第6章

AnaltogetherremarkablemanwasthisnativeofCyrene，whocametoAlexandriafromAthenstobethechieflibrarianofPtolemyEuergetes。Hewasnotmerelyanastronomerandageographer，butapoetandgrammarianaswell。HiscontemporariesjestinglycalledhimBetatheSecond，becausehewassaidthroughtheuniversalityofhisattainmentstobe"asecondPlato"inphilosophy，"asecondThales"inastronomy，andsoonthroughoutthelist。Hewasalsocalledthe"surveyoroftheworld，"inrecognitionofhisservicestogeography。Hipparchussaidofhim，perhapshalfjestingly，thathehadstudiedastronomyasageographerandgeographyasanastronomer。Itisnotquiteclearwhethertheepigramwasmeantascomplimentorascriticism。

Similarphraseshavebeenturnedagainstmenofversatiletalentineveryage。Bethatasitmay，Eratosthenespassedintohistoryasthefatherofscientificgeographyandofscientificchronology；astheastronomerwhofirstmeasuredtheobliquityoftheecliptic；andastheinventivegeniuswhoperformedtheastoundingfeatofmeasuringthesizeoftheglobeonwhichweliveatatimewhenonlyarelativelysmallportionofthatglobe’ssurfacewasknowntocivilizedman。Itisnodiscredittoapproachastronomyasageographerandgeographyasanastronomeriftheresultsaresuchasthese。WhatEratosthenesreallydidwastoapproachbothastronomyandgeographyfromtwoseeminglydivergentpointsofattack——namely，fromthestand-pointofthegeometerandalsofromthatofthepoet。Perhapsnomaninanyagehasbroughtabettercombinationofobservingandimaginativefacultiestotheaidofscience。

NearlyallthediscoveriesofEratosthenesareassociatedwithobservationsoftheshadowscastbythesun。Wehaveseenthat，inthestudyoftheheavenlybodies，muchdependsonthemeasurementofangles。Nowtheeasiestwayinwhichanglescanbemeasured，whensolaranglesareinquestion，istopayattention，nottothesunitself，buttotheshadowthatitcasts。WesawthatThalesmadesomeremarkablemeasurementswiththeaidofshadows，andwehavemorethanoncereferredtothegnomon，whichisthemostprimitive，butwhichlongremainedthemostimportant，ofastronomicalinstruments。ItisbelievedthatEratosthenesinventedanimportantmodificationofthegnomonwhichwaselaboratedafterwardsbyHipparchusandcalledanarmillarysphere。Thisconsistsessentiallyofasmallgnomon，orperpendicularpost，attachedtoaplanerepresentingtheearth’sequatorandahemisphereinimitationoftheearth’ssurface。

Withtheaidofthis，theshadowcastbythesuncouldbeveryaccuratelymeasured。Itinvolvesnonewprinciple。Everyperpendicularpostorobjectofanykindplacedinthesunlightcastsashadowfromwhichtheanglesnowinquestioncouldberoughlymeasured。Theprovinceofthearmillaryspherewastomakethesemeasurementsextremelyaccurate。

Withtheaidofthisimplement，Eratosthenescarefullynotedthelongestandtheshortestshadowscastbythegnomon——thatistosay，theshadowscastonthedaysofthesolstices。Hefoundthatthedistancebetweenthetropicsthusmeasuredrepresented47

degrees42’39"ofarc。One-halfofthis，or23degrees5，’

19。5"，representedtheobliquityoftheecliptic——thatistosay，theanglebywhichtheearth’saxisdippedfromtheperpendicularwithreferencetoitsorbit。Thiswasamostimportantobservation，andbecauseofitsaccuracyithasservedmodernastronomerswellforcomparisoninmeasuringthetriflingchangeduetoourearth’sslow，swingingwobble。Fortheearth，beitunderstood，likeagreattopspinningthroughspace，holdsitspositionwithrelativebutnotquiteabsolutefixity。Itmustnotbesupposed，however，thattheexperimentinquestionwasquitenewwithEratosthenes。Hismeritconsistsratherintheaccuracywithwhichhemadehisobservationthaninthenoveltyoftheconception；foritisrecordedthatEudoxus，afullcenturyearlier，hadremarkedtheobliquityoftheecliptic。Thatobserverhadsaidthattheobliquitycorrespondedtothesideofapentadecagon，orfifteen-sidedfigure，whichisequivalentinmodernphraseologytotwenty-fourdegreesofarc。ButsolittleisknownregardingthewayinwhichEudoxusreachedhisestimatethatthemeasurementofEratosthenesisusuallyspokenofasifitwerethefirsteffortofthekind。

Muchmorestriking，atleastinitsappealtothepopularimagination，wasthatothergreatfeatwhichEratosthenesperformedwiththeaidofhisperfectedgnomon——themeasurementoftheearthitself。WhenwereflectthatatthisperiodtheportionoftheearthopentoobservationextendedonlyfromtheStraitsofGibraltaronthewesttoIndiaontheeast，andfromtheNorthSeatoUpperEgypt，itcertainlyseemsenigmatical——atfirstthoughtalmostmiraculous——thatanobservershouldhavebeenabletomeasuretheentireglobe。ThatheshouldhaveaccomplishedthisthroughobservationofnothingmorethanatinybitofEgyptianterritoryandaglimpseofthesun’sshadowmakesitseembutthemorewonderful。YetthemethodofEratosthenes，likemanyanotherenigma，seemssimpleenoughonceitisexplained。Itrequiredbuttheapplicationofaveryelementaryknowledgeofthegeometryofcircles，combinedwiththeuseofafactortwofromlocalgeography——whichdetractsnothingfromthegeniusofthemanwhocouldreasonfromsuchsimplepremisestosowonderfulaconclusion。

Statedinafewwords，theexperimentofEratostheneswasthis。

HisgeographicalstudieshadtaughthimthatthetownofSyenelaydirectlysouthofAlexandria，or，asweshouldsay，onthesamemeridianoflatitude。Hehadlearned，further，thatSyenelaydirectlyunderthetropic，sinceitwasreportedthatatnoononthedayofthesummersolsticethegnomontherecastnoshadow，whileadeepwellwasilluminedtothebottombythesun。

Athirditemofknowledge，suppliedbythesurveyorsofPtolemy，madethedistancebetweenSyeneandAlexandriafivethousandstadia。These，then，werethepreliminarydatarequiredbyEratosthenes。Theirsignificanceconsistsinthefactthathereisameasuredbitoftheearth’sarcfivethousandstadiainlength。Ifwecouldfindoutwhatanglethatbitofarcsubtends，amerematterofmultiplicationwouldgiveusthesizeoftheearth。Buthowdeterminethisall-importantnumber？Theanswercamethroughreflectionontherelationsofconcentriccircles。

Ifyoudrawanynumberofcircles，ofwhateversize，aboutagivencentre，apairofradiidrawnfromthatcentrewillcutarcsofthesamerelativesizefromallthecircles。Onecirclemaybesosmallthattheactualarcsubtendedbytheradiiinagivencasemaybebutaninchinlength，whileanothercircleissolargethatitscorrespondingareismeasuredinmillionsofmiles；butineachcasethesamenumberofso-calleddegreeswillrepresenttherelationofeacharctoitscircumference。Now，Eratosthenesknew，asjuststated，thatthesun，whenonthemeridianonthedayofthesummersolstice，wasdirectlyoverthetownofSyene。ThismeantthatatthatmomentaradiusoftheearthprojectedfromSyenewouldpointdirectlytowardsthesun。

Meanwhile，ofcourse，thezenithwouldrepresenttheprojectionoftheradiusoftheearthpassingthroughAlexandria。Allthatwasrequired，then，wastomeasure，atAlexandria，theangulardistanceofthesunfromthezenithatnoononthedayofthesolsticetosecureanapproximatemeasurementofthearcofthesun’scircumference，correspondingtothearcoftheearth’ssurfacerepresentedbythemeasureddistancebetweenAlexandriaandSyene。

Thereaderwillobservethatthemeasurementcouldnotbeabsolutelyaccurate，becauseitismadefromthesurfaceoftheearth，andnotfromtheearth’scentre，butthesizeoftheearthissoinsignificantincomparisonwiththedistanceofthesunthatthisslightdiscrepancycouldbedisregarded。

ThewayinwhichEratosthenesmeasuredthisanglewasverysimple。HemerelymeasuredtheangleoftheshadowwhichhisperpendiculargnomonatAlexandriacastatmid-dayonthedayofthesolstice，when，asalreadynoted，thesunwasdirectlyperpendicularatSyene。Nowaglanceatthediagramwillmakeitclearthatthemeasurementofthisangleoftheshadowismerelyaconvenientmeansofdeterminingthepreciselyequaloppositeanglesubtendinganarcofanimaginarycirclepassingthroughthesun；thearewhich，asalreadyexplained，correspondswiththearcoftheearth’ssurfacerepresentedbythedistancebetweenAlexandriaandSyene。Hefoundthisangletorepresent7

degrees12’，orone-fiftiethofthecircle。Fivethousandstadia，then，representone-fiftiethoftheearth’scircumference；theentirecircumferencebeing，therefore，250，000stadia。

Unfortunately，wedonotknowwhichoneofthevariousmeasurementsusedinantiquityisrepresentedbythestadiaofEratosthenes。AccordingtotheresearchesofLepsius，however，thestadiuminquestionrepresented180meters，andthiswouldmaketheearth，accordingtothemeasurementofEratosthenes，abouttwenty-eightthousandmilesincircumference，ananswersufficientlyexacttojustifythewonderwhichtheexperimentexcitedinantiquity，andtheadmirationwithwhichithaseversincebeenregarded。

