El Frío en Enología I. Fundamentos Básicos

8/3/2019 El Frío en Enología I. Fundamentos Básicos.

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?

Agnqce Beg{mkgn

qc`cacbnx{m.ogeirzex.bem

Zerxnhn4 ‗Kg aríe k` kègeiín”

Xkvxe xemnhe hk N`xe`ce D. Nqcgã Mcþnè

K~{kmn nhnzxnhe hkg mcme n{xer



2

>. HKAC@CBCE@KR

BNGE_

K {`n aermn hk gn k`kriín' gn mî hkirnhnhn< n~{kggn n gn ~{k xck`-

hk` n be`qkrxcrk k` {` zrebke hkik`krnxcqe xehn gn hkmî.

K` kakbxe' gn k`kriín kgãbxrcbn k be`qckrxk xehn k` bnger b{n`he

bcrb{gn zer {` be`h{bxer ~{k eze`k {`n irn` rkcxk`bcn n { zne

&kx{an kgãbxrcbn#.

Gn k`kriín mkbî`cbn' è xk`hrínme ~{k rkme`xnr n ge xckmzezrkfcxòrcbe znrn bemzrk`hkr ~{k sn k fnbcn {e hk ãxk hkakbxe hkik-

`krnxcqe b{n`he k k`bk`hín a{kie arexn`he he mnhkrn.

Gn k`kriín ~{ímcbn' onxn be` rkberhnr ~{k k` {`n rknbbcò` beme

k gn akrmk`xnbcò` hkg mexe fns {` hkzrk`hcmck`xe hk bnger.

Gn be`kb{k`bcn ercic`nhn zer ãxn xk`hk`bcn hk b{ng~{ckr

k`kriín n be`qkrxcrk k` bnger' e` n qkbk o{bnhn znrn { nzreqkbfn-mck`xe s exrn c` kmonrie be`xcx{sk {` n{xk`xcbe zreogkmn hk hcaíbcg

eg{bcò`.

Gn xkbègeiín xck`k zrkbcnmk`xk { rntò` hk kr' k` kx{hcnr s

nzgcbnr ge mkhce nhkb{nhe znrn ~{k kn mí`cme gn hkirnhnbcò`

k`kriãxcbn k` bnger' sn ~{k gòicbnmk`xk' ge c`xkrkn`xk k kg nzreqkbfn-

mck`xe mîvcme' s xehe ge ~{k k be`qckrxn k` bnger k k`kriín zkrhchn.

Znrn kqcxnr zkrhchn k` kg xrn`zerxk hk gn k`kriín kgãbxrcbn k rk-

b{rrk ng kmzgke hk ngknbce`k {zkrbe`h{bxern. Znrn kqcxnr zkrhchn

zer retnmck`xe k rkb{rrk ng hckþe nkrehc`îmcbe mî berrkbxe s b{n`he

ãxk è k {acbck`xk ng kmzgke hk ngknbce`k n`xcarcbbcò` s xnmocã` hk

ngxn xkmzkrnx{rn hk a{cò`. Znrn kqcxnr ~{k k` {`n akrmk`xnbcò` eb{rrn`

ge zreogkmn hk znrnhn' hkxr{bbcò` hk nremn' zkrhchn hk ngbefeg' kxb.'

fns ~{k rkb{rrcr xkbègòicbnmk`xk n ~{cxnr kg bnger ik`krnhe' sn ~{k è

zehkme c`bchcr k` ~{k kg hknrreggnhe zer gn rknbbcò` kn mnser ò mk-èr.



8

XKMZK_NX[_N

Nbnhãmcbnmk`xk k {è hk ge he anbxerk bemze`k`xk hk gn

k`kriín bngeríacbn' ck`he kg exre gn k`xrezín.

Gn qnme n hkac`cr beme kg qnger ~{k c`hcbn kg `cqkg' gn ngxcx{h' n gn

~{k k k`b{k`xrn kg bnger. B{n`he mî kgkqnhe k ãxk `cqkg fnognme hk

bngck`xk' e zer kg be`xrnrce' b{n`he ãxk k mî onde fnognme hk aríe.

Zer zrc`bczce' kg bnger ckmzrk ag{sk hkg `cqkg ngxe ng onde' hkg aebe

bngck`xk ng aebe aríe' hkg mcme mehe ~{k kg ni{n ckmzrk bnk hk nrrcon n

nonde ze`ck`he {` ímcg fchrî{gcbe.

KG A_CE

B{n`he ngie kxî mkè bngck`xk ~{k exrn ben' hkbcme ~{k kxn

mî aríe. E kn' ckmzrk ~{k è rkakrcme n ãg' ge fnbkme k` xãrmcè

rkgnxcqe' bemznrî`hege be` exrn ben s k` kakbxe k ní' zer~{k kg aríe è

kvcxk k` xkrmc`n xãb`cbe' xn` ege hkbcme ~{k kxnme kàrcn`he ngie

b{n`he gk kxnme ~{cxn`he bnger.

Nhkmî k {odkxcqe' zer~{k e` nzrkbcnbce`k kèrcngk ~{k

z{khk` qnrcnr< zer kdkmzge4' c beikme xrk rkbczck`xk' bnhn {è be`

ni{n n :´B' ?:´B' s 8:´B s mkxkme {`n mnè k` gn hk :´B s gn exrn k` gn

hk 8: ´B' s nmon n {` xckmze gn nbnme s gn mkxkme k` kg rkbczck`xk

hk ?: ºB' gn mnè ~{k kx{qe k` kg rkbczck`xk hk :ºB. gn èxnrî bngck`xk s

gn ~{k kx{qe k` kg hk 8:ºB gn èxnrî arín.

BNGE_



;

KVZ_KRCE@ HKG BNGE_

Rc bngk`xnme he oegn hkg mcme zke' {`n hk qchrce s exrn hk

nbkre n gn mcmn xkmzkrnx{rn s gn hkzecxnme eork {` oge~{k hk fck-

ge' eokrqnrkme ~{k gn bn`xchnh hk fckge hkrrkxche k mnser k` kg nbkre

~{k k` kg qchrce' g{kie kg bnger be`xk`che zer {` b{krze k zrezerbce`ng n

ngie zrezce hk bnhn kgkmk`xe.

N ãxk /ngie/ bnrnbxkríxcbe k hkèmc`n bnger kzkbíacbe s k {`n

zrezckhnh aícbn c`fkrk`xk n bnhn b{krze' s ~{k ckmzrk k hn rkakrche ng

ni{n' n gn ~{k k gn fn hnhe kg qnger {`chnh. Hcrínme ~{k kvzrkn gn bn-

znbchnh hk {` b{krze hk i{nrhnr kg bnger' { nqchkt hk bnger. Rc nfern gn

he oegn e` hk nbkre zkre {`n hk >: Li s exrn hk ; Li s be` gn mcmn

xkmzkrnx{rn k hkzecxn` eork kg fckge' gn bn`xchnh hk fckge a{`hche zergn zrcmkrn krî heogk ~{k gn hk gn ki{`hn< zer xn`xe' kg bnger hk {` b{kr-

ze k zrezerbce`ng n gn mnn hkg mcme.

Rc nfern e` gn he oegn hk nbkre hk >: Li. Zkre {`n be` 1: ºB s

gn exrn be` 2: ´B s zknme kg ni{n hkrrkxchn' eokrqnrkme ~{k k he-

ogk k` gn zrcmkrn ~{k k` gn ki{`hn< zer xn`xe' kg bnger hk {` b{krze k

zrezerbce`ng n { xkmzkrnx{rn.

Xehn kxn zrezerbce`ngchnhk gn zehkme zgnmnr k` gn aerm{gn4

^ = Bk ¹ m ¹ x

Rck`he4 Bk 4 kg bnger kzkbíacbe' k` Lbng%Li. m 4 gn mnrn k` Li.

x 4 gn xkmzkrnx{rn k` ºB.

^{k rkzrkk`xn gn bn`xchnh hk bnger be`xk`chn zer kg b{krze k` kg

`cqkg hk xkmzkrnx{rn x . Nfern ock`' c c`xk`xnme bngk`xnr ãxk b{krze

hkhk kg `cqkg hk xkmzkrnx{rn x > fnxn kg `cqkg x ? gn bn`xchnh hk bnger

~{k fnorín ~{k {mc`cxrnr znrn geirnrge krín4

^? = Bk ¹ m ¹ x ?

-&^> = Bk ¹ m ¹ x >#

^? - ^> = Bk ¹ m ¹ &x ? - x >#



1

Zer xn`xe' kg bnger `kbknrce n {mc`cxrnr znrn kgkqnr gn xkmzkrn-

x{rn hk {` b{krze hkhk x > n x ? ò kg ~{k fns ~{k ~{cxnr znrn kàrcnrge

hkhk gn xkmzkrnx{rn x ? n gn hk x > k4

^ = B k ¹ m ¹ &x ? - x > #

- 2 ´B

- 8 ´B

: ´B

BNGE_ RK@RCOGK BNGE_ GNXK@XKHK A[RCÒ@

&6: Lbng.#

>:: ´B QNZE_ RNX[_NHE N >:: ´B

> Li NI[N

;26'8: LbngBNGE_ GNXK@XK HK QNZE_



9

BNGE_ RK@RCOGK S BNGE_ GNXK@XK

Fnxn nfern fkme qcxe ~{k xehe n{mk`xe e hcmc`{bcò` hk bnger

qn nbemznþnhe hk gn qnrcnbcò` k` kg mcme k`xche hk gn xkmzkrnx{rn<

zkre fns zrebke k` ge ~{k ãxn berrkze`hk`bcn è xck`k g{inr.

Rc beikme ni{n n ?: ´B s gk {mc`cxrnme bnger' eokrqnrkme

~{k kg xkrmòmkxre ~{k fkme c`xreh{bche k` kggn' k qn kgkqn`he fnxn

ge >:: ´ B' zkre ng ggkinr n ãxk z{`xe gn kbngn hkg xkrmòmkxre ~{khn

acdn' k kmzcktn n kqnzernr kg ni{n be`xk`chn' zkrmn`kbck`he ní mck`-

xrn ~{khk {`n iexn hk ni{n zer kqnzernr.

Ng bnger ~{k k hkxkbxnhe zer {` xkrmòmkxre' qnrcn`he/k`cogkmk`xk/ { xkmzkrnx{rn k hkèmc`n bnger k`cogk. S n~{kg

~{k kxî' zkre è k hn n beèbkr zer {`n qnrcnbcò` hk xkmzkrnx{rn bnger gnxk`xk.

K` xehe zrebke hk bnmoce hk kxnhe k mn`xck`k gn xkmzkrnx{rn

be`xn`xk xn`xe kn a{cò` beme kqnzernbcò`.

Gn bn`xchnh hk bnger ~{k fns ~{k {mc`cxrnr znrn be`ki{cr kxebnmoce hk kxnhe qck`k hnhe zer4

^ = m ¹ Bc

K` he`hk Bc k kg bnger gnxk`xk hk bnmoce hk kxnhe' ~{k znrn kg

ni{n xemn ge qngerk4

Gnxk`xk hk a{cò` -‘‘‘-‘6:': Lbng%Li.

Gnxk`xk hk kqnzernbcò`-‘-;26'8 Lbng%Li.

[@CHNHKR HK BNGE_

Gn {`chnh hk mkhchn hkg bnger k gn bngerín' ~{k k hkac`k beme gnbn`xchnh hk bnger `kbknrcn znrn kgkqnr k` {` irnhe bk`xíirnhe' hkhk >8

n >; ́ B gn xkmzkrnx{rn hk {` irnme hk ni{n.



6

Ng kr kxn {`chnh m{s zk~{kþn' k {xcgctn èrmngmk`xk gn Lcgebn-

gerín' ~{k k {` môgxczge hk gn bngerín ~{k rkzrkk`xn kg bnger `kbknrce

znrn kgkqnr hk >8 n >; ́ B gn xkmzkrnx{rn hk {` Lcgeirnme hk ni{n.

K` kg nriex xãb`cbe rkakrche ng aríe s zer norkqcnr' b{n`he k fnogn

hk /bngerín/ ckmzrk k ãxn rkacrck`he n gn Lcgebngerín.

Xnmocã` hk mn`krn ik`krng k nhmcxk ~{k b{n`he bngk`xnme k

fnogn hk /bngerín/ s c k ng be`xrnrce' ~{cxnme bnger' k fnogn hk/ arcierín/. Gn /arcierín/ k zer xn`xe {`n /bngerín/ zkre `kinxcqn.

