture and soon /' V will pass through the star A, which stands still. When it does, PV will be the hour-circle of A. At the instant chosen PB U the hour-circle of A. The atars inside the circle NK are always above the obaenrer'g horizon. Im ia ill! half of the dinmal orbit of one of the north stars. All the stars inside the circle n its axil. Of ir-angle. The io« it ii the dif- [mint, the atar. Aoa.— We can h ahall change wnyenient, for etery ebaerfer then Tary with rrer. M fixed pointa north pole will race of the atar lanred, for the ose aome fixed ler co-ordinate qnator towarda That ia, from rA< MCMMtMl of th» hour-eireh \ea$ured on th« ahall find oat ) define it aa a -polar diatanoe »ni PA define te atar, and the ich other theae Their relatiTe poaitiona are not aftected by the rotation of the earth, nor by the poaition of the obeerver upon its aarfaoe. He may be in any latitude or any longitude, and hia aenith may be anywhere in the whole aky, but the right aaoenaion and the north-polar diatanoe of each atar remain the lame ne?* ertheleaa. The right aaoenaion of the atar KiiVC. Of a atar at J7 it ia VCE; of a atar at Z> it i» VCED\ of a star at IT it ia V CED W, and ao on. ligL. Aaoenaion and Declination. — Sometimea in place of the north-pokr diatanoe of a atar it ia convenient to nae ita declination. Th» declination of a star is its angular distance north or touth of the celestial equator. The declination of ^ ia BA, which ia 90** minus PA. The rebition between N. P. D. and d ia N. P. D. = 90" - *; d = 90» - N. P. D. North deolinationa are +; South deolinationa are — . The declination ot Z in CZ. CZia equal to P Jf, ainco each ia equal to 90° — PZ. PN meaaurea the latitude of the obaerrer whoae zenith ia Z. (See page 81.) The latitude of a place on the earth's surface is measured by the declination of tts tenith. Thia ia the definition of the latitude which ia need in aatronomy. Oomrdiaatea of a Star.— In what haa gone before we have Been that there are Tarioua waya of expreaaing the apparent positions of stars on the aurfiwe of the oeleatial aphere. That one moat commonly oaed in astronomy ia to gito the right ascension and north-polar distance (or dedination) of the atar. The apparent poaition of the atar ia fixed by these ;. ' jt';&'-^... ' jg5i-"- ' - ' .--!-!-!."i-" 43 ASTBOyOMT. If! >■ 1 two co-ordinates. If we know its distance also, the afoso* lute position of the star in space is fixed by the three co- ordinates. Thus we hare a complete method of describing the positions of the heavenly bodies. Co-ordinates of aik Obserrer. — ^To describe the position of an obserrer on the surface of the earth we have- to giye his latitnds and longitnde. His latitude is the declination of his zenith; his longitude is the fixed angle between his celestial meridian and the celestial meridian of Greenwich (or Washington). Declination in the sky is analogous to Latitude on the earth. Bight ascension in the sky is anal- ogous to Longitude on the earth. Both of these co-ordi- nates depend upon the position of his zenith, since his longitnde is nothing but the angular distance of his zenith west of the zenith of Greenwich. All this is extremely simple, but if it is clearly under- stood the student has it in his power to answer a great many interesting questions for himselt We know, for example, that the sun is in the equator and at the Yernal equinox on March 2l8t of each year. The student can determine for himself what appearances will be presented on that day next year. He may proceed in this way: Draw a circle to reprtdeut the celestial sphere. Take a point, P, of it to be the position of the north pole in the sky. If the observer lives In a phice whose latitude is g> degrees north, his zenith will be 90° — ^ from the north pole measured towards the south. Measure oft 90° — 9> on the circle from P. The end of that arc is the zenith of that observer, Z. PZ is an arc of his celestial meridian. Meas- ure from P through Z 90*, and the end of that are is on the eqqator, Q say. Join P with the centre, 0, of the circle. This line is the direction of the celestial pole. Join and Q, and this line (perpen- dicuUr to PO) is the direction of that point of the equator which is highest above his horizon. Draw the line ZO; this is the vertical line. Throu^O draw JIT 0^ perpendicular to ZO. This is the north and south line of bis horizon. Draw the ovals which repreeent (in BELATION OF THE EABTB TO THE HSAVENa. 43 Iso, the afoso< the three oo- of describing lie position of re to giyehis leclination of between his of Greenwich analogoQS to le sky is aual- ;hese co-ordi- ith, since his of his zenith learly nnder- iswer a great lator «nd at the larances will be Ihisway: Draw loint, P, of it to I observer lives zenith will be DUth. Measure arc is the zenith eridian. Meas* on the eq^ator, rhia line is the lis line (perpen- [uator which is I is the Tertioal Phis is the north >h represent On perspective) the circles of the equator and of the horizon. Assume rpoint, V, of the celestial equator. On March 21st of each year the sun is there. When the sun is at the highest point Q of the equatoi it is noon to this observer. The sun is on Ms meridian. Six houw before this time the sun will rise to him; six hours after he will set It requires twenty-four hours for the point F to be apparently carried all round the equator, and the sun appears to go with the poinC Three months later the sun is about fiO° of right ascension and has a north-polar distance of 8 '^ i? 270°, the sidereal time is 18 hours; and, finally, wh e itar reaches the upper meridian again, it is 24 houi\^ o«- hours. (See Fig. 13, where E O WD is the apparent diurnal {wth of a star in the equator. It is on the meridian at C.) Instead of choosing a $tar as the determining point whose transit marks sidereal hours, it is found more con- ▼enient to select that point in the sky from which the right ascensions of stars are counted — the yemal equinox — the point V in the figure. The fundamental theorem ol si- dereal time is: The hour-atigle of tie vernal equinox, or the sidereal time, ie equal to the right aeeensum of the meri- dian; that is, CV^VG. To aroid coniinnal reference to the stars, we set a clock so that its hands shall mark hours minntes seoondi .MM BSLATtOlt OF TBM MARTU TO TUB HEAVBNa. 46 d. any place its It is then ')' IS away (east- ontinnally in- to 24 honrs. by the honr- the meridian When this me is 6 hoars; 1 is again on apolar star), it ) sidereal time hes the upper (See Fig. 18, I of a star in mining point tnd more con- hich the right equinox — the leorem of d- jMitMx, or the 0/ the meri- re set a dock itesOieoondf at the transit of the vernal equinox, and regulate it so that its hour-hand reyolves once in 24 sidereal hours. Such a clock is called a sidereal clock. Solar Time. — Time measured by the hour-angle of the sun is called true or apparent solar time. An apparent solar day is the interval of time between two consecutive transits of the sun over the upper meridian. The instant of the transit of the sun over the meridian of any place is the apparent noon of that place, or local apparent noon. When the sun's hour-angle is 12 honrs or 180% it is local apparent midnight. The ordinary sun-dial marks apparent solar time. As a matter of fact, apparent solar days are not equal The reason for this will be fully explained later. Hence our docks are not made to keep this kind of time, for if once set right they would sometimes lose and sometimea gain on such time. Ibaa Bdar Time. — A modified kind of solar time is therefore used, called mean eolar time. This is the time kept by ordinary watches and docks. It is sometimes oaUed civil time. Jfean solar time is measured by the hour- angle of the mean sun, a fictitious body which is imagined to move uniformly in the heavens. The law according to which the mean sun is supposed to move enables us to com- pute its exact position in the heavens at any instant, and to define this position by the two co-ordinates right asoensidy, real or assumed. The body chosen determines the Itind of time, and the alraolute length of the unit — the day. The simplest unit is that determined by tiie uniformly rotating earth — the sidereal day; the most natural unit is that determined by the sun itself — the apparent solar day, which, however, is a variable unit; the most convenient unit is the mean solar day, and this is the one chosen for use in our daily life. Comparatiye Lengths of the Mean Solar and Sidereal Say. — As a fact of observation, it is found that the sun appears to move from west to east among the stars, about 1° daily, making a complete revolution around the sphere in a year. It requires 365^ days to move through 360". Hence an apparent solar day will be longer than a side- real day. For suppose the sun to be at the vernal equinox exactly at sidereal noon (0 hours) of Washington time on March 21st; that is, the vernal equinox and the sun are both on the meridian of Washington at the same instant. In 24 sidereal hours the vernal equinox will again be on the same meridian, but the sun will have moved eastwardly by about a degree, and the earth will have to turn through this angle and a little more in order that the sun shall again be on the Washington meridian, or in order that it may be apparent noon on March 22d. For the meridian to overtake the sun requires about 4 minutes of sidereal 'i-4^j^'. 9W^ RELATION OF THE EARTH TO THE UBAVBN8. 47 of the mean Twelve hours The mean each. Each >lar seconds. n, which is in one point: tl or assumed, absolute length ermined by the natural unit ia ar day, which, it is the mean ily life. lad Sidsreal that the snn stars, abont 1 the sphere ugh 360^ than a side- irnal equinox ton time on the sun are ame instant oin be on the iastwardlv by mm through he snn shall order that it the meridian B of sidereal time. Th« true sun does not move, as we have said, uni- formly. The mean sun is supposed to move uniformly, and to make the circuit of the heavens in the same time as the real sun. Hence a mean solar day will also be longer than a sidereal day, for the same reason that the apparent solar day is longer. The exact relation is: 1 sidereal day = 24 sidereal hours = 1 mean solar day = 24 mean solar hours = 0-997 mean solar day. 23h SO" 4* -091 mean solar time, 1-003 sidereal days, 34i> S{" 66*-555 sidereal time, and 866-24222 sidereal days = 865-24222 mean solar days. Local Time.— When the mean sun is on the meridian of a place, as Boston, it is mean noon at Boston. When the mean sun is on the meridian of St. Louis, it is mean noon at St. Louis. St. Louis being west of Boston, and the earth rotating from west to east, the local noon of Boston occurs before the local noon at Tt. Louis. In the same way the local sidereal time at Boston at any given instant is expressed by a larger number than the local sidereal time of St. Louis at that instant. The sidereal time of mean noon is given in the astro- nomical ephemeris for every day of the year. It can be found within ten or twelve minutes at any time by remem- bering that on March 21st it is sidereal hours about noon, on April 21st it is about two hours sidereal time at noon, and so on through the year. Thus, by adding two hours for each month, and four minutes for each day after the 2lBt day last preceding, we have the sidereal time at the noon we require. Adding to it the number of hours since noon, and one minute more for every fourth of a day ***^';v',.': >!i'^''- ^yl'-;Ji^'!■'?*'^"■'■'i■-SJ?-;^^^l!^ 48 ASTRONOMT. on account of the constant gain of the clock (4" dailj), we have the sidereal time at any moment. iirampfo.— Find the Bidereal time on July 4th, 1881, at 4 o'clock A.M. Wc have: k m June 21st, 8 mouths after March Slst; to be X 3, 6 July 8d, 12 days after June 2l8t; X 4, 48 4 A.1I., 10 hours after noon, aeasXy f of a day, 10 8 This result is within a minute of the exact Talue. Belation of Time and Longitude. — Considering our civil time which depends on the sun, it will be seen that it is noon at any and every place on the earth when the sun crosses the meridian of that place, or, to speak with more precision, when the meridian of the place passes under the sun. In the lapse of 24 hours the rotation of the earth on its axis brings all its meridians under the sun in succession, or, which ia the same thing, the sun appears to pass in suc- cession over all the meridians of the earth. Hence noon continually travels westward at the rate of 15° in an hour, making the circuit of the earth in 24 hours. The differ- ence between the time of day, or the local time as it is called, at any two places will be in proportion to their difference of longitude, amounting to one hour for every 15 degrees of longitude, four minutes for every degree, and so on. Vict versa, if at the same real moment of time we can deter- mine the local times at two different places, the difference of these times multiplied by 15 will give the difference of longitude. The longitudes of places are determined astronomically on this principle. Astronomers are, however, in the hmlnt of expressing the longitude of places on the earth like the Sfii itiii' RELATION OF THE a^HTU TO THE HEAVENS. 49 dailj), we , at 4 o'clock k ■ 8 048 16 8 mWi ig our civil 1 that it is en the sun : with more m under the ;he earth on t succession, pass in sue- Hence noon in an hour, The differ- I it is called, ir difference 16 degrees of M) on. Vice i can deter- le difference lifferenoe <^ tronomioaliy in the halnt rth like the right ascensions of the heavenly bodies, not in degrees, but in hours. For instance, instead of saying that Washington is 77° 3' west of Greenwich, we commonly say that it is 6 hours 8 minutes 13 seconds west, meaning that when it is noon at Washington it is 5 hours 8 minutes 12 seconds after noon at Greenwich. This course is adopted to prevent the trouble and confusion which might arise from constantly having to change hours into degrees and the reverse. Where does the Day Change 1— A question frequently asked c .is connection is. Where does the day change? It is, we will suppose, Sunday noon at Washington. That noon travels all the way round the earth, and when it gets back to Washington again it is Monday. Where or when did it change from Sunday to Monday? We answer, wherever people choose to make the change. Navigators make the change occur in longitude 180° from Greenwich. As this meridian lies in the Pacific Ocean, and meets scarcely any land through its course, it is very convenient for this purpose. If its use were universal, the day in question would be Sunday to all the inhabitants east of this line, and Monday to every one west of it. But in practice there have been some deviations. As a general rule, on those islands of the Pacific which were settled by men travelling east the day would at first be called Monday, even though they might cross the meridian of 180°. Indeed the Bussian settlers carried their count into Alaska, so that when our people took possession of that territory they found that the inhabitants called the day Monday when they them- selves called it Sunday. These deviations have, however, almost entirely disappeared, and with few exceptions the day is changed by common consent \n longitude 180° from Greenwich. !-T-':,''"J. 00 ABTROHOMT. DiTKumiATiovi or TnximiAL LoMomrsn. Owing to the rotution of the earth* there is no such fixed correspondence between meridiMis on the earth and among the stars as there is between latitude on the earth and de- clination in the heavens. The observer can always deter- mine his latitude by finding the declination of his zenith, but he cannot find his longitude from the right ascension of his zenith with the same facility, because that right as- cension is constantly changing. To determine the longi- tude of a place, the element of time as measured by the diurnal motion of the earth necessarily comes in. Gon- sider the plane of the meridian of a place extended out to the celestial sphere so as to mark out on the latter the celestial meridian of the place. Take two such places, Washington and S^n Francisco for example; then there will be two such celestial meridians cutting the celes- tial sphere so as to make an angle of about forty-fire de- grees with each other in this case. Let the obsenrer imagine himself at San Fr&ncisoo. Then he may conceive the meridian of Washington to be visible on the celestial sphere, and to extend from the pole over toward his south-east horizon so as to pass at a distance of about forty-five degrees east of his own meridian. It would appear to him to be at rest, although really both his own meridian and that of WashLgton are moving in consequence of the earth's rota- tion. Apparently the stars in their course will first pass the meridian of Washington, and about three hours later will pass his own meridian. Now it is evident that if he can determine the interval which the star requires to pass from the meridian of Washington to that of his own place, he will at pQce have the difference of longitude of the two BELATION OF TUB EARTH TO TUB HEAVENS, fil BRXTOI. no Buch fixed .h and among earth and de- always deter- Df his zenith, ght ascension hat right as- ine the longi- asured by the aes in. Gon* tended out to he latter the such places, >; then there ng the celes- forty-five de- lerver imagine conceive the lestial sphere, liis south-east ty-five degrees 9 him to be at I and that of e earth's rota- will first pass 3e hours later int that if he iqnires to pass bis own plaoe, ide of the two places by simply turning tbe interval in time into degrees at the rate of fifteen degrees to each hour. rw.14. The difference of longitude between any two places de- pends upon the angular distance of the terrestrial (or celes- tial) meridians of these two places and not upon the motion of the star or sun which is used to determine this angular difference, and hence the longitude of a place is the same whether expressed as the difference of two sidereal or of two solar times. The longitude of Washington west from Greenwich is S^ 8*° or 77°, and this is in fact the ratio of the angular distance of the meridian of Washington from that of Greenwich, to 24 hours or 360°. The angle between the two meridiane is ^ of 24 hours, or of a whole circumo fergnoe, ■UJ,.-. iri 69 ASTRONOMT. It iB thus plttin that tlif difference of longitude of any two places is the amne as the difference of their eimultaneoua local times; and this whether the local times spoken of me both sidereal or both solar. MxTHOM Of DiTiBimnjro thi Snrruunoi of Lovei- TTOI Of Two FLAOII ok TBI lASTH. Every purely astronomical method depends upon the principle we have just laid down. It is of vital importance to seamen to be able to deter- mine the longitude of their vessels. The voyage from Liv- erpool to New York is made weekly by scores of steamers, and the safety of the voyage depends upon the certainty with which the captain can mark the longitude and lati- tude of his vessel upon the chart. The method used by a sailor is this : with a sextant (see Chapter III.) the local time of the ship's position is deter- mined by an observation of the sun. That is, on a given day he can set his watch so that its hands point to twelve hours when the sun is on his meridian on that day. He carries a chronometer (which is merely a very fine watch) whose hands point always to Gi-eonwich time. Suppose that when tlie ship's time is 0" or noon the Greenwich time is 3" 20'". Evidently he is w'.dt of Greenwich S" 80". since that is the difference of the simultaneoua local times, and since the Greenwich time is later. Hence he is some, where on the meridian of 60° west. If he has determined the altitude of the pole or the declination of his zenith in any way, then he has his latitude also. If this ehonld be 46° north, the ship is in the regular track between New York and Liverpool, and he can go on with safety. RKLATION OF TUR EARTB TO THE IlKAVKNa. 58 d« of any two simultaneout 68 spoken of SI Of Lovex* ;th. ds upon the able to deter- age from Liv- I of steamers, the certainty tude and lati- a sextant (see ition is deter- B, on a given >int to twehe hat day. He iry fine watch) me. Suppose ho Greenwich mwich 9,^ gO", ii« local times, ce he is some^ as determined t his zenith in this shonld be between New safety. When the steamer Faraday wm Iftving the dirert cable the got her longitude cvury day by comparing hur ship's timv (found by oliser- ralion on Imnrd) with the Qrocnwicli time telcgraplicd iiloug tlie cable and raceived at the end of it which she liad on her dcclc. Longitudes may be determined in the same way on shore. From an observatory, as Wasliington, the beats of a cloclc are sent out by telegraph along the lines of railway; at every railway sUtion and telegraph office the telegraph sounder tients the seconds of the WaMhington clock. Any one who can set his watch to tlie local time of his station and who can compare it with the signals of the Wash- ington clock (which are sent at ATashington noon, daily except Sun- day) can determine for liimsolf the difference of the simuiluneoua local times of Washington and of his station, and thus his own longi- tude cast or west from Washington. mTROM ov DiTiBMnmro tki Latittos or a Plaoi OK TBI EABTH. Latitude from Giroumpolar 9t«n.— In tbo figure sup- pose Z to be the zenith of the observer, UZRN hM me- ria.is. ridian, P the north pole, HR his horizon. Suppose iS^and iS' to be the two points where a eiroumpolar star crosses the meridian^ as it mores around the pole in its apparent "V ■-"■- wxr M '^ m ii k i km,mimimM lm~ 04 ABTJiONOMT. •■f diurnal orbit. P 8 = P S' is the itar's north-polar dii- tance, and P II =

e obiorver'g latitude. ^±_^ = ZP = 00" ^. Therefore 9= 90° ZS^ZS' We can mcaauro Z declination is taken from a catalogue of stars if it is a star, or from the Nautical Almanac if it is the sun. In either case the declination C 'Sf is known. ZQ=QS-\-Z8; qt= 6 -\- H. If the body culminates north of the zenith at flf , ZQ=Q8'-Z8i Ii-pokr di>* RKLATION OF TttB KARTll TO WK IlKAVKNB. 68 This is the method uniformly employed ut sea, where the altitude of the Hun at apparent noon Ih daily measured. ances of the de or by the tor. Hence itude of the in or a Star. r the pole, orsoction of iitor with the r. The alti- ir 8 is meas- itur is on the is known to iian when we I lobeamax- the measured »uce ZS = Z , catalogue of nnnac if it is B known. At 8', Fasaixazxi Aim BmisiAiaTBBf or thi Hiatiwlt BODII& The apparent position of a body on the celestial sphere remains the same as long as the observer is fixed, as haa been shown (see page 20). If the observer changes his ])1iu« and the star remains in the same )M)sition, the ap- Tm. 17. parent position of the star will change. T<> show this let CW be the earth, C being its centre. S* and 8' are the places of two observers on the surface. Z" and Z' are their zenith in the celestial sphere H'P". P is a- star. 8* will see P in the apparent position P'. 8" will see P in the apparent position P*. That is, two different ob- servers see the same object in two different 'apparent positions. If the observer y moves along the surface directly to S*, the apparent position of P on the celes- tial sphere will appear to move fr^m P' to P*. This change is due to the parallax of P. fe ui >j siiM i aaj a a a.' atxx~: < I. 66 ASTRONOMT. The parallax of a body due to a change in the position of the observer, is the alteration in the apparent position of the body caused by that change. If the observer at S* could move to the centre of the earth along the line S'C, the apparent position of P wonld move from P*io P^ It the observer at /S* conld move from S* to C along S'C, the appannt position of P would move from P' to P^. In the triangle P S'C the following parts are known: CP = J = the geocentric distance of P, CiSf' = p' = the radins of the earth at S', and the angle S'PC = P'P P, is the parallax of P. For the change of apparent position of P from P' to P^ is due to the change of the point of observation from S* to a Similarly the angle S'PC = P'PP, is the parallax of P relative to a change of the observer fiom 8' to C. Horixontal Parallax. — Olearly the parallax of P differs for observers differently sitnated on the earth, and it is necessary to take some standard parallax for each observer. Such a standard is the horizontal parallax. Suppose P to be in the horizon of the observer S'; then Z'S'P will be 90°, as will also the angle PS'C. In the triangle S'PC three parts will then be known and the horiiontal parallax (the angle at P when P is in the horizon) can be found. It will be the same for the observer at 5*. When P is in the horizon of S', Z'S'P is a right angle, as is also PS'C. CP and CS' are known and thus the horizontal parallax of P is determined. If CP, the distance of P, increases, other things remain- ing the same, the parallax of P will diminish. mtlm V _ the position ent position ntre of the of P would conid moTe of P would known: tP, of P. ►m P' to P, I from 8' to arallax of P C. a P differa b, and it is sh observer. Suppose P then rS^P the triangle B horiiontal son) can be 5*. When le, as is also le horisontal mgs remain- RBLATtoiT OP ma MAttm fd fan a^Avism. &t The student can prove this foi* himself by dwwing the figure on the same scale as here given, making CP latgen The angles at P (the parallaxes) -.vill become sitiiillei- and smaller the larger C7P is taken. Hence the magnitude of the pai-allax of a star or a plaudt depends upon its distance from us. Suppose an observer at the point P looking at the earth's radius S'C. The angle subttmdcd by that semidiameter is the same as the parallax of P. Hence we may say that the parallax of a body with reference to an observer on the earth is measured by the angle subtended by that semidi- ameter of the earth which passes through the observer's station. As the point P is carried further and further away from the earth, the angle subtended by ^C, for example, becomes less and less. If P were at the- distance of the moon, this angle would be about 67'; if at the distance of the sun, it would be about 8^'. S'C is roughly 4000 miles; it subtends an angle of 57' at the distance of the moon. 70 miles would subtend an angle of about 1', and 3437' would be about 340,000 miles. This is the distance of the moon from the earth. (See pages 4, 5.) Again, 4000 miles subtends an angle of 8*. 5 at the dis- tance of the sun. 470.7 miles would subtend an angle of 1', and 206,264*. 8 would be 97,000,000 miles, and this is about the distance of the sun. By taking the exact values Qf the radius of the earth and of the solar paralkx, this dis- tance is found to be about 93,000,000 miles. The example shows the method of calculating the sun's distance when we have two things accurately given: first, the dimensions of the earth; and second, the parallax «£ the snn. r * tS6 A6TR0N0MT Annual Parallax. — We have seen that for the moon the parallax is about 1°; for the san it is only 8'; for some of the more distant planets it is considerably less. For Jupiter it is aboat 2'; for Saturn less than 1'; for Neptune abont 0'.3. Let us remember what this means. It means that 4000 miles, the earth's radius, would Bubt«nd at the distance of Neptune an angle of only A of a single second of arc. The parallax of the moon is determined by observation, and the observations consist in measuring the angle which the radius of the earth would subtend if viewed from the moon's centre. 57' is an angle large enough to be deter- mined quite accurately in this way. There would be but a small per cent of error. Even 8', the sun's parallax, can be measured so as to have an error of not more than 2 or 3 per cent. But this method will not do to measure anything much smaller than 8'. The parallax of a fixed star, for example, IS not si^si f part as large as the sun's parallax: and this is too minute a quantity to be deduced by these methods. We therefore use for distant bodies a parallax which does not depend on the radius of the earth, but upon the radius of the earth's orbit around the sun. The annual parallax of a body is the angle subtended at the body by the radius of tJie earth's orbit seen at right angles. For example, in ^ig. 18 suppose that Cnow repi'esents the sun, around which the earth 8* moves in the nearly circular orbit S'S'Jff'. S'Cia no longer 4000 miles as in the last example, but it is 93,000,000 miles. Suppose P to be, again, a body whose annual paraUax is S'P C (suppose ing Pi^O to be a right angle). \ _ he moon tbe for some of than 1'; for ins that 4000 e distance of 1 of arc. observation, angle which wed. from the to be deter- ould be but a rallax, can be 9 than 2 or 3 lything much for example, ax: and this ese methods. I which does on the radius subtended at seen at right >w repi'esentfl in the nearly miles as in Suppose P to F C (suppoB- RELATION OF THE EARTH TO THE HEAVENS. 69 Some of the nearest fixed stars have an annual parallax of nearly 1'. Hence the nearest of them are not nearer than 206,264 times 93,000,000 miles. The greater number of them have a parallax of not more than ^'. Hence their distances cannot be less than 10 X 206,264 X 93,000,000 miles. To the student who has understood the simple rules giyen on pages 4 and 5 these deductions will be plain. Fia. la Semidiameten of the Heavenly Bodies.— The angular semidiameter of the sun as seen from the earth is 961'. Hence its diameter is 1922'. Its real diameter in miles is therefore about 880,000, as its distance is 93,000,000 miles. The angular semidiameter of the moon as seen from the earth is about 15^'. Hence its real diameter is about 2000 miles, its distance being about 240,000 miles. In the same way, knowing the distance of any planet and measuring its angular semidiameter, we can compute its dimensions in miles. ■Mi 1 it ' I 1 I !' i I! I ii 1 !• ! i: i : .i CHAPTER Itt. ASTRONOMICAL INSTRUMENTS. General Aeeoimt — ^In a general way we may divide the instraments of astronomy into two claBses, seeing instru- ments and meaauring instruments. The seeing instruments are telescopes; they have for their object either to enable the observer to see 'foint objects 88 comets or small stars, or to enable him to see brighter stars with greater precision than he could otherwise do. How they accomplish this we shall shortly explain. The measuring instruments are of two classes. The first class measures intervals of time. The second measures angUs. A clock is a familiar example of the first class; a divided circle of the second. Let us take these in the order named. The Sefhusting Telescope. — The refracting telescope is composed of two essential parts, the object-glass or objec- tive and the eye-piece. The object-glass is for the sole purpose of collecting the rays of light which emanate from the thing looked at, and for making an image of this thing at a point which is called the /ocu« of the objective. The eye-piece has for its sole object to magnify the image so that the angular dimensions of the thipg looked at ;will appear greater when the telescope is used than when it is not. \ _ ay divide the feeing instra- hej have for I laint objects > see brighter otherwise do. ixplain. The rhe first class asnres angles, ma; a divided ; telescope is glass or objec- !olIecting the ooked at, and rhich is called tify the image ooked at mil tan when it is ASTRONOMICAL iNSTRVMENTa. For example, in the figure suppose BI to bo a luminous surface. Every iioint of it is throwing off rays of light in straight lines in every possible direction. Let us consider the point /. The rays from /proceed m every direction in which we can draw a straight line through I. Suppose all such straight lines drawn. Let 00' be the objective of a tele- scope pointed towards BI. All the rays from / which fall on 00' lie between the lines 10, and I(y. No others can reach the objective, and all others which proceed from / are wasted so far as seeing / with this particu- lar telescope is concerned. The action of the convex lens 0& is to bend every ray which passes through it to- wards its axis BA. 10 is bent down to OF; 10' is bent up to O'/*; and so for every other ray except the ray from / through the centre of Off which is bent neither up nor down, but which goes straight on to i* and beyond. Every one of the rays of light sent out by / between the limits 10 and /O' finally passes through 1*. / is a point of light, and so is r. The point /' is the focus of OO* with respect to /. Sim-rarly B sends out light in every direc- tion. Only those rays which chance to fall between BO and BO' are useful for seeing J9^ith this particular ielesoope. Every one pe used as an if the combina- )f any telescope bjeotive is usn- h6re the arrow shows the direction in which the rays come to it from the object. If wo use a fingle ob- jective we find that the image of the object is colored ; that is, of different colors from its natural tints. We find that by using a double objective made of two Fw».». different kinds of glass this can be corrected. This is ex- plained in Optics under the head of Achromatism or Chro- matic Aberration. Light-gathering Power.— It is not merely by magnifying that the telescope assists the vision, but also by increasing the quantity of light which reaches the eye from the object at which we look. Indeed, should we view an object through an instrument which magnified but did not in- crease the amount of light received by the eye, it is evident that the brilliancy would be diminished in proportion as the surface of the image was enlarged, since a constant amount of light would be spread over an increased surface; and thus, unless the light were very bright, the object might become so darkened as to be less plainly seen than with the naked eye. How the telescope increases the quantity of light will be seen by considering that when the unaided eye looks at any object, the retina can only receive so many rays as fall upon the pupil of the eye. By the use of the telescope it is evident that as many rays can be brought to the retina as fall on the entire object-glass. The pupil of the human eye, in its normal state, has a diameter of about one fifth of an inch, and by the use of the telescope it is virtually increased in surface in the ratio of the square of the diameter of the objective to the square of one fifth of m inchj that is, in the r^tio of the sur/act of the objective «4 ABTRONOMT. :hrll to the surface of the pnpil of the eye. Thus, with a two- inch aperture to our telescope, the number of rays collected is one hundred times as great as the number collected with the naked eye. With a 5-inch object-glass the ratio ia 820 to 1 " 10 2,600 to 1 " 16 •• " " " 6.026 to 1 " 20 " " " " 10.000 to 1 " 26 • 16,900 to 1 When a minute object, like a small star, is viewed, it is necessary that a certain number of rays should fall on the retina in order that the star may be visible at all. It is therefore plain that the use of the telescope enables an observer to see much fainter stars than he could detect wil>> the naked eye, and also to see faint objects much better than bv unaided vision alone. Thus, with a 26-inoh tele- scope we may see stars so minute that it would require the collective light of many thousands to be visible to the unaided eye. Eye-piece. — In the skeleton form of telescope before de- scribed the eye-piece as well as the objective was considered as consisting of but a single lens. But with such an eye- piece vision is imperfect, except in the centre of the field, from the fact that the image does not throw rays in every direction, but only in straight lines away from the objec- tive. Hence the rays from near the edges of the foeal image fall on or near the edge of the eye^piece, whence arises distortion of the image formed on the retina, and loss of light. To remedy this difficulty a lens is inserted at or very near the place where the focal image isformedyforthe purpose of throwing the different pencils (tf rays whieb ^inanat^ fromi ^he several parts of the iiDa|;e, townrcl V^ 'Ul JM«i wm ABTRONOmCAL INSTnUMENTS. 8, with a two- rays collected collected with astol OOtol 25tol OOtol OOtol i viewed, it is Id fall on the I at all. It is pe enables an Id detect witV much better 26-inoh tele- Id reqnire the isible to the pe before de- ras considered such an eye- of the field, rays in every >m the objec- I of the foeal piece, whence }tina, and loss inserted at or armed, for the f rays whiehf e, townrcl tlk9 axis of the telescope, so that they shall all pass nearly through the centre of the eye-lens proper. These two lenses are together called the eye-piece. There are some small differences of detail in the con- struction of eye-pieces, but the general principle is the same in all The figure showi an eye-plec* t<*^' ' Rl iii p I ' « I ill I . ' '5 I, M ASTItOyOMY. XtflaetiBf TaltMopM.— As wo hnvo seen, one essential part of a refracting tvlescHpe is the objective, wliicli brings all the incident rays from an object to one focus, formihg there an image of Hint object. In reflecting telescopes (retlectont) the objective is a mirror of specu- lum niolal or silvered gloss ground to lliu Hlinpe of a paraboloid. The figure shows the action of such a mirror on a bundle of parallel rayh, wliich, after impinging on it, are brought by reflection to one focus F. The image formed at tliis focus may be viewed with an eye- piece, aa in the case of the refracting telescope. The eyepieces used with such a mirror are of tlie kind already described. In the figure the eye-piece would have to be placed to .vni Tta.t». tbe right of the point F, and the observer's head would thus interfere with the incident liglit. Various devices have been proposed to rem- edy this inconvenience, of which the most simple is to interpose a email plane mirror, which is inclined 45° to the line AC, just to the left of F. TIds minor will reflect the rays which are moving towards the focus Fdova (in the figure) to another focus outside of the main beam of rays. At this second focus the eye-piece is placed and the observer looks into it in a direction perpendicular to AC. The Teleicopr in MeMturement. — A telescope is generally thoaght of only as an instrument to assist tbe eye by its magnifying and ligbt-gatbering power in tbe manner we have described. But it bas a very important additional function in astronomical measurements by enabling the astronomer to point at a celeHtial object with a certainty and accuracy otherwise unattainable. This function of the telescope was not recognized for mo^e than htilf a c^u- m 1 ASTRONOMICAL INSTRUMENm 91 ntinl part of a lie incident rays I of Hint object, nirrurof specu- rnlioloiil. Tlio if parallel rayh, n to one focus d with an cyc- le kind already be placed to d thus interfere reposed to rem- to interpose a AC, just U) the noving towards lide of the main placed and the AC. e is generally bhe eye by its 16 manner wo nt additional enabling the ;h a certainty \ function of an h^lf a c^vr tury after its invention, and after a long and rather aori' monious contest between two schools of astronomers. Until the middle of the seventeenth century, when an tistronomer wished to determine the altitude of a celestial object, or to measure the angular distance between two stars, he was obliged to point his sextant or other meas- uring instrument at the object by means of "pinnules." These served the same purpose as the sights on a rifle. In using them, however, a difficulty arose. It was impossible foi I he observer to have distinct vision both of the object and of the pinnules at the same time, because when the eye was focused on either pinnule, or on the object, it waa necessarily out of focus for the others. The only way to diminish this difficulty was to lengthen the arm on which the pinnules were fastened so that the latter should be ai far apart as possible. Thus Tycho Brahe, before the year 1600, had measuring instruments ver/ much larger than any in use at the present time. But this plan only diminished the difficulty and could not entirely obviate it, because to be manageable the instrument must not be very large. About 1670 the English and French astronomers found that by simply inserting fine threads or wires exactly in the focus of the object-glass, and then pointing it at the object, the image of that object formed in the focus could be made to coincide with the threads, so that the observer could see the two exactly superimposed upon each other. When thus brought into coincidence, it was obvious that the point of the object on which the wires were set was in a straight line passing through the wires, and through the centre of the object-glass. So exactly could such a point- ing be made, that if the telescope did not magnify at all Ofi ASrnONOMT. (tho oye-piecij and objcct-gliisa being of oqiiul focal length), a Tory important lidvance would still be made in the ac- curacy of astronomical mciisurcmcnts. This line, passing centrally through tho telescope, we call the line of colli- tnution of the telescope, A B in Fig. 19. If wo have any way of determining it, it is as if we had an indefinitely long pencil extended from the earth to the sky. If the observer rimply sets his telescope in a fixed position, looks through it and notices what stars pass along the threads in tho eye- piece, he knows that all those stars lie in the axis of col> limation of his telescope at that instant By the diurnal motion a pencil-mark, as it were, is thui drawn on the surface of the celestial sphere among th« stars, and th6 direction of this pencil-mark can be deter- mined with far greater precision by the telescope than with the naked eye. CHBOHOMITIBB AlTD OlOOXft We have seen that it is important for various pnrposeB that an observer should be able to determine his local time (see page 62). This local time is determined most accu- rately by observing the transits of stars over the celestial meridian of the place where the observer is. In order to determine the moment of transit with all required accuracy, it is necessary that the time-pieces by which it is measured shall go with the greatest possible precision. There is no great difficulty in making astronomical measures to a sec- ond of arc, and a star, by its diarnal motion, posses over this space in one fifteenth of a second of time (see page 44). It is therefore desirable that the astronomical clock shall not v^ry from a uniform rate more than a few ASTBOyOMICAL JNSTltUMKNTS. c»cal length), B in the no- line, paMing line of colli- tvo have any Bfinitely long the obserrer oks through Is in the eye- axis of col« were, is thus among th« !an be deter- pe than with f)U8 purposes lis local time L most acctt- the celestial In order to red accuracy, > is measured There is no [ires to a seo- I, passes oyer me (see page omical clock than a few hundredths of a sooond in the course of a day. It is not, however, necessary that it should always be perfectly correct; it may go too fast or too slow without detracting from its character for accuracy, if the intervals of time which it tells off — hours, minutes, or seounds — uro always of exactly the same length, or, in other words, if it gains or loses exactly the same amount every hour and every day. The time-pieces used in astronomical observation are the ohronometor and the clock. The chronometer is merely a very perfect watch with a balance-wheel so constructed that changes of tempera- ture have the least possible effect upon the time of its oscillation. Such a balance is called a compensation bal- ance. The ordinary house-clock goes faster in cold than in warm weather, because the pendulum-rod shortens under the influence of cold. This effect is such that the clock will gain about one second a day for every fait cf 3° Cent. (5°.4 Fahr.) in the temperature, supposing the pendulum- rod to be of iron. Such changes of rate would be entirely inadmissible in a dock used for astronomical purposes. The astronomical clock is therefore provided with a com- peneation pendulum, by which the disturbing effects of changes of temperature lire avoided. The correetion of a clock is the quantity which it is necesaary to add to the indications of tlie hands to obtain th« true time. Thus if the correction of a sidereal cloclc is + 1" Kf-OT and the hands point to 810 18" 14'.80, tlie correct sidereal time is 21^ 14" 24*.57. The rate of a chnik is the daily change of its correction; i.e., what it gains or loses daily. wfK n :^i ," ill ill 70 A8TB0N0MT. The Tsaksit Instbvmeht. The Transit Instrument is used to observe the trw.sits of stars over the celestial meridian. The times of these E>^H Fio. 30. transits are noted by the sidereal clock, which is an indis- pensable adjunct of the transit instrument. ■ ..m»i w ASmONOMIOAL INSTRUMENTS. 71 the traR.sits es of these N is an indis- It consists essentially of a telescope TT mounted on an axis VV at right angles to it. Tlie ends of this axis terminate in accurately 'cy\indrical pivots which rest in metallic bearings VY which are shaped like the letter Y, and hence called the Y's. These are fastened to two pillars of stone, brick, or iron. Two counterpoises WIT are connected with the axis as in the plate, so as to take a large portion of the weight of the axis and telescope from the Y's, and thus to diminish the friction upon these and to render the rotation about FFraore easy and regular. In the ordinary use of the transit, the line F F is placed accurately level and also perpen- dicular to the meridian, or in the east and west line. To effect this "adjustment" there are two sets of adjusting screws, by which the ends of F F in the Y's may be moved either up and down, or north and south. The plate gives the form of transit used in permanent observatories, and shows the observing chair G, the reversing carriage B, and the level L. The arms of the latter have Y's, which can be placed over the pivots VV. The Um of eoUimation of the transit telescope is the line drawn through the centre of the objective perpendicular to the rotation axit VV. The retiele is a network of fine spider-lines placed in the focus of the objective. In Fig. 24 the circle represents the field of view of a transit as seen through the eye-piece. The seven vertical lines, I, II. Ill, IV, V, VI, VII, are seven ! fine spider-lines tightly stretched across a hole in a metal plate, and so adjusted a* to be perpendicular to the direction of a | star's apparent diurnal motion. The hori- zontal wires, guide-wira, a and b, mark the I centre of the field. The field is illuminated at night by a lamp at the end of the axis which shines through the hollow interior of the latter, and causes the field to appear bright. "The wires are dark against a bright ground. The line of right is a line joining the centre of the objective and the central one, IV, of the seven vertical wires. The . whole transit is in adjustment when, first, the axis F F is lioriiontal; second, when it lies east and west; and third, when the line of sight and the line of eoUimation coincide. When these condi- tions are fulfilled the line of sight intersects the celestial sphere in the meridian of the place, and when TT \a rotated about F F the line of right marks out. the celestial meridian of the place on the splMre. Ro. Mk IW 72 ASTRONOMY. •*' The clock etandB near the transit instrument. The times when a star passes the wires I-VII are noted. The average of these is the time when the star was on the middle thread, or, what is the same thing, on the celestial mendian. At that instant its hour-angle is zero. (See page 89.) The sidereal time at that instant is the hour-angle of the vernal equinox (see page 44). This is measured from the meridian towards the west. The right ascension of the star which is observed is the same quantity, measured from the vernal equinox towards the cast. As the star is on the meridian, the two are equal. Suppose we know the right ascension of the star and that it is a. Suppose the clock time of transit is T. It should have been a if the clock were correct. The correction of the clock at this instant is thus a — T. This is the use we make of stars of known right ascen- sions. By observing any one of them we can get a value of the clock correction. Suppose the dock to be correct, and suppose we note that a star whose right ascension is unknown is on the wire IV at the tiuie a' by the clock, a' is then the right ascension of that star. In this way the positions of stars, or of the snn and planets (in right ascension only), are determined. Vhb ¥Ki»nTAw CntoLS. The meridian circle is a combination of the transit in- strument with a graduated circle fastened to its axis and moving with it. A meridian circle is shown in Fig. 36. It has two oirclee finely divided on their sides. The grad- uation of each circle is viewed by four microscopes. The microscopes are 90° apart. The cat shows also the hntg- ing leva by which the en-or of level of the ws is found. ASTRONOMICAL INSTRUMENTS. 73 The times The average Idle thread, Tidian. At 39.) angle of ihe 3d from the ision of the osnred from I star is on e know the Suppose the !en a if the lock at this right ascen- ii a value of ^e note that the wire IV lit ascension *8, or of the etmmined. » transit in- its axis and m Fig. S6. The gnid. ciopes. The o theiuuig- is found. The instrument can be used as a transit to determine right ascensions, as before described. It can be also used to measure declinations in the following way : If the telescope is pointed to the nadir, a certain division of I tho . iTcles, J»8 N, is under the first microscope.. "We can irj*ke Ihu nadir a Visible point by placing a hmm of quick- silver below the telescope and locking in it through the tel- escope, v^e shall see tbe wires of the reticle anr! ,.lso their 74 ABTBONOMT. ; i t =! n f reflected images in the quicksilver. When these coincide, the telescope points to the nadir. If it is then pointed to the pole, the reading will change by the angular distance between the nadir and the pole, or by 90° + q>, ^ being the latitude of the place (supposed to be known). The polar reading P of the circle is thus known when the nadir reading N\& found. If the telescope is then pointed to various stars of unknotvn polar distances, p', p", p'", etc., as they successively cross the meridian, and if the circle readings for these stars are P', P", P'", etc., it follows that p'^P'—P; p" = P"_P; p'" = P'" — p., etc. Thus !:he meridian circle serves to determine by observa- tion both co-ordinates of the apparent position of a body. Tee Eqvatobial. An equatorial telescope is one mounted in such a way that a star may be followed through its diurnal orbit by turning the telescope about one axis only. The equatorial mount- ing consists essentially of a pair of axes at right angles to each other. One of these SN (the polar axis) is direct- ed toward the elevated polo of the heavens, and it there- fore makes an angle with the horizon equal to the latitude of the place (p. 31). This axis can be turned about its own axial line. On one extremity it carries another axis L D (the declination axis), which is fixed at right angles to it, but which can again be rotated about its axial line. To this last axis a telescope is attached, which may either be a reflector or a refractor. It is plain that such a tele- scope may be directed to any poir f the heavens; for we can rotate the declination axis until the telescope points to any given polar distance or declination. Then, keeping the telescope fixed in respect to the declination axis, we can lese coincide, in pointed to ular distance , qt being the The polar m the nadir n pointed to >", p'", etc., if the circle c, it follows - P; etc. B by observa- of a body. ih a way that t by turning }rial mount- right angles •is) is direct- nd it there- the latitude bout its own er axis LD angles to it, line. 1 may either such a tele- rens; for we pe points to len, keeping axis, we can ASTRONOMICAL INSTllUMENTS. rm.K. 76 ASTBONOMT. % 1 t rotate the whole instrument as one mass about the polar axis until the telescope points to any portion of the parallel of declination deOned by the given right ascension or hour- angle. Fig. 26 is an equatorial of six-inch aperture which can be moved from place to place. If we point such a telescope to a star when it is rising (doing this by rotating tlie telescope first about its declination axis and then about tlie polar axi»), and fix the telescope in tliis position, we can, by simply rotating tlie whole apparatus on the polar axis, cause the telescope to truce out on the celestial sphere the apparent diurnal path which this star will appear to follow from rising to setting. In such telescopes a driving-clock is so arranged that it can turn tho telescope round the polar axis at the same rate at which the earth it- self turns about i' ■ own axis of rotation, but in a contrary direction. Hence such a telescope once pointed at a star will continue to point at it as long as the driving-clock is in operation, thus enabling the astronomer to make such an examination or obserration of it as is required. TBI SiZTAn. The sextant is a portab e instmment by which the aUituda at celestial bodies or the angular 4iHanu* between them may be measured. It is used chiefly by navigators for determining the lati- tude and the local time of the position of the ship. Knowing the local time, and comparing it with a chronometer regulated on Green- wich time, the longitude become* known and the ship's place is fixed. (See page 53.) It consists of an arc of a divided circle usually 60° in extent, whence the name. This arc is in fact divided into 120 equal parts, each marked as a degree, and theae are again divided into smaller •paces, so that by means of the vernier at the end of the index-arm M8 an arc of 10" (usually) may be read. The index-arm M8 carries the index-^ii M, which is a silvered plane mirror set perpendicular to the plane of the divided arc. The horitonrglau m u also a plane mirror fixed perpendicular to the plane of the divided cirole. Thi8 last glass is fiaad 4a poalUmi. -tnAle the first revolves with the index-arm. Tlie horison-^asi Is divided into two parts, of which the lower one is silvered, Un upper half being transparent. JT is a telescope of low power pointed toward the horizon. glass. By it any ^ * }ut the polar if the parallel ision or hour- [)erture which Ising (doing this I axis and then )8ition, we can, axis, cause tlie pparent diurnal ', to setting. In it can turn tho ich the earth it- iti-ary direction. )ntinue to point tifl enabling the ttion of it as is the aUttudet of them may be mining the lati- Knowing the ilated on Oreen- ship's place is ' 00° in extent, 20 equal parts, !d into smaller '. the index-arm ch is a silvered Ided are. The lar to the plane solves with the iart8, of which Min;nt. J7 is a 188. By it any ASTRONOMICAL INSTRUMENTS. n object to which it is directly pointed can be seen through the untOterei half of the liorizon -glass. Any olher object in Mieume plane can be brought into the same field by rotatiag the index-arm (and tlie index- glass with it), so thai • bewn of liglit from this second object shall ilrfhe tfn Mex-glass at the proper angle, there to be reflected to the horizon-glass, and again reflected down the telescope E. Tlius the images of any two objects in the plane of the sextant miiy be brought together in the telescope by viewing one directly au' .he other by reflection. Wm> ST This imtniment is need daily at sea to determine the ship's position by measnring the altitude of the sun. This is done by pointing the telescope, EB, to the ma-horison, H in the figure, which appears like a line in the field of the telescope, and by moving the index-arm till the image of 78 ASmONOMT. 'Si H the sun, B, coincides with the horizon. The arc read from the sextant at this time is the sun's altitude. From the altitude of the sun on the meridian the ship's latitude is known (see page 52). From its altitude at another hour I ! the local time can be computed. The difference between the local time and the Greenwich time, as shown by the ship's chronometer, gives the ship's longitude. By means of this simple instrument the place of a vessel can be found witnin a mile or so. The above are the instruments of astronomy which best illustrate the principles of astronomical observations. Practical Astronomy is the science which teaches the theory of these instruments and of their application to ob> Bervation, and it includes the art of so combining the observations and so using the appliances as to get the best results. %k ASmONOMWAL EPIIEMERIS. 79 trc read from I. From the p's latitude is another hour snce between hown by the By means can be found jr which best ations. teaches the cation to ob« nbining the get the best The Abtbohomicai Efeemzsis, ob Katttioai Almanao. The Ailronomieal Eplieintrii, or, as it in more commonly called, the Nautical Almanac, is u work iu wliicli celestial phenomena and the positions of the heavenly Imdies uro computed in advance. The usefulness of such a work, especially to the navigator, de- pends upon its regular oppearauce on a uniform plan and upon the fulness and accuracy of its da\a; it was therefore necessary that its Jssue should bo taken up as a government work. An astronomical epiieineris or nautical almanac is now published annually by each of the governments of Germany, Spain, Portugal, France, Great Britain, and the United States. Tliey are printed three years or more be- forehand, in order that navigators going on long voyages may supply themselves in advance. The Ephemeris furnishes the fundamental data from which all our household almanacs are calculated. The principal quantities given in the American Ephemeris for each year are as follows: The positions (R. A. and 8) of the sun and the principal large planets for Greenwich noon of every day in each year. The right ascension and declination of the moon's centre for every Greenwich hour in the year. The distance of the moon from certain bright stars and planets for every third Greenwich hour of the year. The right ascensions and declinations of upward of two hundred of the brighter fixed stars, corrected for precession, nutation, and aberration, for every ten days. The positions of the principal planets at every visible transit over the meridian of Washington. Complete elements of all the eclipses of the sun and moon, v»lth maps sliowing the passage of the moon's shadow or penumbra over those regions of the earth where the eclipses will be visible, and tables whereby the phases of the eclipses can be accurately computed for any place. Tables for predicting the occultations of stars by the moon. Eclipses of Jupiter't satellites and miscellaneous phenomena. Catalogues of Stars.