{illustrationcaption=DIAGRAMTOILLUSTRATEERATOSTHENES’

MEASUREMENTOFTHEGLOBE

FIG。1。AFisagnomonatAlexandria；SBagnomonatSvene；IS

andJKrepresentthesun’srays。TheangleactuallymeasuredbyEratosthenesisKFA，asdeterminedbytheshadowcastbythegnomonAF。ThisangleisequaltotheoppositeangleJFL，whichmeasuresthesun’sdistancefromthezenith；andwhichisalsoequaltotheangleAES——todeterminetheSizeofwhichistherealobjectoftheentiremeasurement。

FIG。2showstheformofthegnomonactuallyemployedinantiquity。ThehemisphereKAbeingmarkedwithascale，itisobviousthatinactualpracticeEratosthenesrequiredonlytosethisgnomoninthesunlightatthepropermoment，andreadofftheanswertohisproblemataglance。Thesimplicityofthemethodmakestheresultseemallthemorewonderful。}

Ofcourseitisthemethod，andnotitsdetailsoritsexactresults，thatexcitesourinterest。Andbeyondquestionthemethodwasanadmirableone。Itsresult，however，couldnothavebeenabsolutelyaccurate，because，whilecorrectinprinciple，itsdataweredefective。InpointoffactSyenedidnotliepreciselyonthesamemeridianasAlexandria，neitherdiditlieexactlyonthetropic。Here，then，aretwoelementsofinaccuracy。Moreover，itisdoubtfulwhetherEratosthenesmadeallowance，asheshouldhavedone，forthesemi-diameterofthesuninmeasuringtheangleoftheshadow。Butthesearemeredetails，scarcelyworthyofmentionfromourpresentstand-point。

Whatperhapsisdeservingofmoreattentionisthefactthatthisepoch-makingmeasurementofEratosthenesmaynothavebeenthefirstonetobemade。ApassageofAristotlerecordsthatthesizeoftheearthwassaidtobe400，000stadia。SomecommentatorshavethoughtthatAristotlemerelyreferredtotheareaoftheinhabitedportionoftheearthandnottothecircumferenceoftheearthitself，buthiswordsseemdoubtfullysusceptibleofthisinterpretation；andifhemeant，ashiswordsseemtoimply，thatphilosophersofhisdayhadatolerablypreciseideaoftheglobe，wemustassumethatthisideawasbaseduponsomesortofmeasurement。Therecordedsize，400，000

stadia，isasufficientapproximationtothetruthtosuggestsomethingmorethanamereunsupportedguess。Now，sinceAristotlediedmorethanfiftyyearsbeforeEratostheneswasborn，hisreportastotheallegedsizeoftheearthcertainlyhasasuggestivenessthatcannotbeoverlooked；butitarousesspeculationswithoutgivinganinklingastotheirsolution。IfEratostheneshadaprecursorasanearth-measurer，nohintorrumorhascomedowntousthatwouldenableustoguesswhothatprecursormayhavebeen。Hispersonalityisasdeeplyenvelopedinthemistsofthepastasarethepersonalitiesofthegreatprehistoricdiscoverers。Forthepurposeofthehistorian，Eratosthenesmuststandastheinventorofthemethodwithwhichhisnameisassociated，andasthefirstmanofwhomwecansaywithcertaintythathemeasuredthesizeoftheearth。Rightworthily，then，hadtheAlexandrianphilosopherwonhisproudtitleof"surveyoroftheworld。"

HIPPARCHUS，"THELOVEROFTRUTH"

Eratosthenesoutlivedmostofhisgreatcontemporaries。HesawtheturningofthatfirstandgreatestcenturyofAlexandrianscience，thethirdcenturybeforeourera。Hediedintheyear196B。C。，having，itissaid，starvedhimselftodeathtoescapethemiseriesofblindness；——tothemeasurerofshadows，lifewithoutlightseemednotworththeliving。Eratosthenesleftnoimmediatesuccessor。Agenerationlater，however，anothergreatfigureappearedintheastronomicalworldinthepersonofHipparchus，amanwho，asatechnicalobserver，hadperhapsnopeerintheancientworld:onewhosetsohighavalueuponaccuracyofobservationastoearnthetitleof"theloveroftruth。"HipparchuswasbornatNicaea，inBithynia，intheyear160B。C。Hislife，alltooshortfortheinterestsofscience，endedintheyear125B。C。Theobservationsofthegreatastronomerweremadechiefly，perhapsentirely，atRhodes。A

misinterpretationofPtolemy’swritingsledtotheideathatHipparchus，performedhischieflaborsinAlexandria，butitisnowadmittedthatthereisnoevidenceforthis。Delambredoubted，andmostsubsequentwritersfollowhimhere，whetherHipparchuseversomuchasvisitedAlexandria。InanyeventthereseemstobenoquestionthatRhodesmayclaimthehonorofbeingthechiefsiteofhisactivities。

ItwasHipparchuswhosesomewhatequivocalcommentontheworkofEratostheneswehavealreadynoted。Nocounter-chargeinkindcouldbemadeagainstthecritichimself；hewasanastronomerpureandsimple。Hisgiftwasthegiftofaccurateobservationratherthanthegiftofimagination。Noscientificprogressispossiblewithoutscientificguessing，butHipparchusbelongedtothatclassofobserverswithwhomhypothesisisheldrigidlysubservienttofact。ItwasnottobeexpectedthathismindwouldbeattractedbytheheliocentrictheoryofAristarchus。HeusedthefactsandobservationsgatheredbyhisgreatpredecessorofSamos，buthedeclinedtoaccepthistheories。Forhimtheworldwascentral；hisproblemwastoexplain，ifhecould，theirregularitiesofmotionwhichsun，moon，andplanetsshowedintheirseemingcircuitsabouttheearth。HipparchushadthegnomonofEratosthenes——doubtlessinaperfectedform——toaidhim，andhesoonprovedhimselfamasterinitsuse。Forhim，aswehavesaid，accuracywaseverything；thiswastheoneelementthatledtoallhisgreatsuccesses。

Perhapshisgreatestfeatwastodemonstratetheeccentricityofthesun’sseemingorbit。Weofto-day，thankstoKepplerandhisfollowers，knowthattheearthandtheotherplanetarybodiesintheircircuitaboutthesundescribeanellipseandnotacircle。

ButinthedayofHipparchus，thoughtheellipsewasrecognizedasageometricalfigure(ithadbeendescribedandnamedalongwiththeparabolaandhyperbolabyApolloniusofPerga，thepupilofEuclid)，yetitwouldhavebeentherankestheresytosuggestanellipticalcourseforanyheavenlybody。Ametaphysicaltheory，aspropoundedperhapsbythePythagoreansbutardentlysupportedbyAristotle，declaredthatthecircleistheperfectfigure，andpronounceditinconceivablethatthemotionsofthespheresshouldbeotherthancircular。ThisthoughtdominatedthemindofHipparchus，andsowhenhiscarefulmeasurementsledhimtothediscoverythatthenorthwardandsouthwardjourneyingsofthesundidnotdividetheyearintofourequalparts，therewasnothingopentohimbuttoeitherassumethattheearthdoesnotliepreciselyatthecentreofthesun’scircularorbitortofindsomealternativehypothesis。

Inpointoffact，thesun(reversingthepointofviewinaccordancewithmoderndiscoveries)doeslieatonefocusoftheearth’sellipticalorbit，andthereforeawayfromthephysicalcentreofthatorbit；inotherwords，theobservationsofHipparchuswereabsolutelyaccurate。Hewasquitecorrectinfindingthatthesunspendsmoretimeononesideoftheequatorthanontheother。When，therefore，heestimatedtherelativedistanceoftheearthfromthegeometricalcentreofthesun’ssupposedcircularorbit，andspokeofthisasthemeasureofthesun’seccentricity，hepropoundedatheoryinwhichtruedataofobservationwerecuriouslymingledwithapositivelyinvertedtheory。ThatthetheoryofHipparchuswasabsolutelyconsistentwithallthefactsofthisparticularobservationisthebestevidencethatcouldbegivenofthedifficultiesthatstoodinthewayofatrueexplanationofthemechanismoftheheavens。

Butitisnotmerelythesunwhichwasobservedtovaryinthespeedofitsorbitalprogress；themoonandtheplanetsalsoshowcuriousaccelerationsandretardationsofmotion。ThemooninparticularreceivedmostcarefulattentionfromHipparchus。

Dominatedbyhisconceptionoftheperfectspheres，hecouldfindbutoneexplanationoftheanomalousmotionswhichheobserved，andthiswastoassumethatthevariousheavenlybodiesdonotflyoninanunvaryingarcintheircircuitabouttheearth，butdescribeminorcirclesastheygowhichcanbelikenedtonothingsotangiblyastoalightattachedtotherimofawagon-wheelinmotion。Ifsuchaninvisiblewheelbeimaginedascarryingthesun，forexample，onitsrim，whileitsinvisiblehubfollowsunswervinglythecircleofthesun’smeanorbit(thiswheel，beitunderstood，lyingintheplaneoftheorbit，notatright-

anglestoit)，thenitmustbeobviousthatwhilethehubremainsalwaysatthesamedistancefromtheearth，thecirclingrimwillcarrythesunnearertheearth，thenfartheraway，andthatwhileitistraversingthatportionofthearewhichbringsittowardstheearth，theactualforwardprogressofthesunwillberetardednotwithstandingtheuniformmotionofthehub，justasitwillbeacceleratedintheoppositearc。Now，ifwesupposeoursun-bearingwheeltoturnsoslowlythatthesunrevolvesbutonceaboutitsimaginaryhubwhilethewheelitselfismakingtheentirecircuitoftheorbit，weshallhaveaccountedfortheobservedfactthatthesunpassesmorequicklythroughone-halfoftheorbitthanthroughtheother。Moreover，ifwecanvisualizetheprocessandimaginethesuntohaveleftavisiblelineoffirebehindhimthroughoutthecourse，weshallseethatinrealitythetwocircularmotionsinvolvedhavereallyresultedinproducinganellipticalorbit。

