a history of science-2-第3部分

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gressed　northward；　another　party　southward；　from　a　given　point　to　the　distance　of　one　degree　of　arc；　as　determined　by　astronomical　observations。　The　result　found　was　fifty…six　miles　for　the　northern　degree；　and　fifty…six　and　two…third　miles　for　the　southern。　Unfortunately；　we　do　not　know　the　precise　length　of　the　mile　in　question；　and　therefore　cannot　be　assured　as　to　the　accuracy　of　the　measurement。　It　is　interesting　to　note；　however；　that　the　two　degrees　were　found　of　unequal　lengths；　suggesting　that　the　earth　is　not　a　perfect　spherea　suggestion　the　validity　of　which　was　not　to　be　put　to　the　test　of　conclusive　measurements　until　about　the　close　of　the　eighteenth　century。　The　Arab　measurement　was　made　in　the　time　of　Caliph　Abdallah　al…Mamun；　the　son　of　the　famous　Harun…al…Rashid。　Both　father　and　son　were　famous　for　their　interest　in　science。　Harun…al…Rashid　was；　it　will　be　recalled；　the　friend　of　Charlemagne。　It　is　said　that　he　sent　that　ruler；　as　a　token　of　friendship；　a　marvellous　clock　which　let　fall　a　metal　ball　to　mark　the　hours。　This　mechanism；　which　is　alleged　to　have　excited　great　wonder　in　the　West；　furnishes　yet　another　instance　of　Arabian　practicality。　Perhaps　the　greatest　of　the　Arabian　astronomers　was　Mohammed　ben　Jabir　Albategnius；　or　El…batani；　who　was　born　at　Batan；　in　Mesopotamia；　about　the　year　850　A。D。；　and　died　in　929。　Albategnius　was　a　student　of　the　Ptolemaic　astronomy；　but　he　was　also　a　practical　observer。　He　made　the　important　discovery　of　the　motion　of　the　solar　apogee。　That　is　to　say；　he　found　that　the　position　of　the　sun　among　the　stars；　at　the　time　of　its　greatest　distance　from　the　earth；　was　not　what　it　had　been　in　the　time　of　Ptolemy。　The　Greek　astronomer　placed　the　sun　in　longitude　65　degrees；　but　Albategnius　found　it　in　longitude　82　degrees；　a　distance　too　great　to　be　accounted　for　by　inaccuracy　of　measurement。　The　modern　inference　from　this　observation　is　that　the　solar　system　is　moving　through　space；　but　of　course　this　inference　could　not　well　be　drawn　while　the　earth　was　regarded　as　the　fixed　centre　of　the　universe。　In　the　eleventh　century　another　Arabian　discoverer；　Arzachel；　observing　the　sun　to　be　less　advanced　than　Albategnius　had　found　it；　inferred　incorrectly　that　the　sun　had　receded　in　the　mean　time。　The　modern　explanation　of　this　observation　is　that　the　measurement　of　Albategnius　was　somewhat　in　error；　since　we　know　that　the　sun's　motion　is　steadily　progressive。　Arzachel；　however；　accepting　the　measurement　of　his　predecessor；　drew　the　false　inference　of　an　oscillatory　motion　of　the　stars；　the　idea　of　the　motion　of　the　solar　system　not　being　permissible。　This　assumed　phenomenon；　which　really　has　no　existence　in　point　of　fact；　was　named　the　〃trepidation　of　the　fixed　stars；〃　and　was　for　centuries　accepted　as　an　actual　phenomenon。　Arzachel　explained　this　supposed　phenomenon　by　assuming　that　the　equinoctial　points；　or　the　points　of　intersection　of　the　equator　and　the　ecliptic；　revolve　in　circles　of　eight　degrees'　radius。　The　first　points　of　Aries　and　Libra　were　supposed　to　describe　the　circumference　of　these　circles　in　about　eight　hundred　years。　All　of　which　illustrates　how　a　difficult　and　false　explanation　may　take　the　place　of　a　simple　and　correct　one。　The　observations　of　later　generations　have　shown　conclusively　that　the　sun's　shift　of　position　is　regularly　progressive；　hence　that　there　is　no　〃trepidation〃　of　the　stars　and　no　revolution　of　the　equinoctial　points。　