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M.M, M i-(t F t., Jn tho Clerk's Offic of the )St DIlet Coiurt fior tih Souti f.-tl4ct of'''Yotk. i.'t:-i i:Ty ^ t''' I'i:. S' SfMIit t & MCOO-t GALt, J, f). BtIDtnFO: u & CO., 83 S -I hl..e.kiau.-st., N., Y'. Ji & li FI1nkin t. iV ]b 1t i A. 01 E.itI: a\uthor rlhs no other apolorgy to present for ofer.ing to the public the following work on " Popular Astronomy" than the mnarked fxlvor with whiclt his Pl'anetary tand Stellar Worlds" has been rcceived, both in this country and in Europe. Tli science of Astronoml y is so rapidly progressivo tlat to keep the public advised of its advances new works are required almost every year. This nay bo offlerd as an additional reason for the present publication. nt the preparation of tle work I have availed myself of so tmany sources of infrnmation that it wtould be quito impt)ossible for tme to specify the authors or the volumes to whichlt I am indebted. The plan and tlhe cast is all my own. I have endeavored to follow the path of real discovery, andt in every insta-nce to present the flcts land phenomena so as to afford to the rteader and student tan opportunity to exerciso his ownl genius in their discussion JV P R Et F A C E. and resolution, beforo oft:ring tihe explanatioi reachled by ancient or mlodern scienco. It is hoped that thit s mlethod otf treatingrt the sulbjct whlicl is t now, (so filr as I ktoow,) mlay avail in exciting a greater inttrest in the examination of those great problemls of the universe whose sctuecsfu solution constitutes the chiof honor of human genius. I.T a feew inst-aces I havo ventured to presenat tho resultts of mly own observattioms, and ha Ove occupied a short spaco in cxhibiting a sketch of new methodts and noYw instlruments which have ben introduced into the observatories at Cinciramati and at Albany. )DU DLtr O-asEx:vt'OI:;~nr, Jtaur'yS 1860. 0 0 N:!,T E N 1 8. OILAPTE2 1. TliO.g 80U'.. T BIS CE:INTtA, t Ot4It OF THI 41 P 1LANs'nETIY YSTB'.5t' ~.tAO: S): S'Covs:'ti- OnI i 1: A.sXNs- - lt. tifle S8out r oof Xigt Ansd leth atlnl Life. -Ti.tot 8u'1s aliq>ar:i'nt Mtito,:t.. t< —'ir,. tlh of te, Y''ar..'.'...Th<..:un's Iirirett Pathlmt 434ons tie.-'ix:xe St;sl.% a C.l ei'.l1-1-t. f4itt )a3rT'nt foti)on noti l'iflrotti. —-Tho Ex.planat ion of 1 tipl':rihus. ——.....oir.telt,s:. — l~ Tei r Pr1riic:ton. 1Dt)iz.coY V 1-. t I': Y 1"' i otII tt*xs<.' —I'}.~ -The< Suln's ].)i4{t:dancIe.'-'Hs-. i11s Io,if'oital Patral lax..tl.ii'.lnort no of tl is Elh:n, m t, —- - ie,' ur d by tho transit otf Vem.-... - T'he Sttun' rel Man tml,' i aslI ticromettl ca l eaRt-l re of 3 fI; I )Itancto:r.- Tlhe I'hySil~.1. nSS)titutl.t on of the4 8utIm.-.Solar 8Iots — T ir I'er.odict..ity.. — l:ypothe Ms d itecul tat......................1............... 13 C:t[APT lR. II:tElP CU1Ylf, TI 1 t FI.ST i:' NLA 4P I. )11 Tt f): O ~ )XISTA iC FltOM TH}1S 80I. lt.S Erl v' ) s.covery.-.l' I C'ult to | bo tEis4,tnt:uishd firom the Stars -. -l ong.;. tionls,~-..Motitm firect 43nd Klietrog'atei,-,-i ai.,. tt'm,, Sl.ti 4ryt.........f tltro of thet O(r1t, —- — Va' ria:t o 4 n )tho t.lttgt.ion 4:xp1latl. N- -— i i1hi'Nods. a-rT sit of M~crery.~ —— r- -itnlinatlton f Mts rery1' Or"lt, —. - ( Mr an )1tDattbinco firom tthe Buttn. Conjonltlttios~. ——.- II'ossa.- -i'uet~vr tattd'tVohltulo.,,,.................... 4t t} i t. M. 80.,X The Fitst Pla'net )isict;verei.'.t MIoe of its )lsicovery.-.- l er l.t1 ^4 to34ni —,. Mor'4 ning. atl1d 4ven1i4 0 tar,- -At 4tticlIt t 1o iof thl St 1n1.-'-I 4tr sue peri r anio l It.fertior itji nt)ti~ lons4..^. et r -St ltt i.-.. l. rirct ftl et t an rir tleo M ot i s. —- Theo l'henomeitont itdiato a Motion of' tin \r\ th. — -'-irt auslt.S of Vetlmu-......i trclina* t.it of the fOrbiti of Ve-lnu to tho the ctiitie^.....4. r ods^-. -Intleralsi of i her Trats^it?.-:..ot.K }w\ edl. }~ of the Ancients~~ —,w —Phat'i ses of \V etU:-. —-ter El^k wgatlons: eqni4sl,- -. o Sattellite yet D)iscovered..-l'..'Stttls lgt ant Il 4at at V enus,,Pjlcr Atttio:iphere,,.,.................. ~..-......~........................ 9, C(l \.' P 1 i: t iV. T f1? BA1t'ftlt'I ANO1) TSf SiATT l'fXIL T11' T:i'41 T1111RI) PiLNE'T IN T.'11 OtRI)I:Rt 0 1.^1i'.i:ANC }Ft:01 Tl}1 SUN.'The- 1rth th'e'ppa re t ilt (.Center of Moti:4, — - To all the Sinse: {t i s fit ]:Le. t,-. T''e (.tecntr of 1the fMottons (of thett Stn,: atndtl oont C:t.-.. l-xlia-tmn of tlhe Ac cltl4eratlito o:f Ithe Orbitlmt M o tifon f thlle. awtnd Mltltoim. -Pto.lt>tms. p ieyls......1'h1e':lxplaation otf Cottleornie{s.- -ho Si' t th-i CtIetor 4 4 f a'l tiotary hatoti4on~,.4-4':'he I E. tht One of t114 Pla,4ne.-... —0 t 0bjl1io n to tfhi 1s1 3 (pot1C13...^ fhie Ans;wer. —.-Sv..- - t1e4 of Jupitter discovterCd 14 ti 1'ls o I: O.- — t't lt ('hOd Systil) stl e-i3cdtdc:l by tIho Nt'w _. —T....'. hol Filtre an,1 MN:'iditr.tt oft. the 1'^tlFrtl. l}t;o detrtertltniinc.'d I-t..Th'e'4rf-th's Mfotions,.. —. tat'im a'nd tl Ht voe fltltion. -A.. Unt otf fTit'en ftrni4shed b1 tLhe 1,t rth's.':1 V od' 1 f t' *il ti. att, --- rth's OrMitut:. Mo)ttiotn,. —'Ver t l:44u4t41 ox 1 t.<... -tiitheliot of j:n'1tt Orb1t.4.1 Its Period of l\o. filti}o1,-...- So3l1ar andl Sidtere a T1io4e,','tt toot,.-'trt evolutiont in h1er 4 Orlit.-. -f er Phalses,. — cileeeltri t:y of htir Ort 1.-.t.l' to iHti.3 of her Ap*l,:ee.- - }.tiii ts. nentt', of hler (rs it'..-, ons Parnllafx a3nd it lSat:'c1-cll.- tr.Sis-I'.: Con.1tlluftt.fi. —-^-'ij ter f Gt 1y iRy al C.:enl ter oiif t3i4l"................................................. 6, vi CO N T E NTS, 8. CI. APT EI i't V. m^AXt-RS, TIlE FOUti'Lt Pi;SLANEI' IN' TlllHE O(iDE OF I)STANtE FROM Tif}f SUN. I'lleioinc-ena 4Ntf M-rs ditilct tt to exldaitn wit thl; u Ea:ithi s thle (enhitr of Mo-< tino (.- <> — j'tt' r Kit l'p'it-tii iit^lntt — S ^-lit'icctliv, t'.l..-4ti I tter I.tiiitmnlleni awi l t Itl.i't liIiit lilt i" t.(li<.-I I tn>* e*t -tr i i r.-Kv t. il-'s hw istd,of tic.t<-. -Tho (t. rit of Mr- an I's t e.t —- - i. h.ler's tn........iiii -tii; Orbit f the'( Ilaa{e(ts.... l-;e'F teh{.)~<.s of tho'lanh'cttry (O)-bits ~xl lu~,l 11-. —110ow th(seC E iri nlltsa tre tobtiIn c^.- t-K el(r's t}nrlii i II.- uo of t his L n w.".-.. l l e it y siils Asl'ect t Mars- I — Snotw Zftlnes. — lotat:ion of thl Planet,. —-1)l.tmeter andt V lue. —-Spe lt;ttion a-s to its Ctato t C ut lor,...................... I 1 C }: A P T' E. ItV. TimI:} ASf OIDX AlS: G i(OUP OP tIr MAL bi LAE, Ti' 1'f1Yi, t IN ThJtO11)3It 0O t DISTiANC(, FROM THEi 8SUN, T'li'o'Itertlphinlctry Si'c t'.s,- -- Kepler~ Spcult ttions..-G realt Intetrval bettttee N tmi atd n tld iliter..}l-i'iictial iIlt - - n: vIetitn tn-"t' f itt.ianet e xit0*t hetwtee) Nf'lrSand iI}ii. t.......Cotn i.v of Astrono es.- a- Ali N^o'I ill OriCtdt o f:(} tS rlrl ftir thV e [U0 imr o wP net.- )-eD!,ovvr of o 0Cetr.s -. -. ——.st Ill the S.'os-W r jH^un^.ei>4t-i-'l li.i} {- v rer a til-'; b t, ~.y G ~... li.e..T N o. w O n'i- r D ist blelt d1( ll v thuo D)i -.coveirr of PaHllas - ---—! ^ ilypothcsk. — O.iD ovvry of Juno k~ndl Vt I' 1. —-,e;Kl'cii (.'Tf. - eir Magittl ude.- -'Forl mof tbeirir.4titwstS. -' ift ti u.t liii l'tit — t-'tli i. — T l3.1tl ".....0.. kil''ti-nlsieVe!c8.tey of Diyt t dis'-covosvie — ed. lece-T t nial 4 ont-(itiudl et.^-wetXtiohi o tof;so t.rSii oCi a1l Axis....................,,.,.....,,,,,................ 1Mag )'1ita!. T;c fan, NT b er T t'T, CRAPTER Vl11. SA'UR8NtT, TA' fE SNt BEVEI FXT AH 31A 0, N'TE T OHf'It OP }I'STLAN(.'E F tROMSt'THEI' ST.;N, sulmt)l O. BY}t C3ONlEn O BIS, A ND A TTENI:E D, e1 i.t t i stf t of 0tt(..ty Pl.{ne. — i l.ht Faint, tAf S a....l' I Ajlrnd ainl- a1s''itit.. it' of Ltts.'lun i.if ttv,I f it Iiot Flit t,e tIii. - -iif t;I'IIi it:t eitf li, kite i sn', t:i t'i. Ter -'TI.t Ii k ts I ta.. GA l5lX.':t'., d cmKATL iNSa.-. —-By o \ i:l:. covlt S ered.- - ih —: iq t git Nue1.IB er^. ~;...Ft r Jh)ishrtIc:s antl Pr t......t.fi rltlt. —'s -Orbit. tte. T Boundarny of thie PX..tletat-y. ystbtea, oos kl wn to ta ie A xnciets..........,....,........................ 15 C INT' E4 N T vS. (C HIAPTEI. IX. it;,AkWS OF MO1TION AND GttVITATION, lThe )i)ertons of ]i'orial AX trii oi.-'.Tloe t of Ph liv-i'i Aptnrit? ~S i$ o th II l$Sov:' v.:.:' r2erl..:'tit'ii:iu Q t! iit Or DIS iANC.t I'ROM Acit i-entitlxv Discove.red bv Sitr NWillian I cheiill. —Ani noiteed a a (.rniel....-.Itsrb it pr,:;vet'UNI - T'IE NIN4li AN) N LAST' }NOWN} FLVANN' IN fTie T 011 Ui'tI OF D)iSTtNC l'OM THill SUN. Ur-alnrs Di)is xveervd by AceifC t. — Ceres t'y te.tl'r. wit hl the io leee........l e. Ileit.-'cover i by M NIthein-ict d CompntriraitOin.. —-— The 1:ii'r l- oiin on f Ilhk4lnus. -. No t thiu to atry known Cli'tise......t As' ed to A-fis l o t)t t xt nlertir o: la i [ et - -N attit of thoe Ex.} xllti at on tto find the ItU k nown Planet.- t J — l ndrti ke n at thUe,m- t ti — e n V td wo Ct- ttil)ter.s it'. i. -iutauon A i.tos'."lsa l':I it? to th:e tUll. knowit Pianio-t: — Isc<>r.ed by thne T'ioe-ts p.- t l- I.s veries lIvi..ti-ngl.-l - S liteltto Detectfed..- Ttfe MaI^sis f Nelttinoe thuts.let^r nitd. — Neptune's Orlbit tiLe Cleumctlijtibl-tg ioundairy of the lta e"itary' Byst)ct,...,,....,,... 6,i C I A PTE IE R XI\ Ar %t12I CO.MTE"i'.t ObItc't oe f D]) adt Il the T}':."arlyvi:.-t Cor ets O r tifes L.a f it (i avitalion MiAn lf,;volvo i s.otw e (:l m of th' (.?h: SO eci,n.;-C ral-ti:> of tCheIo -Curlves. —.(.:'l2Co:t o:f t16.0 8ndik bvy (ewt Ha. —l-Com t of 19 maid' S] tlevts (. o 1et, It —-ts Iitort v.......'s I-etu ll t.I.' if {lhe S(.oar SIN ^. lotm. —- -- T ) iPheno et f'r wbi(c':h'vit-ltatilon IS I-h..:t, p,-i. l.)i t Sli Ileo- itttl.th:ili'ut-t lh,- muitiun: ti- A:,N: t tliltitit i;t,- N r. - i.t...lt-,lti i l~;itt. s f;l;)tlitl in I t cis.P. —t- Nemitil.t is N;it itt t-ci I.no:-su.itl i l ittl t lie it-si:'i-i libi~ l-~ I'.i Sli:titi o r Systeo I oX nc a lob: f N_ h}!:- l.itt ittt-i er. f.i' I t i itol of i v'cdi te tm th ulr tor of t1he tlcvolvi. l?a......or' iuio.. if,i l:'ets an tof.%tllitts................................................... 319 I N T 1 01) DIT C T I 0 N THl great dolme of the heavens, filled wit l a countltUss 1multitudes of stars, is beyond a doubt thl most amalzill spectacele revealed )by the sense of siglt. It lhas excited the iadmiration and curiosity of I-mankint d il lln alges of the cworld. The study of the stars is thereftore coeval'with our race, anl hencc we find many discoverice iII the heaven:s of whose origuin neither history nor tradition can giNv antlay account. lho science of Astrontomyl emlb)racin.g, as it does, all the phtto.men:ca of the celesti al orb:s, has furntished in all ages the g'ratnde.st proble)ns for the Cxercioe of Iumtan genius, In the vprimitve ages its advalnees were Xsl+ow, buat by patient watchiing, and by diligent ati fIa.ithftul records tcra'.nsmitted to posterit y fi'om generation to gelneration, thoe mysteries which fill the heavens were one by one mastered;, mtil at le1mtl:, i our ow.tn age, there rcmains nlo phenomrenon of tmotionr uneXplxaiin ed, while the distance nmanittudts, ma sses, reciprocal influences, and phi\yslical constitution of th}o celestial orbs ttavo been approxima tely revealed. in a former volume an attempt \vs mad to trae toie careler of discovery tl aniton t. thte stas, l to exhibit the suctcessivc steps by which tth genius of mIlatni fintlly rea.tched the soluotion of tle great probliem of the univexrse. tlhe perflrmt ance of that task did not permit the special study of any one object, except so far ast it was rtuired in the march of the general investigation. It is our X X NTftRO ) U CTItON. olject )now to execute what was then promised, anild to examnine in detail the various bodies which arle allied to the sun, constitutting (as we shall find) a. delicately organtizced system of revolvitng worlds, a cornplex mcclanical structure, whtose stability hats challengted the admi ration of all thinkling minds, and whose olrganizabtion has fiurnished tho most profound tfhem s of humat n invest igation. litho plan adopted will lead us to presoent clearly all tho facts arid phenomena resulti:ng f'rom observation; witit these ficts thie student tmay exorcise is own genius in attet mptingt to account for tthe plenomenta, bte fore proceeding to accept tth explanation laid down in thl text. T.o aid the teory and to present a systemnat-tic invelsti g.ation, we shall adopt tle simple order of distance ftroml tho solar orb, colmmencing with tha:.t grt.nd central lumtinary, and proceeding outward fromn plfanet to planet, until wo shall develop all the phenomenal employed in tho discovery of the great law of universal gra'vitation.'With a ktnowledg.t of tli l tt he tsworlds already cxaninted cease to be isolated and arrangl tlhemselves undter the emtpire of gravtitation into a coltplex system, the deolicate relations of whose parts, leatds to new discovery and to the final )perfection of the system of solar satellites. I aving closed our investigatiion of te planets and their tributary worlds, we shall render an account of thoso anomalous bodies called comets, which, by the suddet.. ness of their ap)ttaranco, their rapid and ecctentric lmotions, and tho brilliant trains of light which sometimes attend them1, have excited universal interecst, not unattended witt alarm in all ages of the world. Beforl passing to thle execution of this:ptan, we must examinlne, to soime extent, t tlhe plnomtcena of the nlocturnal INTROD U C TION. i heavens, as the stars furnish the fixed points to which all moving bodies are referred. To the eye the heavens rise as a mighty dome, a vast hollow hemisphere, on whose internal surface the glittering stars remain forever fixed. In case we watch through an entire night, we find the groupings of stars slowly rising from the east, gradually reaching their culmination, and then gently sinking in the west. A more attentive examination enables the eye to detect some of these groups of stars toward the north which ever remain visible, rising, culminating, and descending, but never sinking below the horizon. Every star in this diurnat revolution, as it is called, is found to describe a circle, precisely as if the concave heavens were a hollow sphere to which the stars were attached, and that this hollow globe were made to revolve about a fixed axis, passing through its center. Indeed, we find by attentively watching, that this hypothesis of a spherical heavens accounts for all the phenomena already presented. As the stars are situated nearer to the extremity of the axis of revolution the circles they describe grow smaller and smaller, until, finally, we find one star which remains fixed, and this one must be at the point where the axis of the heavens pierces the celestial sphere. This is called the north star; and the point in which the axis pierces the heavens is called the north pole. The opposite point is called the south pole. Only one half of the celestial sphere is visible at one time above the horizon, but this spherical surface extends beneath the horizon, and forms a complete sphere, encompassing us on all sides, while its center seems to be occupied by the earth. It is true that, in the day-time, the stars fade from the sight in the solar blaze, but they Xii I NT' O ) U CT X N. are not lost; the)y still fill the heavens, as we shall sco hereafter, and the starry sp rtt'lr sweepUts ibroken entirely roudtll tthe eartth [Theset great truths, the diurnal revolution ofl the 1teav-. ens, its sphelrical ibri, tle central position of the earth, thie nortit polar star, tht axis of the ht avew the circleT desc-ribed by the stars, )were among tlhe distcoverites of' primtitive antiquity and are matters of the.m.ost silpleo ob)ser va.tion. Tl.hl spletricatl flrni of the heavens was soon ilitated, and thte rt/iicitd globo becamte one of tihe firt ast strononicatl intstrumlents. On this a rtificial globe certain line.s were drawnl to imitate thoso described in the heacves by the celestial orbs, and as thlese lies must }tncetlfrtdh foirnI at part of our languago we proceed to gi.ve the fitl lowing: Definlitions: -- A. gryat circle is one whose plane passes through] tho center of the sphere. A.sma-:ll circle is one wtose plane does not pass th1ro)ugh the center of0 the sphere..Tlhe axis of the heavetns is an im;,giniary ]ine paissin throught tle center of the earthl, and about whicht the hetavenis appear to revolve onc in ttwenty-four hours. A. 7mzesidia(n is a. great circle passing thlroug tlho hjighlest point of the celestial sphere (called the ze. i-i) ttnd thle axis of tho hea;vens.'1The ecquator or cquintoclia is a great circle, perpentdiculttar to tho axis of the hetavens, and half-tway between the north and south polar tpoints. Theseo ii mptortalnt litnes Ihave beeln emtployed ifom thl carlliest ages in the study of the heavenly bodies, dttl hlaving thoroughly mastered their m.teaniang and position we are preptared to oxamine any clanges of locationt whioit INTRODUCTION. Xiii may be discovered among the vast multitude of shining bodies which go to fill up the concave of the celestial sphere. We shall proceed,. then, without further delay, to the execution of the plan already laid down. CHAPTER I. THE SUN, THE CENTRAL ORB OF THE PLANETARY SYSTEM. DISCOVERIES OF THE ANCIENTS.-THE SOURCE OF LIFE AND LIGHT AND HEAT.-THE SUN'S MOTION AMONG THE STARS.-HIS ORBIT CIRCULAR.LENGTH OF THE YEAR.-INEQUALITY OF THE SUN'S MOTION.-EXPLAINED BY HIPPARCHUS.-SOLAR ECLIPSES.-TIHEIR FIRST PREDICTION. DISCOVERIES OF THE MODERNS.-THE SUN'S DISTANCE.-HIS HORIZONTAL PARALLAX.-IMPORTANCE OF TIIS ELEMENT.-MEASURED BY THE TRANSIT OF V.NUS.-THE SUN'S ACTUAL DIAMETER AND REAL MAGNITUDE. —HIS ROTATION.-THE SOLAR SPOTS.-THEIR PERIODICITY.-SPECULATIONS AS TO THE PHYSICAL CONSTITUTION OF THE SUN. THE sun is beyond comparison the grandest of all the celestial orbs, of -which we have any positive knowledge. The inexhaustible source of the heat which warms and vivifies the earth, and the origin of a perpetual flood of light, which, flying with incredible velocity in all directions, illumines the planets and their satellites, lights up the eccentric comets, and penetrates even to the. region of the fixed stars; it is not surprising that in the early ages of the world, this mighty orb should have been regarded as the visible emblem of the Omnipotent, and as such should have received divine honors. On the approach of the sun to the horizon in the early dawn, his coming is announced by the gray eastern twilight, before whose gradual increase the brightest stars and even the planets fade and disappear. The coming splendor grows and expands, rising higher and yet higher, until, as the first beam of sunlight darts on the world, not a star or planet remains visible in the whole heavens, and 16 THE SUN. even the moon, under this flood of sunlight, shines only as a faint silver cloud. This magnificent spectacle of the sunrise, together with the equally imposing scenes which sometimes accompany the setting sun, must have excited the curiosity of the very first inhabitants of the earth. This curiosity led to a-more careful -examination of the phenomena attending the rising and setting sun, when it was discovered that the point at which this great orb made his appearance was not fi'ed, but was slowly shifting on the horizon, the change being easily detected by the observation of a few days. Hence was discovered, in the primitive agesTHE SUN'S APPARENT MOTION. —In case the sun is observed attentively from month to month it will be found that the point of sunrise on the horizon moves slowly, for a, certain length of time, toward the south. While this motion continues, the sun, at noon, when culminating on the meridian, reaches each day a point less elevated above the horizon, and the diurnal arc or daily path described by the sun grows shorter and shorter. At length a limit is reached; the point of sunrise ceases to advance toward the south, remaining stationary a day or two, and then slowly commences its return toward the north. This northern movement continues; each day the sun mounts higher at his meridian passage, the diurnal arc above.the horizon grows longer and longer, until, again, a northern limit is reached, beyond which the sun never passes. Here he becomes stationary for one or two days, and then commences his return toward the south. Thus does the sun appear to vibrate backward and forward between his southern and northern limits, marking to man a period of the highest interest, for within its limits the spring, the summer, the autumn, and the winter, have TC3 B: 8UN. I7 un thetir cycles, and by their 1union have wrouht out the chainges of thle -year.'The length of tlis irnportant period was, doubtless, first deterit ndittc ly counting the days which elapsed o firo' the, tie, wthicn tihe sunl rose behind soe elid so well-defined nattral o(bject in the horizon until his returll in tlh satlln direction t tthe same point of rising. 0O coursei, these chtanges in tie sun's plae p, were studied with prolfound attentiont. l)lty were amo teng the first elestial phelnomenat discovered, and among the fist demanding explant.tionl.'1Tht stta/s' were fotund rnevt' to chagz e their points ol risin,^ cuhllination, and setting.'.Their diurnat l are renmined tbrever the samel, and the amount of time they retatinlled above thti horizon depended on their dista nce froml' the north polar point. Observatiotn hvint g thus revealed the fact that the stun was lundoubtedly movinfg alternately norith altnd southt,,t more critical research stolwed thte elqually important truthi that this great luminary was slowly shifting it.. }place a1tlllOn11 te t fixed star:s. 1Thi \s was )ot so re(adily deterrminled; but by noting theo brillitant stars which first appeared in the evening, twilighltt after sunset, it wts )oo0n discovered tha.t themse stars (did not lon" re.main' visiCle..tT'h:cid the whole starrly h}~eavens seemtedt, (from )night to night, to be plunging downward to overttake tl secttintg sun, or rather, that the sunl hiniseolf was moumntingl upwtard to m-eet the stars,; att d tllts was discovered a solar ot ion iln a directio0n opposed to tohe diurnal revolution of the heavens. [fllows that half tho angle, A..'.A,"/ measures tho iclination of' tle ecliptic to the equinoctial. Int the earliest ages it wals assumtled that the sur's orbit was absolutely fixed t tamong the stars, and thlat the points it which this tirtle crossted the etiuinoctiadl wero in like tmanrerll inu1variable, Th,eso points of intersection are of the highlest im)porttance. TI h:at one througl whilech t}llo sun pas)ses in going fronlt south to north, is cialed the t,[ernl lEqtioxr while the opposite poilnt, tlhrough whitch the solar or'b pases in gloing from nlorth to south, is called the Atl'utmwnl.f/lqioxt, Onl tlh day of the equinoxes', as the sunms center was then on the equlinolctial, the diurnal arc de-scribted li ttho sllun would lie ono half above, and the other h balf below the htoizon, makildng the length of lday and- nightt precisey equal. Amnong the ancient nations the day of the vernal equilX was tan object of especialt interest, as it heiralded tho coming of spintg, and its approachl w-as marked by tho risingt of a certain bright star in the early dawn of tho morning. Now, in case the vernal and utumt nal equinoxes were invariab1le, tho samet star by its hfeliaca rising, (as it was called,) would mark the crossing of tho equinoctial by the stun in the spring1 and the equality of day and night. After the lapse of few centuries it wats discovered, by the length of tho noon shadow of tho gntomort, tltnt thoe sun had reached the equinoctial point, and yet thl sentinel star did not m.lake its appeait anco, tEithrl the equinox or the star was it motion. It was soon (ecided tlfhat the ve'rnaalland autut nal iueqinoxes arte both slowly moving backwards along t.lho equinoctial, andl thus tite sttt crosses tis celtostial eircle each year a little behindl the ptoinlt of th.e )prce(.cding year. The ancient nations all seotlt to hve attalined to a 22 T 3i1: SU N. knowledge of this great trath, and some of theml are said to lave fixed the period in whicht the vernal equinlox retrogtrdes aroutd the entire heavens, at period of nearly twenty-six thousand yearst; as thiis is a matter of simplo obseirvation, and as the rate of motion can bo obtained by comparing recorded observations, m1fade at intervahls of futr hundred or five hundred years, we may readily credit the statement that this period bcamel known even anterior to tlhe commencement of authentie history. Thlis discovery of the retrocession of tlh equinoxes led to at more crlitical examination of the sun's apparent mtotion. Thils motion had )been assumed to be utunifornlt aand in case this hypothesis could be maintained, the solar orb ought to occupy an equal aounmit of time in passing over tlhe two portions of its orbit north tand south of the cquinoctial, that is, the number of days from the vernal to the autumnal equinox oughlt to be precisely equal to the number of days from0 t the autut nal to the vernal equinox. The (Grceek astronomer I1tipparchus was the first to discover the ilmportant truth that an inequality existed in these two periods,. HIe found from his ownt observa:ttions that tthe sun occupied eiht (ays m1ore in tr'acing tho northern than it did in traversing the southern portion of its orbits. T.lis was a discovery of tho highest import.Itace, as it seemed to involve the then incredible fact, that the lord of ttie celestial sphere, the great source of life, tand light. atnd heatt travelet d amotng the stars witt a vatriatble velocity. Iln ctase the solar orbit was indeed a ct'cle, this inequality of motion seemed to be impossible..The circular figure of the orbit could not be abandoned, neither was it possiblo on philosoptical principles to give up the hyp)o T H::f El S N. 23 thesis:of unliform motion. ]I ere thn was prelselted problem of the deetpest intetest, to preserve the circiltar figure of the solari orbit and the uitt/firt motion of the sun, anlld at the same time render a satisfactory accoint of the ione uality ldiscovelred in the periods durinttg wh icl tho sun rem1ained northi and south of the c(quitoctial. This problemi was solved by Ilip)parhelus and bftroe pro'cceeding to examinel the reasolnimig of the old G(reck, let the stt.udent exercise his own genius in an attempt to explailn the ascertainted faicts. Illitherto it had been assumed, not only that the stun' orlit wtas circltr, andI tlhat his motion was uniforl, but also that the carth occupied tihe ex.act center of the circle in whichl the sucn traveled round the ]teavens. l.By pro-v iotund study Itlilpparelhs discovered t hatt all tlie ftacts could b1) explaine(d by givilng to the earth a position not in the center of the sum's orbit, but somewhatt nearer to that portion of thle solar orbit where jIis motion was most rapid.''his wtill become evident firom the figure. Iict thl cirle ilt A B C ) r ep)rsent the sun's circular orbit^ in which the sun is supposedt to move uniformly. This motion will only appealr uniforlmto to at spectator at the center 0. If the ol server be rem)foved to 0(, and the line E' be drawn perpendicular to 0 0', the portio.n W A. B E of the orbit will re(1uire a longer time for its descriiption than the portion I^ C I1).., and hencein the tformer the sutl will a)ppear to move slower t'han' in the latter. Indeted, it is maniftest th:at; tlte point V, on the line 0 0' prolo'ned, is thle platce of swiftest miotion, while the opposite point V' is tlhat in whlich the sutt will appear to Imovo slowest. 24 T tE SU N. Itipparchttus, not satisfied with thus rendering a general explanat1iont of the Iphoenotlnon, undertook to detetrino the actual plac oft the earth inside thel solar orbit:, or the valut of the distance () 0, whlich is called the cccen.tricity. IltCre is another problem1 for the examination of the student,.t may be solvead by simply knowing how E If "6',,, l.................. mRanty days longer the sun remained northo of th.o equi-. noctial than it did on tl the south of this circle.'thi quantity we have alreadiy given. JBy dividing the circol A B C I) into a ls mttany equal partst as there are days in tho year, and by drawing 3F ^' through tihe conter 0, an.d perptendicultar to V V', we have only to lay off firom Fo to alf te excess in days, and draw f. W4 parallel to Ft f", and it will give at 0'.tO t.eo tru e place of the earthl, anttld 0' will bo the ecccntricity..An o-bserver at (0 will see all phenomecnat, actually detected in t}re sun's miot.ionll, while the circular orbit and unifort m velocity aro rigorously retained. ltaving determinied thoe arth's eccentricity, it was Itow T: 33 S U. 25 v ry easy to calcula.t tihe stnil s place frtom day to day during hiis entilre rvolutiont among tile fixed stars, This was actually< done by thle old astrotnomers; a(nd as the cotmpted places agtreed with those observed withiin the limits of observation, with the rude intllrImenlts thten il use, no furtlh) r advance would lb mrade in the solar mno-. tions. Ecntisc OtF TilE S INr,-. No one has ever beheld tho total dislap)perance of the sun in tho d4ay-time without a feeling of awe creeping through his fiame, and, even now, witen modern scietnce predicts t: thee co ming of tttcsc;tntnazit. Ip)lt.eomc:na with unerritng precisioln, a totail eclipse ofth tiho sun never ftilIs to inspire at certain feeling of glo.omy.ap.-. prehlension. W\hat, then, must hatve been the ellcet in tile rude crages of the worhld of the fitding out of the sun in mid-.course throtugh. the heaverns? Itlnnaln t gll ius, of course, bent all its enerlies to the resolution of the great problemtrs involved in the occurrence of an colipst of thle sun.t T11l first efolrt was directed t) to lth discovery of thle ctseC of these startlintg lphetinmcl:flt; attndl thin once determtined~l tht second tgreat effort was put forth to so mnaster all tte circumstances as not only to Cxplaint tho eclipse but to predict its cormniI. Ai. At 0'F Ax S OLAR:Clt::.......... i:n searching fir t i cause by wi. ch the sun might be hidden, it was at, once evident tflat there was but ote 0object in th}e }tavens suf. fliently large to hide the whole surface of tho.fe sun. T'. his body was thie imoont. Tittms attention wfas directed to tho lunar orb, a3nd it was soon noticed that, while the britglt ttars and planets became visible in thte darkness attending tan eclipse of t:he sun, yet tlce brightest ol.bject in tihe ]thcavent after the sunl wa1ts never visible during an eclipse. Tlue tmoon was fi)nd to move.amon t i e stalr withi a velocity A t 26 T t t;P S N. far greater thlan that of thie sun. It was,:morteovrc seen that the moon's pathi crossed that of the sun twice during every revolution of tthe m1oon, and examtining still more closely, it was discovered that no eclipse of the sun ever occurtred except at the now mioon. Now this rapidly revolving globe was evidently the nearlest to the earth of all the heavenly bodies. It was seen, wvhen a silver crescent, sonm ti lcs to pass over and iide the larger stars which fell in its path; it lwas also fundt thatt ttho moon, though invisible during a solar eclipse, always appearted itmmediately after very neart the sun and as a slendel crescentt of light. Thtese fiats all combined to provo beyond a. question that the sun was eclipsed tby being covZered by the dark bodly of the -moon. The cause of the eclipse was thus reached, and it now remained to rol the plnomenon of its terrors by predicting whenl it might be expected. To plrcedict a solar eclipse with precision is a prol)lle1It of great difficulty, even with the present extended knowledge of the laws and structure of the solar system. And yet wee are intformned that thei old Greek astronomerls sue-: ceeded in the resolution of this complepx problem. Ti.his -may 1ha.v e been done by lonrg and persevering care in the record of these phenolmenalt; lbr in case all thio eclipses visible at any given place are recorded year'fter yeart for a pe;riod of ninteeen years, it will be found tthat for the next period of nineteen ye'ars eclipses wNill lhappf)en on the sa.zet d:ys and in the samet order; so tlat an asttronlmer, whose diligence had been rewarded by the discovery of this grand truth mright acquire thte ]hig:hest. rentown among his countrytmen and throughout the world )y Ihis superior wisdom in predicting the coming of an cclipse, T 1S U. 2I though no specia-l genius was put forth in the resolution of this gre>at problem. WV re not quite certain, however, that the prediction of the first announced solar eclipse nmat y not thave been accomplished by the application of powerful thought and persevereing observation. tn case the effort were now made to predict a solar chlipse; as a starting point we know that no eclipse of the sun ever occurred except at the ne'o moon. Bt ut at th1e time of at total eclipse of the sun the moon is interposed precisely between the eye of the observer and the sun, and a line jointing the centers of theso two great lumlinaries, produced to the earth, passes throulgh the place of the observer. il1enee, on the day andl at the hour of an eclipse thO new mo0on. must )b in the;act of passsiJy fromi one side of the Sutn's patht to the othler. o render an eclipse possible two conditions )tust be filfilled at the same time; the moon must be new,, andf tlhe nioon0's center must be in th}t act of crossiL the sunt's orbit. If the sun's annual route in thle lhea.vens we re marked among tl stars by a line of (golden light, alnd tlhe mooln's m.otion bo attentively warVt:ced, it w.ill bto found thatt at every one of her revolutions slhe crosses tisi grolden line twitce,. Th pointt of her crossing fi:om south to north is called theo moon's tstondiuq n'tode0, wlhilo the pointt of crossing fiomr north to south is the descending node. T'hese nodes (lo not remoain fixed, but are in comp)aratively rapid motion, fand fin-ally accolmplish an entire re'~volut ion aroundtl the teavens,s oiln eC ec!if)tic. If, then, we unite all these facts it will be seen that to producet to any observer an eclipse of the su, tlhe moon, at thtc nttt-, must be} exactly in one of hetr nodes, sott that ttte center of the )moon, the nodte, and the center of the slun, form on .S t I; SE U N. and the samie straight lineo. l [crc, thlen, are tie conditions precedent to a solar eclipse. It now rematins to so tbllow these revolving orbs tas to ble able to anticipate ihe certai occlTurrence of these deteornincdl conditions., We follow, then, fi-on nigiht to nigtlit, te waning moonL shie slowly approaches tthe un; leter lighlt becoltmes a deh iate crescent, just visible in the g'ray twiligttt of mornl'tlintg beftre the rising. of the sun; at length the mIoon tbecomtes invisible, and when shl reappea rs it is on the Olpposite side of the sul, and ther silver crescent of light is just above the setting sun. There was no eclipse be.cause this niew moon did not fall on the sun's path. It is, howevert, easy to martk the tie of now moon, and eq{tually (easy to see and note the time when the mtoon is in her node, or fo the eclipti c, ad by ttus warItching, frontt new moon to new moon, wo may see whether tho interval'fromn the ptass'age f the nod ui t to new mvoon is >,vrow invg slhorter, and at whatt rante it dcreaises, till, inallty, we tsall perceive tltat to the coming of a ctertain new moon:it'm t fiall precisely at tthe node, and on tho day of this coimputed conjunction, to himn w-Io has watched tnd wittd, and ponderedtl, and computed, tho sttun must t it awalty int total eclipse.'C ulihe is thef train of reasoningti and obsc vation which may have first led to t to resolution of thits greuat lproblenc, ltut to whose gnciius we tare i'ntebted for th}is grand discoverny neither history nor tra. it ion furnish anlty inf [rmatlion. In consequenco of the near equality in the apparent diameterss of the sun and moono, and a, slight olhanwge in both due to a clhnge of th e actual distance fiom }the carthI (as will be shown S ereahfter), it somlctitimes hapcipns that the mtoon's daiamroetter is (less ttan thl.eat of the lsun.t tWhenl tl his obtains duri'ng a solar eclitpse there r-emains T UI N s B. 29 larount,. tilo tblack disk of the moon a brillilant ring of solar iglit, arltt the eclipse is said to be taunt/.lr. W''lt th ever the meoow"s ceCter, at theIo 1ne, is not precisely:at the ntlod, but not so rem(ote from it as tihe sum of' the( emi-diamettorl of ttos to obs, t here will beo a pa rti(l obsc 1i'ation of the stun'Wo hlave }resented th ese fllfet in tlhis place, as known to the early astro:olli)ers, lad lt as admirable me tans of exetrcising t tloe powver of thought.1)1 thel: part of those wht o mnay desire to devoto th.t.mselvtcs to the real study of tlhe gtreat ptlenomneila. of nature. Wt will recur to this tsu I jict again when we s-hall have mastered the laws of motion 41and of( gnamvitaation, Suchl is i ranpid survey of tihe discoveries of the an.cients in the.tlstudy of that gre'at orb, whiclt firom its splet:1dorl1, cvc if it e a metre 1ph'antomt of light, justly cottnmaan.8ds our adinti.11t:ion'and dtcsrves our be.st efblrtsto vmaswter its i.ystlriots iovemients and its stiulblintte ptlteOWe noN prIceed to exhibit tihose discoveries tvwichit could sonly be accomptlishet d after m:an had armted htinsolf with instruments ofi great powler antd delicacy, and with a vtision itncreascted a. thousand fold beyond tthat, with' which he is endowed by nature. )Iscvt r'1 s OF'E.n MO i X5tt -The.' rude instru-' iments t em loyett d byII te e:arly ast.ronoml:ers sulliced to fix the p1)lace.s oft the sun (and tth other hea:.venly bodiets with sufficient accuracy to give a. genleral outlinetc of tthe curves they described, and a:s ttlese c'urves, as dcetermined by olbscrtva tion, a -pproximiated thlo circulatr tril, it was coiteluded that the deviations fromt th at exact t figure were only errors of observaition. t Knowitng the periotd in whichl the sunt revolves roundt the heavens, atn the distance of 80 T It: S U N. the observer from the centor of his assumed circular orbit, it was easy to computoe accurately the, stln' placo ainong tle stars on any day of tho ye tar. T'his eomIutationt tbeig lmad e, no instrument then i uso could detect any dilffcrence between the comtputed place and that actteallf heli by the sun. It was, thleolbro, uinphilosophical to doubt the absoluto truth of an hypothesis tihus sustained by the best observations which could then be )made. JIt was not at all dif;icult to observe roughly mere position, tand any error of observation in fixing tlh place of tho sun would, in tho long run, bo cnliminated itd its effects by taking into account a largoe tnumbr of revolutions. Thoe degree of accuracy required in thus fixing the s;un' pltace am)ong:t tho stars was widely diftlrent from1 that (ldemandil1ed in tho M5ASUB^\;Mlo'NT 0': OF T E' $U >S )IS'TANUC,-'1 TheO prin'ciples involvedt iln te solution of this greatt problem wero well understood by tho old Greek astronome:lcrs, and were applied by theit successfully in measuring the distances of inaccessible objects on the surlaco of the earth. The}so principles are so simple that a k]nowledgeo of the very first ruditiments of geometry will suffice to render inttolligible theo ethods which are employed in obtaining tho data for comtputing the distances of the heavenly bodies. Suppose it were required to learn the distance of tho object A tfoml the point 0. ]From 0 send to A the visual ray C A, then lay olf any line frontm ( B perpendicular\ to A (, and measufre its lengtht. From B draw tth visual ray B:I C, anltd leatsure tho angle C1 B1 A. We havo thu.s fornmed a rightt-angled triangle, in which tho anglo at C is a right anglo, the base, ( B, is known by mearumremetnt, and the angloe B A is known in the sameo way, henco may be computed, by tho simplest clementa of trigonometry, tth length of the distanco C A, or tho required quantity. Any error committed in the measurement of the anglet C 11 A grows more powerful in llt effect on C A, in pro-:B.................................................................................................... portion to the number of titmes C: B i must he tatken to measure C A. In our attempt to measure the sun's disitalnce we aro limited to a base line equal in length to the carth's ditameter, and hence it becomes necessary to em:ploy every refinement of art to eliminate as far as possible the errors involved lin the measurement of the anglo (J B A, or its eomplement, the angle ( A -, on which, in the application of these principles to the problem in qtuestion, depentds the measurement of tile sun's distance. this quantity isi tie great key whict untlocks all the mysteries of the entire syste. Uon it t ptends d)t s irectly the mlass, >volume, and density of thl sun, the distalnces, weighlts, and magnit tude of all the platnets, and even thle masses and distances of the fixed stars. Itt is for this reason that tmodern seienco las sparedl neither time nor 82 anT S U N. mot-ey neither siill nor ilngeutity in thte eftrt to reach tan exact solution of tists gatnd problemra }. ltn SOL.AR: PAIRALLAX........... -int caso an observer were located at ttte suttn' cent:r, and froin hiis eyo two vistual rays were drattwn one to the center of the earth, the other tangent to the sptherical surfaco of the earth, tthese rays wtould tl rm an att le with ealch other at the eye of the ob.Qtserver, aind tlhis ang..le is called the sun's hori.:Zouttl iitrtlt[.w,. t.'Thus S represeplnt:mg the sun's center, C the ce'nter of ea.rtti, C0 It a radius of tlh earth trpet:cndiular to tho visual ray S C, adal S It the visuatl ray drattwnt to thie cxtrerity Rt of thte radius, the angle l R. S is the solar part llattt(: in cat s it were p iossible to measltre that aingle(, as the tanglo SO R is a rightt-.a1gle, the remtaining parts of thet triang-le R S C become known by cornpultatation.'lThus it appears that the problem of imnasuining the sun's distalnet from the.earth resolves itself into obtaining tlte value of thoe situ'o's hori.zo'ntai pa.ralltxt( or the angzle under which the earth'i radiut s would bo seen firom tlhe sumt' center. No inst:rmonts ha ve yet been coristructed suff.iienttly delicate to accomplish directly the measure of tlis imnportan t qtualttlity with the requisite precistion..u tt t tero is an indirect tmethod, whicht hlas beten emiploye: by modern astronomerstt to accomplisih tte -lsameo object, which T H E:l: S UN. 8 htas been rewardeld witIt sat islactory succe s. Tlhis tethodl w)e sha ll 1now proceed to explain. F:rom tint mostrt remotto antiquity it has btcc knownt that there are two planitets,.tMercuryl ad enutts, which apt..pear to revolve around the stt, never rocedingl fr't tha.t orb heyond. certain narrow and well defined limitits.'ltie distances from ttheset planets t to the su:t are less than the earth's distance frioml the samie luminary, anlld he'lnce tfhey m-stt att eacht of their revolutions pass between the carth} and sm tll. Modern scie.tnee lhas confirtmned these alte<. ctient discoverties, atnd the telescope ltias even. stow.n that on certain rarie occastions eaich of these planets actualtly past:,ses bet\weent tlhe solar disk and the eye of an observer (3ont the earth1, anid appel tar)t ts as a round ltc siol on the }'igth't sur1t.ce otf the sun. These passages of tie planetts across the:solar disk are called Iranusits, and it IIha Ct n that the trantsits of tVenus furn:ish an aldmirablet m1eans of reduciln the errors involved in the direct tmasureit -.ment of the solar para laxt as we sthall now proceed to explain, Wv will first present thol principle involved, and thln ma llc tie application. Let it b requtired to determine the dt istancte of tho point A. fiom any inaccessible surlfco, as (: ), and that A. A' is the longest 1 b ase linc w ltich can l os si!bly )e em-e ployed.t In case the dist;ane of the po int B' 0 on th} stin ti'ec C 9 D be rtt1quirc, t. en the atigles B A' A.. and c B A.At \ musit be measur ed and their sul, subtrac eted hftllo 80 tf gives br a r aidr to a rngl derA I' A,', or the antgle undter whic the lin e Ae A' wtld bY s pectator att f', Now this antglc because of its minute value, >ay ie difficult to meatasure, anitd we desire to find stome a.1 rt0ilice by whichl this difliculty may be at leas dt dimini.lshed, 84 wnti( s u'. if not entirely removed. Suppose t1thn a m1ateria1 point to )b loca1ted at.1 much nearer to A A.' thatn to C3 D, an observer at - A would see thl point B) projected onl C 1) at B", whil ant observerr at A' would ecO the same point T~') A.^~...,. ) — -~-~. ~t ~ " ~~ ~...: es::.x............... --: C, projeted a t'. Now loet t suppose that tlhe points B:V and B: can be identified and seen as round, black, petrmltlt tneat spots on the remuot ce surl'face ( ); iln ease B is fiur'. ther friom 0C ) thtan from A A', it is c lear tlht thte visual au/yle subtlended by Bi'", as seen fromm A, will be larger tltan the visual angtle subtended by A A, as seten from B' in the prolportion of tihe distancle B B' to the distance JB A'; land iS: Bf' should be 2. times longer tha)n B A', tlen'would. B' h" e. 2} times longer than A.'; and the proble.ml resolves itself into the measurement of the large ang le Bf' A B" instead of the small angle A. B'.:'. iuch is the principle; and we will rnow proceed to iti application. A' is the diameter of thte earth. B is tho planect Ven\usT and (t s.) is a diameter of the solar disk. T'.o an observer -t.t A,'Venuts is seen on thite sun as a }lack spot at <':), while an observer at A.' sees tl: e plan:et pro THE SUN. 85 jected at B'. Venus is about 2- times further from the sun than from the earth, hence B B' is 2- times longer than B A', and therefore B' B" is 2- times greater than A A', or 2- times greater than the diameter of the earth, as seen from the sun, or five times greater than the sun's horizontal parallax; it is therefore but one fifth part as difficult to measure the angle B'A B" as to measure the angle A B' A'. There is another important advantage gained in using the transit of Venus in the measurement of the solar parallax, arising from the fact that modern science has obtained a very exact knowledge of the relative velocity of Venus across the solar disk. f we note, hen, eactly the momet the planet is in If we note, then, exactly the moment the planet is in contact with the solar disk at p, and also at p', this interval of time will give an enlarged measure of the chord pp', described by the planet as seen from the station A. In like manner the observer at AX making the same observa. 36 THE SUN. tions at q and q', we shall obtain the relative lengths of these two chords, and hence an accurate measure of the interval B' B", by which they are separated, or of five times the solar parallax. Although this problem may appear somewhat complex at the first, careful study will render it, in these general outlines, very simple and easily intelligible. Its high value in the measurement of the very most important element in the entire system of the sun and his satellites should secure from the student all the time and attention necessary to its complete mastery. Such is the importance attaching to this great problem, that at the last transit of Venus, governmental expeditions were fitted out at great expense, and observers were dispatched to points on the earth's surface as far asunder as possible, each observer noting, with every precaution, the exact time in hours, minutes, and seconds, from the first contact of the planet with the sun's disk, up to the moment of last contact. It will be seen that the problem, as presented above, is freed from many complications which surround it in practice, such as those arising from the revolution of the earth in its orbit, its rotation on its axis, and the fact that the observers are not located at the extremities of the same diameter of the earth. These and other matters affecting the result being carefully taken into account, we have obtained, for the value of the sun's horizontal parallax, when at his mean distance from the earth, 8".6, or eight and six-tenths seconds of arc, showing that this grand orb is removed from the earth to a distance of about ninety-five millions of miles. We shall recur to the transits of Mercury and Venus when we come to treat of those bodies. .M->>it' i. -..........;. SOLA. A SPOTS T It S U N, 87 t.t li si's tA MA(si NI:t i-t:ItI. -.. lodex t instlrumon.t enablett u to neasure with great exactitudo the a.ilglo subtended'by thie sun' appar'et diameter7 an attglo wioso: valuto at the suu's imean distancel mountt to 8.1"..it at globe removed to a, distatneC of nil.ety-filve rillioil of iniles, a1nd yet having atn apipatrent diameter of 1, 1'", muIst havo a real diameter of ito less thanl Si82O)000 tmiles ilin lengtht, or lmore than one hundred and elcven ti-mes longer than tie diameter of our earth, as woe shail ltereatter sOtc.'Tis t eables us to com)pa ro thet bulk or volume of these two globe., and we find t-hat it would requitre no lss tIhin one mlllion thl ree hundred andi eighty. ftour thousand thur hundred and seventy-two globes as large as thet earthl to fill tlhe vast interior of a h.ollow globe as lben:t as the sun. This is a cotmpariston of' bulk only tie rcla'tive weights of the earth and stut mtiust be consideredl. hI ercaft er It this wondle.trfiul globe excited ounr admiration by tho spilentdor ot it surftce, and its floods of li gh't land heat, how mlust this admira.tion be inrea'sed w itcn wt conterttl plate its great dista nce anld its zgtigantic pr0opl rttions? tlitE PB.SXiIAL:I co'xsir:t.t.t'oIN orF T.r.n.su1... tt:for the aid derived from the tolescope man could never have pau.sed bIyond mi er oe conjecture tas to ~what lies ion the saurtice of the sun. The tclec sop; o lowever, magnifying; thlus'iand times, transplortas thle observer over a' vast prol.porttion of the dista nce separattting thim fromt the solar orbl, and pl an:tts him in space within nincty-fliv ltousand miles of the sun's sur tsleace, there to examine tht e phenomena revealed t is sity t hisig magicix tub., We ima..y therte - fore. regard tho su i's distance as rt duced to thef thousandiltl'h part ofl its acctual value, and'we should'not bo surprised to 1iitd upon a globe of tsch gtraltd prportt ions 38.Ti H St U N. fluctauations and lcanges whiclh, at this reduced distance, may become distinctly visible. This anticipation has rnot been disappointed. Tin sola sptOLA s o theS naked eye the t sun' surface presents a: blaze of insuflTl'rable splendor, and even when this intense light is reduced by the use of tany translucent meditmttit the entire tdik appears evenly shaded, witIh a slight diminution of light around thl cir. teutfarenee, tbut withoutt visi t visible s or iationl. Whten, however, the power of vision is increased ait udred or a:t thousand fo(ld by telescopic aid, and -when the intense heat of the sun and his equally intense light are reduced by the intterlosition of deeply colored glasses, the eye recogttnize a surittco of most wonderful character. Instead of finding the sun evert ywhere equally brilliant, tlhe tielescope shows sometcimes on its surftace btack spols, of very i rregultar figurt, j caed and broken in outline, andt surtrounded by a. penttmmbrta confot min in ftiure to thte ent-.. eral outlitln of the central black spot (called t}he nutclltus,) but of mtuch lighrter shade. Even whiere there are no spots. the;surflac of the ston is by no meants unirmly brillibanLt. The entire surafitc has (.a mo/lied appearaince. w ith delicat pores or points, no one of' wlich can be readily held by te eyeo, but a. group of tthc1m mtay somctithes le seized by thle vision under tt voirable atmtospherio citreut stancts, and can be held lottng en ough to demonstatte tt that these miltte pores do not clhatge tteir rela;tivo )osition, or dislapeaptvtr while under tte eye. Bezsides the mottling of the surficc, te tlestcope detects in the s;olar orb a variety of brighter streaks, cal led fitcPue, whose lappearane tas been connected, as some believe, with the bre aking out of the bltack spots. Watchingt friom day to day a sigle slspot, or a group THE SUN. 39 of spots, on the sun's surface, they are found to advance together in the same direction, slowly to approach the edge of the sun, finally to disappear from the sight, and after a certain number of days to re-appear on the opposite side of the sun's disk, revealing the surprising fact that the sun is slowly rotating on an axis whose position seems to be invariable. In case these spots were absolutely fixed on the sun's surface, they would reveal the exact period in which his rotation is performed, but in consequence of their change of figure, and change of position as well, we can only reach an approximate value of the period of rotation. This is now fixed, by the best authorities, at twenty-five days, eight hours and nine minutes. During the past thirty years M. Schwabe, of Dessau. has given special daily attention to counting' the groups and spots on the sun, and by preserving a record it has been discovered that the amount of solar surface covered by the black spots is not only variable but that periodicity marks this variation. The entire change, from a maximum of spots counted in any year, to the minimum, occupies about five and a half years, and the same time elapses from a minimum to a maximum, making the period from maximum to maximum eleven years. This fact is one of the most surprising revealed in the physical constitution of any of the heavenly bodies, and thus far has baffled the power of human investigation to explain it, while its mysterious character is increased by the fact recently discovered, that this periodicity in the solar spots is identical in duration with a certain variation observed in the intensity of terrestrial magnetism. Thus, it would seem, that a new bond of union is about to be established between the earth we inhabit and that 410 T:II B 1. N. nigotliy orb) whlenc we reccivo otur su lites of lightt at.d Stomte astronotmerts accountt for tho solar spots by sup-.posilngw the sttlt to be a solid, dark, opaque globe, situ. tro tnded by two atimo fttlphres the exterior olie }a ighly luniiiitlous td ga-seous envelope, the interior more dense, and poIse.ss in, g't refleat rlcting pt wer. 1"t spot''.ro supp.toscd to result from- powerful itternal con vulsio is, l'pli eavals floi within breaking throug]h tfhese. two en.-t velopi' and producin, a more extend:td chas.m in tho exttenal tluminous atmospfl>hee I have exam tted the su.rthcee of the 8sutn atnd clos(ly observed the larg.e solar spots twith [a rVcfiacetor of admirablee perlformianlt ee atnd so:tar fron pre, senting an appearance such as the above hypotlhi. e(is \wvouild warrant;, etio cit iro exh ibititon res jembler d th opt'iiitgst ofteAtn ftound by melting through a thick st.ratum of solid ice frion below.v tho spiky tmd jagged outl il of' tho} black nuclett being well rteplr nteittd by al stimilar fi)rmt in the ttpettin//. thiroutgh theo ico, t' ilet tho ptmut bra was ver y fitith-iflly re-prlc'scntedt1 by the ih l'ar. port iolns of' ico tea'ini)g atround th l le opening. I, t is )not to be inf:erred fIron this c>omp:arhisolt tthat t he author tentorta:ins tlhe op;tiion that the extetior of the msui is a, solid c(rust, and that t}heso solar spots are pr:od.uced from thle mlelt-in of th.is crtust )by the action of jinterral fl c s.' Tto cot..parit7sotn is madte fir the purpose of illust ratingt as stlron:gly ats possitible, te tabsolute- appearance of these int xplicablo penoinettilna.t and to present as stroiig at contrast, as tho facts wtarrant to the statemeont mtade by ta distingttishdt astfrontomer, that tho stti's surface, whena viewied by a Ipowerf-uld telescope, resembles " tlho subsidonct of' soo ltloctltcntt cthemicalt precipitatles ti ai trnsparent fluid So lfrx iom thiis t bieinig the cIase the sharp outli.es of tho THE SUN. 41 penumbra surrounding the dark spots has often been seen to cut directly across the minute pores, dividing them sharply and sometimes equally. Recent observations seem to demonstrate that what has generally been considered the solar surface is really the exterior of a cloudy atmosphere beneath the luminous ocean surrounding the sun. Mr. Dawes, by an eye-piece of his own construction, bearing a metallic diaphragm, in which a minute hole is pierced, coincident with the axis of the telescope, has been enabled to make a very critical examination of the solar spots. He finds in the center of the dark spot a smaller opening, which is, as now seen, intensely black, and this is at present regarded as the real surface of the solar orb. The same distinguished observer has announced the discovery of an actual rotation of the solar spots about a central axis. This important fact has given rise to speculation as to the probable cause of these wonderful fluctuations which occur in the solar atmospheres. It is conjectured that these exhibitions may be produced by tremendous storms or whirlwinds resembling those which sometimes sweep over the surface of the earth, and whose vortices, if seen from above, would present an appearance not unlike the spots on the sun. We understand how these tornadoes are generated in the atmosphere of the earth, but it is useless to attempt to conjecture the causes which can produce such amazing effects in the solar atmosphere. INTENSITY OF THE SOLAR HEAT.-Admitting that the heat of the sun falling on the earth is diminished in the ratio of the square of the sun's distance, it is not difficult to form some approximate idea of the intensity of the solar heat at the surface of the sun. By exposing a sur 42 T II S2 U N facc of ice to the l direct action of til sun's heat, whten the suni ws..tearly vertical, Sir Jolhn 1Xlerschcel determined by experiment the thicknexs of the ice meclted in a agivce time. From this and like experiments it is determincd that it would require the combustion of more than one hundr.ed attd thirty thousand tpounds of coal per hour on etach square foot of the sun's surface to produco a hewat equtal to that radiated from the solar orb. Whlen an. i:mage of the sun is received on any s rfac it is fottund that thle central point of the iima;ge is more heated than the parts near tih circurmferene, and tohat the temperature ditmniisheta fromt the equator toward tho poltca T'f sh.'S ATMOSE:RE — These fiacts have been accoluted for by supposing the sut to be surrounded by a dense atmosphetre, and that the heated rays which pass tlhrough the deepecst part of this atmosplhre lose a. portion of their heat, and lftnce the region.s aroundt the disk of the s-tu sthould be, to uts less heatd than those xnear the center of the solar orb. There alre some Xephenomena attendingf a total eclipse of the sun whlich se:em to sustain tLis hypothetsis i of a solar atmlosphere. At the moment the eclipse becomest total, there is seen to burst from the jet black disk of the moon a solrt of halo or glory, radiiating on every side, and presenting a:,pettacle of won>ldterkil grandeur, so mnch so t hat ol the occasion of t eclipse of dJuly, 1842, wittfness ed at I) aviat the entire.popultlace burst into a. sthoutt of wonder and admiration. There also uaptpeared, at the same time, Jflames of fire darting from behind the limb of the moon, re'sembtling mountains of rosce-colored light, rising to the height of forty ori fifty t.hols ahnd ttiles abovtte ts surftac of the sun.1 TH l' 8 U N. 4!btheseJ.lames are knmown to assulte the form of cloudy exhallatio:ns which, it some imltances, seemtl to be drifted like smoke ascelnding i aa calm atmosphere to a. certain level, where it meets at Current and is borne off 1torizon-. tally. t1l eore is another phenoimenon attending the rising and setting of the sun at certain sctasoms of the year in- tho shapo of a vast beam of fiintl, gauzy light, of lenticelar fornm, rising from the pointt of sunset in the evncingf, and stretcting u1pward ini the direction of the sun's path sometitmes 710" or 80~ Ti ls i called the Zoadticrt 1/at, anld tas long been regarded as the evidence of uneondensed ncebulosity, or material a itmosphlere urround ing the equatorial regions of the sun.'lhe central line, or axis, of this lulinous beam does not appear to )e fixed.in position, and Ihence a difficulty arises not re'adily re-. moved by thel hypothesis of a material atmtosphere. S.omt have supposed thlis m.ysterious hftuniltous zone to be ai nibulous ring surrounuding our moon, while others have retarded it as an immense ring of minutt asteroids or mieteora, revolving round the sun, and slowly tubsit(l ing into this grand luminaltry, and by the conversion of their veloc.ity into Iteatl as they fall in a perpetuatl shower on tie sun, or are burned up in the solar atmiosphere, keeping up a supply equal to tloe vast radiation shot forth fr'om te t tn at every momt vey.etof time. Whil' we e are willing to admit thatt a m(atteialt globe, falling into the solar atmtoslcphere, may generato immenese heat, imtn ptro portion to its miagnitude and velocity, it seems quite impossible to adopt the hypothesis that the zodiacal light is either a. m1aterial solar atmosphtere or a ring of revolving meteors, as it extends to such a, vast distalnce from tho sun, tha:t if revolving witht tlte sun, as does our atnmo e44 T If 33ts` U N, st:)lhero wit l t ih the earth, the particles would b) th}'rown yon.d t tIe control of the sun anld would bo dissipated into \'O are compel led to aclknowledge thatt ) u - t he i'entt timei science has renlidered lno sattiisfa:ctory taccountt of ttl ), origitt tof the solar light or'l}eat.t \helnc cotnie tlio exhaustless supply, scattered so lavitsly into space il every direc.tiont we know not.lt, Nithcr.i 1t paossi.l to gitve a t satistfhctory sotltion of the solar spots, or of alny of tio stratllnge t)lphomenati atte.nding their rotation or tran.lslat0ion on1 thio sulnt surfaSce. The idea that torna.tdoescc and tecmpests rat- in theo deep, luminous ocean that slirroninds the sunl, like those Nw'inch fotmctiunes a"itate the amttotsp'herc of theo cartht has noo solid ftundation. A'\e ]know the exciting causes of the t ornadoes oln eatrthl, hut whly such storml-s should exist in the solatr )photosphiere it is in vain to conjecture at preselnt. Doutless the time will com whlen these pholtomtena -t will be explaited. Per-l severting ant d well-direeted observation will, in the endt triutmpl butl these are matters wiict must be consignd to the re.sea.rcches of posterity. C I[ A PT1':1:t 1. MTEXrCUBRY THIE FI.t1ST P I AX\NET IN TIfL O0R1:t)-:R O D)I T[ ANCE FROMA TILE SUN. }x', ItS AB tY.)l:OV::Y.- - - - -l:)rt; tin U R uvgtsLf'nn B;)I'X" - to D,'i':ti> t I i Ai!->...t....lELONT; i'ON,: 1A....... f)'&i' I) ng AND]:O.PitAnt —-- -'llOB. M~ltS'fl;s SiTA'i'[ONAi'RY.'ti i NoF. --— T A NS ^ iT 01, U;.i -(' — i, 1.NA.l N AT' itN E I-N.'tYi S ('.-I — l:T.. iMg.A N I ) Bi:"'TA xm n Su, C. O~ u- -- ( Io IA.,'O..... A. S,.l.. )A.Xt': ANDi No discovery made 1by the ancients gives is a higlielr idea of tie care are and scrutiny wtith wlhicIt their astrono ical observations were conducted th ant. t t ha te fthat the milinte ptlancet. Merclury, so difficult to ie seent, attd so tun-t distXingutisthblo ftiom tlhe fixed stars, was discovered in the very earliest sages of the world. Thlat the brighter plianttelts such as Vtens and Jupiter, whtos brilliancty excetds that. of any of the fixed,stars' sthould tha:ve been detected to -o wandelriltng bodies, even in the remotest antiquity, is by no ieanxs surprisirng. For in watcthingll tie stun rising and the st setting, so as to to ote in tle first instanle, the st-ar n earest to -the su, which were tlhe last to fitade away, aid in the seecondl those stars wich were the first to become visible, thte cha-1ge1 of position of tthe planets Vi 11111 anld Julpiter could not fiil to attract thle tttcttltion of t he student of the teaven but thBo planet AMrcury is so small, and so rarely visible, evein to the ]Ceenest eye thliat it Iis said oper ticus hintisclf, dulring his \ whoil liflt devoted to tthe study of tlhe heavetns, never once caughit it si of this almo;st invisible world. Ci (A ~. 46 M Rf C U R Y Mrcxry, in 1his appearance to to he naked eye, s not distinguslhable from the fixed stars. Il fis close proximity to the sun, t the fct that lie is never visible except near the horizon, o and the intense blrilliancy of his disk give to h-lim that twinkling appearance lwhich dist.inguishtes tthe fixed starts. Ntotwithlistanding all these difficulties the oldest astronomers:managed to acquire a very conplete knowledge of the principal fltts connectcd with the m]ovemt nt of this planet. By a careful and continuous exttamination it Ywas found that AtMrcury never rccmeded more than about twsenty degrees fromt the sun' center. Thre amount of recess, or eltonation as it is called, was soon discovered to be a. variable quantity), a. fact which demonstrated that in cas tthe plane t revolved in at circullar orbit, inclosing thie Stin, tihe sun could not occupy tthe ccnter of this circle. Bly watching the clongations tfom -revottlion to revolut'0ion it w as foiund thatt theyy varied from at tinnilttmum of 160 t12, to a maximum of 20' 48'. Knolwing thle ltamount of this vat.riatito, and watching car'fuily the progressive chanttge it b pcame possible to reaoh a ttolerably tacctuat e ktowlelc ofk the naturot of tile orbit detscribed by the planet in its Yrvolution around thfe san-. It was soon discovered thatit isotmo'ortiot: ofl, his o rbit M[ercury advanced with th:e st in Iris marchl among the fixed statrs, while in oti:er parits of his orbit his motion betame retrograre, and in tli change t'omn direct to retrograde, and t:he. reverse, tle planet apparenAtly ceased to mlove, anld for a short time beca-me stat ioar'y. It will he seen that all these changes are readily act-l coumnted for by supposing the planet to revolve about tlte sun it a circular orbit, the sun being eccentrically 1placed,.If we conceive two visual rays, to bie drawn tl fiom the eyo -t t th U XI b Y, oT of tie observer, and tangent to t-h orbit of Mercurty on the right 1and on the left, the planet, while tlraversing that arc of its olrit intercepted between thee points of contact and nearest to the eye, will miove d'iect; in passing throughl thle point of contact lafter diroct motion eases, it will miove, oft in the direction of the visual ray, antd hence will appear staitnar/fy for a sholrt timo. XIn the larger portion of its orbit (that rem1ote friom the eye) its motion Itnust be opposite to that of thie sun, and hcnce relro..'rade". In coming up to the second point of contact til planet will move along the vist al ray towatrd thi eye of the observerx and henco for a short time will app ear f.tationlary. To atccouti for the variation in tho elontgationt of Aercury, we tmust either suppose thte point of nearest appropach of the planet to the sun, called its perihelion, to lie iln I)totion, or e1se wet muilst suppose lthe spectator to be hilmiself moving, and thus to beiold the planet, its peri}elion ploint, and the sutI, under varying rolations to eacth other. As t oi early astrono' m(rs atssttuned tile imtmolbility of thIo oarti they expltained the variations il thr el ongations of Ai'curely by giving to its perihelion point a: mot ion ot f revolution about thi s n..It is impossible to iollow tite planlet wvith tlte )akedtt eye in its celose approatch to the soltar orb, a its itsfeeble re-. fiectet1d ight:is necessarily )ovr'powered by tile'illiattrcy of, thm su, but by close observation land by marking the positiotns of the plaitneXt at its disappearance and reatppeat - an1te tihe old asitronomers are said t. o have reached to a klnowledgte of theo ftct that thi planet orinctimes e trosse ~tte atnl's ditsk ptroaducing wvhat tt i. ealc.'t a t'ralslit of tcrct,/, itdenticalf in its phenomena i' wii t til trans'it of Venus, alretady spokenl of tin connF ct)in w ithf th. dtF, tcrtlinaltionl of the solar paratllax. In case the plane of the orbit of Mercury were exactly coincidcnt witit the }'lan't of thc sun's appltarent orbit, it is'maniest that every revolution of the ptlalneit would produce a transit. As tlthis) however, is not thle cas, and ats n.o central. transU it call occutr, xc ept when the plan-cet crosses the visual ray drmawn frort the eye of the o)bserver to the sun's center, it is maniftest that t t the platnct Mlrculry, during a central tira.nsit, tmust actuaIlly pass thronlth the edellipl fioomr one sidtl of thlis plane to tie otier. Th'iS point of ptas,:>a th0rough0 the 1plae of t he sun's a)pa rent orbit is called the -f:t/e of the planet's orbit. tlhere are, of courite, two sucht points.'Tie p.latnt passes its dtescet(ndih;n node in mlovilng froml the north to th e south sid te of the ecliltic, tand its asctzenditn nodt e on its return from t}he soutlt to the north side. ft is thflus seen t-hat in order t)o p'roduce a: transit of:Merlcu try there must b,e a conjitmnlioir of the tlat et, its lnode and the sun,'Whtenever thlis conjunctiot. is absl)olute, Mercury will pass across the sun's center.t When it is only tapproxinma te, tho planet will transit a small portion of the sun's disk, or possibly pass without contact at all. An attentive cxamination of the places of thte l'anet, bei:O:e atn aift e a t ransit, led t to a p:retty actcurai te determination of the angle under which the. p lane of the plantct's orbit.i itnclined to the plante of the eclilptic. 1This antgllt' was (q.tproi nuxi'tely determined by the ancients, while Pmodet science fixed it at tthe commencement of thie prweselnt century:it 7t".00'.10". ~..The mtotion of Mh ercurlty in its orbit is morle rapid than thatt of' any of I t ttse p i',laets thus Fr discovered, traveling, as it does, m:ore than one'hundredt t tlousa',nli -lilet an hour, .M E bt c u R t. 49 and pertorning its entire revolution about the sun in about eighty-eight of our days. In case this world hitas the same vtaricty of seasons which mnark the surlace of our own earth, tlhese will follow each other in such apid succession tha t the lontest of them will consist of only atout tthree of our weekss. It is not difficult to compute the intentsity of solar light and heat which hills upon tthe surftace of the planet Mercury, in case thtes be subjected to the a:mn mtodify.ingl influences whichl exist iupon the earth..But as we remain in ignorance of the circumstances which surroutnd this distantt planet, it is vain to spetculate uponl tlhe physical conustitution of a world 1whose close piroximit y to th e sun has thus fhr shut it out from the reaxchl of telescopic examtinlation, The distance of t te planet Mercury fromt tle sun mtay be readily detenrmined, in certain portionls of its orbit, int case we know first the earthtl' distance from thle sattnle orb, For example, conceivei a visual ray to b)e dravwnl from the e arth, tagcent to tIe orbit of AMercury (supposcd, fbo the present, to be circular); place the p)lantet at tthe point of contact, and join the center of the planet with the center of tie sunt; also join the centers of thl earth and su-t the triangle t thus fiorlred, havingt the earth, Mlercury), and the sun ats he voertic.es of its three angles is right —anglcd at Mercury, while the angile at thie ea rth is readily measured, and is nothint more, indeedt th'an the tlontgation, fior the time being, of that ilda et. I hicne, in the right angled-tritangt, we know the anlt'les'and the loti(n>,st side, extending fiomt the earth to tIh( sun,:i and by the simplest principles of trigonotla.etryw, twe l clontlptc the rematining p)rts......