第9章

TherelativeinfertilityofBacon’sthoughtisshownbythefactthathefoundednoschoolandleftnotraceofdiscipleship。TheentirecenturyafterhisdeathshowsnosingleEuropeannamethatneedclaimtheattentionofthehistorianofscience。Inthelatterpartofthefifteenthcentury，however，thereisevidenceofarenaissanceofsciencenolessthanofart。TheGermanMullerbecamefamousunderthelatinizednamedofRegioMontanus(1437-1472)，althoughhisactualscientificattainmentswouldappeartohavebeenimportantonlyincomparisonwiththeutterignoranceofhiscontemporaries。ThemostdistinguishedworkerofthenewerawasthefamousItalianLeonardodaVinci——amanwhohasbeencalledbyHamertonthemostuniversalgeniusthateverlived。Leonardo’spositioninthehistoryofartisknowntoeveryone。Withthat，ofcourse，wehavenopresentconcern；butitisworthourwhiletoinquireatsomelengthastothefamouspainter’saccomplishmentsasascientist。

FromapassageintheworksofLeonardo，firstbroughttolightbyVenturi，[1]itwouldseemthatthegreatpainteranticipatedCopernicusindeterminingthemovementoftheearth。Hemademathematicalcalculationstoprovethis，andappearstohavereachedthedefiniteconclusionthattheearthdoesmove——orwhatamountstothesamething，thatthesundoesnotmove。Muntzisauthorityforthestatementthatinoneofhiswritingshedeclares，"Ilsolenonsimouve"——thesundoesnotmove。[2]

Amonghisinventionsisadynamometerfordeterminingthetractionpowerofmachinesandanimals，andhisexperimentswithsteamhaveledsomeofhisenthusiasticpartisanstoclaimforhimprioritytoWattintheinventionofthesteam-engine。Intheseexperiments，however，LeonardoseemstohaveadvancedlittlebeyondHeroofAlexandriaandhissteamtoy。Hero’ssteam-enginedidnothingbutrotateitselfbyvirtueofescapingjetsofsteamforcedfromthebenttubes，whileLeonardo’s"steam-engine""droveaballweighingonetalentoveradistanceofsixstadia。"InamanuscriptnowinthelibraryoftheInstitutdeFrance，DaVincidescribesthisengineminutely。Theactionofthismachinewasduetothesuddenconversionofsmallquantitiesofwaterintosteam("smoke，"ashecalledit)bycomingsuddenlyincontactwithaheatedsurfaceinaproperreceptacle，therapidlyformedsteamactingasapropulsiveforceafterthemannerofanexplosive。Itisreallyasteam-gun，ratherthanasteam-engine，anditisnotunlikelythatthestudyoftheactionofgunpowdermayhavesuggestedittoLeonardo。

ItisbelievedthatLeonardoisthetruediscovererofthecamera-obscura，althoughtheNeapolitanphilosopher，GiambattistaPorta，whowasnotbornuntilsometwentyyearsafterthedeathofLeonardo，isusuallycreditedwithfirstdescribingthisdevice。Thereislittledoubt，however，thatDaVinciunderstoodtheprincipleofthismechanism，forhedescribeshowsuchacameracanbemadebycuttingasmall，roundholethroughtheshutterofadarkenedroom，thereversedimageofobjectsoutsidebeingshownontheoppositewall。

Likeotherphilosophersinallages，hehadobservedagreatnumberoffactswhichhewasunabletoexplaincorrectly。Butsuchaccumulationsofscientificobservationsarealwaysinteresting，asshowinghowmanycenturiesofobservationfrequentlyprecedecorrectexplanation。Heobservedmanyfactsaboutsounds，amongothersthatblowsstruckuponabellproducedsympatheticsoundsinabellofthesamekind；andthatstrikingthestringofaluteproducedvibrationincorrespondingstringsoflutesstrungtothesamepitch。Heknew，also，thatsoundscouldbeheardatadistanceatseabylisteningatoneendofatube，theotherendofwhichwasplacedinthewater；andthatthesameexpedientworkedsuccessfullyonland，theendofthetubebeingplacedagainsttheground。

TheknowledgeofthisgreatnumberofunexplainedfactsisofteninterpretedbytheadmirersofDaVinci，asshowinganalmostoccultinsightintosciencemanycenturiesinadvanceofhistime。Suchinterpretations，however，areillusive。Theobservation，forexample，thatatubeplacedagainstthegroundenablesonetohearmovementsontheearthatadistance，isnotinitselfevidenceofanythingmorethanacutescientificobservation，asasimilarmethodisinuseamongalmosteveryraceofsavages，notablytheAmericanIndians。Ontheotherhand，oneisinclinedtogivecredencetoalmostanystoryofthebreadthofknowledgeofthemanwhocamesonearanticipatingHutton，Lyell，andDarwininhisinterpretationofthegeologicalrecordsashefoundthemwrittenontherocks。

ItisinthisfieldofgeologythatLeonardoisentitledtothegreatestadmirationbymodernscientists。Hehadobservedthedepositoffossilshellsinvariousstrataofrocks，evenonthetopsofmountains，andherejectedonceforallthetheorythattheyhadbeendepositedtherebytheDeluge。Herightlyinterpretedtheirpresenceasevidencethattheyhadoncebeendepositedatthebottomofthesea。Thisprocessheassumedbadtakenhundredsandthousandsofcenturies，thustacitlyrejectingthebiblicaltraditionastothedateofthecreation。

NotwithstandingtheobviousinterestthatattachestotheinvestigationsofLeonardo，itmustbeadmittedthathisworkinscienceremainedalmostasinfertileasthatofhisgreatprecursor，Bacon。Thereallystimulativeworkofthisgenerationwasdonebyamanofaffairs，whoknewlittleoftheoreticalscienceexceptinoneline，butwhopursuedthatonepracticallineuntilheachievedawonderfulresult。ThismanwasChristopherColumbus。Itisnotnecessaryheretotellthetritestoryofhisaccomplishment。Sufficeitthathispracticaldemonstrationoftherotundityoftheearthisregardedbymostmodernwritersasmarkinganepochinhistory。WiththeyearofhisvoyagetheepochoftheMiddleAgesisusuallyregardedascomingtoanend。Itmustnotbesupposedthatanyverysuddenchangecameovertheaspectofscholarshipofthetime，butthepreliminariesofgreatthingshadbeenachieved，andwhenColumbusmadehisfamousvoyagein1492，themanwasalreadyalivewhowastobringforwardthefirstgreatvitalizingthoughtinthefieldofpuresciencethattheWesternworldhadoriginatedformorethanathousandyears。ThismanborethenameofKopernik，orinitsfamiliarAnglicizedform，Copernicus。Hislifeworkandthatofhisdiscipleswillclaimourattentioninthesucceedingchapter。

IV。THENEWCOSMOLOGY——COPERNICUSTOKEPLERANDGALILEO

WehaveseenthatthePtolemaicastronomy，whichwastheaccepteddoctrinethroughouttheMiddleAges，taughtthattheearthisround。Doubtlesstherewasapopularopinioncurrentwhichregardedtheearthasflat，butitmustbeunderstoodthatthisopinionhadnochampionsamongmenofscienceduringtheMiddleAges。When，intheyear1492，Columbussailedouttothewestonhismemorablevoyage，hisexpectationofreachingIndiahadfullscientificwarrant，howevermuchitmayhavebeenscoutedbycertainecclesiasticsandbytheaveragemanoftheperiod。

Nevertheless，wemaywellsupposethatthesuccessfulvoyageofColumbus，andthestillmoredemonstrativeonemadeaboutthirtyyearslaterbyMagellan，gavethetheoryoftheearth’srotundityacertaintyitcouldneverpreviouslyhavehad。Alexandriangeographershadmeasuredthesizeoftheearth，andhadnothesitatedtoassertthatbysailingwestwardonemightreachIndia。Butthereisawidegapbetweentheoryandpractice，anditrequiredthevoyagesofColumbusandhissuccessorstobridgethatgap。

AfterthecompanionsofMagellancompletedthecircumnavigationoftheglobe，thegeneralshapeofourearthwould，obviously，neveragainbecalledinquestion。Butdemonstrationofthesphericityoftheearthhad，ofcourse，nodirectbearinguponthequestionoftheearth’spositionintheuniverse。ThereforethevoyageofMagellanservedtofortify，ratherthantodispute，thePtolemaictheory。Accordingtothattheory，aswehaveseen，theearthwassupposedtolieimmovableatthecentreoftheuniverse；thevariousheavenlybodies，includingthesun，revolvingaboutitineccentriccircles。WehaveseenthatseveraloftheancientGreeks，notablyAristarchus，disputedthisconception，declaringforthecentralpositionofthesunintheuniverse，andthemotionoftheearthandotherplanetsaboutthatbody。Butthisrevolutionarytheoryseemedsoopposedtotheordinaryobservationthat，havingbeendiscountenancedbyHipparchusandPtolemy，itdidnotfindasingleimportantchampionformorethanathousandyearsafterthetimeofthelastgreatAlexandrianastronomer。

Thefirstman，seemingly，toharkbacktotheAristarchianconceptioninthenewscientificerathatwasnowdawningwasthenotedcardinal，NikolausofCusa，wholivedinthefirsthalfofthefifteenthcentury，andwasdistinguishedasaphilosophicalwriterandmathematician。HisDeDoctaIgnorantiaexpresslypropoundsthedoctrineoftheearth’smotion。Noone，however，paidtheslightestattentiontohissuggestion，which，therefore，merelyservestofurnishuswithanotherinterestingillustrationofthefutilityofpropoundingevenacorrecthypothesisbeforethetimeisripetoreceiveit——particularlyifthehypothesisisnotfullyfortifiedbyreasoningbasedonexperimentorobservation。

Themanwhowasdestinedtoputforwardthetheoryoftheearth’smotioninawaytocommandattentionwasbornin1473，atthevillageofThorn，ineasternPrussia。HisnamewasNicholasCopernicus。Thereisnomorefamousnameintheentireannalsofsciencethanthis，yetposterityhasneverbeenablefullytoestablishthelineageofthefamousexpositorofthetruedoctrineofthesolarsystem。ThecityofThornliesinaprovinceofthatborderterritorywhichwasthenundercontrolofPoland，butwhichsubsequentlybecameapartofPrussia。ItisclaimedthattheaspectsofthecitywereessentiallyGerman，anditisadmittedthatthemotherofCopernicusbelongedtothatrace。Thenationalityofthefatherismoreindoubt，butitisurgedthatCopernicususedGermanashismother-tongue。Hisgreatworkwas，ofcourse，writteninLatin，accordingtothecustomofthetime；butitissaidthat，whennotemployingthatlanguage，healwayswroteinGerman。ThedisputednationalityofCopernicusstronglysuggeststhathecameofamixedraciallineage，andweareremindedagainoftheinfluencesofthoseethnicalminglingstowhichwehavepreviouslymorethanoncereferred。TheacknowledgedcentresofcivilizationtowardsthecloseofthefifteenthcenturywereItalyandSpain。Therefore，thebirthplaceofCopernicuslayalmostattheconfinesofcivilization，remindingusofthatearlierperiodwhenGreecewasthecentreofculture，butwhenthegreatGreekthinkerswereborninAsiaMinorandinItaly。