— Of the same general nature with the Ephe- meris are catalogues of the fixed stars. The object of such a cata- logue is to give tlie right ascension and declination of a number of stars for some epoch, the beginning of the year 1875 for instance, with the data by which the position of each star can be found at any other epoch. JiWI ffff*l : ' . i 80 ASTRONOMr. • 'If To give tlio student a still further idea of tlic Ephemtm, we preseut a stniill portion of uue of iti pages for the year 1882: Febhvabt, 1882— at Oreknwicii Mean Noojt, week. ffS The Bpn's i '; Wed. Thur. FriU. 8»t Bun. Mod. Tuea, Wed. Tkur. Frid. Sat. Bun. Mod. Tues. Wed. Thur. Frid. Bat. 16.8410.141 19.8810.107 »1.M 10.078 28 .3.S 10.040 «1 80 88.88 lO.OOT Apparent right aaoenHion. Diff. fori hour. a. 18.0110.178 817 Apparent declination. 31 84 88.68 9.974 81 88 88.60 9.941 81 88 80.79 9.909 81 86 18.81 81 40 14.88 81 44 10.80 81 48 5.98 81 68 0.43 81 S5 M.16 31 89 47.17 88 8 89.47 83 7 81.07 9.87r 9.816 9.81.') 0.784 9.7S8 9.788 9.698 9.661 9.685 16 16 16 15 16 3 45 87 9 51 83 33.4 5.4 80.9 89.3 80.8 6.1 15 14 35.4 14 55 39.1 14 86 17.7 14 16 51.6 18 57 11.8 18 87 16.9 18 17 9.1 18 56 48 8 18 86 14.9 13 IS 89.8 11 54 88.1 11 88 88.6 Diff. fori hour. +43.81 48.67 44.80 +44.99 45.69 46.86 +47.08 47.66 48.88 48.88 49.4' 50.08 Equation of time to be subtracted from mean time. M. IS 18 14 14 14 14 B. 51.84 58.58 5.01 10.61 16.41 19.40 14 88.60 14 36.01 14 86.65 14 37.51 14 37.68 14 86.99 +50.80 14 85.68 51.18 14 98.53 51.66 14 80.70 +88.14 53.68 68.07 14 17.15 14 18.90 14 7.M 0.818 0.884 0.850 0.916 0.188 0. H. M. s. 30 46 81.70 39 80 18.86 30 54 14.81 18031 0.117 0.084 0.063 0.030 0.011 0.049 0.078 0.104 0.1S4 Sidereal time or riftht aaoenaion of meanaun. 30 88 11.97 81 9 7.93 • 4.48 91 10 1.08 91 18 B7.80 91 17 84.14 91 91 80.70 91 8S 47.36 81 39 48.81 31 88 40.86 31 S7 86.91 31 41 8S.46 0.164 91 46 80.08 0.198 81 40 36.87 0.383 31 68 38.18 The third coiumn shows the R. A. of the sun's centre at Oreen- wich mean noon of eacli day. The fourth column shows the hourly change of this quantity (9.815 on Feb. 12). At Greenwich hours the sun's R. A. was 21 ■> 44'" 10*.80. Washington is fi^ ^ (6^.18) west of Greenwich. At Washington mean noon, on the ISth, the Greenwich mean time was S'*. 18. 0.815 X 5.18 is SO'.SS. This isto be added, since the R A. is increasing. The sun's R. A. at Wash- ington mean noon is tlierefore 21^ 45" 1*.15. A similar process will give the sun's declination for Washington mean noop. In the same manner, the R. A. and Dec. of the sun for any place whose longitude is iinown can be found. The column "Equation of Time" gives the quantity to be sub- tracted from the Greenwich mean solar time to obtain the Green- wich apparent solar time (see page 188). Thus, for Feb. 1, the Greenwich mean time of Greenwich mean nooc is 0^ 0* 0*. Tlie true sun crossed the Greenwich meridian (apparent noon) at 28^ 4ih 08*.66on the preceding day; i.e., Jan. 81. When it was O* 0" ()• of Greenwicli mean time on Feb. 18, it was also 21'' SS" 40'.35 of Greenwich local sidereal time (see the last column of the table), L&i nneri*, wu present [ Noon. n » Sid«iwil time orrlRht Moenuon of meMiaun. 0.818 o.mt 0.8B0 B. 80 80 80 M. S. 48 91.70 fiO 18.98 54 14.81 0.918 0.188 O.ISO 90 91 81 B8 11.97 9 7.98 8 4.48 0.117 0.064 O.OM 91 91 91 10 1.08 18 S7.M 17 M.14 0.080 0.011 O.Ott 91 91 91 81 BO.TO 88 47.95 80 48.81 0.078 0.104 0.184 91 91 91 88 40.86 87 88.91 41 88.48 0.184 0.198 0.888 91 81 46 80.08 40 86.57 08 88.18 centre at Oreen- shows the hourly eenwich hours I is fi^ ^ (6^.18) on the 12tb, the S0-.86. Thtoisto B R. A. «t Wash- lilar process will OP. In the some i whose longitude kntltv to be sub- »btafn the Qreen- for Feb. 1, the isOkO-O*. Tlie noon) at 38^ 46" n Feb. 18, it was time (see the last CHAPTER IV. MOTION OF THE EARTH. AVOBHT IDIAS or THE PUUntTS. It was observed by the ancients that whilr; the great mass of the stars maintained their positionn volatiTdly to each other month after month and year aiter year, there re visible to them seven heavenly bodies which changed thc'ir positions relatively to the stars and to each other. These they called planets or wandering stars. It was found that the seven planets performed a very slow revolution around the celestial sphere from west to east, in periods ranging from one month in the case of the moon to thirty years in that of Saturn, The idea of the fixed stars being set in a solid sphere was in perfect accord with thei( diamal revolution as observed by the naked eye. But it was not so with the planets. The latter, after continued observation, were found to move sometimes backward and sometimes forward; and it was quite evident that at certain periods they were nearer the earth than at other periods. These motions were en- tirely inconsistent with the theory that they were fixed in solid spheres. These planets (which are visible to the naked eye), together with the earth, and a number of other bodies which the telescope has made known to us, form a family or system by themselves, the diro«nsioQ^ pf which, although ASrUOAOMK »i !i I hi i : inconceivably greater tliun niiy wliich wo Imve to doal with at the surface of tlie oiirtli, uru riuito iiiBignitlcuiit when compurod with tlio distiincu wliich .separates us from the fixed stars. Tiio sun being the gn-at central body uf this Bystom, it is called the i-1ie earth the sun seems to perform an annual revolution :vmong the stars, a fact which has been known from early ages. This motion is due to the annual revolution of the earlli round the sun. In Fig, 29 let S represent ihc sun, ABCD the orbit of the earth around it, and ('11 ^GH the sphere of the fixed stars. This sphere, being supposed infinitely distant, must be considered as infinitely«larger than the circle ABCD. Suppose now that 1, 2, 3, 4, 5, 6 are a number of consecutive positions of the earth in its orbit. The line IS drawn from the sun to the earth in the first position is called the radius-vector of the earth. Suppose this line extended infinitely so as to meet the celestial sphere in the point 1'. It is evident that to an observer on the earth at 1 the sun will appear projected on the sphere in the dii'ec- tion of 1'; when the earth reaches 2 it will appear in the direction of 2', and so on. In other words, as the earth revolves around the sun, the latter will seem to perform a revolution among the fixed stars, which are immensely more distant than itself. The points 1', 2', etc., can be I to (IohI with litlcunt when U8 from tho I body of this .>ro are vight I tho urdorof orm tiroguhtr •est, iKjrforniH 9 farthest, in m. 8 to perform :;t which has is due to the 7D the orbit iphere of the litely distant, in the circle ire a number lit. The hne rst position is lose this line sphere in the . the earth at in the direc- ippcar in the as the earth to perform a e immensely , etc., can be r ^, *>.^< m b: IMAGE EVALUATION TEST TARGET (MT-3) 1.0 ^1^ tti ■tt 1^ 12.2 2* u^ ip*" 1.1 S 1^ 12.0 11-25 i U 1 1.6 IIII^B nHI^^ wmM •J' HiotogFaphic ScMioes C(xpQFati0n 23 WMT MAM STMMT W||if|||,N.Y. 14SM CIHM/ICMH Microfiche Series. CIHIVI/iCIVIH Collection de microfiches. Canadian Inttituta for Historical MIcroraproductiona / Inatitut Canadian da micrcraproductlona hiatoriquas 0m^ MOTIONS OF rUE EARTH. 83 fixed by tbeir relations to the yarioug fixed stars, whose places are known. It is also evident that the point in which the earth would be projected if viewed from the sun is always exactly opposite that in which the sun appears as projected from the earth. Moreover, if the earth moves more rapidly in Fia. ».— BsToLonoM ow rvm Eaktb. some points of its orbit than in others, it is evident that the son will also appear to move more rapidly among the stars, and tLut the two motions must always accurately porresppnd to each other, The rftdius-yeotor of the earth in its annual course de- iOrib«B » plane;, wUich in the figure may be represents by H ASTRONOMY. i. k that of the paper. This plane continued to infinity in every direction will cut the celestial sphere in a great cir- cle ; and it is clear that the sun will always appear to move in this circle. The plane and the circle are indiffer- ently termed the ecliptic. The plane of the ecliptic is gen- erally taken as the fundamental one, to which the jjositions of all the bodies in the solar system are referred. It divides the celestial sphere into two equal parts. In think- ing of the celestial motions, it if- convenient to conceive of this plane as horizontal. Then if we draw a vertical line through the sun at right angles to this plane (perpendicular to the plane of the. paper on which the figure is represent- ed), the point at which this line intersects the celestial sphere will be the pole of the ecliptic Let us now study the apparent annual revolution of the sun produced by he real revolution of the earth in its orbit. When the earth is at 1 in the figure the sun will appear to be at 1', near some star, as drawn. Now by the diurnal motion of the earth the sun is made to rise, to culminate, and to set successively for each meridian on the globe. This star being near the sun rises, culminates, and Bets with it; it is on the meridian of any place at the local noon of that place (and is therefore not visible except in a telescope). The star on the right-hand side of the figure near the line C8l prolonged is nearly opposite to the sun. When the san is rising at any place, that star will be setting; when the sun is on the meridian of the place, this star is on the lower meridian; when the sun is setting, this star is rising. It is about 180° from the sun. Now suppose the earth to move to 2. The sun will be seen at 2', near the star there marked. 2' is east of 1'; the sun appears to move among fhe stars (in consec[uenc« of the CHrtb'B annual motion) to infinity in in a great cir- lys appear to } are indiffer- cliptic is gen- i the ]>oBitions referred. It ks. In think- to conceive of a vertical line perpendicular ) is represent- the celestial olution of the th in its orbit. in will appear \)j the diurnal to culminate, e globe. This I sets with it; 1 noon of that tlescope). The the line CSl tien the san is when the sun on the lower is rising. It the earth to the star there o move among ^nual motion) MOTIONS OF THE EARTH. 88 from west to east. The star near 2' will rise, culminate, and set with the sun at every place on the earth. The star near 1' being west of 2' will rise before tlie sun, culminate before him, and set before he does. If, for example, the star 1' is near the equator when the lun is 15° east of it, the star will rise about 1 hour earlier than the sun. When the sun h 30° east of it (at 3', for example), the star will rise 2 hours before the sun. When the sun is 90° east of 1', the star will rise 6 hours before the sun, and so on. That is, when the siin is rising at any place, this star will be on the meridian of the place. When the sun appears in the line VCS 1 prolonged to the right in the figure, the star 1' will be on the meridian at mid- night, and is then said to be in opposition to the sun. It is 180° from it. When the sun appears to be near H, the star 1' will be about 45° or 3 hours east of the sun. Tlio sun will rise first to any place on the earth, and the star will rise 3 hours later, say at 9 a.m. Finally the sun will come back to the same star again and they will rise, cnlmi- nate, and set together. We know that this cycle is about 365 days in length. In this time the son moves 360°, or about 1° daily. This cycle is perpetually repeated. Its length is a sidereal year; that is, the interval of time required for the sun to move in the sky from one star back to the same star again or for the earth to make one revolution in its orbit among the stars. The ancients were familiar with this phenomenon. They knew most of the brighter stars by name. The heliacal rising of a bright star (its rising with Helios, the sun) uwlred the beginning of a cycle. At the end of it, seasons «l4 oropn aii4 the periodical floods of the Nile Iiad repeal 86 ASTRONOMY. ed themselves. It was in this way that ' le first accurate notions of the year arose. The apparent position of a body as seen from the earth is called its geocentric place. The apparent position of a body as seen from the sun is called its heliocentric place. In the last figure, suppose the sun to be at S, and the earth at 4. 4' is the geocentric place of the sun, and is the heliocentric place of the earth. The Smr'B Appabent Path. It is evident that if the apparent path of the sun lay in the equator, it would, during the entire year, rise exactly in the east and set in the west, and would always cross the meridian at the same altitude. The days would always be twelve hours long, for the same reason that a star in the equator is always twelve hours above the horizon and twelve hours below it. But we know that this is not the case, the sun being sometimes north of the equator and sometimes south of it, and therefore having a motion in declination. To understand this motion, suppose that on March 19th, 1879, the sun had been observed with a meridian circle and a sidereal clock at the moment of transit over the meridian of Washington. Its position would have been found to be this; Right Ascension, 23" SS" 83» ; Declination, 0° 30' south. Had the observation been repeated on the 20th and fol- lowing days, the results would have been: March 20, R Ascen. 23" 59°' 2' ; Dec. 0' 21, " 0" 2'°40»; " 0° 22, " 0" 6" 19'; " O' If we lay these positions down on a chart, we shall fnd th^m to he as in Fig. 30, the centra of the sun being south ' 6' South, 17' North, 41' North. %.. first accurate )m the earth position of a Uric place. \t S, and the snu, and G is ho sun lay in ', rise exactly rays cross the uld always be ; a star in the on and twelve t the case, the nd sometiraes a declination. I March 19tb, ivn circle and a lie meridian of and to be this; 0° 30' south, I 20th and fol^ " 6' South, ' 17' North, Ul' North. we shall fnd in being soatk ifOrfONS OF THE EARTH. 87 of the equator in the first two positions, and north of it in the last two. Joining the successive positions by a line, we shall have a representation of a small portion of the appa- rent path of the sun on the celestial sphere, or of the ecliptic. It is clear f roin the observations and the figure that the sun crossed the equator between six and seven o'clock on Uie afternoon of March 20th, and therefore that the eqtia* tor and ecliptic intersect at the point where the sun was at that hour. This point is called the vernal equinox, the first word indicating the season, while the second expresses Fio. SOi— Thb Suit OwMmia tob Equatob. the equality of the nights and days wliich occurs when the sun is on the equator. It will be remembered that this equinox is th6 point from which right ascensions are count- ed in the heavens, in the same way that we count longi- tudes on the earth from Greenwich or Washington. A sidereal clock at any place is therefore so set that the hands shall read hours minutes seconds at the moment when the vernal equinox crosses the meridian of the place. Continuing our observations of the. sun's -apparent coarse for six months from March 20th ^I) Sept^ftiW !23d, vTe 88 ASmolfOMT. should find it to be as in Fig. 31. It will be seen that Fig. 30 corresponds to the right> hand end of 31, bnt is on a much larger scale. The son, moving along the great circle of the ecliptic, will reach its greatest northern declination about June 21st. This point is indicated on the figure as 90° from the vernal equinox, nnd is called the summer sol- stice. The sun's right ascen- sion is then six hours, and its declination 23^° north. The student should complete the figure by drawing the half not given here. The course of the sun now inclines toward the south, and it again crosses the equator about September 22d at a point diametrically opposite the ver- nal equinox. All great oirclee intersect each other in two op- posite points, and the ecliptic and equator intersect at the two opposite equinoxes. The equi- nox which the sun crosses bnt is on a The Ban, > great circle rill reach its declination This point :lie figure as nal equinox, summer sol- right ascen- ours, and its north. The omplete the the half not the snn now e sonth, and the equator I2d at a point >site the ver- great circles er in two op- tbe eoliptio Bctatthetwo I. The equi- n crosses oa 1 called the months from ilon of a day. By the more exact methods of modurti limes it can be determined within less than a minute. It will bo seen that this method of determining the annual appar- ent course of tlic sun by its declination or altitude is entirely inde- pendent of its relation to the flxed stars; and it could be etiually well bpplicd if no stars were ever visible. There arc, tiiereforc, two en- tirely distinct ways of finding when the sun or tlic earth has completed ita apparent circuit around the celestial sphere; tlie one by the transit instrument and sidereal clock, which show when the sun returns to the tame ponition atnong Vu »tart, the other by the measurement of altitude, which shows when it returns to the tame equinox. By the former method, already described, wc conclude that it has completed an annual circuit when it returns to the same star; by the latter when It returns to the same equinox. These two nietiiods will give slightly different results for the length of the year, for a reason to be here- after described. Tha Zodiao and iU DUisiou. — The zodiac is a belt in the heavens, commonly considered as extending some 8' on eucli side of the ecliptic, and therefore about 16° wide. The planets known to the ancients are always seen within this belt. At a very early day the zodiac was mapped out into twelve signs known as the signt of the todiae, the names of which have been handed down to the present time. Each of these signs was supposed to be the seat of a constella- tion after which it was called. Commencing at the vernal eq;;!sox, the first thirty degrees through which the sun passed, or the region among the stars in wliich it was found during tlie month following, was called the sign Aries. The next thirty degrees was called Taurus. The names of all the twelve signs in their proper order, with the approximate time of the sun's entering upon each, are as follows: Ariet, the Ram, Taurus, the Bull, Gemini, the Twins, Caneer, the Crab, Leo, the Lion, Virgo, the Virgin, L^ra, the Balance, Seorpius, the Scorpion, Sagittarius, the Archer, Gaprieomus, the Goat, Aquarius, the Watcr-be.-.rer, Pisces, the Fishes, March 20. April 20. May 20. June 21. July 22. August 22. September 22. October 28. November 28. December 21. January 20. Februaiy 19. e time at which least to a frac> rti limes it can 3 annual appar- is entirely inde- be etiuully well erefore, two en- I lias completed le by the transit sun returns to aeaaurement of juinojc. By the t has completed the latter when rill give slightly son to be here- in the heavens, ich side of the I known to the y early day the the signt of the 1 to the present t of a constclla- rernal equinox, i, or the region )nth following, ees was called r proper order, on each, ore as r23 B. r28. •21. !0. 19. koftoifS OF fits XARta. dl Each olP these signs coincides roughly with a constellation in the heavens; and thus there arc twelve constellations called by the names of these signs, but the signs and the constellations no longer correspond. Altiiough tlie sun now crosses the equator and enters the $ign Aries on the 20th of March, he does not reach the eonttella. lion Aries until nearly a month later. This arises from the precea- sion of the equinoxes, to be explained hereafter. OBUQinTT 07 THS SOIimO. We have already stated that when the sun is at the snm- faior solstice it is about 23^° north of the equator, and when at the winter solstice, about 2'6^" south. This shows that the ecliptic and equator make an anple of about 23^° with each other. This angle is called the obliquity of the eclip- tic, and its determination is very simple. It is only neces- sary to find by repeated observation the sun's greatest north declination at the summer solstice, and its greatest south declination at the winter solstice. Either of these declina- tions, which must be equal if the observations are accurate- ly made, will give the obliquity of the ecliptic. It has been continually diminishing from the earliest ages at a rate of about half a second a year, or, more exactly, about 47' in a century. This diminution is due to the gravitating forces of the pl^iets, and will continue for several thousand years to come. It will not, however, go on indefinitely, but the obliquity will only oscillate between comparatively narrow limits. In the preceding paragraphs we have explained the apparent annual circuit of the sun relative to the equator, and shown how the seasons depend upon this circuit. In order that the student may clearly grasp the entire subject, it is necessary to show the relation ol these apparent move- ments to the actual movement of the earth around the van. 1 To understand the relation of the equator to the ecliptic, we must remcmlier that tiio cele«tinl pole and tlie celostiitl equator hare really no ruferenco whatever to the heavens, but depend solely on the direc- tion of tlie earth's axis of rotation. Tlie polo of the lieitvens is noth- ing more than that |K>int of tlio cele'tdal sphere toward which tlie earth's axis happens to point. If the direction of this axis changes, the position of tlie eeleHtial pole among the stars will change also ; tliough to an observer on the earth, unconscious of tlie change, it would ■eem as if tlie starry sphere moved while the pole remained at rest. Again, tlie celestial equator being merely the great circle in which the plane of the earth's equator, extended out to infinity In every direction, cuta the celestial sphere, any change in tlie direction of ilie pole of the earth would necessarily change the position of ilie equator among the stars. Now the positions of the celestial pole and the celestial equator among the stars seem to remain unchanged tiirough- out the year. (There is, indeed, a minutd change, but it does not affect our present reasoning.) This sliows that, as the earth revolves around the sun, its axis is constantly directed toward nearly the •amo point of the celestial sphere. Thx Siaiovk The conclnsions to which we are thus led respecting the real revolution of the earth are shown in Fig. 32. Here 8 represents the sun, with the orbit of the earth surrounding it, but viewed nearly edgeways so as to be much foreshortened. A B CD are tlic four cardinal positions of the earth which correspond to the cardinal points of the apparent path of the Bun already described. In each figure of the earth iV^ is the axis, N being its north and 8 its south pole. Since this axis points in the same direction relative to the stars during an entire year, it follows that the different lines NS are all parallel. Again, since the equator does not coincide with the ecliptic, these lines are not perpendicular to the ecliptic, but are inclined from this perpendicular bj 23i°. When the earth is at A the sun's north-polar distance (the i cliptlc, we mutt lutor bnre renlly lily OD the direc- lieaveDH Is iiotk- wrard wliicli the kxis changes, the ge nl84> ; though muge, il wouhl iniiliied at rcHt. circle In which nflnity In every direction of the n of the equator al pole and the innged through- but It does not e eiirth ruvotves rurd nearly the 'especting the 32. Here S irroiinding it, oreshortened. 3 earth which tit path of the earth NSin pole. Since ) to the stars ifferent linei iter does not lerpendicalar [leudicuhu* bj distance (the MOTIOm oy THB BAni'lt. 08 angle at the centre of the earth at .1 between the lines to the north polo and to the sun) is li:^"; ut // it is 00°; at C it is 66^°; at D it is uguin 00°, and between 60^ and 113^° the north-polar distance continunlly yaries. This may bo plainer if the student draws the lines SA, S H, SC, SD, and prolongs the lines N8 at each position of the earth. Now the snn shines on only one half of the earth; viz., that hemisphere turned toward him. This hemisphere is left bright in each of the figures of the earth at A, B, V, D. Fw. St.— Oaohh ne. MOTIONS OF THE EARTH. 96 Celestial Latitude ahb Lohoitubs. To describe the positions of the sun and planets in space we need two new co-ordinates. The Celestial Latitude of a star is its angular distance north or south of the ecliptic. The Celestial Longitude of a star is its angular distance from the vernal equinox measured on the ecliptic from west to east. Having the right ascension and declination of a body (which can be had by observation), we can com- pute its celestial latitude and longitude. These co-ordinates are no longer observed (as they were by the ancients), but deduced from observations of right ascension and declina- tion. t'4J .irt....i"- •■wp" CHAPTER V. THE PLANETARY MOTIONS. AnAMxn Airs Rial MoTion ov the PiAnm DefliiitieiUL — The soiar syBtem compriaes a number of bodies of rarious orders of magnitode and distance, sub- jected to many complex motions. Oar attention will be particularly directed to the motions of the great planets. These bodies may, with respect to their apparent motions, be divided into three classes. Speaking, for the present, of the sun as a planet, the first class comprises the 8un and moon. We have seen that if, upon a star chart, we mark down the positions of the sun day by day, they will all fall into a regular circle which marks out the ecliptic. The monthly course of the moon is found to be of the same nature; and although its motion is by no means uniform in a month, it is always toward the east, and always along ov very near a certain great circle. The second class comprises Venus and Mercury. The apparent motion of these bodies is an oscillating one on each side of the sun. If we watch for the appearance of one of these planets after sunset from evening to evening, we shall find it to appear above the western horizon. Night after night it will be farther and farther from the sun until it attains a certain maximum distance; then it will appear to r^tuni towards the sun a^n, and for a whil^ tQ ^ loit THE PLANETARY MOTIONS. 97 : Plaibts. 1 a number of distance, snb- tention will be great planets. arent motions, I a planet, the have seen that ositions of the ar circle which B of the moon ugh its motion ays toward the I great circle. )£ereHry. The Hating one on appearance of ing to evening, srizon. Night a the sun until I it will appear rhil? tQ b9 loit in its rays. A few days later it will reappear to the west of the sun, and thereafter be visible in the eastern horizon before sunrise. In the case of Mercury the time required for one complete oscillation back and forth is about four months; and in the case of Venus it is more than a year and a half. The third class comprises Mars, Jupiter, and Saturn, as well as a great number of planets not visible to the naked eye. The general or average motion of these planets is toward the oast, a complete revolution in the celestial sphere being performed in times ranging from two years in the case of Mars to 164 years in that of Neptune. But, instead of moving uniformly forward, they seem to luvre a swinging motion; first, they move forward or toward the east through a pretty long wrc, then backward or westward through a short one, then forward through a longer one, etc. It is by the excess of the longer arcs over the shorter ones that the circuit of the heavens is made. The general motion of the sun, moon, and planets among the stars being toward the east, motion in this direction is tilled direct; motions toward the west are called retrograde. j nring the periods between direct and retrograde motion the planets will for a short time appear stationary. The planeta Venus and Mercury are said to be at greatest elongation when at their greatest angular distance from the sun. The elongation which occurs with the planet east of the sun, and therefore visible in the western horizon after sunset, is called the eastern elongation, the other the west- em one. A planet is said to be in . onjunction with the sun when it is in the same direction as seen from the earth, or when, «■ it awm to pass b^ the sun, it approaches nearest U> it. 1, i m ASTRONOMY. It is said to be in opposition to the sun when exactly in the opposite direction — rising when the Eun sets, and vice versa.* If, when a planet is in con junction, it is between the earth and the sun, the conjunction is said to be an inferior one; if beyond the sun, it is said to be superior. i Fm. as.— Omn of tbs Fijuim. Axntngements and Motions of the Planeti.— The sun i» tlie real centre of the solar system, and the planets proper revolve around it as the centre of motion. The order of the five innermost large planets, or the relative position of * A planet is in' oonjunetion with tbe sun when it has the aame geocentric longitude; in oppoeition wUen the longitudes differ l^\ THE PLANETAliY MOTIONS. 9% exactly in the ets, and vice it is between said to be an je superior. k — ^The sun Js ilanets proper The order of ye position of it has the aamie uclM differ l^\ their orbits, is shown in Fig. 33. These orbits are all nearly, but not exactly, in the same plane. The planets Mercury and Vemis which, as seen from the earth, never appear to recede very far from the sun, are in reality those which revolve inside the orbit of the earth. The planets of the third class, wliich perform their circuits at all dis- tances from the sun, are what we call the superior planets, and are more distant from the sun than the earth is. Of these the orbits of Mars, Jupiter, and a swarm of telescopic planets are shown in the figure; next outside of Jupiter comes Saturn, the farthest planet readily visible to the nakcid eye, and then Uranus and Neptune, telescopic plan- ets. On the scale of Fig. 38 the orbit of Neptune wonld be more than two feet in diameter. Finally, the moon is a small planet revolving around the earth as its centre, and carried with the latter as it moves around the sun. Inferior planets are those whose orbits lie inside that of the earth, as Mercury and Venus. Superior planets are those whose orbits lie outside that of the earth, as Mars, Jupiter, Saturn, etc The farther a planet is situated from the sun the slower is. its orbital motion. Therefore, as we go from the ntn, the periods of i-evolution are longer, for the double reason that the planet iias a larger orbit to describe abd iAbves more slowly in its orbit. It is to this slower motion of the outer planets that the occasional apparent retrograde mo* tion of the planets is due, as may be seen by studying Fig. 31. The apparent position of a planet, as seen from the earth, is determined by the lino joining the earth and planet. Supposing this line to be continued so as to inter- sect the celestial sphere, the apparent motion of the planet wiU be defiacd by the motion of the point in which the line I ti ■TSS 100 A8TR0N0MT. intersects the sphere. If tliis motion is toward the east, it is direct ; if toward the west, retrograde. The Apparent Kotion of a Superior Planet.— In the figure let S bo the sun, ABODE F tlie orbit of the earth, and HIKLMN the orbit of a superior planet, as Mar%. When the earth is at A suppose Mars to be at H, and let B and /, C and iT, B and Z, E and il, F and JV be corre- sponding positions. As the earth moves faster than Mart rw.si the arcs AB, EC, etc., correspond to greater angles at the centre than HI, IK, etc. When the earth is at ^, Mars will be seen on the celestial sphere at the apparent position 0. When the earth is at B, Mars will be seen at P. As the earth describes AB, Mars will appear to describe OP moving in the same direc- tion as the earth's orbital motion; i.e., direct. When the earth is at C, Mars is at K (in opposition to the sun), and ite motion is retrograde along the small arc beyond QP iu i the east, it [n the figure earth, and b, as Mara, ; H, and let JV be corre- r than Mart mgles at the the celestial I earth is at •scribes AB, ) same direo- When the he sun), and >yond QP ii| THB PLANETARY MOTIONS. 101 the figure. When the earth reaches D the planet has fin- ished its rctrogi-ade arc. As the earth moves from D io E the planet moves from L to M, and the lines joining earth and planet are parallel and correspond to a fixed position on the celestial sphere. The planet is at a station. As the earth moves from Eio Fihe apparent motion of Mara is direct from Q io R; and in the same way the apparent motion of any outer planet can be determined by drawing its orbit outside of the earth's orbit ABODE Fond laying off on this orbit positions which correspond to the points ABCDEF and joining the corresponding positions. It will be found that all outer planets have a retrograde mo- tion at opposition, etc. The Apparent Motion of an Inferior Planet— To deter- mine the corresponding phenomena for an inferior planet the same figure may be used. Suppose HIKLMto be the orbit of the earth, mdAB CD EF the orbit of Mer- ; eury, and suppose iSTand A, /and B, etc., to bo corre- ; spending positions. Suppose HA to he tangent to Mar- '' eury' a orbit. The angle AHS is the elongation of Mer-'l eury, and it is the greatest elongation it can ever have, i Let the student construct the apparent positions of Mar* ' eury as seen from the earth from the data given in the : figure. From the apparent positions he can determine the apparent motions. As Mercury moves from ^^ its ap- parent motion is direct On both sides of the inferior con- '. junction C its motion is retrograde. From D to E it is stationary. Also let him construct the apparent positions of the ran at different times by drawing the lines H8, IS, K8, etc., towards the right The angles between the ap- parent positions of Mercury and the sun will be the elonga- tions of Mercury at yarious times. 102 A8TR0N0MT. TkMry of KplojrelM.— Complicated as tlie apparent motions of the planets were, it wus seen by tlic ancient astruuomers tliat tliey could be represented by n combinatiun of two motions. First, a small circle or epicycle was supposed to move around the earth (not the sun) with a regular, though not uniform, forward motion, and then the planet was supposed to move around the circumference of this circle. The relation of this theory to the true one was this: The regular forward motion of the epicycle represents the real motion of the pinnet around the sun, while the motion of the planet around the circumference of the epicycle is an apparent one arising from the revolution of the eartli around the sun. To explain this we must under- stand some of the laws of relative mo- tion. It is fuiniliitrly known thut if an observer in unconscious motion looks upon an object at rest, the object will appear to him to move in a direction opposite that in wiilcli he moves. As a result of this law, if the observer is unconsciously describing a circle, an object at rest will appear to him to describe a circle of equal size. This is shown by the following figure. Let 6' represent the sun, and ABC DBF the orbit of the earth. Let us sup- pose the observer on the earth carried around in this orbit, but imagining himiielf nt rest at 8, the centre of mo- tion. Suppose he keeps observing the direction and distance of the planet P, which for the present we suppose to be at rest, since it is only the relative motion that we shall have to consider. When the observer is at A he really aees the planet in a direction and distance A P. but imagining himself at a he thinks he see the planet at the point a determined by drawing a Une 8a parallel and equal to ^ P. As he passes from ^ to B the planet will seem to him to move in the opposite direction from a to b, the point b being determined by drawing Sb equal and parallel to BP As he recedes from the planet through the arc B CD, the planet seems to recede from him through bed; and while he movee from left to right through DB the phinet seems to move from ri^t no PlAifETAttr MOTIONS. 108 itioDB of the It tliey could a smull circle not the sun) ind then the of this circle. Tlic regular lOtion of tlie ; around the ng from the around the must under- f relative mo- 1 thut if an motion looks le object will n a direction I moves. As e observer is ; a circle, an ar to him to il size. This g figure. Let ABCDEP Let us sup- enrth carried ut imagining centre of mo- observing the the planet P, re suppose to y the relative e to consider. i A he really pning himself 3d by drawing m ^ to B the ion from a to 1 and parallel arc S CD, the rhile he movea ve from ri^t to left through de. Finally, as he approachv'>8 the planet through the arc efa the planet seems to approach him through EFA, and when lie returns to A the planet will appear nt A, as in the liegln- ning. Thus tlio planet, though really at rest, would seem to him to move over the circle abcdef corresponding to that in which the observer himself was carried around the sun. The planet being really in motion, it is evident that the combined effect of the real motion of the planet and the apparent motion around the circle abedefviW be represented by carrying the centre of this circle P along the true orbit of the planet. The motion of the eartii being more rapid than that of an outer planet, it follows that the apparent motion of the planet through a 6 is more rapid tlian the real motion of P along the orbit. Hence in this part of the orbit tiie movement of the planet will be retrograde. In every other part it will be direct, l»ecause the progressive motion of P will at least overcome, sometimes be added to, tlie apparent motion around the circle. In the ancient astronomy the apparent small circle abedefyru called the epieyele. In the case of the inner planets Mercury and Vmu$ the relation of the epicycle to the true orbit is reversed. Here the epicyclic motion is that of the planet round its real orbit; that is, the true orbit of the planet around the sun was itself taken for the epicycle, while the forward motion was really due to the apparent revolution of the sun produced by the annual motion of the earth. By constructing a figure for this case the student can readily see how tills comes about. Although the obseryations of two thousand yean ago could be tolerably well explained by these epicycles, yet with eyery increase of accuracy in observation new compli- cations had to be introduced, until at the time of Copsb- Hicus (164?) the confusion was very great. The Copemioan System of the World.— Cofebkicus re- vived a belief taught by some of the ancients that the sun was tite centre of the system, and that the earth and plan- ets moved about him in circular orbits. While this was a atq>, and a great step, forward, purely circular orbits for the planets would not explain all the facta. r» 104 ASTRONOMY. From the time of Copernicus (1543) till that of Kep- ler and Galileo (1600 to 1630) the whole question of the true system of the universe was in debate. The circular orbits introduced by Copernicus also required a complex system of epicycles to account for some of the observed motions of the planets, and with every increase in accuracy of observation new devices had to be introduced into thb system to account for the new phenomena observed. In short, the system of Copernicus accounted for so many facts (ad the stations and retrogradatious of the planets) that it could not bo rejected, and had so many difficulties that without modification it could not be accepted. KmjtB's Laws or PLAniiBT Monov. Kepler and Galileo.— Kepler (bom 1571, d. 1630) was a genius of the first order. He had a thorough acquaint- ance with the old systems of astronomy and a thorough be- lief in the essential accuracy of the Oopernican system, whose fundamental theorem was that the sun and not the earth was the centre of our system. He lived at the same time with Galileo, who was the first person to observe the heavenly bodies with a telescope of his own invention, and he had the benefit of accurate observations of the plftnets made by Ttcho Brahb. The opportunity for determin- ing the true laws of the motions of the planets existed then as it never had before; and fortunately he was able, through labors of which it is difficult to form an idea to- day, to reach a true solution. The Periodic Time of a Planet.— The time of revolntion of a planet in its orbit round the 3un (its periodic tinu) can be learned by continnons observations of the planet's course among the stars. Tan PLANETARY MOTIONS. 106 hat of Kep- Bstion of the Dhti circular d a complex he observed I in accuracy ced into thb bserved. In 'or BO manj the planets) y difficulties >ted. [OV. I. 1630) was ;h acquaint* thorough be- lean system, and not the i at the same > observe the vention, and the plftneti )r determin- existed then e was able, an idea to- »f revolution wiodic time) the planet's From ancient times the geocentric positions of the planets had been observed. Those positions were referred to the places of the brightest fixed stars, and the relative places of these stars had been fixed with a tolerable ac- curacy. The time required for a planet to move from one star to the same star again was the time of revolution of the planet referred to the earth. The real motion of the earth was known from observa- tions of the apparent motion of the sun. By calculation it was possible to refer the motions as observed (i.e., with reference to the earth) to the real motions (t.0., those about the sun). It was thus found that the periodic times of the known planets were: jr = 1.0000 Man «. 1.6887 Jupiter a. = 5 ioas Saturn a. = 9.58«^ The cftlcultttion which wo Imve described could be made for every poaition of ouch planet, and tlius ita distances from tlio sun ut every point of its orbit could be determined. The radim-vector of a planet is the line which joins it to the sun. The relative lengths of the radii-veotorea of each pinnet at any time were thus found by observation, in terms of the eurth'H radias«vector = 1. Fra. S7. Suppose iS^to be the sun, and draw lines SP, SP^, SP,, SP,, etc., to the heliocentric positions of a planet at dif- ferent times. On these lines lay off distances 5 P, iSP,, SP,, etc., proportional to the lengths of the planet's radii- vectores determined as above. Join the points P, P„ P„ P„ etc. The line joining these is a visible representation rliliiilWfifflriTillltWIiillW^ ^' j3^' 108 astboMmt. t!. 9 ! of the shape of the planet's orbit, drawn to scale. This shape is not that of a circle, but it is an ellipse, and the sun, S, is not at the centre but at a/ociis of the ellipse. An ellipse is a curve such that the sum of the distances of every point of the curve from two fixed points (the foci) it a constant quantity. ria as. Th» W3ltm.—A i) C P is an elllpM ; 5 and 5* are the fed. By the definition of an tiWpetSP+Pff^AO, and this is true for ereiy point. 8 is the focus occupied by the sun, " the filled focus." A 8 is the leait dittatux of the planet from the sun, its perihelion dutanee; and .4 is the periheUon, that point nearest the sun. C is the aphelion, the point farthest from the sun. 8 A, SD, 80, SB, 8P are ladii- ▼ectores at different parte of the orbit, il C is the major aiis of the orbit = 2a. This major axis of the orbit is twice the mean auanee of the planet from the sun. a. BD is the minor axis, 26. The ratio of 08U> OA is the eeeentrieity of the ellipse. By the definition of the ellipse, again, B8-\- BS'=AO; mdB8 = BSs: a. 'S^ = BO* + Q fl*. or 08= ¥^^'v and the eccentricity of the ellipse is ^=i2L=i*. OA a Keplur't Laws.— By compatations baaed on the observa- tions of Mart made by Tycho Brahb, Keplkb deduced > jun»M iii» n i iwew i»" wn i i ■^ iTHMrwggiiw n to scale. This n ellipse, and the of the ellipse, t of the distances i points (the foci) re the focL By the lis is true for ereiy I filled focus." A 8 I feriluUon dktanee; I. (7is theopAettm, \ 8B, 8P ftie radii- Cis tlie major axis is twice the nuan the minor uis, Sb. the ellipse. By the uidB8 = BSssa. eccentricity of the 1 on the observa- Keplkb deduced TBS PLANSTABT MOTTONS. 100 his first two laws of motion in the solar system. The first law of Keplkb is — /. JSach planet moves around the sun in an ellipse, hav- ing the sun at one of its foci. To understand Law II: Suppose the planet to be at the points P, P„ P„ P„ P^, etc., at the times T, T„ T,, T^, T^, etc. (Fig. 37). Suppose the times T,- T, T,- T,, T,- T^ to be equal. Eepleb computed the areas of the surfaces P SP^, P, 8 P„ P^iS^Pj and found that these areas were equal also, and that this was true for each planet. The second law of Ebf- LEK is — //. The radius-vector of each planet describes equal areas inr equal times. These two laws are true for each planet moving in its own ellipse about the sun. For a long time Kepler sought for some law which should connect the motion of one planet in its ellipse with the motion of another planet in its ellipse. Finally he found such a irelation between the mean distances of the different planets (see table on page 107) and their periodic times (see table on p. 106). His third law is: ///. The squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun. That is, if 7*,, T,, T,, etc., are the periodic times of the different planets whose mean distances are a„ a„ a„ etc., then I*' T*: T;-a,* T* : T* = o/ : a/; etc. etc. 4\ iipMsiiiRP' 4 110 AsTitoyoMr. If T^ and ^ M« the periodic time and the mean distance of the earth, and if T, (= 1 year) is taken as the unit of time and a, as the unit of distance, then we shall have r.' : 1 = a.* : 1 or ^* = 1 or -^ = 1; 7'-l = a-lor^ = lor|| = l; and so on. The data which Kepler had were not quite so accurate as those which we have given, and the table below shows the very figures on which Eepleb's conclunon was based: Mercury 0.2878 0.2408yean 1.018 FeniM 0.6104 0.6151 1.008 JBarlh l.OOdO 1.0000 1.000 Mar$. 1.8740 1.8810 1.004 JvpOer 11.014 11.8764 0.986 BatHrn 88.058 20.4605 1.060 Although the numbers in the third column were not strictly the same, their differences were no greater than might easily have been produced by the errors of the obsw- yations which Kepler used; and on the evidence here given he advanced his third law. The order of discovery of the true theory of the solar system was, then — I. To prove that the earth moved in space; II. To prove that the centre of this motion was the sun; III. To establish the three laws oi Kepler, which gave the circumstances of this motion. „ By means of the first two laws of Kepuek the motions of eadi planet in ite own ellipse became known; that is. the poaition of the planet at any future time could be predicted. For example, if the planet was at P at a time 7, and the question was as to ita place at • subsequent time T. this could be solved by compuUng, first, how i mi sanaMaakw mtmtitmmm ;he mean distance m as the unit of ire shall have 1; T )aite so accurate able below shows UMon was based: 18 years SI (0 [0 \i » 1.018 1.008 1.000 1.004 0.990 l.OSO iolumn were not no greater than Tors of the obsmr- lie evidence here rder of discoTery , then — space; >tiunwa8the8an; 'LEB, which gave he motions of eadi , the position of the For example, if the is as to its place at • imputing, first, how TEE PLAjmfAHF MOTIONS. in large an area woidd be described by the radius-vector in the interval T — T; and second, what the angle at 8 of the sector having this area would be. Then drawing a line tlirough 8 making this angle with the line SP(8ay 8P,), atd laying off the length of the ladiufc Tcctor SP„ the position of the planet iKcame known. From the third law the relative values of tlie mean distancea di, oi, flt, at, etc.. could be determined with great and increasing ac curacy. T From the equation— = 1, a could be determined so soon as Twas ^ ai known. With each revolution of the planet T became known more accurately, as did also a. These laws are the foundations of our present theory of the solar system. They were based on observation pure and simple. We may anticipate a little to say that these laws have been compared with the most precise ol>servations we can make at the present time, and discussed iu all their consequences by processes unknown to Kep- ler, aud that they are strictly true if we make the following modifl- cations. If there were only one planet revolving alxnit tlie sun, then it would revolve in a perfect ellipse, and ol)ey the second law exactly. In a system composed of the sun and more than one planet each planet disturbs the motion of every other slightly, by attraotiag it from the orbit which it would otlierwise follow. Thus neither the first nor the second law can be precisely true of any planet, although they are very nearly so. In the same way the relation lietwoen the orbits of any two planets as expressed in the third law in not prfetM, nlli^ough it is a very close approximation. Xlementt of a Planet's Orbit.— Wlien we know a and b for any orbit, the shape and size of tlie orbit is known. Knowing a we alsd know T, the periodic time; in fact a is found from 7 by Keflbr's law III. If wo know the planet's celestial longitude (L) at a given epoch, say December 81st. 1850, we have all the Oementt necessary for finding the place of the planet in it$ orftU at any time, as has been explained (page 110). The orbit lies in a certain plane; this plane intersects the plane of the ecliptic at a certain angle, which we call the intUnation i. Know- ing I, the plane of the planet's orbit is fixed. The plane of the orbit intersects the plane of the ecliptic in a line, the line :■'•' ,■- j^i.i', u^W ,... • -vji' :.«..:;.•_ \. ;. .v.'*.'. ng from the south ng node; the point north to south is have only the tn. where in the plane lace of the nodes, ilane. This we do node A. ' tlie planet's orbit rihdion, or P. lane of the planet's lion of the line of le position of tlio le sun, and hence B orbit, which fix oeA, whicli enable ace, to be fixed at ' system are now two or three cen- >roximation to the id. . . ,.-..■'; ^.»^Ul*^^; ■»■.;. ■*v)V;'fft.'*\^ CHAPTER VI. UNIVERSAL GRAVITATION. HXWTOH'S LAWB 07 KOTIOV The ceiablishmcnt of the theory of universal gravitation furnishes one of the best examples of scientific method which is to be found. We shall describe its leading features, less for the purpose of making known to the reader the technical nature of the process than for illustrating the true theory of scientific investigation, and showing that such investigation has for its object the discovery of what we may call generalized facts. The real test of progress ia found in our constantly increased ability to foresee either the course of nature or the effects of any accidental or arti- ficial combination of causes. So long as prediction is not possible, the desires of the investigator remain unsatisfied. When certainty of prediction is once attained, and the laws on vhich the prediction is founded are stated in their simplest form, the work of science is complete. To the pre-Newionian astronomers the phenomena of the geometrical htws of planetary motion, which we have just described, formed a group of facts having no connection with anything on the earth's surface. The epicycles of HipPARCHUS and Ptolemy were a truly scientific concep- tion, in that they explained the seemingly erratic motions of the planets by « wngl? aimple ]|tw, In the heliocentric sX W&m »wiMilSIH Nil 114 ASTRONOMY. i : .1 theory of Oopbrnicus this law was still further simplified by dispensing in great part with the epicycle, and replacing the latter by a motion of the earth around the sun, of the same nature with the motions of the planets. But Coper- nicus had no way of accounting for, or even of describing with rigorous accuracy, the small deviations in the motions of the planets around the sun. In this respect he made no real advance upon the ideas of the ancients. Kepleb, in his discoveries, made a great advance in rep- resenting the motions of all the planets by a single set of simple and easily understood geometrical laws. Had the planets followed his laws exactly, the theory of planetary motion would have been substantially complete. Still, farther progress was desired for two reasons. In the first place, the laws of Kepler did not perfectly represent all the planetary motions. When observations of the greatest accuracy were made, it was found that the planets deviated by small amounts from the ellipse of Kepler. Some small emendations to the motions computed on the elliptic theory were therefore necessary. Had this requirement been ful- filled, still another step would have been desirable; namely, that of connecting the motions of the planets with motions upon the earth, and reducing them to the same laws. Notwithstanding the great step which Kepler made in describing the celestial motions, he unveiled none of the ■ great mystery in which they were enshrouded. When Kep< LBB said that observation showed the law of planetary mo- tion to be that around the circumference of an ellipse, as asserted in his law, he said all that it seemed possible to learn, supposing the statement perfectly exact. And it was all that conld be learned from the mere study of the l)laaetar7' motions. In order to connect these motions with VrnVKHSAL QUA VlTAl'ION. 116 ■ther simplified , and replacing the sun, of the . But COPER- n of describing in the motions Bct he made no advance in rep- a single set of iws. Had the •y of planetary mplete. Still, In the first jr represent all of the greatest lanets deviated \. Some small I elliptic theory nent been ful- rable; namely, s with motions me laws. PLER made in li none of the . When Kep. planetary mo- \ an ellipse, as ed possible to xact. And it 3 study of the B motions with those on the earth, the next step was to study the laws of force and motion here around us. Singular though it may appear, the ideas of the ancients on this subject were far more erroneous than their conceptions of the motions of the planets. We might almost say that before the time of Galileo scarcely a single correct idea of the laws of motion was generally entertained by men of learning. Among those who, before the time of Xewtok, prepared the way for the theory in question, Galileo, Huyohens, and HooKE are entitled to especial mention. The general laws of motion laid down by Newton were three in number. Law Firfct: Every body preserves its state of rest or of uniform motion in a right line, unless it is compelled to change ffutt state by forces impressed thereon. . It was formerly supposed tbnt a body acted on by no force tended to come to rest. Here lay one of tbe greatest difiicullies wbicb the predecessors of Nbwtoii found, in accounting for the motion of the planets. Tbe idea tbat the sun in some way caused these motions waa entertained from the earliest times. Even ProLEifTluula vagw idea of a force which was always directed toward the centre of the earth, or, wbidi waa to him tbe same thing, toward tbe centra of th« universe, and which not only caused heavy bodies to fall, but bound the whole universe togetlier. KsriJn, again, distinctly affirms the existence of a gravitating force by whicli the sun acts on the planeU; but he supposed that the sun must also exercise an impulsive forward force to lieep the pl«nets in motion. Tbe reason of thb incorrect idea was, of course, tbat all bodies in motion on the surface of the earth had practically come to rest. But what was not clearly seen befora the time of Nbwtoh, or at least before Oaulbo, waa that this arose from the inevitable resisting forces which act upon all moving bodies upon tbe earth. Law Second: The alteration of motion i* wer propor- tional to the moving force impressed, and i$ made in thi dir^ittn of the right line in wAiVA thot/afee #«||, m ..ii'iTii«gi«Biiwiw^ MiiW' 116 ASTJtONOMT. The first law might be conaidered m a particular caae of thii seo- ond one wliich arises wlien the force is supposed to vanish. The ac- curacy of botli laws can be proved only by very carefully conducted experiments. They are now considered as conclusively proved. Law Third: To every action there ia always opposed an equal reaction ; or the mutual actions of two bodies upon each other are always equal, and in opposite directions. Tliat is, if a body A acts in any way upon a body B, B will exert a force exnctly equal on A in the opposite direction. These laws once established, it became possible to eofeulato the mo- tion of any body or system of bodies when once the forces which act on them were known, and, tie* ttrta, to define what forces were re- quisite to produce any given motion. The question which presented itself to the mind of Newton and his contemporaries was this: Under vhat lav of force teill planets mote round the ran in aeeordanee with KkPlbb's lawe t Supposing a body to move around in a circle, and putting B the mdius of tlie circle, T the period of revolution, HuvoHENshad shown that the centrifugal force of the body, or, which is the same thing, the attractive force toward the centre which would keep it in the dlole. was proportional to -=r But by Krpler'b third law 7* is pro- portional to Bf. Therefore this centripetal force is proportional to -^: that is, to-^. Thus it followed immediately from KEPUtR'i third law that tlie central force which would keep the planeU in their orbits was inversely as the square of the distance from the sun, sup- posing each orbit to be circular. The first law of motion once com- pletely understood, it was evident that the planet needed no force impelling it forward (o keep up iu motion, but that, once started, it would keep on forever. The next step was to solve the problem. What law of force will make a planet describe an ellipse around the sun. having the latter in one of its foci? Or, supposing a planet to move round the sun, the latter attracting it with a force inversely as the square of the dto- tance; what will be the form of the orbit of the planet if it is not cir- cular? A solution of either of these problems was beyond the power of mathematicfauM before the time of Newtos; and it thus remained uncertain whether the planeu moving under the Influence of the «un's gravitation would or would not deapribe eUlfMea. VoaUe, «| CAM of thU see- vanith. The to- ■nfully conducted irely proTed. iy« opposed an vo bodies upon direcliona. yB,B will exert I. oaUeukUeibtmO' 9 foroea which set It forces were re- I which presented iwasthia: Vhdtr n aeeordanet with nd putting H the OHENB had shown the same thing. Id keep it in the bird law 7* is pro- is proportional to Y from Kepucr's be planets in their ■om the sun, sup- notion once oom- needed no force t, once started, it law of force will haying the latter B round the sun, square of the die- Met if It is not cir- bejrond the power 1 it thus remained I Inlluenoe of the Ipeea. Vb>U*i M UmVSRaAL ORAVlTATIOy. 