Meanwhile，astronomersacrossthechannelwerebynomeansidle。InFranceseveralsuccessfulobserversweremakingmanyadditionstothealreadylonglistofobservationsofthefirstastronomeroftheRoyalObservatoryofParis，DominicCassini1625-1712，whosereputationamonghiscontemporarieswasmuchgreaterthanamongsucceedinggenerationsofastronomers。PerhapsthemostdeservingofthesesuccessorswasNicolasLouisdeLacaille1713-1762，atheologianwhohadbeeneducatedattheexpenseoftheDukeofBourbon，andwho，soonaftercompletinghisclericalstudies，cameunderthepatronageofCassini，whoseattentionhadbeencalledtotheyoungman’sinterestinthesciences。OneofLacaille’sfirstunder-takingswastheremeasuringoftheFrenchareofthemeridian，whichhadbeenincorrectlymeasuredbyhispatronin1684。Thiswasbegunin1739，andoccupiedhimfortwoyearsbeforesuccessfullycompleted。Asareward，however，hewasadmittedtotheacademyandappointedmathematicalprofessorinMazarinCollege。
In1751hewenttotheCapeofGoodHopeforthepurposeofdeterminingthesun’sparallaxbyobservationsoftheparallaxesofMarsandVenus，andincidentallytomakeobservationsontheothersouthernhemispherestars。Theresultsofthisundertakingweremostsuccessful，andweregiveninhisCoelumaustralestelligerum，etc。，publishedin1763。Inthisheshowsthatinthecourseofasingleyearhehadobservedsometenthousandstars，andcomputedtheplacesofonethousandninehundredandforty-twoofthem，measuredadegreeofthemeridian，andmademanyobservationsofthemoon——productiveindustryseldomequalledinasingleyearinanyfield。Theseobservationswereofgreatservicetotheastronomers，astheyaffordedtheopportunityofcomparingthestarsofthesouthernhemispherewiththoseofthenorthern，whichwerebeingobservedsimultaneouslybyLelandeatBerlin。
Lacaille’sobservationsfollowedcloselyuponthedeterminationofanabsorbingquestionwhichoccupiedtheattentionoftheastronomersintheearlypartofthecentury。Thisquestionwasastotheshapeoftheearth——whetheritwasactuallyflattenedatthepoles。TosettlethisquestiononceforalltheAcademyofSciencesdecidedtomaketheactualmeasurementofthelengthoftwodegrees，oneasnearthepoleaspossible，theotherattheequator。
Accordingly，threeastronomers，Godin，Bouguer，andLaCondamine，madethejourneytoaspotontheequatorinPeru，whilefourastronomers，Camus，Clairaut，Maupertuis，andLemonnier，madeavoyagetoaplaceselectedinLapland。Theresultoftheseexpeditionswasthedeterminationthattheglobeisoblatelyspheroidal。
Agreatcontemporaryandfellow-countrymanofLacaillewasJeanLeRondd’Alembert1717-1783，who，althoughnotprimarilyanastronomer，didsomuchwithhismathematicalcalculationstoaidthatsciencethathisnameiscloselyconnectedwithitsprogressduringtheeighteenthcentury。D’Alembert，whobecameoneofthebest-knownmenofscienceofhisday，andwhoseserviceswereeagerlysoughtbytherulersofEurope，beganlifeasafoundling，havingbeenexposedinoneofthemarketsofParis。Thesicklyinfantwasadoptedandcaredforinthefamilyofapoorglazier，andtreatedasamemberofthefamily。Inlateryears，however，afterthefoundlinghadbecomefamousthroughoutEurope，hismother，MadameTencin，sentforhim，andacknowledgedherrelationship。Itismorethanlikelythatthegreatphilosopherbelievedherstory，butifsohedidnotallowherthesatisfactionofknowinghisbelief，declaringalwaysthatMadameTencincould\"notbenearerthanastep-mothertohim，sincehismotherwasthewifeoftheglazier。\"
D’Alembertdidmuchforthecauseofsciencebyhisexampleaswellasbyhisdiscoveries。Bylivingaplainbuthonestlife，decliningmagnificentoffersofpositionsfromroyalpatrons，atthesametimerefusingtogrovelbeforenobility，hesetaworthyexampletootherphilosopherswhosecringingandpusillanimousattitudetowardspersonsofwealthorpositionhadhithertoearnedthemthecontemptoftheupperclasses。
Hisdirectadditionstoastronomyareseveral，amongothersthedeterminationofthemutationoftheaxisoftheearth。Healsodeterminedtheratiooftheattractiveforcesofthesunandmoon，whichhefoundtobeaboutasseventothree。Fromthishereachedtheconclusionthattheearthmustbeseventytimesgreaterthanthemoon。ThefirsttwovolumesofhisResearchesontheSystemsoftheWorld，publishedin1754，arelargelydevotedtomathematicalandastronomicalproblems，manyofthemoflittleimportancenow，butofgreatinteresttoastronomersatthattime。
AnothergreatcontemporaryofD’Alembert，whosenameiscloselyassociatedandfrequentlyconfoundedwithhis，wasJeanBaptisteJosephDelambre1749-
1822。Morefortunateinbirthasalsoinhiseducationaladvantages，DelambreasayouthbeganhisstudiesunderthecelebratedpoetDelille。Laterhewasobligedtostruggleagainstpoverty，supportinghimselfforatimebymakingtranslationsfromLatin，Greek，Italian，andEnglish，andactingastutorinprivatefamilies。Theturning-pointofhisfortunecamewhentheattentionofLalandewascalledtotheyoungmanbyhisremarkablememory，andLalandesoonshowedhisadmirationbygivingDelambrecertaindifficultastronomicalproblemstosolve。Byperformingthesetaskssuccessfullyhisfutureasanastronomerbecameassured。AtthattimetheplanetUranushadjustbeendiscoveredbyHerschel，andtheAcademyofSciencesofferedasthesubjectforoneofitsprizesthedeterminationoftheplanet’sorbit。
Delambremadethisdeterminationandwontheprize——afeatthatbroughthimatonceintoprominence。
Byhiswritingsheprobablydidasmuchtowardsperfectingmodernastronomyasanyoneman。HisHistoryofAstronomyisnotmerelyanarrativeofprogressofastronomybutacompleteabstractofallthecelebratedworkswrittenonthesubject。Thushebecamefamousasanhistorianaswellasanastronomer。
LEONARDEULER
StillanothercontemporaryofD’AlembertandDelambre，andsomewhatolderthaneitherofthem，wasLeonardEuler1707-1783，ofBasel，whosefameasaphilosopherequalsthatofeitherofthegreatFrenchmen。
Heisofparticularinteresthereinhiscapacityofastronomer，butastronomywasonlyoneofthemanyfieldsofscienceinwhichheshone。Surelysomethingoutoftheordinarywastobeexpectedofthemanwhocould\"repeattheAEneidofVirgilfromthebeginningtotheendwithouthesitation，andindicatethefirstandlastlineofeverypageoftheeditionwhichheused。\"Somethingwasexpected，andhefulfilledtheseexpectations。
InearlylifehedevotedhimselftothestudyoftheologyandtheOrientallanguages，attherequestofhisfather，buthisloveofmathematicsprovedtoostrong，and，withhisfather’sconsent，hefinallygaveuphisclassicalstudiesandturnedtohisfavoritestudy，geometry。In1727hewasinvitedbyCatharineI。toresideinSt。Petersburg，andonacceptingthisinvitationhewasmadeanassociateoftheAcademyofSciences。Alittlelaterhewasmadeprofessorofphysics，andin1733professorofmathematics。In1735hesolvedaprobleminthreedayswhichsomeoftheeminentmathematicianswouldnotundertakeunderseveralmonths。In1741FredericktheGreatinvitedhimtoBerlin，wherehesoonbecameamemberoftheAcademyofSciencesandprofessorofmathematics；butin1766hereturnedtoSt。Petersburg。
Towardsthecloseofhislifebebecamevirtuallyblind，beingobligedtodictatehisthoughts，sometimestopersonsentirelyignorantofthesubjectinhand。
Nevertheless，hisremarkablememory，stillfurtherheightenedbyhisblindness，enabledhimtocarryouttheelaboratecomputationsfrequentlyinvolved。
Euler’sfirstmemoir，transmittedtotheAcademyofSciencesofParisin1747，wasontheplanetaryperturbations。
ThismemoircarriedofftheprizethathadbeenofferedfortheanalyticaltheoryofthemotionsofJupiterandSaturn。Othermemoirsfollowed，onein1749andanotherin1750，withfurtherexpansionsofthesamesubject。Assomeslighterrorswerefoundinthese，suchasamistakeinsomeoftheformulaeexpressingthesecularandperiodicinequalities，theacademyproposedthesamesubjectfortheprizeof1752。Euleragaincompeted，andwonthisprizealso。ThecontentsofthismemoirlaidthefoundationforthesubsequentdemonstrationofthepermanentstabilityoftheplanetarysystembyLaplaceandLagrange。
