bull bull
187
Mt8o~oe EYTOnlOIJOU TCy EocpaAlJtYCo)Y ~E~OlJtYCo)Y KaTa TOY unoAoYlolJOY Tile noAAanAile ORl080TOlJiae 611J1 r BA6xoumiddot
npoundpiAl~t 2 G l att ToD rrpopMJJ1aToc
Elr Ti]v 7to(J0vaQV JJdir1Jv 7tIOYPQHVOfCOa 1 0 Re6J)1]lta TOU 7tflOa61OltapoiJ TWV r[rU n (JOalyyun v uv lToyfivwv ayvwmiddot arov alllf iov be rov DllOIOV lOQFTIJe~O)lt1U aI c5tevOtiv(it~ 7l(JOr n 3 to d~Oo TI~ywvOIUrfJtxd o1]plio yvwl1rwl OV)Imiddot
uraypeurovwv X-l7]OlJl0llOIOtrnfmiddot TO oVvOAOI rwv b apoundAsOOpoundIOWV
-WeQT71e-10 6Wv al ifiQ(p6Covu nl Mi80601 fWI poundlar[middot urwv TST(lUYW VWV Baoll middot iil (TtWTct(l luivwv tOVTWV VlOAOshyyl(ovrw at y wvm 6lW8tltOFW- $lgo [ auTov ootF1JOb Tflt YWVOufTQ1)(OV o1]J1eiov Yoal 1- ll UTWV a1 ampli PE(oC l1Ta8f(Jai n(l0l1a~aTOA((1ftoij T61 hrn(jvluHUlI 1 ui nlJ)IltOlr1EWr rOtlTWV 1Tgtor n)v P EUTfV Hpj(1 H uV e)IOXo1middotr I aJ dtwJ10gui v 7 OEwmiddot (1]arc TWV ono[(IraquoI trffr t LlE1 TUV E1~1fQJ )((Ji Ul1rpo)1j f1TOllIOpOV
niw liltO)tAUOVdWP (I(Jv(Jaapcvwl) l11ltotcVl1e6W ij nLfV rvr0J XP1](JII(JWL1JOtvrwv T(l yWV0ftTll(Wv U1JPrlWl iUrpa1PEvWJI Q1JVrcraY~ltvwv
_ Elu aywYIi
T6 np61)lJta tou til 6ma90toJtiae TtPOaSIOplaJ-lo() t6)V auvshy-reTQYJt~voov tvo~ CIl1 IlEioo QnaVtatal aUxvol(l~ d e tilv npallv Kata Til v ROKVOO01V ll t ICtamv BEUnpE06vtoov tPIYOOVOJtEtPl KWV l) IKTUOOV aQ) tvo~ ~ai Kcno Tilv poundlnt)OO tv ( Aa ootKGlv toshy1toypatptKoW tpyaol(lIv 6rp t-ramppoo OTav EIvat YVCOOtai 01 Kata npoO~H10l v auv-rEtaYIlEVQl TOU ~v A6yIP alJtti ou Kal t oTageshypa npoaavuToA10Jt OO TG)V 1tapuTTlPl9poundlcrwv 01poundu9uvOEWV ou VltClle9a 01 tqmpJloYfie tfJlt Jtpound96Bou TC IJEta30)i1e TGlV ouvshyte-taYJtEVCJ)V va ampigtowlJev TtlV )middotilPl AUcrlV TOi) npoj3AJ)JtaToe fitol va uROAcent-yiawJtEv tae t1AlIae cruvTpoundtClYJUVCU TOU Kal Tit OTolxefa Tije 6VttOTOXOU eHEljlEOOI TOO OqgtQAlJatoc 0 npoo OtOptOIJOC 6jlmc Tillv KaTO npOOEY71mv OUVTETClyjl~VCOV (moshyTEAd ialtOl TO nAto ApoundnTov KCli ElJaio911ToV ~poc t fie 6)T]e tPyaaiae ocoo)Jtvou btl acicrEl aUTGlv O~elAOjlpoundV npoTO) npo3WIJEV euroIe t6v tEAlKOV unotoYlaIJOV va 6va~l1tilowJtEv KCli QJtopp[woojlpoundV tOO TOXOV torpaAJtcvae aKonpoundUOEtlt Ii 16 TUXOV eorpaAJtpoundvoov oUVl etayJt~vwv XPT]crlll01tOl Il 9tvTQ TPIYOOVOlJeshyTPIKO olJLpoundTa Kata aUVEnpoundl(1V dVal Alav napaKIVl)UVEUIIEVOV v6 OtIlP(lWJtEV tiJv cpyaoiav tfi e ltigtc 6vw poundmAOYfi c T(i)V op9wv nClpaT11pijoeoov elc TCu nEp[nou OUVt poundTClYllevae UlTtVpounde nposhyKU1ttOUV a no Tpeic Jt6vov napaTlPi)oele 6oovoijnote Kat av Clutat 9poundoopo)vta1 aKpla ete
Elc tilv napo)oav tPyamav JtCApoundtWIJEV TOV JtpoaS10pIOIJOV tillv KaTa RpoatYYlo lv OuVteTaYlJtvwv TOI) 6yvcilOTOU all IJE100 Kat Ti c OTagepoc rcpoaavaTOA10l-l0l) t euv t~ abtoi) napCpoundtT]pT]shy9E lolllv l)lpoundu0uvOEWV np61 n ~ J to n)~fl901 t P1YWV0I-l EtPIKO OT)Jt poundTa Aau~6vOvttlt nt 6j11v t6 OUVOAOV tGlv tKTEAEa(C10WV )1poundtpijopoundwv ME1u t Tiv EUPEcrlV tGlv Kat a npoo~YYIOlV auvTpoundtashyYIIEVWV lmoAo-yi~ovtal 01 (aatov VEOV oT]lJpoundiov at a-raSEpai 1tpOoaVaTOAtaJtoO VI tWV SIEu6uvaewv np6e ~V ~KaatOv T6)V XPTlalJton01T]8euroVTWV TP1yWV0JlftP1K6)V OllJlEiwv tv OIIVEXF(Q OE 1l1-leuro01l TlU1) Vm t WV Vi Kcpoundl tl aUtolV EUp(OKOVTCt l Ul lil0shy90)(Jfl~ u1middot E tfi~ Jt EAtTTJ~ TWV liloperoaewv tOi)twv poundvtimL ~OVTa l Ei)1(61we at lavQCta~EVQl OmiddotK01[poundOOEIe il Tel XllOI~onOI T]9EVfa tPIYWVOjJpoundTP1 KD OT)Jeta fOq)ClAJt EVWV oOVtEtOYJtpoundVWV
tteooJtevou 6T L 6 01 6 PI 9uOJlll XavlI ROAOYOJt oe CtK6jJT] Kat tlje 6nfi~ 6RI090to~da I( Tpt(i)V JtDVO V OIll-le(oov anQtpoundl apfet ov K6nOV 1) OAT] tpyaaicpound hEl auvcal8~ JtE yvroJtova tite 6v6Yl(ae toO autol-l6tOU lmOOYOIIOl) dC t OV tllEKTPOVucov unoJoYlat~v
To Jtp6aAT]lJa TiSEtal Ox ciKO)Oueoo~
EI( aT]Jt Eioo 0T60EltOI M aYVroOTOOV OllvtEtay~tvwv XW toKomiddot JtEu9T]oav n to n)ij90C TP lYWVOJt pound-rPIKO ol1Jtpoundia Pj yvcoo-r(i)v
OUVtEtaYUEVCJ)V Xi lVI ICcd tjJEtprST]oav al OIpoundUOUVOft ~ lj (i = 12 0) Zl1tOOVtaL a aUVTEtcryJt~val XW toO OllJtamptOO M Kat il oCcpoundgepa V npooavCtTOAIOjlOO tWV o ~eo9uvopoundwv
N
Pc (X middot - )1 1Yl
M(XIj)
o X
WEOTW Mtt 1) OIEU 9uvOlC t laquovnOTo loOoa elc tfl V aV6yvWatv Ij 7lPoe T6 TPWVO~TPII6v Pi H -ywvia OIEuOUVOEWC Tl)e Mtt EIVQl ( l + V) EI( TOO Pi ~tPOJtEV t 1)V K69poundtOv PjN 1[pO~ t~v M6 H -ywvia uj naplOTQ T~V olOp9WOlV t~ e IJEtP11 geiOT)C olw9uvOewc l np6~ ovaywy1)v t atitT]e de t li v OllvoPGffi)1tVl1v
-+ TlJt1lv TT]e To SIpoundlJ9uvovta OllVl1JtttOVQ toO 8IavUaJtClTo~ MN elvat TW(l1 + V) ouv(lj + V)
-+ toO ot olavUaJJQTOC P iN KaOt Tou np6e t6 npOTnOUI-lEVOV poundIvai
-oov(I + V) ~~(I + V)
-+To JlEtpOV toO Stav0ollatoe PiN ampiOECQ )1(0 tou TmOU
PiN = Z = Z(X 1jI V) =- (X -x) middot OOv (I + V) + + (1jI - IjI) ~~ (I + V) (I)
6 onoroe I-lEta tilv poundKTtAemv tlllv npalewv Y(VEtCn
7 ouvV ( - Xj cruv Ii + WI 11111j) + + T]IJV(Xj lJtl j+ lVi ouvlj ) + Ouvlj(X auvV - 1V T] ~V)-
-~~I(X~~V -i-ljI ouvV) (2)
0Et0Jtev
- Xj auv Ij + V lJtl = hI (3)
Xi 1l-llj + Wi auv Ii = 8i IKai
X ouvV-fI TlIIV =00 (4)