-.namely, thie distances of Mei'rctu'y froml the suni and fi'oml tthe earth. By this, and by other mnethods mlore accurate, it is fltundl 50 M E R I t Ntt that Mercury revolves n an orbit tarould t(he stt, and at a;it ean distance of about thirt} /.'si'x t-mi/ itons of miles. As thl entire.orbit oft thits planet li(.s witint the limits -already assigned, it follows that the planet cttn never be saen in a qua rter of thCe lhe Cavens opposito to the m un, or can ne vet IcYr he in ot.posi/io. Wen nearest to earthtb, atid onl tihe right line jo(itlinglo thl0 sn antd ctt tit, M4erurity is said to be in i"J.f.rior cotjtucttion. W ltn 1it' d istant iro>ll this place it is on the other side of the sun, with respect to the earth, and is then in its superior cotnjune — tion, Th'tl tolescotp hasX detmonstrated thatt this planet pI-asses throgh eiangles jike those presentted by thle moon. When in stuperior eontjtiietion tht planet xwill he seen nearly round, as inl tlhatt po)sition nearly the we wNoltc of't thte illu-. ininated surfitcc is turned toward itite) eye of' the oserver on the cartht. A.s the platitnt tcotlrs round to:its inftrior coijmlttiot the lighlt: gradailt y wanes' until at tinft'rior co'iMauction a iloCltdr Creiscent of great delicacy and beauty is revcaltcd to t re eye, provided tht. plfanoet tdoe-s not loso its lil tt enti. lyin t}o ttpat ssag actross t:: sm\ts dis'these phttases of Metrcu ry prove b eyond questi on( th'e tIct tlhat tlte planet does not shine by its own lig;tlt, lt tlh.t its brilliancy is deri ved 1:fon1 rellectin, thie lig lit of tlho solar orb.'th degre of precisioin reacdied in p.redictingh tho transits otf Mle:ry il(.:icitte.s, with wotndelrft l tfbtrex tho tlrogress of tmodemn astronomy. i the first predIictet tan tsit. xlitit hwats acttually tsvt osered occ urr td:n 631 ttwhe the'lintis of possible error werel fixed by th con- t.. puter at four days; anvd hetice the watch commttenced two ent:ire day8 betlbr tle predicted timte. If the transit hadt taken place iln ite night tinte, tho M EQ U I IY 51 opportunity for veriflcation would have been lost. Vtortunately this was not the case, and the toil and zeal of (assendi wore rewarded with ttie first view of Mercury projected on the solar disk ever witnes:ed by tmortal tman. Nearly two hundred years later, at the beginning of the nineteenth c-entury, the Flrenchi astronomers velntured to assert that ttheir predictions could not be in error more than Jfrty minttes. t'i:he tralnsit which occurred on the 8th.Nov., 1802, verified this assertion very nearly. By att. more careful study of the causms affecting the pl:ac of the planet tbirty -ttlhr year)s later, the discrepancy betweein computation and observation was reduced to only siateen seconds oft time, a quantity very very minute, whoen wl tea into account the variety of causes tafiecting the resoltution of the problemt. Thte ttransits of Mercury recur at certain refguari intervtals rep-eat ing themselves after at cycle of 2 y::t7 years', filing for tho present in the months of IMay antd Novetmber. IH a.ving learned the distance of Mercury fron tht earth, an.d ltaving measured the angle subtended by its diameter, we find its actual mlagnitude to be much smaller thanl that of the earth. Its diametter is but t 8,140 milte, arnd its volume is but 0.068, the earth's volume being counted as unity. In compariso8n with the vast proportions of the sun, ttis little planet sinks into tabsolute insignificance, for if the sun be divided into a. miillion equal parts MNercury would not weigh as muclt as the hattlf of one of theso pa-rts, C( JIA. 1' t I t IAII. VENU8, tf'TX SE"COND P!LANEX T IN T'Ift ORDE.fX OF Di ).i TANC/X, FROttM TtHE SUN. Ti'r 1FI Xfitt Tl>~XfI.: NyirD.t')tS:O t-ont8 o ltr iSCOv Rt., m-I[: LOOAtIOAi tS....1MO.5Nlo'} ANSr 8NVONI - STAn.- A $A'": ttlti' x Or T*I t SUv..-I};g S. P ERtOXIK A^ t, N:P, O C(O t J t. N T'i'., r A }' Ti 0', * —So -. )S t? AN I > ~ f' f.: A Jl:tA MaOifOx.~..t:: I:*'H OMM A IN PEAt' A: MOtION t OFlEt' }iASI -' —.~-TEAN, it'' N)f'i'. - - AJON — i[?.1)'.iINA?iO,f0..... It':g.Or Yrmn! } 1':.$,;; —-'- N"i. 4%At. ON Pin'I AE O}A; C. V iS0 S, —' i'o4 F IR.t:- Ik if Et' i t: or VrBK.. —.. ol??ALio or VwOt o'nm y K U wTOr'ji ti; A<'m'Teirm ni f}:lrAS}S Or V'S;.I ---- - X nSrs.:;. ELOA.ATIONS ti':[..' 3- n'NEfo SitT YN.'r 1:)DC v,; eD,...-.. ut.t.nm:'r X fli A g i,:> Vt.V - }i Aintxs X,;:n. Tll1:: planet is the second in order of distance fiom the Sun: and as it is the Inost brillifant of all the orbs, tith the exception of the sun and moon, it was undoubt~edly the first discovered of all trhe plhanets. The movemeints of the sun and moon raong the fixed stars m1ust lave claimed the attention of the observers of celestial pheinot mena in the earlist ages of the world. In ma rking the risi.jlt and seotting sun, anld in notingt, thle stars which \vcra th'e last to fiade out in the morning twilight and the first to tappear in the evenincg after the settilng of tho 8sun tfhe brilliancy of Ventus cou0ld not fitl to have attracted the attention of the very first observer of celestial phtenomena-,. A A star of nnusual brightnes twas noticed in comparative proximity to the stun in tihe early evening. Theo stuns place, with reference to this object, havitn been carefully marked, itr a few consecutive nights, it was found that the distance b4etween them was rapidly dimini:shing. It twas readily seen that this dimtinution of,'. ~3 v EI N t0 S 56 distance was due to the flct that the brigltt star was apt.Pproeaching the Smtlt for by comtparing its place am:ong titre fixed stars with what it was a tow xniglts previots, thtis star was fouid to have chang ed its position among the qgroup in whtichi it happened to )b located, ant d was cvidently advancing rapidly tow(ard the sun. W ae tare u preselted wYith the exact ithts which -must have lmalrked the diseovery of the first pm',et or nwanderjig 8str over revealed to the eye of man. WV' know not the name of tho discoverr, nor the atgo or nationt to wthich he belon-ged, but we are satisfied that the facts as above stated did undoubtedly occur; and we fid not only prolante authorls but one of the Hlebrewt prophcts rcftIrinng to this planet tmore tban two thousanrd five hundred years ~ ago..lo'.l tudent who detsie.s may easily re-dsiscovert tth planet Venus. She will be readily recognized as the lar'gest at.d brightest of all the star, atrnd will bte f:und ervcr to recedlt from te s t unl m-re than about 47t. From this distance which she reaches at her greatest clongation, the planet will be found, at first slowly, but after — ward more rapidly, to approach thoe soltar orb. She will finally be lost in the superior efftlgence of the suln; and vwhen the ounaided eye ceases to follow hetr in her approach to the s-un, telescopic power will enable the observer to continute is observaitions u ntis l fi natlly, the Bsun's direct beams, mitnglting with those of the planet, she ceases to be visible, and is now lost for a. greater or less period, tore the sun in tit gray morning twilight. She lnow recedes from her central orb, finally reaches her greatest elonglation upon thf e opposite side, stops in her career, returns tagain, anid thus oscillates backwar d anld forward, never passing certain prescribed limits, t6 v vt. u 8s. As already stated, the fact that VcnuS was at. planetnc or twandlfig star must have beco0m known amntt g the very first of sttronomicai dlicoveries; but it required, doubt-. les, a long series of observations to determine the truth that the bright st-ar whicht fo somle months bhad accomlt panied the setting 8sun, and which was at lentgth lot; in the solar bea-ms was the same object which, at a later period, becam le vsible in theo orning dawn;, havinlotg )pased by or across the solar disk. This discovery, however, is said to hat ve been made by the Egyptian priests, and was by them cottmmun icated to the:t reek astronomer, Ii'yll tha gora s, who taught this truth to his countrytmen. it is obvious, Tfrom the above facts, that the pllanet Vntus, like Mtercury, is beyond doubt a true isatellite of theo sn, even to tho minhabitants of the earth, and it is cqually lmanifiest th:at, wihatever be the true relatiotns btetweuln the carth} arnd the sun, ald whichever one of these two bodies may be at rest, one0 thling is certain, the plalnts MeTrcury and Venus ca. ot by any possibility.have the carthtt ir t}heir center of m:otion, iNo mattetr in wihatt region of the healvens the sun may be found at any season of the year, tthese two interior planets ever accolimpany him. As Vemmrs recedes to a greater distance froml tho sun than Mercury,t it follows that her orbit o f rev'olution around the sun.must be th larger of t the wo. We aro thlus etnatbled, by the simplest traiin of reason tand observattion, to fix tile following leti: r.- T'h sun is a central orb, about which revolve, in regular order, two planets, the nearest tof which is MTercury, and next to Mercury, Vtenus, with periods of revolution, readily determtined by the spectator on the earith's surfiac,. These acts arse ex - cccdinglty imtportant: as the primarty ones which lead to the discovery of the ttrue systerm of the universe. V ]! N U S. t15 VlWhen Ve us passes between the ey of the observer and the sun, site is said to be in her inferior coj)tjiutc tion; whten site is dirctly. beyond the sun, with reftretnce to tiie spectator, 8l1e is in her supferior' coijitctioil. Front her infierior to her superior cotnjunction 8se occupies a position west of the sun, rises in the early morning, bhelre the stn, and is klnownl as.Phosphorous, or lutcifter, or tihe orning star. Froltm her stuperior to her inferior conjunction sht e follows the setting sunl; sle becomles our evenintg star, untder the name of Ht.(espclus I'n examitumgnin, the phenomerna involved in the motions of V\enus, and watchting lher carefully' in er app roacI to and in. her recess froi tte sln, it iis foundt that her m ovetatts tre almos;t ientitcl with those of Mercury - —.her mlotions tfr: certain por tion of her revolution being diretl, or like those of the sunt; site th:en becomes sta.tion;t., t lte ) moves backttwatrd or retroradte among the fixed stars, becolmes stationarl)y tX-ain,, and then cormaclces. her direcct Amovement. All these fies atr readily accounted for by adnitittini t tht Ve nus xevo.lves abtout ihe sun in an orbit nearly circular, and that she is viewedt by a sopectator situattcd exterior to her orbit, an.d moving taound the san and Venus in t circle, wvhote plane mattk a snall aegle wvitth (lie plane on which the orbit of Venus lies. I f a visual rt be drawnt friom tht teye of tthe obser.ver, t. taitt t ilt or)it. of V'enus, sould the planet d hapt Jpein to fill thle point of conlt-act, site will appear to mtiove in the direction t thfis ra a-nd, ftio tr the time beitng, will h)e directly advant cin. g to: or recedintg front thet eye of tIhe ob),rver, and tlts will appear st:titlonalry. That the obsterver li isn moti.ont is manil'tbs9t:fi:rom the fact tlh:t t lie direct miovemenv t of Velnus does ncot bear tfthat relationl to the retrograde movem ent which i.s required by sucl ane 5G6 V N U I, htypotheis. Intldeed, if two visual rays were d1ra.w fromt the eye of a sta.tionary observer, tagent, to the orbit of Venus, she would appear to move fi'om one point of cowntact to the oth:er, on t tte hither siide of her olrit, with a dircect lmotion while on the filtthtr side of her orf it,: be-. tween the points of contact, her motion would appear retrongrade. These facts, however, are not presented in mxture, and would be subverted, of course, b)y supposing the s3pectator to lbe in m.otion. In case the spectator were to occupy the lie passing' frtom the sun's cent1re tlhrough Vt'enCus, and to revolve about the sunt in the same period occupied by the planet, then would tlto planet alwaiys bo scntt in intrior conjunction with the sun. As is not the. fitaet in observation, it is m:anliestt that the angular velocity of the spectator is not so great as tlhatt of thte 1)lanet Venus, as ste fially emerges from the stun's trays after heri interior conjunction, be0yond tho litne, joining the sun's center and the eye of the beholder. tere, theln, is another importanlt fiet, which muest be taklen into a:tc count whlen weo shall inquire into the true systemt of na.tture, as presented inL the organization of the planetary wvorlds. in case the eye of tho observer were located in the samei plane in which the orbit of V'enus lies, this plano, passing as it does, through the sun's centel, it is cleta thatt at every, inferior coij tunction of the p1htlet there might be seen a htr'a.sit o/ [:tt" -\\V while at every st) 1 periort cotjunction, the planet would be ouctdf'lu. or h idtden, by passing actually behind the disk of thtt stunt' It Ithappes, however, that the pane of the orbit of nVtlus does not coincide with the plane of the ecliptic, o.r eart'tt's orbit, lthee pla(ttnes are inclinted to each other, under an anglet of 83 23' 28".5, one half of tthe orbit of Venus V E N u S, 5t lying above, or north of tho eliptic, the other half lying below, or south of the ecliptic. The point in wh\ichl Venus passes fromi tte north to the south side of t'he ecliptic is called the dscrending node. She returns frtlom the south t tthe north of this plane trough thou o ascenitd" big.node, and tlhet line joining these two point, is called the lin te of Znodes The t-ransit of Venus, unfortunately foir astrononmial sctice, are of very rare occurronee, and.are sepa.lrated by intervals of time whmich are very unequal.'lT'e per'iods from transit to tranlsit are 812 05, 8, 122, &e., year a lons g paeriod falling in the monllthsf of Jutno and Deccm.ber, As already statedt no transit can occur cxcept wlhen the planet is in the act of passing herl node at her inferoior conjunction, while, at the stame tine, the earth is crossing the olinte of nodes of the )planet p-rolon;ged.,This line of nodes, thought not fixed, moveti very slowly, and at thitis timo crosses tlh etarth's orbit in tlhos re-O gions pasted over by the earth in tih months of June and Dcetmber. After a transit tthe relattive motion of Venus, the earthi and the node of the orbit of Venus, is such ah to render it certain that within eigh t years tanmli other tlrantsit will occur, aiont. It is possible thait any two, or cven all of thes. causes, may combline to produce the phenottmetna prestetecd in the movtements of Ven ust. We s8iall recur ag(ain tt t theso latters wheilc wh e come'e to consitder the grefat problem of the trtte sysitem:c of the tuniverse.'ate extreme brightness of this planet makest it at very b.eauntifitl but lifdielult object for telescop)ic o}servat:iotn. Althought spots ha ve been seen upon the surt:cee of VenM, atnd by their close examination her period ot rotation upon her axtis has tben approximately determited,.I have never been able, at any timel with the powecrful. refractor of th.e C(lincitti Observatory, to mark any welledt-efitd difltterncecs in the ill lumination of her sur. ftle. If we are to. trust to tthe observations of others tho ineualt ities whiich tidiversity the ptlanot YVnums fiar Cexcccd i:t gratndeur tlhoso fouxnd upon our carth. It is stated b)y Mr'. Schroter that, friom hi own observations8 th-e miourmttams of Vextms reach an altitude five or six. times greater than the loftiest mountains of our own: globe. llt Lham been allnrmced b)y several distinguished astronomers that this planet is accotmpanied by a iainuto satellite, but by theo app}ication of tlhe mtost powerful telescopes, duringt tto present century, a:n after tho most rigid examinilatjion, thliB statelment lht not 0been eomfirmled. It wast supposed that during the transit whicth octcu tred in ILt69 the disputed qu1estionl as to the existence of a mloono of Venus would be positively settled. W\\ile th:e planet was distincltly seen as a tdark spot upon the surfie of the sun8 no telescopic power could detect any dark object which mtight be a satellite. Although woe cannot absolutely afflirm that Venu c s bas no.satellite, we lt' ma fly say, that if thero be one it yet remains t o be discovered.'.The atlmount of light and heat which the eartht would rcceive from the sun, if revolving in the orbit of Venus, would bne netarly twice a"s grea that ttow yre civecd; but this does not justify us in concluding thlat the planet Venus ht s tasa mean t emperature nearly double that of tho earth.'We know that a. powerful influence is exerted by the earth's atmosplere to modify the solar hieat. Th:ero may exist an atmosphere surrounding.( Verus such that the temperaturo at her surftcoe may be no g*reater tlhan our own. it is useless, however, as we hatve already ret.marked, for us to speculatet about matters concerninge which w e positive ly know noth}ing. Thero are some n s it-n dication.s in the telescopic appearance of Venus thalt a31 VE NIsI 61 is Sturroltfundle by a.. n oxtte.nded atmosphere. Wh'en pr.e - senting th e tfrmn of a crescent of light, the slender horns are found sometlimes to extendt beyonld thie limits of a scini.circumxfterlnce...a tet only to be accounted for, so far as we know bay admitting attnospherie refraction. C ii A. P T 1' It I V. TIIE I TX\ARTI( A. N I)?ItS SATI&ILLITt: PT1 P THIt RI) P iANEt IN TtJI[- ORDER 01t O IJXSTANCf FRbROM THIEi SUN.:t Iy i ixjTHi }T1-I AP O I' Ai NT C(N.'; t" 0' Mo l itN. — -4T AL. it f 8 t:- I: tS AT O'flt Ac('t t,::: (i'.: t1 O:!Ixi,'Moit ON ( 1 OTi SUN AD iMOON-...... I.'I/)OLIk;M ~ N.]:,'IiLE I..~ ---- ]4.'. ]XLANATtOr OF CO:'t': riNiS, — -'t.H'.. N i'iT, O iEi'tONiS 1 O'.hS1 si) >''t1.}ii.!t,"'I-W. A S It.t'g 1 tSv t 1';'"n}: j.ItI ": S'VMi*o1n4O. —.-rA' toi-'ON A*Ni; /KYOLv'O-~':-.A U't. - O d'..iN 0,If:rEli;asI;ot iN' ii'.A'I.; lO Ol l:IATIO,-.~-A:10'0 1BIinAL k AOl' AtO. —-VI it-ENA, t'ti. soN., —-- iAt I *ox tI t ts f IO Ot:' L i io i.......I' I} O 0 F I;VO LUtON..~ (I'XI~th (NOlr N~i~~l,:)1 I) Ii'ft!or 11 Oon..MO..... M:p T.A,*sl}X- -; i T. AS.'I'-!A nx -.-. —'Eg(}:?Rr'i"CIi.[t'Y 0~ lt:( Of;T.t.....'g-C IYIT.IO) (iF 0 tlg.>'tOfk.-'"'.'][<'NL?,N A'ifO(N VO~ U.t..'I'3t"'li" ~ At[ NtS IA"kALL,'AX ANO |)ts' K r F}T. —- A Pn)8ts'f, ^ t. Co i iA.x.i'A:r' itON,- KN t'x ( G iOAV' t ANV ) CtS N n}: 01 FIt}Lo UE. 1t: I t ancients did not reckon til earth as on of t (he planetary orbs. Thlere sfeemed to be no tanalogy between thle world which w e inhliabit, with its dark, opaque, and diver sihfed sturtace, and thIose brlliti lanlt planets twhlict pur1ied their m1iysterliouts journ't'Cy tal longl the starsi. Bullk as they werc, so deep in spt ac, it wt as very difficult to treah any correct bkno wlo edge of tleir absoluto tmaqnitude, The l, xtthl seemed, to tlo t seses of manl, vastly la-rgfer thtan tany or all of tltese revolving worlds. lAbout tio ealrth at a ixed center, thie vilole colatic re tile theaveni, witlh a ttrll its starry constellations, app6cred to revolve, producing thie alt0ernations of day tand night. Itt wa s not tnnatitural, tllerefore, kntowilag the euntraIl position of the THE EARTH. 63 earth with reference to the fixed stars, to assume its central position with reference to the sun, and moon, and planetary worlds. There is no problem perhaps so difficult as that presented in the attempt to discriminate between real and apparent motion. To all the senses the earth appeared to be absolutely at rest. It could not be affirmed that any one had ever seen it move, or felt it move, or heard it move, while the sense of sight bore the most positive testimony to the motion of the surrounding orbs. It must be remembered that, in the primitive ages, the great objects of observation and study were the sun and moon. Five planets were indeed discovered, at a period so remote that no historic record of the facts of their discovery now exists. They seem to have been known to all the nations of antiquity, and a knowledge of their existence appears to have been derived from a common origin, as we shall have occasion to notice more particularly hereafter. A few of the more obvious phenomena presented in the planetary movements were known and studied by the old astronomers, but when these motions became to them inexplicable, they frankly confessed that these matters must be left for the study and development of posterity. If, then, we confine our attention principally to an examination of the solar and lunar motions, and to the general revolution of the sphere of the fixed stars, in our efforts to determine the true position and condition of the earth, we shall find ourselves compelled, as were the celebrated Greek astronomers, Hlipparchus and Ptolemy, to admit not only the earth's central position, but also its absolute immobility. It is, undoubtedly, central to the moon's motions, and it is equally central to the sun's 6 T 1[ 1; E A It T i[. movemcent; tlht is to say, all the lphtnomn)att of tho solar miotions are as well accounted for by supposing thte catttl to he the center about which the sun revolves, a by sup. posint thle convlrst hypothcsis, that the sun is the ce atcr about i whichl the earth revolves. o8 ftr, then, as theso two great lum-inaeri are concerned, the hypothesis of the eartt's central positiont is well sustaintd, and almost indisputablo. I is only when we extend our investigations to the inferior and superior planetsa, anltd g.athcr together a mul thitude of faitas atd phtenot enat demanding explanation, that we find ourselves nece>ssarily driven into so great coimltlcxity by retainilig the central position of the artll, that at last we begin to doubt. We httavc already noticed tht rtemart ble move. -ments of t-h two planets V'0-nus anvd Merluryl. We s hall find hereafter that phenomena of at like chamracter were presented in the mIovemenlts of Marhs, Jupiter, and:i S.t. turn, acat-t of Ywhich planet wts wadistinguished by its sIa/ions, retr'oyradations, and advances amoln the fixed stars.'the ancients not only adopted tt h hypothesis of tho earths contral.position and immobility, but, for evident reasons, likewise adopted the hypothesis thatt all me.otion \was performed in circulir orbits, tand with utniforra velocity. \We h}ave already se'en, in our examinattion of the solar imotions, that this orb did not move to the eye with unitlorm velocity, but thtis apparent t deviation fr'om. uniformitiy was readily accounted fo r by supposing ttho earth to be placed a little eccentric with reference to tto 8sunts circular orbit t..he same thcts becomingf ktnownn w1itth relrenco to the moon0's m-otion, a. like hypothesis was adopted, and t he arth was iplaced eccentrically wtithin tle lutnar orbit. In mar11kintt the planetary movtemnt.s, they were found, 0however, to dill'cr radically in some THE EARTH. 65 particulars from the movements of the sun and moon. While these great luminaries always advanced in their revolution among the fixed stars, the planets were found, in making their revolution, not only to stop, but for a time actually to turn back, then stop again, and finally to resume their onward movement. No eccentric position of the earth could account for these stations and retrogradations; but a very simple expedient was devised, which rendered a satisfactory account, in the primitive astronomical ages, of these curious phenomena. Retaining the central position of the earth and the circular figure of the planetary orbits, each planet was supposed to revolve on the circumference of a small circle, whose center was carried uniformly around on the circumference of the great circle constituting the orbit of the planet. By such machinery it will be seen that it became possible to render a satisfactory account of the stations and retrogradations of the planets, for while the planet was describing that portion of the small circle in which it revolved, nearest to the eye of the spectator, it would seem to move backward in the order of the fixed stars. Again, in coming directly toward the eye of the spectator, or in moving in the opposite direction along two visual rays, drawn tangent to its small circle, the planet would appear stationary. Such was the general exposition of the Greek astronomer Hipparchus, whose theory was enlarged and extended by his successor Ptolemy, whose theory of astronomy, based upon the central position of the earth, known as the Ptolemaic System, endured for more than fifteen hundred years. It was only after a long lapse of time, and by the discovery of a large number of irregularities in the solar, lunar, and planetary motions, making it necessary (to 006 T IE E:i A It T I. 0rnder at justl account of them) to incroteaset tle numt)er of these smiall circles, wthilt wtere called p.ji../ic/lcXs, tlhat the -twhole sclthme finally beca:e so tcumbrousllt and comnplicatcd thttt, after long and laborious study, extending tltroulgh moreu tlhan thlirty years of diligent obser'vation, t.tch "great.Polish astrolnomer, Coopernicus, foltd himself compelled to abatndon the old hypothesis of the central. Xposition of the earth}t and to attempt at new solutio.n of the greaIt problem of the universe..tn giving uIp the cearth as the centre about which the worlds were revolving, there was little difficulty il selecting the objcet whichl, in greatest probability, occupied the true center. A. ll the mov\ements of the sunl could, without the sligtcst dificultty be transfe;rred to the earth, andt tiut the stun could becolme ccletral to telt ierth, revolving a:ts one amltong tf}e plarnets..!this hvypothesis did not require any change whatever int the computation of those tables which gave from dfay to day the SultitS apparent place lamong thte fixcd stars. Atgint, ai we hailve already seen, the platnets Mercurtty anld Venus were undoubtedly satellites of the sun, whether the sun be at rest or in motiont; and with these sul.gestions, the vigorous mind of Copernicus, transftserring hiiuselT il ihntagination, to the s8m, a.nd thence loolkig out upon the planetary revolutions, ilund tthalt a large numbIer of those complexitiecs and irregularities whicth had so conftun.) ded hit when viewed( firom the elar't's sur8ace wero swept awaytt fr1 ever. When seen ifrom tthe su, as te cenlter of motiton, all the stationtroioss ad it0nf:tio in the planetary revolutions disappeared. The complications in the mlovcmeltts of Melrcury atndl Venus were reducted to perf't:et ordetr and simplicity whenl seen fri'om the sun. Thoe tearth itself assumlled its propter ran among tho TI X E: i tA.t't *. 67 planetalry worlds, dilgnitied by the attendance of its satellite the moon,:and beyond tli earth, the planets Mani.8: Jupiter, and Saturn, perfotrmcd theilr orderly revolution in orbits nearlty circular. Such is the true scheme of nature in its grand outtlincs, as given to the world by Copernicus. It will be seen thatt one of thie rem:arkable features of the old systeml. namely, the luniform cir.cularl movemcnlnt of the planets, wa:ls retained by tlhe Polish as — tronolmer. 1By the luse of eccentrics and epicycics, Copernticus ftound it possible to render a: satisfitctory taccotunt of all t.he phenol.me'na. of t}he solar systeCn known duriln his age. W e can readily comtprehend that a system involving the startling doctrine of the swift rotation of the earth upon its axis, and the rapid flight; of its entire mass, with all its continents, and oceans, and nmountains, lthrogh space, mutst halve been received -by the hum:an mmid with the greatest distrust. tIdeed, there seemed to be to thl eye positive proof thait this bold theory was absolutely faise. i t was urged by lthe a nti-Copernicans, that in case the earth did revolve about the sun in ant orbit of nearly two hundred millions of miles in dilamelter, that t}e point where the axis of rotation, prolongced to the sphere of the fixed stars, pierced the heavent must by necessity t.ravel arounl and describe a curve almong the stars identical with that described by the earth in revolving about the sun. Now, as no such mlotion of tho n)orth polar point was visible to the eye, but ats the axis of the bheavyens remtained for ever fixed among the stars, it proved ibeyond dispute the absolute imilpossihbitlitty of the earth's revolution about the sun. This train of reason.ing was undeniably ttrue, anld the only response whic the Cope.rticans could tmake was tthis: " The earth( does revolve about the' sun; the carth's axis p0rolonged docs 68 T t i i A iT. t. pierce the colestial conceave in successive pointds, describing a (curve precisely like the eartt'ls orbit, and wltho d im-,.I It.r is indeed nearly 200,000,000 of miles; bttt that tite dista etl of the fixed stars is so g1reat, that an o.j^ct lia(t in: this immelnse di.ameter actually slnAinls into an invisible point, on accounlt of the altost inlfiite distanee to whlichl it is removed from tih e y of the beholder;" and witlt this answer the world wal s comipelled to rest satiliced for more thanrt two hundred ycars. T.he doctritne of Copernicus ga.ined a great accession of strength by the invention of the telescole. Xly the use of th:is extraordinary instrumen[t not only were tho ph)ls8c.s of.tMercury and Venus detected, but also tho greater discovery of the satellites of Jupiter, presenting, in this central orb, w'itdh his bour revolving moons,; sort of m1iniature likeness of the grander systemi, having the rutt for its center. The simplicity of the hypothlis presented{ in the Copernican system, thoe nuttmerotus cot.mphieations which it removed fromt the heavtens, and the satisfictory account which it yielded of the discoveries made by the telescope, caused it to be adopted and defended by some of the best mindlls of the age iltmmediately following thatt of Copernicus, among whom none is mlore distinguished than the great IFlorentino astronomer and piloophe ailoso (Galillci, It is hardly necessary to Imelnttiont the htistorical ftact, that tlh old syst}em of atstron(omy, whiIch hatd held its sway over the human m)ind ior more thant 2,000 years, did not fiall without a severe struggle. Thet astronot myi of Ptolemy, and the philosopthy of A.istotle, had take:n so deep a hold of mlankind, tanr were so firilly interwoven with a"ll the systtems of cducation and of science, that we must behold witl astonishmeint the downfall of syst-ems venerable fromt their anll T'n]:tl E A RT:. 6 9 tiquity, and whtose ruin could only be accomrplisied by the desertion of their adherents. T1,.1e FIGURE AND MAGNXTUDE OF THE ARtlA knowledge of thle globular figure of thte earth seemns to have been reached at an early period in the history of astr >onomy. indeed, the concave htavcni, presenting to thle eye a hemisphre above th te horizon, and, undoubtedly extending beneath} the earth, so as to complete the grand hollow sphere, suggested at once that the inclos;ed earth, mTinute in its dimensions when compared with the celces tial globe by whichl it was encompassed, migiht also have the globulavr form. The eurvature of the earth's suriace becomes at once visible to the eye in marking the gradual approach of a ship at sea, At first only the top of the mast can be discovered, even with a glass, all the rmaining parts of the vessel being hidden by the outline of the t.he interposed water. AsB the distance diminish:les morto and more of the ship lifts itself above the horizon, luntili finally, the water-line comes into sight. Th sae mie v.idtence of the rotundity of the earth is fiurlnished by the circular fijrm of the horizon which always sweeps roundl a beholder who ascends to the sulmmit of a loft;y rmounltain, Thus, ware te disposed to adopt the spherica1l fbrm of tho ea.rth in colnseqten1ce of its simplicity, even before we lhave any conclusive demronstration as to its real form. The re ek astronomers comprelt) ndedt the simple I)ro. cerss whereby not only tih ttrute figur e of tlte arth might be obtained, but in caise it were spherical, whereby its real diameter an.d absolute magntitude milght i.be deterimined. This process is remarkably simple. Suppose an tobserver, provided with the means of directing a telescope precisely to the zenith of any given station. and in the '0 T II B BT A R T ii, ze-niith point ite mattrks a star, which fr'om i ts magnittude and positiot li can lt readily find again. Now, leaving this first f st tr.in, td mlovnJ:l dutte Iorth, mtasurit'ng) tie tdistance over vwhich hle passes, he will find that, as he progresses to t towar e ttnortt, the star under examlinaition will leave the t zenith anl: d slowly decline toward the south.;tSuppose the observer to halt, set up his instrument, and find that }is star lhas declined one degree fvomt the zenith toward the- south.,.Thlis demonstrates that he has traveled fromr the first station to the second, over one degree of a great circle of the carthlt, or onte partit in 360 of the entire circumferelnco of the earth..t ffollows that, in case the earth is ceally glotttla r in itfrm i the distance betwevn the stations, multi-. plietd Iy'tO6 v, will give the lngtht of the ecntire circumrncc, aid this ui tntitty, divided by 8. 14 59 (the rastio etttweentt the circuml ference of a circle anl d its diameter), will:ive the value of the eartit's ditameter. It iis by mtetho}ds altllogous to tabove that thte tr.ue figure and actl mgnit ud tof the eartht tlhav been dcettermied. \lltry umttlrous and delicateo. eastures, per. fiormcd in tmanltty paits of the earth's sur.lco, have revealed thle surplrisillg ftact th.at the ttrue figure of the earth is not thlat of a: sphere, but of at: s )pheroidt being: ore tlattened at the poles antd more prottubct rant at ttthe equa-. totr ti}an a true sphlter. We slh ll hereal'fter exhibit tho cause of this relimarkablle let, antd present t some very eurious (aild surprisintcg results and phenomena whicht flow flro1n it. BIly thie tmlost reliable measurle twe find tlhe polar diameter of the earth to be'89:8 I iles. while tho diameter of tlle etuator reaches to 7,9'24, being an t xcess of no less thant twenty-six mtiles, wticht excess would thav to bhe trimmtled off to reduc the t earth to a globular form. T it I I A It T HI. tl tltoE En AwrTS OtIAri o N,-~..- -Weo t have alt ready noticed tho fact that tih Su, als welll as the plnllets thu-s'it desicr ibed, thave ta mliotiont of rotatio: n atbout t a fixed axis, while thle pheltits have also a t motionl of revolutito in their orbits. Since we are compelledt to rcogtizet tho earth as one of the planets, we naturally conclude that it will be di-. tinguished by the samne m:otions which mark tie ongoings of the other planets. We shall it fintd, tindeed, hat thee eartht htts tftree rmotions: a motion of rotation aboult tan a41xis, acomplished iln a period of twenty" ytfbur hours, and producini tit napparent revolution of the sptlhre of tie fixed st aris in the same period. A. mlotion of' ret.o/twtioft. in ian olrbit Awhereby the earth is carried entirely aroutnd the sun, eftfetitn all. those change.s wlhich mlark fupolt tthe e arti. i's sur:ltcce the seasons of the year, andt prouerirtvtgr lait} th t-{ alre {]}Xtt -tl1 ta]}}):11'Cllt (I C.lttt~f}}fl. Of' tt10 ducing at tli same tim e an app. rent revolution of tho stl in a t Ciltl orbiit tllotmo tlhe fixed stars.'The earth htas tha lird l(motion (xlhich we will oxam1ine mt1ore filly herleaft1ter) o neadsioted by tlhe fiact that its axis of rotation does not remtain l onfst:antly pa.trallel to itself.'t.11:A. lf x'.:X TAjIOi...t Let us return to the con.sideration of tl diu tr...! rt'.ollh//ion to lth ilait;antts of the earth, as well'is toi th e student. of asttronoitny, by fit, the lmos t ilporta'l)tnt. motion which} ha.s tbeen re.. vcaltd by tthu:anlt invtigation.tl1 t is, perhaps, impos-.. sible for tihe mind of tmant to form an ly just notion of whatt we call time, except. as its flow is mtea:srted l)y so.me attsoltutelly unifi)rmt sucession of (events. is perfe'tct nitasure of timen1 is:l;:und in the u t ifbrin rotlat-:io:n of the exrm rotaIltion of tho eaarth on its axis aeo obtain, al already statedl, our ultit of time. But ti s rotation is not sensible to lman except by its eftlet on the position o ojects external to the eart h; and hetnce we deterlxinel tle t absoluto p-ereiod of rotation froml ma.rkl.iing, the moml'entl whe\ n a lixed oljcct, such a at sttar passes the meridian of any given place. T"Ihe time elaptsing fiomt this moment up to theo next passage of the sam:t object across the mecridian, suppos'ing the carth to )be immtovable as to its ccent.ral point, would bo the exact mtteasurte Cof the l eriodl of rotattion of the eartht ont its axis. Now, tho cart. Is ct(tote, tin the space of one day ard niglh, or d uritng one rotationt acttual asss over arly 2,r 000:.000) of miles- an(d it would steem ast though totis change of:' poo ition would sensibly aftbetI the return of our star to th}l meridian, but sttur is tht vast distance of tle fixed stars 78 T Ht E A l A t'' T, that vistual rays sent to tlho anme star, fromr theo extremn i ties of at ibase line of 2,000,000 miles in lengtt, are ab.soluteely parallel under the m1ost seareliing inst:rumin tta scrutiny tlhat man hias been able tto make. A,.sidereal lday ~-tthe th ime, whicth elapes bo.twceln th ee onsecutiv re - turns of the same fixed star to anly igiven me11rdian l. is an invariable unit of timea, anl, as such, is extensively used in pr(actical astron.o)my; but in civil lifc, ina.smauclh as all the duties of life are rtgulated by the return of tho sun to the meridian, solar, and not sitdercal time, hla become the great standard in ttio record of alll historic and chronologic events.' nl case the earth did not re-l volve utpon its axis, and had no motion except that of revolution in its orbit around the sun, itl is manit'fstt that in the course of one revolution the carth's ax1is, rema1iningt paratlel to itself; the circle dividingl the illuminated from1 the dark hemisphere of carth wiould take up successively every possible position consistent with its always remnailnin:fg po)rpetdicular t to th line, joining tihe centers of t-ho earth and sun. It is manifest, therefore, that by this revolution around the sut this luminary would )bo caused, to rise tab.ov te tt horizon of any and every place upon tho earth's siurface successively, slowly to sweep across tho leavens, ald at thte end of six 0months again to sinkl: be - neath tlh horizon. If, thet we defitne a solar dayt to be the timeo which celapses from the passate of the sutlt center across any given meridian until it returns to thoe s;ame meidian al ain, one s:uch it da would evidently l)o prloduce d by thle revolution of the eartt in its orbit; hence wte lind a solar day to beo longer than a. sidereal day, because ot' thie fict thaft thle tsun't center is brouglht to the merridian later, in consCequenco of its own\t apparenit motion:. Indeed, wh.ten we como to aexamine care-c THE EARTH. 79 fully the length of the solar day, we find it to be in a state of comparatively rapid change; a fact which we could readily have anticipated, as we know the apparent movement of the sun in its orbit, or rather the real motion of the earth, is changing from day to day. When the earth is in perihelion, or nearest the sun, it then travels with its greatest velocity, and passes over an arc of 1~ 01' 9".9, in a mean solar day, whereas, when the earth is in aphelion, or furthest from the sun, it sweeps over an arc, in the same time, of only 57' 11".5. We thus perceive that the length of a true solar day must vary throughout the year, and for the purpose of obtaining a standard of time the world has adopted what is called a mean solar day, or a day having the average length of all the true solar days in the year. All the time-keepers employed in civil life, such as clocks and chronometers, are regulated to keep mean solar time, while, for the purposes of an observatory, sidereal time is in general use. This, however, is slightly different from the sidereal time already defined. The sidereal clock of the observatory, if perfectly true, would mark Oh. 00m. 00s. at the moment the vernal equinox is on the meridian of the observatory. It would mark the same at the next return, and hence this sidereal day is really a vernal equinox day. Now, as the sun's center appears to sweep round the whole heavens in the space of one year, and by virtue of this motion passes across the meridian of any place and returns to the same again, so, as we have seen, the vernal equinox sweeps around the heavens in a period of 25,868 years, and thus passes from one meridian to the same by virtue of this motion. Thus, a vernal equinox day is shorter than a sidereal day by an amount equal to one day in 25,868 years, a 80 Tfl f B 0 0 N. quantity vry v minutoe intdced, but still insisted ipon, a wc desiro to imtpresl'. upon the nlind of tl:o readert thl dti: ftcrtcn.e bet.weeto those vlarious ilctasutl of tilio. TlH.l-;MOON A SATCllJITH, t 0 m t! tiAR T' -IIn prt. OS tcuti.ng our plalt of investigation weo ust now give saomne account of the moot, as he1 forms, astronomicallt y spe:ak.-. int, at part of tthe planel weltch we call the eartht and w shaltl findl hereafter that \whetn we speak of the oorbit, in which the earth revolves about the sun, tlht real poi.nt tracing that orbit is not the center of the eartth, but t point detertminted by taking into consideration theli fct that the earth anid i.'-ooit murst ble comtbinied, as form ingt a sort of cotmpound planctt, rt volving about tho sut, Of all tho celestial orbs fitlishing objects ftr the 1 ivstig: ttion to man no one of thet canl r1iva l thie moto in the anttiquity of its researches or in the importance and con:plexity of its revolutions. If it,were possible to trace tio histAory of astronomical discovttery it would bo found, beyotnd a doubtl, that tlh irsXt positive alct everr revealed to the sttdcnt of tlhe skies was Ih molltoioi' of t tlhe raCoi tlaaon tSe tfixd stars.'his fact is so obvious th'at any oto who chooser cs to markltc tihe titoo's place by the stars which;s urround her to-nigh t, andw l coinmpare it with her place on to1- torrow nig'ht, will make for himself the great discovery that thli moon is sweepin aroltnd the heavens iln a direction contrary to that t of tho diurnal revolution of the celestial splt re. TIhus, if we mark the place of theo new noon, in the evenin, twilight, whenll she appl'ars as a silver cr1scc:t, eimictrginig fitom the sun's Ibeams, and just; visihble above thto western horizon, we shall find that on the.next evenig, at the same hour, her distance from the horizon will liavo been greatly increased, ant thiis increase of distance pro. T 1g o O N. 831 gressers firom nig.ht to night., until wlye find tihl moon actu-. ally rising in the etast t the te ime tlhe sun is scttintt ilt the west On tleo fbllotwing night, at surctt, the moon will nlot have ris. ls but we will be cm.tl:eplled to wNait tnearly an hour after sunset efotore she becolmes visible above the east.er horizon, and tthus shte advances in her orderly marchl amongt thoe fixed stars, uttil slho circlesc tentir'ely around tthe heavct-ens, passesI- througlht thl solar bettams, and reappears in the west above the sttu, as alt slentlder creselnt. T. I tOO ()N )S ia'VOLs:tON N IN R-i OIR.t.IT,-W..'C ha. ltV alreadty statedl that, int case it a wor possible for the tun'l center to t.%race out in its revolutiton amongt th fixed stars at litne of golden light, visible to tfe eye of tan, this linto woutld be a, regular circle, perlected at / tho close. of ott irevolutiontt atnt evetr atifter repeatedt along1 the sa me identictal ttrak, Suctl however, is not, the crase with our satellite. Ctould the tlmoon's course bo traced t by leavingt berhintd her among the stars a silver thre'ad of lighlt. at thte completionl tf one revolution, t}lis tflhread would tot join oil the ptoint of beginni.ng but t wtould ho more or less reniote, and the t rack de'tscribed in t}he secornd and successive re volutions would Iot coincide witht thatt first described; and thuis we should find a.L mutltiplicity of silver lines sweMeping 1round the circuit of thet heavens, crossilngl each. other, antd interlatci.t. in the most comlnplitc.ed itta;nnertl t tndtus l.mt kint. a t.irdtle, or zone, of' dltfiliito width, beyond whose lilits tihe moonl could inever Upass. The time occupied itn colnplcting oo1 of these revolutions firomn a. given star, until it r.turnts to th tie "reat:ircle of' the heavenli pass'tint thlrouit h the axis tand i thlis star gain, i soon found to be vari ablet, l vitlih certain t na rrow limits. This is called a: side;rf'al revolu-'X' 82' T i.H M.t 0 0 N t tion, and its metan valueI, at telt beginnintg of tthe prosent century, is fixed at 27d, I7h 43m., 1.5 T'e!o most obvioutt s lunar period, howtevr, and that doubItless first discovered, is tlhat ctalled a sy/odical revolutionl, aind is the period clap: g i'o tihe occTurrenc of c flull moon to full J(moon agtain oxr f01oni o1w Nty itot to Inetw mtKIoont a;i:ailn. J.The a.veratge lenogth of tlhis period, wlich is also ctalled a tefan ti ltt iont.i t amtounted, at ti } epochl above mentiot ed, to 2i9d. Il4)h. 441n. 2s. 87. It is within the limits of tfii. po.eriod tlit. tth lo1001 passes through 111e th tose atppoa rances which weN c ll. I'it l0: mo BtN's Pts+:... Il S..-'les... extraordinary changes in tlhe physical aspect of the mooin musltt have petrplexed tho ea rly ast rononlC rs. \'Wile thte stnever remamineit d round and fdll.orhed in all his positions,t mongt tthe fixed stari, tand while all the planets ant d bright stars shotte whith a nearly invariatblhe light, the rtoon passed fiont a state of acttual invtisibility to at condition in wtich her disk was as round as that t of the sun, andt thelnc gttradually losing iher light, finally fiadted fromr the eye si s'ie approached the solar orb. it was soon discovered that these cihanges were in some wtay (dep.tdent strictly tupfon the siun, and not upon th l e too';s pltaeo aong} t}ie fixed stars. A. ny one whto chooses may verify this discovery,: 1:r by locatving the toon'ts place amt ong tht e fixed stars at the ftull, and xaitin t her r1etarn{ to the same place,aga'tin, it will be fi nd tthat slte htas not yct reachfed her figure bf at complete (irctle.,.lndcedt, Ior than two:days'lar re..tqutired, aftr ptassingm the position occupied wthen last ifull, betore she gains the point that shall presenlt -s with ta comtplettly illttumitnedt disk. Tie discovery -of titis truth:t:'tf. i (.'. t t8 J-l.yg. ) t s 4. >t.:r y t i tof' A t l y t y t Ile r loon (9 s a ided undoubtedl y in solving the mtystery of thle moon' phases. It was clearly mnanilest that the moon was re-. Tr I:: M o o N. 83 volving about the earth in an orbit nearly circular.'ilhis wasn evidentt iTom the fot that tlhe moot's appartnt diam iet did not chantge, y 1) y tsy nsible aLiounttt, d(ur ing atn entire revolution, which would have lbeen nipossible ii cease her approach to, or recess'from the earttlI, had been ver ey at i n prt of her orbit. A.nother phen.omenone of startling interest aided greatly in reachting a tre.ru solution of the clhangs of the mlloo)tn. I reelr, of counse, to so r a(nd lunt etlipses. Wo, 1: voe,alr eady refe rred to solar celipses, as being undoubtedly produced by the interposition of the darlk bodty of tlhe',mot0o bet wetten the eye of the spectator and the sun's ditsk..Tiis em.onstrated the Iact that the mtoon in her revoltttion ronlltld the eatrth did sometimes cross the line joiningtm tie elarth'ts centre with tie sun, thlts'produtcing at central sola.r eclipse. It was tlhs manaifestly possible ftbLr the mootn' center t o-cross tih same line at a int lying be'- yolnd tih earth, with reference to the sun. Wt l.hen in thls position, at straight t line drawn through the center of the 8attu, anft throughl the center of the earth, tand p)roduced onwatlrd would pass through the moon's center, and to a perfson there situated, and looking at the sunt, ho{ would find thie solat r sfat e covered by the round dis k of the etirth, thius producint g to tihe lunarita at solar ectlipse.'When thle tmoon was thus situated, it was flund to he shornt of;it very larget.t proptortion of its ligtt, not entitrely f'tdiitg fon the, eye, a's did thlie sulln wheu in total cclipse, but rte'mainint g ixnditin ctily visible, with a dull rddisht color. Now, s tcoulnon observation teachets tu that (evcry op:)aue obp et casts a shadow in a direction oppo-. site to the sourcte of liht, it fo:low Xs thatt te ea rth must cast a shadow in a:\ directiont opposite to tile sniI; anld in caseo this shadowr reaited as s far asthe tmoon's orbit, tih 84' it l M 0 0 oN tooI, in tfaking uip her successivo pos3.itions, would somet tilmes pass into the etarth's shadow. If self:i'-lltmi ous, t h pistatge actross thle earths shadow would occtasion but a triflln. c;lthge in her appcaranco. )t e, howevor, ier light was either wholly or in greater ptart derived frolim tho suntl then i piassing into the earth's shadow, th stretam of lightt from the sun bei1ng intercepted by the carth, the moon0- would lose her brilliatnty, and coutl t only be visible with an obscured lustre. All the iphenotmena presented in at solar as well as a lunar ecelipso combine to demo.nstrate tlhat the light of tlt moont is not inherent or fthat thlis orbA is not a seltf-luinous body;l and all tlhese 1phel:nomena were perftectly accounted for by.admtittiln tite h-ypotl;esis that th:} moon s/hiics.b rf/'ct..'ing t/he ig'ilt if the sunz.'.lhus, during a:t tottd solar eclipse, wheln the:,t ill-uminated hc.mistphcrett of the tmn wtas turned fromnt- the earth, her hither side a ppe8ared a)' olutely hbact', while no lunar eclipse ever occuriedd excve pt at time whiden the moon'slt illutmitnated ihet n iscpt ere w wt holly visible, or at the fullt moon. In passing frot new moonlt to full, it is evident, friom t1he sligh}Ytest reflection, thatt as the moont slowly recetdes fionl'. tlte sunl, in her mtovement rountd the earth, she will turn more and more of' her illuminated hemispvher towards the earth, the whole of which will becotme visible whten- she is precisly opp(osito the t suntt ite t ligt the t dmust tccrease in a reverso ordei in passing from the full moon0 to ttle ntw Thuis, all thie It ts i(and p1 heltoniIat: of tancient as weYll as otf miloder.n disto\very comtbitneto to denl:ostrate thi truth that tine eartlhs satellitte like the p'lanets.t atltready t1reatedt of; is only visible by r flecting th t he liglt ol' the sunt. We te re rady by attnalogy to extend tlti.s reasolning to embrace the earth, and tto believe that our owtn ea rth T U MOOA N. 85 sh};ines to the inhlablitants of other planett (if such there b), by re lect ing t ht ligt of the sun W arec not.eft, htowever to ioere anltlo:gy to demonstrate this truth, as we ihav the mloest positive evidCenco in the pthases of the 1i0noon that the et arth doe's.reflect the solar litght. INo one can httavet tiled to notice th te ct that when tih moonl aptipears as a slender crescentI, her en/tire disk: nmay lb traced, Ihintly visible even to tte naketd oye; but whlen the telescope is applied, we readily distinguishl in lthii darkened ti art all the outlines and pr omitcitent f0atitres whicih becomo visible to the unaided cye whiten tho tnmon is entirely full. Phlis fiint Itninosity is beyond all doubt occasioned by the reflection back again t to to earth of tlhatt light which the earth rellects upon the moont; for ift we consilder. the relative positiolns of the sunt, t)moon, and ea rth, we shall see that tt the t t now mltoon the \whol illtiuinated hemtisphlore of the earth is turned fill:upon her satellite, and at that tirme tthe largest amount of light firom the earth falls upon the sBurace of the m1oon. ttho relative positions of the bodies now slowly change, and as thi moon incteases in light by like degrecs,t thtl earthl loses in light:; and whten thte moolt boimes entirely full, the earth will be to the lunariat n tentirely dark, as her tlon.l:.iuminous hemispltere is thent turned directly to the We ia vo ailready s tated that, during a lunar celipse, the m)-oon remanits dimly visible, T.lins is not due to the.1rc.ictcd lig tt of th. o sent thrown upotl t he moon b)y ithe art t-, hbut aristes t f io tea tt thtt the solar rayts ar so mu tlt bent out of thir cl tli 1r1 cours in pas tsi n i ugh tho eartht's atmosplhere, that ttmanty of them are st ill able to reaclt the mtooI's surtace, andl thus in sonme tdegree to lightl up her disk, oven duritng a central cflipse. 86 TWH IE 0 0 ON. A mid all the variations land etmngel s whlich it -ark the htlnilnsit;y of the moon one tiling reaiXn s altost afbsoL. Iutelty ittvatriable. [No eye ol earth hlts yet seen miore tlita one lhalf of the lunar sphl-:ere.'hle helmtisphre now visible to matn, has (so f1r as we know,)) ever been visil)le, and, except by the intrusion of solme foreign odty, will over remain turned toware d tito i le arth. There are stlight deviations firom the positiv.e ness of t.tis state.clmett to wihie.l wAe shtall have occa-sion to allude hereatfter, >butt the grand truthl remattins, that the s8lame lhmislphero of tle imofo is ever turnedl toward the. e.arth. To account for thli remartkablo fact we are compe'lled tot ac]knowle\dgev a rotation of thle m.oon ont her axis, in tihe exact period emptloyed by her ill her revotlution in lhr t-orlit. If fthe moton had no mtotion of rotation about an axis., te then il the course of her orbital revolu.ttionl every( portion of her surtlfac would come- into view sutc ce'ssively. This explawnation, wt hich it would seeni. ought to be pe}rficetly sat isftctorv, has, in some strangle twayt been not only misunderstood, but denied:tand yet shttould the per - son. most skeptical undertakec to walk round at cetral oh,iect. altwa'ys tn iurlin' Iis -fi':t to the ce.nterl, witlthont as twell ttturtini' Ii is shouldert s:and Ipetrson, lie would trceive a posit ive convx iet:ion of' tlhe truth of our explanatiton of a ma'ost pi actic:tl cha racter. Th i physical ca tuse of this reimarkable flact in the m1oon's hIistory w ill bet duly contsidered hercaftelr. T'lithe sme kind of. observation and reasoning whlich entabltd I'ihpp:archus to determtine the eccetntricity of the Isuns tapp:'ient 0orbit (the earth's real orbit) siltiect to enablet ttis philosoptter to dctermine ttt eccentricity of the tmoon>' orbit, tandt the epicyclical theory gave a. THE MOON. 87 tolerably fair account of the most striking irregularities in the moon's motion. In one respect, however, we find a remarkable difference between the lunar and solar motions. The position of the perihelion of the earth's orbit moves so slowly that for a period of even a hundred years this motion may be neglected without any great error. While the moon's apogee, or least distance from the earth, was found to be sweeping round the heavens with a comparatively rapid motion, following the moon in her course among the stars, so that while in a period of 6,585- days the moon performed 241 complete revolutions with reference to the stars, she made but 239 revolutions with regard to her perigee. Hipparchus succeeded in representing this motion by means of eccentrics and epicycles, and finally was able to tabulate the moon's places with such accuracy as to represent her positions, especially at the new and the full, so as to predict roughly solar and lunar eclipses. Ptolemy discovered, 500 years later, a new irregularity in the moon's motion, which reached its maximum value in what are called the octants, that is, the points halfway between the new moon and her first quarter, and so on a quarter of a circumference in advance round the orbit. New attempts were made to explain these irregularities by a combination of circles and eccentrics. It was, finally, approximately accomplished, but all these facts thus accumulating were preparing the way for the abandonment of an hypothesis which could only be maintained by the imperfection of astronomical observation. The excursions made by the moon, north and south of the ecliptic, or plane of the earth's orbit, were obviously to be accounted for by the fact that this satellite revolved in a planet, uttinclined under a certain angle, to the ecliptic.'Itills t-tang was retadily measured by the ancient., atndt tiought slightly variable, was jixed tIt the beiinntring of our century at 5i) 8' 47"9..f' T L.U N, iARt RALt lIAX AND):DSTA NCE. I-. Xthe rude inl tirtnents Cli mpiloyet d by thle earfly observer is in thltir as: tiononicalt observations were insufillcient itr any delieato worlk antd hence we find them q- (uite ignora'int of thio absolute value of even the moon's parallax, a quantity whic b ilhr exceeds any other parallactic aglte of' the aolar sys tem. WVe have already.Shown (Chap..L) ihow tlte distance of an inaccessible object mn.ay ib obt:ined by mteatsuringM the angles failrmced at the extremities of a given basoe linel by visual rays dra iwn to the objcct, In c as thle base 8lite be very short in proportion to the d:istance to ble mealsured, thle sumt of thie two anllec; thus m:eatsulted wi11 iatpp'roach. in. lt vlue 1800, and tl antgle C at the distant o!bject lr 1n d by the visual rays becolmes smalller in proportion to its distantce. In our atte mpts o to e atsure the solar parallax, using the earth's diameter as a base it was found that the delicacy of modern instruments was inot tadequatet to so difficult at task. This, however, is not ttie e ea when twe coime to (apply them int tllte dctertmin:ation of thle lunar paratll!ax.,Indeed, thie mo on is fti und to be so near t the earth tthat visuatl rays, d:rawn f'om s.pectators att difllterent parts of the earth, not very remote fli': o eacht otiler, to thfe mXoonl's centert fbl1rm with etach othler setnsible angles.; and thus thhe mt} oon, vitewed from diflt... ent stattions, isl projected aiolt dift llrent star's. Whelln tlhe moont s ctnttrt is i th.e absolute horizon, (titat is, in a, p:ltt plassing throuh tro h ie centetr of thle earth and'per.pendiculartts to the terthi's radius drawnt: to tle plaeo of tlie spectato0r), lilne dirawnl fron) tlie center of the ~~~~'-....: 0 X i:: ZA iS. M 0 - CS = =..::-:i:::::!:: Ct ~: lr X~~~,t ~:41w: itt= f,, Ha Wl m < ||H c l1 l* -_ THE MOON. 89 earth and from the eye of the observer unite at the moon's center, under an angle called the moon's horizontal parallax. In case the moon's distance from the earth were constant, this angle would also be invariable. This, however, is not the case, and we find the horizontal parallax reaches a maximum value equal to 1~ 1 24", when the moon is nearest the earth, and a minimum value of 0~53'48," when most remote-the average value being- 0~ 57' 00".9. These angles give for the moon's mean distance from the earth 237,000 miles. As all the computed places of the planetary orbs assume the spectator to occupy the earth's center, we readily perceive that, in the case of the moon, the computed and observed places would never agree, except in one instance, namely, that in which a line joining the center of the earth with the moon's center passes through the place of the observer, or when the moon's center is exactly in the zenith. The effect of parallax on the apparent place of the moon is to sink it below the position it would have held in case it were seen from the earth's center. Knowing the actual distance of the moon, her real diameter is readily determined, and is found to be about 2,160 miles; hence her volume is about oneforty-ninth part of that of the earth. We shall have occasion hereafter to resume our examination of the moon's motions when we come to discuss the physical causes by whose power the planetary orbs are held in dynamical equilibrium, and are retained in their orbits. We now proceed to examine the physical constitution of THE MOON, AS REVEALED BY THE TELESCOPE.The splendid instruments which modern skill and science have furnished for the examination of the distant worlds so far increase the power and reach of human vision, 90 THE MOON. in the case of the moon, as to bring this satellite of the earth comparatively within our reach. A telescope which bears a magnifying power of one thousand times, applied to the examination of the moon's surface, enables the observer to' approach to within 237 miles of this extraordinary world, and even this distance, under the most favorable circumstances, may be reduced by one-half. This, perhaps, is the nearest approach ever made to the moon, and it is at a distance of say 150 miles that we are permitted to stand and examine at our leisure the features which diversify the surface of our satellite. No subject has excited so deep an interest from mere curiosity, as that involved in the actual condition of the moon's surface. Every one desires to know if the other worlds are like our own. Have they oceans and seas, lakes, rivers, islands, and continents? Does their soil resemble our own? Does vegetable life there manifest itself in every variety of grass and flowers, and shrub and tree? Are there extended forests and spicy groves, filled with multitudinous animals, in these far off worlds? And, above all, are these bright orbs inhabited by rational intelligent beings like man? The earnest desire to obtain responses to these and like questions, caused to be received, many years since, with the most wonderful delight and credulity, a statement put forth in America, giving professedly the details of lunar discoveries, said to have been made by Sir John Herschel at the Cape of Good Hope, in which all these questions were most satisfactorily answered. We need hardly say how great was the disappointment when these pretended discoveries proved to be but fanciful inventions. When we call to mind that with a telescope magnifying 2,000 times we are still separated from the moon 120 miles, we TU IX:L M OON. 91 readily perceive the utter impossibility of solving at prets-, ent, directly by vision, the problemt of the moon0sl habitatbility. We know not what may bo accomlplislced by hlumantll genius antd buurnan invention, and after the production of so marvellous an instrument as i tflescope capable of trannsporting the b.eholder to within 120 miles of the slur-1 itee of a body actually removed 217,000 miles, we will not presume to set any specific limnits to futuroe efort.'We can only say that that telescope must become vastly improved in it,< powers of definitiol and developameni t be.foroe we can hope to satisfy ourselves, fironm actual i9nspection, that our satellite is or is no inhabited by a: race witll any of the fiaclties which distinguish man. Let us see what lhas actually been accomplished by telescopic investigation, aFnd although it fials fari short of saitisfying the curiosity of our nature we shtall f1nd much to interest and astonish. We can affirm, then, that the surfict of our' satellite is diversified with hill and. dale, with loft.y mountains and mighlty cavities, with extensive plain.:s andt isolated mountain peaks, not very unlike the sanle fmeatures presented lby our earth. heo hemlisphlree of the m:oon, visible to man, has been studied and miIapped with the greatest care. Indeed, its clevations and depressions have been acceurately mtodeled, the mountain elevations have beeIn )I\asem'd, and tdhe depth)t of theil mighty cavities whiceh distinguish her surtic have all been carefully determined. iTheso measures all de. lpond oni the fitact that the imtooln receives its light ifrom tie sun, and presentxs its surfteo to tthat orb under every angle in tIhe coulrse of it's revolution.'Th1e mountains of the moon00 like those of tle earth, have their summits ilrst lighted by tire rays of tth rising sun, while all the plain boneath, and their rough alnd rugged sides, are ii 02S T d A:t BTilt MOON. fthe deepest darktess. These summits, when so ilnmium atedt glow ani sparkle with ta daztlingt beatuty unsurr.passesd. As th( sun rises, weo perceivc distictitly thi attt1k shitdow of the moiutaint llitng to a treatt distatince on thte ple aint " belshadow ess slowl y decrease il length, a ind their outlines gradtually ctreep 1up tlth ilountain side as the sun reaches tltch r n's mieriditan.'W}hen the sutu b.tegins to deline the s:tiadows idall in tlh opposite dir:cttion, slowly extentd their black -masses over tho distant plairns, and darkness finally g-athers round the mountain sitdes, till again the sulmmntit is altle iullniittIed by the rays of a settingl sun, It i by moans of tthos shadows, whoso ltngtiths are readily determined by m icromlutnical ttmeasuretts that we are enable tto dAeteinine tho heights of the lunar mountainsa andti the depths of tho. lunar cavitiles. This p1rlocess is not more difficult than to determine the elevation of a church stetepo po oter t h lofty objcct by the lengtth of its shadow cast upon a horizontal pltane below. Thoe altitude of th o sun above the horizont at noon: will. give the direction of t:he visual ray pastsing fromt the summiit of tto object to the extremity of its shadow. Knowling the value of thtis ang-le, antd thi mas uired length of the s.hadow cast, we havoe at oneo tho mellans of determtining tho tlevation of the olute; ndoe r examintation, ThesIle Asimple principlh s are readily trans ftrred to tot determination of th heightts tand depth;s of the lunar surhco while tho figuro of the shttadow cast by tho summits of a tmountati range on an extentded plain below, gives to us dalmost as perfect a know ldge of the actua.l forms of the lunar mountlains a thoucgh it were possible actually to tread their lofty summits. Wto find upon the oonh's surtfce a 1ange of mountains lifting thlixmselve above a level counttry and extcnding ............~ ~~~~~~~:;':::..::::~::;::':::::i':':::::ii X::;, ~ ~ a~~:,.:.:::::: i I.,,::~~:::i ~~:B:':::j:.::~. ~:::~ Mitsui::! Ali,..~..,~:"~:: ~~n~~n~~n~~i:;:iii:~:-......:-.... K ~': Sta istic l, r: _::~:::~~~~r..........~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~n:.i~..:~: ~...:.... THE MOON. 93 nearly two hundred miles, which have received the name of the Appenines. This mountain range comes into the sunlight just after the moon has passed its first quarter, and is then one of the finest objects that the telescope reveals to the eye of man. The brilliancy of the illuminated heights and ridges, the absolute blackness of the deep, rocky chasms, the lofty peaks, the rugged precipices, and the deep shadows, all combine to increase the natural grandeur of this extensive mountain range. Let it not be imagined that details in such a scene, such as actual individual rocks, of definite form and outline, are to be seen; but as lights and shades produce the forms of every surface, so these lights and shadows on the moon bring out the absolute forms in the most distinct and perfect manner. The contrasts between the dark and illuminated parts of the moon are far deeper and stronger than on the earth. This arises from the fact that the sunlight on the moon is not reflected or refracted by an atmosphere such as surrounds the earth. The twilight which attends the setting sun and the dawn, which so beautifully announces the coming of day, does not exist for the lunarians. If any eye beholds the rising of the mighty orb of day from those lofty lunar summits which are first illumined by his horizontal beams, no gentle flashings, or rosy tints, or purple hues, but from intense darkness there is an instantaneous burst of brilliant sunlight. The beauty of our dawns and twilights is due to the atmosphere which surrounds the earth, and while we cannot affirm that no such atmosphere surrounds our satellite, we are certain that whatever gaseous envelope may surround the moon on its hither side, its density cannot compare with that of the terrestrial atmosphere. Under very favorable circumstances, with the great refractor of the 94 THE MO N. Cincinnati Observatory, the author has either seen, or fancied he saw, a faint penumbra edging the dark mountain shadows, and clinging to the black outline, as it slowly crept up the mountain side, as the sun rose higher and higher. We shall return to this subject when we come to treat of certain peculiarities attending the eclipse of the sun, and the occultation of stars by the moon. Some of the mountains of the moon reach an elevation of 8 to 10,000 feet above the general level. Here and there we find insulated peaks rising abruptly from extended plains to a height of 6 or 7,000 feet, and in the early lunar morning flinging their long, sharp, black shadows to a vast distance. But the most remarkable feature presented in the lunar surface is the tremendous depths of some of the cavities, and their immense magnitude. Some of them extend beneath the general level of the country to a depth of 10 to 17,000 feet, and their rough, misshapen, precipitous sides, exhibit scenes of rugged sublimity to which earth presents no parallel. Of these cup-shaped cavities, especially in the southern portion of the.lunar hemisphere, the number is beyond credibility; and, in case we admit them to be the extinct craters of once active volcanoes, we are forced to the conclusion that convulsions, such as the earth is a stranger to, have shaken the outer crust of our satellite into a hideousness of form unknown in any region of our planet. Some of these deep cavities are nearly circular in figure, and with diameters of all magnitudes up to twenty miles. Very often the interior will exhibit a uniformly shaded surface, and in the center a conical mountain will lift itself far above this level plain. That these convulsions are of different ages is clearly manifest from the fact that their outlines very T H E l 0 0 N. 95 often overlap one anotler, and the oldest and the newest iormationt s are tints distinctly tlraced by the eye of mntan. So sitar p;and positive is the outline of these extraordinary oljiccts thalt one canlnot but feelol thiat soine sudden bulrnting fortth inili'tt even occur while under telescopic exam,inattion. Onlee indCeed, wtlilc closely inslpecting these seeinilgly voleanie mounttains and craters of the moonl, I was startled by a spectacle t: which, fi:tr a imoment produced' upo-n the mitid (a mos t tt srange sensation. A miighty bird, hue in outline and vast in its propolrtions, suddenly lifted itself above the r:loonl's horizon and slowly ascendedt il its flight toward-s the mof)on's ceniter. It was no lunar bird, how.ever, but olne of earth high ui3 p in the hmeavens, wint,in g its solit ar y flight in the dead of night.t, and:y chl'. crossilt thte ficld, of vision land the lunat r disk. Ahci'ro' tho powe of t it tt ele scop t e lean reacltedti its pres - entt. cont:.ltition of pl.erfecti on the tairker spots- off tlhe m)oon swere a Issiium ed to be seafs antd oceatns; but the power now\ tappliet to the moon dcmost rates tha t e c ot tre t exist at: this timle any considerable bodty of water on the hemiisplhrei frblem tle \ r the earth. Andt yet we find olbjects Bucl i, tiat in case we were gazing upont tihe earth froml the moom.t possessin our actual k nowledge of thi eartths lakes tnd Livers, we should plro)loulnce tle. lm, withoutl hesitat: iot, lake; and rivers.'..Thler iS ono suct:h ol)jec:t xwhicfh 1I ill tdiscribe as often Seen i thlrough thli (inlllcintnti {etrfact:lot. Teet outlinl, is neatrly circularl witlt a: Io fty rainge of lulls on tlhe western and south- v(weter sides'is; ran'ge traduall y sinks in the eaist., ad a.t lb-titiltI sloping b:,achl seeams to extend down to the levetl csurltCe of tie inclo ed lake (ias we l shall call it, tlor wa nt of other language). With thle ihightest telescopic power, under ttie most ivoratble cirtcumstant es, I[ \ ever could deteet 96 THE MOON. the slightest irregularity in the shading of the surface of the lake. Had the cavity been filled with quick-silver and suddenly congealed or covered with solid ice, with a covering of pure snow, the shading could not be more regular than it is. To add, however, to the terrene likeness, into this seeming lake there flows what looks exactly as a river should at such a distance. That there is an indentation in the surface, exactly like the bed of a river, extending into the country, (with numerous islands,) for more than a hundred miles, and then forking and separating into two distinct branches, each of which pursues a serpentine course for from thirty to fifty miles beyond the fork, all this is distinctly visible. I may say, indeed, that just before entering the lunar lake this lunar river is found to disappear from sight, and seems to pass beneath the range of hills which border the lake. The region of country which lies between the forks or branches of this seeming river, is evidently higher, and to the eye appears just as it should do, so as to shed its water into the stream which appears to flow in the valley below. The question may be asked, why is this not a lake and a river? There is no lunar atmosphere on the visible hemisphere of the moon, such as surrounds the earth, and if there were water like ours on the moon, it would be soon evaporated, and would produce a kind of vaporous atmosphere, which ought to be shown in some of the many phenomena involving the moon, but has not yet been detected. What, then, shall we call the objects described? I can only answer that this phenomenon, with many other, presented by the lunar surface, has thus far baffled the most diligent and persevering efforts to explain. In some of these cavities, where the tinting of the level surface is so perfect with an ordinary telescope, THE MOON. 97 when examined with instruments of the highest power, we detect small depressions in this very surface, cupshaped, and in all respects resembling the form and features of the principal cavity. These hollow places are clearly marked by the shadows cast on the interior of the edges, which change as the sun changes, and seem to demonstrate that these level surfaces do not belong to a fluid but to a solid substance. Among what are called the volcanic mountains of the moon are found objects of special interest. One of them, named Copernicus, and situated not far from the moon's equator, is so distinctly shown by the telescope, that the external surface of the surrounding mountains presents the very appearance we would expect to find, in mountains formed by the ejecting from the crater, of immense quantities of lava and melted matter, solidifying as it poured down the mountain side, and marking the entire external surface with short ridges and deep gullies, all radiating from a common center. Can these be, indeed, the overflowing of once active volcanoes? Sir William Her. schel once entertained the opinion that they were, and, with his great reflecting telescope, at one time discovered what he believed to be the flames of an active volcano on the dark part of the new moon. More powerful instruments have not confirmed this discovery, and although a like appearance of a sort of luminous or brilliant spot, has been seen by more than one person, it is almost impossible to assert the luminosity to be due to a volcano in a state of irruption, but is more commonly supposed to be some highly reflective surface of short extent, and for a time favorably situated to throw back to us the earthshine of our own planet. From some of these seeming volcanoes there are streaky 5 98'uH -I MO 0 00 N. radiations or briglht lines', running,:frto a co'mmon center, anrd extending s(metinetlt to gr'teat distanes, Thltese hlavo b (y some been considcered to be lhardened lava streamls o:f great retlctive pot er, 1but, uttn firliunately ftor this hypo.tlths.is the:xy hol'tfleirl way Iunbroken atcross ldp valleys anld abruipt ldeprct sions, xi vl:it1lrt t()n olten matter flowing S lava does could t sibly do. To me y more thy re resemble itllm:lnse uplheavals, l'o ing elevatecd ridtge(s of a, reflecting power gtreater than tlhat of the surlroundilng coiuntry. tWe find on the levol surfaces a: few very direct c^tts, as they may be called, not tunlike thoso tae ton our platnet ifo railway tracks, only ont a giganttic scale, boing miore than at: thousand yards in wxidthi and extending in some instances over a hundred miles in length. What tthso nmay be it is useless to conijectur. We cannot reg",ard themn as the w)ork of sentient beings, and Imust rnatller consider them as abrupt. depressions or failts in the tlunar geography. T'.i MOON's cNTx t. O Ft11.......'