thoughts on man-第70章

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luded　between　these　lines　terminating　in　the　sun；　and　the　base　formed　by　a　right　line　drawn　from　one　of　these　stations　to　the　other；　which　in　this　case　is　the　length　of　the　earth's　diameter。　　I　have　therefore　now　the　three　particulars　required　to　enable　me　to　construct　my　triangle。　　And；　according　to　the　most　approved　astronomical　observations　hitherto　made；　I　have　an　isosceles　triangle；　eight　thousand　miles　broad　at　its　base；　and　ninety…five　millions　of　miles　in　the　length　of　each　of　the　sides　reaching　from　the　base　to　the　apex。

It　is　however　obvious　to　the　most　indifferent　observer；　that　the　more　any　triangle；　or　other　mathematical　diagram；　falls　within　the　limits　which　our　senses　can　conveniently　embrace；　the　more　securely；　when　our　business　is　practical；　and　our　purpose　to　apply　the　result　to　external　objects；　can　we　rely　on　the　accuracy　of　our　results。　　In　a　case　therefore　like　the　present；　where　the　base　of　our　isosceles　triangle　is　to　the　other　two　sides　as　eight　units　to　twelve　thousand；　it　is　impossible　not　to　perceive　that　it　behoves　us　to　be　singularly　diffident　as　to　the　conclusion　at　which　we　have　arrived；　or　rather　it　behoves　us　to　take　for　granted　that　we　are　not　unlikely　to　fall　into　the　most　important　error。　　We　have　satisfied　ourselves　that　the　sides　of　the　triangle　including　the　apex；　do　not　form　an　angle；　till　they　have　arrived　at　the　extent　of　ninety…five　millions　of　miles。　　How　are　we　sure　that　they　do　then？　　May　not　lines　which　have　reached　to　so　amazing　a　length　without　meeting；　be　in　reality　parallel　lines？　　If　an　angle　is　never　formed；　there　can　be　no　result。　　The　whole　question　seems　to　be　incommensurate　to　our　faculties。

It　being　obvious　that　this　was　a　very　unsatisfactory　scheme　for　arriving　at　the　knowledge　desired；　the　celebrated　Halley　suggested　another　method；　in　the　year　1716；　by　an　observation　to　be　taken　at　the　time　of　the　transit　of　Venus　over　the　sun＇50＇。

＇50＇　Philosophical　Transactions；　Vol。　XXIX；　p。　454。


It　was　supposed　that　we　were　already　pretty　accurately　acquainted　with　the　distance　of　the　moon　from　the　earth；　it　being　so　much　nearer　to　us；　by　observing　its　parallax；　or　the　difference　of　its　place　in　the　heavens　as　seen　from　the　surface　of　the　earth；　from　that　in　which　it　would　appear　if　seen　from　its　centre＇51＇。　　But　the　parallax　of　the　sun　is　so　exceedingly　small；　as　scarcely　to　afford　the　basis　of　a　mathematical　calculation＇52＇。　　The　parallax　of　Venus　is　however　almost　four　times　as　great　as　that　of　the　sun；　and　there　must　therefore　be　a　very　sensible　difference　between　the　times　in　which　Venus　may　be　seen　passing　over　the　sun　from　different　parts　of　the　earth。　　It　was　on　this　account　apprehended；　that　the　parallax　of　the　sun；　by　means　of　observations　taken　from　different　places　at　the　time　of　the　transit　of　Venus　in　1761　and　1769；　might　be　ascertained　with　a　great　degree　of　precision＇53＇。

＇51＇　Bonnycastle；　Astronomy；　7th　edition；　p。　262；　et　seq。　

＇52＇　Ibid；　p。　268。　

＇53＇　Phil。　Transactions；　Vol。　XXIX；　p。　457。


But　the　imperfectness　of　our　instruments　and　means　of　observation　have　no　small　tendency　to　baffle　the　ambition　of　man　in　these　curious　investigations。

〃The　true　quantity　of　the　moon's　parallax；〃　says　Bonnycastle；　〃cannot　be　accurately　determined　by　the　methods　ordinarily　resorted　to；　on　account　of　the　varying　declination　of　the　moon；　and　the　inconstancy　of　the　horizontal　refractions；　which　are　perpetually　changing　according　to　the　state　the　atmosphere　is　in　at　the　time。　　For　the　moon　continues　but　for　a　short　time　in　the　equinoctial；　and　the　refraction　at　a　mean　rate　elevates　her　apparent　place　near　the　horizon；　half　as　much　as　her　parallax　depresses　it＇54＇。〃