X TlJtV + wcruvV Q ) bull oM IC p ArpOv6Iln~ T01loypQf+)o Mlal lC~ on EM nO~l)Tr( ~tiov t t EoSPQ f fl r poundvlI fn Acnpo OolJia -01 reQ)O(lIn-oDotpOvOllllCIiIO n pOOOlO MII Orllcn l~ II lOX10ul lJllt TOO nUVCII Il lOlo bullAIIT -Gv Enl jJpoundlITl IlUpU PIOjl liv t Oto J M n O)vnIV1oll
188 HopTlO 1972
6n6Tamp ~ (2) )~pavEl t~v ~opqgt~v
Z = co middot auvlj- ltp TlJllj+ Gj TlIJV + hj bull cruvV (5)
H cruv6peO)(H~ OLpound7tpoundrQL fmc t ov oAy6pI9lJov
n
F = CZZJ = 2 (00 auv li - ltP bull rU1lj + gj llJl V of hi OuvVgt = i - I
= minimum (6)
Oltp[ io~v Aomov yo CtvaCrriaOOjlEV [at tqlIlt t~v BOl9nshyn lCGlv aYvampa-rwv CLl Kui P 51ft tolt 6noialaquo n O1JvOPlTlOlt F AOjlshyllltvpoundL tAaxalIlV ttlltrv
J middotYITo~oyu7fJol
E t~ t~WaOl (6) EXO~V
oF(0) = auv II + cruv~ l~ + + cruvln = [ cr1JV~ Ii Jgt 0
(7)oFo = TUJi + lllll + + ll)Jlln = [lll12 1 1gt 0
Kala aUVpound1tEtOV al ()lot taW (0 Kol ltp OlQ tac 67toiot nF AaIJshyB6vEL ~)a(lcrtn V nllv 6pi~oVQ uno (Llv ~Icrmaeuro(()v
of iiG = 2 (cruVll (00 auv l -ltp 111middottl + gl TlJlV+ hi (H)yV)
+ allyl laquo1) OuvI2-tpmiddot fill 11 + Sa TljlV + hl middot auvV)
+ + auvl (romiddotcruvl -qgt -TlJ1ln- gn lljlV + hll(JWV)=Oo n
A ttLcrOOltJeuro It autOl BuvaVtClL v6 YPOqlOOv
[auv2tj) 6)- [Illd auvlj ] qgt + [gi01Jvlj J rUlV +
+ [h j auvl] auvV = 0
-lllll cruvlj] 00 + 111)1Zj] ql - [Si lll1 li 1middot I1I1Vshy
-(h11l1l] auvV = O
- ( Twl cruvti I
N = [ ~v~v II ] I ~~I)
l(hjauvl j l T ~ [ [g cruvl)
- lSi l1)1lj] -[h i TlI1 ljl J (9)
[gi au 1] - [8 ~~II ~ T =
[hi cruv l ] -hi TW1i] J [ ~~V ]~Ul =n~[] ouvV
)V6IIL tGlv axtopoundwv (9) a ~~LawOpoundL( (8) Tl8EvtClL 6n6 tTtV )1upqgtiiv
(10)
Aal1JlavovtCC ttlC )lepucu napaYwYo~ C1 F roc npoc 1))1 V crovV cupiolr(ouv
of (lll-lvf - 2gmiddot (00 ouv~ - ql ll)Lll + gl 1l11V + h1 middot ouvV)
+ 280 middot (co middot Olv l - qgt ~~l + 80 middot ~~V + h cruW)
+ + 2S (6) auv In - ql TJl1l + gn -1))1 V + h OllvV)n n n
()(O~~ vj = 2h l (w aUv II -ql 11)11 bull gbull TJl1V + hi OwV)
+ 2hmiddot (00 middot Olv 4 ~~ I + 80 ~~v + h cruW) J
+ 2h (m - auvln- ql TJl11n+gn rwV + hn ouvV~n
AI axtow QittCll BovavtQt vO YPQqlOOv
aF2 a(~~V) ~ [Il cruvl1middot co- [ g ~~ I)middot 1 +
+ [g g) ~~V+ [ 8 h) cruvV (II)
(12)
6n6tE 01 (J 1) yivovtOl
I amp(~~Vf bulloF I (lJ)- ~ IT aill 2 of[ claquoJ1)V V)
Eitv 1Jt1lm~tV 6lIv ~v Wcrcocrw ( 10) ~ enocr (13) ypashyqgtpoundt(ll
naputIlPoO)LpoundV lSn
H ~l1it pa N bull Kata OUvpound1tnav lCal d vtlotpoqgt6c tTJ~ N -1 Elval t ctpnywvual Kat cro)1)lupun dx 1tpOC Tl)V Kuplav 010middot YWVIOV tnc AeBO)1tvoo 6tl l) IJTttpa Tt bull dpu Kui tVTAJaYIJ~middot Vll aOtft t 2T dvaL utpayoovllCll 5uvQl1e9a e~ICO)OgtI va (moshy8dE(J)~poundV 6t TO YlVOlJeVOV
T - lt- N IT)
dvalllla tetpayoovlloi KOt (J~I1poundtP~KTJ I1ntpaOEUTllpac tupound~_
EJtuol) Be f llllpa 1M Elval ~1ttall lt ntpOY(J)vultl) Kal aUIl)L emiddot tPLKtl OCtltEPOlt taero to a t)to alL OU)LPct(va Kal SlU lil v 1l1lt pUV M M- T ( T) (15)
H6pTLO~ 1972
[rUJ2ld [hiOUvljP + [ouv2 li ] middot [hTllll jr - 2 [T)IJliOuvlj [hj 11jl1i Jmiddot (hjOuvlj]
JI~3 = [hi h j 1- [TllJ i I j 1 [cruvlj] - ( Tl ~Ili auv1i J
[TlIl2ld lSi auv II J ( h j cruv li ) J [au2 l j 1 [8i T)IJ lj ] [hi Tllllj] - [Tlllt i cruj] ([ gj au I ] [hi 111J Ii I (8j T))Ll j J hI cru lj D
(lllJll lj J (ouv1l J j)- TtIJ II (fU tiJI
dU01JE8a a O1tOOElS(iJIEV K(1T6nv 1tpaEW 611 ta cr1Ol1Eia JI )I OU a TaL va hqlpa08oCv we aOpoicrjlo1a 1E1 POYWVW
11 n OUvaP1flOEOOv 8j = gj (8 Ii) KOt hi = hi (hi Ii) to of crtOt-
1EtO JI = Il hmiddotPPoCETaL WC 69pOlOIlO ytOIleurovoov 1lO aushy1 ~ 2 1
l roV cruOplrOEOO nc tK lOU1 0U 1) ll1)lpa Ma OUVOlaL Va
lE9t 000 tTlV IlOPPrV
(16)
ElC lWV cr1euroOECIv (14) KOj (16) E1OIlEV
I ~F [ ) [ ) I2 iJ(n~V) = gi gi nV + I hi auvV (17)
1 of [ [ ) T cltcruv V) -= 8i hi] T)jJ V r hi hi O)V V
H ltlln 100 V Qla -rtl 61to(av Tl F 1ta poucrtateuro1 aKpOlala (JUY1010V Ti tAUXlOtOV) QiOE10t into t1)1 tlcrrocrewc
of of auvV-~ nV=o (18)oV 0( V) a(cruv V)
AaJIaaVOVtEc on 6~H nlv (17) 1) -reuroAeurou-rQa y[vEtal
~- = 2[ [g g] n V cruv V + [g h) cruv Vshy
- [~ h) n V - (h hj n V auv V ) = deg (19)
(20)
A AUOeuroU t1) c (20) dval
2V =2Vo + k7t
A lilla Aol1tOV toO V oui TaC 6noiac 1) F 1tCLpoucrullEI DKp6shytala dVQl
0 lt V lt T I (21) V~ = Vo + T T lt VI lt 1t
OpftOVlol oE Ka1a 1tPOOpoundY)IOIV n aK1IV(OOV
DpofPavwe fK tGlv OUO lOUtWV l lJlGlV 1 Jlia aVtI(flOl1Et d e 16 lJeYlolOV Kat 1) 6))11 euroI~ 16 euroA6XIltJl OV lflr F dFOOIlpoundVOU 011 euroVblocpeurop6IlE9a 81(i lTlV 1lllliv 100 V tinr aVrIOlOIXEf Etc 16 euro~~6Xl(flOV llie F tiC t1erUOOOJlEV 1t0(0 t K llOv (21) OiQEl Uomiddot -XL0111- nlltv eurolr lV F
H fV AOrltgt Ouvaptr)Ollt EIval
v = r ~V dV
o
of AVtlKa91ltJtlOvleuror Tflv tlIlTlV toO i) V fK 1flr (19) Kat 6AOshy
KAT)POOV1E C AaJla6vOIlEV
F = [g g) ~ V + [h h) auv V + 2 [g h) ~ V cruv V - [h h 1 (22)
E1tEIOt 11 1tOO6T1e [h h ] eurotval 01u9europa Tl Oeuro 1t006T1r
[g gJ n V + [hgt) cruv V
poundlvat 9E1IK6e apI91l6c 010 va A6al] Tl F UaXIOTI1V lLllnv 1tpbtel
(23)
EK 100lOU OUvOYOJlEV OTI
a) Ev [ggt] lt deg t6tE oui vel Icrxu11 1l (23) npeuroJtEt
TlIlV OuvV gt 0
