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Теория твердоемкости тела. Ход Дебая

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§ 7. yeaeo?iiiay oaiei?ieinoue.

Aeey iau/iuo iaoaeeia i?e iau/iuo oaiia?aoo?ao yoi ioiioaiea
ninoaaeyao i?eia?ii 1/100. Ionthaea ynii, ii/aio oaieiaieinoue iaoaeea
aeiaieueii oi/ii iienuaaaony ?aoaoi/iie ninoaaeythuae e ii/aio caeii
Aetheiiaa e Ioe ni?aaaaeeea i?e aunieeo oaiia?aoo?ao.

Ioiaoei oaeaea, /oi oaieiaieinoue N eeiaeia ii O. I?e i/aiue ieceeo
oaiia?aoo?ao yoio eeiaeiue /eai, eioi?ue iau/ii caienuaatho a aeaea

N = O

iiaeii ioaeaeeoue io ?aoaoi/iiai /eaia, eioi?ue no?aieony e ioeth
auno?aa — eae O . Ecia?aiea aeaao iaiin?aaenoaaiioth eioi?iaoeeth i
aaee/eia — ieioiinoe ninoiyiee ia o?iaia Oa?ie. Iai?eia?, aeey
ia?aoiaeiuo iaoaeeia iaaethaeathony aunieea cia/aiey o a niioaaonoaee ni
neacaiiui a ianoiyuea aeaau.

I?ienoiaeaeaiea eeiaeiiai oiaea oaieiaieinoe i?e ieceeo oaiia?aoo?ao
iiaeii iiiyoue neaaeothuei ia?acii. ?anniio?ei ?ani?aaeaeaiea Oa?ie.
Aeeyiea oaiia?aoo?u naiaeeony e aicaoaeaeaieth iaaieueoiai /enea
yeaeo?iiia ia aieaa aunieea o?iaie. Ii yoio aooaeo iiaeao auoue caiaoiui
oieueei a iaeanoe yia?aee ii?yaeea O aaeece . Iu iiaeai neacaoue,
/oi eaaeaeue

Oa?ie/aneia aicaoaeaeaiii yeaeo?iiia a iaoaeea.

yeaeo?ii ec iauaai /enea, i?eia?ii ?aaiiai ( ), i?eia?aoaao
yia?aeth ii?yaeea O. Oaeei ia?acii, iieiue auea?uo yia?aee ninoaaeyao
i?eaeeceoaeueii

Yoi niioaaonoaoao oaieiaieinoe

: -3-

Yeaeo?iiiay
oaieiaieinoue

Yeaeo?iiu a iaoaeeao aeieaeiu aiineoue iaeioi?ue aeeaae a iieioth
oaieiaieinoue. *oiau iaeoe aai, au/eneei n?aaeithth yia?aeth yeaeo?iiia.
Ainiieuecoainy oi?ioeie (1), i?aaeiieaaay, /oe nenoaia yeaeo?iiia
neeueii au?iaeaeaia

I?iaeeooa?aioee?oai yoio ?acoeueoao ii oaiia?aoo?a, o/eouaay , /oi
o?iaaiue Oa?ie oaeaea caaeneo io oaiia?aoo?u(3):

Caeanue eniieueciaaii ?aaainoai e iiouaiu /eaiu aunoaai ii?yaeea ii O.

Yoi i/aiue aaaeiue ?acoeueoao. N?aaiei au?aaeaiea (3) n oaieiaieinoueth
eeanne/aneiai aaca /anoeoe, neaaeai 3/2 . A eaaioiaii neo/aa
?acoeueoao iaiiiai iaiueoa. Aeey naiaiaeiuo yeaeo?iiia ieioiinoue
ninoiyiee i?e yia?aee, ?aaiie yia?aee Oa?ie, ninoaaeyao 3/2 , oae
/oi

-5-

Oiae Aeaaay.

A 1912 a. yoo caaea/o i?eaeeaeaiii ?aoee Aeaaae, ?anniao?eaay oaa?aeia
oaei, eae ecio?iiioth ‘iai?a?uaioth n?aaeo. –

*enei i?iaeieueiuo eieaaaiee (1I,’ a eioa?aaea /anoio (o, o+eo) a iauaia
V yai?a?uaeie n?aaeu niaeanii (14.97) ?aaii

^^-^.o»Aeo. ^

aaea a—nei?inoue ?ani?ino?aiaiey i?iaeieueiuo aiei a n?aaea.

A oaa?aeii oaea iiieii i?iaeieueiuo eieaaaiee aiciiaeiu aeaa iacaaeneiuo
iiia?a/iuo eieaaaiey. Eo /enei e^/ a oii aea eioa?aaea /anoio

^=^-o«^,

aaea N1 — nei?inoue ?ani?ino?aiaiey iiia?a/iuo eieaaaiee.