Gn k~{cqngk`bcn be` exrn {`chnhk k4

> Ly = 61: Lbng.

> B.Q = 12? Lbng.

- >; ´B

- >8 ´B

> bngerín

> Li

hk ni{n



3

KRBNGNR XK_MEMKX_CBNR

B{n`he è rkakrcme n gn mkhchn hk xkmzkrnx{rn' ckmzrk ge

fnbkme k` irnhe bk`xíirnhe' zer~{k `{kxre zní kxî hk`xre hkg îrkn

hk nzgcbnbcò` hkg cxkmn mãxrcbe s kxe k ge zrkbkzxcqe. Fns exrn kbn-

gn ~{k be`qck`k xk`kr k` b{k`xn' n{`~{k xn` ege kn znrn fnbkr bem-

zrk`hkr gn rkgnxcqchnh k` gn ~{k k onn` s gn brkk`bcn k~{cqebnhn hk

~{k zer hkonde hk :´ B sn è kvcxk bnger.

Gn kbngn LKGQC@ kmzcktn be` kg bkre' zrkbcnmk`xk k` kg bkre no-

eg{xe' n -?92 ´B ' z{`xe k` kg ~{k k brkk ~{k `nhn k m{kqk' ~{k `nhn

kvcxk. _kngmk`xk k` kxk z{`xe {` b{krze è xck`k bnger. Gn kbngn BKG-

RC[R' e bk`xíirnhn' xemn' znrn gn xkmzkrnx{rn n gn ~{k a{`hk kg fckge' kg

qnger BK_E s znrn gn xkmzkrnx{rn n gn ~{k k kqnzern kg ni{n' kg qngerBCK@.

Qngerk xemnhe n `cqkg hkg mnr' e kn n > nxmeakrn e ge ~{k k ge

mcme >':22 Li% bm?.

Gn kbngn AN_K@FKCX &hk {e k` ge zník nìgende`k# xemn

beme rkakrk`bcn xnmocã` kg ni{n s kg qnger hk 2?´ A znrn gn a{cò` hkg

fckge s ?>?´ A znrn gn ko{ggcbcò` hkg ni{n.

Gn c`xkrrkgnbcò` k`xrk kggn k cmzgk4

R{ k~{cqngk`bcn e`4

>::´ B = >6:´ A < >´ B = >6:%>:: A = 3%;´ A.

Rc ~{krkme be`qkrxcr {` qnger hkxkrmc`nhe' zer kdkmzge >;´ B< kg

qngerk` gn kbngn Anfrk`fkcx krín4

>;´ B = 2? , >; ¹ 3%; º A = 2? , ?9 = ;3´ A.

Fnbkme fc`bnzcã k` kg be`bkzxe hk ~{k xehe b{krze &n{`~{k {o-dkxcqnmk`xk è znrktbn /aríe/# xck`k bnger fnxn ~{k ggkin ng bkre noeg{-

xe' kxe k n - ?92´ B.

BK@XCI_NHN AN_K@FKCX LKGQC@

Ko{ggcbcò` hkg ni{n >:: ´ B. ?>? ´ A. 292 ´ L.

A{cò` hkg fckge : ´ B. 2? ´ A. ?92 ´ L.

Qnger hk gn kbngn >:: ´ B. >6: ´ A. >:: ´ L.



>:

C@AG[K@BCN HK GN Z_KRCE@

Kxk k {` be`bkzxe cmzerxn`xícme n xk`kr k` b{k`xn znrn bem-

zrk`hkr zexkrcermk`xk kg bcbge arcieríacbe.

Xehe bnmoce hk kxnhe qck`k càg{k`bcnhe zer gn zrkcò` ~{k kmn`xck`k n { ngrkhkher. B{n`he n`xk fnogîonme hk ge zrc`bczce e

ac`ngk hk kbngn xkrmemãxrcbn kzkbcacbnme n `cqkg hkg mnr< sn ~{k' be-

me zer xehe k noche' gn xkmzkrnx{rn ngbn`tnhn zer kg ni{n ~{k kxî k`

ko{ggcbcò` hk`xre hk {`n /eggn n qnzer/ k {zkrcer n >:: ´ B. & hk nfí ~{k

k b{ktn` n`xk ge ngcmk`xe#' mck`xrn ~{k k` irn`hk ngxcx{hk kxn

xkmzkrnx{rn k mkèr hk >:: ´ B.

Rckmzrk k b{mzgk ~{k znrn bnhn gc~{che fns {`n berrkze`hk`bcn

k`xrk gn zrkcò` n gn ~{k kxn emkxche s gn xkmzkrnx{rn n gn ~{k ko{ggk.

Znrn kg ni{n4

S znrn kg rkarcikrn`xk _-?? kxn berrkze`hk`bcn k4

Zrkcò` Li%bm? Xkmz. hk ko{ggcbcò` ´B.

8'1 >86

>'8 >:6

>':22 &>nxm.# >::

:'16; 63

:'28? 9?

:':>? >:

:'::3 ;

Zrkcò` Li%bm? Xkmz. hk ko{ggcbcò` ´B.

8'1 >86

>'8 >:6

>':22 &>nxm.# >::

:'16; 63

:'28? 9?:':>? >:

:'::3 ;



>>

BNGB[GE HK GN BN@XCHNH HK BNGE_

R{zeìnme ~{k beikme > Li hk fckge n -; ´ B s ~{krkme ggk-

qnrge n qnzer n >>: ´ B. Znrn geirnrge' fnorî ~{k {mc`cxrnr bnger k` hc-

qkrn ank' xng beme ~{khn rkzrkk`xnhe k` kg irîacbe4

>.- Bnger k`cogk {mc`cxrnhe ng fckge' znrn kgkqnr { xkmzkrnx{rn hk-

hk - ;´ B n :´ B.

^ = B k ¹ m ¹ &x ? - x > # = > ¹ :';:8 ¹ \:-&-;#] = ?';? Lbng.

?.- Bnger gnxk`xk hk a{cò` hkg fckge' znrn znnr hkg fckge n :´ B. n ni{n

xnmocã` n :´ B.

^ = m ¹ b> = > ¹ 6: = 6: Lbng.2.- Bnger k`cogk znrn znnr kg ni{n hkhk :º B. fnxn >::´ B.

^ = m ¹ bk &x?- x># = > ¹ > &>:: - :# = >:: Lbng.

8.- Bnger gnxk`xk hk qnzerctnbcò` hkg ni{n' znrn znnr hk ni{n n >::´ B. n

qnzer xnmocã` n >::´ B.

^ = m ¹ b>= > ¹ ;26'8 = ;26'8 Lbng.

;.- Bnger k`cogk znrn znnr kg qnzer hkhk >::´ B. fnxn >>:´ B.

^ = m ¹ bk ¹ &x? - x># = > ¹ :'81 ¹ &>>:->>:# = 8'1 Lbng.

Zer xn`xe kg bnger `kbknrce xexng krín4^x = ?';? , 6: , >:: , ;26'8 , 8'1 = 9?;';? Lbng.



>?

BCBGE HK _KA_CIK_NBCE@

N xehe è fn eb{rrche. B{n`he k kqnzern ngbefeg hk `{kxrn

mnè e b{n`he k ngk hk {`n zcbc`n' k`xcme aríe. µN ~{k k hkok5 Kqc-

hk`xkmk`xk' n ~{k `{kxre b{krze kxî nzerxn`he kg bnger `kbknrce znrn

~{k k kqnzerk kg ngbefege kg ni{n' è kxnme rkarcikrn`he' kxnme

zkrhck`he bnger. E kn' b{n`he k kqnzern {` gí~{che ge fnbk noerock`-

he bnger hkg mkhce ~{k kxî k` be`xnbxe be` ãg s zer xn`xe' geirn`he {

rkarcikrnbcò`.

Gòicbnmk`xk' gn kqeg{bcò` k` k`xche be`xrnrce' kg zne hk qnzer n

gí~{che' k kakbx{nrî b{n`he bkhn kg bnger ~{k noerocò. Gn rkzkxcbcò` hk

kxk zrebke hk aermn c`c`xkrr{mzchn k` he`hk k zreh{bk noerbcò` hk

bnger k` kg kgkmk`xe ~{k k ~{ckrk rkarcikrnr zer kqnzernbcò` hk {` ag{c-he s zexkrcer be`hk`nbcò` hkg mcme' qnme n hkèmc`nrgk /bcbge hk

rkarcikrnbcò`/.

Fnorín ~{k rkme`xnrè n zrc`bczce hkg cige VCV s mî be`brkxn-

mk`xk ng nþe >.6?8' b{n`he k zrkk`xò gn xkc hebxerng hk Bnrèx' k` gn

~{k k kx{hcnon kg bcbge xkrmehc`îmcbe eork kg ~{k kxî a{`hnmk`xnhe

kg hk rkarcikrnbcò` s ~{k fes k` hín k beèbk beme BCBGE HK [email protected] aci{rn' rkzrkk`xn' hk`xre hk {` hcnirnmn hk zrkcò`-xkmzkrnx{rn

berrkze`hck`xk n {` hkxkrmc`nhe rkarcikrn`xk' gn kqeg{bcò` hk gnxrnàermnbce`k xkrmehc`îmcbn {archn zer kg mcme.



>2

K` kxk hcnirnmn' gn b{rqn n gn ct~{ckrhn hkg z{`xe bríxcbe /K/' rk-

zrkk`xn gn gí`kn hk nx{rnbcò` hkg rkarcikrn`xk k` { ank gí~{chn. Kg îrkn

n gn ct~{ckrhn hk kxn gí`kn rkzrkk`xn kg gí~{che {okàrcnhe.

Gn b{rqn n gn hkrkbfn hkg z{`xe bríxcbe /K/' rkzrkk`xn gn gí`kn hk

nx{rnbcò` hkg rkarcikrn`xk k` { ank inken. Kg îrkn bemzrk`hchn n gnhkrkbfn hk kxn gí`kn rkzrkk`xn kg in rkbngk`xnhe.

K` gn te`n c`xkrmkhcn' bemzrk`hchn k`xrk nmon gí`kn bekvcxk`

gn he ank' gí~{che s in. Gn zrezerbcò` hk in ~{k fns k` gn mktbgn

qck`k hkac`chn zer gn b{rqn /V/ hk xíx{ge hkg qnzer ~{k k kzkbcacbn` k`

kg hcnirnmn rkng z-c hkg rkarcikrn`xk kzkbíacbe.

Kg bcbge ckmzrk k rkberrk k` k`xche be`xrnrce n gn ni{dn hkg rk-

ged s gn gí`kn kvz{kxn k` kg irîacbe k berrkze`hk` n gn ci{ck`xk

xrnàermnbce`k4

Kqnzernbcò`‡‡‡‡‡‡‡‡.Gí`kn N-O

Bemzrkcò`‡‡‡‡‡‡‡‡. Gí`kn O-B

Be`hk`nbcò`‡‡‡‡‡‡‡. Gí`kn B-H

Kvzn`cò`‡‡‡‡‡‡‡‡‡. Gí`kn H-N

Kqnzernbcò`

Hk`xre hkg bcbge' k berrkze`hk be` gn kqeg{bcò` ~{k kg rkarcikrn`-

xk kvzkrcmk`xn znrn znnr hkg z{`xe /N/' k` kg ~{k xck`k kg mî zk~{kþe

be`xk`che hk bnger s ~{k kxî k` aermn hk mktbgn gí~{chn mî in' fnxn

kg z{`xe /O/' k` kg ~{k fn n{mk`xnhe { be`xk`che k` bnger &è ní {

xkmzkrnx{rn# s k fn xrnàermnhe xexngmk`xk k` in.

Beme be`kb{k`bcn hk kxk bnmoce hk kxnhe' kg rkarcikrn`xk fn hk

noerokr {`n bn`xchnh hk bnger ~{k fn hk bkhkrgk kg mkhce ~{k gk rehkn.Kg c`xkrbnmocnher hk bnger ~{k b{mzgk be` kxn mccò` rkbcok kg èmork

hk KQNZE_NHE_ &c k xck`k k` b{k`xn gn a{`bcò` ~{k b{mzgk# e K@-A_CNHE_ &c k xck`k k` b{k`xn gn nzgcbnbcò`#.