＇54＇　Astronomy；　p。　265。


〃It　is　well　known　that　the　parallax　of　the　sun　can　never　exceed　nine　seconds；　or　the　four…hundredth　part　of　a　degree＇55＇。〃　　〃Observations；〃　says　Halley；　〃made　upon　the　vibrations　of　a　pendulum；　to　determine　these　exceedingly　small　angles；　are　not　sufficiently　accurate　to　be　depended　upon；　for　by　this　method　of　ascertaining　the　parallax；　it　will　sometimes　come　out　to　be　nothing；　or　even　negative；　that　is；　the　distance　will　either　be　infinite；　or　greater　than　infinite；　which　is　absurd。　　And；　to　confess　the　truth；　it　is　hardly　possible　for　a　person　to　distinguish　seconds　with　certainty　by　any　instruments；　however　skilfully　they　may　be　made；　and　therefore　it　is　not　to　be　wondered　at；　that　the　excessive　nicety　of　this　matter　should　have　eluded　the　many　ingenious　endeavours　of　the　most　able　opetators＇56＇。

＇55＇　Ibid；　p。　268。　

＇56＇　Phil。　Transactions；　Vol。　XXIX；　p。　456。


Such　are　the　difficulties　that　beset　the　subject　on　every　side。　　It　is　for　the　impartial　and　dispassionate　observers　who　have　mastered　all　the　subtleties　of　the　science；　if　such　can　be　found；　to　determine　whether　the　remedies　that　have　been　resorted　to　to　obviate　the　above　inaccuracies　and　their　causes；　have　fulfilled　their　end；　and　are　not　exposed　to　similar　errors。　　But　it　would　be　vain　to　expect　the　persons；　who　have　〃scorned　delights；　and　lived　laborious　days〃　to　possess　themselves　of　the　mysteries　of　astronomy；　should　be　impartial　and　dispassionate；　or　be　disposed　to　confess；　even　to　their　own　minds；　that　their　researches　were　useless；　and　their　labours　ended　in　nothing。

It　is　further　worthy　of　our　attention；　that　the　instruments　with　which　we　measure　the　distance　of　the　earth　from　the　sun　and　the　planets；　are　the　very　instruments　which　have　been　pronounced　upon　as　incompetent　in　measuring　the　heights　of　mountains＇57＇。　　In　the　latter　case　therefore　we　have　substituted　a　different　mode　for　arriving　at　the　truth；　which　is　supposed　to　be　attended　with　greater　precision：　　but　we　have　no　substitute　to　which　we　can　resort；　to　correct　the　mistakes　into　which　we　may　fall　respecting　the　heavenly　bodies。

＇57＇　See　above；　Essay　XXI。


The　result　of　the　uncertainty　which　adheres　to　all　astronomical　observations　is　such　as　might　have　been　expected。　　Common　readers　are　only　informed　of　the　latest　adjustment　of　the　question；　and　are　therefore　unavoidably　led　to　believe　that　the　distance　of　the　sun　from　the　earth；　ever　since　astronomy　became　entitled　to　the　name　of　a　science；　has　by　universal　consent　been　recognised　as　ninety…five　millions　of　miles；　or；　as　near　as　may　be；　twenty…four　thousand　semi…diameters　of　the　earth。　　But　how　does　the　case　really　stand？　　Copernicus　and　Tycho　Brahe　held　the　distance　to　be　twelve　hundred　semi…diameters；　Kepler；　who　is　received　to　have　been　perhaps　the　greatest　astronomer　that　any　age　has　produced；　puts　it　down　as　three　thousand　five　hundred　semi…diameters；　since　his　time；　Riccioli　as　seven　thousand；　Hevelius　as　five　thousand　two　hundred　and　fifty＇58＇；　some　later　astronomers；　mentioned　by　Halley；　as　fourteen　thousand；　and　Halley　himself　as　sixteen　thousand　five　hundred＇59＇。

＇58＇　They　were　about　thirty　and　forty　years　younger　than　Kepler　respectively。

＇59＇　Halley；　apud　Philosophical　Transactions；　Vol。　XXIX；　p。　455。


The　doctrine　of　fluxions　is　likewise　called　in　by　the　astronomers　in　their　attempts　to　ascertain　the　distance　and　magnitude　of　the　different　celestial　bodies　which　compose　the　solar　system；　and　in　this　way　their　conclusions　become　subject　to　all　the　difficulties　which　Berkeley　has　alleged　against　that　doctrine。

Kepler　has　also　supplied　us　with　another　mode　of　arriving　at　the　distance　and　size　of　the　sun　and　the　planets：　　he　has　hazarded　a　conjecture；　that　the　squares　of　the　times　of　the　revolution　of　the　earth　and　the　other　planets　are　in　proportion　to　the　cubes　of　their　distances　from　the　sun；　their　common　centre；　and；　as　by　observation　we　can　arrive　with　tolerable　certainty　at　a　knowledge　of　the　times　of　their　revolutions；　we　may　from　hence　proceed　to　the　other　matters　we　are　desirous　to　ascertain。　　And　that　which　Kepler　seemed；　as　by　a　divine　inspiration；　to　hazard　in　the　way　of　conjecture；　Newton　professes　to　have　demonstratively　established。　　But　the　demonstration　of　Newton　has　not　been　considered　as　satisfactory　by　all　men　of　science　since　his　time。

Thus　far　however　we　proceed　as　we　may；　respecting　our　propositions　on　the　subject　of　the　solar　system。　　But；　beyond　this；　all　science；　real　or　pretended；　deserts　us。　　We　have　no　method　f