... wonderful phIfalnomen a presotnted to the eye on tlh visible h misphero of the moon Ihavre bleen rendered in som1e odegree explicable by a ret-arkalloe discovery recently made, t}at the cettlcr of gravit/y of the l0mon docs not cointidot with tlto center) of Jilurte. tthis is not tlho placo to explain h. to this fact has been ascertained.:It is now introduced to present its efi:et, on the hiitihcr portion of thle lunar orb. If the matelrial composing thle moonl was lighter in on(o hcmtisphere tc h that the otler, it is manlt ifetst that the center of gra-vity would fial in tlh hleavier htalf f f the globo. 3'or instance, a globo composed partly of lead and p.artly of wood cottuld not have the center of gravity coincident with the center of the globe; bu it twould lie somewhclro T 1H 1E't 0 O N. 99 ij tloe leadten ttispher e. So it now aptpears that that t center of gracvity of the moonl ist more than 83 mtiles ft0ro the center of figturoe and that th;tis center of gravity falls in the remote thctiisptere, which can nev1'e be seen by mortal eye.'Now, the center of gravity, is the center to whi.ch all heavy bodies gravitate. Abtout it 1a a center the lunar occan and the lunar atmosphere, in case such exist woutt atrra, e thetselves, and the lighter hemtisphero wrould rise above the gfeneralt level, as 1referred to tho center of gravity, to an extreme height of 88 miles, Admitting tit to be true, and as we shall se hereo after the fact appears to be well established, VeC can readily perceive that ino watetr, river, lake oxr sea, s>hould exist on the hither side of the moon, and no perceptible atmospherte cant exist at so g'reat an cl cvation. Even vegetable litf itself could not b)e mltutainetitcd onl ai mountaint tower.ing up to the en'orlmous height of 83 miles; an.d tnco wo oug}tlt to expect the hither side of our satellite to pres.cnt exactly such an appeap'rance as is revetald by tcle scopic inspection. If the centers of gravity and figure ever coincided in the moon) and the changte of form has been produced by some great convu lsion, which has principally expended its firce in ant uphl:eaval of the hltither side of the globe, tihen we Xcan account for thie rouligl, broken, and shiathte.red condition of tho visible surfitce. Lakes and rivers mtay once hiave existed, active volcanoes milight oncel htave p)tored fo:rth tleir la'va streams, while now the dry andi desolate beds alnd thte extinct craters are only to bo seen. Th' constequences which flow from this singular dis-. covery ts to the figure of our satellite are certainly very 100:T 3E Mt OON, rem'tarkabl, and twill doubtless b t.raced with deep interest in futture xamntimattions. (.)cc.t.Tx.rio.,',..... As tle moo is very n earl thle eart l t t1and her disk covers at very considerabl surface in the he ttl a cns int her sweep a ng thle fixed stars, 8she lmust of course cross over t muliltitude of stars in her revolutions. A star thuls hlidden by the m:oon is sa;id to be oedlltCed and tlhes occUttationtts are phenomenallt of special interest on lttany actounts..As a general thing, at star even of the first ilagnitude, in tpasi8ng. under the dlark lil)m of the moon, vanishes from the sight nstalta nleously, as thouglt it were suddenly stricken from existence, and'at its rei:)earalnce its full brilliancy bursts at onc on l the eye. Tlhis demonstratets the fiact that t:h stalrs can 1l nothing,m'ore than luminous points to our senses, even when grisped by tho greatest telescopic powver..A.. strange appearance sometimes attends the occultaslion of stars by them.moon. ITho star comes up to the:tmoon's litmb entirely vanishes tfor a momt ent, then reappeairs, glides on the bright limb of the moon fbr (a second or m-ore, and. then suddenly tldes t iom the sight. Th lish phenllomlenonl as talso anotthert of most startling charac(ter attet-ndinig.sometimes thi total eclipse of the stun, twhen blood.-red streakts in radiations are fttuld to shoot suddenly fromn behind the mtoon's limb, are supposed by some to demonstrate the existence of a lunattr'atmosphere. Mluchl attentiont las been bestowed on the total eclipses of the sun during tho past twent ye1ars, for tho Cexlt.es purposi of solving, if possible, these mysterious radiations of red liglht. Some entertain the opinion tlhat they are duet o t the colored glsses used to softent the intetnse solar lighlt, as seen thl:rough tlhe telescope. We ctan only say that these phcnomte remaint wtitthout satitsictory T I} ], A o 0 0 N 101] cxplaatation, and that tthe pihysical condition of thte xloon is yet a problem1n of the deepest interest. \' can atssrt; thle irreg^ulariticsa of her surfiace, Itlr deep1 cavities and lofty clevations, her extended ptlains antd abrupt mtoutntain peaks', but beyond this our positive ktowledge docs lnot extend. We shall resume the consideration of our satellite when we colme to discuss t he great theory of tuniversal gravitation, CTI h APT EI Vt.MAA, TSil VOURTI(t PLAN.' T IfN JTHE O.IX, O Di-, TANC'E'RO:M THIE UN,.'r.tSNO)U;Xi^A O MA1A,. i)FC xFtICLT TO;XP.r AItN' WI' 1:x }tgH 1i ArTIr- AS'tHrB (RS.:N tlA o0 MsOTliON'.~"OAi):'E"NwIOtK'N SYS'tTEM AP:I>'tEfIl),-.' —1'.:iOYCLg:; OFr MA}:{..,-"...B~;,:' thtwr JNSWtVRUMENTS o AND MOtir: ACOURA't OBSf.xiYAT''ONS>..-.TYC{O ANO K~tuLixR..-.. tK'IE,' it l,,,i s't {Ol' ^ J'- OE'ItO,..tBCLif AN) YIi -,lf Y t.tT.N;IIA$: it.K ti'~~'sI r.1. -S. S.. i O,- -- -.ll-E 1,P'4,;tIL. OisF i 01}'x'l. EPIAt:, N f~'is'iii, —-'t~:.t..I;N" s' ilt Ilt,ANt' At.' 0i:B't:i EXfAtIi).,-Hl.OW''iIE LE.i NMi' At: OitAlNE}A): -fs IttK'lli) iX n ftSCI aii'i. —tts..srt tv I [Vx'. t'si Xi't~xx;x. t.~'BluN u'rsicti Asrint:s'i~........- T..} >," "[t11 g D'LAW,......~...VAVIU }5 "t' THIS L['AWS —.,*"'i'1}:'i tt^K ~81C:IA } Si OT 0 i-: t Ak, -— SNOWN.....: t —O':tA'ION s i-r T'i'i PLANE T,-.i.... 3)IAr.mt'E N,t.s. O OLUMiE,~L':.-.r'Sili..t,.:': itON 4AS'0 ti',i' CLtMAT}i AND f oiO.., THlnT planet i isdistinguished to thi naked eye b)y its brilliantt red lilgh. t and is one of the planets discovered by the ancients. Tlo the old astronomers Mars presenteod an object of special difficulty. Iltvoling as it does in an orbit of great ccentricity, sometimues recedlinfg from thie eatrth to a vast distance, tlhen approaclinig so near as to rival in brilliancy thoe Irgett o planets, Jupiter and Venu-s, on tlie old l1ypothesis of tho central position of the earth, and thle uttifbrm circular motiont of t1he planets, M:tlarN s presentte anoimalies in his revolution most difficultt of explanation. TlBheso complications wero measurably rexmoved by tho great discovery of Copernicus, which released tlhe elarth from: its fialse position, and ga veo to Mars its true center, the s1un; bu t even with this extraordina ry advance in tho direction towards a full solution of the mysterious Imove MARS. 108 ments of this planet, there remained many anomalies of motion of a most curious and incomprehensible character. It will be remembered that Copernicus, in adopting the sun as the center of the planetary orbits, was compelled to retain the epicycle of the old Greek theorists, to account for the facts which still distinguished the planetary revolutions. As in the revolution of the earth about the sun there was an approach to and recess from this central orb, so in the revolution of Mars it was manifest that there was a vast difference between the aphelion and perihelion distances of the planet. The epicycle was then retained to account for this anomaly in the motion of Mars; and it will be readily seen from the figure above how this hypothesis rendered a general explanation of the facts presented for examination. :10.4 Mat A U S. The tlargo circle, having the sun for it' center reprostelt the orbit of Mars, that is, a circtl whose radius is equal to thoe averatge or metanl distance of tlte planet. Tlhei small circles represent tie epicycle, int the cireultivIbree-ic of which the 1lanet revolves with an equablot e inotion, wbhile its center moves unifornmly round onl the circumernrencce of the lar e circle. Wen te planet i att t A, it isin perihelion, or Itneest th su.,Wh il te tecenter of the epicycle perolorts a quarter revolution, the planet also peorfbrms in its epicycle a quarter of a, revolution, and reaches the position B. A half revolution brings. it to tphelione. in (C, and three quarters of a revolution ilt thoi epicycl lotcates the planet at D, and an entire rcvoltion brings itt a gain to A, the point of depiarture. t Thus it will be seen ttat the planet must describe ant o val curvet, t:raced in the figure A 3 C 1), and for general pun.-. thioses ti exposition of the )lenomena: seemid entircly satislftctory. It is true that it only accounted fito the tmovelment fiorl east to west. or in longitudelx wlilo the mlot:ion north and southi of the cartt's orhbit, or in lati-t ttue, wa.s accounted for }y stpposing th pn o t t epicycle to vibrate or rock up and down, or righlt and left of the plane of the ecliptic, while its' cteter movcd tuniformly round in thot great circle constituting tho orbit of the planet. So long as obsorvationl was so deftective as to yite, d lut roug1hit placees of' the hexavenly bodies, the deviations fitom ttho pathl miarled out )b t teoy ot th eor picycles e'scaped detection. Tho erectiont of thie lgreat obsoerv atory oft Utra.nilh tl,r, by tle celebrated astronomer Ti'yc}ho' rattl( adl the fiurnishling it with inlst.rumt nts of tsutpe.erior dttli. cacy, introduced a new era in the his)tory of a1stronomical observation..The: ilnstrutmntts lemployed by Copternlicus MAt S I V..105 were incapable of givitng thle place of a star or planetl with a precision such as to avoid errors amomunt i to even tlh half of one de.gree, or ant4 amounlt of space equal to ti:he sutns apparent (di ameter..The instlrutents employed by'Tycho reduced the errors of observation firom fi:actiotnr of degrrees to fractions of mrinutes of arc, and w\hen thus critically examined, the planett as well as thle sun atul mlool, presented anomalic s of meotion, requirirng to account ibor thenl a lar(ge accumulation of cotmuplexity in the celestial machinery. Such was the condition of theoretic and practical astronomy at the era inatugurated by thot appetaranct e of the celebrated Kepler. This (lis. tingui shied astrlonomer early becato a t devoted advocato of the (Uopernican system of the universe, adoptingt not only the central position of the sun, but also the -acient doctrine of unitform circdular mIotion, and the th teory of: epicyclets. 1The:inves;tigattions of Kepler on tite motions of thie planet 5f:aars commenced after joilning lTycho at tIl'ranijt 1l(erg in 1:.608, andt. based upon the accurate obser.va.tions of this later ast.ronomt er) finally led to the overt-hrowl of the old theory of epicycles and circular lmotion, introlduced ithe true figure of the planetary orbitts, and'witht the elliptical. t:heory of planetary motion, comme0:t nced tlto dawtn of that brighter dacy of modern scicne, whlich in our age sheds its li(ght upon the world. Th1e lhistory of the greatt discoveries of Kepler presnts one of tihe mfost extraordina.ry chapters in tho science of astronomy. It must )be remembler*ed that tho ldoctrine of circular motion, at once so beCautif:ul andl simple, had held its sway over the lhuman miTd for more1 tthan tAwo thousand years. Such, ided, wa ts powr of fscination that even the bold and independent mind of Copcrnicns could not br'eak awnly from its sway. When Kepler 106 MARS. commenced his examination of the movements of Mars it was under the full and firm conviction that the theory of circles and epicycles was unquestionably true. His task, then, was simply to frame a combination such as would account for the new anomalies in the motions of Mars discovered by the refined observations of Tycho. The amount of industry, perseverance, sagacity, and inventive genius displayed by Kepler in this great effort is unparalleled in the history of astronomical discovery. His plan of operation was admirably laid, and if fully and faithfully carried out, could not fail, in the end, to exhaust the subject, and to prove at least the great negative truth, that no combination of circles and epicycles could by any possibility truly represent the exact movements of this flying world. It is useless to enumerate the different hypotheses employed by Kepler. They were no less than nineteen in number, each of which was examined with the most laborious care, and each of which, in succession, he was compelled to reject. Having adopted an hypothesis, he computed what ought to be the visible positions of the planet Mars, as seen from the earth, throughout its entire revolution. He compared these computed places or positions with the observed places, or those actually occupied by the planet, and finding a discrepancy between the two, his hypothesis was thus shown to be false and defective, and must necessarily be rejected. It is curious to note the limits of accuracy in the observed places of the planet, upon which Kepler relied with so much confidence in this bold investigation. Many of the various hypotheses which he worked up and applied with so much diligence, enabled him to follow the planet in its entire revolution around the sun, with discrepancies MARS. 107 between observation and computation not exceeding the tenth part of the moon's diameter. Indeed, the whole error in the computed place of Mars, when compared with its observed place, when Kepler commenced the problem, did not exceed eight minutes of arc, or about one-fourth of the moon's apparent diameter, and yet upon this slender basis this wonderful man declared that he would reconstruct the entire science of the heavens. Having thus framed one hypothesis after another, each of which was in its turn rigorously computed, applied and rejected, this exhaustive process finally brought Kepler to the conclusion that no combination of circles, with circular motion, could render a satisfactory account of the anomalies presented in the revolution of Mars; and he thus rose to the grand truth, that the circle, with all its beauty, simplicity, and fascination, must be banished from the heavens. The demonstration of this great negative truth was a necessary preliminary to the discovery of the true orbit in which Mars performed his revolution around the sun. Complexity having been exhausted in the combination of circles without success, Kepler determined to return to primitive simplicity and endeavor to find some one curve which might prove to be that described by the planet. In tracing up the movement of Mars, as we have seen, the figure of the true orbit was evidently an oval, and among ovals there is a curve known to geometricians by the name of the ellipse. This curve is symmetrical in form, and enjoys some peculiar properties which we will exhibit to the eye. The line A B is called the major axis, and is the longest line which can be drawn inside the curve. It passes from one vertex A to the other vertex at B, and 108 MARS. the semi-ellipse A D B is such that if turned round the axis A B, it would fall on, and exactly coincide with the semi-ellipse, A C B. The line C D is called the minor axis, and is the shortest line which can be drawn in the ellipse. This line divides the figure into two equal portions, exactly symmetrical. C Ad rD The point L is called the center of the ellipse, and divides all the lines drawn through it and terminating in the curve into two equal parts. But there are two points, 0 and 0', called the foci, which enjoy very peculiar properties. If from C as a center, and with a radius equal to A L, the semi-major axis, we describe an arc, it will cut the major axis in 0 and 0', the two foci. Now, in case we assume any point on the curve as P, and join it with 0 and 0', the sum of these lines, 0 P and 0' P, will be equal to the major axis, A B. Such are the distinguishing properties of the curve, which holds the next rank in order of beauty, simplicity, and regularity, after the circle. While the circle has one central point, from which all lines drawn to the curve are equal, the ellipse has two foci, from which lines M A R s. t109 dralwnt to the same point on tthe curve, wheln added togetticr, areL equal in length to the imaj]or axis. When the:imaijor axis of the ellipse is assumed as tthe diam.eter of* a circle, tthe cicumtferetce will wholly inclose the ellipse. tWten the minor axtis is assmted as the dlian:l. tet, the circumttferrenco wtill lie wholly within the ellipse. Whnt tlthe foci 0 atd 0', are very near the center, t tn these circles, and the ellipse lying between them, are very close to eachl other. \Wh1en K epler was compelled to abandon the cirlec and cireular motion as.a rmcans of representing the planettary )rvolutions, et adopted the ellipse as tlt et probable fbir of the orbits of these revolving worlds, and made an especial cfblrt to apply this new figure to a solution of th:e mysteries which still enveloped tho motions of MAars. But h lre a new difficulty presented itself. In the cireclar orbits and epicycles a unitrm mlotion was always accepted, fitt in the ellipse, every point of which is at unequatl distances from th thtl cus, solme law of velocity hiad to be discovered to rentder it possible to computo the planet's place, eveln after the axis of the ellipse had been dettrinted. itero again was otpeied pll) to tho mindat of tih laboriouts philosoplher a widle field of investiiation. Ianty were the hypotheses which hle taitned, computed applied and rejected, but finally fixing the 8sm.t in the fcus the asstm ed elliptic orbit, atd ass sumlting that the line ledrlawn from the sunt''s center to the planet woutld 8weep over cqua'l a(tmountls of area in. t/(tua! times, lie comflputed thi e places of Mars through tan entire revolution.'Theise newly computed places were now compart.ed with those actually filled by the revolvinrgl world, anid (Kpler tf und to his infinite delight that tho planet swpt wt over the precise track which h:is hlypothesis 1 1t0 MA,.tt S. hladt enabled himn to predict, and wlith tant exultation of vietorioult's trimph to w lich the histsoy of p-iure thougtht furnislhes few pa ralsI ll Kepler ranno.nccd to the world. his to J ^first lahws of planetary motion, wliclh may be given as followsx I. wry 1 qplanlctl r.cl.olves in an elilipticatl orbi t about the sunt 7t which o):o't/pies he Jfocus..... f'/ rthciy of thfe ipl/,an onil ever-ttC potint of its orbit is st/h, tuat th1iet line drawn from the /sun to /the pla'net wil t. weep ovel equtl atretais int eqt.l titmes. Atl thle timoe Ktepicer lived, hian gtenius could not hlave won ai grander ttittnlph, for it wats not only a freed the tmind fromt the iron sway of the stools, land fromt the prejtudice.s lwh ich hald becomet vttenertable witl ttho lapse o1f moro than ttwent.ty centltries of ulnyietlding poxwer..No grander cmotiont ever sw lledt thot hm1nan heart thant tho::se which Kepler experiencedl whcel traciln this flery worldt tl.rough Ih is sweelp lamong t fixtctid tatr, h.e tl1tund lie htad truly and. firmly lboutnd It is now cptfiv e planet in c ltainis of adamant., firom whicl in ll fittunre agles it could neve. r e scapc, t.avintg fixed tior all tnimoe tthe ii uroe oft the orbit andtt tlhe law of its orbital velocity. tht.is etxtentdedl notice is duot to the well merited fatlno of K(ler, as well as to tht gtranldeur of thoe laws discovered.'The elliptical theoryt) now succossfully applied to the platnt MItars, was extended rapidly to Mercurll to tte mtooin,} atln inl ordert to all the knotwn planets. We sall therea'fter, in our treatment of the planets, adopt the ellipticat thleory, and to render our language entirely I tite I ligible, wilt proceed to exptlain what is meant by thte elet ~ mentts of tho orbit of a pilalnet. MAIfS, IIt.To dotermo in thle nil/ nitudt c of anly ellipso we must know tIhe longer atnd shorter axis, or the Ione l t ax is andl the distance froma the cent er to tlhe focus, catlled tlh eccentricity. To determine thto position of tle plallnoe of an ellipse, we:must know the position of tlhe line of its inte: sect ion w'ith a given plane, (usu.ally the ecliptic() called t fhe tine of tfnodes and also tle anygle o'/ ilchiatio with this fixed plane. To determine the position of the elliptical orbit in its own plane, we muast knlow the positi.on of thl e vter'lv, o extremity of tlhe iajor axis, called th}e pelrihlion.t And fintally, t ttrace e te planet;after all thesoe matters stha l he knll)ownl as to its orbit, we must know its ptace or ptositiont in its orbit, at at a giveln momentt of tilnet ainid its period of revolution. Noow, every pllaine of every planetary orbit passes throlughT l the tisn's cenltr..Every longet r axist ot every pl:anetary orbit passes throeugh the snt's center and every line of -nodes of all the p:tlanctat ry orbits tpases tlrotugt the Isun's center.'ThIus twe have one point of every axis, line of no des and pla;tnt of every oirbit of the primary platnets. TI'o obtain ti.lt ltongller axis we ha. tve only to measure tlhe tplanets daistance' fitom c the tun wthen in alpheltion tJand iln porlitelionl. IlTh.'s di stanes addet ttreCtlhor makee tile lonfetlr tlais of the ortbit. The perihtelion dtisttance beling knotwn.t w retadtily obtain the eccentricity Itontce the( shorter ax is and fiotlm thsI. the entire ellipse in magn itude. T.'!he lp'oint at whlich. a pailine!t'.passes fromr north't to southtt of thIe c(liptic:is one point in its line of nodes, t he suits center is another, a( d tl hesea determini t te tdir:ction of the line of nodest-. IThe inclination of plane of the 112 M. A ItS. planetr, orbit to the ecliptic is measured by the antglo ftollmd between a< lint e drawn friomn the suitlts center perpertdicular to toh: lie lil of: nodes ien the pliae of the clip.tic, and one percpendicular to the same line at the same poinLt but lying in the plane of the planet's orbit. Th elevation thercfire of the planet above the ecliptic, whenO 90' deg-ireeL fromt the node, will be the at/lte of iltndinAlion. I ia:ving the line of noldes and inclinattion, we can draw the plane. l iavring the perillelion point, lonfger axis aind(1 eccent ricity, wet can construct tand locato the elliptit orbit, and having the tmoment of perilhlionl passaget we c:a trace the planet int its future mxovemerits. Tlte elliptical theory being adopted and extended to all tho ktnown plarntcts succcssfltlly, it becamte ntlmtaife.st to the searching.enius of Keplert that t:hre existed too manty common points of rtsecMtbanco tbetween thles reivolving orbhs not to iltvol vo some common1.n bond wlhich united thlemn into a s chenme of tutual ldeperndencit e. l'th.ey all revolvcedl in elliptical orbits. Thlesoe orbits had otne cotimm frot us th s. t he sunll'T', lines of' nodes altnd Iprincipal axes intereteltcd in the sun. They all obeyed the same law in thleir rcevolution in ttheir orbits, and Keple r now undtlertook the tasl k al, osft hopeless in its chairacter, of discoverinf, some boind of union which might reduce ka rmltitudet of now isolated worlds to an orderly and det - pende'tt system. Tlis problerm occupied the mind of Kepler fIor no l ess than nineteen years, lie t1examinled carefully a.'ll th} eleen.cts o tie planetlry orbits, arnd fina:lly selected the,tmcf. daislta.ces ad ridi times ias t the ol:jects of his spelcial investigattion. Ic found tthat th-e periods of r'volution increased tas tihe planelt was more remote fi'0to MA It. 118 the fsun, but cortlaily not in the exact ratio of the dit-tanee,. T I}1hms~.. Thie Imeat dsta nce of the xet'tt is,. 9o,000,000 t of:ilcs,. Its ptciod f revol\tionl,,. 3651tI- days. Madn distnce otr Mar',.... 14 02,100000,0of miles. Pcriod ofrc volution, *, G. 8 days. In ea the t distances and periodic ticnes wreo exactly prop:ortio.nal, e o hould hiave:.".li But -.,5 nearly, whlile f 111.:9 nearly. linding ithat to simple proportion existed ol. twlcc, tlhese quanttities, Kplt r broke away froin the ratios of geomuetry, wiclt up to his ownt en hald talmost exclusively been emplolye in all astroll.mi. cal invtigatiott, and conceived thl iOd:c td tlhet tl i til dtden secret nni.htlit oe otund in proportiotn existing t betweenti sBne pow ers of the quanttites under consideratiton. Ito lirsat tried the squt'rca, or simple products of the quanti.ttt tics by tl'tmselvs, 1fllere Ito was atgatin unsuccessfiul. l.e1 now rose yet high er and examined tIl relations of the cubes of the periods and distances. But no proplortion was:tund to exist amongt these third powers., At lensgtfh h1e was led by 1)so tl itftluence, lie knew not,'what, as he sas, to try tthe relation between the squtres of the peri-n ods and tlthe cubes of the distances8 thusi II x',ll and'': x''> X'; " and lher la. y the grand os crct, or i f a ny one0t ill pentformi the operati ons above indicatted, al t ad sqtuar the periods of revolution, and cube the mean distatnces, lie will fildt the above quantities to be cqua(l to each oth'r, or, in othi language, lhe will find the squartes of tit periodic lt.se exactlfy nrot7portion(u l to tl cubes of lite iletw' d[i ttances. T. his i called thoe lird tla of. Kepler, and is perh.tap thl grandest and most important of all his wondert'al dis.coveriesd..Through its power thelo worlds are all linked j.4 t A It S. together. The satellites of the planets revolveo in obedionce to it8s sway, and even those extraordinal ry objects, the revolving double stars, are subjectedr to the same controlling law. it resolves at once the most difficult pro.bloems involved in the solar systeml, aftording a simple lmthod of determining the mean distances of all tto planetst b1y reasuringS the miean distance of any one planet. antd by observingt the periods of revolution. As we lhave already seen, the periodic times are reatdily determined from noting the dlays land fractions of days whticht elapse fiom the planet's passage through its inode until it returns to the same node agai,:t. T1is, in case the line of nlodes remnained absolutely fixed, would give the tinme of revolution precisely, and a slightt correction auiffices to correct the error due to thle movement of the nod^es. The determination of the mean tdistance of tho earth, thent becomes the key to a; knowledige of all tio plalnettary distances, frioml which flows the abs olute Intagnlitudes of the planets and their densities. it is lnot, then, surprising that tlepler, seeing the tItgrandeur of the consequences flowing fitomt the great discovery, should hav-te given utterance to his kfelinrgs in language of the mrost lofty enthlusiasm. VWith the knowledge of the three latws discovered by Kepler modern astronomy coummenced a career of won-. dertll success. We shall findl, hereafterl that even these great laws of Kepler are but corollaries to a higher law yet remaitining to be developedt but we prefer to fbllow out the order of exsaminatlion and developmenlt already commenced. Wc resume our discussion of the planet under examination. tt'he clnt:alges in thie atpparent diamleter of Marsl must, of course, b) very great. When ini oppiosition to MARS. AUG. 30.8 H.55 M.1845. MARS,CINCINNATI OBSERVATORY AUG 5 " 1845. M: A It 8. 1re15 the sun, ov on a, line joitning tlhe sn and earh, Mars is only firty-tsveni millions of mniles from our planet, while, on reacting Ills conjunction with the sun, this distance is incretased by thee lentire diameter of the earth's orbit, or.196 millions of miles. \WIhen in opposition Mars shines with great splendor, pr}cscrentin to tthe eye, as tshwn by the telescope, a l.arge an. d well-defined disk, with a surftce distinctly marked wiith permantaent outlines of what lttave een conjcctuttre to 1)o conttlets and oceans. t.l.he polar regions are distinguishted by zones of brilliantt white light, whtich, in consequence of their disappeara, inc under the heatt of summer, and ttheir reappearant e no:a the winter comes o)t, Iha ve bl)een considered as due to snow tand ice, I, have examined these snow zonesi t with tho greatt trefactor of the Cincinnati ObsCervattory, unIder pelctiarly ivxorable circumstancs. To illustrate the Xmode of observation inployed in the determltination of th. o period of rotation of Mars on its axis, and the power of the telescope in the revelation of the physical eonsitit:rtion of this planet, I] append some accoun t of Macdler's observeations, matde in 1.830, and also of those made at the Cincinntati Observatory in 184:5:-.Th last opposition of Maxrs, which occurred on t he 20tht August, 1845, fiurnished a fine opportunity for the inspection of the irregula rities of its surlfce. When itl opplositiont0 the planet ris es ats the sun sets, and the earth1 and planelt tarc: in a straight line, which, by be)ing: pro-i longe(d, passes through the sun. As tih orbit of Mats inclosest that of the earth, it, will 1)0 seeCn fi'irom a little reflection thiat when 1 tMars in opposition it is nearer to the earth than at any other ttime, xn arer t han when in tonljunictioln by the entirl diameter of the earth's orbit, or.190 millions of mtiles. In case the orbits of'Mtars and 11t06} At A it 8. them earthl were exact circles, the distance boetween the two plfantst a.t every opposition woutld be tihe same, but the clliptic figture of thet orbits occasions a. considerable varia.tion in this distanc, and tlhe least l distance possible between the etrth arnd trs will be Nwhen an oppositioln o - curs at tthe thnee that tie earth' is fuirthcst front the suit tand aI.s nearest to the sun. Sucht was.aptroximatcly tie relative positione fslts of the plalets i 1 84t5, and their dlistaInce was then less than it ctan be again for nearly 15. years. During the opposition lwhich} occurred in 18i0, the:. earth and MItars held nearly the s.alme relative positions, Ti. e planet was observed by t)Dr. Macdlr, the proesent distilnguislIed )irector of the Illmperit Obslervatory at Dorpat, ut ssia, assisted by lr. il Beer. l[ hav e translated the fllowing notices frotm Sc machr's journal..........'Thr opposition of Mars which occurred in the month of September- of this year (1880), tand at whiclh time this plalnet appr oachet nearer the earth than it will agaitn for 15 yearst induce(d us to observe the planet as often as tho clouds would permit, in order to determtinol the position and fligre of ita spots; their possible physical Ichangces,antd especially the time- of revolution on its axis. ".tho telescope employed wwas.a Firaxenlthoet- r Refractor, 4t } feet focus.' tlhe opposition occurred on the 19th September, and the lnearest approach to thte ea rth (0,384) on the 14th of itho ame mtlontth In all succeeding opptositilons 1up to 1,845), this distlance amounts to 0. andt even up to 0.65 (the unit beingl the meant distance of the eartht from the sut). On account of the accurate definition of the instru-. mcli.t, te were able to emt ployy a. power of 800 cgenerally,;anld never les than 185). With low imagniftying powt) rs,' the greatest diameter t wae determined to be a, little les MAt A t. 117 thatn 22'". Our observations extended fiomt the 20tht bSptcmlter to the 20th October, during which timne. 17 nigtts, mtore or less favorablc, occurred, and all side-s of Mars camne into view. WThirtly-.five drawinvgs were executed. Itt was not thought advisable to apply at microme-.. ter, as the thicklmess of tihe lines would have produced greater errors in such minute measures thlan ttiose arising firo a1 carefil estimation by the eye. Txhet drawintts were invariably made with the aid of the telescopo. Comlintmonly a little delaty was had, ill tthe undetermlined figure'o of tbie spots visible at thle first glaence separated thenmselves (to the eye) into distinct portion.s On thle 10th Septertmber a. spot was seen so sharp and well defined, and so near the center of the planet, thatt it was selectae to determino the period of rotation, lOni the 14th 8':etember it retrogriaded fiom: the eastern helnmiphere, through tle center to the west tern lhensiatphere, in the course of three thours. its filgure lunlt altered during tfur da'ys and its regularity a;s to rota-f tion left no doubt of its identity and permanencc.''In thre course of 2 hiours Mtars exhibited an entirely dififrenlt appeatranceo Tht e spot (already alluded to) was near the wesitern d|isk of the planet. On the 1I6th it was again observed l and the period of revolution d te duced. lIt wNas invisib l up to thle Imiddle of Octobter, appearing only in the dayt t ime on theo side o te of pllanet next to the eartht. it ft was first; observed again on the 19th October, and thte disk of Mars shlowced itself with euncommon slha srpnes. On thoe southern b(ordetr of the princiijpal spt two r p ots twere sctn, resem'blitig a ruddy sky on the earth. I'}tey ap)peare. d filnter:an htour aftie, atid although they again seemed brighter 118 MARS. they were never again seen red. We also observed a faint spot near the principal one, which was never after visible. X * + * * *;,> " The observations from the 26th September to the 5th October showed to us some very dark spots, which in zone-formed extensions showed a strong contrast to the brightly illuminated surfaces free from spots. A fragment of one of these spots was at the north end distinct and broad, while at the south end it was so small as to be seen with difficulty. Between the pole and the principal spot, there was seen a broad stripe, of less shade, while the northern hemisphere was almost entirely free from spots. Bad weather interrupted the observations from the 5th to the 12th October. " On the 13th, a spot appeared for the first time again, but so near the western disk that we recognized its return only on the 14th. "More accurate observations were had on the 19th and 20th October, when this spot passed the middle of Mars, which movement was observed with all accuracy, and hence a new determination of the period of revolution. Computation gave the magnitude of the invisible part of Mars on the 13th October-0.06, on the 20th, 0.08, of the radius of Mars. "From the beginning of the observations there was seen at the south pole, always with great distinctness, a white, glittering, well defined spot, which has long been observed, and is called the'szow zone.' During the observations it continually diminished up to the 5th of October. Here an increase commenced, yet very slow. On the 10th September we estimated it, =.110; 5th Oct. =. 10, and 20th Oct -.115 of the diameter of Mars. MARS, 119 A: A ~ S.....'1.9 " In case we adopt lcrlcrsh det terination. of inclinal tion and po( si t tio n f tlr ax is o Mar itl r tir e.tnce to its ol':bit, tfta. S(lltt f:}0}tt <:h tt1*S f.}} f:}l3 l.;:tll Oft. tl'ilt t(It.8f10 orbit, te s.outh polo of Mars on the 14th of April, 1.880 must: 1have had its equilox, and onth thle 8th Seil:temlbe, its summer solstice. Te smaillest diaietc.r of thte s >'1w zoe icclurred on tihe 2'l t day after thto sitummer ol.stice, a timelilt wi lcorrtesponds to th last haltf of \ly on thle northerni hemlnisplh-re of the eartl, at which time it is well known we have the greatest heat.'!recedin-tg observers in oppositions, Nwhere the polo was further froml the mtsaximum ttemporature, have seen the' snow zone' mtuclh larg'er, ltthoutgh nearly all reg1.ard it as clham.;geaible in size. t ltese ifcts soeeeml to sustain the hypothesgi' of a cove ring ofl stnow.' A a. furtler confirmiation. of thlis hlypothes:is, we sub-l join thle fllowinvgi cttompultations, by tlt sae psa ter-stns, Th.he previous determinations of the tlderl' ersehel are takcen as the basis of thte calculations. T'his \white polar Irgcion is lnow distinctly visible, and seettlms to be accountedt for in ito other xway Cloiparing the varlious seasons itn.tlMars, Matcdltr filld s fiollows.... " Duration ofi Spri:, Ng c. lcaisphro,,..19.Ma' day t" Stum'sltm., 180 [. Autuini., 1.40 0 Winter,'.. 14' Additng siprin, atnd sumnnier togethelr, and fill and winter, wo lihave..tt.. I Dultltion of Sl1umm:er in N*. ILf to S.,. a to 15) "intetsiy ( ofsm's ligti.t. N, I, to S [t,,,. as 20 to 29': rntingia t)ceso two proportions, tand a ssluing tlhatI bieat and light atre received in equal ratios, it wNill follow tha:t thle south pole, by the greater intensity of solar leat, is more thanll com'npensated for the shortness of its S.uit-. 120 Ait SA. uter. But since ior tl ti winter the proportion of 20 to 29 is reversed, so will the winter of tlhe south pole, lnot only on account of lonigter duration of tcold, blut also firom its greater intensity, be fatr more severe than in the north)t pole. He llcrcwithl agreet tth fac:tcta tlittt preced ing observers have not lost t siglt of the'so s1now one' of the south pole, evetn twen the pole becamt e invisibleC wh\I eoe it fiollows that it m)-lust extend fromr the pole 4t5' degrees and even trlther, while we tunder like circumtstances, couhl not discover any such appearance on tho northl side of'Mars. On the contrary, the brightness of' this portion was exactly like that. of the other parts of the disk." The conclusions reached by the Germlan astronotmer, as abtove, were confirmed in tthe fullest mtanner by the observations mlade at thte Cfiininlati Obsterva to.ry duriwn the opposition of' 118-4):5. 1 will here record some sintgular lhenttllom: connected with thee' snow zono,' which: so far as I I ltotw, have not been noticed elseowhere, On the nitght of July 12th, 1.84t5 this bright polar spXot pre;sented an ap:pearance never exhibiteitd at any pr ecediln or succeedint:S o tbservation In thie vrly center of:the wh:ite surlce was a dtrk / po/ l, whicht retaited its position dluriig' several hours, and was dist tinctly seen by two friends, who lpased ti e nighlit with mel it the obs)ervzatory. It x as mutch darker and )better defined thi.' n any pot pre viou sly or sutbsetuently obse\ved hrc, and, in delt aftertf an ll txamnation o' more tlhan eighty d(ira nwigs of tihe surfiacc of tis planet rby othe ot.rbsrvers at prl'vi(1os:opipsitionts, I fint no notice of a larkl spot ever tia - ing'twenl sCCen in the t'e ihtit snow zon'.e. (On thie tf',llowiilq:n eveningll no: trtace of' a dark,ttpolt was to b) steet llland it 1ha n.evor atfter beet visible. MARS. 121 Again, on the evening of August 29th, 1845, the snow zone, which for several weeks had presented a regular outline, nearly circular in appearance, was found to be somewhat flattened at the under part, and extended east and west so as to show a figure like a rectangle, with its corners rounded. On the evening of the 30th August I observed, for the first time, a small bright spot, nearly or quite round, projecting out of the lower side of the polar spot. In the early part of the evening the small bright spot seemed to be partly buried in the large one, and was in this position at 8h. 55m., when the drawing, No. 1, was made. After the lapse of an hour or more, my attention was again directed to the planet, when I was astonished to find a manifest change in the position of this small bright spot. It had apparently separated from the large spot, and the edges of the two were now in contact, whereas when first seen they overlapped by an amount quite equal to one-third the diameter of the small spot. On the following evening I found a recurrence of the same phenomena. In the course of a few days the small spot gradually faded from the sight and was not seen at any subsequent observation. Should Herschel's hypothesis be admitted, that the bright zone is produced by snow and ice near the pole of the planet analogous to what is known to exist at the poles of the earth, these last changes may be accounted for, by supposing the small bright spot to have been gradually dissipated by the heat of the sun's rays. Its apparent projection over the boundary of the large snow zone may have been merely optical, and the separation may have been occasioned by seeing the two objects in such position as to prevent the one from being projected on the other. Such change may have been 1.22 At I SA I.t producedl by the rotation of Mars on its axis il the space of a few hours. "To deteermine the exact period of rotationi of Mars, Sir William Iterschol instituted a. scies of observations in I77I7,t which were followed by others during the oppo.sition of I.'lt9. i'roml tho first selies ani approximtate period of rotation was obtained, anltd by uniting the ob-,servat ions of I1777 and those of 1."79, and using, 2 41t t8)t9m, as the approximate period of rotation, Iterschel nmade a farther correction, and fixed the rotation at 24h. 89mnt. 21.6 s. Mttaedlfers detecrminatioll in, 1 gavc fior e? fin al result, 24h.t. 8in. IOs., which in 1.832, was corrected anid fixed at 2411. 3nm. 23.7s. In 18839 Mtaedler reviewed tfierschel's obselrvations,'fiomr' whiece his first reiults were deduced, and discovered that after inltroducing tthe ncessary reduction, the dis:crepancy of two m inutte mi lht b e reduced to two seconds', by giviln to JMars one m50ore rotation oi its axis, betweent tfe obse xrvations of:. IT7' and t 79, tltn lt. rschotl ha(t emiploy ed. In t.84), when Mars agtain occupiedt the sa. e relative position thit it it; ad done in 8 it was too far s.outht for obs;;(.'rva ttio at I)orpat..'B-y comii)ini g Mala-edler's observationl made t er in, 18o0o,:eptitbembl1r 14t,. witlh one m't1 de ate t the Cincinnati. Obso rvtory 184, " At.tnust 30 8ht. oil matingiils the corre tions (tldu to g.l(ocentri lton: itude, pthatse. and.) thrration, I[ find the T period tof ro'ttiotl to h}e,ib}t S'it. 20.6s., didllri' ng by only two sec.nds fri)ro AI t dl er s period tas las t corrected. It is fgenerally believed that Marstl is sul1rroulnded by an atimosp)l hre which int mtanty respects resenmbtles our own. MAt s 1t28 In case this beo true, wt may altilcipate the existP nce of belts of clouds, and occasional cloudy regions, which would modify the outline of tile great tracts of sea and llad, andttl would account fbr the rapid chang cs whINich ax r sometimes nelotictd int the Stiu'frac of the planet. Tle. t atxis of the planet is inclined to its orbit (as may readily b deduced from thle rotation of the spots) under an atngle of a little mnor tha:tn 80', hence the variations of climate a:nd te changes of season in Mars will not bo very unlike those Owhich mlark the condition of our own plllaet,. Indeedl, there are nmany strong pointts of resermblance in the planetary fetatulres of the earth and this neighb oring world. The plantts of their orbits are but little inclined to.each other, a little less thal 2'. fhir years are not widely dithirent when we take into account t:he vast periods lwhichl distinguish some of the more dis. tant plan:ets. Tte s8easonits oulght to be nearly alike, alnd tle length of daty and night, asB determtined by the periods of rotationl of the two worlds, is nearly t he s e. In calse tile great geogratlphical outlitcs are ali ke, 1anid seas and continents really diverlsify tthe surf:ace of Mars with ani atntostphlcr and ctlouds, the two worlds ber a strtong resem, lance to eacht other. tto acttual dialeterl'tt M of: altts is o011:1,1r00 mtiles, or a little more than ht lf thle dilametter of otr earth, whVilet its volume is not.amuch grealter thanr onte-telnth part of' the volunie of our titplanet..Tol tIe inlmlabitantslt of Ml:ars (if such there be) the earthl and moon will pr1 set a very be autiftul pair of indi ssolubly united p-laIets, showing all the phlases which are prl'eselnted by tercurty and'Vetnus to our eyes, tie two worlds nfever pairt ing comt'any,'and always'relainting at C. v, IC)'f"'~ 124 hfARI8. as distance of ab)out one quarter of one degree, or about half the roon's aptparent diameter. The amolnt of hieat and light received from the sun by Mars is tabout one half of that whbiclh flls on the earth;l and in ease the planet were placed under the identical cirem.stances wt tich obtat ti on earth, tli equatorial oceans even would be solid ice,'lhis, we ltave every eatson to believe, is not the case, and hence we are inducled to conclude, as in other cases, that the light and heat of the sun are subjected to special m:odifications, by atmott spholri andl other causes, at the surtlaces of each of the worlds dependent on tfis great centratl orb. The reddishl tint which marks the light of MTars llhas been attributed by Sir Johtn.lerschel to the prevailing color of its soil, while hto considers the greenisht hu:e of certain tracts to ditisthi.uslt 1 then as covered with water.tt Tftis is tll pure conjecturel based upon anltogy and derived fro tt our knowledge of whlat exists in our own planet. If wve did not know of the existence of seas ont thie earth, we coutl never cotljecture or surmise ttheir oxistence in any -teighboring world. Under what mod[ificatiou of circumnsttanes sentient beings maty bl) placed, whto itnhabit the neighborig worlds it is vin for tus to It would beo most incredible to assert, as some have dorie, tha:t our planet, so small and insiagniftlant in its pro:portions lwhen compared with otlterx pilanets with whtich it is allied, is the only world in the whole nltiverse filled witt sent ient, rtt l, ati, and intelligent beings capable of coimprehending the grand mysteries of the physical uniVCle'80, CHAPTER VI. THE ASTEROIDS: A GROUP OF SMALL PLANETS, THE FIFTH IN THE ORDER OF DISTANCE FROM THE SUN. THE INTERPLANETARY SPACES.-KEPLER'S SPECULATIONS.-GREAT INTERVAL BETWEEN MARS AND JUPITER.-BODE' EMPIRICAL LAW.-CONVICTION THAT A PLANET EXISTED BETWEEN MARS AND JITPITER.-CONGRESS OF ASTRONOMERS. -AN ASSOCIATION ORGANIZED TO SEARCH FOR THE PLANET.-DISCOVERY OF CERES.-LOST IN THE SOLAR BEAMS.-REDISCOVERED BY GAUSS.-THE NEW ORDER DISTURBED BY THE DISCOVERY OF PALLAS.-OLLER'S HYPOTHESIS.DISCOVERY OF JUNO AND VESTA.-THE SEARCH CEASES.-~RENEWED IN 1845. -MANY ASTEROIDS DISCOVERED.-THEIR MAGNITUDE, SIZE, AND PROBABLE NUMBER. THE worlds thus far examined in our progress outward from the sun have been known from the earliest ages. Those constituting the group under consideration, called asteroids, have all been discovered since the commencement of the present century. The circumstances attending the discovery of CERES, D OF THE ASTEROIDS are replete with interest, and demonstrate the power of the conviction in the human mind that, in the organization of the physical universe, some systematic plan will be found to prevail. In drawing to a scale the solar scheme of planetary orbits, it was readily observed that the distances of the planets from the sun increased in a sort of regular order up to the orbit of Mars. Here, between Mars and Jupiter, there was found a mighty interval, after which the order was restored as to the planets beyond the orbit of Jupiter. As early as the beginning of the seventeenth century, t126 0 A t: $ 1'4 01 I) S, Kt(pler, whoso singular genius was captivated by mystli il numl)ersi a.nd curious analogices conjectured(l the existeneo of an undiscovored planet in this great space whichl in-1 tervltied between AMlars and tJupiter. Tl th thouglit t ltus thrown out relquired no less than two hundred years to tfake root andt yield its lefitimalte firuit. The d(iscovery of ta planet beyond th1e orbit of Saturn, by Sir'Williamt 1lers}ehel, in 1781, greatly strengthened the opinions based on tho orderly arrantIgemet of the interplantetary spaces; and tho.crman astronomer, Bode, by the discovery of at curious relation, which seenied to control th. distances of the planets, gave additional:ft:orce atnd power to the conjecture of (epler.' Tht is l;aw is a very remarkable one, and althougth no explanation could bo given of it, was verified in so many instancets as tal0ost to force one to the conclusion that it must boe a law of nature. Wo present the law itn at simtple firm. Writo the so Oies -. 0, 8, 6 2, 48, 9(, &c. add 4 4 4 4 4 4 4, &c. sutm 4 7 10 1(. 28 52:100, &e. io, if ten bet taken to represent the disttance of tho earti fiom: the sun, the other te-rms of the series will represent with considerable truth the distances oft tih othter tlatnets,. as we will readily perceive, thus:........ h:i'rcr. ty, ~n. Etratlh. Mars. Jupii.r. uSaturn. l.saiu. 4 7 1t0 i. 28 1. 00 196 Th-.e true distances are roughly as under: 8.8 7.2 J10 15,2 t52 9 05, 3 191.8 It is thus seen tthat the actual distances of t;h.e plaftlets agreet it a'most remarkablo manner with thoso obtained THE ASTEROIDS. 127 by the application of Bode's Law, and as no planet was yet known to fill the distance (28) between Mars and Jupiter, it required very little devotion to the analogies of nature to create in any mind a firm belief in the existence of an unknown planet. The German astronomers, at the close of the last century, took up the matter with earnest enthusiasm, and in the year 1800 a congress or convention of astronomers was assembled at Lilienthal, of which M. Shroeter was elected president, and Baron De Zach perpetual secretary. It was agreed to commence a systematic search for the unknown planet, by dividing the belt of the heavens near the sun's path, called the zodiac (and within whose limits all the planetary orbits are confined), among twenty-four astronomers, who with their telescopes should search for the object in question. It was manifest that the unknown planet must be very small, too small to be visible to the naked eye, otherwise its discovery must have been long since accomplished. It might, however, prove to be large enough to exhibit a planetary disk in the telescope, in which event a simple search was all that was required. If, however, it should be too diminutive to show a well defined disk in the telescope, then another method of examination would be required. The planet could. only be detected by its motion among the fixed stars. This, indeed, is the way in which all the old planets had been discovered; but while the naked eye takes in at the same time a large portion of the celestial sphere, the telescope is extremely limited in its field of view, rendering the search laborious and difficult. Were it possible, however, to make an exact chart of all the stars in a given region of the heavens, to-night, if an examination on to-morrow night of 128 THE ASTEROIDS. the same region should show a strange star among those already charted, this stranger might with some probability be assumed to be a planet. A few hours of patient watching would show whether it was in motion, and a few nights of observation would reveal its rate of motion. Such was the mode of research adopted by the society of planet-hunters. The system thus adopted had not been pursued but a few months when a most signal success crowned the effort. On the night of the 1st January, 1801, Piazzi, of Palermo, in Sicily, observed a star in the constellation Taurus, which he suspected to be a stranger. On the following night (having fixed its position anew with reference to the surrounding stars), he found it had changed its place by an amount so large that its real motion could not be doubted. The star was found to be retrograding, or moving backward, and this continued up to the 12th January, when it became stationary. It was soon after lost in the rays of the sun, thus becoming invisible, before any considerable portion of its orbit had been observed, and before Piazzi could communicate his discovery to any member of the society. Piazzi not considering it possible that a planet which had remained hidden from mortal vision from its creation could be discovered with so little effort as had thus far been put forth, conceived that the moving body which he had discovered was a comet, but the intelligence having been communicated to the society, Bode promptly pronounced this to be the long sought planet, an opinion in which he was sustained by Olbers and Buckhardt, Baron de Zach, and Gauss, and I know not by how many other members of the society. It now became a matter of the deepest interest to re T Ht:a A S T.. o X )S. 129 discover thlis stranger after its iteme rgenc fro the sun's lrys, a tals of no littli (tifcllty, as we will see by tlho s]ightest reflection. Tllhe star had been followed through only about 40 of its ort, and on this slender:basis it seemeld talmos$t impossible to erect a superstnructure suic as mitghitt conduct the astronomer to the point. occupied atany given time by tils almost invisible world. We shall see hereafter that this most astonishing feat was successfully accomplished by the Germtan mnathematicitan and astronomerl, ('lauss, thten quite a yountg manl atnd who, inl this carly effort, gave evidence of thalt tigh ability fior which lie became afterwarl so greatly distinguished. Ceres beintg re-discovered, and closely observed, tho data were soon obtailned fr the exact collputation of the elements of its orbit, when it was found to occupy, inl the planetary systenm, the precise position which hlad bteen assigned to it fiftcon years bcelre by Baron de Zach, in accordance'with the indications of the curious empirical rule, already piresented, k1nown as Bto's law. The hlnarmony of the system was thus fully established, the missiingt term i:n:the searies was no tfilted,. Tho vast interplanetary space betwee\n Mar: and Jupiter was the real locality of a discovered world, whose existence had been conjectured by Kepler two hundred yearss before, and whose discovery, by combined systemtatic and scientific examtin.atio.n constituted tthe crowningl glory of tho age(. True, the new planet was exceedingly small when compared with any of the old planett, yet it acknowledged obedience to the great.laws established by IKepler, revolving in an ellipt ical orbit of very ctnlisiderable eccentricity, and sweeping round the Sun in a per iod of about Jfur years and'ntc imon/ths, and at a mztean distance of about 2638 miliots of miles, I30 3! OT 3:1 A ST It 0 IA rO s'tFle tele.scpo yielded but little in.forin)mtiot n as to tho absolute magnitude and condition of Cerses. Its diame. ter has been measured by various asttrnomer s but the re.sults are so discordantt that but little confidence is to placed in th. the t eannot, probably, exceed 1,000 liles, and may bet much letss. It is supposed to be surr'loundt d by an extensive at mospltere, but thlt evidenc e of thtis is not very reliable. iUnder ftvorabl eircumistanc.es, and wVith tt pIowerful telescope, a, d isk cant somiettites be seen, but for the m. (ost part Ceres prescents the appearance of a star of about ttte eighth magnitude. Suchl was tlie condition of astronormy,'lftfbording to those interested cause for Iig't gu tatification in the now kntOwn orderly distribution o f tlhe 1ja ltetttary orbs, whitt a an nouncement was made which was reccceived wvith prof)ound astolnishml ent, as it at once introduced con - fusion precisely at the pointt in which order had been so 1atelty restored. Tlis was th discotvery oft aother smnall planett byt b Olb(rsi of IB:rcmenl revolving in al orbit nearly equal to that occupied by Ceres. Computation alnd observation lunited in fixinl", betyond doubt(, this most extraordinary di scovery, alnd the new anod anomlalous body received the name of Pallas, The exact eclements of the orbit of Ptalas having been determined, it was foiund t.hat a very near approximation to tequality existed between the itean distances and periods of Ctres anda Piallas, as we find below.......: tC:ris' pelorio of revolution,.. 1,682.125 day.'adlas'... l.80.51.0 " Cores' me.anr distance,..... 26ti2, 0,000 mites Paltas' L'.... 263,4356000 t.I cr t we ind the mean distances and periods so nearly equalt that in case tthe plantesi of thie orbits of tlhe two T t11 A3 T i s t 0 1.). 1.3:81 planets hatd chantted to coincide tlees~ two worlds might ttravtl si(d.lt by side foir a long whilo, an)d att a distanlce froim each other only about double the distance sepattratilln the earth from'i: her satellite.'it The distance between. Mars tand Ceres is no less th Itt 1t20 nillions of milet. l. he distatnce ironT CoreCs orbit to thlat of Jupiter is more th-n 280 ml-lionls of ni les, and yet here are two plancts whiclt l)nay approacl t eachl other to within a distance less tlhita half a. million of m1iles. It is true. the eccentrieitics of thle orbits differ greatly, and the inclinations of thltir orbital pla-nes is also very great, so th'at J]'a.llas, by this inclinattion, is ca;rried f:ar beyo(nd the limit wis t}hin which the planetary excursionsl north and south of the ecliptic had been previously con fined. yet. a, time would coime in the countless revolutions of these remattl.rkable worlds when each would fill, at thi same time, points of thie commlon line oft intersection of their orbital plantes, and thes twe to points, owing to tho revolut ions of ther perihelion, migltt, possibly, at somo future period, colme to coincide. jInt catset tlhese speculations werei e within the limits of tho profbable, and if' it were plermnitted to anticipate in the future, the possible collision or union of these m ninuto planetsi, a like train of reasoning, runninsg back intoe tho pa1st, would le.,.ad to the coneclusion that in catse their revolution had beent in progr ss fir nnmtl )bered tagcs, there was a time int the 1'ast, when thelse two independcnt worlds nig-l'ht have occupied the sameo pointt in space, and hence the thoughtt thit tpossibly thtey were friagments of some great ptla'i.et., whicht, by tlho power of some ttrementtt ous interntal convulslion, hatd been burst into many sepa.ratt fratgientets. T lis st1txrange hyIpothesis wias first propounlded by Dr. Otlbers, and has tmet witht more or less ftvor froto 182 THE:I 1` ] AS.LT KtOI tO ) ), succeeding astronomers, even xup to the present day, as we shall see hereator., T rue or ihlse, it soon produced very positive results, for it occasioned a. renewal of the research which had been discontinuxed after the discovery of Ceres, and in a: flew years two more planets were added to the list of astroids. Ti.e search was long continued, and it was not unt:il the rend of fifteen years that bthers and his associates becaeno satisfied that no more discoveries could bo expected to reward their diligence. Thus it becaior a. received do-, trine that in case a large planet had been rent asunder by sonmo intornaIl explosive power, it had been burst into four pieces, and that no other fragments existed sufficiently largo to be detected even by telescopic power. This opinion prevailed up to December,'845, when the astronomlical world was somewhat startled by the announcement of a new asteroid, discovered by fltenkc, of I)rcisen,. this event awakened aittention to this subject, and a now generation of observers entered the field of rescearch, whoseo effrta have resulted in revealing a largo group of small planets, of which no less than fityfive have already been discovered, and their orbits cora.puitted. The theory of theo disruption of one great planet; a s tho origin of the asteroids lias been revived and exten.sively discussed, but thus far no satisflactory conclusion has been reached. So st;rangely are the orbits of theso bodies related to each other that, in case they all laid oni the sanmo plane, they would inl some instances intersect each otheir r xhibiting relations nowhere else f ound in i.tho 8solar system. jNone of tho asteroids are visible to the naked eye, ior are they distingaishable firom the stars with tho telescope, except under the nmost faivorable ci rcumstances, T. tt A ST. It 0: i S..t33 Whon ca reftlly watched some of them exhibit rapidt cthanges in the iintensity of their light, sometimsc sad(dnly itcreatincrsing in brighttness a.lnd alrt)ttin as pidly t: lad ingi out.,IThese- chan;ges ehavo }con accounted ior on t:he supposition tliat these worlds are indeed angular fraglmen t, andt that, rotatitn on an axis, they someti tme present large reflective surfacc, and again anCgular points, from withnce but a sm1all amount of ligltt readeties the earth. As tlhe stars of the smaller tmagnitudes are becoomingt more extensively and accurately charted, their places being dtelrined w'ith great prccision~, we may antiticipate a large increise in the nlumlb\ r of known asteroids during the iretmainder of the current century, and s forward; for if so great a multitudo lhas already been rt a vealed almost without effortt and ntearly by accident,'what must be tle result fwheln a systemlatic schenme of exatminatio.n shall have been executited based on ail ac — curate knowledge of the places of all the stars down to the twelfth maegnitude? We havo justt gtrounlld for supposing that tthero are thousands of these little worlds revolving in space. C PI ATT ~ND.ID BY f OUI It V I F IXT IAN JUFtI:FTR Nss, sTfEt NUF) BY IAA. YONR s. NS A $ 1 PL Pi 3.AN E3t 3l IN TH i ORDER OR 0 )ISTANCE FROM TH SU.i, A o or( E v:-,OO:AxAi'to.- -STA IONARY POIN T'. —....Sr AN. o r: I PlANt:'EI4.itNE,* —-. t)i, -Pri1i.'^'-. —— SY.NO:}40'nAI, I: \VOLl4"i'4 ON G IVES "I71tV,1: l ^ SIIIT EtA,,...';.-RtFAC. O J 1 t. 4 A:It'1 1}1 ANS 4t1:1, 4N IE: " tsItl E l't:ES'.I 9tL s:ACA,- — t l-tP I)t!~ 41 At(t.i A}i'. T{ f) t.. t-. - ~ ii. I' N.. -I N A NC: ~ A A T-: A' INii A,A t,Tn': SATEi I,' T IS OF I.P1 1i1-H - ow 1!OV:'-.-Tt t | >-i MA 4, t - 1'' }: v....1 I 1-0 s 7:1os. o.' t' A3gt};. A.A,- - - - -s i s To. X4;' v s t..oS I;:.5.t....... X.. 4. i 4 (.1t:I'. l-. —.. t"ti O iX lt.. 11 14'^.ttI-.l': i;.' l> l1O1 N A At N., —'14r444t o o o4: v,1 1u4\ (II 1411 i4 t Di4 44'.', 4. -4o7N.a —-'i:~UI ItX passing ^ forol tho dilinlutinvt e astecroid to the mag-... nitude and splendor which distitinguish thle vast orb) wl ielt t0hold tho next position in the planeLtary systyntlt w arove the lmore dispolsed to adopt tho theory that the exceeding (isparity now existingl il the magnitude of theso )eig.l)borint'g wNorlds is ditue to the fct t. hat the asteroids are tbut a few of tho fragments of some objct in wAich they were all once united, Weo shall hereafter present a: stpeculation on. this sul)jeot which scems entitled to co'sidclratt iotl.'lhe tplanlet Jupiter is one of lhe five revolving worlds discovered in tho primitive ages. Its revolutiton anmong tie fixed stars is slow and majestic, comiportitng well with. its vast dimenlsions, and the dignity conterred by fbur tributary world's J U P I XT E R.:1 5 Liko all the old planlets, the ancients had detltermined with considorable precision tho period of revolution of Jupiter, tand cils relatliv position amongf the planeta ry Aworlds.'The pointas inl his orbit where lh becomes stia tionatry, the arc over whtich ht retrog:lradoes, anl d his period of ret rogradation, woere all pretty well determtrined fromt tho early observations. As we, recede to greatter disttances from lthe sun, tho iare of retrogradation dimtinishes in extent, while te the tim employed in describing thetse arcs must by necessity in-l. tcease., Thiis will becomet evident if we recall to mindt the cause of t iis Xpplrent rut retrotgradation. When tho sun, earth, and planet., ara all on: the same stl:raightt line, the earttt and planet being on the same sidte of tfhe sun, then tthe planet tl is tln oplpost ion. The't. cart -t a nd planett starting frtom l ttis line, as tthe eart1h moves tho swifter in its orbit, at the end of, stay, twenty-ifour ll honr the li~ne joining the cartht and planet will take a. direction such tehat it will meet the first line exterior to the orbit of the planet, as seen below:-............ (). P is the lint on which the three rbodies:are found.l on the day of opposition. At the end of, say, twentyfour hourns, tlt earth larives aEt E' it its orbit, tthe planet at P, and then thte planet is seenl from tlh earth in tho 136 JUPITER. direction E'P' S', whereas on the day previous it was seen in the direction E P S. Thus it appears to have moved backwards from S to S' among the fixed stars, while in reality it has moved forward in its orbit from P to P'. Admitting the orbits to be circles and the motions to be uniform, it is very easy to locate the places of the earth and planet on successive days after opposition, and joining those places by straight lines, we should soon reach a position in which the lines thus drawn on consecutive days would be parallel. There the planet would appear stationary among the fixed stars, and there its advance would commence, as is manifest from the figure below:S ~E n which S is the sun, E E' E" E'" the successive places of the earth, P P' P" P"' the successive places of the planet. The lines E P and E' P' meet on the side opposite the sun, the lines E' P' and E" P" also meet on the same side, but E"' P"' and E" P" are parallels, and in P" the planet becomes stationary, and after passing this point, the earth still advancing, the lines joining the earth and planet meet on the side next the earth, and henceforward the motion of the planet, as seen from the J UT P T E iR. 18 /t eartih must continuo to be dircct, until the earth co3ming rounld fagain to occupy the conjunction li, pL trevious to which the stationary point: will bto.ted, td the rettro-t gradation will be comnunctte d..lhe distance of any planet from the unt, iM terms of the earth's distance, may be obtained fhril a mleasure.tmenlt of the are of retrogradation in a. given timen, s:ay twenty-.four hours, provided we know the periodio time in which the earth and planet revolve round the smu.'lTh1is will become evidcnt friom tlh figure below~.. \....^:....... ~~~~~ ~ ~~.... in wlfich S is tho sun, I and P the places of tho earth and pl)anet on the day of opposition, f' and P' their places at the end of twenty-four hoursi, Bi' and, P' Imay be regarded as straight lines, as they arle very short in comtparison wvith the entire cirumfe rent e. As we ar supposed to 1know the periods of revolution of the earth and planet, t1he distances,' EW a:lnd P' t arc fr:actional parts of tlo whole circumlfrenice represented by one, divided by the numiber: of days in the periodic time. Tlho fractioln for the earth is 3, and for Jupiter it is In th rigtt agl trianglo, FiY 0, we know tlho 1[38 J P:I It. value of 1' 3, and the lingle,' 0 1 eq, tual to S'O S' or the rCtrograda.tiont of thie ptlanect. 1::ence the otllor lparts becomo kntown cith cr by construction or tie simplest processes of trigetonolmtry. \We thtues determint the value of E, 0 and aiddint S 3:, wo hlave the valu e1 of S 0. then in tle triangle S P: 0 we have tlio side, ), just eterminied, also tite an'les P' 8 0 alnd ]') 0 8.. Ifence we can: conlrstruct the triangle, or com-n pute by tritgonometry the other parts,. T1hus S P1', the phlant's distance,:becomnes klnown, Int case the periodic times were accurately knownl, and thet orbits were exact circles, this mode of dctetrmtiinglla the distance of a superior planet would be suffticieltly texct, but by t thl third of:Ke)ler's la ws, wtichl tells us that tlie s8quares of the periodic tites are proportional to tlhe c:ubes of the mean distan.ces, w e perceive that thle entire problew of the planetary distances retsolves itself into fixing, with all possible precision, fro.l observation, the periods of revolution, and tihen in obtaint inig the exact distance of anly one of them. We hatve already stated that the interval elapsing fro.t the )pas.rsage of a planet froml one side of the ecliptic to the other, up toto te same again, gives the period of rovolution, in case we correct for the various changces which may take place fiom one node-passagc to thie next. T. iis, however, in t he c.ase of a planet like Jupiter, whose orlb;it'al ptle neatrly coincides with I the ecliptic, becomt es dilllcult as at matter of observation, antd hence some lc:ttter methiod lmust be emttployed.'This is best acclmpished b.y observing the exact timte of opposition, or thl moment wlhen the planet i 1.800 distant fiom the sun..Thel interval betweenl two such oppositions 1s called a syntodical revolutfion, and in case tho earth did not J u X IT u,. 189 move, would )bo tthe planet's period of revolution around tt te sun. t tehse synodical re.volutions would be all procisely equal. oni the hypothtesis of circular orbits andl equable notions. fBut as the planetary orbits are ellipical, and hence the motions variable, the synodical revotiat'l }:lltd fl O1 8 VttE) tflt Sybeltltl i, bIC) lution:s of any planet, as Jtupitor, will vary somtewh1at front each other in duration. It, however a ltarge ntumtber be counted, say, as many as have occurred in a thou-t sand, or even two thousiand ycears, thoe a mean period is deduced of great taccuracy.'.This is possible, as wIe'ha4rve the oppositions of the old planets, rcco.rded by the ancient's with sufflicient precision to be employed in such a discussion. T..o derive the sidereal revolution from the synodical -we have only to consider that the two bodies set out fronm the ame rightt line.'The earth's velocity is knovwn; the timet required lbr tihe earth to overtatke the planet is known (the synodical revolution). The velocit y or rate of th-e platlet's motion is retquired. This is readily ttund by simple proportion. Take the following example..1' meatn solar day the earth travels in its orbit 0"' 856t, A. mlean synodical revolution of Jupiter is observed to )bo equal to 898.807 solatr days. Bs ut the earthl perforilms its revolution, and comes again to thl startingl poin't in 8t6.5).)(56 days, and then tmust travel for 398.86T.65.t. 5 1.8-.O.6i..: days before overtaking Jupiter. But il 863. I11 days, at tile rate of 00.9856 lper diem, tho earthtt will tlravel about 88' 928, and thtis is the whole distance mtade by Jupiter in 898.86T dtays. H*enceo, thi rate per diem is, ^%8::..4 993.4' 559".2, an d at this rate to travel 860 will req uirle 3 0 ~ 4.882d, 14h,;.' 59.,2, 140 j P X T B i. 2mt, whli1ch is tlo tiime occupied by Jupiter in p).erformilng Ilia re voluttion afrountd the suna These mnetthods of investigation, which aro perfectly simple, wtere employed by the ancients, atd used even by (Copemrntics, Kepler, and others, antd furnished the approximate values of the period and distances employed in the researehes of KIeplr, whereby he discovered hie celebrated laws. Pi}trSAt, CONlXSTi: T TUrONtO 3JUP't'l R.