tsnEp (llJVEnOYETat 0 lt V lt T TOlno OTlllaVEI 611 de ltlV 1teuropl1nooOlV airr1)v Tl iT)tou)ltvT) llllTl 100 V euroIvai 1) VI
6) Eav [ggtraquoO -rOleuro h TfIc (23) OUllneuropolvojlEV 6)10100lt 611 1) iI1ToulltVT) Tllll) -roO V Elvot 1) v2 bull
TOIOVTOl p6nroc 6p[tpoundla~ Tl T11l1l TflC )I poundtaaATllfle V Qla ttlV 61toiav 1) Ouvap-rT)OlC F AaJlt3ltiVeuro1 fA-axicr1nv T1JlrV bullAC KashyAeurocrwllEv V 11lV lQJ11V (QU1TlV
Ko-r61ttV lOv ovoodpw Tl IlnTpa l UI etV(U l poundAEtwe roPIO)leuroV11 61tOTE fK llic t~I(fltOOeuroffilt (10) U1tOAOy[tovlm o( tl)lat l(l)V BoTtshy9TJtlK(l)V Oyv6la-tro 00 Kol ql
(24)
TEA-Dlt h lli)V f~t06)(JfwV (4) AlaquowaoVOIlE Tae ~TJ100)lEVCle 11shy
Jlac lGlV DyvcilcrlOO X Kat w
x =00 middot cruvV l IP TlIlV ) (2l)
W = - 00middot T)IJV + IP OUvV
At 11)Iat autat o VTl1tPOOoonEUOUV lae KCl1o 1tPOOeuroY)lolV (J)VshytEloyJ1iVoC loil OYVWO1OU OTlIlE[OO M 01 61tOIot OU euroivai Kal al OKplaEie TOlornal U1tO lit 1tPOi)1t69EOlV On JlE1Cll0 lGW QpoundOolle oov (OK01teVOW Kol (fuVleurotaYlltvClI lplYOOVOIJE1PIKGlV OTJIlEirov) opound uP(Cfiavrol tcrcpoAJdva cr1OLX Eia
4 ETOmoJlbr TW I4aAlJanJv - napaT1pijOEli
rUIlIPWvroc 1tpOe TnV tK1E9eurolOClV )JpoundOooov unEAoyicralJEV lac cr)VTEtClYlltvo~ tou Qui 1tO)ACl1tA1)~ 6u090Tolllae i1l10UIJeuroVOU O11IlEiOU AUllaavoVTEe Uf( OWlY 16 crUVOAOV tampv t KTEAE09euroLshyOGlv lrapotT)P1loE(JJv Toulo CSTlllaivEl 611 10 EUPE9EV OT)IlEtov Elval to 1tUOV m9ovov aacrll TGV de 11)V ol69poundoiv JIae IJ EshylpnOeurooo Kat w euroK roUTDU ouvalClI OO(pClAGlC 6 XPllOIJj01tOIshy11911 liL6 16v lmOAOYI01l6v KPITT) piou Qui IlEOOU TOO olrolou euroVT01tltOlOI Kat onOPPLmOVTal 0[ euroOlDaA)IEVal OK01tEOOpoundIC ti fa OKomu9ivra lP1jW OIlE1PIKel on)ltia focentgtlttlIlfV(J)V ouvshy
190 Mopno 1972
tEtUYJ1EVOOV To KPLtTJP10V 060 lmoAoyiCEtaL ~ t~fl~
EK tGlv (JUVYpoundtOY)lEV(t)V XW EKaatoo VEOU CrU1Eiou 1eCl 1amp1
cruVTEtaylpoundVOOV Xi IV tCigtv cncomUetVTCOV tPlYOJVOIu tl)l)(UlV
Oll)1elWV P i (l1tOfOyi~O)lEV teie yroviu OlEU80V(JEooc
G = lj + Vi (26)
XI - X poundqlG = I (i = 12 n)
J Wj - IV
E tiic axtOEwe (26) OampOO)1poundVOU 6n e[V(lt )vroomi tK rrupomiddot TI1Pit crCWt at tt)lul tGlv lj 96 hOOjlEV n to TtAfl8CX UIUIC Vi TfjC amgepac rrpocraVQtOA10)10Q rlOv oLeu9uvcreoov IiVnOtOLXOUshyaae 1tpOt t D1i til toO OTHldou toutou 1tpaY)JCltoftOLll0dcrru 01(0shyTtElxrtr 01Mza~ 1tP~ to 1tAiOO TampV XPI1O1)lonouo(vtOJV tptshyyroVOJlEtPlKWV Oll)lElOOV AaJl~6vo~IfV TnV )lEOlV nllV V [JJ TOUshytOW Kat tv auvEXeiq EupicrKOILEV rQc OlUqlOp6C
ui=Vm-Vj bull
TOlOUi OTp6Jtcgtc 01 EKWJtOV VtOV crn~HOV 1a)l~voJlev t va 1tLVQKU oLOpOromwv Ui H gecilPl1OlC teDV 1tlvchwv aotGlv tnt~
tPf Trpound1 tOV Eirxep~ EvtOmalJOv ttilv poundOtpaA~v(i)v OKomuatXllv il tOv XPl1allJonot19tVTOJV tHYWVO)UtfP1KOlV Ol1IJmiddotGioov poundalposhyJJtVOlV auvtetaYIJcvrov npuY~tt Oaqgtci) l1U~l1IJtv1 till HOC tK teov OtOp9roOEO)v u or 6rrOiut mpuhOVtal dC tOV 1tlvaKa hoc ~K tGlv vtoov al1)Jelrov TrjJOOUgtpoundl 6tL 11 aViOtOlXOC OKOshy1teumc elvaL )aveao)Jpoundvll tV(l ilIa mgtcTtTlIJanKampC l1~TljtpoundVTl tI)lTv TtilV u to 6noia nepampxovlQ1 cle tou~ olaltpopo~ 1t[vashyKae tampv vpoundoov al1)JEiwv Kat uVTlatolXoCiv de oKonEumlC tOCi a()toD -rPlyrovolle-rpIKoi) Ol1IJamplOU o1)JOVamp1 6tl 01 9poundroPTlOelCCIl OUVletaYIJpoundVal toO aTl)Jeou rOUtOU Elval poundacpaAIJtval
Ava)6yoolt toi) XPTlO1)Jonolou)J~vou 9wSoJJxou Kat tflC btlshyOIWKolltvl1C aKpl~dac OuvOIlpound9a va 6p (OW)JEV to opla ~Vtoe tWV 6no(wv rrpt nEI vei 1tEpthrovtal at lllJat tampv u Kat oOtO) Ka9icrratat ouvatov va poundIJ1nOtEU9allJeV nlv UVWtpoundpW tpyaalav t v-romolloO Kat arcoppiVcwc tGlv poundOqJOAIJevrov OEOOIJEVWV dC lOV TJAEnpOVIKoV imOAOY10tnV
ElHleurolWlSOV 6tt 11 K(m~ lf)v civoottpoo jJEOOOOV Urro M Ylc8EtOa tlllTJ t OO V OUVOTOV va Slacp~P1J t tl 1tptljJlomd roc fiSTl tUxOn KUTa plusmn 2OOg middotEltlall ~ ouvatov yo h G )JLlqUlv d a h l OlUCPOPUV cirro Oiffl)V 86n leamiddottf Tllv i1QtilKoaiov Tf OUvop- 900pound0) tooOtrl9)l[~elQL fJ(poundOEl tou ntpaywvou tampv cL1tocrramiddot acmv tVQ) KUU tnV KMlacrlKliv JJt9000v Mv AallaampvOvtaL UTt 6j1 LV a[ U1tOltTtUaE1C
H napoCan epyacr1a SOVUta l va 9croP1l9t1 t1lc ~v IJtpo~ tou fshyV1ICWtCPOU 1tpOaATUJaw li t11c OLU 1to)Acl1t)Glv omcrflotO)llrov tnEKluOEOOC f 1tUKvroOnm OtUUPBU6VlOlV t PlY(l)vo)Jpound1pudlIV OLKtOOlv ITpaY)Jon 0 nVt1KpoundLllev6~ Uo~ mcOft~ etc napQshy110(av 1tampPl71tCOOL v dvaL vo EltHUXltOjJJV tv l euroVlKOV Itp6YPojJ)Jo pounde tov r41ClPOVLKOV imoAoYlOtftv t 6 01toov tpoltpol)OtOUshyIJEVOV d tci~ OUvtCtOYIlAVW tampv YVO)QtGw t P1YCtlVOjlEtpUOOV 0l1lwirov toJ to bc napatl1POCo)V crtolxEia 96 ouvatol v6 r-vto1tlClJ xat imoppVu t at )oveacrpllv~ 1tUpal l1P1lcrUC i1 to tU Xov crKoltt-u9tvta tPlyrovoll lit pua cno lxda t alpu)lltvrov auvTcayupoundvroo tv CNVeXc(q St til ~oTl6dQ toov unoAo(nrov crtOlXtdmv va CmoAoyiau t o 6P lOTl M~ auVlElaYIlEva tampv Cl1tOUjJtV(JlV GTl jurov co tntoil l Kat tftv CAM l~lV toO 0 rpQh IlUTO ft UOtOU t~ a lgtto)v atimn tczv OtcrEOlv tGlv tPlyOOVOJ4amp~ tPlKWV Ollleiwv t o 61toia XPl1OlIJ01t01n9Tlcrov Bt u t6v imoshyA0YlOIJOV tGlv cruVtCfOYIJEVOOV tOll Euv6ltoV dvm dn d= jdav tOlOUTl1v Jl~9000V U~to)Jatou unol oyuJpoO t v9a ii npocroomshyICtl (J)1l)lCtOXtl nepLOpipoundtot ei~ to voXlatOV dV(Ll C1l6ntlJOv Olei va IJr ri ltroIJEV aVOYKotov OrtCO at I(UtO rrpoctYY101V aUvtctaYIJpoundval lkiam la-v lmo(mv aaOPPTCfOVTat tei talpaAshyJlpoundVO SeSOJl t-va UKOAoJCroVtOl cruvapTnOE1 toO OUVOAOU tampV YEVOJLtVOJV napatTlPiacwv
