Colin F. Gauld- Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications for Teaching About the Nature of Science

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  • 8/3/2019 Colin F. Gauld- Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications

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    LATPBLY QYA BE PFA ZAL@QCQM PB NLUAYPNDGPA ECQN@ _AYNYPGLIA8 G

    IGYA YPQ@^ GL@ YBMA NMZCNIGPNBLY EB_ PAGIFNLD GOBQP PFA LGPQ_A BE

    YINALIA

    IBCNL E, DGQC@

    Yifbbc be A`qigpnbl# Qlnuarynp~ be Lat Ybqpf Tgcay# > Mnifgac Irayialp# Kngmg @btly# LYT#

    ?199# GqyprgcngAmgnc8 idgqc`Jymgrpifgp,lap,gq

    Goyprgip, Obbky N gl` NNN be LatpblyZrnlinzng `auacbz Latpbly `~lgmnigc pfabr~ gl` yfbt fbt np avzcgnly g

    lqmoar be iacaypngc zfalbmalg, Obbk NN fgy raianua` cnppca gppalpnbl erbm fnypbrngly br a`qigpbry oaigqya np `bay lbp

    zcg~ g mghbr rbca nl Latpbly grdqmalp, Fbtauar# np ny nl Obbk NN pfgp ta yaa mbyp icagrc~ Latpbl obpf gy g

    pfabrapningl gl` gl avzarnmalpar, Nl pfny zgrp be pfa Zrnlinzng Latpbl agcp tnpf parrayprngc rgpfar pfgl tnpf iacaypngc

    zfalbmalg gl` `ayirnoa` g lqmoar be avzarnmalpy fa igrrna` bqp pb aypgocnyf pfa yqiiayy be fny pfabr~ nl avzcgnlnld pfa

    zrbzarpnay be ecqn` raynypglia, Np amblyprgpay mbyp icagrc~ pfa gipnunpnay be g yinalpnyp tbrknld gp pfa ebraerblp be

    klbtca`da gl` tbrknld tnpf zfalbmalg tfnif fa `n` lbp eqcc~ ql`arypgl`,

    Nl pfny zgzar pfa enryp be Latpbly yap be avzarnmalpy nlpb ecqn` raynypglia gra `ayirnoa` gl` pfa pfabr~ tfnif

    ql`arcnay fny avzcglgpnbl ny bqpcnla`, G lqmoar be nyyqay grnynld erbm pfny zbrpnbl be pfaZrnlinzng pbdapfar tnpf

    nmzcnigpnbly ebr pagifnld gobqp pfa lgpqra be yinalia gra `nyiqyya`,

    Ka~tbr`y, Latpbl# ecqn` raynypglia# zal`qcqm# lgpqra be yinalia# fnypbr~ be yinalia

    NLP_B@QIPNBL

    PfaZrnlinzng razrayalpa` g lat tg~ be pfnlknld gobqp zf~ynigc zfalbmalg gl` nl np Latpblzrayalpa` g lqmoar be glgc~yay be g ugrnap~ be zfalbmalg parrayprngc mbpnbl# ecqn` mbpnbl gl`

    raynypglia# ybql`# cndfp# gl` iacaypngc mbpnbl, Pfaya tara mgryfgcca` pb zrbun`a bla cgrda grdqmalpebr fny lat gzzrbgif, Pfa qcpnmgpa payp be pfny gzzrbgif &zrayalpa` nl Obbk N. tgy npy goncnp~ pb

    avzcgnl pfa mbpnbl be g ugrnap~ be iacaypngc bohaipy yqif gy zcglapy# ygpaccnpay gl` ibmapy &zrayalpa`

    nl Obbk NNN., Nl zrayalpnld gl bqpcnla be Latpbly grdqmalp nl pfaZrnlinzng mgl~ gqpfbry zrbiaa`erbm pfa pfabr~ nl Obbk N pb pfa yqiiayyeqc avzcglgpnbly be iacaypngc zfalbmalg nl Obbk NNN cgrdac~ndlbrnld pfa iblpalpy be Obbk NN &yaa# ebr avgmzca# Ifgl`rgyakfgr 7>>1# 909-900; @alymbra 7>>?.,

    Fbtauar# bla be Latpbly bohaipnuay tgy pb `amblyprgpa pfgp pfa gcparlgpnua y~ypam zrbzbya`

    o~ @ayigrpay ebr avzcgnlnld pfny mbpnbl fny ubrpav mb`ac tgy nlg`awqgpa &Gnpbl# 7>4?; Kb~r

    7>51# zz,4>-796; Latpbl 74?>"7>5:# Obbk NN# Yaipnbl NV; Obbk NNN# enlgc Dalargc Yifbcnqm;Taypegcc 7>6:# z,010.7, Gy zgrp be pfny zrbdrgmma np tgy laiayygr~ pb yfbt pfa aeeaip be ecqn`y

    yqif gy gnr bl pfa mbpnbl be bohaipy ynlia np tgy lbp zbyynoca nl Latpbly `g~ pb igrr~ bqp

    yqoypglpngc avzarnmalpy bl mbpnbl nl g ugiqqm, Obbk NN be pfaZrnlinzng ny zrnmgrnc~ ibliarla`

    tnpf gl nluaypndgpnbl nlpb pfa lgpqra gl` zrbzarpnay be pfa raynypglia pb mbpnbl zrb`qia` o~ ecqn`y

    gcpfbqdf bpfar pfnldy gra `agcp tnpf nl pfgp obbk gy tacc, Tfnca nl Obbk N Latpbl zrayalpa` pfa

    pfabrapnigc ogyny ebr fny gzzrbgif gl` nl Obbk NNN fa gzzcna` fny rayqcpy pb pfa ql`arypgl`nld beiacaypngc zfalbmalg np ny nl Obbk NN pfgp ta yaa icagrc~ Latpbl gy gl avzarnmalpar, Nl ptb zcgiay

    &nl pfa Dalargc Yifbcnqm ebccbtnld Zrbzbynpnbl 97 gl` nl pfa `nyiqyynbl be Zrbzbynpnbl 0:. fa

    razbrpa` pfa rayqcpy be mgl~ avzarnmalpy nl tfnif fa qya` fny pfabr~ pb avzcgnl mbpnbl pfrbqdf

    ecqn`y,Prqay`acc &7>56o. fgy zbnlpa` bqp pfgp nl Obbk NN Latpbl tgy `agcnld tnpf zraunbqyc~

    qlavzcbra` parrnpbr~ gl` pfgp pfa mgparngc nl pfny zgrp be pfaZrnlinzng ny gcmbyp alpnrac~ brndnlgc&z,701. ybmapfnld tfnif tgy lbp dalargcc~ pfa igya tnpf Obbky N gl` NNN, Oaigqya be pfny np

    iblpgnly g oatnc`arnld gcparlgpnbl be mgpfamgpnigc zrbbe# ornccnglp f~zbpfayny# zqra dqayynld# ocqee#

    gl` zcgnl arrbr &z,70>., Fbtauar# Prqay`acc gcyb grdqa` pfgp pfa ornccnglpc~ nldalnbqy oqp# nl pfa

    al`# cgrdac~ qlygpnyegipbr~ Obbk NN cgn` bqp pfa gragy gl` `aenla` pfa zrbocamy ebr mgl~ be pfa

    maifglnigc rayagrifay be pfa lavp ialpqr~ &7>56g# z,>7.,Nl pfny zgzar Latpbly gzzrbgif pb ypq`~nld ecqn` raynypglia qynld zal`qcqm mbpnbl ny

    bqpcnla` gl` fny rayqcpy gra `nyiqyya`, Pfa ynmzcninp~ be fny avzarnmalpy mgka pfam n`agc

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    igl`n`gpay ebr razcnigpnbl o~ zrayalp `g~ ypq`alpy gl` fny pfabr~ zrbun`ay g icagr avgmzca be pfa

    tg~ Latpbl pfbqdfp gobqp zf~ynigc zfalbmalg, Pfa racgpnblyfnz oaptaal pfabr~ gl` avzarnmalp

    nl Latpbly pfnlknld ny gcyb icagrc~ nccqyprgpa`,

    Pfa enryp ptalp~-lnla zrbzbynpnbly nl Obbk NN zrbun`a gl glgc~yny be bla gl` ptb `nmalynblgc

    mbpnbl ql`ar pfa nlecqalia be raynypgliay tnpf `neearalp `azal`aliay bl pfa uacbinp~ be pfa mbunld

    bohaip, Nl Zrbzbynpnbl 9: Latpbl zrayalpa` pfa pfabr~ tfnif tbqc` algoca fnm pb qya pfa `aig~ nl

    pfa ytnld be g zal`qcqm pb enl` bqp pfa dalargc zrbzarpnay be ecqn` raynypglia,

    LATPBLY PFAB_^ BE FNY ECQN@ _AYNYPGLIA AVZA_NMALPY

    Ypgda 7 Latpbly avzaipgpnbl

    Nl Yaipnbl N be Obbk NN &Zrbzbynpnbly 7 pb 0. be fnyZrnlinzng Latpbl `agcp tnpf pfa zrbzarpnay beraynypglia tfnif ugrnay `nraipc~ tnpf pfa uacbinp~, Nl pfa Yifbcnqm gp pfa al` be pfgp yaipnbl Latpbl

    trbpa

    Fbtauar# pfgp pfa raynypglia be ob`nay ny nl pfa rgpnb be pfa uacbinp~# ny mbra g mgpfamgpnigc f~zbpfaynypfgl g zf~ynigc bla, Nl ma`nqmy ubn` be gcc palginp~# pfa raynypgliay mg`a pb ob`nay gra gy pfa ywqgra be

    pfa uacbinpnay, &Latpbl 74?>"7>5:# z,?00.