-t. —'4VWhen Cxamt in'ted withl p)owrfui ttl e tescopes the surfiace of Jupiter is found to be diversRified with shades of greater oxr Clos depth, tfrmitn parallel bands or -belts, especially about the c(quator of tho planet, Upon these belts well-defined blreaks, irregularities, and spots are discetrned, by mcanms of whicht it is discoveried that th-e acee of Jupiter, visible at any given time, is colmpletely hidden by rotation oln an axis, at netw taco appetaring at' the end of a little Ict.ss than five hotlus. This gives a period of axical rotat. ion of 91h 65m, 49,Ts., as the resultl of investigations similar to those employed in determiing the period of rotation of Mars. When ttt t apparent dia:iter of Jupiter is accurately imeasured, and his distance is taken into consideration, woe find hi' aetual diamteter to bo nearly 90,000 miles, and his volmtt e to b) equal to that of 1,281 globes such as our earth. Thde tdark belts which encircle the equatorial regions of the planet, and Ywhicht revolve with the globe, 8show tha:tt the axis of rotation is very nearly perpendiculttr to tho pla14l of the orbit. Tlhus we have a pllanet twelve hundred and eightyi. one times larger tthan our earth, rotating on an axis, but little inclined to tohe plane of its orbit, int lesst tian ten htour A II I:4I aANI4 VISIA VIIV........:;:..::..:.:.:.:::::d:::: act;::.. d::.;::..... L. - i^i~i^::si..-:n J U I TcI t. 141 of time, and sweepn g rotund the sun in about twelve of our yeart, at a mtean distance of about 485 millions of miles.'the streaCk and datk shadeas whichl distinguisht the equatorial region of Jupiter are by many considered to be belts of clouds floating in th le atImosphereV of the planet, thus indicating the existence of all thle great ole.xe:Nts whiclh distinguish the earth. I:n cotnequene1 of the ftctt thait the axis of Jupiter is very nearly perpenwdicular to the plane of the orbit, thle sun will always pour his rsays8 vertically on the equator of tlte planet. constituting one perpetual suntmer in all parts of the globe. In case light and heat are governed by the sanme lawt whvich hold on the earth, the inhabitants of Jupiter will receive fromt the sutn only one twentyw-seventhl part as much Elight tand heat as falls on the eart.IL What modifications of hceat rmay Ib eflected by the extensive attnmos phere whl ich appears to surround J'upiter it is inpossaiblc to cotnjecture. We may suppose, without reflection, thit a world would be only dimly illumined whose sun was reduced to one twenty-seventith part of that which lights or earth l.. s, however, is not the case, as atny one will crecdit who 1has ever witnessed the l0ood of lightt poured fortih from the smallest portion of the sun's disk in emergting fro total eclipse. The tamlloulnt of light which dfils on Jupiter fr exceeds 1that witich is poured upon the e. rth on a it oderately cloudy day. When we mea sure rigorously with the mlicrometer the tigure of Jupiter's disk, we find a marlked deviation fromn the circular outline. Thi:s is analogous to the figres of the earth and Mars, and indeed the slame peculiarity (of whtich a satisfactory account, will be given hreatt'tcr) (dis-. ttingnishces all the planets. In Jupiter the equatorial diameter exceeds the polar by more than stx thous(aud tmiles. 14.2 J Tf UP I T:.it. We are indebted to the telescope for the revelation of the hltighly interesting factet that:t Jupiter is tttentded by no0 le.s than four 1t 1oo()0lS or satellit:es, nearly all of theml tlar-ger thant our own moon)l. 1These satellites were discovered by G(alileo in 1610, soon after lit habd finished Ilis secotnd telescope, whi:cht as het tells ts, cost himu incredible pains, and whic}l bore a mbxtlfnifSgtt power of )about thirty times. Ithe discovery of these mlooIt of Jupiter nmay be regarded as amongt the umost imptortant results of the application of the t elescope, if we take into account the then0 existing condition of astronomnical science. Thle scienltific world was just in a. transition state. The most honest, itttelligent, and powerfuil minds lhad already adopted the Copernican theory, but in the universities and other e school s of science, as well as in the clhurcll the system of Ptolemy still reckoned among its supporters at host of learned tand digifited men,'IThe beautiful lminiature of the solar systel.' presenter d in Jupiter and his moons, as give8 n L) Cby opctrnicus, coult not fitil to exert a mos1t powerftl influence over all clmndid and uipretjutdiced minds. lere wars prelsented to thle eye a central orb and about it a schlmne of tdependent worlds revol vit' g in citrculayr orbits, and with suclh elertgant siemplicity as to shamle the cumbro0us complexity which distitlulisLed the tpicyclical theory of the old Greek sethool. It is noti at atl surprising tlhat Galileo, the discoveret of t.}iis bean lutiful syt, syst.m l should lhave become one of thIe most.1ar dent slup.porters of the doctrines of Copetrncus.'Itt' eso satollites of Jupiter revolve in orbits whotse p)lane s are nearly coincident wit t t ihe equator of tleir pr imalt'ry.'Thet exterior, or most distant of tIle fiolr, revolves in an orbit solmewha1t incllined to the plane of Jutpiter's cquator but the three inmer satetllites, at every J Ut 1 I T' R, 148 revolution, eclipse lth sun to the inhabitalInts of Jupiter, antd are tlhetmslves eclipsed inl tpassting thlroughl the shadow of their pri'jiary. Tilhe slamte fpllases which mark the revolution of our mloon are also exhibited by Jupiter's moons, und tthe periods of revolution of three of the satellites are so adjusted tlht fone of tthem must1 he full when the othler two are tnew. The nocturntal heavens, a fs seen from this grand orb, must be inexpresibly'magnificent..Besides the slame glittering, coustellations whlich are seen from earth, thet sky of Jupiter may be adorned with no less thitn ftur mtoons, with thefi diverte phasess, ome waxingt, or ( wanting, some just rising or setting, some possibly tjust entering into or emterging from eclipso. lThe whole of this splendid celestial exhibition, sweepim.n ac-ross tehe he averns,'rising, cultdminatint', and settingt in less thantt fivte hours of ou time. Such} arci the scenest witnessed by the inihabittants of J upiter, if suchI tlere be, t.HlK: i Al'trTI.-.l:,;S SOF JP:.......... A. already stated, thec;se tributary \-orlds wtere discovered by G(tailco in.610, On) tlthe eveling' of Januarltytt the Sth of th at.t )Sye havirt ug eoipleted his second telescope, cttpabl e of }bearitn a magnitt. fyintg power of thirty times, ht0 went to hIs garden't ito t at it qualj'it y by an examinationl of J'tupiter. 1.Near the pltanet lhe noticed three small stars;: icarly in a stdraitghlt litne, passing o throgh the ce.nterl of,Jupitr. Hte stup posed thltem to be fixed stars, but ca.refully noted t}feir positnions wit lt reference to Jupiter and to each other. On. the:itllowuigng night, lhe rettmarked that ttthere was a. imanliJest, chttlange int thoe relative places of tlhese stars and the,planet wthi'ch could hardly be accounted ior by tho motion of Julpiter in his orbit. (Gialtileo began to suspect tlhe true nature t of the stars 144 J U P I T E i.t which lad attracted his attention, and seeing clearly the immense imp)orttance of such a discovery, aNwaited with ~great impa.tience the comrling of tho next evenin' to conll firtl his conjectures. Clouds, however, coming up dis.. appointed hiis hopes, and it wavs not unt1il the eve-ning of the 4thIl that te was atgain permitted to direct his telcscope to the planet, when lie found, to his great delight, not only the three stars, still in closo proximlity to the planet, but lie also detected a fourthl one, whose appearance and position were such that tle auttlOtn1nced at- OllCO the discovery of ftour moons resembling our owi, and reovolving about the planet Jupiter as tlhir central orb. Ih is announcement createdt the greatest excitemlent in the astronomicatl world. Its tefect on the old theory of astrolnomy was at once perceived, and the disciples of Ptolemy determinedt that they would never believe in the exisltence of any such pestilent worlds. Sole of them factually refused to do so much as look through the tube of (Galileo, declatringt the whole was a deception, and un-. worthy the a-ttention of a true philosopher.'The discovery was not the less real because its truth was denied, tand to this importantt addition to tthe bodies Iwhich constitute our systenm modern science is indebted for somle of itS most elegtant discoveries.'Thae great distlance at which we are compelled to exanine the.se bodies has rendered it difficult to obtain, even with our mtost delicate instrumentts, satisfactory t measures of the ditameters of these satellites. A.pproximnatte tmeasure's lhave }been obtained from which wee learn that the nearest satellite ha. s a diameter of about 2,500 miles, tho second, 2,068; the third, 2,87; the fiourti 2,800 miles. We namte them in the ordert of thit distances froin tie primary. J U PI TE It. 145 B3y careful measures of the edongatiotts, or greatest dista.nces to which thee bodies recede fioomi their primary, the tatittd and t f'irm of their olrbits lttave bccee well detterinintcd. ^hitc first satellite is thus Xltund to revolve (round Jupiter il Al orbit nearly circular, whose diameter is 260,000 miles in a: period of Id. 18h. 28m. The plane on which the orbit lies is inclined to the plant e of Jupiter's orlbit under an a ngle of 3" 05' 30", or less, by nearly onte-hall, thlan thle ingle made by the rtoon's orbit with that of the ea.rth. The smallness of this angle, the nearness of thoe satellite to its primary, the timmense mxagnitude of the primary and the distance from the sl:tin, combine to produce an eclipse of the first satelltite at every revolution, while, in like mannmer, an eclipse of the sun takes p>lac te quite as frqucently, friom thte iaet that th e shdow of atellite tils onl thie planet at every conjunction of tl e satellite with the stun. These s taterents are not mere conl ctures. They are verified by the telescope, for these eclipses of the sateilite and thte shadows cast on the primary atre distinctly se(en from tho earthl, and ftrnish the datat whereb'y the periods of revolution are dete.rminted with great precision. rWhetn Jupi. ter is in 0opposition it often occurs tlhat the satellite whle oil tlhe itiler side ot tih primary, is seen plrojected on the di8k of the planet as a round. bri'ht spot, wIi le the tshadow of tIhe santet bodyy m:ay be steen t ill close proxinmity Ias a rountd black spot. Any eye, tituatcd within tile limiittos of this shadow, willl witness an eclipse of the stun precisely siuch as is produced on c-rtht by the shadow of the m toon. The passage of th e satellite across the disk of ttJupiter is called ta transit. From this position the moono of Jupiter revolves round half its orbit, and thien by tne(cessity passeis across thle cone of shadow cast by the 1:46 J U P I T " REt. primaryW in a. direction oppositc the sun. 1. cer we behold an clipse of the secondary, as its light is cxtimnguished on entering the shadow, and is only regatined after passingt beyond the limits of the shadow, thus do-e monsl.tratin: g beyond ra doubt the ftlet tha:t, like our moon, these secondaries of Jupiter shine only by reflecting the ligtt of the sun, In case Jupitor were at rest it is evident that the o1bservations of these eclipses would give the exact period of revolution of the s:atellite, whicht would be precisely the interval from one eclipse to the next. Tr1he fact that the eartht i is n motion would not affect the time of recurreonce of the eclipse, for this would be entirely indepelndernt of the place of the spectator, p)rovideld hoe sees the disappearance of the satellite at th:e moment its ligllt is extinguished. It is imanitfest t that the lmotion of Jupiter in his or.bit will chalnge the p)osition of tle atxis orf the shadow-n, and a.s the satellite revolves in the same direction in which the shadow advances, it is clear that the time lrom one eclipse to the next I iilonget r tltan thet true period of revolution of the satcllite, by a quantity easily cotmputed frto the knovwn orbital velocity of the planet, as may be seen fi8'o the figure blow, where...l — S................. A I`': ~~~ --- ~~~~ —- ~- JUPITERI. 147''.i *' 1 -r r ni opp1 4 S is the sun'S place, t, he att eartl, Jupiter in olposiioln M, tlhe satelite in eclipse. At tthe end of one exact revolution of the satelliteC Jupiter Ihas reached J:', the satellite is at M-, but the axis of shadtow is ntow AM/ and the center of tthe eclipse will not occur until the satellite reaches Att l", passing over the angle M" 4t' j'. Tlhis angle is precisely equal to the angular motiolt fromn eclipse to eclipse, at quantity easily determined. Tf'ho satellite will then revolve 8G60, I.t the angle J S J', or..' J ~4", in the intervtal from one eclipsc to the next, hence the rate per hour becomes known, and gives at once the period of revolution. Galileo devoted himti.self for many years to a careful observation of the eclipses of Jupiter's moons, and finally constructed tables whereby these eclipses might be prot dicted witit tolerable precision. I is s8 uccCsesors devoted inuch time to tohe satme subj ect for a reason we will give hereafter. Long study of these phenormena revealed tlhe curious thct th.at the interval firomt one eclipse to the next did not fullil the prediction batsed on the tforegoing reasolning. Tho place of the earth seeced in seome mysterious way connected with the t.ime at which the eclipse occurred.'This may to some appear very reatsorable, but, in act, on the lypothcesis that at the moment of the extinction of a: luminous olject it ceases to be visible, the platco of the earth in its orbit or the position of the observer could in no way alkect the mnomenlt of the satellite's disalppea. rance by entering the shadow of its prii:mary. This will become tmanifest fi'rom a very simple illustration. Suppose the per0sotns in a large circular hlall to be gazitng. on the light of a taper, and the taper is suddenly extinguishecd by being blown out, every observer will certainly los0 the light t the same absolute momentl admitting 1.48 J J P I T;: t,. the fact that the liglht dies at the instantt of extinction to every eye, X.Let us apply this illustration to the eclipses of' Jt'niter':s Inoois. The.ly are only seen wheln the stnlight itll:s oni themm. Cut of from te:tl the snllig}it by entering the shad ow of the primary, aid admnittili this ent:ran'ce to be instantaneous, everly Cye3 everywhere should lose th t te Si t at t ame nmoment of absolute time.'thce carth's position in its orbit oghttt, tltrcetrc, to have no eftict on tthe time of the eclipse, and yet t et.ctame clearly mlnitnittst that the carth's place was in some way connetetd with certain ilrreuflaritries in the intervals of these remote eclipses.'tlhis matter will be best illustratedt from the figure below, in which S represuets ".i the sutn, I' 1X' 4" W"t the earth's orlTit,, J tupiter, and8 tS the satellite. It was foundl that whin the earth was at 14, or nearest to Jupliter, the interval from eclipso to eclipse grew longer as tlh earth receded from J"upiter. At 14' the interval was at a rmaximum. It now diminished by slow degrees, becoming nearly stationttay iat 1\" then lrownl shorter, reached a. tlinillumtl a:t.l}', afte which a slow increase was noticed up to 1i, and so on in every revolution of the earth in its orbit. 1)ue account, of course, muslt be taken of the orbital J UP.T t; T R. 1t49 movement of Jupiter. I:n case the student is ignorant of the explanation of these variations in the synodical revolutlions of tie moon:0s of J upiter, he nmay test hils ownT powers of discovery }by a close examinalttion of theo ttacts ias albove presented. All the satellites gave evidence of the same faets, and the irreularities were fiound to bfllow in the same order reaclting their miaxima,'mini:al, and stationary poilts aIt the same time, or when tit earth was at the same point of it; orbit. Moret ttthan fifty years passed a( way without any satisfactory explanation of the fiacts and ptheti nomen:t above re.corded, when, in t1675, itemet r was at length successfiu in solvingt thie miystery, and tfund it due to the ptogressite,mot/ion f lightf, which up to this timle hadlf been conM.sidered by all lphilosophers as instantanettous in its eflbets; that is, if a luminous body were created, all eyes, 1no nmatter how remotely placed, would see the light at the samtte moment of time. As tee t velocity of light, deduc(e fromn these investigations, is so enormous, no less tlhan 19(2,000 miles in one second, we will enter into tho explanlation somtewhat minutelly. 8uppose a luminolu body, as in thite figure below, at S, suddenly to be cxtinguisihed the stream- of light flowing froml the body is 6' At. B at once cut of; and wIhen tho last particles or wave passes at spect'ator at A., att that tmomenlt l.e will mark the ex. tinction of the ligtht whIile to the spectator at IB tho really extinct luninolts body will re)main visible uYntil ttho lastt partictles of thte stream of its light pass 1B, and then the bodty vanishes to the speetator at B.' Suppose the body to thus dtisap)petar periodically, A aln B wi ll, whilo 3150 J U PIT ER. they rematin stationar'y, note thot intervatls froml one disappearance to the ncext to be precisely equal, and thl:e inl terval, as observed by A, though begininingt at ain earlier absolute mloment of time, will be equal to the interval, as observed at IB. t-, Lot tt now suppose, that after a, disappearance, and before th:e next, A removes to 1, it is maniettlst that the duration or dpeiod whose blegin:ring was observed at A, but whose endinrg was noted at Bl, will be longer than it was before by an amount of time required lor the stretam of lig(ht to pass from A to B. Tthe reverse would be true if B changed his position to A.. Thtes principles are precisely applicable to the caso under consideration. If the earth's orbit were at straight line, with a length equal to A B, the conditions would be identical.'. Th.e nearly circular figure of the earthl's orbit produces the variations already noticted. Wlhen the earth is rapidly recetditg from the source of light, the durantion of the tsy nodical. revolution of Jupiter's mnoon will Ibo increased by thio time required for the light to pass over the space traversed by the earth during the synodic revolution. Trhis. period amoun1ts to somet seventeen days for thlo fourth satellite.:3But the earth tratvels somel 06,000 miles an hour, or in seventeen (days nearly thirty millions of miles, so that th h synodical revolution, twhen longest, will exceed the same period wthen shortest by an amountt equal to the double time required by light to travel 80,000,000 of mxiles. t-tis difflrence between the m)t:ax1itimul andt minimum synodic periods, proved to boe about five Ilinutes, an1d hence it became evident that light l yust fly at the rate of sixty mtillions of' milcs in five minutes or 12,000,000 miles in one minute or 192,000 mniles per second. Should this result appear incredible we shall find J U P t I tl it. 151 hereafter abutindant confirmat0ion of its truth by a train of retasoning and pliettomlnina enti'ely distinct from wvhat haetv just been given. Int ctasc light. ttravcls with at finite velocity we cannot fail to perceivo that this fact will introduce important mnodificatiolns in all obs1 ervations designed to fix tth places of the heaven-ly bodies at a; given moment of time. inco, the earth is,swCeping through space wilt great velocity even th6is fact will produce at certain displacement in tho altpparent 1place of a fixed lumi-nous Ibody. When thlo body under observation i8 in motion, tho velocity of liglht being finite, it ist clear that the light whicht fa:ll on ttho eye of the spectator, and which enables:him to sec tho object, is not t l t itt t the lit eitte tle moment the object is seen. Tins, the planett Julpiter is distant from the earth, say, 480 millions of m1iles. To t travel this distal.neo hiis light lmust occupy no less thtan forty m1inutes, duringl which time tJupitor has advanced in his orbit about onethird of his own diameter. During tie same tam time the earth has traveled in its orbit a certain distance nearer to or furth ier fiom Jupiter, wh:iclh must be taken into account in our efflrti to fix thle absoluto position of tle p ctlat'a center at a given:moment, This subject will be resumed when we come to consider the means and instruments em.1ployed in astronolmiead observttion, The satellites of Jupiter have firnished, in their celipses, the earliest miethod of resolving the great problem of'Ta MinE STrAL LON(1 lDiT ) -.t..t t c positiolt of any place on the earth's surlatce is detecrl-lined by fixingi its distance tfom- thte equator of the earth north or southl, callt e the latitude, and also its distance east or west of anly give meridian line, called the longitude. The first of thleso elements is very rdiy e ly deterlined. In case a place iis 152 J U I' I T.situated on tho equator, its hatit:ude i zero, taid to any spectator at this place, tus awo hlItav already shown, thlo poles of tho earth and heavelns will lie on-,t tho0 hitizoi n. L. eavit n the equatttor and traveling due northe along a mir.iiain lint, t 1 br ever ty degtree we wgo nIorthl it is e:videntl thoe pole of the hIeatvens will ris oe de dge:tabove tth horizoln; and whien we reach the northt ptolo of t te cartIj t the north ptol of ti:e heavens will bo on the zenithl or ninety (dirc:et ahove the horizon. Thus it. appears thatt the h/ttiltude of any place is etqutal to i/te ca ctd.a/wit of t e pl/ole abovte /the horit:zonl o' Ilte p/tace, and to fix tht latitude we have, only to imeasture t:iis angile of c elevation wit t a suit able in strutmenlt: and ailpply certlain: ctrrections, to e.lhereafter explatincei. ItIe.pro')dblem of thie lon/i.tdae does not admit of so easy a solutlionl, o dc.ttoit ino alccurately lot,ittude at sea. is a mllatter of tle 1 tihces.t importlancle to coemrnieco and.l a vi gation, at problelm itr l whose solution martt1itimle nall t:ionls.:a.ve i.n modern tlitnesli ofiered larg:e re wxtarlds. Th satety of at essel its crew and car1 o t, depen tds on le tarn)in g y sorno metlhod its exact position ont the sit [e of tIhe occ an where there are no permtanent, oi)jc{(ts o o our globe to )mark its place; and it. is only ftlom thle celestial spIhereo thatt it itbecomes possible to select fixed objects w tich ): may reveal to t n r the m ariner the dangers by whr licl h is sui rou ided.'TIho latitude, as w'o have seen, is readily ottalintd; not so the longitude, whichl had, up to time o:f G6lileo teen regarded a. alt ost ant:t impossible prob lim at (sea..Thl great F.lorentine astronomnt er staw in thle ct:lii:tes of }tte m Joons of Jup iter the means of solv\ing, this l:ittily imlportanit problemt, and to this end the devoted matny years to most dtiligcent atld careful olbservamtion of t hese JUPITER. 153 eclipses, with a view to be able to predict their coming, months or even years in advance. We will now explain how these predicted eclipses of Jupiter's satellites, conjoined with their actual observation, may be employed in the determination of terrestrial longitude. As the earth rotates on its axis with uniform velocity, the 360 degrees of the earth's equator are fairly represented by twenty-four hours of time. Thus an hour of time is equal to 15~'of longitude, a minute of time is equal to 4' of longitude, a second of time is equal to 4" of longitude. The difference of longitude, then, of any two places on the earth's surface is nothing more than the difference of local time, for a mean time solar clock marks Oh. OOm. 00s. when the center of an imaginary sun, moving with the mean or average velocity of the true sun, reaches the meridian of the place in question. A place west of the first one will have the center of the mean sun on its meridian later by an amount of time equal to the exact difference of longitude. It is clear, then, that if any phenomenon, such as the sudden extinction of a fixed star, could be noted by two observers in different places, each will record the moment of disappearance in his own local time, and an inter-comparison of these records will give at once the difference of longitude between the two stations. Suppose it were possible to predict that the bright star Vega, in the constellation of the Lyre, would suddenly disappear on the first day of January, 1870, at Oh. 00m. 00s. mean time at Greenwich, England, this fact being known and published, vessels at sea on long voyages, in all parts of the globe, having the star above their horizon, by watching for this phenomenon, and by noting the moment of disappearance in their local time, -* 154 J U P It ER 1'E. would detormino their longitudo fr'om (Greenwi'ch. A. 11 observers recordiu.ng the disappiearanfl bctfbr thl ptrodieted tim-n would bo in cast lomgitude, while those recordinjg the same ithe nomeno n lalter tlhan tih pIrdicted tim-e would bo in west longitude, and as mlany lours, minmuttcs atnd seconds west as wa\s indicated byi their local time..Now, at sIea, very simple methods, as wI shall show hlcreafitcr may bo elmployed to obtatin the local time, atnd thus, wore it possible to predict a multitude of such pheltomtnaet as above recordedl occurring every day or two, fior yearas in advance seametin o long voyages:.) p'rovidingll th1cmslves with t hose predictions, would lhave the lmeans of fixing: their longitude as often as anty o0ne of thosoe prt-. dicted phenomena., cotuld be observed, Tho eclipses of the mtoons of Jupiter are precisely like the pheltoientto:it of thie sudden ext-ictiot oft at star.t As thl-so moo nis shine ronly by reflected light, tihe moment }they cu'eter the} st4hadow of their primary they vanlish. filom the sight or are, to all intents ant d tt rptoses, l xti,guished; and as theso eclipses are constantly re'.curringt tat; very 1short mitevalNsGalileo saw at once t]he use to whttih they mightl ble devoted in the resolution of tinis great probleir of terri''slrial lof/ilt'de. Be:fi:ec they could bo thus used it becamtie iececssary to miaster cornpltctely their law1s, so that; tlhe n0momenit of etolpso tt ight bol accutrate ly predi tet 4 yiars iini advtltc'e. Tlu-loug th e ti uscan philo.siopher didl not live lot, 1 e lou.t lg to perl:e at and apply his itre-at dis coery, his suesettc os. rs in:ttmodern times hlavte fully ctarrietd out tnd tapti lictd wllat \was so admirlably cncei ved altd so0 c arefully coi('1t men tccd, Ant attentive exaiinination of tho luminosit)y of Juipi J utp i T E it. I 155 ter's moons00 reveals t1he curious iftct tlint it it fs f'riablet incr g and deas i nng at Tregullar intotrlva.ls, equal to tho periods of revolution in their orbits, whence it h:as been inlferred by Sir Willialm Xerschel and others thlat each of these satellites rotates (like our moon) upon an axis in tho exact time in w:ch liclt t revolves about tho lrilmary. SBATU) RN,,THNJ SETfVtNTtf PIFAN1ET,IN TN'1 t1)RDElI' OF BISTANCE1, FR.,OM TIX E SUN, SURROt )EDtf)'I Y CO)NCI'NT'RIO It:N(GiS ANi) ATTNI-NIED BY -iF T A'SATEI:, tTES. T'1: M.O.s ):sT DISTT or'*tt' 0t, PLD AN,,x:r.,, —IS l,rT:AIN- T, I',C:t)'.' —"V 0' O1I. 1.k''ti.'I' ION.- I' 1 1. 1: I FO',.'' 1ION. —. A D~/' NU IN TK., Oti:t t (.rn VI } t s::)o',...,:' AN OIC R8 S,-V't,: f;.~ I.t.',1: N t 1t3 N:'- t.F I 11(:N$ t o'N tt,'ii'BS Vf; IIN fI. }:ttON OF'.i1; Ji N1.. i..S.'I' ) Two. —-— T N ) sL.itN AN. - T11E. NI, T'1t',l: BNEI 111N1....'111 (1'A:, ii AN t1D 15 Ult 1m SlSutno o1A r11.It', AN);ir ON'Il-; 1: IN.- 1Ns — T ATN'lD SPO's. — -P1.^Ot OF i. OtOr-91' i O1 1. fANtF' AND NIN.-X'1A1rA1ANIs 1.0'F0'lIK KING Ex0 iA INFOF'1XtiM )S! Y Ky ftINO,'Pi}l:1t }1I- IAt c N'I51 AI, NS ) 111i,.ItD)S,~ —. -S —\'N I.; N-iS N I$ (. i it. B1 tA NI' -.'}(}.'tY OIN F'11t1 P1.,lAN.S"AgY SYi'StT, AS 1}'NO\WN''iA(.'N'1}1N i\. Cl-:S.N'N t:t now reach, in our out twatrd journey frot tlhe sun, the 1mot dist3ant world known to the ano inits, rcevollving iln an o.rbit of vast tmagtitutlde, and in a period nearlly thirty tirimes greater than tha t of our earth'. Saturn, on account of his immense. distantce, shines with a fa:inter light than either of the old planets, though still a, con.spie,:uous object amongl the fixed stars. lts. light is rent artal)ly steady, wvithout t-he scintillati0ons which dlis.tillrit is}t tfe t Istars, tad the brilliant glare which is shown by Ve0nus and Jupiter.'lhe're is a yellowisit or golden thue to this planet which is not lost t when seen through tlie most p)owerfult telescopes. Such is the 1planet Saturn as known to the old astrono1efrs, land as seen by the unaided vision. Its movement SATURN. 157 among the fixed stars is distinguished by the same phenomena which we have found to exist among all the planets. Being the most remote of all the old satellites of the sun, its stations are the best defined, its arc of retrogradation the shortest, and the period employed in this retrograde movement is longest. From observations made during opposition, and by trains of reasoning identical with those laid down in our examination of Jupiter, the periodic time and mean distance of Saturn are concluded. Owing to The very slow motion of this planet in its orbit, the earth will pass between it and the sun, or bring it into opposition, in a little over 378 days; that is, Saturn and the earth starting from the same straight line, passing through the sun, the earth makes its revolution, comes up to the starting point, and then overtakes Saturn in about twelve days and three-quarters. The earth's period must then be to that of Saturn as twelve days and three-quarters is to 378, or as one to thirty, roughly. This determination is a matter of such simplicity that any one, almost without instruments, may make the observations which give the data for the computation. The opposition is observed when Saturn is 180 from the sun, and we have only to count the days from one opposition to the next to obtain the synodical revolution. Such were the few facts known to astronomy touching this distant orb prior to the discovery of the telescope. The immense multiplication and extension of human vision effected by the invention and improvement of that instrument is in no case more signally displayed than in the successive revelations which have been made in the physical constitution of Saturn, and the extraordinary 1538 SAT U ItN.:tappe)Ldagcs and estehcmo of dependent worlds now known to revolve atrountd }int. In 1.1.0, the year in which Galileo first applied the tclescope to an examination of the celestial orbs -A.thi year int whicht ht. annllounced the (diswcovery of Jupiter's Imoons-.-. an exaSminaition of Sa-turn resulted in the stralnge land ano-malous discovery that his dis k was not circular, like all the otler plantets, but elolgated, as thoughl two sinaller planets overlaid a larger central one extending somnewhat to the ritght and left of the center. Th.lils'remarkable fitgurle Galileo announced to h'is.' tatronom'ical contentipotrariesi under the fiotr of a l)puzzle produced by a ttranspo'sition of tte Latin sentence'.Alt:issilnmum platet-a tergenimumi observaxi.' {' 1 have observed the most distatt of all the planets to l:e triple."' Tl.his t.mode, of presenting the discovery was adopted by the Florentine astronomer to establish hlis pririoty, a. ilany of his greatot discoveries were claimhed by some of his opt)ponentsl while the truth of all was most obstinately disputed by others. lIt was urgtled, even in the etas of Jutpiter's mtoons, tt tt these were mere illusions, the 1off. spring of the heated imagination of thte iambitious philosoplher', andl that oter e yes could never verity these pretended discoveries. We can readily imiagine whlat must; ihave. been the feelings of G(ailelo when, snot many lmoths atfter tlte discovery of tth triple cll0haracter of Saturn, ho'wa8s compenllced to acknowledtge( that, even as seen8 through hlis mtlost powerfultf telescope, the planet was exactly circular, with an outline ats sharp and plerfect as thatn of Jupiter. ItIc le eaims, tan:it be possible so)tie 1demont has i nocked me "' lile did not live to explain this re 8 A':. t N. 159 marktablh cllehangoel, tut he st tiple forip restor edi, t:and dBiscovered thoso periodical traunsimutatitons of figure. Fifty years latrt, in 1659(, lttuygcns, witlh mlore powerfiel telescopes discovered the true figure of Saturnl, and foiutnd the triple' f/ rmi see by G(a.ltco to b)0 produced )by t the t that the round planet was encircled by at broad tlat ring of immenset diameter, and so situated that tthe specetator on the earth can never see it in a direction perpett ndicular to its planoe. 11 enco, although circutlar in form, the direction of the visual ray gives it an oval or elliptical figure. Itygenl distinctly per ceived the dark spaec intervening be.tween the body of the planet and the rint, rigltt and left, whict had escapiedI thle eye of Galileo with a less perfect telescottp. Ilentce, the!Flotrentine astronolmer only saw the planet elongated,.an d pronounced it triple, iHuygcnr explained the mnys-. tcrious chtangt of figure whticlt had so tprple:xed G(alilco, and found it due to the itact thait the ring is extremely thin so thin, indeed that when the earth chances to hold a place such tha:t thle plitte of the ring produced passes through thhe earth and the ring comes to b6t p)resentcd to the s'pectat(o'r edgewise, not even the t:elescope of It: u ygettnsl could discernt the fibre of ligit presented by the rimn ort circumferne ct of the ritng, when t tus located, and to themll the disappertantee was complete, leaving the planet rontd, lear, and well-defined, titn 1665, w at had hitherto been regarded as onlo lirtat, flatl rin-g-, was obserItvedt to be divided into two pot.tions by a. dark line which, under fit\vorable circunt.tstances, was traced entirely roundll the ring. T'this discovery wa coifirmcd by the heldcr tCssini, int I: 75T who also disc.ovcred theo unetqual brilliancy oft tdoe two rings the outer one being thie brighter. lie also was the first 160 S AT U.N, to anrou t existnce of a dark stripe or belt surroundint the equator of the plantet. Other discoveries, such as additional belts, the shadow of the planet on tho rinj, tte shliadow of the ring on the p)lanet were succcs8 sivcly tlade,as t e te powers of tihetelescope were imp oved, )tDuring the present century miany astronomers assert tho multiple division of thle rintgs of Saturn, and the evidenco is so conclhsive, that the existence of dirk lines, concentrio withl the rin':,s (anld like that whilc severl s the t wo prin-. ciptl ring canot be deniedt, t hoh togthere is every rea. slo to believe that tthese lines are only to be seen occasiolnally. With the full power of thie refractor of tlh (Cainnati )Obtservatory, defining in the most beautiful manner all the other delicate characteristics of Saturt and hlis rings, i have never been able to perceive any trace of any other thant the principal division. lThe bright and datrk belts and certain spots, whicht mark both the surfice of the planet and the ring, have furniis1hed the means of fixing tle period of xrotaition of (the planet on its axis at l0h. 29mn. 16.8s., while the ring revolves on an axis nearly coincident with t1ha't of tth planet in lO. 82n. 1..5s. If we reflect on the structure and position of Saturn' rings, ttie pienollmena attenlding its disappearance and reappearance become readily cxplicable. Tie plane of the ring rloduced indefinitely, iterts.cets tile platne of tIho arth's orbit in a straight line.'Th.istt is calledt the lize of,uodes of the ring. This line of nodes, relailling ltetrly IaralEl to itself, will t itel anifeitly move as the ring mnoves. carr ied with the pflanet in its revoluttion round the t;unt. )turing olne-alrt of Saturn's revolution in its orbit thet smun twill illumine the northern sido of the rings, duringI the other haltf it will shine on the southern side. z z z--- ~ ~ ~ ~ ~ ~ ~~ ~ ~~ ~ ~~ ~ ~~ ~ ~~ ~ ~~ ~ ~~ ~ ~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~ ~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ —-- A T I t N, It t1 T.lhu the ringl, carried by til planet, will fitally come into a: position such t.tt: tht te sunliglit will Ptll on ncitllti side. but on the edge oft the rin.f only, and whent in this position it is 1manlitif.st that the plano of the ring passe.s throxugh thl-e sun. I1f when in this position, tith catrth comie betweeln Saturn and 1the sun a spectator from) the earth's aur'fae will behold the edge of the ring, if visible at all, s a deliate li:ne of litght extendiAtg beyond the disk of the planet, tand puassing through its c ntter. The 1earthl, cxnmo.lving forwardi in its orbit fr'om opposi-.i tion of the planet, will pa1ss tthroug t h planet of tile ring, anld upon the non-illumin.ated side. A Satur moves very slowly in comparpison with the t ac th, whilo the plane of the ring is sweeping fr'om the one side of t}h sun to the other, the earth may pass more th;tan once through the i:plane of tlo ritng, rTpeatttinltg in somet stense, the phetnomnton of disappearance. As Saturn's period of revolution extends to nearly thiry,f of our years, during oncte-l.lf of this period the inhabitants of' th.e carth will behold one side of the rinlg, and during the other hatlf they will look upontt its opposite surfaceo. All the changes fromi the greatest opening of the rina, wlhen the pl:aneCt is;seen like a tmagnificent golden ball, engirdled by its ring of golden lightIt, down to the total disappearance of the ring, require tatbout fifteen yeaXrs. Thenl the reverse changes occur, and all the phases and transmutations are taccomplished in atbout thirty yetar, when0l they are againt rcpeat-ed in the satmel order. Thei distappearance of thte ring, whilch took place in 188, was wattched by the author at the Cinciltlnati Obh)servatory with the p owerfuil refractor1 of t hat;l institution. A. minute fitbre of light iremtained clearly visiblt even when the e of thet ringo was twurnted directly to the 162 SATURN. eye of the spectator. The delicacy of this line far exceeds anything ever before witnessed. When compared with the finest spider's web stretched across the field of view, the latter appeared like a cable, so greatly did it surpass in magnitude the filament of light presented in the edge of Saturn's ring. I had the pleasure of witnessing the phenomena so beautifully described by Sir William Herschel, the movement of the satellites along this line of light, "like golden beads on a wire." This is a consequence of the coincidence of the planes of the orbits of these satellites with the plane of the ring; hence, when the ring is seen edgeways, these orbits will, in like manner, be seen as straight lines, coincident with the line under which the ring is seen. To add to the extraordinary constitution of this wonderful planet, another ring has recently been discovered by Bond, of Cambridge, and by Lassell, of Liverpool, more mysterious, if possible, than those previously known. This ring lies between the planet and the bright ring, and is of a dusky hue, and only discernible in powerful telescopes. Its outline is the same as that of the other rings, with the inner edge of the smaller of which it seems to unite. This extraordinary appendage is so constituted as to reflect but little light, and is sufficiently translucent to permit the body of the planet to be seen through its substance. I have frequently examined this dusky ring with the Cincinnati refractor, and have sometimes been confident that its breadth at the extremities of its longer axis was much greater than that which would be due to an elliptical figure concentric with the bright rings. Knowing, as we do, the distance of Saturn, it is easy, from the measures of the diameter of his surrounding SATURN. 163 rings, to compute their absolute dimensions. The exterior diameter of the larger ring is no less than 176,418 miles, and its breadth is 21,146 miles. The exterior diameter of the second ring is 157,690 miles, leaving a chasm between the bright rings of 1,791 miles across. The breadth of the second ring is 34,351 miles, and the interval between the planet and this ring is 19,090. miles. The thickness of the rings is a matter of conjecture, as it is too minute a quantity to be obtained by any means of measurement at present within our reach. Sir John Herschell does not believe it can exceed 250 miles. A single second of arc, at a distance equal to Saturn, subtends nearly 5,000 miles; so that a bright globe of 5,000 miles in diameter, removed to Saturn's distance, would be covered by the smallest spider's web stretched across the field of view of the eye-piece of the telescope. In case we admit the rings of Saturn to be 250 miles in thickness, then, when seen edgeways, the filament of light seen reflected from the outer circumference is only onetwentieth part the diameter of the spider's web. We pass now to an examination of the SATELLITES OF SATURN.-The largest of these satellites was discovered by Huygens as early as 1665. Four others were discovered some thirty years later by Cassini. Two more were added by Sir William Herschel on the completion and application of his grand reflector in 1789, while an eighth satellite was discovered by two observers, Bond and Lassell, on the same night (Sept. 19th, 1848), the one in Cambridge, United States, the other in Liverpool, England. We have thus, in addition to the anomalous rings which surround Saturn, a scheme of no less than eight dependent worlds, all of which revolve about the central orb in elliptical curves, and in periods 164 8 A T U Rt., varying from twoenttytwo htour to seventy —ninO days. if tlr celestial scealry of Jupiter is rCndered magnificent by the siplCdor of his fourt moons, wat must be the tamatzint g g'ranldeur of the nocturnal t sky of Saturn, a rcht ed fromt horizon to htorizon by his broad, luminon: s girdle (onl which the shadow of the planet, like tlhe dark Iattd of a mighty dial, will mark the hours of the night), tho changes t p)haset eclipses, the occultataions of his ilunl r-i ous moontss and the brilliant background of glitteritg constellations w\hich gem our nocturnal sky, must altogether form ai display of celestial splendor of which the hutmain m:ind can iotrm but tt falint conception. In consequence of the vast distance at whichi the Saturnian system is removed, adl the magnitude and power of the telescope demnanded for- its- examinationt we are as yet comt paratively ig norantt of many itcts, whicih in the case of Jlupiter's moonst, tav been well deter:mined, It will be retmembered that the moons distance L fro the earth is about 237,000 miles. Three of Saturn's moons fall fiar withint this limit, and the tiurth. is but 248,000 mxiles friom its primary. The fifth ist 3:40,000 miles; distant; the sixth, 788,000 miles; tho seventh (latest dis(covercd), is about 1,000,000 mliles dista:t, while tho eighth is removed fronm Saturnl to a distance of nearly 2,800,000 miles, tlhtc nea.retst of the moons, revolving at a. diistatnce of 1.20,000 miles, circulates round thet primary in about tweut:y-tfwo hours and a halt f presen. ting all the phases exhibited by our tmont, in less tthan a ttirticth part of the tilme. Its dishk as seen fro't Saturtt, will surpas the moon's disk in the ratio of ten to one. Of the fivo earliest discovered satellites, two are read:ily seen wtith any good telescope. lThe1c fiv ay now be 1seet by mtany SATURN. 165 refractors and reflectors of modern construction, while the three smallest satellites are only rendered visible by a few of the most powerful instruments in the world. We shall here close what we have to present of the structure of the Saturnian system. We have thus terminated the examination of all planetary bodies known to the ancients, and have added to these the new objects revealed by the telescope, inclosed by the circumscribing orbit of Saturn. Within these limits we find all the phenomena known to the master minds to whom we are indebted for the vast extension of the boundaries of human knowledge in the solar system. Before we pass these old limits, which for so many thousand years were regarded as impassable, we must render an account of the great discoveries, whereby it became possible to achieve the crowning victories of human genius in the planetary regions, and to extend these conquests far beyond the limits of solar influence into regions of space and among revolving orbs, of which the old philosophers had no conception. CHAPTER IX. THE LAWS OF MOTION AND GRAVITATION. THE DEMANDS OF FORMAL ASTRONOMY.-THOSE OF PHYSICAL ASTRONOMY.SYNOPSIS OF THE DISCOVERIES ALREADY MADE.-QUESTIONS REMAINING TO BE ANSWERED.-INQUIRY INTO CAUSES.-THE LAWS OF MOTION DEMANDED.RECTILINEAL MOTION. —FALLING BODIES.-LAW OF DESCENT.-MOTION OF PROJECTILES.-CURVILINEAR MOTION.-FIRST LAW OF MOTION.-SECOND LAW OF MOTION.-MOMENTUM OF MOVING BODIES.-MOTION ON AN INCLINED PLANE. —THE CENTRIFUGAL FORCE.-CENTRAL ATTRACTION.-GRAVITATION. -LAWS OF MOTION APPLIED TO THE PLANETS.-QUESTIONS PROPOUNDED IN PHYSICAL ASTRONOMY.-NEWTON'S ORDER OF INVESTIGATION. —HIS ASSUMBD LAW OF GRAVITATION.-OUTLINE OF HIS DEMONSTRATION.-ITS IMPORTANOC AND CONSEQUENCES.-THE LAW OF GRAVITATION EMBRACES ALL THE PLANiTS AND TIIEIR SATELLITES.-GRAVITATION RESIDES IN EVERY PARTICLE OF MATTER. THE discoveries thus far made among the revolving worlds dependent on the sun have their origin in a rigorous comparison between the actual phenomena presented in nature and the hypothetical facts derived from an assumed theory. Hipparchus and Ptolemy surpassed their predecessors because, on careful examination, they discovered that the motion of the sun and moon and planets, not being uniform, as had been asserted and believed, they explained this irregularity by the hypothesis of an eccentric position in the central orb, thus enabling them to anticipate all the anomalous movements known in the age in which they lived. Succeeding discoveries, adding to the complexity of the theory of eccentrics and epicycles, drove Copernicus to a new center of MOTION AN () AVITAT ION..GO' mnotion in the sun, and this hypothesis, united to thoe old th ory of tepicycles, wras sufficient to tharmolnize the t}hen 1known fitcts of astronomy with the predictions of scientifio meon. tIn0reased a ccuracy of ob)servation hlowvover soon revealed certain unldoubted discrepancies b)et\ween teh absolute places of the heavenly bodites, as given by instumental observation, and their places as obtatined by computation, and after exhausting every possible expedicnt to restore harmony between observation and contputation, finding it; impossible, Kepler, as we have soon, was compelled to abandon the circular theory, as C opcrnicus before him had been forced to relinquish the geocentric hypothesis. In allt this long lapse of many thousands of years the human minld has occupied itself exclusively with tOh great problem of framing an hypothesis which would embrace all the phenomeinat as preseted in the lheavens It was a question as to.here was the center of mrotion, ntot wh\y it was there; -whiat was lte figure of the )lanotary orbits, -not ifwhy this particular figure existed; htow the paI'.ets deviated from a luniform vlot ity in tlheir revolution round the sutn not?th'y they y were aiccelerated and retarded; thowt the periods of revolution aXnd th. timean distances were relatedt not.twhy tlhcy ert t thus related. itn short, the fiacts and riot thie causes occupied th:e exclusive attention of thle freatt ast. rontomers, until tihe sc'ience of lata, or f/lbrmal C(StiroItny, had reacled its limit, and the mindr,! having exhausted this field of invest iga ion, was compelled to turn its attention to causes or to phi.ysicua astronoory. Let us review and condense thOe fats thus far developed by.orinatl astronomy. 16.8 iT It 1. A W S 0 F The planets revolve aabout tlhei su as their commonf center of motion in orbits whose tfigure is nearly, if not quite, elliptical. Tlheir motion is not vuiform ll ut g:rows swifter as they approatch the siun, and loses in velocity after passing their perihelion or nearest point to tile sun. T-he dimensions of the planetary orbits are not abso. Iutely invariable. Ther ae c slightt fluctuations not to be overlooked in the periodic times and meant distances. Tlhe positions of the orbitts in their own planle are sutbject to perpetualt changel very slow in some of the plal ets, but comnparatively rapid in the moon and in tle satellites of other planets. The inclination s of thhe plnes of the planetary orbits to a fixed planet are also in a state of fluctuation. somel angles increasing vwhile others are diminishing. The lines of nodes, in which the plan:es of the orbits of tle planets ttersectte plae of thlC e earth's orbit, are rnot fixed lines.'1hey are foundt on the whole, to retrogratde, but are somentimes fiund to advance in tte order of pltanetary revolution. Thie mroon exhibits anomalonu.s movements, very marked and well-defined, and iwhich are cvidently outside of her elliptic motion, rising above and superior to the general. law of her trevolution fThe molst considertable of these lunar inequalities amounts to:" 20' 80, b.y which quattity slie is alter-. nrately in atdvance tand behind her elliptic place in her orbit. This mot:ion was known to the anctients, having beeln discovered by Ptolemy, and was treadily appreciable by thelt ilmprfict intsttrumlnts lempl.oye.d by thle (.reek c asirounolme -rs. It is 1 kown as the m0oon's c vcio. A secoind inequalit:y, amoitun tin llt to I l called the Mt 0 I. ON AN. ): GRAVItt A O N, moon's'v aria.io, w\as discovered by the Atrabians, an lbyt Ir thtno Ip.sosterlit y, t tlt s:lhowing tih mX1ootstt mootion acceletrted in tlhe quladrttants of her orbit precut.ity her cottjun tions antd opposi:tions, ao:nd retarded in thle aIlttcIrIate qt:tuadran.l tts, A third lunar inequality was called the ann ual cquationa, a name tladopted to express} the fict that t:he moon1lt -place in her1 orbit is for half a year in advance of her elliptic place, and for the other hatlf year behtind it. The line of apsies or longer axis of t( e }lunar orbit pierifoins ta complete revolution in the heaveils in 3232.5 days. Thet line of nodes revolves round the heavens in 6t)9i3.9 days. T.lte ve.ltrnal (eqtuinox i also int motion, sweeping roundt the theavens in 25.808 years, while the north pole of the heattvens r lf rev ol-e roundt the pole of the ecliptic in th samte exact period. Add o to these flacts, all discovered by obselrvation. and reflection, the ngrand discovery of el that the st.qaresl of the periods of revolution are precisely protportional to the cubes of the toean distances of thJe planets, and thatA this and the other tlaws of tKepler govern the satellites, and we Iha.ve a fair exhibition of the grBeatt truths of/r-ma astlronol y, and it is to llanswer wt t}heso phenotmena, exist tlhat phtysicaltt astronomy has1 been cultivated as a science. "Why does a. planettt continue to revolve about the sut? In case it approacht the sun at all, whly lnot continue that approach until it be precipitated on the seurttc of the solar orb? W do these revolving bodies describe el.liptic orbits with the sun always ill the focuis of every orblit:? Why are thle dcviations foiom elliptic motilon.8 T70'':t iE 1,A IV 0 1o wlat tthcy are? and how comnes it thlat tih ellip'tic lc.. rtieltts are in a1 state of prpel'tuatl flu.etluation? \ l'y do not the planetl fall on tih sun, or fty off ito s)act; or stop motionless in their orbits?''What }lholds the earthl to tile sun, or the moon to tthe earth, so thl tt the.y tneer pa.rt ctmpany, and unitedly sweep:haronio usly roundl the sun? Wha. at bonld unites all the sateclites to their primnaricas, and all the-se primaries to 1one central orb? t)o all these interrogatories admit of a sigle answer, or shall we find these phenomenta to spring fi'ro divenrse origins, antd due to a vatriety of' eanses Bcforte it was possible to colsider any one of' these grand prAobdtlem's it }bcam necetssary to reconstruct the old science of mechai nics or mneehat cal phiilosophy, which was contetlmporattneus with thte (-reek astro nonily of.Ptolemy, and at tih tine of Kepler and Galileo exer ted quit as tlI: )werfi l an. inttluence over the human:i:t rind as did the doctrines of Ptolemy and I'ip)parchus.'eli philos0ophy o' Aristotle was tanuglt in all tile slchools, sus. aittied by the inteliuso imnfluenite of' tptrote'sssionl oirg:niza-t tionl atnd rec ived with a fiulness of confidence a.ndl depth of submission which, so fi'r froio tolerating doubt, actuilally prohtibited inquiry., As the planet;s and their s-atellites were blodies in 7mo.tlion, no tdvaunce could be matde in tile inquiry concoern-. in'g att: lses until the true nature of motion and the la. ws by whic.h it wats gfoverned could bo determined. These -laws could o:lfy ibo reveat ld b}y accurate thought and o-l.t servationt and would naturally be hkindependent t of the causte )l'rodullci 1 tI.he motion.,'Th. mo:st o( t vis exa1mple oft mnotio. is wLhere a t:ea'tvy body is dtrotl ed vertically from any height, antd:tfls towatrd the catrtt. (Ob.srvation teaches the -trectilineal path nT 0 t 0 N ANND ( ) i AVITATION:Il 7T of sulch a fia:lling body, as well as its direction, which is towardt the center of the earth. It was a matter of experiment to deter)mine whether the velocit y was uniform or accelerated, and if accelerated, observation alone could detetrmitne the law of acceleration. All th'lis was quite in.dependent of the cause producing the original m1 otion, tlhe reetilin-eal direct ion, thio acceleration, and the direction towa.rd the ea rtlt's center. Aristotle had laid down the law of falling bodies, and asserted tha0t in case tballs of uneq1uatl weight were dtrop-.) ped at th:e saime momenlt from cqutl elevations the heea vitor ball would movet tit swiftcr, nd that the velocity of tho two uballs would hbo directly t proportional to their respective weiglhts. JIt was easy by experiment to prove or disprove titis statement, and Galileo is said to have given tilo first powerful blowt to the l reek pil osophy, by sh}owing experimenltal ly, (Iby dlroppintg batlls of utiequal weight;s from thle smunrit ofl the laing tower of PIis,) that the velocity of tlh ball, tor the time occupied in thl t111, wttas entirely independent of the weight of the ball, thh etsistattlce of the atmlosphere being taken into account. By meastrin the space passed over by a. filling body in equal intervails of titme, it became possi.bIle to detert - amine the law of, dtescntL. and it was thus ftiund that every fidllitig body plassce tnhrough, say, sixteen freet in theo first secold of its tll.'This is the velocity impressed in tle first second of titme, and were tlte body to mnove o0n with t}te velocity thulls acquirled, it would ptass nit ormily over thlirtyw-two fti: et in tle next second of time. Blut it is found tlat thto ve\locity of every failing body is incrcasd in every secotnd of timfe by the same precise velocity tacquiredl inl thie first second, and thus it case a cant on 1T.2 T B' Xfi A WS 0 F batll were )prqjected downward att the rate of a tlhousand fit:t in one second, it would lnot only pass over' one tlousand fitet, but the sixteen additional fictt atquir.t d by a bodlty:ftilling fi'0o a state of rest would be addedtt to the thoustand feet due to the impulsive force of' the g:aunpowder. Againti, in projicting a. body vertically upward, it was discovretd by experiment lthat t at equal elevations in the ascenttt and descent the velocities wtre idtntical and tiths whatttever might be the eauso retardi: ng tlhe asceldiug )otly, or aecele;ratitnr, the desene(dinta one that case t was f(und to excrt its Lbfrce with a coinstant eCetr, G(alileo w\as the first fhilly to develop tle fitcts al)ove;tated, wlhiclt ftictLs nt-manifestly began to couplet 1mo tion a d vclcity with some mysterious cause of acceleration an t.retardation. Thtlt rectilineadl.notion of fidling.bodies naturally led to thi ifnquiry as to t he lin in wich al btody, receiving a single intpulso, would mt ove, if enltirely firee f:' ro tlne infl1uonce of extraneous forces. A ody om a) gt htl ori-. zontally, at tihe comtnientceent of' its inotion seemed to move in a, right line, but a more rigid examination showed that: (the air as a resistinlg metldilm ottt of coltsidlrat:lion) thle butlllet clmnl(eneted t;o fit.l at tthe itmomnent of its ilightt., and actl ually did 11ll in ote second of' time through a, vertical hteight preciscly equat to t:he space it woniuld have filon tthrouglt if dropped ftiromn the muzzle of the gunt. i ttle, tlhen, was ta. deviation:frout a reetillnetal plath ac-1counted flr by ad(ifittin(g a: ctstant.t deflectitn ltbrc precisetly eq.tal to that Iorce wherev.: e it )ntay bo lodged, or whatever it may be.) \thich prioduces tand ac oele.rates the velocity of Hi lling bodies., As th e right lin is tho most perfect of:: all li'nes; and M TIO N AN ) ] V) 0 G A XV I TATION,:l3,a ulnifollrm motion in ta rigltt line i the simplest of all motiotions, Galileo coeived the bidct thte idn case. bodty receive a sin gl im-lpulse ^ivint a. veloo:ity of 0iany ratt per sccottd t thett th bodt y thus set in motion will miove ofi witth untiftorm vetloeity iiy a: sitrai'lt lio, holding the Hdirection itn whic the imp}ul se is applied1 and will thtus lontilnue moving for ever, unless some force o r power he exerted to chane thl te direction or to destroy tho velocity. fThis concieption or hypothesis could not; be proved dirtectl y from experit nuent. A hall perftct ly hard, round land sinooth, slhot on at level surtfcel lik.e ice, wouttl pre. - sewrve its rectilineal patht and its initial velocity tmltutch lontger t ihan if opposed by irregularities of surftace and other xre.istingl causes; and tflt s it beame tlt nanitlfeslt that as th}e Tre sist.:ie to.mtion were tdiminishedl, there was a nearetr ptos itivc and ext periental apilroact to t he veti fica-. iton of the principle laid down by Gta ileco, till fin:idly it becamci a scttled piinciple and iwas at lenthti digti'ficd as the st grlcl lgaw qf m0otio-n. Precviousl to the discovery of ths law tht mind had continue after the cause producing it had ceased to act, and yet thert is nto motion produced by human contrtiv ance, such as the motion of a stone from a: sling, or a ball fromr a. cannon, itn whtich it is not mnanifbest that t ol forcc tpro'duin th" l motion cea se its action after the first:imptulse. Tto, slingv c1annot pursue thot stone once liberatcd, nor t'le poxwdcr withi its eoxtpaisive power fblt ow toh ball once released friom the gun; and thius it is clear that mot. ion. once gtenorated, survives ftor longer or shorter time the direct action of the impulsive fore. So much for rcctilineal motion. We arc indebted to . 74 Tr 1H A w s 0 G(atlileo at.gain f)r the0 second law of motion, or the law by \wlicl we pass from rectilinetal to curvilinear motion. A baal pt)rojcctedl horizontall als we have seen, soon cornti melnccd to fatl1 laway firomel tto straiglht line in which its nmoftion cotmmenced. G-alileo provedl tmhat utinder tlie uititctd eflbct of tte j)rojcctile force, andl the iforeo whichl caused ift to fll t owrd tlh earth, thtl ball would describe at regular C1urve, called a parabola, which is nothltint: moref tirtan an. ellipse, whose matjo*r axi is is fin4itely long. lthis tlcurve may be seen in the form of the jet, whell water or any other fluid spouts fromt an orifice near the bottom off a cylindricatl vessel. Thoe Florcut-inc p1iloso 6 pher in pulrsuin-g this saul cct finally came to gen li to eneralize the principle involved, and dis covered tthat if ta body in milotion at any given rate re-. ceive anl impulse, whose line of direction fio1rs any angle with thte line of direction of the movting body, it will int-. tediately tatke utl a new line of direction, atccordini to a law whichi. may bo thus ann.tounceld:~ -.1t/ two sides of a square or) rcctangle rpreprenst fthe inttensit ies and directions of tweo iatmpusive forces acting at the sa-rtm istant, on a body at the anitle.formed by these sides, Ithen /the bodfy fwhic, att the tend' r one secondt,'wou/tl have beetn fotnd, und.r the impids / of el/tot' force, at th e cxtremti-!t of the side reopesentttig tte f/rce,2 will neithter fJlow /ithe one side of. the re'afqf.t e nor the othera bidlt'til/ ta eii the dircetit of' the tdifaonatl atnd at the end of o01t1 second will be tfound at the e6xtretitly o1f that diagtontt, as ma-y bi more readily com'prlehended fIt'om the figures below.:Lect. be any impulsive force, such, that actin on thet matetrial point iP, in the directiont P B,]: would project it to B in one secontd of tTime, and t' be an imlpulsive force MOTION AND GRAVITATION. 175 which, acting on the same material point P, in the direction P A, would project it to A in one second; then, in case the two forces operate at the same moment on the material point P, at the end of one second it will neither be found at B nor at A, but will be found at C, the extremity of the diagonal of the parallelogram. F /F A. A B C This principle is known as the second law of motion, and is also known as the parallelogram of forces. In these investigations no account has been taken of the weight or mass of the body moved. It was clearly perceived that the force exerted by a body at rest pressing upon any support was precisely proportioned to its weight, and hence a ball weighing ten pounds would bend a spring through ten times the space due to a ball weighing but one pound. Aristotle knowing this truth, and believing that this pressure downward was the moving force, when a body fell freely, asserted the principle that a body would fall with a velocity proportioned to its weight, which, as we have said, was disproved by Galileo in his celebrated experiment at the leaning tower of Pisa. It was manifest, however, that when two balls of unequal weight fell from the same elevation, although they struck the ground at the same moment, or fell with equal velocities, the effect of the blow struck by the heavy body was very different from that produced by the lighter .176 It' t, A \., S A 0 F body. Indeed, it it wasa casy by experineilit, to prove that the cficct was precisoly proportioted to tle weigiht of thl' failing blody, and thal t a. body of ten poun.ds xweaight iwould strtike a blowt tent tilmes more powerful tthan a. one tpotud we ig'ht after l.atlingt throutgh e(ual }:eigtlthtss. I't tawas thtus seen that. to csthiate the c'itect of a blow struck bxy a xnovin:g body we must, take into account not only the velocity but also the weight or imass of tho body.'Thi samte body, with double velocity, doubling its eftfect, in shortt the mass multiplied by the velocity, lt w cal tled the momentZum, beeamctrt the true representative of thtto ffect produced by the blow strltuck by a movitl body. T taving readted clear ideas and true la.ws ont these irni-. porttan;t sulujeets, Galileo gavo his adtcitetion to the circumittt st.ances of m:otion on an ilnclined platno. y'expori meit lie dermol trated that, if thte same body rotll downl ptfns of tho same vertical heiht, but with difterent inotliattions, tho velocity acquired on rea chti the f(oo tt of any one ot thesto ptlanet s will be indetpendent of the inclination tand will always be equal tto the velocity due to the vertical heightt of the inclined pilnte. tIhis discovery jprsent:fed the pr)lt'lnciple of thel third and last law of motion, antd, a'fter muchl discussion, cam to b0 adoptcd as fundltb. mental truth in mecha.anical science, Tl'fhes laws of tmo-. tio.n wore thl result of cleart retasoning, based utlpon accurately conducted experilment, and were rquite itdc.epetndlnt of the actual causes producintt g nlmotion. Bo soon as tl-h ktnowlcdgl o of thelo tsecond lta of motion wavs attained, whoreby it became demonlst-rable that a body set in motion by ta single impulse, at.n t.hen operated.on by a constant power, would de scribo a. curve, it seems strange to us, surromunded as wo now are by teto fitll illutmi.nation of a true science, that this prilncipleo wtas not directly MOT ION A N J) GRAV I T ATI ON, 177 applied to account for the motions of revolution of tho celestial orbs. Kepler, whoso fl'trtilo gc'lius, ever active antd untiriMg, souglit the cause of pla.netary motion, bein'g:igr: nrant of tio laws of motiono i)let that lie must discover and reveal some constafntly iactive power operati.: in tih directiion of thte planetary motion so as to keep lup tho velocity, belicvin" t}ihat without some such ever-active force tho planlets mltust of nccessity stop.'hle succtessotrs, of K.itpler and of (lalilhe:o for fity years, or during thel, i'rst. halfti oft the seventeentt century, felt strongly the necessity of: at physical thleory of the planetary mnotions, without attaint ing to anythiniltg clear or satisftactory. That all heiavy bodies were in some way attracted by the oearth, and that the center of attraction was in th} earthis cnter, was manie st from the fact that every body fatlling rCeely, sought the earth's center. But how a central orce, lodged in thi earth or in the sun, could operate to keep ul) at motion otf revolution round that center, in distant bodies, was the inexplicable mystery. he amnio.nta had al ready remarkied that when a: stone? in a stl i i s whirled rapidly round tim he ad of the slinger, a force is developed which powerfully stretc1hes the string by which tho stone is hold. This:orlce was called tih en/ri/'tfqalforct, and it finally cam.e to be accepted that, in all revolving bodies, thi tendency to y from the ceuter must be generated, and hotncc in the )lanets an(d their satellites a like tendency must exist..Reasoning, th'en upon the two great tacts, that all bodies grtNvitato to the earthl, anid from analogy all bodies equally gravitate to the suni an li thatt all revolvin bodies, by the action of the centrift gal foree generated in their revolution, are disposed to fly from tlhi center : 78 s T t -t J1 A W r 0 o of motiont.B.tiorrelli, of lorenct e in:1666, seems to lavo beten tlhe first to coneeivo tIe ideal tli:.ttl in tllh planetts atlnt tlheir satellites these two forcetis mightit mlutually destroy or counterbalane eachl other, andt leave tlhe planetl iln state of dytnamtical equilibrium to pursue its journery round the sttn. Il'ere we fildt the cgrml of ti:e granid ttheory whiclh aft tle preSllt idaty cnm'tces within its gl'rasp t}h entire ph ysical unlivctrsc of tGtd. It wtas, howeverl uttt the gterm. Ti )11li diid nott preted t to deeonstrate th t h ruthI of lisi, su.'. cs-, lion. To aceompisit this, it becane necessary to deimon-... stlratl t0li la- of the centrifhug'al tlhreo a n tleo law of gia:vitatiolt andI then to sow tlat tthe firstt of these io]rce a1s developefd by the velocity' of revolutioln of any.planet, was' precisely equail to the tbforc of' travitatiot n exerted by the sun at i te distanc tto s which thle pl)anet was removed. Tet law governi ngr thel devetlopilnent of the centruiftugal fortnce ctultd be inves:ttl igatedt experim t entally. A. cord stuft ficieintly strong to Ihold at bod y suspddt froml al fixed point was not strong elnoulfht to liolt the same hodty wlen tmade.. to revoflv about the point, alnd, as tlhe velocity of revolution was increased; ti t strength of' the cord had to be increased. But, it was soon tlund that, with double the velocit.y it cord twice as strong wAould not retain tOh revolvingt body. Th'l ce oe centrifitgal three incretased, therefo.re in a igilher'ratitha thilto simple velocity. flly firther experinment it was discove:red tlhat whTen the velotity of the revolving body was doubledt theC cord Itolding it nusltt be qtuadrtp'tq/d, andI whlen tlh velocity was tripledt the cortd )must't be made ninc-foldt s'tronger, andt henett it becamet finally a fixed principle thai the ct n/rif/tla /fi/rce -i etve'/y rt.oiti hwl/ inicreasCed'with i/te sq/uare ot f l/ e /to %cCl/y. It remained yet to ascerttain AMOTIONA XN ) It ARAVITATION. 1 T 9 i, what way tlis:frcoe was aflt cted by thie distanco of the trevolving body i0'om the center of motion. Thisi was accomtplishli e xporimteittally, and the completo law regu. latinlg tht e dcvlopmnllt of the ccntrifttuigatl: rc iln atl r cvolving bodiesa having 0 been determincd, t.his force, was found to increase as tle stquar of tlhe velocity and to d.creas.c directly as the distlance from t)he center of m).otion increased, With tile knowyledge of tlhis important lawN, we can rleturni to the consideration of the planetary revolutions. Thilat these bodies wtere ur:ged directly fiom the sun by tle actior otf the centriftga'l frce generated by their velocity of revolution could not be doubted, and to counterbalance this ttendency to fly fiomtl the center of nmotion some three precisely equ.al and opposite: muslt exist.'th is fitrce was c.alled the,gramttatin, fbrce, or force of' f ravt ill and the ltaw r ulatinglt t its intensity remalinued to ib discovered. Kepletr had not ail ed to conjecture.o the existence of sotmile sutcl central force )lodged in tlhe sun and in tlho earth. -Ie even went furtliher and conceived the same firnee of atttraction to exist in the mtoon, and filndingl: the tides of thIe ocean to be sway ed( by tlha.t distant, orb, le conceived thlat the same enet ly whicht mani t sted it.self in a heavingt up of the ocean wave, muYst exert' itself with tequal power on tihe siolid mass of fthe earth. lt(hese, lhowever, were mero speculations with.Kepl Aer anld even, in case lit had selrio:usly undertakentl to proscute tlhe( researehl the ignor.ance of the true laws of motion t he.n existing would have rendered anty success i impossible, From t the days of Kepler to those of Newt)ont this great probletm constaitttly occupied the tthoughts of thte most emi.ent philosophetters Was the gravitati.ng tfrce wtthereby 1.80. t'It 1. A W. S 0 F bodies' fll to tlo carthlt' surface a constanlt or va'tribl fhree? Was tt thins tibrc ope atttivne in the distant regions of space? Did its power extend to the mnoolt? and itwas it therc precisely what it should bo in order to countttrba.lance thte energy of the centrifitgal threce? Did this same gratxvitatinlg power dwell in the sun antld other Iplan-t eta; as well as int tlh earth ltl? id tt}h, sun's gravity extetnd to each of thte planets, and: exertt at thlese tdift'reut dtstia:leest an energy equal alnd opposite to tlhe existil centrij:t:ugal.frce dtne to the plainet's distance and velocity? I'rshort, was thiere a ftbrce or ene1rgy tdwellingt in every particle of ponderable lmatter whery every e exist ing particle attracted to itself every other exist.'in. t particl, withb an energy proportioned iln some way to their Yweihtt s land to the distances by whilch they were separ.ate d? Could such a. toree, lotdg'ed cent rail y ill the sunt ind. op eratt.ing'by anty law, convert, t he rectilinear.t tmotion of a body darted. into s bpace b y a single impulse into ellip.. ti:c.l 1mot:iootn a tld at the samtt timet at every point in the elliptical orvbit, pretisly eountl:erpoise th}e ttientriftul Ial firce. du( to t:he planets adistance t.nl ve.t locity'? CA(uld th e stamte ior ceT governeed Iaby tlhe sami laws ant\ d lodgtI ed in tho prilmary 1planets, controlt tho' 1 ovmencnttst of thetir satellites? t'tcstet w\tere the grand itnquiries Vwtilch n enlgrossed tho attention of the gneratioi:it of ph ilosophers which flourislhd fio the timet of Kt(pler and intalileo lup to the: ra. re.ndcrcdl imntuortal hy tlte grand discovery o tf.I - lw toft uiversal travitatioln by.Newtoln. iNt.TO'T0N"'S J)D 8(OVEitY OF TE IA' 0 OV ". iA'VIITA.. ON.. —...o acore now plreparedt to consider thoe trainl of rerasoning emipll)oyt ed by the i nl.islt philNosoher in s ire seiarchles t;r t ile law of g rattvitation. Mltany astrontoer boforo N'owt.on hIad cotnjectured that t.h} ltrce exerted by i tt T ION A X.ND 0 t A V I T A T 1t8 the sun on theo planet, and by thto primrarie on their satellitct decre3tased as the squmare of the disttamt ineretastd, 0or:f:lloed the law oft tthe inverse ratio of the squareotlt c f fth tdistance.'This was inferred from0 thoe considlcration of t cth, t i at tl is attractive energy, called gratv ity, was lodgted in the center of the sun, and issued front tliat center in all possil direction, like lieght emanating t'rom a lutminous point. iAs thie distance increased filo the cenlter ttle force would become le ss intetnse, and migtht i;olow thi law of the decretase in the intensity of lighti which was well known by experimtent to be tthe iverXso ratio of the sqtuare of the distau.co It was one thlin to conjecturoe this to be t he law regulatitng the fbr ce of gra.yity, but quite ta difflcrot tling to demotstrate the t ruth of sucht. a cohjIpcture.'The investtigation a; pur>sued by Newton, antd the discovytrits madet1 by that distitngishcld philosophter, followed lprogrflsivcly in a scries of distin:ct prIopositions, tite destmonst lrations of which wvere reachted at difll.rent periods.'irst, Newton deimonstrated f that assum ingt tlt. th:e tird law of iKpler as a fiact derivetd fiom observation, ats at consequence of thits ictt (combined with the l aw of the ccntrifAtgal f orce,) the gravitation of tie planets to tiro sun:mus-t diminislh in the inverse ratio of the ttsuatre of their respective distlances. T'lh.is demonstration iwas auccomrpli shed by ta train of mathematical reIi asoning, of whe ich we we ill not stop to -give any account att present. It Iwas based, ~however, on tll, astsuimption that the plantaryl: orbits werero circles, antd hence did not ret ethe ca-se of nature. The second step was to prov e to prov ltat in cefae a planett revolvedt iln 4an elliptical orbit, thatat at every point of its revolutionl the ice exe trted on it by th0 suItt or it. .182 TIE S L A; wS 0o gravitat:ron to tl:i solar orb was always il the inverse ratio of the s(tquar e of its distance. TI.bis was equivalent to provilng that: if -t body in stpace, fieeo to move, recoived a singlo iiplltatise and at the same moment was aturactt od to a fixed e4 ntet by a force which diminished as the squttare of th istne lst e at -whicht it operated itnreased, such a body, thus dteltected Irtom its recctilineat l paeth, would describe an ellipse, in whose focus the center of att:rat — tion would be located. The third step in this extraordin ary investigat:ion was to demonstrate t}hat; this gravitavtting power lodcged in tlhe sun, and controlling the planetary movements was iden.tical with t~hatt force exerted hy't the earth over every ftllt.. ing body, and exteTnding' itself to the mtoon, decreasintg mi inttensity in proportion as t tle square of the distalnce increastti a.1 thus o) pposing itself as a precise Cquip)oise at every tnolten t t t o t eit of the ce ntrtifiu:gl forco geneirated by the motion of thiis revolving satellite..The fourth. step required the philosopher to demronstra(te thatt not only did thle plantets tgra vitate to the snn andl the satetllites to their primaries, b tht tht each and every one of tlhset bodies, sun, planet and satellite, gravitated to the other, and thatt each attratctced til other by a force which varied in the inverse ratio of the square of the distance. ulit hitere it waYts f)tund tlht another mattter had to be taken into account. The, energy of gravi..tation did not dtepend alone ont distan-.ce. Thile power exc\trtcd by the s1un oni the planet Jupiter was v(astly greatter tl ha tha1tit exerted bty Sattiurn, t}oulgh Jtupiter was neacly ctquitisttantt frott these two bodies wult1en in con tiunct.ion witht aturn. Newton proved { that tlh powe;r of gravitationt lodged in any body (depeded on thi mass or wcifght of the body, antd hence it the sun'weighedtt MOTION AND GRAVITATION. 