Theideaisperhapsmadeclearerifwepicturetheactualprogressofthelanternattachedtotherimofanordinarycart-wheel。Whenthecartisdrawnforwardthelanternismadetorevolveinacircleasregardsthehubofthewheel，butsincethathubisconstantlygoingforward，theactualpathdescribedbythelanternisnotacircleatallbutawavingline。Itispreciselythesamewiththeimaginedcourseofthesuninitsorbit，onlythatweviewtheselinesjustasweshouldviewthelanternonthewheelifwelookedatitfromdirectlyaboveandnotfromtheside。Theproofthatthesunisdescribingthiswavingline，andthereforemustbeconsideredasattachedtoanimaginarywheel，isfurnished，asitseemedtoHipparchus，bytheobservedfactofthesun’svaryingspeed。

Thatisonewayoflookingatthematter。Itisanhypothesisthatexplainstheobservedfacts——afterafashion，andindeedaveryremarkablefashion。TheideaofsuchanexplanationdidnotoriginatewithHipparchus。ThegermsofthethoughtwereasoldasthePythagoreandoctrinethattheearthrevolvesaboutacentrethatwecannotsee。Eudoxusgavetheconceptiongreatertangibility，andmaybeconsideredasthefatherofthisdoctrineofwheels——epicycles，astheycametobecalled。TwocenturiesbeforethetimeofHipparchusheconceivedadoctrineofsphereswhichAristotlefoundmostinteresting，andwhichservedtoexplain，alongthelineswehavejustfollowed，theobservedmotionsoftheheavenlybodies。Calippus，thereformerofthecalendar，issaidtohavecarriedanaccountofthistheorytoAristotle。Asnewirregularitiesofmotionofthesun，moon，andplanetarybodieswerepointedout，newepicycleswereinvented。

Thereisnolimittothenumberofimaginarycirclesthatmaybeinscribedaboutanimaginarycentre，andifweconceiveeachoneofthesecirclestohaveapropermotionofitsown，andeachonetocarrythesuninthelineofthatmotion，exceptasitisdivertedbytheothermotions——ifwecanvisualizethiscomplexminglingofwheels——weshallcertainlybeabletoimaginetheheavenlybodywhichliesatthejunctureofalltherims，asbeingcarriedforwardinaserraticandwobblyamannerascouldbedesired。Inotherwords，thetheoryofepicycleswillaccountforallthefactsoftheobservedmotionsofalltheheavenlybodies，butinsodoingitfillstheuniversewithamostbewilderingnetworkofintersectingcircles。EveninthetimeofCalippusfifty-fiveofthesesphereswerecomputed。

Wemaywellbelievethattheclear-seeingAristarchuswouldlookaskanceatsuchacomplexsystemofimaginarymachinery。ButHipparchus，pre-eminentlyanobserverratherthanatheorizer，seemstohavebeencontenttoacceptthetheoryofepicyclesashefoundit，thoughhisstudiesaddedtoitscomplexities；andHipparchuswasthedominantscientificpersonalityofhiscentury。Whathebelievedbecameasalawtohisimmediatesuccessors。Histenetswereacceptedasfinalbytheirgreatpopularizer，Ptolemy，threecenturieslater；andsotheheliocentrictheoryofAristarchuspassedunderacloudalmostatthehourofitsdawning，theretoremainobscuredandforgottenforthelonglapseofcenturies。Athousandpitiesthatthegreatestobservingastronomerofantiquitycouldnot，likeoneofhisgreatprecursors，haveapproachedastronomyfromthestand-pointofgeographyandpoetry。Hadhedoneso，perhapshemighthavereflected，likeAristarchusbeforehim，thatitseemsabsurdforourearthtoholdthegiantsuninthraldom；thenperhapshisimaginationwouldhavereachedouttotheheliocentricdoctrine，andthecobwebhypothesisofepicycles，withthatyetmoreintangiblefigmentoftheperfectcircle，mighthavebeenwipedaway。

Butitwasnottobe。WithAristarchusthescientificimaginationhadreacheditshighestflight；butwithHipparchusitwasbeginningtosettlebackintoregionsoffoggieratmosphereandnarrowerhorizons。Forwhat，afterall，doesitmatterthatHipparchusshouldgoontomeasurethepreciselengthoftheyearandtheapparentsizeofthemoon’sdisk；thatheshouldmakeachartoftheheavensshowingtheplaceof1080stars；eventhatheshoulddiscovertheprecessionoftheequinox；——what，afterall，isthesignificanceofthesedetailsasagainsttheall-essentialfactthatthegreatestscientificauthorityofhiscentury——theonetrulyheroicscientificfigureofhisepoch——shouldhavelentalltheforcesofhiscommandinginfluencetotheold，falsetheoryofcosmology，whenthetruetheoryhadbeenpropoundedandwhenhe，perhaps，wastheonlymanintheworldwhomighthavesubstantiatedandvitalizedthattheory？Itiseasytooverestimatetheinfluenceofanysingleman，and，contrariwise，tounderestimatethepoweroftheZeitgeist。ButwhenwereflectthatthedoctrinesofHipparchus，aspromulgatedbyPtolemy，became，asitwere，thelastwordofastronomicalscienceforboththeEasternandWesternworlds，andsocontinuedafterathousandyears，itisperhapsnottoomuchtosaythatHipparchus，"theloveroftruth，"missedoneofthegreatestopportunitiesforthepromulgationoftruthevervouchsafedtoadevoteeofpurescience。

Butallthis，ofcourse，detractsnothingfromthemeritsofHipparchusasanobservingastronomer。Afewwordsmoremustbesaidastohisspecificdiscoveriesinthisfield。Accordingtohismeasurement，thetropicyearconsistsof365days，5hours，and49minutes，varyingthusonly12secondsfromthetrueyear，asthemodernastronomerestimatesit。Yetmoreremarkable，becauseofthegreaterdifficultiesinvolved，wasHipparchus’sattempttomeasuretheactualdistanceofthemoon。Aristarchushadmadeasimilarattemptbeforehim。Hipparchusbasedhiscomputationsonstudiesofthemoonineclipse，andhereachedtheconclusionthatthedistanceofthemoonisequalto59radiioftheearth(inrealityitis60。27radii)。Here，then，wasthemeasureofthebase-lineofthatfamoustrianglewithwhichAristarchushadmeasuredthedistanceofthesun。Hipparchusmusthaveknownofthatmeasurement，sincehequotestheworkofAristarchusinotherfields。HadhenowbutrepeatedtheexperimentofAristarchus，withhisperfectedinstrumentsandhisperhapsgreaterobservationalskill，hewasinpositiontocomputetheactualdistanceofthesunintermsnotmerelyofthemoon’sdistancebutoftheearth’sradius。AndnowtherewastheexperimentofEratosthenestogivethelengthofthatradiusinpreciseterms。Inotherwords，Hipparchusmighthavemeasuredthedistanceofthesuninstadia。Butifhehadmadetheattempt——and，indeed，itismorethanlikelythathedidso——theelementsoferrorinhismeasurementswouldstillhavekepthimwideofthetruefigures。

ThechiefstudiesofHipparchusweredirected，aswehaveseen，towardsthesunandthemoon，butaphenomenonthatoccurredintheyear134B。C。ledhimforatimetogivemoreparticularattentiontothefixedstars。Thephenomenoninquestionwasthesuddenoutburstofanewstar；aphenomenonwhichhasbeenrepeatednowandagain，butwhichissufficientlyrareandsufficientlymysterioustohaveexcitedtheunusualattentionofastronomersinallgenerations。Modernscienceoffersanexplanationofthephenomenon，asweshallseeinduecourse。WedonotknowthatHipparchusattemptedtoexplainit，buthewasledtomakeachartoftheheavens，probablywiththeideaofguidingfutureobserversintheobservationofnewstars。HereagainHipparchuswasnotaltogetheraninnovator，sinceachartshowingthebrighteststarshadbeenmadebyEratosthenes；butthenewchartsweremuchelaborated。

ThestudiesofHipparchusledhimtoobservethestarschieflywithreferencetothemeridianratherthanwithreferencetotheirrising，ashadhithertobeenthecustom。Inmakingthesestudiesoftherelativepositionofthestars，HipparchuswasledtocomparehisobservationswiththoseoftheBabylonians，which，itwassaid，AlexanderhadcausedtobetransmittedtoGreece。HemadeusealsooftheobservationsofAristarchusandothersofhisGreekprecursors。Theresultofhiscomparisonsprovedthatthesphereofthefixedstarshadapparentlyshifteditspositioninreferencetotheplaneofthesun’sorbit——thatistosay，theplaneoftheeclipticnolongerseemedtocutthesphereofthefixedstarsatpreciselythepointwherethetwocoincidedinformercenturies。Theplaneoftheeclipticmustthereforebeconceivedasslowlyrevolvinginsuchawayasgraduallytocircumnavigatetheheavens。Thisimportantphenomenonisdescribedastheprecessionoftheequinoxes。

