a history of science-2-第47章

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　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　the　nature　of　light）　to　exceed　the　refractions　of　the　fixed　stars；　and　that　by　four　or　five　minutes　NEAR　THE　HORIZON；　did　thereby　increase　the　moon's　HORIZONTAL　parallax　by　a　like　number　of　minutes；　that　is；　by　a　twelfth　or　fifteenth　part　of　the　whole　parallax。　Correct　this　error　and　the　distance　will　become　about　60　1/2　semi…diameters　of　the　earth；　near　to　what　others　have　assigned。　Let　us　assume　the　mean　distance　of　60　diameters　in　the　syzygies；　and　suppose　one　revolution　of　the　moon；　in　respect　to　the　fixed　stars；　to　be　completed　in　27d。　7h。　43'；　as　astronomers　have　determined；　and　the　circumference　of　the　earth　to　amount　to　123；249；600　Paris　feet；　as　the　French　have　found　by　mensuration。　And　now；　if　we　imagine　the　moon；　deprived　of　all　motion；　to　be　let　go；　so　as　to　descend　towards　the　earth　with　the　impulse　of　all　that　force　by　which　（by　Cor。　Prop。　iii。）　it　is　retained　in　its　orb；　it　will　in　the　space　of　one　minute　of　time　describe　in　its　fall　15　1/12　Paris　feet。　For　the　versed　sine　of　that　arc　which　the　moon；　in　the　space　of　one　minute　of　time；　would　by　its　mean　motion　describe　at　the　distance　of　sixty　semi…diameters　of　the　earth；　is　nearly　15　1/12　Paris　feet；　or　more　accurately　15　feet；　1　inch；　1　line　4/9。　Wherefore；　since　that　force；　in　approaching　the　earth；　increases　in　the　reciprocal…duplicate　proportion　of　the　distance；　and　upon　that　account；　at　the　surface　of　the　earth；　is　60　x　60　times　greater　than　at　the　moon；　a　body　in　our　regions；　falling　with　that　force；　ought　in　the　space　of　one　minute　of　time　to　describe　60　x　60　x　15　1/12　Paris　feet；　and　in　the　space　of　one　second　of　time；　to　describe　15　1/12　of　those　feet；　or　more　accurately；　15　feet；　1　inch；　1　line　4/9。　And　with　this　very　force　we　actually　find　that　bodies　here　upon　earth　do　really　descend；　for　a　pendulum　oscillating　seconds　in　the　latitude　of　Paris　will　be　3　Paris　feet；　and　8　lines　1/2　in　length；　as　Mr。　Huygens　has　observed。　And　the　space　which　a　heavy　body　describes　by　falling　in　one　second　of　time　is　to　half　the　length　of　the　pendulum　in　the　duplicate　ratio　of　the　circumference　of　a　circle　to　its　diameter　（as　Mr。　Huygens　has　also　shown）；　and　is　therefore　15　Paris　feet；　1　inch；　1　line　4/9。　And　therefore　the　force　by　which　the　moon　is　retained　in　its　orbit　is　that　very　same　force　which　we　commonly　call　gravity；　for；　were　gravity　another　force　different　from　that；　then　bodies　descending　to　the　earth　with　the　joint　impulse　of　both　forces　would　fall　with　a　double　velocity；　and　in　the　space　of　one　second　of　time　would　describe　30　1/6　Paris　feet；　altogether　against　experience。〃＇1＇　All　this　is　beautifully　clear；　and　its　validity　has　never　in　recent　generations　been　called　in　question；　yet　it　should　be　explained　that　the　argument　does　not　amount　to　an　actually　indisputable　demonstration。　It　is　at　least　possible　that　the　coincidence　between　the　observed　and　computed　motion　of　the　moon　may　be　a　mere　coincidence　and　nothing　more。　This　probability；　however；　is　so　remote　that　Newton　is　fully　justified　in　disregarding　it；　and；　as　has　been　said；　all　subsequent　generations　have　accepted　the　computation　as　demonstrative。　Let　us　produce　now　Newton's　further　computations　as　to　the　other　planetary　bodies；　passing　on　to　his　final　conclusion　that　gravity　is　a　universal　force。　　　　　　　　　　　〃PROPOSITION　V。；　THEOREM　V。　〃That　the　circumjovial　planets　gravitate　towards　Jupiter；　the　circumsaturnal　towards　Saturn；　the　circumsolar　towards　the　sun；　and　by　the　forces　of　their　gravity　are　drawn　off　from　rectilinear　motions；　and　retained　in　curvilinear　orbits。