Iieiia /enei eieaaayee a ‘eioa?aaea (v, o+(1\) ^=^(o)^=^+^= 1(14.112)

aaea n — n?aaeiyy nei?inoue oi?oaeo aiei a n?aaea, ii?aaeaeyaiay ec
?aaainoaa

^+-1-—. (14.113) ^ n? o^„.

Ia ?en. 42 ioieoe?iay eeiey ecia?aaeaao ooieoeeth ?ani?aaeaeaiey /anoio
a oaa?ee Aeaaay, a nieioiay eeiey — ?aoaoi/ioth (eaaiyioth) ooieoeeth
?ani?aaeaeaiey, o/eouaathuoth aeene?aoioth no?oeoo?o «?eaoaeea y
niaoeeoe/ioth aeey «niae?aoiiai oaa?aeiai oaea. Ooieoeey ^^ia?aaeaeeaony
yenia?eiaioaeueii ‘ii ?annayieth «aeo.?ieia,aoaa?ao1ei«n»e — /eneaiiuie
iaoiaeaie.

A ea/anoaa oa?iiaeeoeaia/aneiai ‘iioaeoeeaea e?enoaeea ii oi?ioeai
(14.108) e (A4.116) iiaeii au/eneeoue yia?aeth Aaeuei-aieueoea, a ooi«
a « ana ae?oaea oa?iiaeeiaie/aneea ooieoeee oaa?aeiai oaea a
oai?ee Aeaaay (*). Iaeaaei aeey ii?aaeaeaiey oaieiaieinoe a?iua;
iaiin?aaenoaaiii ii oi?ioea (14.109]!au/eneeoue aioo?aiithth yia?aeth A
Aeaenoaeoaeueii, iiaenoaaeyy (14.115) a (14.109), iieo/ei

V oao

?—? 9^ N o* (iv

^^aA ^ ao?^/a)-1 -. (14.117]

Aeey au/eneaiey eioaa?aea a (14.117) aaaaeai iiaoth ia?aiaiioth
o=Eo/a e oaiia?aoo?o Aeaaay

Ai=/1Oo„^ (14.118)

(ii ii?yaeeo aaee/eiu 7ae~ 100— 1000 E). Oiaaea aeey iaeiiai a?aie-aoiia
e?enoaeea iieo/aai

aaea ooieoeey Aeaaay

1>«)=-^1^1. . (14.120)

i

I?e aunieeo oaiia?aoo?ao, O^Oa, a aa?oiai i?aaeaea eioaa?aea ooieoeee
Aeaaay noieo iaeay aaee/eia, iiyoiio a iiaeuioaa?aeueiie ooieoeee o
caaaaeiii iaei; iieaaay a*»\+o, iieo/ei

^EUa^ A^Ai+eEO

/ oaieiai.einoue No=(aeA/aeO)o=2E eiaao eeanne/aneia cia/aiea ^4.103).

I?e aeeceeo oaiia?aoo?ao, A

e oaieiaieinoue , ^(-1) -^-^• ^1) \ " /o 5Ai Oaeei ia?acii, i?e ieceeo oaiia?aoo?ao oaieiaieinoue e?enoaeea i?iii?oeeiiaeueia eoao oaiia?aoo?u («caeii 7"»). Ec (14.119) iaoiaeei au?aaeaiea aeey oaieiaieinoe No ai anae iaeanoe eciaiaiey oaiia?aoo?u: (14.122) Ec yoie .oi?ioeu aeaeii, /oi a oai?ee Aeaaay oaieaaieinoue yaeyaony aeey anao oae iaeiie e oie aea ootha?naeueiie ooieoeeae O{Oi. A?aoee caaeneiinoe No io O/Oa i?eaaaeai ia •?en. 43. Oi?ioea (14.122) aeey oaieiaieinoe, ianiio?y ia i?eaeeaeaiiue oa?aeoa? oai?ee Aeaaay, oi?ioi iiaeoaa?aeaeaaony ia iiuoa. Aeaeueiaeoaa ?acaeoea oai?ee oaieiaieinoe e?enoaeeia naycaii n ioeacii io caiaiu oaa?aeiai oaea iae?a?uaiie n?aaeie e ?anniio?aieai eieaaaiee oaa?aeiai oaea eae eieaaaiee e?enoaeee/aneie ?aoaoee. A oai?ee Aeaaay iiaeii «u/eneeoue yia?aeth Aaeueiaieueoea e ae?oaea oa?iiaeeiaie/aneea aaee/eiu (•).. § 70. Yeaeo?e/aneea e iaaieoiua naienoaa aaeaaeueiuo nenoai Aei neo i? iu ?anniao?eaaee eaeaaeueiua nenoaiu a ionoonoaea iaoieo aieae. ?anniio?ei oaia?ue ^aeaaeueiue aac, ninoiyuee ec iieaeoe, eiathueo iinoiyaiue yeaeo?e/aneee aeeiieueiue iiiaio ?, iaoiaeyueeny a iinoiyaeii iaeii?iaeiii yeaeo?e/aneii iiea n iai?yaeaiiinoueth 6. A ?acoeueoaoa i?eaioe?othuaai aeaenoaey iiey e aeaci?eaioe?othuaai aeaenaiey oaieiaiai aeaeaeaaey onoaiaaeeaaaony oaeia ?ani?aaeaeaiea iieaeoey?iuo aeeeieueiuo iiiaioia, eioi?ia i?eaiaeeo e aicieeiiaaieth iiey?ecaoeee ^> aaeieue yeaeo?e/aneiai iiey:

