a history of science-2-第35章

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f　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　gravity　towards　the　planets　is　the　same　as　towards　the　earth。　For；　should　we　imagine　our　terrestrial　bodies　removed　to　the　orb　of　the　moon；　and　there；　together　with　the　moon；　deprived　of　all　motion；　to　be　let　go；　so　as　to　fall　together　towards　the　earth；　it　is　certain；　from　what　we　have　demonstrated　before；　that；　in　equal　times；　they　would　describe　equal　spaces　with　the　moon；　and　of　consequence　are　to　the　moon；　in　quantity　and　matter；　as　their　weights　to　its　weight。　〃Moreover；　since　the　satellites　of　Jupiter　perform　their　revolutions　in　times　which　observe　the　sesquiplicate　proportion　of　their　distances　from　Jupiter's　centre；　their　accelerative　gravities　towards　Jupiter　will　be　reciprocally　as　the　square　of　their　distances　from　Jupiter's　centrethat　is；　equal；　at　equal　distances。　And；　therefore；　these　satellites；　if　supposed　to　fall　TOWARDS　JUPITER　from　equal　heights；　would　describe　equal　spaces　in　equal　times；　in　like　manner　as　heavy　bodies　do　on　our　earth。　And；　by　the　same　argument；　if　the　circumsolar　planets　were　supposed　to　be　let　fall　at　equal　distances　from　the　sun；　they　would；　in　their　descent　towards　the　sun；　describe　equal　spaces　in　equal　times。　But　forces　which　equally　accelerate　unequal　bodies　must　be　as　those　bodiesthat　is　to　say；　the　weights　of　the　planets　（TOWARDS　THE　SUN　must　be　as　their　quantities　of　matter。　Further；　that　the　weights　of　Jupiter　and　his　satellites　towards　the　sun　are　proportional　to　the　several　quantities　of　their　matter；　appears　from　the　exceedingly　regular　motions　of　the　satellites。　For　if　some　of　these　bodies　were　more　strongly　attracted　to　the　sun　in　proportion　to　their　quantity　of　matter　than　others；　the　motions　of　the　satellites　would　be　disturbed　by　that　inequality　of　attraction。　If　at　equal　distances　from　the　sun　any　satellite；　in　proportion　to　the　quantity　of　its　matter；　did　gravitate　towards　the　sun　with　a　force　greater　than　Jupiter　in　proportion　to　his；　according　to　any　given　proportion；　suppose　d　to　e；　then　the　distance　between　the　centres　of　the　sun　and　of　the　satellite's　orbit　would　be　always　greater　than　the　distance　between　the　centres　of　the　sun　and　of　Jupiter　nearly　in　the　subduplicate　of　that　proportion：　as　by　some　computations　I　have　found。　And　if　the　satellite　did　gravitate　towards　the　sun　with　a　force；　lesser　in　the　proportion　of　e　to　d；　the　distance　of　the　centre　of　the　satellite's　orb　from　the　sun　would　be　less　than　the　distance　of　the　centre　of　Jupiter　from　the　sun　in　the　subduplicate　of　the　same　proportion。　Therefore；　if　at　equal　distances　from　the　sun；　the　accelerative　gravity　of　any　satellite　towards　the　sun　were　greater　or　less　than　the　accelerative　gravity　of　Jupiter　towards　the　sun　by　one…one…thousandth　part　of　the　whole　gravity；　the　distance　of　the　centre　of　the　satellite's　orbit　from　the　sun　would　be　greater　or　less　than　the　distance　of　Jupiter　from　the　sun　by　one　one…two…thousandth　part　of　the　whole　distancethat　is；　by　a　fifth　part　of　the　distance　of　the　utmost　satellite　from　the　centre　of　Jupiter；　an　eccentricity　of　the　orbit　which　would　be　very　sensible。　But　the　orbits　of　the　satellites　are　concentric　to　Jupiter；　and　therefore　the　accelerative　gravities　of　Jupiter　and　of　all　its　satellites　towards　the　sun；　at　equal　distances　from　the　sun；　are　as　their　several　quantities　of　matter；　and　the　weights　of　the　moon　and　of　the　earth　towards　the　sun　are　either　none；　or　accurately　proportional　to　the　masses　of　matter　which　they　contain。　〃COR。　5。The　power　of　gravity　is　of　a　different　nature　from　the　power　of　magnetism；　for　the　magnetic　attraction　is　not　as　the　matter　attracted。　Some　bodies　are　attracted　more　by　the　magnet；　others　less；　most　bodies　not　at　all。　The　power　of　magnetism　in　one　and　the　same　body　may　be　increased　and　diminished；　and　is　sometimes　far　stronger；　for　the　quantity　of　matter；　than　the　power　of　gravity；　and　in　receding　from　the　magnet　decreases　not　in　the　duplicate；　but　almost　in　the　triplicate　proportion　of　the　distance；　as　nearly　as　I　could　judge　from　some　rude　observations。

　　　　　　　　　　〃PROPOSITION　VII。；　THEOREM　VII。　〃That　there　is　a　power　of　gravity　tending　to　all　bodies；　proportional　to　the　several　quantities　of　matter　which　they　contain。

