a history of science-2-第16部分

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r　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　overcome　the　atmospheric　resistance；　and　that；　with　this　qualification；　neither　the　weight　nor　the　material　had　any　influence　upon　the　time　of　oscillation；　this　being　solely　determined　by　the　length　of　the　cord。　Naturally；　the　practical　utility　of　these　discoveries　was　not　overlooked　by　Galileo。　Since　a　pendulum　of　a　given　length　oscillates　with　unvarying　rapidity；　here　is　an　obvious　means　of　measuring　time。　Galileo；　however；　appears　not　to　have　met　with　any　great　measure　of　success　in　putting　this　idea　into　practice。　It　remained　for　the　mechanical　ingenuity　of　Huyghens　to　construct　a　satisfactory　pendulum　clock。　As　a　theoretical　result　of　the　studies　of　rolling　and　oscillating　bodies；　there　was　developed　what　is　usually　spoken　of　as　the　third　law　of　motionnamely；　the　law　that　a　given　force　operates　upon　a　moving　body　with　an　effect　proportionate　to　its　effect　upon　the　same　body　when　at　rest。　Or；　as　Whewell　states　the　law：　〃The　dynamical　effect　of　force　is　as　the　statical　effect；　that　is；　the　velocity　which　any　force　generates　in　a　given　time；　when　it　puts　the　body　in　motion；　is　proportional　to　the　pressure　which　this　same　force　produces　in　a　body　at　rest。〃＇2＇　According　to　the　second　law　of　motion；　each　one　of　the　different　forces；　operating　at　the　same　time　upon　a　moving　body；　produces　the　same　effect　as　if　it　operated　upon　the　body　while　at　rest。

STEVINUS　AND　THE　LAW　OF　EQUILIBRIUM　It　appears；　then；　that　the　mechanical　studies　of　Galileo；　taken　as　a　whole；　were　nothing　less　than　revolutionary。　They　constituted　the　first　great　advance　upon　the　dynamic　studies　of　Archimedes；　and　then　led　to　the　secure　foundation　for　one　of　the　most　important　of　modern　sciences。　We　shall　see　that　an　important　company　of　students　entered　the　field　immediately　after　the　time　of　Galileo；　and　carried　forward　the　work　he　had　so　well　begun。　But　before　passing　on　to　the　consideration　of　their　labors；　we　must　consider　work　in　allied　fields　of　two　men　who　were　contemporaries　of　Galileo　and　whose　original　labors　were　in　some　respects　scarcely　less　important　than　his　own。　These　men　are　the　Dutchman　Stevinus；　who　must　always　be　remembered　as　a　co…laborer　with　Galileo　in　the　foundation　of　the　science　of　dynamics；　and　the　Englishman　Gilbert；　to　whom　is　due　the　unqualified　praise　of　first　subjecting　the　phenomenon　of　magnetism　to　a　strictly　scientific　investigation。　Stevinus　was　born　in　the　year　1548；　and　died　in　1620。　He　was　a　man　of　a　practical　genius；　and　he　attracted　the　attention　of　his　non…scientific　contemporaries；　among　other　ways；　by　the　construction　of　a　curious　land…craft；　which；　mounted　on　wheels；　was　to　be　propelled　by　sails　like　a　boat。　Not　only　did　he　write　a　book　on　this　curious　horseless　carriage；　but　he　put　his　idea　into　practical　application；　producing　a　vehicle　which　actually　traversed　the　distance　between　Scheveningen　and　Petton；　with　no　fewer　than　twenty…seven　passengers；　one　of　them　being　Prince　Maurice　of　Orange。　This　demonstration　was　made　about　the　year　1600。　It　does　not　appear；　however；　that　any　important　use　was　made　of　the　strange　vehicle；　but　the　man　who　invented　it　put　his　mechanical　ingenuity　to　other　use　with　better　effect。　It　was　he　who　solved　the　problem　of　oblique　forces；　and　who　discovered　the　important　hydrostatic　principle　that　the　pressure　of　fluids　is　proportionate　to　their　depth；　without　regard　to　the　shape　of　the　including　vessel。　The　study　of　oblique　forces　was　made　by　Stevinus　with　the　aid　of　inclined　planes。　His　most　demonstrative　experiment　was　a　very　simple　one；　in　which　a　chain　of　balls　of　equal　weight　was　hung　from　a　triangle；　the　triangle　being　so　constructed　as　to　rest　on　a　horizontal　base；　the　oblique　sides　bearing　the　relation　to　each　other　of　two　to　one。　Stevinus　found　that　his　chain　of　balls　just　balanced　when　four　balls　were　on　the　longer　side　and　two　on　the　shorter　and　steeper　side。　The　balancing　of　force　thus　brought　about　constituted　a　stable　equilibrium；　Stevinus　being　the　first　to　discriminate　between　such　a　condition　and　the　unbalanced　condition　called　unstable　equilibrium。　By　this　simple　experiment　was　laid　the　foundation　of　the　science　of　statics。　Stevinus　had　a　full　grasp　of　the　principle　which　his　experiment　involved；　and　he　applied　it　to　the　solution　of　oblique　forces　in　all　directions。　Earlier　investigations　of　Stevinus　were　published　in　1608。　His　collected　works　were　published　at　Leyden　in　1634。　This　study　of　the　equilibrium　of　pressure　of　bodies　at　rest　led　Stevinus；　not　unnaturally；　to　consider　the　allied　subject　of　the　pressure　of　liquids。　He　is　to　be　credited　with　the　explanation　of　the　so…called　hydrostatic　paradox。　The　familiar　modern　experiment　which　illustrates　this　paradox　is　made　by　inserting　a　long　perpendicular　tube　of　small　caliber　into　the　top　of　a　tight　barrel。　On　filling　the　barrel　and　tube　with　water；　it　is　possible　to　produce　a　pressure　which　will　burst　the　barrel；　though　it　be　a　strong　one；　and　though　the　actual　weight　of　water　in　the　tube　is　comparatively　insignificant。　This　illustrates　the　fact　that　the　pressure　at　the　bottom　of　a　column　of　liquid　is　proportionate　to　the　height　of　the　column；　and　not　to　its　bulk；　this　being　the　hydrostatic　paradox　in　question。　The　explanation　is　that　an　enclosed　fluid　under　pressure　exerts　an　equal　force　upon　all　parts　of　the　circumscribing　wall；　the　aggregate　pressure　may；　therefore；　be　increased　indefinitely　by　increasing　the　surface。　It　is　this　principle；　of　course；　which　is　utilized　in　the　familiar　hydrostatic　press。　Theoretical　explanations　of　the　pressure　of　liquids　were　supplied　a　generation　or　two　later　by　numerous　investigators；　including　Newton；　but　the　practical　refoundation　of　the　science　of　hydrostatics　in　modern　times　dates　from　the　experiments　of　Stevinus。