Asayoungman，CopernicusmadehiswaytoViennatostudymedicine，andsubsequentlyhejourneyedintoItalyandremainedtheremanyyears，Abouttheyear1500heheldthechairofmathematicsinacollegeatRome。Subsequentlyhereturnedtohisnativelandandpassedhisremainingyearsthere，dyingatDomkerr，inFrauenburg，EastPrussia，intheyear1543。

ItwouldappearthatCopernicusconceivedtheideaoftheheliocentricsystemoftheuniversewhilehewasacomparativelyyoungman，sinceintheintroductiontohisgreatwork，whichheaddressedtoPopePaulIII。，hestatesthathehasponderedhissystemnotmerelynineyears，inaccordancewiththemaximofHorace，butwellintothefourthperiodofnineyears。ThroughoutaconsiderableportionofthisperiodthegreatworkofCopernicuswasinmanuscript，butitwasnotpublisheduntiltheyearofhisdeath。Thereasonsforthedelayarenotveryfullyestablished。Copernicusundoubtedlytaughthissystemthroughoutthelaterdecadesofhislife。Hehimselftellsusthathehadevenquestionedwhetheritwerenotbetterforhimtoconfinehimselftosuchverbalteaching，followingthustheexampleofPythagoras。Justashislifewasdrawingtoaclose，hedecidedtopursuetheoppositecourse，andthefirstcopyofhisworkissaidtohavebeenplacedinhishandsashelayonhisdeathbed。

TheviolentoppositionwhichthenewsystemmetfromecclesiasticalsourcesledsubsequentcommentatorstosupposethatCopernicushaddelayedpublicationofhisworkthroughfearofthechurchauthorities。Thereseems，however，tobenodirectevidenceforthisopinion。IthasbeenthoughtsignificantthatCopernicusaddressedhisworktothepope。Itis，ofcourse，quiteconceivablethattheagedastronomermightwishbythismeanstodemonstratethathewroteinnospiritofhostilitytothechurch。Hisaddresstothepopemighthavebeenconsideredasadesirableshieldpreciselybecausetheauthorrecognizedthathisworkmustneedsmeetwithecclesiasticalcriticism。Bethatasitmay，Copernicuswasremovedbydeathfromthedangerofattack，anditremainedforhisdisciplesofalatergenerationtorunthegauntletofcriticismandsufferthechargesofheresy。

TheworkofCopernicus，publishedthusintheyear1543atNuremberg，bearsthetitleDeOrbiumCoelestiumRevolutionibus。

ItisnotnecessarytogointodetailsastothecosmologicalsystemwhichCopernicusadvocated，sinceitisfamiliartoeveryone。Inaword，hesupposedthesuntobethecentreofalltheplanetarymotions，theearthtakingitsplaceamongtheotherplanets，thelistofwhich，asknownatthattime，comprisedMercury，Venus，theEarth，Mars，Jupiter，andSaturn。Thefixedstarswereallegedtobestationary，anditwasnecessarytosupposethattheyarealmostinfinitelydistant，inasmuchastheyshowedtotheobserversofthattimenoparallax；thatistosay，theypreservedthesameapparentpositionwhenviewedfromtheoppositepointsoftheearth’sorbit。

ButletusallowCopernicustospeakforhimselfregardinghissystem，Hisexpositionisfullofinterest。Wequotefirsttheintroductionjustreferredto，inwhichappealismadedirectlytothepope。

"Icanwellbelieve，mostholyfather，thatcertainpeople，whentheyhearofmyattributingmotiontotheearthinthesebooksofmine，willatoncedeclarethatsuchanopinionoughttoberejected。Now，myowntheoriesdonotpleasemesomuchasnottoconsiderwhatothersmayjudgeofthem。Accordingly，whenIbegantoreflectuponwhatthosepersonswhoacceptthestabilityoftheearth，asconfirmedbytheopinionofmanycenturies，wouldsaywhenIclaimedthattheearthmoves，IhesitatedforalongtimeastowhetherIshouldpublishthatwhichIhavewrittentodemonstrateitsmotion，orwhetheritwouldnotbebettertofollowtheexampleofthePythagoreans，whousedtohanddownthesecretsofphilosophytotheirrelativesandfriendsonlyinoralform。AsIwellconsideredallthis，Iwasalmostimpelledtoputthefinishedworkwhollyaside，throughthescornIhadreasontoanticipateonaccountofthenewnessandapparentcontrarinesstoreasonofmytheory。

"Myfriends，however，dissuadedmefromsuchacourseandadmonishedmethatIoughttopublishmybook，whichhadlainconcealedinmypossessionnotonlynineyears，butalreadyintofourtimestheninthyear。Notafewotherdistinguishedandverylearnedmenaskedmetodothesamething，andtoldmethatI

oughtnot，onaccountofmyanxiety，todelayanylongerinconsecratingmyworktothegeneralserviceofmathematicians。

"ButyourholinesswillperhapsnotsomuchwonderthatIhavedaredtobringtheresultsofmynightlaborstothelightofday，afterhavingtakensomuchcareinelaboratingthem，butiswaitinginsteadtohearhowitenteredmymindtoimaginethattheearthmoved，contrarytotheacceptedopinionofmathematicians——nay，almostcontrarytoordinaryhumanunderstanding。ThereforeIwillnotconcealfromyourholinessthatwhatmovedmetoconsideranotherwayofreckoningthemotionsoftheheavenlybodieswasnothingelsethanthefactthatthemathematiciansdonotagreewithoneanotherintheirinvestigations。Inthefirstplace，theyaresouncertainaboutthemotionsofthesunandmoonthattheycannotfindoutthelengthofafullyear。Inthesecondplace，theyapplyneitherthesamelawsofcauseandeffect，indeterminingthemotionsofthesunandmoonandofthefiveplanets，northesameproofs。

Someemployonlyconcentriccircles，othersuseeccentricandepicyclicones，withwhich，however，theydonotfullyattainthedesiredend。Theycouldnotevendiscovernorcomputethemainthing——namely，theformoftheuniverseandthesymmetryofitsparts。Itwaswiththemasifsomeshould，fromdifferentplaces，takehands，feet，head，andotherpartsofthebody，which，althoughverybeautiful，werenotdrawnintheirproperrelations，and，withoutmakingtheminanywaycorrespond，shouldconstructamonsterinsteadofahumanbeing。

"Accordingly，whenIhadlongreflectedonthisuncertaintyofmathematicaltradition，ItookthetroubletoreadagainthebooksofallthephilosophersIcouldgetholdof，toseeifsomeoneofthemhadnotoncebelievedthattherewereothermotionsoftheheavenlybodies。FirstIfoundinCicerothatNicetieshadbelievedinthemotionoftheearth。AfterwardsIfoundinPlutarch，likewise，thatsomeothershadheldthesameopinion。

Thisinducedmealsotobegintoconsiderthemovabilityoftheearth，and，althoughthetheoryappearedcontrarytoreason，I

didsobecauseIknewthatothersbeforemehadbeenallowedtoassumerotarymovementsatwill，inordertoexplainthephenomenaofthesecelestialbodies。IwasoftheopinionthatI，too，mightbepermittedtoseewhether，bypresupposingmotionintheearth，morereliableconclusionsthanhithertoreachedcouldnotbediscoveredfortherotarymotionsofthespheres。Andthus，actingonthehypothesisofthemotionwhich，inthefollowingbook，Iascribetotheearth，andbylongandcontinuedobservations，Ihavefinallydiscoveredthatifthemotionoftheotherplanetsbecarriedovertotherelationoftheearthandthisismadethebasisfortherotationofeverystar，notonlywillthephenomenaoftheplanetsbeexplainedthereby，butalsothelawsandthesizeofthestars；alltheirspheresandtheheavensthemselveswillappearsoharmoniouslyconnectedthatnothingcouldbechangedinanypartofthemwithoutconfusionintheremainingpartsandinthewholeuniverse。IdonotdoubtthatcleverandlearnedmenwillagreewithmeiftheyarewillingfullytocomprehendandtoconsidertheproofswhichI

advanceinthebookbeforeus。Inorder，however，thatboththelearnedandtheunlearnedmayseethatIfearnoman’sjudgment，Iwantedtodedicatethese，mynightlabors，toyourholiness，ratherthantoanyoneelse，becauseyou，eveninthisremotecorneroftheearthwhereIlive，areheldtobethegreatestindignityofstationandinloveforallsciencesandformathematics，sothatyou，throughyourpositionandjudgment，caneasilysuppressthebitesofslanderers，althoughtheproverbsaysthatthereisnoremedyagainstthebiteofcalumny。"

InchapterX。ofbookI。，"OntheOrderoftheSpheres，"occursamoredetailedpresentationofthesystem，asfollows:

"ThatwhichMartianusCapella，andafewotherLatins，verywellknew，appearstomeextremelynoteworthy。HebelievedthatVenusandMercuryrevolveaboutthesunastheircentreandthattheycannotgofartherawayfromitthanthecirclesoftheirorbitspermit，sincetheydonotrevolveabouttheearthliketheotherplanets。Accordingtothistheory，then，Mercury’sorbitwouldbeincludedwithinthatofVenus，whichismorethantwiceasgreat，andwouldfindroomenoughwithinitforitsrevolution。

"If，actinguponthissupposition，weconnectSaturn，Jupiter，andMarswiththesamecentre，keepinginmindthegreaterextentoftheirorbits，whichincludetheearth’sspherebesidesthoseofMercuryandVenus，wecannotfailtoseetheexplanationoftheregularorderoftheirmotions。HeiscertainthatSaturn，Jupiter，andMarsarealwaysnearesttheearthwhentheyriseintheevening——thatis，whentheyappearoveragainstthesun，ortheearthstandsbetweenthemandthesun——butthattheyarefarthestfromtheearthwhentheysetintheevening——thatis，whenwehavethesunbetweenthemandtheearth。ThisprovessufficientlythattheircentrebelongstothesunandisthesameaboutwhichtheorbitsofVenusandMercurycircle。Since，however，allhaveonecentre，itisnecessaryforthespaceinterveningbetweentheorbitsofVenusandMarstoincludetheearthwithheraccompanyingmoonandallthatisbeneaththemoon；forthemoon，whichstandsunquestionablynearesttheearth，caninnowaybeseparatedfromher，especiallyasthereissufficientroomforthemoonintheaforesaidspace。Hencewedonothesitatetoclaimthatthewholesystem，whichincludesthemoonwiththeearthforitscentre，makestheroundofthatgreatcirclebetweentheplanets，inyearlymotionaboutthesun，andrevolvesaboutthecentreoftheuniverse，inwhichthesunrestsmotionless，andthatallwhichlookslikemotioninthesunisexplainedbythemotionoftheearth。Theextentoftheuniverse，however，issogreatthat，whereasthedistanceoftheearthfromthesunisconsiderableincomparisonwiththesizeoftheotherplanetaryorbits，itdisappearswhencomparedwiththesphereofthefixedstars。Iholdthistobemoreeasilycomprehensiblethanwhenthemindisconfusedbyanalmostendlessnumberofcircles，whichisnecessarilythecasewiththosewhokeeptheearthinthemiddleoftheuniverse。Althoughthismayappearincomprehensibleandcontrarytotheopinionofmany，Ishall，ifGodwills，makeitclearerthanthesun，atleasttothosewhoarenotignorantofmathematics。