^*=?nia1+?nia! 1, -1^1•^ . ., 1 iaaeue, 1:anno)yaiy :«aa^o o?iaiyie ninoaaeytho i^iei ),05 i.) 1 Iinoieueeo aaeea ]1a?6^iaee11eyaeee, aicaoaeaeathony eio:> iaiii-

1 aia in^ eee; aoi?u. A ^aoeueoaoa a oaieiaieinoue, e 1 aieiaay ‘•
‘ iaaeaeo 3^
aenoe1aeeyai?ai]^ (^aaeaeua aoii i?eieiaaony ca o?o inoeeeeyoi?a, oa»
eae ^oi^ iiaeaa ia?aiauaoueny a o?ao )caiiii ia?iUeueeo.Ay?iu^
^{i?aaeaieyo). Oiaaea caaea/a (aiaeeony e oiio, /oi >u iau 1N^1 oue,
ii/aio oaieiaieinoue iaeiiai inoeeeeyoi?a- aoaea a ?aaia^C^/C^ (Ae{ th 2
eae/iieue-“E.). *oiau ?aoeoue yoo caaea/o, iu nia/aea ?anniio?ei
oaieiaieinoue eaeaaeueiiai

:. ^1.1

1 • • • ‘. ! ” ‘ ” 1 ‘ ‘ aaca,
iineieueeo; oaii »?oeoo?iaA o (a ia onoa iiaeaia o^( iii

‘ aeey aaeIaeueii^i aaca. 1 nea ie n^iae e onoayio aou naycue ia eaeo !
yia?aeae aoiiia^ eaeaae >i(ai,aa^a e aa) oaiia «aoo?ie, ‘.o, oai : ‘(ca. Aoaeai oaeaea n/eoaoue, 410
e1 ?aonaoaa^nth?yoei/ii a a.

•Ia?aeeaeueai (eaaeaeie ei>?aeeUaoii1 ine Ia aiaoeaaono ^^/3 ! aoiiia.;
Ionoue nei?ia’ ue anao) aoii >a iaeeiae yaa & ?a aia v. -; Oiaaea ana
aoiiu !iaeaae&th^ iaeeiaeia a[eiea/(noa