ItismuchinquestionwhetherthisphenomenonwasnotknowntotheancientEgyptianastronomers；butinanyevent，HipparchusistobecreditedwithdemonstratingthefactandmakingitknowntotheWesternworld。AfurtherservicewasrenderedtheoreticalastronomybyHipparchusthroughhisinventionoftheplanosphere，aninstrumentfortherepresentationofthemechanismoftheheavens。Hiscomputationsofthepropertiesofthespheresledhimalsotowhatwasvirtuallyadiscoveryofthemethodoftrigonometry，givinghim，therefore，ahighpositioninthefieldofmathematics。Allinall，then，Hipparchusisamostheroicfigure。Hemaywellbeconsideredthegreateststar-gazerofantiquity，thoughhecannot，withoutinjusticetohisgreatprecursors，beallowedthetitlewhichissometimesgivenhimof"fatherofsystematicastronomy。"

CTESIBIUSANDHERO:MAGICIANSOFALEXANDRIA

JustaboutthetimewhenHipparchuswasworkingoutatRhodeshispuzzlesofcelestialmechanics，therewasamaninAlexandriawhowasexercisingastrangelyinventivegeniusovermechanicalproblemsofanothersort；amanwho，followingtheexamplesetbyArchimedesacenturybefore，wasstudyingtheproblemsofmatterandputtinghisstudiestopracticalapplicationthroughtheinventionofweirddevices。Theman’snamewasCtesibius。WeknowscarcelymoreofhimthanthathelivedinAlexandria，probablyinthefirsthalfofthesecondcenturyB。C。Hisantecedents，theplaceandexacttimeofhisbirthanddeath，arequiteunknown。

Neitherarewequitecertainastothepreciserangeofhisstudiesortheexactnumberofhisdiscoveries。ItappearsthathehadapupilnamedHero，whosepersonality，unfortunately，isscarcelylessobscurethanthatofhismaster，butwhowroteabookthroughwhichtherecordofthemaster’sinventionswaspreservedtoposterity。Hero，indeed，wroteseveralbooks，thoughonlyoneofthemhasbeenpreserved。Theonesthatarelostbearthefollowingsuggestivetitles:OntheConstructionofSlings；

OntheConstructionofMissiles；OntheAutomaton；OntheMethodofLiftingHeavyBodies；OntheDioptricorSpying-tube。TheworkthatremainsiscalledPneumatics，andsointerestingaworkitisastomakeusdoublyregretthelossofitscompanionvolumes。

Hadtheseotherbooksbeenpreservedweshoulddoubtlesshaveaclearerinsightthanisnowpossibleintosomeatleastofthemechanicalproblemsthatexercisedthemindsoftheancientphilosophers。Thebookthatremainsischieflyconcerned，asitsnameimplies，withthestudyofgases，or，rather，withthestudyofasinglegas，thisbeing，ofcourse，theair。Butittellsusalsoofcertainstudiesinthedynamicsofwaterthataremostinteresting，andforthehistorianofsciencemostimportant。

Unfortunately，thepupilofCtesibius，whateverhisingenuity，wasamanwithadeficientsenseoftheethicsofscience。Hetellsusinhisprefacethattheobjectofhisbookistorecordsomeingeniousdiscoveriesofothers，togetherwithadditionaldiscoveriesofhisown，butnowhereinthebookitselfdoeshegiveusthe，slightestclewastowherethelineisdrawnbetweentheoldandthenew。Once，indiscussingtheweightofwater，hementionsthelawofArchimedesregardingafloatingbody，butthisistheonlycaseinwhichascientificprincipleistracedtoitssourceorinwhichcreditisgiventoanyoneforadiscovery。ThisisthemoretoberegrettedbecauseHerohasdiscussedatsomelengththetheoriesinvolvedinthetreatmentofhissubject。ThisreticenceonthepartofHero，combinedwiththefactthatsuchsomewhatlaterwritersasPlinyandVitruviusdonotmentionHero’sname，whiletheyfrequentlymentionthenameofhismaster，Ctesibius，hasledmoderncriticstoasomewhatscepticalattituderegardingthepositionofHeroasanactualdiscoverer。

Themanwhowouldcoollyappropriatesomediscoveriesofothersundercloakofamereprefatorialreferencewasperhapsanexpounderratherthananinnovator，andhad，itisshrewdlysuspected，notmuchofhisowntooffer。Meanwhile，itistolerablycertainthatCtesibiuswasthediscovereroftheprincipleofthesiphon，oftheforcing-pump，andofapneumaticorgan。AnexaminationofHero’sbookwillshowthatthesearereallythechiefprinciplesinvolvedinmostofthevariousinterestingmechanismswhichhedescribes。Weareconstrained，then，tobelievethattheinventivegeniuswhowasreallyresponsibleforthemechanismsweareabouttodescribewasCtesibius，themaster。YetweoweadebtofgratitudetoHero，thepupil，forhavinggivenwidervoguetothesediscoveries，andinparticularforthediscussionoftheprinciplesofhydrostaticsandpneumaticscontainedintheintroductiontohisbook。ThisdiscussionfurnishesusalmostouronlyknowledgeastotheprogressofGreekphilosophersinthefieldofmechanicssincethetimeofArchimedes。

ThemainpurposeofHeroinhispreliminarythesishastodowiththenatureofmatter，andrecalls，therefore，thestudiesofAnaxagorasandDemocritus。Hero，however，approacheshissubjectfromapurelymaterialorpracticalstand-point。Heisanexplicitchampionofwhatwenowadayscallthemoleculartheoryofmatter。"Everybody，"hetellsus，"iscomposedofminuteparticles，betweenwhichareemptyspaceslessthantheseparticlesofthebody。Itis，therefore，erroneoustosaythatthereisnovacuumexceptbytheapplicationofforce，andthateveryspaceisfulleitherofairorwaterorsomeothersubstance。Butinproportionasanyoneoftheseparticlesrecedes，someotherfollowsitandfillsthevacantspace；

thereforethereisnocontinuousvacuum，exceptbytheapplicationofsomeforce[likesuction]——thatistosay，anabsolutevacuumisneverfound，exceptasitisproducedartificially。"Herobringsforwardsomethoroughlyconvincingproofsofthethesisheismaintaining。"Iftherewerenovoidplacesbetweentheparticlesofwater，"hesays，"theraysoflightcouldnotpenetratethewater；moreover，anotherliquid，suchaswine，couldnotspreaditselfthroughthewater，asitisobservedtodo，weretheparticlesofwaterabsolutelycontinuous。"Thelatterillustrationisonethevalidityofwhichappealsasforciblytothephysicistsofto-dayasitdidtoHero。Thesameistrueoftheargumentdrawnfromthecompressibilityofgases。Herohasevidentlymadeacarefulstudyofthissubject。Heknowsthataninvertedtubefullofairmaybeimmersedinwaterwithoutbecomingwetontheinside，provingthatairisaphysicalsubstance；butheknowsalsothatthissameairmaybecausedtoexpandtoamuchgreaterbulkbytheapplicationofheat，ormay，ontheotherhand，becondensedbypressure，inwhichcase，asheiswellaware，theairexertsforceintheattempttoregainitsnormalbulk。But，heargues，surelywearenottobelievethattheparticlesofairexpandtofillallthespacewhenthebulkofairasawholeexpandsundertheinfluenceofheat；norcanweconceivethattheparticlesofnormalairareinactualcontact，elseweshouldnotbeabletocompresstheair。Hencehisconclusion，which，aswehaveseen，hemakesgeneralinitsapplicationtoallmatter，thattherearespaces，or，ashecallsthem，vacua，betweentheparticlesthatgotomakeupallsubstances，whetherliquid，solid，orgaseous。

Here，clearlyenough，wastheideaofthe"atomic"natureofmatteracceptedasafundamentalnotion。TheargumentativeattitudeassumedbyHeroshowsthatthedoctrinecouldnotbeexpectedtogounchallenged。But，ontheotherhand，thereisnothinginhisphrasingtosuggestanintentiontoclaimoriginalityforanyphaseofthedoctrine。WemayinferthatinthethreehundredyearsthathadelapsedsincethetimeofAnaxagoras，thatphilosopher’sideaofthemolecularnatureofmatterhadgainedfairlywidecurrency。Astotheexpansivepowerofgas，whichHerodescribesatsomelengthwithoutgivingusaclewtohisauthorities，wemayassumethatCtesibiuswasanoriginalworker，yetthegeneralfactsinvolvedweredoubtlessmucholderthanhisday。Hero，forexample，tellsusofthecupping-glassusedbyphysicians，whichhesaysismadeintoavacuumbyburninguptheairinit；butthisapparatushadprobablybeenlonginuse，andHeromentionsitnotinordertodescribetheordinarycupping-glasswhichisreferredto，butamodificationofit。Hereferstotheoldformasifitweresomethingfamiliartoall。