"Theorderofthespheresisasfollows:Thefirstandlightestofallthespheresisthatofthefixedstars，whichincludesitselfandallothers，andhenceismotionlessastheplaceintheuniversetowhichthemotionandpositionofallotherstarsisreferred。

"Thenfollowstheoutermostplanet，Saturn，whichcompletesitsrevolutionaroundthesuninthirtyyears；nextcomesJupiterwithatwelveyears’revolution；thenMars，whichcompletesitscourseintwoyears。Thefourthoneinorderistheyearlyrevolutionwhichincludestheearthwiththemoon’sorbitasanepicycle。InthefifthplaceisVenuswitharevolutionofninemonths。ThesixthplaceistakenbyMercury，whichcompletesitscourseineightydays。Inthemiddleofallstandsthesun，andwhocouldwishtoplacethelampofthismostbeautifultempleinanotherorbetterplace。Thus，infact，thesun，seatedupontheroyalthrone，controlsthefamilyofthestarswhichcirclearoundhim。Wefindintheirorderaharmoniousconnectionwhichcannotbefoundelsewhere。HeretheattentiveobservercanseewhythewaxingandwaningofJupiterseemsgreaterthanwithSaturnandsmallerthanwithMars，andagaingreaterwithVenusthanwithMercury。Also，whySaturn，Jupiter，andMarsarenearertotheearthwhentheyriseintheeveningthanwhentheydisappearintheraysofthesun。Moreprominently，however，isitseeninthecaseofMars，whichwhenitappearsintheheavensatnight，seemstoequalJupiterinsize，butsoonafterwardsisfoundamongthestarsofsecondmagnitude。Allofthisresultsfromthesamecause——namely，fromtheearth’smotion。Thefactthatnothingofthisistobeseeninthecaseofthefixedstarsisaproofoftheirimmeasurabledistance，whichmakeseventheorbitofyearlymotionoritscounterpartinvisibletous。"[1]

Thefactthatthestarsshownoparallaxhadbeenregardedasanimportantargumentagainstthemotionoftheearth，anditwasstillsoconsideredbytheopponentsofthesystemofCopernicus。

Ithad，indeed，beennecessaryforAristarchustoexplainthefactasduetotheextremedistanceofthestars；aperfectlycorrectexplanation，butonethatimpliesdistancesthatarealtogetherinconceivable。Itremainedfornineteenth-centuryastronomerstoshow，withtheaidofinstrumentsofgreaterprecision，thatcertainofthestarshaveaparallax。Butlongbeforethisdemonstrationhadbeenbroughtforward，thesystemofCopernicushadbeenacceptedasapartofcommonknowledge。

WhileCopernicuspostulatedacosmicalschemethatwascorrectastoitsmainfeatures，hedidnotaltogetherbreakawayfromcertaindefectsofthePtolemaichypothesis。Indeed，heseemstohaveretainedasmuchofthisaspracticable，indeferencetotheprejudiceofhistime。Thusherecordstheplanetaryorbitsascircular，andexplainstheireccentricitiesbyresortingtothetheoryofepicycles，quiteafterthePtolemaicmethod。Butnow，ofcourse，amuchmoresimplemechanismsufficedtoexplaintheplanetarymotions，sincetheorbitswerecorrectlyreferredtothecentralsunandnottotheearth。

Needlesstosay，therevolutionaryconceptionofCopernicusdidnotmeetwithimmediateacceptance。Anumberofprominentastronomers，however，tookitupalmostatonce，amongthesebeingRhaeticus，whowroteacommentaryontheevolutions；

ErasmusReinhold，theauthorofthePrutenictables；Rothmann，astronomertotheLandgraveofHesse，andMaestlin，theinstructorofKepler。ThePrutenictables，justreferredto，socalledbecauseoftheirPrussianorigin，wereconsideredanimprovementonthetablesofCopernicus，andwerehighlyesteemedbytheastronomersofthetime。ThecommentaryofRhaeticusgivesustheinterestinginformationthatitwastheobservationoftheorbitofMarsandoftheverygreatdifferencebetweenhisapparentdiametersatdifferenttimeswhichfirstledCopernicustoconceivetheheliocentricidea。OfReinholditisrecordedthatheconsideredtheorbitofMercuryelliptical，andthatheadvocatedatheoryofthemoon，accordingtowhichherepicyclerevolvedonanellipticalorbit，thusinameasureanticipatingoneofthegreatdiscoveriesofKeplertowhichweshallreferpresently。TheLandgraveofHessewasapracticalastronomer，whoproducedacatalogueoffixedstarswhichhasbeencomparedwiththatofTychoBrahe。HewasassistedbyRothmannandbyJustusByrgius。Maestlin，thepreceptorofKepler，isreputedtohavebeenthefirstmodernobservertogiveacorrectexplanationofthelightseenonportionsofthemoonnotdirectlyilluminedbythesun。Heexplainedthisasnotduetoanyproperlightofthemoonitself，butaslightreflectedfromtheearth。CertainoftheGreekphilosophers，however，aresaidtohavegiventhesameexplanation，anditisallegedalsothatLeonardodaVincianticipatedMaestlininthisregard。[2]

While，variousastronomersofsomeeminencethusgavesupporttotheCopernicansystem，almostfromthebeginning，itunfortunatelychancedthatbyfarthemostfamousoftheimmediatesuccessorsofCopernicusdeclinedtoacceptthetheoryoftheearth’smotion。ThiswasTychoBrahe，oneofthegreatestobservingastronomersofanyage。TychoBrahewasaDane，bornatKnudstrupintheyear1546。Hediedin1601atPrague，inBohemia。DuringaconsiderableportionofhislifehefoundapatroninFrederick，KingofDenmark，whoassistedhimtobuildasplendidobservatoryontheIslandofHuene。OnthedeathofhispatronTychomovedtoGermany，where，asgoodluckwouldhaveit，hecameincontactwiththeyouthfulKepler，andthus，nodoubt，wasinstrumentalinstimulatingtheambitionsofonewhoinlateryearswastobeknownasafargreatertheoristthanhimself。Ashasbeensaid，TychorejectedtheCopernicantheoryoftheearth’smotion。Itshouldbeadded，however，thatheacceptedthatpartoftheCopernicantheorywhichmakesthesunthecentreofalltheplanetarymotions，theearthbeingexcepted。Hethusdevelopedasystemofhisown，whichwasinsomesortacompromisebetweenthePtolemaicandtheCopernicansystems。AsTychoconceivedit，thesunrevolvesabouttheearth，carryingwithittheplanets-Mercury，Venus，Mars，Jupiter，andSaturn，whichplanetshavethesunandnottheearthasthecentreoftheirorbits。Thiscosmicalscheme，itshouldbeadded，maybemadetoexplaintheobservedmotionsoftheheavenlybodies，butitinvolvesamuchmorecomplexmechanismthanispostulatedbytheCopernicantheory。

VariousexplanationshavebeenofferedoftheconservatismwhichheldthegreatDanishastronomerbackfromfullacceptanceoftherelativelysimpleand，aswenowknow，correctCopernicandoctrine。Fromourlatter-daypointofview，itseemssomuchmorenaturaltoacceptthantorejecttheCopernicansystem，thatwefinditdifficulttoputourselvesintheplaceofasixteenth-centuryobserver。Yetifwerecallthatthetraditionalview，havingwarrantofacceptancebynearlyallthinkersofeveryage，recordedtheearthasafixed，immovablebody，weshallseethatoursurpriseshouldbeexcitedratherbythethinkerwhocanbreakawayfromthisviewthanbytheonewhostilltendstoclingtoit。

Moreover，itisuselesstoattempttodisguisethefactthatsomethingmorethanamerevaguetraditionwassupposedtosupporttheideaoftheearth’sovershadowingimportanceinthecosmicalscheme。Thesixteenth-centurymindwasovermasteredbythetenetsofecclesiasticism，anditwasadangerousheresytodoubtthattheHebrewwritings，uponwhichecclesiasticismbaseditsclaim，containedthelastwordregardingmattersofscience。

ButthewritersoftheHebrewtexthadbeenundertheinfluenceofthatBabylonianconceptionoftheuniversewhichacceptedtheearthasunqualifiedlycentral——which，indeed，hadneversomuchasconceivedacontradictoryhypothesis；andsotheWesternworld，whichhadcometoacceptthesewritingsasactuallysupernaturalinorigin，layunderthespellofOrientalideasofapre-scientificera。Inourownday，noonespeakingwithauthoritythinksoftheseHebrewwritingsashavinganyscientificweightwhatever。Theirinterestinthisregardispurelyantiquarian；hencefromourchangedpointofviewitseemsscarcelycrediblethatTychoBrahecanhavebeeninearnestwhenhequotestheHebrewtraditionsasproofthatthesunrevolvesabouttheearth。YetweshallseethatforalmostthreecenturiesafterthetimeofTycho，thesesamedreamingscontinuedtobecitedinoppositiontothosescientificadvanceswhichnewobservationsmadenecessary；andthisnotwithstandingthefactthattheOrientalphrasingis，forthemostpart，poeticallyambiguousandsusceptibleofshiftinginterpretations，asthecriticismofsuccessivegenerationshasamplytestified。

Aswehavesaid，TychoBrahe，greatobserverashewas，couldnotshakehimselffreefromtheOrientalincubus。Hebeganhisobjections，then，totheCopernicansystembyquotingtheadversetestimonyofaHebrewprophetwholivedmorethanathousandyearsB。C。AllofthisshowssufficientlythatTychoBrahewasnotagreattheorist。Hewasessentiallyanobserver，butinthisregardhewonasecureplaceintheveryfirstrank。Indeed，hewaseasilythegreatestobservingastronomersinceHipparchus，betweenwhomandhimselfthereweremanypointsofresemblance。

Hipparchus，itwillberecalled，rejectedtheAristarchianconceptionoftheuniversejustasTychorejectedtheconceptionofCopernicus。

ButifTychopropoundednogreatgeneralizations，thelistofspecificadvancesduetohimisalongone，andsomeoftheseweretoproveimportantaidsinthehandsoflaterworkerstothesecuredemonstrationoftheCopernicanidea。Oneofhismostimportantseriesofstudieshadtodowithcomets。Regardingthesebodiestherehadbeenthegreatestuncertaintyinthemindsofastronomers。Thegreatestvarietyofopinionsregardingthemprevailed；theywerethoughtontheonehandtobedivinemessengers，andontheothertobemerelyigneousphenomenaoftheearth’satmosphere。TychoBrahedeclaredthatacometwhichheobservedintheyear1577hadnoparallax，provingitsextremedistance。Theobservedcourseofthecometintersectedtheplanetaryorbits，whichfactgaveaquietustothelong-mootedquestionastowhetherthePtolemaicspheresweretransparentsolidsormerelyimaginary；sincethecometwasseentointersecttheseallegedspheres，itwasobviousthattheycouldnotbethesolidsubstancethattheywerecommonlyimaginedtobe，andthisfactinitselfwentfartowardsdiscreditingthePtolemaicsystem。Itshouldberecalled，however，thatthissuppositionoftangiblespheresforthevariousplanetaryandstellarorbitswasamediaevalinterpretationofPtolemy’stheoryratherthananinterpretationofPtolemyhimself，therebeingnothingtoshowthattheAlexandrianastronomerregardedhiscyclesandepicyclesasotherthantheoretical。