    Nl bpfar tbr`y Latpbl `n` lbp oacnaua pfgp raynypglia tgy ragcc~ zrbzbrpnblgc pb uacbinp~ oqp# nl pfa

    n`agc igya# pb pfa ywqgra be pfa uacbinp~, Fa grdqa` pfgp pfa mbunld ob`~ ibccn`a` tnpf pfa

    ypgpnblgr~ ma`nqm &br zgrpnicay be pfa ma`nqm.# avarpa` g ebria bl np gl` ypgrpa` np mbunld, Ne bla

    iblyn`ary pfa ma`nqm pb oa g ibccaipnbl be nl`nun`qgc zgrpnicay pfa uacbinp~# u# nmzgrpa` pb bla bepfaya zgrpnicay ny zrbzbrpnblgc pb pfa uacbinp~# U# be pfa mbunld ob`~, Ne pfa ibccnynbl ny zareaipc~

    acgypni pfa zgrpnica giwqnray gcmbyp ptnia pfa uacbinp~ be pfa mbunld ob`~; ne pfa ibccnynbl ny

    zareaipc~ nlacgypni pfa uacbinp~ be pfa zgrpnica ny gcmbyp awqgc pb pfgp be pfa mbunld ob`~ &yaa

    Latpbly `nyiqyynbl be Zrbzbynpnbly 99 gl` 91., Pfqy g mbra rgzn`c~ mbunld ob`~ zrb`qiay gzrbzbrpnblgcc~ cgrdar uacbinp~ nl pfa zgrpnicay be pfa ma`nqm pfgl g mbra ycbtc~ mbunld ob`~, Pfa

    pnma pgkal pb prglyear g dnual pbpgc gmbqlp be mbpnbl &mbmalpqm. ny nluaryac~ zrbzbrpnblgc pb pfa

    uacbinp~, Pfqy pfa raynypglia# tfnif ny zrbzbrpnblgc pb pfa gmbqlp be mbpnbl cbyp o~ pfa mbunld

    ob`~ zar qlnp pnma ny zrbzbrpnblgc pb ifglda nl mbpnbl zar qlnp pnma# pfgp ny pb mu"&7"U. brU? tfara

    m ny pfa mgyy be pfa ma`nqm yap nl mbpnbl,

    -- ENDQ_A 7 --

    _aearalia pb Endqra 7 yfbty pfgp nl bla yaibl` pfa ob`~ mbuay g `nypglia Uyb pfgp pfa

    mbmalpqm prglyear zar yaibl` ny awqgc pb mu tfara m ny pfa gmbqlp be ma`nqm iblpgnla` nl pfa

    ubcqma prguarya` o~ pfa mbunld ob`~ nl bla yaibl`, Pfqy# erbm Latpbly pfnr` cgt# pfa raynypglia

    pb pfa mbpnbl be pfa mbunld ob`~ ny

    _ = mu &`GU.U`GU?

    tfara `ny pfa `alynp~ be pfa ma`nqm gl`G ny pfa irbyy-yaipnblgc grag zarzal`niqcgr pb pfa `nraipnblbe mbpnbl,

    Latpbl yfbta` nl Obbk NN pfgp fa avzaipa` pfa mghbr iblprnoqpnbl pb raynypglia pb oa

    zrbzbrpnblgc pb pfa ywqgra be pfa uacbinp~# pfa grag be pfa mbunld ob`~ zarzal`niqcgr pb pfa `nraipnbl

    be mbpnbl gl` pfa `alynp~ be pfa ma`nqm &Yifbcnqm ebccbtnld Zrbzbynpnbl 70; Zrbzbynpnbl 99;

    Zrbzbynpnbl 91# Igyay 7-9# Ibrbccgrnay 7-1.,Pfny be ibqrya ny blc~ nl ma nqmy ubn` be gcc palginp~, Nl pfa Yifbcnqm gp pfa al` be YaipnblNNN be Obbk NN Latpbl trbpa

  • 8/3/2019 Colin F. Gauld- Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications

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    Pfa raynypglia be yzfarnigc ob`nay nl ecqn`y grnyay zgrpc~ erbm pfa palginp~# zgrpc~ erbm pfa gpprnpnbl# gl`

    zgrpc~ erbm pfa `alynp~ be pfa ma`nqm, Gl` pfgp zgrp be pfa raynypglia tfnif grnyay erbm pfa `alynp~ be pfa

    ecqn` ny# gy N ygn`# gy pfa ywqgra be pfa uacbinp~; pfa bpfar zgrp# tfnif grnyay erbm pfa palginp~ be pfa ecqn`# ny

    qlnebrm, &Latpbl 74?>"7>5:# z,?6:.

    Latpbl pragpa` qlnebrm raynypglia nl g ynmncgr egyfnbl pb pfa aeeaip be drgunp~ bl gl gyial`nld

    ob`~ gl` fa yqddaypa` pfgp bla mndfp gcyb db bl pb pfa mbpnbl be ob`nay tfnif gra raynypa` nl zgrp

    qlnebrmc~# nl zgrp nl pfa rgpnb be pfa uacbinp~# gl` nl zgrp nl pfa `qzcnigpa rgpnb be pfa ygma uacbinp~,

    Fa zrbun`a` avgmzcay be fbt pfny mndfp oa `bla nl fny `nyiqyynbl be Zrbzbynpnbly 77 pb 70,

    Ypgda ? Latpbly iblyprqipnbl

    Nl `nyiqyynld Zrbzbynpnbl 9: Latpbl oadgl fny glgc~yny be pfa zrbocam be raynypglia pb pfa mbpnbl

    be g i~icbn`gc zal`qcqm o~ qynld pfa ygma ergmatbrk fa qya` tfal `agcnld tnpf pfa uacbinp~ be

    pfa zal`qcqm obo nl pfa igya tfara pfara ny lb raynypglia &Obbk N# Zrbzbynpnbl 1?., Nl Endqra ? pfa

    `ngmapar#OG# be g yamn-inrica razrayalpy pfa zbynpnbl be pfa obo gy np mbuay erbm npy oadnllnld

    zbnlp#O# pb npy al` zbnlp#G &yaa gcyb Endqra 5&g.., Pfa ialpra be pfny zgpf ny Igl`@ gl` `grazbnlpy ybmatfara bl pfa zgpf be pfa zal`qcqm obo yazgrgpa` o~ g ymgcc pnma nlparugc# p, Latpbl

    yfbta`# nl Zrbzbynpnbly 96 gl` 1? be Obbk N pfgp pfa uarpnigc cnla@Any zrbzbrpnblgc pb pfa uacbinp~be pfa obo gp pfa zbnlp@ gl` `a ny zrbzbrpnblgc pb pfa uacbinp~ be pfa obo gp zbnlp `&yaa Dgqc`

    ?::0., Nl Zrbzbynpnbl 17 be Obbk N Latpbl fg` gcrag`~ yfbtl pfgp

    obopfabeTandfp

    zgpfnpygcbldobozal`qcqmblEbria

    C

    I@=

    -- ENDQ_A ? --

    Oaigqya be pfa raynypglia pfa al` zbnlp be pfa enryp ytnld be pfa obo ny pfa zbnlp g tfnif egccyyfbrp beG o~ pfa `nypgliaGg, Gp pfa zbnlp@ pfa uacbinp~# nlypag` be oanld razrayalpa` o~@Any

    razrayalpa` o~ pfa ymgccar caldpf@Egl`# ne erbm pfny zbnlp bl# pfa obo iblpnlqa` qlraynypa` nptbqc` ragif pfa zbnlp M gp pfa caep yn`a be npy zgpf, Ne raynypglia avnypy oaptaal@ gl` `pfa uacbinp~

    gp `ny razrayalpa` o~ pfa cnla `h yb pfgp pfa cnlaeh razrayalpy pfa `airagya nl uacbinp~ oaptaal pfazbnlpy@ gl` ``qa pb pfa raynypglia erbm pfa ma`nqm pfrbqdf tfnif pfa obo ny prguaccnld, Pfa

    zbnlpLrazrayalpy pfa zbynpnbl pfa obo tbqc` lbt ragif ne raynypglia tara xarb gepar pfa zbnlp `gl`B ny pfa ialpra be pfa mbpnbl be pfa obo tfal raynypa` ebr pfa tfbca be npy mbuamalp erbmO pb g,

    Pfa cnla@Kny iblyprqipa` yb pfgp

    obopfabeTandfp

    @gpraynypgliabeEbria

    C

    @K=

    Ypgda 9 Latpbly glgc~yny

    Endqra 9 yfbty mbra `apgnc be pfa radnbl be Endqra 7 oaptaal Igl`@, IEgl` Idgra rg`ngc cnlay

    erbm pfa ialpra# I# gl`dny pfa zbnlp tfara pfa griLh avpal`a` nlparyaipy pfa cnla@E, Pfa rg`nqyIEiqpy pfa grihdgp f, Em ny zgrgccac pb I@ gl` yb ny awqgc pb@`, Ibmzgrnld Endqray ? gl` 9# IL

    = Id# ML = Ef# IM = IEgl`em = `e - @E,

    -- ENDQ_A 9 --

  • 8/3/2019 Colin F. Gauld- Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications

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    Np igl oa yaal pfgp# ne pfa `nypglia@`ny ymgcc# pfa pfraa prngldcay#Eme#Efdgl`E@Igra

    ynmncgr, OaigqyaEmegl`E@Igra ynmncgr

    em

    Em

    em

    @`

    I@

    @E= =

    Edny zrbzbrpnblgc pb pfa `airagya nl uacbinp~ `qa pb pfa raynypglia gl`em ny zrbzbrpnblgc pb pfa

    nliragya nl uacbinp~ `qa pb drgunp~ yb pfgp# erbm Latpbly enryp cgt

    drgunp~pb`qaoboblEbria

    raynypgliapb`qaoboblEbria

    drgunp~beebriapb`qauacbinp~nlNliragya

    raynypgliapb`qauacbinp~nl@airagya=

    Pfgp nyI@

    @K

    em

    Ed=

    Pfqy@E

    I@

    I@

    @K

    @`

    em

    em

    Ed,, =

    yb pfgpEd

    @`

    @K

    @E=

    Oaigqya prngldcayEfdgl`E@Igra ynmncgr

    IE

    @E

    ed

    Ef=

    yb pfgp@E

    @K

    IE

    @E

    @`

    ed

    ed

    Ef,, =

    PfqyEf

    @`

    @K

    IE=

    brML

    @`

    @K

    IM=

    Tfal pfa tfbca mbpnbl ny raynypa` ML,IM= @`,@K, Pfa grag be pfa yfg`a` radnbl@`kK

    ny awqgc pb@`,@Kyb pfgp @`,@Kny pfa grag be pfa tfbca radnblOIgUK, Pfa grag be pfa yfg`a`

    radnbl ML_Y# tfara IM= M_# ny awqgc pb ML,IMyb pfgp ML,IMny awqgc pb pfa grag tfbca

    prgzaxbn`gc radnblGgQT, Pfa grag beGgQTny awqgc pbGg,&IO + Ig. =Gg, gO =Gg,BO =

    grag beOIgUK,

    Ypgda 0 Latpbly gzzcnigpnbl

    Igya 78_ = iblypglp

    Nl pfa ynpqgpnbl tfara_ ny g iblypglp pfa radnblOIgUKny g raipgldca tnpf g caldpf awqgc pbOg gl`

    g fandfp awqgc pb@Kyb npy grag nyOg,@K, Pfqy

    Gg, gO =@K,gO

  • 8/3/2019 Colin F. Gauld- Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications

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    Yb pfgp BU=@K= Gg,

    tfara BUrazrayalpy pfa raynypglia gp pfa ialpra be pfa ytnld,

    PfqyobopfabeTandfp

    Bgp_aynypglia

    C

    .Gg& ?7= [7]

    Igya ?8_ uacbinp~

    Latpbl grdqa` pfgp ne pfa raynypglia tara ymgcc pfa uacbinp~ oaptaalO gl` g ibqc` oa razrayalpa`o~ pfa cnla@Enl Endqra 0 tfaraOEg ny g yamninrica tnpf `ngmaparOg, Fa fg` yfbtl nl pfa

    Ibrbccgr~ pb Zrbzbynpnbl ?1 pfgp# ebr g iblypglp raynypglia# pfa egypayp uacbinp~ biiqrra` gp B# pfaialpra be pfa cnlaOg, Ne pfa raynypglia tara zrbzbrpnblgc pb pfa uacbinp~ pfal pfa fandfp be pfa iqrua

    OKkUg tbqc` oa g iblypglp ergipnbl be pfa fandfp be pfa yamninricaOEg, Nl bpfar tbr`yGKkUg ny gyamn-accnzya tnpf gl grag awqgc pb BU,BO = BU, Og,

    -- ENDQ_A 0 --

    Pfqy BU, Og =Gg, gO

    Yb pfgp GgGg

    BU 774

    ?'=

    /

    Nl bpfar tbr`yobopfabeTandfp

    Bgp_aynypglia

    C

    Gg=

    .& 774 [?]

    Igya 98_ uacbinp~?

    Ne pfa raynypglia tara zrbzbrpnblgc pb pfa ywqgra be pfa uacbinp~ gl` pfa iqruaGEg ny g yamninricapfal pfa iqruaGKkUg ny g zgrgobcg tnpf gl grag 9? Og,BU, Pfqy nl pfny igya BU= Gg gl`

    obopfabeTandfp

    Bgp_aynypglia

    C

    Gg=

    .& 09 [9]

    Latpbl giklbtca`da` pfgp pfa iqruaOEg mndfp lbp oa g yamninrica gl` yb nl igyay ? gl` 9 pfa

    iqruay mndfp lbp oa avgipc~ gl accnzya gl` g zgrgobcg, Fbtauar# fa iblyn`ara` fny iblicqynbly [7]#[?] gl` [9] pb oa icbya albqdf ebr fny zrgipnigc zqrzbyay qynld pfa tbr` lagrc~ ebr gzzrbvnmgpac~

    prqa,

    LATPBLY AVZA_NMALPY NLPB ECQN@ _AYNYPGLIA

    Nl br`ar pb qya fny pfabr~ pb `aparmnla pfa zrbzarpnay be ecqn` raynypglia gy pfa~ gra geeaipa` o~ pfa

    uacbinp~ gl` ynxa be pfa ob`~ tfnif ny mbunld gl` pfa `alynp~ be pfa ecqn` Latpbl yap qz g cbldzal`qcqm gl` ugrna` pfa zrbzarpnay be pfa ob`nay tfnif mg`a qz pfa obo, Fa `ayirnoa` pfa igra

    tnpf tfnif fa `ayndla` pfa yqzzbrp pbtgr`y pfa al` be pfa Yifbcnqm gl` avzcgnla` pfa laa` ebr g

    yqzzbrp yqif gy g klnea a`da tfnif `n` lbp nlfnonp pfa zal`qcqm ytnld, Fa tgy goca pb ugr~ pfauacbinp~ gp pfa cbtayp zbnlp o~ gcparnld pfa `nypglia pfa obo tgy zqcca` ogik erbm npy cbtayp zbnlp

    &Dgqc` ?::0., Fny zrbia`qra tgy pb zqcc ogik pfa obo g klbtl `nypglia gl` ibqlp pfa lqmoar be

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    ytnldy &erbm bla yn`a pb pfa bpfar. ebr pfa gmzcnpq`a pb ra`qia o~ bla andfpf br bla wqgrpar, Fa

    pfal razagpa` pfa avzarnmalp o~ `bqocnld pfa nlnpngc gmzcnpq`a qlpnc fa fg` g yap be rayqcpy nl tfnif

    pfa nlnpngc gmzcnpq`ay ebrma` g dabmaprni yarnay, Latpbl `aparmnla` pfa ynxa beGg ebr pfa enryp

    ytnld o~ yqoprgipnld pfa ynxa be pfa enlgc gyialp erbm pfa ynxa be pfa nlnpngc `ayialp gl` `nun`nld o~

    pfa lqmoar be ytnldy, Qynld fny avzrayynbl [7]# [?] br [9] algoca` fnm pb qya fny ugcqa beGg pb

    enl` pfa raynypglia gp pfa cbtayp zbnlp nl pfgp ytnld,

    Latpbl grdqa` pfgp pfa arrbr nl pragpnld pfa inriqcgr zal`qcqm gy g i~icbn`gc zal`qcqm tgyladcndnoca, Ebr g i~icbn`gc zal`qcqm pfa uacbinp~ gp pfa cbtayp zbnlp be pfa ytnld ny zrbzbrpnblgc pbpfa `nypglia gcbld pfa griOItfnca ebr g inriqcgr zal`qcqm np ny zrbzbrpnblgc pb pfa caldpf be pfa

    ifbr`OI&Dgqc` 7>>6; 7>>>., Pfa zgpf be pfa obo be g inriqcgr zal`qcqm fgy g iblypglp iqrugpqratfnca pfgp be g i~icbn`gc zal`qcqm be pfa ygma caldpf oadnly gp pfa obppbm tnpf pfa ygma iqrugpqra

    gy pfa inriqcgr zal`qcqm oqp pfny iqrugpqra `airagyay gy pfa gldca be pfa yprnld nliragyay, Pfa

    byinccgpnld yprnld caldpf `airagyay gy pfa yprnld mbuay gdgnlyp pfa i~icbn`gc ifaaky, Pfqy# ne pfa

    caldpf be pfa gri erbm tfnif pfa obo ypgrpy npy `btltgr` hbqrla~ ny pfa ygma ebr pfa ptb zal`qcqmy

    pfa ypgrpnld zbnlp ebr pfa i~icbn`gc zal`qcqm ny fndfar gl` pfa uacbinp~ be pfa i~icbn`gc zal`qcqm ny

    cgrdar tfal pfa obo ragifay pfa cbtayp zbnlp,Ebr g inriqcgr zal`qcqm pfa ypgrpnld fandfp ny dnual o~

    C

    ifbr`f

    ?

    .& ?=

    Ebr g i~icbn`gc zal`qcqm pfa ypgrpnld fandfp ny dnual o~

    C

    grif

    ?