Again，weknowthatEmpedoclesstudiedthepressureoftheairinthefifthcenturyB。C。，anddiscoveredthatitwouldsupportacolumnofwaterinaclosedtube，sothisphaseofthesubjectisnotnew。ButthereisnohintanywherebeforethisworkofHeroofaclearunderstandingthattheexpansivepropertiesoftheairwhencompressed，orwhenheated，maybemadeavailableasamotorpower。Hero，however，hastheclearestnotionsonthesubjectandputsthemtothepracticaltestofexperiment。Thusheconstructsnumerousmechanismsinwhichtheexpansivepowerofairunderpressureismadetodowork，andothersinwhichthesameendisaccomplishedthroughtheexpansivepowerofheatedair。Forexample，thedoorsofatemplearemadetoswingopenautomaticallywhenafireislightedonadistantaltar，closingagainwhenthefirediesout——effectswhichmusthavefilledthemindsofthepiousobserverswithbewildermentandwonder，servingamostusefulpurposeforthepriests，whoalone，wemayassume，wereinthesecret。Thereweretwomethodsbywhichthisapparatuswasworked。Inonetheheatedairpressedonthewaterinacloseretortconnectedwiththealtar，forcingwateroutoftheretortintoabucket，whichbyitsweightappliedaforcethroughpulleysandropesthatturnedthestandardsonwhichthetempledoorsrevolved。Whenthefiredieddowntheaircontracted，thewaterwassiphonedbackfromthebucket，which，beingthuslightened，letthedoorscloseagainthroughtheactionofanordinaryweight。Theothermethodwasaslightmodification，inwhichtheretortofwaterwasdispensedwithandaleathersacklikealargefootballsubstitued。Theropesandpulleyswereconnectedwiththissack，whichexertedapullwhenthehotairexpanded，andwhichcollapsedandthusrelaxeditsstrainwhentheaircooled。AglanceattheillustrationstakenfromHero’sbookwillmakethedetailsclear。

Othermechanismsutilizedasomewhatdifferentcombinationofweights，pulleys，andsiphons，operatedbytheexpansivepowerofair，unheatedbutunderpressure，suchpressurebeingappliedwithaforce-pump，orbytheweightofwaterrunningintoaclosedreceptacle。Onesuchmechanismgivesusaconstantjetofwaterorperpetualfountain。Anothercuriousapplicationoftheprinciplefurnishesuswithanelaboratetoy，consistingofagroupofbirdswhichalternatelywhistleoraresilent，whileanowlseatedonaneighboringperchturnstowardsthebirdswhentheirsongbeginsandawayfromthemwhenitends。The"singing"

ofthebirds，itmustbeexplained，isproducedbytheexpulsionofairthroughtinytubespassingupthroughtheirthroatsfromatankbelow。Theowlismadetoturnbyamechanismsimilartothatwhichmanipulatesthetempledoors。Thepressureissuppliedmerelybyastreamofrunningwater，andtheperiodicalsilenceofthebirdsisduetothefactthatthispressureisrelievedthroughtheautomaticsiphoningoffofthewaterwhenitreachesacertainheight。Theactionofthesiphon，itmaybeadded，iscorrectlyexplainedbyHeroasduetothegreaterweightofthewaterinthelongerarmofthebenttube。Asbeforementioned，thesiphonisrepeatedlyusedinthesemechanismsofHero。Thediagramwillmakecleartheexactapplicationofitinthepresentmostingeniousmechanism。WemayaddthattheprincipleofthewhistlewasafavoriteoneofHero。Bytheaidofasimilarmechanismhebroughtabouttheblowingoftrumpetswhenthetempledoorswereopened，aphenomenonwhichmustgreatlyhaveenhancedthemystification。Itispossiblethatthisprinciplewasutilizedalsoinconnectionwithstatuestoproduceseeminglysupernaturaleffects。ThismaybetheexplanationofthetraditionofthespeakingstatueinthetempleofAmmonatThebes。

{illustrationcaption=DEVICEFORCAUSINGTHEDOORSOFTHE

TEMPLETOOPENWHENTHEFIREONTHEALTARISLIGHTED(AirheatedinthealtarFdriveswaterfromtheclosedreceptacleHthroughthetubeKLintothebucketM，whichdescendsthroughgravity，thusopeningthedoors。Whenthealtarcools，theaircontracts，thewaterissuckedfromthebucket，andtheweightandpulleyclosethedoors。)}

{illustrationcaption=THESTEAM-ENGINEOFHERO(ThesteamgeneratedinthereceptacleABpassesthroughthetubeEFintotheglobe，andescapesthroughthebenttubesHandK，causingtheglobetorotateontheaxisLG。)}

Theutilizationofthepropertiesofcompressedairwasnotconfined，however，exclusivelytomeretoys，ortoproducemiraculouseffects。Thesameprinciplewasappliedtoapracticalfire-engine，workedbyleversandforce-pumps；anapparatus，inshort，altogethersimilartothatstillinuseinruraldistricts。Aslightlydifferentapplicationofthemotivepowerofexpandingairisfurnishedinaverycurioustoycalled"thedancingfigures。"Inthis，airheatedinaretortlikeaminiaturealtarisallowedtoescapethroughthesidesoftwopairsofrevolvingarmspreciselylikethoseoftheordinaryrevolvingfountainwithwhichweareaccustomedtowaterourlawns，therevolvingarmsbeingattachedtoaplaneonwhichseveralpairsofstatuettesrepresentingdancersareplaced，Anevenmoreinterestingapplicationofthisprincipleofsettingawheelinmotionisfurnishedinamechanismwhichmustbeconsideredtheearliestofsteam-engines。Here，asthenameimplies，thegassupplyingthemotivepowerisactuallysteam。

Theapparatusmadetorevolveisaglobeconnectedwiththesteam-retortbyatubewhichservesasoneofitsaxes，thesteamescapingfromtheglobethroughtwobenttubesplacedateitherendofanequatorialdiameter。ItdoesnotappearthatHerohadanythoughtofmakingpracticaluseofthissteam-engine。Itwasmerelyacurioustoy——nothingmore。YethadnottheagethatsucceededthatofHerobeenoneinwhichinventivegeniuswasdormant，someonemustsoonhavehitupontheideathatthissteam-enginemightbeimprovedandmadetoserveausefulpurpose。Asthecasestands，however，therewasnoadvancemadeuponthesteammotorofHeroforalmosttwothousandyears。And，indeed，whenthepracticalapplicationofsteamwasmade，towardsthecloseoftheeighteenthcentury，itwasmadeprobablyquitewithoutreferencetotheexperimentofHero，thoughknowledgeofhistoymayperhapshavegivenaclewtoWattorhispredecessors。

{illustrationcaption=THESLOT-MACHINEOFHERO(ThecoinintroducedatAfallsontheleverR，andbyitsweightopensthevalveS，permittingtheliquidtoescapethroughtheinvisibletubeLM。Asthelevertips，thecoinslidesoffandthevalvecloses。TheliquidintankmustofcoursebekeptaboveF。)}

Inrecenttimestherehasbeenatendencytogivetothissteam-engineofHerosomethingmorethanfullmeedofappreciation。Tobesure，itmarkedamostimportantprincipleintheconceptionthatsteammightbeusedasamotivepower，but，exceptinthedemonstrationofthisprinciple，themechanismofHerowasmuchtooprimitivetobeofanyimportance。ButthereisonemechanismdescribedbyHerowhichwasamostexplicitanticipationofadevice，whichpresumablysoonwentoutofuse，andwhichwasnotreinventeduntiltowardsthecloseofthenineteenthcentury。Thiswasadevicewhichhasbecomefamiliarinrecenttimesasthepenny-in-the-slotmachine。Whentowardsthecloseofthenineteenthcenturysomeinventivecraftsmanhitupontheideaofanautomaticmachinetosupplycandy，aboxofcigarettes，orawhiffofperfumery，hemayormaynothaveborrowedhisideafromtheslot-machineofHero；butinanyevent，insteadofbeinganinnovatorhewasreallytwothousandyearsbehindthetimes，fortheslot-machineofHeroisthepreciseprototypeofthesemodernones。

TheparticularfunctionwhichthemechanismofHerowasdestinedtofulfilwasthedistributionofajetofwater，presumablyusedforsacramentalpurposes，whichwasgivenoutautomaticallywhenafive-drachmacoinwasdroppedintotheslotatthetopofthemachine。Theinternalmechanismofthemachinewassimpleenough，consistingmerelyofaleveroperatingavalvewhichwasopenedbytheweightofthecoindroppingonthelittleshelfattheendofthelever，andwhichclosedagainwhenthecoinslidofftheshelf。Theillustrationwillshowhowsimplethismechanismwas。

Yettotheworshippers，whoprobablyhadenteredthetemplethroughdoorsmiraculouslyopened，andwhonowwitnessedthisseeminglyintelligentresponseofamachine，theresultmusthaveseemedmystifyingenough；and，indeed，forusalso，whenweconsiderhowrelativelycrudewasthemechanicalknowledgeofthetime，thismustseemnothinglessthanmarvellous。Asinimaginationwewalkuptothesacredtank，dropourdrachmaintheslot，andholdourhandforthespurtofholy-water，canwerealizethatthisisthelandofthePharaohs，notEnglandorAmerica；thatthekingdomofthePtolemiesisstillatitsheight；thattherepublicofRomeismistressoftheworld；thatallEuropenorthoftheAlpsisinhabitedsolelybybarbarians；

thatCleopatraandJuliusCaesarareyetunborn；thattheChristianerahasnotyetbegun？Truly，itseemsasiftherecouldbenonewthingunderthesun。

