a history of science-2-第41章

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vault　at　once　to　the　full　expression　of　this　law；　though　he　had　formulated　it　fully　before　he　gave　the　results　of　his　investigations　to　the　world。　We　have　now　to　follow　the　steps　by　which　he　reached　this　culminating　achievement。　At　the　very　beginning　we　must　understand　that　the　idea　of　universal　gravitation　was　not　absolutely　original　with　Newton。　Away　back　in　the　old　Greek　days；　as　we　have　seen；　Anaxagoras　conceived　and　clearly　expressed　the　idea　that　the　force　which　holds　the　heavenly　bodies　in　their　orbits　may　be　the　same　that　operates　upon　substances　at　the　surface　of　the　earth。　With　Anaxagoras　this　was　scarcely　more　than　a　guess。　After　his　day　the　idea　seems　not　to　have　been　expressed　by　any　one　until　the　seventeenth　century's　awakening　of　science。　Then　the　consideration　of　Kepler's　Third　Law　of　planetary　motion　suggested　to　many　minds　perhaps　independently　the　probability　that　the　force　hitherto　mentioned　merely　as　centripetal；　through　the　operation　of　which　the　planets　are　held　in　their　orbits　is　a　force　varying　inversely　as　the　square　of　the　distance　from　the　sun。　This　idea　had　come　to　Robert　Hooke；　to　Wren；　and　perhaps　to　Halley；　as　well　as　to　Newton；　but　as　yet　no　one　had　conceived　a　method　by　which　the　validity　of　the　suggestion　might　be　tested。　It　was　claimed　later　on　by　Hooke　that　he　had　discovered　a　method　demonstrating　the　truth　of　the　theory　of　inverse　squares；　and　after　the　full　announcement　of　Newton's　discovery　a　heated　controversy　was　precipitated　in　which　Hooke　put　forward　his　claims　with　accustomed　acrimony。　Hooke；　however；　never　produced　his　demonstration；　and　it　may　well　be　doubted　whether　he　had　found　a　method　which　did　more　than　vaguely　suggest　the　law　which　the　observations　of　Kepler　had　partially　revealed。　Newton's　great　merit　lay　not　so　much　in　conceiving　the　law　of　inverse　squares　as　in　the　demonstration　of　the　law。　He　was　led　to　this　demonstration　through　considering　the　orbital　motion　of　the　moon。　According　to　the　familiar　story；　which　has　become　one　of　the　classic　myths　of　science；　Newton　was　led　to　take　up　the　problem　through　observing　the　fall　of　an　apple。　Voltaire　is　responsible　for　the　story；　which　serves　as　well　as　another；　its　truth　or　falsity　need　not　in　the　least　concern　us。　Suffice　it　that　through　pondering　on　the　familiar　fact　of　terrestrial　gravitation；　Newton　was　led　to　question　whether　this　force　which　operates　so　tangibly　here　at　the　earth's　surface　may　not　extend　its　influence　out　into　the　depths　of　space；　so　as　to　include；　for　example；　the　moon。　Obviously　some　force　pulls　the　moon　constantly　towards　the　earth；　otherwise　that　body　would　fly　off　at　a　tangent　and　never　return。　May　not　this　so…called　centripetal　force　be　identical　with　terrestrial　gravitation？　Such　was　Newton's　query。　Probably　many　another　man　since　Anaxagoras　had　asked　the　same　question；　but　assuredly　Newton　was　the　first　man　to　find　an　answer。　The　thought　that　suggested　itself　to　Newton's　mind　was　this：　If　we　make　a　diagram　illustrating　the　orbital　course　of　the　moon　for　any　given　period；　say　one　minute；　we　shall　find　that　the　course　of　the　moon　departs　from　a　straight　line　during　that　period　by　a　measurable　distancethat：　is　to　say；　the　moon　has　been　virtually　pulled　towards　the　earth　by　an　amount　that　is　represented　by　the　difference　between　its　actual　position　at　the　end　of　the　minute　under　observation　and　the　position　it　would　occupy　had　its　course　been　tangential；　as；　according　to　the　first　law　of　motion；　it　must　have　been　had　not　some　force　deflected　it　towards　the　earth。　Measuring　the　deflection　in　questionwhich　is　equivalent　to　the　so…called　versed　sine　of　the　arc　traversedwe　have　a　basis　for　determining　the　strength　of　the　deflecting　force。　Newton　constructed　such　a　diagram；　and；　measuring　the　amount　of　the　moon's　departure　from　a　tangential　rectilinear　course　in　one　minute；　determined　this　to　be；　by　his　calculation；　thirteen　feet。　Obviously；　then；　the　force　acting　upon　the　moon　is　one　that　would　cause　that　body　to　fall　towards　the　earth　to　the　distance　of　thirteen　feet　in　the　first　minute　of　its　fall。　Would　such　be　the　force　of　gravitation　acting　at　the　distance　of　the　moon　if　the　power　of　gravitation　varies　inversely　as　the　square　of　the　distance？　That　was　the　tangible　form　in　which　the　problem　presented　itself　to　Newton。　The　mathematical　solution　of　the　problem　was　simple　enough。　It　is　based　on　a　comparison　of　the　moon's　distance　with　the　length　of　the　earth's　radius。　On　making　this　calculation；　Newton　found　that　the　pull　of　gravitationif　that　were　really　the　force　that　controls　the　moongives　that　body　a　fall　of　slightly　over　fifteen　feet　in　the　first　minute；　instead　of　thirteen　feet。　