I F A lIif Jr Theory L nd probl(~ IlL S or lIlalr0i~ N~w Yo r t t 962
2 Y v rJlmih d ftIlocle d~1 nl Qlnclrtll urrb F1 ~menl de I theoshyric d u IrililUlr l1 t l~t lS tlqutl dell ob8e r vaUo IUl P actl 11163
3 J 1 cvttN l1 t1t llod es ~6dliIQlIe pttllr la dttcrtilinatifm deA demiddot forrn Hlo(ul dta b ) rr abs PaJ1~ 19 66
L P Tardi - G LMlat~rlL T1lUC de Gtod~Rle Tome I rase II Pant tiM
5 J M Ttftlltra Theo or tile Iltl Jus lnlfnt or norm a lly distributed ohserv aliooJ Amsterdam 1950
La detection des donnees erronees dans Ie calcul
du relevement multiple Pa D G Vlachos-
R l ume
D Bns ce lte etude on traitc Ie problCI11C de la determination des coordonnecs approchecs d un point inconllu par rele ve shynlfm t sur n ~ 3 points an cicns (de coordonn~~~ connues) en tenant compte de toutCi las visecs et en np pliquant la M~thode des Moindrcs Carris Au moyen de ces coordonneshy
es on peut determiner lilS gi ements de chacun d es paints anciens d rm (Mduire I co nstantes d oricnlation des direcshytions partielles ains i que leur valeur moycnne Ensuite on calcule les correc tions de comrJensallon u ) tude desquclles pen n e l une detection Cacile c t certaino d-es visces aberran tes ou des poinls dappui de coordonnees rllusses
bull DOUUr I[lg~ule Llr A r Ono l1J (-Topoglapll ede I U nl e l1i tt~hn I QIJO a -~Is l anl II la C)f re de 1 II r(lOom IQ C160dt squc de l Unlvcnltt d Atbe[Let YIl a~b mn llch lI IIIptl m6 de I U IlIYl~it6 OAlhtnca U ultre 1ech nlqulI dmiddotAlbfl t ~
188 HopTlO 1972
6n6Tamp ~ (2) )~pavEl t~v ~opqgt~v
Z = co middot auvlj- ltp TlJllj+ Gj TlIJV + hj bull cruvV (5)
H cruv6peO)(H~ OLpound7tpoundrQL fmc t ov oAy6pI9lJov
n
F = CZZJ = 2 (00 auv li - ltP bull rU1lj + gj llJl V of hi OuvVgt = i - I
= minimum (6)
Oltp[ io~v Aomov yo CtvaCrriaOOjlEV [at tqlIlt t~v BOl9nshyn lCGlv aYvampa-rwv CLl Kui P 51ft tolt 6noialaquo n O1JvOPlTlOlt F AOjlshyllltvpoundL tAaxalIlV ttlltrv
J middotYITo~oyu7fJol
E t~ t~WaOl (6) EXO~V
oF(0) = auv II + cruv~ l~ + + cruvln = [ cr1JV~ Ii Jgt 0
(7)oFo = TUJi + lllll + + ll)Jlln = [lll12 1 1gt 0
Kala aUVpound1tEtOV al ()lot taW (0 Kol ltp OlQ tac 67toiot nF AaIJshyB6vEL ~)a(lcrtn V nllv 6pi~oVQ uno (Llv ~Icrmaeuro(()v
of iiG = 2 (cruVll (00 auv l -ltp 111middottl + gl TlJlV+ hi (H)yV)
+ allyl laquo1) OuvI2-tpmiddot fill 11 + Sa TljlV + hl middot auvV)
+ + auvl (romiddotcruvl -qgt -TlJ1ln- gn lljlV + hll(JWV)=Oo n
A ttLcrOOltJeuro It autOl BuvaVtClL v6 YPOqlOOv
[auv2tj) 6)- [Illd auvlj ] qgt + [gi01Jvlj J rUlV +
+ [h j auvl] auvV = 0
-lllll cruvlj] 00 + 111)1Zj] ql - [Si lll1 li 1middot I1I1Vshy
-(h11l1l] auvV = O
- ( Twl cruvti I
N = [ ~v~v II ] I ~~I)
l(hjauvl j l T ~ [ [g cruvl)
- lSi l1)1lj] -[h i TlI1 ljl J (9)
[gi au 1] - [8 ~~II ~ T =
[hi cruv l ] -hi TW1i] J [ ~~V ]~Ul =n~[] ouvV
)V6IIL tGlv axtopoundwv (9) a ~~LawOpoundL( (8) Tl8EvtClL 6n6 tTtV )1upqgtiiv
(10)
Aal1JlavovtCC ttlC )lepucu napaYwYo~ C1 F roc npoc 1))1 V crovV cupiolr(ouv
of (lll-lvf - 2gmiddot (00 ouv~ - ql ll)Lll + gl 1l11V + h1 middot ouvV)
+ 280 middot (co middot Olv l - qgt ~~l + 80 middot ~~V + h cruW)
+ + 2S (6) auv In - ql TJl1l + gn -1))1 V + h OllvV)n n n
()(O~~ vj = 2h l (w aUv II -ql 11)11 bull gbull TJl1V + hi OwV)
+ 2hmiddot (00 middot Olv 4 ~~ I + 80 ~~v + h cruW) J
+ 2h (m - auvln- ql TJl11n+gn rwV + hn ouvV~n
AI axtow QittCll BovavtQt vO YPQqlOOv
aF2 a(~~V) ~ [Il cruvl1middot co- [ g ~~ I)middot 1 +
+ [g g) ~~V+ [ 8 h) cruvV (II)
(12)
6n6tE 01 (J 1) yivovtOl
I amp(~~Vf bulloF I (lJ)- ~ IT aill 2 of[ claquoJ1)V V)
Eitv 1Jt1lm~tV 6lIv ~v Wcrcocrw ( 10) ~ enocr (13) ypashyqgtpoundt(ll
naputIlPoO)LpoundV lSn
H ~l1it pa N bull Kata OUvpound1tnav lCal d vtlotpoqgt6c tTJ~ N -1 Elval t ctpnywvual Kat cro)1)lupun dx 1tpOC Tl)V Kuplav 010middot YWVIOV tnc AeBO)1tvoo 6tl l) IJTttpa Tt bull dpu Kui tVTAJaYIJ~middot Vll aOtft t 2T dvaL utpayoovllCll 5uvQl1e9a e~ICO)OgtI va (moshy8dE(J)~poundV 6t TO YlVOlJeVOV
T - lt- N IT)
dvalllla tetpayoovlloi KOt (J~I1poundtP~KTJ I1ntpaOEUTllpac tupound~_
EJtuol) Be f llllpa 1M Elval ~1ttall lt ntpOY(J)vultl) Kal aUIl)L emiddot tPLKtl OCtltEPOlt taero to a t)to alL OU)LPct(va Kal SlU lil v 1l1lt pUV M M- T ( T) (15)
H6pTLO~ 1972
[rUJ2ld [hiOUvljP + [ouv2 li ] middot [hTllll jr - 2 [T)IJliOuvlj [hj 11jl1i Jmiddot (hjOuvlj]
JI~3 = [hi h j 1- [TllJ i I j 1 [cruvlj] - ( Tl ~Ili auv1i J
[TlIl2ld lSi auv II J ( h j cruv li ) J [au2 l j 1 [8i T)IJ lj ] [hi Tllllj] - [Tlllt i cruj] ([ gj au I ] [hi 111J Ii I (8j T))Ll j J hI cru lj D
(lllJll lj J (ouv1l J j)- TtIJ II (fU tiJI
dU01JE8a a O1tOOElS(iJIEV K(1T6nv 1tpaEW 611 ta cr1Ol1Eia JI )I OU a TaL va hqlpa08oCv we aOpoicrjlo1a 1E1 POYWVW
11 n OUvaP1flOEOOv 8j = gj (8 Ii) KOt hi = hi (hi Ii) to of crtOt-