X。SCIENCEOFTHEROMANPERIOD

WehaveseenthatthethirdcenturyB。C。wasatimewhenAlexandriansciencewasatitsheight，butthatthesecondcenturyproducedalsoinHipparchusatleastoneinvestigatoroftheveryfirstrank；though，tobesure，HipparchuscanbecalledanAlexandrianonlybycourtesy。IntheensuinggenerationstheGreekcapitalatthemouthoftheNilecontinuedtoholditsplaceasthecentreofscientificandphilosophicalthought。ThekingdomofthePtolemiesstillflourishedwithatleasttheoutwardappearancesofitsold-timeglory，andacompanyofgrammariansandcommentatorsofnosmallmeritcouldalwaysbefoundintheserviceofthefamousmuseumandlibrary；butthewholeaspectofworld-historywasrapidlychanging。Greece，afterherbriefdayofpoliticalsupremacy，wassinkingrapidlyintodesuetude，andthehard-headedRomanintheWestwasmakinghimselfmastereverywhere。WhileHipparchusofRhodeswasinhisprime，Corinth，thelaststrongholdofthemain-landofGreece，hadfallenbeforetheprowessoftheRoman，andthekingdomofthePtolemies，thoughstillnominallyfree，hadbeguntocomewithinthesphereofRomaninfluence。

JustwhatsharethesepoliticalchangeshadinchangingtheaspectofGreekthoughtisaquestionregardingwhichdifferenceofopinionmighteasilyprevail；buttherecanbenoquestionthat，foronereasonoranother，theAlexandrianschoolasacreativecentrewentintoarapiddeclineataboutthetimeoftheRomanrisetoworld-power。Therearesomedistinguishednames，but，asageneralrule，thespiritofthetimesisreminiscentratherthancreative；theworkerstendtocollatetheresearchesoftheirpredecessorsratherthantomakenewandoriginalresearchesforthemselves。Eratosthenes，theinventiveworld-measurer，wassucceededbyStrabo，theindustriouscollatoroffacts；AristarchusandHipparchus，theoriginatorsofnewastronomicalmethods，weresucceededbyPtolemy，theperfecteroftheirmethodsandthesystematizeroftheirknowledge。Meanwhile，intheWest，Romeneverbecameatrueculture-centre。ThegreatgeniusoftheRomanwaspolitical；theAugustanAgeproducedafewgreathistoriansandpoets，butnotasinglegreatphilosopherorcreativedevoteeofscience。Cicero，Lucian，Seneca，MarcusAurelius，giveusatbestareflectionofGreekphilosophy。Pliny，theoneworld-famousnameinthescientificannalsofRome，canlayclaimtonohighercreditthanthatofamarvellouslyindustriouscollectoroffacts——thecompilerofanencyclopaediawhichcontainsnotonecreativetouch。

Allinall，then，thisepochofRomandominationisonethatneeddetainthehistorianofsciencebutabriefmoment。WiththeculminationofGreekeffortintheso-calledHellenisticperiodwehaveseenancientscienceatitsclimax。TheRomanperiodisbutatimeoftransition，marking，asitwere，aplateauontheslopebetweenthoseearlierheightsandthedeep，darkvalleysoftheMiddleAges。Yetwecannotquitedisregardtheeffortsofsuchworkersasthosewehavejustnamed。Letustakeamorespecificglanceattheiraccomplishments。

TheearliestoftheseworkersinpointoftimeisStrabo。ThismostfamousofancientgeographerswasborninAmasia，Pontus，about63B。C。，andlivedtotheyear24A。D。，living，therefore，intheageofCaesarandAugustus，duringwhichthefinaltransformationinthepoliticalpositionofthekingdomofEgyptwaseffected。ThenameofStraboinamodifiedformhasbecomepopularizedthroughacuriouscircumstance。Thegeographer，itappears，wasafflictedwithapeculiarsquintoftheeyes，hencethenamestrabismus，whichthemodernoculistappliestothatparticularinfirmity。

Fortunately，thegreatgeographerhasnotbeenforcedtodependuponhearsayevidenceforrecognition。Hiscomprehensiveworkongeographyhasbeenpreservedinitsentirety，beingoneofthefewexpansiveclassicalwritingsofwhichthisistrue。TheotherwritingsofStrabo，however，includingcertainhistoriesofwhichreportshavecomedowntous，areentirelylost。Thegeographyisinmanywaysaremarkablebook。Itisnot，however，aworkinwhichanyimportantnewprinciplesareinvolved。RatherisittypicalofitsageinthatitisanelaboratecompilationandacriticalreviewofthelaborsofStrabo’spredecessors。Doubtlessitcontainsavastdealofnewinformationastothedetailsofgeography——preciseareasanddistance，questionsofgeographicallocationsastolatitudeandzones，andthelike。Buthoweverimportantthesedetailsmayhavebeenfromacontemporarystand-point，they，ofcourse，canhavenothingmorethanhistoricalinteresttoposterity。Thevalueoftheworkfromourpresentstand-pointischieflyduetothecriticismswhichStrabopassesuponhisforerunners，andtotheincidentalhistoricalandscientificreferenceswithwhichhisworkabounds。Beingwritteninthisclosingperiodofancientprogress，andsummarizing，asitdoes，infulldetailthegeographicalknowledgeofthetime，itservesasanimportantguide-markforthestudentoftheprogressofscientificthought。WecannotdobetterthanbrieflytofollowStraboinhisestimatesandcriticismsoftheworkofhispredecessors，takingnotethusofthepointofviewfromwhichhehimselflookedoutupontheworld。Weshallthusgainaclearideaastothestateofscientificgeographytowardsthecloseoftheclassicalepoch。

"Ifthescientificinvestigationofanysubjectbetheproperavocationofthephilosopher，"saysStrabo，"geography，thescienceofwhichweproposetotreat，iscertainlyentitledtoahighplace；andthisisevidentfrommanyconsiderations。Theywhofirstundertooktohandlethematterweredistinguishedmen。

Homer，AnaximandertheMilesian，andHecaeus(hisfellow-citizenaccordingtoEratosthenes)，Democritus，Eudoxus，Dicaearchus，andEphorus，withmanyothers，andafterthese，Eratosthenes，Polybius，andPosidonius，allofthemphilosophers。Noristhegreatlearningthroughwhichalonethissubjectcanbeapproachedpossessedbyanybutapersonacquaintedwithbothhumananddivinethings，andtheseattainmentsconstitutewhatiscalledphilosophy。Inadditiontoitsvastimportanceinregardtosociallifeandtheartofgovernment，geographyunfoldstousacelestialphenomena，acquaintsuswiththeoccupantsofthelandandocean，andthevegetation，fruits，andpeculiaritiesofthevariousquartersoftheearth，aknowledgeofwhichmarkshimwhocultivatesitasamanearnestinthegreatproblemoflifeandhappiness。"

Strabogoesontosaythatincommonwithothercritics，includingHipparchus，heregardsHomerasthefirstgreatgeographer。Hehasmuchtosayonthegeographicalknowledgeofthebard，butthisneednotdetainus。Wearechieflyconcernedwithhiscommentuponhismorerecentpredecessors，beginningwithEratosthenes。Theconstantreferencetothisworkershowstheimportantpositionwhichheheld。Straboappearsneitherasdetractornoraspartisan，butasonewhoearnestlydesiresthetruth。Sometimesheseemscaptiousinhiscriticismsregardingsomedetail，norishealwayscorrectinhisemendationsofthelaborsofothers；but，onthewhole，hisworkismarkedbyanevidentattemptatfairness。Inreadinghisbook，however，oneisforcedtotheconclusionthatStraboisaninvestigatorofdetails，notanoriginalthinker。Heseemsmoreconcernedwithprecisemeasurementsthanwithquestioningsastotheopenproblemsofhisscience。Whateverheaccepts，then，maybetakenasvirtuallythestockdoctrineoftheperiod。

"Asthesizeoftheearth，"hesays，"hasbeendemonstratedbyotherwriters，weshallheretakeforgrantedandreceiveasaccuratewhattheyhaveadvanced。Weshallalsoassumethattheearthisspheroidal，thatitssurfaceislikewisespheroidaland，aboveall，thatbodieshaveatendencytowardsitscentre，whichlatterpointiscleartotheperceptionofthemostaverageunderstanding。However，wemayshowsummarilythattheearthisspheroidal，fromtheconsiderationthatallthings，howeverdistant，tendtoitscentre，andthateverybodyisattractedtowardsitscentrebygravity。Thisismoredistinctlyprovedfromobservationsoftheseaandsky，forheretheevidenceofthesensesandcommonobservationisalonerequisite。Theconvexityoftheseaisafurtherproofofthistothosewhohavesailed，fortheycannotperceivelightsatadistancewhenplacedatthesamelevelastheireyes，andifraisedonhightheyatoncebecomeperceptibletovisionthoughatthesametimefartherremoved。Sowhentheeyeisraiseditseeswhatbeforewasutterlyimperceptible。Homerspeaksofthiswhenhesays:

"’Lifteduponthevastwavehequicklybeheldafar。’

Sailorsastheyapproachtheirdestinationbeholdtheshorecontinuallyraisingitselftotheirview，andobjectswhichhadatfirstseemedlowbegintoliftthemselves。Ourgnomons，also，are，amongotherthings，evidenceoftherevolutionoftheheavenlybodies，andcommon-senseatonceshowsusthatifthedepthoftheearthwereinfinitesucharevolutioncouldnottakeplace。"[1]