Kg hcnirnmn rkng hkg _-?? ~{k k kvze`k k` gn zîic`n >; znrn gn

be`hcbce`k hk xrnonde k` {`n {`chnh kàrcnhern' kqnzern`he n {`n zrk-

cò` hk ; Onr &berrkze`hck`xk n xkmzkrnx{rn hk :´B.# s be`hk`n`he n

{`n zrkcò` hk >9'6 Onr &berrkze`hck`xk n {`n xkmzkrnx{rn hk 8:´B.#'

hn kvnbxnmk`xk gn kqeg{bcò` {archn ng znnr hkhk {`n k`xngzcn hk 662

LD%Li fnxn {`n hk >.:29 LD%Li.



>8

Bemzrkcò`

Kg in rkarcikrn`xk ~{k ngk hkg kqnzernher k` kg z{`xe /O/' k nzc-

rnhe zer kg bemzrker s n{mk`xn { zrkcò` hk aermn cek`xròzcbn fnxn

ggkqnrge ng z{`xe /B/.

Gn mccò` k ggkqnr kg in n ondn zrkcò`' fnxn gn zrkcò` mî ngxn

~{k kvcxk k` kg z{`xe /B/' n{mk`xn`he xnmocã` { xkmzkrnx{rn hkoche

ng xrnonde hk bemzrkcò` ~{k k xck`k ~{k rkngctnr znrn be`ki{cr kxk

ac`.

K` kg kdkmzge ~{k kx{hcnme s c` xk`kr b{k`xn' zãrhchn hk bnrin

k` qîgq{gn' gn xkmzkrnx{rn hk ngchn k berrkze`hkrín be` 1:ºB ark`xk n

ge :ºB ~{k xk`ín k` gn k`xrnhn.

Be`qck`k fnbkr èxnr ~{k ge bemzrkerk nbxôn` beme oemon

qeg{mãxrcbn' sn ~{k beme qkrkme zexkrcermk`xk kxn bnrnbxkríxcbn

xck`k {`n irn` cmzerxn`bcn.

Be`hk`nbcò`

Kg in rkarcikrn`xk n gn ngchn hkg bemzrker k` kg z{`xe /B/' kxî

rkbngk`xnhe' zer xn`xe' n { k`xrnhn k` {` c`xkrbnmocnher hk bnger' kqe-

g{bce`nrî kàrcî`hek hk mn`krn k`cogk' fnxn ngbn`tnr gn gí`kn hk n-

x{rnbcò` hkg in' s be`xc`{n`he be` gn bkcò` hk bnger k` kg bnmoce hk

kxnhe ~{k xck`k g{inr fnxn be`qkrxcrk xexngmk`xk k` gí~{che.

Kg c`xkrbnmocnher' ~{k xck`k zer mccò` kxn a{`bcò`' k hkèmc`n

BE@HK@RNHE_.

Gn mccò` hk`xre hkg bcbge hkg be`hk`nher' k gn hk bkhkr bnger. K

kg kgkmk`xe ~{k fn hk kgcmc`nr kg bnger noeroche zer kg rkarcikrn`xk k`

kg kqnzernher mî kg noeroche k` kg bemzrker &k~{cqngk`xk xãrmcbe

hkg xrnonde hknrreggnhe#.

Gn chkn ~{k fn hk ~{khnr hk kxk bemze`k`xk' k ~{k hkok bkhkr

{`n irn` bn`xchnh hk k`kriín. K` `{kxre bne xkòrcbe' fn hk znnr hkhk{`n k`xngzcn hk >.:16 LD%Li n {`n hk 662 LD%Li.



>;



>1

Qîgq{gn hk Kvzn`cò`

Hk`xre hkg bcbge' xck`k gn mccò` be`xrnrcn n gn hkg bemzrker< kxe

k' fnbk ondnr gn zrkcò` hkg gí~{che rkarcikrn`xk n { ngchn hkg be`hk`n-

her &k` `{kxre bne >9'6 Onr# fnxn gn zrkcò` n gn ~{k k k`b{k`xrn kg

kqnzernher &ci{ck`he be` kg kdkmzge ; Onr#.

Kxn bníhn hk zrkcò`' k rkngctn zer gn irn` ezecbcò` ng zne hk

rkarcikrn`xk ~{k xck`k gn qîgq{gn' ng fnbkrk znnr zer ercacbce m{s zk-

~{kþe. Kxk hkbkè hk zrkcò`' k rkngctn c` ~{k xkìn g{inr qnrcn-

bcò` hk gn k`kriín c`xkr`n hkg rkarcikrn`xk' kxe k' { k`xngzín.

[@CHNHKR A_CIE_CACBNR

Kg be`d{`xe aermnhe zer ge b{nxre kgkmk`xe be`xcx{sk`xk hkg

bcbge' {`che k`xrk c zer {`n x{okrín hk mnxkrcng s xnmnþe be`qk`ck`-

xk' rkbcok kg èmork hk {`chnh arcieríacbn' s kg kgkmk`xe ~{k k hkzgn-

tnrî' cmz{gnhe zer kg bemzrker hkhk {è n exre bemze`k`xk' k kg

ag{che rkarcikrn`xk. Gn aci{rn ci{ck`xk rkzrkk`xn kg k~{kmn arcieríacbe

hk {`n {`chnh hk cmzgk bcrb{cxe s be`hk`nbcò` zer ncrk. Rk fn` nhcbce-

`nhe kgkmk`xe hk be`xreg' ki{rchnh s mkhchn ~{k zer {z{kxe' è c`-

xkrqck`k` znrn `nhn k` kg zrebke bngeríacbe.



>9



>6

AG[CHER _KA_CIK_N@XKR

Kg rkarcikrn`xk nbxôn beme mkhce hk xrn`zerxk hk bnger hkhk kg

kqnzernher fnxn kg be`hk`nher. Gn zrezckhnh mî cmzerxn`xk be` ãxn

hkac`cbcò` k eoqcn' s k ~{k xkìn {` irn` bnger gnxk`xk hk kqnzernbcò`'

k hkbcr' {`n irn` bnznbchnh hk noerbcò` hk bnger. Beme kg kgkmk`xe

k`bnrinhe hk gn be`h{bbcò` k kg bemzrker s xck`k {`n bnznbchnh hk

xrn`zerxk acdn' ge ~{k be`qck`k k ~{k kg rkarcikrn`xk zkk m{bfe' xkìn

{`n irn` mnn s zebe qeg{mk` sn ~{k' rkberhkme' ~{k kg bnger k zre-

zerbce`ng n gn mnn.

N`xci{nmk`xk k kmzgknon` kg n`fíhrche {ga{ree' kg bger{re hk

mkxcge s kg nme`cnbe' zkre n{`~{k b{mzgckre` be` { bemkxche krn` k`

m{bfe bne c`kacbnbk e zkgciree' ck`he xòvcbe ò kvzgecqe.Fes k kmzgkn` ge hkrcqnhe bgernhe s ag{ernhe hk ge fchrebnr-

o{re' ~{k rkô`k` {è rk~{ccxe hk ki{rchnh mnserk s ~{k rkô`k`

gn zrezckhnhk hk kr4

@e càgnmnogk. @e kvzgecqe. @e xevcbn.

@e crrcxn`xk. Cèhere. ^{ímcbnmk`xk kxnogk.

Kg irnhe hk xevcbchnh mkhche zer kg erin`cme nmkrcbnè

/[`hkryrcxkr Gnoernxerck/ ~{khn kxnogkbche k` kvzkrcmk`xnbcò` e-ork n`cmngk s qck`k rkagkdnhe k` gn ci{ck`xk xnogn4



>3

@EMK@BGNX[_N HK GER _KA_CIK_N@XKR

Gn èrmn c`xkr`nbce`ngk zrkbrcok` ~{k znrn hkèmc`nr {`

rkarcikrn`xk k fnin be` gn gkxrn _ ki{che hk {è `ômkre.

Ge èmork ~{k èrmngmk`xk k {n` hk /arkò`/ ò /arcik`/ ò

/Lngxre`/' è e` mî ~{k èmork rkicxrnhe zer gn kmzrkn anorc-

bn`xk hkg rkarcikrn`xk s ~{k k` kxk bne k berrkze`hk` n /H{ze`x/'

/Fekbfx/ s /Lngc-Bfkmck/ rkzkbxcqnmk`xk.

Rc` k`xrnr k` zrea{`hchnhk ~{ímcbn' hcrkme ~{k gn èmk`bgnx{-

rn `{mãrcbn xck`k gn ci{ck`xk bgnqk4

Gn bcarn hk gn {`chnhk' c`hcbn kg `ômkre hk îxeme hk Agôer.

Gn bcarn hk gn hkbk`n mkè {è' c`hcbn kg `ômkre hk îxeme hk

fchròikè.

Gn bcarn hk gn bk`xk`n mî {è' c`hcbn kg `ômkre hk îxeme hk

bnroeè.

Kg `ômkre hk qngk`bcn gcork hkg bnroeè k nx{rn` be` îxeme

hk bgere.

K` kg bne hk ~{k berrkze`hk {` bkre n gn bcarn hk gn bk`xk`n' k

emcxk' rk{gxn`he {`n èmk`bgnx{rn hk òge he bcarn .

Zer kdkmzge4

_->?

? îxeme hk agôer.

>-> = @cìô` îxeme hk fchreikè< zer xn`xe' ng ~{khnr he

qngk`bcn gcork' xk`hrî he îxeme hk bgere. .

:,> = > îxeme hk bnroeè.

Zer xn`xe4 BF Bg? A?' hcbgere-hcag{er-mkxnè.

_-??

? îxeme hk agôer.

?-> = > îxeme hk fchreikè s zer xn`xe' > îxeme hk bgere.

:,> = > îxeme hk bnroeè. ^{ímcbnmk`xk4 BF Bg A?' meèbgere' hcag{er-mkxnè.



?:

_->>8

8 îxeme hk agôer.

>-> = : îxeme hk fchreikè s zer xn`xe' ? îxeme hk bgere.

> , > = ? îxeme hk bnroeè.

^{ímcbnmk`xk4 B? Bg? A8' hcbgere-xkxrnag{er-kxnè.

K cmzerxn`xk rkngxnr he nzkbxe.

[è' ~{k n{`~{k hc{kgqk` ngie ng ni{n' kxn eg{ocgchnh qnrcn be`

gn xkmzkrnx{rn' s nznrxk hk ge kakbxe berrecqe hk gn mcmn z{khk erc-

ic`nr zreogkmn hk eoxr{bbcò` zer beìkgnbcò` hk gn qîgq{gn hk kvzn`-cò`' c è k fn xk`che zrkbn{bcò` {acbck`xk hk fnbkr {` o{k` qnbce s

xehn gn hkmî zrîbxcbn arcieríacbn hk aermn erxehevn.

Exre' ~{k k xrnondn` n zrkce`k ~{k z{khn` ebcgnr èrmngmk`xk

k`xrk >: s ?: Li%bm? s {` mn`xk`cmck`xe hkakbx{ee hk è nzrkxnr

x{krbn' hkb{chnr ge

`cqkgk hk nbkcxk' kxb.'

z{khk` zkrmcxcr ~{k kgbcrb{cxe k ~{khk c` in

zer a{in.

Rc` g{inr n h{hn'

kg rkarcikrn`xk òzxcme

krín kg ni{n' cè a{kk

zer { c`bemznxcocgchnh

be` ge nbkcxk' zer {irn` zehkr evchnxcqe s

{ zrkce`k hk xrnonde

kvxrkmnhnmk`xk ondn.

Xck`k {` irn` bnger hk

qnzerctnbcò` s {zkrn

be` brkbk xehn gn zre-

zckhnhk hk ge hkmî.



?>



??

BEMZE@K@XKR HKG BCBGE HK _KA_CIK_NBCE@

N{`~{k gn aermn' s fnxn gn mn`krn hk nbx{nr z{khk` kr hcakrk`-

xk k` a{`bcò` hk gn nzgcbnbcò` ~{k k gk ~{ckrn hnr' e be` ge ag{che ~{k

k qnsn` n mn`cz{gnr' kg zrc`bczce hk a{`bce`nmck`xe ckmzrk k c`ngxk-

rnogk. Fns ~{k mn`xk`kr {`n zrkcò` hk kqnzernbcò` s {`n zrkcò` hk

be`hk`nbcò`' ck`he kg bemzrker kg bemze`k`xk k`bnrinhe hk kgkqnrgn

s gn qîgq{gn hk kvzn`cò` kg hk rkh{bcrgn.