If　the　Arabs　were　wrong　as　regards　this　supposed　motion　of　the　fixed　stars；　they　made　at　least　one　correct　observation　as　to　the　inequality　of　motion　of　the　moon。　Two　inequalities　of　the　motion　of　this　body　were　already　known。　A　third；　called　the　moon's　variation；　was　discovered　by　an　Arabian　astronomer　who　lived　at　Cairo　and　observed　at　Bagdad　in　975；　and　who　bore　the　formidable　name　of　Mohammed　Aboul　Wefaal…Bouzdjani。　The　inequality　of　motion　in　question；　in　virtue　of　which　the　moon　moves　quickest　when　she　is　at　new　or　full；　and　slowest　at　the　first　and　third　quarter；　was　rediscovered　by　Tycho　Brahe　six　centuries　later；　a　fact　which　in　itself　evidences　the　neglect　of　the　Arabian　astronomer's　discovery　by　his　immediate　successors。　In　the　ninth　and　tenth　centuries　the　Arabian　city　of　Cordova；　in　Spain；　was　another　important　centre　of　scientific　influence。　There　was　a　library　of　several　hundred　thousand　volumes　here；　and　a　college　where　mathematics　and　astronomy　were　taught。　Granada；　Toledo；　and　Salamanca　were　also　important　centres；　to　which　students　flocked　from　western　Europe。　It　was　the　proximity　of　these　Arabian　centres　that　stimulated　the　scientific　interests　of　Alfonso　X。　of　Castile；　at　whose　instance　the　celebrated　Alfonsine　tables　were　constructed。　A　familiar　story　records　that　Alfonso；　pondering　the　complications　of　the　Ptolemaic　cycles　and　epicycles；　was　led　to　remark　that；　had　he　been　consulted　at　the　time　of　creation；　he　could　have　suggested　a　much　better　and　simpler　plan　for　the　universe。　Some　centuries　were　to　elapse　before　Copernicus　was　to　show　that　it　was　not　the　plan　of　the　universe；　but　man's　interpretation　of　it；　that　was　at　fault。　Another　royal　personage　who　came　under　Arabian　influence　was　Frederick　II。　of　Sicilythe　〃Wonder　of　the　World；〃　as　he　was　called　by　his　contemporaries。　The　Almagest　of　Ptolemy　was　translated　into　Latin　at　his　instance；　being　introduced　to　the　Western　world　through　this　curious　channel。　At　this　time　it　became　quite　usual　for　the　Italian　and　Spanish　scholars　to　understand　Arabic　although　they　were　totally　ignorant　of　Greek。　In　the　field　of　physical　science　one　of　the　most　important　of　the　Arabian　scientists　was　Alhazen。　His　work；　published　about　the　year　1100　A。D。；　had　great　celebrity　throughout　the　mediaeval　period。　The　original　investigations　of　Alhazen　had　to　do　largely　with　optics。　He　made　particular　studies　of　the　eye　itself；　and　the　names　given　by　him　to　various　parts　of　the　eye；　as　the　vitreous　humor；　the　cornea；　and　the　retina；　are　still　retained　by　anatomists。　It　is　known　that　Ptolemy　had　studied　the　refraction　of　light；　and　that　he；　in　common　with　his　immediate　predecessors；　was　aware　that　atmospheric　refraction　affects　the　apparent　position　of　stars　near　the　horizon。　Alhazen　carried　forward　these　studies；　and　was　led　through　them　to　make　the　first　recorded　scientific　estimate　of　the　phenomena　of　twilight　and　of　the　height　of　the　atmosphere。　The　persistence　of　a　glow　in　the　atmosphere　after　the　sun　has　disappeared　beneath　the　horizon　is　so　familiar　a　phenomenon　that　the　ancient　philosophers　seem　not　to　have　thought　of　it　as　requiring　an　explanation。　Yet　a　moment's　consideration　makes　it　clear　that；　if　light　travels　in　straight　lines　and　the　rays　of　the　sun　were　in　no　wise　deflected；　the　complete　darkness　of　night　should　instantly　succeed　to　day　when　the　sun　passes　below　the　horizon。　