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-(I)()I(li~ 50tlt9 (9)11(9 = JtlZ = JH lDi]3 nolt9 bull ~~ = 11 (1)1

-IJO llJ10LOJdou ID) DI1QlI 103IfQXd3lL~ QL JQdu ClOA1f1(l)()lDAV Q01 SoJQ( Q tI JC030Q()lOl) Jtl03(3lnD lD13O)I iJtXd9 10)1

01UI1Dl)d3llrtno to(l)1shy

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Aui KUl(lllCl1o 6n6~ Itl )erno T01XOOj1U1U t6 Evepy6v jJfjKOC elvul Taov 11pound to 43 tf)c litullttPOU )lCiC 6nfl die EXU 7tpota9fj 6no 6 P6j1ltepCHov lCai aino Bioet CU)upcuvol)vta OEOOPTttCu Kat 7fipUj1Qll1C6 QltOtttO)1Uto

5 Mijxo xVuuro

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7 nvoprp ~Q(j KvpuroOecnJ(JTOV

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H 7tClp6ACIIIl( TOO nu9jlevot 00 axfHtao L KUIJQto9pauOtoo Clu~nvr1 TJV auvnJEatTtv aVaKAaOero~

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8 EXE(j[UU toii XlIUOTOOeOVOmiddotcov

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Elt t1l v dootfJv lEqlupav flt )jlvnt OOaallKoov ~M911oav al Att~ SluOtaaEIC

6la)1epoc 6Ttampv l ~ 30 tK

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( ETtUUVlilQ 6rrti)Y ) A1tOAOOV BIUl1EpctT6v 0196 Emcpavtlu cS latpntOu 1tMlICOC

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Kat opxnv amptoy va etgtpe9j jllu crxEOl lt )1Etu~U ti)v Ek 16 LX l )lelE9ampv a teal v etc Illav B100l-lfVllV XPOVlKnV CfTlllJtiV

TOtl ll1tOaOtllt 05ato~ 11 oui tampv OnlUv doxropoDaa tvamp tol 6aJullou Ou tiupE8f1 tlC tfc yYooOTfc 6TtO lIv OOPUOllK1V aXIishyOetil auvpoundxda

EK tf c taXlrtTltoc T1 pofr SovQjJE9a va )TtOAoltOWIJEV ilv anOOAEIUV eurovcPletalt EK T1c fitacpoptl tl1c tVEprElat TOf) tttf(gtshyXOIJEVOU ICOJlCLTOC ICUi toO avaKAw)JCVOu [OIOUt-OU eo EUp(UIJEV Ov aovtEampOtnV avaditOEOlI

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55 layou6ploC 1971

tK trlt KatQICOpUllOO Olotpilroo nAaK6lt Kat t00 dlt Qn60molv oTa9poundpoO poundlCtpound1O~tvoo tOLXOU QvadQoecolt

0 nu9f)v tftc SE~O~poundVrlt poundIVai ftfiJ~ QUa 6Xl ICOt QWYKlV Kot dlt t6 poundnhcwov tol) Ot08EPOO toixou alOICMiOEOOI t rlt nAroshyt~e ti ota8Epdlt lCatoOKEUre 0 toIxolt 6vOICMlOEWe 8E(i)PEitOl IDe dlC~1ttov oltLI~Q

Al a T1V n)ftpll KOtov610IV tv OOVExciQ StOY va y ivU KOshyAc1x 6vnAIlJttfl IwE ltOUpyio toi) ICUI-I0tOOpoootOU

Aui t6 LX r ICOt to dlt a v t6 uVQllEp6IJEVa ~e-yt91nopatTJPoOshyjJSY on jtia SlaipOpEtlK1 niEOlC Etlt t6e Suo n)EOpOe trC SlashytpfttOU nAalC6c Sl~ IOUPYE[ pOf)v tK Tf) lt Jt)eupfilt tf)lt l0~ljtpoundshyV1lt 1tttoecoe 1tPOC t6v eaAaI-l0Y (OE~CIjJEvt)V) oui tltLIv 6nulV

Aui vgt a Sa oxrUJCItloS(i)ol IltoC) G)v 6ndlv QVAoi UOCltOlt x apolCTTlPlotllCo i poundKtEIV6jJEVQI KOi n)lpoOVtpoundlt pa9jJl06v t6v 8clA~OV H ICIVf1tllCT tYEPYpoundIO tll 6001 tt poT) olaplCEi OlOXampTEOETal tyt6lt toO SaAitlJou AI poundloptoooOI on 6 mEolV 6shyMnvallJit~ollltO4gt teuroi)v 6nGlv de T6v 9n)CljJOV1lpOKa)oi)Vltposhytpoyampc avir~wolv tf) e tvt6C to) 9ojJ(i)ou 0t6SW1lt ICOt nanoshyotaole a CJlJllCpUVpoundtOL

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jJoe KpoundVOOtal 1tpolCaJoulJpoundvrov UVtIOTOXWY o ()AlU GoOtOe tICshyXUVOI-IpoundVCI)V poundJ( tampv taro ftp6e Ta Elw toO 9aJollou

nU)lV 96 npoKJl1efl inOOAClo tvcPYEialt Kat I nopojJtvouoa tvtp-yELa 90 aolJ~Ju Cgtlt do ouvloTlOOa TOO aJtEpxOJltvou aVUICAwjltyOU KlIJlOtOlt

Ed JtApoundovlntOTlecTol Otl 6 OUVtpoundJEOTf)lt SICJpoundOOECollt (ICOJlOTor) t00 Ota8EpoO Tolxou 6valCAtl0poundCI)lt (Tre J(atoOKcurlt) Elval TshySt ttd 0 OOOIJpoundVEOtpoundpov

6tv e6 ElvaL 1J110tv Ete IT)v nEpifttcoow t~alpEtllClile ~EYOAOU IJlICOOt KOjJOtroV

A()~ lila Otpofh)~ll pol[v

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H t~(OQXHlt toO Bernoulli ou1 CJTpofh)d)oll potty hEI n[vIJOPshy~~y

P V 1 dtpy+ 2g +Z+g dl ~ C( ) ( I )

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p v =-- + shy (2)

y 2g OftOO Zl = Z = Z

XpEla~Etat to aTlJlPtov J va CvplOKEtat were ft ttoOapE~ o~ashyI-IttpO~ 6Jtl)lt )JQKpav t00 toxou TOtE at YELtOvlxal TaXVTntEe EIYQt QIJEATTta lCal hOjlEV VI = O

H Ouvol-IldlnlWIlt Ete TO OT[jlETov 1 (JUlJlJl6lvO)lt 1tp6t t1)v rpajl shyIICllV euroIecop(ay PQOtrov uo()tCl)V Elval

amptou k = L2n = apl91J0c lCUjtatoov

v = tiloc KUJUltOC

Y =- nuJCV6tTJ C toO G6atolt

P J ve kt -TOtE EXOEV = Z y

Aetoc9a tftlOlllt On 0 tOrXOlt elVOl tOoOv MfttOC 6)atE ~ 6shynie uampnoc vo 1p6ovn twlt to OllJlEio 2 ICal lhl it OtaelJl1 toO uSaTOlt tvt6t toO ICOjUlTOepo6aou QVEPXpoundal ICQt lCattpXEtoL 6jJOI01J6PpOOt Pt Oil netoLlt a dVol ~la I-Iwaa 0ti9jJl

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V~ = x = taxliTtle a())oO 13oaTOt

AVTIJ(a910tGgtVw o iYtolk toult Opooe Ei~ tf)v 2 txollEI

yekZ_z +O + Z+ l all l =Q-Z+ Xl +z+2 ad~ gDl 2g gt

xl0 kt a + - + - - (PI - centII) = ve (3)

2g B dl

Kata tOv Roberfson ouvuIJE8a va Yp6jIOOIJEV

2

a ~ J- - dVi5l (~ - q)) = at Yd = (ft ) I

IJt S t6 anotdeOIJOtiKOV Il~KOlt t lUv 6nUlv npooSloPl~OIlEVOV poundIC tlllt YEOOIlElpiac CoO CJTo~l ou OHCi)V Kat Elva I avcIaptltov tr~ taxuI1tor