ItwasEuleralsowhodemonstratedthatwithincertainfixedlimitstheeccentricitiesandplacesoftheapheliaofSaturnandJupiteraresubjecttoconstantvariation，andhecalculatedthatafteralapseofaboutthirtythousandyearstheelementsoftheorbitsofthesetwoplanetsrecovertheiroriginalvalues。
II
THEPROGRESSOFMODERNASTRONOMY
ANEWepochinastronomybeginswiththeworkofWilliamHerschel，theHanoverian，whomEnglandmadehersbyadoption。Hewasamanwithapositivegeniusforsiderealdiscovery。Atfirstamereamateurinastronomy，hesnatchedtimefromhisdutiesasmusic-teachertogrindhimatelescopicmirror，andbegangazingatthestars。Notcontentwithhisfirsttelescope，hemadeanotherandanother，andhehadsuchgeniusfortheworkthathesoonpossessedabetterinstrumentthanwasevermadebefore。Hispatienceingrindingthecurvedreflectivesurfacewasmonumental。Sometimesforsixteenhourstogetherhemustwalksteadilyaboutthemirror，polishingit，withoutonceremovinghishands。Meantimehissister，alwayshischieflieutenant，cheeredhimwithherpresence，andfromtimetotimeputfoodintohismouth。
Thetelescopecompleted，theastronomerturnednightintoday，andfromsunsettosunrise，yearinandyearout，swepttheheavensunceasingly，unlesspreventedbycloudsorthebrightnessofthemoon。Hissistersatalwaysathisside，recordinghisobservations。
Theywereintheopenair，perchedhighatthemouthofthereflector，andsometimesitwassocoldthattheinkfrozeinthebottleinCarolineHerschel’shand；butthetwoenthusiastshardlynoticedathingsocommon-placeasterrestrialweather。Theywerelivingindistantworlds。
Theresults？Whatcouldtheybe？Suchenthusiasmwouldmovemountains。But，afterall，themovingofmountainsseemsaliliputiantaskcomparedwithwhatHerschelreallydidwiththosewonderfultelescopes。Hemovedworlds，stars，auniverse——
even，ifyouplease，agalaxyofuniverses；atleastheprovedthattheymove，whichseemsscarcelylesswonderful；
andheexpandedthecosmos，asmanconceivesit，tothousandsoftimesthedimensionsithadbefore。
Asamerebeginning，hedoubledthediameterofthesolarsystembyobservingthegreatoutlyingplanetwhichwenowcallUranus，butwhichhechristenedGeorgiumSidus，inhonorofhissovereign，andwhichhisFrenchcontemporaries，notrelishingthatname，preferredtocallHerschel。
ThisdiscoverywasbutatriflecomparedwithwhatHerscheldidlateron，butitgavehimworld-widereputationnonetheless。Cometsandmoonsaside，thiswasthefirstadditiontothesolarsystemthathadbeenmadewithinhistorictimes，anditcreatedaveritablefurorofpopularinterestandenthusiasm。IncidentallyKingGeorgewasflatteredathavingaworldnamedafterhim，andhesmiledontheastronomer，andcamewithhiscourttohavealookathisnamesake。Theinspectionwashighlysatisfactory；andpresentlytheroyalfavorenabledtheastronomertoescapethethraldomofteachingmusicandtodevotehisentiretimetothemorecongenialtaskofstar-gazing。
Thusrelievedfromtheburdenofmundaneembarrassments，heturnedwithfreshenthusiasmtotheskies，andhisdiscoveriesfollowedoneanotherinbewilderingprofusion。Hefoundvarioushithertounseenmoonsofoursisterplanets；bemadespecialstudiesofSaturn，andprovedthatthisplanet，withitsrings，revolvesonitsaxis；hescannedthespotsonthesun，andsuggestedthattheyinfluencetheweatherofourearth；inshort，heextendedtheentirefieldofsolarastronomy。Butverysoonthisfieldbecametoosmallforhim，andhismostimportantresearchescarriedhimoutintotheregionsofspacecomparedwithwhichthespanofoursolarsystemisamerepoint。Withhisperfectedtelescopesheenteredabysmalvistaswhichnohumaneveeverpenetratedbefore，whichnohumanmindhadhithertomorethanvaguelyimagined。Hetellsusthathisforty-footreflectorwillbringhimlightfromadistanceof\"atleastelevenandthree-fourthsmillionsofmillionsofmillionsofmiles\"——lightwhichleftitssourcetwomillionyearsago。Thesmalleststarsvisibletotheunaidedeyearethoseofthesixthmagnitude；thistelescope，hethinks，haspowertorevealstarsofthe1342dmagnitude。
ButwhatdidHerschellearnregardingtheseawfuldepthsofspaceandthestarsthatpeoplethem？Thatwaswhattheworldwishedtoknow。Copernicus，Galileo，Kepler，hadgivenusasolarsystem，butthestarshadbeenamystery。Whatsaysthegreatreflector——arethestarspointsoflight，astheancientstaught，andasmorethanonephilosopheroftheeighteenthcenturyhasstillcontended，oraretheysuns，asothershold？Herschelanswers，theyaresuns，eachandeveryoneofallthemillions——suns，manyofthem，largerthantheonethatisthecentreofourtinysystem。
Notonlyso，buttheyaremovingsuns。Insteadofbeingfixedinspace，ashasbeenthought，theyarewhirlingingiganticorbitsaboutsomecommoncentre。Isoursunthatcentre？Farfromit。Oursunisonlyastarlikealltherest，circlingonwithitsattendantsatellites——ourgiantsunastar，nodifferentfrommyriadotherstars，notevensolargeassome；amereinsignificantsparkofmatterinaninfiniteshowerofsparks。
Noristhisall。Lookingbeyondthefewthousandstarsthatarevisibletothenakedeye，Herschelseesseriesafterseriesofmoredistantstars，marshalledingalaxiesofmillions；butatlasthereachesadistancebeyondwhichthegalaxiesnolongerincrease。Andyet——sohethinks——hehasnotreachedthelimitsofhisvision。Whatthen？Hehascometotheboundsofthesiderealsystem——seentotheconfinesoftheuniverse。
Hebelievesthathecanoutlinethissystem，thisuniverse，andprovethatithastheshapeofanirregularglobe，oblatelyflattenedtoalmostdisklikeproportions，anddividedatoneedge——abifurcationthatisrevealedeventothenakedeyeintheforkingoftheMilkyWay。
This，then，isouruniverseasHerschelconceivesit——
avastgalaxyofsuns，heldtoonecentre，revolving，poisedinspace。Butevenherethosemarvelloustelescopesdonotpause。Far，faroutbeyondtheconfinesofouruniverse，sofarthattheawfulspanofourownsystemmightserveasaunitofmeasure，arerevealedothersystems，otheruniverses，likeourown，eachcomposed，ashethinks，ofmyriadsofsuns，clusteredlikeourgalaxyintoanisolatedsystem——mereislandsofmatterinaninfiniteoceanofspace。SodistantfromouruniversearethesenowuniversesofHerschel’sdiscoverythattheirlightreachesusonlyasadim，nebulousglow，inmostcasesinvisibletotheunaidedeye。
AboutahundredofthesenebulaewereknownwhenHerschelbeganhisstudies。Beforethecloseofthecenturyhehaddiscoveredabouttwothousandmoreofthem，andmanyofthesehadbeenresolvedbyhislargesttelescopesintoclustersofstars。Hebelievedthatthefarthestofthesenebulaethathecouldseewasatleastthreehundredthousandtimesasdistantfromusasthenearestfixedstar。Yetthatneareststar——somorerecentstudiesprove——issoremotethatitslight，travellingonehundredandeightythousandmilesasecond，requiresthreeandone-halfyearstoreachourplanet。
Asiftogivethefinishingtouchestothisnovelschemeofcosmology，Herschel，thoughinthemainverylittlegiventounsustainedtheorizing，allowshimselftheprivilegeofonebeliefthathecannotcalluponhistelescopetosubstantiate。Hethinksthatallthemyriadsunsofhisnumberlesssystemsareinstinctwithlifeinthehumansense。GiordanoBrunoandalonglineofhisfollowershadheldthatsomeofoursisterplanetsmaybeinhabited，butHerschelextendsthethoughttoincludethemoon，thesun，thestars——alltheheavenlybodies。Hebelievesthathecandemonstratethehabitabilityofourownsun，and，reasoningfromanalogy，heisfirmlyconvincedthatallthesunsofallthesystemsare\"wellsuppliedwithinhabitants。\"Inthis，asinsomeotherinferences，Herschelismisledbythefaultyphysicsofhistime。Futuregenerations，workingwithperfectedinstruments，maynotsustainhimallalongthelineofhisobservations，even，letalonehisinferences。Buthowone’segotismshrivelsandshrinksasonegraspstheimportofhissweepingthoughts！
Continuinghisobservationsoftheinnumerablenebulae，Herschelisledpresentlytoanothercuriousspeculativeinference。Henotesthatsomestargroupsaremuchmorethicklyclusteredthanothers，andheisledtoinferthatsuchvariedclusteringtellsofvaryingagesofthedifferentnebulae。Hethinksthatatfirstallspacemayhavebeenevenlysprinkledwiththestarsandthatthegroupinghasresultedfromtheactionofgravitation。