BEMZ_KRE_KR

@e eb{znme n~{í ege hk ge ngxkr`nxcqe' k hkbcr' n~{kgge ~{k

oemokn` in nzreqkbfn`he kg hkzgntnmck`xe hk {` zcxn` k` {`n bnmc-n. Oîcbnmk`xk k {` bci÷kþng ~{k znrxck`he hk {` meqcmck`xe bcrb{gnr

ge xrnh{bk k` meqcmck`xe ngxkr`nxcqe hk ge zcxe`k k` gn bnmcn. Hk-

zk`hck`he hk gn cx{nbcò` hkg mexer hk nbbce`nmck`xe' k bgncacbn` k`4

Nockrxe.

Rkmcfkrmãxcbe.

Fkrmãxcbe

K` ge nockrxe' kg bci÷kþng ngk a{krn hk gn bnrbnn znrn kr meqche

zer {` mexer cx{nhe k` kg kvxkrcer.

K` ge kmcfkrmãxcbe' kg kdk hkg mexer k zregeìnbcò` hkg bci÷k-

þng hkg bemzrker' kxn`he k` gn mcmn bnrbnn' zkre ck`he nbbkcogk

hkhk kg kvxkrcer.

K` ge fkrmãxcbe' k zckrhk gn nbbkcocgchnh hk ge kmcfkrmãxc-be' ng kr eghnhn gn bnrbnn hkg bemzrker.

Xn`xe k` ge fkrmãxcbe beme k` ge kmcfkrmãxcbe' kg mexer hk

nbbce`nmck`xe kxî hk`xre hkg bcrb{cxe hk rkarcikrnbcò`' s kxî rkarcikrn-

he zer kg zrezce in rkarcikrn`xk.

S nfern qck`k gn kxkr`n zrki{`xn... µb{ng k mkder5 s n~{í eb{rrk

beme k` ge o{kè qcè hk hcakrk`xk te`n hk zreh{bbcò`' e` ... hcak-rk`xk.



?2

Brcxkrce hk kgkbbcò`

K` gn zîic`n ci{ck`xk k kvze`k` kbbce`k s hkxnggk hk be`-

xr{bbcò` hk ge xrk xcze ~{k z{khk` hnr g{t eork kg n{`xe s qnme n

c`xk`xnr kvze`kr {`n krck hk qk`xndn k c`be`qk`ck`xk' ~{k bnhn {è

xck`k ark`xk n ge hkmî s ~{k z{khk` hkac`cr ngiô` brcxkrce hk kgkbbcò`.

Ge bemzrkerk fkrmãxcbe

Xck`k` k` zrcmkr g{inr {`n gcmcxnbcò` hk zexk`bcn arcieríacbn' sn

~{k kg zrezce cxkmn be`xr{bxcqe gk cmzchk cr n xnmnþe {zkrcerk zer

kdkmzge n ;:: mm. hk hcîmkxre hk bnrbnn. R{ irn` qk`xndn' ~{k ng kxnr

kvk`xe hk {`ce`k rebnhn s d{`xn be` kg kvxkrcer' k kxî kqcxn`he kgzreogkmn hk gn a{in hk in. R{ c`be`qk`ck`xk' ~{k c ngie eb{rrk k` {

c`xkrcer' fn hk mn`hnrk n {`n bnn kzkbcngctnhn znrn ~{k zer mkbn`c-

tnbcò` z{khn nbbkhkr ng c`xkrcer.

N~{í fnorín ~{k zrki{`xnr... µ~{k xn`xe zer bck`xe hk nqkrín xck`k

bnhn {è hk èexre k` kg bemzrker fkrmãxcbe hkg arcieríacbe hk bnn5

Ge bemzrkerk kmcfkrmãxcbe

Xck`k` k` znrxk gn qk`xndn hk ge fkrmãxcbe k` b{n`xe n kvk`bcò`

hk a{in' c k xck`k {` mí`cme hk b{chnhe k` qcicgnr kg kxnhe hk gn

{`ce`k. Ark`xk n ge nockrxe zrkk`xn gn hkqk`xndn hk ~{k n ci{nghnh

hk zexk`bcn noerochn' gn zexk`bcn arcieríacbn k mkèr &xnmocã` eb{rrk

k` ge fkrmãxcbe# k`xrk {` 2 n {` ;+< gòicbnmk`xk k hkok' n ~{k' kg rk-

arcikrn`xk kxî reon`he bnger ng mexer kgãbxrcbe' k` qkt hk reonrge k` kgkqnzernher beme krcn hkknogk znrn eoxk`kr kg kàrcnmck`xe zrkxk`hc-

he.

Fns ~{k remzkr {`n gn`tn k` be`xrn hk gn chkn ik`krngctnhn hk ~{k

ge bemzrkerk k /~{kmn`/< fes k` hín' ge onr`cbk kmzgknhe xck`k

{` zehkr hckgãbxrcbe ngxícme s gn zrexkbbce`k be`xrn eorkxkmzkrnx{-

rn s eorkc`xk`chnhk e` kvxrnerhc`nrcnmk`xk kakbxcqn' fnbck`he bnc

cmzecogk ~{k xng kqk`x{ngchnh z{khn eb{rrcr.



?8

Ge bemzrkerk nockrxe

Zrkk`xn` gn qk`xndn n`xk nz{`xnhn s xnmocã` ~{k z{khk` {nrk

be` b{ng~{ckr cxkmn mexrct &mexer kgãbxrcbe' hk kvzgecò`' kxb.#' zkre

xck`k` kg c`be`qk`ck`xk hk gn a{in hk in zer kg zrk`nkxezn' ~{k k

hcze`k k` kg kvxrkme hkg bci÷kþng ~{k ngk ng kvxkrcer' rkh{`hn`he k`

{` mn`xk`cmck`xe m{bfe mî kqkre s zer xn`xe mî bnre.

Rkn b{ng kn kg xcze' fns {` bemze`k`xk a{`hnmk`xng k` kg irnhe hk oe`-

hnh ~{k {` bemzrker z{khk xk`kr s k kg hk { mn`xk`cmck`xe zkrcòhc-

be berrkbxe' ní beme kg hk xehe ge hkmî bemze`k`xk hkg bcrb{cxe arc-

ieríacbe.

XK@HK@BCNR NBX[NGKR

Kg irn` hknrregge xkbègòicbe k` gn anorcbnbcò` hk bemzrkerk'

d{`xe be` kg bnhn qkt mî ngxe bexe hkg mn`xk`cmck`xe' fn` hkbn`xnhe gn

anorcbnbcò` hk {`chnhk arcieríacbn aermnhn zer qnrce bemzrkerk hk

xcze fkrmãxcbe e kmcfkrmãxcbe' ark`xk n gn ezbcò` hk {` òge bemzrker

nockrxe. Gn hcqccò` hkg rckie hk nqkrín e nèrmngchnhk' k exrn rntò`

cmzerxn`xk ~{k fn ns{hnhe n kxk zrebke hk qnrcnbcò` hk brcxkrce.



?;



?1



?9

QN_CNBCE@ HK GN ZEXK@BCN A_CIE_CACBN

N qkbk' è k`be`xrnme n`xk gn `kbkchnh hk ~{k {` hkxkrmc`n-

he bcbge arcieríacbe a{`bce`k k` rkiímk`k hk xkmzkrnx{rn hcakrk`xk s

zer xn`xe' gn zexk`bcn arcieríacbn {mc`cxrnhn xnmocã` ge krî.

Znrn nqkrci{nr gn rnte`k ~{k càg{sk` n gn zexk`bcn arcieríacbn k`

bnhn rãicmk`' fkme hk rkb{rrcr n gn kvzgcbnbcò` {` zebe mî k` zrea{`-

hchnh hkg a{`bce`nmck`xe hkg bemzrker.

R{zeìnme {` bemzrker hk {` òge bcgc`hre' xng s beme k ci`c-

acbn k` gn aci{rn.

K` gn aci{rn N' kg zcxò` k k`b{k`xrn k` { z{`xe m{krxe càkrcer<

fn ggkinhe ng ac`ng hk gn bnrrkrn hkbk`hk`xk s xehe kg bcgc`hre kxî ggkè

hk in n gn zrkcò` hk kqnzernbcò` Z:' k` gn O' kg zcxò` fn kmzktnhe {

bnrrkrn hk bemzrkcò`' gn qîgq{gn hk nzcrnbcò` s hkbnrin kxî` bkrrn-

hn' kg qeg{mk` eb{znhe zer kg in hcmc`{sk s zer xn`xe n{mk`xn {

zrkcò`.

K` gn B' gn zrkcò` c`xkrcer k ci{ngn be` gn zrkcò` hk hkbnrin Z>

norck`he s hkdn`he kbnznr kg in bemzrcmche be` hcrkbbcò` ng be`hk`-

nher.

K` gn H' kg zcxò` fn ggkinhe n { z{`xe m{krxe {zkrcer' ~{khn`he{` kznbce be` {`n hkxkrmc`nhn bn`xchnh hk in k` kg c`xkrcer hkg bcgc`-

hre n gn zrkcò` Z>' ~{k è z{khk ngcr.



?6

Kxk kznbce hkèmc`nhe /kznbce m{krxe /ci`cacbn èrmngmk`xk

{` 2 ò 8+ hk gn bnrrkrn hkg zcxò` s k cmzrkbc̀ hcogk znrn zrkqk`cr ge

hnþe ~{k zehrín` ercic`nr gn hcgnxnbce`k {archn zer kg zcxò`' ockgn s

bci÷kþng.

K` gn K' kg zcxò` fn kmzktnhe { bnrrkrn hkbk`hk`xk' zkre gnqîgq{gn hk nzcrnbcò` è zehrî norcrk s zer xn`xe' è nzcrnrî in hkg

kqnzernher &~{k k kg ac` zkrki{che#' fnxn ~{k gn zrkcò` hkg in' ~{k

kxnon be`xk`che k` kg kznbce m{krxe' kn ci{ng n gn hk nzcrnbcò` Ze'

Beme qkme' kg kznbce m{krxe xck`k {`n càg{k`bcn `kinxcqn k` kg

qeg{mk` rkng oemoknhe zer {` bemzrker hk {`n hkxkrmc`nhn bcgc`hrn-

hn e qeg{mk` ikemãxrcbe onrrche zer kg mcme.

N~{í k b{mzgk gn rkgnbcò` hk ge ink4

Z > ¹ Q > = Z ? ¹ Q ? = L

Hk n~{í k hkh{bk' hk ~{k b{n`xe mnser k gn rkgnbcò` hk bemzrk-

cò` Z>%Z? xn`xe mkèr krî kg qeg{mk` rkng nzcrnhe s zer xn`xe mkèr

gn zexk`bcn arcieríacbn {mc`cxrnhn zer kg bemzrker.

KACBCK@BCN QEG[MKX_CBN

Rk hkèmc`n ní' n gn rkgnbcò` kvcxk`xk k`xrk kg qeg{mk` kakbxcqe

oemoknhe s kg qeg{mk` ikemãxrcbe onrrche zer {` bemzrker.

Zehrín zk`nrk ~{k kxk qnger z{khk kr fnggnhe hk aermn xkòrcbn

kiô` gn kb{nbcò` n`xkrcer' zkre kxe è k zecogk sn ~{k fns exre anb-

xerk ~{k mexcqn` ~{k kn hcakrk`xk kg qeg{mk` rkng oemoknhe' xngk be-

me4

Zãrhchn hk in zer hkakbxe hk nd{xk hk qîgq{gn e zcxe`k.Bngk`xnmck`xe hkg in rkarcikrn`xk' b{n`he k`xrn k` be`xnbxe be`

gn znrkhk hkg bcgc`hre.

_kh{bbcò` hkg qeg{mk` nzcrnhe zer kg nbkcxk rkarcikrn`xk hk gn

znrkhk hk gn bnmcn s hk gn bnoktn hkg zcxò`.

In rkarcikrn`xk hc{kgxe k` kg nbkcxk kvcxk`xk hk`xre hkg bcgc`hre.

Beme xehe kxe anbxerk e` cmzecogk hk kqng{nr hk aermn xkò-

rcbn' xehe ge anorcbn`xk hk bemzrkerk xck`k` { b{rqn hk kacbck`bcn

qeg{mãxrcbn mkhchn k` on`be hk zr{kon s ~{k èrmngmk`xk gn hn` kà{`bcò` hk gn rkgnbcò` hk bemzrkcò`.