ElsewhereStrabocriticisesEratosthenesforhavingenteredintoalongdiscussionastotheformoftheearth。Thismatter，Strabothinks，"shouldhavebeendisposedofinthecompassofafewwords。"Obviouslythisdoctrineoftheglobe’ssphericityhad，inthecourseof600years，becomesofirmlyestablishedamongtheGreekthinkersastoseemalmostaxiomatic。WeshallseelateronhowtheWesternworldmadeacuriousrecessionfromthisseeminglysecurepositionunderstimulusofanOrientalmisconception。Astothesizeoftheglobe，StraboisdisposedtoacceptwithoutparticularcommentthemeasurementsofEratosthenes。Hespeaks，however，of"morerecentmeasurements，"

referringinparticulartothatadoptedbyPosidonius，accordingtowhichthecircumferenceisonlyaboutonehundredandeightythousandstadia。Posidonius，wemaynoteinpassing，wasacontemporaryandfriendofCicero，andhencelivedshortlybeforethetimeofStrabo。HismeasurementoftheearthwasbasedonobservationsofastarwhichbarelyroseabovethesouthernhorizonatRhodesascomparedwiththeheightofthesamestarwhenobservedatAlexandria。ThismeasurementofPosidonius，togetherwiththeevenmorefamousmeasurementofEratosthenes，appearstohavebeenpracticallythesoleguideastothesizeoftheearththroughoutthelaterperiodsofantiquity，and，indeed，untilthelaterMiddleAges。

Asbecomesawriterwhoisprimarilygeographerandhistorianratherthanastronomer，Straboshowsamuchkeenerinterestinthehabitableportionsoftheglobethanintheglobeasawhole。

Heassuresusthatthishabitableportionoftheearthisagreatisland，"sincewherevermenhaveapproachedtheterminationoftheland，thesea，whichwedesignateocean，hasbeenmetwith，andreasonassuresusofthesimilarityofthisplacewhichoursenseshavenotbeentemptedtosurvey。"Hepointsoutthatwhereassailorshavenotcircumnavigatedtheglobe，thattheyhadnotbeenpreventedfromdoingsobyanycontinent，anditseemstohimaltogetherunlikelythattheAtlanticOceanisdividedintotwoseasbynarrowisthmusessoplacedastopreventcircumnavigation。"Howmuchmoreprobablethatitisconfluentanduninterrupted。Thistheory，"headds，"goesbetterwiththeebbandflowoftheocean。Moreover(andherehisreasoningbecomesmorefanciful)，thegreatertheamountofmoisturesurroundingtheearth，theeasierwouldtheheavenlybodiesbesuppliedwithvaporfromthence。"Yetheisdisposedtobelieve，followingPlato，thatthetradition"concerningtheislandofAtlantosmightbereceivedassomethingmorethanidlefiction，ithavingbeenrelatedbySolon，ontheauthorityoftheEgyptianpriests，thatthisisland，almostaslargeasacontinent，wasformerlyinexistencealthoughnowithaddisappeared。"[2]

Inaword，then，StraboentertainsnodoubtwhateverthatitwouldbepossibletosailaroundtheglobefromSpaintoIndia。

Indeed，somatter-of-factaninferencewasthisthatthefeatofColumbuswouldhaveseemedlesssurprisinginthefirstcenturyofourerathanitdidwhenactuallyperformedinthefifteenthcentury。Theterrorsofthegreatoceanheldthemarinerback，ratherthananydoubtastowherehewouldarriveattheendofthevoyage。

Coupledwiththeideathatthehabitableportionoftheearthisanisland，therewaslinkedatolerablydefinitenotionastotheshapeofthisisland。ThisshapeStrabolikenstoamilitarycloak。Thecomparisondoesnotseempeculiarlyaptwhenwearetoldpresentlythatthelengthofthehabitableearthismorethantwiceitsbreadth。Thisidea，Straboassuresus，accordswiththemostaccurateobservations"bothancientandmodern。"

Theseobservationsseemedtoshowthatitisnotpossibletoliveintheregionclosetotheequator，andthat，ontheotherhand，thecoldtemperaturesharplylimitsthehabitabilityoftheglobetowardsthenorth。AllthecivilizationofantiquityclusteredabouttheMediterranean，orextendedofftowardstheeastataboutthesamelatitude。Hencegeographerscametothinkofthehabitableglobeashavingthesomewhatlenticularshapewhichacrudemapoftheseregionssuggests。WehavealreadyhadoccasiontoseethatatanearlierdayAnaxagoraswasperhapsinfluencedinhisconceptionoftheshapeoftheearthbythisidea，andtheconstantreferencesofStraboimpressuponusthethoughtthatthislong，relativelynarrowareaoftheearth’ssurfaceistheonlyonewhichcanbeconceivedofashabitable。

Strabohadmuchtotellusconcerningzones，which，followingPosidonius，hebelievestohavebeenfirstdescribedbyParmenides。Wemaynote，however，thatothertraditionsassertthatbothThalesandPythagorashaddividedtheearthintozones。

ThenumberofzonesacceptedbyStraboisfive，andhecriticisesPolybiusformakingthenumbersix。ThefivezonesacceptedbyStraboareasfollows:theuninhabitabletorridzonelyingintheregionoftheequator；azoneoneithersideofthisextendingtothetropic；andthenthetemperatezonesextendingineitherdirectionfromthetropictothearcticregions。Thereseemstohavebeenagooddealofdisputeamongthescholarsofthetimeastotheexactarrangementofthesezones，butthegeneralideathatthenorth-temperatezoneisthepartoftheearthwithwhichthegeographerdealsseemedclearlyestablished。Thatthesouth-temperatezonewouldalsopresentahabitableareaisanideathatissometimessuggested，thoughseldomorneverdistinctlyexpressed。Itisprobablethatdifferentopinionswereheldastothis，andnodirectevidencebeingavailable，acautiouslyscientificgeographerlikeStrabowouldnaturallyavoidtheexpressionofanopinionregardingit。

Indeed，hisownwordsleaveussomewhatindoubtastotheprecisecharacterofhisnotionregardingthezones。Perhapsweshalldobesttoquotethem:

"Lettheearthbesupposedtoconsistoffivezones。(1)Theequatorialcircledescribedaroundit。(2)Anotherparalleltothis，anddefiningthefrigidzoneofthenorthernhemisphere。

(3)Acirclepassingthroughthepolesandcuttingthetwoprecedingcirclesatright-angles。Thenorthernhemispherecontainstwoquartersoftheearth，whichareboundedbytheequatorandcirclepassingthroughthepoles。Eachofthesequartersshouldbesupposedtocontainafour-sideddistrict，itsnorthernsidebeingofone-halfoftheparallelnextthepole，itssouthernbythehalfoftheequator，anditsremainingsidesbytwosegmentsofthecircledrawnthroughthepoles，oppositetoeachother，andequalinlength。Inoneofthese(whichofthemisofnoconsequence)theearthwhichweinhabitissituated，surroundedbyaseaandsimilartoanisland。This，aswesaidbefore，isevidentbothtooursensesandtoourreason。

Butletanyonedoubtthis，itmakesnodifferencesofarasgeographyisconcernedwhetheryoubelievetheportionoftheearthwhichweinhabittobeanislandoronlyadmitwhatweknowfromexperience——namely，thatwhetheryoustartfromtheeastorthewestyoumaysailallaroundit。Certainintermediatespacesmayhavebeenleft(unexplored)，buttheseareaslikelytobeoccupiedbyseaasuninhabitedland。Theobjectofthegeographeristodescribeknowncountries。Thosewhichareunknownhepassesoverequallywiththosebeyondthelimitsoftheinhabitedearth。

Itwill，therefore，besufficientfordescribingthecontouroftheislandwehavebeenspeakingof，ifwejoinbyarightlinetheoutmostpointswhich，uptothistime，havebeenexploredbyvoyagersalongthecoastoneitherside。"[3]

WemaypassoverthespecificcriticismsofStrabouponvariousexplorationsthatseemtohavebeenofgreatinteresttohiscontemporaries，includinganallegedtripofoneEudoxusoutintotheAtlantic，andthejourneyingsofPytheasinthefarnorth。ItisPytheas，wemayadd，whowascitedbyHipparchusashavingmadethemistakenobservationthatthelengthoftheshadowofthegnomonisthesameatMarseillesandByzantium，hencethatthesetwoplacesareonthesameparallel。ModerncommentatorshavedefendedPytheasasregardsthisobservation，claimingthatitwasHipparchusandnotPytheaswhomadethesecondobservationfromwhichthefaultyinductionwasdrawn。Thepointisofnogreatsignificance，however，exceptasshowingthatacorrectmethodofdeterminingtheproblemsoflatitudehadthusearlybeensuggested。Thatfaultyobservationsandfaultyapplicationofthecorrectprincipleshouldhavebeenmadeisnotsurprising。

Neitherneedweconcernourselveswiththedetailsastothegeographicaldistances，whichStrabofoundsoworthyofcriticismandcontroversy。Butinleavingthegreatgeographerwemayemphasizehispointofviewandthatofhiscontemporariesbyquotingthreefundamentalprincipleswhichhereiteratesasbeingamongthe"factsestablishedbynaturalphilosophers。"Hetellsusthat"(1)Theearthandheavensarespheroidal。(2)Thetendencyofallbodieshavingweightistowardsacentre。(3)

Further，theearthbeingspheroidalandhavingthesamecentreastheheavens，ismotionless，aswellastheaxisthatpassesthroughbothitandtheheavens。Theheavensturnroundboththeearthanditsaxis，fromeasttowest。Thefixedstarsturnroundwithitatthesamerateasthewhole。Thesefixedstarsfollowintheircourseparallelcircles，theprincipalofwhicharetheequator，twotropics，andthearcticcircles；whiletheplanets，thesun，andthemoondescribecertaincirclescomprehendedwithinthezodiac。"[4]

