a history of science-1-第31章

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feature　of　this　document　in　which　the　calculation　of　the　sand…　grains　is　contained。　〃It　was　known　to　me；〃　says　Archimedes；　〃that　most　astronomers　understand　by　the　expression　'world'　（universe）　a　ball　of　which　the　centre　is　the　middle　point　of　the　earth；　and　of　which　the　radius　is　a　straight　line　between　the　centre　of　the　earth　and　the　sun。〃　Archimedes　himself　appears　to　accept　this　opinion　of　the　majority；it　at　least　serves　as　well　as　the　contrary　hypothesis　for　the　purpose　of　his　calculation；but　he　goes　on　to　say：　〃Aristarchus　of　Samos；　in　his　writing　against　the　astronomers；　seeks　to　establish　the　fact　that　the　world　is　really　very　different　from　this。　He　holds　the　opinion　that　the　fixed　stars　and　the　sun　are　immovable　and　that　the　earth　revolves　in　a　circular　line　about　the　sun；　the　sun　being　at　the　centre　of　this　circle。〃　This　remarkable　bit　of　testimony　establishes　beyond　question　the　position　of　Aristarchus　of　Samos　as　the　Copernicus　of　antiquity。　We　must　make　further　inquiry　as　to　the　teachings　of　the　man　who　had　gained　such　a　remarkable　insight　into　the　true　system　of　the　heavens。

ARISTARCHUS　OF　SAMOS；　THE　COPERNICUS　OF　ANTIQUITY　It　appears　that　Aristarchus　was　a　contemporary　of　Archimedes；　but　the　exact　dates　of　his　life　are　not　known。　He　was　actively　engaged　in　making　astronomical　observations　in　Samos　somewhat　before　the　middle　of　the　third　century　B。C。；　in　other　words；　just　at　the　time　when　the　activities　of　the　Alexandrian　school　were　at　their　height。　Hipparchus；　at　a　later　day；　was　enabled　to　compare　his　own　observations　with　those　made　by　Aristarchus；　and；　as　we　have　just　seen；　his　work　was　well　known　to　so　distant　a　contemporary　as　Archimedes。　Yet　the　facts　of　his　life　are　almost　a　blank　for　us；　and　of　his　writings　only　a　single　one　has　been　preserved。　That　one；　however；　is　a　most　important　and　interesting　paper　on　the　measurements　of　the　sun　and　the　moon。　Unfortunately；　this　paper　gives　us　no　direct　clew　as　to　the　opinions　of　Aristarchus　concerning　the　relative　positions　of　the　earth　and　sun。　But　the　testimony　of　Archimedes　as　to　this　is　unequivocal；　and　this　testimony　is　supported　by　other　rumors　in　themselves　less　authoritative。　In　contemplating　this　astronomer　of　Samos；　then；　we　are　in　the　presence　of　a　man　who　had　solved　in　its　essentials　the　problem　of　the　mechanism　of　the　solar　system。　It　appears　from　the　words　of　Archimedes　that　Aristarchus；　had　propounded　his　theory　in　explicit　writings。　Unquestionably；　then；　he　held　to　it　as　a　positive　doctrine；　not　as　a　mere　vague　guess。　We　shall　show；　in　a　moment；　on　what　grounds　he　based　his　opinion。　Had　his　teaching　found　vogue；　the　story　of　science　would　be　very　different　from　what　it　is。　We　should　then　have　no　tale　to　tell　of　a　Copernicus　coming　upon　the　scene　fully　seventeen　hundred　years　later　with　the　revolutionary　doctrine　that　our　world　is　not　the　centre　of　the　universe。　We　should　not　have　to　tell　of　the　persecution　of　a　Bruno　or　of　a　Galileo　for　teaching　this　doctrine　in　the　seventeenth　century　of　an　era　which　did　not　begin　till　two　hundred　years　after　the　death　of　Aristarchus。　But；　as　we　know；　the　teaching　of　the　astronomer　of　Samos　did　not　win　its　way。　The　old　conservative　geocentric　doctrine；　seemingly　so　much　more　in　accordance　with　the　every…day　observations　of　mankind；　supported　by　the　majority　of　astronomers　with　the　Peripatetic　philosophers　at　their　head；　held　its　place。　It　found　fresh　supporters　presently　among　the　later　Alexandrians；　and　so　fully　eclipsed　the　heliocentric　view　that　we　should　scarcely　know　that　view　had　even　found　an　advocate　were　it　not　for　here　and　there　such　a　chance　record　as　the　phrases　we　have　just　quoted　from　Archimedes。　