Here　was　surely　a　suggestive　approximation；　yet；　on　the　other　band；　the　discrepancy　seemed　to　be　too　great　to　warrant　him　in　the　supposition　that　he　had　found　the　true　solution。　He　therefore　dismissed　the　matter　from　his　mind　for　the　time　being；　nor　did　he　return　to　it　definitely　for　some　years。　｛illustration　caption　=　　DIAGRAM　TO　ILLUSTRATE　NEWTON'S　LAW　OF　GRAVITATION　（E　represents　the　earth　and　A　the　moon。　Were　the　earth's　pull　on　the　moon　to　cease；　the　moon's　inertia　would　cause　it　to　take　the　tangential　course；　AB。　On　the　other　hand；　were　the　moon's　motion　to　be　stopped　for　an　instant；　the　moon　would　fall　directly　towards　the　earth；　along　the　line　AD。　The　moon's　actual　orbit；　resulting　from　these　component　forces；　is　AC。　Let　AC　represent　the　actual　flight　of　the　moon　in　one　minute。　Then　BC；　which　is　obviously　equal　to　AD；　represents　the　distance　which　the　moon　virtually　falls　towards　the　earth　in　one　minute。　Actual　computation；　based　on　measurements　of　the　moon's　orbit；　showed　this　distance　to　be　about　fifteen　feet。　Another　computation　showed　that　this　is　the　distance　that　the　moon　would　fall　towards　the　earth　under　the　influence　of　gravity；　on　the　supposition　that　the　force　of　gravity　decreases　inversely　with　the　square　of　the　distance；　the　basis　of　comparison　being　furnished　by　falling　bodies　at　the　surface　of　the　earth。　Theory　and　observations　thus　coinciding；　Newton　was　justified　in　declaring　that　the　force　that　pulls　the　moon　towards　the　earth　and　keeps　it　in　its　orbit；　is　the　familiar　force　of　gravity；　and　that　this　varies　inversely　as　the　square　of　the　distance。）｝　It　was　to　appear　in　due　time　that　Newton's　hypothesis　was　perfectly　valid　and　that　his　method　of　attempted　demonstration　was　equally　so。　The　difficulty　was　that　the　earth's　proper　dimensions　were　not　at　that　time　known。　A　wrong　estimate　of　the　earth's　size　vitiated　all　the　other　calculations　involved；　since　the　measurement　of　the　moon's　distance　depends　upon　the　observation　of　the　parallax；　which　cannot　lead　to　a　correct　computation　unless　the　length　of　the　earth's　radius　is　accurately　known。　Newton's　first　calculation　was　made　as　early　as　1666；　and　it　was　not　until　1682　that　his　attention　was　called　to　a　new　and　apparently　accurate　measurement　of　a　degree　of　the　earth's　meridian　made　by　the　French　astronomer　Picard。　The　new　measurement　made　a　degree　of　the　earth's　surface　69。10　miles；　instead　of　sixty　miles。　Learning　of　this　materially　altered　calculation　as　to　the　earth's　size；　Newton　was　led　to　take　up　again　his　problem　of　the　falling　moon。　As　he　proceeded　with　his　computation；　it　became　more　and　more　certain　that　this　time　the　result　was　to　harmonize　with　the　observed　facts。　As　the　story　goes；　he　was　so　completely　overwhelmed　with　emotion　that　he　was　forced　to　ask　a　friend　to　complete　the　simple　calculation。　That　story　may　well　be　true；　for；　simple　though　the　computation　was；　its　result　was　perhaps　the　most　wonderful　demonstration　hitherto　achieved　in　the　entire　field　of　science。　Now　at　last　it　was　known　that　the　force　of　gravitation　operates　at　the　distance　of　the　moon；　and　holds　that　body　in　its　elliptical　orbit；　and　it　required　but　a　slight　effort　of　the　imagination　to　assume　that　the　force　which　operates　through　such　a　reach　of　space　extends　its　influence　yet　more　widely。　That　such　is　really　the　case　was　demonstrated　presently　through　calculations　as　to　the　moons　of　Jupiter　and　by　similar　computations　regarding　the　orbital　motions　of　the　various　planets。　All　results　harmonizing；　Newton　was　justified　in　reaching　the　conclusion　that　gravitation　is　a　universal　property　of　matter。　It　remained；　as　we　shall　see；　for　nineteenth…century　scientists　to　prove　that　the　same　force　actually　operates　upon　the　stars；　though　it　should　be　added　that　this　demonstration　merely　fortified　a　belief　that　had　already　found　full　acceptance。　Having　thus　epitomized　Newton's　discovery；　we　must　now　take　up　the　steps　of　his　progress　somewhat　in　detail；　and　state　his　theories　and　their　demonstration　in　his　own　words。　Proposition　IV。；　theorem　4；　of　his　Principia　is　as　follows：　〃That　the　moon　gravitates　towards　the　earth　and　by　the　force　of　gravity　is　continually　drawn　off　from　a　rectilinear　motion　and　retained　in　its　orbit。　〃The　mean　distance　of　the　moon　from　the　earth；　in　the　syzygies　in　semi…diameters　of　the　earth；　is；　according　to　Ptolemy　and　most　astronomers；　59；　according　to　Vendelin　and　Huygens；　60；　to　Copernicus；　60　1/3；　to　Street；　60　2/3；　and　to　Tycho；　56　1/2。　But　Tycho；　and　all　that　follow　his　tables　of　refractions；　making　the　refractions　of　the　sun　and　moon　（altogether　against　t