?3

[` kdkmzge rkng hk gn b{rqn anbcgcxnhn zer ge anorcbn`xk' kxî

rkagkdnhe k` gn aci{rn ci{ck`xk4

BNZNBCHNH A_CIE_CACBN KRZKBCACBN

Znrn ~{k z{khn qkrk hk {`n mn`krn be`xrnxnhn gn càg{k`bcn hk

gn xkmzkrnx{rn hk kqnzernbcò` s be`hk`nbcò` k` gn zexk`bcn arcieríac-

bn' qnme n bngb{gnr znrn hcakrk`xk qngerk gn zexk`bcn rkakrchn n {` m2

hk in nzcrnhe zer kg bemzrker znrn kg rkarcikrn`xk _-?? &kg mî {{ng

k` `{kxrn {`chnhk#' hk nb{krhe be` ge qngerk k`be`xrnhe k` gn xn-

ogn berrkze`hck`xk ng /A_CIK@/ ?? kvz{kxn k` zîic`n n`xkrcerk.

Kg bîgb{ge kxî eoxk`che zer gn nzgcbnbcò` hk gn kb{nbcò`4

^ = m ¹ &c > - c ? #

He`hk4

^ = Zexk`bcn arcieríacbn kzkbíacbn.

m = Mnn hk > m2 hk in _-??.

c > - c ? = Hcakrk`bcn hk k`xngzcn k`xrk qnzer s gí~{che.



2:

Zehkme bemzreonr ~{k znrn {`n mcmn xkmzkrnx{rn hk be`hk`-

nbcò`' zer kdkmzge 8:ºB.' gn bnznbchnh arcieríacbn znn n kr hk 112'6

Arci. znrn {`n xkmzkrnx{rn hk kqnzernbcò` hk -;ºB. n kg qnger hk >:32';

Arci. znrn {`n xkmzkrnx{rn hk kqnzernbcò` hk >:ºB.

Gn bnznbchnh zer xn`xe fn n{mk`xnhe `nhn mkè ~{k k` {`18'9+' hk kxnr kqnzern`he n -;ºB. n kxnr kqnzern`he n , >:ºB.

Zer kg be`xrnrce' znrn {`n xkmzkrnx{rn hk kqnzernbcò` hk :ºB.' gn

bnznbchnh znrn {`n xkmzkrnx{rn hk be`hk`nbcò` hk 8:ºB.' k hk 966';

Arci. ark`xk n 1;;'2 Arci.' znrn {`n be`hk`nbcò` hk 1:ºB.

B{n`he k xrnh{bk n zerbk`xndk' k`be`xrnme ~{k fn hcmc`{che

k` {` >1'3+. Rc nhkmî hkg xkrmexîxcbe n`xk qcxe' be`chkrnme kganbxer zrkexîxcbe' gn qnrcnbce`k hk gn zexk`bcn arcieríacbn ~{khn` m{-

bfe mî nirnqnhn beme qnme n xk`kr ebncò` hk bemzreonr.

Hk gn xnogn hkg _-??' eoxk`kme ge qngerk4

Xkmzkrnx{rn ́ B -; : ,; ,>: ,8: ,1:

Zrkcò` Nxm. 8'2:?; ;':96: ;'3;29 1'3298 >;';131 ?8'1?>6



2>

K`xrn`he k` gn xnogn hk kacbck`bcn qeg{mãxrcbn hk gn aci{rn n`xk-

rcer be` ge hnxe hk gn rkgnbce`k hk bemzrkcò` eoxk`chn znrn ge qn-

gerk be`xkmzgnhe n`xkrcermk`xk' eoxk`kme4

_b &-;´' 8:´# = >;';131%8'2:?; = 2'1>3

_b &>:´' 8:´# = >;';131%1'3298 = ?'?88

_b &:´' 8:´# = >;';131%;':96: = 2':11

_b &:´' 1:´# = ?8'1?>6%;':96: = 8'683

Rc be` kxe qngerk k`xrnme k` gn xnogn' k`be`xrnme gn ci{ck`-

xk kacbck`bcn qeg{mãxrcbn4

Kq & -;º' 8:º# = 6:+

Kq &>:º' 8:º# = 69'6+

Kq & :º'8:º# = 62+

Kq & :º'1:º# = 92+

_kngmk`xk `{kxre bemzrker fczexãxcbe be` {` qeg{mk` oemokn-

he xkòrcbe hk >m2%f. kxî nzcrn`he ge zerbk`xndk n`xk kvz{kxe. Zer

xn`xe' gn zexk`bcn arcieríacbn kzkbíacbn ~{khn k` hkac`cxcqn hnhn zer geqngerk4

& -;º' 8:º# = 112'6.:'6 = ;2>': Arci.%f

&>:º' 8:º# = >:32'; . :'696 = 31:'> Arci.%f.

& :º' 8:º# = 966';. :'62 = 1;8'; Arci.%f. & :º'1:º# = 1;;'2.:'92 = 896'8 Arci.%f.

Rc be`chkrnme beme n`xk {`n mcmn xkmzkrnx{rn hk be`hk`n-bcò` hk 8:ºB.' gn qnrcnbcò` ~{k {ark hk kxnr kqnzern`he n -;ºB.' n kxnr

kqnzern`he n >:ºB.' k hk 6:'6+. Kxn qnrcnbcò` be`krqn`he be`xn`xk

gn kqnzernbcò` n :ºB.' ci`cacbn ~{k hk znnr hk 8:ºB. n 1:ºB. k` be`hk`-

nbcò`' {ze`k {`n hcmc`{bcò` hk ?1'3+.

‗K@ BE@BG[RCE@' [@ N[MK@XE HK GN _KGNBCÒ@ HK BEMZ_K-RCE@ GK BE__KRZE@HK [@N HCRMC@[BCE@ HK GN ZEXK@BCN A_CIE_ÍAC-

BN HK GN [@CHNH K@A_CNHE_N.”



2?

ZEXK@BCN A_CIÒ_CACBN S K@K_ICN NORE_OCHN ZE_ BEMZ_KRE_ XCZE



22

KQNZE_NHE_KR

Fnognrkme n~{í kvbg{cqnmk`xk hk ge mî {{ngk' e kn' hk ge

hkèmc`nhe /kvzn`cò` kbn/ e /kvzn`cò` hcrkbxn/< k` kgge' gn ngc-

mk`xnbcò` hkg kqnzernher k rki{gnhn zer {`n qîgq{gn hk kvzn`cò`' hk

mn`krn ~{k kg rkarcikrn`xk k kqnzern xexngmk`xk k` kg c`xkrcer hk ge

x{oe.

B{n`he kg ag{che n kàrcnr k ni{n' ngm{krn hk kxcgkìgcbeg' e ngiô`

exre gí~{che' bemô`mk`xk è rkakrcme n ãg beme /kàrcnher hk ni{n

hk kvzn`cò` kbn/.

Rc kg ag{che kàrcnhe k ncrk' k gk hkèmc`n

/onxkrín hk kvzn`cò` hcrkbxn/.



28

K@A_CNHE_KR HK NI[N

Kvcxk` aermn be`xr{bxcqn hcqkrn' zer kdkmzge kg rkzrkk`xn-

he nrrcon k hk /x{oe k` fer~{cggn/' mck`xrn ~{k kg hk gn aci{rn c-

i{ck`xk k hk /x{oe rkbxe/.



2;

Kg ni{n n kàrcnr bcrb{gn zer kg kznbce ~{k ~{khn k`xrk kg c`xkrcer

hk gn bnmcn s kg kvxkrcer hk ge x{oe' ck`he eogcinhn n rkberrkr {` bcr-

b{cxe k` tcitni' kiô` gn hczecbcò` hk {`n krck hk onagk e kznrnherk.

Kxe kznrnherk k bngb{gn` hk

aermn kvfn{xcqn' xn`xe k` { kznrnbcò`

beme k` kg kimk`xe bcrb{gnr ~{k k ber-

xn' k` nrn hk {` mnser nzreqkbfnmck`-

xe hkg c`xkrbnmoce xãrmcbe.

Kg rkarcikrn`xk bcrb{gn zer kg c`xkrcer hk ge x{oe' fnbck`he xn`xe

rkberrche beme zer bîgb{ge fnsn` ngche' be` kg ac` hk ~{k gn qkgebchn-

hk kn` ezxcmn s kg rk`hcmck`xe hk c`xkrbnmoce mnser. Xnmocã` k

hcze`k`' k` kg c`xkrcer hk ge x{oe zer ge ~{k znn kg rkarcikrn`xkgí~{che' {`n kxrkggn hk ng{mc`ce hk zkracg kzkbcng' be` kg mcme ac` hk

n{mk`xnr rk`hcmck`xe.

ONXK_CN HK KVZN@RCE@ HC_KBXN

Kxn aermnhn zer {` krzk`xí` hk x{oe hk beork s {` be`d{`xe e

zn~{kxk hk ngkxn hk ng{mc`ce ògchnmk`xk {`che ng krzk`xí` hk x{oe hk

beork' me`xnhe k` {` mnrbe mkxîgcbe4 kg ncrk cmz{gnhe zer qk`xcgnhe-rk k fnbk znnr n xrnqã hk kxk /rnhcnher/ zreh{bcã`hek { kàrcn-

mck`xe.

Kg hckþe hk ge bcrb{cxe hkg rkarcikrn`xk' kgkbbcò` hkg hcîmkxre

hk bnzcgnrk hk ngcmk`xnbcò` hk bnhn bcrb{cxe' qkgebchnhk hkg ncrk' `ômk-

re hk ngkxn zer z{ginhn' kxb.' e` znrîmkxre ~{k nbxôn` hkbccqnmk`xk

k` kg rk`hcmck`xe hk c`xkrbnmoce s ~{k zer {z{kxe fn hk kr mkxcb{ge-

nmk`xk bngb{gnhn.



21

BE@HK@RNHE_

Gn mccò` hkg be`hk`nher hk`xre hkg bcrb{cxe arcieríacbe k gn hk

kàrcnr s be`hk`nr kg in rkarcikrn`xk zrebkhk`xk hkg bemzrker' zer

bkcò` hk bnger n {` ag{che kvxkrcer.

Kg bnger ~{k kg rkarcikrn`xk xck`k ~{k hccznr k` kg be`hk`nher' k

{mn hkg ~{k noerocò k` kg kqnzernher &zexk`bcn arcieríacbn hk gn {`c-

hnh# s n~{kg ~{k k fn zreh{bche k` kg bemzrker zer kg xrnonde rkngctn-

he k` gn bemzrkcò`.

N xcx{ge càermnxcqe' kvze`kme n be`xc`{nbcò` {`n xnogn hk

/bekacbck`xk hk zreh{bbcò` xãrmcbn/ ~{k zkrmcxk beèbkr kg bnger ~{k

fn hk hccznrk k` kg be`hk`nher k` a{`bcò` hk gn xkmzkrnx{rn hk kqn-

zernbcò` s be`hk`nbcò`' be` ege m{gxczgcbnr gn zexk`bcn arcieríacbn hk gn{`chnh zer kg bekacbck`xk k`be`xrnhe k` kggn.

BEKACBCK@XK HK Z_EH[BBCE@ XK_MCBN K@ BEMZ_KR:_KR FK_MKXCBER s RKMCFK_MKXCBER

@ermngmk`xk' kg anorcbn`xk hk k~{cze arcieríacbe hn beme hnxe

a{`hnmk`xngk gn zexk`bcn arcieríacbn s gn zexk`bcn noerochn hk aermn

~{k z{khk bngb{gnrk aîbcgmk`xk kg bnger n hccznr k` kg be`hk`nher.

Zer kdkmzge4 Zexk`bcn arcieríacbn --;:.::: Aci.%f.

Zexk`bcn noerochn-- ?: Ly.

Kg bnger n hccznr k` kg be`hk`nher4

^=;:.::: ,?: ¹ 61: = ;:'::: , >9.?:: = 19.?:: Lbng%f.