AninterestingpracticaldiscoverymadebyTychowashismethodofdeterminingthelatitudeofaplacebymeansoftwoobservationsmadeatanintervaloftwelvehours。Hithertoithadbeennecessarytoobservethesun’sangleontheequinoctialdays，aperiodofsixmonthsbeingthereforerequired。Tychomeasuredtheangleofelevationofsomestarsituatednearthepole，whenonthemeridian，andthen，twelvehourslater，measuredtheangleofelevationofthesamestarwhenitagaincametothemeridianattheoppositepointofitsapparentcircleaboutthepolestar。Halfthesumoftheseanglesgivesthelatitudeoftheplaceofobservation。

AsillustratingtheaccuracyofTycho’sobservations，itmaybenotedthatherediscoveredathirdinequalityofthemoon’smotionatitsvariation，he，incommonwithotherEuropeanastronomers，beingthenquiteunawarethatthisinequalityhadbeenobservedbyanArabianastronomer。Tychoprovedalsothattheangleofinclinationofthemoon’sorbittotheeclipticissubjecttoslightvariation。

TheverybrilliantnewstarwhichshoneforthsuddenlyintheconstellationofCassiopeiaintheyear1572，wasmadetheobjectofspecialstudiesbyTycho，whoprovedthatthestarhadnosensibleparallaxandconsequentlywasfarbeyondtheplanetaryregions。Theappearanceofanewstarwasaphenomenonnotunknowntotheancients，sincePlinyrecordsthatHipparchuswasledbysuchanappearancetomakehiscatalogueofthefixedstars。Butthephenomenonissufficientlyuncommontoattractunusualattention。Asimilarphenomenonoccurredintheyear1604，whenthenewstar——inthiscaseappearingintheconstellationofSerpentarius——wasexplainedbyKeplerasprobablyproceedingfromavastcombustion。Thisexplanation——inwhichKeplerissaidtohavefollowed。Tycho——isfullyinaccordwiththemostrecenttheoriesonthesubject，asweshallseeinduecourse。ItissurprisingtohearTychocreditedwithsostartlingatheory，but，ontheotherhand，suchanexplanationispreciselywhatshouldbeexpectedfromtheotherastronomernamed。ForJohannKepler，or，ashewasoriginallynamed，JohannvonKappel，wasoneofthemostspeculativeastronomersofanyage。Hewasforevertheorizing，butsuchwasthepeculiarqualityofhismindthathistheoriesneversatisfiedhimforlongunlesshecouldputthemtothetestofobservation。Thankstothishappycombinationofqualities，Keplerbecamethediscovererofthreefamouslawsofplanetarymotionwhichlieattheveryfoundationofmodernastronomy，andwhichweretobelargelyinstrumentalinguidingNewtontohisstillgreatergeneralization。TheselawsofplanetarymotionwerevastlyimportantascorroboratingtheCopernicantheoryoftheuniverse，thoughtheirpositioninthisregardwasnotimmediatelyrecognizedbycontemporarythinkers。Letusexaminewithsomedetailintotheirdiscovery，meantimecatchingaglimpseofthelifehistoryoftheremarkablemanwhosenametheybear。

JOHANNKEPLERANDTHELAWSOFPLANETARYMOTION

JohannKeplerwasbornthe27thofDecember，1571，inthelittletownofWeil，inWurtemburg。Hewasaweak，sicklychild，furtherenfeebledbyasevereattackofsmall-pox。Itwouldseemparadoxicaltoassertthattheparentsofsuchageniusweremismated，buttheirhomewasnotahappyone，themotherbeingofanervoustemperament，whichperhapsinsomemeasureaccountedforthegeniusofthechild。Thefatherledthelifeofasoldier，andfinallyperishedinthecampaignagainsttheTurks。

YoungKepler’sstudiesweredirectedwithaneyetotheministry。

AfterapreliminarytrainingheattendedtheuniversityatTubingen，wherehecameundertheinfluenceofthecelebratedMaestlinandbecamehislife-longfriend。

Curiouslyenough，itisrecordedthatatfirstKeplerhadnotasteforastronomyorformathematics。Butthedoorsoftheministrybeingpresentlybarredtohim，heturnedwithenthusiasmtothestudyofastronomy，beingfromthefirstanardentadvocateoftheCopernicansystem。Histeacher，Maestlin，acceptedthesamedoctrine，thoughhewasobliged，fortheologicalreasons，toteachthePtolemaicsystem，asalsotoopposetheGregorianreformofthecalendar。

TheGregoriancalendar，itshouldbeexplained，issocalledbecauseitwasinstitutedbyPopeGregoryXIII。，whoputitintoeffectintheyear1582，uptowhichtimetheso-calledJuliancalendar，asintroducedbyJuliusCaesar，hadbeeneverywhereacceptedinChristendom。ThisJuliancalendar，aswehaveseen，wasagreatimprovementonprecedingones，butstilllackedsomethingofperfectioninasmuchasitstheoreticaldaydifferedappreciablyfromtheactualday。Inthecourseoffifteenhundredyears，sincethetimeofCaesar，thisdefectamountedtoadiscrepancyofaboutelevendays。PopeGregoryproposedtocorrectthisbyomittingtendaysfromthecalendar，whichwasdoneinSeptember，1582。Topreventsimilarinaccuraciesinthefuture，theGregoriancalendarprovidedthatonceinfourcenturiestheadditionaldaytomakealeap-yearshouldbeomitted，thedateselectedforsuchomissionbeingthelastyearofeveryfourthcentury。Thustheyears1500，1900，and2300，A。D。，wouldnotbeleap-years。Bythisarrangementanapproximaterectificationofthecalendarwaseffected，thougheventhisdoesnotmakeitabsolutelyexact。

Sucharectificationasthiswasobviouslydesirable，buttherewasreallynonecessityfortheomissionofthetendaysfromthecalendar。Theequinoctialdayhadshiftedsothatintheyear1582itfellonthe10thofMarchandSeptember。Therewasnoreasonwhyitshouldnothaveremainedthere。ItwouldgreatlyhavesimplifiedthetaskoffuturehistorianshadGregorycontentedhimselfwithprovidingforthefuturestabilityofthecalendarwithoutmakingtheneedlessshiftinquestion。Wearesoaccustomedtothinkofthe21stofMarchand21stofSeptemberasthenaturalperiodsoftheequinox，thatwearelikelytoforgetthatthesearepurelyarbitrarydatesforwhichthe10thmighthavebeensubstitutedwithoutanyinconvenienceorinconsistency。

Buttheoppositiontothenewcalendar，towhichreferencehasbeenmade，wasnotbasedonanysuchconsiderationsasthese。Itwasdue，largelyatanyrate，tothefactthatGermanyatthistimewasunderswayoftheLutheranrevoltagainstthepapacy。SoeffectivewastheoppositionthattheGregoriancalendardidnotcomeintovogueinGermanyuntiltheyear1699。ItmaybeaddedthatEngland，understressofthesamemannerofprejudice，heldoutagainstthenewreckoninguntiltheyear1751，whileRussiadoesnotacceptitevennow。

AstheProtestantleadersthusopposedthepapalattitudeinamatterofsopracticalacharacterasthecalendar，itmightperhapshavebeenexpectedthattheLutheranswouldhavehadaleaningtowardstheCopernicantheoryoftheuniverse，sincethistheorywasopposedbythepapacy。Such，however，wasnotthecase。Lutherhimselfpointedoutwithgreatstrenuousness，asafinalanddemonstrativeargument，thefactthatJoshuacommandedthesunandnottheearthtostandstill；andhisfollowerswerequiteasintoleranttowardsthenewteachingasweretheirultramontaneopponents。Keplerhimselfwas，atvarioustimes，tofeeltherestraintofecclesiasticalopposition，thoughhewasneversubjectedtodirectpersecution，aswashisfriendandcontemporary，Galileo。AttheveryoutsetofKepler’scareertherewas，indeed，questionastothepublicationofaworkhehadwritten，becausethatworktookforgrantedthetruthoftheCopernicandoctrine。Thisworkappeared，however，intheyear1596。ItborethetitleMysteriumCosmographium，anditattemptedtoexplainthepositionsofthevariousplanetarybodies。

Copernicushaddevotedmuchtimetoobservationoftheplanetswithreferencetomeasuringtheirdistance，andhiseffortshadbeenattendedwithconsiderablesuccess。Hedidnot，indeed，knowtheactualdistanceofthesun，and，therefore，wasquiteunabletofixthedistanceofanyplanet；but，ontheotherhand，hedeterminedtherelativedistanceofalltheplanetsthenknown，asmeasuredintermsofthesun’sdistance，withremarkableaccuracy。

Withthesemeasurementsasaguide，Keplerwasledtoaveryfancifultheory，accordingtowhichtheorbitsofthefiveprincipalplanetssustainapeculiarrelationtothefiveregularsolidsofgeometry。Histheorywasthis:"Aroundtheorbitoftheearthdescribeadodecahedron——thecirclecomprisingitwillbethatofMars；aroundMarsdescribeatetrahedron——thecirclecomprisingitwillbethatofJupiter；aroundJupiterdescribeacube——thecirclecomprisingitwillbethatofSaturn；nowwithintheearth’sorbitinscribeanicosahedron——theinscribedcirclewillbethatofVenus；intheorbitofVenusinscribeanoctahedron——thecircleinscribedwillbethatofMercury。"[3]

Thoughthisarrangementwasafancifulone，whichnoonewouldnowrecallhadnotthetheorizerobtainedsubsequentfameonmoresubstantialgrounds，yetitevidencedaphilosophicalspiritonthepartoftheastronomerwhich，misdirectedasitwasinthisinstance，promisedwellforthefuture。TychoBrahe，towhomacopyoftheworkwassent，hadtheacumentorecognizeitasaworkofgenius。HesummonedtheyoungastronomertobehisassistantatPrague，andnodoubttheassociationthusbegunwasinstrumentalindeterminingthecharacterofKepler’sfuturework。Itwaspreciselythetraininginminuteobservationthatcouldavailmostforamindwhich，likeKepler’s，tendedinstinctivelytotheformulationoftheories。WhenTychoBrahedied，in1601，Keplerbecamehissuccessor。Induetimehesecuredaccesstoalltheunpublishedobservationsofhisgreatpredecessor，andthesewereofinestimablevaluetohimintheprogressofhisownstudies。