117 first, to reach a satisfactory solution, Newtom attacked the problem in another direction, sUrting from llie gravitation, not of the sun, but of the earth, as explained in the following section. OBATXTAnov nr not ExAYura The reader is probably familiar with the story of New- ton and the falling apple. Although it has no anthorita- tiye foundation, it is strikingly illustrative of the method by which Nbwtok must have reached a solution of the problem. The course of reasoning by which he ascended from gravitation on the earth to the celestial motions was as follows: We see that there is a force acting all over the earth by which all bodies are drawn toward its centre. This force is called gravitation. It extends without sensible diminution to the tops not only of the highest buildings, but of the highest mountains. How much higher does it extend? Why should it not extend to the moon? If it does, the moon would tend to drop toward the earth, just as a stone thrown from the hand drops. As the moon moves round the earth in her monthly course, there must be some force drawing her toward the earth; else, by the first law of motion, she would fly entirely away in a straight line. Why should not the force which makes the apple fall be the same force which keeps her in her orbit? To answer this quetition, it was not only necessary to calculate the intensity of the force which would keep the moon her- self in her orbit, but to compare it with the intensity of gravity at the earth's surface. It had long been known that the distance of the moon was about sixty ndii of the earth, from measures of her parallax (see page 67). If this force diminished as the inverse square of the distance, thea «t the moon it woald be only j^^ as great as at the M-lfrHrWTftMaii 118 ASTRONOMY. surface of the earth. On the earth a body falls sixteen feet in a second. If, then, the theory of gravitation were cor* rect, the moon ought to full towards the earth 3,^7 °^ ^^'' amount, or about -^ of an inch in a second. The moon being in motion, if we imagine it moving in a straight line at the beginning of any second, it ought to be drawn away from that lino ^ of an inch at the end of the second. When the calculation was made it was found to agree ex- actly with this result of theory. Thus it was shown that the force which holds the moon in her orbit is the same force that makes the stone fall, diminished as the inverse square of the distance from the centre of the earth. It thus appeared that central forces, both toward the sun and toward the earth, varied inversely as the squares of the distances. Kepler's second law showed that the line urawn from the planet to the sun would describe equal arcus in equal times. Newtox showed that this could not be true unless the force, which held the planet was directed toward the sun. Wo have already stated that the third law showed that the force was inversely as the square of the distance, and thus agreed exactly with the theory of gravitation. It only remained to consider the resultf of the first law, that of the elliptic motion. After long utA laborious efforts, Newtok wus enaoled to demonstrate rigorously that this law also resulted from the law of the inverse square, and could result from no other. Thus all mystery disappeared from the celestial motions; and planets were shown to be simply heavy bodies moving according to the same laws that were acting here around us, only under very different cir- cumstances. All three of Keplbb's laws were embraced in the single law of gravitatian toward the sun. The sun at- tracts the planets as the «arth attracts bodies here »roand w^ ' #)» (4-. '« ^ ^ UNIVERSAL GRAVJTATJOK. lift 8 sixteen feet ion wore cor- *> siVt ot this The moon straight liiio druwn nway f the second, to agree ex- s shown that . is the same IS the inverse earth. )wurd the snn squares of the .hclineurawn qual areus in Id not l>e true rectcd toward d law showed the distance, Eivitation. It irst law, that rioQs efforts, nslythat this ) square, and f disappeared shown to be one laws that different oir« embraced in The sun at- re»roandlw« K«tul AotlftB of tk« 71«MU.—ny NRWTOM'stlilnl law of motion, cacli pluiiet mu8t nltrnrt the lun with n force equnl to that which the nun exertH upon the planet. The moou nloo must attract the earth as nuich ns the earth attracts the moon. Sucli being the case, it must l>e highly probable that the planets attract each other. If so, Keplkk'h laws can only be an approximation to the trutli. The sun, Itoing imineniwly more massive than any of tlie planets, overpowers their attraction upon each other, and makes the law of elliptic mo- tion very nearly true. But still the comparatively small attraction of the planets must cause some deviations. Now, deviations from the pure elliptic motion were known to exist in the case of several of the planets, notably in that of the moon, which, if gravitation were universal, must move under the influence of the combined attraction of the enrih and of llie sun. Newton, therefore, attacked the com- plicated problem of the determination of the motion of the moon under tiie combined action of these two forces. He showed in a general way that its deviations would \te of the same nature as those shown by observation. But the complete solution of the problem, whicli required the answer to be expressed in numbere, was beyond his power. OntTitation Reiidet in each Particle of Katter.— Still another question arose. Were these mutually attractive forces resident in the centres of the several bodies attracted, or in each particle of the matter composing them? Nsw- TOK showed that the latter must be the case, because the smallest bodies, as well as the largest, tended to fall toward the earth, thns showing an eqnal gravitation in every sepa- rate part. It was also shown by Newton that if a planet were on the snrface of the earth or outside of it, it woald be attracted with the same force as if the whole mass of the earth were concentrated in its centre. Putting together the various results thus arrived at, Nswroir was able to formnlate his great law of universal gravita- i^on in these comprehensive wot6b: " Fverp . particle of matter in the universe attracte every other particle with a force directly at the maetes of the two partielet, and ?fSESP?S«»i; 1^"" - ,. .-I^^^i^, Vi&iHtiiiiUlSJ ^si^^^ss^s^ms^s^sss^S^SSSS^ 120 ASTRONOMY. \nver$ely at the tquart of the distance which separate* them:* To ihow the nature of the attractive force* among theM Tarioua particle*, let us represcot by m und m' the mawM of two attracting bodies. We may conceive the body m to be compoMd of m par- tides, and the otiier body to be composed of m' particles. Let us conceive that each particle of one body attracU each particle of the other with a force ^. Then every particle of m will be attracted by eochof tiie m' particles of the other, and therefore the total attractive force on eacli of tlie m particles will be -^. Each of tite m partlclea being equally subject to this attraction, tiie total attractive force be. tween the two bodies will bo ~ When a given force acts upon a body, it will produce less motion the larger the bo«ly is, tlie aeeel- entHng force being proportional to the total attracting force divided by the moss of the Inxiy moved. Therefore the accelerating force whicli acts on tlic body m', and whidi determines tlio amount of motion, will be ^; and conversely the accelerating foree acting on tiie body m will be represented by tlie fraction — &I1I A 1W Oir TEE THIOBT OF OlATITAnoV. The real natnre of the great discovery of Newton is so frequently misunderstood that a little attention may be given to its elucidation. Gravitation is frequently spoken of ai if it were a theory of Nbwtow's, and very generally received by astronomers, but still liable to be ultimately rejected as a great many other theories have been. Not infrequently people of greater or less intelligence are found making great efforts to prove it erroneous. Newtok did not discover any new force, but only showed that the motioni of the heavens could be ateounted for by a force which we aU know to exist Grartation (Latin ^roi>»W»— Meh separates ing these rariout >t two attractiDg poMd of f>t par larticlea. Let ui I particle of tlie I be attracted by e total attractive if the m partlclet iictivo force be> force acts upon xly li, the aecel- \g forcu divided «;elcmtiDg force the amount of force acting on rAnov. ^EWTOK is 80 ition may be lently spoken erj generally be altimately B been. Not nee are found Nbwtow did red tbat the For by a force in gravitd*— VNl VERSAl GkA VltA TlOif. 121 weight, heaviness) is the force which makes all bodies here at the surface of the earth tend to fall downward; and if any one wishes to subvert the theory of gravitation, he must begin by proving that this force does not exist. This no one would think of doing. What Newton did was to show that this force, which, before his time, had been recognized only as acting on the surface of the earth, really extended to the heavens, and that it resided not only in the earth itself, but in the heavenly bodies also, and in each particle of matter, however situated. To put the matter in a terse form, what Newton discovered was not gravitation, but the universalitif of gravitation. It may be inquired, is the induction which snpposei gravitation universal so complete as to be entirely beyond doubt? We reply that within the solar system it certainly is. The laws of motion as (Bstablished by observation and experiment at the surface of the earth must be considered as mathematically certain. It is an observed fact that the planets in their motions deviate from straight li:>» - in a certain way. By the first law of motion, such de ation ' can be produced only by a force; and the direction and intensity of this forc^ admit of being calculated once that the motion is determined. When thus calcuUted, it is found to be exactly represented by one great force con- stantly directed toward the sun, and smaller subsidiary forces directed toward the several planets. Therefore no fact in nature is more firmly established than that of uni- versal gravitation, as hud down by Niwton, at least within the sokr system. We shall find, in describing double stars, that gravita- tion is also found to act between the components of a great number of such itun. It it certain, thfrefore, that at m ASrMNdkt. If ■■'■i': i': least some stai^ gravitate toward each other, as tl.o bodies of the solar system do; but the distance which separates most of the stars from each other and from our snn is so immense that no evidence of gravitation between individual stars and the sun has yet been given by observation. Still, that they do gravitate according to Newton's law can hardly be seriously doubted by any one who understands the subject. The student may now be supposed to see the absurdity of supposing that the theory of gravitation can ever be subverted. It is not, however, absurd to sup))ose that it may yet be shown to be the result of some more general law. Attempts to do this are made from time to time by men of a philosophic spirit; but thus far no theory of the subject having much probability in its favor has been propounded. iV »;w**w^i.*i**ii* ;r, as tl.o bodies Krhich separates tm our snn is so nrecn individoal jrvation. Still, ton's law can tio understands > the absurdity on can ever be suppose that it ) more general I time to time ir no theory of favor has been CHAMEU Vrt. THB MOTIONS AND ATTRACTION OP THE MOON. Each of the planets, except Merairy and Venus, is at- tended by one or more satellites, or moons as they are sometimes familiarly called. These objects revoke around their several planets in nearly circular orbits, accompany- ing them in their revolutions around the sun. Their dis- tances from their planets are very small compared with the distances of the latter from each other and from the sun. Their magnitudes also are very small compared with those of the planets around which they revolve. Considering each system by itself, the satellites revolve around their central planets, or "primaries," in nearly circular orbits, and in each system Kepler'8 laws govern the motion of the satellites about the primary. Each system is carried around the sun without any derangement of the motion of its sev- eral bodies among themselves. Our earth has a single satellite accompanying it in this way, the moon. It revolves around the earth in a little less than a month. The nature, causes, and consequences of this motion form the subject of the present chapter. Thx Moob'8 Monon Airs Teamxil That the moon performs a monthly circuit In the heavens Is a fact with which we are all familiar from childhood. At certain time* we .eehernewly emerged from thetun'a rays in theweatem twilight, and then we call her the now moon. On each succeeding evening 124 ASTRONOMY. we see her further to the east, so that in two weeks she is opposit* tl sun, rising in the east as he sets in tlie west. Continuing her course two weeits more, slie has approached tlie sun on the other side, or from tiie west, and is once more lost in his rays. At the end of twenty-nine or thirty days, we see her again emerging as new moon, and her circuit is complete. The sun has been apparently moving toward the cast among the stars during the whole month, so that during the interval from one new moou to the next the moon has to make a complete circuit relatively to the stars, and to move forward some 80' further to overtake the sun, which has also been moving toward the east at the rate of 1° daily. The revolution of the moon among the sUrs is performed in about 27^ days,* so that if we observe when the moon is very near some star, we shall find her in the same position relative to the star at the end of this interval. Tlie motion of the moon in this clrouit differs from the apparent motions of the planete in being always forward. We have seen that the planeU, though, on the whole, moving toward the east, are effected with an apparent retrograde motion at certain intervals, ow- ing to the motion of the earth around the sun. But the earth is the real centre of the moon's motion, and carries the moon along with it in its annual revolution around the sun. To form a correct idea of the real motion of these three bodies, we must imagine the earth per- forming iu cireuit around the sun in one year, and carrying with it the moon, which makes a revolution around it in 27 days, at a dis- tance only about -^^ that of the sun. PhaiM of the Moon,— The moon, being a non-laminona body, shines only by reflecting the light falling on her from some other body. The principal source of light is the sun. Since the moon is spherical in shape, the sun can illumi- nate one half her surface. The appearance of the moon varies according to the amount of her illuminated hemi- sphere which is turned toward the earth, as can be seen by studying Fig. 39. Here the central globe is the earth; the circle around it represents the orbit of the moon. The - rays of the sun fall on both earth and moon from the right, the distance of the sun being, on the scale of the * More enetlj, r.mei*. ^iMmmiiV:\!tic;r''m * B she i* oppositlr Continuing her un on the other liya. At the end merging as new been apparently whole month, so > next tlie moon rs, and to move ch has also been le revolution of days.* so that if re shall find her this interval, tm the apparent i have seen that i the east, are a intervals, ow- the earth is the an along with it correct idea of le the earth per* »rrying with it 7 days, at a dis- lon-lominoas I on her from ht is the ran. ! can illami- >f the moon mated hemi- m be seen by is the earth; moon. The on from the scale of the MOTIONS AND ATTRACTION OF THE MOON. 126 figure, some 30 feet. Eight positions of the moon are shown aronnd the orbit at A, E, C, etc., and the nght- hand hemisphere of the moon is iUuminated in each posi- tion. Outside these eight positions are eight others show- ing how the moon looks as seen from the earth in each position. At A it is "new moon," the moon being nearly between Vtob Mi the earth and the ran. Its dark hemisphere is then trnn- ed toward the earth, so that it is entirely invisible. The sun and moon then rise and set together. At E the obserrer on the earth sees about a fourth of the iUuminated hemisphere, which looks like a crescent, a0 shown in the outside figure. In this position a great deal of light is refl«oted from the earth to the moon, rendering 126 ASTnoNOitr. the dark part of the latter visible by a gray light. Thi« appearance is Bometimes called the "old moon in the new moon's arms." At C the moon is said to be in her " first quarter," and one half her illuminated hemisphere is visi- ble. The moon is on the meridian at 6 p.m. At Q three fourths of the illuminated hemisphere is visible, and at B the whole of it. The latter position, when the moon is opposite the sun, is called "full moon." The moon rises at sunset After this, at H, D, F, the same appearances are repeated in the reversed order, the position D beinir called the " lust quarter." Thx TiBtt H is not possible in an elementary treaUse to give a comnlete ae- .TaniVntl'T"' ^^V"™ ""•"' '«^'"' duei tbe S oMhe Bun and moon. A general account may be presented which will tw Wffldent to show the n.t«™ „f tbe iects'^rodu^ and o7 Ih Let us consider the earth to be composed of a solid centr* sar rounded by an ocean of uniform (and luTvery grea depth S moon exerciws an attraction upon every particlJ of the earth's masi «.Hd and fluid alike. The attraction of ule whole mooT(^) ™^^ a particle m is — ^, where p is the distance frt.m the centre of the moon to m. If m is one of the solid particles of the earth It cannot ■olid particles move, since the earth proper is rigid If m is a fluid particle, it is free to move in obedience to the forties impressed upon It. Tlio attraction of JTis proportional to -*-; that is. the particjes nearest Mm most attracted, apd.on the whole thi wajer^ the part of the earth nearest the'm'ook iiil be .J^i f The moon also attracts the solid parts of the earth moi« th.. .i.- the same efect as if there was another moon M exactly ODDodte to Jf. TlH» elevation of the water under Jf ■ w ' aoriw aouE m .^ M that under Jf. on account of the incre«ed disScTfSK *^ 'v«^!ft5' »y light. Thi8 oon in the new e in her " first lisphere is visi- f. At G three liblo, and at B 1 the moon is 'he moon rises le appearances lition D being e a complete ac- tbe effect of tbc d which will be ed and of their «Hd centre sar- at) depth. The be earth's mass, moon (M) upon le centre of the earth, it cannot «s all the other ice to the f oitiea »lto-^-;thatis, the whole, the II be raised to- more than she oduces exactly tly opposite to ! qoite as gnat from Jr. MOTIONS AND ATTRACTION OF THE MOON. 127 Thus the moon's action tends to elevate the whole mass of water on the line joining her centre « ilh the cenl.-e of the ca'"'. ""fjl"* »» "J not only on the part of this line nearest the moon, but also on that '"l-hU dev"i^'of the waters of the ocean above their mean level is called the tide. The tidal effect of the moon produces a distortion of Se spherical shell of water which we have supposed to f "^""d Uie earth and elongates this shell into the shape of an ellipsoid, the longer Rxis of which is always directed to the moon. Now as the moon Tv^ a^und the earth once in 24^ 54-. this ellipsoidal shape must S^move with her. The crest of the wave directly under M would come back to the same meridian every 24- 54". The outer crest (under M') would come W 27- after the first, so there would be two A,gh UdLltany one meridian every (lunar) day. The fla'. (and largest) S tide would be at the time of the moon's visible transit over he mfrldiun The second high tide would be 12^ 27- later, when the moon was on the lower meridian of the place. The high tides occur when there Is more water than the mean depth, and between these high tides we should »'«'«><»«; 'J«>f;/''0 ?n eS. lunar day. Similarly there wouUl be two high tides dally at eacrmerullan, due to the attractive force of the sun. These would have a rl^rlod of 24 hours and could not always agree with the unar hirii tides When the solar and lun:ir high tides coincided (at new aS fu I moon), then we should have the highest UigU tides and the lowest low tUles. (These arc the Spring tides, so called.) When the mZ and the sun were 90» apart (moon at first and third quarter . Ihrwe should have the lowest high tides and the highest low tlde^ ^Z iSprXclfg U of the moon is to that of the sun a. 800 U to 855 The great mass of the sun compensates in some degree for oppose each other. The relaUve heights are as 800 +885 : 800 - 855. or as la to 5 approximately. The explanation above relates to an earth covered by an ocwn ot uniform depth. To fit it to the facU as they are. a thousand c Ir- cuSces must be taken into aocount. which depend upon the mSlng effects of continents and islands, of deer and Bhallow ^ of currente and winds. Practically, the high tide at any sU- tion I. predicted by adding to the time of the moon's transit over its merldUna quantity determined from obeorvatioB w4 not from ibeoty 128 ABTHONOMr. :! IffMU «f tiM XMm .pM tk« Itftk'i l«UMo«.-Ai the tide-waTe moves It meeu. with resisiauce due to friciion. The amount of thia rasistance u subtracted daily from the earth's energy of roution The tides act on the earth, in a way. as if they wen a light friction'- brake applied to an enormously heavy wheel turning rapidly The wheel has been set to turning, and, so far as we know, it will never have any more rotative energy given to it. Every subtracUon of energy, however small, k a positive and irretrievable loss. The lunar tides are gradually, though very slowly, lengthening the day Since accurate astronomical observations began there has been no dmrvaHonal proof of any apprectable change in the length of the day. but the change has been going on nevertheless. _i As the tide-WATe le amount of this ergy of roUtion. « a light friction- ig rapidly. The low, it will nerer 7 subtraction of eloas. . lengthening the in there has been the length of the CHAPTER VIII. ECLIPSES OP THE SUN AND MOON. Eclipses are phenomena nriBing from the shadow of one hody being cast upon another, or from a dark body paaaing oyer a bright one. In an eclipse of the sun, the shadow of the moon sweeps over the earth, and the sun is wholly or partially obscured to observers on that part of the earth where the shadow falls. In an eclipse of the moon, the latter enters the shadow of the earth, and is wholly or partially obscured in consequence of being deprived of some or all of its borrowed light. The satellites of other planets are from time to time eclipsed in the same way by entering the shadows of their primaries ; among these the satellites of Jupiter are objects whose eclipses may be observed with great regularity. THI EAETH*! taASOW AHD FBVmiBXA. In Fig. 40 let 8 represent the sun, and E the earth. Draw straight lines, DBF and J^BV, each Ungent to the sun and the earth. The two bodies being supposed spherical, tliese lines will be the inteisections of a cone with the plane of the paper, and may be taken to represent that cone. It is evident that the cone B YB will be the outline of the shadow of the earth, and that irrithin this cone no direct sunlight can penetrate. It is therefore called the earth's «AadlMe-«MW. Let us also draw the lines BBP and PBP' to represent the other cone tangent to the sun and earth. It is then evident that within the region VBP and VBP' the light of the sun wiU b« partially but not entirely cut off, 130 ASTRONOMT. Dimeniiona of Shadow.— Let ui investigate the distance E V from the centra of tbc eartli to tbe vertex of tlie sliudow. Tlie triangles VEB and V8D are siiniiar, Imving a riglit angle at B and at D. Hence VE:ED= VS : 8 D = ES : {HD- EBf. So if we put I = VE, tlie lengtli of tlio shadow measured from the centre of tlio earth. r= E8, the radius-vector of the earth, B= 8D, the radius of the sun, p = EB, the radius of the earth, we have l=VE = E8X EB 81) -EB Tm. 40.— row o» ■uaov. That is, I k expresaed in terms of known quontltiM^ imi thtw la known. The radius of the shadow dimlnisliea uniftmnly with the diatanco «s wo go outward from the «arth. At any distanoo s from tlie earth's centre it will be ei^ua) to II —'^P, for this formula fives the radius p when s s= <^ and the diameter aero wkcn f = < as it should.* • It wlllbe noted that this ezprtMkm is not, i1goraitol7 sfMU^b the I dlooMter of the ihadow, Iwt (he ahorteat dlitiince fram a potoit on (ta osatral IliM to its conioai pnifsoo. Tliis dtatance is ineaaared ia a tfirsdioB XB parpen- dienlartoDB.wheraiMtlM diameter would lie perpendleular totho aidS^A anditahaU-laaclhwoMldJMalttUei * — listance E V from ow. The triangles igle at B and at D. -KBj. from tke centre of J itltiMb Md tims H with |he distance itanoo t from tlie his formula fires > when I = I as it rSfMttW.tlMI apotatoa (taoMtral dJTMtkmXBpeipen- Mlartotteaitti^i;, ECLIPSES OF THE SUN AND MOON. loufm cr THi Xooi. 181 The mean distance of the moon from the earth is abotit 60 radii of the latter, and the length E Vot the earth's shadow is 217 radii of the earth. Hence when the moon passes through the shadow she does so at a point less than three tenths of the waj from Eio V. The radios of the shadow here will be 'Vrf^ <>' ^^^ radius E B ot the earth, a quantity which we readily find to be about 4600 kilo- metres. The radios of the moon being 1736 kilometres, it will be entirely enveloped by the shaduw when it passes through it within 2864 kilometres of the axis EVot the shadow. If its least distance from the axis exceed this amount, a portion of the lunar globe will be outside the limits BV ot the shadow-cone, and will therefore receive a portion of the direct light of the sun. If the least distance of the centre of the moon from the axis of the shadow is greater than the ram of the radii of the moon and the shadow — that is, greater than 6336 kilometres — the moon will not enter the shadow at all, and there will be no eclipse proper, thongh the brilliancy of the moon is diminished wherever she is within the pennmbral region. Wlien an eclipse of the moon occurs, the phases are laid down in tlw almanac. (See Fig. 40.) Botipaiing the moon to he moving arouad the earth from helow upwiud, its advancing edge first meets the Iwundaiy BP' of the penumbra. The time of this ooouireaoe is given in the almanac as that of " moon entering penatthra." A small portion of the suslight is then cut off from the advaodng edge of the moon, and this amount constantly increases until the edfe icadies the houndary ^ F of the shadow. It is cuffons, however, that the eye can scarcely delect any diminution in tlife liriiliaaey of the moon until she has almost toudied Uie boundary of tlte «hado«< The observer must not, therefore, expect to detect the OOfniuf eclipse witn vary nearly Uif lips |ivei| ip t)ie stpaoae as that 183 ASTRONOMY. of "moon entering ■hadow." At this happens, the advancing portion of tlie lunar disk will be entirely lost to view, as if it were cut off by a rather lll-deflned Hoe. It takes the moon about an hour to m6ve over a distance equal to her own diameter, so that if the eclipse is nearly central the whole moon will be immersed in the shadow about an hour after she flrst strikes it. This is the time of beginning of total eclipse. 80 long as only a moderate portion of the moon's disk is in the shadow, that portion will be entirely invisible, but if the eclipse becomes total the whole disk of the moon will nearly always be plainly visible, shining with a red coppery light. This is owing to the refraction of the sun's rays by the lower straU of the earth's atmosphere. We shall see hereafter that If a ray of light D B passes from the sun to the earth, so as Just to grau th« latter, it is bent by refraction more than a degree out of its course, so that at th>i distance of the moon the whole shadow of the earth Ui filled with t; repreaent the low will remun the shadow in li of the moon's letres. This is from the Murth Wo tnOfofOTO conclude thst when the moon passes between the earth and the sun, the former will be very near the vertex V of the shadow. As a matter of fact, an observer on the eurth'a surface will sometimes pass through the region C VC, and sometimes on tho other side of V. Now, in Fig. 40, still supposing BBS to be the moon, and <8Di)' to be the sun, let us draw the lines DBf and DBP tan. gent to both moon and sun, but crossing each other between these bodies at b. It is evident that an observer outside the space PBBP will see the whole sun, no part of the moon being project- ed upon it; while within this space the sun will be more or less obscured. The whole obsoured space may be divided into three regions, in eaeh of which the character of the phenomenon is dif- ferent. First, we have the region BVB forming the shadow-cone proper. Here the sunlight is entirely cut off by the moon, and darkness is therefore complete, except so far as light may enter by refraction or reflection. To an observer .at V the moon would exactly cover the sun. the two bodies being apparently tangent to cnch other all around. Secondly, we have the conical region to the right of F between the lines B V and B Fcontinucd. In this region the moon is seen wholly projected upon the sun. the visible portion of the latter presen.' ng the form of a ring of light around tlie moon. This ring of light will be wider in proportion to the apparent diameter .of the sun, the farther out we go, because the moon will appear smaller than the sun, and its angular diameter will diminish in a more' rapid ratio than that of the sun. This regton is that of annvlar tdip»e, because the sun will present the appearance of an annulus or ring of light around the moon. Thirdly, we have the region PB V and FB V, which we notice is eontinuoas, extending around the interior cone. An observer here would see the moon partly projected upon the sun, snd there, fore a certain part of the sun's light would be cut off. Along the inner boundary B Y and B V tlie obscuration of the sun will be complete, but the amount of sunliglit will gradually increase out to the outer boundary BPB P, where the whole sun is visible, This region of partial otiaeuration is called the jwniraitria. To aiww more eleariy the phenomena of sofaur eeHpsM, iri present Miotber figure reprvssnting the penambnt Of the mooo thrown upon 'm 1" 184 ASTRONOMY. the cftrth.* The o»t«r of (he two circlee 8 lepreMnU the limb of Um ■un. The exterior Inngcntt which niKrk the boundary of the ihadov eroM each other nt Y before reaching the earth. The earth (K) being a little beyond the verlei of the iluulow, there can be no total eclipae. In thia oHe an obaerver In the penumbral region, VO or DO, will aee the moon p*rtly projected on the nin, while If he chance to bo altuatcd at O he wll'i we au annular eclipae. To iiliow how this is, wa draw dotted iiaes from tangent to the moon. The angle iMtween these lines ripraaents the apparent diameter of the moon as seen from the eartli. Continuing them to the sun, tliey show the apparent dkmeter of the moon as projected upon the sun. It will bo seen that, In \\%a case supposed, when the rertex of the shadow 'is between tlia earth and moon the Utter will necessarily appear rra. 41.— rievu or Sbabov mb Amirilab Boumb. smaller than the sun, and the observer will aee a portion of the solar disk on all sides of the moon, as shown in Fig. 48. If the moon were a little nearer the earth than it is represented in Fig. 41, it* shadow would reach the earth in the neighborhood of 0. We should then have a total eclipse at each point of the earth on which it fell. It wilt be seen, however, that a total or annuhur •clipse of the sun is visible only on a very small portion of the earth's surface, because the distance of the moon clianges ao little that tlie Mfth can nevnr be far from the vertex V of the shadow. As the •n will be acted that all the icurN of aelipsM ai* Mosspaiiljr drawn ve. mwheoioCproiwrtloib BMllyth* sua is400tiaMO thedlsttiii^of.themooii, wMsfc agaia Is eottaMstharadiasaC the earth. But It wa^lil |ie entlrelj ion- passtMe to draw a flfure o< this propertlon; we are theretors obliged to i i HBHHl th» sarth la fig. 4Baalaftertttsat(MpiB,itnd the moon «i«mrlir halt wer Ntwsaa tt)9 earth and sua. M limb of Um >f the •hador' trlh(/?) being I total fclipM. or DO, will chance to be low bow Ibis I. The angle f the moon ■■ ibey ibow I be •un. It will 1 Ibo iliadow laarily appear ow. the cwitre of which Is always to the ediptic ZS. mTmooii*. orbit to repn^nted by CD. At O U- eelipw to eMtial and tom. at J" It to iiartial, and at X there to bwreiy an eeUpee. is an even chance timt an edlpae will occur; toward the lower limit (18* -7) the ebances increase to certainty; toward the upper one (W.*) they diminish to aero. The corresponding limits for an eclipse of tbe moon are V and 18*' ; that is. If at the moment of full moon the distance of the moon from her node is greater than 12i° no eclipee can occur, while If the distance is less than 8° an eclipse Is certain. We may pat the mean limit at 11*. Since. In the long- run, new aud fuH moon will occur equally at all disUnces from the node, there will be, on the average, aiiteen edipaes of the sun to eleven of the moon, or nearly fifty per cent more. If, at the moment of new moon, the distance of the moon from the node is leas than lOi* there will be a central eclipse of the sua, and If greater than tiiia there will not be such an eclipse. The K-i 138 ASTBONOMT. eclipse limit may range half a degree or more on each side of this mean value, owing to the varying distance of the moon from the earth. Inside of 10° a central eclipse may be regarded as certain, and outside of 11° as impossible. If the direction of the moon's nodes from the centre of the earth were invariable, eclipses could occur only at the two opposite months of the year when the sun had nearly the same longitude as one node. For instance, if the longitudes of the two opposite nodes were re- spectively 64° and 284°, then, since the sun must be within 18° of the node to allow of an eclipse of the moon, its longitude would have to be either between 43° and 66*, w between 822° and 246". But the sun is within the first of these regions only in the month of May, and within the second only during the mouth of November. Hence lunar eclipses could then occur only during the months of May and November, and the same would hold true of central eclipses of the sun. Small partial eclipses of the latter might be seen occasionally a day or two from the beginnings or ends of the above months, but they would be very small and quite rare. Now, the nodes of the moon's orbit were actually in thft above directions in the year 1878. Hence during that year eclipses occurred only in May and No- vember. We may call these months the seasons of eoUpaes for 1878. There is a retrograde motion of the nooh's nodes amouhting to IQi" in a year. The nodes thus move back to meet the sua' in ita annual revolution, and this meeting occurs about 80 days earlier every year than it did the year before. The result is that the season of eclipses is constantly shifting, so that each season ranges through- out the whole year in 18-6 years. For instance, the season corre- sponding to that of November, 1878. had moved back to July and August in 1878, and will occur in May, 1882, while that of May, 1878, will be shifting back to November in 1888. It nuy be interesting to illustrate this by giving the days in which the sun is in conjunction with the nodes of the moon's orbit during several years. Awtadinfllode. 1879. 1880. 1880. 1881. If! 1888. 1884. January SM. January 6. December 18. November 80. November 18. October 25. Octobers. Descendiiir iTo^. 1879. July 17. June 27. June 8. May 80. Mayi. 1884. April IS. 1885. MaivbSS. 1880. lasi. 1888. sach side of this moon from tbe irded as certain, itre of th« wrtli opposite months ude as one node. ) uodes were re- be within 12° of Itude would hare and 246°. But e month of Majr, •▼ember. Henoe mtha of May and I eclipses of the een occasionally ove months, but lie nodes of the a th* year 1878. I Uttf fend No- ot eoUpJMS for « amouhting to t the sua in its M days earlier I that the season ranges through- lie season oorre- •ck to July and le that of May, le days in which n's orbit during Node. yl7. ieS7. leS. yao. rillS. rah as. EOLIPSSS OF THE SUN AND MOON. 1S9 During these years, eclipees of the moon can occur only within 11 or 12 days of these dates, and eclipses of the sun only within IS or 16 days. In consequence of the motion of the moon's node, three Taiying angles come into play in considering the occurrence of an eclipse: tbe longitude of the node, that of the sun, and that of the moon. One revolution of the moon relatirely to the node is accomplished, on tbe average, in 27 21222 days. If we calculate tbe time required for the sun to return to the node, we shall find it to be 846-6201 days. Now, let us suppose the sun and moon to start out together from a node. At the end of 846>6201 days tbe sun, baring apparently performed nearly an entire revolution around the celcsthil sphere, will again be at tbe same node, which has moved back to meet it. But the moon will not be there. It will, during the interval, have passed the node 12 times, and the 18th passage will not occur for a week. The same thing will be true for 18 successive returns of the sun to the node; we shall not find tbe moon there at the same time with the sun; she will always have passed a little sooner or a little fatter. But at the 19th return of the sun and the 242d of the moon, the two bodies will be in conjunction witUn half a degree of the node. We find from tlie preceding periods that ' iv turns of the moon to the node require 688S.887 days. sun 6SeS.780 The two bodies will therefore pass the node within 10 hoars of each other. This conjunction of the sun and moon will be the Mid new moon after that from which we started. Now, one lunatton (that is, the interval between two consecutive new mooas) is, in the mean, 28.S80S88 days; 228 lunations therefore require 6688.12 days. The new moon, therefore, occurs a little before the bodies reach the node, the distance from the latter being that over whidi the moon moves in 0*.086. mr the sun in 0'.490. This distance is 28' of are, somewhat less than the apparent semldiameter of either body. This would be the smallest distaaoe from either node at which any aeW moon would occur during the whole period. The next nearest m>> proaches would have occurred at the 8Sth and 47th lunations re^ieo- tively. The 8Sth new moon would have occurred about 6* befoM the two bodies arrived at the node from Which We started, aUd tha 47th about li* put the opposite node. No other new moon wooM «enir so near • node before the 228d one, wMeh. iswe hare jui* .^ML weald ooeurO*ar wast of tbe Boda. ThIspethMlaf MtatW tmmmnsmtii.-^,. 140 ABTRONOMY. moons, or 18 yean 11 days, was called the Saro* by the ancient as- tronomers, and by means of it tliey predicted ecli|>8e8. Tlie possibility of a total eclipse of the sun arises from the occa- sional very slight excess of the apparent angular diameter of the moon over that of the sun. This excess is so slight that such an eclipse can never last more than a few minutes. It may be of inter- est to point out tlie circumstances whicli favor a long duration of totality. These are: (1) That the moon should be as near as possible to the earth, or, technically speaking, in perigee, because its angular diameter as seen from the earth will then be greatest. (2) That the sun should be near its greatest distance from the earth, or in apogee, because then its angular diameter will lie the least. It is now in this position about the end of June; hence the most favorable time for a total eclipse of very long duration is in the summer moiiths. Since the moon must be in perigee and also be- tween the earth and sun, it follows tliat the longitude of the perigee must l)e nearly tliat of the sun. The longitude of the sun at the end of June being 100°, this is the most favorable longitude of the moon's perigee. (8) Tiie moon must be very near the node in order tliat the centre of the shadow may fall near the equator. The reason of this condi- tion is that the duration of a total eclipse may be considerably in- creased by the rotation of the earth on its axis. We have seen that the shadow sweeps over the earth from west toward east with a Telocity of about 8400 kilometres per hour. Since the earth rotates in the same direction, the velocity relative to the observer on the earth's surface will be diminished by a quantity depending on thia velocity of rotation, and therefore greater the greater the velocity. The velocity of rotation is greatest at the earth'* equatnr, where it amounts to 1660 kilometres per hour, or nearly half tba Telocity of the moon's shadow. Hence the duration of a total adlpM may, with- in the tropics, be nearly doubled by the earth's rotation. When all the favorable circumstance* comUne in the way we have just de- Bcribet^, the duration of a total eclipae within the tropics will be about seven minutes and a lialf. In our latitude the maximum du- ration will be somewhat lea*, or not Imx from six minute*, but it i* only on very rare occasions, hardly once in many centuric*, that all these favorable conditions con be expected to concur. Oeaaltattoa «< Stan by th* Mean.— A phenomenon wliieh, geooMt- rically considered, is analogous to an eclipae of the *un ia the ocmil- tation of a star by the moon. Since all the bodie* of the solar syat«M •re nearer titan the fixed stars, it is evident tluit th^ auiat tnm maim by the ancient at- )8eil. C8 from the occa- r diameter of tlie liglit that such an [t may be of inter- long duration of ! to the earth, or, l^ular diameter as listance from the meter will be the ' June; bence the duration is in the igee and also be- ide of the perigee if Ibe sun at the longitude of the er that the centra son of this condl> ! considerably in- re have seen that ward east with a the earth rotates observer on the spending on this ater the velocity, equator, where it U the Telocity of KdlpMmay, wiih- ■tioo. When all re have just de- e tropics wiU be ke maximum du- linutes, but it is enturics, that all r. 1 which, geomat- sun is the ooeui- the solar tymim SCLtPSm Of THE SUN AND MOON. 141 time to time pass between us and tlie stars. The planets are, how- ever, 80 small that sucl\ a passage is of very rare occurrence, and when it does happen the star is generally so faint that it is rendered invisible by the superior light of tlie planet before the latter touches it. But the moon is so large and her angular motion so rapid that she passes over some star visible to the naked eye every few days. Such phenomena are termed oeeuUatiotu of $tar» by the moon. It must not. however, l»e supposed that tliey can be observed by the naked eye. In general, the moon is so bright that only stars of the first magnitude can be seen in actual contact with her limb, and even then the contact must be with the unilluminated limb. OHAfTDK IX. l!:-l THE EARTH. Our object in the present cliaptcr is to trace tlie efiFects of terrestrial gravitation and to study the changes to which it is srbject in various places. Since every part of the earth attracts every other part as well as every object upon its surface, it follows that the earth and all the objects that we consider terrestrial form a sort of system by them- selves, the parts of which are firmly bound together by their mutual attraction. This attraction is so strong that it is found impossible to project any object from the sur- face of the earth into the celestial spaces. Every particle of matter now belonging to the earth must, so far as we can see, remain upon it forever. Mam avd Biviitt or tex Eaktk. The mass of a body may be defined as the quantity of matter which it contains. There are two ways to measure this quantity of matter: (1) By the attraction or weight of the body— this weiglit being, in fact, the mutual force of attraction between the body and the earth ; (2) By the inertia of the body, or the amount of force which we must apply to it in order to nuke it move with a definite velocity. Mathemati- cally, Uiere is no reason why these two methods should give the same result, but by experiment it is found that the attraction of all bodies is proportional to their inertia. In other words, all bodies, whatever their chemical constitution, fall exactly the same number of feet in one second under the influence of gravity, supposing them in a trace tlie effects 1 changes to which every part of the every object upon Dd all the objects )f system by them- K>und together by 1 is so strong that ject from the sur- 8. Every particle Qust, 80 far as we Eastk. us the quantity of ty of matter: (1) By lit being, in fact, tbe id tlie eartli; (2) By whicli we must apply elocity. Mathemati- sliould give tbe same traction of all bodies , all bodies, whatever ae number of feet in apposing them in • THE EARTH. 148 vacuum and at the same place on the earth's surface. Although the mass of n body is most conveniently measured by its weight, yet mass and weiglit must not be confounded. The weight of a body is the apparent force with which it is attracted toward the centre of the earth. This force is not the same in all parts of the earth, nor at dif- ferent beiglits above the earth's surface. It is therefore a variable quantity, depending upon the position of the body, while tbe mass of the body is sometliing inherer' , of the rocks composing the mountain was determined by experiment. The mass, M, of the mountain was VxD; that is, a known quantity. A plumb-line set up at the south end of the mountain wab attrucled away from the true vertical toward the mountain; that is, toward the north. A plumb-line at the north end of the mountain was attracted toward the south. The amounts of these deviations were measured, and they ^/ere due to the muss of the mountuio. Hence a measure of Its attractive force was obtained. The actual process of determining the deviations of the plumb- lines y and 5 was this: The latitude of the stations 8md Nvien determined. These were nothing but the decliuations of the xenitlu . of Jfand 8, the seniths being determined by the directions of plumb- lines at each station. The difference of latitudes of N and 8 by ^ astronomiml observations was known in arc and therefore in feet If the mountain had no attraction on the plumb-lines, this differ ence in feet would be the same as the distance apart of the two stations determined by tlie topt^rnphical survey. But it was differ- ent and the amount of the difference was a measure of the attraction of this particular mass. This is the general principle according to which the relation of mass and attraction ia determined. As the mass of the mountain and its attraction was known, the density of the wliole earth ooald he determined. The earth's maaa (M') was equal- to IW TOh»ii0 i V) i\m»\f density (2)'). {to yolwne was known, its I'ii 146 A8TR0N0MT. nam wu known, bacMin it miut be nich h to tttnust bodi« with forcM measured by tlieir weights, and hence iu density wu deter- mined from this experiment. The actual result was that the earth waa 4*7 times as dense as water. Otiier researches give about 5-6 for the density of the earth; this is more than double the average specific gravity of the roclis which compose the surface of the globe: whence It follows that the inner portions of the earth are much more danae than the outer parts. LAWI OV TimUSTUAL OlATITATIOV. The earth being very nearly spherical, certain theorems respecting the attraction of splieres may be applied to it. The demonstrution of these theorenu requires the use of the Integral Calculus, and will be omitted here, only the conditions and the results Iwing stated. Let us imagine a hollow shell of matter, of which the internal and eitemal surfacea are both spheres, attracting any other mass of matter, a small particle we may suppose. This particle will be attracted by every particle of the shell with a force inversely as the square of iU distance from it. The total attraction of the shell will be tlie resultant of this inflnity of separate attractive forces. Thkorkm I.— If th» particle be tmteide the ahell, it will be attraeied a$iftke vhole moM pose a body either outside the sphere or on its aurface. If we con- oalT« tlie apbeie as made up of a great number of spherical shells, the attracted point will be external to ail of them. Since each ahell attracts as if its whole mass were in the cent.e, it follows that the whole sphere attracts a body upon the outaide of ita surface as if its entire maaa were concentrated »; its centre. Let us sow uappom the attracted particle inaide the splien, as at P, Fig. 45. and imagine a spherical surface FQ oonoantric with the sphere and paaalng tbrouf^ the attraeted particle. f|a^ ^ 4k\\ that p«rtio«i of the sphere lyiaf' Mnci bodlM with density wu deter- HTM that the ewtb ircbes glTe ftbout louble the average rface of the globe: rth are much more .TIOV. leorems respecting riie demonstmtion Calculus, and will >ults being stated. 1 the internal and ny other mass of s particle will be ee inversely aa the m of the shell will ve forces. it will be attraeUd itt centre, the opponte attrat' matter whereaboufe nt attraetion of tK* «, let us first sup- irface. If we con- ipherical shells, the « external to all of ibell attracts as if I in the centic, it ole sphere attracts taide of its surface irere concentrated MM the attracted )heie, M at P, Fig. spherical surface h the sphere and attracted particle. tlie sphere lyiaf^ THK EARTH. 147 geometry, 4 )r^- Dividing by the square of the distance r, wo see 8 ouUide this spherical surface will be a uphcrical shell having thn particle Inside of It, and will therefore exert no iitiractioii whntever on the particle. That portion inside the surfnce will constitute n sphere with the particle on its siirfnco, nnd will therefore attract ns if all this portion were concentrated in the centre. To flnil what this attraction will be, let us lirst suppose the whole sphere of equal density. Let us put a, the radius of the entire sphere. r, the distance PCot the particle from the centre. TlietoUl volume of matter inside the splicre PQ will then be, by geometry,-5)rr*. Dividing by the squan o that the attraction will be represented by 4 that is. inside the sphere tlfe attraction will be directly as the dis- tance of the particle from the centre. If the |Hirticle is at the sur- 4 face we have r = a, and the attraction is -^ na. Outoide tiie sur- face the whole volume of the sphere -g « «' will attract the particle, 4 a* and the attraction will be ^ « -:. If we put r = o in this formula, o I we shall have the same result as before for the surface attraction. Let us next suppose that the density of the sphere varies from its centre to its surface, so as to lie equal at equal distances from tlie centre. We may then conceive of it as formed of an infinity of con- centric spherical shells, each homogeneous in density, but not of the same density as the others. Tlieoreros I. and II. will then still apply, but their result will not be the same t» in the case of a homo- geneous sphere ior a particle inside the sphere. Referring to Tig. 45, let w put D, tlie mean density of the shell outside the particle P. 2)*, the mean density of the portion P Q inside of P. We shall then hav« : Volume of the shell, 4 ' (a* — r*)- Volume of the inner nphera, 8 int*. Mas^ pf the sh9ll = vol. X Z> = 4 » i) (a» — r»). Mass of the 141 ASTROJfOMfT. : MaM inner •?««« = ▼ol. x I^ =» J- * ffr*. Mnu of the whoU iplwra = •U!n of moMOi it •hell »nd Inner sphere ■ jj- « ( /> a» + (D" - U) H|i Attraciion of the whole iphere upon » point M lU lurfhce ■ Attraction of tlio inner ipliere (Ihe mne Mthat of the Whole iheU) _ Mkm 4 ^ „. upon » point at i* = -^- = g- « ■t' ^ If, OS in tlie awe of the earth, the density continually Increases to- ward the centre, the Tnlue of Df will increase adto, as r diminislies, so that gravity will dlininlsli less rapidly than In the case of a home ffeneous sphere, and may. in fact, actually Increase as we descend. To show this, let us suhlract the attraction at Pfrom that at the sur. face. The difference will give : Diminution at P = J^ « (^a + (D* - 2>) -,- iXr ^ Kow let us suppose r a very little less than a, and put r =« a -rf; d will then Im the depth of the particle below the surface. Cubing this value of r, neglecting the higher powen of 0, and dividing by a«, we find ^ = a -8d. SubatltuUng in the above equation, the diminution of gravity at P beeomes 3 « (82) -VD^i. We see that if 8 D < 3 /)'— that is. If the density at the surfuce is less tl w" I of the mean density of the whole Inner mass— this quan- tlty will become negative, showing that the force of gravity will be less at the surfuoe than at a small depth in the interior. But it must ultimately diminish, because it is neoesMirily «ero at the centre. It was on this principle that Profesaor Airt determined the density of the earth by comparing the vibrations of a pendulum at the bottom of the Harton Colliery, and at the surface of the earth in the neigh- borhood. At the bottom of the mine the pendulum gained about 2'-5 per day, showing the foroe of gravity to be greater there than at the surface. Fraou AiB Kijonnnxi ov no Iaihl If the earth were fluid and did not rotate on its axis, it would auiume the form of a perfect sphere. The opinioQ irhoto iphtra a + (/)'- iDf*)i t iu turflwfl m Ui« whole sbell) My inereMM to* r dimiDisliM, w CBM of a homo, u we deacend. I Uut at the aur- -^ Dfry i put r St a — rf; rface. owen of d, and g in the above at the lurfiice ii mau — thii quan- f gravity will be lor. But it muat It the centre. It Bd the density of tm at the bottom uth in the neigli- iim gained about ater thexe tban at ) on ita axis, it , The opinioQ TUK EARTH. 149 is entertained that the earth was once in a molten state, and that this is the origin of ita present nearly spherical form. If we give such a sphere a rotation upon its axis, the centrifugal force at the equator acts in a direction op- posed to gravity, and thus tends to enlarge the circle of the equator. It is found by mathematical analysis that the form of such a revolving J9uid sphere, supposing it to be perfectly homogeneous, will be an oblate ellipsoid ; that is, all the meridians will be equal and similar ellipses, having their major axes in the equator of the sphere and their minor axes coincident with the axis of rotation. Onr earth, however, is not wholly fluid, and the solidity of its conti- nents prevents its assuming the form it would tn 9 if the ooeiui covered its entire surface. By the figure of the earth we mean, hereafter, not the outline of the solid ani liquid portions respectively, but the figure which it would assume if its entire surface were an ocean. Let us imagine canals dug down to the ocean level in every direc« tion through the continents, and the water of the ocean to be admitted into them. Then the onrved surface toaohing the water in all those canals, and coincident with the sur- face of the ocean, is that of the ideal earth considered by astronomers. By the figure of the earth is meant the figure of this liquid surface, without reference to the inequalities of the solid surface. We cannot Hty that this ideal earth is a perfect ellipsoid, because we know that the interior is not homogeneons, but all the geodetic measures heretofore made are so nearly represented by the hypothesis of an ellipsoid that the lat- ter is a very close approximation to the true figure. The deviations hitherto noticed are of so irreguk ^ oharaoter that they have not yet been reduced to anj •: ; uun Ikw, 160 ASTBONOMT. The largest which have been observed seem to be due to the attraction of mountains, or to inequalities in the den> sity of the rocks beneath the surface. Method of Triangulation. — Since it is practically impossi- ble to measure around or through the earth, the magnitude as well as the form of our planet has to be found by com- bining measurements on its surface with astronomical ob- servations. Even a measurement on the earth's surface made in the usual way of surveyors would be impracticable, owing to the intervention of mountains, rivers, forests, and other natural obstacles. The method of triangulation is therefore universally adopted for measurements extending over largo areas. (Ill, li ;lii '■;■''■■ ¥\ Vta. it^.