\"ThattheMilkyWayisamostextensivestratumofstarsofvarioussizesadmitsnolongeroflastingdoubt，\"
hedeclares，\"andthatoursunisactuallyoneoftheheavenlybodiesbelongingtoitisasevident。Ihavenowviewedandgaugedthisshiningzoneinalmosteverydirectionandfinditcomposedofstarswhosenumber……constantlyincreasesanddecreasesinproportiontoitsapparentbrightnesstothenakedeye。
\"Letussupposenumberlessstarsofvarioussizes，scatteredoveranindefiniteportionofspaceinsuchamannerastobealmostequallydistributedthroughoutthewhole。Thelawsofattractionwhichnodoubtextendtotheremotestregionsofthefixedstarswilloperateinsuchamannerasmostprobablytoproducethefollowingeffects:
\"Inthefirstcase，sincewehavesupposedthestarstobeofvarioussizes，itwillhappenthatastar，beingconsiderablylargerthanitsneighboringones，willattractthemmorethantheywillbeattractedbyothersthatareimmediatelyaroundthem；bywhichmeanstheywillbe，intime，asitwere，condensedaboutacentre，or，inotherwords，formthemselvesintoaclusterofstarsofalmostaglobularfigure，moreorlessregularaccordingtothesizeanddistanceofthesurroundingstars……
\"Thenextcase，whichwillalsohappenalmostasfrequentlyastheformer，iswhereafewstars，thoughnotsuperiorinsizetotherest，maychancetoberatherneareroneanotherthanthesurroundingones，……andthisconstructionadmitsoftheutmostvarietyofshapes……
\"Fromthecompositionandrepeatedconjunctionofboththeforegoingformations，athirdmaybederivedwhenmanylargestars，orcombinedsmallones，arespreadinlong，extended，regular，orcrookedrows，streaks，orbranches；fortheywillalsodrawthesurroundingstars，soastoproducefiguresofcondensedstarscuriouslysimilartotheformerwhichgaverisetothesecondensations。
\"Wemaylikewiseadmitstillmoreextensivecombinations；when，atthesametimethataclusterofstarsisformingattheonepartofspace，theremaybeanothercollectioninadifferentbutperhapsnotfar-
distantquarter，whichmayoccasionamutualapproachtowardstheirowncentreofgravity。
\"Inthelastplace，asanaturalconclusionoftheformercases，therewillbeformedgreatcavitiesorvacanciesbytheretreatingofthestarstowardsthevariouscentreswhichattractthem。\"[1]
Lookingforward，itappearsthatthetimemustcomewhenallthesunsofasystemwillbedrawntogetheranddestroyedbyimpactatacommoncentre。Already，itseemstoHerschel，thethickestclustershave\"outlivedtheirusefulness\"andarevergingtowardstheirdoom。
Butagain，othernebulaepresentanappearancesuggestiveofanoppositecondition。Theyarenotresolvableintostars，butpresentanalmostuniformappearancethroughout，andarehencebelievedtobecomposedofashiningfluid，whichinsomeinstancesisseentobecondensedatthecentreintoaglowingmass。
InsuchanebulaHerschelthinksheseesasuninprocessofformation。
THENEBULARHYPOTHESISOFKANT
Takentogether，thesetwoconceptionsoutlineamajesticcycleofworldformationandworlddestruction——
abroadschemeofcosmogony，suchashadbeenvaguelyadumbratedtwocenturiesbeforebyKeplerandinmorerecenttimesbyWrightandSwedenborg。Thisso-called\"nebularhypothesis\"assumesthatinthebeginningallspacewasuniformlyfilledwithcosmicmatterinastateofnebularor\"fire-mist\"diffusion，\"formlessandvoid。\"Itpicturesthecondensation——
coagulation，ifyouwill——ofportionsofthismasstoformsegregatedmasses，andtheultimatedevelopmentoutofthesemassesofthesiderealbodiesthatwesee。
PerhapsthefirstelaborateexpositionofthisideawasthatgivenbythegreatGermanphilosopherImmanuelKantbornatKonigsbergin1724，diedin1804，knowntoeveryoneastheauthoroftheCritiqueofPureReason。Letuslearnfromhisownwordshowtheimaginativephilosopherconceivedtheworldtohavecomeintoexistence。
\"Iassume，\"saysKant，\"thatallthematerialofwhichtheglobesbelongingtooursolarsystem——alltheplanetsandcomets——consist，atthebeginningofallthingswasdecomposedintoitsprimaryelements，andfilledthewholespaceoftheuniverseinwhichthebodiesformedoutofitnowrevolve。Thisstateofnature，whenviewedinandbyitselfwithoutanyreferencetoasystem，seemstobetheverysimplestthatcanfollowuponnothing。Atthattimenothinghasyetbeenformed。Theconstructionofheavenlybodiesatadistancefromoneanother，theirdistancesregulatedbytheirattraction，theirformarisingoutoftheequilibriumoftheircollectedmatter，exhibitalaterstate……Inaregionofspacefilledinthismanner，auniversalreposecouldlastonlyamoment。Theelementshaveessentialforceswithwhichtoputeachotherinmotion，andthusarethemselvesasourceoflife。Matterimmediatelybeginstostrivetofashionitself。Thescatteredelementsofadenserkind，bymeansoftheirattraction，gatherfromaspherearoundthemallthematteroflessspecificgravity；again，theseelementsthemselves，togetherwiththematerialwhichtheyhaveunitedwiththem，collectinthosepointswheretheparticlesofastilldenserkindarefound；
theseinlikemannerjoinstilldenserparticles，andsoon。Ifwefollowinimaginationthisprocessbywhichnaturefashionsitselfintoformthroughthewholeextentofchaos，weeasilyperceivethatalltheresultsoftheprocesswouldconsistintheformationofdiversmasseswhich，whentheirformationwascomplete，wouldbytheequalityoftheirattractionbeatrestandbeforeverunmoved。
\"Butnaturehasotherforcesinstorewhicharespeciallyexertedwhenmatterisdecomposedintofineparticles。Theyarethoseforcesbywhichtheseparticlesrepeloneanother，andwhich，bytheirconflictwithattractions，bringforththatmovementwhichis，asitwere，thelastinglifeofnature。Thisforceofrepulsionismanifestedintheelasticityofvapors，theeffluencesofstrong-smellingbodies，andthediffusionofallspirituousmatters。Thisforceisanuncontestablephenomenonofmatter。Itisbyitthattheelements，whichmaybefallingtothepointattractingthem，areturnedsidewayspromiscuouslyfromtheirmovementinastraightline；andtheirperpendicularfalltherebyissuesincircularmovements，whichencompassthecentretowardswhichtheywerefalling。
Inordertomaketheformationoftheworldmoredistinctlyconceivable，wewilllimitourviewbywithdrawingitfromtheinfiniteuniverseofnatureanddirectingittoaparticularsystem，astheonewhichbelongstooursun。Havingconsideredthegenerationofthissystem，weshallbeabletoadvancetoasimilarconsiderationoftheoriginofthegreatworld-systems，andthustoembracetheinfinitudeofthewholecreationinoneconception。
\"Fromwhathasbeensaid，itwillappearthatifapointissituatedinaverylargespacewheretheattractionoftheelementstheresituatedactsmorestronglythanelsewhere，thenthematteroftheelementaryparticlesscatteredthroughoutthewholeregionwillfalltothatpoint。Thefirsteffectofthisgeneralfallistheformationofabodyatthiscentreofattraction，which，sotospeak，growsfromaninfinitelysmallnucleusbyrapidstrides；andintheproportioninwhichthismassincreases，italsodrawswithgreaterforcethesurroundingparticlestounitewithit。Whenthemassofthiscentralbodyhasgrownsogreatthatthevelocitywithwhichitdrawstheparticlestoitselfwithgreatdistancesisbentsidewaysbythefeebledegreeofrepulsionwithwhichtheyimpedeoneanother，andwhenitissuesinlateralmovementswhicharecapablebymeansofthecentrifugalforceofencompassingthecentralbodyinanorbit，thenthereareproducedwhirlsorvorticesofparticles，eachofwhichbyitselfdescribesacurvedlinebythecompositionoftheattractingforceandtheforceofrevolutionthathadbeenbentsideways。Thesekindsoforbitsallintersectoneanother，forwhichtheirgreatdispersioninthisspacegivesplace。Yetthesemovementsareinmanywaysinconflictwithoneanother，andtheynaturallytendtobringoneanothertoauniformity——thatis，intoastateinwhichonemovementisaslittleobstructivetotheotheraspossible。Thishappensintwoways:firstbytheparticleslimitingoneanother’smovementtilltheyalladvanceinonedirection；and，secondly，inthisway，thattheparticleslimittheirverticalmovementsinvirtueofwhichtheyareapproachingthecentreofattraction，tilltheyallmovehorizontally——i。e。，inparallelcirclesroundthesunastheircentre，nolongerinterceptoneanother，andbythecentrifugalforcebecomingequalwiththefallingforcetheykeepthemselvesconstantlyinfreecircularorbitsatthedistanceatwhichtheymove。Theresult，finally，isthatonlythoseparticlescontinuetomoveinthisregionofspacewhichhaveacquiredbytheirfallavelocity，andthroughtheresistanceoftheotherparticlesadirection，bywhichtheycancontinuetomaintainaFREECIRCULARMOVEMENT……