-EXO~EV trdOTlt V = X

d~ = X J(at Sl aVTllCotQOtaOErolt d~ tf)v (3)

) a + ~ l _ X= vek 1 (4)2g g

x J(ot x Suwa t va OUOXEtL060 III 0 a tcpaPjlO~OjltVI1C tflt OXtOEmlt ouvcxdalt EK Qlmllt 6JL(1Jlt nPOKUntEI jJ(a IJTt Ypa~shy~IKI olaqlOptlCT tSlo(l)ltJl~ it 6no(o Stv hEI 00lt Mow ~(Q tIC TJ)V OUVJlerov OtOIXpoundICI)OampI oovaptrloEro

AuvataL illUDC va ylVl] ll t~tOroOIC aovT)9nlt Mv bAOICAlPffiOltDjJEV

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ktt11J1 ao1v Efe nlv (4) nymiddottl toO opou ve H otaollCaoia o6TTl OftaMillEt 6 [690lt EfC t1iv olatpoplKTtV tliOroOlV tlQ 1tQPOshy~VpoundI Tt Iota 0 111CT) Ol)lallllCn nleolC nonola tnEvcPyel cl lt Ta jt6pla 00 OOaoe EIlt ttv 1tEPIOXllv toO SlaTpfltoo OLXOU Oli shytOO poundXO~EV

o kb

I I eshy5=11 ve kz dz =v -kh

-h jltoov f600lt

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Tropa T) ~OTJ tl~ij TOO Paeoue toO Opou lC It gt ouvatat va ypQlpfi

1- e- kh kh ~at

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k = A TJI atI (6)ve IJEaOV p69~

56 lavou6plor 1971

T6lE 11 tloQ)al~ (4) yiVETQl

Xl 0 a+ - +- x = A l1~crt (7)

19 g

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o abO ) gt J idA (8)

- h(t

R TQxrn v x eylVC 6Vf~aplrpo~ tol) z de TnV l~iawaIV (7) lxVTIKael crt1lVt~ TrV )I(ltJ11V TIIHy Ouva)lKfjc mpoundacwc toO POshyBOlle ti ttlv t~l a(i)olV (4)

Ol aUAol uOator OJltTh PEOUV OLQ )lia-au troy JIEIlOVWJIEVroV 01[ampv 6rt6TE d lt TIl E~awOv (8) 1tPE1tEI VIl Elaax9r1 Kal TO OLQllEpamiddot TOV 100 [oixall

~Av oVOIlCtOOOJlEV m t 6 ~VEpY6v o01tEpar6v 101E hO)IIv

m ~~ Aw (9)

6ltoU Aj EmcpoVlla T6)v 01TroV

Kat Aw - OlVOAtKTJ pound1tIcpnvELQ loD lOXOU

M~ dA = dAJ = mdA w = mdz(1) OUVatOL va )paipti ti (8)

o

aD ~ Jxmdz == imh (10) -h

l1ui 1fj~ (10) tl1tOOEI1(VUETOl6n npo oui ~eOoo TO)v61tWV dVOI icrl1 ItpO~ 10 jJctpov KatTt (bo1totov n crta9J1111oD UOOTO~ poundvt6~ laC 9a)ajJou altPXS1al ti KOtEpXStOl

T6tc t-(ojJpoundv o b X a mh a

0 b 1 = rnh a

Al tlV1(I(OtacrT60EWC st~ 1tlv (7) 7IPOI(U1t1Sl

h )Ol a ob (a+ -- - -+-- o=Al1jJol (11)

mh 2g mgh

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B AbojJEV lhl

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11 UvtIKatacrlCtOE(L)( toO DO d~ Cliv (l 1)_ -Exoj1poundv

(12)

(3)

ob 1 0

t 6 --1- = - EupioKOjlEI tEAII(ampr mgl cu

(14)

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(15)

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(16)

61tOU H Ellal 16 e6poc 100 a (ovE~oKa1EaOOJlO) Kal ltp r OlOshy(popa ltpOOE(I)C jJEtcUU v KOt o Oi fiPOl H KO cp OUV(tV10l vo 1tPOcrOlOPIOOoDv pound1( to)V 0106cp6)1 1fI~ (12) aVtlKaelOtampVTeuro~ totl~ 6pou~ a a Kol a 1fj~ t~CchoEroc (16) Etc 111V ~~(OWOll (15) Ex 1f1r aVtllC010CtaoEroc 1tPOxil1t1poundl

_ _ ( Bo ) (17)centI_SCP l- o l fro l Kat H = A [Bo + (1-00)) ]- (18)

R pi~o tti~ (18) ouvo1al va 6v0J1006~ n Kat 161E 6X0J1EV 11 = [Ber + ( I - a~ fro) ] - T (19)

OUtOO 16 H 10 Et)pO~ laD 0 (6vE~OKoTE~oa~) ~Kltppale1a 010 TaD YlV0J1tvou 1oD aoVtLACcrOl) jJqc9uverpoundooc 11 JCQl TOO A 011A tOC SOpolX llj~ jtAOl1C lIJ1tic Tn~ OUVaJ1IKfI~ mtoEOyen j3QshySou

(20)a - nA (cr - ~) 11 KOt cp OlOOlTaL (mo 1amp 1 t~IOroosOlv (19) 1(0t (17) OVTlcTolXox

0EroPTU1Q 1(1)1 iaoOul6fLwv l pyOlv KOTO Lorentz

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H K1Vl1TLI(n poundvepYElo 11)V ono[ov ltlOKet ll )JOVUC ~Crpo~ 100 OOOTOo E1tt 100 I(0J10106pouoou ElvOl

(~)2~ _ ~ mh 2g 19 0

~v0 1) KlV11tlKf) poundVEPYSIO Tf~ KIVOU)ltIl1l Emcpovdo tOC ilSoshytO~ Ko6roc gxowv Q1toSEx9f dvo 110AO J1tKpf) tv OUYKptOSI J1e l1)V KlVltlKtlV fVEPYtlOV T6)V oOampv U001oc (Jels)

lovou6ploC 1971 57

H KlVltlKI) tVpoundPYEIO npo)rou paOJloO d e tl)v lovaoo aapoue b D

elval (--) ~ To noOov TfiJ J1EtOalaa~OJltvl1 e poundvEPYElaemh 2g imoAoY~Etal dv JtOAAQltAoOlaOO)jJEv 16v K6BE lvov 6rr6 aoshytOUe to u~ 5potX btl 10 p6 poC toi) ooaToe K08e OUAOO yxdAj Ka i OAOKAl1J)(bOU)JlEV 5Al1 V tl)v t rrHpavElov obtGw

To lpyov to rropay6J1EVOV uno rit c K1VlltlK1) e tvEpyetoe dVOl iOov jJe t6 6AO KAr proJlO KOta TOV XPOvov t1)c jJ EtoPtlla(oJltshyVTlC evepYEioe o 000 OE 6pOl napayoov TO aino a ov vYOO Kota nEPloooV KUJ10tO C 011Mar

t+T b 2

Jdt J (mh) g (yxdAj) I t Aj

tH

= Jdt JI ( ~ti ) ~ (YidA) I middot t Aj

Eli t1c 10 6jl(Oe hOJ1EV it = ~h a 5nouit ExU tflv OUtl)v

tlJ1nV KOTa JlilKOC tGlv ouMlv GOOtoe

EK tOOtrov npolliimtEl

I+T l+T

Jy (~S 11 Ajdl = JY CS t+T I+ T

(21)~ f 1 l dl = f D l il l dl t

At OnO AUtOl 1lllot tttBl10av Ele tOe ~lcrroOele )6ytp toO 6n to tpyov dVOl )Jov6JLpoundtpov Kat lipo aV~QPtl1tOV SUU9U VOEroc EK tile (20) npo lCtnttu