-~k. Pi«r or nn Twaaawi Tbiamwilatioii ikak Pasis. Triangulation is executed in the following way : Two points, a and b, a few miles apart, are selected as tlie extremities of a base- line. They must be so chosen that their di>tnnce apart can be accu- rately measured by rods ; the intervening ground should therefore be as level and free from obstruction as possible. One or more ele- vated points, E F, etc., must be visible from one or Iwth ends i>i the baae-lins. By means of a theodolite and by observation of the pole- star, the directions of these points relative to the meridian are accu- rately observed from each end of the base, as is also the direction ab of the base-line itself. Suppose .J^* to be a point visible from each end of tbe base. th«ii iq the tria:igle abFyie have the len(;th ab^ THB EAllTH. Iffl to be dae to B in the den- cally impossi- lie magnitude Dund by com- 'onomical ob- irth's surface mpracticable, i, forests, and angulation is ats extending BAB Pahs. : Two points, a mities of a base- Kirt can be accu- should therefore One or more ele- Imtb ends o; the ition of the pole- eridian are accu- > the direction a 6 'iaible from each the length a (dfh termined by actual measurement, and the angles at a and h deter- mined by observations. With these data the lengths of the sides ai^aud b Faxe determined by a simple computation. The observer tlien transports his instruments to F, and determines in succession the direction of tlie elevated points or hills D EOHJ, etc. He next goes in succession to each of these hills, and determines the direction of all the others which are visible from it. Thus a net- work of triangles is formed, of which all the angles are observed with the theodolite, while the sides are successively calculated from the first base. For instance, we have just shown how the side aFia calculnted; this forms a base for the triangle EFa, the two remain- ing sides of which are computed. The side ^^forms the base of the triangle O EF, tlv sides of which are calculnted, etc. In this operation more angles are observed than are theoretically necessary to ciilculatc the triangles. This surplus of data serves to insure the detectiua of any errors in the measures, and to test their accura«-y by tlie agreement of their results. Accumulating errors are further guarded against by measuring additional sides from time to time as opportunity offers. Chains of triangles have thus been measured in Russia and Sweden from the Danube to the Arctic Ocean, in England and France from the Hebrides to Algiers, in this country down nearly our entire At- lantic coast and along the great lakes, and through shorter distances in many other countries. An cast and west line is now being run by tlie Coast Survey from tiie Atlimtic to the Pacific Ocean. Indeed it may be expected tliat a network of triangles will be gradually ex- tended over the surface of every civilized country, in order to con- struct perfect maps of it. Suppose that we take two stations, a and j, Fig. 46, situated north and south of each other, determine the latitude of each, and calculate the distance between them by means of triangles, as in the figure. It is evident that by dividing the distance in kilometres by the dif- ference of latitude in degrees we shall have the length of one degree of latitude. Then if the earth were a sphere, we should at once hare its circumference by multiplying the length of one degree by 860. It is thus found that the length of a degree is a little more than 111 kilometres, or between 69 and 70 English statute miles. lU circum- ference is therefore about 40,000 kilometres, and its diameter between 13,000 and 18,000.* * When the metric syBtem was originally dMisned by the Vyencb, It was in- tended tliat the kUometi* should be nin of Um dlitaiice tram the pole ot the earth to the eqnator. This would make a degree of the meridian eqaal, on Hw avwage. to XUk UlomMtwa. But the metre aottiaUy adfl|)taa Is vimAj^lA •BlnchtboitadM. Iftd AstnoKOitT. Owing to the ellipticity of the earth, the length of one degree varies with the latitude and the direction in which it is measured. The next step in the order of accuracy is to find the mngiiitude and the form of the earth from measures of long arcs of latitude (and sometimes of longitude) made in different regions, especially near the equator and in high latitudes. But we shall still find that dif- ferent combinations of measures give slightly different results, both for the magnitude and the ellipticity, owing to the irregularities in the direction of attraction which we have already described. The problem is therefore to find what ellipsoid will satisfy the measures with the least sum-total of error. New and more accurate solutions will be reached from time to time as geodetic measures are extended over a wider area. The following are among the most recent results: Fm.47. the ear til's polar semidiameter, 6855 • 370 kilometres; earth's equatorial ■emidiameter, 6877>877 kilometres ; earth's compreesion, ^^.^ of the equatorial diameter ; earth's eccentricity of meridian, 0'06819. An- other result is that of Captain Clarkb of England, who found: polar semidiameter, 685((>459* kilometres; equatorial semidiameter, 6S78-191 kilometres. O eeg i a p k l e aad O assentrie latitodMi.— An obvious result of the ellipticity of the earth is that the plumb-line does not point toward the earth's centre. Let Fig. 47 lepreaent a meridional section of the earth, N8 being the axis of rotation, B Q the plane of the equator, and the position of the observer. The line HS, tangent to the * Captain Clabxb's remlU are glren in f«et. the polar radiiM toinK ao,8B4,MS fset, the eqnatorial aa,8l6,aoiL These numbers are in the praportlM MB :«i. of one degree it is measured, magnitude nod f latitude (and especially near 1 find that dif- »t results, both rregularities in escribed. The y the measures !urnte solutions >s are extended (recent results: J Tax SAJiTB. 158 «arth at 0, will then jreprescnt the horizon of the obserrer, while the line Z If', perpendicular to HB, and therefore normal to the earth •Jit 0. will be ihe verlioul as determined by the plumb-line. The angle OJf'Q, or ZO Q', which, the observer's zenith makes with the equa- tor will then be his astronomical or geographical latitude. This is the latitude which in practice we always have to use, because we are obliged to determine latitude by astronomical observation, and not by measurement from the equator. We cannot determine the direction of the true centre C of the earth by direct observation of any kind, but only the direction of the plumb-line, or of the perpen- dicular to A fluid surface. ZOQ is the astronomical latitude. If, however, we conceive the line COt drawn from the centre of tlie earth Uirougli 0, z will be the observer's geoeentrie tmith, while the angle O C Q will be his geoeentrie latitude. It will be observed that it is the geocentric and nottlie geographic latitude which gives the true position of tlie observer relative to the earth's centre. The difference between tlic two latitudes is the angle CON' otZOt; this is called tlic angle of tlie vertical. It is zero at the poles and at the equator, be- ouise hero the normals pass through the centre of the ellipse, and it attains its mnximnm of 11' 80" at latitude 46°. It will be seen that the geocentric latitude is always. less than the geographic. In north latitudes the geocentric zenith is south of the apparent zenith, and in southern laUtudcs north of it; being nearer the equator in each case. *f rth's equatorial on, f^.T of the 008819. An- d, who found: semidiameter, I result of the it point toward I section of the of tlw equator, tangent to the Mtknsm-.am. MvnuK or thi lAXTtfa Ajjm, ob Phomuov or thi Saunrozif. UdeTMl uid Squinoctial Ymt.— lu^dewribing theftppar- ent motion of the Bun, two ways of finding the time of its apparent rerolntion around the sphere were described; in other words, of fixing the length of a year. One of these metliods^consisU in finding the interral between sucoessive MiMgia of the nm throngih theeqninozes, or, which is the ,|nHBe thing, across the plane of the eqnator, and the other Iby finding.wben it retnms to the same posititiun. Two thoQiand years ago Hippabchub fonnd, by amfumg his own obserrations with tho«e made two cm- ianm bKCeie t^ Tumkharis, Uuit thoie Ipo -Htttltods of 154 A8TB0N0MT. fixing the length of the year did not give the same resnlt. It had previously been considered that the length of a year was abont 365^ days, and in attempting to correct this period by comparing his observed times of the sun's pass- ing the equinox with those of Timocharis, Hipparchus found that the length required a diminution of seven or eight minutes. He therefore concluded that the true length of the equinoctial year was 365 days 5 hours and about 63 minutes. When, however, he considered the return of the sun not to the equinox, but to the same position reUtive to the bright star Spica Virginis, he found that it took some minutes more than 365^ days to complete the revolit- tion. Thus there are two years to be distinguished, the tropical or equinoctial year and the sidereal year. The first is measured by the time of the sun's return to the equinox; the second by its return to the same position relative to the stars. Although the sidereal year is the correct astronomical period of one revolution of the earth around the sun, yet the equinoctial year is the one to be used in civil life, because the change of seasons depends upon that year. Modern determinations show the respec- tive lengths of the two years t« be : 366"> 6" O" 9' = 365"".25636. ,, 365" S"" IS- 46" = 365«.a4220. , Sidereal year, Equinoctial year. It is evident from this difference between the two yeain that the position of the equinox among the stars must be changing, and that it mast mbve toward tiie west, because the equinoctial year is the shorter. This motion is called tha precession of the equinoxes, and amounts to about 50'' per year. The equinox being simply the point in which the equator and the ecliptic intersect, it is evident that it _ji,,^„„„tj.-.l*SI le same resnlt. ingth of a year correct this the son's pass- HlPPABCHUS »n of seven or :he true length and about 63 ) return of the sition reUtive 1 that it took ite the revold- nguished, the xl year. The return to the same position il year is the 1 of the earth bhe one to be tsons depends >w the respeo* 65"".25636. ,, S5*.a4220. , the two yeairs stars must be west, because >tion is called to about 50^' >int in which ident that it TEE BASTE. 166 can change only through » change in one or both of these circles. Hipfarchus found that the change was in the equator and not in the ecliptic, because the declinations of the stars changed, while their latitudes did not. Since the equator is defined as a circle everywhere 90° distant from the pole, and since it is moving among the stars, it follows that the pole must also be moving auiong the stars. But the pole is nothing more than the point in which the earth's axis of rotation intersects the celestial sphere: the position of this pole in the celestial sphere depends solely upon the direction ot the earth's axis, and is not changed by the motion of the earth around the sun. Heuce precession shows that the direction of the earth's axis is continually changing. Careful observations from the time of Uippab- CHCS until now show that the change in question consists in a slow revolution of the pole of the earth around the pole of the ecliptic as projected on the celestial sphere. The rate of motion is such that the revolution will be completed in between 25,000 and 26,000 years. At the end of this period the equinox and solstices will have made a complete revolution in the heavens. The nature of this motion will be seen more clearly by referring to Fig. 88, p. 98. We have tliere represented tlie earth in four poai- tions during its annual revolution. We have represented the axis as inclining to the right in each of these positions, and have described il as remaining parallel to itself during an entire revolution. The phenomena of precession show that this is not absolutely true, but that, in reality, the direction of the axis is slowly changing. Tbia change is such that, after the lapse of some 0400 years, the north pole of the earth, as represented in the figure, will not incline to the ri^t, but toward the observer, the amount of the inclination remain* ing nearly the same. The result will evidently be a shifting of the seasons. At D we shall have the winter solstice, because the north pole will be inclined toward the observer and tlierefon from the sun, fA 166 ASTROKaur. 'I while at A we sball have the venial equinox instead of the winter solstice, and so on. Id 6400 years more the north pole will be inclined toward the left, and the seasons will be reversed. Another interval of the same length, and the north pole will be inclined from the observer, the seasons being shifted through another quadrant. Finally, at the end of about 25,800 years, the axis will have resumed its original direction. Precession thus arises from a motion of the earth alone and not of the heavenly bodier. Although the direction of tlie earth's axis changes, yet the position of this axis relative to the crust of the earth remains invariable. Borne have supposed that precession would result in a change in tlie position of the north pole on the surface of I .(. r». A the earth, so that the northera i«|^ons would be covered bj the ocean as a result of the different direction in which the ocean would be carried by the centrifugal force of the earth's rotation. This, bow- ever, is a mistake. It has been shown that the position of the poles, and therefore of the equator, on the surface of the earth, cannot change except from some variation in the arrangement of the earth's interior. Scientific investigation has yet shown nothing to indicate any probability of such a change. The motion of precession is not uniform, but is subject to several small inequalities which are called nutathn. TBI Oauu w PuMsmov. The cause of preoesdon, ete., is illuslratcd in the flgura, iirtMi shows a spherical earth surrounded by a ring of natter atv«b»«q||p- tor. If the mxik were really spherical there would he «o prMN^WL It is^ bosf«ver, cUipwHdal with a protubenaoe at^lw npi» r . -ftht Bad of the winter d toward the left, rral of the aame the ohaerrer, the Finally, at the lumed its original I alone and not of the earth's axis I crust of the earth precession would on the surface of le covered hj the I the ocean would ition. Thi8,bow- lition of the poles, the earth, cannot sent of the earth's Dthing to indicate subject to aereral tiM figure. i|riM> i»tteratv«be«K|{|a- i he «o pTMNsiUp. ■-r TffB SAnTH. vn effect of this protuberance is to be examined. Consider the action between the sun and earth alone. If the ring of matter were absent, the earth would revolve about the sun as is shown in Fig. 82, p. 98 (Seasons). We remember that the sun's N. P. D. is W at the equinoxes, and 66i° and 118^° at the solstices. At the equinoxes the sun is in the direction Cm; that is, NOm is 00°. At the winter solstice the sun is in the direction Oe; NCe = 113i°. It is clear that in the latter case the effect of the sun on the ring of matter will be to pull it down from the direction Cm towards the direction Ce, An opposite effect will be produced by the sun when its polar distance is 66i°. The moon also revolves round the earth in an orbit inclined to the eqiutor. and in every position of the moon it has a different action on the ring of matter. The earth is all the time rotating on its axis, and these varying attractions of sxm and moon are equalized and distributed since different parts of tlie eartli are successively presented to the attracting body. "The result of all the complex motions we have described is a conical motion of the earth's axis JV G about the line CB. The earth's shape is not that given in the flgtire, but it is an ellip- soid of revolution. The ring of matter is not confined to the equator, but extends away from it in both directions. Tiie effects of the forces acting on the earth as it is are however, similar to the effects we have described. CHAPTER X. . t lu i h « i* i CELESTIAL MEASUREMENTS OF MASS AND DISTANCE. XbB GZUniAI fklALE Of KSAnrUlCEHT. The uuitB of length and mass employed by astronomws are necessarily different from thope used in daily life. The distances and magnitudes of the heavenly bodies are never reckoned in miles or other terrestrial measures for astro- nomical purposes; when so expressed it is only for the pur- pose of making the subject clearer to the general reader. The units of weight or mass are also, of necessity, astro- nomical and not terrestrial. The mass of a body may be expressed in terms of that of the sun or of the earth, but never in kilogrammes or tons, unless in popular language. There are two reasons for this course. One is that in most cases celestial distances have first to be determined in terms of some celestial unit— the earth's distance from the sun, for instance — and it is more convenient to retain this unit than to adopt a new one. The other is that the values of celestial distances in terms of ordinary terrestrial units are for the most part uncertain, while the corre- sponding values in astronomical units are known with great accuracy. An extreme instance of this is afforded by the dimensions of the solar system. By a series of astronomical observa- tions, investigated by means of Keplkb's laws and the theory of gravitation, it is possible to determine the forms forms I \im J AND DISTANCE. nrSEMXHT. yed by astronomers in daily life. The ily bodies are never ueosures for astro- is only for the pur- the general reader, of necessity, astro- is of a body may be )r of the earth, but I popular language. One is that in most be determined in 's distance from the anient to retain this B other is that the ordinary terrestrial Q, while the corre- B are known with id by the dimensions tronomical observa- leb's laws and the ietermine the forms MEASUREMENTS OF MASS AND DISTANCE. 159 of the planetary orbits, their positions, and their dimen- sions in terms of the earth's mean distance from the sun OS the unit of measure, with great precision. Keplek's third law enables us to determine the mean distance of a planet from the sun when we know its period of revolu- tion. All the major planets, as far out as Saturn, have been observed through so many revolutions that their periodic times can be determined with great exactness— in fact within a fraction of a millionth part of their whole amount. The more recently discovered planets, Uranus and Nep- tune, will, in the course of time, have their periods deter- mined with equal precision. Then, if we square the peri- ods expressed in years and decimals of a year, and extract the cube root of this square, we have the mean distance of the planet with the same or^cr of precision. This distance is to be corrected slightly in consequence of the attractions of the planets on each other, but these correc- tions also are known with great exactness. Again, the eccentricities of the orbits are exactly determined by care- ful observations of the positions of the planets during suc- cessive revolutions. Thus we could make a map of the planetary orbits so exact that the error would entirely elude the most careful scrutiny, though the map itself might be many yards in extent. On the scale of this same map we could lay down the magnitudes of the planets with as much precision as our instruments can measure their angular semidiameters. Thus we know that the mean diameter of the sun, as seen from the earth, is 32'; hence we deduce from formulse already given on pages 5 and 67 that the diameter of the sun is .0093083 of the distance of the sun from the earth. We oau therefore, on our supposed map of the solar system. 160 ABTROhOMT. I < ! I lay down the sun in its true size, according to the scale of the map, from data given directly by observation. In the same way wo can do tliia for each of the planets, the earth and moon excepted. There is no immediate and direct way of finding how large the earth or moon would look from a planet; whence the exception. But without further special research into this subject, we shall know nothing about the scalt of our map. That is, wo have no means of knowing how many miles or kilo- metres correspond in space to an inch or a foot on the map. It is clear that in order to fix the distances or the magni- tudes of the planets according to any terrestrial standard, we must know this scale. Of course if we can learn either the distance or magnitude of any one of the planets laid down on the map, in miles or in semidiameters of the earth, we shall be able at once to find the scale. But this process is so difficult that the general custom of astrono- mers is not to attempt to use a scale of miles, but to employ the mean distance of the sun from the earth as the unit in celestial measurements. Thus, y^ astronomical langnage, wo say that the distance of Mercury from the sun is 0.387, that of Venus 0.7^3, that of Mars 1.523, that of Saturn 9.539, and so on. But this gives ns no information respect- ing the distances and magnitudes in terms of terrestrial measures. The unknown quantities of our map are the magnitude of the earth and its distance from the sun in terrestrial units of length. Could we only take up a point of observation on the sun or a planet, and determine ex- actly the angular magnitude of the earth as seen from that point, we should be able to lay down the earth of oar map in its correct size. Then, since we already know the size of the e«rth in terrestrial units from geodetic surteys we, MEASURKMENTa CV MASS AND DISTANCE. 161 ng to the scale of ervation. In the planets, the earth diate and direct moon would look nto this subject, ' our map. That any miles or kilo- k foot on the map. ces or the magni- rrestrial standard, e can learn either I the planets laid idiametera of the e scale. But this iistom of astrono- les, bat to employ trth OS the unit in lomical language, L the sun is 0.387, 3, that of Saturn formation respect- nns of terrestrial our map are the e from the sun in ly take up a point md determine ex- as seen from that earth of our map lady know the size Ddetic surveys w«, should be able to find the scale of our map, and thence the dimenfions of the whole system in terms of those units. It ifill be seen that what the astronomer really wants is not so much the dimensions of the solar system in miles as to express the size of the earth in celestial measures. This, however, amounts to the same thing, because having one, the other can be readily deduced from the known magnitude of the earth in terrestrial measures. The magnitude of the earth is not the only n known quantity on oor map. From Eepleb's laws we can deter- mine nothing respecting the distance of the moon from the earth, because unless a change is made in the units of time and space, they apply only to bodies moving around the sun. We must therefore determine the distance of the moon as well as that of the sun to be able to complete our map on a known scale of measurement MiAiuxii or m fkiLo An ltoax Paxauax. The problem of distances in the solar system is reduced by the preceding considerations to measuring the distances of the sun and moon in terms of the earth's radius. The most direct method of doing this is by determining their respective parallaxes, which we have shown to be the same as the earth's angular semidiameter as seen from them. In the case of the sun, the required parallax can be deter- mined as readily by measuring the parallaxes of any of the planets as by measuring that of the sun, because any one measured distance on the map will give us the scale of our map. Now, the planets Venus and Mars occasionally come much nearer the earth than the sun ever does, and tbeir parallaxes also admit of more exact measurement 168 A8TR0K0MT. The parallax of the sun ia therefore detcrmin* , not by ob- aenrations on the sun itself, but on these two planets. The general principles of the method of determining the parallax of a planet by simultaneous observations at distant stations will be seen by referring to the figure. If two observers, situated at S* and 8", make a simultaneous observation of the direction of the body P, it is evident that the solution of a plane triangle will give the distance of P from each station. In practice, however, it would Flo. 48. be impracticable to make simultaneous observations at distant stations; and as the planet is continually in motion, the problem is a much more complex one than that of pimply solving a triangle. This is the method of determining the parallax of the moon. Knowing the actual figure of the earth, observa- tions of the moon made at stations widely separated in latitude, as Paris and the Cape of Good Hope, onn be com- bined so as to give the parallax of the moon and thni its distance. On precisely the same principles the parallaxes ot Yww ox Mars have been determined. iin» !/ not by ob- ro planeta. letormining the itions at distant figure. If two a flimultaneoai P, it is evident ;ive the distance iwever, it woald observations at tually in motion, le than that of ) parallax of tho e earth, obaerVa- ely separated in ope, onn be cbm- >on and thai its )s the parallaxes MEASUJiBMEIfTS OF MASS AND DISTANCE. 163 Mmt PftrtUu frMi Traaaito of ▼•&«••— When Vtnui ia at ber in. ferior conjuucliona ahe Id Itetwecu tliu iun and the curtli. If the orbit of Vtnu$ lay in tlie ecliptic, aiiu would bo projected on tlie auii'a diilt at every inferior conjunction. Tlie inclination of her orbit is, however, about 8)°, and thus the tmntittot Venu$ occur only when Venui happens to be near the node of her orbit at the time of inferior conjunction. When this occurs she is seen to pass ncroaa the sun's disk. In the last figure, if P is the place of Venui at such a time, and If Ibe disk of the sun is PP', then an observer at 8f' will see V*nu$ at P' and one at S' will see her at P. Tho distance. PP' can be meac^rcd directly, or it can be calculated by ob^rviug th6 time required for V*nu* to pass across the chord of the sun's disk at P' and across the chord at P. It is obvious that these chords are of different lengtli. The parallax of Venut («') is the angle subtended by tho earth's, radius at P; the parallax of the sua («) Is the angle subtended by the earth's radius at P|. If a Is the distance of the earth from Vtnu$, and If b Is the distance of the earth from the sun, we know that the earth's radius e will sub- tend an angle at F«nu< of - = ir*, and at the sun of -^ = ir (see page 6). That U,e = tm' = iJi and «' = -.«. ft is leO; and a is about 0.26 at the time of a transit. Hence f^ = 9.8it. What we really measure is the difference of the parallaxes n* And x, and thus, by employing the transit of Venus to measure the sun's ^ parallax (8".8), we are enabled to use an angle 2.8 times as large, or about 25". Even this Is • very dffHcuU ihatter: it is hardly possible by any one set of measuros-of the solar parallax to determine the latter without an uncertainty of ^^ of iu whole amount. In the distance of the ittn this corresponds to an uncertainty of nearly half a million of miles. Astronomers have therefore sought for other methods of determi|iiog the sun's distance. Although some of these may be a little more certain than measures of. parallax, there Is none by which the distance of the sun itf miles can be determined with any approximation to the accuracy which characterizes otber celestial meiwures. 'Othtr MMHodi of Determining Solar Purillax.— A very interesting and probably the most accurate method of meaduring the sun's distance depends upon a knowledge of the Telocity of light. We shall hereafter see that the time 164 ASTRONOMY. required for light to pass from the son to the earth is known with considerable exactness, being very nearly 498 seconds. This time can be determined still more aecuratefy. K then we can determine experimentally how many miles or kilometres light moves in a second, we shall at once have the distance of the sun by multiplying that quantity by 498. The velocity of lig^t is about 300,000 kilometres per second. This distance would reach about eight times around the ewth. It is seldom poasible to see two points on the earth's surface more than n hundred kilometree apart, and distinct vision sjt distances of more than tweaty kilometres is rare. Hence io determine experimentally ttic time required for light to pass between two terrestrial sta- tions requires the measurement of an interval of time which, even under the most favorable cases^ can be only a fraction of a thousandth of a second. Methf)ds of doing it, however, have been devise#, and the vel jcity of Kghfr would seem to be about 299,900 kilometres per 8eeond>. Multiplying this by 498, we obtain 149,350,000 kilometres (a little less than 93,000,000 miles) for the disfamee of the SUB. The time required for light to pass horn the sun to the earth is still uncertain by nearly a second, but l&is value of the sun's distance is probably tiie best yet ob- tained. The corresponding^ vmlue of the- sun's panBiC is 8'.81. Yet other methods of detemin^ng the sun's dirtaBov are given by the theory of gra<4t«tion. It is found hf mathematical investigation that the motion of the moon is subject to several inequalities, hnving the sim's horiwnilil parallax as a factor^ If the position of the moon owdt Hv determined by observation with the same easotOMK tMr j)he ponHoa^ » 9^ v/^ nlwiet c»n (whidl il^ewwi^lKD^ IjIa earth is known ly 498 seconds, uocuratefy. If many miles or [I at once have at quantity by 000 kilometres ut eight times see two points red kilometree ire than twenty erimentally Idic terrestrial sta- terval of lime 1^ can be only a !thr>dB of doing el jcity of Kght «8 per seeontf. 1,000 kilometres distanee of the ^m' the sBtt to' econd, bat l&is Im best yet ob* Hin's panBaK is Ban's dirtaBov It is fottod fijr t of the moon ia Hut's horiMartri 1 moon oaoit Hv ^i«<«HH*«iH MEASUREMENTS OF MASS AND DISTANCE. 166 this would probably afford the most accurate method of determining the solar parallax. Brief Hlitory of Detarmiiiatioiu of the SoUr PutlUz.— The dctermi- natioa of the distance of tlie sun must at all times have been one of the most interesting scientific problems presented to the human mind. The first known attempt to effect & solution of the problem was made by Aristarchus, who flourished in the third century before Christ. It was founded on the principle that the time of the moon's first quarter will vary with the ratio between the distance of the moon and Sim, which may be shown as follows. In Fig. 50 let E represent the earth, M the moon, and S the sun. Since the sun always illuminates one lialf of the lunar globe, it is evident tliat when one rtekflOL half of the moon's disk appears illuminated the triangle ^ JT^muat be right-angled at M. The angle MBS can be determined by measurement, being equal to the angular distance between the sun and the moon. Having two of tiie angles, the third can be deter- mined, because the sum of the three must make two right angles. Thence we shall have the ratio between E M, the distance of the moon, and E8, tlie diatance of the sun. by a trigonometrical computation. Then knowing the distance of the moon, which can be determined with comparative ease (see page 182), we have the distance of the sun by multiplying by this ratio. Aristabchcs concluded, from his suppoied measures, tliat the r.ngle MBS waa three degrees less than EM 1 a right angle. We aliould then have ^^- = rrr vr^ nearly, since 8* ia ^ of 57* and B8 = 57° (sec page 6). It would follow from tiiis tluit tli» tm wM 19 timea the diatancQ ot it» moon. We now know 166 A8TB0N0MT. that this result is entirely wrong, and that it is so because it is im- possible to determine the time when the moon is exactly half illumi- nated with any approach to the accuracy necessary in the solution of the problem. In fact, the greatest angular distance of the earth and moon, as seen from the suu — that is, the angle ESM— is only about one quarter the angular diameter of the moon as seen from the earth. The second attempt to determine the distance of the sun is men- tioned by Ptoleht, though Hippakchus may be the real inventor of it. It is founded on a somewhat complex geometrical construc- tion of a total eclipse of the moon. It is only necessary to state the result, which was that the sun was situated at the distance of 1210 radii of the earth. This result, like the former, was due only to errors of observation. So far as all the methods known at the time could show, the real distance of the sun appeared to be infinite; nevertheless ProiiBMY's result was received without question for fourteen centuries. Th3 first really successful measure of the parallax of a planet was made upon Mar$ during the opposition of 1672, by the first of the two methods already described. An expedition was sent to the colony of Cayenne to observe the declination of the planet from night to night, while corresponding observations were made at the Paris. Observatory. From a discussion of these observations. Cab- siNi obtained a solar pandlax of 9". 5, which is within a second of the truth. The next steps forward were made by the transits of Venua in 1761 and 1769. The Itsading civilized nations caused obser- vations on tliese transits to be made at various points on the globe. The method used was vsry simple, consisting in the determination of the times at which Venu* entered upon the sun's disk and left it •gain. The absolute times of ingress and egress, as seen from differ- ent points of the globe, might differ by 20 minutes or more on ac- count of parallax. Tlie results, however, were found to be discord- ant. It was not until more than half a century had elapsed that the observations were systematically calculated by Enckb of Qermany, who concluded that the parallax of the sun was 8" .578, and the dis- tance 95 millions of miles. In 1854 it began to be suspected that Enokb's value of the parallax was much too small. Hansen, from the theory of the moon, found the parallax of the sun to be S" .916. This result seemed to be con- firmed by other observations, especially those of Man during 1868. It was therefore concluded that the sun's parallax was probably be- tween 8" .90 and 9" .00. Subsequent researches have, however, been diminishing thia Ttlue. In 1867, from a discustioa of itll Ui«t data MBASUREMUNfS Of MAB8 AND DISTANCE. 167 lecause it is im- jtly half illumi- 1 the solution of of the earth and r— is only about seen from the the van is meu- le real inventor Eitrieal construc- isury to state the listanee of 1210 iras due only to lown at the time d to be infinite; >ut question for : of a planet was ' the first of tlie was sent to tlie the planet from ere made at the bservatious, Gas- hin a second of y the transits of ons ca\ised obser- its on the globe, be determination s disk and left it seen from differ- i or more on ac- nd to be discord- 1 elapsed that the :ke of Germany, .578. and the dis- ue of the parallax ' the moon, found seemed to be con- Van during 1868. was probably bc- ^ve, howeTef. been o of W tl>«t d»ta which were considered of value, it was concluded by one of the writers that the most probable parallax was 8". 848. The measures of the velocity of light reduce this value to 8". 81, and it is now doubtful whether the true value is any larger than this. All we can say at present is that the solar parallax is probably be- tween 8". 79 and 8". 83, or, if ouUide these limits, that it can be very little outside. Relative Masses or the Suh and Flakets. In estimating celestial masses as well as distances, it is necessary to use what we may call celestial units; ihiit is, to take Uie mass of some celestial b>xly as a unit, instead of nny multiple of the pound or kilogram. Tlie reason of this is that the rntiu» between the musses of the planetary system, or, which is the same thirtg, tlie mass of e.ich body in terms of that of some one body ns the unit, can be; de- tcrmiped independently of the mass of nny one of them. To express a mass in kilogrammes or other terrestrial units, it is necessary to find the mass of the earth in such units, as already explained. This, however, is not necessary for astronomical purposes, where only the relative masses of the several planets are required. In estimating the masses of the individual planets, that of the sun is generally taken as a unit. The planetary masses will then all be very small fractions. The mass of the sun being 1.00, the mass of Mercury is ^Jcti; " " Venu» is tT^m\ " '• " " JEa>'« sun. Knowing the latter, we can determine the mass of the suu rvlstivo o tbr earlii, which is the same thing as determining the astronor^r '"^) niisi of the earth, that of the sun being unity. This mny be cle:triy seen by re- flecting that when we know the radius of the eariL's orbit we rnn determine how far the earth moves aside froo* .> .might line in oua second in consequence of the attraction of tho lui;. This muticn measures the attractive force of the sun at the distance of the eutb I ttJBlW.Mga g'i .iW 168 A8TR0N0MT. Compnring it with the attractive force of the earth, and making allowance for the difference of distunccs from centres of the two boilics, we determine the ratio between their masses. Tlie following table shows, for different values of the solar paral- lax, the corresponding ratio of the masses, and distance of the sun in terrestrial measures: DiaTAMCB or trk Sl'M Solar M Parallax. P" In eqMRtorial radu of the earth. In mllUona of miles. In millions of kilometres. 8'. 77 835684 23519 93.208 150.001 8". 78 834598 28492 98.102 149.830 8'. 79 383398 28466 92.996 149.660 8". 80 832262 23439 92.890 148.490 8". 81 331182 23413 92.785 149.320 8'. 82 330007 23386 92.680 149.161 8". 88 338887 23360 92.575 148.982 We have said that the solar parallax is probably contained Iwtween the limits 8". 79 and 8". 88. It is certainly hardly more than one or two hundredtlis of a second without them. So, if we wish to ex- press the constants relating to the sun in round numbers, we may say that — Its matt is 830,000 times that of the earth. Its dMtanee in miles is 93 millions, or perhaps a little less. lU distance in kilometres is probably between 149 and 150 mil- lions. til, and making tres of tbe two the solur parol- ice of the Bun in Sum In millions of kilometres. 150.001 149.890 149.6tf0 148.490 149.320 149. ISl 148.983 ntained Itetween ore than one or we wish to ex- imbcrs, we may tie less. 19 aud 160 mil- CHAPTER XL TKE BEPBACTION AND ABERRATION OP LIGHT AND TWILIGHT. Aivofranio BBnAcmar. Wnsv we qieak of the place of a planet or star, we n«a- ally mean its true place; i.e., its direction from an ob- server situated at the centre of tbe eartb. We have tbowi in the section on parallax how observations which are .necessarily taken at tbe surface off the earth are reduced to what they would have been if the observer were situated at the earth's centre. We have supposed tbe star to be projected on the celestial sphere in the prolongation of the line joining the observer and the star. The ray from the atw was considered to si^er no deflection in passing throng the stellar spaces and through the earth's atmos- phww. Bat from the principles of physics, we know that Booh a InminouB ray passing from an empty space (as the fltellM- Bpaoei prehirt^ are), and through an aitmosphere, matt Boiier • refeactioo, as every ray of light is known to do ni -pMirinf from a tam into a denser medittm. As we MB^tite stw in tito diteetion in which its light enters ihe rnyo Hint is, m wo {urojeet the star on the celestial sphere byiprokm^iog this light-bewn backward into space— there 9-i:'!: Mm^tfpfmuAiiiukjitMmttata the star Irom refrac- twa. W« mtjj recall » tew deflnitions from physics. The ray which toavM tbe Mar and imj^tiges on the outer surface of tbe «arth'a at- ABTRONOMT. ^mgi mospbcre is called the incident ray; after its deflection by the attnos* phere it in called the refracted ray. The difference between these diiections is called the aetronomieal refraction. If a normal is drawn (perpendicular) to the surface of the refracting medium at the point where the incident ray meets it, the acute angle between the incident ray and the normal is callM the angle of incidence, and the acute angle between the normal and the refracted ray is called the angle of refraction. The refraction itself is the difference of these angles. The normal and both incident and refracted rays are in tlie same vertical plane. In Fig. 51, SA is the ray incident upon the surface ^.^ of the refracting medium BBAN, AO is the refracted ray, MNWxo normali ,8^ Jf and CAN the angles nt incideuco and refrac- tion respectively. Produce CA back- ward iij the direction A ff: 8 A S is the refraction. An observer at G will see the star 8 as if it were at S. AS is the apparent direction of the ray coming from the star 8, and 8 is the apparent place of the star as affected by refraction. St.— Refiuctioii. This explanation supposes the space above BB' in the figure to be entirely empty, and the earth's atmospherei, equally dense throughout, to fill the space below. .&i?'. In fact, however, the earth's atmosphere is most dense dt the surface of the earthj and gradually diminishes in density to its exterior boundary. . Therefore we must sup- pose the. atmosphere to be divided into a great number of parallel layers of air, and by assuming an infinite nnmr her of these we may also assume that throughout each one of them the air is equally dense. Hence the preoediog figure will only represent the refraction at a single one of these layers. The path of a ray of light through the at* mosphere is not a straight line like A C, but a curve, l^^e may suppose this curve to be represented in Fig. 02, where >n by the attno»> e between these normal is drawn im at the point een the incident the acute angle nd the refracted le of refraction. is the difference le normal and ^racted rays are plane. In Fig. idcut upon tlio racting medium refracted ray. IJf and CAN Qco and refrac- aduce CA baclc- I Aff.'SAB ia laerver at G will !ut direction o| ]^aee of the star e BB' in the 3 atmosphere^ below. -ffi?', I most dense diminishes in we must Bup- »t nnmber of infinite namr loat each one the preoediQg single one of iroogh the at? a curre. Ve rig. 02, where HEFRACTION AND ABERRATION OF LIGHT, m the number of layers has been taken very small to avoid confusing tho drawing. Lot C be tho centre and A a point of the surface of the earth; let Shoa star, and >S^e a ruy from the star which is refracted at the varioiis layers into which we suppose the atmosphere to be divided, and which finali ' enters tho eye of an observer at ^ in tho apparent di.oction S'A. He Vm. as.— BKFRAonoR or Lathh or Alfe. will then see the star in the direction S* instead of that of ^S", and ■'J AS', the refraction, will throw the star nearer to his zenith Z. The angle 8' A Z 19 the apparent zenith distance ot S; t^e.true zenith distance of S is ZA iS, and SA may be assumed to coincide with iS^0, as for all heavenly bodies except the moon it pra<;tioally does. The line Se pro- ABTR0N0M7. longed will meet the line AZ'\n% point above A, eoppoie at v. Quantity and Effeeti of Xefraotion. — At the zenith the refraction is 0, at 45° zenith distance the refraction is about l^ and at 90° it is 34' 30"; that is, bodies at the zenith distances of 45° and 90° appear elevated above their tme places by V and 34^' respectively. If the snn has just risen — that is, if its lower limb is just in apparent contact with the horizon — it is in fact entirely below the true horizon, for the refraction (35') has elevated its centre by more tlian its whole apparent diameter (32'). The moon is full when it is exactly opposite the sun, and therefore, were there uo atmosphere, moon-rise of a full moon and sunset would be simultaneous. In fact, both bodies being elevated by refraction, we see the full moon risen before the sun has set. On April 20th, 1837, the full moon rose eclipsed before the (ran had set. TWIUOHT. It is plain that one effect of refraction is to lengthen the duration of daylight by causing the snn to appear above the horizon before the time d! his geomeirieal rising and after the time of true sunset. . Daylight is also prolonged by the reflection of the sun's rays (after snnset and before sanrise) from the small parti- cles of matter suspended in the atmosphere. This i»o- duces a general though faint illumination of the atmos- phere, just as the light scattered from the floating particles of dnst illuminated by a sunbeam let in through a titmSk in a shntter may brighten the whole of a darkened room. The sun's direct rays do not reach an Te A, BUppOM the zenith the raotion is about s at the zenith bovo their tnie e Ban has just pparent contact below the true )d its centre by posite the sun, moon-rise of a eouB. Ic fact, ire see the full iril 20th, 1837, tad set. to lengthen the 4) appear above ieal rising and ion of the sun's the BDudl p«rti- ere. This iffo- of the stmoB- ioating particles brongh a €iadc urkened reoin. Ametfer on tiie TWIUOST. 178 earth after the instant of sunset, since the solid body of the earth intercepts them. But the sun's direct rays illuminate the clouds and the suspended particles of the upper air, and are reflected downwards so as to produce a general illumination of the atmosphere. In the figure let -4 ^ CZ> be the earth and A an observer on its surface, to whom the sun S is just setting. ^ a is the horizon of A; Bbot B; Cc of C; Dd otD. Let the no. Bs. circle PQR represent the upper layer of the atmosphere. Between ABGD and PQR the air is filled with sus- pended particles which will reflect light. The lowest ray of the Bun, SAM, just grazes the earth at A ; the higher rays iS^iVand SO strike the atmosphere above A and leave it at the points Q and B. Each of the lines SAPM, SQN, is bent from a straight course by refraction, bat SB is not bent since it just touches the upper limit* of ASTRONOilV. n lii ft*;. Ji the atmosphere. The space MA li C DB ia the earth's shadow. An observer at A receives the (last) direct rays from the sun, and also has his sky illuminited by the reflec- tion from all the particles lying in the space PQJiT which is all above his horizon A a. An observer at B receives no direct rays from the sun. It is after sunset. Nor does he receive any light from all that portion of the atmosphere below A /' M; but,the por- tion PRx, which lies above his horizon U b, is lighted by the sun's rays, and rofloets to B a portion of the incident rays. This ttoilight is strongest at R, and fades away gradu- ally toward P. To an observer at C the twilight is derivoJ from the illumination of the portion PQz which lies above his horizon Cc. ^ To an observer at Z> it is night. All ol the illt^mated atmosphere is below his horizon />rf. The student should notice for himself the twilight arch which appears in the west after sunset. It is morti marked in summer than in winter; in high latitudes than in low ones. There is no true night in England in midsiiinmer, for example, the morning twilight beginning before the evening twilight has ended ; and in the torrid zone there is no perceptible twilight. Abebbatioh ahd the Motioh of Liokt. , Besides refi-action, there is another cause which prevents our seeing the celestial bodies exactly in the true direction in which they lie from us; namely, the progressive mo- tion of light. We see objects only by the light which emanates from them and reaches our eyes, and we know F is the earth's lust) direct rays ted by the reflec- space PQRT B from the sun. y light from all M; but^the por- i b, is lighted by of the incident des away gradu- erivoJ from the lies above his the illi^mated th0 twiUght arch t is mote marked des than in low in midsummer, ining before the torrid zone there F LlOKT. , le which prevents the true direction progressive mo- the light which es, and we know REFRACTION AND ABERRATION OF LIGHT. 175 that this light requires time to pass over the space which separates us from the luminous object. After the ray of liglit once leaves the object, the latter may move awaiy, or even be blotted out of existence, but the ray of liglit will continue on its course. Consequently when we look at a star, we do not see the star that now is, but the star that was several years ago. If it should be annihilated, we should still see it during the years which would be required for the last ray of light emitted by it to reach us. The velocity of light is so great that in all observations of ter- restrial objects our vision may be regarnomenon of an entirely dif- ferent character, which coiifii-mcd the theory. He was then engaged in making observations on the star y Dra- conia in order to determine its parallax. The effect of parallax would have been to make the declination of the star greatest in June and least in December, while in March and September the star would occupy an interme- diate or r e^rn p iptical axis of a "WSS-^ ■^ -wrrw^iwif fs^r^-- IMAGE EVALUATION TEST TARGET (MT-3) 1.0 1.1 if EM 1^ £ lit 12.0 lit in 1^ U4 6" Photographic SdSices Corporation 'jmm 23 ¥I«T MAM STIHT VfilSTW,N.Y. 14SI0 (7U) •72-4503 «' CIHM/ICMH Collection de m Ife. REFRACTION AND ABERRATION OF LIGHT. 177 _ telescope, and 8 a star from which emanates a ray moving in the true direction SAB'. Per- haps the student will have a clearer conception of the subject if he imag- ines AP to be a rod which an ob- server at B seeks to point at the star S. It is evident that he will point this rod in such a way that the ray of light shall run accurately along its length. Suppose now that the ob- serrer is moving from B toward B' with such a velocity that he moves J^"- H from B to B' during the time required for a ray of light to move fi?om A to B'. Suppose, also, that the ray of light 8A reaches A at the same time that the end of his rod does. Then it is clear that while the rod is moving from the position AB to the position A'B', the ray of light will move from A to B', and will therefore run accurately along the length of the rod. For instance, if b is one third of the way from B to B', then the light, at the instant of the rod takirig the position i a, will be one third of the way from A to B', and will therefore be accurately on the rod. Consequently, to the observer, the rod will appear to be pointed at the star. In reality, however, the pointing will not be in the true direction of the star, but will deviate from it by a certain angle depending upon the ratio of the velocity with which the observer is carried along to the velocity of light This presupposes f ;iat the motion of the observer is at right angles to that of a ray of light. If this is not his direction, we must resolve his velocity into two components, one at right angles to the ray and one pAfiaW to it. The latter will not a^e^t jibe apparent di- 178 ASTRONOMY. rection of the star, which will therefore depend entirely upon the former. Effeott of Aberration.— The apparent displacement of the heavenly bodies thus produced is called the aberration of light. Its effect is to cause each of the fixed stars to ascribe an apparent annual oscillation in a very small orbit. The nature of the displacement may be conceived of in thfe following way: Suppose the earth at any moment, in the course of its annual revolution, to be moving toward a point of the celestial sphere, which we may call P. Then a star lying in the direction P or in the opposite direction will suffer no displacement whatever. -A star lying in any other direction will be displaced in the direction of the point P by an angle depending upon its angular distance from P. At 90° from P the displacement will be a maii- mnm. Now, if the star lies hear the pole of the ecliptic, its di- rection will always be nearly at right angles to the direc- tion in which the earth is moving. A little consideration will show that it will seem to describe a circle in conse- quence of aberration. If, however, it lies in the plane of the earth's orbit, then the various points toward which the earth moves iu the course of the year all lying in the eclip- tic, and the star being in this same plane, the apparent motion will be an oscillation back and forth in this plane, and in all other positions the apparent motion will be in art ellipse more and more flattened as we approach the ecliptic. The maximum displacement of a star by aberration is 20'. 44. The connection between the velocity of light and the dii*- tance of the sun is such that knowing one we can infer the other. Let us assume, for instance, that the time required for light tp reach us from the sun is 498 seqopds, which .-.ai^/.«^w»- rr^-'■.■-r™»¥w^lnr, REFRACTION AND ABERRATION OF LIGHT. 179 depend entirely displacement of i the aberration le fixed stars to very small orbit. Aceived of in thb moment, in the loving toward a y call P. Then pposite direction star lying in any direction of the angular distance t will be a maii- »e ecliptic, its di- gles to the dii-ec" btle consideration I circle in conse- 3 in the plane of toward which the ying in the eclip- tic, the apparent rth in this pliane, Ition will be in an ■oach'the ecliptic. ierrationi8 20'.44. light and the dii^- I we can infer the the time required )8 secopds, which is probably accurate within a single second. Then know- ing the distance of the sun, we may obtain the velocity of light by dividing it by 498. But, on the other hand, if we can determine how many miles light moves in a second, we can thence infer the distance of tlie sun by multij)lying it by tiie same factor. During the lust cen- tury the distance of the sun was found to be certainly be- tween 90 and 100 millions of miles. It was therefore correctly concluded that the velocity of light was some- thing less than 200,000 miles per second, and probably between 180,000 and 200,000. This velocity has since been determined more exactly by the direct measurements at the surface of the earth already mentioned. »fS*=f.'.^.'-^-'--'ft«]«r--^ CHAPTER XII. CHRONOLOGY. AffiBOKOiaoAL MBAsntxs 07 Tim. The intimate relation of astronomy to the daily life of mankind has arisen from its aiffording the only reliable and accurate measure of intervals of time. The fundamental units of time in all ages have been the day, the month, and the year, the first being measured by the revolution of the earth on its axis, the second, primitively, by that of the moon around the earth, and the third by that of the earth round the sun. Of the three units of time just mentioned, the most nat- ural and striking is the shortest; namely, the day. It is so nearly uniform in length that the most refined astro- nomical observations of modern times have never certainly indicated any change. This uniformity, and its entire freedom from all ambiguity of meaning, have always made the day a common fundamental unit of astronomers. Ex- cept for the inconvenience of keeping count of the great oamber of days between remote epochs, no greater unit would ever hwe been necessary, and we might all date our letters by the nnmber of days after Chbist, or after any other fixed date. The difficulty of r.^membering great numbers is such that a longer unit if absolutely necessary, even in keeping the reckoning of time for a single generation. Such a unit on. ;he daily life of m\j reliable and be fundamental tbe montb, and evolution of tbe by tbat of tbe hat of the earth d, the most nat- tbe day. It is tst refined astro- 5 never certainly and its entire ave always made bronomers. Ex- int of tbe great no greater unit ight all date our 18T, or after any tumbers is snch even in keeping on. Snob a nnit CHRONOLOGT. 181 is tbe year. Tbe regular changes of seasons in all extra- tropical latitudes renders this unit second only to tbe day in tbe prominence with which it must have struck tbe minds of primitive man. These changes are, however, so slow and ill-marked in their progress tbat it would have been scarcely possible to make an accurate determination of the length of the year from tbe observation of tbe sea- sons. Here astronomicd observations came to tbe aid of our progenitors, and, before tbe beginnings of history, it was known that the alternation of seasons was due to the varying declination of the sun, as tbe latter seemed to perform its annual course among the stars in the " oblique circle" or ecliptic. Tbe seasons were also marked by tbe position of certain bright stars relatively to tbe sun; that is, by those stars irlsing or setting in the morning or evening twilight. Thus arose two methods of measur- ing the length of tbe year — tbe one by the time when the snn crossed the equinoxes or solstices;- tlio other when it seemed to pass a certain point amoiig the Stars; Atfwis have already explained, these yours were 8)igiit]y different, owing to the procession of the oquinoUps,.'th0'fir«t or equi- noctial year bcinb; a Tittle Ict^s ami the ^fcbiid dt' sidcrcatl year u litUo greater than 3<)5i4ttys. . Tire number of days in n }'ie«r is too great to udmit of their Wing easily rcmembereSi wiilinnt iiny t)roak;Vm intermodiutL' iH»riod is tliereforc ncocKsary. Such a, period is measured by the revolntion of tbe moon lu^onnd- the earth, or, more exactly, by the, recurrence of hew moon, which takes place, on the average, at the end of nearly 29i days. The nearest round number to this is 30 dayf>, and 12 periods of 30 days ^ch only lack 6^ days of being a year. It has therefore been common to consider a year i i i ; t 162 ASTRONOMT. as made up of 12 months, the lack of exact correspondence being filled by various alterations of the length of the month or of the year, or by adding surplus days to each year. , , ,, The true lengths of the day, the month, and the yenr having no common divisor, a difficulty arises in attempting to make months or days into years, or days into montlis, owing to the fractions which will always be left over. At the same time, some rule bearing on the subject is neces- sary in order that people may be able to remember the yenr, month, and day. Such rules are found by choosing some cycle or period which is very nearly an exact number of two units, of months and of days for example, and by dividing this cycle up as evenly as possible. POBKATIOir OT CAUHDAXB. The montlis now or heretofore in use among the peoples of the dolKs may for the most part be divided Into two classes. (1) The lunar month pure and simple, or the mean interval be- tween successive new moons. (2) An approximation to the twelfth part of a year, wilhout respect to the motion of the moon. Tlw lunar Month. -Tlie mean Interval iK-tween consecutive new moons beinir nearly 20i days. It was conmu.ti in llic use of the pure lunar month to have months of 29 and 30 days aliernUcly. This supposed perloil. however, will fall short by a day in ah(,ut 2i years. Tills defect was remedied by Introducing cycles containing rather more months of 80 than of 29 .lays, the small excess «.f long months being spread uniformly through the cycle. Thus the Greeks »"«l « «"y«>« of aaa months, of which 125 were full or long months, and 110 were short or deficient ones. We see that the length of this cycle was 8940 days (125 X 80 + 110 X 29). whereas the length of 285 true lunar months is 285 X 29.58088 = 6989.688 days. The cycle was therefore too lone by less than one third of a day. and the error of count would amount to only one day in more than 70 years. The Mohammedan^ «nin. took » cycle of 860 months, which they divided into 169 short Sdm tongones. The length of thU cycle wm 10681 days, whUe Borrespondonce length of the 18 days to each I, and the year s in attempting fs into montlis, left over. At ubjoct is neces- ember the year, choosing some cact number of cample, and by (he peoples of tlie asses; meuu interval be- sar, wilhoiUri'spect n consecutive new lite use of tlic pure iilternUcly. Tliis ' ill about 2i years, tiiiningriitliernioro long months licing Greeks had a cycle inths, and 110 wcro li of this cycle was th of 285 true lunar cycle was therefore rror of count would %e Mohammedans, vided into 100 short B 10681 days, 'while OBSONOLOOT. 