a history of science-1-第52章

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yptian　territory　and　a　glimpse　of　the　sun's　shadow　makes　it　seem　but　the　more　wonderful。　Yet　the　method　of　Eratosthenes；　like　many　another　enigma；　seems　simple　enough　once　it　is　explained。　It　required　but　the　application　of　a　very　elementary　knowledge　of　the　geometry　of　circles；　combined　with　the　use　of　a　fact　or　two　from　local　geographywhich　detracts　nothing　from　the　genius　of　the　man　who　could　reason　from　such　simple　premises　to　so　wonderful　a　conclusion。　Stated　in　a　few　words；　the　experiment　of　Eratosthenes　was　this。　His　geographical　studies　had　taught　him　that　the　town　of　Syene　lay　directly　south　of　Alexandria；　or；　as　we　should　say；　on　the　same　meridian　of　latitude。　He　had　learned；　further；　that　Syene　lay　directly　under　the　tropic；　since　it　was　reported　that　at　noon　on　the　day　of　the　summer　solstice　the　gnomon　there　cast　no　shadow；　while　a　deep　well　was　illumined　to　the　bottom　by　the　sun。　A　third　item　of　knowledge；　supplied　by　the　surveyors　of　Ptolemy；　made　the　distance　between　Syene　and　Alexandria　five　thousand　stadia。　These；　then；　were　the　preliminary　data　required　by　Eratosthenes。　Their　significance　consists　in　the　fact　that　here　is　a　measured　bit　of　the　earth's　arc　five　thousand　stadia　in　length。　If　we　could　find　out　what　angle　that　bit　of　arc　subtends；　a　mere　matter　of　multiplication　would　give　us　the　size　of　the　earth。　But　how　determine　this　all…important　number？　The　answer　came　through　reflection　on　the　relations　of　concentric　circles。　If　you　draw　any　number　of　circles；　of　whatever　size；　about　a　given　centre；　a　pair　of　radii　drawn　from　that　centre　will　cut　arcs　of　the　same　relative　size　from　all　the　circles。　One　circle　may　be　so　small　that　the　actual　arc　subtended　by　the　radii　in　a　given　case　may　be　but　an　inch　in　length；　while　another　circle　is　so　large　that　its　corresponding　are　is　measured　in　millions　of　miles；　but　in　each　case　the　same　number　of　so…called　degrees　will　represent　the　relation　of　each　arc　to　its　circumference。　Now；　Eratosthenes　knew；　as　just　stated；　that　the　sun；　when　on　the　meridian　on　the　day　of　the　summer　solstice；　was　directly　over　the　town　of　Syene。　This　meant　that　at　that　moment　a　radius　of　the　earth　projected　from　Syene　would　point　directly　towards　the　sun。　Meanwhile；　of　course；　the　zenith　would　represent　the　projection　of　the　radius　of　the　earth　passing　through　Alexandria。　All　that　was　required；　then；　was　to　measure；　at　Alexandria；　the　angular　distance　of　the　sun　from　the　zenith　at　noon　on　the　day　of　the　solstice　to　secure　an　approximate　measurement　of　the　arc　of　the　sun's　circumference；　corresponding　to　the　arc　of　the　earth's　surface　represented　by　the　measured　distance　between　Alexandria　and　Syene。　The　reader　will　observe　that　the　measurement　could　not　be　absolutely　accurate；　because　it　is　made　from　the　surface　of　the　earth；　and　not　from　the　earth's　centre；　but　the　size　of　the　earth　is　so　insignificant　in　comparison　with　the　distance　of　the　sun　that　this　slight　discrepancy　could　be　disregarded。　The　way　in　which　Eratosthenes　measured　this　angle　was　very　simple。　He　merely　measured　the　angle　of　the　shadow　which　his　perpendicular　gnomon　at　Alexandria　cast　at　mid…day　on　the　day　of　the　solstice；　when；　as　already　noted；　the　sun　was　directly　perpendicular　at　Syene。　Now　a　glance　at　the　diagram　will　make　it　clear　that　the　measurement　of　this　angle　of　the　shadow　is　merely　a　convenient　means　of　determining　the　precisely　equal　opposite　angle　subtending　an　arc　of　an　imaginary　circle　passing　through　the　sun；　the　are　which；　as　already　explained；　corresponds　with　the　arc　of　the　earth's　surface　represented　by　the　distance　between　Alexandria　and　Syene。　