〃For　the　revolutions　of　the　circumjovial　planets　about　Jupiter；　of　the　circumsaturnal　about　Saturn；　and　of　Mercury　and　Venus　and　the　other　circumsolar　planets　about　the　sun；　are　appearances　of　the　same　sort　with　the　revolution　of　the　moon　about　the　earth；　and　therefore；　by　Rule　ii。；　must　be　owing　to　the　same　sort　of　causes；　especially　since　it　has　been　demonstrated　that　the　forces　upon　which　those　revolutions　depend　tend　to　the　centres　of　Jupiter；　of　Saturn；　and　of　the　sun；　and　that　those　forces；　in　receding　from　Jupiter；　from　Saturn；　and　from　the　sun；　decrease　in　the　same　proportion；　and　according　to　the　same　law；　as　the　force　of　gravity　does　in　receding　from　the　earth。　〃COR。　1。There　is；　therefore；　a　power　of　gravity　tending　to　all　the　planets；　for　doubtless　Venus；　Mercury；　and　the　rest　are　bodies　of　the　same　sort　with　Jupiter　and　Saturn。　And　since　all　attraction　（by　Law　iii。）　is　mutual；　Jupiter　will　therefore　gravitate　towards　all　his　own　satellites；　Saturn　towards　his；　the　earth　towards　the　moon；　and　the　sun　towards　all　the　primary　planets。　〃COR。　2。The　force　of　gravity　which　tends　to　any　one　planet　is　reciprocally　as　the　square　of　the　distance　of　places　from　the　planet's　centre。　〃COR。　3。All　the　planets　do　mutually　gravitate　towards　one　another；　by　Cor。　1　and　2；　and　hence　it　is　that　Jupiter　and　Saturn；　when　near　their　conjunction；　by　their　mutual　attractions　sensibly　disturb　each　other's　motions。　So　the　sun　disturbs　the　motions　of　the　moon；　and　both　sun　and　moon　disturb　our　sea；　as　we　shall　hereafter　explain。　　　　　　　　　　　〃SCHOLIUM　〃The　force　which　retains　the　celestial　bodies　in　their　orbits　has　been　hitherto　called　centripetal　force；　but　it　being　now　made　plain　that　it　can　be　no　other　than　a　gravitating　force；　we　shall　hereafter　call　it　gravity。　For　the　cause　of　the　centripetal　force　which　retains　the　moon　in　its　orbit　will　extend　itself　to　all　the　planets　by　Rules　i。；　ii。；　and　iii。　　　　　　　　　　　〃PROPOSITION　VI。；　THEOREM　VI。　〃That　all　bodies　gravitate　towards　every　planet；　and　that　the　weights　of　the　bodies　towards　any　the　same　planet；　at　equal　distances　from　the　centre　of　the　planet；　are　proportional　to　the　quantities　of　matter　which　they　severally　contain。

〃It　has　been　now　a　long　time　observed　by　others　that　all　sorts　of　heavy　bodies　（allowance　being　made　for　the　inability　of　retardation　which　they　suffer　from　a　small　power　of　resistance　in　the　air）　descend　to　the　earth　FROM　EQUAL　HEIGHTS　in　equal　times；　and　that　equality　of　times　we　may　distinguish　to　a　great　accuracy　by　help　of　pendulums。　I　tried　the　thing　in　gold；　silver；　lead；　glass；　sand；　common　salt；　wood；　water；　and　wheat。　I　provided　two　wooden　boxes；　round　and　equal：　I　filled　the　one　with　wood；　and　suspended　an　equal　weight　of　gold　（as　exactly　as　I　could）　in　the　centre　of　oscillation　of　the　other。　The　boxes　hanging　by　eleven　feet；　made　a　couple　of　pendulums　exactly　equal　in　weight　and　figure；　and　equally　receiving　the　resistance　of　the　air。　And；　placing　the　one　by　the　other；　I　observed　them　to　play　together　forward　and　backward；　for　a　long　time；　with　equal　vibrations。　And　therefore　the　quantity　of　matter　in　gold　was　to　the　quantity　of　matter　in　the　wood　as　the　action　of　the　motive　force　（or　vis　motrix）　upon　all　the　gold　to　the　action　of　the　same　upon　all　the　woodthat　is；　as　the　weight　of　the　one　to　the　weight　of　the　other：　and　the　like　happened　in　the　other　bodies。　By　these　experiments；　in　bodies　of　the　same　weight；　I　could　manifestly　have　discovered　a　difference　of　matter　less　than　the　thousandth　part　of　the　whole；　had　any　such　been。　But；　without　all　doubt；　the　nature　of　grav