eee N,^—,- eae/aoii '°E. ^ Aeey eaeaaeueiiai aaca oaieiaieinoue ia caaeneo io oaiia?aoo?u, a aa cia/aiea (3 eae/iieue -°E) oi?ioi niaeanoaony n ecia?aieyie aeey iaeiiaoiiiuo aacia. Oaieiaay yia?aey, i?eoiaeyuayny ia eaaeaeoth noaiaiue naiaiaeu aoiia ioiineoaeueii i?ino?ainoaaiiuo eii?aeeiao, ?aaia IO12. Oaia?ue caaea/a aaeeth/aaony a auaiaea aeey oaa?aeiai oaea o?aaiaiey, aiaeiae/iiai au?aaeaieth (3.14). I/aaeaeii, /oi aeey oaa?aeiai oaea oaeie auaiae iaeuecy aeoaee?iaaoue, oae eae aoiiu oaa?aeiai oaea ia oaea?ythony i noaieo ninoaea, e aeaaeaiea ?aaii ioeth. Iiaeao iieacaoueny, /oi o?aaiaiea (3.14) aiiaua iai?eiaieii aeey ethauo oaa?aeuo oae. Iaeiaei cia/aiea yoiai o?aaiaiey i/aiue aaeeei e ia ia?aie/eaaaony oai iniaui neo/aai, aeey eioi?iai iii auei auaaaeaii. Ia eaaeaeia ii?iaeueiia eieaaaiea nenoaiu i?eoiaeeony oaieiaay yia?aey AeA/2 (a i?aaeaeueiii neo/aa aunieeo oaiia?aoo?). Iao?oaeii ii?aaeaeeoue, eae i?ienoiaeeo eciaiaiea yia?aee aa?iiie/aneiai inoeeeeyoi?a. Eieaaethueeny aoii iaeaaeaao e eeiaoe/aneie, e iioaioeeaeueiie yia?aiyie. Iaa yoe ninoaaeythuea ia iinoiyiiu; oieueei eo noiia, iauay yia?aey Ao, yaeyaony eiinoaioie.. A oa/aiea ia?eiaea eeiaoe/aneay yia?aey eciaiyaony io ioey aei Ao. N?aaeiaa cia/aiea eeiaoe/aneie yia?aee a aeaenoaeoaeueiinoe ?aaii oi/ii A-?I, oaeia aea n?aaeiaa cia/aiea eiaao e iioaioeeaeueiay yia?aey. Aniiiiei, oaai aeey aaca a caieiooii iauaia oaieiaay yia?aey aoiia, ioianaiiay e eaaeaeie eii?aeeiaoa aai ia?aiauaiey, ninoaaeyao ?iaii !nO/2. Aniiiiei oaeaea, /oi aeey aaca any oaieiaay yia?aey anoue yia?aey eeiaoe/aneay, a iioaioeeaeueiie yia?aeae aa» ia iaeaaeaao. I?aaeiieiaeei, /oi aeey inoeeeeyoi?a n?aaeiyy eeiaoe/aneay yia?aey Ao/2 eiaao aaee/eio )nO/2. Oiaaea iauay \ oaieiaay aia?aey eaaeaeiai inoeeeeyoi?a ?aaia IO, a noiia?iay oaieiaay yia?aey anaai oaa?aeiai oaea, ninoiyuaai ec ^ aoiiia, aoaeao ninoaaeyoue Ai=5^O. (3.15) Ec yoiai au?aaeaiey neaaeoao, /oi iiey?iay oaieiaieinoue oaa?aeuo oae ?aaia N„,,a=3^& eae/iieue- °E= CE eae/iieue-*E. (3.16) Aeey oaiia?aoo? auoa aeaaaaaneeo yoi o?aaiaiea aeaao eeanne/aneia cia/aiea a eae/iieue '"E. Ioiaoei, /oi yoi ?iaii aaeaia aieueoa cia/aiey oaieiaieinoe CE/2 aeey eaeaaeueiiai aaca, iineieueeo inoeeeeyoi? iiaeao iaeaieeaaoue oaiei e a aeaea iioaioeeaeueiie yia?aee. E o?aaiaieth (3.15) iiaeii i?eeoe e ae?oaei iooai, eioi?ue ?anniao?eaaeny ?aiaa. Yoio auaiae iniiaai ia oii, /oi eaaeaeue niinia iiaeiuaiey aia?aee aeiioneaao iaeaieeaaiea aa a eiee/anoaa 1aO/2 ia eaaeaeoth noaiaiue naiaiaeu. Oaieiaay yia?aey eeiaeiiai inoeeeeyoi?a neeaaeuaaaony ec aeaoo neaaaaiuo: aaee/eiu AA/2, i?eoiaeyuaeny ia aeieth eeiaoe/aneie yia?aee, e aaee/eiu 1nO/2 — aeeaaea iioaioeeaeueiie yia?aee. Neaaeiaaoaeueii, oaieiaay yia?aey oaa?aeiai oaea, ?anniao?eaaaiiai eae niaieoiiinoue e^ inoeeeeyoi?ia, iiyoue ?aaia ^1nO. Iaiaoiaeeii iiae/a?eiooue, /oi a?aoiaiou, i?eaiaeyuea e auaiaeo o?aaiaiey (3.16), a i?eioeeia ei??aeoiu, ii eniieueciaaiiua eiee/anoaaiiua niioiioaiey aeaeaei ia anaaaea oi/ii io?aaeatho ?aaeueiia iieiaeaiea aeae. Ciay, /oi oaieiaay yia?aey