a history of science-1-第43章

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osophers　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　apparent　size　of　the　moonwhich；　as　we　have　seen；　Aristarchus　has　already　measuredhe　is　able　to　tell　us　that；　the　sun　is　〃more　than　5832　times；　and　less　than　8000〃　times　larger　than　the　moon；　though　his　measurements；　taken　by　themselves；　give　no　clew　to　the　actual　bulk　of　either　body。　These　conclusions；　be　it　understood；　are　absolutely　valid　inferencesnay；　demonstrationsfrom　the　measurements　involved；　provided　only　that　these　measurements　have　been　correct。　Unfortunately；　the　angle　of　the　triangle　we　have　just　seen　measured　is　exceedingly　difficult　to　determine　with　accuracy；　while　at　the　same　time；　as　a　moment's　reflection　will　show；　it　is　so　large　an　angle　that　a　very　slight　deviation　from　the　truth　will　greatly　affect　the　distance　at　which　its　line　joins　the　other　side　of　the　triangle。　Then　again；　it　is　virtually　impossible　to　tell　the　precise　moment　when　the　moon　is　at　half；　as　the　line　it　gives　is　not　so　sharp　that　we　can　fix　it　with　absolute　accuracy。　There　is；　moreover；　another　element　of　error　due　to　the　refraction　of　light　by　the　earth's　atmosphere。　The　experiment　was　probably　made　when　the　sun　was　near　the　horizon；　at　which　time；　as　we　now　know；　but　as　Aristarchus　probably　did　not　suspect；　the　apparent　displacement　of　the　sun's　position　is　considerable；　and　this　displacement；　it　will　be　observed；　is　in　the　direction　to　lessen　the　angle　in　question。　In　point　of　fact；　Aristarchus　estimated　the　angle　at　eighty…seven　degrees。　Had　his　instrument　been　more　precise；　and　had　he　been　able　to　take　account　of　all　the　elements　of　error；　he　would　have　found　it　eighty…seven　degrees　and　fifty…two　minutes。　The　difference　of　measurement　seems　slight；　but　it　sufficed　to　make　the　computations　differ　absurdly　from　the　truth。　The　sun　is　really　not　merely　eighteen　times　but　more　than　two　hundred　times　the　distance　of　the　moon；　as　Wendelein　discovered　on　repeating　the　experiment　of　Aristarchus　about　two　thousand　years　later。　Yet　this　discrepancy　does　not　in　the　least　take　away　from　the　validity　of　the　method　which　Aristarchus　employed。　Moreover；　his　conclusion；　stated　in　general　terms；　was　perfectly　correct：　the　sun　is　many　times　more　distant　than　the　moon　and　vastly　larger　than　that　body。　Granted；　then；　that　the　moon　is；　as　Aristarchus　correctly　believed；　considerably　less　in　size　than　the　earth；　the　sun　must　be　enormously　larger　than　the　earth；　and　this　is　the　vital　inference　which；　more　than　any　other；　must　have　seemed　to　Aristarchus　to　confirm　the　suspicion　that　the　sun　and　not　the　earth　is　the　centre　of　the　planetary　system。　It　seemed　to　him　inherently　improbable　that　an　enormously　large　body　like　the　sun　should　revolve　about　a　small　one　such　as　the　earth。　And　again；　it　seemed　inconceivable　that　a　body　so　distant　as　the　sun　should　whirl　through　space　so　rapidly　as　to　make　the　circuit　of　its　orbit　in　twenty…　four　hours。　But；　on　the　other　hand；　that　a　small　body　like　the　earth　should　revolve　about　the　gigantic　sun　seemed　inherently　probable。　This　proposition　granted；　the　rotation　of　the　earth　on　its　axis　follows　as　a　necessary　co