a history of science-2- 第17部分

　is　now　familiar　to　every　one；　a　cannon…ball　dropped　from　the　level　of　the　cannon's　muzzle　will　strike　the　ground　simultaneously　with　a　ball　fired　horizontally　from　the　cannon。　As　to　the　paraboloid　course　pursued　by　the　projectile；　the　resistance　of　the　air　is　a　factor　which　Galileo　could　not　accurately　compute；　and　which　interferes　with　the　practical　realization　of　his　theory。　But　this　is　a　minor　consideration。　The　great　importance　of　his　idea　consists　in　the　recognition　that　such　a　force　as　that　of　gravitation　acts　in　precisely　the　same　way　upon　all　unsupported　bodies；　whether　or　not　such　bodies　be　at　the　same　time　acted　upon　by　a　force　of　translation。　Out　of　these　studies　of　moving　bodies　was　gradually　developed　a　correct　notion　of　several　important　general　laws　of　mechanicslaws　a　knowledge　of　which　was　absolutely　essential　to　the　progress　of　physical　science。　The　belief　in　the　rotation　of　the　earth　made　necessary　a　clear　conception　that　all　bodies　at　the　surface　of　the　earth　partake　of　that　motion　quite　independently　of　their　various　observed　motions　in　relation　to　one　another。　This　idea　was　hard　to　grasp；　as　an　oft…repeated　argument　shows。　It　was　asserted　again　and　again　that；　if　the　earth　rotates；　a　stone　dropped　from　the　top　of　a　tower　could　not　fall　at　the　foot　of　the　tower；　since　the　earth's　motion　would　sweep　the　tower　far　away　from　its　original　position　while　the　stone　is　in　transit。　This　was　one　of　the　stock　arguments　against　the　earth's　motion；　yet　it　was　one　that　could　be　refuted　with　the　greatest　ease　by　reasoning　from　strictly　analogous　experiments。　It　might　readily　be　observed；　for　example；　that　a　stone　dropped　from　a　moving　cart　does　not　strike　the　ground　directly　below　the　point　from　which　it　is　dropped；　but　partakes　of　the　forward　motion　of　the　cart。　If　any　one　doubt　this　he　has　but　to　jump　from　a　moving　cart　to　be　given　a　practical　demonstration　of　the　fact　that　his　entire　body　was　in　some　way　influenced　by　the　motion　of　translation。　Similarly；　the　simple　experiment　of　tossing　a　ball　from　the　deck　of　a　moving　ship　will　convince　any　one　that　the　ball　partakes　of　the　motion　of　the　ship；　so　that　it　can　be　manipulated　precisely　as　if　the　manipulator　were　standing　on　the　earth。　In　short；　every…day　experience　gives　us　illustrations　of　what　might　be　called　compound　motion；　which　makes　it　seem　altogether　plausible　that；　if　the　earth　is　in　motion；　objects　at　its　surface　will　partake　of　that　motion　in　a　way　that　does　not　interfere　with　any　other　movements　to　which　they　may　be　subjected。　As　the　Copernican　doctrine　made　its　way；　this　idea　of　compound　motion　naturally　received　more　and　more　attention；　and　such　experiments　as　those　of　Galileo　prepared　the　way　for　a　new　interpretation　of　the　mechanical　principles　involved。　The　great　difficulty　was　that　the　subject　of　moving　bodies　had　all　along　been　contemplated　from　a　wrong　point　of　view。　Since　force　must　be　applied　to　an　object　to　put　it　in　motion；　it　was　perhaps　not　unnaturally　assumed　that　similar　force　must　continue　to　be　applied　to　keep　the　object　in　motion。　When；　for　example；　a　stone　is　thrown　from　the　hand；　the　direct　force　applied　necessarily　ceases　as　soon　as　the　projectile　leaves　the　hand。　The　stone；　nevertheless；　flies　on　for　a　certain　distance　and　then　falls　to　the　ground。　How　is　this　flight　of　the　stone　to　be　explained？　The　ancient　philosophers　puzzled　more　than　a　little　over　this　problem；　and　the　Aristotelians　reached　the　conclusion　that　the　motion　of　the　hand　had　imparted　a　propulsive　motion　to　the　air；　and　that　this　propulsive　motion　was　transmitted　to　the　stone；　pushing　it　on。　Just　how　the　air　took　on　this　propulsive　property　was　not　explained；　and　the　vagueness　of　thought　that　characterized　the　time　did　not　demand　an　explanation。　Possibly　the　dying　away　of　ripples　in　water　may　have　furnished；　by　analogy；　an　explanation　of　the　gradual　dying　out　of　the　impulse　which　propels　the　stone。　All　of　this　was；　of　course；　an　unfortunate　maladjustment　of　the　point　of　view。　As　every　one　nowadays　knows；　the　air　retards　the　progress　of　the　stone；　enabling　the　pull　of　gravitation　to　drag　it　to　the　earth　earlier　than　it　otherwise　could。　Were　the　resistance　of　the　air　and　the　pull　of　gravitation　removed；　the　stone　as　projected　from　the　hand　would　fly　on　in　a　straight　line；　at　an　unchanged　velocity；　forever。　But　this　fact；　which　is　expressed　in　what　we　now　term　the　first　law　of　motion；　was　extremely　difficult　to　grasp。　The　first　important　step　towards　it　was　perhaps　implied　in　Galileo's　study　of　falling　bodies。　These　studies；　as　we　have　seen；　demonstrated　that　a　half…pound　weight　and　a　hundred…pound　weight　fall　with　the　same　velocity。　