Yet；　as　we　now　see；　the　heliocentric　doctrine；　which　we　know　to　be　true；　had　been　thought　out　and　advocated　as　the　correct　theory　of　celestial　mechanics　by　at　least　one　worker　of　the　third　century　B。C。　Such　an　idea；　we　may　be　sure；　did　not　spring　into　the　mind　of　its　originator　except　as　the　culmination　of　a　long　series　of　observations　and　inferences。　The　precise　character　of　the　evolution　we　perhaps　cannot　trace；　but　its　broader　outlines　are　open　to　our　observation；　and　we　may　not　leave　so　important　a　topic　without　at　least　briefly　noting　them。　Fully　to　understand　the　theory　of　Aristarchus；　we　must　go　back　a　century　or　two　and　recall　that　as　long　ago　as　the　time　of　that　other　great　native　of　Samos；　Pythagoras；　the　conception　had　been　reached　that　the　earth　is　in　motion。　We　saw；　in　dealing　with　Pythagoras；　that　we　could　not　be　sure　as　to　precisely　what　he　himself　taught；　but　there　is　no　question　that　the　idea　of　the　world's　motion　became　from　an　early　day　a　so…called　Pythagorean　doctrine。　While　all　the　other　philosophers；　so　far　as　we　know；　still　believed　that　the　world　was　flat；　the　Pythagoreans　out　in　Italy　taught　that　the　world　is　a　sphere　and　that　the　apparent　motions　of　the　heavenly　bodies　are　really　due　to　the　actual　motion　of　the　earth　itself。　They　did　not；　however；　vault　to　the　conclusion　that　this　true　motion　of　the　earth　takes　place　in　the　form　of　a　circuit　about　the　sun。　Instead　of　that；　they　conceived　the　central　body　of　the　universe　to　be　a　great　fire；　invisible　from　the　earth；　because　the　inhabited　side　of　the　terrestrial　ball　was　turned　away　from　it。　The　sun；　it　was　held；　is　but　a　great　mirror；　which　reflects　the　light　from　the　central　fire。　Sun　and　earth　alike　revolve　about　this　great　fire；　each　in　its　own　orbit。　Between　the　earth　and　the　central　fire　there　was；　curiously　enough；　supposed　to　be　an　invisible　earthlike　body　which　was　given　the　name　of　Anticthon；　or　counter…earth。　This　body；　itself　revolving　about　the　central　fire；　was　supposed　to　shut　off　the　central　light　now　and　again　from　the　sun　or　from　the　moon；　and　thus　to　account　for　certain　eclipses　for　which　the　shadow　of　the　earth　did　not　seem　responsible。　It　was；　perhaps；　largely　to　account　for　such　eclipses　that　the　counter…earth　was　invented。　But　it　is　supposed　that　there　was　another　reason。　The　Pythagoreans　held　that　there　is　a　peculiar　sacredness　in　the　number　ten。　Just　as　the　Babylonians　of　the　early　day　and　the　Hegelian　philosophers　of　a　more　recent　epoch　saw　a　sacred　connection　between　the　number　seven　and　the　number　of　planetary　bodies；　so　the　Pythagoreans　thought　that　the　universe　must　be　arranged　in　accordance　with　the　number　ten。　Their　count　of　the　heavenly　bodies；　including　the　sphere　of　the　fixed　stars；　seemed　to　show　nine；　and　the　counter…earth　supplied　the　missing　body。　The　precise　genesis　and　development　of　this　idea　cannot　now　be　followed；　but　that　it　was　prevalent　about　the　fifth　century　B。C。　as　a　Pythagorean　doctrine　cannot　be　questioned。　Anaxagoras　also　is　said　to　have　taken　account　of　the　hypothetical　counter…earth　in　his　explanation　of　eclipses；　though；　as　we　have　seen；　he　probably　did　not　accept　that　part　of　the　doctrine　which　held　the　earth　to　be　a　sphere。　The　names　of　Philolaus　and　Heraclides　have　been　linked　with　certain　of　these　Pythagorean　doctrines。　Eudoxus；　too；　who；　like　the　others；　lived　in　Asia　Minor　in　the　fourth　century　B。C。；　was　held　to　have　made　special　studies　of　the　heavenly　spheres　and　perhaps　to　have　taught　that　the　earth　moves。　So；　too；　Nicetas　must　be　named　among　those　whom　rumor　credited　with　having　taught　that　the　world　is　in　motion。　In　a　word；　the　evidence；　so　far　as　we　can　garner　it　from　the　remaining　fragments；　tends　to　show　that　all　along；　from　the　time　of　the　early　Pythagoreans；　there　had　been　an　undercurrent　of　opinion　in　the　philosophical　world　which　questioned　the　fixity　of　the　earth；　and　it　would　seem　that　the　school　of　thinkers　who　tended　to　accept　the　revolutionary　view　centred　in　Asia　Minor；　not　far　from　the　early　home　of　the　founder　of　the　Pythagorean　doctrines。　