\"Theviewoftheformationoftheplanetsinthissystemhastheadvantageovereveryotherpossibletheoryinholdingthattheoriginofthemovements，andthepositionoftheorbitsinarisingatthatsamepointoftime——nay，more，inshowingthateventhedeviationsfromthegreatestpossibleexactnessintheirdeterminations，aswellastheaccordancesthemselves，becomeclearataglance。Theplanetsareformedoutofparticleswhich，atthedistanceatwhichtheymove，haveexactmovementsincircularorbits；andthereforethemassescomposedoutofthemwillcontinuethesamemovementsandatthesamerateandinthesamedirection。\"[2]
Itmustbeadmittedthatthisexplanationleavesagooddealtobedesired。Itistheexplanationofametaphysicianratherthanthatofanexperimentalscientist。Suchphrasesas\"matterimmediatelybeginstostrivetofashionitself，\"forexample，havenoplaceinthereasoningofinductivescience。Nevertheless，thehypothesisofKantisaremarkableconception；
itattemptstoexplainalongrationallinessomethingwhichhithertohadforthemostpartbeenconsideredaltogetherinexplicable。
ButtherearevariousquestionsthatatoncesuggestthemselveswhichtheKantiantheoryleavesunanswered。
Howhappensit，forexample，thatthecosmicmasswhichgavebirthtooursolarsystemwasdividedintoseveralplanetarybodiesinsteadofremainingasinglemass？Weretheplanetsstruckfromthesunbythechanceimpactofcomets，asBuffonhassuggested？
orthrownoutbyexplosivevolcanicaction，inaccordancewiththetheoryofDr。Darwin？ordotheyowetheirorigintosomeunknownlaw？Inanyevent，howchanceditthatallwereprojectedinnearlythesameplaneaswenowfindthem？
LAPLACEANDTHENEBULARHYPOTHESIS
Itremainedforamathematicalastronomertosolvethesepuzzles。ThemanofallotherscompetenttotakethesubjectinhandwastheFrenchastronomerLaplace。Foraquarterofacenturyhehaddevotedhistranscendentmathematicalabilitiestothesolutionofproblemsofmotionoftheheavenlybodies。
WorkinginfriendlyrivalrywithhiscountrymanLagrange，hisonlypeeramongthemathematiciansoftheage，hehadtakenupandsolvedonebyonetheproblemsthatNewtonleftobscure。LargelythroughtheeffortsofthesetwomenthelastlingeringdoubtsastothesolidarityoftheNewtonianhypothesisofuniversalgravitationhadbeenremoved。TheshareofLagrangewashardlylessthanthatofhisco-worker；butLaplacewilllongerberemembered，becauseheultimatelybroughthiscompletedlaborsintoasystem，and，incorporatingwiththemthelaborsofhiscontemporaries，producedintheMecaniqueCelestetheundisputedmathematicalmonumentofthecentury，afittingcomplementtothePrincipiaofNewton，whichitsupplementsandinasensecompletes。
IntheclosingyearsoftheeighteenthcenturyLaplacetookupthenebularhypothesisofcosmogony，towhichwehavejustreferred，andgaveitdefiniteproportions；infact，madeitsothoroughlyhisownthatposteritywillalwayslinkitwithhisname。
Discardingthecrudenotionsofcometaryimpactandvolcaniceruption，Laplacefilledupthegapsinthehypothesiswiththeaidofwell-knownlawsofgravitationandmotion。Heassumedthattheprimitivemassofcosmicmatterwhichwasdestinedtoformoursolarsystemwasrevolvingonitsaxisevenatatimewhenitwasstillnebularincharacter，andfilledallspacetoadistancefarbeyondthepresentlimitsofthesystem。Asthisvaporousmasscontractedthroughlossofheat，itrevolvedmoreandmoreswiftly，andfromtimetotime，throughbalanceofforcesatitsperiphery，ringsofitssubstancewerewhirledoffandleftrevolvingthere，subsequentlytobecomecondensedintoplanets，andintheirturnwhirloffminorringsthatbecamemoons。Themainbodyoftheoriginalmassremainsinthepresentasthestillcontractingandrotatingbodywhichwecallthesun。
LetusallowLaplacetoexplainallthisindetail:
\"Inordertoexplaintheprimemovementsoftheplanetarysystem，\"hesays，\"therearethefivefollowingphenomena:Themovementoftheplanetsinthesamedirectionandverynearlyinthesameplane；themovementofthesatellitesinthesamedirectionasthatoftheplanets；therotationofthesedifferentbodiesandthesuninthesamedirectionastheirrevolution，andinnearlythesameplane；theslighteccentricityoftheorbitsoftheplanetsandofthesatellites；
and，finally，thegreateccentricityoftheorbitsofthecomets，asiftheirinclinationshadbeenlefttochance。
\"BuffonistheonlymanIknowwho，sincethediscoveryofthetruesystemoftheworld，hasendeavoredtoshowtheoriginoftheplanetsandtheirsatellites。
Hesupposesthatacomet，infallingintothesun，drovefromitamassofmatterwhichwasreassembledatadistanceintheformofvariousglobesmoreorlesslarge，andmoreorlessremovedfromthesun，andthattheseglobes，becomingopaqueandsolid，arenowtheplanetsandtheirsatellites。
\"Thishypothesissatisfiesthefirstofthefiveprecedingphenomena；foritisclearthatallthebodiesthusformedwouldmoveverynearlyintheplanewhichpassedthroughthecentreofthesun，andinthedirectionofthetorrentofmatterwhichwasproduced；
butthefourotherphenomenaappeartobeinexplicabletomebythismeans。Indeed，theabsolutemovementofthemoleculesofaplanetoughtthentobeinthedirectionofthemovementofitscentreofgravity；
butitdoesnotatallfollowthatthemotionoftherotationoftheplanetsshouldbeinthesamedirection。
Thustheearthshouldrotatefromeasttowest，butneverthelesstheabsolutemovementofitsmoleculesshouldbefromeasttowest；andthisoughtalsotoapplytothemovementoftherevolutionofthesatellites，inwhichthedirection，accordingtothehypothesiswhichheoffers，isnotnecessarilythesameasthatoftheprogressivemovementoftheplanets。
\"Aphenomenonnotonlyverydifficulttoexplainunderthishypothesis，butonewhichisevencontrarytoit，istheslighteccentricityoftheplanetaryorbits。
Weknow，bythetheoryofcentralforces，thatifabodymovesinaclosedorbitaroundthesunandtouchesit，italsoalwayscomesbacktothatpointateveryrevolution；
whenceitfollowsthatiftheplanetswereoriginallydetachedfromthesun，theywouldtouchitateachreturntowardsit，andtheirorbits，farfrombeingcircular，wouldbeveryeccentric。Itistruethatamassofmatterdrivenfromthesuncannotbeexactlycomparedtoaglobewhichtouchesitssurface，fortheimpulsewhichtheparticlesofthismassreceivefromoneanotherandthereciprocalattractionswhichtheyexertamongthemselves，could，inchangingthedirectionoftheirmovements，removetheirperihelionsfromthesun；buttheirorbitswouldbealwaysmosteccentric，oratleasttheywouldnothaveslighteccentricitiesexceptbythemostextraordinarychance。Thuswecannotsee，accordingtothehypothesisofBuffon，whytheorbitsofmorethanahundredcometsalreadyobservedaresoelliptical。Thishypothesisisthereforeveryfarfromsatisfyingtheprecedingphenomena。
Letusseeifitispossibletotracethembacktotheirtruecause。
\"Whatevermaybeitsultimatenature，seeingthatithascausedormodifiedthemovementsoftheplanets，itisnecessarythatthiscauseshouldembraceeverybody，and，inviewoftheenormousdistanceswhichseparatethem，itcouldonlyhavebeenafluidofimmenseextent。Inordertohavegiventhemanalmostcircularmovementinthesamedirectionaroundthesun，itisnecessarythatthisfluidshouldhaveenvelopedthesunasinanatmosphere。Theconsiderationoftheplanetarymovementsleadsusthentothinkthat，onaccountofexcessiveheat，theatmosphereofthesunoriginallyextendedbeyondtheorbitsofalltheplanets，andthatitwassuccessivelycontractedtoitspresentlimits。