1EtO JI = Il hmiddotPPoCETaL WC 69pOlOIlO ytOIleurovoov 1lO aushy1 ~ 2 1
l roV cruOplrOEOO nc tK lOU1 0U 1) ll1)lpa Ma OUVOlaL Va
lE9t 000 tTlV IlOPPrV
(16)
ElC lWV cr1euroOECIv (14) KOj (16) E1OIlEV
I ~F [ ) [ ) I2 iJ(n~V) = gi gi nV + I hi auvV (17)
1 of [ [ ) T cltcruv V) -= 8i hi] T)jJ V r hi hi O)V V
H ltlln 100 V Qla -rtl 61to(av Tl F 1ta poucrtateuro1 aKpOlala (JUY1010V Ti tAUXlOtOV) QiOE10t into t1)1 tlcrrocrewc
of of auvV-~ nV=o (18)oV 0( V) a(cruv V)
AaJIaaVOVtEc on 6~H nlv (17) 1) -reuroAeurou-rQa y[vEtal
~- = 2[ [g g] n V cruv V + [g h) cruv Vshy
- [~ h) n V - (h hj n V auv V ) = deg (19)
(20)
A AUOeuroU t1) c (20) dval
2V =2Vo + k7t
A lilla Aol1tOV toO V oui TaC 6noiac 1) F 1tCLpoucrullEI DKp6shytala dVQl
0 lt V lt T I (21) V~ = Vo + T T lt VI lt 1t
OpftOVlol oE Ka1a 1tPOOpoundY)IOIV n aK1IV(OOV
DpofPavwe fK tGlv OUO lOUtWV l lJlGlV 1 Jlia aVtI(flOl1Et d e 16 lJeYlolOV Kat 1) 6))11 euroI~ 16 euroA6XIltJl OV lflr F dFOOIlpoundVOU 011 euroVblocpeurop6IlE9a 81(i lTlV 1lllliv 100 V tinr aVrIOlOIXEf Etc 16 euro~~6Xl(flOV llie F tiC t1erUOOOJlEV 1t0(0 t K llOv (21) OiQEl Uomiddot -XL0111- nlltv eurolr lV F
H fV AOrltgt Ouvaptr)Ollt EIval
v = r ~V dV
o
of AVtlKa91ltJtlOvleuror Tflv tlIlTlV toO i) V fK 1flr (19) Kat 6AOshy
KAT)POOV1E C AaJla6vOIlEV
F = [g g) ~ V + [h h) auv V + 2 [g h) ~ V cruv V - [h h 1 (22)
E1tEIOt 11 1tOO6T1e [h h ] eurotval 01u9europa Tl Oeuro 1t006T1r
[g gJ n V + [hgt) cruv V
poundlvat 9E1IK6e apI91l6c 010 va A6al] Tl F UaXIOTI1V lLllnv 1tpbtel
(23)
EK 100lOU OUvOYOJlEV OTI
a) Ev [ggt] lt deg t6tE oui vel Icrxu11 1l (23) npeuroJtEt
TlIlV OuvV gt 0
tsnEp (llJVEnOYETat 0 lt V lt T TOlno OTlllaVEI 611 de ltlV 1teuropl1nooOlV airr1)v Tl iT)tou)ltvT) llllTl 100 V euroIvai 1) VI
6) Eav [ggtraquoO -rOleuro h TfIc (23) OUllneuropolvojlEV 6)10100lt 611 1) iI1ToulltVT) Tllll) -roO V Elvot 1) v2 bull
TOIOVTOl p6nroc 6p[tpoundla~ Tl T11l1l TflC )I poundtaaATllfle V Qla ttlV 61toiav 1) Ouvap-rT)OlC F AaJlt3ltiVeuro1 fA-axicr1nv T1JlrV bullAC KashyAeurocrwllEv V 11lV lQJ11V (QU1TlV
Ko-r61ttV lOv ovoodpw Tl IlnTpa l UI etV(U l poundAEtwe roPIO)leuroV11 61tOTE fK llic t~I(fltOOeuroffilt (10) U1tOAOy[tovlm o( tl)lat l(l)V BoTtshy9TJtlK(l)V Oyv6la-tro 00 Kol ql
(24)
TEA-Dlt h lli)V f~t06)(JfwV (4) AlaquowaoVOIlE Tae ~TJ100)lEVCle 11shy
Jlac lGlV DyvcilcrlOO X Kat w
x =00 middot cruvV l IP TlIlV ) (2l)
W = - 00middot T)IJV + IP OUvV
At 11)Iat autat o VTl1tPOOoonEUOUV lae KCl1o 1tPOOeuroY)lolV (J)VshytEloyJ1iVoC loil OYVWO1OU OTlIlE[OO M 01 61tOIot OU euroivai Kal al OKplaEie TOlornal U1tO lit 1tPOi)1t69EOlV On JlE1Cll0 lGW QpoundOolle oov (OK01teVOW Kol (fuVleurotaYlltvClI lplYOOVOIJE1PIKGlV OTJIlEirov) opound uP(Cfiavrol tcrcpoAJdva cr1OLX Eia
4 ETOmoJlbr TW I4aAlJanJv - napaT1pijOEli
rUIlIPWvroc 1tpOe TnV tK1E9eurolOClV )JpoundOooov unEAoyicralJEV lac cr)VTEtClYlltvo~ tou Qui 1tO)ACl1tA1)~ 6u090Tolllae i1l10UIJeuroVOU O11IlEiOU AUllaavoVTEe Uf( OWlY 16 crUVOAOV tampv t KTEAE09euroLshyOGlv lrapotT)P1loE(JJv Toulo CSTlllaivEl 611 10 EUPE9EV OT)IlEtov Elval to 1tUOV m9ovov aacrll TGV de 11)V ol69poundoiv JIae IJ EshylpnOeurooo Kat w euroK roUTDU ouvalClI OO(pClAGlC 6 XPllOIJj01tOIshy11911 liL6 16v lmOAOYI01l6v KPITT) piou Qui IlEOOU TOO olrolou euroVT01tltOlOI Kat onOPPLmOVTal 0[ euroOlDaA)IEVal OK01tEOOpoundIC ti fa OKomu9ivra lP1jW OIlE1PIKel on)ltia focentgtlttlIlfV(J)V ouvshy
190 Mopno 1972
tEtUYJ1EVOOV To KPLtTJP10V 060 lmoAoyiCEtaL ~ t~fl~
EK tGlv (JUVYpoundtOY)lEV(t)V XW EKaatoo VEOU CrU1Eiou 1eCl 1amp1
cruVTEtaylpoundVOOV Xi IV tCigtv cncomUetVTCOV tPlYOJVOIu tl)l)(UlV
Oll)1elWV P i (l1tOfOyi~O)lEV teie yroviu OlEU80V(JEooc
G = lj + Vi (26)
XI - X poundqlG = I (i = 12 n)
J Wj - IV
E tiic axtOEwe (26) OampOO)1poundVOU 6n e[V(lt )vroomi tK rrupomiddot TI1Pit crCWt at tt)lul tGlv lj 96 hOOjlEV n to TtAfl8CX UIUIC Vi TfjC amgepac rrpocraVQtOA10)10Q rlOv oLeu9uvcreoov IiVnOtOLXOUshyaae 1tpOt t D1i til toO OTHldou toutou 1tpaY)JCltoftOLll0dcrru 01(0shyTtElxrtr 01Mza~ 1tP~ to 1tAiOO TampV XPI1O1)lonouo(vtOJV tptshyyroVOJlEtPlKWV Oll)lElOOV AaJl~6vo~IfV TnV )lEOlV nllV V [JJ TOUshytOW Kat tv auvEXeiq EupicrKOILEV rQc OlUqlOp6C
ui=Vm-Vj bull
TOlOUi OTp6Jtcgtc 01 EKWJtOV VtOV crn~HOV 1a)l~voJlev t va 1tLVQKU oLOpOromwv Ui H gecilPl1OlC teDV 1tlvchwv aotGlv tnt~
tPf Trpound1 tOV Eirxep~ EvtOmalJOv ttilv poundOtpaA~v(i)v OKomuatXllv il tOv XPl1allJonot19tVTOJV tHYWVO)UtfP1KOlV Ol1IJmiddotGioov poundalposhyJJtVOlV auvtetaYIJcvrov npuY~tt Oaqgtci) l1U~l1IJtv1 till HOC tK teov OtOp9roOEO)v u or 6rrOiut mpuhOVtal dC tOV 1tlvaKa hoc ~K tGlv vtoov al1)Jelrov TrjJOOUgtpoundl 6tL 11 aViOtOlXOC OKOshy1teumc elvaL )aveao)Jpoundvll tV(l ilIa mgtcTtTlIJanKampC l1~TljtpoundVTl tI)lTv TtilV u to 6noia nepampxovlQ1 cle tou~ olaltpopo~ 1t[vashyKae tampv vpoundoov al1)JEiwv Kat uVTlatolXoCiv de oKonEumlC tOCi a()toD -rPlyrovolle-rpIKoi) Ol1IJamplOU o1)JOVamp1 6tl 01 9poundroPTlOelCCIl OUVletaYIJpoundVal toO aTl)Jeou rOUtOU Elval poundacpaAIJtval