Q = ~A~~(al-P)

a = alA avv(ot - ltpl

OvnKOelCrTaVlEe ot d e 1nV 21 hOJ1EV

L+T t+T

f I(01lA)oov(al -Ijraquo l dl= f D I (a~A)middotauv(al-Ijraquoldl t

t+T t+T

~ O1lA f loov(al-Iraquo l dl = D f l oov(a( -P) l dl (22) t

At OnOAUtOI tljlat tav OAOKAl1proJ1Qtrov oty onOltofiv t~hOlttshypov rrpoOoXTtv liv to 6PLOV QAOKAT]PIDaEroe unEPPalvu to ishyIllOO toO KUKAOU dC to orrotov 1)JlIKUKA10V Ouv(at - fP) poundIvol BcnKOv

ToOto dVOl 1gt- _2

~_6 1= a

(al- Iraquo =- z bull ~

Ij) + _2 toJ~ (at - 1raquo = Z ~ (=- a

Tote f TIII1l toO OOPIOjlt VOO OAOKAl1PCoJ101Oe elval L7rAal~ otshynAooo poundKeVTlC Tfic OllVOptnOECOlt OMKATJPIDaEme llexPl to ~~Iau tv~ )(1)KAou 6 oOT11~ T11~ ~e6Sou ~ (22) ylvol

+ 2

201lA j-o- auv (a1 - 1raquo dl = l)-n2

o

ill + 2

= 2D j-o- a )vl (crt _ Ql) dt

~ bull

I I I 0

a~A I- ~~ (al-Iraquo- - ~~(al-ljraquo = J+ 0 30 _ 2

L - shylOP te2

~~2(o shy w) J 40 4I -n2

bull

(23)

E1)~ pUnOJ1EV 611 b YP0JljlIICOe crUvtEMCrTtiC anocratoEooe D Elval OUvap tT)at e t~ KUKJlKilo aUXVOt11tOe toO KOjlOt Oe a Kat tofl EOpOOe ti)e tOAaVttOOECi)e tilo trrujKlvEfa~ toO Goot oe tvtOo tofl 8aAOJlOU lA AnaAEicpovtpounde to D b t Glv t~Oooapoundrov (1 3) Kal (23) Eupicncojlpoundv

B__4_ (~)2 T)Aa (24)38 mh

AVllKOBIOTlUvrec TO 11 ti e t~lOwcEoo~ (19) de tnv (24) ~XOJJpoundv

B = _ 4_ (~) Aa --c==~=c--cshy3ng mh 1820-1+ (l - a tro)

OWCoVOjlpoundv aJ1POtEpa 10 J1poundAl1 poundIe t 6 tEtpt)oovov

a ) [4A ( b )] B + 8 1 (I - - - j = - - - shyro l a t 3n8 mh

B + B ~ -a) - I + [ 1 ( 1 - -cr ) - I ]1 - shy( rot o 2 rot 0

= [~(_b) ] + [ ~ (l- ~) _]I3ng mh 2 rot 01

_ I (l-~) _I- (25) 2 6)1 a

OUtro t o 9edgtPl1Jlo t bv (OOOOVOllrov lpyrov SloEI Iday )IOVOS1shyK1)V AlXHV oui tOv OOVtEAtOttlV a1tOoptaEroe B OuvapttiOE ~ tGlv S~ocpOprov napoJlttpcov toO KUjlatOepoualOO

0poundlOIlTlcnlt (t~ttQO) ~~ tvltpy(W

PAy Kat T) OUVOjJlC 6nooptaEUlt tto poundIltJ(lxnroe (J5) Elval nproshyou a09J1ofi CoC np6e el 1) n pOYjJOtlK1l arrIDAEla tvpoundp(poundiac Elval OuvStlicllpoundVll III til tClXiltTltO toO 06AOO GOOlO jlt tOV opov

OEUTt pO O poBJ1o) 6 OnoLo nOpOoO1o~poundtal dO tflv (7)

H 6nc1J)E~a til e K1VTJtlKflt hepyEiae ouvatot vO 6noOoBn ete QUo croVttAECrT6e Mfa JlIKpa anooAElo 6rpEfAEtai poundIe l1)V tplaflv d e t6 tarotpoundpLKOV to(xrojla ta 6rrGW lly TO n6XOC tOO toxoo Elval J1ampyOAUtEPOV ono lvo IlllCPOv nOAAOnAacrlov 1ftc alQJltshytPOU tG)v onlllv

H na poOoQ 9ampoopto 6J1IDt BttEl roe npo07l6BFOlV 6n t6 1tOXO~ t OO to ixoo slval ioov J1t tilv lhojlEtpOV -raw 6nGll arrO tae 0shyno(oc OnaJ OOlOVTnl va 0~poundA90uv obAol uaotoexCllpic rrAEoplshyKae -rP IfkC ~ dJ tYI rrpofYoOJlpoundYTV 1fEpi1TTlO(uV

T6 JlcyoAmEpov Iltpoc tfl c dft(J)AElo~ tfl~ tVEpye1W OIpEi AttOl de ttlV ttOTtAmOlV Koi SIaoK6pnlOlV toD aOAoll btl tGlv 860 OWCCIlV -roO o latp~ tou toixou 6noo fI K1Vl1UKfI t VtpYEtu tGlv

sa IQvou6piO~ 1911

(l1raquo~V ~ctetp6nll de (J1POPIA6gtSl Doilv h [fie 6no(aC (teamiddot Cl(J1acrE~) Mv ~navepXamptQl de 1]1 npoCEpav

T6n 6)ollAllp0C 11 tCtXUTTlC tOO QUAoO g SlQaKOpnCltOl J6shy

rqJ TOG 1ldgt5o~ toO ftEPIPliUoVTOC aircflv (HiQtoc

R anooJELQ EvepyEtac euroIe T1V jJovtloa papooc tOO uyponElvat x2amp T6tpound to nocrbv tfle 6nooAElac eVEPYEtac elval (Oov npoc

TO Ytv6~vov cO 2i Slll T6 pupae ToD jl0pou UOUTOC TOO pAshy

anal Korll tJflKOC tvOc vri)lotoc 5101 6AOtc)TpooOil me npoc 1111 SUqlUVEIQV TOO OLOtpTjroll Toixou

middotHtOl

(26)

R Qn6JutoC C11l toO xhpTlOIj10nOl911 ot6n QTtcDApoundICl poundYepshyydac pound1vo j10VOIJEtPolt (OXI OIOVVOJ10tllCit) S)aofl UYpound16pshyTltOlt elC Tfle lhampu9uvoeroc jJeurota06oEoolt [ftc tVEPYetac

dAJ= mdAw

anau dAw = dz(l) AVtlKa9tOtG)ftElt Etc TTlV (26) npOICOn1amp1

o dE 1middot1 = f y _x_ mdz (27) 2g

-h

AqlOO 0 x dval aVE~6pTlltOv toO Z Ol 6)oKAIlProaEltOlt d gtshyptQKO)JpoundV

~= myh Ixi (28)d 2g

Tflv ~OTIV tqlItv otaalCopn(creroc 1i1c tVllpyamptaC oov6)1amp90 va

u1toAoyfcrro)leV OL 6AOICAnprocre~ au ~ roc ltp6c t61 Kil shy

CAe evoe KWaTOC Kat Ola OIQtptaeroc Sui Tfllt 1tePU~SOl 811shy)n8~

(29)

EqJapJl6lovttc TaC t~lcrGJO ellt (10) teal (20) Aa)l~UVo llpoundv

b b ()( - ffih a m h OTA avv crt - ltp)

I I= CA ) i auv(cr -~) I (30)

AvtllcaecrtampVt~ -rae (28) Kat (30) de v (29) rtPOKOrttEI

I+T c- I f myh ( bOT]A )E =1 2S rnh l auv(cr-~)Idt

I I+T

-- I myh (blt11]A) fE ____ --- 1lt1Uv(-~)ld (ll)T 2g mh

I

msh 00 = - shy

6b

At aVTlKUtQcrtacrpound(i)lt pound1lt fly (32) npOKU1ttEl

~ =2 myh (lt11]A g ) (33)311 g OWl

t F1VQI 6 )ltcror 6po TfI ~ cutwhiac ti c t vepyeiac btl toO KUshyjJuto9paootoo KQTa n v l)UiPKeurolQV )ltllt 7tepI6BOl)