188 the true length of 890 lunar months is 10081.018 days. The count would tlierefore not be a day in error until the end of about 80 cycles, or nearly 23 centuries. This month therefore follows the moon closely enough for all praclical purposes. Months other than Loaar.— The complications of the system Juat described, aud the consequent ditficuliy of making the calendar month represent the course of the moon, are so great that the purs luuar month was generally abandoned, except among people whose religion ruquircd Important ceremonies at the time of new moon. In such cases the year has been usually divided into 12 months of slightly different lengths. The ancient Egyptians, however, had 12 mouths of aO days each, to which they added 5 supplementary days at the close of each year. Kinds of Tear.— As we find two different systems of months to have been used, so we may divide the calendar years into thne classes, namely: (1) The lunar year, of 12 lunar months. (8) The solar year. (ji) The combined luni-solar year. Ths Luar Tosx.— We have already called attention to the fact that the time of recurrence of the; year is not well marked except hj astronomical phenomena which the casual observer would haidlj remark. But the time of new moon, or of beginning of the month, is always well marked. Consequently it was very natural for people to begin by considering the year as made up of twelve lunations, the error of eleven days being unnoticeable in a single year unless can* f ul astronomical observations were made. Even when tliis error was fully recognized, it might be considered better to use the regular year of 12 lunar months than to use one of an Irregular or Tuying number of months. The Moliammedans use such a year to this day. Thi Bolar Tsar.— In forming this year, the attempt to meesarethe year by revolutions of tlie moon is entirely abandoned, aud its length is made to depend entirely on the change of the seasons. The solar year thus indicated is that nrost used in both ancient and modem times. Its length has been 'rtjown to be nearly 865^ days from the timesof the earliest iMtronc^^'x, and the system/idopted in onr cal- endar of having three years of 165 days each, followed by one of 806 days, has been employed in China from the remotest historic times. Tliis year of 865^ days is now called by us the Julian Ttar, after Jin.n;s GisaAB, from whom we obtained it. The Voteaie Oydo.— These considerations will enable ns to under* stand the origin of our own calendar. We begin whh the Hetonic Cyide of the andent O.rseks, which still regulates some reHgioutfes- - -f^5^'-.;«--?^> :f i"»C1;-ir.'T-*^ 184 ABTRONOMT. tivftli, although it hM dinppeared from our civil reckoning of time. The neceisity of employing lunar months osused the Greeks great ilifflculty in regulating tlieir calendar so as to accord with their rules for religious feasts, until a solution of the problem was found by Meton, about 488 b.c. The discovery of Metom was that a period or cycle of 6040 days could lie divided up into 285 lunar months, and also into 10 solar years. Of these months, 125 were to be of 80 days each and 110 of 20 days each, which would, in all, make up the re- quired 6040 days. To see how nearly this rule represents the actual motions of the sun and moon, we remark that: Days. Hours. MIn. 885 lunations require 6080 16 81 10 Julian years require 6080 18 10 true solar years require 6080 14 27 We see that though the cycle of 6040 days is a few hours too long, yet if we take 285 true luirnr months, we find their whole dura- tion to bo a little less tiian 10 Julian years of 865^ days each, and a little more than 10 true solar years. The problem was to take these 285 months and divide them up into 10 years, of which 12 should have 12 months each and 7 should have 18 months each. Tiie long years, or those of 13 months, were probably those corresponding to the numbers 8, 5, 8, 11, 18, 16, and 10, while tiie first, second, fourth, sixth, etc., were short yeara. In general, the montlis bad M and 80 days alternately, but it was necessary to substitute a long month for a short one every two or three years, so tiiat in the cycle there should he 125 long and 110 aiiort months. Ooldm Vuibtr.— This ia simply the number of the year in the Motonic Cycle, and is said to owe its appellation to the enthusiasm of tiie Oreeks over Mbtom'b discovery, the authorities having ordered tlie division and numbering of the years in the new calendar to be inscribed on public monuments in letters of gold. The rule for find- ing the golden numlier is to divide tlie number of the year by 10 and add 1 to the remainder. From 1881 to 1800 it may be found by sim- ply subtracting 1480 from the year. It is employed in our church calendar for finding the time of Easter Sunday. The jraliaa Oaleadar.— The civil calendar now in use throughout Christendom had its origin among the Romans, and its foundation was laid by Jclics CiHSAB. Before hfai time, Rome can hardly be said to have hvA a chronological system, the length of the year not being prescribed by any invariable rule, and being therefore changed from time to time to auit the caprice Or to omnpua the endt of the CBttONOtOOY. 18» ;koDiDg of time, be Greeks great with their rules in was found by as that a period nar moDtlis, and to be of 80 days make up the re- sents the actual lours. MIn. 16 81 18 14 27 few lioura too leir whole dura- ays each, and a divide them up lis each and 7 le of 18 months, 5. 8. 11. 18. 16, ere short years, tely, but it was le every two or M long and 110 the year in the the enthusiasm having ordered calendar to be he rule for find- I year by 19 and e found by sim> 1 in our church use throughout ; its foundation i can hardly be of the year not erefore changad the endtof the. rulers. Instances of tliis tampering disposition ore familiar to the hitturical student. It is said, for instance, tliat the Oauls having to pay a certain monthly tribute to tlie Romans, one of tlie governors ordered the year to be divided into 14 months, in order lliat tlio pay days might recur more rapidly. A year was fixed at 865 days, with the addition of one day to every fourth year. The old Roman months were afterward adjusted to the Julian year in such a way as to give rise to the somewliat irregular arrangement of months which wo now have. Old aaA Xew Itylas.— Tlie mean length of the Julian year is 865} days, about 11} minutes greater than that of tlie true equinoctial year, which measures the recurrence of the seasons. This difference is of little practical importance, as it only amounts to a week in a thousand years, and a change of this amount in that period is pro- ductive of no inconvenience. But, desirous to iiave the year as cor- rect as possible, two changes were introduced into the calendar by Pope Oreoory XIII. with this object. They were as follows : (1) The day following October 4, 1582, was called the 15th instead of the Sth, thus advancing the count 10 days. (2) The closing year of each century. 1600, 1700, etc., instead of being always a leap-year, as in the Julian ciilendar. is such only when the number of the century is divisible by 4. Tlius while 1600 remained a leap-year, as before. 1700, 1800, and liMO were to be common years. This change in the calendar was speedily adopted by all Catholic countries, and more slowly by Protestant ones, England holding out until 1752. In Russia it has never Iteen adopted at all. the Julian calendar being still continued without change. The Russian reckon- ing is therefore 12 days behind ours, the ten days dropped in 1582 being increased by the days dropped from the years 1700 and 1800 in the new reckoning. This modified calendar is called the Oregorian OaUndar, or Ifeu l^te, while the old system is called the JuUan QOendar, or OM Style. It is to be remarked that the practice of commencing the year on January let was not universal until comparatively recent times. The most common times of commencing were. perlAipa. March 1st an gether as the nu^ planett, to distinguish them from the two hun- dred or more minor planett of Group 8. The formal dafinitions of the various classes, laid down by Sir Wiluax Hbbsohbl in 1808, ara worthy of repetition : FAIL rSTEM. I a central body, lor planets, with ad an unknown manent members ppear, and move around the sun, siting the system ollows : e Earth, Mar$. Atteroidi, revolving atum, Uranut, aod g about the planets, revolving in very metimes classed to- from the two hun- srmal dafinitions of owcHBL in 1800, am arnucTURE of the solar system. 191 Planets are celestial bodies of a certain very considerable slee. They move in not very eccentric ellipses about the sun. The planes of their orbits do not deviate many degrees from the plane of the earth's orbit. Their motion about the sun is direct (from west to east). They may have satellites or rings. They have atmospheres of I ! Fia. S6w— Raunvi Soiricaa or nn FUMifs. considerable extent, which, however, bear hardly any sensible pro. portion to their diameters. Their orbito are at certain considerabhi distances from each other. AstereUs, now more generally known as maatt or minor pfoMtt, are oekstial bodies which move about the sun in orbiU, «iUier of little or 199 ASTRONOMY. of considerable eccentricity, the planes of which orbits maj be in- clined to the ecliptic nt any angle whatsoever. They may or may not have considerable atmospheres. OomeU are celestial bodies, generally of a very small mass, though how far this may be limited is yet unknown. Tliey move in very *!l Tm. M.— Aptabxmt M Aomnrou or thb Scm as bbkn raoii Dmnaumr Fbimn. eccentric ellipses or in parabolic arcs about the t'Un. The planes of their motion admit of the greatest variety in their situation. Tlw direction of their motion is also totally undetermined. They liaTe atmospheres of very great «xtent, which sliow themselvos in vaHil wltMn tM MW'i i 8TRUCTURB OF THB SOLAR ST8TBM. \n I surface. Or again, conceiTe of the force of gravity at the surface of the Tarious bodies of the system. Al the sun it is nearly 28 times that known to us. ▲ pendulum beating seconds here would, if transported to the sun. vibrate with a motion more rapid than that of a watob-balance. The muscles of the strongest man would not support blm erect on tb* aurfaoe oi the sun : even lying down be would cruali himself to death under hia own weight of two tons. We may by these iUuatrations get some rough idea of the meaning of the numbers in these tables, and of the iacapabiiUy of our Ihniled ideas to comprehend the true dimensions of even the aukr system. ^SSm^j^ii:^.^^^-- ■ -.51 198 ASTRONOMY. 1^ m t v m rn 'mmmmfe H^m '^' f* ■ J ii w *» n « w ^ e JO t« ^, US 52 {2 S9 9 3® s; 2 22 f2 8 Is 8 S : SI) 9 9' no) O 1-* DA CO 00 eco 5 IS 3 »e» s g .9 « a 3 § I OQ 3 STRUCT VRB OF THE SOLAR aYSTBM. \m n i ® s s s s a T^ 00 ^ JH ei ^ 1^ s s s s OO M '<<• « 5^ S: g S S gS $ S 2S P 9 S 8 8 Z 2 8"!" °- Ik * -3 -g S ^ ^ »i e« 40 e. © th O "-i $ S OQ S I o 4) * . . & M I & & U> P § S S 0t 9 00 *^ 9 9 ■^ T* S « 0) 04 « ■ t-' t^ -^ s g s af I TF S S S ^ 9 op M 10 »• t^ ^ g O O 00 t> 1-1 o o S S S 3 8 04 e« « t^ t^ e» jg g e e e o e «o t> e 58 e ^ e o 8 8 8 8 8 % •H 1-« 1^ IH f>4 IS . 44 190 3 8 Ti CHAPTER IL THE BUH. OmoAi IhwmMMt. To enable the natare of the phenomena of the an n to be dea/lj nndenitood, we preface oar aoconnt of iti phyiical conatitation bj a brief aanamary of iii main feataret. Pkotoiphere. — To the simple Tieion the san presents the aspect of a brilliant sphere. The risible shining aurfact of this sphere is called the phofotphere, to distinguish it from the body of the sun as a whole. The apparently flat surface presented by a riew of the photoiph«re is called the snn's di»k. ipAlA— When the photosphere is examined with a tele- scope, small dark patches of taried and irregular outline are frw^uently foiind upon it. These are called the iolar tpoti. aetat t e a .-^Vhen the spots era obeei^ed from day to day, they are fonnd to moTeorer the snn's disk from east to west in soeh a way as to show that the snn rotates on it« axis in a period of 26 or 29 days. The ran, therefore, has axi$, poltt, end tquator, like the earth, the axis being the line Mound which it roiatea. iMolai.— Oronpa of minute apecka brighter than the general anrfaoe of the aun are often aeen in the neighbor- hood of Bpota or ^where. They ar0 called /«<;«/<«. i the Ban to be ot its pbyiical ftfataret. in presentg the hining aur/act distingnish it apparently flat ir« is called the ed wHh a tele- 'egnktf outline ailed the solar from day to sk from east to rotates on its therefore, has axis being the bter than the the neighbor* i/acula. TBM btllt. 901 Obromof^rt, or Sierra,— The solar photosphere is cot- ered i.y a layer of glowing vapors and gases of very irregu- lar depth. At rhe bottom lie the rafon of Many metals, iron, etc., tsiatnised hj the forvont heat which reigns there, while the upper portions are oompcsed principally of hydrogen gas. This vaporous atmosphere is commonly called the ehromosp1m% aoBMtimes the mstm. It ia«i- tirely invisible to direct vision, whether with the telescojie or naked eye, except for a few seconds about the beginning or end of a total eclipse, but it may be seen on any clear day through the spectroscope. Premiaeaeei^ Frotuheraaeea, or Sod rhnofc— The gases of the chromosphere are frequently thrown up in irregular masses to vast heights above the photosphere, it may be 60,000, 100,000, or even 300,000 kilometres. Like the chromosphere, these masses have to be studied with the spectroscope, and can never be directly seen except when the sunlight is cut off by the intervention of the moon during a total eclipse. They are then seen as rose-colored flames, or pilot of bright red clouds of irregukr and fantas- tic shapes. i Ooraaa.— During total eolipoes the sun irseen to be en- veloped by • mass of soft white light, much fainter than the ehromoophoro, and extending out on sill sidof far be- yond the highest prominences. It is brightest around the edge of iho tun, and fades oft toward its onter boundary, by insensible gradations. This halo of light is called the eoroM, and is a very striking object during a total eclipse. f4Ml* Ml IMMNM sf fM ¥kHmilk$n.—thi disk 6f the sna is d^ esflar in shiipe, ntf ttMter #hiit fide of tb« ittn*s gliAe b turned tif- • •'V.Hfjff^ l f^ . sod ASTRONOMY. ward us, whence it follows that the sun itself is a sphere. The aspect of the disk, when viewed witu the naked eye, or with a telescope of low power, is that of a UTiifortn bright, shining surface, hence called the photogpJiert. With a telescope of higher power the photosphere is seen to be dlTersified with groups of spots, and under good con> Fnk IB.— KanovLATiD AaaAiiaBinHT or tu Sm'a Otom a photognnAu) ditions the whole bums has a mottled or curdled appearance. Thii mottling is caused by the presence of cloud-like forms, whoM out- lines though faint are yet distinguishable. The background is also covered with small white dots or forms still smaller .than tlks c]ouda» here. Theaapect itli a telescope of face, hence called r the photosphere under good con> ipearance. Thia rou, whoM out- digiound ia alto than thjB clouda» i THR 6UN. 908 These are the " rice-grains," so called. The clouds themseWes are composed of small, intensely bright bodies, irregularly distributed, of tolerably definite shapes, which seem to be suspended in or super- posed on a darlier medium or background. The spaces between the bright doU vary in diameter from 2' to 4' (about 1400 to 2800 kilo- metres). The rice-grains themselves have been seen to be composed of smaller granules, sometimes not more than 0'.8 (185 miles) in diameter, clustered togetiicr. Thus there have been seen at least three orders of api^gation in the brighter parta of the photosphere: the larger cloud-like forms; the rice- grains; and, smallest of idl, the granules. Light and Heat from the Photoiphere. — The photosphere is not equally brig] it all over the apparent disk. This is at once evident to the eye in observing the son with a tele- scope. The centre of the disk is most brilliant, and the edges or limbs are shaded off so as to forcibly suggest the idea of an absorptive atmosphere, which, in fact, is tl^e cause of this appearance. Such absorption occurs not only for the rays by which we see the sun, -the so-called visual rays, but for those which have the most powerful effect in decomposing the salts of silver, the so-called chemical rays, by which the ordinary photograph is taken. The amount of heat received from different portions of the sun's disk is also variable, according to the part of the apparent disk examined. This is what we shoald expect. That is, if the intensity of any one of these radiations (as felt at the earth) varies from centre to circomference, that of every other should also vary, since they are all modifi- cations of the same primitive motion of the sun's con- stituent particles. But the constitution of the sun's at- mosphere is such that the law of variation for the three classes is different The intensity of the radiation in the sun itself and insido of the absorptive atmosphere is prob- 1- y*^ ■JMIMMBBES Jjt! '- ifn mi MTRONOMT. ably nearly constant. The ray -vrbidi leaves the centre of the sun's disk in passing to the earth liaiiiiias the smallest possible thickness of the solar atmosphere, while the rays from points of the sun's body which appear to us near the limbs pass, on the contrary, through the maxi- mum thickness of atmosphere, and are thus longest sub- jected to its absorptiye action. This is plainly a rational explanation, since the part of the sun which is seen by us as the limb varies with the position of the earth in its orbit and with the position of the sun's surface in its rotation, and has itself no physical peculiarity. The various absorptions of different classes of rays correspond to this supposition, the more refrangi- ' ble rays, violet and blue, suffering most absorption, as they must do, being composed of waves of shorter wave-length. Amount of Heat Emitted by the Sun.— Owing to the absorption of the solar atmosphere, it follows that we re- ceive only a portion — perhaps a very small portion — of the rays emitted by the sun's photosphere. If the sun had no absorptive atmosphere, it would seem to us hotter, brighter, and more blue in color. Exact notions as to how great this absorption is are hard to gain, but it may be said roughly that the best authorities agree that although it is quite possible that the sun's at- mosphere absorbs half the emitted rays, it probably does not absorb four fifths of them. The amount of this absorption is a practical question to us on the earth. So long as the central body of the san continues to emit the same quantity of rays, it is plain that the thickness of the solar atmosphere determines the nnm- ber of wttoh rays reaching the earth. If in former timet this atmosphere was much thicker, then less heat would tei>iwii i »j" i M^ ^ ^^^^ ".';«>'■■ eaves the centre "th tnmnM the itmosphere, while hich appear to us irough the maxi- shas longest sab- since the part of b varies with the h the position of tself no physical different classes e more refrangi- •sorption, as they ter wave-length. — Owing to the Hows that we re- mall portion— of «, it would seem Dior. 'ption is are hard e best authorities ;hat the snn's at- it probably does itical question to body of the son rs, it is plain that rmines the anm- in fonner timM less hc»t would THS SUIT. d06 have reached the earth. Glacial epochs may be explained in this way. If the central body of the sun has likewise had different emissive powers at different times, this again would produce a variation in the temperature of the earth. Amount of Hest Badikted. — There is at present no wny of dctermin- ing accurately either the absolute amount of heat emitted from the central body or the amount of this heat stopped by the solar atmos- phere itself. All that can be done is to measure (and that only roughly) the amount of heat really received by the earth, without attempting to define accurately the circumstances which this radiation has undergone before reaching the earth. PomUiET has experimented upon this question, making allowance for the time that the sun is below the horizon of any place, and for the fact that the solar rays do not in general strike perpendicularly but obliquely upon any given part of the earth's surface. His con- clusions may be stated as follows : if our own atmosphere were re- moved, the solar rays would have energy enough to melt a layer of ioe 9 centimetres thick over the whole earth daay, or a layer of about 82 metres thick in a year. This action is constantly at work over the whole of the sun's sur- face. To produce a similar effect by the combustion of coal would require that a layer of coal 5 metres thick spread all over the sun Should be consumed every hour. This is equivalent to a eontinuotu evolution of 10,000 horse-power on every square foot of the sun'i surface. If the sun were of solid coal and produced its own heat by combustion, it would bum out in 6000 years. Of this enormous outflow of heat the earth receives only nvnbnw ^* *'*'® expressed the power of even this small frac- Uoiifof ihe sun's heal in terms of the ice it would melt daily. If we compute how much coal it would require to melt the same amount, and then further calculate how much work this coal would do, we Shan find that the sun sends to the earth an amount of heat which is equivalent to one horse-power continuously acting for every 80 square feet of the earth's surface. Most of this is expended in main- taining the earth's temperature; but a small portion, about -i^, is stored away by animals and vegetables, and this slight fraction it the souroe upon which the human race depends. If this were with- drawn the race would perish. Of the total amount of lient rndiated by the sun the earth receives 6at an imfgniflcnnt share. The ruii is capable of heating the oitlre •urface of a sphere whose rnilius is the earth's mean distance t6 the ■I.: V' d06 A8TR0N0MT. nine degree that the earth is now heated. The surface of such a sphere Is 2,170,000,000 times greater than tlie angular dimensions of the earth as seen from tlic sun, and licnce the earth receives less than one two-billioDth part of tlie soliir radiation. The rest of the solar rays are, so far as we know, lost in space. lelar Temperature.— From tiic amount of heat actually radiated by the sun, attempts liave been made to determine the actual tempera- ture of tiie solar surface. The estimates reached by various authori- ties differ widely, as the laws which govern the absorption within the solar cnvelopo are almost unknown. Some such law of absorp- tion has to be supposed in any such investigation, and the estimates have differed widely according to the adapted law. Skcchi estimates this temperature at about 6,100,000° C. Other estimates are far lower, but, according to nil sound pliilosophy, the temperature must fur exceed any terrestrial temperature. There can be no doubt that if the temperature of the earth's surface were sud- denly raised to that of the sun, no single chemical element would re- main in its present condition. The most refractory materials would be at once volatilized. We may concentrate the heat received upon several square feet (the surface of a huge burning-lens or mirror, for instance), examine its effects at the focus, and, making allowance for the condensation by the lens, see what is the minimum possible temperature of the •un. The temperature at the focus of the lens cannot be higher than that of the source of heat in the sun ; we can only concentrate the heat received on the surface of the lens to one point and examine its effects. If a lens three feet in diameter be used, the most refractory materials, aa fire-clay, platinum, the diamond, are at once melted or ▼olatilized. The effect of the lens is plainly the same as if the earth were brought closer to llie sun. in the ratio of the diameter of the focal image to that of the lens. In the case of the ku' of three feet, allowing for the absorption, etc.. this distance is yet greater than that of the moon from the earth, so that it appears that any comet or planet so close as this to the sun, if composed of materials similar to those in the earth, must be vaporized. UiHt^ BW-fPOn ASB Faodxjil A very cursory examination of the sun's disk with a small tcle- ■cope will generally abow one or more dark spots upon the, photo- ■friiere. These are of various sizes, from minute black dots 1' of 3' in dhuneter (1000 kilometres or less) to large spoto several minutes of are in extent fi^n'^'-^' '-^^■^■•*'"^ 'ho surface of such a ngulnr diiiiciisious of irth receives less than riie rest of the solar ; actually radiated by I the actual temperu- d by various authori- lie absorption vithiu I such law of absorp- >n, and the estimates aw. e.lOO.OOO' C. Other )uud philosophy, the ipcraturo. There can h's surface were sud- cal element would re- :tory materials would n several square feet for instaucc), examine for the condensation e tcmperuturo of the cannot be higher than only concentrate the point and examine its 1, the most refractory are at once melted or « same as if the earth )f the diameter of the theleii' of three feet, e is yet greater than ears that any comet or of materials similar to isk with a small tcle- ipots upon the.piioto* lite blaciL dots 1' Of 2' spots several minutes THE 8UN. 207 Solar spots generally have a dark central nu^V>» i* o( course perpendi^qlKr to it. fore •pproxinmtely chiefly confined to >ni about 10° to SS' ■ region ipota «re arc much more rare witli tlie apols, but mottliugB of iig^t live with the surfaoe leir motiona must be i shows the appear- lenting the apparent at times of the year. >r on the earth, seem lerver mqst be in the kths are ellipses, and ses are most oblique, be plane of the solar the ecliptic is abotit di^qhtr to it. me" ill THB 8Uy. 900 Vatiir* of til* Spott.— The sun-spota are really depres ■ions in the photosphere, as was first pointed out by Ax- DRBW Wilson of Glasgow in 1774. When a spot is seen at the edge of the diik, it appears as a notch in the limb, and is FM. M.— AfTAMnr Path or Solar Spot at DimasKT SsAaoHS. dliptioal in shape. As the rotation carries it farther and farther on to the disk, it becomes more and more nearly oirci'lar in shape, and aftor passing the centre of the disk , the i^pearanoes take place in reverse order. These obaerratioiis were ex|dained by Wilsoh, and more fully bj Sir WnutM ffwicwp.. b^ suppoeinK t)M w^ to coaslrt 9f aa fah 310 ABTRONOMT. terior dark cool mMi, surrounded by two layers of clouds. The outer layer, which forma the risible pbotosplicre, waa supposed ex- tremely brilliant. Tlie inuer layer, which could not be seen except when a cavity existed in the photosphere, was supposed to lie dark. The appearance of the edges of a spot, which has been duscrihed as the penumbra, waa supposed to arise from tliose dark clouds. Tiie spots themselves are, according to this view, nothing but openings through both of the atmospheres, tiie nueletu of the spot being simply the black surface of the inner sphere of the sun itself. Ttaia theory. Fig. 02, accounu for the facta aa they were knoi^n n*. aa.— ArPCAaAMOc or a Stct xbab nm Lma a»d imAB ibb Caaraa or thb Sini. to HsRSOBaL. But when it is confronted with the questions of the cause of tlie sun's heat and of the method by which this heat haa been maintained constant in amount for centuries, it breaks down completely. The conclusions of Wilsoh and Hbrschbl, that the spots are depressions in the sun's surface, are undoubted. But the existence of a cool central and solid nucleus to the sun is now known to be impoasible. The apparently black centres of the spota are so mostly by contrast If they were seen against a perfectly black background, they would appear very bright, as haa been proTed b^ photometric menauren. ^nd a cool solid naclem li«nfatl| IrtntfittWitiwarmnK rs of clouds. The I, waa Biippoaed ex- not be seen except ipposed to bo (hirk. 8 been described ub dark clouds. The tiling but opeuinga le spot being simply self, I they were known i AMDimiBTBB ;h0 questions of the irhich this heat hu les, it breaks down Ibrschbl, that the Ddoubted. But the to the sun is now centres of the spots against a perfectly right, as has been lUd nacleiis )i«n^tl| TBE BUN. 911 such an atmosphere as HEiiscnKi. sup^ iA would soon become gas- eous by the conduction and radiation of the heat of the photosphere. The supply of solar heat, which has been very nearly constant dur- ing the liistoric period, in a sun so constituted would haye sensibly diminished in a few hundred years. For ihese and other reasons the hypothesis of Hkrscbbl must be modified, sare as to the fact that the spots are really cavities in the photosphere. Hnmber and Periodieity of Solar Spots. — The number of Bolar spots which come into view raries from year to year. Although at first sight this might seem to be what we call a purely accidental circumstance, like the occurrence of cloudy and clear years on the earth, observations of sun- spots establish the fact that this number xatiea periodically. The periodicity of the spots will appear from the following sum- mary: From 1828 to 1881 the sun was without spots f>n only 1 day. In 1888 From 1888 to 1840 In 1848 From 1847 to 1851 In 1808 From 18S8 to 1881 In 1887 ISVdaya. 8 " 147 " 3 " 198 •• no day. 195 days. Every 11 years there is a minimum number of spots, and about 5 years after each minimum there is a maximum. If, instead of mere- ly counting the number of spots, measurements are made on solar photographs of the extent of tpotUdarea, the period comes out with greater distinctness. This periodicity of the area of the solar spots appears to be connected with magnetic phenomena on the earth's surface, and with the number of auroras visible. It has been sup- posed to be connected also with variations of temperature, of rain- fall, and with other meteorological phenomena such as the monsoons of the Indhm Ocean, etc. Tlio cause of this periodicity is as yet un- known. It probably lies within the sun itself, and is similar to the cause of the periodic action of a geyser. As the periodic variations of the spots correspond to variations of the magnetic needle on the earth, it appear* that there in a connection of an unknown natuis between the sun and the earth. 212 ABTRONOMT. \ , % t ': TBI Sxnr'i CnoMosPHixK avb Coioita. nraomraa of Tot»l leUpm.— The Ijcgiiinlng of n total iolor eclipse is marked simply by llio small black notch made in the luminous disk of the sun by the advancing edge or limb of the moon. Tills always occurs on the western half of the sun, as the moon moves from west to cast In lis orbit. An hour or more must elapse before ihe moon has advanced sufficiently far in its orbit to cover the sun's disk. During this time the disk of the sun is gradu- ally hidden until it becomes a thin crescent. The actual amount of the sun's light may bo diminished to two thirds or three fourths of Its ordinary amount without its Ixjlng •trlkinfrly perceptible to the eye. What is first noticed is the change which takes place in the color of the surrounding landscape, which begins to wear a ruddy aspect. This grows more and ir.ore pro. nounced, and gives to the adjacent country that weird effect which lends so much to tin impresslveness of a total eclipse. The reawm for the change of color is simple. We have already said that the Bun'a atmosphere aUo:bs a large proportion of the bluer rays, and aa this absorption Is dcTiendcnt on the thickness of the solar atmosphere through which the rays must pass, it. Is plain that Just before tlio sun is totally covered the rays by which we sec it will be redder than ordinary sunlight, as they are those which come from points near the sun's limb, where they have to pasa through the greateat thick- ness of the sun's atmosphere. The color of the light becomes more and more lurid up to the mo- m-iXki when the sun has nearly disappeared. If the spectetor is upon th 1 ?np of a high mountain, he can then begin to see the moon's ■hrdow rushing toward him at the rate of a kilometre in about a aecond. Jtist as thp shadow reaches him there ifc a sudden increase of darkness; the brighter atars begin to shine in ^e darli lurid sky, the thin crescent of the sun breaks up into small points at dote of lijrht, which suddenly disappear, and the moon itself, an intensely black ball, appears to hung isolated in the heavens. An insUint afterward the corona is ^:een surrounding thfi black di!>k of the moon with a soft effulgence quite different from any other light known to us. Near Ihe moon's limb It is intensely bright, and to the naked eye uniform in structure; V or IC from the limb this Inner corona has a boundary more or less deflned.and from this extend streamers and wlng8 of fainter and more nebnioaa light These are of variona shapes, sizes, and brilliancy. No two aolw ^paea ^et qbsepre^ hay^ been ^\\}ffi in tUia respect, It THE SUN. 21B DBOVA. of K total folar )tch made in the ;e or limb of the of the 8UD, ns the )ur or more must far in its orbit to ! the sun is gradu- liminislicd to two witliout its Iwing ticcd is llie change landscape, wliich ire and iriore pro. vcird effect which ipse. The reason iady said that the bluer rays, and u B solar atmosphere just before the sun rill be redder than from points near the greatest thick- urid up to the mo- 9 spectator is upon to see the moon's smetre in about a a sudden increase le darli lurid sky, points or dots of Itself, an intensely s. )iinding thn black llfferent from any is intensely bright, W from tlif limb ned.and from this re nebulous light ;y. No two eoUHr These appearances, though clinngpable, do not change the moon's shadow requires to pass from Vancouver's Island to Texas, for example, which is some fifty minutes. Superposed upon tliese wings may lie seen (sometimes with the naked eye) tiie red flames or protulierances which were flrst discov- ered during a solnr eclipse. These need not be more closely de- scribed here, OS they can now be studied at any time by aid of the spectroscope. The total phase lasts for a few minutes (never more than six or sevenX «>d during tliis time, as tiie eye becomes more and more accustomed lo the faint light, the outer corona is seen to stretch further and further away from the sun's limb. At the erllpso of 1878, July 20th, it was seen to extend more than 6° (about 9,000,000 miles) from the sun's limb. Just before the end of the total phase there it a sudden increase of the brightness of the sky, due to the increased illumination of the earth's atmosphere near the observer, and in a moment more the sun's rays are agnin visible, seemingly as briglit as ever. From the end of totality till tlie last contact tha phenomena of the flrst half of the eclipse are repeated in inverse order. Telaseopie Aapeet «f the Oereaa.— Sudi are the appearances to the naked eye. The corona, as seen through a telescope, is, however, of a very compUoated structure. The inner corona is usually com- posed of bright strisB or fllaments separated by darker bonds, and some of these latter are sometimes seen to lie almost totally black. The appearances are extremely irregular, but they are often as if the inner corona were made u|t of brushes of light on a darker back- ground. The corona and red prominences are sohtr appendages. It was formerly doubtful whether the corona was an atmosphere belonging to the sun or to the m»n. At the eclipse of 1860 it was proved by measurements that the red prominences belonged to the sun and not to the moon, since the moon gradually covered them by its motion, they remaining attached to the sun. The corona has also since bivn shown to lie a solar appendage. Oasaeas Vatwe ef the Prealawees.— The eclipse of 1868 (July) was total in India, and was observed by many skilled astronomers. A discovery of M. JAifSSBN's will make this eclipse forever memora- ble. He was providc«l with a spectroscope, and by It observed the prominences. One prominence in particular was of vast size, and when the spectroscope was turned upon it, its spectrum was discon* tinuone, showing the bright lines of hydrogen gas. The brightness of the spectrum was so marked that JAnanni deter. miB#d to keep his spectroccope dsed upon it even after the rcappear> -SBW I Jje di4 ASTRONOMr. ri«. •S.-Svu'i QoKoaA PVBiM nu Ecum ov Jolt M, Itn, Am*' ■ t Swt M, 1SI9. m^» . imj" ^m it TBK 8VK. ^ib fence of (unliglit, to lee hoir long It could be followed. It wrh found that Us ■pectruin could ittill be seen ufter the return of complete lun- linht; and not only on that day, but on Kubaequent dayi, ainilhir phenoniuna could be obaerved. One great diftlculty wait conquered in an Inttant. The red flames which formerly were only to be seen for a few moments during the comparatively ruro occurrences of total eclipses, and whose obserra- tion demanded long and expensive Journeys to distant parts of the world, could now be regularly observed with all the facilities offered by a fixed observatory. This great step In advance was independently made by Mr. Locx- Tm. 64.— Vowa or tsi Soua Paoimnnoia as i TSR, and his discovery was derived from pure theory, unaided by the eclipse itself. By this method the prominences have been carefully mapped day by day all around the sun, and it has been proved that around this body there is a vast atmosphere of hydrogen gas— the ehnmo^then or aierra. From out of this the prominences are pro- jected sometimes to heights of 100,000 kilometres or more. It will be necessary to recall the miln facts of observation which are fundamental in the use of the sjMctroKOope. When a brilliant point is examined with the spectroscojjii;, it is spread out by the prism into a band— the spectrum. Using two prisms, the spectrum be* longer, but the light of the surface, being spiMQ over a 216 AaiRONOMT. Ill greater area, is enfeebled. Three, four, or mora prisms spread out the spectrum proportionally more. If the spectrum is of an incan- descent solid or liquid, it is always continuous, and it can l)e en- feebled to any degree; so that any part of it can be made as feeble as desired. This method is precisely similar in principle to the use of the tele- scope in viewing stars in the daytime. The telescope lessens the brilliancy of the sky, while the disk of the star is kept of the same intensity, as it is a point in itself. It thus becomes visible. The spectrum of a glowing gas will consist of a definite number of lines, say three— A, B, C. for example. Now suppose the spectrum of this gas to be superposed on the continuous spectrum of the sun; by using only one prism, the solar spectrum is short and brilliant, and every part of it may be more brilliant than the line spectrum of the gas. By increasing the dispersion (the number of prisms), the solar spec- trum is proportionately enfeebled. If the ratio of the light of the bodies themselves, the sun and the gas, is not too great, the continu- ous spectrum may lie so enfecbletl that the line spectrum will be visible when superposed upon it, and the spectrum of the gas may tlien be seen even in the prvsence of true sunlight. Such was the process imnginod and successfully carried out by Mr. Lockyer, and such is in essence the method of vivwing the promiuences to-day adopted r Tki Gnroaal IpMtnw.— In 1860 (August 7th) a total solar eclipse was visible in the United Stales. It was probably observed by more astronomers than any prececrutnre of the sun cannot be kept up by the mere combustion of its materials. If the sun were solid carbon, and if a constant and adequate supply of oxygen were also present, it has been shown that, at the present rate of radiation, the heat arising from the com- bustion of the mass would not last more thau 6000 years. An explnnntion of the solnr heat and light has tieen sufrgestfd, which (lepciids u|M>n the fact tliut great imiouiils of lieiit ami light are procluftKi by the ollision uf two. rnpiUly moving lipuvy iNulies, or even by the pasmge nf a heavy lto*l> like a mctiorile tlirougb Die earth's atmosphere. In fact, if wc had a certain mass availaltle with which to produce beat in the sun, and if this mass were of the best poasible materials to produce heal by burning, it cua be Khown that, by burning it at the surface of the sun, we should pntduce vastly less heat than if we simply allowed it to fall into the sun. In the iMt caae, if it fell from the earth's distance, It would give 0000 times man beat by its fall than by its burning. : ne teait velocity with which a body from space could fall upon ^ sub's surfMe it In the neighborhood of .SM nilee in a leoond of JSSSWB igi«a^^ai*«Sijii(«!^fe,-ia» <>SiyMM&;; 218 ASTRONOMY. 'I •• I;! uSSi time, snd the Telocity may be as great as 850 miles. The meteoric theory of solar heat is in effect that the heat of the sun is kept up by the impact of meteors upon its surface. No doubt immense numbers of meteorites fall into the sun daily and hourly, and to each one of them a certain considerable portion of heat is due. It is found that, to account for the present amount of radiation, meteorites equal In mass to the whole earth would have to fall into the sun every century. It is extremely improbable that a mass one tenth as large as this is added to the sun in this way per century, if for no other reason because the earth itself and every planet would receive far more than its present share of meteorites, and would become quite hot from this cause alone. There is still another way of accounting for the tun's constant supply of energy, and this has the advantage of appealing to no cause outside of the sun itself in the explanation. It is by supposing the heat, light, etc., to be generated by a constant and gradual contrac- tion of the dimensions of the solar sphere. As the globe cools by radiation into space, it must contract. In so contracting its ultimate constituent parts are drawn nearer together by their mutuhl attrac- tion, whereby a form of energy is developed which can be trans- formed into heat, light, electricity, or other physical forces. This theory is in complete agreement with the known laws of force. It also admits of precise comparison with facts, since the laws of heat enable us, from the known amount of heat radiated, to infer the exact amount of contraction in inches which the linear dimensions of the sun must undergo in order tliat this supply of heat may be kept unchanged, as it is practically found to be. With the present size of the sun, it is found that it is only necessary to sup- pose that its diameter is diminishing at the rate of about 220 feet per year, or 4 miles per century, in order that the supply of heat radiated shall be constant. It is plain that such a change as this may be taking place, since we possess no instruments suffleiently delicate to have detected a change of even ten times this amount since the in- vention of the telescope. It may seem a paradoxical conclusion that the cooling of a body may cause it to become hotter. This indeed is true only when we suppose the interior to be gaseous, and not solid or liquid. It it, however, proved by theory that this law holds for gaseous i We cannot say whisther the sun has yet begun to liqtief| in his interior parts^and hence it is impossible to predict, at present the duration of his constant radii^on. Theorjr 3W!; I TUB SUN, 819 les. The meteorie » sun ia kept up by into the sun daily insiderable portion present amount of u-th would have to improbable that a un in this way per h itself and every bare of meteorites, the sun's constant pealing to no cause B by supposing the id gradual contrac- the globe cools by racting its ultimate lieir mutual attrac- lich can be trans* »1 forces, le known laws of Ih facts, since the if beat radiated, to I which the linear this supply of heat d to be. With the Y necessary to sup- about 220 feet per )ly of heat radiated ge as this may be Iciently delicate to [ount since the in- cooling of a body true only when we I or liquid. It it, gaseous masses. ' twgnn to liqtie^; «8ible to predict ii^on. Thaorjf shows us that after about 5,000,000 years, the stin radiat- ing heat as at present, and still remaining gaseous, will be reduced to one half of his present yolnme. It seems prob* able that somewhere about this time the solidification will hare began, and it is roughly estimated, from this line of argument, that the present conditions of heat radiation cannot last greatly over 10,000,000 years. The future of the sun (and hence of the earth) cannot, as y)Q see, be traced with great exactitude. The past can be more closely followed if we assume (which is tolerably safe) that the sun up to the present has been a gaseous and not a solid or liquid mass. Four hundred years ago, then, the snn was about 16 miles greater in diameter than now; and if we suppose this process of contraction to have regu- larly gone on at the same rate (an uncertain supposition), we can fix a date when the sun filled any given space, out even to the orbit of Neptune; that is, to the time when the solar system consisted of but one body, and that a gas- eous or nebulous one. It will subsequently be seen that the ideas here reached d posteriori have a striking analogy to the h priori ideas of Kant and La Place. It is not to be taken for granted, however, that the amount of heat to be derived from the contraction of the sun's dimensions is infinite, no matter how large the prim- itive dimensions may have been. A body fallin^^ from any distance to the snn can only have a certain finiie velocity depending on this distance and the mass of the sun itself, which, even if the fall be from an infinite distance, cannot exceed, for the sun, 350 miles per second. In the same way the amount of heat generated by the contraction of the sun's Tolnme from any size to any other is finite and not infinite. MO ABTRONOMY. !:• It has been shown that if the sun has always been radi> ating heat at its present rate, and if it had originally filled all space, it has required 18,000,000 years tu contract to its present volume. In other words, assuming the present rate of nuliution, and taking the most faTorable case, the age of the sun docs not exceed 18,000,000 years. The earth is, of course, less aged. The supposition lying at the base of this estimate is that the radiation of the sun has been constant thronghont the whole period. This u quite unlikely, and any changes in this datum affect greatly the final number of years wiiich wo have assigned. While this number may be greatly in error, yet the method of obtaining it seems, in the present state of science, to be satisfactory, and the main conclusion remains that the {Nist of the sun is finite, and that in all probability its fntnro is a limited one. The exact number of centuries that it is to last are of no moment even were the data at hand to obtain them: the essential ]i.-)int is that, so far as we can see, the sun, and incidentally the solar system, has a finite past and a limited fntnro, and that, like other natural objects, it passes through its regular stages of birth, vigor, decay, and death, in one order of progress. mmmm •«mJ-; .. i tn I ilways been radU I originally filled to contract to its ling the present ▼orablo case, the KK) years. Tlio osition lying at Ation of the sun period. This m um affect greatly ssigncd. While i the method of >f science, to be jns that the ]>a8t ility its fntnro is irics that it is to it hand to obtain I we can see, the a finite past and tnral objects, it rigor, decay, and OHAPTER in. THE INFERIOR PLANETB. Monovi An AfPionL Trb Infflrio planets are those whose orbits lie between the sun and the orbit of the earth. Commencing with the more distant ones, they comprise Vtnu* and Mercury. The real and apparent moiiuns of these planets have already been briefly described in Part I., Chapter V. It will be rememliered that, in accordance with Keflkb's third law, their periods of revolution around the sun are less tlun that of the earth. Consequently they OTertalte the latter lietween suocewive inferior conjunctions. The interval between these conjunctions is about four months in the case of Mer- cury, and between nineteen and twenty mouths in (hat of Yentu. At the end of this period each repeats the same series of motions relative to the sun. What these motion* are can be rendily seen by studying Fig. 95. In the first place, suppose llie earth at any pioint, S, of iu orliit, and if we draw a line. E L at EM, from E. tangent to the orUt of either of tliese planets, it is evident that the angle which this line malies with that drawn to the sun is the greatest elongation of the planet from the sun. The orbits being eccentric, thk elongaUim varies with the position of the earth. In the case of JTsrswy it rsages from 16* to 86*, while ia the esse of Vetuu, V- oiMt of whicfa is nearly circular, it varies very little from 45*. TbjS'O phaets, tiwrefote, seem to have an cscUladog motion, first swiofiBf Ito. a& ^appi^iFiiw 9M A8TROK0M7. Wta. M.— Appamsiit MAamrrou am TMM DuK or MiaoiniT. toward the east of the sun, and then toward the west of it, as already explained. Since, owing to the annual revolution of the earth, the sun has a constant eastward motion among the stars, these planets must haTe, on tlie whole, a corresponding though intermittent motion in the same direction. Therefore the ancient astronomers supposed their period of revolution to be one year, the same as that of the sun. If, agahi, we draw a line ESC from tlie earth through the sun, the point /, in which this line cute tiie orbit of the planet, or the point of inferior conjunction, will be the least distance of the planet from the earth, while the second point C, or the point of superior conjuiiclion, on the opposite side of the sun, will be the greatest distance. Owing to tlie difference of these distances the apparent magnitude of these planets, as seen from iho earth, is subject to great variations. Fig. 66 shows thcMS variations in the ease of Mnvurjf, A representing its apparent magnitude when at its greatest distance, B when nt its mean distance, and C when at ito least distance. In the cose of Venut (Fig. 67) the variations are much greater than in that of Mercury, the greatest distence. 1.73, being more than six times the least distance, which is only 0.28. Tiie variations jf apparent magnitude are therefore great in the same proportion. In thus representing the apparent angular magnitude of these planets, we suppose their whole dislcs to be visible, as they would be if they shone by their own light But since they can be seen only by the reflected light of the sun, only those portions of the disk can be seen which are at the same time visible from the sun and from the earth. A very little consideration will show that the proportion of the dbk which can be seen constently diminishes as the planet ap- proaches the earth, and looks larger. When the planet is at ita greatest distance, or in superior conjunction (0, Fig. 65), lu whole illuminated hemisphere can be seen from the earth. As it moves around and approaches the earth, the illuminated hemisphere is gradually turned from us. At the point of greatest elongation, M or L, one half the hemisphere is visible, and the planet has the form of the moon at first or:second quarter^ At it «l>proachea inferior conjunction, the apparent visible disk aasumea the form of a crescent, which becomes thinner and thinner as tba |danet approMhea4lie aun. westof it, M already Ion of the earth, the I stars, these planets I intermittent notion itronomers supposed same as that of the through the sun, the planet, or the point e of the planet from the second point C, iperior conjunction, lide of the sun, will distance. Owing to these distances the ido of these planets, earth, is subject to be«) variations in the lagnitude when at its I, and G when at its I variations are much distance, 1.73, being \\ is only 0.28. Tlie e great in the same magnitude of these l>lc, as they would be y can be seen only by ns of the disk can Im le sun and from the lat the proportion of lies as Uie planet ap- i superior conjunction Ban be seen from the earth, the illuminated he point of greateat ) is visible, and the cond quarter As it visible disk assumes r and thinner at the THK INFERIOR PLANETS. Fig 68 shows the apparent disk of Jforeufjr at various times during iU synodic revolution. The planet will appear brightest when this dUk lins the greatest surface. This occurs about half way between greatest elongation and inferior conjunction. In consequence of the changes in the brilliancy of these plancU produced by the variations of distance, and those produced by the Fio. ar.-AMPiMWT MMimvDn of ma Dme o» Vamm. variations in the proportion of illuirinated disk virible from the earth, partially compensating each oUier, their actual brilliancyto not subject to such great variations as might have been expectMl. As a genend rule, Mercury shines with a light exceeding that of a ■Ur of the first magnitude. But owing to iU proximity to the sun, • I ) • « ( ( Ito. M.— Amuuiraa or Maaoaav at Dvnanr FonRa or ns Oaarr. It can never be seen by the naked eye except in the west a short time after sunset, and In tiie east a little before sunrise. It is then of necessity near the horixon. and therefore does not seem so bright aa If It were at a greater altitude. In our latitudes we mi^t almoat lav that It is never ▼UUo except la the monilDf or evenlog twilight 994 ASTRONOMT. i\ On the other hand, the plnnet Venua is, next to the inn and moon, the moat brilliant object in tlie heavens. It is so much brijrhter than any fixed star that there can seldom be any difllculiy in identi- fying it. The unprac(i:*ed observer might under some oircumatances find a difficulty in distinguishing between Venut and JupiUr. but the different motions of tiie two pluneU will enable him to distin- guish tliem if they are watched from night to night during several weeiis. Atmoiphiu um Rotatiov or Mibovit. The various phases of Mercury, as dependent upon iu rarious positions rohttive to the sun, liuve already been shown. If the planet were an opnque sphere, witliout inequalities and witiiout an atmos- phere, the apparent disk would always be bounded by a circle on one side and an ellipse on the other, as represented in the flgtire. Whether any variation from this simple and perfect form has ever been detected is an open question, the balance of evidence being very strongly in the- negative. Since no spots are visible upon It. it would follow that unless variations of form due to inequalities on its sur- face, such as mountains, can bo dcti-cted, it ia Impossible to deter- mine whether tlie planet rotates on its axis. We may reganl it as doubtful whether any evidence of nn atmos- phcrc of Mercury lias been obtained, and it is certain that we know nothing definite respecting its physical constitution. ATMosPHni An BoTAnov ov Ymu. As Venu$ somvlinies comes nearer the earth than any other pri- mary planet, astronomers have examined its snrface witli great at- tention ever since tlie invention of thct telescope. But no concliisive evidence respecting tlie rotation of (he piniat and no proof of any changes or any inequalities on its furface have ever been obtained. Atmoiphare ef Taans.— The evidence of nn atmoepliere of V»mv$ is licrliaps more eonclusivo than in tlic case of any ntlier planet. When Vetiua is observed very near its inferior oonjnnction, and when it therefore prescnto the view of a very thin crcsrent, it is found that this crescent extends oyer moro than |80*. This wouhi lie evidently inipoMibie unless the sun illuminated more than ooff half the planet. We therefore conclude that Venm$ hlia an Mmoa- phere whicii exercises so powerful a refraction upon the liglit of the sun that the latter illuminates several degrees more than one half the globe. A phenomenon whicii muf>t be attributed to the same cause b»» s«)f epal timea b^n observed during trMi«im 9f f^TlifA Pnrip| ■^'«llili»IIIMWtllii|«MHW1lltre than one half the 9d to the same cause 9ff«»Hf«. Pnrip| I TUB iNrwrnon PiANSTa. tiM tnoiit of Decembe r 8th, 1874, most of the observers who enjoyrd % line steady atmosphere saw that when Vtnu$ was partially pro- jected on the sun, the outllfie of that part of its disk outside the sun could be distinguished by a delicate line of light. From these several obser^ationa It would seem that the refractive power of the atmosphere of Fmim Is greater than that of the earth. Teabirs or MftBovBT An Vivm. When JKMViHy or Ymut peases between the earth and sun, so as to appear projeelad on the sun's disk, the phenomenon Is called a trmntU. If these planets moved around the ann in the plane of the ecliptic, it la evident that there would be a transit at every inferior conjunction. The longitude of the deacending node of Mmnmrjf at the preaent time is 227°, and therefore that of the aareading node 47'. Tiie earth has these longitudes on May 7lb and November 9lh. Since a transit can occur only within a few degrees of a node, M«reur}f cau transit oitly within a few days of tliese cpocha. The longitude of tlie descending node of Vtnui is now about 808^ and therefore that of the aMMnding node is 76*. The earth has theat longitudes on June 8th and Decismber 7th of each year. Transits of Venut ean therefore oeeur only within two or three daya of these I ef Traasits sf Msreiry.— The following table shows the dates of occurrence of tranaits of Mtreury during the present cen- tury. Tliey are separated into May transiu, which occur near tlie descending node, and November once, which occur near the ascend- inir node. November trannits are the most numeroua, because JUratry is then nearer the sun, and the transit limita are wider. 1798, May 8. 1802, Nov. 9. 1889, May 8. 1818. Nov. 11. }84t. May 8. 1888, Nov. S. 18T8. May «. 1888. Nov. 7. 1881, May 9. 1848, Nov. 10. 1881. Nov. 18. 1808, Nov. 5. 1881, Not. 7. 18B4, Nov. 10. s( Traaafts af TesM.