    .& ?=

    Ynlia pfa ypgrpnld fandfp ny zrbzbrpnblgc pb pfa ywqgra be pfa uacbinp~ gp pfa obppbm pfa rgpnb be pfa

    uacbinp~ ebr pfa inriqcgr zal`qcqm pb pfgp be pfa i~icbn`gc zal`qcqm ny awqgc pb &ifbr`"gri.,Latpbl icgnma` pfgp pfa rgpnb be pfa zarnb`y ebr pfaya zal`qcqmy ny &gri"ifbr`., Fbtauar# ne

    bla ibmzgray pfaya rgpnby bla enl`y pfa~ gra blc~ gzzrbvnmgpac~ awqgc?, Ebr avgmzca# ebr g ypgrpnld

    gldca be 9::

    pfa rgpnby `neear o~ gobqp :,1! &Kn`` % Ebdd ?::?., Latpbl `n` lbp hqypne~ fny icgnm

    oqp gl grdqmalp fa mndfp fgua qya` ny pfa ebccbtnld, Pfa zal`qcqm oboy obpf ypgrp gp rayp gl` pfa~

    prguac pfa ygma `nypglia gcbld gcmbyp n`alpnigc zgpfy, &Pfa fandfp gobua pfa cbtayp zbnlp gp pfa

    oadnllnld ebr pfa inriqcgr zal`qcqm ny 74,?7 nlif tfnca pfgp ebr pfa i~icbn`gc zal`qcqm ny 74,5?

    nlif g `neearalia be blc~ :,07 nlif,. Latpbl mg~ fgua pfal ynmzc~ iblicq`a` pfgp pfa pnma pgkal ny

    nluaryac~ zrbzbrpnblgc pb pfa enlgc uacbinp~,

    Latpbly iblicqynbl erbm fny `nyiqyynbl be Zrbzbynpnbl 9: tgy pfgp pfa `airagya nl gmzcnpq`a

    gepar bla ytnld be pfa zal`qcqm `qa pb raynypglia tgy zrbzbrpnblgc pb pfa raynypglia v caldpf be pfazal`qcqm &awqgpnbly [7]# [?] gl` [9]., Nl pfa Dalargc Yifbcnqm fa raypgpa` pfny nl g ebrm tfnif

    raearra` blc~ pb pfa zrbzarpnay be pfa mbpnbl be pfa obo gl` lbp pb pfa zal`qcqm, Nl pfny ebrm pfa

    `airagya nl gmzcnpq`a ny zrbzbrpnblgc pb pfa raynypglia v &zarnb`.?, Gyyqmnld pfgp pfa raynypglia gp

    pfa obppbm tgy zrbzbrpnblgc pb U?

    pfny magly pfgp pfa `airagya nl gmzcnpq`a tgy zrbzbrpnblgc pb U?

    vP

    ?, Fbtauar# Latpbl fg` gcrag`~ ypgpa` pfgp U&i~icbn`."U&inrica. = &gri"ifbr`. gl` pfgp

    P&i~icbn`."P&inrica. = &ifbr`"gri. yb fny iblicqynbl tgy pfgp pfa `airagyay nl pfa gmzcnpq`a ebr ginriqcgr zal`qcqm gl` g i~icbn`gc zal`qcqm tnpf pfa ygma caldpf gl` pfa ygma gmzcnpq`a tara

    lagrc~ awqgc, Pfqy fa oacnaua` pfgp fny qya be inriqcgr rgpfar pfgl i~icbn`gc zal`qcqmy `n` lbp

    nlprb`qia yqoypglpngc arrbry nlpb fny avzarnmalpy,

    -- PGOCA 7 --

    Latpbly `gpg ebr pfa 09 avzarnmalpy fa razbrpa` nl pfa Yifbcnqm ebccbtnld fny `nyiqyynbl be

    Zrbzbynpnbl 97 gra dnual nl Pgoca 7 gl` g drgzfnigc yqmmgr~ ny zrayalpa` nl Endqra 1, Fny qlnp be

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    `nypglia tgy pfa Aldcnyf nlif &pb oa `nypnldqnyfa` erbm pfa Zgrny nlif. 7? be tfnif mgka qz gl

    Aldcnyf ebbp tfnif ny awqgc pb :,9:1 mapra, Fny qlnp be tandfp &br mgyy. tgy pfa prb~ bqlia tfnif

    ny awqgc pb ?6,91 drgmy, Fa igrrna` bqp pfraa mgnl yarnay be avzarnmalpy pb amblyprgpa

    rayzaipnuac~ pfa `azal`alia be pfa raynypglia bl &g. pfa uacbinp~ be pfa obo# &o. pfa `ngmapar be pfa

    obo gl` &i. pfa `alynp~ be pfa ecqn`,

    -- ENDQ_A 1 --

    @AZAL@ALIA BL PFA UACBINP^ BE PFA OBO &Igyay 7-7?.

    Latpbl qya` igyay 7-5# nl tfnif fa magyqra` pfa lqmoar be ytnldy rawqnra` ebr pfa zal`qcqm

    gmzcnpq`a pb `airagya o~ bla andfpf# pb nluaypndgpa pfa `azal`alia be pfa raynypglia bl uacbinp~,

    Pfa zal`qcqm caldpf#C# tgy 7?5 nlifay gl` pfa zal`qcqm obo fg` g `ngmapar be 5,641 nlifay gl`g mgyy be 14,976 bqliay, Latpbl zcgia` g mgrk bl pfa tnra yqzzbrpnld pfa obo gp g zbnlp 7?7

    nlifay &C. erbm pfa yqzzbrp, Oafnl` pfny mgrk fa zcgia` g rqcar tfnif tgy qya` pb cbigpa pfa

    zbynpnbl be pfa mgrk gy pfa zal`qcqm byinccgpa`, Pfa ugcqay nl pfa yaibl` gl` pfnr` ibcqmly be

    Pgoca 7 gra pfa `nypgliay mbua` o~ pfny mgrk tfal `ayial`nld gl` gyial`nld, Np igl oa yaal erbmpfa dabmapr~ be pfa ynpqgpnbl pfgp pfa rgpnbGg"Cebr pfa mgrk ny awqgc pbGg"C ebr pfa obo, Pfa

    magyqra be pfa uacbinp~ ny pfa nypglia prguacca` nl pfa enryp `ayialp, Ebr g dnual i~icbn`gc zal`qcqmpfa gri caldpf prguacca` `qrnld pfa enryp fgce be pfa enryp ytnld ny zrbzbrpnblgc pb pfa uacbinp~ gp pfa

    obppbm be pfa zgpf &Dgqc` ?::0.,Ybma be pfa ugcqay ebr pfa lqmoar be byinccgpnbly nl ibcqml 1 be Pgoca 7 iblpgnl ergipnbly, Nl

    gl agrc~ tbrknld zgzar qzbl tfnif pfny Yifbcnqm ny ogya` &Ibfal 7>47# z,7:9. Latpbl avzcgnla`

    fbt fa grrnua` gp yqif ugcqay, Ebr avgmzca# nl igya 5 tfara pfa lqmoar be byinccgpnbly ny 9?> pfa

    obo tbqc` oa gobua npy pgrdap be 15 nlifay gepar > ytnldy oqp oacbt pfa pgrdap gepar 7: ytnldy,

    Latpbl lbpa` pfa gmbqlpy o~ tfnif pfa klbp tgy gobua br oacbt pfa pgrdap gl` qya` pfaya ugcqay

    pb aypnmgpa pfa lqmoar be ytnldy tfal pfa pgrdap tgy ragifa`,Latpbly avzaipgpnbl pfgp pfa raynypglia tbqc` oa zrbzbrpnblgc pb pfa ywqgra be pfa uacbinp~

    tgy iblenrma` ebr cgrdar uacbinpnay o~ `nun`nld pfa ugcqay ebrGg&tfnif gra pfa ogyni magyqray be

    raynypglia giibr`nld pb awqgpnbly [7]# [?] gl` [9]. o~ pfa ywqgra be pfa gri prguacca` &tfnif ny pfa

    ogyni magyqra be uacbinp~ gp pfa obppbm be pfa ytnld. nl pfa enryp `ayialp ebr igyay 7-5,

    Nl fny mbra raenla` glgc~yny fa gyyqma` pfgp pfny raynypglia tgy mg`a qz be pfraa ibmzblalpy

    zrbzbrpnblgc# rayzaipnuac~# pb U# U9"? gl` U

    ?, Fa dgua lb ragybl ebr pfny gl` np gzzagry pb oa g zqrac~

    ebrmgc gyyndlmalp, Fny zraunbqy pfabrapnigc `nyiqyynbl fg` blc~ `agcp tnpf raynypgliay zrbzbrpnblgc

    pb U:# Ugl` U

    ?, Qynld igyay ?# 0 gl` 5 gl` gl avzaipgpnbl pfgpGg = GU + OU

    9"?+ IU

    ?Latpbl

    `aparmnla` pfa ugcqay beG#O gl` Itfnif algoca` fnm pb igciqcgpa pfa racgpnua ynxay be pfaya pfraaibmzblalpy ebr `neearalp uacbinpnay, Nl br`ar pb `aparmnla pfa raynypglia erbm pfa gobua awqgpnbl

    Latpbl qya` awqgpnbly [?] gl` [9] pb grrnua gp

    Caldpf

    IUOUGU

    Tandfp

    _aynypglia ?09?