183 a thousand or ten thousand times as much as a planet, its energy at equal distances would, by so much, exceed that put forth by the smaller orb. The fifth and final step in this sublime, intellectual ascent to the grand law of the physical universe, required the philosopher to prove that the force, power, or energy, now called gravitation, lodged in the sun, planets and satellites, pervaded equally every constituent particle of each of these bodies, and did not dwell alone in the mathematical center of the sun or planet. In short, it was required to show that every ponderable particle of matter in the whole universe possessed and exerted this power of attraction in the direct proportion of its mass, and in the inverse ratio of the square of the distance at which its energy was manifested. In case these propositions could be clearly and satisfactorily demonstrated, an instant and absolute revolution must commence in the whole science of astronomy, and the business of future ages would be nothing but the verification of this one grand controlling law, in its application to the phenomena presented in the movements not only of the sun's satellites and their attendants, but in those grander schemes of allied orbs revealed by telescopic power in the unfathomable regions of the sideral heavens. We shall now exhibit an outline of the demonstration accomplished by Newton to prove that the law of universal gravitation, as above announced, was the exact law according to which the earth exerted its attractive power on the moon, and held this globe steady in its orbit. The intensity of any force, as we have seen, is measured by the velocity it is capable of producing in a heavy particle in any unit of time, as one second. The earth's 1 84 Tv 1: I. A W 8 0 r'avity at tlhe surftac is meoastured thent by the spaco thr.ougl.f. whicll t l ody ftlIs in a second of tin:e, which spacet (aS e xpttimnt dcmonsltrats) is about sixteen fcct. I.t easo it wcere p}ossible to tmeasumre with absolute precision tho sp.ace througth which at body fials at the level of tho seat and t1 he at the sun1mmit of at mountainl (if there wero any sucht) 4. 000 lmiles high, it would be easy to Yerify thet tlruth of the tassumed law 1y actual experiment' }utit Ino mouIntain e xist on the cart th's. sutrface whost e heihlt.t is tomparabxle with tho lengthlti of ttl earth's tadius, and ats it is absolutely impo:issible to ascend vertically above the earth to an*y consi(dcrablo heighht Newton soon saw that 1no tmeanls existed on0 th. surtflace of the earth whereby the t1ruth or falshlood of hIis atssumt-ed hypjothliesis miglht be aserttained,. In tt his dilemma hli conceived th ideaLt that the mtoon might be employed in the experiment, not by arresting; her mo1tion at. d dropping her literally to tho car tIh, but by co0nsidering the earth.a's attfractive power as the cause of her deflection( fr0om a rietilinrcal meovement.'tI one sense the moon0 is perpetually tllling to the earth, as may be readily conpreolended from a. examination of the figure below..., %" I \ " MO TIO. N AND It A VITATX ON. 18. LXEt il represent tile ttear't's center,: a point of tIh moOrl'st otrbi t, in whIich she i at rest with no lthre what.ever operatingt on herx.' Now let an impulse he atpplied to the moon, in the direction M Mi""', ta:fngent to the orbit, or perpenidicular t ttihe line M.f,, and with such intens ity that at the end of one second of tinl the moon w ill lba fomud at M"t, eturni the moon to 7, and concei ving'..er to dr.l. U t;'l, her to hdrop toward the earth, under tho power ofl the carths attr actionl let us suppose thiat site passes over tihe disttance? M Ml" in xone second. In ease the m:ooln 1) b} rouglht hack afgain to M, and the imnp ls he now applied, antd att the ilst.'ant the moonl darts olf along the straight line All M'", sire is seized by the earth's attractive power, and l, bndig-t at once under ttese conloinlmed influences, s}ht commtences her elliptic al orbit, and at the end of one second is:filund alt;, passitng over a. sort of curvilinear diagonal of tho parallelot gra fort leld on t two sidels }'M' and l \5I I Now it is inainbst that thet line AMl" M7" is qult ita to 1 l M, thatt is, tia tl t h att ount yt wh icil the imoon is deflected from a: rightt line is prcliscly tie amount by whinch she fi ls to the earth in one second of t ine. The pr oblem tOhen resolved itse i nto a cornputation of the line 41':t', or the distance throughl which the moon ought to fall in one secondl in case the assumed law of travition be tiruo and the exact measurement l tt strunelitally of the distancot) l'I tho spact through which the mIoon did tal 1 in one second,.An exact equa1lit'y between thtese0 two (quantities would etaltisht tth law of the decrease of the earth's power of atrl f action to bl in the invers ratio of the square ofj the distance. It will be seen that to compute how itr a: body would fall in one secondl, wlhen relmoved to tlhe mloon"'s distantce in case the earth's gravity be diminis hed as th e squawre of 1.8'6 t. t c XI A 8 0' the. distance increases, is a: matter involvinlg lo diflticulty or unclrtainty wlhatver int case we know whi:lt tihe moo's distance is. Itn lik:e mannier, to obtatin the space througlt whiich th1e moon all tut:ly ialls to thl earth in o:ne secolnd or minute of tine, knowing her distatnce, adtnittting lher orblit to be circular, and wassumitng that tw k now her periodic time, is a probilem of easy solution. Tl'he ciiof difficulty lay it acc-omplishing an accurate determiniation of thie loon's distance from the eartIh, a matter which could not; be determined without an accurate knowledge of the earth's diameter or ratdius, s we have already seen. WXhen -Newton commenced }il investi"attiont tile mlcasurfsc which had been executed of tan arc oin the meridian, whereby the entttire circumIiernco of thle eatrit 1migltt be obt aitned anld its diameter comtptted, were cotimpa ratively imperfect, yielding olty an a tpproximate v alue of tihe carthls radius. As this quantity w\as the unit elmployed in the sr of te as toono's distance, an}y error in its value would be repeated some sixty tilcs in the value of tlihe moon' distance, and as the gravity of tiho earth was assumed to decrease as the square of the distance iltlcreased, we perceive thaet any error in the radius of the earth would operate fiatally onl tth solution of thiis p:roblem, invtolving the liat of the ml'ost conlmprthesive and ftt r.. reachinug hypotthesis over conceived by thet hIutllanl mtind. Untfortunately It r Newton, the valut of' tho enarthtl's diametert, mptlloy td in hlis first computatilons, was in ernlolr, and in excui tiong thi coinputation the values o{f' the space through whichl the moon owg/t! to 1ill, and the.space throug)h which she.did fill, wtere discrepant by att amtoulnt equal to tihe siixth part of the entire quantity. So greawt a ldisag'retment was iiatal to the theory in tho t0 T I 0 N AN X. t A VI TA TIO N. 18 truitllloving and exact m1ind of Newtoll and for lmany years 1he abantdoned all hope of dtmoinst'ratingt tho tri'tlt of hi.s favorito hypothesis. Still his m)ind was in somot wa.y powerfully impressed with the contvictionl that hoe had divined the true law of nature, and hl returned aglain attltd acgailn to his colputations in the hope of remtoving the1 discrepa-ncy b)y detecting some utmetrical error. It was impossiblc, however, to lilld an. error where none ex-. isted, and ior a timo the great philosopher abandoned all Lhopt of aeeomplbhing thiti the grandest of all the efibrts of his own sublim:e genius. 1uch wasa the colndtion of tihis investitgation when at now detterination of the vatlue of the earth'st diameter ywas accomplished in t'rancfe by the measutremtent of at are of the t err'stria:l meridiatn. t la.ving obtained this new value of the eartlh's diameter, N'ewton resuined once more the consideration of the problelte whicht htad 8so -long occupied his thoughts. T'IM nOw value was substituted Ifor the l the e mloont's (distance being now aceurattely known- — tho 8pace throughl which a body would fill in a unit of time, under the l-\sper of gravitation, when rtemoved to this netw distance, was rapidly computed. tIn like imanner the distance tlhrough which the moon must acttutlly Itl was also obtained by usin.tgt the newt value of the earth'si diameter. It would be inmpossiblet to fiorm any just idea of the in-. ttnse em ttotions which must lhave aitated thle mind of tlho!.;English philosopher while engaged in bringing these last computations to at closet.'Upon a: comparisonl of thle re.t sults n1ow reached th icroe thung' consequenes ot incalcul able value. No less thanl nineteen years of carnest study, of proflund th-outght, and of tit most latborious invesltigation, thd already been exhausted on this grand proobltem anld now wtithi at few minm utest t tho fate of the 188 T J.' J.t A wt o OF' ftheory and tho ftitm of tho astronomrn' were to t o bo or ever fixed. No wtonder, thitn, t ttat wo ae told thatt Cven thle giant l intcltlect of iNewton reeled and stagerd t tiunder tlhe trcmcndous excitemenlt of the I:tlloentt; e d steeitfl that the figres were so shapitng thoemsolvcs as inrtvitably to roy the diestroepaey t discrepancy which had so lon existed overcomo by his emlotions, Now ton was compelled to ask tho assistane of a f itend to finish the numerical cofmprutatiot. and when completed it was found that the space through' whtichl th.o moon did fall in a: unit of time was idcentical t with' tIhe space throughl which shie oulht to:fall, in case her mlovements wvere controlled by a po\weC lodged in thlle artht centre, and decreasing in energy as ti t lquare of the distanco at which it operated wa. in. creased. Hlcro was presented th1e fiirst positive proof of tho )prevalence of' that tuniversal law of mutual attraction whicht energizes every particle of polndtlet ble matter existingl int thte universe. Tlhe earth's 8 power of attraction was thus shown to exert itself accordling to a fixed law, in detlecting the mtoon froml tth rectilincal pathI it would otlhenrwise have tfolovwed, convcrtin;g its tmotioln into onl1 of revolution, giving to its orbit the elliptical form, and maintaining at every point of its revolution the most exact anl d perfect equilibrium. I.t.may:, lla)s, srh ecm extratordinary lthat so mu.lch co0tsequence should thave been attached by Newton 1 to the succtessful t'demonstration'of thlis particulart problem..If lie had alrtt eadty shown thttt the sun's attraction upon the Iplanett s itllowed the law of the inverse ratio oft the sq.uare of tihe ldist-ance, and thatt thc lhe same law ptIrcvatiled in tlho att.racti.o o f thte sun upon any one planet at di ftrelnt points of its orbit whty retga.rd as a. matltter of such M O T t 0 A N 1) G Rt A V I: TAT 0 N' t, 1.89 htight valttu the demonistration of thle fact that the earth't attraction uipon thli moon Iwas governed by th-t samet identical law. t'lho answer 1: think, may be readily given,'.The greatt problem was t. litis )ocs one law reigAn sIupreome over all the ponderable mIassCes of thl- phl:ysical universe, or are there mtany subordinate lawts holding their sway in tie divere systems a dis wd bodils ich are revealed l)y sig}t? tit ihlt not be tthat the sun wotld fattract the ptlanets attcctrdin to 0one law, wAhil theO pla nets might attract their s atclhte accordin-gta to a dibllrent lawt? l7By ldemonstrtatiltga that tihe earth controlled tle moon by tho aall preciset' power, whereby the stitn conltrolledt the planlets, it wars demtonstratedt- that the ponderable matter of the eartht was identical in character with thle ponderlable matter of thle sunl, anttd fromr this it:ftllowed that as the earth wts one of the planets controll.ed by the power of gcravitation of' the sutt, tO li(kewise the other planet:s which were controlled by the same power mst b)e coin-. posed of tponderabt-llc iatter, governed by the same laws whichl rei^n in the sunt alnd eart. VWe perc ive tten,h that ti.;s demonstration, executedt by New ton, in whtich lhe proves thaft the earth's attrac.tion. contirolled the moont. deserves the hlig l rankt wthichl e ihas assigned it, fort it is nothing less, when contjoined'with hisi previous demonstratitons t tan p)rovi ng ttat every gl.obe which shlines in space, plantet and satellite, and sun, are but parts of one mightt system lid Cied togetther by ilndissoluble Iotnd, )otrming one grand scheme.t int which each exertas its ilnluentce upon the othel, the wholoe controlled by one su preme and l ll-pervatditg law I't only renm:ined now to extend by demonlstration tlhe empiret' oft the law tof universal gra\vitation ove.r each. 1. 90 T I. I, i A W S 0,' particle of malttertc composing the several worlds. ThInis was a probtleo of no ordinary difficulty; t'or New\ton soon discovered tthat in case a mass of ponderai le maltter were fastioned into t}lhe shapte of at spherc,t that for tall the p)urptoses of cormputation it woutld be sa;fie to consider tile entire glo)e ts ct Contcentrated il one singtle point at tle centre. Observation taught that all the planlets, as well as their satellites were bodies of globutlar form, and hence in applying thle law of universadl gratvitation to the study andl eon-mputattion of their movmnts, the same results twould }. obtained by admittirng tho whole lfo tre otf attratctiont belotning: to to these bodies to bo conecnt.ra.ted in their central Upoint,: o to Ibe distributed amo)g thl dillft'rent pariticles compos:.Sing the glo:be.'t o slow, then,1 thlat gra.vity resided in every particle ctlposing a globe: and not in its cent.ral -point, was an imipossible things, so ftar as' the distant worlds were concerned. In tIhe world whichl we inlihabit, \however, and wIhre we can study its indi-. vidual (dportio ns, and whero we can penetrate to certain deptlhs toward its center( it may not be inpos;sible to learn whether the power of gravitationl dwells in every ponderable atomI which goes to tmake itp thle entire earth, 0or \hether it is concentrated in the central point Thterae e severatl metlhods which may ble lmployed to ascerttailn w lhother there be any pomwer of att.action -in s'parat'tt portions of the earth or in the crust of tho earth. t' he clibet. of a hitgh mountain on the direction. of' the pl:ttiumb-litn (whliclh at the level of' the sea: holds a. direction pterpendictlar to the surtlcett) in ctasin:g it. to devi" ate fito n this di cttion, may )0e measuredl with suflit cient Saccuracy to demonlstatt te (ie power of attracttion cxisting in the mounttain, Suct an experit en tt, howtcver, MOT. ION A N) ( I At V I T A T IX N, 91. could not le employed to demonstrate that tlhe lawt of universal griavitatiot prevailed amrng thlit pt articles corni posing tlie moluitain, it would only show that there owas a tpower of attraction exerted by tlie mounttain and in catts e e kne ew thie extact atnount of deviation of the plumb.line fromn the vertical, and the mag-nitude of thle mounfain,: as well as the rlaw according: to wtich its attractive powter was exerted, we could th th obtait n the qnantity of mnatter contained in the mountain mass..A second methold lmay be employed to ascertain whtether thti whole power of gravitationl is lodged int tlhe center of the earth or is distributed amtong all its constlit.ent ptartticles. 1fT it were -poXsiblo tto poenetrato toward tie earth's cent:?r, a thousaid miles below tleo sturlfce, ind thlt erl drop a hteavy body, and measur the spacet thtrough which ic th lsf in a unit of time, if this measured space shouldt be identical with thatt over which} tile blody oughtl to ftill on theli supposition that its velocity (tde. pended simply on its distatnce fr'o tho center, such an ex.periment would demontstrato that the eamrthls ra1lvitatin t force resided in the central point alonet thlis experirelt caln nolt:,ot plerfot.rmed in the exact manner announced, b)tt it tcat ei c, ant d has been sutbstan:tially tt0erofired wit ve.ry gre-ait delicacy, inh the following imanner: It: is fi:loultt itat a penidulul of g.ivlen lengthl will vibrate seIoids at tte et quator of the ea rtt.If th is ptenulu be removed nearer to thi e eartt:'s center by carrying it toward tlhe piolCts thit power of gravita tion producting its vibtratiotm thertby' growinug morl e iJntciaeso, tlih ptendutlumt will vibitte mnor than sixty timtes in a nminute, andt thus the ltn il xt. of vi } atl'io llSin a giv-en t time bcomes a v.ery exact means of measurint tie distance of any point on tie earthttt surftce frit om its center.',hese experiments, 192 fT f I: I, A WC 8 0 I' hlowever, are pertbrlned uponl tlhe eartlh's sur cfia. I, in-. stead of removingl 1 the penduluxm from the e to t l e tor toward the poles', anlt thereby reducing its distatnce fromt the earl.th's center), this distance were reduced Iby the same laounttt by transporting the pendulum verticatlly downwar(d into a deep lmine —-if distance alone fromi the center be the cause a.flecting the time of the vibration of the pendutluml t —— then tile nu:mtber of vibrations in a unit of tinne will he the sameC in. the mine as at a point on the ex.terior equitldistaint frt om the earthls cetelr.'When th is experiment comes to be pertfi:bred it is bfound that there is a. great dififrence between the -numltber of vibratlins in the interiorl when compared witht tho numtber of vibrations at the exterior at oequal distances r orthe center, in tany lunit of time, say a mean solar (da:l clearly domlonstrating thatt tIhe mattter of the e arth, lying above the p})endulum located in the mine, produces a v\ii'ery sclnsible and ip.owerful efbect upon tie numtiher of its vibrations. liere, agttain we fitd itimnpotssible, fr'om thins experi-.metit, to determine tti exact la which r u at:les the attirative power of tho individutal parIticls com.l)posinrg the eartt, but we do demonst -rate the fitct that the earth's gr(avity is not concentrated at its center, but dwell.s ac,contiilt. to some law, in all the atoms vwhich cotmp)oste it ma:ss; and this law,t we ll e sall provo hcre ft:er is Inlono other than the great law of universal gr.ravitation. lit is imposh. sible to lfrm a jtust idea: o:-t the vast iiport. antl. whlich attaches to thi grand discovery of'Ntwton. It worked out, inst;'tly a(nd absolutely, a comp-Il.te rlevolution inl thte Iolt0 science e of astrtontomy. Prelvious to the discovery of the law of universal. gravitation t all the obsef'rvatio..s upont the stars and planets, which had been acItcumlati nig'[i so many eOnturies, could only be re. MOTION AND ( R A V I T A T 0 N. 193 gaxrdd ias so many isolated facts, halv.ig 1no specific rclationl tie one to the other. The1 planetts wtee independent orbs. movin througlh space in orbi'ts pectliar to thllcselve, and only united by tt h si t gle teact tlhat the sun constituted the colmmon center of revolution. 1The discovery made by Newton converted th:is scheml e of isolated orldIs into a grand nechanical system, wherein each orb was ldepetndent upon every other, each satellite aflecting every other, and the whtole colmplex sc.heme gra.Nvitating to tlhe cominmoil center, whllich exerted a pr.edominant power ovr ach and every one of these revolving worlds, T'hose eccen tric bodies which we denonminate comets, whl ose albrupt appenlaranlce in tlhe heavens with their glowfiinf tratis of liht, whose rapid mtovt tments and sudden disappeara.nce htave excited such a deep interetst in all tages of thte world, wtere ound tnot to be exempt, aitS wo slitall herea lter show, ftrom the empire of gravitatiot, 9 CHAPTER X. THE LAWS OF MOTION AND GRAVITATION APPLIED TO A SYSTEM OF THREE REVOLVING BODIES. A SYSTEM OF TWO BODIES.-QUANTITIES REQUIRED IN ITS INVESTIGATION.FIVE IN NUMBER.-SUN AND EARTH.-SUN, EARTH AND MOON, AS SYSTEMS OF THREE BODIES.-TIT SUN SUPPOSED STATIONARY.-CHANGED FIGURE OF THE MOON'S ORBIT.-SUN REVOLVING CHANGES THE POSITION OF THE MOON'S ORBIT.-SOLAR ORBIT ELLIPTICAL.-EFFECTS RESULTING FROM THE INCLINATION OF THE MOON'S ORBIT.-MOON'S MOTION ABOVE AND BELOW TIlE PLANE OF THE ECLIPTIC.-REVOLUTION OF THE LINE OF NODES.-SUN, EARTH AND PLANET, AS T THE THREE BODIES.-PERTURBATIONS DESTROY THE RIGOR OF KEPLER'S LAWS.-COMPLEXITY THUS INTRODUCED.-INFINITESIMAL ANALYSIS.-DIFERENCE BETWEEN GEOMETRICAL AND ANALYTICAL REASONING. WE shall now present, as clearly as we Can, without the aid of mathematical reasoning, the application of, the laws of motion and gravitation to the circumstances arising in a system of three bodies mutually affecting each other. We will commence even with a simpler case, and suppose a solitary planet to exist, subjected to the attractive power of one sun, and that these are the only bodies in the universe. Let us consider what quantities are demanded to render it possible for the mathematician to take account of the circumstances of motion which will belong to this solitary world. First of all, it is evident that the quantity of matter contained in the sun, or its exact weight, must be known, for the energy or power of the sun varies directly as its mass, and two suns, so related that the weight of one is tenfold greater than that of the other, the heavier one MI 0 TO N AND) t A V I T A TIO N, 195 will exertt a power of attraction tnclfold greater than the ligtlter one. In' the secotnd place, we mlust Xkvow tlhe distance of the planct fromtn tle lstu, for tleo powve of the tu's attract tion decrelases ats tes t squareto of tlte disltanc at wtich. it operates increasest; so that if at a distance of \nity it exerts an attractivo force which w\ maiy call onelC, at at distance l ttol tfiso force will be diminlisled to o'ne-fourt t; att a distance tf/ee to onie-inth; at a distance foJ r to one-sixteenth; at ta distance telt to the one hundredtt part of its first value..lnt tte third place, theo mass or wCeight of thle'planet must, be ktnown for not only does the slun attract its plalnet, but in turn thte plancet attlraects tit sln, tand t:hle intensity of this attracteion, which affects thle motion of the plantlet as well as thatt of tlih sunt, dep:ends exclusively upon the mass or weight of the planet. III the fiawlth place, we rmust know the intensity (f lthe imtpusitte frce whicht:is employed to stiart the planet inl its orbit, for upon the intensity of this ftre will tile initial velocity of the planet depend, anrd we see readily that the formi of the orbit as to curvature will depend upon the initial velocity. Theo greater trhis velocity the more nearly will tle turvature of the orbit coincide with ti straight line inl which the plIanet would thave mnoved in case tt had been v opterated upon by the impulsive tbrce a lontte,.in the fiftih place, before we can completely master the circumstances of motion to the planet, we must know the direetion in wh icht the impulse is applied, for upon this direction it is mantifest thatt the fitgur of the orbit will depelnd. tIf tlhe imnpulsive force )bo applied in a. direc.. tion passing through the t1tsun's ctCtre, and towtard t.he 196 T It B T, A W 5 0 F s tll, it 1s clear tlat t the lancet will simply fall to tle 8su iln a straihflt linte. I it it met witlt no re.sistatci it wtould pass t;i hrougll h and beyondfl tti sun's center umntil its ve locity woulid be lntirely over cotne by tlto attract ion of gravitationt x wlten it would stopX::fll taain to the sun, ant Id thus vibrate lt evcr v in a rigtt line. In ctset tho direct. ion of the impuflse is oblite to tle line joining the planet and the sun, (tihe angloe falling within ce.rtainl limnits of tvalue,) thlen the planet will describte an elliptical fitlgure t its revolution around tlhe sun, and will rttnl precisely t teo tt point of departture to repeat the same identical curve, with thle stam velocities pritciscly at eaclt of tht points of its orbit, in: the saino exact order for tvere. Iln oxamining tho peculiarities whilch} dNistin lgi ishl t t:e mr ovemt nts of tli s revolvin.g hody, we sIall fintd as a necessary consequence of the laws tunder whlicI it move s tl4at its,motion must: be lowest t at t point tofit t olf it vwhtere it is fauthest. fiom t}he sun, L wavin th}is point as it tap:l'oahelt thi sun, its velocit t y ntst rapidly incretase. antd will reach its mainstim att the pelrihlion of its o0rbwit, lwhelro, beming nearest to the sunt it will nmove, w it its swiftest velocity. R.eCtding nowtt fir(l the center of attraction it will lose it.s velocity by the same degrees with wh ich it was autg ented, and wtill againt pTass its ap lIelion with its slowest velocity.'tus we perceive that tte mnovements off a sinf'le planet trevotlving' a.bout the ot0ly sun in existence tare ma.t-rked itlt great simplicitty: andt in case the mathtct ati.ciatt lktows tilr'.cisely tho live tqtantities already named, viz tlie 81t18.timSS, Ilth pflaf nt1 dis/ttic th: e plandets 1. ttss, the in.t ttnsily qf lthe impl)lsivet/orce^ 1, and the di' ection' / t' fhis fiPcet, it its not at attll dificult to determintie atll the cir-: cumstances otf notion of tht planete, aitd to predict its AOTION A N ) G At VITA T' 0 N. 19t7 place i i ts orbit w ith absoluto precision at the endl of ten thousand revolationts. W'e will not at irct apr tt tempt to sow how }t\o these five quant ities imay )be obtained, Tihso determ i iations belong to the depart ment. of instrumental afstronomny, t subtject wh}ich wvill be trea-ted after closincg what we have to say on the appltication of the law of gravitation to the inove1lents of a: system of three bodies. ln case the pl;ants htad )beent formed of a. manterial such as to )be attlracted lby the sun, -but not to attract each otlher, and if ftle satellites hatd b.een composed of a Imaterial such:I. to be attracted by their prlirimaries only, then thle elcmtents of the orb.lits of all these rcvlvigit htdie would 1 havle remained for ecrer absolutely invariable. So soo0n tthen as accurate obstervation stt'l} ould have furnished tti five quant:ities required in detertinining tthe circum-.. stances of motion in any revolving botdy, 11mathlitatleical computation would havtre fittetd an invarialle orbit to tacht 0one of these bodies, and would have fiurnished by calculation the exact place of each one of these bodies in atll comnling tinie. T".}he wlhole system would hltavo b)een one of perfiectt equtilibrinlm, and although comtplexity wo, ld iave presented itself apparently in thf interlacingt rtvoIntions of these revolving worlds, yet aV bsolute simtplicity, comllinled with- short Pteriodical changl-es, would htve restt ored achtl one of thtese bodtics to tlh exact position occupied when first launched iil its orbit. This, however, is not the case of nature. Tb{lec siun not only att rcts the planets, but also attracts their satellites,. The primnary planets not only attract their satelltites,.lbut.i attrctact fi otlher and thu\s not a singlo body exists ilt the whole untiverse wvlhich is not depentdent upon Cevery othler. 198 Tr.I I.T A w s 0o. \We haveo already seen that in case the sun with one Iplatlet were the only objects in existence, that having trace|d tihe planet in 0one single. revolution round t the sun, the vtariations of motion thus developed would bt e repeated without the sligIttest clmng: in any succccding revolu-. tioln for ail comting time. Suppose tis solitary planet to be the eatrtt, and that from a knowledge of the we ight of the sun, the distance of tit earth fromt the sun, the weigtht of tthe earth, the intensity of the impulsive force, andtt the directiton in which th-at force is atpplied to start the carth iits orbit, we deter1mine thTe e lements of its orbit. T..he flrm of this orbit, its magnitude attd ptosition int space will r.w - matin. absolutely ilnvariatble, ant the chanls of miotion in the first revolution will be repeated exacttly in all succe(edingt revolutions. L.ot us now addt to our systemi of two bodies a third body, tas thle moonl. In: case thlt sun itad no etxistence, or was remioved to an infinite dis-. trance ten, t the circlumstances of motion in the moon, once determined, would remain absolutely invarialtde but the tmoTient we unite the three bodies, the sun, euarth and moon, into at system of three orb, uttualy rdetpetntent utpo0 each. othr, the perfiection and sim.,licity t whlich:marks a. systemt oft two b.odies is tox:r ever destr':oyed, land modifications are at oncet iroduced into th ito te otion of the earth revolving aroundl tthe sut, and alo into tlat of the moon revolvitg around ttl lth earth of an exceedlintly complex.iand difficult charactert and rtquiring the }hig-th-. est developm ents tof mathematical lanadlysis to graIpple1 suetcessf.tlly wxith this.great problem of It/he the bodites. The soluttion of this plroblem hla ttVtl b.}e positively aceomplishdt, but approximations of twonderflul delic cy have boen reachled by the successors of Nwt:, so tlhat MOTION AND GRAVITATION. 199 for all practical purposes in astronomy this approximate solution may be fairly regarded as absolute. As the plan laid down in this work does not admit the use of any but the simplest mathematical elements, we shall only trace out, in general terms, the consequences which must follow from the introduction of a third body into a system of two revolving orbs, and, for the purpose of fixing our ideas, we will suppose the earth and moon to be our two bodies. The moon's orbit, in magnitude, and figure, and position, is supposed to be known; her period of revolution and the circumstances of her motion in her orbit are also supposed to be accurately determined. The earth being fixed in position, and the moon performing her revolution under the laws of motion and gravitation, let us now add to this simple system a third body, the sun; and to render our investigation as simple as possible, we will adopt the hypothesis that the earth continues at rest, but that a new force, namely, the sun's attraction, now commences to exert its influences upon the moon. In order still further to simplify the case, let us suppose the sun's center to be situated in the prolongation of the longer axis of the moon's orbit, and that the moon, in passing through her aphelion, will cross the line joining the centers of the earth and sun. Under this configuration it is clearly manifest that the figure of the moon's orbit will be changed, because the attractive power of the sun will. certainly increase the distance to which the moon travels from the earth, for the velocity with which the moon moves away from her perihelion point will be reinforced by the attractive power of the sun, and thus her aphelion distance will be increased. By the same reasoning, it will appear that her perihelion distance will be somewhat diminished, and 200 T: E t A. w S o) thus1 the lon'ger axis will be increa8sed in lngtlt, aind tthe period of rcvolution of tlle rnoon w\llt in likt Itt matlner bo inlcr eased.'Th'ese ct.:haing llaXinP bct n once t accol i plishicd and tiho i0noon having taken utp }he new orbit un.der the actionl of the n1w forces, so lontg 1as these forces retmain constaut, that is, so long as tile sutil remains fixed in position, the now orbit will remain as invariable as did the old before ttte introduction of til sun. All the clhantges accom.pis}hed by thie sn's power, wherebtly tle new orbit is inmade to difler:from thl old, are called, in astronoyrn, jwerl-tturbati/ts, and thie sin is called the distiurbitn bodly. Let;i us now stuppose t.lt sun, retain'inl its distance from the carttl, to start. from its position ot thle prolon:gation of' til tlongetr axis of thle mool's orbit, and to colmelnc.e a xrevoldution around the earth. in a circular orbit; lying in t}le plane of tilo nmoo'ns orbit. A. little rellection will slow us that thie:lmoent, the distukrbirng bIody cot0lrmlences to rumove. the direction of its attractive power uponl tthe revolvin l, mloon. will betgin to change; a n ew set of disturbances will now colmmence, not afiecting tlre newil figttre of the mnoon's orbit, bu-t chtanlgiln ttte p.osition of th t principal lines of thre orbit in its own platne for it is cletarly tmanifeist that tihe strongest power will be exerted to dra.w th:e moon away t'frontm the earth on the line joillinlt thie ccnte1rs of thle eartl and sunl; and ltencc thie aphelion point of thoe mtoo's orbit will necessarily try to follow this moving line. e.'tle subject cwill be madet plainter by an examination of' the figure blolow, in which. tl represents ttl e arth in tihe focus of tite moon's orbit)1, S the place of the stin ot the pl rolgactionc of Ml: the llonger axis, P thle prtiee't", and the:ap1.. gee{ ot te:l moon.'s orbit. In c:ase the sun b}e reoved 3T OTION ANT) ( I A IT AT i ON. 20 to S', aad there rom in tationary, it is manife. t t:hat eaclh ti tile moon crose lhe line EI S' it will be s)ub- jctetdt te nt e inuce to ot t l itunc to d t away fromtw the earth at It:; tand in case the sun remain stiation.t. - ~,,....' /................... I.......N, ary fr a sufticiently long titntle at each: of the:r0oon1' revo\ltions, thle point NM will approattch Ml a n{ finally it will actually itlt oln AtM, where it will remain fixed, so lon asr the sun is stationary..In cfast I.owever tite su ain at dvances in the same direction, the apogee of the moon will again advance, and should the s un, by succe)ssive steps, slowly perforl anl entire revolution, pausing at eacih step sufilciently lontg )br thi moonst apIogee to come upt ) to the ltin joining the ccnters of the earth antd sun; when the revolution of, the sun shatll have been com 1pleted th. e revolution of the xnoon's apogee will, in like mranter, have been fitnished. It, instead of supposing the suit to advance by sutccessive steps' we admit his uniform progress, it is clearly aiai. i st that in eacht revolution of the moon, the apogee of her orbit must advan1tce a certain amounlt in th direct:iont of the sunt' motion, tand in the end, a4 complete revolution. of the tmoo's apogee will be accomtplished under t.he distturbintt infltuence of tile sun's atttraction,' i 202'r t Iu n A \V 0 OF We }have seen th-at, if tho sun were stratiionary his disturbit(ng power would only go to changet the figt'urel of the tiooo1is orit, le itavi.g the direction of the longe1r axis 1undisturbed. The revolution of the sun in at (ircular orbit; by slow degreesls accon)plishes an enti ire revolution of the apogee, or of the linte of apsidels, (and thus in I c ios the line of attpsides should perforlt its revolution in a period which shall be an exact multiple of the period of thoe sun'su revolutilon, tlh:n at the end of 0one such cycle the tmo.o will thave tipass tl tlhroug all tht chantes which can arise ft-ltom the disturbinogl ii influencell of tlh sunl..The.;sec changel s will tlcrefibri be strictly periodical, andf in tlhe end the moon will return to its first position, and \wil rfcpeat. t:}he samttc ide ntical cltlhanges fore')ver. We will now consider the solar orbit to bo elliptical. This involvcs, by necessity, a perpetual chtange i)n tho lsun's distance, antd as his disturbing power varies in in — tensity inversely witit thli square of Itis distance, it is manitlibest tlhtt this vtl aiattiont in the disturbing ftl)rcc w ill iitt roduce at cort-responding variation into tlte fi:ure of tlhe tmoon0t's orbit. If the sutn bI) supposed to advnce toward the earth and tlte imoolt, in thte directiont offl thei lilne of attpides, its disturbint t power would beo exerted to draw the moon tfrtlher tI omat: tte earth the nearer t.il stun ap-t) prloachted in other language. to increase thte magnitudet of the m1-1,oovts orbit and thie period of her revolut0ion, aT1his action will be varied in case the sun recedt e fron the earth alo-ng the sameI line, and if this iap.proach and recess were mt ade by successive steps, a't intet.rvals suf-t iciently long to allow the rtnoot's orbit to assutlme a fixed lt'a-rn, thlen t(.ne vibrationl of the sun a(lva.lnci.ng ain:td re.ceding through equatl space, would work out al serics (o cltantgCis i ln e lte frm of tho mtoon:s orbit identical with MO TI ON N A N D t tVI T A T I r N. 203 thoseo accomtplished by each stuceesive vibration, wtilte it all thl so cthtanges tThe direction ot tile line of apsides would t1treniaiin fixed. ilt' now we suppose the advance ail recess of the sun to be efifc'tctd by its re'volution in an elliptic orbitt, then we shall litd tite chtanges of figtno in the moott'l orblit, just notic:ed, as due to the sun's change of distance, will te co(ttt:netd with an advantlce and fintal comptlete revolut;ionl oft the fil1e of apsides; and aditittingt tihe figure of thie:unIs orbit to remailn untltaneed, atnd t.he p:rincipal axis of its orbit to remtaintl fi. xd Iforever inl pos ition, at timot will conic wh0.en thle stn will htave bcen presented to thte mIoon in every possible p1)osition, and all the chlantres iI the figitre of te h mnoon' orbit, and the revolution of ttie line, o; apsits of the moon's f orblit., due to the revolutiou of the sttt in his orbit, will htavte )eie accomlislthed, ThtO nmovilng hodiies return to their primitive points of cideplarturc, a.d a. new cycle of lchanges begtins to )b repeated, i t (the samne order forever. lThui}s itt we have supposed the lite of apsides of tfho sun's orbit to remaitl ixed in position and uncltan.fted in. }lenttht, lIt is inmatllitst that a revotltioin o' thfl filre of apsidhcs of the sun.'s orbit, definite in period antld tlultituati.ons ill its lengtt also pe.riodical, Nwotld introdtluce addtitioial tfluctuations int the toootls miotion) amtl in th lelgth and position of the printcipal axis otf ler olrbit. lBut while. w rise in complexity, and w hilet the periods Ir(uiitc for ellcting atll these changes expand into atges, wc still rccognize the great fatct tlat /t. riodicil/t reit — mlaitlstis atid that inl the elnd, aft time trmtimattiton of a. vast cyc le ttem revolv ina bodies must return al.' in to their points to de pazrmture to repeatt the same idtt licaltt eic'ttlta lthtrouglh c'ndle.Css ages. 204 THE LAWS OF In all our reasoning thus far we have supposed that the three bodies under consideration always lie in the same plane; in other language, that the planes of the orbits of the moon and earth coincide. This, however, is not the case of nature. As we have already seen, the moon's orbit is inclined to the plane of the ecliptic under an angle of about 5~-the line of intersection of the two planes being called the line of the moon's nodes, which line must, of course, always pass through the earth's center. We shall now proceed to take this inclination into consideration, and ascertain whether the sun's disturbing force has any, and if any, what effect on the position of the line of nodes, and on the inclination of the moon's orbit. For this purpose let us suppose the earth to be stationary, and that the line of nodes of the moon's orbit holds a position perpendicular to the line joining the centers of the earth and sun, and that the moon starts from her ascending node to describe that portion of her orbit lying above the plane of the ecliptic. The power of attraction of the sun will manifestly exert itself in such manner as to cause the moon to deviate from its old orbit and to describe a new orbit, which will lie in all its points a little nearer to the plane of the ecliptic. The moon will not, therefore, rise in this superior part of her orbit as high above the plane of the ecliptic as she did before her motion was disturbed by the sun; and in descending to pass through her node she will clearly reach the plane of the ecliptic quicker than she did when undisturbed, and pass through her node at a point nearer to herself than that occupied by the former node: in other language, the old node comes up to meet the advancing moon, and thus takes up a retrograde motion. hO T. ION AN ) t RAV tTI 1 ON. 205 Lot uts now examine ttoe motion of tloe Inoon in that portion of her orbitb lying beneath the pla.ne of tho e teli.ptic and rmlost remot e fi nr the sun. ll.ere the sun's disturbing il tluence will be dimilislhed somewhat, in consequcnce of the increased distanco at which it operates, but its eftloct will mnanl:fcstly b to cause thto moon to descrend ilmore rapidly and to reach a lower point beneatht the Ccliptic than when undisturbed, increasing the inl.timatiol of the platne of the orbit, alnd causing the moon to reacht lher ascending node ait. point earlier than when u.ndisturbed, and thus producin alt retroces ion1 or retro grado motion of the linel of nodeta.'Il us it appCars tlht il the lon5 rtt th o stun's tdituring influeonc will tend to eitiante within ccrtain lilits the angle of inelination of the mnoon's orbit; aind inldeed, if the carth weret fixed in posit:ion, would finally destroy thlis iltclination entirely, reducing: the lano of th0e m-oon'0s orbit to absolute coilnci.. denco with t}hait of the earth; but as teo mo 0on is ca.rried bly the earth arotund the stun, and as the moonl's orbit in the coturse of ant entire'revolution of the earth is thus presented to the sun at opposite points of thte orbit tunder rei'verso circumlstances' there is a compensation acoe-.lt plis}hed, so ifr as thle ialnle of inclination is concernel, and. also a(t partial comp})ensation in the retro1CgreCssi)o oft the line of nodes offtihe mIoon1's orbit, but not sucht ats to iproelnt, in the ex'ndl a. complete revolution of tbe mltooislt nodes in a period which \wo hatve already steen amountst to cightee. ye tars and two -hu.dred and ninleteen dalys. W'\o have t:luts att mlpted to present a general account of the effhet of a disturbing fo!rce.'These sam e samprinciple:s ttmy he cxtendet.d yt fi rther, and will give a general idea of theo e'lects prodtuced by the planets and their satetites upon each otlher, 206 T' t: A W S 08 it, If wo return ftlo.r a. momentlt to the hypot.tt:l si that tho carthI is th y plct revolving about the osun, thle miagnitu.de of its orbit: as well as ttir lelngth and.tt position Of the line of aplsides' wIill rlemain fior ever fixed. f1 however, we inttlodluce into our system a new planet revolving in an orbit interior. to tthat of' the eartt, whatever fotrce is (scxertcet xipo)t0 thte earth by the atttractive ptower of' this new planet will go to reintorce thl powerr exerted by tile sun; aln heltce the disturitng itluenlce of thle'lan tlet Avill t td to dilinisiudlt tIhe magnitude of tihe ea rti' s orbit, and to idereaetse its periodic; time. If the disturbi)tng planet revolve irt the same directiont with the cartll, >by apl)yi) the rettasonintl, hit:herto used we slhll find that its ciftc:t x will be to ca:use thoe perilhelion point of the earth's orbit to advance and ret.rcat dutritngi th e revolution oft the d(istturbingt body, always leaving, howlever, a slight, p iroponder'anceo of til ad:tlvancintg movement1t over thle retrogra(e.f In case the dlisturbing body revolve in anl orbit ex-. terior to that of the tearth, then its cli:ct will be to expand the eartths orbit tand to incretase the periodic tiime, while tthe influence exerted upon) th lo position of' the line of apsides will, in the long rut:' prodtu an adv ance. 1The reasoning' hlift itlherto Ceployed with referenco to tohe inclination of thle tmoon0's orbit to thel ecliptic is (lireetly applicable to the (teli.ct; produced by any planet upon the inclination of the orlbit of tany othltr planet t as relfrred to a fixed p'lan. Talke the c:autht fbr esxa-mplt, and l. et us consideir' the efle. of any Plt clf ay plaet ither intortior or ex terior uponl the inclinationt of ttis p)lian to any fixed plane. S l s.to tlong as th Ile dist urbing body is evolving it that part (of its orbit lyinlg below the plaitnet of, tho eclip>. ti the tetndency of the istturtbing tfiree will tbe to draw thle'arth: l f'rom its utidisturb}.ead path bt low tte pliane ort a Mt O N X A N G - i A V I TA T I N. 20tO fixed ecliptic, whle this cfleet will be revesed wh enover tile distturbin planet shall lpas tlrough tihe pln of the celptiptic, ad cotmnt nce t ite de sription of ttat part of its orbit whlich licsh a bove this plane.' roim the ab'tove reasoningt it is clearly mar.ifst that as not ta solitary platnet or satellite is motving tludisturlt led under thle at tractive p-ower of its primary ilody, not onet of the teatvenltly bod ie s describes ritorously an elliptic orbit, nor does the line joinitn the sun with any planlet sweep over preciset ly equal ar.nea in equal tie.s, noithert are the squarles of the periodic timetcs of' the Ipanets exactly proportioned tot to tle cues of teir miean distances from) the sun1. iIl short, every latw of I.Ktp'ler, whereby perfei'ct h}ar1:monyt seemed to be ijntroduccd amtolongl the lheavenly lbotdies. is now seen to tail in consutquctcet of the law of universal gravit ation and we filnd ourselves surro.uled tyt a: tproblnfe of wolnderful,grandt urt but of almost inlfillite complexity. Befiore thtis problem clan be filtly solved wo must mleatsureo tte distanco whliclh separattes every l4 ian t fom the sun, and whicht divides every satellite from its primary; we mus tttl 4 te h st weih the un a all lstil )planets tian every siatellite; we mitust determine the exact periods of revolution of ea:ch of these rctvolving; worlds; and when all this is tacctomlpslihed, to trace out the reciprotca influt!unces of etach upon the other detmands powe.rs of reasoning fir t traiscclldin.: the abiilities of the most p)owertful.genius' a lnd henco the mintld musit cither ftrel't:o thce resolution of this p)robltcmn or prepare filo itself some t enmta'l machIhilnery which shall give to though. t.andt reason the saint mlechani cal advantages which are ol - tti:tCed lori the phys-'ic'a powfers of thle body by the in-t v\tltiont an.d costructtion of' thle mighty tengin' of lmodern ineehatrn i..s 208 if H, A AW S oF h'll'is has actuatlly been accomplished in the discovery and gradual perftct tion of a branclh of mathtlemtics called the inf/iniic's'imndal aw.lysis. IJp to the tinto of Newton, tle indtl( employed (alone the reasoning of geormetry in tlt exainittnation and discussion of the problems pnresented in the hteavens. I>lven Newton himself was conltteitt to publisht to the world the resuIlts of the application of thie law of gravitation to the movemt0ent of tihe planets and their sate llites under a geometricat l fo'lm, cxh.iitintt in the use of these old tmitltods, a sort of gigantic power which lias ever remained as a monument of his wonder-. tul. ability.:le waNs, however, fully conscious of thle fact, that the mintd demlanded for its use, iln a fill ilnvestiliation of the phlysical universlac -in the pursuit of these flying worlds, journeytint g througl e t i spe ad uchl a crowd of disturbtlingt influtncne. -a ftr mort1 e subtle, pliable, (and powerfull mental itacinery tlhan that fulrnish.ed in the cumtbrous forms ofg ecorl Cetrical'treasoning. Conscious of this wanlt the genitus of Newton supplied the dl ic:iencyt and gave to tle world tite tiin/ite/simt al ana/qysi, whlich, ta im lproved and extended by the successors of the gtreat.'iEnglish philosophecr, las enablled man to accomlplislh result:s whiichl seemt to pl.ace him almos tt t taon t thle cods Th1e plan1 of our work (does not permit anyt atttempt to explain the nature and )powers of tlins tnw method of reasoning. We can only illustnrate ilmperflctly the diffcr. ence between the lse of geometry and anait lysis.'tho demonst;ratilon of a pmroblemt by geometry detmanids that thle tmind shall comprehtnd and oldt the first step in the I rain' of re:tso:nlinilg, then. whileit tthe first is htld thell secol: d mnlst be comtpre ltitded, atnd wh il itently ho1lding tlhese two' stepjs, tihe third niust be lmastered ailt( }hctld while MT 0 tt f N A ND I) O( t r V A V T T I[ 0 N, 209 the mrind advances to the fourth step; thus plrogrssing with a: constamlttly accumulating we ight oppressieng tlc attenlation, and tending to crush antd destroy fiurtlthor fllortto advtance till, finally, th1e steps becoln so numterous and comlplex that only those possesscd of at genius of surp)assing vtior are able to reach in safety the last step, antlid rs thus gsthe full demont'tlstration of' t he problem, Suct is the reasoning of geometry. Ttlhat of analysis is entirely ditbrcnt, I lIer the great eflbrt; is put forth to mnaster fully andti perftctly the conditions of the problem, tand then to fisten up.on the piroblem thtus mastered the an.t alyticatl machlinery tdemanldedt in its resolutionl. This once accompiJlish:ed, the mind puts il rth1 its elergy and accoi.. plishes the first step, aln matiy there stol and r est, in t.he tull confidenc thatt awhat has beont gainetd cantt nevr be lost. )ays, eveln months mlay pass, before the l problema be ressutmnc but. in this lapse of time there is no loss, and the investigation mnay be taken up precisely where it wats left 1off; and so one step after anot.helr tmay be tak'en, eatch depetndeit on the other, but each in some setns terecotypted as the mind adv ances, and remainintin fixed without the putting fortt of iany mlental efAbrt; to retalil it. In short, g(eometry demiands a vigor of mind suffi:i-. cnt to grasp, and toldd a tt t}h sate s1 instant, every link in the l *ongaest anid most compltx chain oft reasoniii whiloe ana.lysis only requires a power o f genius sutfiicient to deal with individual links in succession; thltls, in t} en td, rcn'tachiitng the conclusion by short tand comparfativcly easy mentalt mlarches. (1.11 J." l' XC It I ~ INSTIRUJMENTAL ASTRONOMY. Ms}tu{O~>FR O(4 ITAINIlN(O " f}t [' O} I'ltg I Y. or' — i -. SI i ti't,'N i tAW NO AT I MAS.. O A PLANLi' Wi' H A' 8A'fLIR --'lt \Vt;tlN(o sk -.P r A.V NN NO.SATtI,IlT -P m-o!Pout Vrut N sut Surutuf ut ul 1 LA A ut) 1)04 u txi}K sri hit {ti;tA:Ytt~lo. D -' —"IN' li.LNYAI. t1; tfW}EpN I}k. Atl:tis...'i tgtr:t StEixt.tti':- Ts'it0}ft OlTi'AINFo. -'" lNSi'"i AN't i.tlti*Xt i reat tas tlhat of the earth't s moon; and Itc hnce J upritcr's attrac — tion to counterb-alance this ttendency to fly fromn the cetlter mustt be one l(.ndred folt greater t}a that of the earth. Thiis is on the hypothesis of equal distanles. Btaut if Jupiter's moon be) stupposed to be twice as reioto froml its prilmatry, and to revolve ten times as rapid as 1our moon,1r t1he will it be demonstrated tdhat Jupiter is one hundred times heavier, onl account of the 8squarte of the velocity of the revolvinog moon but this weight must be multiplied by the square of two on acecount of the double distance at whiclh it acts, lilente undert thso circumstances Jupiter would be 400 times as theavy as the c:artlh. Th'us, to determinei the weight of a planet in terms of, the earth'fs weig lt [ as untity, we lmust learnt thte exact distance attd periodictl time of our mtt)ooln and also theic interval by which the planet and its mooni are (separated, as well as t.hel period of revolution of the satellite, all of which again demand the use of ir'struments of a high order of accuracy and delicacy. T. WtE,]l.A PLSANIE.PT itAVINxt I NO.SATEli, ITI..........'..,Three of tthe platints, viz.; Mercury,'Venus and Mars1, so 216. I N'T R t if M1 N T A SI A ST R N O fM Y. tfar as Imown, are not accompanied by a moon. Theo prceditn', ethodi of obt)tiainlig thle l-Onass or weight will not at'pply to eithfer of theseO planet.t, It is only after tactjuiint g a v ery texct knowledge of thei ove mntlts of the planets whose imasses ma:y be derived from0 their satellites tfhat it buecotes possible to determline the weights of the rematinitn planets..Let ts uppose thatt tI}te earth' alone revolved atrotund the sun8 and that its orbit was perleetly determnined. hIn ant exterior orbit of known dimensions let us 1place tile plane. t Mars. This will at 011nc modif the tltrmer orbit of tlh eartt, and thle cthange will depend, in quantity, upon the mass of the tnew pl;anet; and iin case it became possible to measure thcse changers thcir values will give itie weight of thte body producing them. thiet same hypothesis remaining with refereoce to th: carth'sa otrbit, we may ima1gi ne the new planet, to revolve in thle orbit of Venuis, interior t o to that of t.( earlth, and the same kind of investigation will lead to the detcrrmina.-lia tionr of the mass of this interior planelt. We shal ssee hereaft:er that certain periodical co>mets, tvoral. t ly locatedt fitrn ish t the mens of corrolorat in g the reosults reached iby the abotve train of reasoning(, by tIhe datat thewir p1erttrbations furnish for reaching tIhe marss of thle plancet producitng these effects. T'o Wi:::t'li: ST:,:rilS............ efet produced by thle mt1oon oi tthe earth in ca.sitn ti ie figurte of its orbit to sy to ad to under t ho ti ur tte oon8's attractive powe furnishes tga:in tih data whterc!by itho moon's mass tay be deternlined. In the case of imany satellites to the same planet, their effcts on each other being. carefully determined, furnlishl the means of computin their l masses. This htowevert is a: difficult probleml, aldt ot e int which a X N S T U A I N T A LX ASTR ON Y 0. 21T solutiion las been iebcted only in the system of Jupiter.'the imasses of tite satllites ofh t hte tlr superior ipla1net1 have as yet not been obtailned with any reliable certainty. VWe have thls presented methods by which the nmasss of thte sun, planets alnd sBatellites'may be ob}ta ined, lprovided certain measurements can be made, which tnmeasure.ments dtemandi the aid of powerfil and accurate intS'utt T"'le distances separatvfing the sut and planets, and separating the primnaries and their satcllites, mtust be ohtained befor e we can trace the history of any one of these revolving worlds. We hatve already explained the processes by whitich thee earth's distance fi'orn the sun maity be obtained by the use of the phenomena. atttending the t.ranisit of V'1enus. Thi}s lproblem aga.in demanded itnslru.. ment.al wteasureiment. A.dmlitting thi earth's distance from the sun to b)e 0lnoviw, Kepler's third law1 will give the distances of all tile plan:etts of our system), provided wie thave obtained their periods of revolution around tho sun. t..hot method of obtaining the periodie times las also bcen exp lained, and in this proces:s instrutmental tmttsutremtiens are demanded. in like n:annert, to reach the periods and distances of the satellites, their elon gations, occultatitio and eclip)ses, must, b0 carefully nmeasuried tand noted, dtemaliding instruments of at higih order. ITo itrce at planet or satellite, in addition to the quan. tities already pointed out, wo have seen tlhat we mu1st know the intensity of ite impulsive force by which it was projected in its orbit.:tlt wv ve thae seen that tho i ntensity of any iltmpulse is mesured tby the velocity it Is capabtle. of producinlg int a ttit of tite. A dmit t ing,. 218 IX ST. ft U M EN TA. A STR 0 NO Y. thecn, that we know the distalnce of a planet frtom tile sunt atnd4 its period of revolution, we knt ow the velocity with which it moves, in case its orbit be circular. The eartht, tbr cxampl, in 3G5:1 days accoinplishcs a jour1.ney round the sutn ill a circle whtose diameter is t190,00,000 and whose cirTcumference ijS equal t to tis quantity taken 8.1415.ti t im es. llence, by dividing the numlber of miles traveled in the entire circuit by the nuirt)er of days occupied in the journey, we have the rate per diem, or velocity. I)ividing the spatce tpassed over in one day by 24, we have the rate per hour, and finally may obtain the rate per secondt. If tle orb1lit bot not circular, we can atlwa ys find a cirmcle whie, fbr a very sIh(ort }distancei will coincide with an elliptic or other curv, and on this circle we may suppose the planet to move ftr a very short time, as one sec ond, with uniform velocity, and th spate Spasso t e over int this unit wilt again measure tlhe intCsity of tihe imt)pulsiv e Int'e at tilis part o te f l t orbit. HIe.re a: iagin we havc pI ttresupli scd a knowledge of the tmagnitude and figure of tho eclliptic orbit belfore t i the intesity of tle impulsive force cani be rachied, anld to determine these quantities instrlumenltal Imeasuremetnt is ddemandedIc requirin inslrttmentts of great perfection..The last quantityy denmandled by tie ma-thetmaticiant in writinlg out thle historyti of a pl )anet nmovinlg ill space is ttle dircltion of tie ilmpulsive tbreo pt jojet in t it its orbit.'Thiis is readily obttaiied when. we siall htiavi learned the exact direction of at ]tine tangent to any point of tlte p'la;ttary orbit; fort the direction of til impulst must always be tanlgent to the rve descritbld 1b thl body set in motion. If we join the planet with thte sunt bty a right line, this line will fibm tan angle with tangfent INS T E X NTA N ASTRONOMY. 219 to the planetatzry orbit; atnd we shall filnd hereafter thatt the natuvr of the orbit will depend upon the value of tl:is angle, or in otlter langlage, oll the direction i l wlhich the impulso isl applied. Titnles we find that not a single quantity of the five required to detert ilne the circumstances of nmotion of a, body revolving liunder the laws of motion and gravitatitonl can be treached without instrumental t e asutremctt!; so that our entire knowledget of the phylsical universe hatngs at latst on the accuracy and perfection of the inshrutments wht ich have been inventedl and constructed ir aking these metasures, a fItc't wvich tlevates instrumen.tal astronomy. to a position of( the highest dignity and inlportInco. T'he measures de-manded in inrstrumental astronomy are divided into two great classes. In tlhel jrs! cltss all the measures of position are absohttc, thlat is, a star or planet whose platce is thus determined is located onl the celestial sphiere, alnd fixed for the mtomtent in position by a mieasure of its distanceo, say, frolom the north pole of tlho heavens al ong the are of a great circlo, and also its dnis.. tance measured on the equinoctial firom the vernal cqui.. nox, or firom some other fixed points which may ha ve beo-en selectetd, In the second class al the measures are retl-ive or dif' /t/tlir' a; that is, an interval between two points in close proximity is determined. To tltis class beltong the m easutres of the diamteters of the stun andl moto and tplanets; the clonga.tiont s of the satellites from their primariets; the metasures of the transits of YtVenus alld Mtercur'y ac(ross the disk of thto sun; tie mea csures of the solar antd tlunar spots; the distanccs betweten the double and multiple stars; in short, a.ll those measures involving mere diltlbrence of position. 220 XN'.T It U IM N TA, AT 8 rT t ON OM,Y..EactS of these classes of measures dtemands: its own pccltitar talld appropriate instt mentll ttl e of thlem involvingt the data require'd in the solution of the sublimest'proble: is of celestial science. We shtall now proceed to exhlibit anl outline of tho structure of a few of tlhe mrost iriportaitt instruments n'he-. lon'ging to tthese two elass es' only fibr the purl pse of proesenting. tie extraorditnary di ficult ies w}tich must,he met and coltuered in the seeminigly simple mechtanical:pobleml of fixing the place of at star in the celestial sphtere. For the purpose of giving position to the heavenly bodies astronomers refer t them to the surface of a celcstial sphere, whose poles are the points in wlhich the earth's axis prolog ed pi'erces the sphere of the fixed stars:. PTo dete'rmine ta pointt ont tthe surl'tee of any sphere we tmust fix its distance on the are of a great circle fromt the north )ole and we must also know the distance of thie meridian line oni which it is located, fromt a fixed tmeridian. A..st. ronomlners have chosen for thteir prime meriditan that one whitch pas.ses thtlought the vernal equinox, and as the celestial sphere revolves to our senses with uniform vo.elocity once in twentyt-four hours, the vernal equinox will come att thte end of th}is period to the meridian of the'flace from whence it started. Any object, therefore, vhichl crosses the meridian of a given plate an hour laterl than the vernal equinox has its place fixed somewvdherei on' the circumferenc of a known meridianl, or }tour circle. If at the same time its distance firom the northl pole can be determined, its position oit the celestial sptere will be positively defined byy these two elencntLs. As we Itave alretdy seen, tlte vernal equinox is IX NS T RU 1 i 3 N 1' X T A S T Rt 0 N 0 O' Y. 221 thei point in twhic)t the greatt circle oF the heavens, cut out: t:y the indefinite extension of the plan f e of tle earthas orbit, intersectst thle equimnocttial circle, or tihat circle cut from tite cclcestial spherie: y the indefinite extensionl of thle planle of the earth's equator. If' thte vernal e(quinox were a'bsolutely fixed, andl if in titatt point a star were lo-t cated, this st:ar would revolve witth all tim othier stars of the heatvens once in tvwenty -fbur siderealt hours. ITo marki thie movemen it of this vernal equinox ast ronomel employ the sidereal clock, whose dial is divided into tt; wonty-t-our hours, and wiiicel, whenl pr)(.fc(tly adjusted, will mark Oh. Oi.t Os. at the momntentt the vernal; equinox is on t}t ]mirlidi.an of the placte where the clock is l)caitdl. A.ll poirnts on the celestial sphtere will pass the tnmeridian nccetssarily att ink. t ltets of time mark ingt tIle poition of the hour circle in whlict they arc located, relative to tho e p:imte mcridtian patssing throuhll tlthe veit.'ial equinox..The se interva.ls oft time which elapse b}et.wCeei tile tpasstge of the vernal equinox across the imeriditan of a given place, iand the passage of any lheavernly body acrosS the s.amet tmeridian, are called rsi4hdt tsceen:sitns. T lu a star which follows the vernal equinox, after ait interval of 21,. 10:m 20s, mas ma rked b y a perfiet sidereal clock, ias a. right ascetsion of 2tt..O. 20s. l Thu. s, to fix the place of any heavenly body on the celestiatial sphere, two i nstruments halve been devisedl thli o one having fb1r its object to inecasuret. rlh pohtr dis-. lances. while th:e otlher is oeilployed in th:c lemeasurem)entt oft riy/tt slcf t'csioitns; the first of thes is denominated a ui.t(/rl cire'/c, while the second is called at frat si itWe shall firstt consider the prirciples involved in the construction of tho transit instrutent. Th: is in8strument .222.. tN S T R S R M N T A L A S t 0 0 M Y consists of a telescope emounted upt)onl a txis perpendlicular to the axis of the tube of the telescope.'Thlis per tpeindicular axis terminates at each extremity in) two pivots of equal size and perfectly cylindrical in fotrm. To give sulpport to this instrument at solid pier of masonry is built) restintg upon a firm foundation, and isolated from the surrounding building. On the upper surflace of this stone pier two stone columnttl are placed, whose centers are sptarated by a' distance equal to the length of tthe axis of the transit; ol te top.s of these columnlls metallic plates are fastenled, to which metal pieces are attactthed(, cut into tihoe shape of the letter Y. If in t}hese Y's thio pivots of thle transi t beo laid t in case thle axis be pre:cisely level, and lying due east and west, then the axis of tlh telescope, or visual ray, be)ing carried around t te healvens, by revolvi)ng the instrumtent in its8 Y's will describle a meridian line whtich will pats throlugh't the north pole of the heavens. If this meridian line could be rendered visible it would be tpossible to note tLhe passage of any star or other heavenly body across t}is visible meridian. This can:not be accomplished d(irectly, but the samet end is reached lby stretching a delicate filatmnent. of spider's web acro ss the center of a mettallic ring, and placingt it in the focus of the cye-piece of the telescope; lwhen this spider's wIe) is lighted up by a lamip, throught a suit-abile orifice, it is seen as a delicate golden line of ligh; t stretch-t ing acrotss t ie field of view, and res.ting on the dark balckgrounditl of the Ileave lcs. trevolving the ring which INbears t}he spider's web, we tmay bring this web) to coincide, throughout its entire lengtth, wiith at tt ru meridlian line, and tlius, in reality, we procure for ourselves a visible lmeridian qutite as perifect for our purpose: as athoiugh it were an actual line of light, swee ping from ni orth to soutlh Z".: INSTRUMENTAL ASTRONOMY. 223 across the celestial sphere. To render visible the axis of the telescope, or to direct the visual ray, another spider's web is stretched across the field of view, in direction perpendicular to the first, and precisely in the center of the field, so that by their intersection these spiders' webs form a point of almost mathematical minuteness. Let us now examine what is demanded in the construction of the transit to render it an instrument perfect in performance. The object-glass and the eye-piece, forming the optical portion of the telescope, should be perfect in their figure and adjustments; the tube in which they are placed should be perfectly rigid and inflexible; the optical axis or line of collimation should be exactly perpendicular to the horizontal axis on which the instrument revolves; the pivots should be exactly equal to each other, and precisely cylindrical in form; the horizontal axis should lay in a direction exactly east and west, and should be absolutely level. In connection with the transit we require a perfect time-keeper. The clock, when properly adjusted, will mark Oh. OOm. OOs. at the moment the vernal equinox is seen to pass the visible spider's line meridian of the telescope; it must then move uniformly during the entire revolution of the heavens, and mark the zero of time again when the vernal equinox returns to the meridian line. Such are the mechanical demands required in the construction and use of the transit and clock; but to obtain a perfect result the observer is required to perform his part in the operation; he must note the exact instant at which the vernal equinox passes the visible meridian, so as to set his sidereal clock; this being accomplished, to obtain the right ascension of any heavenly body he must seize the precise mo 224 x4 IN2 S T RUt M E NT A t A O 8 O T It 0 NO M.t Y i2tC, as. marsked by Ilis clock, at Nwhich the ccnter of tho object under observattion patss e tol:e mieridian.l To a obtai.n, then, the elemllt of right ascensiont required to fix the place of a heavenly bodty a; t a given tmoment,;wo require a per fect transit, perlbectly iadjusted a pt r,lefct clock, perictly rattedI and a peri ecte observerl witl a per- fect method of subdividina time into minute iract iolls.;Not one siglte one of these demands can ever bte mot. Il;vcn admittini g t te possible construction of a per.efict in8trument, every chang t)e of temperature will tefect certain chi-ngcs in th e miaterial of whIlich it is comltiposed. No two pivots can possibly- b e made a exactly equalt nor )pr - cis cy cylindrical in fbirm and sould s the observer succeed in placing the axis of tins transit;iso as to lie east and west, as well s well horizonta.l, it will not rernain in tlthi position for even a single hour of time. fIt the clock bo adjustetd so a to mark the exact: zero of titme and to move off with a unifrm rate, this rate will soon sensibly chang e and must bet carefully vwatched even from htour to htourt.'T!lho observer himself is but an ilmperfect and variable machine, utterly incatpable of mtarking the exact moments required, his work being sul}ijcct to errors, whose values fluctuate from day to day; and to addt to allc these difliculties, the atmolsplher wlicht surrounds tho carth not only possesses the power of d iverting the rays of light from ttheir reotilineal patt, butt becatuse of its conlsta nt fluctuations and ltcan ttt.i. produces a treonmulous or0 dancing motion in tflh stars under obsc.rvattion whvlic(h, to a certain extent, renders it i mpossible to do exact work, even with p:'ertfect instruments and por t observ.ers, could such be foun ttd.'We will now examt inet the instrumental man s requi red to determineui the second clement, the i/oriht polar dis. T N B T R U M E iN T A T A sT IIO 0 NO0 M Y. 22f. t10ttue, rwhich isj demanded.l in fixitng the place of a httavenly body. f'or this purpose let 1:s tsupipotS a t cttitllie circle to be permaniently lastened to the horizontal axis of the transit, hiaving its center in the central line of t}e a.xis, and its. plane )pelrpenidicular to this lilne. LeC't tu suppost the t}trim of thtls circle to be dividedl into de.tgrcs, nmnulte:s and seconds of are, atnd this division to flave been pertectly accomnplislied. fr t us direct tihe tranksit telescope precisely to the north pole of the heCavens, and whten.t t sdirected let us fix upoit tthe st:on pier a pertmanent tmark or pointer, directed to the Zlero point on thte divided circle. As \e turnt the tiltranllit aw vay frotre tlie north pole towattrd the southtt the zero poi'nt on the citrchle will in lik aer ave t' thni e fixed pointer, aXnd thuls tilte d(i l1tanc froml thie Iortht pole to any object to which t tlte tlete ay "y be directedt will Ibe rad oi t tle dlivided circlhl fromt the zero round to tihe division to whlich the pointer directs. Sucht an istrument is called a.'meridian,. circl. HI[crc again new nmeitchait al diflicultice prisent themselves. Ihlic centerti of thie circle, tllet pritt ion of tie divisions upon its circm nterltcne are mn.atters whticht catnnotl be accomplished witth absolute a-, curatcy and t even if tis ere p)os sibl, thtey are liable to chtangtes to which all mlaterial is suttjectcd at every mo.menitt.'ltti slame is true of the stLability of thle pointer, anly change in,0 wthose po sition must involve anl error inl the tmeastured )lorth polar distanlce, titus far we lhav supposed that in otur l;clostial sphere we have two fitd pointstt of reftrence, itnamely, the verunttl eqtftttox atndlt t orth pt-iol'ar pointL tUn iforttntately ibr tle obseIrver, a:ttn to incretase t1e diliCtultices by wtlich tie is surroundted, neither of these poinlts remains absolutely fixed, and even their rate of mnovement is not unit8;: 22. IN s T B U I META ASTRONOMiY ibrmt; andil thus one diflicutlty rises above fanlother, ul:t1 Ininatittg in t.lh fiact that even tihe ligjht whereby oljects becomte visible doet:s not dart through space l with infinito velocity, butt winlits flight with a mt casurable speed, which, when conjoined with the speed of the carth's revolution in its orblit sensibly changes the apparent place of every ottject under examination. Add to this long catalohgue of difliutit:ics the factt that the earth's rotation ott its axis is rapidly revolving tmhe observer, his in.struments and o)servatory, at a possible rate of a thousand nmile anl hour' and some idea may be fitried of thle embarrassments underi which astronotmer are compelled to work out tho res olution of the great probllems of' the heaCvels. tlaving presented this array of diffitcultic, we shall rot undertak.e to show in every instance by wlniat preciso lltans tihey are overcome. 