a history of science-1-第51章

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nd　less　than　forty…three　to　six。　〃Proposition　seventeen。　The　bulk　of　the　sun　is　to　that　of　the　earth　in　greater　proportion　than　6859　to　27；　and　less　than　79；507　to　216。　〃Proposition　eighteen。　The　diameter　of　the　earth　is　to　the　diameter　of　the　moon　in　greater　proportion　than　108　to　43　and　less　than　60　to　19。　〃Proposition　nineteen。　The　bulk　of　the　earth　is　to　that　of　the　moon　in　greater　proportion　than　1；259；712　to　79；507　and　less　than　20；000　to　6859。〃　Such　then　are　the　more　important　conclusions　of　this　very　remarkable　papera　paper　which　seems　to　have　interest　to　the　successors　of　Aristarchus　generation　after　generation；　since　this　alone　of　all　the　writings　of　the　great　astronomer　has　been　preserved。　How　widely　the　exact　results　of　the　measurements　of　Aristarchus；　differ　from　the　truth；　we　have　pointed　out　as　we　progressed。　But　let　it　be　repeated　that　this　detracts　little　from　the　credit　of　the　astronomer　who　had　such　clear　and　correct　conceptions　of　the　relations　of　the　heavenly　bodies　and　who　invented　such　correct　methods　of　measurement。　Let　it　be　particularly　observed；　however；　that　all　the　conclusions　of　Aristarchus　are　stated　in　relative　terms。　He　nowhere　attempts　to　estimate　the　precise　size　of　the　earth；　of　the　moon；　or　of　the　sun；　or　the　actual　distance　of　one　of　these　bodies　from　another。　The　obvious　reason　for　this　is　that　no　data　were　at　hand　from　which　to　make　such　precise　measurements。　Had　Aristarchus　known　the　size　of　any　one　of　the　bodies　in　question；　he　might　readily；　of　course；　have　determined　the　size　of　the　others　by　the　mere　application　of　his　relative　scale；　but　he　had　no　means　of　determining　the　size　of　the　earth；　and　to　this　extent　his　system　of　measurements　remained　imperfect。　Where　Aristarchus　halted；　however；　another　worker　of　the　same　period　took　the　task　in　hand　and　by　an　altogether　wonderful　measurement　determined　the　size　of　the　earth；　and　thus　brought　the　scientific　theories　of　cosmology　to　their　climax。　This　worthy　supplementor　of　the　work　of　Aristarchus　was　Eratosthenes　of　Alexandria。

ERATOSTHENES；　〃THE　SURVEYOR　OF　THE　WORLD〃　An　altogether　remarkable　man　was　this　native　of　Cyrene；　who　came　to　Alexandria　from　Athens　to　be　the　chief　librarian　of　Ptolemy　Euergetes。　He　was　not　merely　an　astronomer　and　a　geographer；　but　a　poet　and　grammarian　as　well。　His　contemporaries　jestingly　called　him　Beta　the　Second；　because　he　was　said　through　the　universality　of　his　attainments　to　be　〃a　second　Plato〃　in　philosophy；　〃a　second　Thales〃　in　astronomy；　and　so　on　throughout　the　list。　He　was　also　called　the　〃surveyor　of　the　world；〃　in　recognition　of　his　services　to　geography。　Hipparchus　said　of　him；　perhaps　half　jestingly；　that　he　had　studied　astronomy　as　a　geographer　and　geography　as　an　astronomer。　It　is　not　quite　clear　whether　the　epigram　was　meant　as　compliment　or　as　criticism。　Similar　phrases　have　been　turned　against　men　of　versatile　talent　in　every　age。　Be　that　as　it　may；　Eratosthenes　passed　into　history　as　the　father　of　scientific　geography　and　of　scientific　chronology；　as　the　astronomer　who　first　measured　the　obliquity　of　the　ecliptic；　and　as　the　inventive　genius　who　performed　the　astounding　feat　of　measuring　the　size　of　the　globe　on　which　we　live　at　a　time　when　only　a　relatively　small　portion　of　that　globe's　surface　was　known　to　civilized　man。　It　is　no　discredit　to　approach　astronomy　as　a　geographer　and　geography　as　an　astronomer　if　the　results　are　such　as　these。　What　Eratosthenes　really　did　was　to　approach　both　astronomy　and　geography　from　two　seemingly　divergent　points　of　attacknamely；　from　the　stand…point　of　the　geometer　and　also　from　that　of　the　poet。　