Ava)6yoolt toi) XPTlO1)Jonolou)J~vou 9wSoJJxou Kat tflC btlshyOIWKolltvl1C aKpl~dac OuvOIlpound9a va 6p (OW)JEV to opla ~Vtoe tWV 6no(wv rrpt nEI vei 1tEpthrovtal at lllJat tampv u Kat oOtO) Ka9icrratat ouvatov va poundIJ1nOtEU9allJeV nlv UVWtpoundpW tpyaalav t v-romolloO Kat arcoppiVcwc tGlv poundOqJOAIJevrov OEOOIJEVWV dC lOV TJAEnpOVIKoV imOAOY10tnV
ElHleurolWlSOV 6tt 11 K(m~ lf)v civoottpoo jJEOOOOV Urro M Ylc8EtOa tlllTJ t OO V OUVOTOV va Slacp~P1J t tl 1tptljJlomd roc fiSTl tUxOn KUTa plusmn 2OOg middotEltlall ~ ouvatov yo h G )JLlqUlv d a h l OlUCPOPUV cirro Oiffl)V 86n leamiddottf Tllv i1QtilKoaiov Tf OUvop- 900pound0) tooOtrl9)l[~elQL fJ(poundOEl tou ntpaywvou tampv cL1tocrramiddot acmv tVQ) KUU tnV KMlacrlKliv JJt9000v Mv AallaampvOvtaL UTt 6j1 LV a[ U1tOltTtUaE1C
H napoCan epyacr1a SOVUta l va 9croP1l9t1 t1lc ~v IJtpo~ tou fshyV1ICWtCPOU 1tpOaATUJaw li t11c OLU 1to)Acl1t)Glv omcrflotO)llrov tnEKluOEOOC f 1tUKvroOnm OtUUPBU6VlOlV t PlY(l)vo)Jpound1pudlIV OLKtOOlv ITpaY)Jon 0 nVt1KpoundLllev6~ Uo~ mcOft~ etc napQshy110(av 1tampPl71tCOOL v dvaL vo EltHUXltOjJJV tv l euroVlKOV Itp6YPojJ)Jo pounde tov r41ClPOVLKOV imoAoYlOtftv t 6 01toov tpoltpol)OtOUshyIJEVOV d tci~ OUvtCtOYIlAVW tampv YVO)QtGw t P1YCtlVOjlEtpUOOV 0l1lwirov toJ to bc napatl1POCo)V crtolxEia 96 ouvatol v6 r-vto1tlClJ xat imoppVu t at )oveacrpllv~ 1tUpal l1P1lcrUC i1 to tU Xov crKoltt-u9tvta tPlyrovoll lit pua cno lxda t alpu)lltvrov auvTcayupoundvroo tv CNVeXc(q St til ~oTl6dQ toov unoAo(nrov crtOlXtdmv va CmoAoyiau t o 6P lOTl M~ auVlElaYIlEva tampv Cl1tOUjJtV(JlV GTl jurov co tntoil l Kat tftv CAM l~lV toO 0 rpQh IlUTO ft UOtOU t~ a lgtto)v atimn tczv OtcrEOlv tGlv tPlyOOVOJ4amp~ tPlKWV Ollleiwv t o 61toia XPl1OlIJ01t01n9Tlcrov Bt u t6v imoshyA0YlOIJOV tGlv cruVtCfOYIJEVOOV tOll Euv6ltoV dvm dn d= jdav tOlOUTl1v Jl~9000V U~to)Jatou unol oyuJpoO t v9a ii npocroomshyICtl (J)1l)lCtOXtl nepLOpipoundtot ei~ to voXlatOV dV(Ll C1l6ntlJOv Olei va IJr ri ltroIJEV aVOYKotov OrtCO at I(UtO rrpoctYY101V aUvtctaYIJpoundval lkiam la-v lmo(mv aaOPPTCfOVTat tei talpaAshyJlpoundVO SeSOJl t-va UKOAoJCroVtOl cruvapTnOE1 toO OUVOAOU tampV YEVOJLtVOJV napatTlPiacwv
I F A lIif Jr Theory L nd probl(~ IlL S or lIlalr0i~ N~w Yo r t t 962
2 Y v rJlmih d ftIlocle d~1 nl Qlnclrtll urrb F1 ~menl de I theoshyric d u IrililUlr l1 t l~t lS tlqutl dell ob8e r vaUo IUl P actl 11163
3 J 1 cvttN l1 t1t llod es ~6dliIQlIe pttllr la dttcrtilinatifm deA demiddot forrn Hlo(ul dta b ) rr abs PaJ1~ 19 66
L P Tardi - G LMlat~rlL T1lUC de Gtod~Rle Tome I rase II Pant tiM
5 J M Ttftlltra Theo or tile Iltl Jus lnlfnt or norm a lly distributed ohserv aliooJ Amsterdam 1950
La detection des donnees erronees dans Ie calcul
du relevement multiple Pa D G Vlachos-
R l ume
D Bns ce lte etude on traitc Ie problCI11C de la determination des coordonnecs approchecs d un point inconllu par rele ve shynlfm t sur n ~ 3 points an cicns (de coordonn~~~ connues) en tenant compte de toutCi las visecs et en np pliquant la M~thode des Moindrcs Carris Au moyen de ces coordonneshy
es on peut determiner lilS gi ements de chacun d es paints anciens d rm (Mduire I co nstantes d oricnlation des direcshytions partielles ains i que leur valeur moycnne Ensuite on calcule les correc tions de comrJensallon u ) tude desquclles pen n e l une detection Cacile c t certaino d-es visces aberran tes ou des poinls dappui de coordonnees rllusses
bull DOUUr I[lg~ule Llr A r Ono l1J (-Topoglapll ede I U nl e l1i tt~hn I QIJO a -~Is l anl II la C)f re de 1 II r(lOom IQ C160dt squc de l Unlvcnltt d Atbe[Let YIl a~b mn llch lI IIIptl m6 de I U IlIYl~it6 OAlhtnca U ultre 1ech nlqulI dmiddotAlbfl t ~
H6pTLO~ 1972
[rUJ2ld [hiOUvljP + [ouv2 li ] middot [hTllll jr - 2 [T)IJliOuvlj [hj 11jl1i Jmiddot (hjOuvlj]
JI~3 = [hi h j 1- [TllJ i I j 1 [cruvlj] - ( Tl ~Ili auv1i J
[TlIl2ld lSi auv II J ( h j cruv li ) J [au2 l j 1 [8i T)IJ lj ] [hi Tllllj] - [Tlllt i cruj] ([ gj au I ] [hi 111J Ii I (8j T))Ll j J hI cru lj D
(lllJll lj J (ouv1l J j)- TtIJ II (fU tiJI
dU01JE8a a O1tOOElS(iJIEV K(1T6nv 1tpaEW 611 ta cr1Ol1Eia JI )I OU a TaL va hqlpa08oCv we aOpoicrjlo1a 1E1 POYWVW
11 n OUvaP1flOEOOv 8j = gj (8 Ii) KOt hi = hi (hi Ii) to of crtOt-
1EtO JI = Il hmiddotPPoCETaL WC 69pOlOIlO ytOIleurovoov 1lO aushy1 ~ 2 1
l roV cruOplrOEOO nc tK lOU1 0U 1) ll1)lpa Ma OUVOlaL Va
lE9t 000 tTlV IlOPPrV
(16)
ElC lWV cr1euroOECIv (14) KOj (16) E1OIlEV
I ~F [ ) [ ) I2 iJ(n~V) = gi gi nV + I hi auvV (17)
1 of [ [ ) T cltcruv V) -= 8i hi] T)jJ V r hi hi O)V V
H ltlln 100 V Qla -rtl 61to(av Tl F 1ta poucrtateuro1 aKpOlala (JUY1010V Ti tAUXlOtOV) QiOE10t into t1)1 tlcrrocrewc
of of auvV-~ nV=o (18)oV 0( V) a(cruv V)
AaJIaaVOVtEc on 6~H nlv (17) 1) -reuroAeurou-rQa y[vEtal
~- = 2[ [g g] n V cruv V + [g h) cruv Vshy
- [~ h) n V - (h hj n V auv V ) = deg (19)
(20)
A AUOeuroU t1) c (20) dval
2V =2Vo + k7t
A lilla Aol1tOV toO V oui TaC 6noiac 1) F 1tCLpoucrullEI DKp6shytala dVQl
0 lt V lt T I (21) V~ = Vo + T T lt VI lt 1t
OpftOVlol oE Ka1a 1tPOOpoundY)IOIV n aK1IV(OOV
DpofPavwe fK tGlv OUO lOUtWV l lJlGlV 1 Jlia aVtI(flOl1Et d e 16 lJeYlolOV Kat 1) 6))11 euroI~ 16 euroA6XIltJl OV lflr F dFOOIlpoundVOU 011 euroVblocpeurop6IlE9a 81(i lTlV 1lllliv 100 V tinr aVrIOlOIXEf Etc 16 euro~~6Xl(flOV llie F tiC t1erUOOOJlEV 1t0(0 t K llOv (21) OiQEl Uomiddot -XL0111- nlltv eurolr lV F