AnapahlTOV c5)J~ tIval va dproJlEV )l iav crXEm v (UlV evepshyYEIG)V TOO pound1tEPXO)l t VQU KOjJQtOC Kat TaU anEP10)lEVOU

0 piooe 6pltgtlt tfte )Lpoundtalgtoaao t11~ evEpy~(ae lgtul T6 1CAatOt -HUe KOpOcentie KOjlatOC oui rilJ1Qta jlIKPOO EUPOllC poundIvaI

- ya l E= Z- CG (34)

61COU a - TO dgtpoc KUJlaTOC

lCat C( - 11 tUXOTTlC 6jlUOoc KUJ1(ltWV

H to1o111 laquo CG SUI pa9~o uBata etVat t6 filllOU tftc tOXOTTltl (pacrpoundwe

en _ ~ _ 1- gT I g = L 2 2 2~ == 2 (- 20

AVtlKa9lOTUlVTtt Ele TflV (34)

-=- yaig Ea = 4ltf (J5)

-A SCXO(jJ~IfY 6n ouMv J1~polt ti ~ t vcp(E iac JlEtaP l ~6~ctal ti Rl OOcV tocgt t1tITt)poundOVtOC OropalOC TOtt dYQI TtPOlpQvampc On 1 t vtpYGlu tol) tlVtuvaICAroJltvou ICUJlUTOC Elvallan Jl6 TIiv tvtpshyYpoundlay toO btpxojlpoundvOU E)attOu1lvllC KIlTCt TO no06v tfle un-Qshyhtac trti tou KUjlat09patXHoLl

--Er = -E (J6)

r - aVtaVQ)( ACoJlEVOV (ICOJlQ) i btcPX6jlpoundvoV (lCUjla)

AVtlKU810tlUVTpoundlt e[c tilv (36) npOI1gtlttEI

yarg ya j g shy

- -_-- -E4ltJ 4cr

(a) 4cr_r = 1- --- E (37) a1 ya g

j

AVTtKa810tGlvTEC Tflv (J3) etc t1)v (37) npOKlmtpoundl

(~)2 = 1 -~2~ (OTlAQ) a[ ya~ g J1t g orol

Kat

(38)

EK ~ (5) ~xo~v l_eshy kI1

A=a kh

6nou a to EUpOC toO Jlovjlou OJJlQtOC tnt tfle TtI)006pound00C TO) KUjluW8paix1too H Oxtcnc jle-ta~igt toD crtJVTpoundAtcrtOI) K KUjla~ toov [uOtoc OSQtOC Kat Ttl auxv6t11TOc a crUjlqgtIDVUX TtpOC TflY yp~ilv 8poundoopluv XCI ~ ~~

59 TcxyU(Q XpOYIKQlavouapLO~ 1971

AV1lKa91(16)I1E~ d~ 1flV (5) npo)(u1tlE1

1 _ e-ahg A=a -- -shy

a hg Kat

~l1Ag = goTla ( 1 _ e-ahll )

ow Soo 0 1 hfg

(J9)

T6 EUPOC toe jJovljJou ICUjJpoundl10C t ni tftc npoooWEOO C to ICUjJUmiddot toapaultTtou MVU1Ut vei avtlICCttOoTaafi Sux toO lLapoOjJQtoC to poundiJpGW TO poundnEPxojltvou )(Qi toO onepxojJEvOU l(ujJao~

(40)

an Onou npOKUnttt

a = a j (I + R) (41)

d~ lLVTlKQTQataotwlt d~ trv (J9) poundOPlOICOjJpoundV

8 mgh [ (l _e-OOI)]Rt=l-_____ ~(t+R)So~ 11 - - - shy31t 63006 o h g

(42)

2a1 HI T6 lCajlnu)ov to ercpoundPx0jJeuroVOl J(ujJQtOlt L L pound[vm jJia

napajJpoundtpolt npoundov xpljaljlo~ an6 T6 poundopo~

Eloa)oV[pound~ ~j poundl~ 11v (42) Kai fXOVtE~ on 0fl IV

HI J HI 1 HI 2ft I HI 2n shy - 2 ~ T L to ~ T L -K - T L og

dv(u (43)

T6tE npOKmtEI

8 mil (HI ) ( oh )R ~ I --- - - - (1+ R) -- x3 Soo L g

)( [ (l - e~lg)J (44) 11 o thg

dTjAQSl 6 auvtEAEotfl~ 6lEUPUVOE~ 11 nEpihEI t6 R Kat 6() lQtm 10 eurol(qlpaaOtl roC oKOAOUa~

bull 1

EK-ftc (19)txojiEI 11 = [810 + (1 _ )2]-2

If 4A ( b)] l 1 ( omiddot )])18 102 = -- -- 0 + - 1 - shy 3ftg mh 2 ooa

__I (1_~)2 2

an 01l0U EupiOKOjJEV SIU 6 Tj

EI( ampv

aj

(1 + R) (I _e--o 11IB)

big

at = - (~) oi L

npOKUmtt

ng ( ~) (I + R) (l _ e-g2hg)

ah

B~~aB~ _ b_ ~ -- 6 anESElxe~ Kal EI~ T~V (14)rnh uoo

T6tpound ~AO (~)2 = 4g ( ~l) (1 + R) 1 _ e- olbS

3ng mh 35004h 0shy

Al aVtlJ(a1aat6opound~ etc t1)v (45) npoICUntEl

-1212

(46)[ - ( 1 shy ~) rI + -H - )

]

H mu16tTjlt ~h = 0 tij~ (14) SUvotal va tpound6a elc 16~ (44) Kat (46) XQt va 56xn) lOoSuVQj10Ut pound~tailiaELC SUI t(1)1 6noloov 5u

lQV1QI al 1IupajJpoundtpoL to KUjJQt09pau010u 10 ~J(qlpaaeampOlv antooO1poundpu

(47)

(48)

napaTl1Pita fU va e1tlAu6t1 Sui 111 lt jlE96Bol 1ampV OUlOOX tKwV 1tpoocntorcov

H t~iCJooat~ (47) Olv5ua~o~tvTJ j1E 11v (48) BiSEL t6v cruvTE)emiddot EK tijlt ~Opqllj~ tij~ t~lOdlCJ((i) t~6ro~poundv to aulln~paOj1a on atilv CLVtaVUKAaOsrolt R E(val tp[tOU llaa~o aAAQ OOVQtal t cruxv6tTjc OO~ftpoundplcptpEtal til OUVtOVotf~ Kal npuyan

60 lavou6pl0C 197

6 O1)VteAeuroCftf~ 6vtIlYalCw(JcroC R te[vEl npO eva crUyl(euroI(~H IJEvOV 6p9L16v 6Tav TO cr tdvu npor to Jlloiv Tl np6r TO anE pOV KQi yiVETCtI pound)CtxLOTor Stu )IpoundPLKar tvolCl)lpoundaOUC lLJHie toO a KQi ola -olv OUXVOtlt1l aOYfOvtolloD

A( t~lOWaeuroLr ai~rtaL otv hou oocpelr (PltCl) )ucreLr m 1Cp~ R twt Sui TOOTO Mv Quvctldla va MlcrOOj1EV Illav lJeuroylotT1v t11ltl v Etc to R OUttolt ampOtE vei KO TIl)1jOOjUv de 11 v O1lxv6Tl1to auv tOVlOJIO)

E)t)cp6loav O)l(ilr CIa ti1r IJE90cSou TUV OlOSOXUCGlv npocren aEroV Kat ~crxdiLli(Jal1(Jav etc ta olaYPcllljJOta 1 ~Wlt 6 eie TU 6noTa ~vJtoJlev em 6 OUVOYl0J10r )QJJfaveL xoopav ampray f CJuXV()t llC to) euro1tpoundPlOjleurovOU KUJllltOC 1tAncrntllJ tilv qgtUOIK1V (Ju(v6t lt1l 100 KU)IOT09pau(Jlou npcrYjJll to 6notoy aUjJpaishyVEL Kal etc I-lllxavLlCac to IlvroocreuroLr EtC Tn oxfUIata ainQ to