    9

    7:4

    774

    ++

    =

    Pfa egipbr 4"7: nl pfa yaibl` parm ny pfa magl be 4"77 gl` 9"0 ebql` nl awqgpnbly [?] gl` [9],

    Latpbl zrayalpa` pfa `gpg ebr igyay 4-7? nl tfnif pfa gmzcnpq`a tgy ra`qia` o~ bla wqgrpar

    be pfa nlnpngc `ayialp ypgpnld pfgp pfaya rayqcpy tbqc` zrbun`a mbra giiqrgpa nlebrmgpnbl pfgl igyay7-5 oqp fa pbbk pfanr glgc~yny lb eqrpfar, Fa trbpa8 N cagua pfa igciqcgpnbl pb yqif gy gra `nyzbya`

    pb mgka np' Np ny nlparaypnld pfgp pfa ugcqay beGgebr pfa igyay 7-5 gra iblynypalpc~ cgrdar pfgl pfbya

    ebr pfa ibrrayzbl`nld igyay 4-7?, Bla ragybl ebr pfa `neearalia ny pfgp# gy pfa zal`qcqm byinccgpay#npy uacbinp~ `airagyay# pfa raynypglia `airagyay gl` pfa ugcqa beGg`airagyay tnpf agif ytnld,

    Pfqy# `nun`nld pfa `neearalia oaptaal pfa enryp `ayialp gl` pfa cgyp gyialp o~ pfa lqmoar be ytnldy

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    dnuay pfa guargda `airagya zar ytnld gl` lbp pfa airagya ebr pfa enryp ytnld, Oaigqya pfa ymgccar

    `airagyay ebr pfa cgpar ytnldy nl igyay 4-7? gra bmnppa` nl igyay 7-5 pfa guargda ugcqay beGgebr

    igyay 7-5 gra cgrdar pfgl ebr pfa ibrrayzbl`nld ugcqay ebr igyay 4-7?, Ne bla gyyqmay g zgrpniqcgr

    `azal`alia bl U&br bl pfa gmzcnpq`a. ebr pfa ugcqa beGg nl agif ytnld np ny zbyynoca pb `arnua g

    mbra giiqrgpa aypnmgpa beGgebr pfa enryp ytnld &qynld# ebr avgmzca# pfa Dbgc Yaakpbbc nl MY

    Aviac., Pfa ugcqay ebrGgqynld pfny mapfb` gra mqif icbyar ebr pfa ptb yapy be rayqcpy,

    @AZAL@ALIA BL PFA @NGMAPA_ BE PFA OBO &Igyay 7-?5# ?4.

    Nl igyay 79-7> Latpbl qya` g obo tnpf g ymgccar `ngmapar &? nlifay. gl` tandfp &?5,?1 bqliay.

    pfgl ebr igyay 7-7? tfnca mgnlpgnlnld pfa ygma caldpf ebr pfa zal`qcqm, Ebr pfaya igyay fa ibqlpa`pfa lqmoar be ytnldy pb ornld gobqp g ra`qipnbl nl pfa gmzcnpq`a be bla andfpf, Ebr igyay ?:-?5 pfa

    avzarnmalpy tara razagpa` ebr g ra`qipnbl nl gmzcnpq`a be bla wqgrpar oqp pfaya rayqcpy tara lbpglgc~ya` nl pfaZrnlinzng,

    Latpbl glgc~ya` igyay 71# 74 gl` 7> qynld pfa ygma ebrm be racgpnblyfnz ebrGggy ebr igyay

    ?# 0 gl` 5 gl` ebql` pfgp pfa rgpnb be pfa uacbinp~ ywqgra` ibmzblalpy be raynypglia `arnua` erbm

    pfa ugcqay beIebr igyay ?# 0 gl` 5 gl` igyay 71# 74 gl` 7> &ebr tfnif ibrrayzbl`nld uacbinpnaytara pfa ygma. tgy 4,99"7 tfnca pfa rgpnb be pfa ywqgray be pfa `ngmapary tgy 77,6"7, Fa grdqa`

    pfgp ne bla pbbk nlpb giibqlp pfa raynypglia be pfa pfrag`# tfnif fa aypnmgpa` pb oa dragpar pfgl gpfnr` zgrp be pfa tfbca raynypglia be pfa cayyar zal`qcqm# pfa enryp rgpnb oaibmay &4,99 :,99."&7,::

    :,99. br 7:,1"7 g ugcqa tfnif ny icbyar pb pfa rgpnb be ywqgray be pfa `ngmapary,

    Latpbl ragcnya` pfgp pfa aeeaip be pfa pfrag` tbqc` oa racgpnuac~ cayy ebr dcboay tnpf cgrdar

    `ngmapary gl` fa igrrna` bqp gl avzarnmalp &igya ?4. tnpf g dcboa be `ngmapar 76,41 nlifay gl`

    mgyy ?:6 bqliay, Pfa zal`qcqm caldpf tgy 7??,1 nlifay, Pfa rayqcpy be pfny avzarnmalp tara

    ibmzgra` pb pfbya erbm igya 5 gl`# ynlia pfa zal`qcqm caldpfy tara `neearalp# pfny laiayynpgpa` pfa

    prglyebrmgpnbl be zal`qcqm zgrgmapary ebr igya ?4 pb pfbya be igya 5 oaebra g iblicqynbl ibqc` oa

    ragifa`, Fa ebql` pfa rgpnb be raynypgliay pb oa 4"7 gl` pfa rgpnb be pfa ywqgra be pfa `ngmapary pb oa

    4,0"7,

    @AZAL@ALIA BL PFA @ALYNP^ BE PFA ECQN@ &Igyay ?6-09.

    Latpbl igrrna` bqp g yarnay be avzarnmalpy nl tfnif pfa obo be g zal`qcqm mbua` pfrbqdf gnr

    &igyay ?6-97G. gl` pfal pfrbqdf tgpar &igyay 9:T-95., Erbm igyay ?6 gl` 97G nl gnr Latpbl

    `aparmnla` pfa ugcqay beG gl` Inl pfa avzrayynblGg= GU + IU?, Fa ragcnya` pfgp fa ibqc` lbp

    ynmzc~ qya pfa gri caldpf gy g magyqra be pfa uacbinp~ gp pfa obppbm nl tgpar oaigqya pfa uacbinp~tgy mqif cayy nl tgpar pfgl nl gnr ebr pfa ygma zal`qcqm zgrgmapary, Fbtauar# fa grdqa` gy fa

    `n` tfal ibmzgrnld pfa oafgunbqr be inriqcgr gl` i~icbn`gc zal`qcqmy, Fa ragybla` pfgp ne pfauacbinp~ be pfa zal`qcqm nl tgpar tara pb oa nliragya` yb np tgy pfa ygma gy pfgp ebr pfa zal`qcqm

    nl gnr pfa pnma pfa obo yzalp prguaccnld pb pfa obppbm be npy zgpf tbqc` oa `airagya` nl pfa ygmargpnb, Pfqy# ynliaGg ny zrbzbrpnblgc pb raynypglia v &pnma.

    ?gl` ne pfa raynypglia tara zrbzbrpnblgc

    pb U?#Gg tbqc` oa qlifglda` gl` lb arrbr tbqc` oa nlprb`qia` o~ gyyqmnld pfgp pfa magyqra be

    pfa uacbinp~ be pfa zal`qcqm obo prguaccnld pfrbqdf tgpar tgy pfa caldpf be pfa gri,

    Ne pfny iblicqynbl tara prqa pfal# ebr igyay 97G gl` 97T#_&tgpar."_&gnr. =Gg&tgpar."Gg&gnr. = L&gnr."L&tgpar. = 191"7,?, Qynld fny ugcqay beG gl` Iebql` zraunbqyc~

    Latpbl pfal grdqa` pfgp_&gnr[U?]."_&gnr. = 06,75"57,47 tfara_&gnr[U

    ?]. ny pfa ibmzblalp be pfa

    raynypglia `qa pb pfa gnr tfnif ny zrbzbrpnblgc pb U?

    erbm tfnif fa iblicq`a` pfgp_&tgpar."_&gnr

    [U?]. = 147"7, Pgknld nlpb giibqlp pfa egip pfgp pfa pfrag` tgy pbpgcc~ nmmarya` nl gnr oqp lbp

    pbpgcc~ nmmarya` nl tgpar# Latpbl# tnpfbqp gl~ eqrpfar `apgncy# grrnua` gp fny iblicqynbl pfgp

    _&tgpar."_&gnr[U?]. tgy gobqp 61: pb 7# pfgp ny gy# pfa `alynp~ be pfa tgpar pb pfa `alynp~ be pfa gnr#

    lagrc~,Latpbl igrrna` bqp eqrpfar avzarnmalpy ebr tfnif fa `bay lbp zrbun`a gcc pfa `apgncy, Fa

    ragcnya` pfgp# nl ybma igyay# fny uayyac tgy pbb ymgcc ebr pfa ynxa be pfa obo gl` fa trbpa

  • 8/3/2019 Colin F. Gauld- Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications

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    >

    N nlpal`a` pb fgua razagpa` pfaya avzarnmalpy tnpf cgrdar uayyacy# gl` nl macpa` mapgcy# gl` bpfar cnwqbry

    obpf fbp gl` ibc`; oqp N fg` lbp pfa canyqra pb pr~ gcc8 gl` oayn`ay# erbm tfgp ny gcrag`~ `ayirnoa`# np

    gzzagry yqeeninalpc~ pfgp pfa raynypglia be ob`nay mbunld ytnepc~ ny lagrc~ zrbzbrpnblgc pb pfa `alynpnay be

    pfa ecqn`y nl tfnif pfa~ mbua,

    Pfa cgyp avzarnmalp fa `ayirnoa` nl pfny Yifbcnqm tgy bla pb `aparmnla pfa raynypglia `qa pb

    pfa gapfar, Pfa gapfar tgy ibliazpqgcnya` gy g ecqn` tfnif lbp blc~ encca` amzp~ yzgia oqp gcyb

    zarug`a` pfa nlparnbr be ybcn` bohaipy, Fa yqyzal`a` g tbb`al obv bl pfa al` be g pfrag` 77 eaap

    cbld pfal `rat np gyn`a gobqp 5 eaap# gccbta` np pb byinccgpa gl` lbpa` pfa zbynpnbl be pfa obo gepar

    bla# ptb gl` pfraa ytnldy, Pfa obv tgy pfal encca` tnpf mapgc, Tfal eqcc pfa tandfp be pfa obv

    tgy 46 pnmay pfa ibmonla` tandfp be pfa amzp~ obv# pfa gnr nl np gl` pfa pfrag` grbql` np, Tfalgccbta` pb byinccgpa# pfa encca` obv pbbk 44 ytnldy pb ragif pfa enryp mgrk, Latpbl tgy nlparaypa` pb

    yaa ne pfny `neearalia tgy `qa pb pfa aeeaip be pfa gapfar bl yqregiay nlyn`a pfa obv gy tacc gy bl pfabqpyn`a yqregia, Qynld pfa racgpnblyfnz [7]# [?] br [9]# lgmac~#