That　this　sudden　change　does　not　occur；　Alhazen　explained　as　due　to　the　reflection　of　light　by　the　earth's　atmosphere。　Alhazen　appears　to　have　conceived　the　atmosphere　as　a　sharply　defined　layer；　and；　assuming　that　twilight　continues　only　so　long　as　rays　of　the　sun　reflected　from　the　outer　surface　of　this　layer　can　reach　the　spectator　at　any　given　point；　he　hit　upon　a　means　of　measurement　that　seemed　to　solve　the　hitherto　inscrutable　problem　as　to　the　atmospheric　depth。　Like　the　measurements　of　Aristarchus　and　Eratosthenes；　this　calculation　of　Alhazen　is　simple　enough　in　theory。　Its　defect　consists　largely　in　the　difficulty　of　fixing　its　terms　with　precision；　combined　with　the　further　fact　that　the　rays　of　the　sun；　in　taking　the　slanting　course　through　the　earth's　atmosphere；　are　really　deflected　from　a　straight　line　in　virtue　of　the　constantly　increasing　density　of　the　air　near　the　earth's　surface。　Alhazen　must　have　been　aware　of　this　latter　fact；　since　it　was　known　to　the　later　Alexandrian　astronomers；　but　he　takes　no　account　of　it　in　the　present　measurement。　The　diagram　will　make　the　method　of　Alhazen　clear。　His　important　premises　are　two：　first；　the　well…recognized　fact　that；　when　light　is　reflected　from　any　surface；　the　angle　of　incidence　is　equal　to　the　angle　of　reflection；　and；　second；　the　much　more　doubtful　observation　that　twilight　continues　until　such　time　as　the　sun；　according　to　a　simple　calculation；　is　nineteen　degrees　below　the　horizon。　Referring　to　the　diagram；　let　the　inner　circle　represent　the　earth's　surface；　the　outer　circle　the　limits　of　the　atmosphere；　C　being　the　earth's　centre；　and　RR　radii　of　the　earth。　Then　the　observer　at　the　point　A　will　continue　to　receive　the　reflected　rays　of　the　sun　until　that　body　reaches　the　point　S；　which　is；　according　to　the　hypothesis；　nineteen　degrees　below　the　horizon　line　of　the　observer　at　A。　This　horizon　line；　being　represented　by　AH；　and　the　sun's　ray　by　SM；　the　angle　HMS　is　an　angle　of　nineteen　degrees。　The　complementary　angle　SMA　is；　obviously；　an　angle　of　（180…19）　one　hundred　and　sixty…one　degrees。　But　since　M　is　the　reflecting　surface　and　the　angle　of　incidence　equals　the　angle　of　reflection；　the　angle　AMC　is　an　angle　of　one…half　of　one　hundred　and　sixty…one　degrees；　or　eighty　degrees　and　thirty　minutes。　Now　this　angle　AMC；　being　known；　the　right…angled　triangle　MAC　is　easily　resolved；　since　the　side　AC　of　that　triangle；　being　the　radius　of　the　earth；　is　a　known　dimension。　Resolution　of　this　triangle　gives　us　the　length　of　the　hypotenuse　MC；　and　the　difference　between　this　and　the　radius　（AC）；　or　CD；　is　obviously　the　height　of　the　atmosphere　（h）；　which　was　the　measurement　desired。　According　to　the　calculation　of　Alhazen；　this　h；　or　the　height　of　the　atmosphere；　represents　from　twenty　to　thirty　miles。　The　modern　computation　extends　this　to　about　fifty　miles。　But；　considering　the　various　ambiguities　that　necessarily　attended　the　experiment；　the　result　was　a　remarkably　close　approximation　to　the　truth。　Turning　from　physics　to　chemistry；　we　find　as　perhaps　the　greatest　Arabian　name　that　of　Geber；　who　taught　in　the　College　of　Seville　in　the　first　half　of　the　eighth　century。　The　most　important　researches　of　this　really　remarkable　experimenter　had　to　do　with　the　acids。　The　ancient　world　had　had　no　knowledge　of　any　acid　more　powerful　than　acetic。　Geber；　however；　vastly　increased　the　possibilities　of　chemical　experiment　by　the　discovery　of　sulphuric；　nitric