Hr a t R = - H poundOXpound0Il10911 roc ouvapt1)alC toO -- onou W ETvill

I ro ft CPUOLK1 Ou(v6t1)lt toO OllotfUlatolt KUjIot09pouutou Kat KOta

mgh(14) ro = - 61)

EKOCJt11 Ko~nuA11 ovrlnpoooonEuEI roplO~evalt nopa~poundtpoOl ton KUjLllmGpouOmu I(at WPtOjLeuroVOV UVoC tn))Iotoc

Ymv9uJ1iso)1tV On jLpoundyaA11 tnlXv6tlle KUjLatoc a 6vnutOtIEI dc JI1KPa J1TilCll ICU)lOtOe L ft BE )IlKpa ete )lEyOAa )lnX11 lCilshy

2ngJlatoe L KCIta nlV1 kg _ --shy

T6 otOypa)ljLo 1 Kol fl pound~(Ol1)Ote (47) Elval to KaAUtpoundpov )IEaOV lCaTOV01lOEcolt tle e7tlOpaatOOe toO onotEApoundO~OttICOil OlCl1tpoundpashytoO m poundni ti1c AErroupYlar toO ICUjLatotlpaUcHou

middotOaov to m 1tA1OtllSlJ ltp~ TO jL11Mv 6 lh6tP1toC 1otxoc toc KUjlQt06pouOtoU hEl [0pound0001) avtQvaKAOOIV Kat t6 R n) 1OIQshysEI1tpOr ~V OPlOV 01tWC n KQ)I1tUA1 Q ToO 6tayp 1 rEVlKW C 0shyOOV to m UYOAOlVIJ (Cmo t6 jL11OpoundV) 6oov T6 R poundAQtlOOtOL KOL n OuxVOt1)e OUVtOVlOjLOO yiVEtat UV1)AOtcpa OnA OllVTO VlaJl~ )OJlf3OVEI xwpav Ol(l )lllCpa J1rK1) KUjIOfOC

Elc ta 0(aypa)lJ10to 23 Kal 4 0(1)PEUV1l911 n bdopaolC tf)~ a)shy)ay~ to) p690u h Kol toO nAarOUC b tlc OEs(ljLEVnC evcp tv nopa))l~ t1 SLciJlEtpoC tampv onoov Kai 1l un60taole tOUtOl~ olamptllP1Sll OtaSEpO

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ToOto OlllllkllvpoundL 61av Ola

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poundAOt1OUjlEVOU toO )6101) ~l middotOtov Ot nivo 1tp6e t6 JIllOEv

t6 R ttheL np6e iva OPIOV poundS(UPOUIlEll t tie TtEPI1ttOOOtltIlC a uvrovlojlou T6 cpaLVOjleVOV tOlO EfCpoundI3Ef3Cl1ooeurol1 lCai npoundIPQjla tI KWr

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L 0 OuvtCALoti dVaKAQOpoundw R 1poundlVEl poundAOTtOUIlpoundVO alJ~nshyVOJltvou 10) unotdpoundO)1aTIKOO olonEpatoD m ti tAoTtOI))JtV1l~

H i tiie OXCOCli 7

2 0 OuVtOVLojl6C ActjlP6vCl xihpav El tllV ncploxlv IlEyaAtgtshyTepooov ~I1KGgtV KU)1a[oc ~avoJltvwv toO nMtoue b toO ~amiddot aoue h 1(01 tflo CmOTCAcOllanK~C anootOcr(CJ) 0 lampV 6nwv toi Cu)lot09pOUOlol)

middotOAal af nopOjlFtPOI t oO Ku~(no9paucJTol) SUVaVtOl va 1tpoamiddot OIOPloOwOtv E6KOAWe UQlPOI)~Evrov tiJ a rroT6EOjLontd i imocmlocroe S [rov 6nampv Kat TOU tl1tOteuroAEOjlUttKOO 6WHEpatoO

0 Robertson lgt1tOOEllCvUEl ffilt anOtEAEOjlaTIlCnV anbcrtctm r

KALI(UgtV cmampv to gv Coi poundV t otTOV tIle OIO~tj)OU n)~ Ultile t~ Kao n)v geCLlj)lav tooV Pranul Kui Tictjcns 6upioI(0)1poundV [I a tlr 1 KetTal jl ETO~U toO 8mAaalOU J(ai tl1t ~uoou 1tAOTOLk tampy ttshytpaYOlvIlCrov Onwv

To tlnotWO~a[lJ(ov ota1tpoundpoT6v lOoUTal )It t6 A(Iv6)JeurovOV totl yero)JETPlCOU ol anepOtOU tn t ~Q Katoll1Aov Ollvtpound)fcrn v

T6 )1tYES~ toO crUVTt)Wto( Toumu t lapfimt t1C ttic Scopoundwe toO abAof) Cioome cile npoe tTlv tnuj)aVEtav ii ooe 1tp6e yEltOVlshyKOlX a uAoUe

0 OUvrpoundAEcrtfl~ 061 etvaL nX 1 tAoxOtn UJl1l laquo lituO 8ui JIfov ScluJlcvt1v andpwv OtaOtQOEOlV Kat ti t tlv onolov ()(p[oovral ilhiuOpoundt Ollv91Kal 6142 tllV nEpt1ttWOlV evoc lCujlaT09pauOlOU 0010e AajlflavEl nOAo ~C)UAUtEpaC Tllltle

R Katmpa au)1lpU)vo 6nola EmtpounduxSll ~poundTalu TampV Qn01pound AfO~t6TWV T~V EloGxreOlv (47) Kui (48) Kut twv nElp0jLOTOlV oUl

eurova KUJluT09pauOCTlV jlE KUK)I 1io 61t6~ liTO oUl Iltov anonmiddot AeOJlOtlK1V a71oOToolV 01tltUv lan v )1E TnV uno TOO Roberlson 1tPOtElvO~UCvrov 0llA 4(J tv OllVOOOOjlc9 JIE ha OUVT6Ae(JulV [OOv jLt 077

E+ap~oy~ bull

Oe 1tOpaSCly~a np6t cpapJl011v TaW OVOOttpco 9fllploov t~cshyAt)n 11 It1~ pin1rool lti t~ t nAwT~~ ieq)Upoe Tfje AI)JVllC OuoshyatV)KtWV )1t 1U t~l1 c lkSojlpoundvo

a) Iuv~91lC tUXUTlle aVEIlOlJ t 5 (1l)la ooplolroc)

~) Mpound)iOt11 1Orunllt aVEjIOU 25 (J1IAIU rlgtpla(wc)

y) OW-OC ICUlla1Oe Jlpound[olo 19 Kai 22 n60 (57-67) tIC 0) 1tcpioooC KU)1a1oc )1eTa~u 20 I(ai 33 0poundUT6pOAE1tta (OA)

pound) ICUKA11Cf1 croxv6t1l~ 00 = 24 S)- I

Q peo= 80 60 (loovnp6~v~ueGlv~q~upa)(24S )

ll) OlojL poundTPoc OnOlv 10 noS (O1tQpUlT1l Troe J1LKpoTepa tol) OUVll-SouC i)wolX ICUjLOTOe)

9) dlfotEAEOJlallK1 a1t601acne 01tGgtv 43 10 (tfie OlOjIEWOU)

bull middotA~tpopIlV o n o uto 1ltou8rIYlTit E P Ricbey 1l10 ou roplOKOI-OL dlt tfa4gt~I hnl 01111001(001 f(gtu yuTl~ UV 16 Report 19 10C 1966 TOO obtol) nUVCIt I UTTl~IOJ Tflo Washil1IOil O)6nKGJ l it TO clWKMliIlBYO KO)IQTQ do l1v AIjVTjv OliQOIYK1W OIlUU 01 ouo IlMuTul yt 9l)pol

61 Iavouaploc 1971

I) bullAROcrtClOlC 61twv 20 R6cS ~~ roY RPOICUReEl Q1tOtEAEcrIJOeIKOV 077 middot 0196 middot g 80 middot 12b= 61 noli - 186 ~cSLll tPl1 t ov