    T

    _

    C

    LgyialpEnlgc`ayialpNlnpngck

    C

    kGg=

    '

    =

    ".&

    Latpbl iblicq`a` pfgp pfa tfbca raynypglia be pfa obv tfal eqcc# fg` lbp g dragpar zrbzbrpnbl

    pb pfa raynypglia be pfa obv# tfal amzp~# pfgl 46 pb 44, Yazgrgpnld pfaya raynypgliay nlpb ptb

    ibmzblalpy pfgp `qa pb pfa bqpar yqregiay gl` pfgp `qa pb pfa nllar yqregiay - fa iblicq`a` pfgp

    pfa raynypglia be pfa amzp~ obv nl npy nlparlgc zgrpy tncc oa gobua 1::: pnmay cayy pfgl pfa

    raynypglia bl pfa avparlgc yqzareninay [yqregiay] pfgp ny# pfa raynypglia be pfa gapfar# ne gl~# tgy uar~

    ymgcc,

    Latpbl zbnlpa` bqp pfgp pfny avzarnmalp ny racgpa` o~ mambr~# pfa zgzar oanld cbyp nl tfnif Nfg` `ayirnoa` np; yb pfgp N fgua oaal bocnda` pb bmnp ybma ergipnblgc zgrpy# tfnif gra ycnzp bqp be m~

    mambr~; gl` N fgua lb canyqra pb pr~ np gdgnl,

    @NYIQYYNBL

    Nl mgl~ rayzaipy Latpbly pragpmalp be pfa zrbocam be ecqn` raynypglia ny yndlneniglpc~ `neearalp

    erbm pfa tg~ pfny zrbocam tbqc` oa pgikca` pb`g~ ayzaingcc~ nl a`qigpnblgc yappnldy, G lqmoar be

    eagpqray be Latpbly tbrk nl pfny grag gra `nyiqyya` nl tfgp ebccbty,

    Pfa dabmaprnygpnbl be lgpqra

    Pfa pfabr~ zrayalpa` gobua nccqyprgpay pfa gzzrbgif pb ql`arypgl`nld zf~ynigc zfalbmalg tfnif

    Latpbl g`bzpa` gl gzzrbgif `ayirnoa` o~ Kb~r gy pfa dabmaprnygpnbl be lgpqra &Kb~r 7>51#

    zz,5-4; Taypegcc 7>>:., Zf~ynigc racgpnblyfnzy ibqc` oa mgzza` o~ gl` glgc~ya` pfrbqdf

    dabmaprnigc racgpnblyfnzy, Pb`g~ pfa amzfgyny nl yinalia pagifnld ny bl gcdaorgni rgpfar pfgl

    dabmaprnigc mb`acy, Bla eagpqra be Latpbly pragpmalp be Zrbzbynpnbl 9: ny pfa icbya racgpnblyfnz

    oaptaal pfa dabmaprnigc `ngdrgm gl` pfa zf~ynigc ynpqgpnbl, Pfa ogya cnla#OG nl Endqra?#razrayalpy pfa zgpf be pfa zal`qcqm obo gl` pfa uacbinp~ be pfa obo ny razrayalpa` o~ uarpnigc cnlay

    ypgrpnld erbm pfa zgrpniqcgr zbynpnbl be pfa obo bl pfgp cnla, Pfa raynypglia gp@ ny razrayalpa` o~pfa cnla@K, Nl agif igya pfara tgy g `nraip racgpnblyfnz oaptaal g `~lgmnigc br knlamgpni ugrngoca

    gl` g cnla bl pfa `ngdrgm gl` pfa ibllaipnbl oaptaal `ngdrgm gl` ynpqgpnbl ny lbp `neeniqcp pb drgyz,Pfa raynypglia ny `nraipc~ racgpa` pb pfa `airagya nl pfa gmzcnpq`a be pfa zal`qcqm gy np mbuay

    pfrbqdf pfa ecqn`,

    -- ENDQ_A 5 --

  • 8/3/2019 Colin F. Gauld- Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications

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    Fbtauar# pfny ny lbp gctg~y yb nl pfaZrnlinzng gl`# nl ybma igyay# tfnca Latpbl zrbun`a` gdabmaprnigc ybcqpnbl pb g zrbocam ybmapnmay pfa cnlk oaptaal pfa `ngdrgm gl` pfa ynpqgpnbl tgy lbp

    agy~ pb ibliazpqgcnya, Fny pragpmalp be Zrbocam 0 &Zrbzbynpnbl ?>. nccqyprgpay pfny zbnlp tacc, Pfny

    zrbocam ny Yqzzbynld pfgp g ob`~ byinccgpnld nl g i~icbn` ny raynypa` nl g `qzcnigpa rgpnb be pfa

    uacbinp~8 pb enl` pfa raynypglia nl agif zcgia yb# nl zgrp# nl pfny zrbocam Latpbl gppamzpa` pb ybcua

    pfa ygma zrbocam fa `agcp tnpf nl Zrbzbynpnbl 9:, Latpbl cbbka` ebr g mgpfamgpnigc glgcbdqa ebrpfa zf~ynigc y~ypam fa tgy ypq`~nld gl` ebr mgl~ be pfa Zrbzbynpnbly nl Obbk NN pfny tgy ogya` blpfa f~zarobcg, Nl Endqra 5&g. g zal`qcqm obo tbqc` mbua erbmO pbG ne pfara tara lb raynypglia

    tfnca# gy g rayqcp be raynypglia# np mbua` erbmO pb g, Iny pfa cbtayp zbnlp gl`@ ny gl~ zbnlp blpfny zgpf, Latpbl yap qz pfa f~zarobcg nl Endqra 5&o. nl br`ar pb enl` g tg~ be `aparmnlnld pfa

    raynypglia avzarnalia` o~ pfa obo gy np mbua`, Fa ypnzqcgpa` pfa ebccbtnld nl br`ar pb oadnl fny

    glgc~yny8

    GragZNAW

    GragZNPY

    OI

    Ig= &pfny `aenla` pfa zbynpnbly beY# Zgl` W.

    GragNAE

    GragNCP

    BW

    BY=

    GragZNLM

    GragZNAW

    IX

    OI= &pfny `aenla` pfa zbynpnbl beM.

    GragZND_

    GragZNAW

    I@

    OI= &pfny `aenla` pfa zbynpnbl be_.

    tfara IXny awqgc pb pfa caldpf be pfa zal`qcqm,Ebccbtnld fny glgc~yny be pfa ynpqgpnbl Latpbl iblicq`a` pfgp

    GragZNLM

    GragNDFGragNAEBW

    B_

    drgunp~beEbria

    @gp_aynypglia'

    =

    .&

    Gcpfbqdf pfny ebrmgcc~ ybcua` Latpbly zrbocam np igl agync~ oa yaal pfgp cnppca be pfny glgc~yny

    gccbty ebr gl nlpqnpnua ql`arypgl`nld be pfa zrbocam npyace gl` Latpbl giklbtca`da` pfny tfal fa

    g`mnppa` Fbtauar# o~ ragybl be pfa `neeniqcp~ be pfa igciqcgpnbl o~ tfnif pfa raynypglia gl` pfauacbinp~ gra ebql` o~ pfny Zrbzbynpnbl# ta fgua pfbqdfp enp pb yqohbnl pfa Zrbzbynpnbl ebccbtnld, Nl

    Zrbzbynpnbl 9: fa zrbun`a` pfa acadglp gl` dalargcnya` glgc~yny be pfa zrbocam be ecqn` raynypglia gy

    np gzzcna` pb g i~icbn`gc zal`qcqm gl` tfnif ny bqpcnla` gobua gcpfbqdf pfa gzzrbvnmgpnbly mg`a

    nl pfny ybcqpnbl ral`ara` np cayy rndbrbqy pfgl pfa Aqicn`agl mb`ac tfnif Latpbl gppamzpa` pb

    amqcgpa nl pfaZrnlinzng,

    Zcgqynoca gzzrbvnmgpnbly tnpfbqp rndbrbqy hqypnenigpnbl

    Nl g lqmoar be zcgiay Latpbl gzzagry pb cgik pfa mgpfamgpnigc pbbcy pb zrbiaa` nl fny glgc~yny gl`

    mgkay gzzrbvnmgpnbly bl pfa ogyny be pfanr gzzgralp zcgqynoncnp~, Ebr avgmzca# tfnca fny pfabr~ nyogya` bl fny glgc~yny be pfa mbpnbl be g i~icbn`gc zal`qcqm# nl fny avzarnmalpy fa qya` g ynmzca

    inriqcgr zal`qcqm, Fa mg`a g igya &bqpcnla` zraunbqyc~ nl pfny zgzar. pfgp lauarpfacayy fny pfabr~ibqc` oa gzzcna` pb fny avzarnmalp aual pfbqdf pfny igya cgika` pfa rndbqr be bpfar zgrpy be fny

  • 8/3/2019 Colin F. Gauld- Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications

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    glgc~yny, Ynmncgrc~# fa icgnma` pfgp# nl Endqra 0# pfa iqruaOehg tgy g yamninrica br gp cagyp

    lagrc~ g yamninrica g zcgqynoca gyyqmzpnbl ebr tfnif fa zrbun`a` ybma hqypnenigpnbl,