It　is；　however；　matter　of　common　experience　that　certain　bodies；　as；　for　example；　feathers；　do　not　fall　at　the　same　rate　of　speed　with　these　heavier　bodies。　This　anomaly　demands　an　explanation；　and　the　explanation　is　found　in　the　resistance　offered　the　relatively　light　object　by　the　air。　Once　the　idea　that　the　air　may　thus　act　as　an　impeding　force　was　grasped；　the　investigator　of　mechanical　principles　had　entered　on　a　new　and　promising　course。　Galileo　could　not　demonstrate　the　retarding　influence　of　air　in　the　way　which　became　familiar　a　generation　or　two　later；　he　could　not　put　a　feather　and　a　coin　in　a　vacuum　tube　and　prove　that　the　two　would　there　fall　with　equal　velocity；　because；　in　his　day；　the　air…pump　had　not　yet　been　invented。　The　experiment　was　made　only　a　generation　after　the　time　of　Galileo；　as　we　shall　see；　but；　meantime；　the　great　Italian　had　fully　grasped　the　idea　that　atmospheric　resistance　plays　a　most　important　part　in　regard　to　the　motion　of　falling　and　projected　bodies。　Thanks　largely　to　his　own　experiments；　but　partly　also　to　the　efforts　of　others；　he　had　come；　before　the　end　of　his　life；　pretty　definitely　to　realize　that　the　motion　of　a　projectile；　for　example；　must　be　thought　of　as　inherent　in　the　projectile　itself；　and　that　the　retardation　or　ultimate　cessation　of　that　motion　is　due　to　the　action　of　antagonistic　forces。　In　other　words；　he　had　come　to　grasp　the　meaning　of　the　first　law　of　motion。　It　remained；　however；　for　the　great　Frenchman　Descartes　to　give　precise　expression　to　this　law　two　years　after　Galileo's　death。　As　Descartes　expressed　it　in　his　Principia　Philosophiae；　published　in　1644；　any　body　once　in　motion　tends　to　go　on　in　a　straight　line；　at　a　uniform　rate　of　speed；　forever。　Contrariwise；　a　stationary　body　will　remain　forever　at　rest　unless　acted　on　by　some　disturbing　force。　This　all…important　law；　which　lies　at　the　very　foundation　of　all　true　conceptions　of　mechanics；　was　thus　worked　out　during　the　first　half　of　the　seventeenth　century；　as　the　outcome　of　numberless　experiments　for　which　Galileo's　experiments　with　failing　bodies　furnished　the　foundation。　So　numerous　and　so　gradual　were　the　steps　by　which　the　reversal　of　view　regarding　moving　bodies　was　effected　that　it　is　impossible　to　trace　them　in　detail。　We　must　be　content　to　reflect　that　at　the　beginning　of　the　Galilean　epoch　utterly　false　notions　regarding　the　subject　were　entertained　by　the　very　greatest　philosophersby　Galileo　himself；　for　example；　and　by　Keplerwhereas　at　the　close　of　that　epoch　the　correct　and　highly　illuminative　view　had　been　attained。　We　must　now　consider　some　other　experiments　of　Galileo　which　led　to　scarcely　less…important　results。　The　experiments　in　question　had　to　do　with　the　movements　of　bodies　passing　down　an　inclined　plane；　and　with　the　allied　subject　of　the　motion　of　a　pendulum。　The　elaborate　experiments　of　Galileo　regarding　the　former　subject　were　made　by　measuring　the　velocity　of　a　ball　rolling　down　a　plane　inclined　at　various　angles。　He　found　that　the　velocity　acquired　by　a　ball　was　proportional　to　the　height　from　which　the　ball　descended　regardless　of　the　steepness　of　the　incline。　Experiments　were　made　also　with　a　ball　rolling　down　a　curved　gutter；　the　curve　representing　the　are　of　a　circle。　These　experiments　led　to　the　study　of　the　curvilinear　motions　of　a　weight　suspended　by　a　cord；　in　other　words；　of　the　pendulum。　Regarding　the　motion　of　the　pendulum；　some　very　curious　facts　were　soon　ascertained。　Galileo　found；　for　example；　that　a　pendulum　of　a　given　length　performs　its　oscillations　with　the　same　frequency　though　the　arc　described　by　the　pendulum　be　varied　greatly。＇1＇　He　found；　also；　that　the　rate　of　oscillation　for　pendulums　of　different　lengths　varies　according　to　a　simple　law。　In　order　that　one　pendulum　shall　oscillate　one…half　as　fast　as　another；　the　length　of　the　pendulums　must　be　as　four　to　one。　Similarly；　by　lengthening　the　pendulums　nine　times；　the　oscillation　is　reduced　to　one…third；　In　other　words；　the　rate　of　oscillation　of　pendulums　varies　inversely　as　the　square　of　their　length。　Here；　then；　is　a　simple　relation　between　the　motions　of　swinging　bodies　which　suggests　the　relation　which　Kepler　bad　discovered　between　the　relative　motions　of　the　planets。　Every　such　discovery　coming　in　this　age　of　the　rejuvenation　of　experimental　science　had　a　peculiar　force　in　teaching　men　the　all…important　lesson　that　simple　laws　lie　back　of　most　of　the　diverse　phenomena　of　nature；　if　only　these　laws　can　be　discovered。　Galileo　further　observed　that　his　pendulum　might　be　constructed　of　any　weight　sufficiently　heavy　readily　to　overcom