~ 10 middot 24-I middot04 3 0196m = R 2020

H 6vrotpoundpOO tllJit fl 6no[0 ICETtOl1tAlWlov Tfc ltd6EotfC ttJlitCraquoK) tvepyov olORCpatOV 077 OJ96 poundrt0)1l8CUEtOl ano laC t~lcrccrpoundlC (47) 1C01 (48) c c tJlcpaivEtat

t) EuJlcpwvroC npoc tei oUlypallJlatCI 2 froamp 5 Sao ot rot = 12 6 d c toV t1t6IJEVOV RivolCa CJlVtc)tOl1l C QVaKMlOpoundroamp R YlvttO I t)6XI01Olt 011) 6 KJ~ llato9poucrtTl C 61tocrpalvc a t6 IlE1a)ulpoundpoV ~ltpoC t~C hEpmiddot nINA= 1 ydac

P EUVtEMOtitC clVlaValCJiLaerolt

ExovtCC un OV I V tli 6vrotpoundPlaquol KCIt PltcrEl eft c t~lcrclgtcrEroC (14) 1tpOICUntEI

I HI

I HI

L eo 002 - i - = 005

b dc noonc = I 4 I 5

6 I 7 I 4

5 I 6 I 7 I I

I

I I I0 middot 8)shy 1 II- -10 083 075 069 065 080 076 074 072

15 065 050 040 Oll 062 056 052 049

20 039 bull bull bull 044 036 Oll 033

r--shy25 bull 000 009 019 028 026 029 033

30 016 044 059 068 032 043 052 058

35 077 087 091 093 066 077 082 085

40 096 097 098 098 091 094 095 096

45 099 099 099 099 098 098 098 099

bull ApvlllllCnt tlJlat trnop60poundlCtOL

62 lavou6pl0i 1971

nef(JpaTX~ 6teevv7]ot

Tn rtElpallcua ftp6t ~~baaw lfit OltOMOEOOlt tGlv h ho6)Cj) KUshyjJQro9pauOr(()v fYlvov eit 10 ~pyacrtliplDY toO TIaVEltlCtljllOU tftc 006moy)([ool

H ouilptX EIXEY 6p90YOOVIKlV StatOIlTlV 1lllKOOt 164 noSGlv 1tMtoolt 4 noS Kal l3a90u 35 noS Et~ to iKpQ [ftc 61to~ ~t01toepoundt1i6fcrav SUo KEKlljJtVQ ~1thtpoundOa nopIOt(1)vra til nllshypal(ov

HpeuvMllcrav 6 nmm ICUPCtt09pQLlOrlbv fa a1tottAtCf)Jara tti)v OJtolrov noplOLQvtQt dt EllaypaIJIuna

bullAvdlva~ tWlI n cauoTlxWv anOT8iEuprl-rlm

Eli taW SlIlYPOjlJU1trov ayoJlpound9a t tli t6 OIraquo)ldpaoJlo 6[1 6 nU ov d OOOtlK6 tlgtnot dv(u 6 SUI KUICAI1CG)V onoov (6 lByOIlE VOJex 2) OOrOi tlamplOpound TOY Ju p6tepov ltruVTE)poundcrt1V dvcucAQOCCJ19 ltui

elval OXEtlK(Olt Avc~ptTl[oC ~K t(1)v ol(uuaoEIDv Tfle ( ~) KUP10111TOlt tlano uj1(vQO 6jlOlC toD )JEyt90u~ aotf1 ~ (Tfilt tll pshyt6tlltO) tgta rfoOnn Kat 0 mJVtE)eat~ avadlur~ ToCto drccliEIX911 9poundroP11tLKa~ (Blayp 6) Kai rreuropaIJatt K6l~(liui1 paIJ 9)

Mla tin cUSEta crVy~PlOLC ~utta~o tll)v 9rroP11ttKWv Kat nEtshy~an1(rov aTtotcAeuroOWitcov rXiil v611IJCl ilv KOtaat~ ouvatov va 1tPOOlSlOPI09~ 1100lK auxVOtlle toO OAOU ouatilJato~ toO lCU~ato9paucrtou

R 110ou cngtXvOtTle tvolt owmiddottpntou KU~(lto9paucrtou eK 1(1)shylC)l1(Glv 01tGlv OUVQtal va EopEatl oui tPic Ilt9000u e tKu9poundlmiddot 011lt de to geroPl1tlKOV ~epoe (nmoc 14) Aihf lcroOtal Ola tva lCU~oto9paootllv lCOKAIKGlv onlbv toO Seuttpou rimou IJt 002 = 701 0)-8

BacrEl QUt~~ t~e tt~fte tcrxtlhucr911 de t6 ol6ypaIJ)Ia 11 1l KQ~shytril)n tou OUVtEAEotoD avad6oECO( ~ aut11 npOKUTttEI poundK tf~ eE(J)pi~ Kol poundK tampv ftElpall6tcov 01tOO Kai yivpoundtal crUyKpIOle Iltmligt tOOV

~ Av oi )aIroIJEV un 6wlV Kat tCi mpa))Iata ta oTtora 01tEtotpshyXOV1UI ICUtcI 1(1)V OtEcayro)) v tGw 1tElpaIJCtta)v tote ouva)lE9a va ELTtffiIJfV Ott tCt eE61PlltlICO Kol 1tElpCljlQtIKcl anot(Apound(JIJUm oXt66v cru~rovoCv

gt0

R-~ M

co

h_rvnrt 11 OJ 1l=t OItH

llio04J)

~ 1~ ~

~0 0 0 5- D 1 ~-~ uP ~ -0

0

~~OOO7

~

I~m b-Ctn-H

~j 111 mor C-ooQoi 10 1

n gt0

o 0

- ~

JLdYI 2 EwuAtUTr QVQJ(AelUeW ~eaeUhIJEVO~ i K TOV uw-6vaCTIJOV Jd8ot xal nAdtov TOV x VIJOTo8(1otiOTOV

0

h-J)S5JJ 011 mmiddoto511

-)045

0 d () J 1()yemiddot J EllIHAEOt~ QVQgttJO(JEtJ) otnla~nue TOV nAClTOV

teV ~VpOtoOeavoto~

10 tlom7middot

~

n-Olll1 ~1H1Iae

t tImiddotou)i 8-011 m r IS11

a -(-M

06

04

iwl)1

0

r~5Jj 11 Qn~t)

(11 lill

~ _O~~

o 0 t~ 0 -gt -gt

11elYi 5 Lwre)ean da~Adotw ovvG)njuu TlJ cmottAeshyopatl)tij anocnaoew TeOV 01lWl

15 0 1 lo 2

rmiddot05l3l ~Qn11L 1~~~7ol ~

30

LvvTeha-nj QloxAdoew OVVaeTrJoe _ lh

tOv )(VuOTO yo

62 lavou6pl0i 1971

nef(JpaTX~ 6teevv7]ot

Tn rtElpallcua ftp6t ~~baaw lfit OltOMOEOOlt tGlv h ho6)Cj) KUshyjJQro9pauOr(()v fYlvov eit 10 ~pyacrtliplDY toO TIaVEltlCtljllOU tftc 006moy)([ool

H ouilptX EIXEY 6p90YOOVIKlV StatOIlTlV 1lllKOOt 164 noSGlv 1tMtoolt 4 noS Kal l3a90u 35 noS Et~ to iKpQ [ftc 61to~ ~t01toepoundt1i6fcrav SUo KEKlljJtVQ ~1thtpoundOa nopIOt(1)vra til nllshypal(ov