0 o far as regartds1 the mioveinente of the vernatl equinox and the north pole, the most extended and t elaborate observations have been mtado through a long series of years by the best instrumicttts andt the imost skillful observers antd these tlhav been re.duced autd discussed lby the most able mathemn:ticians, unttil by dilfftrent methods astronomer;s lave reached to so perfect a knowledge of the values of the errort due to these two caumes that it scems as though nto greater ap' - proxinlmation to accuracy can be made by the same amcthods. tlhat correction (tue to the movement of the vernal equiil)ox is called precession.; thtat due to the movement of tlh north polo is called n7ta/tion) of which we shall give a more accurate account hereafter.'Th error arising iroi) the velocity of light, conmbined w o orith the orbita and rotary l0mo tion of the cart}h is calle(d atbrration.. Thlis suttljcet will also )b treated hleratfttt, Of) the thitee:pinciptal instrtumental errors, that arising firom wantt of INSTRUM.ENTAL ASTRONOMY. 227 exact perpendicularity in the position of the axis of the telescope to the horizontal axis of the transit is called the collimation error, and may be detected and measured by mechanical means; its effect is to cause the visual ray to pierce the heavens east or west of the true meridian, and in the revolution of the transit this point of piercing will describe a small circle of the sphere, instead of the great meridian circle, which it ought to describe. The error arising from a failure to place the transit axis in a truly horizontal position iscalled the level error; its effect is to cause the visual ray to pierce the heavens east or west of the true meridian, and the point of piercing, by the revolution of the transit on its axis, will describe a great circle of a sphere inclined to the true meridian, under an angle equal to that which the axis of the transit makes with the horizon, or equal to the level error. The failure to place the axis of the transit precisely east and west gives rise to what is called the azimuthal error. This causes the visual ray or line of collimation of the telescope to pierce the heavens on the true meridian only when directed to the zenith. This point of piercing, by revolving the transit on its axis, describes a great circle, which departs from the true meridian at the zenith, under an angle precisely equal to the azimuthal error. Methods have been devised for measuring these various errors, and for computing their effect upon the apparent places of the heavenly bodies. The rays of light by which every object is rendered visible, as we have already stated, on entering the earth's atmosphere are bent from their rectilineal path, giving rise to a source of error called refraction. The laws governing the direction of the light, as affected by the atmosphere, have been carefully studied, so that at 228 INSTRUMENTAL ASTRONOMY. present it is possible to compute with great exactitude the change of place of any object under observation due to the effects of refraction. The flexure of the tube of the telescope, under the various circumstances by which it may be surrounded, have been thoroughly investigated, while the exact figure of the pivots of the axis has been subjected to the most rigorous mechanical tests; in short, all the mechanical deficiencies in the instrument have occupied the attention of many of the best minds for the past two hundred years, and thus slow but steady advances in accuracy have been accomplished. To remedy the errors arising from the perturbations of the atmosphere, as well as those arising from personal error in the observer, in seizing the moment of transit across the visible meridian line, several spider's lines, commonly called wires, parallel to each other, have been introduced into the focus of the eye-piece of the transit, and thus the instant at which the star passes each one of these wires being noted as accurately as possible, the average of all gives a better result than could have been obtained from any one wire. To remedy the defects arising from the imperfect divisions, from imperfect centering, and from changes of figure in the circle from whence the north polar distances are read, it is usual to have four pointers, and even sometimes six, by means of which the north polar distance is read in as many places on the divided circle, the average of all giving a better result than any one reading. These pointers, as we have named them, are in reality powerful microscopes, permanently fixed in the heavy stone pier, on which the instrument rests, and having their visual ray fixed by the intersection of spiders' webs, as in the principal telescope. NSTR, U t.ME NTAL A S TIt 0 N. 29.I')rom tlihese st'lrumltt il:eimperfections we pass to those whltic:ih b1elong:, to the clock, and hlere,trai te aW e coin})ltldt to worik witht an imtpe:fect imachine. No clock lias ever been mtade whicSh can keep perfect timoc and the g-eiat ohijtet of the observer is to learn the peculiarities of his clock, to determineA its doviations fir*o absolute 4ace.ltcy, and to be able to matrk these deviations, if possible, friom mntinute to minlute, T'I1h observer, havi)ing mastered all the sources of error above descri bedt next comeslt to the eonsideratiotn of his own persott l ditlevitions from accuracy Int attempting to lmark the imomlent tit t hich a star crosses his visible meridian.'To o)bs.rvt c the transit of a.star acrt(s the meridian, he'lace.s himseltf, att the t'ra.nsit. instrumentt, enttle in ltis iotet-book thie hour and minute fromu tthe tece otfthe coclk, then fixing h1 is eve thlrou:gh the telescope upon the star. antd countitan thle beats of the pe.ndulult,1 he i:bll ows tho st ar as1 it slowly advances to the meridian wire. Between somiet two ibates thus counted the star crosses the wire..lThe observe r holds in his mindt as w el aws he can tlh star'ts peostition at thle close of the beatt betlre the patss'ae, andt at t ti close of the next t beat after tho ptlssa,.te. ari, mentally subdividing this spacec passed over in one secont into ten equial parts, lie estimates how man11y of these Iparts precede the passage of the star across the e riiant atnd these patts atre the fractio)s or tenths of t' seco id, which matrk the time of t ransit. Thu's li adds to the cntury int his note-book already made the numinber otf beatst of the penduttlu and also Pte1 f'ractions of a. seconti'above obtained, and tius the0 time of tlransit is obtainted, approxi.mall. d t t he' t te nth ptart of one second. of time-t In thte method of observing: transits just explained so 2.80 I N T RII U M -a NI T A 1, A S3 t t A RONOMY. iany thintg are demanded of the observer thiat I}s atteoltion cannot be given exelusively to t the deterilation of thle motmIoentt of transit; lio must keep lup the coutt of the clock beat; hie -must -hold i his mind the intcrval ptaseds over by the star firom one b0 eat to the next during the transit; Ith must divide this space by estimation into telths; 1-it must assitgn the tnumtber of tenths which precede the transit: lie must enter th seconds and tclent in his note-bo ok- keeping tup the count of the beatst of the p(endulmn, and tihs pl'ass, from one wire o tothe next successively through attll the system of wires, so that in this mu'lttiormi eflort his powers of attention are taxed beyond what they are able to bear, and it is tnly by long practice tat attny valuabl e results are ever retached. T1}ue observer also finds that his modes of obsetrvatiot often. lead hinm into fidlse habits. l ie may markt tlhe time from his own menital couttrt of the beat, rather than fri'n the sozud of tlie heat itself: or Ite may fid h imself rlunning into the htabit of fixing his tenth}s of seconds predominantly in one or two portions of thie scale of tentihs. It is antitfei.st that in a. thotusald observations tle ttentth} of a, second on which the transit aflls ought, to be uniftibrly divided't aonltt the whole number. Thlis there s'huld bl a itumdredt observations in whict t:le time of transit should fitll on tlh first tenth of a second, a Ihundred obseirttatlons il which the thtime shouldM: fhal onl on the second entil, and so ou lr e ch of thei tenthsl.:But lan >oserver may fim l wi hen he )comes to examine a thoustand o i o bservationsl that two ori three hundred are ente.red ats i1 ll-. intg on t1he third tenthtl and tthree or tlur hundred as ftlling on the seventhl tenttt, Tlis o0inly detmonstrates that le tias tillen into Ilabital errort due to the fitct that lie is colmpelled to estimatc. Ini attemlpting to I tN S'.TRU M N T A L ASTRONOMY. 231 CSCes:ca fromn this particular etrror, and finding himself too mtucht attachlmd to onet portion oe tis stal, of tenths, he is very likely to fall into the other extroeme, tt and thus 1ho finds himtself a variable instrument, alwaty importiect even in these.leitinnato sources of error. By studying his owni peculiarities more trigortously, and cotmparing himself wi th othes, it will be foittund that in case thet two persons compared ould cu at the same time look through the satme telesxope at the same star coting 1up to cross the sat-r}e mcridian wire, each attemptitngt to note the moment of passage, by listeni ng to e the eat of the s.ame clock, the recorded times would diftlr, one of the observers being unliformlyll in advtance of thle other. Should this experimcnt be repeated, at the end of a month, with everyi po.sible preccautionl tuhe dif;l'reCnee betwveen the two obse rvers will in general be found to ttchange, dttmonstratingt thalt one or thle other or both htave va ried inl this particutla and that an inter.-comparisnon of their observat ions now mtade by th}e fori r dikctrenceo would plroduce iaccurate results. This diffcrrence is ttwhat is denomtinated ttchnlically personal cquatioft and is supl)potsed. to a.rise fi' oml the ftct that time) is rteal ly an Fclc. Intnt inl the operation of the sens ths: at tttwo persons listening to t ee sase sound, las th sarp crack of' a pis — tol, the sense of hearingi of the one. may periformnt its otf ico of ctnveying this sound to the brain more rapidtly than thle othetr, t( taht th thmt sthae tmnay ble 1asserted of the sense ofi sight. F.or tle l'purpose of comparing t. the observattions of (dif. ft'rent astlro:nomers, it lbecoine's necessary to deterilme tle peulia.rities of each, and it w ould be a matter of grceat importa'nce if it vweret poss.ible to fix son1e abs tolute stuandard to which all observattions nuight be reduced. th ins is 232 XX S t R rUM N rr TA T A ST R ONO M Y accompElis}held so fr as the three in strutrmenal e rrors antld thel c/lock error are concerned, by actually tapiplying'a cotreet.ion which redu'ces each obsrervation to what it would have been. in ease none: of tlese clrro'IS hatd existed. Tho samie tmay be said of the correction a pplied for refraction and:fr aberration, As to pre cccsion, the posit iton of the equinoctial pointd stuplposing it to mnove with it.s tmean 6r average t velocit:y, is always given fi r, tle etpot h t to which the o.bservat-ion is referred. 1Ie observa tions are also reduced fir paralttax whe'never thi cdlemeni bcomnes sensible, tand are thus recorded as though tthe observer wer e loca;ted at the center of the t earth. To taecomlplisah thle inttercomtinparson of obs.ervations mlade at diffll-ret obser vatories thl oret yet remains the reduction due to di(tf/,r/ence or/f iitit.ude, and that depending utpon the p'er$son.-t pct.ttliarities of the observers,.The high demtand fi:or accuracy in instru mental otbser vation can onily be fully appreciated by those actua:lly 5engaged it' t he computattion of thre p lac es of t:t tevetly bodies. Observat:ions are valua.e l einl the ratio of tih sqtuares of their pro)bable errors: tlhatt is, if one seot of observatio-ns cane b produced in whlich the probtal.lo er'rors remain tamong the tentls of seconds of f time, while in another soet of observat:ions the errorls.are driven into the hltndredths of secondst, rl aore but one tenlth part as targe as the fi rmet: then the second set will be a thundrcd fol more vatuabll than the tirst. Th.iis principle atpplies. to all observations, but their e arsoe distanese so gireat and some m:otions so slow t t tat even the best and mtost delicate methods oft observation hitherto appl'tied fifil a(ltot'f(her t o neasu e o the to a e ot to halleciate the oth:er.'l his renmark is especially truit when applied to tho distance atd mtovemen ts which are found in the reg0ion I N ST Rt M EN T Af fA, A S T R 0 NM 0;. 0 2t ) 23 of the fixed stars. Among these remote obiccas, while in some instances thle motion is sutfficietly rapid to be detected and approxim'ately metasured, even in a sinlett year, in other instance, ad by fi r the larger Iltttmb11er, these motions are so slow that they must accumulate fir hundreds of yetars to beco-ime apprctiablc and mlnasurable by the mtost refitned and porfect instrumentis hitherto pr-. pared by:human skill..In the tthree great departments of astronomy there is but one in which there is much hope for increased fiacility antd accurtacy. ThI great laws of -motion and gravitati on t tare no doubt perfectly determlinnedt. T ihe matlthetmatical formnulte whetrby thlese laws are applied to the cittnm — ttanues of motion of the planets and their satellites tarce niow broutgttt to great simplicity and perfection; and if it were possiblo to ive to v the physical astronomer pejf'i:et datat le wvould be able to obtain perfect results. \We iknow by gm fetotlry tthat the areta of a rectangle is t ie productt of itrs base by its altitude. Tilfs rule or ifrmtula is abt.solutely accuratel and whenever we wish to apply it to det.terminte thte ameit of any particular rectangle we must t first accompishl tth mechanical measurementclttt of the length of the base an1 td altitude. To do this pcrfie:ctly is impos-. sible, but approximt ate results may bo reached of greater or less precision in proportion to the accuracy of the intst truments em-ployed, and the time and pains expendle upon t.ht wAork. Thus one measure mat y reduct thte proablc errors to onle huntdredth of an itnch, whtile in;tllother the error may only reach one thousandth of the satme unit,; tr like manner thie t heory tand fbrmulta of physictal iastron.tomy are nearly, if not (quite perfect, while, nhowever, the olb\ervations whene we derive the data. to be used in 23-84: I N S' T uIt, U ti. N T A L, A 8 T R 3. 0 M Y. cominptt:ation are, as we have scon, comlparatively imlperfeet:. T:hoe author of tlis work ha:s attempted to contrti. butt someth ling to tho accuracy and tacility of astronomlica1 obstervtion,.tPhe follhowintg is a brief account of the circumstances attending the invention of this now tmode of observation, now kitnown tas TH..i AlMEIRI'CAN MHT1IEIOI) OF TiANSITS.-'nl tile autumntt of the year 1848, the late Professor S. C. Walker, then of the o Utited States Coatst Survey, wavs engaged with ie at tihe Cincintnati ObservaItory in a series of observa. tions, having fio trhs.ir obiject the dteterlmination of tthe diflti~brcnc of longitttdt betwen the otbservatoriess of Pt ila.: delpthiti- anttd Cincinnati. It comtpar.it g our clocks or citronoe:lrters with thtose of Pthiladelphiat, ant observer at.Philadelphlia listening to the clock-beat touchetd the lomagtnetic key of the telegraph wire att every eatt and we received at Cincinnalti atn audible tickh every second of time, wtich was cartfiully noted, and thts our clocks were compared.. lThere wNere two sources of errol' in this maetitod of compatrisont8 arising fromt an inperfecet imitation of tlie clock —beat by the Philadelphiat operator, also froml our noting the a.'rrivl of thlat beat in Cincinnati. On tho 26th of Octob(er, 1848, Protessor Watlker, while coinversintg on this sulject, irstn presen-ted to me the me -. chanical problem of cau'ing the clock to send its own }eats Iby tele.-grapht:4 firom oneo station to tilet otler, or what amounted to the same t lig, thin te probtltem of c(nve/. ing time itnto space. as a lready sexpltailned; t'or in. ca,-o the cltockt could send its own. beats by telegraplt1 and these beats could )be received ton a uniformly flowing time scale, tite start transit could be als]o sent by tele'graph) and received on the same scalet; and thus a. new method of INS 8 TR U 5 E14 N T A L A S T R 0 ON 0 2M Y 8. 35 transits would att atonce spring from the resolution of the first mcclhanical problemL. I was inlormed by Professor Warlker that the proble-m had already been presented to others, but,:o fr s e w, d nc b so tl as e w ad n ver d. The iull value of the idea was at once appreciated; tand on the samte cvenlinlg at common brass clock, the only one then in the observatory, was made to record its own beats by the use of the electro-magnct on a Mtorse fillet. The problem once solved, nothing tmore remained thtan to elaborate such 1machinery as would render it po)ssi:blet to apply this new discovery or invention to the delicate alt positivc detantds of astro:nomical oblservations. ItI is well known that signals are transmtitted alotng at line of telegraphic wire by closing or by breaking the Awir circuitt over which the electricity passes from po 0le to polo of the battery. The finger of the telegraphic operator, by touching a 1magnetic key, " breaks or ma:kes " the circuit:, and thus either interrupts or starts the tlow o'f lectricit:y, The'probletm of cansing a clock to record its beats telegraphically was then nothin-g more than to contrive sxomo method whereby the clock might be made (by the use of some portion of its own:machinery) to take the place of the linlyger of thel living, intelligent operator, and - make" or break" tihe elect.ric circuit. Tlhe grand difficulty did not lie in causing: the clock to play the part of lan automaton in tlhis ptis e parcis rticular, but it did lie in causing the clock to (at;e automl atically, and at the same ttimte perfitorn p)rfet tl y its gfreat ftllction of a timrte-keeper.'This became a matter of great difficutty and delicacy; o to tax any sr )tion of the clock machinery with a, duty beyond the ordinary.and contemplated demanlds of the maker.t, seemed at once to involve tho'machine in iimp)ertlfct and irrgullar action. After due reflection it was decidet to apply to 280 I N$gTRU U MENTAL ASTI0ONOMY. the petRndubt. for a: minuto a imomit of power-, wi}hlreby tho l'nakin;l., or brea1' iin,: the electric c'ircuait, mni;itn t hio acoitIplislhtcd with the it reatest chaonce of.I: c(eaing any iljrlo ciltcot ort t1ic goingt of tlhe clock. The. principio wthicht guidedi in ttis slecction was, that Vw ought lt to go to tile Ipinimo mover (wllict in this case was the clo0c weiglht-s, tand. whi-ich could not be tinyployed ) antld ftiling to re.act the p1rinme lmover, Yw shoutl select the nearestl piece of michatismin to it, whlich in the clock is the pendul.I.um. A secodi point e arlyd y ler y experinment anid reflection was this: that th. e making or breaking of the cir. cult rilust be accomplished by thte use of mercury, and not by t a s -olid metallic connection. Thlet metthod evolved andtt1 t based on these two principle) s is the one which ttas been't in use now fobr mlore than ten years in t:heC Cincin.. nati Obsc)rvatory. lThte simplest, possible mtlethod of cautsing tthe pendulumi to " tmake " the circuit mnay be described as follows A..ttach to the under suritlc of the clock ipe)itdultum with gtum shellac a small bit of wire bent thus t)- -............... - thtn rightt and left of' the point over which the pendluilum vibrates when lowest place two small globules of mercury, into each of which there shall dip a wire firomn tlhc poles of thte battery. N'ow, as thle pondulu swings over t}he globules of mercury, the two.points oft the attttahed wire will fitallty come, for one lmomentt, to lip in thel melrculry cups, and thus make a momlCnt:ar br/idye, over which tth current of electricity may tpass tom polo to pole]. Thtis mocthlod, amtong others, ]having been triecd, was soon. abtandoned as uncertain and irregul ar in i ts ere.sutts. and the fillo'tv.ing plan was adoptedl A. s-tiall cross of delicate wire was mtounted on a:t short axis of' the same matetria:l ptassin~g throu'gh thIet point of INSTR UMENt.A At STRONOMY. 0 T Y 237 union of the fiur arms constitutinl, the cro.ss. T..is axis was then phlaced horizontal t on a metallic support, in Y's, wher e it igt vibrateit, provided the top steri of the cros.s could be in some way attached to the pendulum of the clock, and the L. cross " should thus rise land ftl at its outer stem as the pendultum swings l)backwta.rd and lforward. Thet }t metallic fiamre h)ea ring tlhe 8 cross'' also bore a s111all glass tube bent at right angles. This was filled wit mercury, and into one extremity one wire froml tie pole of thle tattery twas made to dip; the other wiri e was |nastd flastt by a binding screw to thie ietallie stan:d bearing the "cross, and thus every t time the'tcross') dipped into the tmercury in the bent tube, the el:ctricity passed through the metallic firame, up the verti4al standards bearilng the axis of tIe cross, along the axis to the stem, and down the stemt into the mercury, and finally through thle mercury to tlhe other pole of the battery. Thus at every swing of the pendulum the circuit was ma.d, and a suitable app:aratus migh-lt, b.y tIhe clectro-matgtct, record t ach alternate second of time, The amnount of of power required of the pend ulum to give motion to tle delicate wire-cross wats ahnost it ins(tnsibtle, as tlte stems nearly counterpoised each olther in every position. tere, however, there was great difficulty i lu prtcturing a fibre suliiciently mimlt:e:and. ela:stic to constitutt the physicald union between tihe top stlem of thte cr'oss and the clock pendulum. Various materials wcer tried, amorn otlters a delicate thutman hair, the very fitnst that ould be I obtained, but t}tis was too coarse atnd stiff: Its wtant of pliaincy and elasticity gave to to the miuto "wir.e-cross at irre gulatr motsion), and causedt it to trebotud fromi t lhe globule of mercury inito whlich it shlould 238 I N ST R t ME NTA., AST O NO MY. thavte plunCged, After mlany fruitless efibrts, an appeal was mlade to an a.rtistan of wonlderfil dextelrity; tlt assist;nlee of thle spitder was invoked; his wei,) perltc ictly elastic and.perfictly pliable, waas firnislhcd, and this mat terial connection between t-he wirce-cross and tth clock p!ndulum proved to be exactly the thling required. In 1'roof of this remark I need only stato the it et that one singe Bpider's twe hlas fulfilled tie dclicato dutty of moving the wire-cross, lifting it, tad again permittilng it to dip into the mercur evey every scond of tiloe fr a -period of m-oreth than three yeanrst I ow tmuch longer it miglht have ltithfully prfoermed tI.o same service I know not, as it then became,necessary to break this adm)irable bond, to make some changes in the clock. Here it will be seen the samoe webl was exp-anded and contracted each second during this whole period, and yet never, so tfar as could be o)1served, lost any portion of its elasticity. The clock was thus tmadeo to clos e te lectric circuit in tie mtost perfect mtanner; tand inasmuchl as the resistance opposed to the pendulum by the " wir\ecross " wats a. constant quantity and very minute, thus acting prc — cisely as does the resistance of the atmosphere, the clock(, once rlegulat:ted with the " cross" as a portion of itO machinmtery, moved with its wonted st-eadinessi and nnitb rmity. T'hus one grand point was gained. The clck was now ready to record its own beats automatically anld with abso.ute certainty, without in any way ta fiet ing tthe regularity of its movement. I t was early oljectIed to tihe mercuriial connection jlust described, thlat ill a short: t:ilme the surface of the:mercury wotuld becomet oxidized, and thus refuse to transmlit the current of elcctricity; but experiment demoinstrated that the exfltosiont produced by thi electric disch]1arge at every dip I N S t R i E N TAi ASTR f ONO A 2'9 into the mlercurty thirw off the oxide formed, and left the )olished st'rfice of tlhe globule of mercury in a pertict state to receivo the next passage of the electricity. So far as known, all other methlKos are now abandoned, and the mtercuria connection is the only one in use. Tiu: T' vXrj scAi. - -.. The: clock being now prepatred to record its beats, accura ely and uniformly, the next ilaporttant step was to obtaintt if possible, a unitformly ioving time-scale, which slhould be applicable to the practiecal demiands of the astronomer. In case the fillet of paper used in the Mor(se telegraph could have been made to flow at a uniform ratte upon its surfice, the clock could now record its b)eats, appearingt as dots separated from each other by equal intervals. But it was BO soon tt the pI)faper could not be made to flow unifbrmtly; and event ad t}is been po ssible, ta single nightt's work would demand for its record utch a vast lrtamount of tpapert that this m.ethod was inapplicable to practice. After caretttl deliberation, the' revolving disk" was selected as the best possible surface on lwhicht the record of time and observation could bt made. The tpeferen.tcle was given to the disk over the cylinder fbor the following reasons.:h-^'l. unifotrm revolution of tho disk could b.e more readily reached. The record on tthe disk was atlways under the eye in every part of it at tthe same timel whileu on' the revolviwn cyvlnder, a portion of the lwork was alwayis invisible. One)t disk. could be sub)stitutitd for another with greater ease, and in a sithorter titme; and the r as re of thtt frac tions of seconds could be mtore rapidly and accurately perorinmed olt the disk thlIan on thle cylinder. After much thought and experiment idt was decided to.adopt "am' take circuit." and' " at dotted scale" rather than .24:.0 XN S T If U tM E N T A t A 8 T It 0 N 0 M Y at break circuit" and a't lineatr scale;t ard II think it will be seen hereafter t hat in this selection the choice has.,cbeen fully justified in practice. Tlhese ptit::s being scttled, the lmelhanic eals problres entte-d for solution were the followhing: First, To invent somte imathicry whlich could give to a disk of, stay, twenty inchel dialmeter, rounted on at verticalai axis, a motion sucht that it should revolve unitormtly once in each mitintute of time; andt second o connect with this disk the machiwnery which should enable the clock to record on the disk etach alternate second of timel i in the shatpe of a delicate round dot, JtJhirdt t'he apparatus which should enable thl ob ). server to record on the same disk the exact imolent of the transit of a star tacross the tmeridianl or thle occurrence of a ny otlier phenonimenon. Thet first of these problems was by 1ai' the most difli.cult and, indeed, its perlfct solution 1remai ns yet to 1)o accolmplish ied, thou.gh, for any practical astronomical putrpose, the probletm as been solved in more th-aul one way. Tl.he plan adopted in the Cincinnatti Observatory Imay be described as follows:.- The clock -ttwork m' achtetcry cmlployed to give to the great equatorial telescope a- utfori i motion equal to that of the eartth's rotation, on its axis, oftered to me the first obvious approximate;solution of the problle uinder consideratiion.. Thu-is mtachiinery was accordinglly app lied to t1he motion of the disk, or ratCer to frluhi(te tlhe motion of revolution, tlis motion )bing tproltuced y. dlescenditg, weigh.t, after the flashion of an ordinary clock, It twas soon discovered tlhatt the lj'frantenholel r clock," as t is machine is called, was not cont.'petent to produce a motion of sucht untifbrmiity as was now required. Severa l. odifications were made withI a, pl:sitiv\e g;nHat. but a'fter long stud y it t: w- titialyl dis I N S T Rt t N' T Ar 1 A S8 T 0 N 0 M Y. 241. covered t that when the achiry was brought into pe.r — fott tdjust:tment, tic dynattrical equilibriumt obtalined \was ai etqujilfiii:t lm of instability; tlat is, if io.t tt otion sucth as produced a revolution in one exact minute, it }bhgian to lose, this loss or decrement in vclocitty wtet ol itreatsiing, or if it commttenced to rtgaini, the ticrem.ent went, on0 increasinlg at cach revolution of the disk. Now all these delicate chantges could be watched with the rost pcrfect. certainty; as in case the disk revolved tniformtly once,a minutet. thenl thOe seconds' dots would fi:l.l in such ta mannert) (as we shall see directly), tfhat the dots of the samet recorded seconds would radiate froml the center of the disk in- a straigiht line. Any deviation from this line would be marked with the utmost delicacy downi to the thousanudth of a second. Blly longi and careftl study, it was at length discovered, thlat to makl any change in, the velocity of the disk, to increase or decrease quickly its.motioln, in short, to restore the dynamlical eq uilibritum, the winding ]key of the "' Frauelnhofbi clock" wtas thle po)itt of the matchinery where the ext.ra h}elping ftrcoe shoi}uld be applied; and it was fi:und that a per.t s8ot of ordinary intelligeCnce stationed at the disk, and wvith his inxgers on this key, could, whenever le. noticed a slig[ht deviation firom uniformity, att once, by slight as-.. sistanec, restore tihe equilibriuml when the machine would perlhapi contimue its pertrmancr e perfectly fior several milnutes, when again some slight; ace le'-ration or r..etardation mivcght I be required from the sentinel posted as an auxiliary,'T.}ho mechanical problem now demanding solution was very clearly announced. It was this' l{equircd to co:nst.lruct:t an autom-,tlaton \which sohould taklo tha e pltce otf tho intelligenti sentinel, wat:c tho g)int.' of the disk., and in0. 0 0'-/,, U 9 I NSTR I UM E N TA, A S T 0, 0 T N MY. staidtly corrcct any acceleration or retatlrdatt0iol. Tlhis, in tact, is tlie great problem in altl effort, to secure unifoirm nototion osf rotation..ttis roblc' was rcesolved tltorcticatlly, in mtlany ways, several' of which imethods weorel ex.e cuted mcchanically without success, as it was ttluna thtt the machtine stationed as a, sentinll to regulatet the going of the disk was too weak, and was itself carried off by its too powerfill antagonist. The tollowing method \ was, hltowever, i the endt entirely successul. Upon tho axis of the winding key, already menictioned, a tootihed wheel was atta-ched, tilh ge'arin g beg so adt justedl thfat one revolution of this wheel sthould produce a wholtle lmtiber of revolutilols of the disk. The circlumftereltncl of t this wheel was cut into a certain numl ber of notthes, so that, as it revolvedt, one of these notche:s would reaht l tIhe highxtest point once in t\wo sccotds of time. Bty moamns of an clectrotmagnet a stmall cylinder or rol ler, a t lthe extretnity of lever armt, \as m1ade to ftRl into thle highest notct of the tootted wheel at thl end of every two secondsl. In case the disk was revolving exactly on1e0 a minute, the roller, driven by the sidereal clock, ltby mans of a:tn electro-n:vtagnllet,:fil1l toth the botto of the notch, andtI..peifolted no service whi ttever; but, iln cae tlh disk b:egan.t to sttaci kl its vclotcity, t thl nt thle roller f(.l. O tt tl he re.t:r tea ting ic ) imtted ltace of tlthe notcl all tl tan tt l,'..... ward; tl bty a mniutc amount the 1t: rd diskt wti ilc, ot n tt tli contrary, ishold thte variatiuon mtt.front a. muiif', veloci(y piresent: itseh inf i an't acceleratt. inc.lt thent tethe troller stratttck onl the}t advan cing ftace of the notch, and thu thus tendedt slowly to restort tht cqtili'irium. I',et it e) remembered' that thtis delicate r egulator hits hut min:ut amount t of service to peoritorml. It is ever onl guard: and detectitng, as it X N 5 T U M N AT A 2 A S T 3 0 M O;Y. 243 does instantly, any disposition to change, at 0once applies its restoring power, iand thnts )lrescrv8s tan Oxctedingly lear approach to exacit uniftbrity of revolution. this reg:ulator operates th rough all the whcel- work, and thius acctomplisihe a restoration by mirtito increeticnts oxr dccrenments spread over ]:many iniiutets of tinme. Withi at uniitorimly revolving disk, stationary inl position, we should accomplish exactly, and very perfectly, thei record of one m11:tutte of tine;mc presenltitng on tlc re- cording surftee thirty dots at equal antgulanr intervals on thio circumterent o of a circle. Tt o receive the Iime dolts of the next mninuto on a circle of larger diamteter, re — quitttd either th(at thl recording pen should cihtang posiition, or that at ith end of each revolution the di.sk itself sitould nmove away firom the pen by a s8mall amount. We chose to remove the disk. T..'o accomplisht accurately tthe chaenge, of pos.ition of tte disk, at tire end of each revolution, tho entiret mtacitine was mountted on wivhels on a. smiall railway track, and by a very delicate lmeeltcanical tarmratgement accomplished its own elhaxnge of positi'ton lbtween the lifty-1nitti and sixtieth second of every minute. THE't!COUr1 NG.PENS.... —-.xfc.t Inow remains tonly to do.scrtibe tlo simrplte mach inery by hy wich the clock records its beats, ant d thtl observer lmakes the record of liis obser-' va tion. VThel.se instruments are ctalted tihe r ecordin /,ptC'tht belongitnl to t tite clock is ca(lledtl thi time tt; tho one used tby tthe o)bserver the ohbsrct Uvi p. i Thley are constructed andd operate in the tillowing ut" natlitse A mlnetaillic ari is constructed w ith a. sitort axis, pet.rpendic.ular to its lengtht. The extrem.tities of tlt:is axis are pivots wiorkintg in the jtaw of a metallic framte, whi'h supports te xi of thee ltis in, e t horizolntal positiotn. Tte 2:44 X INS r 1r tM E NTA, T ASTRONOMY, lo.nger armi of the pen reaches over into t:le cerntr of the (i)k, and iN rmed aIt its extremnity w ith a seel point or sty1 s. U: aon the tlon ar n.of t th pent ar nd neartt the atxis is located a piece of soft iron denominatedtt artn (a.ml'tf e) and beneath this armature an elcctro-n:tagnet is firnily fixed.'Ti.is mlagnt is phlaed on the circuit clost(d by tihe wire-cr'oss vibralting with the clock peitnlulumt and thus, at every dip of the cross into the mercury cup, thle armaltare of the pen is suddenly drawn down on the head of tile malnett ) and the momentl the circuit is broken a. spring acting on the short armx of the pen lifts it friomt the head of th e maget. It is readily seenl that in this wayy the sly/lus )brought down by a sudden shock or blowN oni the materia;tl platced on the revolving disk to receive tile record. Tmte pen is so t4adjustd that in case thei armlature )b simply placed and hla by altnd oil the heatd of the lmagnet.t; th steel point of the sty/fhs d:cs not quite touch tih recording surltlfc onl the disk. Th ela Csticity of the loffng a rm ofi tthe pen is, tlhereofri a.t l:mattter of the greatest 1moment, foir this elasticity causes the'pen to tmake a simplet dot, by at sudde-n blow and dre coil; whereats were tle pen non-lastic, there wotuld be a drag ibr tht ttie during which tlie magnet holds the peci, which would at once dest-roy tIle unitiormnity in the going of the disk. A pen constructed in precisely thle sname waty, mand itl:acedl att righlt angles to thl ftormer, so that the points of the two pens fill ini close proximlity otl tih diisk, is Olperatetd by a maLgnet matde by a circuit closed at vwiill I, tile iintgr of the observer; tand thus he is enabldt to throw\ ldown upon tuhe tie t scale a d(ot., which, fillint It lbetwt.een,some t)O-sec)nd d(ots on thet diiskl records trhe exSct instiant of any pheno mnon under w5observation. I N 8 T UMT NTA 1I AST RON0 OM Y 21.5 Whten the disk is filled, weo lave only to lift it fr.om its socket and replace it with a new disk. To read thei tie tt scale it is only necesary to mark on tthe disk fom tthe clock fitco ti time denoted by any one (dot; for?example, 2h., I.in. 00s. The circle next outsid e will tbe 12 h. lt6n: tht next circle 12 1t. Ii7m., &e.; while tli filrst or tmarked rtadius of dots will be tte 0 second of all the mirnites, tlte n1ext in order will be the second, the next the fbiurth, ail so on to tlth 58th and 0 second again. Thus we read t.le scale as rapidly as we re-ad a clock face, for the hour, nminix ute and second; and it. only remt ains to construct ai: achinle for meaturing the fractions of seconds. T'Pu.ANOU.1.:Al,'r M i:CRo;.-.........T tOis instrumient is very tsimtple. T ake a common tcatrpnter's two-tfoot rule; cut away the inner portion of o e f tIe leti for ti:wo —ttirdts of its lengtht and insert a piece of plane g las; draw fromt the centre of the joinit with a: diamoutnd point, on tle under surfiace of this glass, a delicate straiiht line, and blacken by rubbing iln black lead pencil. Thej arm is of this micrometer arle a little longer tthan tile radius of the disk. To the left hand arm, at its outer extremity, attacht a smatll brass ale, divided into second-s and tenthls, tand make it, 8say,. 2. seconds in len gth. W hen the two legs are closed the black line on the glass will retad 0 -on thlis scale of secolnds. At te joint drill a small hole, and at tite center of the disk to be measured etrect a s-mall vertical pint to fit tins i ohle. Lay tle instrunlent on t1 o. disk, the pin lbeing insertedi iin tile hole, an1d thus tlho fraction of secottnds may be measured with an y degree of prc.ision. Suttc is;an outline of the machilnery now ti use in thto Dudley O)blse rvatory at Altbany, alnd at the Cincinnati Obs ervtory. 2l6 X:: S t 1:M).tM 1 NTA A f T i R 0 NOM i Y. As woe have seen, inl the old method of t irallsit thet at" tletion of tile o:bsorver twas divided amtong manyr ob }ccts. I to was comlpolletd to keep up the countinttlg of thte:clock bouttt to estinato theo s)ace passed over by the star under observation it a second of time; to subdividet ttis space by estimation into tentlm; to write down in his notcbook the observed:moment of triansit across each of the wires, and all this while his eye continued to follow the movement of the object under observation. To t'ive tlto observer titme to make his record, the spider's lines or wires were necesst.arily sepa)rated by such an interval fir'o eacht other thatt seve ral seconds would lbe required by the star to pass firom one to the other, a-nd thus. but fet' wires could be employed in transit observations. In the it3nw mlethod thte observer is released fiom a ll responsibility witth rcbrence to time, countingl of clock bheat, estilmation of spaces, or entries inl note-book. 1The clock records its owt beat., and the oblserver 1ha's nothing to do lbut touch a mag:tetic key att the exact mtomlent itt whicth his star is bisected by the meridian wire. Thil touch records the moment of observed transit, and as this record is accomplishedd almost instantaneousl. y, the ohserver is ready to record the transit tacross the next wire, and thus the inttrval between the wires maxy be gr eatly reduced, and their mumber extended al most indefil itely. While in the old method long practice was required to make an accomplished observer (the best of whom could not record{ more than the transits on seven wires), in t:he new method a l fw nightl.s of practice gives all desiratble. experience, and tthe observer may record the transits acros s as many a.s fifty wires, should so large a. lntmber ever be desirable under any circuimstanles. It is fitou in thte use of this melthod that erroneous habits of obser IN' ST It tl f N J T A tl A S'i tC fT f) 0 NO Yl. 247 vation tmay cither boe entirely avoided or dete:ctedtt, adtt tltus corrected, It ilturnishes tlhe -nleanls on-f mei:attsr, with great accuracy the value of persot nat qlaiothn and has deilonstrated, indeed, that the large dibrtlences existing between observers, amfounting in somue illtanccs to I a witlole stcctnd of time, are cnot due to physiologica-l constitution, but almost entirely to fils8 habits of observation. I[t has furnished the iteanrs of measuring the tattount'of tile which clapscs between the occurrence of anty lil,noinhon fallinilg within tire grasp of the senscs of sig ht and llearing, and the possible record by the toucth of t maignetie key. In this operatitiont there re three distinct processes, the sense of siilt, for example, conveys to tho b)rain intformation of the occurrence of tih extettrna.l yph.cnomenon; thhe mind thus pereeives, and the will issues an order to thte nerves to record; the nerves executoe this order. Thus fart it hats been impossib)let to ascertain the amlount of time occupied in each of these procestses, but the sum of tile times, or that elapsitlng between thie m ment of occurrence of a phenomentton and its record, l-as been measured both for the sense of sight and the sense of hear'ing, itn a large nltumber of persons of both sexes and of all ages. PFrom the.s experiments it has been atscertained thatt while dififrent intdividuatls present promi-. nent anid marked difilernces, these dilffrenceC; are only found to exist in the hundredtlls of at' second of time, and not, as hIas been imagin,ed in whole secoins. Inl ceon-l lducting thecsc ecxperit ents it was ascertained that all ob-. servers, without at. single exception, in attempting to tmarkt tlie momrent at whicht at star crossed a wire, a.nttici" pated tlhe momenlct of transit, and tli recorded time was tthus in advance of tie t rue tine t. laving learned tlhi factt thle observer is placed upon his gtuard, tnd is f r 248 INSTRUM ENTAL ASTRONOMY. nished with the means of correcting this false habit, and of bringing himself up to a standard of positive accuracy. Another advantage derived from this mode of observation arises from the fact that it imposes but a slight tax upon the nervous system, and hence an observer is able to continue his work without exhaustion for a much longer period of time. We have mentioned that one of the most hidden sources of error lies in the uncertainty of the rate of going of the clock. The old methods furnish the means of ascertaining with comparative accuracy how much the clock has lost or gained in twenty-four hours; and if this quantity should amount only to a fraction of a second, it is almost impossible to assert that this loss or gain may not have occurred even a hundred times, or possibly a thousand times during the twenty-four hours. By causing two or more clocks to record their beats upon the same time-scale, the new method furnishes the means of inter-comparison between these clocks, even from second to second, if required, and thus from a record of this kind may be obtained a positive standard of time. The electro-magnetic method of observation in connection with the system of telegraphic wires, now extended over nearly all the civilized world, furnishes a very rapid and exact method of determining the difference of longitude between any two points. This difference of longitude is nothing more than the time which elapses from the transit of a star across the meridian of one place until it crosses the meridian of the other place. In case the two observatories whose difference of longitude is required are connected by telegraph, and are furnished with the electro-magnetic apparatus, the observer in the eastern TX NS T R U M:NTA L ASTI R0 XNO M. 249 observatorly may stend to hIls corrcspolndnt by telegraph t}lt. moment of t:ransit of tthe 8tar tacross his ow eridia. Ite will rcceive in rettiurrn by telegrapht the noncentt tlio same star crosses tile meridian of tho western observatory, and in case tte observations are perfecttly mntad, transmit.. ted with infinitil velocity along- the wires, antl recorded with} perfect accuracy, tite result will be absolutely perict. Tho comntmon errors of observation are readily elitinl — ated, tlie errors of recording, in like manner, are tasily detected arid meaisuredt and the only mattler of difilieulty wilich remains is to ascertain whethter the message s'ent along t te wire traves at att. nile rate, and if sot to determline,wha.tt this ratet ma)ly be, T.'to ctlveritsion of ttlimto into space, and tho delicacy of the machinery now et:lpioyedt in recording and subdividing tine, hlas flurnishled tht means of meatsurin ti e velocity ith which signals are trantsmitted along:I the wires of the tclegraph. No doubtt this velocity is modified by a. vtricety of circum.n stance, and may depelnd upon the direction in which tlhe tel(graplthic wire is laid, thoe csaon of the year, tohe tem:t perature of tlh eartit and atmosphere, but none of' these causes can inteirfere to to mar th 1accuracy of the work e-l' - ployed for longitude purlpoes; fbr there is no difficulty in determining the exact velocity with whiich the signaltts are transnmintted by the wires at the tilme of observation. T..h.tse are a. few atlong ma:ny advanta.ges which }ha ve b}cnt gained by the conversion of time into space, and thle apt plication of this pritniple to the otservattiont of astionom:ical transits. ThIIe author lr as attemi)ted to add somnIething to the ficility and accuracy of' the detettmiattion of ntor./ /oi.iftr dtistances, the second zgreat. elemo-ent employed in fixing the pltace of at hleavenly body..As already explained, 250 IN STRU MENTAL A ON A T 0 O M this clcm.ent is reachlited by the division of a circle attached to th,.e axis of t te t ransit, and the accuracy of0 tlhe w0ork.dependtts upont the perfectiol of tlese divisio:ns the tperl )iaielllt:!C f the fiture of the circle, t},he permacnence in th 1tlae p of the readniqg microscopet, an tho preisit on atttainlabtle in readinglm the subdivisiiorns of the cirlel. As the errors which ari Os front tlese diffirent sources are fouinft to le comparativetly large, for thte mleasurcerit oft tn ll tdi rcetces of north polar' distatnct s or small vartc of spaett resort has been had to other anid more delicato tmel aIticea ieo tttrivanies', he'1nce the invcention and l con-. tlructionl of the variousin' lc's m mer now in use, a.ll of which depend flr their accuracy upon the performai.nco of a.micromt eteri screw. Very extended cxperiments witht these in.st runents first crteted a. doubt in mty own mind as to the accuracy with which tle nicrormeter screw would repeat its own meatsures.'his doubt, a ddtedt to the fit tlhat thte mleasurement bylt t the mic rometer were very slow a:nd tedio:s, gave rise to th t cOffrt whticth:ha resulted int the constiruct'tion of a new systemt whereby diflrenles of northt potlar1 distance may be detteninted wtith great traplidity and precision, which principle can readily xBe cx — tended:t to the determination of absoluto north polar distancots. A description of the mtachinery employ ed' for this purposo ma1)y be found elsewhere. We are only concerned htere to notice some of tho possibl)e advantages of this new method of north polar distances. t will only state t:hat tho ma lohinery employed in all its joints andtt connections is of the simplest kind, alld eerywhtrec visible to t he eye. ThCere is no concealed lport ion, as il tie scre'w micromet) ter, no joints to grow impelfect by wcaritng,tl and no strong re sistance to chatng the figur of antly part: of the n tchinery. If the t:ube of the tele. I N STR tM 5 E N T A L A S T: R 0 NO, M Y. 2 >5. scope, loaded as it is withl tile \tcigl;t of the olj0ct. glass and cyc-picce, and its own weiglt, can bet depct-ded uponl to retain its figure wilttout a'counterpoiset it, is absolutely certain thatl the declinatiottr. zm.r, which inl the 1new method is attachedt to the axis of[ the tra nsit, if perkectly counterpoised and hearing no weight whatever, can be relicd upon }]i~t't..l tr'1tt b;ftt\ tt-) \ t \\Aflt\' I01) twe p to retaint its fitllre. tlhe lower exttremity of this arl, mtovingo as it does in north polar distan8 e, with the litne of collimation of the tolescope, by a connecting balr, gives ilmotionl to the a xis of the reading mieroscope, wihich, beincg direct ed to a. distant sctlet mtIagniifies irt a. very high ratio y metchanical means thi are th are throutgh which tho transit rc.volves in the plane of the mteridian. Thus it twill be seen thtat tiis new min tliodt is nothing m1lore thant thie use of a.lecAh aic al mayn/tr ier, and the only question is, can the seale le so divided ta to read'seconds of are, andt c anit bi 1 n)0 ade of i nvariable lengthl? iThere is little difficulty in accomlplishing both of these olbjects, finr scales ha:ve already been divided with such prccision that no error amounting, to tihe /ih dretdlt part of a sinlce sficou. of alrc couldt possibly exist. atnd it order to retainl an intvarible lengthi in the scale allt tlt s ncch essary is to grade it upon ai surtace constuttuing one ftce of at rectangular tube; fill this tube with water and br'okc. t ice, and thus a permanent temperature of 82: may be htatd for any lentgth of time. T'o Imeasur te t exa:ct valutt of the divisions oni the scale we have only to crn — l)oy teltiei divisions in mtasuring around the entire circtumfreenlce of the circle attachled to the axis oft tthe trasit. Sup)pose the lentgth of the scale to boe sixty m6il'nuto:. apptroxtimately, then if this length is contailned 360 times in the whole cireumtference, its approximate value becomes its absoluto valluoe and. at all events this experimenat 252 INSTRUMENTAL ASTRONOMY. furnishes the means of determining the absolute value. Thus while the circle furnishes the means of measuring the scale, the scale furnishes in return the means of measuring the subdivisions of the circle. These amount only to 360, and may be reduced even to the fifth part of this number, should practice prove this reduction desirable. This small number of divisions can rapidly be read up with a scale of invariable length, and by performing this reading at temperatures widely different a correction for temperature may be determined with great exactness. In the old circle, as there are no less than ten thousand divisions, and as there exists no permanent scale for the reading of these divisions, it becomes almost impossible to learn their actual values and to tabulate their errors, hence astronomers have been compelled to rely to a great extent upon the assumed accuracy of the subdivisions of their circles, as received from the hands of the manufacturer. By a combination of the electro-magnetic method, with the new method of measuring north polar distances, a very simple, convenient, and accurate instrument is obtained for recording the places of the stars or other heavenly bodies with great rapidity and exactitude, rendering it possible to construct, in a comparatively short time, a very extended and exact catalogue of the places of all the fixed stars, clearly visible, with any optical power. We have thus presented a rapid sketch of the old and new methods of fixing the elements for the determination of the heavenly bodies, it only remains in this connection to speak of the optical power of the telescope. These instruments are divided into two great classes, called reflecting and refracting telescopes. In the reflecting telescopes the rays of light from the external ob I N S T. U i ME N T A L, A STI 0N Y. 203 joct, plaTssingl down the tubo of the tlcescopeo, fall upon a.t mtetallic tinirtor or spe)lcurtlmt, whose Surfhet, perf.ecttly p(oli s-ed, has thie figure of a paraboloid of revolution, Being retlected by thins surfiace the rayt of lightt are concent trate(d at a certatin point, called thle focts, where an intent sely luminous itmage of the object is fortmcd,'his )Jiflta. is then examined bIy a magnifyjling glat, or teye piece, ant.d its dimension:s expanded to any required deIn; the refractlin t:lescope t i.o t light tilis upon what is called the o0jecct-yhtss, a powerfil lens, fwhich conllcentrate.s, by refrtaetiotn, the rays of light which piss througlh it; thus forming an image of tihe oljcct at the ibal p.oinIt. Th.-is im'e:tao is tthen examined, as in tth rcoflectilng t.elescolopt by eyc-picce: havingt difilrent Imagnt. f.lying power0s. I Hitherto it hats been ttund impracticablo to construtet oJ1jct1..y'lasses of any very considerable d(iameter, the large.st of tlhse glatsses in use not excetedi sixteen to t wenty ln inces n diatmeter*.'Thelse narrow limits do nlot exist, however, in thle construction of t}he meit.alic mseclat/a which belong to the retleting telescopt; and httleno wo find( gi'gantic instrument lIave been conl stru: ted by difte.rent obs\ervers, one of which, now in us by loId }'4"l)ss, has a speculumtl of Ino less than six fret inl diA,(,.}f}'t:!{O(.;t'-4,AYA.tAil-. —-.t''{};~1iy I {y ti.,','.Oi, itlt — t'tii.I i t.)F "tilt ]I'i".'.. iti t:i i'L t..... ):ti.'tO if "O X t-:.: iN l:t\i ANtM:*I.(.[N;$......."'4,-t'ti "3FO''I.'S,5,.t[F',"'{i. } t IAtJif, Arf4t'; fil-'It<,.~tll-::8 I"f3 t]. - ANt'$ t.TNSt.;Ri. - * T TS. s. T X N ii N. r i. 1 i i ini. tt 1 01C i'UKAA8 NV, oy:i:.tFiti~' —— "t'ii. IF,} A 1:> i t JI;i l DSCO' *;l' OF A^ NK AW XIt K 1", xl I' O P tL A S"i:'T. lr wats lrcnt rkct d at the close of our invstisgation (f tit SBaturnian systen tm iatt t this planet inelosedt by its orbit all the obtjects belonging to tho sol al systCe w\iltci weret known to tie k ncint and wXhose ptcnomnena, as observed and recorded in aill time, furntished tle datla for the discovcry of Kepler' s laws and the law of lt iver sal gratvitation, as fitally revealed by N Xewton. Whiloe many of the mtodet.t astt.rolnomitc s, firom t In txal'in ation of tth inter- lant l1at tt lp t tces, h ad ventured to smligrst the pro- bable existcie of a lairge planet revolvilng in an orbit interlledi atc bet\ weenu tlhose of XMasl and J upit.er, tno one had venltured to predict the possible dis: covery of planets lying exterior to thie miglty orbit o Saturntl, flrou thlt very dawXn otf astoronomy this 1)lan1uet had teld tho position of sentitnel on the outposts of tho plane tary syste, atld many strong ni nds h t ad long e Ct 025f8 U 11 A N U. t:ttaxnedA the opinionl tlat no othter bodies existd xt e rieor to tlhe orit orbt of r1aturn for'ting a pat of tthe sclmt1e of worlds revolvinlg a1round thl'e stt. Suchl, indeed waNs the prtevalence of thhis opinion thtat whcen iln 1.781, Sir W illialt Ilerischlell, in a course of systtl:temtic explottion of the heavcn;s, discovcrcd4 an object hawvint a well-definet d pltanctaiy disk, an. wihose movemenot aniong the fixed stars bectame measurabl, c ven at thL e end of aL few hours' lhe did not even suspec t t this flw ol:ject to )be a planet, but announced to the world that tle had d(iscovered at'mo1st extraorditnary comet, without any of the ulsual hIziness whlich attends these bodiese but presentint g a clear and well defined plehitattry disk.'Tils n ewly-discovercd object soon att racted universal atecttion. It was; observed at the roya l observatory at G - reenwich, and the t hein astronomer royalr, D)r. Markecblyie, was the first to suspect its ptlanetary chiaracter. IEltbrits were imade by several computer.s to to give to the new coicet, as it was called, a, parabolic orbit; this, iow.-. vert was fiound to be impossible, and it was very soon0 fund that tht e t newlyt discovered object was revolvingr around t he sun in ant orbit nearly circular in fiorn,' lying in a plante, nearly eoincident with the ecliptic, antd cornpletitng its miglhty revolution in a period of nro le ss t1than eif/hty-tt.o yfears. It must be remtembered tthat these extraortdinary discoveries and annou ncement s were t made at the end of a; very short; Cxaminationt while t}h lperiods of revolution of all the old planetts jhad bctte obttairnd tirom actual otlservation, th;roughl long centuries of pal)ti.enttt w\(tatching. TIhe periodic l time of this last tdi - coe'retd of all the. planets, wiich, by the old lmethod of watclting its return to t the sameo fixed start, could not have been dctcermio ned in ltss tlthan iglhty.-atwo yearst' anid vetle URANUS. 259 then only approximately, was, by the new method, based upon the law of universal gravitation, guided by the results of a few nights of accurate observation, and worked out by the powerful formulae of analytic reasoning, given to the world with accuracy after only a few months of investigation. This is the first illustration of the change wrought in the whole movement of astronomical science by the great discoveries of Newton, and by the almost equally extraordinary step accomplished by Descartes, in fastening the powers of analysis upon geometry. All the circumstances of motion of this planet were rapidly investigated; the eccentricity of its orbit; the position of its perihelion; the inclination of its orbit to the plane of the ecliptic; the position of its line of nodes; the measure of its actual diameter; the determination of its various distances from the sun, all these and many other peculiarities were accurately determined from actual observation and computation. These facts strike us with the more astonishment when we reflect that the planet Uranus is removed to a distance of eighteen hundred millions of miles from the sun, and that, although its actual diameter is thirty-five thousand miles. it is absolutely invisible to the naked eyed, and, when seen through the most powerful telescope, presents a disk of only the five hundredth part of the apparent diameter of the sun. At such an immense distance it has been impossible thus far to determine anything with reference to the precise figure of Uranus. The discoverer of the planet thought that he saw a flattening at the poles, but subsequent observation has not confirmed this announcement. We have only, therefore, analogy to induce us to believe that this planet, like all the others, rotates upon an axis, and that, consequently, its figure is that 260 URI A US. of the elipsoid and not of the sphere. The immense maglnitude of tlte orbit of iUranus, when cotipared wyitht that of the eartht, eauste t8 is planet to retrogr'ade over -an aro of otnly 3)3 86t' but the durationl of the retrograde motion extenlds otvr:a period of tno less than one h:undred aind fity-one days. No telescope lhas yet been a.t)le to discern, )upon the sufit'ice of Uranus, any spot or belt, or any well.defined point, distinguished from thee entire surflatce, so tliat we have no inmeans thus:tfir, of fixing tth periodl of rotation upon its axis. The almounllt of light and heat received by tUranus, admitting the ltaw of diminutltion, which seemis to govern these elements, could only be the quartet r part of thlat received by the planet Satturtn w.}ile the tappitartit dit ametet-r of the sun, as seen from'Urainuts, would be less than the thirtietht part of his diaimeter, as seent from' the eartlh. his plancet is surroundXed by at least tour satellitcs. TIwot others twere annoutnced by Sir Wi..t rslel, wYho not 0ol'y ve, v' t0heir distances but their periods of revo lutliont yet no telescope lha since been able to detect theso mi.nute points of lighlt and their ver y existence i8 nowl doubted by many of the blest observers. iFour of tio s.atellites ha-d been studied, with tmuch care, tand their periods of r'volutionl and tfheir mc ean d(istances htlad bceun well determinled:. Of thesce thet second atnd. l iurth are o111st.. readily seen, and ditfibeent astron1omerl s have obt;ained results which t gree with each other wit lhin comptlaratively sntall limits of teror. Thus, tthc ctttler i. t.ers l fixed th}e ptr.)tiod o)f revolution of t.he second satellite, in the oirer of distantee, at 8d. 16. i. fit6n. 5s, Sir John ]['erschel tmade:.l tlthe sanie period twenty-six seconds longer. D)r. I. atl ontt, of M.\luich, obt.ained, fi' this same period, a value of 8d. I1h:. 6G1. T28 3. T' The period of trevolu URANUS. 261 tion of the fourth satellite, in the order of distance, as determined by Lamont, amounts to 13d. llh. 07m. 06s.3. The period of revolution of the nearest satellite is about five days and twenty-one hours, while the third satellite in order of distance performs its revolution in a period of about eleven days. These are among the most difficult of all the objects revealed to the eye by telescopic power. After Sir Wm. Herschell no one for many years was able to see any of these satellites, the forty-foot reflector of Herschel having gone into disuse. In 1828, Sir John Herschel, after many unsuccessful attempts, by confining himself in a dark room for many minutes previous to observation, and thus giving to the eye great acuteness, succeeded in detecting two of these satellites. In 1837, Lamont, with the powerful refractor of the royal observatory of Munich, managed to follow, with tolerable certainty, the two larger satellites, and occasionally obtained glimpses of two others. At this time there are four or five telescopes in the world capable of showing these four satellites, under favorable circumstances. I have frequently seen two of them with the Cincinnati refractor, but they are certainly objects of great difficulty, and only to be discerned under the most favorable circumstances in the observer, and under the best possible conditions of atmosphere. Enough, however, has been determined with reference' to these four satellites to warrant the assertion of a fact of most extraordinary character, and nowhere else to be found in the whole range of the solar system, namely, that their orbits are nearly perpendicular to the plane of the ecliptic, and that their motions are retrograde. We have seen that all the planets revolve in orbits whose planes are nearly coincident with the plane of the eclip 262 U IR A xNU t tic: that they all r1evolve in the stame dir'etion aroundlt tte sun,; that the t ant adall the planets rotate on t heir axes in the same direction int which they revolve in t(eir orhbits. Wt,' haIve fotund, ill like matlner that all the satellites of every iplanet revolve around their pIriniarics in the samet direction, and in pl-anes nearly coincident with the plansc of the equators of their primaries; so that it became a settled opinion that there was but one direction( in whicht any rotation or revolution could bo perftoried bya member of the planetary system; and thus whten the asteroids were discovered, although there were consider.able deviations in the angles of the inclination of the planess of their orbits fr'o those of the old planets, yet in every instance their motions are found to be direct. hese satellites of Uranus presentt, then, tile only examp:le of retrograde mtovementlmtt among tnhe legitimate m embers of thle solar system. \We shall see htcreaftter that aontlg thei comets (which imay be regartded as satellites of t.ho sun ) ttere are a flew which presernt this s:atte anoml)aly of retrogtrade movement, yet this is not Inarly so su'rprisint g s to thiso ftii t lotin ls Inoal o tionl aolltOlng the satcllite' o:f a prl iatt' planct.'Wo shall retturn to the consideration of titis st'ject wheln w come 0 to discuss the cos:motgoy of' the' uni verse. If \we recall to tnitind the relations whichl exist bet.ween te dista'sttltC ant d periodic tilmes of' tUrants and Sat tur we( shatl ltt ttind thlath theseo two plantett'h wlett w.i>ar.: to c:. t(l otlIcr or' whcnt in cin junction, arte s:eIrated byt dista.tl of( albout. ninec htudrt d milliols of' miles,.'Wheln mt inst Icreote li'oiom ea.Ith other, thli tlis stance of sep ):ratic)it is inreased I; lby tI(e twhole diameter of the orbit of l Satur or by eighteen }tundttred m-illions of miles, as will be treadily sc!ent fr-om;l the filgure, in which S relpresentt s the sun,11 UR A N US. 263 A and B the places of Saturn and Uranus when in conjunction, while B' represents the place of Uranus in the opposite part of its orbit, or when in opposition to the sun. Thus the distance between the planets when located at BI V S JA B A and B is just equal to the interval between their orbits, while this interval is increased as Uranus recedes from B up to the time that it reaches B', and on reaching this point, Saturn being supposed to occupy the point A, the two planets will be separated by a distance of about twenty-seven hundred millions of miles. Since Saturn performs its revolution in about twenty-nine years and a half, and Uranus performs its revolution in about eightytwo years, the interval from one conjunction to the next is readily computed to be about forty years. This extraordinary change of distance produces a corresponding change in the reciprocal influences exerted by these planets upon each other. The same remark is applicable to the configurations of Jupiter and Uranus, and may be extended indeed to all the planets. Thus we perceive that the greatest possible effect to draw Uranus closer to the sun will be produced when all the planets 204..: U ItR A N U S. lie oln the same strtaitght line, and oi the same side of the Sllttt, Th.e pit'cvaltlencc of the lat of universal gra.vitttion, wheroby every particle of maltter in ttie universe feels the attraction of every otlier particle, unites all tIhe planets and their slateltllites into one grand schemel of revolving worlds, int which cach is ustbjected to the influence of all the othelrs. Aiftter the discotvery of Uranus an effort was made to assign to thi planet a curve owhose magnitude and positio werte derived fromt observations embracint but'at small p)otion of its orbit, This, of course, was.a mattCr of ncesity, fior even one roevolut ion has not yet been completed by Urlanus since thle date of its dis.covery in 1 81J. The orbit assigned to the pl anet was sutficiently accurate to trace tbackw;ard its movement amrllon the fixed stars. This was done in thle ho tIpe thtat the pIlaet might hav e been seen and its place recorded as at fixed star by some of tht early astron)omrs. If it should happen thlt. t the cotinptted place of' the platnet shotuld coincide with the recorded place of tt sttar of tho same:'magnitude as the platnet, then at suspicion would arise tha t thilis star and.t tlle planet were one and the same tbody. Ift on directincg the telescope to the point once occtpicd by the star tl. e t iec s l uld te stlbet fl(ond vaca,it, thtis etvidence would be almost conclusive thiat thue tsuptposed star was actuilly tih pltant. Bl:ty aIt examntination of this Filln it is fk i ndit wthat t thle planelt'f'ranus had been obse rved, and its place carefilly rccorded by no lerss tlhan three astronomers} each of wh lomet ad steen it severalff titnes, without lany suspicion of its planetairy chtl-aracte. r l.'tle atironomer fltanst e ed was the first whto had mistaken tlis planet flor a star nearly nitnety yteairs lbe ifre its ditts co(vryi by Sir William I terschell. It was sul.)bsequ(ettly URANUS. 265 observed by Bradley, by Mayer, and by Le Monnier, who fixed its place no less than twelve times during the period from 1750 to 1771. These ancient observations furnished an opportunity to test the accuracy of the computed elements of the orbit of the new planet, and to correct these elements in case they were found to be sensibly in error. This work was executed in a most faithful and exact manner by M. Bouvard, who also computed tables predicting the places of Uranus for many years in advance. It was supposed with reason that these tables would point out the places of Uranus with the same certainty as those of Saturn and Jupiter, computed by the same astronomer, gave the places of these planets. In this the hopes of the astronomical world were disappointed, and this extraordinary discrepancy between computation and observation gave'rise to the discovery of an exterior planet, as we shall now relate. 12 CHAPTER XIII. NEPTUNE, THE NINTH AND LAST KNOWN PLANET IN THE ORDER OF DISTANCE FROM THE SUN. URANUS DISCOVERED BY ACCIDENT.-CERES BY RESEARCH WITH THE TELESCOPE. -REDISCOVERED BY MATHEMATICAL COMPUTATION.-TIIE PERTURBATIONS OF URANUS.-NOT DUE TO ANY KNOWN CAUSE.-ASSUMED TO ARISE FROM AN EXTERIOR PLANET.-NATURE OF THE EXAMINATION TO FIND TIlE UNKNOWN PLANET.-UNDERTAKEN AT TIlE SAME TIME BY TWO COMPUTERS.COMPUTATION ASSIGNS A PLACE TO THE UNKNOWN PLANET.-DISCOVERED BY THE TELESCOPE.-DISCOVERIES RESULTING.-A SATELLITE DETECTED.THE MASS OF NEPTUNE TIIUS DETERMINED.-NEPTUNE'S ORBIT THE CIRCUMSCRIBING BOUNDARY OF THE PLANETARY SYSTEM. THE discovery of Neptune is undoubtedly the most remarkable event in the history of astronomical sciencean event without a parallel, and rising in grandeur preeminently above all other efforts of human genius ever put forth in the examination of the physical universe. The planet Uranus was discovered by the aid of the telescope, not exactly by accident, but still without any expectation on the part of the discoverer that his examination of the fixed stars would result in the addition of a: primary planet to the system. Indeed, as we have seen, so little did the astronomical world then anticipate the discovery of a new planet that the announcement by Sir William Herschel that he had detected a most remarkable comet was accepted on all hands, and it was only continued observation that finally compelled astronomers to NEPTUNE. 