He　found　this　angle　to　represent　7　degrees　12'；　or　one…fiftieth　of　the　circle。　Five　thousand　stadia；　then；　represent　one…fiftieth　of　the　earth's　circumference；　the　entire　circumference　being；　therefore；　250；000　stadia。　Unfortunately；　we　do　not　know　which　one　of　the　various　measurements　used　in　antiquity　is　represented　by　the　stadia　of　Eratosthenes。　According　to　the　researches　of　Lepsius；　however；　the　stadium　in　question　represented　180　meters；　and　this　would　make　the　earth；　according　to　the　measurement　of　Eratosthenes；　about　twenty…eight　thousand　miles　in　circumference；　an　answer　sufficiently　exact　to　justify　the　wonder　which　the　experiment　excited　in　antiquity；　and　the　admiration　with　which　it　has　ever　since　been　regarded。　｛illustration　caption　=　　DIAGRAM　TO　ILLUSTRATE　ERATOSTHENES'　MEASUREMENT　OF　THE　GLOBE　FIG。　1。　AF　is　a　gnomon　at　Alexandria；　SB　a　gnomon　at　Svene；　IS　and　JK　represent　the　sun's　rays。　The　angle　actually　measured　by　Eratosthenes　is　KFA；　as　determined　by　the　shadow　cast　by　the　gnomon　AF。　This　angle　is　equal　to　the　opposite　angle　JFL；　which　measures　the　sun's　distance　from　the　zenith；　and　which　is　also　equal　to　the　angle　AESto　determine　the　Size　of　which　is　the　real　object　of　the　entire　measurement。　FIG。　2　shows　the　form　of　the　gnomon　actually　employed　in　antiquity。　The　hemisphere　KA　being　marked　with　a　scale；　it　is　obvious　that　in　actual　practice　Eratosthenes　required　only　to　set　his　gnomon　in　the　sunlight　at　the　proper　moment；　and　read　off　the　answer　to　his　problem　at　a　glance。　The　simplicity　of　the　method　makes　the　result　seem　all　the　more　wonderful。｝　Of　course　it　is　the　method；　and　not　its　details　or　its　exact　results；　that　excites　our　interest。　And　beyond　question　the　method　was　an　admirable　one。　Its　result；　however；　could　not　have　been　absolutely　accurate；　because；　while　correct　in　principle；　its　data　were　defective。　In　point　of　fact　Syene　did　not　lie　precisely　on　the　same　meridian　as　Alexandria；　neither　did　it　lie　exactly　on　the　tropic。　Here；　then；　are　two　elements　of　inaccuracy。　Moreover；　it　is　doubtful　whether　Eratosthenes　made　allowance；　as　he　should　have　done；　for　the　semi…diameter　of　the　sun　in　measuring　the　angle　of　the　shadow。　But　these　are　mere　details；　scarcely　worthy　of　mention　from　our　present　stand…point。　What　perhaps　is　deserving　of　more　attention　is　the　fact　that　this　epoch…making　measurement　of　Eratosthenes　may　not　have　been　the　first　one　to　be　made。　A　passage　of　Aristotle　records　that　the　size　of　the　earth　was　said　to　be　400；000　stadia。　Some　commentators　have　thought　that　Aristotle　merely　referred　to　the　area　of　the　inhabited　portion　of　the　earth　and　not　to　the　circumference　of　the　earth　itself；　but　his　words　seem　doubtfully　susceptible　of　this　interpretation；　and　if　he　meant；　as　his　words　seem　to　imply；　that　philosophers　of　his　day　had　a　tolerably　precise　idea　of　the　globe；　we　must　assume　that　this　idea　was　based　upon　some　sort　of　measurement。　The　recorded　size；　400；000　stadia；　is　a　sufficient　approximation　to　the　truth　to　suggest　something　more　than　a　mere　unsupported　guess。　Now；　since　Aristotle　died　more　than　fifty　years　before　Eratosthenes　was　born；　his　report　as　to　the　alleged　size　of　the　earth　certainly　has　a　suggestiveness　that　cannot　be　overlooked；　but　it　arouses　speculations　without　giving　an　inkling　as　to　their　solution。　If　Eratosthenes　had　a　precursor　as　an　earth…measurer；　no　hint　or　rumor　has　come　down　to　us　that　would　enable　us　to　guess　who　that　precursor　may　have　been。　His　personality　is　as　deeply　enveloped　in　the　mists　of　the　past　as　are　the　personalities　of　the　great　prehistoric　discoverers。　For　the　purpose　of