\"Intheprimitiveconditioninwhichwesupposethesuntohavebeen，itresembledanebulasuchasthetelescopeshowsiscomposedofanucleusmoreorlessbrilliant，surroundedbyanebulositywhich，oncondensingitselftowardsthecentre，formsastar。Ifitisconceivedbyanalogythatallthestarswereformedinthismanner，itispossibletoimaginetheirpreviousconditionofnebulosity，itselfprecededbyotherstatesinwhichthenebulousmatterwasstillmorediffused，thenucleusbeinglessandlessluminous。Bygoingbackasfaraspossible，wethusarriveatanebulositysodiffusedthatitsexistencecouldhardlybesuspected。
\"Foralongtimethepeculiardispositionofcertainstars，visibletotheunaidedeye，hasstruckphilosophicalobservers。MitchellhasalreadyremarkedhowlittleprobableitisthatthestarsinthePleiades，forexample，couldhavebeencontractedintothesmallspacewhichenclosesthembythefortuityofchancealone，andhehasconcludedthatthisgroupofstars，andsimilargroupswhichtheskiespresenttous，arethenecessaryresultofthecondensationofanebula，withseveralnuclei，anditisevidentthatanebula，bycontinuallycontracting，towardsthesevariousnuclei，atlengthwouldformagroupofstarssimilartothePleiades。Thecondensationofanebulawithtwonucleiwouldformasystemofstarsclosetogether，turningoneupontheother，suchasthosedoublestarsofwhichwealreadyknowtherespectivemovements。
\"Buthowdidthesolaratmospheredeterminethemovementsoftherotationandrevolutionoftheplanetsandsatellites？Ifthesebodieshadpenetratedverydeeplyintothisatmosphere，itsresistancewouldhavecausedthemtofallintothesun。Wecanthereforeconjecturethattheplanetswereformedattheirsuccessivelimitsbythecondensationofazoneofvaporswhichthesun，oncooling，leftbehind，intheplaneofhisequator。
\"Letusrecalltheresultswhichwehavegiveninaprecedingchapter。Theatmosphereofthesuncouldnothaveextendedindefinitely。Itslimitwasthepointwherethecentrifugalforceduetoitsmovementofrotationbalanceditsweight。Butinproportionasthecoolingcontractedtheatmosphere，andthosemoleculeswhichwereneartothemcondenseduponthesurfaceofthebody，themovementoftherotationincreased；
for，onaccountoftheLawofAreas，thesumoftheareasdescribedbythevectorofeachmoleculeofthesunanditsatmosphereandprojectedintheplaneoftheequatorbeingalwaysthesame，therotationshouldincreasewhenthesemoleculesapproachthecentreofthesun。Thecentrifugalforceduetothismovementbecomingthuslarger，thepointwheretheweightisequaltoitisnearerthesun。Supposing，then，asitisnaturaltoadmit，thattheatmosphereextendedatsomeperiodtoitsverylimits，itshould，oncooling，leavemoleculesbehindatthislimitandatlimitssuccessivelyoccasionedbytheincreasedrotationofthesun。Theabandonedmoleculeswouldcontinuetorevolvearoundthisbody，sincetheircentrifugalforcewasbalancedbytheirweight。Butthisequilibriumnotarisinginregardtotheatmosphericmoleculesparalleltothesolarequator，thelatter，onaccountoftheirweight，approachedtheatmosphereastheycondensed，anddidnotceasetobelongtoituntilbythismotiontheycameupontheequator。
\"Letusconsidernowthezonesofvaporsuccessivelyleftbehind。Thesezonesought，accordingtoappearance，bythecondensationandmutualattractionoftheirmolecules，toformvariousconcentricringsofvaporrevolvingaroundthesun。Themutualgravitationalfrictionofeachringwouldacceleratesomeandretardothers，untiltheyhadallacquiredthesameangularvelocity。Thustheactualvelocityofthemoleculesmostremovedfromthesunwouldbethegreatest。Thefollowingcausewouldalsooperatetobringaboutthisdifferenceofspeed。Themoleculesfarthestfromthesun，andwhichbytheeffectsofcoolingandcondensationapproachedoneanothertoformtheouterpartofthering，wouldhavealwaysdescribedareasproportionaltothetimesincethecentralforcebywhichtheywerecontrolledhasbeenconstantlydirectedtowardsthisbody。Butthisconstancyofareasnecessitatesanincreaseofvelocityproportionaltothedistance。Itisthusseenthatthesamecausewoulddiminishthevelocityofthemoleculeswhichformtheinnerpartofthering。
\"Ifallthemoleculesoftheringofvaporcontinuedtocondensewithoutdisuniting，theywouldatlengthformaringeithersolidorfluid。Butthisformationwouldnecessitatesucharegularityineverypartofthering，andinitscooling，thatthisphenomenonisextremelyrare；andthesolarsystemaffordsus，indeed，butoneexample——namely，intheringofSaturn。
Innearlyeverycasetheringofvaporwasbrokenintoseveralmasses，eachmovingatsimilarvelocities，andcontinuingtorotateatthesamedistancearoundthesun。Thesemasseswouldtakeaspheroidformwitharotatorymovementinthedirectionoftherevolution，becausetheirinnermoleculeshadlessvelocitythantheouter。Thuswereformedsomanyplanetsinaconditionofvapor。Butifoneofthemwerepowerfulenoughtoreunitesuccessivelybyitsattractionalltheothersarounditscentreofgravity，theringofvaporwouldbethustransformedintoasinglespheroidicalmassofvaporrevolvingaroundthesunwitharotationinthedirectionofitsrevolution。Thelattercasehasbeenthatwhichisthemostcommon，butneverthelessthesolarsystemaffordsusaninstanceofthefirstcaseinthefoursmallplanetswhichmovebetweenJupiterandMars；atleast，ifwedonotsuppose，asdoesM。Olbers，thattheyoriginallyformedasingleplanetwhichamightyexplosionbrokeupintoseveralportionseachmovingatdifferentvelocities。
\"Accordingtoourhypothesis，thecometsarestrangerstoourplanetarysystem。Inconsideringthem，aswehavedone，asminutenebulosities，wanderingfromsolarsystemtosolarsystem，andformedbythecondensationofthenebulousmattereverywhereexistentinprofusionintheuniverse，weseethatwhentheycomeintothatpartoftheheavenswherethesunisall-powerful，heforcesthemtodescribeorbitseitherellipticalorhyperbolic，theirpathsbeingequallypossibleinalldirections，andatallinclinationsoftheecliptic，conformablytowhathasbeenobserved。Thusthecondensationofnebulousmatter，bywhichwehaveatfirstexplainedthemotionsoftherotationandrevolutionoftheplanetsandtheirsatellitesinthesamedirection，andinnearlyapproximateplanes，explainsalsowhythemovementsofthecometsescapethisgenerallaw。\"[3]
ThenebularhypothesisthusgivendetailedcompletionbyLaplaceisaworthycomplementofthegrandcosmologicschemeofHerschel。Whethertrueorfalse，thetwoconceptionsstandasthefinalcontributionsoftheeighteenthcenturytothehistoryofman’sceaselesseffortstosolvethemysteriesofcosmicoriginandcosmicstructure。Theworldlistenedeagerlyandwithoutprejudicetothenewdoctrines；andthatattitudetellsofamarvellousintellectualgrowthofourrace。Markthetransition。Intheyear1600，Brunowasburnedatthestakeforteachingthatourearthisnotthecentreoftheuniverse。In1700，Newtonwaspronounced\"impiousandheretical\"byalargeschoolofphilosophersfordeclaringthattheforcewhichholdstheplanetsintheirorbitsisuniversalgravitation。In1800，LaplaceandHerschelarehonoredforteachingthatgravitationbuiltupthesystemwhichitstillcontrols；
thatouruniverseisbutaminornebula，oursunbutaminorstar，ourearthamereatomofmatter，ourraceonlyoneofmyriadracespeoplinganinfinityofworlds。Doctrineswhichbutthespanoftwohumanlivesbeforewouldhavebroughttheirenunciatorstothestakewerenowpronouncednotimpious，butsublime。
ASTEROIDSANDSATELLITES
Thefirstdayofthenineteenthcenturywasfittinglysignalizedbythediscoveryofanewworld。OntheeveningofJanuary1，1801，anItalianastronomer，Piazzi，observedanapparentstarofabouttheeighthmagnitudehence，ofcourse，quiteinvisibletotheunaidedeye，whichlateronwasseentohavemoved，andwasthusshowntobevastlynearertheearththananytruestar。Heatfirstsupposed，asHerschelhaddonewhenhefirstsawUranus，thattheunfamiliarbodywasacomet；butlaterobservationproveditatinyplanet，occupyingapositioninspacebetweenMarsandJupiter。ItwaschristenedCeres，afterthetutelarygoddessofSicily。