XKMZK_NX[_N HK

KQNZE_NBCÒ@ K@ ´ B X¤ hk

Be`hk`nbcò`

k` ´B-?; -?: ->; ->: -; : ; >:

>.89 >.8> >.21 >.2> >.?9 >.?2 >.?: >.>9>.;> >.8; >.23 >.28 >.2: >.?1 >.?2 >.?:

>.;; >.83 >.82 >.26 >.22 >.?3 >.?1 >.?2

>.1? >.;8 >.89 >.8? >.29 >.22 >.?3 >.?1

>.13 >.1: >.;2 >.89 >.8? >.29 >.22 >.?3

>.99 >.16 >.1: >.;2 >.89 >.8? >.29 >.22

2:2;

8:

8;

;:

;;



29

XCZER HK BE@HK@RNHE_KR

Hkzk`hck`he hkg ag{che ~{k k kmzgkk znrn be`ki{cr ~{k k be`-

hk`k kg in rkarcikrn`xk' k hcxcì{k` he xcze4 rkarcikrnhe zer ni{n s

rkarcikrnhe zer ncrk.

Be`hk`nbcò` zer ni{n

Kg mî bemô`mk`xk kmzgknhe k kg hkèmc`nhe /meèogeb ferc-

te`xng c`{`hnhe hk bnrbnn s fnt hk x{oe/ ' n~{í rkzrkk`xnhe<

Kg rkarcikrn`xk k`xrn zer gn znrxk {zkrcer' k k`b{k`xrn be` kg fnt

hk x{oe n {`n xkmzkrnx{rn mî ondn' bkhk bnger s k be`hk`n eork gn

{zkracbck kvxkrcer hkg fnt hk x{oe zer b{se c`xkrcer bcrb{gn ni{n. Ge

x{oe hkg fnt ik`krngmk`xk e` hk beork be` ngkxn kvxkrcerk znrn be`-

ki{cr {`n mnser {zkracbck hk xrn`mccò`. Gn bnrbnn s ge bnoktngk k`

nbkre. Gn geìcx{hk' `ômkre hk zne hkg ni{n' qkgebchnh' hczecbcò`

hk x{oe' kxb.' fn` hk kr zkrakbxnmk`xk bngb{gnhn s xck`k` {`n kèrmkcàg{k`bcn k` gn xrn`mccò` hk bnger.

Be`hk`nbcò` zer ncrk

Kg rkarcikrn`xk bcrb{gn zer kg c`xkrcer hk {` krzk`xí` ~{k k nxrn-

qknhe zer {`n berrck`xk hk ncrk zreh{bchn zer {è qk`xcgnherk. Kg kr-

zk`xí` hk x{oe &ik`krngmk`xk hk beork# hcze`k hk {` zn~{kxk hk ngk-

xn &ik`krngmk`xk hk ng{mc`ce# n ac` hk be`ki{cr {`n mnser {zkracbckhk xrn`mccò`. Kg be`d{`xe k k`nmogn k` {` mnrbe mkxîgcbe znrn hnrgk

rcichkt< rkbcok k`xe`bk kg èmork hk /onxkrín be`hk`nhern/.



26

QNGQ[GN HK KVZN@RCE@ XK_MERXNXCBN

Kxk kgkmk`xe hkg bcbge arcieríacbe' k kg k`bnrinhe hk mn`xk`kr kg

bn{hng `kbknrce hk gc~{che rkarcikrn`xk' n xrnqã hkg kqnzernher' znrn

be`ki{cr gn zrkxnbce`k arcieríacbn rk~{krchn' be` kg mîvcme rk`hc-

mck`xe. Rc gn bn`xchnh hk gí~{che k zk~{kþn' gn {zkracbck hkg kqnzernher

è k nzreqkbfn kacbntmk`xk4 mck`xrn ~{k' c gn bn`xchnh hk gí~{che k

kvbkcqn' è xck`k g{inr gn bemzgkxn kqnzernbcò`' be` be`kb{k`bcn irn-

qk.

Znrn be`ki{cr gn bn`xchnh hk gí~{che zrkbcn k` kg kqnzernher' gn

qîgq{gn qnrín kg irnhe hk nokrx{rn hkg ercacbce hk zne' hk {`n mn`krn

n{xemîxcbn' nbx{n`he hkg mehe ci{ck`xk4

Gn zrkcò` hkg o{goe ~{k nbxôn k` gn znrxk {zkrcer hkg hcnarnimn'xk`hck`he n norcr kg ercacbce hk zne' k be`xrnrrkxnhn zer gn hk kqnzern-

bcò` &xemnhn mkhcn`xk kg kb{ngctnher hk zrkcò`' k` gn gí`kn hk nzcrn-

bcò`# s gn hkg m{kggk ~{k xck`hk n bkrrnrge.

Kg k~{cgcorce znrn {`n be`hcbce`k hkxkrmc`nhn' k be`ci{k

b{n`he gn zrkcò` hkg o{goe' k ci{ng n gn {mn hk gn hk kqnzernbcò` s gn

hkg m{kggk. Rc k` kxk z{`xe n{mk`xn gn bnrin xãrmcbn hkg kqnzernher' kg

gí~{che xkrmc`nrî n`xk hk kqnzernrk' n{mk`xn`he { xkmzkrnx{rn< kxk

n{mk`xe k xrn`mcxche n gn mktbgn hk gí~{che-in k`bkrrnhe k` kg o{goe'n{mk`xn`he { zrkcò` s zer xn`xe' norck`he kg zne hk gí~{che fnxn

be`ki{cr rkxnogkbkr kg z{`xe hk k~{cgcorce. Rc zer kg be`xrnrce' hkbck`-

hk gn bnrin xãrmcbn' gn xkmzkrnx{rn hkg in n gn ngchn hkg kqnzernher

hkbck`hk s zer xn`xe' gn zrkcò` k` kg o{goe hk gn qîgq{gn xnmocã`' bk-

rrn`he kg zne hk gí~{che ng kqnzernher.



23

GN [@CHNH K@A_CNHE_NµBE@HK@RNHN ZE_ NC_K E BE@HK@RNHN ZE_ NI[N5

Gn hccznbcò` hkg bnger k` kg be`hk`nher kmzgkn`he {` mkhce {

exre k ckmzrk mexcqe hk h{hn zer znrxk hkg {{nrce hk {`n c`xngn-

bcò`. Gk fn` hcbfe.... gk fn` bemk`xnhe .... /~{k gn hk ni{n k mkder ~{k gn

hk ncrk/ s n~{í ~{khn kxn`bnhe b{ng~{ckr rnte`nmck`xe. C`xk`xkme ze-

`kr ngi{`n g{t k` kg n{`xe.

Fnognme hk ni{n rkb{zkrnhn be` xerrk hkdn`he hk gnhe exrn nzgc-

bnbce`k be` ni{n zkrhchn sn kn hk zete' rce. kxb. Kg zrc`bczce hk a{`bce-

`nmck`xe hk {`n xerrk hk rkarcikrnbcò`' k kg kàrcnmck`xe hkg ni{n nzre-

qkbfn`he kg bnger ~{k noerok znrxk hk gn mcmn b{n`he k kqnzern' k`-

arcn`he ng rkxe ~{k ~{khn. @e k` qnè k` ngi{è zník k gk hkèmc`n/xerrk kqnzernxcqn/.



8:

Gòicbnmk`xk kxnme kqnzern`he kg ni{n z{rn s k` kg ni{n ~{k

~{khn' k kxî c`brkmk`xn`he gn bn`xchnh hk ngk' kgkqn`he gn be`bk`-

xrnbcò` hk gn xkmchn bng.

Kvcxk {` nrrnxrk hk iexn hk ni{n n bn{n hk gn berrck`xk hk ncrk

~{k k brkn be` ge qk`xcgnherk ~{k z{khk xk`kr qngerk bemzrk`hchek`xrk kg :'? s kg :'6+ hkg bn{hng hk ni{n k` bcrb{gnbcò`.

N ac` hk ~{k è zreirkk hk aermn zkgciren gn be`bk`xrnbcò` hk

bng' fn hk rkze`krk ng mkè gn mcmn bn`xchnh hk ni{n ~{k k kqnzerò

s hkdn`he kbnznr gn ~{k eork zer kg rkoenhkre e ock` zer kg ircae hk

z{rin hk gn xerrk.

Zer xn`xe' kg ni{n be`{mchn k` {`n xerrk znrn hccznr >::.:::

Lbng%f k4

Ni{n kqnzernhn4 >::.:::%;23 = >6; g%f.

Ni{n nrrnxrnhn4 >::.:::%; v :'::; = >:: g%f.

Ni{n rkz{kxn = Ni{n kqnzernhn = >6; g%f.

Rck`he4 ;23 kg bnger gnxk`xk hk qnzerctnbcò` hkg ni{n'

; kg ngxe xãrmcbe hkg ni{n n gn k`xrnhn s ngchn.

K` rk{mk`' kxnme be`{mck`he 89: g%f. znrn kgcmc`nr gn>::.::: Lbng%f.

B{n`he qknme kg bîgb{ge hkg bekacbck`xk igeong hk xrn`mccò` hk

bnger' qkrkme ~{k k qn` {mn`he gn rkcxk`bcn xãrmcbn. Gn /bng/

xck`k gn znrxcb{gnrchnh n`òmngn ~{k k fnbk cèg{ogk b{n`xe mnser k gn

xkmzkrnx{rn s beme kg z{`xe mî bngck`xk e` ge x{oe hkg be`hk`n-

her' k crî hkzecxn`he k` kgge aermn`he {`n bnzn ~{k cmzchn ~{k k

xrn`mcxn kg bnger.

Gn rkzkrb{ce`k eork kg bcbge arcieríacbe e` c`mkhcnxn s k rk-

agkdn` k` gn kb{nbcò` ik`krng hk xrn`mccò` hk bnger4

^ = L ¹ R ¹ Θx.

Rc L k qn fnbck`he bnhn qkt mkèr znrn ~{k zkrmn`ktbn be`xn`-

xk gn ci{nghnh' `kbknrcnmk`xk fn hk fnbkrk mnser kg Θx .



8>

Beme kxn Θx hkac`k gn hcakrk`bcn kvcxk`xk k`xrk gn xkmzkrnx{rn hk

k`xrnhn hkg ni{n s gn hk be`hk`nbcò`' bnhn qkt k fnrî mnser gn xkmzk-

rnx{rn hk be`hk`nbcò`.

Beme qkínme k` gn zexk`bcn kzkbíacbn' b{n`xe mnser k gn xkmzk-

rnx{rn hk be`hk`nbcò` mkèr k gn zexk`bcn arcieríacbn.Nhkmî hkg zreogkmn hk gn /bng/ kxî kg hkg mn`xk`cmck`xe ng xrn-

xnrk hk {` bcrb{cxe nockrxe kvz{kxe n rkbeikr xehe xcze hk kgkmk`xe

kvxrnþe< kg be`xreg hk ngin be` zreh{bxe ~{ímcbe< kg qnbcnhe hkz{ã

hk gn znrnhn s { gcmzcktn be`kb{k`xk' kxb.

K` be`hk`nbcò` zer ncrk è kqcxnme hk xehe kxk renrce hk hcac-

b{gxnhk ng xk`kr {` ag{che gcmzce s irnx{cxe.

Kg zer~{ã è k fn hcz{kxe fnxn nfern be` mî zrea{cò` gn be`-hk`nbcò` zer ncrk fns ~{k nbfnbnrge ô`cbnmk`xk n nzkbxe xkbègòic-

be k` { anorcbnbcò`.

Be`xr{bxcqnmk`xk e` onxn`xk hcakrk`xk. Mck`xrn ~{k kg hk

ni{n kxî aermnhe zer {` fnt hk x{oe hk beork hk`xre hk {`n bnrbnn

hk nbkre be` {`n hcmk`ce`k rkh{bchn< kg hk ncrk' aermnhe zer x{oe

hk beork s ngkxn hk ng{mc`ce' fn hk xk`kr irn`hk hcmk`ce`k ng kr

m{s zk~{kþe kg bekacbck`xk hk xrn`mccò` hk bnger be` rkzkbxe ng ncrk s

zer xn`xe' kvcicr irn`hk {zkracbck hk xrn`mccò`. Hk ngi{`n aermn kbe`chkrnon ~{k gn be`hk`nbcò` zer ncrk fnoín ~{k bcrb{`brcocrgn ô`c-

bnmk`xk n ge nbe`hcbce`nherk hk ncrk hk xcze hemãxcbe.