Keplerwasnotonlyanardentworkerandanenthusiastictheorizer，buthewasanindefatigablewriter，anditpleasedhimtotakethepublicfullyintohisconfidence，notmerelyastohissuccesses，butastohisfailures。Thushisworkselaboratefalsetheoriesaswellascorrectones，anddetailtheobservationsthroughwhichtheincorrectguesseswererefutedbytheiroriginator。Someoftheseaccountsarehighlyinteresting，buttheymustnotdetainushere。Forourpresentpurposeitmustsufficetopointoutthethreeimportanttheories，which，asculledfromamongascoreorsoofincorrectones，Keplerwasabletodemonstratetohisownsatisfactionandtothatofsubsequentobservers。Statedinafewwords，thesetheories，whichhavecometobearthenameofKepler’sLaws，arethefollowing:

1。Thattheplanetaryorbitsarenotcircular，butelliptical，thesunoccupyingonefocusoftheellipses。

2。Thatthespeedofplanetarymotionvariesindifferentpartsoftheorbitinsuchawaythatanimaginarylinedrawnfromthesuntotheplanet——thatistosay，theradiusvectoroftheplanet’sorbit——alwayssweepsthesameareainagiventime。

ThesetwolawsKeplerpublishedasearlyas1609。Manyyearsmoreofpatientinvestigationwererequiredbeforehefoundoutthesecretoftherelationbetweenplanetarydistancesandtimesofrevolutionwhichhisthirdlawexpresses。In1618，however，hewasabletoformulatethisrelationalso，asfollows:

3。Thesquaresofthedistanceofthevariousplanetsfromthesunareproportionaltothecubesoftheirperiodsofrevolutionaboutthesun。

Alltheselaws，itwillbeobserved，takeforgrantedthefactthatthesunisthecentreoftheplanetaryorbits。Itmustbeunderstood，too，thattheearthisconstantlyregarded，inaccordancewiththeCopernicansystem，asbeingitselfamemberoftheplanetarysystem，subjecttopreciselythesamelawsastheotherplanets。LongfamiliarityhasmadethesewonderfullawsofKeplerseemsuchamatterofcoursethatitisdifficultnowtoappreciatethemattheirfullvalue。Yet，ashasbeenalreadypointedout，itwastheknowledgeofthesemarvellouslysimplerelationsbetweentheplanetaryorbitsthatlaidthefoundationfortheNewtonianlawofuniversalgravitation。Contemporaryjudgmentcouldnot，ofcourse，anticipatethisculminationofalatergeneration。WhatitcouldunderstandwasthatthefirstlawofKeplerattackedoneofthemosttime-honoredofmetaphysicalconceptions——namely，theAristotelianideathatthecircleistheperfectfigure，andhencethattheplanetaryorbitsmustbecircular。NotevenCopernicushaddoubtedthevalidityofthisassumption。ThatKeplerdareddisputesofirmlyfixedabelief，andonethatseeminglyhadsosoundaphilosophicalbasis，evidencedtheiconoclasticnatureofhisgenius。Thathedidnotrestcontentuntilhehaddemonstratedthevalidityofhisrevolutionaryassumptionshowshowtrulythisgreattheorizermadehishypothesessubservienttothemostrigidinductions。

GALILEOGALILEI

WhileKeplerwassolvingtheseriddlesofplanetarymotion，therewasanevenmorefamousmaninItalywhosechampionshipoftheCopernicandoctrinewasdestinedtogivethegreatestpossiblepublicitytothenewideas。ThiswasGalileoGalilei，oneofthemostextraordinaryscientificobserversofanyage。GalileowasbornatPisa，onthe18thofFebruary(oldstyle)，1564。Thedayofhisbirthisdoublymemorable，sinceonthesamedaythegreatestItalianoftheprecedingepoch，MichaelAngelo，breathedhislast。PersonsfondofsymbolismhavefoundinthecoincidenceaforecastofthetransitfromtheartistictothescientificepochofthelaterRenaissance。Galileocameofanimpoverishednoblefamily。Hewaseducatedfortheprofessionofmedicine，butdidnotprogressfarbeforehisnaturalproclivitiesdirectedhimtowardsthephysicalsciences。MeetingwithoppositioninPisa，heearlyacceptedacalltothechairofnaturalphilosophyintheUniversityofPadua，andlaterinlifehemadehishomeatFlorence。ThemechanicalandphysicaldiscoveriesofGalileowillclaimourattentioninanotherchapter。OurpresentconcerniswithhiscontributiontotheCopernicantheory。

GalileohimselfrecordsinalettertoKeplerthathebecameaconverttothistheoryatanearlyday。Hewasnotenabled，however，tomakeanymarkedcontributiontothesubject，beyondtheinfluenceofhisgeneralteachings，untilabouttheyear1610。Thebrilliantcontributionswhichhemadewereduelargelytoasinglediscovery——namely，thatofthetelescope。Hithertotheastronomicalobservationshadbeenmadewiththeunaidedeye。

Glasslenseshadbeenknownsincethethirteenthcentury，but，untilnow，noonehadthoughtoftheirpossibleuseasaidstodistantvision。Thequestionofpriorityofdiscoveryhasneverbeensettled。Itisadmitted，however，thatthechiefhonorsbelongtotheopticiansoftheNetherlands。

Asearlyastheyear1590theDutchopticianZachariasJensenplacedaconcaveandaconvexlensrespectivelyattheendsofatubeabouteighteenincheslong，andusedthisinstrumentforthepurposeofmagnifyingsmallobjects——producing，inshort，acrudemicroscope。Someyearslater，JohannesLippershey，ofwhomnotmuchisknownexceptthathediedin1619，experimentedwithasomewhatsimilarcombinationoflenses，andmadethestartlingobservationthattheweather-vaneonadistantchurch-steepleseemedtobebroughtmuchnearerwhenviewedthroughthelens。

Thecombinationoflensesheemployedisthatstillusedintheconstructionofopera-glasses；theGermansstillcallsuchacombinationaDutchtelescope。

Doubtlessalargenumberofexperimenterstookthematterupandthefameofthenewinstrumentspreadrapidlyabroad。Galileo，downinItaly，heardrumorsofthisremarkablecontrivance，throughtheuseofwhichitwassaid"distantobjectsmightbeseenasclearlyasthosenearathand。"Heatoncesettoworktoconstructforhimselfasimilarinstrument，andhiseffortsweresofarsuccessfulthatatfirsthe"sawobjectsthreetimesasnearandninetimesenlarged。"Continuinghisefforts，hepresentlysoimprovedhisglassthatobjectswereenlargedalmostathousandtimesandmadetoappearthirtytimesnearerthanwhenseenwiththenakedeye。Naturallyenough，Galileoturnedthisfascinatinginstrumenttowardstheskies，andhewasalmostimmediatelyrewardedbyseveralstartlingdiscoveries。Attheveryoutset，hismagnifying-glassbroughttoviewavastnumberofstarsthatareinvisibletothenakedeye，andenabledtheobservertoreachtheconclusionthatthehazylightoftheMilkyWayismerelyduetotheaggregationofavastnumberoftinystars。

Turninghistelescopetowardsthemoon，Galileofoundthatbodyroughandearth-likeincontour，itssurfacecoveredwithmountains，whoseheightcouldbeapproximatelymeasuredthroughstudyoftheirshadows。Thiswasdisquieting，becausethecurrentAristoteliandoctrinesupposedthemoon，incommonwiththeplanets，tobeaperfectlyspherical，smoothbody。Themetaphysicalideaofaperfectuniversewassuretobedisturbedbythisseeminglyroughworkmanshipofthemoon。Thusfar，however，therewasnothingintheobservationsofGalileotobeardirectlyupontheCopernicantheory；butwhenaninspectionwasmadeoftheplanetsthecasewasquitedifferent。Withtheaidofhistelescope，GalileosawthatVenus，forexample，passesthroughphasespreciselysimilartothoseofthemoon，due，ofcourse，tothesamecause。Here，then，wasdemonstrativeevidencethattheplanetsaredarkbodiesreflectingthelightofthesun，andanexplanationwasgivenofthefact，hithertourgedinoppositiontotheCopernicantheory，thattheinferiorplanetsdonotseemmanytimesbrighterwhennearertheearththanwheninthemostdistantpartsoftheirorbits；theexplanationbeing，ofcourse，thatwhentheplanetsarebetweentheearthandthesunonlyasmallportionoftheirilluminedsurfacesisvisiblefromtheearth。

OninspectingtheplanetJupiter，astillmorestrikingrevelationwasmade，asfourtinystarswereobservedtooccupyanequatorialpositionnearthatplanet，andwereseen，whenwatchednightafternight，tobecirclingabouttheplanet，preciselyasthemooncirclesabouttheearth。Here，obviously，wasaminiaturesolarsystem——atangibleobject-lessonintheCopernicantheory。InhonoroftherulingFlorentinehouseoftheperiod，GalileonamedthesemoonsofJupiter，Mediceanstars。

Turningattentiontothesunitself，Galileoobservedonthesurfaceofthatluminaryaspotorblemishwhichgraduallychangeditsshape，suggestingthatchangesweretakingplaceinthesubstanceofthesun——changesobviouslyincompatiblewiththeperfectconditiondemandedbythemetaphysicaltheorists。Buthoweverdisquietingfortheconservative，thesun’sspotsservedamostusefulpurposeinenablingGalileotodemonstratethatthesunitselfrevolvesonitsaxis，sinceagivenspotwasseentopassacrossthediskandafterdisappearingtoreappearinduecourse。Theperiodofrotationwasfoundtobeabouttwenty-fourdays。

Itmustbeaddedthatvariousobserversdisputedpriorityofdiscoveryofthesun’sspotswithGalileo。Unquestionablyasun-spothadbeenseenbyearlierobservers，andbythemmistakenforthetransitofaninferiorplanet。Keplerhimselfhadmadethismistake。Beforethedayofthetelescope，hehadviewedtheimageofthesunasthrownonascreeninacamera-obscura，andhadobservedaspotonthediskwhichbeinterpretedasrepresentingtheplanetMercury，butwhich，asisnowknown，musthavebeenasun-spot，sincetheplanetarydiskistoosmalltohavebeenrevealedbythismethod。Suchobservationsasthese，howeverinteresting，cannotbeclaimedasdiscoveriesofthesun-spots。Itisprobable，however，thatseveraldiscoverers(notablyJohannFabricius)madethetelescopicobservationofthespots，andrecognizedthemashavingtodowiththesun’ssurface，almostsimultaneouslywithGalileo。OneoftheseclaimantswasaJesuitnamedScheiner，andthejealousyofthismanissaidtohavehadashareinbringingaboutthatpersecutiontowhichwemustnowrefer。

ThereisnomorefamousincidentinthehistoryofsciencethantheheresytrialthroughwhichGalileowasledtothenominalrenunciationofhischerisheddoctrines。Thereisscarcelyanotherincidentthathasbeencommenteduponsovariously。Eachsucceedinggenerationhasputitsowninterpretationonit。Thefacts，however，havebeenbutlittlequestioned。Itappearsthatintheyear1616thechurchbecameatlastarousedtotheimplicationsoftheheliocentricdoctrineoftheuniverse。