— For many oenturiea paat and to wmx »w»»l«» of r«»*M ocdir in » cycle mor* ^xnvi *•» rtoie of ■imii»mm; I S36 ABTRONOMT. N ?:; d Mercury. It happens that F«n«« makes 18 reTolutions sround the ■un ia nearly the aame time that (he earth makes 8 revolutions; that is, in eight years. During this period there will be S inferior con< junctions of Venut, because the latter has trade 5 revolutions more than the earth. Consequently, if we wait sight years from an inferior conjunction of Venu$, we shall, at the end of tliat time, have another Inferior conjunction, the fifth in regular order, at nearly the same point of the two orbits. It will, therefore, occur at the same time of tiie year, and in nearly the same position relative to the node of Venut. After a pair of transits 8 years apart, an interval of over 100 years must elapse before the occurrence of another pair as is shown in the following tabic. The dates and intervals of the transiU for three cycles nearest to the present time are as follows: Interrals. 1518, June 3. 1761, June 5. 3004, June 8 8 years. 1526, June 1. 1681, Dec. 7. 168», Dec. 4. 1760, Junes. 1874, Dec. 0. 1883, Dec. 6. !»>13, June 6. 105i 2117, Dec. 11. 8 31S6, Dec. 8 131i SVPrOOD IXTBAMBBOinUAL PlAHlTI. Some astronomers are of opinion tliat there is a small planet or a group of planets revolving around the sun inside th-.. orbit of Mercury. To this supposed planet the name Vvkan has Ix^n given; but astronomers generally discredit the existence of any such planet of considerable size. The evidence in favor of the existence of such planets may be divided into three classes, as follows, whiub will be considered in their order: (1) A motion of the perihelion of the orbit of Mercury, supposed to be due to the attraction of such a planet or group of planets. CD Transits of dark bodieti acrqss the disk of the sun which have Inen supposed to be seen by varans observers during the past cen- tury. (8) TIm obeervation of certain unidentified objects by Professor Watson and Mr. Lbwib Swirr during the total eclipse of the sun, July 28tb, 1878. (1) In 1858 Lb Verribb made a jareful collection of all the obser- vations on the transits of Mercury which had been recorded since the invention of the telescope. The result of that investigation waa BJtWMIOTMWiiil 'olutioDi around the s 8 revolutions; that III be 5 inferior con< e 6 revolutioni more ears from an inferior It time, have another at nearly the same iur at the same time ttive to the node of val of over 100 years >lr as is shown in the Ihe transits for three neS me 9. ic. 11. X.B Intwrrals, 8 years. lOIH " 8 " laii " I is a small planet or inside th-. orbit of \tkan has Ix^en given; » of any such planet luch planets may be viU be considered in Df Mermry, supposed roup of planets. f the sun which have I during the past cen- objects by Professor tal eclipse of the sun, etion of all the obser- •n recorded since the tat investigation waa ■T-» THE INFERIOR PLANETS. 227 that the observed times of transit could not bo reconciled with the calculated motion of tho planet, as duo to the gravitation of the other bodieii of the solar system. He found, however, that if, in addition to the changes of the orbit due to the attraction of the known plauets, he supposed a motion of the perihelion amounting to 80 ' ill a century, the observations could all be satisfied. Such a motion might be produced by the attraction of an unlinown planet inside the orbit of Mercury. Since, however, a single planet, in order to produce this effect, would have to be of considerable size, and since no such object had ever been observed during a total eclipse of the sun, he concluded that there was prolwbly a group of planets much too small to be separately distinguislied. (3) It is to be noted that if such planeU existed they would fre- quently pass over the disk of the sun. During the past fifty years the sun has been observed almost every day with the greatest assiduity by eminent observers, armed with powerful instruments, who have made the study of the sun's surface and spots the principal work of their lives. None of these observers has ever recorded the transit of an unknown planet. This evidence, though negative in form, is, under the circumstances, conclusive against tlie existence of such a planet of such magnit-ide as to be visible in transit with ordinary instruments. (8) The observations of Professor Watbom during the total eclipse above mentioned seem to afford the strongest evidence yet obtained in favor of the real existence of the planet His mode of proceeding was briefly this: Sweeping to the west of the sun during the eclipse, he saw two objects in positions where, supposing the pointing of bis telescope accurately known, no fixed star existed. There is, how. ever, a pair of known stars, one of which is about a degree distant from one of the unknown objects, nnd tlie other about the same distance and direction from the second. It is probable that Professor Watsoh 'a supposed pUnots were this pair of stan. Since the above was written Prof. Watboh'b observations have been repeated under exceptionally favorable circumstances at the eclipse of May 6. 1888, and no trace of his supposed planets was seen, while much smaller stars were observed. ii i I'l I i :i' / aiiiiL CHAPrER IV. THE MOON. Whrn it became clearly understood that the earth and moon were to be regarded as bodies of one class, and thut the old notion of an impassable gulf between the character of bodies celestial and bodies terrestrial was unfounded, the question whether tlio moon was like the earth in all its details became one of great interest. The point of most especial interest was whether the moon could, like the earth, *je peopled by intelligent inhabitants. Accordingly, when the tcicscope was iuvcnted by Galileo, one of the first objects examined was the moon. With every im- provement of the instrument the examination became more thorough, so that at present the topography of the moon is much better known than that of the State of Arkansas, for example. With every improvement in the means of research, it has become more and more evident that the surface of the moon is totally unlike that of our earth. There are no oceans, seaa, rivers, air, clouds, or vapor. We can hardly suppose that anime* '^r vegetable life exists under such cir- cumstances, the funu«.mental ooqditions of raoh existence on our earth being entirely wanting, We might almoit ai well suppose a piece of granite or lay» to be the abode of life OS the surface of the moon. The l«n|^h of one mile on the moon would, m wen from iiNiwwiiaiwrtfMtiiW^^ -rn at the earth and le clan, and that een the character was unfounded, he earth in all ita he point of most 1 could, like the ts. Accordingly, JLEo, one of the With every im- mination became opography of the b of the State of ns of research, it the surface of the b. There are no We can hardly ts under such oir< of inoh existence 9 might almost as o be the abode of )nld, M wen froni TSB MOON. 339 the earth, subtend an angle of about 1* of arc. More exactly, the angle subtended would range between 0'.8 and O'.O, juscording to the varying distance of the moon. In order that an object may be plainly vIsIIjIo to the naked eye, it must subtond an angle of nearly 1'. Consequently a magnifying power of 60 is required to render a round object one mile in diameter on the surface of the moon plainly visible. Starting from this fact, we may readily form the following u.jie, showing the diameters of the smallest objects that can be seen with different magnifying powers, always assuming that vision* with these powers is perfect: Power 60; diameter of object 1 mile. Power IfiO; diuneter 2000 feet Power 800; diameter 600 feet ■ Power tOOO; diemeter 8U0 feet. Power 9000; diameter 100 feet If telescopic power could he increased indefinitely, there would of course be no limit to the minuteness of an object visible on the moon's surface. But the necessary imper- fections of all telescopes are such that only in extraordinary oases can anything be gained by increasing the magnifying power beyond 1000. The influence of warm and cold cur- rents in our atmosphere will forever prevent the advan- tageous use of high magnifying powers. After a certain limit we see nothing more by increasing the power, vision becoming indistinct in proportion as the fower is increased. It is hardly likely that an object less than 600 feet in extent can ever be seen on the moon by any telescope whatever, unless it becomes possible to mount the instrument above the atmosphere of the earth. It is therafore only the great Itatures on the rarfaoe of the moon, and not the miiint« ones, which can be nwde out with the telescope. ■ .■■it^ii^l^ttKSff^sU0$S^\ i I 'I 980 ABTRONOMT. :5s fta. 691— Aanor or nn Mboii's SnurMB. OhMMUr «f tht Mem'i luliMa.— The moat atriking point of dif- ference between tlio earth and moon ia aeen in the total abaence frrai the latter of anything that loolu like an undulating aurfaea. No ■.■^^'iT?ilB«MMWii«WrtffllMii ■ 11 I 33d ABTRONOMT. light Mid HMt of tha Koon.— Many attempts have been made to mensiirc the ratio of the light of tlie full moon and that of the sun. Tlie rusults have been very discordant, but all have agreed in show- ing that the sun emits several hundred thousand times as mu6h light as the full moon. The last and most careful determination is that of ZOluibr, who finds the sun to be 618,000 times as bright as the full moon. Tiio moon must reflect the heat as .veil as the light of the sun, and must also radiate a small amount of its own heat. By collecting the moon's rays in the focus of one of his large reflecting telescopes, Lord RosBB was able to show that a certain amount of heat is actually received from the moon, and that this amount varies with the moon's phase, as it should do. As a general result of all his researches, it may l>e supposed that about six sevenths of the heat given out by the moon is radiated and one seventh reflected. Is there any Ghaage en the lufiMe ef the Moon 1 — When the sur- face of the moon was first found to be covered by craters having the appearance of vdlcanoes at the surface of the earth, it was very naturally thought that these supposed volcanoes might be still in activity, and exhibit themselves to our telescopes by their flames. Not the slightest sound evidence of any incandescent eruption at the moon's surface has been found, however. Several instances of supposed changes of shape '^' 'catvres on the moon's surface have been described in recent time . The question whether these changes are proveu ' n which the opinions of aalronomers differ. Tlie difficulty c ; ',i ag a cer- tain conclusion arises from the fact that each feb<.u have been made to md tliat of the sun. laye agreed in show- I times as mu6h light termination is that of as bright as the full light of the sun, and t. By collecting the !ting telescopes, Lord at of heat is actually tries with the moon's all his researches, it iieat eiven out by the ion 1 — When the sur- }y craters having the 3 earth, it was very «8 might be still in ipcs by their flames, scent eruption at the pe '!' 'catwres on the ne . Dveu ' n which ty t ' - '., og a cer- li feb<.ume regard the appa- only to differences in 'im^ CHAPTER V. THE PLANET MARS. Beiobiftiov OV THB Flahxt. Mara is the next planet beyond the earth in the order of distance from the sun, being about half as far again as the earth. It has a decided red color, by which it may bo readily distinguished from all the other planets. Owing to the considerable eccentricity of its orbit, its distance, both from the snn and from the earth, varies in a larger propor- tion than does that of the other outer planets. At the most favorable oppositions, its distance from the earth is about 0.38 of the astronomical unit, or, in round numbers, 67,000,000 kilometres (35,000,000 of miles). This is greater than the least distance of Venut, but we can nevertheless obtain a better view of Mars under these circumstances than of Venus, becsuse when the latter is nearest to us its dark hemisphere is turned toward n>-, while in the case of Mars and of the outer planets tl o hemisphere turned toward us at opjwsition is fully illumi- nated by the sun. The period of revolution of Mars around the sun is a little less than two years, or, more exactly, 687 days. The snoceasive oppositions occur at intervals of two years and one or two months, the earth having made during this in- terval a little more than two revolutions around the sun, wd the planet Mars a little more than one. The dates of ■' s m immmH m mimmmmgmmi*m'- J f ■t i 984 ABTRONOMT. seTeral past '^nd f ature oppositions are shown in tho fol- lowing table: 1881 Decemlicr 26tb. 1884 January 81«t. 1886 March 6lh. Owing to the unequal motion of the planet, arising from the eccentricity of its orbit, the intenrals between suoces- siye oppositions vary from two years and one month to two years and two and a half months. Mara necessarily exhibits phases, but they are not lo well marked as in the case of Venus, because the hemisphere which it presents to the observer on the earth is always more than half illuminated. The greatest phase occurs when its direction is 90° from that of the sun, and even then six serenths of its disk is illuminated, like that of the moon, three days before or after full moon. The phases of Mar» were observed by Galileo in 1610. B«tatioa «r Han.— The early telescopic obeervers noticed that the disli of Man did not appear uniform in color and brightnesa, Imt lud a variegated aspect. In 1886 Dr. Robbht Hooks found that the marliings on Mart were permanent and moved around in such a way as to show that the planet revolved on its axis. The markings given in his drawings can be traced at tlie present day, and are made use of to determine the exact period of rotation of the planet. So well is the rotation fixed by them that the astronomer can now determine the exact number of times the planet has rotated on its axis since these old drawings were made. The period has been found to be 24^ 87* 98* '7, a result which appears certain to one or two tenths of a second.' It is therefore leas than an hour greater than the period of roUttion of the earth. •nfMS ef Xais. — ^Tbe most interesting result of these markings on Man is the proliabiUty that its surface is diversified by land and water, covered by an atmosphere, and altogether very shnilar to the surface of the earth. Some portions of the surface are of a dedded red odor, and thus give rise to the well-known llery aspect of the planet Other parts are of a greenish hue, and are therefore top* poaed to be seas. The most striking features are two brilliant white gftitiiMiii ihown in tho fol- iinltcr 26tb. lary 81st. Bh6lh. met, ariaing from i between saoces- ine month to two ay are not lo well I the hemisphere ) earth is always est phase occurs lie son, and even , like that of the K>n. The phases 0. ■en noticed that tha tnd brightncsi, but Hooks found that ed around in nicli a lit. The marliings resent day, and are Ation of tlie planet, istronomer can now I lias rotated on its le period baa been ra certain to one or lan an hour greater of these markinga ifsifled by land and Tery similar to the >oe are of a dedded I llery aspect of the 3 are therefore sup- I two brilliant white ■>"ti aw TBS PLANET MARS. 236 regions, one lying around e»ch pole of the planet. It has been sup- posed that this appearance is due to immense masses of snow and ice surrounding the poles. If this were so, it would indicate that the processes of evaporation, cloud formation, and condensation of ▼apor into rain and snow go on at ihe surface of Man as at the sur- face of the earth. A certain amount of color is giren to this theory by supposed changes in the magnitude of these ice-caps. But the problem of establishing such changes is one of extreme difficulty. The only way in which an adequate idea of this difficulty can be formed is by the student himself looking at Man through a telescope. If he will then note how hard it is to make out the different shades of light and darkness on the pknet, and how they must vary in aspect under different contlitions of clearness in our own atmosphere, he will readily perceive that much evidence is necessary to esUbiish great changss. All we can say, therefore, is that the formation of the ice-«api in winter and their melting in summer has some evi- dence in its favor, but is not yet completely proven. BAItUITU OT KiJM^ Until the year 1877 Man was supposed to have no satellites, none having ever been seen in the most powerful telescopes. But in August of that year Professor Hall, of the Naval Observatory. Instituted a systematic search with the great equatorial, which resulted in the discovery of two such objects. These satellites are Iqr far the smallest celestial bodies known. It is of course impossible to meaaure their diameters, as they appear in the telescope only as poinU of light The outer satellite is probaUy about tdx miles and the inner one about seven miles in diapeter. TIm outer one was seen with the telescope at a disUnce from the earOi of 7,000,000 timea this diameter. The proportion would be that of a ball two inches in dhuneter viewed at a distance equal to that between the cities of Boston and New York. Such a feat of telescopic seeing is well fitted to give an idea of the power of modem optical instruments. Professor Hall found that the outer satellite, which he called JkimM, nvolves around the planet in 80^ 16", and the inner one, oiled PMm, in T' 88". The ktter ia only 6800 jnilea from the centre of Jfori, and less than 4000 miles from its surface. It would therefore be almost possible with one of our telescopes on the sur- ftoe of Man to see an object the aixe of a hufge animal on the ■atellite. This short distance and rapid revolution make the inner satellite m\ M AsmONOMt. of Ibn one of the most iolemting bodies with which wo nre «6 qiwintt^l. It perfornu ■ reTulution iu iu orbit iii lew ilwii half the time that Mar$ ravolTea ou iu iizis. Iu couaequenco, to the inbab- iuuts of Jfart it would eeem to rise iu thu went aud wt iu the east. It will be remembered that the revolution of the moon around tlM earth and of the earth on iu aiia are both from weat to eaat; bat Um latter rarolntlon being the more rapid, the apijarent diurnal motfon of the moon is from east to west. In the case of the inner satellite of Man, however, this is reversed, and it therefore appeara to move in the actuiU direction of its orbiul motion. The rapidity of ita phases is also equally remarkable. It is less than two hours from ■ew moon to first quarter, and no on. Thus the inhabitants of Man may see their inner moon pass through all iu phases from new to full and again to new iu a single night. wm&m wm IBstew* Ii which wo nre i^ II IcM ilwii half Um enc«, to Ui« inhab* aud wt iu the vuL t muon ftruund Uw real to eut; bat Um ntdiaml motfoa the inner aatelllto e appenra to moTe he rapidity of ita I two hours from ihabitanta of Jfora from new to CHAPTER VI. THE MINOR PLANETS. Whbk the Boli*^ «v«tein was flrat mapped out in its tnie proportions by Cv .»j!^icu8 and Kepler, only six primary planets were known; namely, Mercury, Venus, the Earth, Mara, Jupiter, and Saturn. These succeeded each other according to a nearly regular law, as we have shown in Chapter I., except that between Mara and Jupiter a gap was left where an additional planet might be inserted, and the order of distances be thus made complete. It was therefore supposed by the astronomers of the seventeenth «nd eighteenth centuries that a planet might be found in this region. A search for this object was instituted to- ward the end of the last century, but before it had mode much progress a planet in the place of the one so long expected was found by Piazzi, of Palermo. The discov- ery was made on the first day of the present century, 1801, January 1st. In the course of the following seven years the astronom- ical world was surprised by the discovery of three other pUmets, all in the same region, though not revolving in the same orbits. Seeing four small planets where one large one onght to be, Olbbbs was led to his celebrated hypothesis that these bodies were the fragments of a large planet which had been broken to pieces by the action of lome unknown force. 338 ASTRONOMY. f A generation of astronomers now passed away without the discovery of more than these fonr. In 1845 a fifth planet of the group was found. In 1847 three more were discorered, and discoveries have since been made at a rate which thus far shows no signs of diminution. The num- ber 1)08 now reached 225, and the discovery of additional ones seems to be going on as fast as ever. The frequent announcements of tlie discovery of planets which appear in the public prints all refer to bodies of this group. The minor planets are distinguished from the major ones by many characteristics. Among those we may men- tion their small size; their positions, all being situated be- tween the orbits of Mara and Jupiter; the great eccentrici- ties and inclinations of their orbits. VamlMr vf Bautll PUnato.— It would be interesting to Icnow how many of tlicse planets tlicre are in all, but it is as yet imimssible even to guess at tlio number. As already stated, fully 200 are now known, and tlie number of new ones found every year ranges from 7 or 8 to 10 or 13. If ten ndditional ones are found every year dur- ing the remainder of tlie century. 400 wUl tlien have been dis- covered. A minor planet presents no sensible disk, and therefore looks ex- actly like a small star. It can be detected only by its motion among the surrounding sUrs, which is so slow that hours must elapse before it can be noticed. Kagaltudss. — It is impossible to make any precise measurement of the diameters of the minor planets. These can, however, be esti- mated by the amount of lir'^t which the planet reflects. Supposing the proportion of light reflected about the same as in the case of the larger planets, it is estimated that the diameters of the three or four largest, which are those first discovered, range between 800 and 600 kilometres, while the smallest are probably from 20 to 60 kilometres in diameter. The average diameter of all that are known is perhaps less than 160 kilometres; that is, scarcely more than one hundredth that of the earth. The volumes of solid bodies vary as the cubes of their diameters; it miglit therefore take a million of these planets to make one of the size of the eiirili. / id Bwajr without In 1845 a fifth three mor^ were ) mudo at a rate on. The nnm- >ry of additional . The frequent ts which appear liis group, from the major 'se we may men- sing situated be- great eccentrici- ting to know bow ret in)|)088ible even rully aOO nro now f year ranges from nd every year dur- :n bare been d<8> herefore looka ex- T its motion among must elapse before ise measurement of , bowevor, be esti- tflects. Supposing in tbe case of tbe f tbe tbree or four tween 800 and 600 !0 to 60 kilometres ) known is perbaps lan one bundredtb iry as tbe cubes of [>f tbese planets to THE MINOR PLANETS. 330 loTB «f Orbits.— Tlie orbits of tbe minor planets are mucb more ecct uric Ibaii those of tbe larger ones; tbeir distance from tbe sun tbercforo varies very widely. Orifia sf the Viaer naaeU.— The question of tbe origin of tbese bodies was long one of great interest. The features which we have described ttssociute themselves very naturally wltli the bypotbesis of Olbkrs, that wc here have the fragmenU of a single large planet which in tbe beginning revolved In iU proper place between tbe orbits of Mar$ and Jupiter. No support has been given to Olbcbs' bypotbesis by subsequent investigations, and it is no longer consid- ered by astronomers to have any foundation. So far as can be Judged, tbese bodies have been revolving around tbe sun as separate planett ever since the solur system itself was formed. •"'"'V-^^^'v L. CHAPTER VII. JUPITER AND HIS SATELLITES. TBI FiAvn JumsB. Jupiter is much the largest planet in the system. His mean distance is nearly 800,000,000 kilometres (480,000,- 000 miles). His diameter is 140,000 kilometres, corre- sponding to a mean apparent diameter, as seen from the snn, of 30'. 5. His linear diameter is about ■^, his surface is T^, and his volume t^itt th»t o' the snn. His mass is T-rfrr, and his density is thus nearly the same as the sun's; vit., 0.24 of the earth's. He rotates on his axis in 9" SS" 20*. He is attended by four satellites, which were discorered by Galileo on January 7th, 1610. He named them, in honor of tlie Medicis, the Medicean stars. They are now known as Satellites I, II, III^ and IV, I being the nearest. The surface of Jupiter has been carefully studied with the telescope, particularly within the past twenty years. Although further from us than Mars, the details of his disk are much easier to recognize. The most characteristic features are given in the drawings appended. These featui-cs are, first, the dark bands of the equatorial regions, and, secondly, the cloud-like forms spread over nearly the whole surface. At the limb all these details become indistinct, »nd finally vanishi %\vw indicftting « DiHMii JVPITBB AXD HIS BATELUTBB. HL "ES. te system. His stres (480,000,- ometres, oorro* seen from the ; ^, his surface His mass is le as the sun's; I his axis in irere discovered inmed them, in tr». They are V, I being the iy studied with twenty years. I details of his t characteristic •ended. These the equatorial 18 spread oyer 1 these details 8 indicating « highly absorptive atmosphere. The light from the centre of the disk is twice as bright as that from the poles. The bands can be seen with instruments no more |)owcrful than those used by GAUiiio, yet he makes no mention of them. The color of the bands is reddish. The position of the bands varies in latitude, and the shapes of the limiting curves also change from day to day; but in the main tliey remain as permanent features of the region to which they belong. Two such bands are aanally vimble, but often f^TL— ' ▼iDnr ov Svramktm mm a*TBums. more are seen. Hkbmhbl, in the year 1798, attributed the aspects of the bands to zones of the phinet's atmos- phere more tranquil and less filled with clouds than the re- maining portions, so as to permit the true surface of the planet to be seen through these zones, while the prevailing clouds in the other regions give a brighter tint to these latter. The color of the bands seems to vary from time to time, and their bordering lines sometimes alter with such rapidity as to show that these borders are formed of some- thing like clouds. Tho olon<|§ ^l^pmeelv^ ^j^ ^ily be aeen at times, and L ASTRONOMY. I lib thoy liave every variety of abupe, aometimos appearing ai brilliant circular wbite masses, but oftonor thoy are similar in form to a aeries of white cumulus clouds such as arc frequently seen piled up near the horizon on a summer's day. The bands themselves seem frequently to be veiled over with something like the thin cirrus clouds of our at- mosphere. Vm. 71.— TauMoono Vww or Jtmnn, Hm OM no wm A SAnum um m Ibabow Bueh olouds can be tolerably socurstely observed, and may be used to determine the rotatloa-time of the planet. Tlieae obaervations show that the clouds have often a motion of their owb, which is also evident from other oondderatlons. The following results of observation of spots situated in various ngions of the planet will illustrate this: (108 appearing ai r thoy are similar )udB Buoh ai aro k on a Bummor'a intly to be Teilod olouda of oar at- JVI'JTElt AXD UIS HATKILITA'S. Oamini 166S, Hbrkrki. 1778, HUIKBRL 1779. SCHROKTRB. 1788, Bub and MIdlcr . 1885, AiBT 1888, soHMioT Idea, M8 A* w. f. rotation-time = 9 M 00 = 9 08 40 s: 9 60 48 = 9 06 CO s: 9 55 20 = 9 68 81 ta 9 S6 M lARB iin m tmjkBom ed, and nuy be med TImm obflerrationa r own, which ia alao situated in ▼arioua Thi (Unuini or Jtrnm. ■•tima af thr *r>ti!'Utas.— Tlie four satellites more about Jvpttm> from weat to eatt a nearly circular orbits. When one of these satellflea passes between the sun and Jupittr, it casts a shadow upon fvfit»t't disk (Me Fig, 78) precisely as the shadow of our moon is ^lit' \i rni; . 944 ASTRONOMY. thrown upon the earth in a solar eclipse. If the gatellUe passes through Jupiter't own shadow in its revolution, nn eclipse of this satellite takes place. If it passes between the earth and Jupiter, it is projected upon Jupiter's disk, and we liave a transit; if Jupiter is between the earth and the satellite, an occultatlon of the latter oc- curs. All these phenomena can be seen with a common telescope, and the times of observation are all found predicted in the Nautical Almnnae. These shadows being seen black upon Jupiter't surface, show timt tills planet shines by reflecting the light of the sun. Teleseopie Appaaranea «f the lateUitM.— Under ordinary circum- stances, the satellites of Jupiter axe seen to have disks; that is, not to be mere points of light. Under very favorable conditions, mark- ings have been seen on these disks. The salellites completely disappear from telescopic view when they enter the shadt w of the planet. This seems to show that neither planet nor satellite is self-luminous to any great extent. If the satellite were self-luminous, it would be seen by its own light; and if the planet were luminous, the satellite might be seen by the re- flected light of the planet. The motions of these objects are connected by two curious and iiuporunt relations discovered by La Place, and expressed as fol- lows: I. 37m mean motion of (he fint eatOUte added to twice the mean mo- tion of the Oiird it exaetty equal to three timet the mean motion of the leeoiid. II. ^ to the mean longitude ef the fret tateKte tM add twice the mean longitude of the third, and tubtraet (Arse timet the mean longitude if the eteond, the difference it alreayt 180°. The fint of these relations is shown in the following table of the mean daily motions of the satellites: Satellite I hi one day moTM. 2(IS*.48W «• n " " lOr.8748 " III •• " 60°.8177 •« IV " " ai'.STll Motion of Satellite 1 808°.48»0 Twice that of Satellite m 100°.6854 Sum 804M844 Three times motion of SatelUte TL 804MaM Observations showed tliat this condition was fulfilled as exactly «■ possible, but the discovery of La Plack consisted in showing that if the approximate coincidence of the mean motions was opce ettftb- ; the satellite passes D, nn eclipse of this earth and Jupiter, it transit; if Jupiter is ion of the latter oc- I common telescope, licted in the NdutietU K)n Jupiter's surface, ;ht of the sun. ler ordinary circum- ve disks; that is, not ble conditions, mark- elescopic view when seems to show that any great extent. If !en by its own light; ight be seen by the re- by two curious and ind expressed as fol- to twiee the mean mo- he mean motion ef ih» tM add titiee the mean I mean longitude c«-- . iv,--:4***WWi^''w-'= \ ! ¥ CHAPTER VIII. BATUKSr AND ITS SYSTEM. OxvxBAL Dnoumov. Saturn is the most distant of the major planets known to the ancients. It revolves around the sun in 29^ years, at a mean distance of about 1,400,000,000 kilometres (882,000,000 miles). The angular diameter of the ball of the planet is about 16'. 2, corresponding to a true diameter of about 110,000 kilometres (70,600 miles). Its diameter is therefore nearly nine times and its volume about 700 times that of the earth. It is remarkable for its small density, which, so far as known, is less than that of any other heavenly body, and even less than that of water. It revolves on its axis in 10" 14'° 24% or less than half a day. Saturn is perhaps the most remarkable planet in the solar system, being itself the centre of a system of its own, altogether unlike anything else in the heavens. Its most noteworthy featuie is a pair of rings which surround it at a considerable distance from the planet itself. Out- side of these rings revolve no less than eight satellites, or twice the greatest number known to surround any other planet. The planet, rings, and satellites are altogether called the Saturnian system. The general appeannoe of this system, as seen in a small telescope, is shown in Fig. 74. BATURN AND ITS ST8TEM. 947 •r planets known sun in 29^ years, ),000 kilometres ter of the ball of > a true diameter s). Its diameter >lume about 700 )le for its small than that of any bat of water. It than half a day. le planet in the a system of its the heavens. Its a which surround met itself. Out- eight satellites, irround any other es are altogether ral appeannoeof shown in Fig. 74. To the naked eye Saturn is of a dull yellowish color, shining with about the brilliancy of a star of the first mag- nitude. It varies in brightness, however, with the way in which its ring is seen, being brighter the wider the ring appears. It comes into opposition at intervals of one year and from twelve to fourteen days. The following are the Ito. 74.— TtaaKiono Yaw or nn SAumtoAK Bnrmt. times of some of these oppositions, by studying which one will be enabled to recognize the planet: 1882 November 14th. 1883 November 28th. 1884. December 11th. During these years it will be best seen in the autumn and winter. When viewed with a telescope, the physical appearance of the ball of Saturn is quite similar to that of JuinUr, 1^ AsmoyoAfT. (^ li ■a having light and dark belts parallel to the direction of its rotation. Tes Rnrcn or SATinur. TLe rings are the most wmarkablo and characteristic feature of tile Saturiiian system. Pig. 75 gives two views of tbe ball and rings. The upper one shows one of their aspects as actually presented in tlie telescope, and the lower one shows what the appearance would be if the planet were viewed from a direction at right angles to the plane of the ring (wliich it never can be from tbe earth). The first telescopic observers of Hilurn were unable to see the rings in their true form, and were greatly perplexed to account for the appearance wliicli the planet preM.>nted. Oami.eo descrilied the planet as " trl-corporale," the two ends of the ring having, in his imperfect telescope, the appearance of a pair of small pluneU at- tached to the central one. "On eacli side of old Utturn were ser- vitors who aided liim on his way." This supposed discovery was announced to his friend Kbplkb in this logogriph : "smaismrmilmepoetalcTmibuncnugltsviras," which, being trans- posed, becomes — "Aitissimum planetam tergeminum observavi" (I liave observed the most distant planet to be tri-form). The phenomenon constantly remained a mystery lo iU first ob- server. In 1910 lie had seen the planet accompanied, as he supposed, by two lateral stars; in 1012 the latter had vanished and the central body alone remained. After that Oalilbo ceased to observe Satitm. The appearances of the ring were also incomprehensible to Hb- VBLitJS. GAssBNDt, and othera. It was not until lOSS (after seven yeara of observation) that the celebrated Hctghers discovered the true explanation of tbe remarkable and recurring series of phenom- ena present by tiie tri-corporate planet. He announced his conclusions in the following logogriph: "aaaaaa ccccc d eeeee g h iiiiiii 1111 mm nnnnonnnn oooo pp q rr a ttttt uuuuu," which, when arranged, read— " Annulo cingitur, tonui, piano, nusquam coherente, ad eclipticam inclinato" (it is girdled by a Uiir plane ring, nowhere touchinir in- clined to the ecliptic). *' , Thia description is complete and accurate. In 1676 it was found by Cassihi, tliat what HmroBJora had seen as a single ring was really two. A division extended all the way aroand near tbe outer edge. This division is shown in tlie flguns In 18SQ the Vmm. Bokd. of Harvard College Observatory. fMiad direction of its iteristic feature of the ball and rings. :ually presented in appearance would -ight angles to the arth). unable to see the ilcxed to account }ami.bo descrilted ring having, in his small planets at- I Untune were ser- sed discovery was lich, being trans- (I have observed ry to ite first ob- d. as lie supposed, id and the central to observe Saturn. rehensiblo to Hr- 1095 (after seven HB discovered the series of phenom- •gogriph: nn oooo pp q rr s ite, ad eclipticam iicre touching, in- roBKJra had seen ided all the waj 1 in the flguns. Mervatoiy, fomd l-lfeSiS;-- / Jl I ' t St 1^ ASTRONOMf. that then wu a third ring, of a dusky and nebulous aspect, inside the other two, or rather attached to the inner edge of the inner ring It is therefore known as Bwwf « duiky ring. It hud not been before fully described owing to its darkness of color, which made it a difBcult object to see except witli a good telescope. It is not separated from the bright ring, but seems as if attached to It. The latter shades off toward iu inner edge, and merges gradually into the dusky ring. The latter extends about half way from the inner edge of the bricht ring to the ball of the planet Aspeet of the Blogi.— As Saturn revolves around the lun, the plane of the rings remains parallel to itself. That is, if we consider a straight line passing through the centre of the planet, perpendic- ular to the plane of the ring, as the axis of the latter, this axis will Mways point in the same direction. In this respect the motion is similar to that of the earth around the sun. The ring of Saturn is inclined about ST to the plane of its orbit. Consequently, as the planet molTaa around the sun. there is a change in the diiecUon in Which the nm ehines upon it similar to that which produces the change of seaeona upon the earth, as shown in Pig. 82. The oarreiponding changes for Saturn are shown in Fig 76 Dur- ing each revolution of Saturn \.Ub plane of the ring passes through the sun twice. This occurred in the years 1862 and 1878. at two oppoeite points of the orUt. us shown in the figure. At two other points, midway between these, the sun shines upon the plane of the ring at ito greatest incUnatioa. about 27°. Since the earth is Jinle more thaa one tenth aa far from the sun as Saturn is. an obwsrver ^ways sf«8 Saturn nearly, but not quite, as if he were upon the sun Hence at, certain times the rings of Saturn are seen edgeways; while at otiier times they are at an inclination of 27°, the aspect depending upon the position of the planet in ito orbit. The followlng\re Uio times of some of the phases: 1878. Pebraaiy 7th.-The edge of the ring was turned toward tiie sun. It could then be seen only as a thin line of light 1886.-The planet having moved forward 90°, the souUi side of tiie rings may be seen at an inclination of 27°. IWl, Deoember.-The planet having moved 90° further, tiie edge of the ring is again turned toward tiie sun. 1809.— The north side of the ring is Inclined toward tiie sun. and is seen at iu greatest inclination. »». "w The rings are extremely thin in proportion to tiieir extent Oon' sequently, when tiieir edges are turned toward theeartii, tiiey aDma^ as a tiiin line of light, which can be seen only witii wiwerful Sk •cope* With such telewsopes. tiie planet appeara as if it w«k SATUBN AND ITS STSTBM. 261 lous aspect, in8ideth« >r the inner ring. It not been before fully :b made it a difficult • not separated from The latter shades off into the dusky ring. ler edge of the bright iround the sun, the liat is, if we consider le planet, perpendic- I latter, this axis will espect the motion is he ring of Saturn is Consequently, as the ;e in the direction in which produces the ig. 83. wn in Fig 76. Dor- ring passes through 13 and 1878, at two ure. At two other on the plane of the » the earth is JlUle urn is, an obserror were upon the sun. en edgeways; while lie aspect depending e following are the 3 turned toward the light lie south side of the 0° further, the edge iward the sun, $3aA their extent Oon^ 3 earth, tfaey appear rith powerful tele^ tears as if it w«i« pierced through by n piece of very fine wire, the ends of which pro- ject on each side more than the diameter of the planet. It has fre- quently been remarked that this appearance is seen on one side of the planet, when no trace of the ring can be seen on the other. There is sometimes a period of a few weeks during which the plane of the ring, extended outward, passes between the sun and the earth. Tiiat is, the sun shines on one side of the ring, while the other or dark side is turned toward the earth. In this case it seems to be established that only the edge of the ring is visible. If this be so, the substance of the rings cannot be transparent to the sun's rays, else it would be seen by the light which passes through it Ceastitutien *t tIpevBiats vt latan'.— The nature of these objects ha» been a subject '&>th.bf wonder and of investigation by mathema- ticians and astronomers ever since they were discovered. They were at first supposed to be solid bodies; indeed, from their appearance it was difficult to copceive of them as anything else. The question Uien arose: What keeps them from falling on the planet? It was shown by La Placb that a homogeneous and solid ring surroundbig the planet could not remain in a state of equilibrium, bat must be pncipltated upon the central ball by the smallest disturbing force. AarnoNOMT. I M It ia now establiMhed beyond reasonable doubt tbnt the ringa do not form a continuous mass, but are rtiilly a countluss multitude of small separate particles, each of which revolves on ito own account. These sutullites are individually far too small to be seen in ony teleKope. but so numeroua that when viewed from the distance of the earth they appear aa a continuous mass, like particles of dust floating in a sunbeam. 1 SATUXITES OV BAtDBV. Outside the rings of Saturn revolve iu eight satellites, the order and discovery of which are siiown in the following table: Dtstaaoe Mo. Nami. from PUuiet. DiacoTerer. Data of DlacoTery. 1 Mimas 8-3 Herscliel 1789. September 17. 2 Encelodus 4-8 Herscliel 178d, August 28. tf Tethys 5.:i Ciifisini 1684. March. 4 Dione 0-8 Cassini 1684, March. ft Rhea 0-5 Cassini 1«72, December 28. 7 Titan Hyperion 20-7 20-8 Huyshens 16S5, March 25. 1848, September 16. 8 Japetus 64-4 Cassini 1671, October. The distances from the planet are given in radii of the latter. The satellites Mimat and Hyperion are visible only in the moat powerful teleM»pea. The brightest of all ia Titan, which can be seen in a teleacope of the snialle«t ordinary size. Japettu has the remarkable peculiarity of apptoring nearly as bright as lOan when seen west of the planet, and so faint as to be visible only in large telescopes when on the other side. This appearance is explained by supposing that, like our moon, it always preaenta the same face to the planet, and that one side of it is dark and tlie other side light. When west of the planet, the bright side is turned toward the earth and the satel- lite ia visible. On the other aide of the planet, the dark side ia turned toward ua, and it ia nearly invisible. Most of the remaining five aateiiites can ordinarily be seen with teleacopes of moderate power. that the ringa do not H multitude of amiill iwD account. These in any telescope, but :e of the earth they I dust floating in a satellites, the order ng table: Data of DlscoTery. 1789. September 17. t78d, Augustas. 1684. March. 1684, Miiich. L«7a, December 28. t«S5, Marches. 1848, September 10. 1871, October. 11 of the latter. The the moat powerful li can be seen in a has the remarkable k when seen west of rge telescopes when by supposing thut, e to the planet, and ht. When west of earth and the satel- dark side is turned the remaining five [ moderate power. CHAPTER IX. THE PLANET URANUS. Uranus was discovered on Murch 13lli, 1781, by Sir William Herscuel (then an amateur observer) with a ten-foot reflector made by himself. He was examining a portion of the sky near H Oeminorum, wlien one of the otufs in the field of view attracted his notice by its ])eculiur appearance. On further scrutiny, it proved to ]iave a planetary disk, and a motion of over 2' per liour. Heuschel at first supposed it to be a comet in a distant part of its orbit, and under this impression parabolic orbits were com- puted for it by various mathematicians. None of these, however, satisfied subsequent observations, and it was finally determined that the now body was a planet revolv- ing in a nearly circular orbit. We can scarcely compre- hend now the enthusiasm with which this discovery Avas received. No new body (save comets) had been added to the solar system since the discovery of the third satellite of Saturn in 1684, and all the major planets of the heavens had been known for thousands of years. Uranus revolves about the snn in 84 years. Its apparent diameter as seen from the earth vai'ies little, being about 3'. 9. Its true diameter is about 50,000 kilometres, and its figure is, so far as we know, exactly spherical. In physical appearance it is a small greenish disk with- d64 AsrnoKoMr. M out markings. It is possible tliat the centre of the disk is slightly brighter tiiun the edges. At its nearest approach to the earth, it Khines us a star of the sixtli magnitude, and is just visible to an acute eye when the attention is directed to its place. In small telescopes with low powers, its appearance is not markedly diflFerant from that of stars of about its own brilliancy. Sir William IIerscuel suspected that Uranus was ac- companied by six ButuUites. Of the existence of two of those satellites there has never been any doubt. None of the other four satellites de- scribed by Uersciiel lias ever been seen, and he was undoubtedly mistaken in supposing them to exist. Two ailditional ones voro discovered by Lasskll in 1847, and they are, with the Hatollites of Mara, the faintest objects in the solar system. Neither of them is identical with any of the missing ones of Herschel. As Sir William Her- 8CHEL had susi^ected six satellites, the following names for the true satellites are generally adopted to avoid confusion: Dikn. I. Arul , Period= 2.620888 II. Uti^rid " = 4.144181 III. Titania, Herscuel'b (II.) " - 8.708897 IV. 06«w». Hkbschei/s (IV.) " =18.463269 It is likely that .^m/ -...ries in' brightness on different sides of the planet, and the same phenomenon has also been suspected for Titania. The most remarkable feature of the satellites of Uranui is that their orbits are uearly perpendicular to the ecliptic instead of having a small inclinstioii to that plane, like those of all the orbits of both planets and satellites previously known. To form a correct idea of the position of the orbits, we must imagine them tipped over until their north pole is nearly 8° below the ecliptic, instead of 80° :'J>'?S)#S «l3l centre of the disk is ts nearest approach e sixth magnitude, len tlio attention is es witli low powers, ; from that of stars liat Uranus was ac> lites thoro Ims never four satellites de- seen, and he was >em to exist. Two lSSELL in 1847, and faintest ohjects in lentical with any of Sir William Heb- fuUowing names for to avoid confusion: ...Period = 2.520888 ... •' = 4.144181 ... " ~ 8.705897 ... " =18.463269 ;htnes8 on different enomenon has also lites of Uranut is that he ecliptic instead of those of all the orbits vn. To form a correct igine them tipped orer ecliptic, instead of 90° .. .■■ TIIK PLANET VltANUft. 960 above it. The pole of the orbit which ghoiild be considered as the nortli one I'' tliat from whlcli, if nn observer loolc down upon n re- volving body, llie latter would seem to turn in a direction oppoBil* tliat of the hundw of a watch. Wlicn the orbit is lipi>cd over more than a riglil nngle, the motion from a point in the direction of tlie north pole of the ecliptic will seem to be the reverse of tids; It is therefore sometimes considered to be retrograde. This term is fre- quently ivpplieti to the motion of tlio satellites of Uranut, but is ratiier misleading, since tlie motion, being nearly perpendicular to the ecliptic, is not exactly expressed by the term. The four saU-llitcs move in tlie same plane. This fact renders It highly prolmble tli llie planet Urannt revolves on its axis in the same plnno with the orbits of the satellitea. and is tlierefore an oblate splieroid like the earth. This conclusion is founded on the consid* erntlon tliut if tlie planes of the satellites were not Icept togetlier by gome cause, they would gradually deviate from each other owing to the attractive force of the sun upon the planet. The different satel- lites would deviate by different amounU, and it would Iw extremely improbable that all the orbits would at any time be found in the same plane. Since we see tiiem in the same plane, we conclude that some force keeps them there, and the oblateness of the planet would cause such a force. ^■^ CHAPTER X. THE PLANET NEPTUNE. After the planet Vranua had been observed for some thirty years, tabJos of its motion were prepared by Bou- VABD. Ho had as data available for this purpose not only the observations since 1781, but also observations extend, ing back as far as 1695, in which the planet was observed and supposed to be a fixed star. As one of the chief diffi- culties in the way of obtaining a theory of the planet's motion was the short period of time during which it had been regularly observed, it was to be supposed that these ancient observationa would materially aid in obtaining exact accordance between the theory and observation. But it was found that, after allowing for all perturbations pro- duced by the known planets, the ancient ond modem observations, though undoubtedly referring to the same object, wore yet not to be reconciled with each other, but differed systematically. Bocvard was forced to omit the older observations in his tables, which were published in 1830, and to found his theory upon the modern observa- tions alone. By so doing, he obtained a good agreement between theory and the observations of the few years immediately succeeding 1820. Bocvard seems to have formulated the idea that a pos- sible cause for the discrepancies noted might be the exist- ence of an unknown planet, but the meagre data at his disposal forged him to leave the subject nDtonched, In ':^.>H$iii Wmmmmu.^^^ observed for some 1 prepared by Bou- is purpose not only bservations extend- ilanet was observed 9 of the chief diflS- Jry of the planet's iring which it had apposed that these aid in obtaining 1 observation. But pertnrbtttions pro- oicnt and modem rring to the same itii encli other, but forced to omit the were published in le modern observa- a good agreement of the few years lie idea that a pos- night be the ezist- leagre data at his Dt UDtonched, In THK PLANET NBPTUNB. 307 1830 it was found that the tables which represented the motion of the planet well in 1820-25 were 20' in error, in 1840 the error was 90', and in 1846 it was over 120'. These progressive and systematic changes attracted the attention of astronomers to the subject of the theory of the motion of Uranu$. The actual discrepancy (120') in 1845 was not a quantity large in itself. Two stars of the magnitude of Uranus, and separated by only 120', would be seen as one to the unaided eye. It was on account of its systematic and progressive increase that suspicion was excited. Several astronomers attacked the problem in various ways. The elder Stbutk, at Pulkova, prosecuted a search for a new planet along with his double-star obser- vations; Bbssbl, at Koeiiigsberg, set a student of his own, Flsmino, at a new comparison of observation with theojy, in order to furnish data ^or a new determination; Abaqo, then Director of the Observatory at Paris, suggested this subject in 1845 as an interesting field of research to Ls Vbrbixb, then a rising mathematician and astronomer. Mr. J. 0. Adams, a stndent in Cambridge University, England, had become aware of the problems presented by the anomalies in the motion of Uranu», and had attacked this question ai early ai 1843. In October, 1845, Adams oommnnioated to the Astronomer Royal of England ele- ments of a new planet so situated as to produce the per- turbations of the motion of Uranus which had actually been observed. Such a prediction from an entirely un- known stndent, as Adams then was, did not carry entire conviction with it. A series of accidents prevented the unknown planet being looked for by one of the largest teleaoopee in England, and so the matter apparently dropped. It may be noted, however, that we now know I w 258 ASTRONOMY. AnAMs' elemonts of the new planet to have been so near the trnth that if it had been really looked for by the power- ful telescope which afterward discovered its satellite, it could scarcely have failed oi detection. Bessbl's pupil Flemino died before his work was done, and Bessel's researches were temporarily brought to an end. Strut e's search was unsuccessful. Only Lb Vbr. BIER continued his investigations, and in the most thorough manner. He first computed anew the pertur- bation of Uranus produced by the. action of Jupiter and Saturn. Then he examined the nature of the irregulari- ties observed. These snowed that if th€> were caused by an unknown planet, it coula uot bo between Saturn and Uranus, or else Saturn would have been more afFected than was the case. The new planet was outside of Uranus if it existed at all, and as a rough guide Bode's law was invoked, which indicated a distance about twice that of Uranus. In the summer ot 1846 Le Yerbieb obtained complete elements of a new planet, which would account for the observed irregularities in the motion of Uranus, and these were published in France. They were very similar to those of Adams, which had been communicated to Professor ChaL' LIS, the Director of the Observatory of Cambridge, Eng- land. A search was immediately begun by Challis for such an object, and as no star-maps were at band for this region of the sky, he began mapping the surrounding stars. In so doing the new planet was actually observed, both on August 4th and 12th, 1846, but the observations remain- ing unreduced, and so the planetary nature of the object was not recognized. t ■.jaitfflfe^','5'-^ L ave been 80 near for by the power- 1 its satellite, it s work was done, y brought to an Only Lb Vbb- d in the most mew the pertur- I of Jupiter and of the irregalari- ; were caused by reen Saturn and en more affected i if it existed at i invoked, which \Uranus. In the >niplete elements !or the observed and these were lilar to those of Professor Qhal- ambridge, Eng- HALLis for such d for this region nding stars. In iserved, both on rvaiions remain- re of the object ■'■LI i.ip mm THE PLANET NEPTUNE. In September of the same year Lb Yebrier wrote to Dr. Qallb, then Assistant at the Observatory of Berlin, asking him to search for the new planet, and directing him to the place where it should be found. By the aid of an excellent star-chart of this region, which had just been completed, the planet was found September 23d, 1846. The strict rights of discovery lay with Le Yebrier, but the common consent of mankind has always credited Via. 77. Adams with an equal share in the honor attached to this most brilliant achievement. Indeed, it was only by the most unfortunate succession of accidents that the discovery did not attach to Adams' researches. One thing must in fairness be said, and that is that the results of Lb Ver- BIBB, which were reached after a most thorough investi- gation of the whole ground, were announced with an en- tire confidence which, perhaps, was lacking in the other oaso. mi \ : '", t^'p'>Vr' ^ -' ^ ' " ' ^TTT .J r*'?:T:^^^>W"^;%T7S^T^/* fas.fiL'W^.'S*irwi'''«.«<«wufw«» M 260 A8TR0N0MT. This brilliant diacorery created more enthusiasin than eyen the discovery of Uranus, as it was by an exercise of far higher qualities that it was achieved. It appeared to savor of the marvellous that a mathematician could say to a working astronomer that by pointing his telescope to a certain small area, within it should be found a new major planet. Yet so it was. The general nature of the disturbing force which re- vealed the new planet may be seen by Fig. 77, which shows the orbits of the two planets, and their respective motions between 1781 and 1840. The inner orbit is that of Uranus, the outer one that of Neptune. The arrows passing from the former to the latter show the directions of the attractive force of Neptune. It will be seen that the two planets were in conjunction in the year 1822. Since that time Uranus has, by its more rapid motion, passed more than 90° beyond Neptune, and will continue to increase its distance from the latter until the begin- ning of the next century. Our knowledge regarding Neptune is mostly confined to a few numbers representing the elements of its motion. Its mean distance is more than 4,000,000,000 kilometres (2,775,000,000 miles); its periodic time is 164.78 years; its apparent diameter is 2.6 seconds, corresponding to a true diameter of 55,000 kilometres. Gravity at its surface is about nine tenths of the corresponding terrestrial surface gravity. Of its rotation and physical condition nothing is known. Its color is a pale greenish blue. It is attended by one satellite, which was discovered by Mr. Lassbll, of England, in 1847. The satellite requires a telescope of twelve inches' aperture or upward to be well seen. Vf-ss^i^r^.a:^ I enthuBiasm than by an exercise of d. It appeared to aatician could say ig his telescope to be found a new a; force which re- >y Fig. 77, which id their respective inner orbit is that 'une. The arrows how the directions will be seen that in the year 1822. lore rapid motion, and will continue r until the begin- mostly confined to nts of its motion. 