GALILEO　AND　THE　EQUILIBRIUM　OF　FLUIDS　Experiments　of　an　allied　character；　having　to　do　with　the　equilibrium　of　fluids；　exercised　the　ingenuity　of　Galileo。　Some　of　his　most　interesting　experiments　have　to　do　with　the　subject　of　floating　bodies。　It　will　be　recalled　that　Archimedes；　away　back　in　the　Alexandrian　epoch；　had　solved　the　most　important　problems　of　hydrostatic　equilibrium。　Now；　however；　his　experiments　were　overlooked　or　forgotten；　and　Galileo　was　obliged　to　make　experiments　anew；　and　to　combat　fallacious　views　that　ought　long　since　to　have　been　abandoned。　Perhaps　the　most　illuminative　view　of　the　spirit　of　the　times　can　be　gained　by　quoting　at　length　a　paper　of　Galileo's；　in　which　he　details　his　own　experiments　with　floating　bodies　and　controverts　the　views　of　his　opponents。　The　paper　has　further　value　as　illustrating　Galileo's　methods　both　as　experimenter　and　as　speculative　reasoner。　The　current　view；　which　Galileo　here　undertakes　to　refute；　asserts　that　water　offers　resistance　to　penetration；　and　that　this　resistance　is　instrumental　in　determining　whether　a　body　placed　in　water　will　float　or　sink。　Galileo　contends　that　water　is　non…resistant；　and　that　bodies　float　or　sink　in　virtue　of　their　respective　weights。　This；　of　course；　is　merely　a　restatement　of　the　law　of　Archimedes。　But　it　remains　to　explain　the　fact　that　bodies　of　a　certain　shape　will　float；　while　bodies