    Tfal fny zal`qcqm oboy mbua` pfrbqdf tgpar# Latpbl ragcnya` pfgp pfa uacbinp~ gp pfa cbtayp

    zbnlp tbqc` oa yndlneniglpc~ cayy pfgp pfgp dnual o~ pfa racgpnblyfnz oaptaal gri &br ifbr`. caldpf

    gl` uacbinp~ qya` ebr g zal`qcqm nl gnr, Fbtauar# fa grdqa` &tnpfbqp `apgnca` glgc~yny oqp tnpf

    raearalia pb eagpqray be fny pfabr~ zrayalpa` agrcnar nl pfny zgzar. pfgp ne pfny ygma racgpnblyfnz taragyyqma` lb yndlneniglp arrbr tbqc` oa nlprb`qia` nlpb fny iblicqynbly,

    Pfaya avgmzcay gra nl`nigpnbly pfgp Latpbl# tbrknld tnpf g pfabr~ pfgp `n` lbp eqcc~ zarebrm

    pfa eqlipnbl tfnif fa nlpal`a` np pb# lauarpfacayy zrbiaa`a` bl pfa ogyny be tfgp mndfp ragyblgoc~

    oa gyyqma` aual tfara fa tgy lbp goca pb aypgocnyf pfa ugcn`np~ be pfbya gyyqmzpnbly,

    Pfa qya be rgt `gpg

    Tfal igrr~nld bqp fny avzarnmalpy Latpbl pbbk dragp igra pb alyqra pfgp fny magyqramalpy tara gygiiqrgpa gy zbyynoca, Nl pfaya avzarnmalpy fa qya` cbld zal`qcqmy gl` raenla` fny avzarnmalpgc

    paiflnwqa gy fa zrbdrayya` nl fny nluaypndgpnbly, Pgoca 7 iblpgnly nlebrmgpnbl gobqp 95 igyay ebrtfnif Latpbl zrbun`a` yqeeninalp `apgnc ebr qy pb klbt mbyp be pfa racauglp zgrgmapary gl` yb

    ifaik fny igciqcgpnbly, Ebr igyay 94-09 gl` pfa bpfar igyay fa razbrpa` nl pfa Dalargc Yifbcnqm

    ebccbtnld Zrbzbynpnbl 97 pfa `apgnc ny nlyqeeninalp ebr pfny pb oa `bla gl` ta fgua pb pgka Latpbly

    tbr` ebr fny iblicqynbly, Nl fny `nyiqyynbl be pfa nmzcnigpnbly be fny `gpg Latpbl glgc~ya` blc~ 7:

    be pfbya igyay cnypa` nl Pgoca 7 gl` lb malpnbl ny mg`a be zbyynoca arrbry nl pfa `gpg, Erbm igyay 7-

    5 fa qya` igyay ?# 0 gl` 5 pb `aparmnla pfa ibaeeninalpyG#O gl` Inl pfa racgpnblGg= GU + OU9"?

    + IU? gl` ndlbra` igyay 7# 9 gl` 1, Igyay 4-7? tara caep pb pfa rag`ar pb glgc~ya,

    Gcpfbqdf Latpbl `auacbza` fny pfabr~ nl Obbk NN pb `agc tnpf raynypgliay tfnif tara

    iblypglp# zrbzbrpnblgc pb U# br zrbzbrpnblgc pb U?

    fa dnuay lb ragybl ebr nlprb`qinld fara g

    ibmzblalp zrbzbrpnblgc pb U9"?

    ,

    Nl mgl~ igyay &ebr avgmzca# igyay 7# 9 gl` 1 br 4# > gl` 77.# ne bla gzzcnay pfa ygma glgc~yny pb

    pfa `gpg tfnif Latpbl ndlbra`# ladgpnua ugcqay gra bopgnla` ebrG brO, Np ny zbyynoca pfgp Latpbltgy gtgra be pfny gl` yb bmnppa` pfaya rayqcpy erbm fny razbrp, Bl pfa bpfar fgl`# pfa igyay fa `n`

    nlicq`a tara pfbya tnpf cgrdar ugcqay beUebr tfnif pfa U? ibmzblalp tbqc` oa avzaipa` pb

    `bmnlgpa,

    Lbtg`g~y gcc pfa `gpg tbqc` oa qya` gl` arrbry aypnmgpa` pb enl` iqruay be oayp enp yb pfgp lbgugncgoca nlebrmgpnbl ny ndlbra`, Pfa zrayalia be ladgpnua ugcqay ebrG brO tbqc` mbyp cnkac~ oa

    gpprnoqpa` pb avzarnmalpgc arrbr,

    _aiblincngpnbl oaptaal rayqcpy gl` avzaipgpnbly

    Nl gcc be pfa avzarnmalpy `ayirnoa` gobua pfara gra mghbr `nyirazglinay oaptaal pfa rayqcpy tfnif

    Latpbl bopgnla` erbm fny avzarnmalpy gl` fny avzaipgpnbly, Pfa `azal`alia be raynypglia bl pfaywqgra be pfa uacbinp~oragky `btl ebr ymgcc ugcqay beU# gl` pfa zrbzbrpnblgc `azal`alia be

    raynypglia bl pfa ywqgra be pfa `ngmapar be pfa obo br pfa `alynp~ be pfa ecqn` tgy egr erbm avgip, Nlgcc pfaya ynpqgpnbly Latpbl ybqdfp g ragybl ebr pfa `neearalia oaptaal fny avzarnmalpy gl` fny

    avzaipgpnbly gl` pfa raiblincngpnbl ny lbp gctg~y iblunlinld, Ebr avgmzca# fa nlprb`qia` g rbqdf

    aypnmgpa be pfa raynypglia be pfa pfrag` &tnpf lb giibqlp be fbt fa bopgnla` pfny. pb raiblinca

    avzarnmalpgc rayqcpy nl igyay 7-5 gl` 79-7> tnpf pfa rgpnb be `ngmapary tfnif tgy 77,9"7, Pfa rgpnb

    be raynypgliay oaebra mb`nenigpnbl tgy 4,99"7 tfnca gepar mb`nenigpnbl tgy 7:,1"7,

    Nl ibmzgrnld raynypgliay nl tgpar gl` gnr fny avzarnmalpy nl`nigpa` pfgp pfa rgpnb tgy 14:"7,Fa rndfpc~ zbnlpa` bqp pfgp pfa pfrag` tgy nmmarya` nl gnr tfnif avarpa` g raynypglia bl pfa pfrag`

    oqp pfa pfrag` tgy lbp nmmarya` nl pfa tgpar yb gcc pfa nrracauglp ugrngocay tara lbp iblprbcca`

  • 8/3/2019 Colin F. Gauld- Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications

    12/19

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    g`awqgpac~, Fa ypgpa` tnpfbqp yqzzbrp pfgp ne pfa pfrag` tara eqcc~ nmmarya` nl tgpar pfa rgpnb

    tbqc` oa 61:"7# tfnif ny lagrc~ pfa rgpnb be pfa `alynpnay be tgpar gl` gnr, &Gp ?::I pfa rgpnb ny

    gobqp 69:"7., Fbtauar# ne pfa nlebrmgpnbl fa dgua gobqp pfa raynypglia be pfa pfrag` tfal

    `nyiqyynld igyay 79-7> nl pfa avzarnmalp qynld g ? nlif obo ny qya`# pfa rgpnb yaamy pb oa blc~

    515"7, Np ny lbp icagr fbt fa grrnua` gp pfa rgpnb be 61:"7, Nl pfa pfnr` a`npnbl be pfaZrnlinzng

    Latpbl qya` pfraa `neearalp ugcqay ebr pfa tgpar pb gnr `alynp~ rgpnbl 61: fara# 65: nl pfa

    Yifbcnqm gepar Zrbzbynpnbl 0: tfal fa nluaypndgpa` pfa raynypglia pb egccnld ob`nay# gl` 64: nl pfaYifbcnqm gepar Zrbzbynpnbl 1: nl tfnif fa nluaypndgpa` pfa yzaa` be ybql` nl gnr, Taypegcc &7>49.

    zbnlpa` bqp pfgp# nl pfa ugrnbqy `rgepy be pfa enryp a`npnbl be pfaZrnlinzng nl tfnif fa `ayirnoa` fny

    nluaypndgpnbly nlpb pfa yzaa` be ybql`# Latpbl pamzbrgrnc~ g`bzpa` >:: gl` >1: oaebra yappcnld

    bl 64: ebr pfny rgpnb# gzzgralpc~ pb enl` pfa bla tfnif oayp yqnpa` fny `gpg, Pfaya mndfp oa avgmzcay

    be tfgp Prqay`acc igccy eq`da egipbry &7>56o# z,70>., Taypegcc &7>49. nl`nigpa` g lqmoar be bpfar

    zcgiay nl pfaZrnlinzng tfara Latpbl gzzagry pb fgua mgyygda` fny rayqcpy pb ornld gobqp g icbyar

    enp oaptaal pfabrapnigc zra`nipnbly gl` avzarnmalpgc rayqcpy,

    Prqay`acc &7>56o# z,>7. zbnlpy bqp pfgp nl Obbk NN be pfaZrnlinzng Latpbl# qynld pfa lat

    zf~yniy# tgy agcnld tnpf zfalbmalg tfnif fg` lauar oaebra oaal pragpa` nl pfny tg~, QlcnkaObbk N nl tfnif fa tgy ebccbtnld nl pfa ebbpypazy be bpfar lgpqrgc zfncbybzfary# nl Obbk NN fa tgy

    prag`nld lat drbql`, Prqay`acc nl`nigpay pfgp mbyp be tfgp Latpbl trbpa nl Obbk NN tgy egcya&Prqay`acc 7>56g# z,>7. oqp pfgp lauarpfacayy tfgp Latpbl gifnaua` pfara tgy lbpatbrpf~ gl` mqyp

    oa hq`da`# lbp giibr`nld pb tfgp ta klbt lbt oqp o~ tfgp tgy klbtl nl pfa 74pf ialpqr~,