ApparentlyitseemedcleartothechurchauthoritiesthattheauthorsoftheBiblebelievedtheworldtobeimmovablyfixedatthecentreoftheuniverse。Such，indeed，wouldseemtobethenaturalinferencefromvariousfamiliarphrasesoftheHebrewtext，andwhatwenowknowofthestatusofOrientalscienceinantiquitygivesfullwarranttothisinterpretation。Thereisnoreasontosupposethattheconceptionofthesubordinateplaceoftheworldinthesolarsystemhadeversomuchasoccurred，evenasavaguespeculation，totheauthorsofGenesis。Incommonwiththeircontemporaries，theybelievedtheearthtobetheall-importantbodyintheuniverse，andthesunaluminaryplacedintheskyforthesolepurposeofgivinglighttotheearth。

Thereisnothingstrange，nothinganomalous，inthisview；itmerelyreflectsthecurrentnotionsofOrientalpeoplesinantiquity。WhatisstrangeandanomalousisthefactthattheOrientaldreamingsthusexpressedcouldhavebeensupposedtorepresenttheacmeofscientificknowledge。YetsuchaholdhadthesewritingstakenupontheWesternworldthatnotevenaGalileodaredcontradictthemopenly；andwhenthechurchfathersgravelydeclaredtheheliocentrictheorynecessarilyfalse，becausecontradictorytoScripture，therewereprobablyfewpeopleinChristendomwhosementalattitudewouldpermitthemjustlytoappreciatethehumorofsuchapronouncement。And，indeed，ifhereandthereamanmighthaverisentosuchanappreciation，therewereabundantreasonsfortherepressionoftheimpulse，fortherewasnothinghumorousabouttheresponsewithwhichtheauthoritiesofthetimewerewonttomeettheexpressionoficonoclasticopinions。TheburningatthestakeofGiordanoBruno，intheyear1600，was，forexample，anobject-lessonwellcalculatedtorestraintheenthusiasmofothersimilarlymindedteachers。

DoubtlessitwassuchconsiderationsthatexplainedtherelativesilenceofthechampionsoftheCopernicantheory，accountingfortheotherwiseinexplicablefactthatabouteightyyearselapsedafterthedeathofCopernicushimselfbeforeasingletext-bookexpoundedhistheory。Thetext-bookwhichthenappeared，underdateof1622，waswrittenbythefamousKepler，whoperhapswasshieldedinameasurefromthepapalconsequencesofsuchhardihoodbythefactofresidenceinaProtestantcountry。NotthattheProtestantsofthetimefavoredtheheliocentricdoctrine——wehavealreadyquotedLutherinanadversesense——butofcourseitwascharacteristicoftheReformationtempertoopposeanypapalpronouncement，hencetheultramontanedeclarationof1616mayindirectlyhaveaidedthedoctrinewhichitattacked，bymakingthatdoctrinelessobnoxioustoLutheraneyes。Bethatasitmay，theworkofKeplerbroughtitsauthorintonodirectconflictwiththeauthorities。Buttheresultwasquitedifferentwhen，in1632，Galileoatlastbrokesilenceandgavetheworld，undercoveroftheformofdialogue，anelaborateexpositionoftheCopernicantheory。Galileo，itmustbeexplained，hadpreviouslybeenwarnedtokeepsilentonthesubject，hencehispublicationdoublyoffendedtheauthorities。

Tobesure，hecouldreplythathisdialogueintroducedachampionofthePtolemaicsystemtodisputewiththeupholderoftheoppositeview，andthat，bothviewsbeingpresentedwithfullarrayofargument，thereaderwaslefttoreachaverdictforhimself，theauthorhavingnowherepointedlyexpressedanopinion。Butsuchanargument，ofcourse，wasspecious，fornoonewhoreadthedialoguecouldbeindoubtastotheopinionoftheauthor。Moreover，itwashintedthatSimplicio，thecharacterwhoupheldthePtolemaicdoctrineandwhowaseverywhereworstedintheargument，wasintendedtorepresentthepopehimself——asuggestionwhichprobablydidnogoodtoGalileo’scause。

ThecharacterofGalileo’sartisticpresentationmaybestbejudgedfromanexample，illustratingthevigorousassaultofSalviati，thechampionofthenewtheory，andthefeebleretortsofhisconservativeantagonist:

"Salviati。Letusthenbeginourdiscussionwiththeconsiderationthat，whatevermotionmaybeattributedtotheearth，yetwe，asdwellersuponit，andhenceasparticipatorsinitsmotion，cannotpossiblyperceiveanythingofit，presupposingthatwearetoconsideronlyearthlythings。Ontheotherhand，itisjustasnecessarythatthissamemotionbelongapparentlytoallotherbodiesandvisibleobjects，which，beingseparatedfromtheearth，donottakepartinitsmotion。Thecorrectmethodtodiscoverwhetheronecanascribemotiontotheearth，andwhatkindofmotion，is，therefore，toinvestigateandobservewhetherinbodiesoutsidetheearthaperceptiblemotionmaybediscoveredwhichbelongstoallalike。Becauseamovementwhichisperceptibleonlyinthemoon，forinstance，andhasnothingtodowithVenusorJupiterorotherstars，cannotpossiblybepeculiartotheearth，norcanitsseatbeanywhereelsethaninthemoon。Nowthereisonesuchuniversalmovementwhichcontrolsallothers——namely，thatwhichthesun，moon，theotherplanets，thefixedstars——inshort，thewholeuniverse，withthesingleexceptionoftheearth——appearstoexecutefromeasttowestinthespaceoftwenty-fourhours。Thisnow，asitappearsatthefirstglanceanyway，mightjustaswellbeamotionoftheearthaloneasofalltherestoftheuniversewiththeexceptionoftheearth，forthesamephenomenawouldresultfromeitherhypothesis。Beginningwiththemostgeneral，Iwillenumeratethereasonswhichseemtospeakinfavoroftheearth’smotion。Whenwemerelyconsidertheimmensityofthestarrysphereincomparisonwiththesmallnessoftheterrestrialball，whichiscontainedmanymilliontimesintheformer，andthenthinkoftherapidityofthemotionwhichcompletesawholerotationinonedayandnight，Icannotpersuademyselfhowanyonecanholdittobemorereasonableandcrediblethatitistheheavenlyspherewhichrotates，whiletheearthstandsstill。

"Simplicio。Idonotwellunderstandhowthatpowerfulmotionmaybesaidtoasgoodasnotexistforthesun，themoon，theotherplanets，andtheinnumerablehostoffixedstars。Doyoucallthatnothingwhenthesungoesfromonemeridiantoanother，risesupoverthishorizonandsinksbehindthatone，bringsnowday，andnownight；whenthemoongoesthroughsimilarchanges，andtheotherplanetsandfixedstarsinthesameway？

"Salviati。Allthechangesyoumentionaresuchonlyinrespecttotheearth。Toconvinceyourselfofit，onlyimaginetheearthoutofexistence。Therewouldthenbenorisingandsettingofthesunorofthemoon，nohorizon，nomeridian，noday，nonight——inshort，thesaidmotioncausesnochangeofanysortintherelationofthesuntothemoonortoanyoftheotherheavenlybodies，betheyplanetsorfixedstars。Allchangesareratherinrespecttotheearth；theymayallbereducedtothesimplefactthatthesunisfirstvisibleinChina，theninPersia，afterwardsinEgypt，Greece，France，Spain，America，etc。，andthatthesamethinghappenswiththemoonandtheotherheavenlybodies。Exactlythesamethinghappensandinexactlythesamewayif，insteadofdisturbingsolargeapartoftheuniverse，youlettheearthrevolveaboutitself。Thedifficultyis，however，doubled，inasmuchasasecondveryimportantproblempresentsitself。If，namely，thatpowerfulmotionisascribedtotheheavens，itisabsolutelynecessarytoregarditasopposedtotheindividualmotionofalltheplanets，everyoneofwhichindubitablyhasitsownveryleisurelyandmoderatemovementfromwesttoeast。If，ontheotherhand，youlettheearthmoveaboutitself，thisoppositionofmotiondisappears。

"Theimprobabilityistripledbythecompleteoverthrowofthatorderwhichrulesalltheheavenlybodiesinwhichtherevolvingmotionisdefinitelyestablished。Thegreaterthesphereisinsuchacase，somuchlongeristhetimerequiredforitsrevolution；thesmallerthespheretheshorterthetime。Saturn，whoseorbitsurpassesthoseofalltheplanetsinsize，traversesitinthirtyyears。Jupiter[4]completesitssmallercourseintwelveyears，Marsintwo；themoonperformsitsmuchsmallerrevolutionwithinamonth。JustasclearlyintheMediceanstars，weseethattheonenearestJupitercompletesitsrevolutioninaveryshorttime——aboutforty-twohours；thenextinaboutthreeandone-halfdays，thethirdinseven，andthemostdistantoneinsixteendays。Thisrule，whichisfollowedthroughout，willstillremainifweascribethetwenty-four-hourlymotiontoarotationoftheearth。If，however，theearthisleftmotionless，wemustgofirstfromtheveryshortruleofthemoontoevergreaterones——tothetwo-yearlyruleofMars，fromthattothetwelve-yearlyoneofJupiter，fromheretothethirty-yearlyoneofSaturn，andthensuddenlytoanincomparablygreatersphere，towhichalsowemustascribeacompleterotationintwenty-fourhours。If，however，weassumeamotionoftheearth，therapidityoftheperiodsisverywellpreserved；fromtheslowestsphereofSaturnwecometothewhollymotionlessfixedstars。Wealsoescapetherebyafourthdifficulty，whicharisesassoonasweassumethatthereismotioninthesphereofthestars。Imeanthegreatunevennessinthemovementoftheseverystars，someofwhichwouldhavetorevolvewithextraordinaryrapidityinimmensecircles，whileothersmovedveryslowlyinsmallcircles，sincesomeofthemareatagreater，othersataless，distancefromthepole。Thatislikewiseaninconvenience，for，ontheonehand，weseeallthosestars，themotionofwhichisindubitable，revolveingreatcircles，while，ontheotherhand，thereseemstobelittleobjectinplacingbodies，whicharetomoveincircles，atanenormousdistancefromthecentreandthenletthemmoveinverysmallcircles。Andnotonlyarethesizeofthedifferentcirclesandtherewiththerapidityofthemovementverydifferentinthedifferentfixedstars，butthesamestarsalsochangetheirorbitsandtheirrapidityofmotion。Thereinconsiststhefifthinconvenience。Thosestars，namely，whichwereattheequatortwothousandyearsago，andhencedescribedgreatcirclesintheirrevolutions，mustto-daymovemoreslowlyandinsmallercircles，becausetheyaremanydegreesremovedfromit。

Itwillevenhappen，afternotsoverylongatime，thatoneofthosewhichhavehithertobeencontinuallyinmotionwillfinallycoincidewiththepoleandstandstill，butafteraperiodofreposewillagainbegintomove。Theotherstarsinthemeanwhile，whichunquestionablymove，allhave，aswassaid，agreatcircleforanorbitandkeepthisunchangeably。