Thoughunpremeditated，thisdiscoverywasnotunexpected，forastronomershadlongsurmisedtheexistenceofaplanetinthewidegapbetweenMarsandJupiter。
Indeed，theywereevenpreparingtomakeconcertedsearchforit，despitetheprotestsofphilosophers，whoarguedthattheplanetscouldnotpossiblyexceedthemagicnumberseven，whenPiazziforestalledtheirefforts。Butasurprisecamewiththesequel；fortheverynextyearDr。Olbers，thewonderfulphysician-
astronomerofBremen，whilefollowingupthecourseofCeres，happenedonanothertinymovingstar，similarlylocated，whichsoonrevealeditselfasplanetary。
Thustwoplanetswerefoundwhereonlyonewasexpected。
Theexistenceofthesupernumerarywasapuzzle，butOlberssolveditforthemomentbysuggestingthatCeresandPallas，ashecalledhiscaptive，mightbefragmentsofaquondamplanet，shatteredbyinternalexplosionorbytheimpactofacomet。Othersimilarfragments，heventuredtopredict，wouldbefoundwhensearchedfor。WilliamHerschelsanctionedthistheory，andsuggestedthenameasteroidsforthetinyplanets。Theexplosiontheorywassupportedbythediscoveryofanotherasteroid，byHarding，ofLilienthal，in1804，anditseemedclinchedwhenOlbershimselffoundafourthin1807。Thenew-comerswerenamedJunoandVestarespectively。
Therethecaserestedtill1845，whenaPrussianamateurastronomernamedHenckefoundanotherasteroid，afterlongsearching，andopenedanewepochofdiscovery。Fromthenonthefindingofasteroidsbecameacommonplace。Latterly，withtheaidofphotography，thelisthasbeenextendedtoabovefourhundred，andasyetthereseemsnodearthinthesupply，thoughdoubtlessallthelargermembershavebeenrevealed。Eventhesearebutafewhundredsofmilesindiameter，whilethesmalleronesaretootinyformeasurement。Thecombinedbulkoftheseminorplanetsisbelievedtobebutafractionofthatoftheearth。
Olbers’sexplosiontheory，longacceptedbyastronomers，hasbeenprovenopentofatalobjections。Theminorplanetsarenowbelievedtorepresentaringofcosmicalmatter，castofffromthesolarnebulaliketheringsthatwenttoformthemajorplanets，butpreventedfrombecomingaggregatedintoasinglebodybytheperturbingmassofJupiter。
TheDiscoveryofNeptuneAswehaveseen，thediscoveryofthefirstasteroidconfirmedaconjecture；theotherimportantplanetarydiscoveryofthenineteenthcenturyfulfilledaprediction。
Neptunewasfoundthroughscientificprophecy。
Noonesuspectedtheexistenceofatrans-UranianplanettillUranusitself，byhair-breadthdeparturesfromitspredictedorbit，gaveoutthesecret。Noonesawthedisturbingplanettillthepencilofthemathematician，withalmostoccultdivination，hadpointedoutitsplaceintheheavens。Thegeneralpredicationofatrans-UranianplanetwasmadebyBessel，thegreatKonigsbergastronomer，in1840；theanalysisthatrevealeditsexactlocationwasundertaken，halfadecadelater，bytwoindependentworkers——JohnCouchAdams，justgraduatedseniorwrangleratCambridge，England，andU。J。J。Leverrier，theleadingFrenchmathematicianofhisgeneration。
Adams’scalculationwasfirstbegunandfirstcompleted。
Butithadoneradicaldefect——itwastheworkofayounganduntriedman。Soitfoundlodgmentinapigeon-holeofthedeskofEngland’sAstronomerRoyal，andanopportunitywaslostwhichEnglishastronomershaveneverceasedtomourn。Hadthesearchbeenmade，anactualplanetwouldhavebeenseenshiningthere，closetothespotwherethepencilofthemathematicianhadplaceditshypotheticalcounterpart。
Butthesearchwasnotmade，andwhiletheprophecyofAdamsgathereddustinthatregrettablepigeon-hole，Leverrier’scalculationwascomingon，histentativeresultsmeetingfullencouragementfromAragoandotherFrenchsavants。Atlastthelaboriouscalculationsprovedsatisfactory，and，confidentoftheresult，LeverriersenttotheBerlinobservatory，requestingthatsearchbemadeforthedisturberofUranusinaparticularspotoftheheavens。Dr。GallereceivedtherequestSeptember23，1846。Thatverynightheturnedhistelescopetotheindicatedregion，andthere，withinasingledegreeofthesuggestedspot，hesawaseemingstar，invisibletotheunaidedeye，whichprovedtobethelong-soughtplanet，henceforthtobeknownasNeptune。Totheaveragemind，whichfindssomethingaltogethermystifyingaboutabstractmathematics，thiswasafeatsavoringofthemiraculous。
Stimulatedbythissuccess，LeverriercalculatedanorbitforaninteriorplanetfromperturbationsofMercury，butthoughprematurelychristenedVulcan，thishypotheticalnurslingofthesunstillhauntstherealmoftheundiscovered，alongwithcertainequallyhypotheticaltrans-Neptunianplanetswhoseexistencehasbeensuggestedby\"residualperturbations\"ofUranus，andbythemovementsofcomets。Nootherveritableadditionsofthesun’splanetaryfamilyhavebeenmadeinourcentury，beyondthefindingofsevensmallmoons，whichchieflyattesttheadvanceintelescopicpowers。
Ofthese，thetinyattendantsofourMartianneighbor，discoveredbyProfessorHallwiththegreatWashingtonrefractor，areofgreatestinterest，becauseoftheirsmallsizeandextremelyrapidflight。OneofthemispoisedonlysixthousandmilesfromMars，andwhirlsabouthimalmostfourtimesasfastasherevolves，seemingthus，asviewedbytheMartian，toriseinthewestandsetintheeast，andmakingthemonthonlyone-fourthaslongastheday。
TheRingsofSaturnThediscoveryoftheinnerorcraperingofSaturn，madesimultaneouslyin1850byWilliamC。Bond，attheHarvardobservatory，inAmerica，andtheRev。
W。R。DawesinEngland，wasanotherinterestingopticalachievement；butourmostimportantadvancesinknowledgeofSaturn’suniquesystemareduetothemathematician。Laplace，likehispredecessors，supposedtheseringstobesolid，andexplainedtheirstabilityasduetocertainirregularitiesofcontourwhichHerschelbadpointedout。Butabout1851ProfessorPeirce，ofHarvard，showedtheuntenabilityofthisconclusion，provingthatweretheringssuchasLaplacethoughtthemtheymustfalloftheirownweight。
ThenProfessorJ。Clerk-Maxwell，ofCambridge，tookthematterinhand，andhisanalysisreducedthepuzzlingringstoacloudofmeteoricparticles——a\"showerofbrickbats\"——eachfragmentofwhichcirculatesexactlyasifitwereanindependentplanet，thoughofcourseperturbedandjostledmoreorlessbyitsfellows。
Mutualperturbations，andthedisturbingpullsofSaturn’sorthodoxsatellites，asinvestigatedbyMaxwell，explainnearlyallthephenomenaoftheringsinamannerhighlysatisfactory。
Afterelaboratemathematicalcalculationscoveringmanypagesofhispaperentitled\"OntheStabilityofSaturn’sRings，\"hesummarizeshisdeductionsasfollows:
\"Letusnowgathertogethertheconclusionswehavebeenabletodrawfromthemathematicaltheoryofvariouskindsofconceivablerings。
\"Wefoundthatthestabilityofthemotionofasolidringdependedonsodelicateanadjustment，andatthesametimesounsymmetricaladistributionofmass，thateveniftheexactconditionswerefulfilled，itcouldscarcelylastlong，and，ifitdid，theimmensepreponderanceofonesideoftheringwouldbeeasilyobserved，contrarytoexperience。Theseconsiderations，withothersderivedfromthemechanicalstructureofsovastabody，compelustoabandonanytheoryofsolidrings。
\"Wenextexaminedthemotionofaringofequalsatellites，andfoundthatifthemassoftheplanetissufficient，anydisturbancesproducedinthearrangementoftheringwillbepropagatedarounditintheformofwaves，andwillnotintroducedangerousconfusion。
Ifthesatellitesareunequal，thepropagationsofthewaveswillnolongerberegular，butdisturbancesoftheringwillinthis，asintheformercase，produceonlywaves，andnotgrowingconfusion。Supposingtheringtoconsist，notofasinglerowoflargesatellites，butacloudofevenlydistributedunconnectedparticles，wefoundthatsuchacloudmusthaveaverysmalldensityinordertobepermanent，andthatthisisinconsistentwithitsouterandinnerpartsmovingwiththesameangularvelocity。Supposingtheringtobefluidandcontinuous，wefoundthatitwillbenecessarilybrokenupintosmallportions。