That　all　the　planets　mutually　gravitate　one　towards　another　we　have　proved　before；　as　well　as　that　the　force　of　gravity　towards　every　one　of　them　considered　apart；　is　reciprocally　as　the　square　of　the　distance　of　places　from　the　centre　of　the　planet。　And　thence　it　follows；　that　the　gravity　tending　towards　all　the　planets　is　proportional　to　the　matter　which　they　contain。　〃Moreover；　since　all　the　parts　of　any　planet　A　gravitates　towards　any　other　planet　B；　and　the　gravity　of　every　part　is　to　the　gravity　of　the　whole　as　the　matter　of　the　part　is　to　the　matter　of　the　whole；　and　to　every　action　corresponds　a　reaction；　therefore　the　planet　B　will；　on　the　other　hand；　gravitate　towards　all　the　parts　of　planet　A；　and　its　gravity　towards　any　one　part　will　be　to　the　gravity　towards　the　whole　as　the　matter　of　the　part　to　the　matter　of　the　whole。　Q。E。D。

〃HENCE　IT　WOULD　APPEAR　THAT　the　force　of　the　whole　must　arise　from　the　force　of　the　component　parts。〃

Newton　closes　this　remarkable　Book　iii。　with　the　following　words：　〃Hitherto　we　have　explained　the　phenomena　of　the　heavens　and　of　our　sea　by　the　power　of　gravity；　but　have　not　yet　assigned　the　cause　of　this　power。　This　is　certain；　that　it　must　proceed　from　a　cause　that　penetrates　to　the　very　centre　of　the　sun　and　planets；　without　suffering　the　least　diminution　of　its　force；　that　operates　not　according　to　the　quantity　of　the　surfaces　of　the　particles　upon　which　it　acts　（as　mechanical　causes　used　to　do）；　but　according　to　the　quantity　of　solid　matter　which　they　contain；　and　propagates　its　virtue　on　all　sides　to　immense　distances；　decreasing　always　in　the　duplicate　proportions　of　the　distances。　Gravitation　towards　the　sun　is　made　up　out　of　the　gravitations　towards　the　several　particles　of　which　the　body　of　the　sun　is　composed；　and　in　receding　from　the　sun　decreases　accurately　in　the　duplicate　proportion　of　the　distances　as　far　as　the　orb　of　Saturn；　as　evidently　appears　from　the　quiescence　of　the　aphelions　of　the　planets；　nay；　and　even　to　the　remotest　aphelions　of　the　comets；　if　those　aphelions　are　also　quiescent。　But　hitherto　I　have　not　been　able　to　discover　the　cause　of　those　properties　of　gravity　from　phenomena；　and　I　frame　no　hypothesis；　for　whatever　is　not　deduced　from　the　phenomena　is　to　be　called　an　hypothesis；　and　hypotheses；　whether　metaphysical　or　physical；　whether　of　occult　qualities　or　mechanical；　have　no　place　in　experimental　philosophy。　。　。　。　And　to　us　it　is　enough　that　gravity　does　really　exist；　and　act　according　to　the　laws　which　we　have　explained；　and　abundantly　serves　to　account　for　all　the　motions　of　the　celestial　bodies　and　of　our　sea。〃＇2＇

The　very　magnitude　of　the　importance　of　the　theory　of　universal　gravitation　made　its　general　acceptance　a　matter　of　considerable　time　after　the　actual　discovery。　This　opposition　had　of　course　been　foreseen　by　Newton；　and；　much　as　be　dreaded　controversy；　he　was　prepared　to　face　it　and　combat　it　to　the　bitter　end。　He　knew　that　his　theory　was　right；　it　remained　for　him　to　convince　the　world　of　its　truth。　He　knew　that　some　of　his　contemporary　philosophers　would　accept　it　at　once；　others　would　at　first　doubt；　question；　and　dispute；　but　finally　accept；　while　still　others　would　doubt　and　dispute　until　the　end　of　their　days。　This　had　been　the　history　of　other　great　discoveries；　and　this　will　probably　be　the　history　of　most　great　discoveries　for　all　time。　But　in　this　case　the　discoverer　lived　to　see　his　theory　accepted　by　practically　all　the　great　minds　of　his　time。　Delambre　is　authority　for　the　following　estimate　of　Newton　by　Lagrange。　〃The　celebrated　Lagrange；〃　he　says；　〃who　frequently　asserted　that　Newton　was　the　greatest　genius　that　ever　existed；　used　to　add'and　the　most　fortunate；　for　we　cannot　find　MORE　THAN　ONCE　a　system　of　the　world　to　establish。'　〃　With　pardonable　exaggeration　the　admiring　followers　of　the　great　generalizer　pronounced　this　epitaph：　　〃Nature　and　Nature's　laws　lay　hid　in　night；　　　God　said　‘Let　Newton　be！'　and　all　was　light。〃

XIII。　INSTRUMENTS　OF　PRECISION　IN　THE　AGE　OF　NEWTON　During　the　Newtonian　epoch　there　were　numerous　important　inventions　of　scientific　instruments；　as　well　as　many　improvements　made　upon　the　older　ones。　Some　of　these　discoveries　have　been　referred　to　briefly　in　other　places；　but　their　importance　in　promoting　scientific　investigation　warrants　a　fuller　treatment　of　some　of　the　more　significant。　Many　of　the　errors　that　had　arisen　in　various　scientific　calculations　before　the　seventeenth　century　may　be　ascribed　to　the　crudeness　and　inaccuracy　in　the　construction　of　most　scientific　instruments。　Scientists　had　not　as　yet　learned　that　an　approach　to　absolute　accuracy　was　necessary　in　every　investigation　in　the　field　of　science；　and　that　such　accuracy　must　be　extended　to　the　construction　of　the　instruments　used　in　these　investigations　and　observations。　In　astronomy　it　is　obvious　that　instruments　of　delicate　exactness　are　most　essential；　yet　Tycho　Brahe；　who　lived　in　the　sixteenth　century；　is　credited　w