a history of science-1-第46章

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　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　the　historian；　Eratosthenes　must　stand　as　the　inventor　of　the　method　with　which　his　name　is　associated；　and　as　the　first　man　of　whom　we　can　say　with　certainty　that　he　measured　the　size　of　the　earth。　Right　worthily；　then；　had　the　Alexandrian　philosopher　won　his　proud　title　of　〃surveyor　of　the　world。〃

HIPPARCHUS；　〃THE　LOVER　OF　TRUTH〃　Eratosthenes　outlived　most　of　his　great　contemporaries。　He　saw　the　turning　of　that　first　and　greatest　century　of　Alexandrian　science；　the　third　century　before　our　era。　He　died　in　the　year　196　B。C。；　having；　it　is　said；　starved　himself　to　death　to　escape　the　miseries　of　blindness；to　the　measurer　of　shadows；　life　without　light　seemed　not　worth　the　living。　Eratosthenes　left　no　immediate　successor。　A　generation　later；　however；　another　great　figure　appeared　in　the　astronomical　world　in　the　person　of　Hipparchus；　a　man　who；　as　a　technical　observer；　had　perhaps　no　peer　in　the　ancient　world：　one　who　set　so　high　a　value　upon　accuracy　of　observation　as　to　earn　the　title　of　〃the　lover　of　truth。〃　Hipparchus　was　born　at　Nicaea；　in　Bithynia；　in　the　year　160　B。C。　His　life；　all　too　short　for　the　interests　of　science；　ended　in　the　year　125　B。C。　The　observations　of　the　great　astronomer　were　made　chiefly；　perhaps　entirely；　at　Rhodes。　A　misinterpretation　of　Ptolemy's　writings　led　to　the　idea　that　Hipparchus；　performed　his　chief　labors　in　Alexandria；　but　it　is　now　admitted　that　there　is　no　evidence　for　this。　Delambre　doubted；　and　most　subsequent　writers　follow　him　here；　whether　Hipparchus　ever　so　much　as　visited　Alexandria。　In　any　event　there　seems　to　be　no　question　that　Rhodes　may　claim　the　honor　of　being　the　chief　site　of　his　activities。　It　was　Hipparchus　whose　somewhat　equivocal　comment　on　the　work　of　Eratosthenes　we　have　already　noted。　No　counter…charge　in　kind　could　be　made　against　the　critic　himself；　he　was　an　astronomer　pure　and　simple。　His　gift　was　the　gift　of　accurate　observation　rather　than　the　gift　of　imagination。　No　scientific　progress　is　possible　without　scientific　guessing；　but　Hipparchus　belonged　to　that　class　of　observers　with　whom　hypothesis　is　held　rigidly　subservient　to　fact。　It　was　not　to　be　expected　that　his　mind　would　be　attracted　by　the　heliocentric　theory　of　Aristarchus。　He　used　the　facts　and　observations　gathered　by　his　great　predecessor　of　Samos；　but　he　declined　to　accept　his　theories。　For　him　the　world　was　central；　his　problem　was　to　explain；　if　he　could；　the　irregularities　of　motion　which　sun；　moon；　and　planets　showed　in　their　seeming　circuits　about　the　earth。　Hipparchus　had　the　gnomon　of　Eratosthenesdoubtless　in　a　perfected　formto　aid　him；　and　he　soon　proved　himself　a　master　in　its　use。　For　him；　as　we　have　said；　accuracy　was　everything；　this　was　the　one　element　that　led　to　all　his　great　successes。　Perhaps　his　greatest　feat　was　to　demonstrate　the　eccentricity　of　the　sun's　seeming　orbit。　We　of　to…day；　thanks　to　Keppler　and　his　followers；　know　that　the　earth　and　the　other　planetary　bodies　in　their　circuit　about　the　sun　describe　an　ellipse　and　not　a　circle。　But　in　the　day　of　Hipparchus；　though　the　ellipse　was　recognized　as　a　geometrical　figure　（it　had　been　described　and　named　along　with　the　parabola　and　hyperbola　by　Apollonius　of　Perga；　the　pupil　of　Euclid）；　yet　it　would　have　been　the　rankest　heresy　to　suggest　an　elliptical　course　for　any　heavenly　body。　A　metaphysical　theory；　as　propounded　perhaps　by　the　Pythagoreans　but　ardently　supported　by　Aristotle；　declared　that　the　circle　is　the　perfect　figure；　and　pronounced　it　inconceivable　that　the　motions　of　the　spheres　should　be　other　than　circular。　This　thought　dominated　the　mind　of　Hipparchus；　and　so　when　his　careful　measurements　led　him　to　the　discovery　that　the　northward　and　southward　journeyings　of　the　sun　did　not　divide　the　year　into　four　equal　parts；　there　was　nothing　open　to　him　but　to　either　assume　that　the　earth　does　not　lie　precisely　at　the　centre　of　the　sun's　circular　orbit　or　to　find　some　alternative　hypothesis。　In　point　of　fact；　the　sun　（reversing　the　point　of　view　in　accordance　with　modern　discoveries）　does　lie　at　one　focus　of　t