\"Weconclude，therefore，thattheringsmustconsistofdisconnectedparticles；thesemustbeeithersolidorliquid，buttheymustbeindependent。Theentiresystemofringsmust，therefore，consisteitherofaseriesofmanyconcentricringseachmovingwithitsownvelocityandhavingitsownsystemofwaves，orelseofaconfusedmultitudeofrevolvingparticlesnotarrangedinringsandcontinuallycomingintocollisionwithoneanother。
\"Takingthefirstcase，wefoundthatinanindefinitenumberofpossiblecasesthemutualperturbationsoftworings，stableinthemselves，mightmountupintimetoadestructivemagnitude，andthatsuchcasesmustcontinuallyoccurinanextensivesystemlikethatofSaturn，theonlyretardingcausebeingtheirregularityoftherings。
\"Theresultoflong-continueddisturbancewasfoundtobethespreading-outoftheringsinbreadth，theouterringspressingoutward，whiletheinnerringspressinward。
\"Thefinalresult，therefore，ofthemechanicaltheoryisthattheonlysystemofringswhichcanexistisonecomposedofanindefinitenumberofunconnectedparticles，revolvingaroundtheplanetwithdifferentvelocities，accordingtotheirrespectivedistances。
Theseparticlesmaybearrangedinseriesofnarrowrings，ortheymaymovethroughoneanotherirregularly。Inthefirstcasethedestructionofthesystemwillbeveryslow，inthesecondcaseitwillbemorerapid，buttheremaybeatendencytowardsarrangementinnarrowringswhichmayretardtheprocess。
\"Wearenotabletoascertainbyobservationtheconstitutionofthetwoouterdivisionsofthesystemofrings，buttheinnerringiscertainlytransparent，forthelimbofSaturnhasbeenobservedthroughit。
Itisalsocertainthatthoughthespaceoccupiedbytheringistransparent，itisnotthroughthematerialpartsofitthatthelimbofSaturnisseen，forhislimbwasobservedwithoutdistortion；whichshowsthattherewasnorefraction，and，therefore，thattheraysdidnotpassthroughamediumatall，butbetweenthesolarorliquidparticlesofwhichtheringiscomposed。
Here，then，wehaveanopticalargumentinfavorofthetheoryofindependentparticlesasthematerialoftherings。Thetwoouterringsmaybeofthesamenature，butnotsoexceedinglyrarethatarayoflightcanpassthroughtheirwholethicknesswithoutencounteringoneoftheparticles。
\"Finally，thetwoouterringshavebeenobservedfortwohundredyears，anditappears，fromthecarefulanalysisofalltheobservationsofM。Struve，thatthesecondringisbroaderthanwhenfirstobserved，andthatitsinneredgeisnearertheplanetthanformerly。
Theinnerringalsoissuspectedtobeapproachingtheplaneteversinceitsdiscoveryin1850。Theseappearancesseemtoindicatethesameslowprogressoftheringstowardsseparationwhichwefoundtobetheresultoftheory，andtheremarkthattheinneredgeoftheinnerringismoredistinctseemstoindicatethattheapproachtowardstheplanetislessrapidneartheedge，aswehadreasontoconjecture。Astotheapparentunchangeablenessoftheexteriordiameteroftheouterring，wemustrememberthattheouterringsarecertainlyfarmoredensethantheinnerone，andthatasmallchangeintheouterringsmustbalanceagreatchangeintheinnerone。Itispossible，however，thatsomeoftheobservedchangesmaybeduetotheexistenceofaresistingmedium。Ifthechangesalreadysuspectedshouldbeconfirmedbyrepeatedobservationswiththesameinstruments，itwillbeworthwhiletoinvestigatemorecarefullywhetherSaturn’sringsarepermanentortransitoryelementsofthesolarsystem，andwhetherinthatpartoftheheavensweseecelestialimmutabilityorterrestrialcorruptionandgeneration，andtheoldordergivingplacetothenewbeforeoureyes。\"[4]
StudiesoftheMoonButperhapsthemostinterestingaccomplishmentsofmathematicalastronomy——fromamundanestandpoint，atanyrate——arethosethatrefertotheearth’sownsatellite。Thatseeminglystaidbodywaslongagodiscoveredtohaveapropensitytogainalittleontheearth，appearingateclipsesaninfinitesimalmomentaheadoftime。Astronomersweresorelypuzzledbythisactofinsubordination；butatlastLaplaceandLagrangeexplaineditasduetoanoscillatorychangeintheearth’sorbit，thusfullyexoneratingthemoon，andseemingtodemonstratetheabsolutestabilityofourplanetarysystem，whichthemoon’smisbehaviorhadappearedtothreaten。
Thishighlysatisfactoryconclusionwasanorthodoxbeliefofcelestialmechanicsuntil1853，whenProfessorAdamsofNeptunianfame，withwhomcomplexanalyseswereapastime，reviewedLaplace’scalculation，anddiscoveredanerrorwhich，whencorrected，leftabouthalfthemoon’saccelerationunaccountedfor。
Thiswasamomentousdiscrepancy，whichatfirstnoonecouldexplain。ButpresentlyProfessorHelmholtz，thegreatGermanphysicist，suggestedthatakeymightbefoundintidalfriction，which，actingasaperpetualbrakeontheearth’srotation，andaffectingnotmerelythewatersbuttheentiresubstanceofourplanet，mustinthelongsweepoftimehavechangeditsrateofrotation。Thustheseemingaccelerationofthemoonmightbeaccountedforasactualretardationoftheearth’srotation——alengtheningofthedayinsteadofashorteningofthemonth。
Againtheearthwasshowntobeatfault，butthistimethemooncouldnotbeexonerated，whiletheestimatedstabilityofoursystem，insteadofbeingre-established，wasquiteupset。Forthetidalretardationisnotanoscillatorychangewhichwillpresentlycorrectitself，liketheorbitalwobble，butaperpetualchange，actingalwaysinonedirection。Unlessfullycounteractedbysomeopposingreaction，thereforeasitseemsnottobe，theeffectmustbecumulative，theultimateconsequencesdisastrous。
TheexactcharacteroftheseconsequenceswasfirstestimatedbyProfessorG。H。Darwinin1879。Heshowedthattidalfriction，inretardingtheearth，mustalsopushthemoonoutfromtheparentplanetonaspiralorbit。Plainly，then，themoonmustformerlyhavebeennearertheearththanatpresent。Atsomeveryremoteperioditmusthaveactuallytouchedtheearth；must，inotherwords，havebeenthrownofffromthethenplasticmassoftheearth，asapolypbudsoutfromitsparentpolyp。Atthattimetheearthwasspinningaboutinadayoffromtwotofourhours。
Nowthedayhasbeenlengthenedtotwenty-fourhours，andthemoonhasbeenthrustouttoadistanceofaquarter-millionmiles；buttheendisnotyet。Thesameprogressofeventsmustcontinue，till，atsomeremoteperiodinthefuture，thedayhascometoequalthemonth，lunartidalactionhasceased，andonefaceoftheearthlooksoutalwaysatthemoonwiththatsamefixedstarewhichevennowthemoonhasbeenbroughttoassumetowardsherparentorb。Shouldwechoosetotakeevengreaterlibertieswiththefuture，itmaybemadetoappearthoughsomeastronomersdissentfromthispredictionthat，assolartidalactionstillcontinues，thedaymustfinallyexceedthemonth，andlengthenoutlittlebylittletowardscoincidencewiththeyear；andthatthemoonmeantimemustpauseinitsoutwardflight，andcomeswingingbackonadescendingspiral，untilfinally，afterthelapseofuntoldaeons，itploughsandricochetsalongthesurfaceoftheearth，andplungestocatastrophicdestruction。
Buteventhoughimaginationpausefarshortofthisdirefulculmination，itstillisclearthatmoderncalculations，basedoninexorabletidalfriction，sufficetorevolutionizetheviewsformerlycurrentastothestabilityoftheplanetarysystem。Theeighteenth-centurymathematicianlookeduponthissystemasavastcelestialmachinewhichhadbeeninexistenceaboutsixthousandyears，andwhichwasdestinedtorunonforever。
Theanalystofto-daycomputesboththepastandthefutureofthissysteminmillionsinsteadofthousandsofyears，yetfeelswellassuredthatthesolarsystemoffersnocontradictiontothoselawsofgrowthanddecaywhichseemeverywheretorepresenttheimmutableorderofnature。
COMETSANDMETEORS
Untilthemathematicianferretedoutthesecret，itsurelynevercouldhavebeensuspectedbyanyonethattheearth’ssereneattendant，\"Thatorbedmaiden，withwhitefireladen，Whommortalscallthemoon，\"
couldbeplottinginjurytoherparentorb。Butthereisanotherinhabitantoftheskieswhosepurposeshavenotbeensimilarlyfreefrompopularsuspicion。NeedlesstosayIrefertotheblacksheepofthesiderealfamily，that\"celestialvagabond\"thecomet。