H fV AOrltgt Ouvaptr)Ollt EIval
v = r ~V dV
o
of AVtlKa91ltJtlOvleuror Tflv tlIlTlV toO i) V fK 1flr (19) Kat 6AOshy
KAT)POOV1E C AaJla6vOIlEV
F = [g g) ~ V + [h h) auv V + 2 [g h) ~ V cruv V - [h h 1 (22)
E1tEIOt 11 1tOO6T1e [h h ] eurotval 01u9europa Tl Oeuro 1t006T1r
[g gJ n V + [hgt) cruv V
poundlvat 9E1IK6e apI91l6c 010 va A6al] Tl F UaXIOTI1V lLllnv 1tpbtel
(23)
EK 100lOU OUvOYOJlEV OTI
a) Ev [ggt] lt deg t6tE oui vel Icrxu11 1l (23) npeuroJtEt
TlIlV OuvV gt 0
tsnEp (llJVEnOYETat 0 lt V lt T TOlno OTlllaVEI 611 de ltlV 1teuropl1nooOlV airr1)v Tl iT)tou)ltvT) llllTl 100 V euroIvai 1) VI
6) Eav [ggtraquoO -rOleuro h TfIc (23) OUllneuropolvojlEV 6)10100lt 611 1) iI1ToulltVT) Tllll) -roO V Elvot 1) v2 bull
TOIOVTOl p6nroc 6p[tpoundla~ Tl T11l1l TflC )I poundtaaATllfle V Qla ttlV 61toiav 1) Ouvap-rT)OlC F AaJlt3ltiVeuro1 fA-axicr1nv T1JlrV bullAC KashyAeurocrwllEv V 11lV lQJ11V (QU1TlV
Ko-r61ttV lOv ovoodpw Tl IlnTpa l UI etV(U l poundAEtwe roPIO)leuroV11 61tOTE fK llic t~I(fltOOeuroffilt (10) U1tOAOy[tovlm o( tl)lat l(l)V BoTtshy9TJtlK(l)V Oyv6la-tro 00 Kol ql
(24)
TEA-Dlt h lli)V f~t06)(JfwV (4) AlaquowaoVOIlE Tae ~TJ100)lEVCle 11shy
Jlac lGlV DyvcilcrlOO X Kat w
x =00 middot cruvV l IP TlIlV ) (2l)
W = - 00middot T)IJV + IP OUvV
At 11)Iat autat o VTl1tPOOoonEUOUV lae KCl1o 1tPOOeuroY)lolV (J)VshytEloyJ1iVoC loil OYVWO1OU OTlIlE[OO M 01 61tOIot OU euroivai Kal al OKplaEie TOlornal U1tO lit 1tPOi)1t69EOlV On JlE1Cll0 lGW QpoundOolle oov (OK01teVOW Kol (fuVleurotaYlltvClI lplYOOVOIJE1PIKGlV OTJIlEirov) opound uP(Cfiavrol tcrcpoAJdva cr1OLX Eia
4 ETOmoJlbr TW I4aAlJanJv - napaT1pijOEli
rUIlIPWvroc 1tpOe TnV tK1E9eurolOClV )JpoundOooov unEAoyicralJEV lac cr)VTEtClYlltvo~ tou Qui 1tO)ACl1tA1)~ 6u090Tolllae i1l10UIJeuroVOU O11IlEiOU AUllaavoVTEe Uf( OWlY 16 crUVOAOV tampv t KTEAE09euroLshyOGlv lrapotT)P1loE(JJv Toulo CSTlllaivEl 611 10 EUPE9EV OT)IlEtov Elval to 1tUOV m9ovov aacrll TGV de 11)V ol69poundoiv JIae IJ EshylpnOeurooo Kat w euroK roUTDU ouvalClI OO(pClAGlC 6 XPllOIJj01tOIshy11911 liL6 16v lmOAOYI01l6v KPITT) piou Qui IlEOOU TOO olrolou euroVT01tltOlOI Kat onOPPLmOVTal 0[ euroOlDaA)IEVal OK01tEOOpoundIC ti fa OKomu9ivra lP1jW OIlE1PIKel on)ltia focentgtlttlIlfV(J)V ouvshy
190 Mopno 1972
tEtUYJ1EVOOV To KPLtTJP10V 060 lmoAoyiCEtaL ~ t~fl~
EK tGlv (JUVYpoundtOY)lEV(t)V XW EKaatoo VEOU CrU1Eiou 1eCl 1amp1
cruVTEtaylpoundVOOV Xi IV tCigtv cncomUetVTCOV tPlYOJVOIu tl)l)(UlV
Oll)1elWV P i (l1tOfOyi~O)lEV teie yroviu OlEU80V(JEooc
G = lj + Vi (26)
XI - X poundqlG = I (i = 12 n)
J Wj - IV
E tiic axtOEwe (26) OampOO)1poundVOU 6n e[V(lt )vroomi tK rrupomiddot TI1Pit crCWt at tt)lul tGlv lj 96 hOOjlEV n to TtAfl8CX UIUIC Vi TfjC amgepac rrpocraVQtOA10)10Q rlOv oLeu9uvcreoov IiVnOtOLXOUshyaae 1tpOt t D1i til toO OTHldou toutou 1tpaY)JCltoftOLll0dcrru 01(0shyTtElxrtr 01Mza~ 1tP~ to 1tAiOO TampV XPI1O1)lonouo(vtOJV tptshyyroVOJlEtPlKWV Oll)lElOOV AaJl~6vo~IfV TnV )lEOlV nllV V [JJ TOUshytOW Kat tv auvEXeiq EupicrKOILEV rQc OlUqlOp6C
ui=Vm-Vj bull
TOlOUi OTp6Jtcgtc 01 EKWJtOV VtOV crn~HOV 1a)l~voJlev t va 1tLVQKU oLOpOromwv Ui H gecilPl1OlC teDV 1tlvchwv aotGlv tnt~
tPf Trpound1 tOV Eirxep~ EvtOmalJOv ttilv poundOtpaA~v(i)v OKomuatXllv il tOv XPl1allJonot19tVTOJV tHYWVO)UtfP1KOlV Ol1IJmiddotGioov poundalposhyJJtVOlV auvtetaYIJcvrov npuY~tt Oaqgtci) l1U~l1IJtv1 till HOC tK teov OtOp9roOEO)v u or 6rrOiut mpuhOVtal dC tOV 1tlvaKa hoc ~K tGlv vtoov al1)Jelrov TrjJOOUgtpoundl 6tL 11 aViOtOlXOC OKOshy1teumc elvaL )aveao)Jpoundvll tV(l ilIa mgtcTtTlIJanKampC l1~TljtpoundVTl tI)lTv TtilV u to 6noia nepampxovlQ1 cle tou~ olaltpopo~ 1t[vashyKae tampv vpoundoov al1)JEiwv Kat uVTlatolXoCiv de oKonEumlC tOCi a()toD -rPlyrovolle-rpIKoi) Ol1IJamplOU o1)JOVamp1 6tl 01 9poundroPTlOelCCIl OUVletaYIJpoundVal toO aTl)Jeou rOUtOU Elval poundacpaAIJtval
Ava)6yoolt toi) XPTlO1)Jonolou)J~vou 9wSoJJxou Kat tflC btlshyOIWKolltvl1C aKpl~dac OuvOIlpound9a va 6p (OW)JEV to opla ~Vtoe tWV 6no(wv rrpt nEI vei 1tEpthrovtal at lllJat tampv u Kat oOtO) Ka9icrratat ouvatov va poundIJ1nOtEU9allJeV nlv UVWtpoundpW tpyaalav t v-romolloO Kat arcoppiVcwc tGlv poundOqJOAIJevrov OEOOIJEVWV dC lOV TJAEnpOVIKoV imOAOY10tnV
ElHleurolWlSOV 6tt 11 K(m~ lf)v civoottpoo jJEOOOOV Urro M Ylc8EtOa tlllTJ t OO V OUVOTOV va Slacp~P1J t tl 1tptljJlomd roc fiSTl tUxOn KUTa plusmn 2OOg middotEltlall ~ ouvatov yo h G )JLlqUlv d a h l OlUCPOPUV cirro Oiffl)V 86n leamiddottf Tllv i1QtilKoaiov Tf OUvop- 900pound0) tooOtrl9)l[~elQL fJ(poundOEl tou ntpaywvou tampv cL1tocrramiddot acmv tVQ) KUU tnV KMlacrlKliv JJt9000v Mv AallaampvOvtaL UTt 6j1 LV a[ U1tOltTtUaE1C