"Theimprobabilityisfurtherincreased——thismaybeconsideredthesixthinconvenience——bythefactthatitisimpossibletoconceivewhatdegreeofsoliditythoseimmensespheresmusthave，inthedepthsofwhichsomanystarsarefixedsoenduringlythattheyarekeptrevolvingevenlyinspiteofsuchdifferenceofmotionwithoutchangingtheirrespectivepositions。Orif，accordingtothemuchmoreprobabletheory，theheavensarefluid，andeverystardescribesanorbitofitsown，accordingtowhatlawthen，orforwhatreason，aretheirorbitssoarrangedthat，whenlookedatfromtheearth，theyappeartobecontainedinonesinglesphere？Toattainthisitseemstomemucheasierandmoreconvenienttomakethemmotionlessinsteadofmoving，justasthepaving-stonesonthemarket-place，forinstance，remaininordermoreeasilythantheswarmsofchildrenrunningaboutonthem。

"Finally，theseventhdifficulty:Ifweattributethedailyrotationtothehigherregionoftheheavens，weshouldhavetoendowitwithforceandpowersufficienttocarrywithittheinnumerablehostofthefixedstars——everyoneabodyofverygreatcompassandmuchlargerthantheearth——andalltheplanets，althoughthelatter，liketheearth，movenaturallyinanoppositedirection。Inthemidstofallthisthelittleearth，singleandalone，wouldobstinatelyandwilfullywithstandsuchforce——asuppositionwhich，itappearstome，hasmuchagainstit。Icouldalsonotexplainwhytheearth，afreelypoisedbody，balancingitselfaboutitscentre，andsurroundedonallsidesbyafluidmedium，shouldnotbeaffectedbytheuniversalrotation。

Suchdifficulties，however，donotconfrontusifweattributemotiontotheearth——suchasmall，insignificantbodyincomparisonwiththewholeuniverse，andwhichforthatveryreasoncannotexerciseanypoweroverthelatter。

"Simplicio。Yousupportyourargumentsthroughout，itseemstome，onthegreatereaseandsimplicitywithwhichthesaideffectsareproduced。Youmeanthatasacausethemotionoftheearthaloneisjustassatisfactoryasthemotionofalltherestoftheuniversewiththeexceptionoftheearth；youholdtheactualeventtobemucheasierintheformercasethaninthelatter。Fortheruleroftheuniverse，however，whosemightisinfinite，itisnolesseasytomovetheuniversethantheearthorastrawbalm。Butifhispowerisinfinite，whyshouldnotagreater，ratherthanaverysmall，partofitberevealedtome？

"Salviati。IfIhadsaidthattheuniversedoesnotmoveonaccountoftheimpotenceofitsruler，Ishouldhavebeenwrongandyourrebukewouldhavebeeninorder。Iadmitthatitisjustaseasyforaninfinitepowertomoveahundredthousandastomoveone。WhatIsaid，however，doesnotrefertohimwhocausesthemotion，buttothatwhichismoved。Inanswertoyourremarkthatitismorefittingforaninfinitepowertorevealalargepartofitselfratherthanalittle，Ianswerthat，inrelationtotheinfinite，onepartisnotgreaterthananother，ifbotharefinite。Henceitisunallowabletosaythatahundredthousandisalargerpartofaninfinitenumberthantwo，althoughtheformerisfiftythousandtimesgreaterthanthelatter。If，therefore，weconsiderthemovingbodies，wemustunquestionablyregardthemotionoftheearthasamuchsimplerprocessthanthatoftheuniverse；if，furthermore，wedirectourattentiontosomanyothersimplificationswhichmaybereachedonlybythistheory，thedailymovementoftheearthmustappearmuchmoreprobablethanthemotionoftheuniversewithouttheearth，for，accordingtoAristotle’sjustaxiom，’Frustrafitperplura，quodpotestfieriperpauciora’(Itisvaintoexpendmanymeanswhereafewaresufficient)。"[2]

Theworkwaswidelycirculated，anditwasreceivedwithaninterestwhichbespeaksawide-spreadundercurrentofbeliefintheCopernicandoctrine。Naturallyenough，itattractedimmediateattentionfromthechurchauthorities。GalileowassummonedtoappearatRometodefendhisconduct。Thephilosopher，whowasnowinhisseventiethyear，pleadedageandinfirmity。HehadnodesireforpersonalexperienceofthetribunaloftheInquisition；butthemandatewasrepeated，andGalileowenttoRome。There，aseveryoneknows，hedisavowedanyintentiontoopposetheteachingsofScripture，andformallyrenouncedthehereticaldoctrineoftheearth’smotion。Accordingtoatalewhichsolongpassedcurrentthateveryhistorianmuststillrepeatitthoughnoonenowbelievesitauthentic，Galileoqualifiedhisrenunciationbymutteringtohimself，"Epursimuove"(Itdoesmove，nonetheless)，asherosetohisfeetandretiredfromthepresenceofhispersecutors。Thetaleisoneofthosefictionswhichthedramaticsenseofhumanityiswonttoimposeuponhistory，but，likemostsuchfictions，itexpressesthespiritifnottheletteroftruth；forjustasnoonebelievesthatGalileo’slipsutteredthephrase，sonoonedoubtsthattherebelliouswordswereinhismind。

Afterhisformalrenunciation，Galileowasallowedtodepart，butwiththeinjunctionthatheabstaininfuturefromhereticalteaching。Theremainingtenyearsofhislifeweredevotedchieflytomechanics，wherehisexperimentsfortunatelyopposedtheAristotelianratherthantheHebrewteachings。Galileo’sdeathoccurredin1642，ahundredyearsafterthedeathofCopernicus。Keplerhaddiedthirteenyearsbefore，andthereremainednoastronomerinthefieldwhoisconspicuousinthehistoryofscienceasachampionoftheCopernicandoctrine。Butintruthitmightbesaidthatthetheorynolongerneededachampion。TheresearchesofKeplerandGalileohadproducedamassofevidencefortheCopernicantheorywhichamountedtodemonstration。Agenerationortwomightberequiredforthisevidencetomakeitselfeverywhereknownamongmenofscience，andofcoursetheecclesiasticalauthoritiesmustbeexpectedtostandbytheirgunsforasomewhatlongerperiod。Inpointoffact，theecclesiasticalbanwasnottechnicallyremovedbythestrikingoftheCopernicanbooksfromthelistoftheIndexExpurgatoriusuntiltheyear1822，almosttwohundredyearsafterthedateofGalileo’sdialogue。Butthis，ofcourse，isinnosenseaguidetothestateofgeneralopinionregardingthetheory。Weshallgainatruegaugeastothisifweassumethatthegreaternumberofimportantthinkershadacceptedtheheliocentricdoctrinebeforethemiddleoftheseventeenthcentury，andthatbeforethecloseofthatcenturytheoldPtolemaicideahadbeenquiteabandoned。Awonderfulrevolutioninman’sestimateoftheuniversehadthusbeeneffectedwithinabouttwocenturiesafterthebirthofCopernicus。

V。GALILEOANDTHENEWPHYSICS

AfterGalileohadfeltthestronghandoftheInquisition，in1632，hewascarefultoconfinehisresearches，oratleasthispublications，totopicsthatseemedfreefromtheologicalimplications。Indoingsoherevertedtothefieldofhisearlieststudies——namely，thefieldofmechanics；andtheDialoghidelleNuoveScienze，whichhefinishedin1636，andwhichwasprintedtwoyearslater，attainedacelebritynolessthanthatofthehereticaldialoguethathadprecededit。Thelaterworkwasfreefromallapparentheresies，yetperhapsitdidmoretowardstheestablishmentoftheCopernicandoctrine，throughtheteachingofcorrectmechanicalprinciples，thantheotherworkhadaccomplishedbyamoredirectmethod。

Galileo’sastronomicaldiscoverieswere，aswehaveseen，inasenseaccidental；atleast，theyreceivedtheirinceptionthroughtheinventivegeniusofanother。Hismechanicaldiscoveries，ontheotherhand，werethenaturaloutputofhisowncreativegenius。Attheverybeginningofhiscareer，whileyetaveryyoungman，thoughaprofessorofmathematicsatPisa，hehadbegunthatonslaughtupontheoldAristotelianideaswhichhewastocontinuethroughouthislife。AtthefamousleaningtowerinPisa，theyoungiconoclastperformed，intheyear1590，oneofthemosttheatricaldemonstrationsinthehistoryofscience。

Assemblingamultitudeofchampionsoftheoldideas，heproposedtodemonstratethefalsityoftheAristoteliandoctrinethatthevelocityoffallingbodiesisproportionatetotheirweight。

ThereisperhapsnofactmorestronglyillustrativeofthetemperoftheMiddleAgesthanthefactthatthisdoctrine，astaughtbytheAristotelianphilosopher，shouldsolonghavegoneunchallenged。Now，however，itwasputtothetest；Galileoreleasedahalf-poundweightandahundred-poundcannon-ballfromnearthetopofthetower，and，needlesstosay，theyreachedthegroundtogether。Ofcourse，thespectatorswerebutlittlepleasedwithwhattheysaw。Theycouldnotdoubttheevidenceoftheirownsensesastotheparticularexperimentinquestion；

theycouldsuggest，however，thattheexperimentinvolvedaviolationofthelawsofnaturethroughthepracticeofmagic。Tocontrovertsofirmlyestablishedanideasavoredofheresy。Theyoungmanguiltyofsuchiconoclasmwasnaturallylookedataskancebythescholarshipofhistime。Insteadofbeingapplauded，hewashissed，andhefounditexpedientpresentlytoretirefromPisa。

Fortunately，however，thenewspiritofprogresshadmadeitselffeltmoreeffectivelyinsomeotherportionsofItaly，andsoGalileofoundarefugeandafollowinginPadua，andafterwardsinFlorence；andwhile，aswehaveseen，hewasobligedtocurbhisenthusiasmregardingthesubjectthatwasperhapsnearesthisheart——thepromulgationoftheCopernicantheory——yethewaspermittedinthemaintocarryonhisexperimentalobservationsunrestrained。Theseexperimentsgavehimaplaceofunquestionedauthorityamonghiscontemporaries，andtheyhavetransmittedhisnametoposterityasthatofoneofthegreatestofexperimentersandthevirtualfounderofmodernmechanicalscience。Theexperimentsinquestionrangeoverawidefield；butforthemostparttheyhavetodowithmovingbodiesandwithquestionsofforce，or，asweshouldnowsay，ofenergy。Theexperimentattheleaningtowershowedthatthevelocityoffallingbodiesisindependentoftheweightofthebodies，providedtheweightissufficienttoovercometheresistanceoftheatmosphere。Laterexperimentswithfallingbodiesledtothediscoveryoflawsregardingtheacceleratedvelocityoffall。Suchvelocitieswerefoundtobearasimplerelationtotheperiodoftimefromthebeginningofthefall。Otherexperiments，inwhichballswereallowedtorolldowninclinedplanes，corroboratedtheobservationthatthepullofgravitationgaveavelocityproportionatetothelengthoffall，whethersuchfallweredirectorinaslantingdirection。