    Latpbly gppamzpy pb raiblinca fny rayqcpy tnpf fny avzaipgpnbly ny p~znigc be ybmabla oragknld

    lat drbql` gl` pfny ny hqyp pfa zbynpnbl be Latpbl tfal nluaypndgpnld pfa ibmzcav zfalbmalg

    `nyiqyya` nl Obbk NN be pfaZrnlinzng, Ta yaa fara ybmapfnld be gl nl`nun`qgc yinalpnyp gp tbrk

    `bnld gcc fa igl pb yfbt pfa ugcqa be fny zbynpnbl rgpfar pfgl pfa ibmzcapa`# eqcc~ nlypnpqpnblgcnya`#

    bohaipnua yinalia be pavpobbky,

    @neearalia oaptaal parrayprngc gl` iacaypngc zf~yniy

    Parrayprngc zfalbmalg gra ibmzcav tnpf pfa bqpibmay oanld pfa rayqcp be mgl~ nlecqaliay tfnca

    iacaypngc zfalbmalg# `agcp tnpf nl Obbk NNN gra mbra ynmzca gl` cayy zrbla pb qlzra`nipgoca

    nlecqaliay yqif gy ernipnbl# raynypglia# pqroqcalia gl` yb bl, Pfa enp oaptaal Latpbly pfabr~ be

    ialprgc ebriay zrayalpa` nl Obbk N gl` pfa gyprblbmnigc `gpg zrayalpa` nl Obbk NNN ny mqif icbyar

    pfgl ebr pfa zfalbmalg `nyiqyya` nl Obbk NN, Gy egr gy zbyynoca# Latpbl gppamzpa` pb iblprbc

    igraeqcc~ nrracauglp ugrngocay oqp# gy fa `n` lbp eqcc~ ql`arypgl`nld pfa zfalbmalg fa tgy `agcnld

    tnpf# fa tgy lbp gctg~y gtgra be pfa lgpqra be pfaya nrracauglp ugrngocay,

    Zgrp be Latpbly zqrzbya nl trnpnld Obbk NN tgy pb raeqpa @ayigrpay pfabr~ be zcglapgr~mbpnbl nl tfnif pfa zcglapy tara igrrna` grbql` pfa Yql o~ ecqn` ubrpniay &Latpbl 74?>"7>5:#

    Obbk NN# Yaipnbl NV; Obbk NNN# Enlgc Dalargc Yifbcnqm; Taypegcc 7>6:# z,010., Latpbl `nyiqyya`

    inriqcgr mbpnbl nl ecqn`y nl Zrbzbynpnbly 17# 1? gl` 19 be Obbk NN, Gp pfa oadnllnld be pfaebccbtnld Yifbcnqm fa iblicq`a`8

    Falia np ny mglneayp pfgp pfa zcglapy gra lbp igrrna` rbql` nl ibrzbragc ubrpniay; ebr# giibr`nld pb pfa

    Ibzarlnigl f~zbpfayny# pfa zcglapy dbnld rbql` pfa yql raubcua nl accnzyay# fgunld yql nl pfanr ibmmbl

    ebiqy; gl` pfa rg`nn `rgtl erbm pfa yql `ayirnoa gragy zrbzbrpnblgc pb pfa pnmay, Oqp lbt pfa zgrpy be g

    ubrpav igl lauar raubcua tnpf yqif g mbpnbl, &Latpbl 74?>"7>5:# z, 9>1.

    IBLICQYNBL

    Pfa mgparngc zrayalpa` gobua dnuay nlyndfp nlpb Latpbly dabmaprnigc zrbia`qra gl` avzarnmalpgc

    paiflnwqa, Pfara ny mqif pfgp ypq`alpy igl cagrl erbm tfgp Latpbl `n , Ebr avgmzca# fny

    avzarnmalpy igl oa razcnigpa` gl` pfa rayqcpy glgc~ya` qynld fny pfabr~; gcparlgpnua aypnmgpay beGg

    tfnif pgka nlpb giibqlp pfa ra`qipnbl nl ynxa be pfny `neearalia ebr agif yqiiayynua ytnld igl oa

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    `arnua`; iqrua-enppnld paiflnwqay igl oa qya` pb glgc~ya fny btl rayqcpy &zrayalpa` nl Pgoca 7. gl`

    pb prglycgpa tfgp fa `n` nlpb mbra mb`arl parmy; pfa gyyqmzpnbly fa mg`a pb algoca fny `gpg pb enp

    fny avzaipgpnbly igl oa avzcbra`; gl` mbra raialp ql`arypgl`nld be pfa lgpqra be unyibqy `rgd

    &zrbzbrpnblgc pb U. igl oa nlprb`qia` nlpb fny glgc~yay, Gcc be pfny nlubcuay ibmnld pb glql`arypgl`nld be fny mb`a be pfbqdfp nl bpfar tbr`y zcginld blayace nl Latpbly yfbay gl`

    oadnllnld pb gzzraingpa pfa `neearaliay oaptaal tfgp Latpbl `n` gl` tfgp ta tbqc` `b tnpf fny

    zrbocam pb`g~, Pfa avzarnmalpy gra ynmzca albqdf lbp pb rawqnra ybzfnypnigpa` nlyprqmalpgpnbl gl`pb oa giiayynoca pb ypq`alpy nl mgl~ iblpavpy, Pfa~ gcyb yfbt pfa dalnqy be Latpbl tfal bla

    oadnly pb gzzraingpa pfa pfnlknld be g mgl gp pfa ebraerblp be pfa `auacbzmalp be maifglniy,

    LBPA

    7 Gnpbl &7>4?. zbnlpa` bqp pfgp# nl yznpa be Latpbly aeebrpy# pfa ubrpav pfabr~ ecbqrnyfa` bl pfa

    iblpnlalp tacc nlpb pfa 74::y, Mgl~ Aqrbzagl yinalpnypy fg` prbqoca tnpf Latpbly pfabr~ oaigqya

    np yaama` pb oa ogya` bl pfa avnypalia be biiqcp ebriay gp g `nypglia tfara pfara tgy lb zf~ynigc

    iblpgip oaptaal pfa nlpargipnld bohaipy, Gcc pfa bohaipnbly pb pfa Igrpayngl ubrpniay fg` oaal klbtebr g cbld pnma, Bl pfa bpfar fgl`# gy g igqya# pfa gpprgipnbl tgy hqyp gy qlgiiazpgoca gy np fg` oaal

    ebr buar g ialpqr~ &Gnpbl# 7>4?# z,?04.,? N gm nl`aopa` pb Gcgl Ammarybl gl` Mnifgac Ebtcar ebr faczeqc ibmmqlnigpnbly gobqp pfa

    zarnb` be g inriqcgr zal`qcqm ebr cgrda gmzcnpq`ay,

    _AEA_ALIAY

    Gnpbl# A,H,87>4?# Pfa Ubrpav Pfabr~ be Zcglapgr~ Mbpnbl# Yinalia Fnypbr~ Zqocnigpnbly# Lat ^brk,

    Ifgl`rgyakfgr# Y,8 7>>1# Latpbly Zrnlinzng ebr pfa Ibmmbl _ag`ar# Bvebr` Qlnuarynp~ Zrayy#Bvebr`,

    Ibfal# N,O, 7>47# Nlprb`qipnbl pb Latpbly Zrnlinzng# Igmorn`da Qlnuarynp~ Zrayy# Igmorn`da,@alymbra# @,8 7>>1, Latpbly Zrnlinzng8 Pfa Ialprgc Grdqmalp, Draal Cnbl Zrayy# Yglpg Ea#

    LM,

    Dgqc`# I,E,8 7>>6# Ibccn`nld Zal`qcqmy# Iblyarugpnbl be Mbmalpqm gl` Latpbl$y Pfnr` Cgt#

    Gqyprgcngl Yinalia Pagifary Hbqrlgc# 00&9.# 94-96,Dgqc`# I,E, 7>>># Qynld Ibccn`nld Zal`qcqmy pb Pagif Latpbl$y Pfnr` Cgt# Pfa Zf~yniy Pagifar#

    94# ?1-?6,

    Dgqc`# I,E,8 ?::0# Pfa Pragpmalp be I~icbn`gc Zal`qcqm Mbpnbl nl Latpbl$yZrnlinzng# Yinalia

    gl`A`qigpnbl,79# 559-549,Kn``# _,O, % Ebdd# Y,C8, ?::?# G Ynmzca Ebrmqcg ebr pfa Cgrda-gldca Zal`qcqm Zarnb`# Pfa

    Zf~yniy Pagifar# 0:# 67-69,

    Kb~r# G,8 7>51# Latpblngl Ypq`nay, Ifgzmgl % Fgcc# Cbl`bl,Latpbl# N,8 74?>"7>5:# Pfa Mgpfamgpnigc Zrnlinzcay be Lgpqrgc Zfncbybzf~# &prglycgpa` erbm pfa

    pfnr` a`npnbl o~ Gl`rat Mbppa gl` raunya` o~ Ecbrngl Ighbrn.# Qlnuarynp~ be Igcnebrlng Zrayy#

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    PGOCA 78 Latpbly zal`qcqm `gpg

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    74

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    76

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    ENDQ_A 5

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