Timeoutofmindthesewanderershavebeensupposedtopresagewar，famine，pestilence，perhapsthedestructionoftheworld。Andlittlewonder。Hereisabodywhichcomesflashingoutofboundlessspaceintooursystem，shootingoutapyrotechnictailsomehundredsofmillionsofmilesinlength；whirling，perhaps，throughtheveryatmosphereofthesunataspeedofthreeorfourhundredmilesasecond；thendartingoffonahyperbolicorbitthatforbidsitevertoreturn，oranellipticalonethatcannotbeclosedforhundredsorthousandsofyears；thetailmeantimepointingalwaysawayfromthesun，andfadingtonothingnessastheweirdvoyagerrecedesintothespatialvoidwhenceitcame。NotmanytimesneedtheadventofsuchanapparitioncoincidewiththeoutbreakofapestilenceorthedeathofaCaesartostamptheraceofcometsasanominousclaninthemindsofallsuperstitiousgenerations。
Itistrue，ahardblowwasstruckattheprestigeoftheseallegedsupernaturalagentswhenNewtonprovedthatthegreatcometof1680obeyedKepler’slawsinitsflightaboutthesun；andanevenharderonewhenthesamevisitantcamebackin1758，obedienttoHalley’sprediction，afteritsthree-quartersofacenturyofvoyagingbutintheabyssofspace。Provedthustobowtonaturallaw，thecelestialmessengercouldnolongerfully，sustainitsrole。Butlong-standingnotorietycannotbeliveddowninaday，andthecomet，thoughproveda\"natural\"object，wasstillregardedasaverymenacingoneforanotherhundredyearsorso。Itremainedforthenineteenthcenturytocompletelyunmaskthepretenderandshowhowegregiouslyourforebearshadbeendeceived。
Theunmaskingbeganearlyinthecentury，whenDr。
Olbers，thenthehighestauthorityonthesubject，expressedtheopinionthatthespectaculartail，whichhadallalongbeenthecomet’schiefstock-in-tradeasanearth-threatener，isinrealitycomposedofthemostfilmyvapors，repelledfromthecometarybodybythesun，presumablythroughelectricalaction，withavelocitycomparabletothatoflight。Thisluminoussuggestionwasheldmoreorlessinabeyanceforhalfacentury。ThenitwaselaboratedbyZollner，andparticularlybyBredichin，oftheMoscowobservatory，intowhathassincebeenregardedasthemostplausibleofcometarytheories。Itisheldthatcometsandthesunaresimilarlyelectrified，andhencemutuallyrepulsive。
Gravitationvastlyoutmatchesthisrepulsioninthebodyofthecomet，butyieldstoitinthecaseofgases，becauseelectricalforcevarieswiththesurface，whilegravitationvariesonlywiththemass。Fromstudyofatomicweightsandestimatesofthevelocityofthrustofcometarytails，Bredichinconcludedthatthechiefcomponentsofthevariouskindsoftailsarehydrogen，hydrocarbons，andthevaporofiron；andspectroscopicanalysisgoesfartowardssustainingtheseassumptions。
But，theoriesaside，theunsubstantialnessofthecomet’stailhasbeenputtoaconclusivetest。Twiceduringthenineteenthcenturytheearthhasactuallyplungeddirectlythroughoneofthesethreateningappendages——in1819，andagainin1861，oncebeingimmersedtoadepthofsomethreehundredthousandmilesinitssubstance。Yetnothingdreadfulhappenedtous。Therewasapeculiarglowintheatmosphere，sothemoreimaginativeobserversthought，andthatwasall。Aftersuchfiascosthecometarytraincouldneveragainposeasaworld-destroyer。
Butthefullmeasureofthecomet’shumiliationisnotyettold。Thepyrotechnictail，composedasitisofportionsofthecomet’sactualsubstance，istributepaidthesun，andcanneverberecovered。Shouldtheobeisancetothesunbemanytimesrepeated，thetrain-formingmaterialwillbeexhausted，andthecomet’schiefestglorywillhavedeparted。SuchafatehasactuallybefallenamultitudeofcometswhichJupiterandtheotheroutlyingplanetshavedraggedintooursystemandhelpedthesuntoholdcaptivehere。Manyofthesetaillesscometswereknowntotheeighteenth-
centuryastronomers，butnooneatthattimesuspectedthetruemeaningoftheircondition。ItwasnotevenknownhowcloselysomeofthemareenchaineduntiltheGermanastronomerEncke，in1822，showedthatonewhichhehadrediscovered，andwhichhassincebornehisname，wasmovinginanorbitsocontractedthatitmustcompleteitscircuitinaboutthreeandahalfyears。Shortlyafterwardsanothercomet，revolvinginaperiodofaboutsixyears，wasdiscoveredbyBiela，andgivenhisname。Onlytwomoreoftheseshort-periodcometswerediscoveredduringthefirsthalfoflastcentury，butlatterlytheyhavebeenshowntobeanumerousfamily。NearlytwentyareknownwhichthegiantJupiterholdssoclosethattheutmostreachoftheirellipticaltetherdoesnotletthemgobeyondtheorbitofSaturn。Theseaforetimewanderershaveadaptedthemselveswonderfullytoplanetarycustoms，forallofthemrevolveinthesamedirectionwiththeplanets，andinplanesnotwideoftheecliptic。
Checkedintheirproudhyperbolicsweep，madecaptiveinaplanetarynet，deprivedoftheirtrains，thesequondamfree-lancesoftheheavensarenowmereshadowsoftheirformerselves。Consideredastomerebulk，theyareverysubstantialshadows，theirextentbeingmeasuredinhundredsofthousandsofmiles；buttheiractualmassissoslightthattheyarequiteatthemercyofthegravitationpullsoftheircaptors。Andworseisinstoreforthem。Sopersistentlydosunandplanetstugatthemthattheyaredoomedpresentlytobetornintoshreds。
Suchafatehasalreadyovertakenoneofthem，undertheveryeyesoftheastronomers，withintherelativelyshortperiodduringwhichtheseill-fatedcometshave。
beenobserved。In1832Biela’scometpassedquiteneartheearth，asastronomersmeasuredistance，andindoingsocreatedapaniconourplanet。Itdidnogreaterharmthanthat，ofcourse，andpassedonitswayasusual。Theverynexttimeitcamewithintelescopichailitwasseentohavebrokenintotwofragments。
Sixyearslaterthesefragmentswereseparatedbymanymillionsofmiles；andin1852，whenthecometwasdueagain，astronomerslookedforitinvain。Ithadbeencompletelyshattered。
Whathadbecomeofthefragments？Atthattimenoonepositivelyknew。Butthequestionwastobeansweredpresently。Itchancedthatjustatthisperiodastronomerswerepayingmuchattentiontoaclassofbodieswhichtheyhadhithertosomewhatneglected，thefamiliarshooting-stars，ormeteors。ThestudiesofProfessorNewton，ofYale，andProfessorAdams，ofCambridge，withparticularreferencetothegreatmeteor-showerofNovember，1866，whichProfessorNewtonhadpredictedandshowntoberecurrentatintervalsofthirty-threeyears，showedthatmeteorsarenotmeresporadicswarmsofmatterflyingatrandom，butexistinisolatedswarms，andsweepaboutthesuninregularellipticalorbits。
PresentlyitwasshownbytheItalianastronomerSchiaparellithatoneofthesemeteorswarmsmovesintheorbitofapreviouslyobservedcomet，andothercoincidencesofthekindweresoonforthcoming。Theconvictiongrewthatmeteorswarmsarereallythedebrisofcomets；andthisconvictionbecameapracticalcertaintywhen，inNovember，1872，theearthcrossedtheorbitoftheill-starredBiela，andashowerofmeteorscamewhizzingintoouratmosphereinlieuofthelostcomet。
Andsoatlastthefullsecretwasout。Theawe-
inspiringcomet，insteadofbeingtheplanetarybodyithadallalongbeenregarded，isreallynothingmorenorlessthanagreataggregationofmeteoricparticles，whichhavebecomeclusteredtogetheroutinspacesomewhere，andwhichbyjostlingoneanotherorthroughelectricalactionbecomeluminous。Sowidelyaretheindividualparticlesseparatedthatthecometarybodyasawholehasbeenestimatedtobethousandsoftimeslessdensethantheearth’satmosphereatsea-
level。Hencetheeasewithwhichthecometmaybedismemberedanditsparticlesstrungoutintostreamingswarms。
Sothicklyisthespacewetraversestrewnwiththiscometarydustthattheearthsweepsup，accordingtoProfessorNewcomb’sestimate，amilliontonsofiteachday。Eachindividualparticle，perhapsnolargerthanamilletseed，becomesashooting-star，ormeteor，asitburnstovaporintheearth’supperatmosphere。Andifonetinyplanetsweepsupsuchmassesofthiscosmicmatter，theamountofitintheentirestretchofoursystemmustbebeyondallestimate。Whatastoryittellsofthemyriadsofcometaryvictimsthathavefallenpreytothesunsincefirsthestretchedhisplanetarynetacrosstheheavens！