Here，then，isacuriousminglingoftruthanderror。ThePythagoreandoctrinethattheearthisroundhadbecomeacommonplace，butitwouldappearthatthetheoryofAristarchus，accordingtowhichtheearthisinmotion，hasbeenalmostabsolutelyforgotten。Strabodoesnotsomuchasrefertoit；

neither，asweshallsee，isittreatedwithgreaterrespectbytheotherwritersoftheperiod。

TWOFAMOUSEXPOSITORS——PLINYANDPTOLEMY

WhileStrabowaspursuinghisgeographicalstudiesatAlexandria，ayoungmancametoRomewhowasdestinedtomakehisnamemorewidelyknowninscientificannalsthanthatofanyotherLatinwriterofantiquity。ThismanwasPliniusSecundus，who，todistinguishhimfromhisnephew，afamouswriterinanotherfield，isusuallyspokenofasPlinytheElder。ThereisafamousstorytotheeffectthatthegreatRomanhistorianLivyononeoccasionaddressedacasualassociateintheamphitheatreatRome，andonlearningthatthestrangerhailedfromtheoutlyingSpanishprovinceoftheempire，remarkedtohim，"Yetyouhavedoubtlessheardofmywritingseventhere。""Then，"repliedthestranger，"youmustbeeitherLivyorPliny。"

TheanecdoteillustratesthewidefamewhichtheRomannaturalistachievedinhisownday。AndtherecordsoftheMiddleAgesshowthatthispopularitydidnotabateinsucceedingtimes。Indeed，theNaturalHistoryofPlinyisoneofthecomparativelyfewbulkywritingsofantiquitythattheeffortsofcopyistshavepreservedtousalmostentire。Itis，indeed，aremarkableworkandeminentlytypicalofitstime；butitsauthorwasanindustriouscompiler，notacreativegenius。Asamonumentofindustryithasseldombeenequalled，andinthisregarditseemsthemoreremarkableinasmuchasPlinywasapracticalmanofaffairswhooccupiedmostofhislifeasasoldierfightingthebattlesoftheempire。Hecompiledhisbookintheleisurehoursstolenfromsleep，oftenwritingbythelightofthecamp-fire。

Yethecitesorquotesfromaboutfourthousandworks，mostofwhichareknowntousonlybyhisreferences。DoubtlessPlinyaddedmuchthroughhisownobservations。Weknowhowkeenwashisdesiretoinvestigate，sincehelosthislifethroughattemptingtoapproachthecraterofVesuviusontheoccasionofthatmemorableeruptionwhichburiedthecitiesofHerculaneumandPompeii。

DoubtlessthewanderinglifeofthesoldierhadgivenPlinyabundantopportunityforpersonalobservationinhisfavoritefieldsofbotanyandzoology。Buttherecordsofhisownobservationsaresointermingledwithknowledgedrawnfrombooksthatitisdifficulttodistinguishtheonefromtheother。Nordoesthisgreatlymatter，forwhetherascloset-studentorfield-naturalist，Pliny’straitofmindisessentiallythatofthecompiler。Hewasnophilosophicalthinker，nogeneralizer，nopath-makerinscience。Helivedatthecloseofagreatprogressiveepochofthought；inoneofthosestaticperiodswhennumberlessobserverspiledupanimmensemassofdetailswhichmightadvantageouslybesortedintoakindofencyclopaedia。Suchanencyclopaediaistheso-calledNaturalHistoryofPliny。Itisavastjumbleofmoreorlessuncriticalstatementsregardingalmosteveryfieldofcontemporaryknowledge。Thedescriptionsofanimalsandplantspredominate，buttheworkasawholewouldhavebeenimmenselyimprovedhadthecompilershownamorecriticalspirit。Asitis，heseemsratherdisposedtoquoteanyinterestingcitationthathecomesacrossinhisomnivorousreadings，shieldinghimselfbehindanequivocal"itissaid，"or"soandsoalleges。"Asingleillustrationwillsufficetoshowwhatmannerofthingisthoughtworthyofrepetition。

"Itisasserted，"hesays，"thatifthefishcalledasea-starissmearedwiththefox’sbloodandthennailedtotheupperlintelofthedoor，ortothedooritself，withacoppernail，nonoxiousspellwillbeabletoobtainadmittance，or，atallevents，beproductiveofanyilleffects。"

Itiseasilycomprehensiblethataworkfortifiedwithsuchpracticaldetailsasthisshouldhavegainedwidepopularity。

Doubtlessthenaturalhistoriesofourowndaywouldfindreadiersaleweretheytopandertovarioussuperstitionsnotaltogetherdifferentfromthatheresuggested。Theman，forexample，whobelievesthattohaveablackcatcrosshispathisaluckyomenwouldnaturallyfindhimselfattractedbyabookwhichtookaccountofthisandsimilarimportantdetailsofnaturalhistory。

Perhaps，therefore，itwasitsinclusionofabsurdities，quiteasmuchasitslegitimatevalue，thatgavevoguetothecelebratedworkofPliny。Butbethatasitmay，themostfamousscientistofRomemustberememberedasapopularwriterratherthanasanexperimentalworker。Inthehistoryofthepromulgationofscientificknowledgehisworkisimportant；inthehistoryofscientificprinciplesitmayvirtuallybedisregarded。

PTOLEMY，THELASTGREATASTRONOMEROFANTIQUITY

AlmostthesamethingmaybesaidofPtolemy，anevenmorecelebratedwriter，whowasbornnotverylongafterthedeathofPliny。TheexactdatesofPtolemy’slifearenotknown，buthisrecordedobservationsextendtotheyear151A。D。Hewasaworkingastronomer，andhemadeatleastoneoriginaldiscoveryofsomesignificance——namely，theobservationofahithertounrecordedirregularityofthemoon’smotion，whichcametobespokenofasthemoon’sevection。Thisconsistsofperiodicalaberrationsfromthemoon’sregularmotioninitsorbit，which，aswenowknow，areduetothegravitationpullofthesun，butwhichremainedunexplaineduntilthetimeofNewton。Ptolemyalsomadeoriginalobservationsastothemotionsoftheplanets。Heis，therefore，entitledtoarespectableplaceasanobservingastronomer；buthischieffamerestsonhiswritings。

Hisgreatworkshavetodowithgeographyandastronomy。IntheformerfieldhemakesanadvanceuponStrabo，citingthelatitudeofnofewerthanfivethousandplaces。Inthefieldofastronomy，hisgreatservicewastohavemadeknowntotheworldthelaborsofHipparchus。Ptolemyhasbeenaccusedoftakingthestar-chartofhisgreatpredecessorwithoutduecredit，andindeeditseemsdifficulttoclearhimofthischarge。Yetitisatleastopentodoubtwhetherbeintendedanyimpropriety，inasmuchasbeallalongissedulousinhisreferencestohispredecessor。Indeed，hisworkmightalmostbecalledanexpositionoftheastronomicaldoctrinesofHipparchus。NoonepretendsthatPtolemyistobecomparedwiththeRhodesianobserverasanoriginalinvestigator，butasapopularexpounderhissuperiorityisevidencedinthefactthatthewritingsofPtolemybecamepracticallythesoleastronomicaltext-bookoftheMiddleAgesbothintheEastandintheWest，whilethewritingsofHipparchuswereallowedtoperish。

ThemostnotedofallthewritingsofPtolemyistheworkwhichbecamefamousundertheArabicnameofAlmagest。ThiswordiscuriouslyderivedfromtheGreektitle，"thegreatestconstruction，"anamegiventhebooktodistinguishitfromaworkonastrologyinfourbooksbythesameauthor。Forconvenienceofreferenceitcametobespokenofmerelyas，fromwhichtheArabsformthetitleTabairalMagisthi，underwhichtitlethebookwaspublishedintheyear827。FromthisitderivedthewordAlmagest，bywhichPtolemy’sworkcontinuedtobeknownamongtheArabs，andsubsequentlyamongEuropeanswhenthebookagainbecameknownintheWest。Ptolemy’sbook，ashasbeensaid，isvirtuallyanelaborationofthedoctrinesofHipparchus。Itassumesthattheearthisthefixedcentreofthesolarsystem，andthatthestarsandplanetsrevolveaboutitintwenty-fourhours，theearthbeing，ofcourse，spherical。ItwasnottobeexpectedthatPtolemyshouldhaveadoptedtheheliocentricideaofAristarchus。Yetitismuchtoberegrettedthathefailedtodoso，sincethedeferencewhichwasaccordedhisauthoritythroughouttheMiddleAgeswoulddoubtlesshavebeenextendedinsomemeasureatleasttothistheoryaswell，hadhechampionedit。Contrariwise，hisunqualifiedacceptanceofthegeocentricdoctrinesufficedtoplacethatdoctrinebeyondtherangeofchallenge。

TheAlmagesttreatsofallmannerofastronomicalproblems，butthefeatureofitwhichgaineditwidestcelebritywasperhapsthatwhichhastodowitheccentricsandepicycles。Thistheorywas，ofcourse，butanelaborationoftheideasofHipparchus；

but，owingtothecelebrityoftheexpositor，ithascometobespokenofasthetheoryofPtolemy。WehavesufficientlydetailedthetheoryinspeakingofHipparchus。Itshouldbeexplained，however，that，withbothHipparchusandPtolemy，thetheoryofepicycleswouldappeartohavebeenheldratherasaworkinghypothesisthanasacertainty，sofarastheactualityoftheminorspheresorepicyclesisconcerned。Thatistosay，theseastronomersprobablydidnotconceiveeithertheepicyclesorthegreaterspheresasconstitutingactualsolidsubstances。