267 accept the new object as a planet. In the case of the discovery of the first asteroid we find a systematic organization of astronomical effort to detect a body whose existence was conjectured, on the single ground of the harmony of the universe, or that the law of interplanetary spaces, interrupted between Mars and Jupiter, would be restored by finding a planet revolving within that vast interval. Hence a search was commenced which consisted in examining every star in the region of the ecliptic, to ascertain whether its place was already laid down on any known map or chart of the heavens. Now it is evident that if it were possible to make a perfect daguerreotype of any region of the celestial sphere, say to-night, and the same could be effected on the following night, the comparison of these two pictures would exhibit to the eye any change which may have occurred in the interval from the one picture to the other; and hence if a star was found on the second and not on the first picture, this star might fairly be suspected to be a planet, or the same suspicion would attach to a star found on the first, but missing on the second picture. Now, a map of the heavens, so far as it includes the correct places of the stars, answers our purpose quite as well as the daguerreotype, and any star found in a region well charted, but not laid down on the map, may be fairly suspected to be a planet. A few hours of examination will show it to be at rest or in motion. If in motion, then its planetary character is decided. This method of research has been employed in the discovery of all the asteroids, and there is but one example in which a more powerful and searching examination became necessary. This was in the case of the asteroid Ceres, which, as we have seen, was discovered by Piazzi, 268,..: t T U N E, at a timote v'when but few obtsrvations coutld b)0 made previous to its beiinr lost in tie nrays of tdhie sun. Por af) t lont, titme it seemed almost a.t opoless task to lundrttak the re-discovery of the planet, as tthe telscopoe vwoulld be contpol'led to grope its way slowly round the lheavens in tlhe reltion of thil eoliptic, oma'trin. every star with its placet ill the clbart I. tlis dilelmina matlt ain-ica aa.lysis essn:yed to erect a structurt e on te nar.row basis of the tewy observation s obtained by Pi a zi, whereon ttie itistrui-tllntatl asdtronomer 1miglht stand anld point'tis tcles.icopto to thep precise poilt octcupied by ti lost tplanet. The gnius of (eaus succeeded in this herculean tastk and i when t tlh teble (scpe wa-s pointed to the heavens in ttho exact pltace,,inicated by the (taring computor, tlhere, in toe field of view, shone the delicate and beauti.fitl litght of the ltont lost planet.'I hs was certainly a most wonderful triumttph of analyt i reasolmning yet in this case the planet had be.n discovered, was known to exist, and lad been observed over 4: o)ut of tihe 360 of its recvolution round the sun. On this basis of 4," it wasz possible to rise to a knowletldge of the pianc.t's pos ition at the end of a few monfths of timne.' lle case of the discovery of Neptlne is eottirely difiRl-t uet. tere no planet was known to exist, to t eleseopie powe er, towever great, had ever seen it. IFor atges it had rovolved rounld tlhe sun in its vast orbit, iar bteyond tho uttmost known verge of the planetary system, unfiathom-.lt tably buried from hutman ga - arnd ftom human ktnowledge. -No sage of ant iqutity ltad ever dreamted of its existenct. TIhle tfertile brain of even tKpler hlad fa iled to imagine its being and it th l powerl l pelienetratio of.Newton' gigan}tic i intellect had 1 itiled to pierce to the fir off region. inhabitted by this unikt nowwi andt solitary planet, N E P T;U N E. 269 Indeed, witlh the ]knowledge which existed prior to tlhe discovery of Uramtsi no humian gc nius', }owevr liiglty, could l ave p.assted tlh tren endoul in, terval wtic S'ep::rat s't the orbits of Saturn and Neptune fioom each other. The discovery of an iatermediate planet wAas requisite to f.t.rnish a firm foothold to hitm who would adventure to pIass gulf of not less than 2,000 millions of miles at its mt r i rowest place.'We shall now proceed to relate tthe cilrcumnstances wlich led to the discovery of Ncptunie. As alreatdy statedl a carefitl and elaborate study of the orbiit of Uranusi hIad( been accomplished by 71,. I:ouvttard, atnd tables giving t the computed places of thits planet hald )oeeni prepared by the same sa astronomer. it was not anticipated thatt these tables would be absolutely perleet, even if based on perfect observations. Wo must remenmbei that each body of the solar systemn atflcts every other, and thence no single set of observations are sufficient to give a perfect[ orbit. In case all the other worldis ero blotted out of existence, and there remained only tte sunt anmd U'ranus, then three perfect observations of tlhe planet' t platce would suffice to determinei positively all the elements of its orbit and fix forever all the cireum — t.anecs of its mIotion. We shall call the figure of tlle orbit of tUranus, obtained under the above hypothesis, the normal Jitfure, and the ellipse llwhich it would tdescribe abfout th e sun, unIder the uabove circumstancl s, the normal0 dt ellipse. It no w w e introduce another plan et into our system, a,S for ecxasmple, Saturnl it is p)ossiblo, as we laave alreatdy seten, to compute the exact amount of powter exerted by SLaturn to disturb the movementsl of i;Uranus, ad to change thte figure of its orbit. Jn like mannt1er, by addin' successively all the interior planets, 0~~~y tteitro 2T70 N ET 1 U X I. it is p">ossi.le to colmpute tlhe iei'rttrlttions that each produces upon tlhe orbit of tany particular one, until, finaflly, by xusing all thtte power of analytic r'.easonring, thle i tmttan Itinmd inay reach to at comnplett knowledge of all possible dcrang ements product d ]by the colmbined actiton of alt l existintg known causes of perturblation. Suippi.sing our knowledge in this way' to becomei per-. fcet as to tthe movcmecnts and orbit of Ura'sis, we can lthcn predict its plaes i all comi timte, ttand these predictions, b eingi' alrantge ill taibular tt r ) ay be v wrif d; lby compariso' in after years with the ooblse.erved places of the planet. tIf n-owt a new planet were addced to t tle sys'ten. revoltving a in an orbit exteriorl to that toft ttUalts, perturbattio itv oltid arise froml the introduction of th:is disturbing body iitto our systeml which wouldM at once causel the planet to dCviatle hfroml its lpredicted t(rack, and tthe obstervcd taInd ct putedl placcs would no loni.ger:agrcc. Wte cant pere'ivo at once, i'so tis statenent of tlh irollia,11 tlhat tles te very discreptanlcies l:et twc the old triack atnd the new (onie l pursued by thle tplancet, would fgive us a clue wherebly it l migtt becotime possible to determin,: in slpace, the positiont of tthe disturbing' body. )Dilitult and lincomp, trltt si le as tile tablov e ptrob t )m't' atpatt'r'. it i"s tf'r i Is tdillcutlt that the ote tac tually pre:sent'ed in nturae. We ha ie supIposed te li' norlmld Ilri:pc; i lt i tiltitit:. It b Iim tlvli' ta1t,oh I lhtt tIi:8 xlx|l.n i i cilice::c, dc-scribcid by U.?ramnus, to l,) knovwni whI,:rce:a.s ill,reaiuty, x' this very lli tt t(e oat to t'ca dnctern t:, i' of' r1al:ni nt of the m t ost s'rc.in. t ant. d powr: x l cIlara'i t:ctr, w hil the wole pro t:tlm wa s allmo.t: opels tt slc.:-.ly e. mhbtrassti(d bt ttht faci th tIt the mxvct ent's of UI rantI Us \wltc.r acttally llheing ll distutrb:,d all tire time by ttie unItknoV')n body whot:e position in space was required..As t1e, normtal: orbit could only bo dctermlinel d by a serics of tp N I Tt I X N 271t p)roxinlltions, biased upon the ob!sterved places of th planet, it was int(posible, in anly one of thtese apI:ttoxt nati o'ts, to for Unranus frtoml tlie disturbing c(tlects of thie unknown }b)lody. It was on ly, thcreforc, by compari ng with each otho-er the results reachet d by these successive alpproxim..atiotn t tthe orbit of'Uranus that it becttear ma-nifeist that no increase of ectturacy was beingt reached lby tiese sace cessive efobrtos andt after every mknown cattuse of disturbancoe had been c.artefuilly taken into accoiut, at grald conclusiotn was finalfly reached that lzno satisfactory account could be rendered movements of tie oveaus by Ut e com(bitned eftects of all tknownt disturbitn c. ustes. T'o reach ti (s conclusion required investig iations of the most p'rootbund and labtorious character, but before it ^vtas possible to explaint these tanonm0alous mtovements of JUr.tnu a problcllm of fir greater diffiaculty remained to be solvi.ed, involving n:othlittg leC than a determinlation of thte w.tiht of the tuniown planet, its distance fri'm the sunt, the wtture otf its orbit, a nd its positiont in the Ihteaven: att a particulart timet, itndicatingt the region to which ite telfet scope must be pointed to render visible what hatd hitterto retmaltined for ag es unseeni by the eye of' man:t. t.'o those who havo gfiven but little attecnt.ion to the study of these extraordimary problems an atttemptl to re-. solve a: question like t hat just presented may seem to:e: eveni pre.sulmpt:I uous. yet when we conic to examineto the circums tantces, we sYhall see dimly a way whereby we may reacht a certaint approximalte knowledttge of the pl]ace of:' thiis unknown l world,'lThe fact: tthat the pf'l:nes of the orbits of all the more distant planets are net rly coincident with thie celiptic revduced the examination to the great circle in the hteavens cut out by thel indefilite extension of this plane.'t.lhis 2TS2 N E P T j N X. is a most imitportant. consideration, and but for this fbortunate circumstance no powers of research could over have iade even the most distant approximation to the place of the unknown tlanet. T'i e empirical law of Bt.odet whoretby it senleed thlat tihe order f of dtistanes of the planets was gj'overnedl as"t signedt to to the hyptothetical world a distance about double that of Uranus, or say 83,600 millions of iles friom the stl,. aAssming this a ti the probabltllte distance, tle third of Kepl:er's laws would determineio the period of revolution of the world whose position was sought. It remained )now to assign a.) mass and position to the plane:t such as would render a satisfactory account of the perturbations of Uranus, wtiich remaine: d outstandting after the known tcauses of distturbance were exhtausted. T[.o accotmplish this let us recall to mind the fact that in case the mean distance of the disturbingl body had betl rightly selected, then the interval between Uranus antd the unknown, when in conjunction, would be about 1,800 millions of milues..In this position the disturbingt force would exhibit its mnsaximtum power in a t.wofold senIe: first, to causett UTranus to recedo to its greatest distalnce frtom the sunt; and, second to cause the same planet to lag beh}ind the place it would otherwise }htave reacied. TIn tth above figure let T I[J U1'' represent the comltputed orbit o' UratJns as existintg under1. thle combJinled influence of all known (causTest the ptlace of tlhe unknownttt., w lhen it conjunction with t'lranu s at U'. lit is mianifestst ttat t}he'orce exerted by P oln ranllIs will tend to accelerate its velocity in comitlg up to conjunction, and to cause t}he patIt described to lie outsi(de the computed ptathl alongt the dotted line, the pla.net really reachling tho lt point U" in-t.. t'' N Et P f tu. 2783 st(iet d of' it tlt ulttdistiurl:b I orbit. Leaving tthis )oilnt thio ib'rce exerted by the tuntknoun woutld rOversae its olbcet, and a rctailation would conmmnco, and bty slow f L ^~ -..'; degrees rcc(ed.ig:fi'o the disturbing body, it would igadually retu11 to til utiidistturbed orbit, land there contitu1e until thlo periodt for ttio next conjunctioln ightt approacith, Such) is a routgh exlibition of the reasoninig wltichl wast temployted to narrow the limits of reseltarct ill the etll:rt to point tt tlelesc3ope to tohe unknown cause of the pertt turbations of lhanttus. oN'O accoutot, of course, ca(n bo givjen of tle mathemiatical treattmlentt of tlln problenl. lit was iundertaken at albott tise sam tim0e by A damst, of ngliantd, and tby L Vetrr ier, of Paris. tac}t computel, unkl)nown t tle otherl reacheld a restlt lalmtost identical. Ieo'\Venileri comnmunicated hlis solution to the Acadenly of'Scoiences on tht. 8;.1st Aug uiIn t 18A? and on the evel - n(g of the 18th1 September, 184of, r. Gtallc, of oBetrlin directetd tieo telescope to tbe point in which thlie rench gefo:eter declarced the ttun(lnowli\ planet woul ble t )ld.. 2 7 4I N EI P T1 U N I A. star of the eighth magtnitudo a:ppeared in the field of vicw, wrhose place was notlt laid dotwn otn a.y kno)wn chlart.. Spiniolt v;S is at onco aroused thlat t.his mtight possibly hbe tthe pleanet of comIputationl, and yet it: steetcd incredii)t thalt at probloint fir surpt''ssitng in dtificutty any tvwhich htad vet r btl en attenteptd by tllmant gCeniulns shloulld thus iat the filrst Ceflert hlave been solved with such inarvolouis i preccision. The suspected star was examined with the deepest itnterest in the Ihpo that it t might exhibit- a planetary disk. In this, how'ever t lh ast00ronomer was unsuccessful, andt there rveCmaincd but one method by which its planetaIry cl}aractetr m)iglht be detcrmined, tha t o f watcthing stuf ficiently lon" to detet its tmotion. Th.lis z proce.s, how-. ever, 1must have tried very sorely the patience of tile ob01) server, as the meotion of the planet at so great a: dis..tanco as three thousand six huldred mlillions of milcs was so slow as to require three cntire tmot ths to p as over a space equal to tho apparent diameter oft the 11moon. 1'e position of thl susp:ected star harving been accurlately determinilted on the first liglht o ofbservation, it becameti evident on the nextt nightl t:hat the statr hlad moved b)y an amount such as was itirly due to t lie slow motionAt of so vtast anl orbit, it could )be none otl'er than the uniknown planet!.A success atlmost infinitely beyond tho expectations of tthe most psangsuint o complttte r had crowned this might0y efflrt, and the amazing intetlliglenlee that theC planet was found startled the astrolnomical world. The planet was soont rcognize d tby the astronometrsn in every part of the world.'lthe clemrentis assigned by oif Verrier t andl Adat ns by computation were accelpted every-. w}here with ml ost iuntlhesita.ti'ng ftith in their accura1cy, tan'd N E P tT U N ti. 275 it was be.lieved tliatt it only remamined fior the t. elscoitpe to vority tlhe compltltations oft theso e most, wotderlitl m::tt:}1:cmltticiais..111 tt;is tle, ast rtonomical world wete destill(d to meet a most remarkable disappointmfent.''e iO rew.planet proved^, indced) ttaquate to ac.tcount ftr all thle tanomalous itIovemeuttt oti jf U'anrus while in all its cltiments it diffi;ered so widely ftio those of thte cmputed hypothetit cl planet tha.t thte cornputed atnd real planet could not in any wafy be rtega1ded as tit stlame o,,dy. T.he first rest.'iction p:roved to he correct.l for the orbit of the new plan.tet (afterwards namtlled Neptune) (did coilt(.ide talmost exactly witl the plano of the ecliptic.'lThe ecttnd restrictiont based on the exttension of Bode's law of in,terpltiaet:ary spaces, was fa'lsi ilied in the event, fior here( the: law of.Bode fitiled, 1and the distance of theo ttrue planet wa;s nearly 5",000 m.illiolns of mtiles le.ss t than that of tle co puted 1one.''ttlt th ird restriection due to the appdtilicati.ion of iKel.leCr's third lawt is verifiedi in the real planet; but as tih dis(... tanc:e of th.e lunl.town was asstumed greatly -to larrge of coturse thie )perio-dic time depending ont tlis distance was8 also too l;tart. e i' I s lIy necessi ty involved t 1a error iin the 1tmass assumed l or th;fe, ulknotwn., whose erronel' ous dis.tance de.mandted, of c ourset an. er'ron)ios maltwss gr'teC1 than that of tilh true p:tlanctt at y.et: notw ithstanditng thel tmatnit.tudc of' the terrors tof t tt n se elementits, the comlp)tetrs uwccc~cdcJd int pointing thle t elescope within loess than one (degree of the actual place of the bod(y which had causedl the anoialons movements otf U.tlranus'We xwill. endea. vor to render aI brief accountt of this mods:t astonl > - "' - v'" r' -I -= - ~ ~ - u~ m - - - -~ -I( -~_ -. -f -C3 -1 il 3~ ~. rJ'~ ^5 -: h i^r *I ^^^^^^ ^ r "i.^. rL. ^ ^ T ^^^' -rr C' rJ - v r * C:~C:-. -. "' I - r'-i ^ 11 i I ^ il -I= g r^ ir iJ 111 i/ " ^^ r ~ ~ ~ ~ ~~C'7 -, -J -c, C c ~ Ct -~~~~~~~~~~~~~~~~~~~~~~~~C ^ ~ C C.:~ - "" - -. 0 _ -.' C:'' -' tI ~* ~ *C: JCI~l3. - -i -''i C-: - - 1 I ^' I. r* -. i^^' C:^^ ^^~~~~~- I' C-.^ - ^^ i y r_ l~ l~ r r "" ^ ^j ^ ^I^ ^I^i ^ ^ 5 1 ^ C: ~ ~ ~ ~ ~ ~ ~ ~ ~ 4 -':r c =" *Ir~~~~~~~~~~C 3 A'~'1* C- r* cc r3~ " ~~~~ rr r~C -.N ^^1 cl ^f~ ^ ^ I ^ 11" g I I! Clb Y 1 1,8 ^ ^ I ^ I ^ a i~^ 1^ 11: 111 1111 *- 111 H Ilr^II '80 N u P x N.,. mote p)trimary.'1lhe great refiactor- have certainly discovered tihe existenco of 0110 satellite, and anMother is suspected.'Tl'h discovery of this one satellito of Nol.ptulo becomes, ntder all thle cirumstances, a matter of deep interest, as it enables us to deteriintc the mass or weilaht of the primary, a matter of the first mom.enilt in cormputing the effiet. of the p)lanet as a disturbingl body. Th. satollito is found to perform- its revolution about the primary in a period of about five days tand twenty-ono hours, and a at mean distance of 23fl thousa d miles, or nearly equal to the distance of our moon frout thie earth. In ease theso distances aro assunmed to be exactly equal, thetn as at thi same distance the ccntrifuiqal force in-l crease.s as the square of t vh velocity, and as the velocity of' Neptunc's moon is about tou1 r and a }talf timnes greatert thian that of our 0moon1 it: centrifu.tal torco in it> orb( it must be 4:5 x 4..i.5 eq(ual to about twenty timtes tile centrift.l.al folrc of tile 1moon1. Now, the atttraetive tbrce of Neptune is exactly propoirtioned to its weighlt or 1mass and hencro to counterbalance this centrifugal torce in }is satellito,'wltic.is twenty time as great as titat of tile moon, tbi maAs of Neptml must be t.wenty tines as tgreat as that of the earth. T..ltus has been revealed not ono world, but two.the one containing a mass of matter suileiient to brm 1no le: ttan twenty worlds a.s heavy as our (art....... the otheir ia satellite, indeed, of the first, yet sulhffiently hlare, to send back to us, at a,. dist"inc of 3,000 millions of miles, the light of til sunl cnect bed by its d.ispersion over this vast distance to thle one thousandth part of the intensity it pours on our earth. W t t av t ea id l tahe. known I oundary of that mighty conf(tederatlion of revol vin lt orbs which, wilist they acknowledge in:the 0 most speci'ic ma nner a imutatal detieindI N b P T U N 28:1. nc are all ct rolled by the predomrniatingw infiueneo of., the sunn.I which occupieds, thle common focus of all thoir Orbits, and around which they 1011 all ro d shine in obedioneo to theo grand law orf universal gravitation. Woe shall now retrace our steps toward the sun, and consider za rernarkafble cllals,,:s of bodies;. which for age w ro regarded as evanescent meteors, suddenly blazing athswat the sky, and as suddenly fading from the vision, never )morc to reappear. Modern science has given to these bodies determinate orbits, awl in some instances, as wo shall see, has assigned them a permanent place among tho satellites of the sun, CHAPTER XIV. THE COMETS. OBJECTS OF DREAD IN THE EARLY AGES.-COMETS OBEY THE LAW OF GRAVITATION AND REVOLVE IN SOME ONE OF THE CONIC SECTIONS.-CHARACTERISTICS OF THESE CURYES.-COMET OF 1680 STUDIED BY NEWTON.-COMET OF 1682 NAMED " HALLEY'S COMET."-ITS HISTORY.-ITS RETURN PREDICTED. PERIHELION PASSAGE COMPUTED.-PASSES ITS PERIHELION 13TH APRIL, IT59.-ELEMENTS OF ITS ORBIT.-PHYSICAL CONSTITUTION.-NUCLE NVELOPES.-TAIL.-INTENSE HEAT SUFFERED BY SOME COMETS IN PERIHELO. -DISSIPATION OF THE COMETIO MATTER.-ENCKE'S COMET.-A RESISTING MEDIUM.-DEDUCTIONS FROM OBSERVATION.-BIELA'S COMET.-DIVIDED.NUMBER OF COMETS. IN all ages of the world these anomalous objects have excited the deepest interest, not only among philosophers, but among all classes of men. The suddenness with which they sometimes blaze in the sky, the vast dimensions of their fiery trains, the exceeding swiftness with which they pursue their journey among the stars, the rapid disappearance of even the grandest of these seeming chaotic worlds, have all combined to invest these bodies with a power to excite a kind of superstitious terror which even the exact revelations of science cannot wholly dispel. History records the appearance of these phenomena, and in general they were regarded as omens of some terrible scourge to mankind, the precursors of war or pestilence or famine, or at the very least announcing the death of some prince or potentate. Some of the ancients, of course, rose above these superstitious ideas, and the T E 0M E,..I. T S. 288 o Amn philopli r Seneca. cvean entertained the op iion thlat tlese eOrratic bodie.s would some dtay' Mfll within thlo doinaiin of hlum'an knowledge, thlt their patis among tlie stars would eve btually b traced, and that lthey would be f1ound vin thle end to hb)e permanent imembers of the solar system. l low ecmAarkably this prediction has been veried will appealr in the concise sketch we are about to preiseint. Tbhe discovery of' thoe law of universal gravitation wa followed )by a Uhiameaical demonstration- also acco-t' plislhed by tlie great Egliltsh phlilosophcr, wIliell was the reverse o("If the probir.nit ln had jjust solved, anid may be anuiioilnced as nfollows w )ien, the inlensily/ of a f ixd cenhral forlce decreasin in po./wer as the squares oqf the distances increase, (1(1nd the dir cltion and intlentsi/q/ of (Ii inmpulsive frc)e opertalinty to set in molio:. a hodiy suhject to Ihe central poner lReqairnd, h/c * s, tare and /igw e Qf thei path dt esicribed by the recoicinq Provious to tlic resolution of this problem Newton naturally expected to find the curve sought to e ani ellipse. Tie sun was tho source of a fixed central ftrce which oheyed the haboe law.'The planets were retained in I their orbits Iby tinsI emit al force. These described ellipses in their r1evt dAtion around the sol, and it was natural to conclude that the solution of the inverse probleni would lead to tIn el1iptic orbit. On clornmpleting the solutioln and reac'hiing the maitlematid exjpresion rpcsent illng{ the orbit t wa found not to be tie usual expresslion Ifor thn oliie^ arid after ca'ctifil examinati proved to bo the og'r'l expression eilbnacing within its gras p no less than foisi' curves, the circle, the ellipse, tho parabola, avd the hyperbola. These eurve; are allied in 284 THE COMETS. a most remarkable manner, having certain properties in common, and having in one sense a common origin. They may all be obtained by cutting the surface of a cone by a plane passing in different directions, as may be seen from the figure below. Let A be the vertex, and C D E A r /G........ O /l \ IV \/ L the circular base of a cone seen obliquely. Any plane passed parallel to the base, or perpendicular to the axis A B, will cut from the surface a circle, as F E G. A plane passed obliquely to the axis will cut from the surface an ellipse, as M 0 0'. Any plane passed parallel to the side of the cone A C will cut the curve T W X, called a parabola, and any plane passed parallel to the :r CO E S 0 ii B,:., 285 axis of tihe cone A. B will cut out from the surihco the cureI[ I 1 Called an I-up'pebo/a.'hesc curves are thus all derived from the coniio suraco by intersectig it with a plane, alnd are henco called conic sections. Now, ai little examaitnation will allow us that while tho circle arid ellipse are rc-e.cerig(5 curves of limited cxtcint, this is'not thoe case with the parabola and hiy per)ola., If the colnic surfaeo were indefinitely exteml.ed below the base, itt is evident t that the cutting plane X W'T )obeing parallel to the side A. (, could never cut thiat p}articular line, anid hence tihe parabola, departing froin thie point, iU aind passing through T and X, would extend in.. definitely on thio surfice of thle cone withlout ever comi.'t.ing too'etheri tliougi thio curves would atpproach each ot..her fit. ever. Thus the parabola is the limit of all possible ell ipses for it is manifesthat as tthe cultting phlalne3 beconsl- more and more nearly parallel to the side A C, t s tlie xis of the ellipse cut out grows longer ald longer and just at the poin't where parallelism is readiched tlhe parabola is formed, and it is only an ellipse with ain infinitely elongated axis. While it is seen that the branches of the parabola ap-. prtoatch each other, and may be said to come to gether at; an infinite distance from the vertex at WV, this is not the case with the branches of the hyperbola. )Departingt from the vertex 1 anid passing the points K and l., the branches of the hyperbolat recede fom ea.ch other ior ever, losing by slow degrees their curvature, until at ait inflnitoe distance tlhe curves degenerate into st. raight lines, and thus continue to recede fur1 ever. Such are se)ioe oft the general characteristics of these remarktable curves T,}hey all, like, the ellipse ha tv an majo.r 9axis, on cach 1side of which they are sy nmetrical. t'y tall i ato at 286 THE COMETS. least one focus, possessing special properties. They all have a vertex lying at the extremity of the major axis and the nearest point of the curve to the focus; and, strange as it may seem, in either one of these curves mathematical analysis demonstrated that a satellite of the sun might revolve under the law of universal gravitation. The elliptic orbits of the planets and the circular orbits of some of the satellites of Jupiter presented examples in the heavens of two of these curves, and it occurred to the sagacious mind of Newton that the hitherto unexplained eccentricity of the cometary revolutions might be accounted for by finding that they revolved around the sun in ellipses of great eccentricity, or possibly in parabolic, or even in hyperbolic orbits. The English astronomer had the opportunity of putting to the test this grand idea by the appearance of a great comet in 1680, which displayed a train of light of wonderful dimensions and seemed to plunge nearly vertically downwards from the pole of the ecliptic, made its perihelion passage with almost incredible velocity, and with a speed always diminishing as it receded from the sun again swept out into the unfathomable depths of space. To this comet Newton first attempted to apply the law of gravitation, and to assign it an orbit among the conic sections. This could be done in the same manner from observation as in the case of a planet. Having obtained as many places of the comet as possible among the fixed stars, it remained to see whether any elliptic orbit or any parabolic orbit could be assigned the comet which would at the same time pass through all these observed places. If this could be done, then it would become possible from this known orbit to predict the places of a comet as of a planet, and in the event of the orbit prov THE COMETS. 287 ing elliptic, then the return of the comet to its perihelion might be computed and announced. The comet of 1680 was carefully studied by Newton, and its orbit was found to be an extremely elongated ellipse, approaching very nearly to the form of a parabola, but while its physical features and its near approach to the sun made it an object of extraordinary interest, the exceeding velocity with which it swept around the sun rendered it difficult to execute exact observations, and hence this comet was not well adapted to demonstrate the truth of the rigorous application of the law of gravitation to the orbital movements of these eccentric bodies. Another great comet appeared two years later, in 1682, to whose history there attaches a special interest, on account of the fact that it was the first of these bodies shown to have a permanent orbit in connection with the solar system, and the first whose periodic time was sufficiently well computed to render it possible to predict its return. This comet bears the name of the great English astronomer Halley, to whom we are indebted for the computation of the elements of its orbit-a problem, at the time it was executed, far more difficult than any belonging to the whole range of physical astronomy. The elements of the orbit of a comet are nearly identical with those which fix the magnitude and position of a planetary orbit. To obtain the magnitude of the cometary ellipse we must have two elements, the length of the major axis and the perihelion distance. To obtain the direction of the longer axis we must have the position of the perihelion point; this point, being joined to the sun's center, gives the direction of the major axis. To obtain the position of the plane of the orbit we must have the place of the ascending or descending node, and also the 288 T t COM T X SI. ircinttaliou of thle plaln of the comctary orbit to that of the ecliptic. ITf in addtition to thetse Olelmenllt we tavo thle limie of perieltion passage, then it becolmets possible to wtbllow the comot in its erratic mrovemnnts witlh at crtalinty almost as great as that with which the orderly movemenits of the planets are pursued, O)n the appearance of ite great comet of' 10;82, 1 alley undertook the laborious atnd hitherto unaeccomplished task of computing rigoroutsly the lelments of its orbit, which task lie accoi:nplished aftert incredible labor in t het most matsterly manner. It then occurred to him to gatther up al}} ltist:>l]X ( Yitfl Ptft l~tGO htO llC Rltt)0xtltttlCC or all historic details with refirence to the appearance of' comlts, as well as all astronomictal observattions, so tat by etxatmination anld intter-comparison lie might letarn whether anty recorded cotmet had ever pursued the satio track in t1he heavens whictl had just bceen passed over by the comeut of 1682. In the course of this histortical itn. ve stigation lie Itnd t tat cometst somewhat resembling ilt physical tappearante and traversing nearl y the saie regions of space lpassed over by his lown comlet had a}p- peared inl the years 11581 and 1607, and now again in t1.682. these epoch-s are separated by an interval of between seventy.-five iand seventy-six years, an d I1alley, after l long and labori.o.us computtationt annor\lued tlhat in 1.59, tlhree quarters of a century from the date of the prediction, this tsame comet twould again return to our system! i o can r'teadily sympathize with tihe ft tintgs of this reat ast'0tronomer when we fitnd him appeahlingt to posterity to remembetr, in the event of his prediction boing veriftdie that such a4n occurrence s t.he return of a comet was ir s t atlmoun.ced by an EXngtSlishfan. As the ye'ar I1.5 ) approattheld, the prophetic declaration of' Ih1alley excited an untlttuua interest thlroughout the alstronom ical TH'atE CoMEi Tna'S, (289 worldlt. T ro: predict the exactt point in the helavcens to which tile telescope) mlust beo directed to catch theo first ftaintl grlimllps of the retulrningt stlrai:ter, and to g0ive the daite of its periheillion pa.ssage:, re(:uiredt inveastigations of so high an order, that in case they had been demanlded of JIialyley, scventy.-six yearis before, the tthenl existing conrdition of mathematical and physical.scienc would not lave firnisltCed the means ifr their acottomplislnnent. }Ithe whole suhljeet of planetary perturlbations hadt by thi limno been tolerably well developed, andtl the laborious taisk of ctm1puting the disturbitng intluene of Jupiter and Saturn twals tutlderitalken by Clairautt, assis-ted by:11, i, ando and by a lady, Madamn L.epanutc, whiose name stands in honorablo unionl with the two profound mathematicians. After manty monthst of indefltigablt e lt.abor the comnpute)r:s ann0ounced that for want of time they lid been compelled to omit several mIatters which might, tmake a difft rence of th'irty days, one way or the oth er, in the return of the comet, b)ut that withint these limits this lofng lost celestial Nwanlderer would pas.s his perihelion on the t18th April, IT.. The. limits of error were justly chosen, for tho conet actually returned tand )passe;d its perih}elion on the /12th of rch, t t hel predicted time. This. successful computation settled lfor ever the doc-t trine of tlie cometary orbits, and denmonistrated:be.yond doubt their sub:jectiont to the attractive piower of the sun, and that this orb extended itsi iflne to tthe prolbund depths of space, to which thto comet descended during its jourtney of seventyr-six years. It was further establishcd that Ill le)y s comet was a p'ermanent mtember of tihe solar systcem, p rforming its orbital revolution around tthe sunl. in an exceecdingly elongatedt ellitpse, but witI a regularity equal to tthat of the ptlanets. Ift was furthert (lcn 6 290 TU iT ti CO I M E t'S tcerm.ined that the entnire mass of the comet was very in 4cO:h:: sidcratlode, as no account of" tilis m, was made iln the lcorm itations br pert Ora:ttioi, wlIi itl: t masses' o J...pi tr anld Sat urn required to o h nowin with precision. This comet inAs rettuned a second -l time sirtco its discovery!y II'ally, wlhen its elements were ore more accurattly - tained by mainy modern astronomers. and perhllaps best of'l by.:irma,, ~t. VcWs!pt,ih(idn, who predicted its perihtlion paIssage, after an absence of scvcnty.-six tyears, to wititin Jie dI/ s/ FhlTis iappearanc tool placi att th closet of 1835. We sh.all have occasion to recur to ti:is coamett again when.we come to spoak of their phliysical eon stitut ion.'Westphalen ftrn:ishes the f.ollowing as thl actual dihtemenions on f 0 I Falley'S comt..........:'I:enhi ih }lion':Us::t nic'.,.,''100,1 (000 mileo.. Al'on' * h 3A-... -:...0.(.)0 i: ltto of tlic maio' axis *,.'4'(; "''pf'1 Brea.:lh~o/'tho or:bit.,.....:;,!:f00,000 "fc It: isi; thutis se. tlat in its journeiy firon the sun: this comet cro0 es: the orbits of all the known l lanet:: and passes thc Ibmoundi'ar, of Ntcptunt e more than tlhre t Julnr hl illiorns oF mi ile.:..I Ji.avi l tlh us n d im.ions;trated the sttuordination of these csxtraordinartiy odis to tfl: law of universa'l raita io a0n.. to tih' rec tived laws of motiott wet C will proct':1d1 to cxamiunenoc their i'P.Y:-..AL::, l CONS' lI I ION..........I-Tl soi d c arrtlt wo in.habi it. thte miooul), hersat'llite, thoe suI a.ii ll tat II e t ilanl i ot, arel. co1pact musss of ni:iattr tof' difib'ring l:;itic, tlut of firl. eoml)pact milatterials. lt. Ite cimet.')1! tl'o c' mt as a: clstes, seeCit to b vax 1tl)o s''tn'SSc, flu' ila l e n111sutbstant.ial tihain the lighltest sumntmer cloudt111) and1 in getneral THE COMETS. 291 transparent, or at least translucent, even in their most condensed portions. This is evident from the fact that the minute stars are still visible with undiminished light when seen sometimes through a depth of cometary matter millions of miles in extent. Comets in general consist of anucleus or head, the center of force and the most condensed portion of their matter. Around this head there is seen usually a vaporous envelope or atmosphere of greater or less extent, sometimes evidently divided into concentric layers of nearly globular form. Many comets, on approaching the sun, undergo extraordinary physical changes in the head or nucleus, which experiences an excessive agitation, flinging out jets or streams of fiery light in a direction towards the sun, which assume many and strange forms, sometimes spreading out into a fan-shaped figure, and rapidly fading in intensity, as they recede from the nucleus. This phenomenon is almost invariably attended or followed with another even more remarkable-the throwing off a train of luminous matter, called the tail, in a direction opposite the sun, and sometimes extending to a prodigious distance. Thus the tail of the great comet of 1680, already mentioned, according to the computations of Sir Isaac Newton, reached to a distance of more than 140 millions of miles, while only two days were occupied in projecting this inscrutable and mysterious appendage to this enormous distance. The form of the tail is usually that of a hollow paraboloid, the nucleus occupying the focus, and thus the tail, as it recedes from the head, seems to diverge into two streams of light, while the axis or central line is comparatively dark. Sometimes, as in the great comet of 1858, the region immediately behind the nucleus on the axis is jet black-the intensity of this blackness 2972 T1 nE 1.' C o M E tS trow ing less IUad less along thie axis lltil it finallty tide out int tihe tgeneral luitiniosity of tlhe taii. Thite nIcleus is slomethitltes toleolably well dt tefintt, and )prosel' nts a planetar.y disk of greater or' letss mn)anlititude. t s not intendedI to assert thaIt ther are nae 0o ct.s wincht are solid bodies, at least in solme portion of thlci ct(etral masses. Ilndced, if we are to credit tie cordds slome lhave been seen in the act of crossing tlhe disk of tlo e sunfl when they hatve appeared as 1ro'nd, w\ell defined, eircut Iar black spots, exactly like the planets Veins an1d lM.cr enury, when seen in the same condition on the bright sntr. lace of the s r ti Il. )r the most prt, tholwver, we know t.halt tthese bodies do not lt tprelsnt ay evidence of solidity. Tl'lciir heaIds or mnllei are ill defined when examsnined by ptower tul teletscopes, atndt theitr gaseous condllition is:detmon t stra;tetd by the fiaet that they expalnd and contract tieir dimltensions with g reat Irapidity, according to circmlstance:.B, ~This contraction generally takes place as t}e comet approaches its perithlihon pastget, whicht is certainly a very curious lhiet, and quite contrary to wlat we would expect, as tihe excessive heat. to which a, cornet must eo subjected in perihelio ought (as would seem) to greatly exp and its dimenllsilons. It is doubtliess owing to thte fiact that tliis elnormous lhca:t extends its iniluence so far that the vaporo1s massl is expande d and raified to sch a degree as to!:becomt e absolutely transp)arentt andt invisiblel and it is only'llhen released fr4om titis intense heat by rec ess friom tlh sutn tiliat a condensation takes plat, and thus tiles seem8.ing, dic.menisions of the comnet increases. It is diflicult to comtiprhelnd thowt soine of' thtse bodies. in tthtir n eartest tl)plproa.chli t til te sun, are not abtsolutely burned up alnd dissipated. fitor ever.'he great comet 0o 1.I80S, wten ill perihlelio. was only about 1.47,000 rniles distan.t, firom thec sui's surfacc; ind admittint g tlt the h et of tlto sun.li diminihes a.s at:.tc square of tlle distance intrcates Newton cotliputtd tthat thwe comet was asulbjected to a htleat O )000 tilmes ml.ore intense tla tn thmt. of red hot'iron. tlhe gr'eat comlet of 1843 is computed to hve atpproached thel s's ssurface to withi1 half the above distancea, and Swi Johntt lefrsehell comxputes thatt the intensity of the hetat then ex — pe.rienced lby tins comelt wais 471000 times greater thlan thle hceat of tihe sun as received a t the eartlth or more than twentytt eigl t t ine greater than the heat concentrated at the fiocus of a llns of thirtty-two incltes diameter, whtich melteld agate atnd rot c rstal, it an dissipated these i refiactorty solids into an invisible tas I After pa.ssin' under the influence of such intense heat, it: seemrs talost impossile tha t any \well defined tftrm should ever b recovered, and yet, the comet of 1680 land thatl of:14 fitna lly receded friom tt s the sun, ettthlclus in some m ysterious -way slowly gathering up its dispversed pattrltielhcs d swteeping awaty into tihe depth}s of8 spatce at wel\l-defintedt ltuminitous ot}jcet, not in any sensibleR de gree ilnjured in its florm or iaiignitudc by tlis lfiery ordeal.'The netl.elops of comets atnd their tails ar by far tlhe most ins1rutal1le probtlms of nature. ()Of these ptheno.mena no sat f i1story account ihas yet beh l relndered. The envelopes of thi comnct of 1858 were beautiftul inl fbrm, withlt a well dlmtiCd cirtcu lar outline, in whose center thie nucleus blazed with its fiery ligh. Tihe diameter of this steemingly globular mass chl'anct d from lnigh t to.nigh't. Its texture varietd; sometimes etvenly Iand bheautifutlly shaded and gauzehlc-li i its surface, and sometimes this ga.uzy surtAco broken by dark and[ irregular patches. A.;t IX~~ C' 2904 iT It E C 0 M II TS scondil conctnittie spi' lierohc became visible,.lai'itert in its outlinlt t.lian thlt,.inte.tior onlti and fin llty ta thtirdt crcile dimly )prented 1it outlie, very a int, at'id only to be scatn in powerfut ttlscot.ps, tun tlcr fi:t\vorabi circutnstt.ics. The beautifli fiorins exhibited in these envelt es alnd ret.ained by thlttI sceimsl to detmonst.ll:e tlte etxistence of som:e tentral repulsive torce located in tthe nutelcus, tand capable of holdjuit these igaseous partt icles in quilitbunt. \W.ia:t ttis thiree 1`may be it is vain to cooj:ecture. I till enveltope of the luclt us is i ca )phclomeno sllurpassin the 1re1ach of hu.itant t1hou1ht, w4lt s:ll wt sa ay of the still more mysterious and incomptrche etsiblt phll nofll eta pr sctnted in the t ails of comets? Wio Iave alroadly said tl t these tails are lthrown o:itt in dilrection fppos/ ith,: s the ti as the co met approttachlts its pcriht ioit(-t passagtlCfe. As the comet sweeps arouind thet sun with atlmost incotnceivtable \vloc0ity, the ttail retafits its di-. Irction, julst as thoutg its axis were a solit bit of ilron passing throut i t h te nucleus to the sun aind m lhal ging on the center of the sola:r orb. This b, b t extetndiln outt to the fitrtthest extremity. of the tail, sonctetittns 120 illions of' milcs beyond the nucleus, sweeps round angularly with tequall rapidity at every point, so that its rectilincar figure is preservdt in this tremendlous sweep. In cast the tatil vwer con posed of pondertlable particles, obtedient to the laws of gravitation and mIotion, this would be imnpossible,i ior if wet consider eacl pa.rticle an. indepe. ndt et body, dctsc..rili:lg o atn elliptic or tparaiolic orbi t lu. the sun, t}te laiws of tlhir iotion wtould coimipel the ntmore distatnt pa.rticles to g beltindl t nearer ones in ai ngtilar velocity. If no ctomet ever exhibited any other ttan ttis peculiar T": G EA CO M ET O F 1858, KNOWN A "DONATIS COMiL T" T I E C 0 c,M.. o 4.. 2... 5 fttlorm of tail, straighlt antd direcled tf)'ro the sun, wo mitiht firale as n hpypothesis whict could a.counit it:.: tlte nt.ct.s but: in oine instances titCre, are mn. ni tails to thte 0:t1 ntucltl a nd these n.ot st r aiht, but: t c.uliv like ai tcimtiar, It o ther cases thtwere are two taitnl the onc, as Msual directedl from hto stmn tlhe other poiinting towatrds the source of light. Societincs thie pricijpal tai is straight, atnd itl. t he direction fit'lo thte sunit while a lJatenal ray shooting frio the 11iteltnus m-ay fotinm t iti. thie atxis of the tail tan atle of thirtty or even sixty degrees. We have aldre.ady said that t te tail swingst atroundl the sun in the pe hrielion p t, pas it sg preserving its forL andl diretionl, anl d hencte wien the comnet is receding Itroin tho ttin, the tail, in all it v at dilCnsiols, is driven )beftore the head of the comnet, preceding the nucleusl as it sweeps outwatrd into sace. Iln sone instances corruscations hlave bieen noticed to take plaeo in these t gran.d but mysterious appetl dages, darti tng with incredible velocity from the i'ry ntucleus to the extremity of the ai, anti ti a thu1s flath.1ing backwards aid fit wardls tlike a magnificent auroral displayt Th.o question arises, What are these luminous displays tArehe the tails of corets coinposed of poitndratblle mtattter? If. so do they yield obedtience to the known laws of motion and gravitation? Is there any itmattter i'n the universe whichl may iever becotme huttilous, but is it. tpondera ci? ( Can tlhes tails e 1be -1la tore ctfoect prloducedt on the swaves of light emtitted by the sufl itn t:ssinig th}roiu t the tmassf cmftictar'y matterot? The se -and many o(tlitr qtustion;st eiqally difficult p r-sent tiheitselves in tlis cotnncttion. iShe re-.absorption of t:he taiil into the Ithead would seet to demonstrate that the matter co(ulmposing the tail was ponderable, -whlile tlte faitis alreadty stated 296 Cc iJ THE C' 0o t I T S. as tho te riid fornm it'csrvcd1 by the tail hi sweepingl arountd the suntl positively contradicts thtl hypotheAsis. One tiling woe kllow comctazry m1atter is ponderabtlo mattter, and obeys t he laws of w motion and gravitattionl is swayed by the sun and by the pltanets, and in all particultats comnplict witlithe laws governinwg otlr ponder..able matter. )This wte 1know, bectaust, as we ha:ve seen, it is possible to predict the return of a, comet revolving even in so great a period as seventy-five yeas, and such preldietions hlave been rigorously verifi(ed. Itt case any )portion of this pondelrable matter were abso nrbed int tlh suntt o dissipated by the intlense heat which it sulffers in the periht ion passage, then would. the mass of the cometnU grow less at each return, and the periodic tine wxould slowly diminish. There is one comet, tnameld after its illustrious discoverer, lnke, whose history for tfhe past thirty years has been followed with high interest,.because it i.s now a fixed truth that at each returnll its >perihlclion passtag'eC is acclerated by about two tand a halft lhouras. It revolves in tan elliptitcal orit of small dimnenlsions comparatively, and performis its revolution around the sun in a period of only.1,203 t days, or about three and a th ird years. By assuming the existenee of a. rare rteisting f meditt, Proecssor Eneke has succeeded in a ccounting fior the acceleration in the motion of these conetts, atn' td tis hypotthesis has been generally lreceived. In case it. truth becomes establishled it involves remote conisequencel s from whtich thlte mind naturally revolts; for i' theire be at Incdium capable of destroying any ptortionn of the velocity of E:tcke's comet, thi same resist(anel mItaus ilt in lie mann.t er destroy a partt of the t oital velocity cf every planettt a.t satellite, iand sooner o latetr each int its turn1t. must btty slow degreet s tapproacht the sun, andt i THE COMETS. 297 the end this grand central orb must become the grave of every planet and satellite and comet I Such an hypothesis is combatted, possibly disproved, by the fact that its influence has not yet been discovered on any one of the planets or on any satellite. It may be argued that on these solid substantial bodies it would require ages to produce sensible effect, while on the vaporous ethereal mass of Encke's comet even an almost evanescent medium might produce a sensible effect, even in a single revolution of 1,205 days. May it not be possible to account for the decrease of the periodic time of Encke's comet without having resort to an hypothesis involving the destruction of the entire universe? In case we admit that it loses a portion of its ponderable matter at each perihelion passage, then there must result an effect like the one observed, the comet slowly approaching the sun, to be dissipated entirely, however, before absolutely falling on the surface of the central orb. However, it is useless to speculate. The facts now in our possession are not sufficient to enable us to render a satisfactory account of the various phenomena in the physical constitution of these bodies which have been enumerated, and we can only hope that the diligence and pertinacity with which this branch of astronomy is now pursued, may before long eventuate in removing from the science this only source of doubt and uncertainty. In the meanwhile the conclusions reached by Sir John Herschel, from an extended and careful observation of all the phenomena presented by Halley's comet in 1835, 6, have been strengthened by the facts recorded both in Europe and America of the great comet of 1848. All the observations go to demonstrate — 13* 298 THE COMETS. 1. That the surface of the nucleus nearest the sun becomes powerfully agitated, and finally bursts forth into luminous jets of gaseous matter. 2. That this matter, with an initial velocity driving it towards the sun, is by some unknown repelling force driven backwards from the sun, and drifted outward from the sun to vast distances forming the tail. 3. That a portion of this vaporized material is not subject to this repulsive force, but remains under the influence of some equally inscrutable central power lodged in the center of the nucleus, and forming the corona or envelope, and assuming forms of great delicacy and beauty. 4. That the force which ejects the tail cannot be gravitation, as it acts with a power and in a direction opposed to this central power. 5. That the power lodged in the nucleus, and by whose energy the particles composing the tail are again reabsorbed into the head, cannot be gravitation, as the minute mass of the comet could not by its gravitating power bring back the particles flung off to such enormous distances. In this catalogue of inscrutable phenomena we must place the remarkable fact of the splitting up of a comet into two distinct portions. A comet of short period, known as Biela's comet, revolving in about six and three quarter years, was recognized as early as 1826, as a permanent member of the solar system. This comet, at its appearance in 1832, excited a profound sensation, in consequence of the prediction that it would cross the earth's path, thereby creating the greatest alarm among the ignorant lest this crossing might occasion a collision between the comet and the earth. T 11 (Os 0 M vif s. 2)99 Thie prediction was veCrfied, but while, the comet was in the act of' crossingte the (1erntl's track or orbit, the eart ii rwas ma::iry 1nill ons of miles rem- oved itfro this special. point of intersNection. T'hi.e apptlarance in'1846( was again rei nered memoradble by the s trange p thnomnron already mentiont'ed.. t ih actualt scveration of the, comnct into two bodies, distinc ttand separate each ometary in its appearance, and each alternaItelSy pretIfpndratti ng l in aptlprenti main:gitude and hrit lli:aIcy.' It'hes two co tets possessed all the e(hlaraCtl tcrist ics wthici mark tlhese anomalous bodies. Each had its mItclettus its cnvelope, and its tail. I'.tIe first indication of a sepairation occur.red as earlys as tillt t 1lt 1)Dcelniber, 1845. By the liddle of Januariy, 184, the scpa.rattion was coiripliete, and was well observcd in u11rope and Amterica. BIty the beginnitg of Mafirch the i terva.l hadl increased to a maxntAimis whe n itt was tabot t one-third as great as the tappl).reltt, diamneter of the fl(0oon. tro. thlis time the co(mip}taniont cimlt t be(gan to fitde, tremltaiin iaintly visiblet up to the lath March.t. A.fter this the old cttmnet reml aineldt singt l atnd finally 1disappea.red. Ilertc \we thave pheCtnomiittte of the most extraorldinary chat|racter.'Wa it con'. vlsion could have s p lit tl is cltebulots t;mass into ltwt ditit nlt fraiinnts?t W lhat twoindelCf power could thave occasioltned tlie malterntations in the irntensity of their t ightt? Wh.at mysterious )bon0d could }thae united tlhese severed tand separated bodies, a nd c.ttausCitd tI tl to viirate about their common ccter of gra.v ity? Ita v e thel sc bodiecs been pernl:t lnlently re-uttit:ed? or will they ever appenar as individual and independent ob)ects l These questi.ons it is now impossible to answer, TuI X; S NUMt:BE:R OF COMETS fa r exceeds thtat of the planets 300 i lt H.; 0 M E:TS. tand their satellites, anid, ilndeed, judging frioin the list of recordeld coimet, and tat i to acont thki fi:tct th tt m.-ult-itudes of these bodies d must esc.ape noti c entiretly by their lreainlin.t above th the hiorizonl.h int t e day timie, we art forced to the conclusionl that tetcy tare not to be ntlmberdlt l:b hundreds or thousands, but probably l)y myillions.,'hey sieem to obey no law as to the inclit ation oat their orbits or the direction of thelir imotions. Some appear to pluiot e vertically downward fom the very pole of the ecliptic, whtile others rise upward fiom beslow th:is plane in a, direction d&iametrically opposite. i' heir planeus are inclined undttert all angles, and thelltir p)erihelioit points are at all dis'tances fromx the sun. Son me revolve in- orblits of rtoderate eccentricity, while others sweep taway intto space iln paralbolic or even in hyperbolic orbits' never tagain to visit our system unless arrested 8and divtrlted fiomn their path by some di1sturbing power. 1tl c migty li.tL depths to vwhich some of these bodies penetratte into spaet, sweeping, as they must, vastly beyond the boundary of the Aplanetlary systemi, would excite a doubt in the mi-nd as to whether there lmight. b room entl ough in spate ir the ltundisturbed revolution of these wondlrfthl. objects. Wo shall see hereaft:er that pirofliund. itnvst iga tiot1s have ainswered thisi inquiry. atnd displ lled every doubt as to the' grandeur oft the scle on w0lhich the untive'se is built, Iin the Appetndix will be found the elements orf the orb'its of stuch comets ta arreg rg.arded perm:anen: t memtt bersw of the solar system. We here clo.se our examinattion of the various class-es of atttctndantt s on the solar orb. We find t}is mightty syste iet of revolvintg worlds composed of bodies which arc diverse in their physicat constitution. som ore dmore lns T I. X: 0 t: T S. 801 tmld solidt tltUan the (earth ont which we dwell, soint fitr in0ore ill and unsubistantialt than the tttmosphrc wo breathle...i.all obledient to the trand controlling poower of tht central orb, while nto one is relieved from t}he disittrbi'tg influenlce ot every other.....a vast comiplicatted display of celestial tmeltt istmt, w1. hose ( equilibrlium adtt stability pre)sentst tlhe grandest problemor r,nan iIt-. vest igeatio t o i to be wfud i theleholo universe of matter. CHAPTER XV. THE SUN AND PLANETS AS PONDERABLE BODIES. [ERAL CIRCUMSTANCES OF THE SYSTEM.-THE SUN.-HIS DIAMETER AND MASS.-GRAVITY AT THE SURFACE.-MERCURY.-HIS MASS AND PERTURBATIONS.-VENUS AS A PONDERABLE BODY.-LONG EQUATION OF VENUS AND THE EARTH.-TIIE EARTH AND MOON AS HEAVY BODIES.-FIGURE AND MASS OF THE EARTH.-PRECESSION.-ABERRATION.-NUTATION.-MARS.HIS MASS AND DENSITY.-GRAVITY AT HIS SURFACE.-TIIE ASTEROIDS.JUPITER'S SYSTEM.-SATURN.-HIS MOONS' AND RINGS AS PONDERABLE BODIES.-URANUS.-NEPTUNE.-STABILITY OF TIE WIIHOLE SYSTEM. HAVING now completed a rapid survey of the bodies which owe allegiance to the sun, and having reached to a knowledge of those laws which extend their empire over all these revolving planets, we come to the consideration of the modifications which are introduced into the circumstances of motion of each of these worlds, by the fact that it is subjected to the influence of all the others. As under the great law of universal gravitation every particle of matter in the universe attracts every other particle of matter with a force which varies inversely as the square of the distance and directly as the mass, it follows that each planet and comet and satellite of the entire system of the sun are, to a greater or less degree, affected by the attraction of every other. We have already considered generally the great problem of the " three bodies"-a central, a disturbing, and a disturbed body. The train of reasoning there presented PONDERABLE BODIES. 303 is now to be carried out and extended in succession to the planets and their satellites. Before proceeding to examine the changes wrought in the orbits of the planets and their satellites by the action of all the disturbing forces, we will make a more general examination of the various elements of the planetary orbits, to learn, if possible, whether any of these elements are subjected to changes which are merely periodic in their character, returning after intervals, longer or shorter, to their normal condition, to repeat the same changes in the same order for ever. We desire also to inquire whether any of the elements are subjected to perturbations which always progress in the same direction, and if so, whether these changes in any way involve the destruction of the system as such. This is undoubtedly the grandest problem ever propounded to the human mind, for it is neither more nor less than an inquiry into the perpetuity of the great scheme of worlds dependent on the sun. It demands a vision which shall penetrate the future ages to predict the mutations and their effects at the end of these ages. It will not be expected that in such a treatise as this we are to enter into an exhaustive discussion of this great subject. We can do little more than announce the results reached by the profound investigations of the great mathematical successors of Newton. We shall commence, then, by an inquiry touching those elements of an orbit which involve the well-being of a planet, or its fitness to sustain the animal and vegetable life which exists on its surface. The figure and magnitude of an orbit are determined by the length of the major axis and by the eccentricity, and in case but one planet existed, these are the only 804 Ti t E S UN A N 1:) PLAN1 ETS oletments whoste alue could in any way aftc t the physical conditionT of the planet so fiar as its supply of ligt a nd heat received firom the sun areo concerned. In tlin c:so tle position of thte orblit i its own plane (determined by thet p/lce of thte p' erihelion point) and also thle position of the planet of the orbit, as reforired to any fixed plane, (deterninted by thXe l(t nI o/f itcliWttUtiont aind inte o' nodes), and also the epoch( (or place of the planet ilt its orltbit at a. iven momentl: ot of time), all those qtuantities wvould not in any degree afIetr the actual condition of the planet; butt as no planet is isolated, atnd as each is sub-.l jetted t ttht influeltee of every other, it.becomnes a,lmatter of grave importance to ascertain whether therl l e e any lucttat ions in tlte values of all tltesoe elements whelther these fluctuations are( confined withlin any specific limits and whether, if thus confined, any iniurious ftbet can'result to thost eltements which involve tthe well-being of any plmanet,; anld finally, whether theri bce e any gularantee otib the perpetuity of the p)lalletary systle it the colldition now existent. In ctase tie planes of the orbits of all the planetts wtere coincident., thtlen thte intvest:.igationls would be confined to the fluctuation in the values of the major atxes, tecen-. tricities and perilelia,; but fit'om the reasolning atre ady presented in the problem of; tlhe three bodies," we have seen thatt if we considert tthe relation of two iplat.t lets whtos orblitls ar etinl.i.ed ulnder tany ani lo, in tlheil reciprocal influlenle, if we assume thl plate of tthe orbit of' one of ttese planets, l; r'examptle, the earttl as fixed ini position,:and thte plane of the otlher planet's orbit ( as Mars) as incli'ned4 to thtis, under a gtiven ag.g'let, it is cle(arly rma:tnitfist thlat the di8stturbing influence of' the earth on Mars will be reversed when Mars passes throufgh thet plante of' the A. S P O N 1.) t B n i BO, ) I: S. f05 earthl's orbit. Sulppsco wee could place our eye in the pi'ololgationt of tlh line of intrcsection of thi two orbits, tlic,e we shoutld see thelm as two straight lines, inclinecd to each other, as in the fiiuro below, in which S represenItst x../? -T/..........................................................................,,................................. the place of the suni, 11:4' places of the eartht, and MA aind AM' places of tMars. Now, wlhen Mars all the eartIt are on tthe sam le side of the sun, or the line of nodes, Mars asctending towairds', atbove the )plalte of the earth}t's olrbit the ftree exerted }tby the earth on the a(tscenditng planlet tends to draw it downward to the ecliptic, and hetnce it will not quite reach the elevation Ml', antd thus all thihs whie te tplane of the orbit of Mars wtill boe forbm itnq a less and l essanglo with the ecliptic.'Tlle xlonienlt Ihowever, the planet reach ts its lighest elevation and cottnenlces to de scend to wards the ecliptic to pass its deseeidin-tg nodlc tthen the eath remaining stattionary, will pull the planet towards its own plalne, and hence the descent will be mtade steeper, 1land tile angle of inclination of the orbit of Marls will while tlhe pla'net thlus descends, he alwasys i;crctsit(,. bfollowing Mars below the pltano of t}te ecliptic, the earth r':eaining las btclore, twe see that here the telitdency is to pull Mars up to the etartht's orbit, 800(6 T:I El SU N AN 1) xP A X i Tr u1tI tlenilne. it will not quite reach tho pont M, or t0Io inclin.atiolt in t ins dimsCotnt. bolow tie ce.liptio will dimtitis/h..From t bis poi nt, as \Mars bemis to asen.d,' thi carth s at.t.;raetive elnerr y will1 cause it to.asfeltind 1ol rattidly, a nd will make t it ) stass it tscend mntg node earlier th.an ift undisturbcdi and as it eontes up faster, it mlust ascetnd a steet(pr grade, or the intcl(tntion. will incr1easo. T.'I us wo see that.IMtars, in ascending or descending to pl)SS cither node, will both fascend and desscend by a steeper trado because of the cartIh's attract'ionl, while in pias>'ing fiio either.node to t the highest and lowest poinwts of its o rf bi t t th e n oeate to' will operat tomke the plan tet reacht points less rettote from the ecliptic titanl if undistlurb)ed antd ltenet to asend and descend withl a smaller angle of inclination. Now, N a carefil inspection will show that tho eflects product d by tte earthl on lMats, while. situa.ted at J', will be greater in tihe thalf oft the orbit of Mars whiche lies above the celiptic, and at tie end of onte revolution an exact coinpents:tltion tma) y not be et lited, so that the int-. crease of the angle of imclinatiiou may nott be exacItly equial to tlhe dtecrease..tBut as thl eearthl is revolving, a timne will come when this body will occutpy the point E,'lnd then tilte most powerftl eftu et will bthe plrodtlced when Mars is below the ecliptic, and inl aetIse the orbits lare cirtultar anI exact symillmetryt exiting, att thte end of' a cer. ta.ri cycle the inclinations will be exactly restoredl Th11e fict that, thl orbits of the planets are elliptical in ii'guri' canntot in an ty wy -less.e the fi(rce of' thte reasoning we have einployed; i t tcan only posttpoetlo' o to aoe remote period the fitnal restoration of. tlhe inclinattions of th{ planetary orbits. UIlnder t hol powerful and ii masterly tantaIlysis of L agraange thi'js slubect was completeltty exhltastted and a result reacthed which in the followitng pro A 8 P 0 N 1) K It A'B L t1 10.1) 1 I s. 807 po.sitioa0 glnaralntee the lstability of the i}t liciattioi.t ts tht rout-g all aes:C.: —..'1t f th l vass or weight of every planet bc inulltiplied by thle'jtuare root t of its mjor axi:t andl this producttt bo mul1tiplied by tIhe tanlgentt of the angle of icliation of the ptlane oft the plathetary orb'it to ta tixed plaln, land thl.es )pr1xilct.s be added togeth'tcr,: ttheir sllum will be conlst:atly the salMt.C Now: wNe will show hereafter that the lmaor tSaxes re m.tain nearlytt invariable, the tiasses of the planets are al. solutely so, and hetncte tl third fitetor of the iproducet, the tangent ofI te it tfinatiol, ca onl y t ary witthit narrow liits returlnin g at the. end of a vast cycle to the p.rittni tive value. We shall see hereaftert how ipt:l)ortanlt the stability of the inclir:tattion of thile earth's orbit is to thie twell-ein g of the living andt sentienlt beintgs now on the eiarthl's surfac:e. We procced to.examine the chalnges oft the tilts of nodf s due to perturbat.tion. ilt.s changes are allied to thioso of inc4lialtiton and art i ltdee d a necessary eonse qumnee of tho ls ane cLt gs, as nmay re'adily ibe shlown. ~...Si -- ~ ^~ 0O8 Til l':. K U 1T iB N ). PLA B N N ETS tIlor this pil'rposo we return to thle fig:ure alreadtyw emntployed, usingl tlto sa. m planlts Mars and thi' earth regarildiit tlt inontcir:nts of aN11s to bo disturbed by tho ea rth's attraction. "We Ia vre allready so ten thait in case Marts be at MA5, tho earth btein at.. l i.: tho planet, in descenditt gl its orbit to tlhe line of nodes> seen as in 8, (the eye of thet spectator b'einlt. int tie pro)lngation of the line of nodes) tduringtt the entirte descenlt tlte planet will bo drawn down to the plano of thel ecliptic I. EE' on a steeper gradt e t:han the normal onte M, and lhence thle plante will pass throutl the ecliptic eartlier than if undisturb:ed, or at a point whilch will be cen somewhere between 8 and 1j. Thus during t'i ds ti eet node will go blackwards to meet tie plantet, or will retro frade. Passing below t tie cliptic, tie planet contin uing to descend, will, s we ha ve s een, be preventedt by the dist.urbing, body froni'relaching a point so low as M', and hencel if its patIh flor a mtoment were'aIty where produced backwards, thits line would meet the ecliptic at siome point always aIpproachltii:g t, or hero agtain the line of 1od1cs retrogreadles.'The ste, reasoni wvill show that with the above configuration the retrogradiation of the line of nodes lmust continue wtith unequal velocity during the entire rcvolutiton of the planet. In other eonfigtrations there is somctinmes an advanle of tihe 1nod, but in tlhe long'utl it is easily demotistrated that the: nodes otf all the plane.tary orbits on antty fixed plane will retrograde ntmd plerrfoirm entire revolutiotns in pe.riods of g(reate.r or less duration. T'}is perp)ctuatl recess of the lines of node(s in o0ne direction dots not in i anty wlay af.ect the physical condition of at plantet, but serves ant adtniratble anl d nt cessary purpose in securing final sttablility in the planetary systemt by AS PONDERABLE BODIES. 309 presenting the disturbed orbits to the disturbing bodies under all possible configurations. We shall not attempt to exhibit in full the reasoning by which the variations of the remaining elements are shown to be periodic, when periodicity is essential to stability, or progressive when progression does not involve destruction, but from a single figure deduce, if possible, the great principles involved in this wonderful problem. S Ei: Let S represent the sun, E the earth, and P any planet disturbed by the earth, and let us suppose that undisturbed in any small portion of time it would reach P', but subjected to the influence of the earth's attraction it reaches P' in the same time. The question is, in what way does this change affect the elements of P's orbit? We have already seen the effect on the inclination and line of nodes. These elements do not affect the magnitude of the orbit nor the position of that orbit in its own plane. The magnitude and position depend on the length of the major axis, eccentricity and perihelion point. Let us examine these in order, commencing with the length of the major axis. :}10 T Hl SUN ANi) PD. AN iN T S'We suppOse l': planit P to h iro iovi, when undisturbledt wit i itts: tnormal elliptic vet ocl ity, ald otf coI rsi on reoacni g IP the lo.nrei r axis of its orbit l andt in. ttct all the elotnetts itretin iriutncangcd in vatluet but bein dtsturlblcd, l so is to be pi:revented ftitom reachig P"i anld beingt compelled to rea ht'I?", will tins compulsion mierely chtlngc thet tposition of tthe planetary orbit, or will itl inc(reas or dec rease the lentgth of tte major axi s?:Ke(pler's tlird ltaw tells us tilat the squares of tlhe periodic tnilies are proportional to tlhe cube}s of the t:major axeCs, a,,tld fro this relation it is malnieitast that any chlaT-.e in the el.liptic ve\locity of a planet must m t ltange tihe period of its revolution, and this involves a change by ncctessity in tlte major axis of thte orbit. lthe question of cltttng1 in the tnmajor axis, theilc recstives itself into an inquiry as to whethter the disturbantcoe ]l:s prodtucied at'. y chtang( i- 1lite elipiic vt/lociy of tle tlisturbte planet. A.t the firs't glance it many seemO impossible to dr(.1tt a planeit oirom its norma.tnii elliptic p:athf witlout aftlectinl its velocit y I l', is )towever, is not the fac't. If a body mftovingtt in a st aighlit li ttand a ftorce be a:pplicdl to it plerl'pdieul toa th to th direc tion of its.otion t t.lis tre. will tnotit in tanly tdetgree:ifeoct the velocitvy, but oitly the di ectitn of thie mi oving hod't. Ttls a b.tal fitrd firom i rille onl te ti cAk of ta: fixed or mt ov ing l'oa t, wit it the sa-ltme initial force, will reaeh tie)l opposite shtore in the same timeo, lint its direction of a.bsolute motion. is clta:.nge.d if fired l om a mov ing boat. from what it woul be ift wuld b it' shot fri-ll o.tt'at rest. So a flyigll ptlaet tmi be sulbtected to the action of ) fu:no a lwat\yst)r pr tndlicular t to the directlion of its motion, whtich fit2rce may pushf it fromlt its 1nor:,mal patli, butt cannot affect its elliptical velcitiy. AS PONDERABLE BODIES. 311 Such a force, then, can have no influence on the length of the major axis, or on the periodic time of the revolving body. Now, every force is capable of being changed into three other forces whose combined action will produce the same effect as the primitive force, as in the figure. I'/ | P/, es d. ection ani......... _________V Let P P"" represent the direction and intensity of any force; on this line as a diagonal construct the solid figure a parallelopiped. Then the sides P P', P P" and P P'" will represent the direction and intensity of three forces, which would produce the same effect as the force p p'"'. P! IP"". Precisely in this way the disturbing force exerted by the earth on the planet P can be converted into three other forces, whose combined effect shall be identical with the original force. Two of these forces shall lie in the plane of the planet's motion, the one tangent to the orbit, or in the exact direction of the planet's motion, the second perpendicular to the direction of motion, or normal to the orbit, and the third perpendicular to the plane of the orbit of the planet. Now, from what we have said, it is clear that but one -t ~ ~ -a - C ~ 3C a -:i <^~~~~~~~~~~~~~~ 7*OC r s' ~ ~-t - ^ 0 0 ^ ^~~~~ 0 0. >^ t ^cr * 1111^ re - i c# * ^ i3 IO - /^ ^5 1:.3'3-. 11, ^~ ^ 51* IS^/ /~~~~~ \ \lC llll~il _ ",oU ~, emOC ~ ^ J ^ \ \ / - \ / ^^5 ^ ^~~ i. $ C _* ~oi;_ ( g; <; - III^ \ / C' / I a H C t < I:; 1 I ^ 1 5 ^ \ \^ ^' "0 - / - ^1^^~ ~ ~~~~~~~~- -.^!'''^ ^,o^^^1 ^^8^ ^-^ e -^^ ^ ^^- ^^ ^^^o^' ^ ^' ^^ ^ ^ ^ ^ ^ o ^ ^-~ —- ^ g^ ^^^^^^ ^-r 5 ^ ^^s >-~~~ o < -f,-' ". -- rc ^^^^^ r "-0.^^ o ^ 0- ^ 9. " ^ ^ ^ ^~~ >-t' r. -^ - a' y" V -o o?? ^ A S P OND) BI- tA tB, E a1o ) I E,-S. 81.3 lthis positiIon the tan gntial force being nothin-g, tIhe ma1jo axis ist utndisturIIbed ly t, As P -moves towards P)ti e direction of the f'rce exerted by E ceases to be l t o s's orbjt:>, atld m- y be replaeed by a normal and a tan-. gentiat l tirce. The tangenltial force frito P3 towards P' is manitfestly in oppositiont to the motion of P in its orbit, and tle refirce retards it:s inotion, and ttius decreases its lmajor axis; but there is a point P" symmetnr ticatlly placed with rel'reneltC to P, were' tho tangCntial ibrcc is in, tlt opposite direction, and in an qual degreeo becom) es an acctelrat.tinlit firce antd whatever the inmjor axis might loso in leng,:tl. firom the disturbing power at P', it would gain from the samie power when it comtes to occtupy the point P". So that if E should remain fixed during an entire revolutieon of BP, a compensation would be eflected, tand the velocity of thle planlt on reachingl its point of dleparturl would be identical with that with which it started, arnd lhence the m.ajor axi, thougt it would hlave lost and gained, would in the end 1)0 restored to its primitive value. If thet orbits were elliptical and their matjo axes were coinc ident th}e same reasoning from symmetry would still hoXl}d goord,.land demonstrate the restoration of the major axis ani d las acti and rectiLon are always equal, it is manifeist[ thait.t by fixing P and causing.lN!, to revolve, the chlangcs wroughft by Ol on P would:now 1be wrought by P. on il, oEnly in tie reverse order —...... at is, wherever P was accelerated by E, E will be retarded by P, and vice Admlitting thle rmajor axes to ie inclined to each otlher destiroys the. symmletry of the figure, allid an exSactt restoratito is not eec'tte in one revolutilon; but as tihe rperihelia of tlte planetary orbits are atlli i a m0otion, tihe thim 14 o314 THE S UN A:ND) 1P:LA:SNE will colme when a coincidence of the major axes will bo Cilefcted, and if there be at certain amount of outstanllding U. mtlcon)ponsatcd vetloeity, whenc the cointcidcnel take.s place, the action will bo revolrsed, anid att tlhe end of one tratnd revolution of the lmajor axes fiom coincidelnce to coincitdenco the restoration will be completed, and the axe-sx will roturn to their primtitive value. HIcere we are comlpelled to leattve the proble-m, and simply state the t result which a cormplete solut1ion hlas eCffeted. We tare agan indebted to I:grangetl for the retsoluttion of ttis moost important of all tlhe problemts involving theo stability of the sola.r system, w\ho presents' the final result as follows:.........' if the masss of each planet be multiplied:t thle squar root.of tithe major axis of its orbit. and tllis protdut by tlh sq(Juarle oh thei tangenm t of the incli tnation of the orbit to, fixed ptlne, atld atl these products be added twoetcihert their sum will be con'stantly the same:, not. matter what variations exist in the systemttn. Tlte Ilmas or weight of eacht planet ins i ilv abltc, whil the loss or aint in t.he valucs of tlh m jor axes is always counterpoised by ttho gain or loss in tle inclination of the orbits,::t tu iand thus ihe long run, in cyclec of vast periods, a cotnpletc Irestorationt of thl matjor axcs:is fully ac.omplishied. and tlh system in t lis piriticulr retlttus to ints tAe liat t a considered th lt of two out iot'We httve thsl f;tr contt idcered t4le..lf:t.t: of twi out: oft the thtree fbrcl s into which a dist urbig frce ntay bo de. - con posed. het normal conmpollent remain to e e xranE iied. "'l"Tis acts it a. dircetion. norm iantl to th t curve dc.::rilbcd l. tli. planet, or pt)rpeoldicular to the tai ngent to the orbit at the point occupi(ed by the plam tt W shall not enter into any extended txatnination of tlis sub. AS P 0 ) ON H A iB,t.: 0 B t o S, 3. 