inoeeeeyoi?a eiaao ii?yaeie eO (ii aeieacaiiiio auoa), iiaeii au/eneeoue aiieeooaeo eieaaaiee aoiia. I?e iaeneiaeueiii niauaiee o^yen yia?aey inoeeeeyoi?a noaiiaeony oeaeeeii iioaioeeaeueiie. Iineieueeo yoa yia?aey ?aaia ie^aen/2 (ni. oea. 3.1), A 2Ao o/» ^iaen-^—ae— ) • ! Aeey aoiia, o eioi?iai eiyooeoeeaio oi?oainoe «i?oaeeiu» a )» 25 i1i (niaeanii ioeaiea «, naeaeaiiie a § 2 aeaiiie aeaau), Oeaen i?e eiiiaoiie oaiia?aoo?a eiaao ii?yaeie 0,2 A. Yoio ?acoeueoao oi?ioi niaeanoaony n yenia?eiaioaeueiuie ecia?aieyie aoiiiuo_niauaiie ?aioaaiianeeie Iaoiaeaie. § 5. Oeoeooaoeee aia?aee Ec o?aaiaiee, i?eaaaeaiiuo a i?aaeuaeoueo ?acaeaeao, aeaeii, /oi oaieiaay yia?aey oaa?aeiai oaea aic?anoaao io ioey (i?e aaniethoiii ioea oaiia?aoo?u) aei ianeieueeeo nioai eaei?ee ia iieue i?e eiiiaoiie oaiia?aoo?a. A n?aaeiai yoa yia?aey eiaao ii?yaeie IO a ?an/aoa ia eaaeaeoth ninoaaeythuoth eieaaaiee aoiia (eee ieiei 0,025 i ia aoii i?e eiiiaoiie oaiia?aoo?a). Ia ia?aue acaeyae iiaeao iieacaoueny, /oi i?e iiauoaiiuo oaiia?aoo?ao yia?aey aoaeao ?ani?aaeaeaia ?aaiiia?ii iaaeaeo anaie aoiiaie, ii ia naiii aeaea yoi ia oae. Aeey eieaaaiee aoiiia oa?aeoa?iu oeoeooaoeee yia?aee eieaaaiee eaaeaeiai aeaiiiai aoiia. Eieaaaiey aoiiia ?aaeueiiai e?enoaeea aanueia neiaeiu, ii ea/anoaaiiua iniaaiiinoe yoiai yaeaiey iiaeii eaaei i?iaeaiiino?e?iaaoue ia iiaeaee ec aeaoo iau/iuo iayoieeia. Ionoue o?aineyoeeiiiie neiiao?ee ?aoaoee, aeinoaoi/ii ?aoeoue nenoaio o?aaiaiee o?aoueae noaiaie. Ecaanoii, /oi yoe eieaaaiey ?aoaoee eiatho aeae e,==e?ao?1a(i(A)^2ao?(^-TH- (7.16) e Eieaaaiey ?aoaoee iiaeiaiu aeonoe/aneei noiy/ei aieiai, eioi?ua oaeaea yaeythony neio?iiii e acaeiii iacaaeneiuie. A aeaeueiaeoai iu aoaeai ?aceaaaoue eaaeaeue oei eieaaaiee ia aeaa aaaouea aieiu, aieiiaua aaeoi?u eioi?uo eiatho i?ioeaiiieiaeiua ciaee. A eaaioiaie iaoaieea ioaeaeueiua oeiu eieaaaiee ?anniao?eaathony oaeei aea iooai, eae e a eeanne/aneie oeceea. Yia?aee yoeo eieaaaiee aeene?aoiu. e ?aaiu ('/ae + /) A a niioaaonoaee n o?aaiaieai (6.18). Eaaioiaua /enea y (e») iiaeii ?anniao?eaaoue eae /enea »oiiiiia' eee caoeiauo eaaioia n yia?aeae th. Oiiiiai i?eienuaaaony eiioeuen, ?aaiue nei), aaea n—nei?inoue caoea. I?iecaaaeaiea 1)?e?*2ao??-(1—1')1 (7.17) e • ?aaii ioeth, anee 1 + A. Anee eieaaaiey ?anniao?eaathony eae ooieoeee aaeoi?ia ?aoaoee, oi iie aeieaeiu iaeaaeaoue naienoaii ioe,aiaiiaeueiinoe. Eo iiaeii a iauai neo/aa ?anniao?eaaoue eae aieiiaua ooieoeee oiiiiia. ^ Oae eae eiatho ianoi aeaa iiia?a/iuo e naeai i?iaeieueiue oeiu eieaaaiee. Niaianoeiuo n eaaeaeui aieiiaui aaeoi?ii, oi oeiu eieaaaiey, eee ninoiyiey oiiiia, aeieaeiu oa?aeoa?eciaaoueny „nieiiaie ia?aiaiiie' ^, eioi?ay iiaeao i?eieiaoue o?e cia/aiey. Aeey oi?iuaiey caiene yoa nieiiaay ia?aiaiiay, aaea yoi aiciiaeii, iioneaaony. Ianiio?y ia oi /oi iiiyoea oiiiia yaeyaony ia aieaa /ai ia?aciui au?aaeaieai, iii ana aea iieacii, iicaieyy iauaaeeieoue noaoenoe/aneea oai?ee aaciia?aciiai e oaa?aeiai ninoiyiee. Anee iaicia/eoue yia?aeth oiiiia /a?ac a, a /enei oeiia eieaaaiee a aaneiia/ii iaeie iaeanoe aaeece a /a?ac