000,000 kilometres e is 164.78 years; orresponding to a avity at its surface I terrestrial surface condition nothing Ine. It is attended ly Mr. Lasssll, of ires a telescope of well seen. CHAPTER XI. THE PHYSICAL CONSTITUTION OF THE PLANETS. It is remarkable that the eight large planets of tlie solar system, considered with respect to their physical constitu- tion as revealed by the telescope and the spectroscope, may be divided into four pairs, the planets of each pair liaving a great similarity, and being quite different from the ad- joining pair. Heronry and Venos. — Passing outward from the sun, the first pair we encounter will be Mercury and Venus. The most remarkable feature of these two planets is a negative rather than a positive one, being thu entire absence of any certain evidence of change on their surfaces. We have al- ready shown that Venus has a considerable atmosphere, while there is no evidence of any such atmosphere aroiind Mercury. They hare therefore not boon proved alike in this respect, yet, on tlie other hand, they have not bKsn proved different. In every other "-espect than this xhe sin, :iarity appears perfect. No permanent markings have ever bet:, certiriit'v seen on the disk of either. If, fA is possible, the atmonhcro of both planets is filled with clouds and vapor i.o chnv^e, no openings, and no formations among these clouc^ m.uses are visiMe from the earth. Whnn- ever either of tijese planets is in fi certain pcsidon rulative to the earth and the sun H seemingly presents the same appearanut., ani nut the slightest change occars in that i if 1:= 262 ASTRONOMY. appearance from the rotation of the planet on its axis, which every analogy of the solar system leads us to believe must take place. When studied with the spectroscope, the spectra of Mer- cury and Venus do not differ strikingly from that of the sun. This would seem to indicate that the atmospheres of these planets do. not exert any decided absorption upon the rays of light which pass through them ; or, at least, they absorb only the same rays which are absorbed by the at- mosphere of the sun and by that of the earth. The one point of difference is that the lines of the spectrum pro- duced by the absoipUon of our own atmosphere ap^iear darker in the spectrum of Venus. If this were so, it would indicate that the atmosphere of Venus is similar in constitution to that of our earth, l)ccauso it absorbs the same rays. But the means of measuring the darkness of the lines are as yet so imperfect that it is impossible to speak with certainty on a point like this. The Earth and Mars. — These planets arc distinguished from all the others in that their visible surfaces are mark- ed by permanent features, which show them to be solid, and which can be seen from the otlicr heavenly bodies. It is true that we cannot study the earth from any other body, but we can form a very correct idea how it would look if seen in this way (from the moon, for instance). Wherever the atmosphere was clear, the outlines of the continents and oceans would be visible, while they would be invisible where the air was cloudy. Now, so far as we can judge from observation, 'uade at so groat a distance, never much less than forty millions of miles, the planet Mars presents to our telescopes very much the same general appearance that the earth would if L )IaDet on its axis, leads us to believe he spectra of Mer- from that of the bhe atmospheres of )sorptiou upou the ; or, at least, they t)sorbed by the at- Q earth. The one the spectrum pru- .tniosphere ap^iear this were so, it ''enus is similar in use it absorbs the g the dui'kness of it is impossible to arc distinguished mrfaces are mark- them to be solid, avenly bodies. It li from any other dea how it would on, for instance), le outlines of the while they would ervation. 'uade at 1 forty millions of ir telescopes very ;he eerth would if PHTSlOAL CONSrtTtrTtON OF TBB PLANETS. 263 observed from an equally great distance. The only ex- ception is that ihe visible surface of Mars is seemingly much less obscured by clouds than that of the earth would be. In other words, that planet has a more sunny sky than ours. It is, of course, impossible to say what conditions we might find could we take a much closer view of Mars : all we can assert is, that so far as wo can judge from this distance, its surface is like that of the eai th. This supposed similarity is strengthened by the spectro- scopic observations. Jupiter and Satnrn. — The next pair of planets is Jupi- ter and Saturn. Their peculiarity is that no solid crust or surface is visible from without. Tn this respect they differ from the earth and Mars, and resemble Mercury and Venus. But they differ from the latter in the very important point that constant changes can be seen going on at their surfaces. The preponderance of evidence is in favor of the view that these planets have no solid crusts whatever, but consist of masses of molten matter, surrounded by envelopes of vapor constantly rising from the interior. This view is further strengthened by their very small specific gravity, which can be accounted for by supposing that the liquid interior is nothing more than a compara- tively small central core, and that the greater part of the bulk of each planet is composed of vapor of small density. That the visible surfaces of Jupiter and Saturn are cot- ered by some kind of an atmosphere follows not only from the moLion of the cloud forms seen there, but from the spectroscopic observations. XTranna and Heptune. — These planets have a strikingly similar aspect when seen through a telescope. They differ L 264 ASTRONOMY. from Jupiter and Saturn in that no changes or variations of color or aspect can be made out upon tlieir surfaces; and from the earth and Mars in the absence of any {lerma- nent features. Telescopically, therefore, we might classify them with Mercury and Venus, but the spectroscope re- veals a constitution entirely different from that of any other planets. The most marked featin-es of their spectra are very dark bands, evidently produced by the absorption of dense atmospheres. Owing to the extreme faiutness of the light which reaches us from these distant bodies, the regular lines of the solar spectrum are entirely invisible in their spectra, yet these dark bands which are peculiar to them have been seen by several astronomers. This classification of the eight planets into pairs is ren- dered yet more striking by the fact that it applies to what we have been able to discover respecting the rotations of these bodies. The rotation of the inner pair, Mercury and Venus, has eluded detection, notwithstanding their comparative proximity to us. The next pair, the earth and Mars, have perfectly definite times of rotation, because their outer surfaces consist of solid crusts, every part of which must rotate in the same time. The next pair, Jupiter and Saturn, have well-establish ed times of rotation, but these times are not perfectly definite, because the surfaces of these planets axo not solid, and dif- ferent portions of their mass may rotate in slightly different times. Jupiter and Saturn liave also in commou a very rapid rate of rotation. Finally, the outer pair, Uranus and Neptune, seem to be surrounded by atmospheres of such density that no evidence of rotation can bo gathered. Thus it seems that of the eight planets only the central four have yet certainly indicated a rotation on their axes. vMk langes or variations pon their surfaces; ienco of any ])erma- e, we might classify le spectroscope ro- from that of any res of their spectra by the absorption xtreme fuiutness of distant bodies, the Bntirely invisible in ich are peculiar to lers. « into pairs is ren- b it applies to what ig the rotations of ner pair, Mercury withstanding their xt pair, the earth imes of rotation, solid crusts, every le time. The next [•established times perfectly definite, not solid, and dif- n slightly difFerent in commou a very uter pair, Uranus )y atmospheres of n can bo gathered, s only the central Du on their axei. J CHAPTER XII. METEORS. PHEMonirA AKB CAvnEs or ][iraoB& DuBiNO the present century evidence has been collected that countless masses of matter, far too small to be seen with the most powerful telescopes, are moving through the planetary spaces. This evidence is afforded by the phenomenu of "aerolites," "meteors," and "shooting- stars." Although these several phenomena have been ob> served and n>>te so great an evolu- iwer. this question f beat. Heat is a and a progressive on more npid we METBORS. 267 fhake the body warmer. By simply blowing air against any com- bustible body with sufficient velocity it can be set on Are, and, if incombustible, the body will be made red-hot and finally melted. Experiments to determine the degree of temperature tlius produced have been made which siiow tiiat a velocity of about 50 metres per second corresponds to a rise of temperature of one degree Centi- grade. From this the temperature due to any velocity can be readily cnlnuiated on the principle that the increa&e of temperature is pro- poi'tionul to tlie "energ}'" of the particles, which again is propor- tional to the square of tlie velocity. Hence a velocity of 600 metres per second would correspond to a rise of 100° above the actual tem- perature of the air, so tiiat if the latter was at the freezing-point the body would be raised to tlie temperature of boiling water. A velocity of 1500 metres per second would produce a red heat The earth moves around the sun with a velocity of about 80,000 metres per second; consequently if it met a body at rest (he concus- sion between the latter and the atmosphere would correspond to a temperature of more than 800,000°. This would instantly dissolve any known substance. It must be remembered that when we speak of these . enormous temperatures, we are to consider them as potgntial, not actual, tem- peratures. We do not mean that the body is actually raised to a temperature of 800,000°, but only that the air acts upon it as if it were put into a furnace heated to this temperature; that is. It is rapidly destroyed by the intensity of the heat. This potential temperature is independent of the density of the medium, being the same in the rarest as in the densest atmosphere. But tiie actual effect on the body is not so great in a rare as in a dense atmosphere. Every one knows that he can hold his hand for some time in air at the temperature of boiling water. The rarer the air the higher the temperature the hand would bear without injury. In an atmosphere as rare as ours at the height of 60 miles, it is probable that the hand could be held for an indefinite period, though its temperature should be that of red-bet Iron; hence the meteor is not consumed so rapidly as if it struck a dense atmosphere with planetary velocity. In the latter case it would probably dis- appear like a flash of lightning. The amount of heat evolved is measured not by that which would result from the combustion of the body, but by the «w viva (energy of motion) which the body loses in the atmosphere. The student of phystte knows that motion, when lost, is changed into a definite amount of heat. If we calculate the amount of heat which is equivalent to the energy of motion of a pebble having a velocity AH i ■m r 1 368 ASTBONOMT. of 20 miles a second, we shall And it sufflcient to raise about 1800 times tiie pebble's weigiit of water from the freezing to the Imiling point. This is many times as much heat as could result from burn- ing eveci Uit most combustible body. The deti> lue nature ns that pro- iddeoly condensed in lind it. I in the way just de- E phenomena depend and the direction and r to the earth. With isible OS to be entirely there. Even of those ; and the loudest deto* 1. On rare occasions ! earth without being luced by its passage I melting and destroy- g unchanged. Whra ' the atmosphere, the I generally broken to i single aerolite, but a been made to deter^ his is effected by two mrt and mapping out I. In the case of very rith considerable pre- cidental obserrers in uses. This observo- n of the parallax of a ince to be Tisible at a miles. The separate an of them. They eight, and therefore the rays of the sua. tmoaphere rises to a h greater height thaa MKTBOnS. XXTZOBIO SHOWIM. As already stated, the i»hcnomenft of shooting-stars may bo seen by a careful observer on almost any clear night. In general, not more than three or four of them will be seen in an hour, and these will be so minute as hardly to attract notice. But they sometimes fall in such numbers as to present the appearance of a meteoric shower. On rare occasions the shower has been so striking as to fill the beholi « ' with terror. The ancient and mediffival records contain m v accounts of these phenomena which have been brought * t through the researches of antiquarians. It has i ,.g been known that some showers of this class occur at an interval of about a third of a century. One was observed by Humboldt, on the Andes, on the night of November i2th, 1799, lasting from two o'clock until day- light. A great shower was seen in this country in 1833, and is well known to have struck the negroes of the Southern States with terror. The theory that the showers occar at intervals of 84 years was propounded by Glbers, who predicted a return of the shower in 1867. This pre- diction was completely fulfilled, but instead of appearing in the year 1867 only, it was first noticed in 1866. On the night of November 13th of that year a remarkable shower was seen in Enrope, while on the corresponding night of the year following it was again seen in this conntiy, and, in fact, was repeated for two or three years, gradually dy- ing away. The oconrrence of a shower of meteors evidently shows that the earth encounters a swarm of meteoroids. The re- currence at the same time of the year, when the eart his in the same point of its orbit, shows that the earth meets 1 270 ASTRONOMY. tho swarm at the same point in successivo years. All the motooroids of tho swurm must of course bo moving in the same diruction, elso they would soon bo widely scattered. This motion is connected witli the radiant point, a well- marked feature of u meteoric shower. XadUat Polat. — Suppose that, during a meteoric k)i<> v>ir, we iivirk the path of each meteor on a star-map, nti in tlic flgiii - t;° we con tiniio the paths backward in a straight line, we sliali lnui ili.t thi'> all meet near one and tlie same point of tiio celcstiul sphere; '!, d. i^, they move as if they all rndiated from this point. The latfr is, therefore, called the radiant point. In the figure the lines do not all pass accurately through tlie same point. Tiiis la owing to the un- avoidnlilo errors made in marking out the path. It is found that the riidiant point is ulviys in the same position among the stars, wherever tho observer iiiti >' be situated, and that M tk» $tan apparenUy movt toward the uett, fhe radiant point mova vith them. The radiant point is due to the fact that the ra<>it he bodies iiem in Mioir passage line seen by an ob- Ircle of tlie celestial to be the centra. If patlis of the meteors, }f the spliere through irill, therefore, be the Just been said it will idicates the direction le earth. If we also moving in space, we irtli, and thus deter- nce. It is not a diffl- and velocity of the on and velocity, the Dg calculated. he velocity of the nined from obsei'' w. fVV.;^ IMAGE EVALUATION TEST TARGET (MT-3) 1.0 ^''^ ta m m ysiiu 116 6" Fhotographk} Sdmces Ccffparatian 23 WKT MAIN STIMT Wr»rM.N.Y. I4SM (71«)t7S.4S03 i.wo-KJ'ms ^m t^m M&&itSM »' i CIHM/ICMH Collection de I \ . ..-WVit and that of the idependently with- nomers, neither of : the other. Gom- swarma of meteor' Olds which cause the November showers move in the same orbit with this comet. The comet passed its perihelion in January, 186G. The most striking meteoric shower commenced in the following November, and was repeated during several years. It seems, therefore, that the meteoroids which produce these showers follow after Tempel's comet, moving in the same orbit with it. This shows a curious relation between copiets and meteors, of which we shall speak more fully in the next chapter. When this fact was brought out, the question naturally arose whether the same thing might not be true of other meteoric showers. Other Showers of lleteori.— Although the November showers (which occur about November 14) are the only ones so brilliant as to strike the ordinary eye, it has long been known that there are other nights of the year (nota- bly August 10) in which more shooting-stars than usual are seen, and in which the large majority radiate from one point of the heavens. This shows conclusively that they arise from swarms of meteoroids moving together around the sun. The ZodiMkl Light.— If we observe the western sky during the winter or spring months, about the end of the evening twilight, we shall sec a stream of faint light, a little like the Milky Way, rising obliquely from the west, and directed along the ecliptic toward a point south-west from the zenith. This Is called the todiaeal Ught. It may also be seen In the east before daylight in the morning during the autumn months, and has sometimes been traced all the way across the heavens. Ite origin is still involved in obscurity, but it seems probable that it arises from an extremely thin cloud either of meteoroids or of semi-gaseous matter like that composing the tail of a comet, spread all around the sun in Me the earth's orbit. lU spectrum Is probably that of reflpcted sunlight, a result which gives color to the theory that It wises from a cloud of meteoroids revolv- ing round the sun. ^'^^M^ii^ii^.i^h^^-:wJ.^=^^!-rK-lh II CHAPTER XIII. COMETS. Aspect of Cohkts. Comets are distinguished from the planets both by their aspects and their motions. They ccme into view without anything to herald their approach, continue in sight for a few weeks or months, and then gradually vanish in the distance. They are commonly considered as composed of three parts: the nucleus, the coma (or hair), and the tail. The nucleus of a comet is, to the naked eye, a point of light resembling a star or planet. Viewed in & telescope, it generally has a small disk, but shades off so gradually that it is difficult to estimate its magnitude. In large comets it is sometimes several hundred miles in diameter. The nucleus is always surrounded by a mass of foggy light, which is called the coma. To the naked eye the nucleus and coma together look like a star seen through a mass of thin fog, which surrounds it with a sort of halo. The nucleus and coma together are generally called the Jiead of the comet. The iail of the comet is simply a continuation of the coma extending out to a great distance, and always di- rected away from the sun. It has the appearance of a stream of milky light, which gi-ows fainter and broader as it recedes from the head. Like the coma it shades off so gradually that it is impossible to fix any boundaries to it. The length of the tail varies from 3" or 3° to 90° or lanets both by their ) into view without inue in sight for a lally vanish in the ■ed us composed of air), and the tail. ked eye, a point of ived in b telescope, Ics off so gradually ^nitude. In large miles in diameter, y a mass of foggy ;he nuked eye the tar seen through a ith a sort of halo. 3uorally called the }ntinnation of the !e, and always di- 3 appearance of a inter and broader coma it shades off any boundaries to 3" or 3° to 90° op I > i )»W. i ''l (Tgi.. COMETS. 275 more. Generally the more brilliant the head of the comet, the longer and brighter is the tail. The above description applies to comets which can be plainly seen by the naked eye. Half a dozen telescopic comets may be discovered in a single year, while one of the brighter class may not be seen for ten years or more. When comets are studied with a telescope, it is found that they are subject to extraordinary changes of structure. Fio. TV.— Tnnoono Ooior without A Nvouro. no. 00.— Tbuwomo Comr wm A NrcutDS. To understand these changes, we must begin by saying that comets do not, like the planets, revolve ai'onnd the sun in nearly circular orbits, but always in orbits so elongated that the comet is visible in only a very small part of its course. See page 278, Fig. 82.) THB YAPOBOVS EHyEIOFE& If a comet is very small, it may undergo no cltanges of aspect during its entire course. If it is an unusually bright one, a bow surrounding tlie nucleus on the side toward tlie sun will develop as the comet approaches the sun. This bow will gradually rise up and spread out on all sides, finally assuming the form of a semi- circle having the nucleus in its centre, or, to speak with more pre- cision, the form of a parabola having the nucleus near its focus. The two ends of this parabola will extend out further and further so M to form a part of tb« tail, and finally be lost in it. Other bows Li 276 AftTltOXOMT. will successively form around the nucleus, nil slowly rising from It like clouds of viipor. These distinct vaporous mosses are culled the entelopea : they slimic oil grmluidiy into the coma so as to \>e witli difficulty distinguished from it. and indeed may Ims considered as part of it. Tiicsc appearances arc apparently caused by masses of vapor streaming up from tliat side of the nucleus nearest tiie sun. and grad- ually spreading around the comet on each side. The form of a bow is not the real form of the envelopes, but only the apparent one in which wo see them projected against tlie bacliground of the sky. Perhaps their forms can be best imagined by supposing the sun to bo directly above the comet, and a fountain, throwing a liquid hori- zontally on all sides, to be built upon that part of the comet which is uppermost Such a fountain would throw its water in the form of ft sheet, fftlUng on all sides of the cometic nucleus, but not touch. Wta. 81.— FoMunoM ov EimLons. ing it. Two or three vapor surfaces of this kind are sometimes seen around the comet, the outer one enclosing each of the inner ones, but no two touching each other. The Physical CoNsniimoH or CoMXTa To tell exactly what a comei. is. we should be able to show bow all the phenomena it presents would follow from the properties of mat- ter, as we learn them at the surface of the earth. This, however, no one has lieen able to do. many of the phenomena being such as we should not expect from the known constitution of matter. All we can do, therefore, is to present the principal characteristics of comets, as shown by observation, and to explain what is wanting to reconcile these characteristics with the known properties of matter. In the first place, all comets which have been examined with the spectroscope show a spectrum composed, in part at least, of bright lines or bftnds. The positions and characters of these bonds leftYe M COMETS. 917 slowly rising from It moRses are culled tlie ■onin 80 as to \te witli r Im3 considered ns part d liy masses of vapor rest tiic sun, and grad- Tlie form of a bow ' the apparent one in cicground of the sliy. supposing the sun to browing a liquid hori- 't of the comet which its water in the form ucleiu, but not touch- id are sometimes seen ih of the inner ones, F COMXTa ! able to show bow all be properties of mat- I. This, however, no !na being such as we 1 of matter. All we racteristics of comets, ) wanting to reconcile of matter. n examined with the rt at least, of bright ' these bands lekYe ao doubt that carbon, hydrogen, and nitrogen, and probably eaeygen ar« present in the cometary matter. More than twenty comets have been exiimined since the invention of the spectroscope and all agree in giving the same evidence. In some recent comets toditim has also been discovered. In the last chapter it was shown that swarms of minute particles called meteoroids follow certain comets in their orbits. This is no doubt true of all comets. We can only regard these meteoroids as fragments or debrit of the comet. On this tlieory a telescopic comet which has no nucleus is simply a cloud of these minute bodies. The nucleus of the brighter comets may either be a more condensed mass of such bodies or it may be a solid or liquid body itself. If the reader has any difHculty in reconciling this theory of de- tached particles with the view already presented, that the envelopes from which the tail of the comet is formed consist of layers of vapor, he must remember that vaporous masses, such as clouds, fog, and smoke, are really composed of minute separate particles of water or carbon. Vormation of ths Comet's Tail. — The tall of the comet is not a per- manent appendage, but is composed of the masses of vapor which we have already described as ascending from the nucleus, and after- ward moving away from the suu. The tail which we see on one evening is not absolutely the same we saw the evening before, a por- tion of the latter having been dissipated, while new matter has taken its place, as with the stream of smoke from a steamship. The motion of the vaporous matter which forms the tail being always away from the sun, there seems to be a repulsive force exerted by the sun upon it. The form of the comet's tail, on the supposition that it is composed of matter driven away from the sun with a uni- formly accelerated velocity, has been several times investigated, and found to represent the observed form of the tail so nearly as to leave little doubt of its correctness. We may, therefore, regard it as an observed fact that the vapor which rises from the nucleus of the comet is repelled by the sun instead of being attracted toward it, as larger masses of matter are. No adequate explanation r.'l this repulsive force has ever been given. , Konon or CkmiTi. Previous to the time of Newton, no certain knowledge respecting the actual motions of comets in the heavens had been acquired, ex- cept tlMt they did not movb around the sun in ellipses like the planets. 278 ASTRONOMY. When Newton investigAted the mathematical results of the theory of gravitation, he found that a body moriiig under the nttraction of the Bim might describe either of tlie three conic lectioiiH, the eliipse, parabola, or hyperbola. Bodies moving in an ellipse, as the planets, would complete their orbits at regular intervals of time, according to laws already laid down. But if the body moved in a parabola or an hyperbola, it would never return to the sun after once passing it, but would move off to inflnity. It was, therefore, very natural to conclude that comets might be bodies which resemble the planets in moving under the sun's attraction, but which, instead of describing Fro. n.— Eujrno and Pakabouo Obbits. an ellipse in regular periods, like the planets, move in parabolic or hyperbolic orbits, and therefore only approach the sun a single time during their whole existence. This theory is now known to be essentially true for most of the observed comets. A few are indeed found to be revolving around the sun in elliptic orbits, which differ from those of the planets only in being much more eccentric. But the greater number which have been observed have receded from the sun in orbita which we are un- able to distinguish from parabolas, though it is possible they may be eitremely elongated ellipses. Comets are therefore divided with re< COMETS. 279 esults of the theory ler the Attraction of iectioii8, the ellipse, ipse, as tlie planets, of time, according ed in a parabola or fter once passing it, ire, very natural to inblo the planets in stead of describing ins. )Te in parabolic or le sun a single time le for most of the I r«volTing around of the planets only umber which have s which we are un- issible they may be re divided witli re« spcct to their motions into two classes; {I) periodic eomett, which are known to move in i-llipiii; orbits, uml to return to tiiu sun at fixed in- tervals; and (2) parabolic eumeU, apparently moving in parabolas, never to return. The first discovery of the periodicity of a comet wns made by IIai,- hBY iu connection willi the ^reat comet uf 1602. Examining the records of past observations, he found tliat a comet moving in nearly the same orbit with that of 1682 had been seen in 1607, and still another in 1581. He was therefore led to the conclusion that these three comets were really one and the same object, returning to the sun at intervals of about 76 or 76 years. Ho therefore predicted that it would appear again about the year 1758. Tlie comet was flrst seen Fla. n.— Obkt of BUujr's OoiiaT. on Christmas-day, 1758, and passed its perihelion March 12th, 1759, only one month before the predicted time. At present it is possible to predict the places of some of the best known periodic comets almost as accurately as the positions of the planets. We give a figure showing the position of the orbit of Hallkt's comet relative to the orbits of the four outer planets. It attained its greatest distance from the sun, far beyond the orbit of Ntptutu, about the year 1878, and then ccmmencrd its return Journey. The figure shows tlio position of the comet iu 1874. It was then far be- yond the rci^h of the most powerful telescope, but its distance and direction admit of being calculated with so much precision that a telescope could be pointed at it at any required moment. iiL« 380 AsrnoyoMT. BlMABKABLI COMITI It is familiarly known that bright comctd were in former years objects of great terror, being supposed to presage the fall of empires, tlie death of monarchs, the approach of earthquakes, wars, pestilence, and every other calamity which could afflict mankind. In showing the entire grouudlessnoss of such fears, science has rendered one of its greatest benefits to mankind. In 1456 the comet known as Hallet's, appearing when the Turks wore making war on Christendom, caused Wn. 84.— Mdal or nn OmuT Comr of IMMl. such terror that Pope Calixtus ordered prayers to be offered in the churches for protection against it. This is supposed to be the origin of the popular myth that the Pope once issued a bull against the comet. The number of comets visible to the naked eye, so far as recorded, has generally ranged from twenty to forty in a century. Only a small portion of these, however, have been so bright as to excite universal notice. Comet of 1680. — One of the most remarkable of these brilliant comets is that of 1680. It inspired such terror that a medal, of which wo present a figure, was struck upon the Continent of Europe to quiet apprehension. A freo translation of the inccription is : " The star threatens COMETS. I nets were in former ipposed to presage rchs, the approach rery other calamity lowing the entire IS rendered one of llet's, appearing iristendom, caueed or IMMl. jred prayers to be against it. This lar myth that the (t. aked eye, so far as enty to forty in a se, however, have ce. narkable of these pi red such terror Sgure, was struck apprehension. A rhe star threatens evil things; trost only I God will turn them to good." • Whot makes this comet especially rcmorkable in history is that Newton calculated its orbit, and showed that il moved around the sun in a conic section, in obedience to the law of gravitation. Great Comet of 1811.— It has a period of over 8000 years, and its aphelion distance is about 40,000,000,000 miles. Qrtftt Comet of 1848.— One of the most brilliant comet* which have apiwarcd during the present century was thai of February, 1843. It was visible in full daylight close to the sun. Considerable terror was caused in some qu•^ ters lest it might presage the end of the world, which had been predicted for that year by Miller. At perihelion it pMsod nearer the sun than any other body has ever been known to pass, the least distance being only about one fifth of the sun's semidiometer. With a very slight change of iU original motion, it would have actually fallen into the sun. Oreat Comot of 1868.— Another comet remarkable for the length of time it remained visible was that of 1868. It i> frequently called after the name of Donati, its first discoverer. No comet visiting our neighborhood in recent times has afforded so favorable an oi.portunity for study- inc it« Phyical constitution. Its greatest brilliancy occurred about the beginning of October, when its tail was 40' in length and 10" in breadth at its outer end. Its period is 1960 years. "7^,p;;7;;,;^;;7ri.ouid notu* the c«re which ««"""'"»• "'j»»V'; .<«(AtioD hu t«ken to m«ke it cousolalory. to make it rliymc. sod S^^irimplid?; U.C year of the comet hy wri.iug cerUiB Romwt numeral* krger than llie otiier letleri. ^ii 1 i Ito. 8K,--DoiiAn*a Ooot or im. COMETS. 988 Great Comet of 1882. — It is yet too soon to speuk of the results of the observutions on this magnificent object. Its splendor will not soon be forgotten by those who have seen it. Eneke'i Comet ud the Xeristing Medium.— Of telescopic comets, that which has been most investigated by astronomers is linown ns Enckk's comet. Its period is between three and four years. Viewed witli a telescope, it is not different in any respect from otlier tele- scopic comets, appearing simply as a mass of foggy light, somewhat brighter near one side. Under the most favorable circumstances, it is just visible to tlie naked eye. The circumstance which has lent most interest to this comet is that the olwcrvations which have been made upon it seem to indicate that it is gradually approaching tho sun. Encke attributed this change in its orbit to the existence in space of a resisting medium, so rare as to have no appreciable effect upon the motion of the pliuiets, and to be felt only by bodies of ex- treme tenuity, like the telescopic comets. The approach of the comet to the sun is shown, not by direct observation, but only by a gradual diminution of the period of revolution. It will be many centuries before thii period would be so far diminished that the comet would actually touch the sun. If the change in the period of this comet were actually due to the cause which Ekcke supposed, then other faint comets of the same kind ought to be subject to a similar Influence. But the Investiga- tions which have been made in recent times on these bodies show no deviation of the kind. It might, then'fore, be concluded that the change in the period of Enckb'b comet must be due to some other cause. There is, however, one circumstance which leav^ us in doubt. Enckb's comet passes nearer the sun than any other comet of short period which has been observed with suiflcient care to de- cide the question. It may, tlierefore, be supposed that the resisting medium, whatever it may be, Is densest near the sun, and does not extend out far enough for the other comets to meet it. The question is one very dIfDcult to settle. The fact is that all comets exhibit Blight anomalies in their motions which prevent us from deducing oouclusions from them with tho same ceruinty that we should from those of the planeU. One of the chief difHculties in Investigating the orbits of comets with all rigor is due to the difficulty of obtaining accurate positions of the centre of so ill-deflned an object as the nudeos. u i!rt" PART III. THE UNIVERSE AT LARGE. II INTRODUCTION. In our studies of the heavenly bodies, we have hitherto been occupied almost entirely with those of the solar sys- tem. Although this system comprises the bodies which are most important to us, yet they form only an insignifi- cant part of creation. Besides the earth on which we dwell, only seven of the- bodies of the solar system are plainly visible to the naked eye, whereas some 2000 stars or more can be seen on any clear night. The material universe, as revealed by the telescope, con- sists principally of shining bodies, many miUions in num- ber a few of the nearest and brightest of which are visible to the naked eye as stars. They extend out as far as the most powerful telescope can penetrate, and no one knows how much farther. Our sun is simply one of these stars, and does not, so far as we know, differ from its fellows in any essential characteristic. From the moat careful estimates, it is rather less bright than the average of the nearer stars, and overpowers them by its brilliancy only because it is so much nearer to us. The distance of the stars from each other, and therefore from the sun, is immensely greater than any of the dis- tances which we have hitherto had to consider in the soIm i^^m^s^mss^t-'- 286 ASmONOMT. system. In fact, the nearest known star is abont seven thousand times as far as the planet Neptune. If we sup- pose the orbit of this planet to be represented by a child's hoop, the nearest star would be three or four miles away. We have no reason to suppose that contiguous stars are, on the average, nearer than this, except in special cases where they are collected together in clusters. The total number of the stars is estimated by millions, and they are probably separated by these wide intervals. It follows that, in going from the sun to the nearest star, we would be simply taking one step in the universe. Tlie most distant stars visible in great telescopes are probably several thousand times more distant than the nearest one, and we do not know what may lie be3'ond. The point wo Avish principally to impress on the i-eader in this connection is (hat, although the stars and planets pre- sent to the naked eye so great a similarity in appeiirance, there is the greatest possible diversity in their distances and characters. The planets, though many millions of miles away, are comparatively near us, and form a little family by themselves, which is called the solar system. The fixed stars are at distances incomparably greater — the nearest star being thousands of times more distant than the farthest planet. The planets are, so far as we can see, worlds somewhat like this on which we live, while the stars are suns, generally larger and brighter than our own. Each star may, for aught we know, have planets revolving around it, but their distance is so immense that the largest planets will remain invisible with the most powerful tele- scopes man can ever hope to construct. The classification of the heavenly bodies thus leads us to this curious conclusion. Our sun is one of the fomily of )wn star is about seven )t Neptune. If we sup- represented by a child's iree or four miles away, contiguous stars are, on pt in special cases where ers. itimatcd by millions, and leso wide intervals. It to the nearest star, we in the universe. The telescopes are probably it than the nearest one, )eyond. ) impress on the i-eader he stars and planets pre- milarity in appciirance, Tsity in their distances >ugh many millions of iT us, and form a little died the solar system, comparably greater— the mes more distant than re, so far as we can see, i we live, while the stars righter than our own. , have planets revolving nmense that the largest the most powerful tele- net. r bodies thus leads us to is one of the family of THE UNIVERSE AT LARGE. 387 stars, the other members of which stud the heavens at night, or, in other words, the stars are suns like that which makes the day. The planets, though they look like stars, are not such, but bodies more like the earth. The great universe of stars, including the creation in its largest extent, is called the stellar system, or stellar universe. We have first to consider how it looks to the naked eye. i#; m » -i CHAPTER I. C0N8TELLATI0N& Oekekal Aspect or the H£AyBH& When we view the licttvens with the unassisted eye, the stars apiiear to be scattered nearly at random over the surface of the celestial vault. The only deviation from an entirely random distribution which can be noticed is a cer- tain grouping of the brighter ones into constellations. A few stars arc comparatively much brighter than the rest, and there is every gradation of brilliancy, from that of the brightest to those which are barely visible. We also notice at a glance that the fainter stars outnumber the bright ones; so that if we divide the stars into classes ac- cording to their brilliancy, the fainter classes will contain the most stars. The total number one can see will depend very largely upon the clearness of the atmosphere and the keenneas of the eye. There are in the whole celestial sphere about 6000 stars visible to an ordinarily good eye. Of these, however, we can never see more than a fraction at any one time, because one half of the sphere is always below the horizon. If we conld see a star in the horizon as easily as in the zenith, one half of the whole number, or 3000, would be visible on any clear night. But stars near the horizon are seen through bo great a thickness of atmosphere as greatly to obscure their light; consequently only the I ra HXAyXH& ho unassisted eye, the at random over the >nly deviation from an :an be noticed is a ccr- }8 into constellations, brighter than the rest, •illiancy, from that of iirely visible. Wo also • stars outnumber the B stars into classes ac- ter classes will contain ill depend very largely ro and the keenness of celestial sphere about r good eye. Of these, than a fraction at any liere is always below the the horizon as easily as number, or 3000, would , stars near the horizon :ness of atmosphere as consequently only the CONSTELLATIONa. 289 brightest ones can there be seen. As a result of this ob- scuration, it is not likely tliat more than 2000 stars can ever be taken in at a single view by any ordinary eye. About 2000 other stars are so near the south pole that they never rise in our latitudes. Hence out of the 6000 supposetl to be visible, only 4000 ever como within the range of our vision, unless we make a journey toward the equator. The Oalaxy.— Another feature of the heavens, which is less striking than the stars, but has been noticed from the earliest times, is the Galaxy, or Milky Way. This object consists of a mngnificent stream or belt of Avhite milky light 10° or 15° in brcadlh, extending obliquely around the celestial sphere. During the pjiring months it nearly coinciiles wiili our horizon in the early evening, but it can readily be seen at all other times of the year spannini? the heavens like an arch. It is for a portion of its length split longitudiually into two parts, which remain separate through many degrees, and are finally united again. The student will obtain a better idea of it by actual examination than from any description. He will see that its irregularities of form and lustre are such that in some places it looks like a mass of brilliant clouds. Lnoid and Teleicopio Stan. — When we view the heavens with a telescope, we find that there are innnmerable stars too small to be seen by the naked eye. We may there- fore divide the stars, with respect to brightness, into two great classes. Lofiid Stan are those which are yisible without a tele- scope. TelMOopie Stan are those which are not so visible. When Galilbo first directed his telescope to the heav- 990 ASTRONOMY. ens, about the year 1610, ho perceived that the Milky Way was composed of stars too faint to bo individually seen by the unaided eye. We thus have the interesting fact that although telescopic stars cannot be seen one by one, yet in the region of the Milky Way they arc so numer- ous that they shine in masses like brilliant clouds. Huy- OHENS in 1656 resolved a large portion of the Galaxy into stars, and concluded that it was composed entirely of them. Kepleh considered it to be a vast ring of stars surround ing the solar system, and remarked that the sun must be situated near the centre of the ring. This view agrees yery well with the one now received, only that the stars which form the Milky Way, instead of lying around the solar system, are at a distance so vast as to elude all our powers of calculation. Such aro in brief the more salient phenomena which are presented to an observer of the starry heavens. We shall now consider how these phenomena have been clas- sified by an arrangement of the stars according to their brilliancy and their situation. KAOHinrsu ov the Stabs. In ancient times tlie stars were arbitrarily clnssifled into siz orders of magnitude. The fourteen briglitest visible in our lati- tude were designated as of the first magnitude, while tboae which were barely visible to the nalced eye were said to be of the sixth magnitude. This classificatioD, it will be noticed, is entirely arbi- trary, since there are no two stars which are absolutely of the same brightness; that is, if all the stars were arranged in the order of their actual brilliancy, we should find a regular gradation from the brightest to the faintest, no two being precisely the same. There- fore the brightest star of nny one magnitude is about of the same brilliancy with the faintest one of the next higher magnitude. Be- tween the north pole and 85° south declination there are: iTT'--,. COmTELLA TI0N8. 291 red that the Milky t to bo individually hare the interesting mnot be seen one by »y they arc so numer- lliant clouds. Huy- u of the Galaxy into )8ed entirely of them, ig of stars surround hat the sun must be g. This view ugroos , only that the stars of lying around the st as to elude all our tt phenomena which starry heavens. We nena have been clas- rs according to their Stabs. rarily cinnifled into six litest visible in our Ihti- litude, wliile those wliich I said to lie of the siztli noticeu, is entirely arbi- ire absolutely of the same arranged in the order of gular gradation from the cisely the same. There- ude is about of the same t higher magnitude. Be- tion there are: 14 stars of the flrst magnitude. 48 " second 16a " third 818 " fourth 854 " flftli 8974 " sixth 5855 of the first six magnitudes. Of these, however, nearly 2000 of the sixth magnitude are so faint that tliey can bo seen only by an eye of extraordinary lieenness. A star of the second magnitude is four tenths as bright as one of the first; one of the third is four tenths as bright as one of the second, and so on. THB GomTKILATIOVS AITS HAMU Of THB BTABE The earliest astronomers divided the stars into groups, called constellations, and gaye special proper names both to these groups and to many of the more conspicuous stars. We have evidence that more than 8000 years Imfore the commence- ment of the Ciiristian chronology the star Siiiu; the brightest in tlie heavens, was known to the Egyptians under the name of Soithii. The seven stars of the Oreat Bear, so conspicuous in our northern sky, were known under that name to Homer and Hesiod, as well as the group of the P'eiada, or Seven Stars, and the constellation of Orion. Indeeil, it would seem that all the earlier civilized nations. Egyptians, Chinese, Greeks, and Hindoos, had some arbitrary divi- sion of the surface of the heavens into irregular and often fantastic shapes, which were distinguished by names. In early times the names of heroes and animals were given to the constellations, and these designations have come down to the present day. Each object was supposed to Iw painted on the surface of the heavens, and the stars were designated l>y tlieir position upon some portion of the object. The ancier of stars of Ruch classes will long prevent tiic accumulation of statistics on this question; but tliis much is certain, that in special regions of the sliy. which have been searchingly examined by rarious telescopes of successively increas- ing apertures, the numl>er of new stars found is by no means in pro- portion to the increased instrumenlal power. If this is found to be true elsewlioro, the conelusitin may Iw that, after all, tbe stellar sys- tem can be experimentally shown to be of finite extent, and to con- tain only a finite number of stars. We have already staled timt in the whole sky an eye of ayeragn power will see about 6000 stars. With a telescope this number is greatly increased, and the most powerful telescopes of modern times will probably show more than 20,000,000 stars. As no tnistworthy estimate bus ever been made, there is great uncertainty upon this point, and the actual number may range anywhere between 15,000,000 and 40.000,000. Of this number, not one out of twenty has ever been catalogued at all. The southern sky lias many more stars of the first seven magni- tudes than the norlliern, and the zones immediately north and south of the equator, although greater in surface than any others of the same width in declination, arc absolutely poorer in such stars. Tills will be much better understood by consulting the graphical representation on page 294. On this chart are laid down all the stars of the British Association Catalogue (a dot for each star), and beside these the Milky Way is represented. The relative richness of tlie TarioUs zones can be at once seen. The distribution and number of the brighter stars (1st to 7th magni- tude) can be well under8toou.'.-is«tM*UKf« VoystKlJ.ATtONS. m i In M 314, 03« hilars rrom llio flfHl to llic 9.5 magnltudcg nrc cnu- nu!ruU in the short time of 4^ hours, and remains of 4™ for 20 minutes. It then com- „'ii?MWW«»(L'4ii)fc -^ ^mfi^^aaifim i IRY STARS. BIABLE. taut light. Since the stars variable in bril- iod of a variable star it goes through all its rilliancy. Mint Cell (o Ceti) and bont twelve times in test brightness (some- sometimes not above lly decreases for about the nakerl eye, and so i. From the time of 3 time of its maximum , or the interval from days, but this period e star at the maxima iable star since 1667. pitnde; after remain- In the short time of ainutes. It then com- ■t^tmm9umia!0i»^tts. ■-. VABlABLE AND TEMPOltABt STAtiS. 2^ mences to increase in brilliancy, and in another 3i hours it is again of the 2d magnitude, at which point it remains for the rest of its period, about 2" 12". These two examples of the class of variable stars give a rough idea of the extraordinary nature of the phenomena they present. A closer examination of others discloses minor variations of great complexity and apparently with- out law. About 90 variable stars are well known, and as many more are suspected to vary. In nearly all cases the mean period can be fairly well determined, though anomalies of various kinds frequently appear. The principal anomalies are: First. The period is seldom constant. For some stars the changes of the period seem to follow a regular law; for others no law can be fi^jed. Second. The time from a minimum to the next maxi- mum is usually shorter than from this maximum to the next minimum. mrd. Some stars (as /3 Lyra) have not only one maxi- mum between two consecutive principal minima, but two such maxima. For ft Lyra, according to Arqelandeb, 3* a"* after the principal minimum comes the first maxi- • mum; then, 3* 7" after this, a secondary minimum in which the star is by no means so faint as in the principal mini- mum, and finally 8* 3" afterward comes the principal maxi- mum, the whole period being 12* 21" 47«. The course of one period is illustmted In the following Uble, supposing the period to begin at 0* 0*. Opposite each phase to given the inten^ty of light in terms of r ^y^ = !• 998 A8TnomM7. , t PhMM of ^ Lorrs. Principal Minimum o* Qb First Maximum 8* 2'' Second Minimum ,\ 6* 9'' Principal Maximum 9* 12'' Principal Minimum ]2* 22" ReUUre Intoniity. 0.40 0.88 0.58 0.89 a4o The periods of 94 well-determined variable stars being tabulated, it appears that they are as follows: Ptoriod between No. of Stan. 18 1 4 4 5 9 14 18 Period between No. of Stank Id. and 20 d. 20 50 50 100 100 150 150 200 200 250 250 800 800 850 850 d. and 400 d. 400 460 450 500 500 550 650 600 600 650 650 700 700 750 18 8 8 1 , 1 :s = 04 It is natural that there should be few known variables of periods of 500 days and over, but it is not a little remarkable that the periods of over half of these variables should fall between 250 and 450 days. The color of over 80 per cent of the variable stars is red or orange. Red stars (of which 600 to 700 arc known) are now receiving close attention, as there is a strong likelihood of finding among them many new variables. The spectra of variable stars show changes which appear to be connected with the variations in their light. TXMFOBAST OB VlW STAXI. There are a few cases known of apparently new stare which have suddenly appeared, attained more or less brightness, and slowly de- creased in magnitude, either disappearing totally, or finally remain- ing as comparatively faint objecta. The most famous one was that of 1572, which attained abrightness ReUUr* Intoniity. .... 0* Ofc 0.40 .... 9* 2" 088 .... 6* 9* 0.58 .... 9* 12'' 089 .... ]2* 22- 040 le stars being tabulated, 1 between No. of Stem and 400 d. 18 460 8 600 8 S50 MO 860 1 700 , 760 1 2 = = 04 wn variables of periods arkable that the periods Iween 260 and 460 days, e stars is red or orange, ire now receiving close ding among them many [es wbich appear to be TAXI. Y new stars which have ghtness, and slowly dc- itally, or finally remain- ich attained abrightness tmmaiti VAlttASLB AifD mitPoniRT STAM. SOd greater than that of Biriut or JupUtr and approached to Venu$, being even visible to the eye in daylight. Ttcho Brake first observed this star in November, 1672, and watched its gradual increase in light until iu maximum in December. It then began to diminish in bright- ness, and in January, 1573, it was fainter than ^upUer. In February it was of the 1st magnitude, in April of the 2d, in July of the 8d, and in October of the 4th. It continued to diminish until March, 1574, when it became invisible, as the telescope was not then in use. Its color, at flret intense white, decreased through yellow and red. Wlien it arrived at the 6th magnitude its color again became white, and so remained till its disappearance. Tycho measured iU distance carefully from nine stars near it, and near iU place there is now a star of tlie 10th or 11th magnitude, which is possibly the same star. The history of temporary stars is in general similar to that of the star of 1672, except that none have attained so great a degree of bril- liancy. More than a score of such objects are known to have ap- peared, many of them before the making of accurate observations, and the conclusion is probable that many have appeared without recognition. Among telescopic stars there U but a small chance of detecting a new or temporary star. Several supposed cases of the disappearance of stars exist, but here there are so many possible sources of error that great caution is necea- sary in admitting them. Two temporary stars have appeared since the invention of the spec- troscope (1850). and the conclusions drawn from a study of their spec- tra are most important as throwing light upon the phenomena of variable stars in general. The general theory of variable stars which has now the most evi- dence in its favor is this: These bodies are, from some general cause not fully understood, subject to eruptions of glowing hydrogen gas from their interior, and to the formation of dark spots on their sur- faces. These eruptions and formations have in most cases a greater or less tendency to a regular period. , . . «, In the case of our sun (which is a variable star) the period is 11 years, but in the case of many of the stars it is much shorter. Ordi- narily, as in the case of the sun alid of a large majority of tiie stars, the variations are too slight to affect the total quantity of light to any visible extent. But in the case of the varial)le slors this spot-producing power and the liability to eruptions are very much greater, and thus we have changes of light which can be readily perceived by the eye. Some additional strength is given to this theory by the fact just men- tioned, that so large a proportion of the variable stars are red. It is well kao«n that glowing bodies emit a larger proportion of red rays and 3i tf 800 ABTROlfOMT. a smaller proportion of blue ones the cooler tlicy become. It is there- fore probable that the red stars have the lenst heat. This being the case, it is more easy to produce spots on tlieir surface; and if their outside surface is so cool as to become solid, the glowing hydrogen from the interior when it did burst through would do so with more power than if the surrounding shell were liquid or gaseous. There is, however, at least one star of which the variations mny be due to an entirely different cause; namely, Algol. The extreme regu- larity with wliich the light of this object fades awny and disappears Buggest<« the possibility that a dark body may be revolving around it, and partially eclipsing it at every revolution. Tlie law of variation of its light is so different from that of the light of other variable stars as to suggest a different cause^ Most others are near their maximum for only a small part of their period, while Al^ is at its maximum for nine tenths of it. Others are subject to nearly continuous changes, while the light of Algol remains constant during nine tenths of its period. »em m0 ^ t mmvk tlicy become. It is there- St lieat. Tliis being tbe lieir surface; and if Ibcir (I, tlie glowing liydrogcn I would do so with more quid or gaseous, icli tlie variations may be Algol. Tlie extreme regu- idcs awny and disappears ty be revolving around it, in. The law of variation ght of other variable stars B are near their maximum Algol is at its maximum early continuous changes, during nine tenths of its t!ltA!»Tt:ft 111. MULTIPLE STARS. Chasaotxb or DoraiB amd Multiflb Staxi. When we examine the heavens with telescopes, we find many cases in which two or more stars are extremely close together, so as to form a pair, a triplet, or a group. It is evident that there are two ways to account for this appear- ance. 1. We may suppose that the stars happen to lie nearly in the same straight line from us, but have no connection with each other. It is evident that in this case a pair of Btars might appear double, although the one was hundreds or thousands of times farther off than the other. It is, moiwver, impossible, from mere inspection, to determine which is the farther off. 2. We may suppose that the stars are really near together, as they appear, and are to be considered as forming a con- nected pair or group. A couple of stars in the first case is said to be optically double. Stars which are really physicaUy connected are said to bo phyneally double. If th« lucid stars are equally distributed over the celestial sphere, tbe chances are 80 to 1 against any two being within three minutes of e«5h other, and the chances are 500.000 to 1 against the six visible stars of the PtowMfc* being accidentally associated as we see thetn. When the millions of telescopic stanaie conridered. there it a gnatw dod ABTItdrnMY. Fia. W.— Tta QoiamwiM Sub probability of such accidental juxtaposition. But the probability of many such cases occurring is so extremely small that astronomers regard all the closest pairs as physically connected. Of the 600,000 stars of the first ten magnitudes, about 10,000, or one out of every 90, has a companion within a distance of BO" of arc. This proportion is many times greater than could possi- bly be the result of chance distribution. There arc several cases of stars which appear double to the naked eye. e Lyra is such a star and is an interesting oli- ject, from the fact that eacli of the two stars which compose it is itself double. This minute pair of points, capable of being distinguished as doub!e only by the most perfect eye (without the tele- scope), is really composed of two pairs of stars wide apart, with a group of smaller stars between and around them. The flguie ahowa the appearance in a telescope of consider- able power. Bevolatioaa of BenUe Stars— Binary Vysteau.— It is evident that if double stars are endowed with the property of mutual gravitation, they must be revolving around each otlier, as the earth and planets revolve around the sun, else they would be drawn to- gether as a single star. The method of determining the period of revolution of a binary star is illustrated by the figure, which is supposed to rep- resent the field of view of an in> verting telescope pointed toward tlie south. The arrow shows the direction of the apparent diur- nal motion, Tlie telescope is supposed to be so pointed that tite brighter star may >ie in the centre of tlie field. The num- bers around the surrounding circle then show the angle of position, supposing the smaller star to be in the direcUon of the number. 