Perhaps　no　man　in　any　age　has　brought　a　better　combination　of　observing　and　imaginative　faculties　to　the　aid　of　science。　Nearly　all　the　discoveries　of　Eratosthenes　are　associated　with　observations　of　the　shadows　cast　by　the　sun。　We　have　seen　that；　in　the　study　of　the　heavenly　bodies；　much　depends　on　the　measurement　of　angles。　Now　the　easiest　way　in　which　angles　can　be　measured；　when　solar　angles　are　in　question；　is　to　pay　attention；　not　to　the　sun　itself；　but　to　the　shadow　that　it　casts。　We　saw　that　Thales　made　some　remarkable　measurements　with　the　aid　of　shadows；　and　we　have　more　than　once　referred　to　the　gnomon；　which　is　the　most　primitive；　but　which　long　remained　the　most　important；　of　astronomical　instruments。　It　is　believed　that　Eratosthenes　invented　an　important　modification　of　the　gnomon　which　was　elaborated　afterwards　by　Hipparchus　and　called　an　armillary　sphere。　This　consists　essentially　of　a　small　gnomon；　or　perpendicular　post；　attached　to　a　plane　representing　the　earth's　equator　and　a　hemisphere　in　imitation　of　the　earth's　surface。　With　the　aid　of　this；　the　shadow　cast　by　the　sun　could　be　very　accurately　measured。　It　involves　no　new　principle。　Every　perpendicular　post　or　object　of　any　kind　placed　in　the　sunlight　casts　a　shadow　from　which　the　angles　now　in　question　could　be　roughly　measured。　The　province　of　the　armillary　sphere　was　to　make　these　measurements　extremely　accurate。　With　the　aid　of　this　implement；　Eratosthenes　carefully　noted　the　longest　and　the　shortest　shadows　cast　by　the　gnomonthat　is　to　say；　the　shadows　cast　on　the　days　of　the　solstices。　He　found　that　the　distance　between　the　tropics　thus　measured　represented　47　degrees　42'　39〃　of　arc。　One…half　of　this；　or　23　degrees　5；'　19。5〃；　represented　the　obliquity　of　the　eclipticthat　is　to　say；　the　angle　by　which　the　earth's　axis　dipped　from　the　perpendicular　with　reference　to　its　orbit。　This　was　a　most　important　observation；　and　because　of　its　accuracy　it　has　served　modern　astronomers　well　for　comparison　in　measuring　the　trifling　change　due　to　our　earth's　slow；　swinging　wobble。　For　the　earth；　be　it　understood；　like　a　great　top　spinning　through　space；　holds　its　position　with　relative　but　not　quite　absolute　fixity。　It　must　not　be　supposed；　however；　that　the　experiment　in　question　was　quite　new　with　Eratosthenes。　His　merit　consists　rather　in　the　accuracy　with　which　he　made　his　observation　than　in　the　novelty　of　the　conception；　for　it　is　recorded　that　Eudoxus；　a　full　century　earlier；　had　remarked　the　obliquity　of　the　ecliptic。　That　observer　had　said　that　the　obliquity　corresponded　to　the　side　of　a　pentadecagon；　or　fifteen…sided　figure；　which　is　equivalent　in　modern　phraseology　to　twenty…　four　degrees　of　arc。　But　so　little　is　known　regarding　the　way　in　which　Eudoxus　reached　his　estimate　that　the　measurement　of　Eratosthenes　is　usually　spoken　of　as　if　it　were　the　first　effort　of　the　kind。　Much　more　striking；　at　least　in　its　appeal　to　the　popular　imagination；　was　that　other　great　feat　which　Eratosthenes　performed　with　the　aid　of　his　perfected　gnomonthe　measurement　of　the　earth　itself。　When　we　reflect　that　at　this　period　the　portion　of　the　earth　open　to　observation　extended　only　from　the　Straits　of　Gibraltar　on　the　west　to　India　on　the　east；　and　from　the　North　Sea　to　Upper　Egypt；　it　certainly　seems　enigmaticalat　first　thought　almost　miraculousthat　an　observer　should　have　been　able　to　measure　the　entire　globe。　That　he　should　have　accomplished　this　through　observation　of　nothing　more　than　a　tiny　bit　of　Egyptian　territory　and　a　glimpse　of　the　sun's　shadow　makes　it　seem　but　the　more　wonderful。　Yet　the　met