ie/aneeo ooieoeee ioaeaeueiuo oeiia eieaaaiee. A /anoiinoe, naiaiaeiay yia?aey aoaeao ?aaia /-'==^[^a— A71i(1 —a-^)](a)ea==CE/. (7.20)

1)

Aaeaeo iineaaeiaai oneiaey i?aaay /anoue ?aaainoaa (7.19) i?e aunieie
oaiia?aoo?a aoaeao ?aaia CE/Ae aeey ethaie ooieoeee »(«). I?e ieceeo
oaiia?aoo?ao ea?atho ?ieue oieueei iaaieueoea cia/aiey yia?aee a, a aeey
yoeo yia?aaoe/aneeo o?iaiae e?enoaee iiaeii ?anniao?eaaoue eae
eaeaaeueiue oiiiiiue aac. ?ani?aaeaeaiea iaeiioiiiiiuo ninoiyiee ii
eiioeuenai eaeaioe/ii niioaaonoaothuaio ?ani?aaeaeaieth aeey iaoa?eaeue*
iuo /anoeoe, o. a. (4iO/E^)?”(1?. O/eouaay naycue iaaeaeo eiioeuenii e
yia?aeae, iieo/ei ?ani?aaeaeaiea ii yia?aeyi

» (a) ^=-1^^ (7.21)

-aianoi (6.16); a yoie oi?ioea iiiaeeoaeai 3 o/eouaathony o?e cia/aiey
«nieiiaie ia?aiaiiie”. Oaieiaieinoue i?e iinoiyiiii iauaia aeey ieceeo
oaiia?aoo? ii (7.21) e (7.19) aoaeao ?aaia

„ ,. 12iO(/aO)’ O a* e ^^—-^–) (?A^^-

ue

Eioaa?ae aeaao oieueei /eneaiiue iiiaeeoaeue, oae /oi oaieiaieinoue
i?iii?oeeiiaeueia eoao oaiia?aoo?u. *oiau auaanoe oi?ioeo aeey
eioa?iieyoeee iaaeaeo iaaeaaeiuie cia/aieyie oaieiaieinoe i?e aunieie e
ieceie oaiia?aoo?a, iu i?aaeiieiaeei, /oi au?aaeaiea (7.21) ni?aaaaeeeai
ieaea ii?aaeaeaiiiai i?aaeaea yia?aee, oiaaea eae ca aai i?aaeaeaie

n aeaoiy oeiaie eieaaaiee e ninoiyieai n iaeiei oeiii eieaaaiey eee ia?aoii. I?ioeannu oaeiai ?iaea ecaanoiu iiae iacaaieai o?aooiiiiiuo noieeiiaaiee. Iao?e/iua yeaiaiou a iauai neo/aa ia?auathony a ioeue, eiaaea inouanoaeyaony noiie?iaaiea ii oceai ?aoaoee, oae eae yeniiiaioeeaeueiua ooieoeee iaiytho ciae e nie?auathony. Iaen/acathuea iao?e/iua yeaiaiou niioaaonoaotho oieueei oaeei i?ioeannai, a eioi?uo 1-E'+A==0 (7.24) eee ^•(1+A+A)=2ae. (7.25) Yoe oneiaey niaianoii n oneiaeai E == E' == \E" i?eaiaeyo e oiio, /oi yeniiiaioeeaeueiua ooieoeee noaiiayony ?aaiuie aaeeieoea. Noiia a (7.23) a niioaaonoaee n yoei inoaaony eiia/iie, anee oaeiaeaoai?ythony oneiaey (7.24) eee (7.25). Caeii nio?aiaiey yia?aee a ia?aoiaea au?aaeaaony a o?aaiaaiee, /oiau /anoiou 'auee naycaiu niioiioaieai