H napoCan epyacr1a SOVUta l va 9croP1l9t1 t1lc ~v IJtpo~ tou fshyV1ICWtCPOU 1tpOaATUJaw li t11c OLU 1to)Acl1t)Glv omcrflotO)llrov tnEKluOEOOC f 1tUKvroOnm OtUUPBU6VlOlV t PlY(l)vo)Jpound1pudlIV OLKtOOlv ITpaY)Jon 0 nVt1KpoundLllev6~ Uo~ mcOft~ etc napQshy110(av 1tampPl71tCOOL v dvaL vo EltHUXltOjJJV tv l euroVlKOV Itp6YPojJ)Jo pounde tov r41ClPOVLKOV imoAoYlOtftv t 6 01toov tpoltpol)OtOUshyIJEVOV d tci~ OUvtCtOYIlAVW tampv YVO)QtGw t P1YCtlVOjlEtpUOOV 0l1lwirov toJ to bc napatl1POCo)V crtolxEia 96 ouvatol v6 r-vto1tlClJ xat imoppVu t at )oveacrpllv~ 1tUpal l1P1lcrUC i1 to tU Xov crKoltt-u9tvta tPlyrovoll lit pua cno lxda t alpu)lltvrov auvTcayupoundvroo tv CNVeXc(q St til ~oTl6dQ toov unoAo(nrov crtOlXtdmv va CmoAoyiau t o 6P lOTl M~ auVlElaYIlEva tampv Cl1tOUjJtV(JlV GTl jurov co tntoil l Kat tftv CAM l~lV toO 0 rpQh IlUTO ft UOtOU t~ a lgtto)v atimn tczv OtcrEOlv tGlv tPlyOOVOJ4amp~ tPlKWV Ollleiwv t o 61toia XPl1OlIJ01t01n9Tlcrov Bt u t6v imoshyA0YlOIJOV tGlv cruVtCfOYIJEVOOV tOll Euv6ltoV dvm dn d= jdav tOlOUTl1v Jl~9000V U~to)Jatou unol oyuJpoO t v9a ii npocroomshyICtl (J)1l)lCtOXtl nepLOpipoundtot ei~ to voXlatOV dV(Ll C1l6ntlJOv Olei va IJr ri ltroIJEV aVOYKotov OrtCO at I(UtO rrpoctYY101V aUvtctaYIJpoundval lkiam la-v lmo(mv aaOPPTCfOVTat tei talpaAshyJlpoundVO SeSOJl t-va UKOAoJCroVtOl cruvapTnOE1 toO OUVOAOU tampV YEVOJLtVOJV napatTlPiacwv
I F A lIif Jr Theory L nd probl(~ IlL S or lIlalr0i~ N~w Yo r t t 962
2 Y v rJlmih d ftIlocle d~1 nl Qlnclrtll urrb F1 ~menl de I theoshyric d u IrililUlr l1 t l~t lS tlqutl dell ob8e r vaUo IUl P actl 11163
3 J 1 cvttN l1 t1t llod es ~6dliIQlIe pttllr la dttcrtilinatifm deA demiddot forrn Hlo(ul dta b ) rr abs PaJ1~ 19 66
L P Tardi - G LMlat~rlL T1lUC de Gtod~Rle Tome I rase II Pant tiM
5 J M Ttftlltra Theo or tile Iltl Jus lnlfnt or norm a lly distributed ohserv aliooJ Amsterdam 1950
La detection des donnees erronees dans Ie calcul
du relevement multiple Pa D G Vlachos-
R l ume
D Bns ce lte etude on traitc Ie problCI11C de la determination des coordonnecs approchecs d un point inconllu par rele ve shynlfm t sur n ~ 3 points an cicns (de coordonn~~~ connues) en tenant compte de toutCi las visecs et en np pliquant la M~thode des Moindrcs Carris Au moyen de ces coordonneshy
es on peut determiner lilS gi ements de chacun d es paints anciens d rm (Mduire I co nstantes d oricnlation des direcshytions partielles ains i que leur valeur moycnne Ensuite on calcule les correc tions de comrJensallon u ) tude desquclles pen n e l une detection Cacile c t certaino d-es visces aberran tes ou des poinls dappui de coordonnees rllusses
bull DOUUr I[lg~ule Llr A r Ono l1J (-Topoglapll ede I U nl e l1i tt~hn I QIJO a -~Is l anl II la C)f re de 1 II r(lOom IQ C160dt squc de l Unlvcnltt d Atbe[Let YIl a~b mn llch lI IIIptl m6 de I U IlIYl~it6 OAlhtnca U ultre 1ech nlqulI dmiddotAlbfl t ~
190 Mopno 1972
tEtUYJ1EVOOV To KPLtTJP10V 060 lmoAoyiCEtaL ~ t~fl~
EK tGlv (JUVYpoundtOY)lEV(t)V XW EKaatoo VEOU CrU1Eiou 1eCl 1amp1
cruVTEtaylpoundVOOV Xi IV tCigtv cncomUetVTCOV tPlYOJVOIu tl)l)(UlV
Oll)1elWV P i (l1tOfOyi~O)lEV teie yroviu OlEU80V(JEooc
G = lj + Vi (26)
XI - X poundqlG = I (i = 12 n)
J Wj - IV
E tiic axtOEwe (26) OampOO)1poundVOU 6n e[V(lt )vroomi tK rrupomiddot TI1Pit crCWt at tt)lul tGlv lj 96 hOOjlEV n to TtAfl8CX UIUIC Vi TfjC amgepac rrpocraVQtOA10)10Q rlOv oLeu9uvcreoov IiVnOtOLXOUshyaae 1tpOt t D1i til toO OTHldou toutou 1tpaY)JCltoftOLll0dcrru 01(0shyTtElxrtr 01Mza~ 1tP~ to 1tAiOO TampV XPI1O1)lonouo(vtOJV tptshyyroVOJlEtPlKWV Oll)lElOOV AaJl~6vo~IfV TnV )lEOlV nllV V [JJ TOUshytOW Kat tv auvEXeiq EupicrKOILEV rQc OlUqlOp6C
ui=Vm-Vj bull
TOlOUi OTp6Jtcgtc 01 EKWJtOV VtOV crn~HOV 1a)l~voJlev t va 1tLVQKU oLOpOromwv Ui H gecilPl1OlC teDV 1tlvchwv aotGlv tnt~
tPf Trpound1 tOV Eirxep~ EvtOmalJOv ttilv poundOtpaA~v(i)v OKomuatXllv il tOv XPl1allJonot19tVTOJV tHYWVO)UtfP1KOlV Ol1IJmiddotGioov poundalposhyJJtVOlV auvtetaYIJcvrov npuY~tt Oaqgtci) l1U~l1IJtv1 till HOC tK teov OtOp9roOEO)v u or 6rrOiut mpuhOVtal dC tOV 1tlvaKa hoc ~K tGlv vtoov al1)Jelrov TrjJOOUgtpoundl 6tL 11 aViOtOlXOC OKOshy1teumc elvaL )aveao)Jpoundvll tV(l ilIa mgtcTtTlIJanKampC l1~TljtpoundVTl tI)lTv TtilV u to 6noia nepampxovlQ1 cle tou~ olaltpopo~ 1t[vashyKae tampv vpoundoov al1)JEiwv Kat uVTlatolXoCiv de oKonEumlC tOCi a()toD -rPlyrovolle-rpIKoi) Ol1IJamplOU o1)JOVamp1 6tl 01 9poundroPTlOelCCIl OUVletaYIJpoundVal toO aTl)Jeou rOUtOU Elval poundacpaAIJtval
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I F A lIif Jr Theory L nd probl(~ IlL S or lIlalr0i~ N~w Yo r t t 962
2 Y v rJlmih d ftIlocle d~1 nl Qlnclrtll urrb F1 ~menl de I theoshyric d u IrililUlr l1 t l~t lS tlqutl dell ob8e r vaUo IUl P actl 11163
3 J 1 cvttN l1 t1t llod es ~6dliIQlIe pttllr la dttcrtilinatifm deA demiddot forrn Hlo(ul dta b ) rr abs PaJ1~ 19 66
L P Tardi - G LMlat~rlL T1lUC de Gtod~Rle Tome I rase II Pant tiM
5 J M Ttftlltra Theo or tile Iltl Jus lnlfnt or norm a lly distributed ohserv aliooJ Amsterdam 1950
La detection des donnees erronees dans Ie calcul
du relevement multiple Pa D G Vlachos-
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D Bns ce lte etude on traitc Ie problCI11C de la determination des coordonnecs approchecs d un point inconllu par rele ve shynlfm t sur n ~ 3 points an cicns (de coordonn~~~ connues) en tenant compte de toutCi las visecs et en np pliquant la M~thode des Moindrcs Carris Au moyen de ces coordonneshy
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