Thesestudieswereassociatedwithobservationsonprojectiles，regardingwhichGalileowasthefirsttoentertaincorrectnotions。Accordingtothecurrentidea，aprojectilefired，forexample，fromacannon，movedinastraighthorizontallineuntilthepropulsiveforcewasexhausted，andthenfelltothegroundinaperpendicularline。Galileotaughtthattheprojectilebeginstofallatonceonleavingthemouthofthecannonandtraversesaparaboliccourse。Accordingtohisidea，whichisnowfamiliartoeveryone，acannon-balldroppedfromthelevelofthecannon’smuzzlewillstrikethegroundsimultaneouslywithaballfiredhorizontallyfromthecannon。Astotheparaboloidcoursepursuedbytheprojectile，theresistanceoftheairisafactorwhichGalileocouldnotaccuratelycompute，andwhichinterfereswiththepracticalrealizationofhistheory。Butthisisaminorconsideration。Thegreatimportanceofhisideaconsistsintherecognitionthatsuchaforceasthatofgravitationactsinpreciselythesamewayuponallunsupportedbodies，whetherornotsuchbodiesbeatthesametimeacteduponbyaforceoftranslation。

Outofthesestudiesofmovingbodieswasgraduallydevelopedacorrectnotionofseveralimportantgenerallawsofmechanics——lawsaknowledgeofwhichwasabsolutelyessentialtotheprogressofphysicalscience。Thebeliefintherotationoftheearthmadenecessaryaclearconceptionthatallbodiesatthesurfaceoftheearthpartakeofthatmotionquiteindependentlyoftheirvariousobservedmotionsinrelationtooneanother。Thisideawashardtograsp，asanoft-repeatedargumentshows。Itwasassertedagainandagainthat，iftheearthrotates，astonedroppedfromthetopofatowercouldnotfallatthefootofthetower，sincetheearth’smotionwouldsweepthetowerfarawayfromitsoriginalpositionwhilethestoneisintransit。

Thiswasoneofthestockargumentsagainsttheearth’smotion，yetitwasonethatcouldberefutedwiththegreatesteasebyreasoningfromstrictlyanalogousexperiments。Itmightreadilybeobserved，forexample，thatastonedroppedfromamovingcartdoesnotstrikethegrounddirectlybelowthepointfromwhichitisdropped，butpartakesoftheforwardmotionofthecart。Ifanyonedoubtthishehasbuttojumpfromamovingcarttobegivenapracticaldemonstrationofthefactthathisentirebodywasinsomewayinfluencedbythemotionoftranslation。

Similarly，thesimpleexperimentoftossingaballfromthedeckofamovingshipwillconvinceanyonethattheballpartakesofthemotionoftheship，sothatitcanbemanipulatedpreciselyasifthemanipulatorwerestandingontheearth。Inshort，every-dayexperiencegivesusillustrationsofwhatmightbecalledcompoundmotion，whichmakesitseemaltogetherplausiblethat，iftheearthisinmotion，objectsatitssurfacewillpartakeofthatmotioninawaythatdoesnotinterferewithanyothermovementstowhichtheymaybesubjected。AstheCopernicandoctrinemadeitsway，thisideaofcompoundmotionnaturallyreceivedmoreandmoreattention，andsuchexperimentsasthoseofGalileopreparedthewayforanewinterpretationofthemechanicalprinciplesinvolved。

Thegreatdifficultywasthatthesubjectofmovingbodieshadallalongbeencontemplatedfromawrongpointofview。Sinceforcemustbeappliedtoanobjecttoputitinmotion，itwasperhapsnotunnaturallyassumedthatsimilarforcemustcontinuetobeappliedtokeeptheobjectinmotion。When，forexample，astoneisthrownfromthehand，thedirectforceappliednecessarilyceasesassoonastheprojectileleavesthehand。Thestone，nevertheless，fliesonforacertaindistanceandthenfallstotheground。Howisthisflightofthestonetobeexplained？Theancientphilosopherspuzzledmorethanalittleoverthisproblem，andtheAristoteliansreachedtheconclusionthatthemotionofthehandhadimpartedapropulsivemotiontotheair，andthatthispropulsivemotionwastransmittedtothestone，pushingiton。Justhowtheairtookonthispropulsivepropertywasnotexplained，andthevaguenessofthoughtthatcharacterizedthetimedidnotdemandanexplanation。Possiblythedyingawayofripplesinwatermayhavefurnished，byanalogy，anexplanationofthegradualdyingoutoftheimpulsewhichpropelsthestone。

Allofthiswas，ofcourse，anunfortunatemaladjustmentofthepointofview。Aseveryonenowadaysknows，theairretardstheprogressofthestone，enablingthepullofgravitationtodragittotheearthearlierthanitotherwisecould。Weretheresistanceoftheairandthepullofgravitationremoved，thestoneasprojectedfromthehandwouldflyoninastraightline，atanunchangedvelocity，forever。Butthisfact，whichisexpressedinwhatwenowtermthefirstlawofmotion，wasextremelydifficulttograsp。ThefirstimportantsteptowardsitwasperhapsimpliedinGalileo’sstudyoffallingbodies。Thesestudies，aswehaveseen，demonstratedthatahalf-poundweightandahundred-poundweightfallwiththesamevelocity。Itis，however，matterofcommonexperiencethatcertainbodies，as，forexample，feathers，donotfallatthesamerateofspeedwiththeseheavierbodies。Thisanomalydemandsanexplanation，andtheexplanationisfoundintheresistanceofferedtherelativelylightobjectbytheair。Oncetheideathattheairmaythusactasanimpedingforcewasgrasped，theinvestigatorofmechanicalprincipleshadenteredonanewandpromisingcourse。

Galileocouldnotdemonstratetheretardinginfluenceofairinthewaywhichbecamefamiliaragenerationortwolater；hecouldnotputafeatherandacoininavacuumtubeandprovethatthetwowouldtherefallwithequalvelocity，because，inhisday，theair-pumphadnotyetbeeninvented。TheexperimentwasmadeonlyagenerationafterthetimeofGalileo，asweshallsee；

but，meantime，thegreatItalianhadfullygraspedtheideathatatmosphericresistanceplaysamostimportantpartinregardtothemotionoffallingandprojectedbodies。Thankslargelytohisownexperiments，butpartlyalsototheeffortsofothers，hehadcome，beforetheendofhislife，prettydefinitelytorealizethatthemotionofaprojectile，forexample，mustbethoughtofasinherentintheprojectileitself，andthattheretardationorultimatecessationofthatmotionisduetotheactionofantagonisticforces。Inotherwords，hehadcometograspthemeaningofthefirstlawofmotion。Itremained，however，forthegreatFrenchmanDescartestogivepreciseexpressiontothislawtwoyearsafterGalileo’sdeath。AsDescartesexpresseditinhisPrincipiaPhilosophiae，publishedin1644，anybodyonceinmotiontendstogooninastraightline，atauniformrateofspeed，forever。Contrariwise，astationarybodywillremainforeveratrestunlessactedonbysomedisturbingforce。

Thisall-importantlaw，whichliesattheveryfoundationofalltrueconceptionsofmechanics，wasthusworkedoutduringthefirsthalfoftheseventeenthcentury，astheoutcomeofnumberlessexperimentsforwhichGalileo’sexperimentswithfailingbodiesfurnishedthefoundation。Sonumerousandsogradualwerethestepsbywhichthereversalofviewregardingmovingbodieswaseffectedthatitisimpossibletotracethemindetail。WemustbecontenttoreflectthatatthebeginningoftheGalileanepochutterlyfalsenotionsregardingthesubjectwereentertainedbytheverygreatestphilosophers——byGalileohimself，forexample，andbyKepler——whereasatthecloseofthatepochthecorrectandhighlyilluminativeviewhadbeenattained。

WemustnowconsidersomeotherexperimentsofGalileowhichledtoscarcelyless-importantresults。Theexperimentsinquestionhadtodowiththemovementsofbodiespassingdownaninclinedplane，andwiththealliedsubjectofthemotionofapendulum。

TheelaborateexperimentsofGalileoregardingtheformersubjectweremadebymeasuringthevelocityofaballrollingdownaplaneinclinedatvariousangles。Hefoundthatthevelocityacquiredbyaballwasproportionaltotheheightfromwhichtheballdescendedregardlessofthesteepnessoftheincline。

Experimentsweremadealsowithaballrollingdownacurvedgutter，thecurverepresentingtheareofacircle。Theseexperimentsledtothestudyofthecurvilinearmotionsofaweightsuspendedbyacord；inotherwords，ofthependulum。

Regardingthemotionofthependulum，someverycuriousfactsweresoonascertained。Galileofound，forexample，thatapendulumofagivenlengthperformsitsoscillationswiththesamefrequencythoughthearcdescribedbythependulumbevariedgreatly。[1]Hefound，also，thattherateofoscillationforpendulumsofdifferentlengthsvariesaccordingtoasimplelaw。

Inorderthatonependulumshalloscillateone-halfasfastasanother，thelengthofthependulumsmustbeasfourtoone。

Similarly，bylengtheningthependulumsninetimes，theoscillationisreducedtoone-third，Inotherwords，therateofoscillationofpendulumsvariesinverselyasthesquareoftheirlength。Here，then，isasimplerelationbetweenthemotionsofswingingbodieswhichsuggeststherelationwhichKeplerbaddiscoveredbetweentherelativemotionsoftheplanets。Everysuchdiscoverycominginthisageoftherejuvenationofexperimentalsciencehadapeculiarforceinteachingmentheall-importantlessonthatsimplelawsliebackofmostofthediversephenomenaofnature，ifonlytheselawscanbediscovered。

Galileofurtherobservedthathispendulummightbeconstructedofanyweightsufficientlyheavyreadilytoovercometheatmosphericresistance，andthat，withthisqualification，neithertheweightnorthematerialhadanyinfluenceuponthetimeofoscillation，thisbeingsolelydeterminedbythelengthofthecord。Naturally，thepracticalutilityofthesediscoverieswasnotoverlookedbyGalileo。Sinceapendulumofagivenlengthoscillateswithunvaryingrapidity，hereisanobviousmeansofmeasuringtime。Galileo，however，appearsnottohavemetwithanygreatmeasureofsuccessinputtingthisideaintopractice。ItremainedforthemechanicalingenuityofHuyghenstoconstructasatisfactorypendulumclock。

Asatheoreticalresultofthestudiesofrollingandoscillatingbodies，therewasdevelopedwhatisusuallyspokenofasthethirdlawofmotion——namely，thelawthatagivenforceoperatesuponamovingbodywithaneffectproportionatetoitseffectuponthesamebodywhenatrest。Or，asWhewellstatesthelaw:

"Thedynamicaleffectofforceisasthestaticaleffect；thatis，thevelocitywhichanyforcegeneratesinagiventime，whenitputsthebodyinmotion，isproportionaltothepressurewhichthissameforceproducesinabodyatrest。"[2]Accordingtothesecondlawofmotion，eachoneofthedifferentforces，operatingatthesametimeuponamovingbody，producesthesameeffectasifitoperateduponthebodywhileatrest。