It　was　not　strange；　then；　that　the　man　who　was　finally　to　carry　these　new　opinions　to　their　logical　conclusion　should　hail　from　Samos。　But　what　was　the　support　which　observation　could　give　to　this　new；　strange　conception　that　the　heavenly　bodies　do　not　in　reality　move　as　they　seem　to　move；　but　that　their　apparent　motion　is　due　to　the　actual　revolution　of　the　earth？　It　is　extremely　difficult　for　any　one　nowadays　to　put　himself　in　a　mental　position　to　answer　this　question。　We　are　so　accustomed　to　conceive　the　solar　system　as　we　know　it　to　be；　that　we　are　wont　to　forget　how　very　different　it　is　from　what　it　seems。　Yet　one　needs　but　to　glance　up　at　the　sky；　and　then　to　glance　about　one　at　the　solid　earth；　to　grant；　on　a　moment's　reflection；　that　the　geocentric　idea　is　of　all　others　the　most　natural；　and　that　to　conceive　the　sun　as　the　actual　Centre　of　the　solar　system　is　an　idea　which　must　look　for　support　to　some　other　evidence　than　that　which　ordinary　observation　can　give。　Such　was　the　view　of　most　of　the　ancient　philosophers；　and　such　continued　to　be　the　opinion　of　the　majority　of　mankind　long　after　the　time　of　Copernicus。　We　must　not　forget　that　even　so　great　an　observing　astronomer　as　Tycho　Brahe；　so　late　as　the　seventeenth　century；　declined　to　accept　the　heliocentric　theory；　though　admitting　that　all　the　planets　except　the　earth　revolve　about　the　sun。　We　shall　see　that　before　the　Alexandrian　school　lost　its　influence　a　geocentric　scheme　had　been　evolved　which　fully　explained　all　the　apparent　motions　of　the　heavenly　bodies。　All　this；　then；　makes　us　but　wonder　the　more　that　the　genius　of　an　Aristarchus　could　give　precedence　to　scientific　induction　as　against　the　seemingly　clear　evidence　of　the　senses。　What；　then；　was　the　line　of　scientific　induction　that　led　Aristarchus　to　this　wonderful　goal？　Fortunately；　we　are　able　to　answer　that　query；　at　least　in　part。　Aristarchus　gained　his　evidence　through　some　wonderful　measurements。　First；　he　measured　the　disks　of　the　sun　and　the　moon。　This；　of　course；　could　in　itself　give　him　no　clew　to　the　distance　of　these　bodies；　and　therefore　no　clew　as　to　their　relative　size；　but　in　attempting　to　obtain　such　a　clew　he　hit　upon　a　wonderful　yet　altogether　simple　experiment。　It　occurred　to　him　that　when　the　moon　is　precisely　dichotomized　that　is　to　say；　precisely　at　the　half…the　line　of　vision　from　the　earth　to　the　moon　must　be　precisely　at　right　angles　with　the　line　of　light　passing　from　the　sun　to　the　moon。　At　this　moment；　then；　the　imaginary　lines　joining　the　sun；　the　moon；　and　the　earth；　make　a　right　angle　triangle。　But　the　properties　of　the　right…angle　triangle　had　long　been　studied　and　were　well　under　stood。　One　acute　angle　of　such　a　triangle　determines　the　figure　of　the　triangle　itself。　We　have　already　seen　that　Thales；　the　very　earliest　of　the　Greek　philosophers；　measured　the　distance　of　a　ship　at　sea　by　the　application　of　this　principle。　Now　Aristarchus　sights　the　sun　in　place　of　Thales'　ship；　and；　sighting　the　moon　at　the　same　time；　measures　the　angle　and　establishes　the　shape　of　his　right…angle　triangle。　This　does　not　tell　him　the　distance　of　the　sun；　to　be　sure；　for　he　does　not　know　the　length　of　his　base…linethat　is　to　say；　of　the　line　between　the　moon　and　the　earth。　But　it　does　establish　the　relation　of　that　base…line　to　the　other　lines　of　the　triangle；　in　other　words；　it　tells　him　the　distance　of　the　sun　in　terms　of　the　moon's　distance。　As　Aristarchus　strikes　the　angle；　it　shows　that　the　sun　is　eighteen　times　as　distant　as　the　moon。　Now；　by　comparing　the　apparent　size　of　the　sun　with　the　ap