HpeuvMllcrav 6 nmm ICUPCtt09pQLlOrlbv fa a1tottAtCf)Jara tti)v OJtolrov noplOLQvtQt dt EllaypaIJIuna

bullAvdlva~ tWlI n cauoTlxWv anOT8iEuprl-rlm

Eli taW SlIlYPOjlJU1trov ayoJlpound9a t tli t6 OIraquo)ldpaoJlo 6[1 6 nU ov d OOOtlK6 tlgtnot dv(u 6 SUI KUICAI1CG)V onoov (6 lByOIlE VOJex 2) OOrOi tlamplOpound TOY Ju p6tepov ltruVTE)poundcrt1V dvcucAQOCCJ19 ltui

elval OXEtlK(Olt Avc~ptTl[oC ~K t(1)v ol(uuaoEIDv Tfle ( ~) KUP10111TOlt tlano uj1(vQO 6jlOlC toD )JEyt90u~ aotf1 ~ (Tfilt tll pshyt6tlltO) tgta rfoOnn Kat 0 mJVtE)eat~ avadlur~ ToCto drccliEIX911 9poundroP11tLKa~ (Blayp 6) Kai rreuropaIJatt K6l~(liui1 paIJ 9)

Mla tin cUSEta crVy~PlOLC ~utta~o tll)v 9rroP11ttKWv Kat nEtshy~an1(rov aTtotcAeuroOWitcov rXiil v611IJCl ilv KOtaat~ ouvatov va 1tPOOlSlOPI09~ 1100lK auxVOtlle toO OAOU ouatilJato~ toO lCU~ato9paucrtou

R 110ou cngtXvOtTle tvolt owmiddottpntou KU~(lto9paucrtou eK 1(1)shylC)l1(Glv 01tGlv OUVQtal va EopEatl oui tPic Ilt9000u e tKu9poundlmiddot 011lt de to geroPl1tlKOV ~epoe (nmoc 14) Aihf lcroOtal Ola tva lCU~oto9paootllv lCOKAIKGlv onlbv toO Seuttpou rimou IJt 002 = 701 0)-8

BacrEl QUt~~ t~e tt~fte tcrxtlhucr911 de t6 ol6ypaIJ)Ia 11 1l KQ~shytril)n tou OUVtEAEotoD avad6oECO( ~ aut11 npOKUTttEI poundK tf~ eE(J)pi~ Kol poundK tampv ftElpall6tcov 01tOO Kai yivpoundtal crUyKpIOle Iltmligt tOOV

~ Av oi )aIroIJEV un 6wlV Kat tCi mpa))Iata ta oTtora 01tEtotpshyXOV1UI ICUtcI 1(1)V OtEcayro)) v tGw 1tElpaIJCtta)v tote ouva)lE9a va ELTtffiIJfV Ott tCt eE61PlltlICO Kol 1tElpCljlQtIKcl anot(Apound(JIJUm oXt66v cru~rovoCv

gt0

R-~ M

co

h_rvnrt 11 OJ 1l=t OItH

llio04J)

~ 1~ ~

~0 0 0 5- D 1 ~-~ uP ~ -0

0

~~OOO7

~

I~m b-Ctn-H

~j 111 mor C-ooQoi 10 1

n gt0

o 0

- ~

JLdYI 2 EwuAtUTr QVQJ(AelUeW ~eaeUhIJEVO~ i K TOV uw-6vaCTIJOV Jd8ot xal nAdtov TOV x VIJOTo8(1otiOTOV

0

h-J)S5JJ 011 mmiddoto511

-)045

0 d () J 1()yemiddot J EllIHAEOt~ QVQgttJO(JEtJ) otnla~nue TOV nAClTOV

teV ~VpOtoOeavoto~

10 tlom7middot

~

n-Olll1 ~1H1Iae

t tImiddotou)i 8-011 m r IS11

a -(-M

06

04

iwl)1

0

r~5Jj 11 Qn~t)

(11 lill

~ _O~~

o 0 t~ 0 -gt -gt

11elYi 5 Lwre)ean da~Adotw ovvG)njuu TlJ cmottAeshyopatl)tij anocnaoew TeOV 01lWl

15 0 1 lo 2

rmiddot05l3l ~Qn11L 1~~~7ol ~

30

LvvTeha-nj QloxAdoew OVVaeTrJoe _ lh

tOv )(VuOTO yo

63 middotIQou6ploli 1971

10

1 ~ o01 tiL-omL L -

i t 1=(( 013 a

0

R -= Hr Hi

~ - 0 25 0 050

bull l Ou 02 150middot

0 middot200 0

00 05 to 5 20 25 30

~-~ 2nh 9 L

lUbullI1dpQa~a

EK t~0 eptUvno dmofixOl1 5tt Ol6 CJXpoundtKGlo IllKPO f6911 6 oU1shytP11T0O KUlloto9paucrtllO Slo Pv IppOjJQ ovoJ()acreroo t1n1tAtov (tolt 0[ n)rotui YEIpUPOI) dvm unotEAfcrllanK6v jJlOov a 1t 0 PshyP 0 IJI 11 0 e Ol 0 tijo tvcp-ypoundiac T~V KUllatU)v

H YtCilIlftP1Kfl jJoPPt1 h-aOTOU KJlluto9 po()(JtoJ ~(tL TnV (SIshyK TTlO PUOIKrV oJxv6t1ltu (tSlocruxv6t11TU) H cwxv6Tlle

o

bull b_OG i7 o J ~ LJ~ j

to OH)

Ol -

b 05i)7 b middot 0 333

tI - C1fH

n-I ~rc~

U II9(ION

o

00 05 10 15 20 25 0 2h 2rt h

g L

changt 10 poundWrtkOT1~ dyax~ampOtW~ ntleQl(lTt~d~ GlYQ(HryCJtt

TO V naTO~ rotgt x1JjJoroOeovarov

10

OJgt T =O~JR r

H

0 LQ t~~ n H )(l llat

bull -i OOlt10 2 ~ oo

00 05 5 20 25O~ 0 w

o

01

8

c R

ODL_-plusmn_-~~~~--=~==~oo ~ m m m ~ ~ H ~ bull

0 - p- (wr~

Juiye 12 ileo1k1p rpcloporo rij~ dvaxJwptv1]( b t eyElw VpOTO

ailtlj ad ctlta1tOKp(VCtO~ 1tp6c tT)V croxv6t11tQ udo IlOPCPfl C n jJQTOe euroIe TfV 6PICfOpoundiOov 9tOtv AVtlCftP6cpcolt de tTv cfiPIshyOIlampVllV eampOW lntoAo-yICttQl fl ~e-tpeftal f) OuXv6tI toO tdt shyYo~~vou XUPClICtllPlOTtKOO KUjJQt~ Kal KOtOCfKtoattOl KUjJQshyTo9pouOTn~ tSIO(J)xv6t11T~ KQTO t6 SUVltlt6v t~C QCrtf1c ~t trv toO KUIlOTO O OUfOl f1ttteox9ljOov cruvttApoundltttat 6VQK)6~ tf1lt t6~fcnc 010 frolt 020 Sui np6oqlopov OUXvOTflTU tot) KUIJQroepaOOtou

InvoUapiOi 1971

ArcESEix911 eloLtL On E1[t)rxQVEtaL OUVtEAECJ1Tl 030 oui rva 6PKElO JIE)oAoV opL9J16v JO)jlOTOOV

H 9Eoopia EOOOOOE dav Xpooqlov IJEOOOOV oui Tilv EKtI~nOOlv ~C MLoopy1aC tOO KUjlOT09poUOTOU j18 KUKAKac 6noc Kat rrMKQ jliKPOO OOXEtiKamp~ 1TaxQUC

H AEtOopy(a KUllat08pault1Tou 6AA11~ YECOj1EtPLKliC ~oprpflc (~e ti ~e OlO OOXlOOj1ampV 6pI~ovticoe fI Ka-ralCopurpCOC) rcpoOOOtOshyPLo9Elcra 6rc6 rcElpalJatlKCt ESay6j1EVa onEoEiXell on poundIvai 6oPKEtlI 6~oia 118 tilv toO KUj1Qt08paoOOTOO IJ8 01[l1C KUKAiKfjC otatOjlfl~

Ila KamAA)ou rcpocrapllori1~ rll~ pamK~~ (ivaAucrEroc poundIVai eU KOAOe 6 lmO)oYlOOJlOC n OlaJlOprpwoLC wv (iAA~ lloPltPi1e bdcrlle lCaaUA(i)V nlJlat09pauooCUv