a o?aooiiiiiuo noieeiiaaieyo. Anee iaicia/eoue /enei oiiiiia a ?aaiiaaniii ninoiyiee /a?ac ?i(0= „-«,(1)/»a_1 ' oi ia?aaiiaaniia ?ani?aaeaeaiea ii?aaeaeyaony a aeaea ^)^i(1)(1 +^. aaea v—iaecaanoiay ooieoeey io 1. A neo/aa noaoeeiia?iiai a?aaeeaioa oaiia?aoo?u yoa ooieoeey aeieaeia oaeiaeaoai?youe eeiaoe/aneiio o?aaiaieth, iiaeiaiiio (3.15): • ^'^=!{^^)-"^—"o- - A {v (A) + v (I - v (1))) I'. (7.27) A yoii o?aaiaiee eiyooeoeeaiou A e A caaenyo io o?ao aieiiauo aaeoi?ia e niioaaonoaothueo /anoio e iieiinoueth ii?aaeaeythony n iiiiuueth oai?ee aiciouaiee. Aaee/eia E ?anniao?eaaaony eae iai?a?uaiay ia?aiaiiay, iineieueeo a?aaeeaio oaiia?aoo?u ii?aaeaeyaony oieueei a i?aaeaeao oaeeo iaeanoae, eioi?ua aaeeee ii n?aaiaieth N ia?eiaeii e?enoaeee/aneie ?aoaoee. O?ieea aieiiauo aaeoi?ia niioaaonoaoao i?ioeannai ia?aa?ina. ?aoaiey yoii o?aaiaiey aua ia iieo/aiu. Iiea aua iaaiciiaeii au/eneeoue eiee/anoaaiii oaieii?iaiaeiinoue e?enoaeeia, i?e/ai iaoaiaoe/aneea o?oaeiinoe a ?aoaiee o?aaiaiey (7.27) ia yaeythony aaeeinoaaiiui i?aiyonoaeai e yoiio. N iiiiuueth ooieoeee ?ani?aaeaeaiey ae(1) eiyooeoeeaiou ia?aiina iiaeii iieo/eoue oieueei iin?aaenoaii o?aaiaiey (1.13), e eioi?iio yoa ooieoeey iaiin?aaenoaaiii ia i?eiaieia. Iaeiaei oai?ey aeaao aiciiaeiinoue iieo/eoue iieoeiee/anoaaiiua ?acoeueoaou, eioi?ua iaoiaeyony a niioaaonoaee n yenia?eiaioii. Iaeaeaii, /oi i?e aunieeo oaiia?aoo?ao eiyooeoeeaio oaieii?iaiaeiinoe i?iii?oeeiiaeai OeO. Yoi i/aiue oi?ioi niaeanoaony n oai?aoe/aneei ?acoeueoaoii, auoaeathuei ec oaiia?aoo?iie caaeneiinoe eiyooeoeeaioia o?aaiaiey (7.27). Eiaaea oaiia?aoo?a nieaeaaony, aa?iyoiinoue 6 c*e. 1189. i?ioeannia ia?aa?ina caiaoii oauaaao e ?ieue yoeo i?ioeannia a ia?aciaaiee oaieiaiai nii?ioeaeaiey e?enoaeeia i?e ieceeo oaiia?aoo?ao no?aieony e ioeth. I?eia?aoatho cia/aiea ae?oaea i?ioeannu, eae, iai?eia?, ?anniyiea oiiiiia ia aeaoaeoao ?aoaoee eee a?aieoeao ca?ai; e caeanue niiaa yenia?ae-iaioaeueiua ?acoeueoaou niaeanothony n auaiaeaie oai?ee. Oai?ey yaeaiee ia?aiina a e?enoaeeao e a eeanne/aneeo aeeaeeinoyo a ianoiyuaa a?aiy aua ianiaa?oaiia ii ?yaeo i?e/ei. A eeanne/aneie aeeaeeinoe ieacuaaaony o?oaeiui oi/ii onoaiiaeoue oa iee?ioece/aneea neo/aeiua i?ioeannu, io eioi?uo caaeneo iaia?aoeiinoue; ii ooieoeee iieaeoey?iiai ?ani?aaeaeaiey e eo ioeaiea iaoiaeyony a iaoeo ?oeao. A e?enoaeeao iiae?iaiua naaaeaiey ia yeaiaioa?iuo neo/aeiuo i?ioeannao iaaeiaoaoi/iu aeey auaiaea niioaaonoaothueo ooieoeee ?ani?aaeaeaiey. E niaeaeaieth, iu iaei /oi iiaeai neacaoue i eaaioiaie oai?ee aeeaeeiai ninoiyiey. Yenia?eiaioaeueiua enneaaeiaaiey aeeaeeiai aaeey, aeatho iaoe?iua aeaiiua, eioa?i?aoaoeey eioi?uo a ianoiyuaa a?aiy i?iaiaeeony ii/oe oeaeeeii ia iniiaa iiaeaeueiuo i?aaenoaaeaiee, ia naycaiiuo n eaeie-eeai ooiaeaiaioaeueiie oai?eae. Iiiuoee auaanoe au?aaeaiey aeey ?ani?aaeaeaiey yia?aaoe/aneeo o?iaiae e oa?iiaeeiaie/aneeo ia?aiao?ia aaaeoony, ii iiea eeoue n ia?aie/aiiui oniaoii. Iaeiaei a yoii ioiioaiee eiathony iaiaaeaaeeaathuea ia?niaeoeau. Iae/ii i?eieiaaony, /oi ieaeiea aicaoaeaeaiiua ninoiyiey aeeaeeiai aaeey aeieaeiu ?anniao?eaaoueny eae oiiiiiue aac, ia ioee/athueeny io ninoiyiee e?enoaeee/aneeo ?aoaoie. Yoa oi/ea c?aiey iiaeoaa?aeaeaaony ecia?aieyie oaieiaieinoe, eioi?ay ieacaeanue i?iii?oeeiiaeueiie 7^ i?e oaiia?aoo?a ieaea 0,6° E. Iaeiaei a aeeaeeinoyo oiiiiu ia iiaoo ?anniao?eaaoueny n iiiiuueth eeiaeiuo i?aia?aciaaiee eii?aeeiao aoiiia. Ioaeaeueiua eieaaaiey iiaeii ii?aaeaeeoue oieueei eae i?ino?ainoaaiiua eiiiiiaiou Oo?uea a ?aceiaeaiee ieioiinoe. Ianiio?y ia yoo o?oaeiinoue, iiiaea aaoi?u aeinoeaee iaeioi?uo oniaoia a ii?aaeaeaiee aeeaaea oiiiiiuo ia?aiaiiuo a ooieoeeth Aaieeueoiia e a o?aaiaiey aeaeaeaiey. ' Oai?ee i?eaeaony i?aiaeieaoue aua na?ueaciua iaoaiaoe/aneea o?oaeiinoe, ii iiaeii iaeeaeaoue, /oi iia iinoeaiao aieueoeo oniaoia a eco/aiee eaaioiauo aeeaeeinoae. 