Gn c`xngnbcò` hk {`n {`chnh hk be`hk`nbcò` zer ncrk be` qk`xcgn-

herk nvcngk' fn hk fnbkrk k` kznbce gcork' kvk`xe hk eoxîb{ge ~{k

z{khn` cmzkhcr kg zne hkg ncrk' xn`xe k` gn k`xrnhn n gn onxkrín be`hk`-

nhern' beme k` gn ngchn hk ge qk`xcgnherk. Kxî` hckþnhn znrn kr

c`xngnhn n gn c`xkmzkrck s zer xn`xe z{khk` kr hcz{kxn kznbce è

nzreqkbfnogk beme xkbfe s xkrrntn.



8?

ZEXK@BCN A_CIE_CACBN K@ NI[N S K@ NC_K

Rckmzrk k eodkxe hk hcb{cò` kxk xkmn n gn fern hk zreskbxnr

{`n c`xngnbcò`.

_kxer`n`he n gn zexk`bcn arcieríacbn kzkbcacbn hk {` bcbge arcieríac-be' qkme ~{k kakbxcqnmk`xk b{n`xe mnser k gn xkmzkrnx{rn hk be`hk`-

nbcò` mkèr k gn zexk`bcn arcieríacbn. Qnme k`xe`bk n bemzreonr ~{k

hcakrk`bcn hk xkmzkrnx{rn z{khk` fnokr k` nmoe bne.

Gn xkmzkrnx{rn hk zreskbxe znrn gn he be`hk`nbce`k e`

èrmngmk`xk4

K` ni{n = Xkmzkrnx{rn k`xrnhn ni{n , >: ´B = 2: , >: = 8: ´B

K` ncrk = Xkmzkrnx{rn hkg ncrk nmock`xk , >8 ´B = 2; , >8 = 83 ´B

Kakbxcqnmk`xk krín k` be`hcbce`k èrmngk' càkrcer gn hk ncrk

~{k gn hk ni{n. Zkre h{rn`xk gn ãzebn hk qk`hcmcn k` m{s zebn te`n

kznþegn k {zkrn gn xkmzkrnx{rn mkhcn nmock`xk hk ?;ºB.' zer xn`xe4

K` ncrk = ?; , >8 = 23 ´B.

K` be`bg{cò`' n qkbk' k` be`hk`nbcò` zer ncrk' gn zexk`bcn arc-

ieríacbn hk gn {`chnh z{khk kr mnser ~{k gn mcmn be`hk`n`he zer

ni{n.

Rc be`chkrnme kg be`xkvxe xexng hk gn c`xngnbcò`' z{khk ngcr

k`kriãxcbnmk`xk hkanqernogk gn be`hk`nbcò` zer ni{n ark`xk n gn hk

be`hk`nbcò` zer ncrk. k` kakbxe' gn zexk`bcn noerochn znrn {`n mc-

mn zexk`bcn arcieríacbn {mc`cxrnhn krî`4

Zer kg bemzrker 4 Be`hk`nbcò` zer ncrk = Be`hk`nbcò` zer ni{n.

Zer qk`xcgnbcò`4 Ge hk gn onxkrín hk be`hk`nbcò`

p Ge hk gn xerrk hk kàrcnmck`xe

Zer oemon hk ni{n arín 4 Be`hk`nbcò` zer ncrk = Be`hk`nbcò` zer ni{n.

Zer oemon ni{n be`hk`nbcò` 4 @e kvcxk k` be`hk`nbcò` zer ncrk.

G{kie k` gn c`xngnbcò` hk be`hk`nbcò` zer ni{n' z{khk fnokr {`

be`{me k`kriãxcbe {zkrcer hkoche n gn oemon ~{k {mc`cxrn kg ni{n n

gn xerrk ~{k k c`kvcxk`xk k` gn be`hk`nbcò` zer ncrk. Zer xn`xe' k` qk`-

hcmcn' n ci{nghnh hk zexk`bcn arcieríacbn zreh{bchn' gn zexk`bcn noerochn

zer {`n c`xngnbcò` be`hk`nbcò` zer ncrk' z{khk kr mkèr ~{k k` {`nhk be`hk`nbcò` zer ni{n.



82

OEMON HK BNGE_

Zecogkmk`xk gn h{hn mî e mkè ik`krngctnhn eork kxk xãrmc-

è ~{k kxî n `cqkg hk bnggk zer kr bnhn qkt hk mî arkb{k`xk {e' kn

zrkbcnmk`xk kg qebnoge. ^{ctî fnorín ~{k fnognr hk {`chnhk ~{k oem-

okn` bnger.

K` kg k~{kmn ~{k rkzreh{bínme kg bcbge arcieríacbe' ng fnognr hkg

kqnzernher ge fnbínme beme {` c`xkrbnmocnher ~{k xk`ín zer mccò`

bnzxnr bnger hkg mkhce ~{k gk rehknon' e kn' kàrcnon kxk mkhce.

Zer kg be`xrnrce' kg be`hk`nher krn kg c`xkrbnmocnher ~{k xk`ín

zer mccò` bkhkr bnger e kn' bngk`xnr n exre mkhce.

Z{k ock`' b{n`he {` bcrb{cxe arcieríacbe ge nzreqkbfnme znrn

bnzxnr bnger' e kn' kàrcnr' ge hkèmc`nrkme /[@CHNH K@A_CNHE_N/ '

s c ge nzreqkbfnme znrn bngk`xnr' ge hkèmc`nrkme /OEMON HK BN-

GE_/.

[`n {`chnh nbe`hcbce`nhern hk qk`xn`n bgîcbn' k bemzerxn beme

kàrcnhern znrn kg c`xkrcer hkg >: bng. he`hk kxî s bngkanbxern znrn gn bn-

ggk. Rc èexre k` c`qckrè aícbnmk`xk gk hcãkme {` icre hk >6:´' kxn-me n`xk {`n oemon hk bnger zer ge ~{k rkzkbxn ng nzreqkbfnmck`xe' sn

~{k' kxnme reon`he bnger ng ncrk hk gn bnggk s ge kxnme c`xreh{bck`he

k` gn fnocxnbcò` n nbe`hcbce`nr. K zrkbcnmk`xk gn c`qkrcò` hk bcbge' kg

bnmoce hk . znzkgk fnbck`he ~{k kg be`hk`nher k bemzerxk beme kqn-

zernher s ng be`xrnrce' ge ~{k hk {`n mn`krn n{xemîxcbn k rkngctn k` gn

{`chnhk be` oemon hk bnger ~{k k bemkrbcngctn`. [`n qîgq{gn hk b{n-

xre qín k gn k`bnrinhn hk be`ki{cr kxn c`qkrcò`.

Beme zrc`bczce' sn a{k k`{`bcnhe zer BN_@EX' n{`~{k x{qe g{inr

{` hknrregge zexkrcer zer Gerh LKGQC@ s { zrc`bczce hk bemkrbcngctn-

bcò` a{k k` kg >.3;: k` ge KK.[[.

Gn oemon hk bnger zer xn`xe' k {` cxkmn hk nzreqkbfnmck`xe

k`kriãxcbe k` kg ~{k' kg bnger kvcxk`xk n {` `cqkg hk xkmzkrnx{rn onde' k

ggkqnhe n {` `cqkg hk xkmzkrnx{rn ngxe' k` he`hk xck`k g{inr { nzreqk-

bfnmck`xe.



88

Gn oemon hk bnger k hkèmc`n` be` he nzkggche. Kg zrcmkre rkzrk-

k`xn kg ag{che hkg b{ng k kvxrnk bnger s kg ki{`he kg ag{che ng ~{k k bk-

hk s he`hk xck`k g{inr { nzreqkbfnmck`xe. Hk kxn aermn z{khk` kvcxcr

gn bemoc`nbce`k ci{ck`xk4

ncrk-ncrk<

ncrk-ni{n<

ni{n-ncrk<

ni{n-ni{n.

Rckmzrk {rik gn zrki{`xn hk ~{k bn`xchnh hk bnger zehkme kv-

xrnkr n {` ncrk n :ºB. e' zer è hkbcr' be` xkmzkrnx{rn mî ondn. Z{k

ock`' xehe ag{che fnxn kg bkre noeg{xe' e kn' -?92ºB. xck`k bnger s zer

xn`xe z{khk kr kvxrníhe' kg zreogkmn rnhcbn k` k`be`xrnr gn aermn hkbe`ki{crge.

Kg bnger ckmzrk qn hkg aebe mî bngck`xk ng mî aríe' zer xn`xe' c k

~{ckrk kvxrnkr bnger hk {` ncrk n ->;ºB.' ge ~{k k fnrî k brknr {`n be`-

hcbce`k hk -?:ºB ò ?;ºB' hk aermn ~{k kg bnger n /`cqkg ngxe ->;ºB/ znk

ng /`cqkg onde -?:ºB/.

Qegqck`he n gn aci{rn hk rkakrk`bcn' kg bekacbck`xk hk kacbck`bcnk`kriãxcbn' qck`k hkac`che zer gn rkgnbcò`4

B.K.K. = gí`kn NO , gí`kn OB % gí`kn OB = Bnger bkhche k` kg be`hk`nh.% Bnger hkg xrnonde hk bemzrkcò`

Kg arcieríacbe hk bnn' znrn èexre k bemzerxn beme {`n oemon

hk bnger. Kvxrnkme kg bnger hk ge ngcmk`xe be`xk`che k` { c`xkrcer

mkhcn`xk kg beìkgnher &kqnzernher# s kxk bnger k bkhche ng nmock`xkhkg rkbc`xe he`hk kxî kg arcieríacbe zer gn rkdcggn zexkrcer

&be`hk`nher#.

Xk`kme rkngmk`xk {`n oemon hk bnger ncrk-ncrk.



8;

X_N@RMCRCE@ HK BNGE_. NRZKBXER IK@K_NGKR

Xn`xe kg kqnzernher beme kg be`hk`nher e` c`xkrbnmocnherk

hk bnger' ní beme ge hcxc`xe kgkmk`xe ~{k g{kie qnme n kmzgknr

znrn kg kàrcnmck`xe hkg mexe e hkg qcè. K `kbknrce zer xn`xe' xrnxnr

kxk xkmn n{`~{k kn hk mn`krn emkrn znrn ~{k z{khn erck`xnrk hk

ngi{`n mn`krn' kg brcxkrce hk kgkbbcò` hk ge bemze`k`xk hk gn c`xngn-

bcò`' hk be`xreg hk xkmzkrnx{rn e hk kxnocgctnbcò`.

Kg bnger bkhche zer {` mkhce n {`n xkmzkrnx{rn x > n exre n {`n

xkmzkrnx{rn x ? qck`k hkac`che zer gn kb{nbcò`4

^ = L ¹ R ¹ &x> - x?#

K` he`hk4

^ = Bn`xchnh hk bnger bkhchn k` Lbng.%f.

L = Beka. igeong hk xrn`mccò` hk bnger k` Lbng%m? ¹ f ¹ ´B

R = R{zkracbck hk be`xnbxe hk ge mkhce k` m?

&x> - x?# = Hca. hk xkmzkrnx{rn k`xrk ge he mkhce k` ´B.

K` kg zrebke hk c`xkrbnmoce xãrmcbe' gn xkmzkrnx{rn c`cbcng x>

hkbck`hk zn{gnxc`nmk`xk s gn x? n{mk`xn' rntò` zer gn ~{k ng bnoe hk

{` bckrxe xckmze gn hcakrk`bcn hk xkmzkrnx{rn sn è krî x> - x? c è ~{k

fnorî hcmc`{che s zer xn`xe gn bn`xchnh hk bnger xrn`mcxche krî mk-

èr.

Znrn be`chkrnr kxn qnrcnbcò` k c`xreh{bk k` gn aòrm{gn n`xkrcerkg be`bkzxe hk xkmzkrnx{rn mkhcn geinríxmcbn Θxm. ~{k hkac`k gn hcak-

rk`bcn hk xkmzkrnx{rn h{rn`xk xehe kg zrebke.

Gn kb{nbcò` ik`krng hk gn xrn`mccò` hk bnger ~{khn hk gn aermn4

^ = L ¹ R ¹ Θxm.



81

BEKACBCK@XK IGEONG HK X_N@RMCRCE@ HK BNGE_

B{n`he gn xrn`mccò` xck`k g{inr k`xrk he ag{che ~{k kxî` kzn-

rnhe zer {`n znrkh' kg bnger fn hk xrn`mcxcrk n gn {zkracbck hk gn zn-

rkh' nxrnqknr zer be`h{bbcò` xehn gn znrkh fnxn k`be`xrnr gn exrn {-

zkracbck s zer ac`' xrn`mcxcrk ng exre mkhce.