5 ject, i:tt d will onld V S my that tils ctone ponnt of the d(istulbing' fotrcci e s risc to a i movxctme'tt ill tthe pctrilion pointis of tlit planuetiary orbits, sormntirns a(:ltdan.cing theOls poiltts, soneltimls lving telii t a ret'rortade inotion, andt in some instatncs t'.:tpodu in:S osci llationis. lhiesio clbects are lnecessarily mlixed tup and combined with thoste produced by th e acttion tof the tlattgenttial force, tfor ats we lhave stee, tthe effltt of this force goet to ilcretase or decrease ttihe value of thte mtalor axis but tno intcrease or dec rease of the atjor axis ctan take plac without a correspontding change in the cec ntrticity, so that these chaItngs thu itS odiicd ts I o iei byi th the otler, iilnally hecomi exceedilgly coimplcx anid can onily be traced and coml puted y the application of the higlhst )powers of analytic etasoning. The co mpt-lity is further increased fromt the faet that ill the consideratl tiion of the entire Irolcm of prturbations the vartyitnt distuances of the distuarblinf and distut:rble bodies nm st be ri orously t ak en into account, and mtay modify antd even reverse t flcts due c t sim ply to diriec-. tion. ith d ificulties so extraordinaItry and diversified, with corunplications and complexities mutually x: tending to each o}tler. involving mlovxemenl ts so silow as to trc. qtuire acXes tbr their ctomipleltitonl, it is a mlatter of amatct menttt that t theil ttlllttll nlt ind iast achieved coanipcete sttccss confictct e vlniOtounce the ch llanges to itll withit narrow antd inocuous limits, while in the end, after a cycle of incdalcutlate fmillions of years, tlto entire system of plaInets and satellites shall returt once m or eo t:teir prim:itiv condi tion to start aaint onf tir lendless cycles of eolnfitgmation and chantge iThere rematins one ore source whesnc aises an ac 80t16 TH SUN AN PLANETS cumulattl1i of dis tiurbancel progressivO in thte sa met direction through} definite cycles of tgreater or l]eset duratiton I meat th} c cfclcets due to ta.netr' comttlmetnsurtUbi/ity of t}te periods of revolution of thle disturl)ed and distturbing tplan ets.'Tihe near er thi a pproaotth to commensurabili t the longer will be the duration of the re.suitinl ilncquality. AW shta lave occasion t to res li s subjl'ct i n our (exntnination1 of the circurnstances of disturballnc belongling to aci individual planet, whtllch we sthall -noYw }proceed to examline briefly, eoliomelllig at the stun, and procccdin' outwards. I'itt.) SUN C(tN'sM E>IM):tII) AS A GRAVITATitN BOIS D,.O.Y.,\ We shldal now return to tlhe great cenlter of the pl-anetlary worlds witht at fll klnoc)wlede of theo lawst of motion and grtvitatittion, land provide(d with t h instruellntal means of Securinll those delicate tmeasures whelxc)reby the solar orb.tt-ay 1e detetrminiledI il dtisftiactc t:1/ol/te antd w.ei gt. A A.,.,-.n.u-.:',''......................................... We h1ave already explained hlow these quantities may be obtained, and we onow pres ent the rc8sults of exact measures andt atl ccuralte ctIlomputation. tIle 8u1n's miean distance ftrom)l thie eaxrth mraiy be taken at ninetyt-five il-. lions of milcs t. y exact t measures the mean diameter of the siun subtends an angle equal to 8.0.1' ".8 amd ant 9 days. This 1quant iiy mnultiplied by 5, produces 2 9)19..6) tI —i l.hat is, dtlnring tthe timet ivolved in thte long' cycle of 2i)21 days there Ithave ot1clrrlted five conljunlletions of thi,e eartIt ald V\ uso distributed equally around the orbits of tlie planets. If we examine tlhe figure bolow and suppose 8, V atnd to A S 1* 0 N) D:R JtA t I 14 B 0 1;) I E s.. 29 r'tl.'l'cent the places of the sun, of V'ellu aInd the earth, at the cotmlmllecelnllet of ta great Cycleo of 2, 921. dlays, at the tend of o1e sytnodic revolution of Venus Vt and.ti' will bo t h places of the two planiets. SAt thi cndt of the E/ 0/ /......... 3 -\ secornd synodic revolution the planets will e)o in V" and Itand:,, a tndt thus tley wil pass roundi the orbits, making t.heir conjunctions at intervals of 588.9 days, and: separated by ares, equal to onet-lifth part of 860t T, Lt ins ow carcGfitty examine tlhe reciprocal influence of V and J. Btartnii romn the places V and Fi] in the figure, Vrnius will tike tio lead, anxd will tend to drag, forward tho earthl, \while the earth will pull back the pltanett, and as the planets sweep around thte sut n'Venus overtaktes t}h eartht a't \V":''", aneld as the eartt is tnow in advance, it will acceleratVenu and w ill turn be retarded.'thus a itpartial comttpetnsation is elctedI, nalt the motions of tieo pjlanetst retturn ntcarly to what they were at the 8t0B ) Tt 1 I-: SU N.AN) P.' A N I f S start. Th }is sant proc i s repeated at eveCry conjun-. tioll; rld ii clase the plainet:s fall exactly on the riightt linc. S V I. at tile entd of fivo of thels^ co{)unlctifos a com)Iplcte ret'storatiotn would bte effctted. But this is nlot sexactly true. l llThe periods are not precisely cqual, tiand tih fifth coljutjction docs not fat11 on S V' E, but on a dotted line a: little behindtt the positi:on S V Ii. Tlheroe will, tlhretfre, remt)ain a very small amltlount of outstand-. ingj perturl)ation at tthe close of one g'reat cylet, which. will go on accumutt lating so long as the dotted line fidlls in;tie same hal. f of the earttli's orbit; But the diflbretnce.ettwcen 2,921.1[60 day s and 2,922 8 is 0.852, and by this ftia.ttion of o0e tday is the earth later than Venus in reachingtt the pointt of departure..Ience, the conijtunction of the ptlanets must Ilhve taken place oni a line behlind th;at of the forlmer colnjunction, whose position nmy be readily corlputed. Thle daily miotion of Ve nus is o.61 2, wi}ile tlhat of the earth is 0)V.(85, at(n tths Vent18s gains daily on the earth by an amtount equal to 1.61-2. 0.9.8.;.... Le:.27.X t S V E be the line of the first 0....... 0..' V' /................................. —..- I,""~ conjunction. At the end of thlirteen revoiutiotns of Venus she returnst to the point V, while the earth is in the pofint, requir-ng ytt 0.852 dayst to reatch. t' ctIus n1s1t.1: ttherelfrc,. hlave t:passed the cartt oil some line azs S \V EI such tthat tVenuts will avce gained 0.852 da ys on tihc earth wh en shle larrivcs at V. But the idaily t.otiIo of Venus is I.'.6 1.2, and il tlhe fraction of one tday 0.852, s}he will move 1".612 x 0..:8 1 ".1 78. I nce, AiS P N 0. 1 R..A I., B; 0 1) I Es. 8, f. the now line of conjunction B V' E" m1ust Il 11 belintd t;tlc t1(: firlfS t:,E t}X}S t to tilt. l/or..'Id ltrsher osition. andt tthus tlfe ltife of odte(is of tihe ring t ill revNolve ast ( do the linest'. of 1nodesi of the planetairy orbits;and tlis is precisely wl at we indtt to be true of the ine of etquinoxes, or tie line cutt by the latte of this etquatorial rinlg tfr'o thl (plan of thet ecliptic. t producinti: as we have seen, at rltrocct.:sion of the eq(tinoctial po)int, at d a precession of t te tile i'of tthe equinox. Il' I t AtN 01' TtlE l EA RTllS AX iS Is t pfhtltinomletno spl'riingin:g." out of the saine causes iproditcinllg pt'ecessioit. If w' ct lsidti er tthe axis of the earth ias ta ilfileoxible itar, p.'ssin.iu throughl the earth's center and perptiendiculart' to the eq utor, exte.(tdinlg inldefilitely in oppMosite dircetionlls, to the cclestial sphctrt,, it is cle ti that 3ny tilti gl of tth AS P N ) I DRA B L E B 0D ES. 88'T earth's equatorial ring will cqually tilt the axis of the earth.'This is actually seen in the slow revolutlion of the pole of' the teart:hl.s equator around the pole of the ecliptic in a: eriod ptri ecisely equal to tlhat,employedt in the revolution of the equinoxes. Nutation is hut a s8ut hordinate fluctuation whereby the pole of the equator, insteadt of desecrihbinl an exact circle aroundt the pole of the ecliptic, makes certain short excursions a little on the inside and on the outside of this circle, in a period whichl tagres exactly with that occupied by the revolution of' the nodes of tihe mlooon's orbit. Tlls at onte sutlrestS the, m1oon to be thel principal cause of this nodding of the eartht's axis, and, indeed, nmodern analysis has pointed out the origin of tle movemellnt and thas accurately computed its value. In all we have se sa.-id e w arie supposed the etquator and ecliptic to coincide. Thtis, however, is not the case of nature. Th.ese planes are inclined to ctitt other, and hencee e find the sun producing results (anatlogtous to those already traced to the moon) on the mass of protutlcrai: t mt atter surrounding the earth's equator. The exact values of these consstants of pr'eccssionmttl and nutat Tion will be filund in the Appendix. lte greatest pa'1ins ]lave been bhestowed on their determiination, as they are of the first importaltnce in fixingr the ab. olute l plE)ees of all the }hetavcnly bodies. I]O:('tR: oF tHt: AEtltwrI:' ORBT 0 *]..- The elli 4ipticity of the earth's orbit is slowly wearing away, under the combinted influence of all the planets. 1The eccentricity at thle co('1nmencement of the present century amnilounted to 0.0(tI 673858, the sentii-major axis being considered as unity.'lThe amount by whiclt this quantity is diccreatsed in at h d. l ed yt. ears is 0.0000411t6, e1 t us reduce thelse I.. 088 T 1t B S U N A N 1) 1, A N B'.gS fiQture: s to int:eolliX:iible qut:atit:i s. 1'tli oe0n0'tr-icity is tllo distan:tce lt::flron th( c(ntr of' t e elip te to th}e ficus, and in Tnills' is et(qt:t to 0. i0 1() 8^ 8 x 90,, 000) 0(I)t) 00 itt 0) Th.is (iluatity dec(reasles i n oe lt(11 lttct ye'aris byt 0.000 041' x95,t3 Ox,0000095()f).(}0..:..); iles. If, now,O we divide vie 5H4t 100 t)'by 9 t.8,:, t}h quotiet I 405t-1- will 1).,0 tho nium1bt)e of centuries Nw}tich ilnnt clapts bet) tbre t)ho e(arth.'s I (.bitN w'ill b'etome an exactwt circle at: the p)tresent rate otf e(lT'tf:,. It is ascertained b1. a b rigorous: 11 taltictal in vestigatito of tiis grei'at plro>blemt tlitat s0 s(,10 as tthe circular figwure is reaied'l by the c arths orbit thle sa11e caluses reve.rsei it eets, nd t:lilie cirtulr' fi.utl et is lost, antd thle cce: trieitt y of tho elliptic fig urie slotwly itereiastcs until finally, tt tte clid of a vast perlio. t}te.orXi!;nal turfi0n of' tlhe otb)lit is ret.aiined, t to e at tint lost: and tltus an cexpta'nsion andlti cotutact t ill ti aks tlte tistory of tle earthl' o01.rit vib:lr-atingt tltrouit pet. riods of t 11ime s welli ting into il lilions of' ves(: rs,. tlhi::ange in t.. t fig.uri of tihe earth's o rbit t lrioduces a. Itite.0 Niangu in thel1 mtean, motion oft t le tm ootl: w:it'h'1tl titwast, iti.t.ter ]ion-a I ye'1rs oft the.lt iostt t: la:oiout t(ts r1 searcI:til:ally'i\ trat e t to otS true orttig )-r y 1. tlt Pla e..e. fih:t I. thatotdtI tlto iool was mllov ing'Istr i)t-t modernt 1 thai it. an.ciet i.ties: t bec.am t3 evidttenlt friomi a (compalrlt on of tlhet m}nodern aInd t anci t(:t eet lipst;t:s.:lt:tthes ecIp:i):es can only (.occur'whiten tile sun, ea. -rt}t an:d moon occu p1'y tlhe s'am-e tri:ght line ne. r al.ts 1.tr t b ttence. their.tr.t r'eco( giv es a vwery'precist e ktnowledg of, the rel atti-ve position (.o tore, tI-t tr.o })oodie(.s. It. thltuts be.'tamle manltti est. tlhat the:tvonera)t, spet:ed witll)whii: ti. m:ont asmvi inh he:iir orbnit. was slow\tly ill(.'l'reasii:gtt'ttll r i cintury to centu. Tt1y "li () lowt s nlec IT Ssairily ftoml thle fitt thiatt the loss of ec.lnti'lriitly )by tho AS t 0 P ).N I It A B; tI" B 0 f 1n t S t38O orbit re'noves- tile earth bhy a snnall amounttt: (on thett a.'1velra'Tt) further ft o thol e sun.'This (carics bot tl teo ctrt land lher stlttellite by so muc away lPom tIn dist l urbtfin, l ini luonce of' tle sun:n leaving to tho earth a more exclusive control of theo moon.i.A.s the stun is outside tie mo'st.'s orbit with refei're:nce. to the earth, his att raction wiill in-l crease tiher narntude oftie m'oon I''s orbit, a: d itt t of course, lier periodic tiite. AnIy dirlniution of tlte slutI' di sturtbt i'i powor will thlerefi(lro by so much permn:it thie mooinl to approtach th Ie eatrth, amt to incroaciXse ter veloc(ity of revo-. lution and lthi' is is precisely what observat ition h rev\:lealed witht reftrence' to our satellite durin, the 0entire period tihat history hlas recordedt thoe M'progreCs of' atronomty.'This grtv'adual acceleration mntll coontnineu up to the Itino when the tarth's orbit shallt {)econe exactly circulatr in f'tortn. 1This limoit once attatined, as thtis orbi t slowly r csumes its elliptic ftr:il-m, the accelerationt of the moo:n': omealn;motion is conv erted into retardati onit: arnd t hus oat the end of va nightty period thtis cltutt will b.e entiretly destroyed, tand the moaon and eartht return to t heT:ir prini-. tive condit.ion.'IThis actlcriation of' tChe mean miotion. of thlle 1mt1oon is so slowt tihat fromt the ea'rliest::recordt of eclipses ily tlhe fabylonians dot wn to the prese.nt tite, sotmte,500 years, t:}le )moon ltas,got in atdvance of her nmt:an ptl]a bl) about t:lt: r t:1;ie tim}lt'o her. ownl ditamleter. Tl.e I fIct abl)tove related inMdieato wit.h how muhelltl dii-i gence tti the noo's maveotin st. 9 been t l studied.''ittougth shlie is our nearest neilhborm and c:onsequently more direc tly tundertt tile eye of:. the astro:nomer-) than any othter t:ea vcnl.ly bodty, her notionts: haxe been more complex and difitli ult of lperet t expsl' ition tthan ant y ob!ject ill the I Iaveins. ti ice re1cnt investi:t:tlions of' the ti'uropea:l:and 34[:0 I t i: S U N AND P, AN E T S.AnIeicaln astsalrooisers and nr- tleltletiaticians seel to have finally conquetredtb tlis rcfrcttaory satellitc, so tlhat 1:1ow it btesolnecs possible to unravel hert involved and intricaite lmarctl amxtongl tilo stars witht such precision tlhat we can fix her place with certainty for even thousands of years. MARS AS A PON)DEtiABIL: BODI)Y.- hi...s planet revolves in tant orlit of such eccentricity as to Iprecstet very tmarlked difterences il tie power of atttraction of the sunt on0 tlhe planet twhen at its geatest and lea.st distances,. Its meant distance is.142 millions of m:iles, g'i -ing ts semti-lnimjor axis a length equtal to 71 millions of miles. Thec eccen-. tricity of the orbit (tile distance between tlhe center1 and fiocus of tle cllipse) tamounts to nearly one-tenrth of this quantity, or to about,6.4 mtillions of miles. 1 F1ence, the perihelion distance is 64.6 millions of' itlils, while the lapielion distfance is 77.4 millions of miiles. T'le attractive power exerted by tthe sun in perihelion will be gre'atter thin that exerted in aphelion in the ratio of (T. 4)' to (64.6)>, or as 5.991 to 4,1 12, or nearly as 3 to 2. To resist this increased power of attraction in periholio tte planet must there mrove with a ft r higher velocity t}han when in its aphelion. All these deductions frirom theory are verified by observation, It was from an examination of tite movement:. of Mtars that IKepcler deduced his celebrated laws. these laws we have.had occasion to use constantly in our comtputations, but in consequence of tit mtutual actions of the planets, not one of these law.s is rigorously tirue.'1The orbits of the planets are not exactt ellipses: nor do they so revolve tlhat thle lines joining, them with the slun sweep over precise equal spaces in etualt timles, norn are ti1 squares of tlte periods of revolution, precisely popiort.io aml to the AS P 0 N ) E. I A t )i 0 ] ) 1I 1 8. M. cubes of the mean distances; but the failurl in tihce laws is due enctirely to cre pertur ba tlt, and t in ctase a simgle planct existed revolving aroundt the sun, they would t(itall b scruputlously Ifillet.d.'lTh ptlanet Mtars was, however, well situatted for t.heC exanmitat.tion cotlductcd by. Kepler..tis i.bcom s tna'iitst if we call to mind the great distance separating Mars a;:llt Jl:uiter, and the conparat ively small distur)bance whiich the earth can produce. To present this p'robletm still clearer let us suppotse the earth, Ma'rs and Jupiter to be in conj.unction, and situated ta in the figure. Tthen ~~~...~.~ ~~~.I.....-.~~-;.. ithe distance from S t'o E is 05 nilliions of miles, from- S to M 1.42 millions, ftom S to J 890 millions of miles. Httence the distance E M is:114-........ 9 4T mrillions of miles, while the distance M J is 890 -142..: ^6 8 i::: illions of miles. W' will first compute the power of attraction of Jupiter on Mars, as compared with the power of tho sun. iif thle masses were equal the energy of Jtupliter would, on ac.count of the greater distlance, be reduced Ihelow that of tihe sun in the ratio of (142)' to (648)', or nearly as I to 21. But the masses are not equal, f'tr the sun weighs ias tmuch as 3,502 such globes as Jtpiter, ttand helnet by colnmbingiln tthes castes of reductionlt we tind thie fi'oce exerted b1y Jtupiter to be less than th:at exe rted by the stun in the ratio of 1. to'3,502 x 21, or tas I to I 1.5,54.2. Let: us now see what ft t rc the. earth exerts ont Mars, lwhen compareld wit the sun's fire. A. the eartt is 841 2. T:li. S/U N A N) PLA N S.. Uneartler to Mars thlan thie sutll iin case t}he Stl ald eta rth were of eltqual awei'htts their lenery at;: ar s wou bt i the ratio of (1 2) to i o s 7, o 20,164 to 2,2,') or nearly in th}e ra.tio of 9 to 1. 1But thle lsun weighls as mIutiehi as 85:1,9306 earthis, and ift we divide 4 1,93( "' y 9, we obtain: 9',4 tas at quotient, I anid }ent uo the p}t ower of the Sto n tt tars is to tlhe power of the ea:rth as,9 4, to 1. It t is thus seen thatt the earth is more psow rt ll thantt Jupiter to disturb Mars in tlie rati.o of 1. 15.,42 to 8.1t: 18 7, or tint the o of about t. T'o exhibit, mrtlte clearly the n itlltto ehartacter of th}ie cf[lcts: of the earth mand: of' JupItiter on thiis pltanet, let us compute teite stpice thilrough} whicht at body would illl in one s.cortdl it as fr flremlioved frot thie sun as i1ars., We J av tle alreadt sen that graivity at tie sollatr surf e is 2 8.7 g eater thiat at the surfate of the eart.h. At the etarthi gravit y irmpriesses suehl a velocity on a. fall in, body tl:tt: it passes over sptace of 1.(.1.. et in the first set cond of time; thlerclrn.,In a body att t.e sunt' surtl'co would ftil th:rotugth a space represtncted by 2 8.7 x G.'.l...... f461 feet it the first second of its fill. t f we rem:ovet ttle tlling. body to doutile the tdist.atco firomn thle sun's centtr, tie force:of tite sutl'sl gratvity is reducted to one tquarter, and htence the splaco pIassewd over by the filling body at two units from tltie cnter of the st n will be'- }..f. 11l.5.25 feet.:ut Mars' distitance ftrol: the un tis 1t4 millions of mi'les, whtoile tlie solar radits is 44:1.500 miles in otilier words. a i iling bodtRy, emtovled to ite tli ae ostce f IMa'rs firomt tie snt, is about 3 tinmes mtor te frnot rot the sun's ceantef tfha w}tcenl on tlte sun's surlace;:(nd thle e ier1y of' [ the sutl's gravity would be reduced a1t thlis distance ilt t he ratio of (1.)' to (82)1, or as 1. to'1,024() so that a body would fall AS PONDERABLE BODIES. 343 in one second, if as far removed from the center of the sun as is the planet Mars, through a space represented by 46 =0.45:0194 feet. To what extent will this quantity be affected by the attraction of the earth? The answer is given in the result already reached that the power of the earth is only the thirty-nine thousand four hundred and thirty-seventh part of that of the sun, and hence the falling body will only pass over the additional space represented by the minute fraction ~-4 4 S0 = 0.000011, or about the one hundred thousandth part of one foot. These quantities look to be minute and quite unworthy of notice, and yet from these small disturbing effects, accumulating through ages, arise all the amazing changes which are progressing among the elements of the planetary orbits. We will not extend these details, but refer for further particulars to the Appendix. tFpE ASTEROIDS AS PONDERABLE BODIES.-As yet we have no certain knowledge of the magnitude or masses of these minute worlds. We are assured that they are subjected to the laws of motion and gravitation, and that the elements of their orbits are undergoing the same modifications to which the elements of the orbits of all the planets are subjected. These planets are disturbed principally by the action of Jupiter, as we may readily determine by an examination of the masses and distances of the two nearest planets, inside and outside the orbits of the asteroids. The mean distance of the group from the sun is about 2.5 times the earth's distance. The distance of Mars, in terms of the same unit, is 1.5, and the distance of Jupiter from the sun is 5.2. Hence, from the mean distance of the asteroids to Jupiter is 5.2-2.5= 2.7, and from the 8344 T'J1.r: U UN AND 1) I, A N E T S same to T-Mar is 2.5..5.:1::::.0. IctccG, if o Ma:. rs- and J piter were equall it weightt til power of Mah over thle central asterotid would exceed the power of Jupiter in the ratio of (2.7)" to (L.0), or in the rati)o ot 7. to 1. nBut Jupiter is 2:56 times heavier than Mars, awnl hence hIis powert will be intcreased in like proportion, and the attraction oft Mars wiill be to that of Jupiter as 7.T, to 25(; or as I to 85 nearly. I ence we perceive thait Jtupiter is the principal disturhi1ber int the movcmcents of' the astceroids. For furtheri partlticulars the reader will contsult the Appendix. J.UPIx:TER AND uls SATIRLLITES AAS HIAVY B011)l'DIES.- Th is plane, t is not only hetavier, but its volume is much gre-ater than that of any one of the planets. Being 5,2 firther from the sun tha tha e carth, it will be attracted by a power dlimniished in tthe ratio of the square of 5.2 to 1, or as 27 to I nearly. The weightt of Jupiter is to that of the earth as 338 to 1, and in case his diamete r were exactly equal toh thatt of the earth, a: body weiqghing one pound at thi terrestrial equator would weigh,at the equator of this plianet 388 pounds. But the diameter of Jtupiter is 90,734: m1iles, land its radius 45^,3)77 mtiles, or more thian ten tites the radius of t}he carth. Ills attraction on a body tupo tihe surface will therefore be reducet d on accounxt of this tfe-. fbold distance to the one hundrcdthl of 3)88 poundsl or to 38.88 polundsl or, if the colmputation be madI e Itprccisely, tlts result gives us. 2.81 as the w'eilght of 0one terrestrial pound at thte equator of this planct. Thie student canti conpute t hl reductiont in the gravity of the planet i at the equator ari sing fromt the action of the centriftl"i l itrcCe the planet revolving on its a xis in 91). 55m. 27s T'he principal disturber of Juptiter is the planet Sattrn. A. S 0 N 1;) i R A ftB P 1)l K Sf I8.'ronm tlhe sun to J'ptitter is 5.2, thi ea.rtt's dista:nce bein.g 1, lJrom Jutpiter to Bcaturln'tlh:e distan ce i s d..t inn tilho s.an(: tterns..U lleTteo, if'ttatural w\tiglt'd as mlit as the si4nt, his pxower' over Jupitte: would bol grea:tert int the ratio oft 2) to (8.2), or T 274 to ( 18.l: or ts 1.4t7 to:.t I-3ut thl( slun weighlss tis attttmu as 8,502 S at trn, and helvte htis power 4 over J'npiter' w ill exceedt thait of Satutrni in tlte ratio of.::, to:. xor as:2,:8}0 to I.' ti, of cours.i' is tIh ratio of the.1 f ci ese whent theflt lanetsl are ill (:oijun cl'tion. X\Wlent i ln opp)osition tti e inttrval betwetncti themtt is incrct ase.iT d tht diain eter of the orbit of Jupiter, or t:y:.0-, anid itnts it becom es:14:.i inisteiad of 4.8 and int this p. itiol the disturbing powI4er of Sat'nt is 1 rftledu it tlI ratio of (l1.47)'4 to (4t.3)8 or as 2t1.(l 09 to 1.8.44, or as 1 2 to 1. Wo li havt e alrseady seen hoi we ean asceirtain tho weigtt; tof' tli is planet observing tih period of revolution of Iris satellites and by mttasurint g their dtitsta:neo.:iy taling these qnantititt flromthe t bh tale int the Al}ppendix t.li tttudtet ttnay compute readily the mass of Jupiter' as corifpa're wit Al thait of the enarth,. tthf cceuuntricity of tihe orbit of this planet amounts to 0.04:81., the sem i-major at 8 I being tunity, or the distanco filom tlie ttenter of t:toe ellipse to tih focus is equtal to (2^4I2,500,t000) x 00481 -1:::t:1,664 2, 0 mile s. This qutantiity is now sl\owly in',cret8sing, and gainls teverl y Cyear in lengttt T888 miles. Thi s is i due to thte disturbitngl in'. lutent o of the surrounding planets, and after an i:numense pelriod w ill retclt a. lim-it beyond which it calnno(t pass. The r ieltc lnt will then be converted into decremtent, andt a. llimit lein t::,g again reacild, thoe orbit in its f:igur thus oscillates between tlihese- limits in ctalcutable, but (so firn as I. know) in periods not yet calculated. S ty` 846 0 T I:t ] S U N A N P L AN'ST S T.he same fact is tiue of tlhe inclinat ion of the ptano of Jupiter's orbit to that of the ecliptic. )On the 1 st January, 1840, tlhis inclination antounte(dt to.t 18' 42".4. Its prl sCent animtal decrease is 0", 2 a1d shottldl this co)l tinue, at the end of about 200,000 years these Iplanes would coincide, T'lhis, lhowever, c(an never tatke iplace,...The de'reaseo finally comest to be converted into increatse, andf tihus the plane of tlh orbit of Jupiter may be said to rock to and fro on the plane of the ecliptic in periods reachingt: to even mill ions of years. We have already noticed a source of pert urbation in thie case of Venus and the earth, arising fro to the approximate conttmcnsurability of the periods of revolution of these planets. A like cquatliou, as it is called, exists in t;l case of Jupiter atnd Saturn. 1Five icrliods of tJuptiter arte 211 663, andt two of Saturn's periods taret 2.1 51 days; so that. in case the planets start at t any givenl time frot a coitjunction, at tle end of five revolutionls oft' Jlpiter andll two of Saturn, the planets will return to nearly thte ^a:ne lpoints of their orbits alnd to tito sme treIltive positions. Bu tt tile synoldical period, or te til ile ftolam conjunction to contjnction of these planets is 7, 4)^3. days, and three titmes thist quantity anounts to 21,76"tt02. Iliene we perceive Jupiter in this period wIill ilave p'..-:tor)ted five revolutions antld 21 760 ~211,66. t" (days over, while Saturn will describe two revolutionls and 24 () d;ys over, and dutrt ing tlese excesses tlt pltants tadvtnce in t heir respective orbits 8$ 6', lThus ever y thill eonjunction will fill 80 6(' in advttanc e of tlhe f:orer one, and the comjuniction line will be thu-s carried round the entire ortbit t in t tbout 4 t imes x T21,760 days, ori in 1,68 years, at the end of which cycle the satme exact condition will ie restolred, attd all the pertturlations in the satte A 0 ON 1;) E i A B t; BO 0 J) I S,. 847 itln cor:ptltely obliteratcd, provided the figures of the orbits rellcailt unclittngd. Indeed, a restoration is effiected partially anid talttost comtpletely in colisequCincc of tho triple cot)junctioto which takes place in til period of 21.,760 days. Thfese coinjunctions fitl at lpointt s o)n the orbits 1i20' apart, anid ttlus tend to (efect a: restorationt whicli is only fully perfected, howevero at the end of the grieat cycle of 2,648 years. ll cro we fild again the cause whtich prevents the laws of Kepler fI'omi being riigoroutsly aptplicableo to the pl'anet- ary movements,. In case Jupiter existcd alone, thten teo line dlrawnl from thfe ptlatet to th e suil would sweep over eqatl tareas in equal timos, as it is carried by tthe planet 0arountd the sunt. But thet association of tie two t planlets renders the applicationl of tht is law io lotnger poCssible. Jfup)iter is dr(agged.ack by S attArn, andt Saturn. is dIragged forward by J,upiter wheltcn thly start oft firont their litte of c(litunction; but here comles in a miost wonderful co.nlpenlsattion itt the fact that whatever Jupiter's miotion loses by the disturbing influence of' Sat:tturn Saturn's mtot-. tion gains by the disturbitng i)fluetnee of Jupiter. So that tite sum. of the areas swept over by. tlhe lines joinling tle two plantets with tlte sun will atlways be ctqp.atl im eqpttl times. Wc shall ot extend further ur notices o f the results arisinit f'om the actie aton of gravitationt on the platlets and their satet lite.s.h i....... g I ttr detiscussed to so.iml extent, t he tutttual pertturbations of 1Uanus and.Neptunte inl a fo'rmter chapter. \We will clo-se by ain extension of the principle laid down in the case of Jupiter tai d Saturn to thte ontliro planttetary system. If at atty moment lines were driawn. fromt thie center of the sutl to ea ch of the planets it the 3.18 48( Tt'f t 8i V' N AN ) Pt A Xi E T. entire systtm, antd tIom thle cont.er of each: oif t}o pl:tanets to their Crespeetivt sa1tellitoes tlie arealtts swept over by aIll tlheI c.s lfilie. tius dr:t il l always ile ctqual in t equal times. Thus while not at solitary }pliinet or satellite cani follow tin t l aw of equal areas, tho comt bilcitd sRlmecrt3 is }lounlld by it ti thle most..igorous tnnir.t atu i C' thet amrount of ar'ea desc.ribejd by the entire systet in one thou were deter't:.inet to-tday, ant d bt e sent dowilt to plts. terity, at thnot ofl tent toltosand years' a like comnIp utation )1bein.g ttade, ticlh saml e identi catl retsult will be r.teac ed, provided t(lh system remaint frec fr[olni any disturbitn.g infihtneot e exterior to its elf I1t et as, 1theretfre, tthe stin with all t is p lanelt t antid lcomerts is ittet, inee driftsipg throult spce into otiler ste:lltar.rei]ons' the time may come when} the fix d stars Jimay so disturb thte str11 of t /Ie af i t' s as to lpotfintt out tlearly the Ilfct that tou system has positive'ly cttliatige its Ioca.t.oll in space. i t 81<10G:'e'c will closo our discustsion of the sun anld Iiis sate.llites iby the examiitation oit an lthpotheslis whlic has b)ee propoun'ted to taccountlt f:or the peculiar organiz:attion of tiis vast schlentm of revolvilg w)orlds. CHAPTER XVI. THE N E ULA HYPOTHESIS. TII, ARRANGEMENT OF THEt SOLAR SYSTEM. —-TIIE PlIENOMENA FOR WHICB GRAVITATION IS RESPONSIBLE.-THE PIIENOMENA REMAINING TO BE AcCOUNTED FOR. NEBULOUS MATTER AS FOUND IN COIETS. —NEBULOUS MATTER POSSIBLY IN THE HEAVENS.-TIE ENTIRR SOLAR SYSTIEM ONCE A GLOBE OF NIEBULOUS MATTER.-MOTION OF ROTATION.-RADIATION OF IIEAT. —CONDENSATION AND ITS EFFECTS.-RINGS DISENGAGED FROM TIHE EQUATOR OF TIlE R EVOLVING MASS.-FORMATION OF PLANETS AND OF SATELLITES. IN our examination of the scheme of worlds which revolve around the sun we have found that the orbits of the planets are all nearly circular, that their planes are all nearly coincident with the plane of the ecliptic, and that this plane is nearly coincident with the plane of the sun's equator; that the planets all revolve in the same direction around the sun, and that the sun and planets and satellites all rotate on their axes in the same direction; that the periods of revolution grow shorter in the planets and satellites as their distances from their primary grows less; that the sun rotates on his axis in a shorter period than that employed in the revolution of any planet; that every planet accompanied by satellites rotates on its axis in a less time than the period of revolution of any satellite. The law of gravitation is not responsible for any of these facts, and in case we compute the chances of such an organization coming into being by accident, we shall .850 TIi E NE B: U I, A t t Y PO t H SIS, find but one cbhance in so lmany mtillions thalt we arce compelled to look to some htighl r cause than imore aceident to account for so great a triltt.itude of comibined plhenomena. We have said that gravitation is not responsible for tlhe fticts above stated. 11n case at solitary planet b) projected with a: given force, and in a given direction about the stun, and at a giveni distance, it will revolve, as we have seeen, in one of four curves, alnd in any one of these curves it will be held equally byt tle law of gravitation. The plante in which it revolves nmay assumt e any angetl with at fixed plane, the direction of the revolution mayhy be the same or contrar'y to that tin whichl the sun rotates, tle orbit niaty be a circle, an ellipse, a parabotla, or an hypetr. blola, anrid yet the p:lanet shall revolve, subject to the law of cgravitation. It ilay rotate on its own axis cither with or agaiist its rvolution i iti iO ritrt and in cas e ivwe gi to this planett a satellite, the same statements are true with reference to this attendant. So thatt so fttr ass the law tof gravitation is concerned, there might have been amonog the pla.nets all the diversity in the fobr.l of their orbits inl tie atgles of their inclilnation to ta fixetd plante, and in the direction of their motions, as arte found atmong the comets, and yet each objt ea would hItre been subject to the greatt law of untiversal gravtitaition. We cant lot, ttherefore, affirm tthat the peculiar st rueture of the solar system results frtiomt the laws of motiton tand gravitation, with out pre-supposing: a conldition of tm:tter entirely dilfrentt fi0om tthat now (recogntized at s existinlg in the planlets and their satellites. We have already noticed the wondertfil constitution of the comets. 3In these bodies is found at kind of mlattetr which htas been termed nbotdt/sf il whichl the minute particlcs are sepa - TIf t E N E 1 U L A I1tt Y POT IEt IS. 81 t rated by some repulsive force, anid tlhe entire mass is but a vapor of tlhe most refined tenuity. Among the stellar regions the telescope lias revealed obecicts whose light, is so fiint and whose formis are so ill defined that. they iatve been regarded by many astrono-0. imerss of high reputation to be analogous to the comets in. their m.aterial, cxhibiting the primitive or primordial con-. dition of the matter composing the physical utniverse. This conjecture (for it is notbing more) may be t.rte or faise, but its truth or fialsehood cannot in any way afleec theli crdibility of the theory or hypothesis we are about. to present. The present condition of matter cannot inll any way be assumed to be- the only condition in which it ever existed, sinc e w now know it to be subject to extrtaor(dinary chanlges and most wonderful modift eatfions. Let us, thenl suppose that. a time once was when tlhe sun and all its planets and their satellites existed as one mighty globe of nebulous iatter, whose diai tier fitr execeded the present diameter of the oribit of Neptune, that to this stupendous globe a motion of rotation was given, and that its heat is' slowly lost by radiation, and let us endeavor to follow tile changes which must flow from the loss of heat and the operation of ttho laws of motion and gravitation, and learn whether friom this par ient mass a scheme of planets and satellites such as now exist can b}) generated. Wo prefer to present tlo reasoning'in tlie language of M. Pontecoulent, one of thel most eminent of tihe illustrious disciples of Newton- merely premising that in ease the central rota.ting mass contracts by loss of heat that a time" must come when, in consequence of tihe increased velocity.of rotation, tihe force of gravity of a particle at the equator will be overcome by the centrifitl gal force generated by tieo velocity of rot.ation, and hence .I852.... TIt [. NE E, II, A I. Y l t 0 It IS "I S.t ftat tnes or rilngs of vapor or nebultltous maittine must cveC Itu lally >bo I tt i the pianoe ofi t the cqiua:.tor of: the revo vlvi f o':...- -C -. " tlisco zonles ins lt haave begutn by lir'c latifng roIdlt thei stt n the )1 fori of conci.cntric rin's, the mlost volatile moleculoe of waich:t have fLtrmedt tle suiperior part, and t:lt most coitidensdtei the infertior ipart. If all the t1buloust moltiecules of which these ringt s are comlposed lIad continued to tool without disunluititng. thly would hia:.vo (emlcd by inuilr: a liquid or solid rin Bu13at thlo regularu constitution.which all parIt of thli ring would require fbr thlat anld \whvich thely would have ncdcd to pre.'ser}v whilst cooling, would m.ake this phlienomenonit extrtemely t ar. Accordingly the solar system presents 01oly one intsta'nce of this, that of the rin,(gs of Sattur,. (Ioetlrally ti}r r'in must hl.ve broken intto several parts, whlicht hatr ctiotinitue to cirelatte'tolnd tile sun: and withl ai l:Irst eqti:al velocityt whttile att th}t sam e t:ilme, in col sequolnlce of tileir separatiton tilcy would acqtuire at. rotatory mot.iont round their respective cenlters of gravity; altnd as the molecttles oft i ttsuperior part of th.e ri{ngt that is to say, those furtthest ftom the center ofIo t lthie suit, h}ld e.tttcssairily tmi absolute velocity greater tthan the iinolecules of thoi in-.feriolr part whichl is Itnetaest it, the y ri otatoy t ion, com — mon to all the frag'nc nts, must always htave lbe( en iln the samett dircetioll as the or bituat motion.: o I l ev er, ift alter their di ision. one of thltese (frag tr mientl Itas been sutfficietly superior to thte ofthersf to unitl thtm to it' by its attrtactiolt, they \will }havte t1nited only tta mlass of vaporl whichl by t}le continuat. llI ition of all its fprts imU, ltusi t etave iasstumitd tile foirm of ta spheroid ltlatlieed at tle poles and elonga.i ted in the direction of its equator. l1.ere, then, are rings of vapor left by the successive rce THE NEBULAR HYPOTIESIS. 353 treats of the atmosphere of the sun, changed into so many planets in the condition of vapor circulating round the sun, and possessing a rotatory motion in the direction of their revolution. This must have been the most common case; but that in which the fragments of some ring would form several distinct planets possessing degrees of velocity must also have taken place, and the telescopic planets discovered during the present century seem to present an instance of this; at least if it is not admitted with Olbers, that they are the fragments of a single planet, broken by a strong interior commotion. It is easy to imagine the successive changes produced by cooling on the planets whose formation has been just pointed out. Indeed, each of these planets, in the condition of vapor, is, in every respect, like one of the nebula in the first stage; they must, therefore, before arriving at a state of solidity, pass through all the stages of change we have just traced in the sun. At first the condensation of their atmosphere will form round the center of the planet a body composed of layers of unequal density, the densest matter having, by its weight, approached the center, and the most volatile reached the surface, as we see in a vessel different liquids ranged one above another, according to their specific gravity to arrive at a state of equilibrium. The atmosphere of each planet will, like that of the sun, leave behind it zones of vapor, which will form one or several secondary planets, circulating round the principal planet as the moon does round the earth, and the satellites round Jupiter, Saturn, and Uranus, or else they will form, by cooling without dividing, a solid and continuous circle, of which we have an instance in the ring of Saturn. In every case the direction of the rotatory and orbitual motion of the satellites or the ring 354 THIE NEBULAR HYPOTHESIS. will be the same as that of the rotatory motion of the planet; and this is completely confirmed by observation. "The wonderful coincidence of all the planetary motions, (a phenomenon which we cannot, without infringing the laws of probability, regard as merely the effect of chlance,) must then be the result even of the formation of the solar system on this ingenious hypothesis; we see also why the orbits of the planets and satellites are so little eccentric, and deviate so little from the plane of the solar equator. A perfect harmony between the density and temperature of their molecules in a state of vapor would have rendered the orbits rigorously circular and made to coincide with the plane of this equator; but this regularity could not exist in all parts of such large masses; there has resulted the slight eccentricities of the orbits of the planets and satellites, and their deviation from the plane of the solar equator. " When in the zones abandoned by the solar atmosphere there are found molecules too volatile either to unite with each other or with the planets, they must continue to revolve round the sun, without offering any sensible resistance to the motions of the planetary bodies, either on account of their extreme rarity, or because their motion is effected in the same way as that of the bodies they encounter. These wandering molecules must thus present all the appearances of the zodiacal light. " We have seen that the figure of the heavenly bodies was the necessary result of their fluidity at the beginning of time. The singular phenomenon presented by the rigorous equality indicated by observation among the lesser motions of rotation and revolution of each satellite, an equality rendering the opposed hemisphere of the moon forever invisible to us, is another obvious conse T IEI NEN B i1 1A I I{ Y P0T H, S. 305 tquence ot tins hypotlesis. Indeed, sup osing that tIhe sli'lhtcst. d(ifiretnct hal d existed betw' en t1:l mean mtoit tion of rott: ion and revotluti(on. our satellite, wh:ile it was in tlte state otf vaportt o of fluiditry tIthe attra.ction oFt tho eartht would have elon latied tIe lu.nar splheroid in. ttho direction of its axis towa:.rds the eartht. lTh}e s.amle attrc:t.. tieons would lhave tendedt to diminiish insensibly thle (liffe..l once betweeln tihe rtotatory and orbitat l t oti iont s of tih )t0m,'o, so as to con:fine to narrow limits a condition stufficient to cause the axis of its equato, r directed tow:ards t thIe eart, to b)e sujtect only to a: species of }'periodicat l ia tlncit lrg const:ittuting tthe phel'nlenonl of libltra.. tion. If these oscill ations ar)e not ntow obsrett ved, it is hte. eansc they hIave ceased to exist in consc4quence of tile resist:ance they have encountered in the comrse of time, even as tihe oscillations of the terrestrial atxis in tihe interior of thle eart:h, arising from the iit. al state of mo-. tion, 1have bteen (iestroyedl antd as indeed al tl e motions oft the he:tave1ly bodies have disa-ppeared whi ch have ntot ihad a }perm'ttt.'tt cause. " The principasl tthenomiena of the planetatry systemt are the relbre exl. Iai ed with. great.t fticility by i the )hypothesis lwe tar exa.mininttl, and as t tl1 th es successive changet}.f, of at n).ulous mass and tlhe tlcavint:g of a part of its tsubstance by coolingf afree with all the letadinr phtenor l mi.ens it 1 mu st bel allowted a. hi,glh ldegree of probabilit:y, Int this Ihyvpottesis the tbrna tion of the planets womild niot h}Iave hln simultane ous' they have bee. created suctcsl.sively\ at intervals of lagest tt oldest are thlose whic arc furtlhe st: fromr tlhe sun and the satollitecs are of a more recent ldate than their relspective pllaets. lt nmay an examination of the constitution of each planet we may 860 Ti E N E B U 1 A t Y POT ESIS go bcack to the epoch of its florma-tion, and assign to each its place in the chronology of the universe. ft is likewise seen that the velocity of the ortittual 1motion of each planlet, as it is now, mllust differ little fiomn that of tlh rotatory motion of the sunt at the period wheint the planet ws detached from its atmlosphlere. Andt as the rotatory motion is accelerated in proportion as th soltar molecules are c:nfitnc.d by cooling, so that the sum1 of the areas whiclt they describe round the center of gravity would relaint. always the same, it follows revolutionary motiot must bo so mutlch more rapid as the planett is nearer the sut, ts is seel by observation. It likewise results that the duration of the rotation either of the sunt or of at planet lmust be shorter than the duration of the nearest body which circulates round them; this observation is completely confilrmed even in those cases where the diftertnce between the duration of the two motions mtust:,be ve:ry slightt. Tius the interior riing of Saturn beilng very close to the plantet, the duration of its rotation must be almost equal, but a little longer thtan that of the plalnect, " The observations of 1 erschiel give, indeed, 0.432 as the (duration of thet rotat ion of tihe ring, and 0.427 as that of the p 0lanet t; why, then, should we not admiit tlat t}is ritng tias been formed by the condensation of the at)mostphere of Saturn, whicht ftrm-erly extelided to it? We may perthaps deduce fiom the latws of mechantjis and thfl actual ditmelsions of the snn, anthl thee kntown durali.ti{lon of its rotation, the relation existing between tthe.radius vector of its surfacite and the time of its rotation in tie difbrent stages of concentratiotn throutgh which it ias passed.'the thirdI, law of' Kepller would be tno longer the Irt mere sult of observation; it would be di T Bi E NI B U L A t Y P 0 T t 81, 8 T rcctly deduced froml t.lt primordial laws of thle lh'avently bodies. i;n thils system tthe particulaxr forml of tho planetst tihe flatteningi at the poles, an bun ling outt at tlo cquatt tol' iS 0only tleo lnee.-ss.ary eoisequenco of the laws of' tho equilibriuml of fluids, tand easily explains the gr(ater part of the phenormenatt t observed by geologists in the constitution of the tlerrestrial.globe, which appear inexplicable, if it is not adnmitted that thie eartht and planets have been ori0inally fluid, Let us now see what is tite origin and part assigned to comets byI this hypothlesis.:tLa, Place su1pposes t.hat they do not belong to tl the planetary systetm, and lie re3ga:trds 1 t thetm as masses of vapor fotrmed by thle agglomnera tion of the lumninous matter diffused in all parts of the universe, and wandering by chance in thre vtarious solar systemts. Comets would thus be, in relatiof to the planetary system, what tht aerolites are in relation to tlie earth, with which they seem to have no original con.nection, When a comet apt-proaches stuficiently neart tlhe regions of space occupied by our0 systemt to cnt'er into the sphere of tle sunt's influencet ttie attraction of that luminary, combined with thle velocity acquired by the comet, causes it to describe an elliptic or hyperbolic orbit. Blut as thle direction of this velocity is quite artitrary, comets must miove in every direction and in every part of tlhe sky, "'r the cotft ai orbits will, t1hen, have every inclina.tion to the ecliptic; and this Iypothetsis t hi explaints Cquall y well the great eccentricity by which tlhey ar te usually efircted.:tIndeed, if the curves described by comets are ellipses, they must be grteatly Ielongated, since their major axes are at least tequal to tte radius of tho 358 THE: N.EBULAR HIYPOTHI:EIS.. sphere of the sun's attraction; and we must consequently be able to see only those whose eccentricity is very great, and perihelion distance inconsiderable; all others, on account of their minuteness and distance, must always be invisible, unless at least the resistance of the ether, the attraction of the planets, or other unknown causes diminish their perihelion distance, and bring them nearer the terrestrial orbit. The same circumstances may change the primitive orbits of some comets into ellipses, whose major axes are comparatively small; and this has, probably happened to the periodical comets of 1759, 1819, and 1832. The laws of the curvilinear motion likewise show that the eccentricity of the orbit chiefly depends on the direction of the comet's motion on its entering the sphere of the sun's attraction; and as this motion is possible in every direction, there are no limits to the eccentricities of the orbits of comets. "If, at the formation of the planets, some comets penetrated the atmospheres of the sun and: planets, the resistance they met would gradually destroy their velocity; they would then fall. on those bodies describing spirals, and their fall would have the effect- of causing the planes of the orbits and equators of the planets, to remove from the plane of the solar equator. It is, therefore, partly to. this cause, and partly to those we have developed above, that the slight deviations we now perceive must be attributed. Such is a summary of the hypothesis of La Place on the origin of the solar system. This hypothesis explains, in the most satisfactory manner, the three most remarkable phenomena presented by the planetary motions. T U E N U BU LAR Y POT 17 t 88, 8t5: 9 L^ 1st mlic iotion f:t tthe planets in the same direct ion, and narly:in thi te same plano. d.t ltT}h motatt of X t the stellites in t}te,samt direction as tlheir pl: nets. 3dl. IThe siitn lar coinciidence in direction of the ro.lltotr andt orbitual motions of the planets and the sun, whlichl in othter syt:tems wo tuld preslent inexplicable) ditlicultties. " tlte no less remarkable plhenoimena of -the snalliss of the eccentricities and inclinations of tile planetary orbits a. r also a nlecssari y consllequence of it, while we seto at t}he same tilnle why tie orbits of t;he comiets depart fi'om this gttenctral law, anld lmay be very ccentric, and hav:e tanly itlclina tiotn whtaterer to tohe ecliptic. Tlhe fiat — tetni, ft intte ft t1 oft' ItI e ifl nets, s!hown oil tthe arthtl by thc eclliarl'menlt t of de(Pre-es of (the Ieridian:. avnid by tihe r'Cleeli u tt l icrtase of weigtttr in go. from the equator to the poles. is o0nl'y thte result of ttte attraction of their mollteiules whil i t tey were.yet in a state of' vapor, comnbiited twith th:c ceittri fugal force p rodticd t byt the rotatory mlotioin imtpro.t.:ed ton thit: fltuid Ilmass. ior. a-t slhot, tlon t:he pll:eno:tn:':a. presesnlttedtl by thio motie ona; anld the:or)n11i o:i thie heavel ly' bodie: therc are non wI icht cannot e ex. platied w eithi e't: ii't i. ility ty t'y the ucc,1100( ssiv c'( et'a-tl t tionl o:f' tire solar system; and t I lt-'ore tlhis systet.'i is exainiined the morie we arc led t:o aclknowledge it; p:robabilit. v.'' t.'tdoubti\:Wedlyt i s fI:, li:'C Place las ht:imselst:f staid,: a - ]potlttesis no4t totittldd ofn ob):;evationt or ctallc:dation lI ust Io\N vits pre; en t tl It):i w itht. xtrteme difidencetl this, it wvill!be Iran't ed: uttr st: ac t e bsat tl t utioI i ll t iand aLgem.I lnt of so> na l irt i'tr. l cts.' al l the marks o:f ptitoabitity. BIcIt wlltU, in ily topinioni pri'ncipally dist.inguishes it friomn 03f60 TII: N:t U. A tR I YPOTH I r I t 8 8S. the ordinary theories concerning the tformation of systems, is the identity lwhict it establislhe between the solar systenl and the stars splread so profisely thlrough thel s>y. A.ll the phenomenatl of nature are connected. atll flow from a few simple and general lawts, and tile task of the t1man e of genius consists in discovering? those secret connec.tions, those unknown relations which connect. the phienomena wlich iappear to tthe vulgar to hlave no analogy. Iln going fr'oml a pltinotlmcnon of which ttie primitive law\ is easily pe rceived, to another in whiclt particular circuistances complicate it so as to conceal it from nt, lie sees them all flowing f'rom the samle sourcet and the secret of nature becomes his possession. Thu ts the lawsl of the elliptic imotion of tho planets led Newton to lte grea t pritnciple of universal gtravitation, whichlt- te would lhavte sought for in vain in the less sileplC phlleomenal of the rotatory motion of tile earth, or the flux and reflux of the sea. But this great principle being once discovered, tll the circurnstances of the planetary motions were exptlaitned, even in thleir minutest details, and the stability of tle solar system was itself only the necessary onmsequetnce of its contfoiration. withoutt wh\vichl, as Newton t hought:: (ld would be constantly obliged to re'touch his work.1 in order to render it scure. sLae: IPlace, extending to all thte stars: and consequently to the stun the ilode of condenstation bl-y which the nebula: are chantged into stars, hias connected the origin of the planetary sys-. tern with thle primlordial latws of i-notion. without recuirring to any hypotthesis butt tlht of attraction. lie ihas, thelrelfre extended to the fixed sta;r tlh greatt law of l'uni iversal gravt\itation, which is probably the onily efficient principle,of thte creation of tlte physical wNorld, as it is of its preservatiotln. T 1u E. N.8B.1 U1.. A t.11 Y P.T t 81 I S. t.l) t.1 cll is a brief outline of one of the mosAt subliineo s:-ceiltlatoions tlitt h:as ever resulted firom.- theo (fltrts ot luttn':.tan tltouglit. ItI carrl'ies ui back to tthlat gra.nld eii)l-}it whie.n n''t thf begI ctinll (-od crleated tlio heavens and.. the earth',"'whetn matttter was first called into be.ingt in its.uit~ lfrined nIebulouts condition and "( tlh earth was without1 tfin and void," and darkness covered the Imiglht.y dee otf tnifatholmable space.. But the Spirit of God mloved il tlh boundless flood of vaporous matter: cattered thiro ugtl the da rkt pfrofund, and gave o to ealc particle its now leterna funltiot, impressed the lawsf of gravitation alt motstionl, selected the g trantd ccnters about which1 the germsll of s, d tsa systems should fiorm, and in infinite wisdom tdrew tho plan of tthat one schOeme whlict h oi l.ave ath - tcenpted to examine, among the millions thlat shine in splendor. throughlout th boundless oempire of space. 5ls X{ fi}t gt0t~f;}t\tt} )tL] >1t.> }}l.iXt(t8st AP I: i'I N J') I X................................ TAI BL. E T|I':S O () EL EI 1 NTl:f xtt s.,SOLAR ELEMENTS, EOCi: lSr 1 JA., 1801. OL:lt:i;')L'ss'N' 1':l' lr'S r.' 1 ]- C I f- I J -A N%) I'So denm Jo:it:ittudo........................... 280~ 39' 10". 2 L::gitud,: orf the4 1 p-eiRce......................, 20 - 0 o 05"'.0 ( tr ato s t Ct euation ofr ce.te. tr.....4............. $ 55'.. l.)o:trease: of S:.n Itt i one.yer....,i,......... *...... 0".. *3 t'clinttion of axis to the e': liptc.,,.......,........ 82 + 4 00'0 Motion inl a man olar day..................... * 30 00 0 Mot0iown of 1)(rio i'4 i. 305 days.. f......... t.......... 1 01 "9.Apparentt diametr.........,.............,... 32' 12:', toan 1ftori)ont par alla x.....,.......t..t..... 81'4 6 Rota14tion i mean solar........................ 600711 4.,11 Os Trim of pa.ssig over on1 dcgrco of ne)an longitudo.. 11 24.h 20 58. s8 ck nl iit'v of C orbit em3 m) )ajor 1.)..,.f.,.s......01 A 538 Volume (earth as 1).........................,........ 1 1 5225 M earth as 1)........... o.............. 354930 Mean.i disltaco' in miles........,.,................ 95,000,0(00 Same earth s 1 i 14 )................................... 23981 Donktyv (eart 1 a 1)..,,.,.......................... 0.2 50 Dl)mncter itt J1miles.......,,,......................... 888.14t ('iGravity at eqiuator.................................. A3.81 it o4n ( e'rw(1 of timeo bodies foi0 ll 1fc loet............... 462.03.G reatestr d.ta.eo, n....... d.r............,.,...........................4 1"fI:xm OF Tl ORBIT O V PiECh, EIO(U JiAN X, 0:east distanc:'oe, m,,,.. unit................. 0504 1 Ec:i nti iti (o -a xi jor as )................. ~,,,1..,21.. 5.. I205( 1.8 83G A tA 1: E t XX An nuat vart ation of sont (decr eas).............. 0.000,000,03866 StSihootil r3oxiatluron- n t *( 8" 91 13 O 1 Siere aul revoluti on in days.......,............... 8.9;9284 1 i01111 Ii hi d..o,..,.,,.,,,. I' 1111k \vsita"i ol:ol it,. imn da s. 7 3' 1 1 ct 1 ot' acit n,.......... 4 1' 0 t 3.00 L')nlisi t ot o t.;..t t S t;l ) oe t + *............... 34 * 0 i 4*9 31 z'; t 0_ Anmuat varton It of. a mo.,,..,...,........... 10.0 Irclination otorbit to ocliti.......................... S I 32 ** G 00' 13'".30 I. lltul vartiation t ll sl,,,,,,,.....,............... 00" eia. ( daily s 1o0tion in or bit.....,.......... 245' 32'.6 lTim of roisi1x ti n n,...............,,,....., 21. 05 m 28 S tiknationl of a (xis t:o ecliptics b................... Unc.rt 4 n,'_.it ar. is t d iao eter. a i t t s l... t 6 t t DItametcr li mile s,............................. 9...........,0 - (earilst bc',,........................... O.i. S'iodical revolution inll days................. 83.'00 oJ', nitudo of the p*riho liot........................ 1 24 1-1'1 25.6 A iual var iation o l s (dc teae).,............... S',onicitudo of the ast iendling node.................'5i 1 29.8 Anrniual vafati..flton of. -aa-'o (decr eas)...................... 90.50 Inclin:lation of orbit to th*,s ecliptic....r................. 3'23" 3 "A Mea:n daily.o.tion Ilt orbit....................... 0'.8 A lintt o lotiotn 01n ait (I......... i'5 1 I tIim. o f ( 1 otati t ) ) on "i Sl, I t............................ h 21. 2it Inequlation8 of axIS to th elti,.,,,,,,,.....,.., Unc *}*,,e rtait n A 1 P E N I) I X. 365 Apparent dmiametr... I..I.,........................O....... " D)iameoter i nilcsa..,,...................,,,..........896 D)iameter (eartihs being 1.),........ 0.. 95 Voh.lnmo (Calh's i )> ~in,:.......................~........,....0960 1Nlnnw: or weight (e:itl's: ing I).......,....,.....,.., 89I f)cnsity (canrthil.in 1t).....'............................ igti received at pcriilclio ni (earth's btilg i)...,,............... 1 Same aI t aphelion (earth's l 1ing I)............................ \'eigilt of a tenerrial pond. or gravity..................... 0. 90) S1paco e:illoel tihirough il one sccornd orf timo, in flit.. 1.,,,,,,.. 4. I M;LEMENTS 0:1? THIE )ARI:IIt, lsr JAN., 1801. 3lean distano in mil,..............................,,.,,, 95,000,000;reatcn t distane-. (n:mean distance 1)...................! I i alt Leas:at (distamnc,, same unit.,,.,........................... 0.98322:9 Moan sidereal rovolution (solar days)............ 365d 01h OCit 09,0; Me;al tropical revolution,........,5....,.... 3 05: Olh 4iSin 4l9s. Mean arnialisc revolutie o n.................... 3U5d Oii i 3m 49s,3 Ilovolution of thel sin's prigoee (solar days)...............,4t, 5,10193 Mean tLongitudo (20'" for aberration)................ 100~ 39' 10'". Earth's motion in plrihelio in a mean solar day........ 13 01' 09".9 Mean motlion in a solar day........................ 0O 5)9 038"33 Mean inotion in a sidereal day................... 0059' 59 ". i Motion in aphelion i a meal siolar day... 00 51' 11",50 Meau loangitudle aof perihelion....,................. 99" 30' 05".0 Arirual mnotion of petrihelion (east).......................... 11".8 Sinite refei tled to lth ecliptic............................. I' 01",9 C(olntdl.eto tropicil revolution of same in year,........... 20,981 Oh:,iqiiity of th! ecliptic.......................... 23 2' 56".5 Annnald diminnti on of srao.,.........,,,.. 0".45'/ Nlatrtia n (sni:i-axis mnajor).......................... 9".4 l:rece::sion (anreat ); Ira'-solar...................... 50".4 irces::ioir t in lonaitude.................. 50...... Conipleto rovolution of vernal eqininox in yea........... 25, Lnlar mnitation in lon oit............................ 1 ".5 9 Sola'r tatiotn in longitudo,.,.....,.<................., 1':.1 37:Eceenttiieit of orlbit (semi-axi:s major 1)............ 0. 010 6835 AnualI decreaseo.................. 0.00000i103 Ilaily ciec leration of sidereal over ticail solir atime......... 3' 55".91 F;rom vernal eqtinox to suniniuer solstice............... 92d 21i 50m From summer sostice to autumanal cquin.ox......... 9t3d 1.3 4:h:a ')'3'? 8(66 A P P E N ]) I X. I From ar iturmlnat ecq\uinox to winterl solstice.,.......... 89d 1. 1h.t4t Ir'-o}i winter Isolstic to vernal equinox............. 89Xd 01h 33t NM:t. (un as I; )........,t....t. t...............* 0.0000028173:l;)nsityi (water a;s 1).,................................. 5.6e.t iMan d munetr in m les,,,,...................19 t G:Pol~, " "................................... I898 I~:~q,~atord ".,....,...................,..'i92:.: icentri in'gatl toree at equator.................. 00034 ight arr ives from the son in.....,............ I.... 8 13".3.l..A. \ A be tin t...,. t.,................................ 20"i25 [EMM ENXTS OF Til 1tX MOONN.-.....0.} [ StrAN, X1801. Mean distance ft)'om th eoarth (earth's radius 1)..+.... 0.2 3433 Mean isdoreal revolution in days...........,'27.3,216001 dicant s^nodhital revolttio n in days.. t.......+....*... 9. 5305887* t:eeiitrieity of )i, * *......................*......... 0 54 908070 Mean f reolution of notdes i i dy,......,......, 07.. 93.: 91 080 Mean revolution of a}o}g0' e o in da *ys..........., 323'2.5i 343 Ic:tn tlonittudo of node at' epochi................. 13 53' 1'.7 Me.'an lungitude of pcrigee......................,.. 2('0G" 1I0' 0/5. Mean ir:clina tion of lrbit. 5.,..,...... 8 x9.,.:ean lniudtta of110 JilUxt nt at seoch................... II'8 1 1 8".3 Ma:s (ea: 1)..................................... 0.0 1 130 I I)iarnete in mile.....,,...................... 216, 21 -De Ifsittv (eart i as 1)..,..*...,.,...,......... 0. 55 *6 G:ravity or weight of one terrestrial pound..............,. 0.16 BISiei s >i1 in ono second, in fiot......,......................... C, I)J iametor (ieartt'h a-I 1).,...............................t., 0.2:Deni sit (water as 1)................................... t:enaton of ax................,......'.............8 M;,>ximul Ievec}ion................................. 1~. t 2. " varia tion.........,,,,...,..........,.,.,,5 3,:42:,0 i arilmal equation................... I 1V 1' 0 l ]oil:,t::: dhlxx....................' 01''. 0:} r-'ny " "'..,.............,,.... 53' 48",0 Maxla r i) appar ent dianwt. o e, 3......~..*..,<.,..,..... * 3l"._, 4Mean ii,'"~} *}............,I (.......,.... +.0t Mini aa t ti.......-,..t.............. 2' 1* t21 Minimm'. 2"....................,.,.,..f. 3' 21. 2;et.(>>.~~~I.X~ ~ s;(~~ b $ ~C* *4*+***+$6M4*, <+ - _ ". ^' > w 0 r. W S r'. _ ^.... ^ i - 7 I 7 I _ _ ~ ~ ^ G1 *^ ^ ^ =:: ~ _ d - l^ I * *: w' *,, G *^' a II, i * I * * rr,~ * **F cku~dC,,, w, h * h;," - M 2'': ^ ~ ~~~~~' r*- i ~~~ i L-~ *L W~I 2' *' *' * * ~ * * w * ^ ^* I'. * >~ i I I-^r ~ s " ~ W. ^ l lg P1 C 1 ^~~~ * * * * " * " "~ ^. w s'^ <~ + "5 * + sIM + ~ " %W 3 J *4 E *+*ft U *h " )" i* " "- a * C i ~' v *, *s *'- i *, r+ 4. * t * o C J. 5 * o + * + + ^ C - F C * o^^^^ _ c' ~' _r ~.a" *~ ~-,;~ X~c~~~ c * 8 C'.~'C; r^~ " ->v d,*t _ ~ t! _' i tt %'' ji -~, r ~4 st5* O,4w: = V + U,; r! O S e:. e *,... ~ ~"~~~3r\C~ * ~ g~o 868 APPE N I) X.::12. t't -::*( ~:~~~~~ <:: "~~'' / ~~~~~~~~~~~~~~~~~~~~"~ - II:li?4:' - ~.-.:: x.:'.. -:':.:' -''i ~~~ *'-.:: l.. k'""( -~;:~?: if,:';. W. ~,; ~~. * ~;* I *.:, ~::...., ~,: ~~~' "i ^:'.*'.<:*:::";..'-.-'.::.;: "'~. -::..}i...5:::'~.k~: ~,'..:.~. ~::,~~: >:i.,:.:+'-.; ~:.'.i:::. ~<:~. ~:~~'":L: ~ ~~ ^ "~:*:~i~~:~.'?:: o:'. ~~~:.<:~~~;~~, >~, ~.:~ ~,~~~:;'t~:'.......... ^1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-. —'^ ^^'!M S~t /2 ">"'-" -7>~~~~~~~-n:x 4 ~>~~~ ~ f-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.:; <141":i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i -.'" "'+ "-''+'+'''" +~~~~~~~~~~~~~~~~~~~~~~~~~~~k. Z'7'+4'4,~~~~~~~~~~~~~~~~I'- ~ -- fjfj'^ S: ^ ^ ^ ^,~;~.<: ^~^~M.^ >>^l~?<:.<^*>~^~~~<^>~^^ Olc^ < ^l -C..............................................................:!. i.::...:::'~:: Z:.''~.~.~:.. $........ ~:................... ~..;:.. -:.. &:..'.6..::.-..:..:...:...................... ^~~~~~~~~~~~~~~~~~~~~~~~~~~l IIJ I~.... i................................................. ^ ^ ~< ^ ^ ^~'t~~~~~~~~~~;. -f.7< i *..*.:.,'! ~- * ~'b *, ^' l~ o^:o ^::,.*: b. *:o,o e.~..~~::.. i-,:.%.. ~:,~ *~?~.'.:s..~~"::o,.: ^~~~~~~~~~~~~t I lt i l't< I~ ~ ~~0 -i — ^`-4 I~' r^.- 0-';' I: -<^ -.- ^ ^ ^ ^ ^ ^' n ^^W >..................................................^ ^;~ ^ ^ ^ < > o ~'..'~: ~i ^ - ^?i - ^~~~~~~~~~~~.* ~~'~ ": -.< ^ <.JO ^ >?~~ ^1 ~~?~~ ^ ^ t * ^ ^'^ ^ -^ ^ fc> ^ ^ ^ ^ ^ ^ ^ ^ -^ ^ *,- ^:.<~l ^-^ ^ ^^ S <-, <..~0. *~ ~^^ s^ " -^^ yi ~?- ~ ^ ^S II'l^^"a^a^;a^a'"' ^ i j; ^ ^ ^ l li~~~~~~~~~~~i^:^S~~a'l JYO IN 3) I X. ELMMI' TS' OF JUPITfI FOl. T[I:!t i..sc JAN., 151i0. Me, is t ance from th in. milen,.,c,,,,.,.. 491,,"5 000 Simtt (eotarit adistanct as 1),..., 20 iO'reatC"t disatieO, c Sae,,....... 5t,45 3 61t13 L'a' t distianc.'a e <,,trtnit.,.,..,,,, ~....5.. 1.9 t 8 1:tceotricit (samc taxis jOtt'........1),......*,. 0,04235 A.lntmal varn'"iation of sa e (hinease).........,,000001....3 Si!ral rot dl0u t oio n' in idays ),,,.........,4 33' 84803' nor ittal ci:revolutionl day,.....,,.,,.,,,11 t 8. Longitude of thle perihelion......................... I l 45' 3'.8 A ntual variaiol of:on i'eo (increasi e)......................... 5 Lotig itu or the asendh g ot:t e..C.ol....... I.,,,,. 98 348' 3.i'8 A in.ltt vxriationt of i meo (decrease)..,..,,.,,,.... t1,00 loclomtio^n tof or(bit to thot to eliptc,. *........ 1t8' 4' 4 A:itiual variatiot of sam (dcreasce)....,... 0!3 M.an daily mnotio in orbiti............................. 4' 5': Time of rot atlo on axi,.,................. h 26 tcl:inaition of axis 11 tho t eoli ti......,,..,. 8. 5.' 30" A!jp:-aront dbiaieler......,................................. 38".4 1itiamter mitt milesi I,,,.,.,.,........,.. ** 1 0.10 iantototer (eariths being I1),........... 11'5; Votlut, e' (-:aSto.s bOig ]1) t.......,,., ~.....'.: 141t ) 1. Mum or w eigh t (:.th's bolo:~::g 1),........................ 34.738 sity (arth's being 1)................................ 3 Lih t roceitved at pm'iheliol. (e artt s bS in S )...... 1.....0108 Btamt at. aphclion (eoartl's bim'' 1)............... 0330 Weig-t of a tverlkttit l oiuilt or gravity....,,,,,.... 41 Sac it 1lh n throui gh iIInU.td one t o of time in c,. tt t:' c.'... 39A I E FS 0 JOU R liElR1 SATELIJTE IT No. NI o EcCeT:srlnCt'. Sidte al revolutiot i day...... hI..,.. d:'18h 3 06 NI an disttaiet ('tipitti' radius 1)i..I................ 0 Itit'Siititt,'o itt d ihit I t t~ n jd'toi'.0 (1 fl 0 l In: linat:ion of orblit to a ixe'd plIme,.............. 0"' 00' 00",0 ncl.inationt of tis plate to Jupliter'ts eqtiator*..... 0 0" 0' ".0 Ma.s, that ofJupitr beinmg 1000,000,000............ Ii 328 No, 2. NOtt al Ec:.':ir, Sid:ereal revolhtion in days,...,....... 3d t eh 14mt 36.393s Mean dista ce (Jupit ers radi s i 1).................... 9.6., 34 A P fE N 1) I 8 Aqliiflatuion of orbit to a fixed pl ne,............ 0 2' 5!' l init. ofn 0i tu. t1. oiii I'iii t.. Jnulpitersi qut-.: t...... 00 01 " 05" hetrroae re voh:ion of node1.s on xfi i paAn in. veari 29,1 Mas: Jupite rs be'n: I,.000,004 0000,., "......... 25235 o0, 3. I-B';NT'RIT' SnA.i Sideirei rovooluiion in da.'d 03h 42m;33.:,2 fean (distaneo (tnlpitcr radius 1). )..,.,., i 15,3524i tcliiat ioni of' orbit to a fixed phano........... 0 12 20' eliito.t~ioi:n of t!is plane to Jupit. re cqcatort...... 0 05' 02" -be:tr(o rade. rovol.iiion of iodes o:t fi.xed pane iu yeara 141. 90 No. 4.:-I:i:N'T: Y B.A.it.i Bidera;l rovotio it draeysn...o in.... 16(d 1.OTh alo3" 40"'0"'.'......d.. 28, M.eani dis:t4n:, (Jupitef' radius beinog 1.). 2'19" 8 35 Tncli:atbion of orbit to a fixed plano............... 0' 1.4it' 58" Inclin:afitio of this plae. to Jupiters equator....... 0 4' 04 it-roi:rado:revolution of node on fixed plano in years, 031,000 ]i:1iM I\NTS OF,8A.T N7 EI5 R01 TH 1' svT JAN., 184.0, Mean diiimco 4omi tdii sil iit n mii ei,,.,...,..,.... 90Oi205,00 Snom' (ieirthis edisltaie:e 1).*.... 9538850 c,:eal,'. distianc.,e, Isainemo.io,,,,,,t...,............, 9.0044~222 leiitrieit (elm i-axis major as 1).......,056026 5 Ain uda variationi of sanm (dero a..)..... 0, 0001..4 ide.eal ire;oliutoiu in das................ I. 10 i55. 191 O I i06 B'v'iodieial. ivoluiiio in dia:v.........1..... 378>090 Longi udei. of ttlie jprihlionli.....,......... 54...5'. 41", A nmiual variation of same (inioreas'.:).......... 1'"3 iLon:iiudo of'b die nsce:dio'oe nodoe............ 1 1' I 4';.1 ATood var'iidon o oame (decrea),.). 3..41.)...... 10",54 liinaiod. of rbil to dhe ec:ipii,...i....,2.0?9 o.....,' Amtd variation of... (deea............... (0, i..01 Mean. dalily motioi in m orbit............'..0...... 20 ".6 Time of ro'tatiorn on axis 10....... tlh t9m I:7 I:eliml'ation of axin t1o it'h cei *ie,..., *................ 49' A. ppant b di ameteir,,1,1)..'j........:':. iamet:r 1el. mil e: s ~ ~............*......*....<..*..* I 5,02 0 ])iam. et.r (enari.h'a b.g 1).,.....,,.~ -..,..,~.02?. Yotm'ne (e'alrth beim"g l)>............ "..0..:1.0 1sia:,iort wvt:l (earfli': ein'g ) )..,,..,.......... * 1 )02468 872 A IP:BX I D X. De)e.s;sty (earth' being 1)............S.........., 0i38 ttlght 1r eOeved 1at pe rihl..:t (artt s b oinh i)................ *0 23 Same at aphioes (earlisls being 1)....*............ e..00 9 9 VWeight of a teirrstrial pmrtd or gravity*................. 1.09 Spact hlilen throug'h it onie scccd of tno t le'tL............. 1.{ ILEM; XN VTS O' SATUtN'$ S ATELLT I No. I, MIMAt Siderea l re volutbio n in day-3............. Od:221 3Minm?.19Mean di,:stance (Saturls radius I)............... Vpe'........................ Mlfl'alt lol tii fit~ t it eat Opochl4t....................... 251:: 4$'E itcnrtriei:' and PerutStuti in,.........V Uuknown, No, 2. Ex l'tts. Sidetreal revoluttio: ill davs............... d 0h l 3 O.T: i pt och a tl.t..tif,i ( t.tttts t, t......I......1 1 S 1: ctiitct t.it... t..... t.t. it.............. V t:t;6.0 Mea i longcitud t at ep oh..................0 4. 3 E ec anricity aud Pt. -Saturlnsum. l....0. i iwn, No. 4. tus. iteral rv'oluition in day...... Id 411 1im 25it 0 ttNO. 4. isttt:M1ear. distanco (/% tr:s radius 1),.............. 0.8398 I EI toch........................................... S l i 1e lc longA i do ai epot h.......i,,......,,... 32 i 4ti'" xceentrieity an4 Ilerl.Satl iu,,.................inert^i. Si dere.al revoltion m days..*............... 4d4 12h 25.n 1i0 Ss Mean dista c: (Sam iv's radius 1).................... >.: i.:S:} Epoceh,,........................................... 1 Longitude at epoch,~............,.,353:44' 00". 10i 1trieity.and Pier Saturnir l~,.....*....... X-feS, t i.No, 0, VtIrA. Sidereal rvttio..,..t........... I 2 2 *i* 41 n 2 i 5.t " s tMean dist ance (Satutn t ra ius t1)...,.....,Lt,. I i50 t $;..l.A-< tSOS4Xt t )*** **+ 4+: *+*:.3iSy?1}.1;.^ A yS~.r 2f. Xw:e t.t<}b aStexy C tttS.l tS}tZ S }) X+b; S )S A P v: 1) N 1)1 N. 373' + AP IND X * * DI* deoant lnc'ttude at epoth................ 2.. 24"i lee n trietr...............,.,*t....*,* 0, 0293 longitude of.I — Satmrumt n,......'...,.. 025 38' 31" No.':t:Y PItx. SidereaiI r.,.vot^..s.,.......,.,**........... 21 0*h O0i 4 0.Ss Other oht'esnis uitantown.t INo. 8 JXA TS:., Sideral rt volu tion...~...... t.d 9:i 71 53:m 40{,4 Mean dlistnc (- aturn's radius 1)..s............ 6t. 9 0 Mean Iongitudec at epochI,....2...0..... t 3' 48" Ecoieni itit and Peri-Saturniumt.....*..,..., Un tnow. EILMINTS OF URANUS FOB TUB: laSr JAN, 18140. Mean distannce triom tho n in ril es..1.......,8 28,000 Same (earth's di-tanc a 1)...................... 19'.182:9 OG xatest distanuc am: u nit.,,...................... 20,0' 130 eaSust distant o sae mio t uni........................... 18, S.2 8848 tIe.entriityi (soeni-axis major as 1).,.................... 0 04 6 t00 nAin l variation of samno.......,........,........ Pki.. Lonrgitude of the as endin*g node t......... * t * * 8 4Xtt 8 Annumal variation of samn (deerease)..,............ 3.,.o05 Inelinationt o' orbit to the eodiptic......... 0~ 4' 2 9'.. Annual variation of satme (in.rcase)................. 0.0. Mema da'il motion in orbit.,.,........... 42 t4 Tim" of rotation on axis...........*.............'Unknown. In..liation of axis to the ecliptic.........*........ Uni sl ame ter ( art hs h being 1),,.......................... 4.34 yohitoi (earth's being 1.)................................, a5 Masl or weight (eart^'s being )............ *...+....... Ii'.. 1 I YT4 APP iEND X D)easitv (arths bting.............................. 0180 lSig t recteivod at pesrihei:lion (cartihs bein:.: 1).,,,...............002 Same at apei a (caird B:s, bein, 1,).....,................... 00, Weiglit of a trrestal poutnd or gravityl.,,......,.. 0,fiG Spaco fa tnlen tiThroug mon e slt cond l of time in fi:et:.......... 12.3 I!bEMiENTS OF.11.0S' SATE NLLIT IS, lS~idereal revolution in days,......,..,.. 2,t.h 29m 2).1fi; 51ean di(staycc:,~*................................... r f 40 Not 4'' I' lini f+ti u' S; vidS.real rotvoiltioll in days 2 t.......,........ ld 3h 2i 8. 9 0s AlI.tt t ( 4:c t t t. e * ( *i. a*e t e * * 1 o: I. x I X ~ ~ *Z MS eal d ista n ve......................... 10.31. No 4. 0 tO:n:mOx. S.t.'.t tt N I t At t ider.dl revolt o n in days..,........ d h i.m tIt, *. 3 1.'2.,i eas d. ta o............................,......... 22I S TIoI.E T O4iF NET.NE I T I A N, i854,i liii liii ttit'i titt i 014)11 lit I nt * * *I+ J* It t * Alt Sn ttS S XIt nttt n tt. 0 n in:atio ditano af tho:sa iit e ilp................. nk:o4w0n00 Samo (o l'' di;sth c.11:::.,'. as 1)....).........,*,..........*... 3t0,0360 rea.s (.::t.7 3d tlao, ms.. ni t.,....., t.................... I..... 3 i0[}: 8,I A: nu 3 var <, ia t ion o f a, ~...~...... *.................. kno 8ynodicat rcvoluthon in d;v^................................ 3iT...88 l,.gitmio of the terih,:!ion,.................., 5,... 4 I'2' 5:g*" lgitudc of ih aseonding node,............. I.30 30' I 2':'. annualt variation of suno~,...................,. Un ikt 4'wI 8 Inoliatiott o i iorbi t to the -l ipl.;..~.............. 1. 40' ".0.An at t l vat'! l O?i tts..sam................ U 1, lO W 1t fMe an d aily mot o t in or tbit,, X..~........<................. 2 209''29' 19"} linatia to 8the eclpt.,......... 11.' 3* 1G ThIo A lann.'!xis.:.......................81 1T ttEeee nic ty....................................... 0.5 5 5 9 eno.d ays............ 2, 8d26 Bl:et..........................................') IcO\ S Coti::t' 114 1 S, S:p c.Timtto t pe ril h io n passago..., h 1 * m 531 lnc0 llnation to th e liptie,.............S.... 2 54:' 45' The o-axi s.......................... t *..* b * * i 0 46.e( rt\ieity,................................... * 0. 6 725, 6t.Period iol days.............. 1,,*.* * 0 d)}: S [irecs;.,.t.........t th A............ Theo of pe.il.lioin pa:.ago,.................. l 13m 3I,Long ude of perislelio>ant.s.................. 110 8' 3 2$,aongidaed of ite as eeding node,.n...... 102'39':I Inclinatlio to t10 cl: Iiptio,.....,.,,..., 30 5' i0 " Priod in d-ays.............................. 30,2d 2 Pir.tft...... f. *............. * TChis comtI which w, oblsr e doublo I, 184 wY a s!;1it dtIi ed a; I Us re itr;as Int 18ti