87.— Poanoii-AiMUi Stab. DooBia But the probabiHty of ' BDiall that aMtroDotners nected. Of the 600,000 MX), or one out of every of arc. This proportion greater than could possi* It of chance distribution, reral cases of stars which ,0 the nailed eye. e Lyra nd is an interesting oli- ract that eacli of the two npose it is itself double, tir of points, capable of shed as doub!e only by ct eye (without the tele- IT composed of two pairs apart, with a group of between and around I a telescope of consider- «.— It is evident that if ' of mutual gravitation, mov-Amui ov a Donna Stab. in tbe direction of the f.^ MULTIPLE STABS. 303 Fig. 87 is an example of a pair of stars in which the position- nncle Is about 44°. . , , .i.« If by measures of this sort extending through a series of years, the .llstance or position-angle of a pair of stars is found to change p«i- odicaUy, it shows lliat one star is revolving around tl»e other. Such a pair is called a binary ttar or binary ,y»Um. The only disliuction which we can make between binary systems ond ordinary double stars is founded on the presence or absence of this observed motion. It is probable that nearly all the very close double stars are really binary systcns. but that many hundreds of years are required to per- form a revolution in some Instances, so tliat the motion has not yet been detected. . ..« t . .^» The discovery of binary systems is one of great scientific interest, because from them we loam that the law of gravitation includes the stars as well as the solar system in its scope, and may thus be regarded as truly universal. CHAPTER IV. NEBULA AND CLUSTERS. < i; DnOOVBBT OF Hebvls. In the star-catalogues of Ptolemy, Hevelius, and the earlier writers, there was included a class of nebulous or cloudy stars, which were in reality star-clusters. They ap- peared to the naked eye as masses of soft diffused light of greater or less extent. In this respect they were quite analogous to the Milky Way. In the telescope, the nebu- lous appearance of these spots vanishes, and they are seen to consist of clusters of stars. As the telescope was improved, great numbers of such patches of light were found, some of which could be re- solved into stars, while others could not. The latter were called nebula and the former star-clusters. About 1656 HuYQHENS described the great nebula of Orion, one of the most remarkable and bnlliuiit of these objects. During the last century Messier, of Paris, made a list of 103 northern nebula), and Lacaille noted a few of those of the southern sky. Sir William Herscbel with his great telescopes first gave proof of the enormous number of these masses. In 1786 ho published a catalogue of one thousand new nebulae and clusters. This was fol- lowed in 1789 by a catalogue of a second thousand, and in 1802 by a third catalogue of five hundred new objects of this class. Sir JoHi^ Herscsel added about two thou- NEBULJl AND CLUSTERS. 805 ERS. [.S. , Hevelius, and the ;Ia88 of nebulous or '-clusters. They ap- Boft diffused light of Bct they were quite telescope, the nebu- 18, and they are seen at nnmbers of such which could be re- iot. The latter were ters. the great nebula of id bnlliuiit of these siER, of Paris, made CAiLLB noted a few VlLLIAM HeRSCBEL )of of the enormous nblished a catalogue ters. This was fol- nd thousand, and in 3red new objects of ed about two thou- Mnd more nebul». The genend c. .logue of nebulas and clusters of stars of the latter astrouomor, published in 1864, contains 6079 nebulae. Over two thirds of these were first discovered by the Hbrschels. GLunnoATiox of Hibto* aw CwrmBa In rtudvlnir these objects, the first question we meet Is this: Are all thSi tt. clustei of sfr. which look diffused only because t^yZ rSsUnt that our tele««>pe. cnnot d««tlnguUh them Bepu- S 'tor are some of them in reality what they seem to bo ; namely, ''K ^Tnl^rol 1784 and 1785. Sir W..u.- H-b-chk. tool Z Slt^iew. He considered the Milky Way "»«»»«»« ».u\» LXeriL of .tn«. and all nebuto naturally ««ned to him to L« but Bear in a general mllklnesa or nebulosity. « , j jt. ^n ItIi: however. hU view, underwent a change. He had dls. covered a MftuioM tar (properly so called), or a sUr which was un- S^ly rimtar to tb!r«Jfounding .tars, and which was encom. Dossed by a halo of nebulous light. j .. _ HTsays: "Nebul. can be elected so that an Insensible gradation •hSfuike place from a coarse duster like the Pto«to do^u to a milky nebulosity like that in OHon, every intermediate step bein? repScnted. This tends to confirm the hypothesis that all are com- Doswi of Stan more or less remote. ^ comparUon of Uie xmoatremet of the series » •«T" «""' f and a nebulous star. Indicates, however, that tht mbuMtg about th, ttariitutof a ttarrg nature. " Considering a typical nebulous star, and supposing the nucleus and chevelure to be connected, we m.iy. first, suppose the whole to be of stars. In which case either the nucleus Is enormously larger than other stars of Ito stellar magnitude, or the envelope is composed of sUrs Indefinitely small; or. second, we must odmit that thTitar \» involved in a Mning fluid of a nature U>taUy unknou,n to **'"The shining fluid might exist Independently of stars. The licht of this fluid Is no kind of reflection from tlie star in the centre If this matter is self-luminous. It seems more fit to pro- duce a star by Ite condensation than to depend on the star for Its ezlstcnc*!. ^r.aif^g.'-^^4^'''/t--^. 806 ASTRONOMY. " Both diffused nebulositiea and planetary nebulte are better ac« counted for by the liypothesis of a shining fluid than by supirasing tliem to be distant stars." This was the flrst exnct statement of the idea thnt, beside stars and star-clusters, wo have in tlio universe a totally distinct series of objects, probably much more simple in tlieir constitution. Observa- tions on the spectra of these bodies have entirely conflrmed the con- clusions of Herbchbl. Nebulae and clusters wer« divided by Hbimchbl into classes. He WtB. IB.— flnoAL VmMOtk. applied the name planetetrjf tiOula to certain circular or elliptic nebulsB which in his telescope presented disks like the planeto. ^ral tubidm are those whose convolutions have a spiral shape. This class is quite numerous. The different kinds of nebulss and clusters will be better under, stood from the cuU and descriptions which follow than by formal definitions. It must be remembered that there is an almost infinite Tkriety of such shapes. ry nebulce are better ms fluid than by supiwBing le idea that, beside Btara totally distinct scries of r constitution. OI)serva- llrely cooflrmed Uie con- lacHSL into classes. He NBBVL^ AND CLU8TSBB, 4 tain circular or elliptic dislu lilie the planets, ive a spiral shape. This •a wlil be belter under, i folloir than by formal era ia an almost inflnit« na. n.—Vn Omma ob 308 AtnnoNOMT. Btab-Clvstiu The moBt noted of all the cliiHter» i« the I^eiade*. wlitoli Imve al- ready been brh'tly dt-dcrllK'd in fonnccllon with the couglelhition Tauni». Tlie nverngc niikcd eye on erwily diHtinguliih fix hIius wltlilii It, but under favoruble conditions ten, eleven, twelve, or more stuncnn be counted. WItIt tlio tclegcoiM), over n hundred stara are «een. The cluHtcrs represented in Flg». 90 ond 91 are good cxamplvR of tlieir cluwei. The first is globular and contains sovernl tliousand sninll stun. Tlie second is u cluster of about 200 stars, of mngni- tudcs varying from the ninth to the thirteenth and fourteenth. In which the Itrighter sUrs are scattered. Fia. M.— OiiOBOijui Ouwraa. no. 91 — CoMPaaaaaii Cixtfnm, Clusters nre probably Kibject to central powers or forces. This waa seen by Sir WiLMAM HBBScmet in 1789. He says: " Not only were round nebula and clusters formed by central powers, but likewise every cluster of sUrs or nebula that shows a prndual condensation or increasing brightness toward a centre. This theory of central power is fnlly established on grounds of ob^ servation which cannot be overturned. " Clusters can be found of 10 diameter with a certain degree of compression and stara of a certain magnitude, and smaller clustcra of 4', 8', or2' in diameter, with smaller stara and greater compreasion. und so on through resolvable nebulae by imperceptible steps, to tb« 'eiadet, wlitcli Imve al- with the constellutini) diHtiiiguUh fix Mlius leven, twelve, or more or n huiidiftl 8Ur8 are are good example* of tains Mvernl tliousand It 200 stars, of mngni- ntb oud fourtfcentli, ia 91 — CoMpaaauii CLonm, venorforcei. This wot [ernys: ten formed by central or nebula that shows a Iness toward a centre. shed on grounds of ob^ ivlth a certain degree of de, nnd smaller dustera ind greater comprewion, perceptible steps, to tU« HKDUL.IS AND CLUSTK118. 809 smaller and faintest [and mo«t diManll ncbiilie. Otiicr vUxnWn there are wlilcli le.»,l to tliu iM-llef llmt either tliey iirc more eomprcHKetl or are'c.)inp<»'«'e of Sirin$, but no eptcd). The coolest ipounds of metallic netallic elements un- or Sight. r give information in iition, but have been velocity in kilometres i; to or receding from The theory of such a lark lines, as a, b, e, II. Prom laboratory lines of incandescent ; relative position as iferred that the solar ;en in its absorptive And three dark lines same as tliat^jof the nsilion the same, but I the fuinler spectrum also similar; that is, less, blackness, nebu- ed that (he ttar really le existence has been ts shifted toward either the violet or red end of the spectrum by a small yet measurable amount. Repeatetl experiments by different instruments and observers show always a shifting in llie same direc- tion and of like amount. The figure shows the shifting of the F line in the spectrum of ««««, compared with one fixed Une of hydrogen. This displacement of the spcctml lines is to be ac- counted for by a motion of the star toward or from the earth. It is shown in Phy- sics that if the source of the light which gives the spectrum o', b', d is mov- ing away from the earth, this group will be shifted toward the red end of the spectrum; if toward the eartli, then the whole group will be shifted toward the blue end. The amount of this shifting is a function of the velocity of recession or approach, and this velocity in miles per second can be calculated from the measured displace- ment. This has been done for many stars. The results agree well, when the difflcult nature of the research is considered. Tlie rates of motion vary from insensible amounts to 100 kilometres per second ; and In some cases agree remarkably with the velocities computed from the proper motions and probable parallaxes. Fio. 93.— F Lnn m Brwrnnm or 8nm». 1 ,1 CHAPTER V. MOTIONS AND DISTANCES OF THE STARS. Pbofeb MoTion. We have already stated that, to the unaided vision, the fixed stars appear to preserve the same relative position in the heavens through many nentnries, so that if the an- cient astronomers could again see them, they could hardly detect the slightest change in their arrangement. But accurate measurements have shown that there are slow changes in the positions of the brighter stars, consisting in a motion forward in a straight line and with uniform velocity. These motions are, for the most part, so slow that it would require thousands of years for the change of position to be perceptible to the unaided eye. They are called proper motions, since they are peculiar to the star itself. In general, the proper motions even of the brightest stars are only a fraction of a second in a year, so that thouaands of years would be required for them to change their place in any striking degree, and hundreds of thousands to make a complete revolution around the heavens. Pbopbb MoTioir or thk Sqv. It is a priori evident that stars, in gonertil, must have proper motions, when once we admit the universality of PHE STARS. inuided vision, the elative position in > that if the an- they could hardly rrangement. But lat there are slow itars, consisting in rud with uniform Dost part, 80 slow for the change of cd eye. They are tcnliar to the star 1 of the brightest in a year, so that sd for them to pee, and hundreds Intion around the iVH. {onenil, must have he universality of MOTIONS AND DiatANCHS OF THE! STAttS. 315) gravitation. That any fixed star should be entirely at rest would require that the attractions on uU sides of it should be exactly balanced. Any change in the position of this star would break up this balance, and thus, in gen- eral, it follows that stars must be in motion, since all of them cannot occupy such a critical position as has to be assumed. If but one fixed star is in motion, this affects all the rest, and we cannot doubt but that every star, our sun included, is in motion by amounts which vary from small to great. If the sun alone had a motion, and the other "stars were at rest, the consequence of this would be that all the fixed stars would appear to be retreating en masse from that point in the sky toward which we were moving. Those nearest us would move more rapidly, those more distant less so. And in the same way, the stars from which the solar system was receding would seem to be approaching each other. If the stars, instead of being quite at rest, as just supposed, had motions proper to themselves, then we should have a double complexity. They would still appear to an observer in the solar system to have motions. One part of these motions would be truly proper to the stars, and one part would be due to the advance of the sun itself in space. Observations can show us only the remltant of these two motions. It is for reasoning to separate this resultant into its two components. At first the question is to deter- mine whether the results of observation indicate any solar motion at all. If there is none, the proper motions of stars will be directed along all possible lines. If the sun does tnily move, then there will be a general agreement m the resultant motions of the stars near the ends of the line t;'!' m Asrnoxowf. { \V ■ along which it. moves, while those at the sides, io to e^k, will show comparatively less systematic effect. It is as if one were riding in the rear of a railway train and watching the rails over which it has just passed. As wo recede from any point, the rails at that point seem to come nearer and nearer together. If we were passing through a forest, we should see the trunks of the trees from which we were going apparently come nearer and nearer together, while those on the sides of us would remain at their constant distance, and those in front would grow further and further apart. These phenomena, which occur in a case where we are sensible of our own motion, serve to show how we may deduce a motion, otherwise unknown, from the appear- ances which are presented by the stars in space. In this way, acting npon suggestions which had been thrown out previously to his own time, Herschel demon- started that the sun, together with all its system, was mov- ing through space in an nnknown and majestic orbit of its own. The centre round which this motion is directed cannot yet be assigned. We can only determine the point in the heavens toward which our coarse is directed — '* the apex of solar motion." A number of astronomers have since investigated this motion with a view of determining the exact point in the heavens toward which the sun is moving. Their results differ slightly, but the points toward which the sun is moving all fall in the constellation Hercules. The amount of the motion is such that if the sun were viewed at right angles to the direction of motion from an average star of the first magnitude, it would appear to move about one tkiird of a second per year. •■■"«a>ij>Tt'- he sides, Ho to e^k, ic effect. It is as if iy train and watching . As wo recede from 1 to come nearer and t, wo slionld see the ere going apparently e those on the sides listance, and those in apart. a case where we are ) show how we may n, from the appear- I in space. ons which had been I, Herschel demon- its system, was mov- majestic orbit of its I motion is directed determine the point Be is directed — " the ce investigated this e exact point in the Ting. Their resalta d which the snn is >-culea. The amonnt were viewed at right om an average star X to move about one MOTIONS AND MSTANCBB OF THE BTAB8. 316 DUIAVOIS OV THX FIZXS 8TABI. The ancient astronomers supposed aU the fixed stars to be situated at a short distance outside of the orbit of the planet Saturn, then the outermost known planet. The idea wa« prevalent that Nature would not waste space by leaving a great region beyond Saturn entirely empty. When Copernicus announced the theory that the sun was at rest and the earth in motion around it, the problem of the distance of the stars acquired a new interest. It was evident that if the earth described an annual orbit, then the stars would apiMjar in the course of a year to oscillate back and forth in corresponding orbits, unless they were so immensely distant that these oscillations were too small to bo seen. The apparent oscillation of Saturn pro- duced in this way was described in Part I. It amounts to some 6° on each side of the mean position. These oscilla- tions were, in fact, those which the ancients represented by the motion of the planet around a small epicycle. But no such oscillation had ever been detected in a fixed star. This fact seemed to present an almost insuperable difficulty in the reception of the Copemican system. Very natural- ly, therefore, as the instruments of observation were from time to time improved, this apparent annual oscillation of the stars was ardently sought for. The problem is identical with that of the annual parallja of the fixed stars, which has been already described. This parallax of a heavenly body is the angle which the mean distance of the earth from the snn subtends when seen from the body. The distance of the body from the sun is inversely as the parallax (nearly). Thus the mean distr: ^9 of Saturn being 9.5, its annual parallax exceeds 6°, while t i 816 ASTUOyoitY. that of Neptune, which is three times as far, is about 2*^. It was very evident, without telescopic observation, that the stars could not have a parallax of one half a degree. They must therefore be at least twelve times as far as Saturn if the Copernican system were true. When the telescope was applied to measurement, a con- tinually increasing accuracy began to be gained by the improvement of the instruments. Yet for several genera- tions the parallax of the fixed stars eluded measurement. Very often indeed did observers think they had detected a parallax in some of the brighter stars, but their succes- sors, on re})eating their measures with better instruments, and investigating their methods anew, found their conclu- sions erroneous. Early in the present century it became certain that even the brighter stars had not, in general, a parallax as great as 1', and thus it became certain that they must lie at a greater distance than 200,000 times that which separates the earth from the sun. SuooetBs in actually measuring the parallax of the stars was at length obtained almost simultaneously by two as- tronomers, BsssELof Kdnigsbergand STRUVE'of Dorpat. Bessel selected 61 Cfygni for observation, in August, 1837. The result of two or three years of observation was that this star had a parallax of 0'.35, or about one third of a second. This would make its distance from the sun nearly 600,000 astronomical units. The reality of this parallax has been well-established by subsequent investigators, only it has been shown to be a little larger, and therefore the star a little nearer than Bessel supposed. The most prob- able parallax is now found to be 0'.51, corresponding to a distance of 400,000 radii of the earth's orbit. The distances of the stars are sometimes expressed by 1C8 as far, is about 2*^. sopio observation, tlmt : of Olio hulf a degree, welve times as fur ob iro true. measurement, a con- to be gained by the Yet for several genera- eluded measurement, ink tbcy had detected stars, but their succes- ith better instruments, w, found their conclu- ciit century it became hud not, in genera), a Bcame certain that they ,n 200,000 times that lun. purulhix of the stars ultaneonsly by two as- nd STRUVE'of Dorpat. ation, in August, 1837. 1 observation was that about one tliird of a ce from the sun nearly eality of this parallax ent investigators, only ger, and therefore the oscd. The most prob- 51, corresponding to a It's orbit >metime8 expressed by MOTIONS AND DISTANCES OF THE STAltS. 317 the time required for light to pass from them to our sys- tem. The velocity of light is, it will be remembered, about 300,000 kilometres per second, or such as to pass from the sun to the earth in 8 minutes 18 seconds. The time required for light to reach the earth from some of the stars, of which the parallax has been measured, is as follows : 8*Am. a Oentauri 61 C^gni. ...... 21.185 Lelande.. fi Centauri ft Catnoptia 84 Oroomliridec 21,258 Lelande.. 17.415 Oeltzvn.. SirivM a Lyra Ymh. 8-5 6-7 6-8 «.9 9-4 10-5 119 181 10. 7 17-9 Stab. 70 Ophiuehi t UrMB Mtijorit Areturuii y Draeoni* ItiaOOroombndge. Patarit 8077 Brndky 85 llegoM a Auriga 6 Draeoni* YMurt. 191 24-8 25-4 85-1 85-9 42-4 401 64-5 70- 1 129- 1 OHAl»TER VI. CONSTRUCTION OF THE HEAYENa The visible uniTerae, as revealed to us by the telescope, ia a collection of many millions of stars and of several thon- sand nebnlae. It is sometimes called the stellar or sidereal system, and sometimes, as already remarked, the stellar universe. The most far-reaching question with which astronomy has to deal is that of the form and magnitude of this system, and the arrangement of the stars which compose it. It was once supposed that the stars were arranged on the same general plan as the bodies of the solar system, being divided up into great numbers of groups or clusters, while all the stars of each group revolved in regular orbits round the centre of the group. All the groups were supposed to revolve around some great common centre, which ' was therefore the centre of the visible universe. But there is no proof that this view is correct We have already seen that a great many stars are collected into clus- ters, but there is no evidence that the stars of these dusters revolve in regular orbits, or that the dusters them- selves have Any regular motion around a common centra. The lint Mtmnomer to make a canf ul study of the amngeawnt of the atara with a view to learn the atnicture of the heavena was Sir WtUAJM HsiiaciRL. HsBacmBL's method of atiidy waa founded on a mode of observo. Hi ; VI. THE HEAVEN& Bd to UB by the telescope, is stars and of several thon- alled the stellar or sidereal lady remarked, the stellar ing qncstion with which the form and magnitade sment of the stars which stars were arranged on the of the solar system, being f groups or clasters, while red in regular orbits ronnd e gronps were sapposed to nmon centre, which ' was B nniverse. view is correct We have tars are collected into dns- that the stars of these or that the clasters thom- ronnd a common centre. »f ul study of the amngenwiit nictura of the heayena wm Sir ounded on a mode of observa- COHSTRUCTIOy OF THE HKA VEHS. 319 lion which ho CBlIci targauaing. It consinloil in polnling a power- ful lelescope low.ml varloun purl- of lliu hcuveiis uuil '"H^^t.rl.ai.lng by ..climl count liow thick the sturn were in lucli regicu. M s aOToot rorteclorwas provi.kd wHli such iii. eyepiece timi in looking Into il ho woulil see a porliou t)f tlie heavens ..Imut 15 in di.inieler. A circle of this si7* on lh« celcMl..! sph.ro has uh..ut one quarter ho apparent surface of ihe sun. or «f the full n«Hni. On Hmlng tho ulwpo in any direction, a greater <.r le« number of stars were nearly always visible. Tbc^c were counted, and ilio direction in which the telesa.pe pointed was noted. Gauges of this kind were inado in all parU of the sky at wliich Im could |H>int his instrument, and the result* were tabulated in Ihe order of right ascension. Tho following Is an extract from the gauges, an.l gives the average number of stars in each lleUl at tho p«»lnlH noted in right aKcnsion and uorlh-p«>lar distance: a A N. p. D. W to W. No. of sun. RA. N. P. D. 7B»toW. No. or SUuu h. 15 in 16 16 m. 10 47 an 87 9.4 • 10.6 18.6 18.6 h.l 11 Vi \l 14 44 4V 8.1 4.6 8.9 8V« In UiU small Uible. It Is plain that a diffctenl law of clustering or of distrlbiitlon obtains in llie two regions. The number of these stars in certain portions is very great, ror example. In the Milky Way tids number was as great as 116.000 stars In a quarter of an hour In some cases. ... , , Hkmchei. supposed at ftrst tliat he completely resolvetl tho whole Milky Way Into smalt stom. ThU conclusion he subsequently modi- "It Is very probable that the great stratum called the Milky Way Is tint In which the sun is placed, though perhaps not In the very cen- tre of iu Ihickneaa. _ , . , , •• We gather Ibis from the appearance of ibe Gidaxy. which seems to encompass the whole heavens, as it certainly must »lo if the sun la wltb'n It. For. suppose a number of stars arranged between two parallel plane*, indefinitely extended every way. but at a given con- siderable distance from each other, and calling this a sidereal stratum, nn eye placed wiewUere wHWu H will sge all tUe stars in the dlrw J» MiST'" 810 A8TR0N0MT. ' '4 i lion of the planes of tlie stratiiin projected into n grcnl ciiclv, wlileh will appear lucid on account of (lie accumulation of llie Hiars, wkilr L Ik * f •' T ' . ♦ f 1 1.; » f .! > ' , •*■ y, Fio. 9S.— HBUOHn'a Trjomt or the SmxAa Sthsm. the rest of the heavens, at tlie sides, will only Fecm to be fcnttcred orer with constellations, more or less crowded. ac<;ording to the dls- ifiiiii' iiiiwiiiii miiwi rr. CONSTRUCTION OF TIIK IIK.WKNS. 331 l«l Into n grent tiiclc, which umulation of the Hiars, while ■Hx Srcuum Stmsm. ill only Fecm to be ccnttcred Dw^ed, iic<;ordlng to the dig- tsncc of tlio plnnes. or number of Mnr« contained in Uic thitknoM or siiieH of tlie Rtratum." Th«» in Hkrschki.'h tigure im wyciU S within the Htrnlum f any slinpe. according to the length, brcadili, and height of the stratum. " Suppose that a smaller stratum pq sliould branch out from ihe former in a certain «lircclion, and tiiat it also is contained lietwccn two puraiiel planes, so that Iho eye is contidned wiiliin the great stratum soniewliere Itefore the separation, and not far from llie place where lliu stnila are still unitetl. Then tills second stratum will not lie piojeeled into a brijthl circle like the former, but it will be «?en as a lucid branch pKM-ewling from the first, and returning into it again at a distance less than a" semicircle. "In the tigure liic stars in Ihe small stratum p? will be projectwl into a bright arc riitt P. which, after Its separation from llie circle CBD, unites with it again at I\ "If tlie iKiuiKling surfan-s are not parallel planes, but irregidarly curved surfacc-s. anulogoiis appearances must result." The Milky Way. as we see it with the naked eye, presents the as|M>ct which has liecn Just accounted for. in Its general appearance of a girdle around the heavens and in its bifurcation at a certain point, and Heiuchei.'8 explanation of this appearance, as Just given, has never been seriously qucstionwi. One doubtful point remains: are the stars in Pig. IW scattered all through the space 8—abpd1 or are they near its bounding planes, or clustered in any way wHhln this space so as to produce the same result to the eye as If uniformly distributed T HBRacHBi. assumed that they were nearly equably arranged all through the space in question. He only examined one other arrange- ment—viz., tbiit of a ring of stars surrounding the sun— and he pro- nouuce«l against auch an arrangement, for the reason that tiiere is absolutely nothing in the slxe or brilliancy of the sun to cause us to suppose It to be the centre of such a gigantic system. No reason ex- cept its Importauce to us personally can be alleged for such a sup- 832 ASTHOAOMy. potitinn. By llio nMiimptloni of Vlij. «8, cai li titur will Imve ill own rippcarnniti of n paiiixy or milky wny. wlilcli will viiiy nccoid- ttiff to ilio Nituatinn of lliu Nliir. Such an rxpltumtioii will nccouiit for llie general nppenrnnciH of the Milky Way iiudof the rent of the iiky. ■uppo«inKllicatiirNci|ually or nearly equally «liitrll»uled in 8piice. On thin auppoflilion, the lyitcm muat be ilee|>er wliciv the »lur» appear mure niimvroui. ..-s^ammm V\fi. 08, cui'li Hlur will Imve lit y wny. wlikli will viiry nccoid- for llie general appcnronceH of ky, RiipponinK »■« •tiirH eiiually or On tliis auppoiilion, tlie lyitein ur more numuroiii. CHAPTER VII. COSMOGONY. A THEORY of the o|.,ration8 by which the universe re- ceived it8 present form and arrangement is called Cosmog- ony. Thia subject does not treat of the origin of matter, but only of its trunaformations. Three systems of Cosmogony have prevailed among thinking men at different times: (1) That the universe had no origin, but existed from eternity in the form in which we now see it. This was the view of the ancient philosophers. (2) That it was created in its present shape in a mo- ment, out of nothing. This view is based on the literal sense of the words of the Old Testament. (3) That it came into its present form through an ar- rangement of materials which were before " without form and void." This may be called the evolution theory. It is to be noticed that no attempt is made to explain the origin of the primitive matter. The last is the idea which has prevailed, and it receives many striking confirmations from the scientific discoveries of modem times. The latter seem to show beyond all rea- sonable doubt that the universe could not always have existed in its present form and under its present condi- tions ; that there was a time when the materials composing it were masses of glowing vapor, and that there will be a «# .;!^: yl 324 ASTRONOMY. time when the present state of things will cease. The ex- planation of the processes through Avhich this occurs is sometimes called the nebular hypothesis. It waa first pro- pounded by the philosophers Swedenborg, Kant, and Laplace, and, although since greatly modified in detail, their views have in the main been retained until the present time. We shall begin its consideration by a statement of the various facts which appear to show that the earth and planets, as well as the sun, were once a fiery mass. The first of these facts is the gradual but uniform in- crease of temperature as we descend into the interior of the earth. Wherever mines have been dug or wells sunk to a great depth, the temperature increases as we go down- ward at the rate of about one degree centigrade to every 30 metres, or one degree Fahrenheit to every 50 feet. The rate differs in different places, but the general average ic near this. The conclusion which we draw from this may not at first sight be obvious, because it may seem that the earth might always have shown this same increase of tem- perature. But there are aeveral results which a little thouglit will make clear, a'Luough their complete establish- ment requires the use of the higher mathematics. The first result is that the increase of temperature can- not be merely superficial, but must extend to a great depth, probably even to the centre of the earth. If it did not so extend, the heat would have all been lost long ages ago by conduction to the interior and by radiation from the surface. It is certain tliat the earth has not received any great supply of heat from outside since the earliest geological ages, because such an accession of heat at the earth's earface wonld have destroyed all life, and even f.1^;^'.-rT'>"'-".^>-fr\'V^.**-'*^''S'T*>^<-^ "'"«"■ ■•' -^^v-^JbV''- COSMOGONY. 325 gs will cease. The ex- li Avliich this occurs is hesis. It waa first pro- DENBORG, Kant, and itly modified in detail, !en retained until the bj a statement of the )w that the earth and ce a fiery mass, radual but uniform in- id into the interior of seen dug or wells sunk icreases as we go down- ; centigrade to every 30 to every 50 feet. The the general average k c draw from this may B it may seem that the i same increase of tcm- results which a little leir complete cstablish- mathematics. ise of temperature can- ist extend to a great >f the earth. If it did all been lost long ages and by radiation from earth has not received fiide since the earliest scession of heat at the fed all life, and even melted all the rocks. Therefore, whatever heat there is in the interior of the earth must have been there from be- fore the commencement of life on the globe, and remained through all geological ages. The interior of the earth being hotter than its surface, and hotter than the space around it, must be losing heat. We know by the most familiar observation that if any ob- ject is hot inside, the heat will work its way through to the surface by the process of conduction. Therefore, since the earth is a great deal hotter at the depth of 30 metres than it is at the surface, heat must be continually coming to the surface. On reaching the surface, it must be radiated oft into space, else the surface would have long ago become as hot as the interior. Moreover, this loss of heat must have been going on since the beginning, or at least since a time when the surface was as hot as the interior. Thus, if we reckon backward in time, we find that there must have been more and more heat in the earth the further back we go, so that we must finally reach back to a time when it was 80 hot as to be molten, and then again to a time when it was so hot as to be a mass of fiery vapor. The second fact is that we find the sun to be cooling off like the earth, only at an incomparably more rapid rate. The sun is constantly radiating heat into space, and, so far as we can ascertain, receiving none back again. A small portion of this heat reaches the earth, and on this portion depends the existence of life and motion on the earth's sur- face. The quantity of heat which strikes the earth is only about TTinn^innr «' tl^*' which the sun radiates. This fraction expresses the ratio of the apparent surface of the earth, as seen from the sun, to that of the whole celestial Inhere. 1^ m 326 ASTRONOMY. m:^ m^^ Since the Bun is losing beat at this rate, it must have had more heat yesterday than it has to-day ; more two days ago than it had yesterday, and so on. Thus culculating back- ward, we find that the further wo go back into time the hotter the sun must have b^en. Since we know that heat expands all bodies, it follows that the sun must have been larger in past ages than it is now, and we can trace back this increase in size without limit. Thus we are led to the conclusion that there must hare been a time wlien the sun filled up the space now occupied by the planets, and muat have been a very rare mass of glowing vapor. The plan- ets could not then have existed separately, but must have formed a part of this mass of vapor. The latter was there- fore the material out of which the solar system was formed. Tho same process may bo continued into the future. Since the sun by its radiation is const mf: Voing heat, it must grow cooler and cooler as ages ai ,. -^, and must finally radiate so little heat that life anc :: ...^.lon can no longer exist on our globe. The third fact is that the revolutions of all the planets around the sun take place in the same direction and in nearly the same plane. We have here a similarity amongst the different bodies of the solar system, which must have had an adequate cause, and the only cause which has ever been assigned is found in the nebular hypothesis. This hypothesis supposes that the snn and planets were once a great mass of vupor, as large as or larger than the present solar system, revolving on its axis in the same plane in which the planets now revolve. The fourth fact is seen in the existence of nebulae. The spectroscope shows these bodies to be masses of glowing ..is g a^a sgag^ s ^ a I rate, it must have had ay ; more two days ago rims calculating back- go back into time the ice we know that heat lie snn must have been and we can trace back Thus we are led to the in a time when the sun the planets, and muat ring vapor. The plan- arately, but must have The latter was thcre- the solar system was nned into the future. msi viit: looing heat, it res ai V. .\ and must fe anc i.^jion can no itions of all the planets same direction and in ;re a similarity amongst stem, which must have ly cause which has ever ular hypothesis. This and planets were once larger than the present I in the same plane in stence of nebulae. The > be masses of glowing COSMOGONY. 837 vapor. We thus actually see matter in the celestial spaces under the very form in which the nebular hypothesis sup- poses the matter of our solar system to have once existed. Since these masses of vapor are so hot as to radiate light and heat through the immense distance which separates us from them, they must be gradually cooling off. This cool- ing must at length reach a point when they will cease to be" vaporous and condense into objects like stars and planets. We know that every star in the heavens radiates heat as our sun does. In the case of the brigliter stars the heat radiated has been made sensible in the foci of our telescopes by means of the thermo-multiplier. All the stars must, like the sun, be radiating heat into space. A fifth fact is afforded by the physical constitution of the planets Jupiter and Saturn. The telescopic examina- tion of these planets shows that changes on their surfaces are constantly going on with a rapidity and violence to which nothing on the surface of our earth can compare. Such operations can be kept up only through the agency of heat or some equivalent form of energy. But at the dis- tance of Jupiter and Saturn the rays of the sun are entirely insufficient to produce changes so violent. We are there- fore led to infer that Jupiter and Saturn must be hot bodies, and must therefore be cooling off like the sun, stars, and earth. We are thus led to the general conclusion that, so far as our knowledge extends, nearly all the bodies of the universe are hot, and are cooling off by radiating their heat into space. The idea that the heat radiated by the sun and stars may in some way be collected and returned to them by the operation of known natural laws is equally untenable. It il •{- 8S8 ASTRONOiir. m m\ iH a fundumental principle of the laws of heat that " the hitter ciiii never pass from u cooler to a warmer body,'* and that a body can never grow warm or acquira heat in a space that is cooler than the body is itself. All differences of temperature tend to eciualixe themselves, and the onl/ state of things to which the universe can tend, under its present laws, is one in which all space and all the bodies con- tained in space ure at a uniform tem]ieratnre, and then all motion and change of tem])erature, and hence the condi- tions of vitality, must cease. And then all such life as ours must cease also unless sustained by entirely new methods. The general result drawn from all these laws and facts is, that there was once a time when all the bodies of the universe formed either a single mass or a number of masses of fiery vapor, having slight motions in various parts, and different degrees of density in different regions. A grad- ual condensation around the centres of greatest density then went on in consequence of the cooling and the mutual at- traction of the parts, and thus arose a great number of nebulous masses. One of these masses formed tlie ma- terial out of which the sun and planets arc supposed to have been formed. It waa probably at first nearly glob- ular, of nearly equal density throughout, and endowed with a very slow rotation in the direction in which the planets now moTC. As it cooled OiT, it grew smaller and smaller, and its velocity of ruUition increased in rapidity. The rotating mass we have described must have had an axis around which it rotated, and therefore an equator defined 88 being everywhere 00° from this axis; In consequence of the increase in the velocity of rotation, the centrifugal force would also be increased as the mass grew smaller. This force varies as the radius of the circle described by COSMOOONT. 329 i\v8 of heat that " the ) a Wanner body," and acquii'c heat in a space !lf. All diffci-ences of nselves, and the onl/ se can tend, under its I and all the bodies con- jieratnre, and then all and hence the condi- lien all snch life as ours entirely new methods. II these laws and facts 1 all the bodies of the or a number of masses s in various parts, and •ent regions. A grad- >f greatest density then ngand the mutual at- >se a great number of asses formed tlie mo- lanets arc supposed to y at first nearly glob- ughont, and endowed irection in which the u, it grew smaller and increased in rapidity. i most have had an axis ore an equator defined axis. In consequence tation, the centrifugal 10 mass grew smaller. :he circle described by any particle multiplied by the square of its angular velocity. Hence when the masses, being reduced to half the rrnlnis, rotated four times as fust, the centrif ugal force at the equa- tor would be increased ix4', or eight times. The gravi- tation of the ma83 at the surface, ocing inversely as the square of the distance from the centre, or of the radius, would bo increased four times. Thorofcio as the masses continue to contract, the centrifugal force increases at a more rapid rate than the central attraction. A tunc ^vould therefore come when they would balance each other at the equator of the mass. Tbe mass would then cease to con- tract at the equator, but at the poles there would be no centrifugal force, and the gravitation of the mass would grower stronger and stronger. In consequence the mass would at length assume the form of a lens or disk very thm in proportion to its extent. The denser portions of this lens would gradually be drawn toward the centre, and there more or less solidified by the process of cooling A point would at length be reached, when solid particles would begin to be formed throughout the whole disk. Tliese would grad- ually condense around each other and form a single planet, or they might break up into small masses and form a group of planets. As the motion of rotation would not be altered by these processes of condensation, these planets would all be rotating around the central part of the mass, which is supposed to have condensed into the sun. It is supposed that at first those planetary masses, being very hot, were composed of a central mass of those sub- stances which condensed at a very hi-h temporatnre, sur- rounded bv the vapors of those substances which were more volatile. We know, for instance, that it takes a much higher temiwaturc to reduce lime and platinum to vapor :it 330 ASTRONOMT. tluin it does to reduce iron, zinc, or magnesium. There- fore, in tlio original planets, the limes and earths would condense first, while many other metals would still bo in a state of vapor. The planetary masses would each bo afFccted by a rotation increasing in rapidity as thiy grew smaller, and would at length forpi masses of melted metals and vapors in the same way as the larger mass out of which the sun and planets were formed. These masses would then condense into a planet, with satellites revolving around it, just as the original mass condensed into sun and )>lanct8. At first the planets would be so hot its to bo in a molten condition, each of them probably shining like tho sun. They would, however, slowly cool off by the radiation of heat from their surfaces. So long as they remained liquid, the surface, as fast as it grew cool, would sink into the in- terior on account of its greater specific gravity, and its place would bo taken by hotter material rising from the interior to the sarfaoe, there to cool off in its turn. There would, in fact, be a motion something like tJmt which occura when a pot of ccld water is set upon the fire to boil. Whenever a mass of water at the bottom of the pot ii lieated, it rises to the surface, and the cool water moves down to take its place. Thus, on the whole, so long as tho planet remained liquid, it would cool off equally throughout its whole mass, owing to the constant motion from tho centre to tho circumference and back again. A time would at length arrive when many of the earths and metals would begin to solidify. At fii-st the solid particles would be carried up and down with the liquid. A time would finally arrive when they would become so large and numerous, and tho liquid part of tho general mass -■ ^■■i? ! ;'^g!g«r';#lfeteA.^^<^ iMte-. COSMOGONY. 881 r magnesium. There- IHC8 and earths would stals would still bo in nusses would each bo rapidity as thiy grew lasses of melted metuls rger mass out of which These masses would h satellites revolving ondensed into sun and )t as to bo in a molten shining like the sun. »flf by the radiation of they remained liquid, ould sink into the in- scific gravity, and its terial rising from the >fl In its turn. There hing like Umt which t upon the lire to boil, bottom of the pot ji the cool water moves bhe whole, so long as raid cool off equally ) the constant motion ) and back again. A any of the earths and irat the solid particles the liquid. A time uld become so large of the general mass become so viscid, that the motion would be obstructed. The planet would then begin to solidify. Two views have been entertained respecting the process of solidifica- tion. According to one view, the whole surface of the planet would solidify into a continuous wast, as ice forms over a pond in cold weather, while the interior was still in a molten state. The interior liquid i.v.nld then no longer come to the sui m-p a cool off, and could lose no heat except what was conducted through this crust. Hence the subsequent cooling would be much slower, and the globe would long remain a mass of lava, covered over by a comparatively thin solid crust like that on which we live. The other view is that, when the cooling attained a cer- tain stage, the centrAl portion of the globe would be solidified by the enormous pressure of the superincumbent portions, while the exterior was still fluid, and that thus the solidification would take place from the centre out- ward. It is still an unsettled question whether the earth is now solid to its centre, or whether it is a great globe lof molten matter with a comparatively thin crust. Asti^mers and physicists incline to the former view ; geologists to the lat- ter one. Whichever view may be correct, it appears cer- tain that there are great lakes of lava in the interior from which volcanoes are fed. It must be understood that the nebular hypothesis, as we have explained it, is not a perfectly established scientific theory, but only a philosophical conclusion founded on the widest study of nature, and pointed to by many otherwise disconnected facts. The widest generalization associated fT 889 ASmONOMT. PI with it is that, so fur us wo can see, tlic iiiiivoi'so is not self- Bustuining, but is a kind ot orgiini^m whiuh, like all other orgunisms we know of, nuiat come to an end in consoqncnco of t!..^8e very laws of action which keep it going. It must have liud u beginning within a cortuin number of years which we cannot yet cnlcniute with certninty, but which cannot mnch exceed 20,000,000, and it must end in u chaos of cold, dead globes at a calcniable time in the future, when the sun und stars ghall have radiated away all their heat, unless it is re-creuted by the action of forces of which we at present know nothing. THE END. ■n ic iinivoi'BO is not self- I which, like all other in end in coiigoqncnco op it going. It mnst ain niimlicr of yriirs certainty, but which it must end in a chaos time in the future, idiatod away all their ion of forces of which INDEX. W- Thw Index Is iulcndod to point oul tbe sul.JccU trcnlcd in the work, nnd furiher. to give reference- to tbe pnges where technical terms are defined or expluined. Aberration-constant, value oi, 178. Aberration of Hglit, 174. Achromatic tclcHCoiJO descrlbwl, 68. Adams's work on perturbations of Uranus, 250 Aibt'b determination of the den- aity of the enrtli, 148. Algol (variable sUr), 296. Altitude of a star defined, 18. Angles, 8. Annular eclipses of the sun, 186. Apparent place of a star, 16. Apparent time, 45. Abibtarchcs determines tlie so- lar parallax, 165. Asteroids defined, 191. Asteroids, numlier of, 226 in Astronomical Instruments (in general), 60. Astronomy (defined), 1. Atmosphere of the moon, 281. Atmospheres of the planets, See Mercury, Venus, etc. Axis of the earth defined, 21. Azimuth defined, 19. Bkbsgi/b parallax of 61 Cygnl (1887), 816. Binary stars. 802. BoDE'ii law 8tule«l, 198. Bond's discovery of the dusky ring of Saturn, 1860,250. Bouvard's theory of Uranus, 256. Bradley discovers aberration In 1729. 176. Calendars, how formed, 182. Cassim discovers four satellilcs of Saturn (1684-1671), 852. Catalogues of stars, general ac- count, 79. Celestial sphere, 4 4. Centre of gravity of the solar system, 194. Chronology, 180. Chronometers, 68. Clarke's elements of the earth, 152. Clocks, 68. Clusters of stars. 808. Comets, general account, 274 Comets' orbits, 277 Comets' tails, repulsive force, 277. •4, 884 INDEX. }'i ^i-'f Comets, their phyricnl constitu- tion, 276. Comets, their spcctrn, 277. Conjunction (of n pianet with the sun) detlned, 97. Consteiltttions, 288. Construction of tlielieavcn8,817. Coordinates of a star defined, 1«, 87. COPERNICUB, 108. Correction of a clock defined, BO. Cosmogony, 822. Corona, its spectrum. 216. Day, how sulMlivided into hours, etc., 187. Days, mean solar and solar, 46. Declination of a star defined, 41. Distance of tlie fi.ved stare, 814. Distribution of the stars, 818. Diurnal motion, 21, 22. Dominical letter, 186. DoNATi'B comet (1858), 281. Double (and multiple) stars, 801. Earth (the), general account of, 142. Earth's density, 142. Earth's dimensions, 151. Earth's mass, 142. Eclipses of the moon, 181. Eclipses of the sun and moon, 129. Eclipses of the sun, explanation, 182. Eclipses of tlio sun, physical phenomena, 212. Eclipses, their recurrence, 186. Ecliptic defined, 84. Elements of the orbito of the ma- jor planets, 198. Elongation (of a planet) defined, 97." Encke's comet, 288. Encxk'b value of the solar paral- lax, 8".578, 166. Epicycles, tlielr theory, 102. Equation of time, 188. Equator (celestial) defined. 21. Equntoriui telescope, description of, 74. Equinoxes, 87. Eye- pieces of telescopes, 62. Fabkitius observes solar spots (1611). 207. Figure of the earlii, 148. Future of tiic solar system, 882. Galaxy, or milky way, 819. Galileo olwcrves solar spots (1611), 207. Galileo's discovery of satellites of Jupiter (1610), 240. Galle first observes Neptune (1846), 259. Geodetic surveys, 150. Golden number, 184. Gravitation extends to the stars, 808. Gravitation resides in each par- ticle of matter, 119. Gravitation, terrestrial (its laws), 146. Greek alphabet, 1 *. Gregorian calendar, 185. Hallet predicts the return of a comet (1682), 279. Hall's discovery of satellites of Mars, 285. Hansen's value of the solar par- allax. 8'.92. 166. Herschbl (W.) discovers two satellites of Saturn (1789), 252. Uerschel (W.) discovers two satellites of Uranus (1787). 254 INDKX. 38R [e'b comet, 388. ik'b yaliie of the lolnr paral- ;, 8".578. 166. ycles, their theory, 103. tlion of time, 188. ttor (culestini) tleflned. 31. itoriul telcgci)[)e, description ,74. Iiioxes, 87. pieces of telescopes, 63. RiTius observes solar spots JU), 207. ire of the carlli, 148. [ire of the solar system, 883. ixy, or milky way, 819. ,ii,EO olmerves solar spots 611), 307. .ii.Eo'8 discovery of satellites : Jupiter (1610). 340. .LE first observes Neptune 846). 250. Kletic surveys, 150. den number. 184. kvitation extends to the stars, 08. ivitation resides in each par- icle of matter, 1 10. ivitation, terrestrial (its laws), 46. ioV. alphabet, 1 *. igorian calendar, 185. lLLET predicts the return of a iomet (1683), 270. iU.'B discovery of satellites of tfars. 385. onsen's value of the solnr par- illnx. 8'.03. 166. iiucHBL (W.) discovers two Balellites of Saturn (1789), 353. CRBCHEii (W.) discovers two satellites of Uranus (1787), 254 IlEB«iiKt(W.) discovers Uranus (1781). 358. Hehsoiibl'b catalogues of nebu- Ite, 805. Hersciie..'b star-gauges, 318. Hbrschkl (W.) states that tlie solar system is in motion (1788), 813. IlEHBCnELB (W.) views on the nature of nebula*, 805. HiFFARCHUs discovers preces- sion, 158. Hooke'm drawings of Mars (1666), 384. Horizon (celestial— sensible) of an observer defined, 17, 30. Hour-angle of a star defined, 89. HnootNs' determination of mo- tion of stara in line of slglit, 810. HuoaiMB first observes the spec- tra of nebulte (1864). 809. HuYOHENB discovers a satellite of Saturn (1655). 353. HuTOHENB discovers laws of central forces. 116. Hdyohenb' explanation of the appearances of Saturn's rings (1656). 348. Inferior planets defined. 99. Intramercurial planets. 336. Jahbocn first observes solar pro- minences in daylight. 318. Julian year. 184. Jupiter, general account. 340. Jupiter's rotation-time. 343. Jupiter's satellites, 348. Kakt'b nebular hypothesis, 838. Kkplbr'b laws enunciated, 109. Laplace's nebular hypothesis. Laplace's investigation of tlie constitution of Saturn's rings, 252. Laplace's relations between the mean motions of Jupiter's satel- lites, 248. Lassell tliscovere Neptune's sat- ellite (1847), 260. Lassrll discovers two satellites of Uranus (1847), 254. Latitude (geocentric — geogra- phic) of a place on tlie earth de- fined, 8, 81, 41, 15t. Latitude of a point on the earth Is measured by the elevation of the pole, 81. Latitudes and longitudes (celes- tlal) defined, 95. Ijilitudcs (terrestrial), liow deter- mined, 58. Le Vebribr computes the orbit of melorlc shower, 271. Lb Verribk's researches on the tlieory of Mercury. 236. Le Verbikr's work on perturba- tions of Uranus. 357. Light-gathering power of an ob- ject-glass, 68. Light-ratio (of stars) is about 3.5, 395. Line of colUmatlon of a telescope, 71. Local time, 47. Lockybr'b discovery of a spec- troscopic method, 316. Longitude of a place, 9, 10. I..ongitudo of a place on tlic earth (how determined), 60. 53. liongitudes (celestial) defined, 05 Lucid stars defined, 389. ^ - INDEX. t V Luiur plittMH, nodei, etc. A« Moon'ii phuHt'i. node*, etc. Mu«nlfyiiig iK)W«r of au eye- piece, M. Mujor pUnoU deflDetl. 191. Mure, physlcul (lewjripllou, 288. Man, rot itlon, 384. MursH ialellUe* dlHCOvered by iiAix (1877). aaa. MA8KBLYNR dotermliiw the den- sity of tko enrlli, 149. MaM of tha BUD in roUtlnn to miU8e« of planets, 167. Mean aolir limo doflned. 45. Mercury'* ntinospliere, )a44. Mercury, ll» apparent niotloua. Meridian (celetllul) defined, 27. Meridian circle, 73. Meridians (terreatrlal) dcflnctl, 27. Metonic cycle, 188. Meteoric showers, 26». Meteort and comets, their re- lation. 271. Meteors, their cause, 265. Milky Way, 288. Milliy Way. its general iliape ac- cording to HEnscHEL, 818. Minor planets deflntd. 181. Minor planets, general account, 887. Mlra Cetl (variable star), 296. Months, different kinds, 182. Moon, general account, 82a Moon'B light ttAw o' ^« ■""' 883. Moon's phases, 188. Moon's parallax, 161. Moon's surface, does U change? 883. Motion of stars In the line of siglit, 810. Nadir i)f au observer detlneti, 18. Nuiitinil uliuaiiac dexcnbed, "9. Nebulu! uuU clusters in geuund, 804. Nebulu,'. tlielr i-pectra. 809. Nebular liypolliesls slaletl, 828. Neptune, iliacovery of, by La Veuuibh and Adamb (1846), 256. Neptune, general account, 256. Neptune's satellite, 360. New stars, 298. Nkwton (I.) calculates orbit of comet of 1680. 280. Nkwtok (I.). Laws of Force, 115. ObjcctWes, or object-glasses, 60. Obliquity of tlie ecliptic. 91. Occultatlons of stars by the moon (or planets), 140. Olbebs's hypothesis of the ori- gin of nsteroitls. 289. OI.BERB pn-dlcts the return of a meteoric shower, 269. Old style (In dates). 185. Opposition (of a planet to the sun) defined. 85. Parallax (annual) defined, 68. Parallax (horizontal) defined, 66. Parallax (in general) defined, 60. Parallax of the sun, 161. Parallax of the sUrB, general ac- count. 814. Parallel sphere defined, 88. Penumbra Of I lit- earth's or moon's shadow. 181. Photosphere of the sun, 301. PiAZZi discovers the first asteroid (1801), 887. INDEX. 887 of ulnra in the line of 810. t ttu olMwrvordefliioti, 18. 1 uiiniiiiitc licHcnlwd, *». and ciuHleni in geuunil, , llieir i.pfclra, 800. • liyputiieais ttuled, 832. f, liiscovery of, by Lb iiBH Hud Adamb (1846), c, general account, 209. e'8 MtLllite, 200. m, 298. N (I.) calculatea orbit of t of 1680. 280. iM (I.). Laws of Force, Te», or obJect-glaMe«, 60. lly of tlie ccliplic. 91. ttions of stars by the moon laneU), 140. a's liypotlic8l« of the orl- )f nfitcroiilB, 289. a prt-dicta tlio return of a lorio sliower, 269. ^1e (in dates). 185. it ion (of a planet to the defined. 85. IX (annual) defined, 88. i\x (horizontal) defined, 56. ax (in general) defined, 60. ax of the sun, 161. ax of the stara, general ac- Dt, 814. el sphere defined, 28. nbra Of I lit earth's or moon'a dow. 181. tsphere of the tun, 201. !i discoven the flrat Mteroid »1), 387. Planeta, tlieir relative size oxhib Itod, 191. Planetary uebul«B defined, 806. Planets; seven bodies so called by the ancients, 81. Plancto, their apparent and real motions, 96. Planets, their phyalcal conatltu- liun, 261. Poles of the celestial sphere de- fined, 21. PomUiKT'a measure! of iolar ra- dUtion, 205. Practical astronomy (daflned), 78. Precession of the quinoxes, 158. Prime vertical of an obaerrer de- fined, 19. Problem of three bodies, 119. Proper motiona of stars, 812. Proper motion of the sun, 813. Ptolemt determines the solar parallax, 166. Radiant point of meteors, 370. Radius vector, 107. Reflecting telescopes, 66. Refracting telescopes. 60. Refraction of light in the atmos- phere, 169. Resisting medium in space, 981. Reticle of a transit inatrumen*, 71. Retrogradationa of the planeU explained, 100. Right aacensitm of a star defined, 40. Right ascensions of stars, how determined by observation, 72. lUght sphere » ' J M lill» H..M^ i Mir« <»W