7.3. /^-oai?aia Aieueoeiaia A ?acae. 2.) e 6.2 oai?ey ?aaiiaaniuo ninoiyiee auaiaeeony ec iinooeaoia, eioi?ua ia iaycaoaeueii yaeythony neaaenoaeyie i?eioeeiia aeeiaieee. Enneaaeiaaiea aiciiaeiith iaoaie/aneiai iainiiaaiey oai?ee oaieiaiai ?aaiiaaney i?eaiaeeo e aaaeiui auaiaeai, eioi?ua e?aoei ?anniao?eaathony a yoii ?acaeaea. ?annoaeaeaiey ia?aie/eaathony eeanne/aneie oai?eae; niioaaonoaothuea eaaioiaiiaoaie/aneea aeieacaoaeuenoaa ianeieueei aieaa neiaeiu, ii i?eioeeieaeueii ie/ai ia ioee/athony. A y?aiaea/aneie oai?aia, auneacaiiie Iaeiaiii e Ae?e-aioii '), ooaa?aeaeaaony, /oi /?acau/aeii oe?ieee eeann aeeiaie/aneeo nenoai iaeaaeaao iniaaiiinoueth «caauaaoue' naie ia/aeueiua oneiaey aeaeaeaiey ii enoa/aiee ioiineoaeueii iaeiai a?aiaie. A niioaaonoaee n, yoei oaciaay o?aaeoi?ey iie?uaaao iiaei?ino?ainoai iinoiyiiie yia?aee n ii/oe ?aaiiia?iie ieioiinoueth. N?aaeiea ii a?aiaie io iaoaie/aneeo aaee/ei i?eaeeaeathony e ia caaenyoei io a?aiaie i?aaeaeueiui cia/aieyi, eioi?ua i?aeoe/anee niioaaonoaotho n?aaeiei cia/aieyi oai?ee ?aaiiaaniuo ninoiyiee. Ni?aaaaeeeainoue yoie oai?aiu caaeneo io oneiaey, /oi yia?aey yaeyaony, ii nouanoao, aaeeinoaaiiui «eioaa?aeii aeaeaeaiey*, o. a. aaeeinoaaiiie ooieoeeae eii?aeeiao e eiioeuenia, eioi?ay inoaaony ia caaenyuae io a?aiaie. Anee i?eiyoue yoo oi/eo c?aiey, ninoiyiea oaieiaiai ?aaiiaaney aeieaeii, ii ii?aaeaeaieth. I?aaenoaaeyoue niaie n?aaeiaa ii a?aiaie-io anao ninoiyiee aeaeaeaiey iaoaie/aneie nenoaiu. Iieiinoueth aeiioneathony niiioaiiua oeoeooaoeee, eioi?ua i?eaiaeyo e a?aiaiiui ioeeiiaieyi io ?aaiiaaney. Iaeiaei caeanue iao ianoa aeey eaeeo au oi ie auei iaia?aoeiuo i?ioeannia. Ii yoie i?e/eia oaeie iiaeoiae aeaeae io eaai?aoi?iuo oneiaee. Ae?oaiai ?iaea ioaao ia aii?in aeaao ^-oai?aia, eioi?oth iu caeanue i?aaenoaaei a aa ia?aiia/aeueiii aeaea. Aa auaiae aeai aeey aacia, ii iiaeao auoue iaiauai. ') Y?aiaee/aneay oai?aia iaeaieaa iieii ?anniio?aia a ?aaioao A. ss. Oei/eia (ni. aeiiieieoaeueioth eeoa?aoo?o [240—48{). I?eaeiaeueiue iiaeoiae e y?aiaee/aneie i?iaeaia e iaia?aoeiinoe a oa?iiaeeiaieea iiaeii iaeoe o I. N. E?ueiaa (ni. aeiiieieoaeueioth eeoa?a-oo?o {25\).—I?eI. ?aae. 6* N oi/iinoueth aei /eneaiiiai iiiaeeoaey yoa ioeaiea niaiaaeaao n i?aaeiei ?acoeueoaoii (4.44). Iaoa ?annoaeaeaiea a nouiinoe naiaeeony e oiio, /oi yeaeo?iiu, ?aniieiaeaiiua a aeoaeia ?ani?aaeaeaiey Oa?ii, ii/oe «ia /oanoaotho» aeeyiey oaiia?aoo?u. Eo ninoiyiea ii?aaeaeyaony i?eioeeiii Iaoee, eioi?ue o?aaoao, /oiau yeaeo?iiu caiieiyee ana o?iaie, ii ia iicaieyao ei aoi?aaoueny ae?oa e ae?oao ia o?iaaiue. Ia oaeeaeoaeueii iiyoiio, /oi yeaeo?iiu, ?aniieiaeaiiua a aeoaieeo aioo?aiieo iaiei/eao eiiiuo inoiaie, ia neaaeoao i?eieiaoue ai aieiaiea i?e au/eneaiee oaieiaieinoe oaa?aeiai oaea, ii e?aeiai ia?a aei oao ii)), iiea oaiia?aoo?a ia noaiao noieue aaeeea, /oi iie niiaoo -aicaoaeaeaoueny oa?ie/aneei iooai.

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