Ked h (i)v EPyaotlPlaK(J)v ~pEOVampV (urEoELXe11 6oK61l11 on 1j hAOYti tllc JlOprpllc toO Ku~at08paixHou 9a Exl] ouaaaOOIshyKflv ~rriopaootV elc t6 (3opoc KilL tl)v oarrovllv TOO KUllQt08pa() ootOO

Iut ti1e tporrOltOlllOECOlt UOPIlO)iK(i)V iV(i)V ftapa~poundtp(i)v 00vashytat va tporcO ltOl119a Oaltppamplt Kill t ICOjlrru)11 MlroupylaC toO KUjlat08pauOOTou

~Av lCa~ n 9ecop[a 6oVE1UUx9T) oia (016tTTac KUIlCttCOV pa8erov boatrov dVQl Suvatl) nErrEKTClOOlC allrliC Kat otll EVOU~IleOOIl 1) KUIlQTa 6o(3a9(i)v oMtcov ola fne xpllcrtllorrolooeco~ (i)v avnshylt1TOtXroV KanUi))rov crUvapTi]ooErov t(i)v ftlpoundOWlV Olll a h6~ atote KUjJata

EVOlQrp~pov elval 6tt til 9EroplltLKo KaL rrupallatlKa O1[oeshyJoj1ata illv OOKLIlWV o OvEltpoovllcrav apKEtU iKCtvOTrOllltlKa

bullH rcpoP)Erp9Efoa QltOOBEcrl~ ttC 6vClK)w~V11e EVEp yc( ac Tli)V ICUJlancrllwv Etc to J3 tf)e (1TEPXOlleVlC TOlaUll C dVOl iv xashypaKtllPIOTLKOV rcoooov Kal 8ltEn6x811 IlE Iliav KOtOcrlCEUTlV rro)0 )OYIKWV OiaOt6oOErov

OrrUlcrSltoe Il EtpcrEi~ dC 1tp6turra 0))0 LiC rpUOLKOV 1tEPIshypaAAOv aVElllwv KUlJlhcuv eo elval ltOAU XPOIIlOI 1[pOC 1IPOOshyOLOPLOII0V 00 EI~ cl(acrtlv mpimcuOtv KCltaUllAot~pOU KUIlClshyt09paoOtou 1[POKtIIleuroVOU va KatacrKEuacr9fl aoBapov EPYOV

BpAloypa~(a

Technical iH))ort No 25 100 1 91))

1 P Rillhev CK Solllil UnlvOrS lty of Wasblngton Coll ege of Engin eering Dcparlmenl of Civil Engineering

Uni vt rsily or WaIhlnglon COllcj(e or En gineering Department or civil Eng ineering

RenbC~d WavCls In Lake Wi_l it lnglnn Teehn ical Reporl No 10 E I~ R idley amp lU Nece

Att Jnua lion or dlC I) Wa ter WLVe8 B y a Porou VolJed Dreakwater Tetmlca r ( IJort 0 2(1 A P 1fchell C K Sollitl

I h = p690~ oE~allrvfI~ KOllaT09paucrou

2 b _ rcAoTO~ ocla evfj ~ Ku~aQ8pa6otoo

3 Aj = b up6vElo orrampv

4 Aw UVO)IK1l ETrUpaVELo lha-rptou dDK6C

5 m ~ _ cl1[oteMOOllanKlj olarrepatot11e

6 0 QrcoTEkecrllamct 61[OotaOl~ On(Uv

7 a OWIpOpo aT691111C uoaot EV6c ~C OelOIlEvfC toD ICU)laT06paooTOu

8 a eopoc E1tlrpnvEIClKOn KOllOtOe = H2

9 EOPoc tneuropxoll~VOU KUllaTocal

LO EOpOC 601tEPXOIlEVOU KUlIlltOlt (6vaKAWIIEvOU KUjlamiddotar )

11 HI KUllaoc

12 Hr oor 6l[EPxOj1~VOU KUllaoc (ovaK)ro~tYOl KU)lashy0)

HrllR H Ou VfeAEO(1)e 6vaKAacrEUllt

14 v lJ1CEPOVWOlC ICUjlOalt (crTa8jlTl hlltpavEiae KOllaoc)

Hi 1 15 C gt= L = KajlrrUOv Klllao~

16 a = T2n ~ yrovlald cruXVlHllC

17 (i) qmotKn OUXV6tllC to) KUllnt09pClOOtOU

18 T 1Teurop[OOOC KUIlCloc

19 L Ilf)Kor KUllatalt

20 H UOC KU)laOC

21 E cruvOJIKTt tvtpYEla auAoO 8rcEvEpyoOcra fllti tTlV j1ov6oa )l1)KOUC 00 Ku~a06po6crtoo

22 ~ cruve)eOTTlt (OLeUPUVOO(roc)

23 0 OuvteApoundotLi~ ampltocrpecrw

Porous Breakwater c E Markakll

Summary

The progress made and the an ticipated in the future exshypansion of the nOCl lill g stru ctures in general makes il imshypera tivu to increlt-llte tho inlettsl on the orious energy reshysources enclosed in the waves nafnely its oncha ining de shyviati on or its absorption in order- to avuid its des Luclive results

FaCing the wave energy by the known voluminous gravity

breakwaters (onsis ting o f artificial o r natural blocks asshysumes very expensive structures

The somiddotcalled pnrulIlttic or hydraulic breakwaters ha ve been s tudied (making usc of compressed air and tubes with nozies or water under pressure) to break and diffuse the enclosed energy however unsuccesfully until the preshysc nt time due to the high cost o r thelr operation

The so-presented porous breakwater as a simple structurbull bull Horn In Crele j 911 n rnduoled a SurVll y E nglnef r In lUi n nd Ar bUectu r kl Emlln eerlnQ for w () rks o r any kina with erurineering u CIvil Huginter in t l 3t SinCe he workf (l ln hla HnI(IIHtring and of roada hr ldBtll e tc etc He Mi Apeclalized In 0061iol II lructu re COflsllu o Uon Office for a ll kl mls Mlinly oeculllC d with -S ialiea and a nd Is one or Ult few In the world SIICclali1tng In theile 5tru ctu rts

lavou6pto~ 1971 T(XVLk t

~~~----------------~--

withou t a ny operaLion expen-fs f onsisLs of a perfora ted pla te a t a suitabl l3 di s tance from the wave fron t a nd of a bo t tom 50 that a n oblong box is (armed with suitable depth the s ide surface of which in the divection or the waves is bei ng pe rformed (porous )

This porous brea kwat er povides a very importa nt means o[ energy absorp tion

More par ti cul a rly by coordin atin g the frequency on the one hand of the waves a nd on the o ther of the breakwa t l3r (own frequency or the sys tem ) the wave oscill a tion in th e horizonta l sense is transromed to i ts rea ter ex tent into a vertical oscilla tion inside the box due to the wa terle vel inside moving laquoupwa rds and downwa rds bull

In the case of a com plete coord ina ti on it is evident th a t the cons tr1tly a ttar-ked s id e opposi te th e perroreated pla te of the box shall rc(~ i ve ouly a s imple hydros tati c pressure

XPOVLKO 6S

Through a theoriti cal cal cula ti on vhich vas verifi ed by tests also-until th t jI t~5e n t time-il was found that the most s uitable bre akwa ter is Uw one h ving circular holes

The so-caned pe rCorman r -A effi ciency of the breakwa ter (na mely the ra tio or t he in coming to the oul g-o ing wave) which theordically sh ould be tero has provt1d 10 reach va lues ra ll gin~ from 010 La 0 20 a nd tor a great number o( variou wa ye up to 030

ft is e vident the pursultd absorption or the wave lt n( lgy which i5- ex l rr mely intere ting mainly in th e non Ling slr ushycLures and mor t spnc ifi c aJl y as 0 thei r anchourage and transve r~ rr sj ~ tan ce (oscilla ti on abo uL the trans (rse ax is)

At the p resen t pa per the theore ti ca l discussion of the porous breakwater is ex posed mainly while ~s a summa ry the re al so exposed the conclusions of the theore tical and experimental r(lsench