Xehe kg zrebke xck`k { rkzrkk`xnbcò` n`ngíxcbn zer4

&>%L# = &>% ξ > # , &k% μ #, &>% ξ ? #

K` he`hk4

L = Bekacbck`xk igeong hk xrn`mccò` hk bnger.

ξ > = Bekacbck`xk hk xrn`mccò` hkg mkhce > n gn znrkh.

k = Kzker hk gn znrkh.

μ = Be`h{bxcqchnh xãrmcbn hkg mnxkrcng hk gn znrkh.

ξ ? = Bekacbck`xk hk xrn`mccò` hkg mkhce ? n gn znrkh.

Gn hczecbcò` k` aermn c`qkrn' rkzrkk`xn gn rkcxk`bcn ng zne

hkg bnger s gòicbnmk`xk gn rkcxk`bcn k qn` {mn`he. Hk kxn aermn

b{n`he gn znrkh kxî aermnhn zer qnrcn bnzn hk hcqkre mnxkrcngk' k

m{s cmzgk bngb{gnr kg bekacbck`xk igeong4

&>%L# = &>% ξ > # , &k% μ #, &k¸% μ¸#, &k¸¸% μ¸¸ #, ‡ ,&>% ξ ? #

Be` kxe fns ~{k fnbkrk n gn chkn hk gn irn` hcacb{gxnh be` gn ~{k

b{k`xn kg zreskbxcxn hk c`xkrbnmocnherk hk bnger n gn fern hk fnbkr kg

bîgb{ge hkg bekacbck`xk L ' z{k fns ~{k rkb{rrcr n gn nzgcbnbcò` hk aòrm{-

gn ik`krngmk`xk hk xcze kvzkrcmk`xng.



89

Z_EBKRE HK BNGB[GE

N xíx{ge hk kdkmzge' qnme n kvze`kr gn aerm{gn ~{k ezerxn` kg

bîgb{ge hkg bekacbck`xk igeong hk xrn`mccò` hk bnger znrn {` c`xkrbnm-

ocnher m{gxcx{o{gnr' ggnmnhe xnmocã` /fnt hk x{oe s bnrbnn/ hk nbkre

cèvchnogk be` x{oe hk ?1%?6 mm. hk hcîmkxre' kznrnhe k`xrk kdk 22

mm. s hcz{kxe n xrkoegcgge.

Kg zrcmkr zne k kg bîgb{ge hk ξ >' bekacbck`xk hk xrn`mccò` hkg

ni{n n gn znrkh kvxkrcer hkg x{oe.

K hk nzgcbnbcò` gn kb{nbcò` hk @{kgx .

@{ = ξ > ¹ &Hk % μ# = :'2; ¹ a ¹ _k :';9 ¹ Z r E.2>

K` he`hk4

Hk = Hcîmkxre kvxkrcer hkg x{oe k` m.

μ = Be`h{bxcqchnh bngeríacbn hkg ni{n k` Lbng%m%f%´B

a = _kgnbcò` hk hcxrco{bcò` ikemãxrcbn hk ge x{oe.

_k = @ômkre hk _ksègh = Q ¹ &Hk % Ϟ #

Z r = @ômkre hk Zrn`h > = H ¹ Ͼ ¹ B z

Rck`he n { qkt4

Q = Qkgebchnh hkg ag{che k` kg ni{n k` m%ki.

Ϟ = Qcbechnh bc`kmîxcbn k` m?%ki.

B z = Bnger kzkbíacbe k` Lbng%Li%´B

Ͼ = Hk`chnh k` Li%m2.

[`n qkt fnggnhe ξ > fn hk berrkicrk k` a{`bcò` hkg `ômkre hk acgn

hk x{oe s hkg îì{ge hk c`bchk`bcn hk gn berrck`xk eork kgge.



86

Kg ki{`he zne k kg hk bngb{gnr kg ξ ? <bekacbck`xk hk xrn`mccò`

hkg mexe n gn znrkh c`xkr`n hkg x{oe. K` kxk bne k nzgcbnogk gn aòrm{-

gn4

@{ = :':29¹&_k ->6:# ¹ Z x > , &h f %G# =ξ ? ¹ &Hk % μ #

Bngb{gnhe kxe bekacbck`xk znrbcngk k bngb{gn kg igeong ~{k

zehrín kr zer kdkmzge4

>%L = >%1:19 , > ¹ >: %>8 , >%>231'6

Hk n~{í k hkh{bk4

L = >:;: Lbng%m?%f%´B.

Beme bekacbck`xk igeong hk xrn`mccò` hk bnger.

Qkme gn irn` bn`xchnh hk anbxerk ~{k c`xkrqck`k` k` kg bîgb{ge hk

kxk bekacbck`xk' hkhk ge z{rnmk`xk aícbe' xkrmehc`îmcbe s fnxn ge

hk xcze qnrcnogk' k` ge ~{k k c`bg{sk a{`hnmk`xngmk`xk gn qkgebchnh.

Zer xn`xe' {` c`xkrbnmocnher fn hk kr bngb{gnhe znrn bnhn bne

kzkbíacbe' nxk`hck`he ng zrebke ~{k k qn n hknrreggnr' kxnogkbck`he

{`n anmcgcn hk b{rqn' k` a{`bcò` hk gn qkgebchnh s hk n~{í hkxkrmc`nr

b{ng krín kg bemzerxnmck`xe ~{k xk`hrín znrn hcakrk`xk be`hcbce`k hk

n~{kggn ~{k gk crqckre` hk onk znrn kg zreskbxe.

Be`qck`k fnbkr èxnr ~{k kg anbxer hk xrn`mccò` hk bnger k a{`-

bcò` xnmocã` hkg xckmze.

Kxk hnxe krqcrî znrn hkxkrmc`nr k` {`n be`hcbce`k kzkbíacbn

kg xckmze `kbknrce znrn { kàrcnmck`xe e bngk`xnmck`xe' sn ~{k fns

zrebke k` kg ~{k kxk hnxe z{khk ggkinr n be`xcx{cr kg nzkbxe a{`hn-

mk`xng hkg zreogkmn k` kx{hce.

?%2:'9; :'8?

-2



83

QNGE_KR @E_MNGKR MNR [R[NGKR

Hk`xre hkg xkrrkè kègòicbe' zehrín` kr hk c`xkrã gn rkgnbcò` hk

bekacbck`xk hk xrn`mccò` bnger ~{k hkxnggnme s ~{k kxî` bngb{gnhe

zer hcakrk`xk aòrm{gn be` {acbck`xk rcier bck`xíacbe s be`chkrnhn k`

{` nmzgce bnmze hk nbx{nbcò`4

C`xkrbnmocnher hk zgnbn ‡‡‡‡‡‡‡‡‡‡‡‡..‡?.;:: n 2.::: Lbng.%m?.f.´B C`xkrbnmocnher x{o{gnr hk x{oe k` x{oe‡‡‡‡.. >.::: n >.8:: Lbng.%m?.f.´B. C`xkrbnmocnher m{gxcx{o{gnr &bnrbnn s x{oe#‡. 9:: n >.>:: Lbng.%m?.f.´B.

Zgnbn rkarcikrn`xk {mkrichn‡‡‡‡‡‡‡‡‡...‡. >;: n ?;: Lbng.%m?.f.´B. Kqnzernher hk rnbnherk‡‡‡‡‡‡‡‡‡‡‡‡‡‡‡.. ;EE n 9;: Lbng.m?.f.´B

Heogk bnmcn k` hkzòcxe‡‡‡‡‡‡‡‡‡‡‡‡‡‡. >;: n ?;: Lbng.%m?.f.´B Heogk bnmcn è ncg.-nmo. &ncrk k` bngmn#‡‡‡‡‡‡ . 6 n >? Lbng.%m?.f.´B Hkzòcxe rkarcikrnhe zer h{bfn Cèv ‡‡‡‡‡‡‡...>?: n >;: Lbng.%m?.f.´B

Fckrre-Kzevc . ‡‡‡...>8: n >9: Lbng.%m?.f.´B X{oe è ncg-nmock`xk &ncrk k` bngmn#‡‡‡‡‡‡‡‡‡... 6 n >? Lbng.%m?.f.´B Hkzòcxe-nmock`xk &ncrk k` bngmn#‡‡‡‡‡‡‡‡‡‡‡‡.. 2 n ; Lbng.%m?.f.´B

_k{gxn znrnhòdcbe kg qnger k`be`xrnhe b{n`he k rkarcikrn` zer

h{bfn' sn ~{k hk c`mkhcnxe {rik gn chkn ~{k kg bekacbck`xk hk xrn`mc-

cò` hk bnger fn hk kr mnser znrn kg nbkre cèvchnogk ~{k znrn kg fckrrebe` kzevc. Rc` kmonrie' ge bîgb{ge rkngctnhe znrn {` hkzòcxe hk qkrxc-

bng hk b{nxre mkxre hk ngx{rn k` nbkre cèvchnogk hk ? mm. hk kzker s

hk kxk mcme hkzòcxe k` fckrre be` ; mm. hk kzker rkb{ockrxe hk

{`n bnzn hk zc`x{rn kzevc hk :'; mm. hk kzker s zer nzgcbnbcò` hk gn

aòrm{gn4

@{ = & ξ ¹ G% μ # = :'>?3 ¹ && Θx ¹ i ¹ G # % X ¹ Ϟ # ¹ Zr

Ge qngerk eoxk`che e`4

L &cèv.# = >28 Lbng %m? f ´B

L &fckrre# = >;2 Lbng %m? f ´B

?%2

2 ?



;:

C@AG[K@BCN HK GN HC_KBBCE@ HK GN BE__CK@XK

K` gn zròvcmn aci{rn' k fn rkzrkk`xnhe hk mn`krn irîacbn kg ag{de

hk bnger ~{k xck`k g{inr k`xrk he ag{che n hcxc`xn xkmzkrnx{rn.

Znrn {`n mcmn be`hcbce`k' kg qnger hk gn hcakrk`bcn hk xkmzk-rnx{rn mkhcn geinríxmcbn 1xm hkzk`hk k` irn` mkhchn hk beme k fnin

bcrb{gnr n ge he ag{che s be`kb{k`xkmk`xk fnrî qnrcnr b{ng~{ckrn hk

ge qngerk ~{k c`xkrqck`k` k` gn aòrm{gn ik`krng hk )gn xrn`mccò` hk

bnger.

^= L ¹ R ¹ xm

Rc be`chkrnme {` bne zrîbxcbe berrkze`hck`xk n gn be`hcbce-

`k4Xkmzkrnx{rn k`xrnhn hk mexe = ?;ºB

Xkmzkrnx{rn ngchn hk mexe = >;ºB

Xkmzkrnx{rn k`xrnhn hk ni{n = 9ºB

Xkmzkrnx{rn ngchn hk ni{n = >?ºB

Ge qngerk hk ge c`brkmk`xe hk xkmzkrnx{rn mkhce geinríxmcbe

e`4

K` be`xrnberrck`xk >:'2´ B.K` k~{cberrck`xk . . . 6'29´ B.



;>

Zer xn`xe' znrn xrn`mcxcr {`n mcmn bn`xchnh hk bnger s {ze`ck`-

he ~{k ge bekacbck`xk hk xrn`mccò` hk bnger kn` ci{ngk' k zrkbcn

{`n {zkracbck hk xrn`mccò` {zkrcer k` {` ?2+ hk be`xr{crk kg c`-

xkrbnmocnher k` k~{cberrck`xk n fnbkrge k` be`xrnberrck`xk.

K` gn zrîbxcbn s n kvbkzbcò` fkbfn hk ge hk zgnbn s hk ge x{o{gn-

rk hk x{oe k` x{oe' è k zrkk`xn` k~{cberrck`xk e be`xrnberrck`xk

z{rn' cè ~{k ckmzrk e` br{tnhn.

Kg bîgb{ge hk gn hcakrk`bcn mkhcn geinríxmcbn' k rkngctn xk`ck`-

he k` b{k`xn {è bekacbck`xk hk berrkbbcò` ~{k e` a{`bcò` hkg `ômkre

hk bnmoce hk hcrkbbcò` k` gn berrck`xk s hkg îì{ge hk c`bchk`bcn eorkgn {zkracbck hk be`xnbxe.



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