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Билеты по Курсу физики для гуманитариев СПБГУАП

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1.A-ai e iana, i?eioeei yeaeaaeaioiinoe. A-ai-aeae iaoa?ee, eio.
Iaeaaeaao ianie iieiy. A-ai neaaaaony ec yeaiaioa?i. /anoeoe.A-ai
anaaaea eieaeeciaaii aia?aie/aiiie /anoe i?ino-aa. Aai iieiae. iiaeii
caaeaoue n iiiiuueth ia?aie/. /eneai ia?aiao?ia (noaiaie naiaiaeu). Mana
oa?-coao eie-ai iaoa?ee. Yoioi?ioee?iaea ea/anoaaiiay. I?aaeeueiaa
aiai?eoue, /oi iana-iaeia ec iniiaiuooa?aeoa?enoee iaoa?ee,
ii?aaeaeythuay aa eia?oeeiiiua e a?aa-iua na-aa. A O.Iuethoiia iana
?ani-eanue, eae eie-ai a-aa. Iiiyoea ianu aaae a iaoaieeoE.Iuethoii,
aeaaay ii?aaeaeaiea eiioeuena – p=mv. Iannie ii iacaae eiyo.
i?iii?oe-iinoe m, iinoiyiioth aeey oaea aaee/eio. Yeaeaaeaioiia
ii?aaeaeaieaianu auoaeaao e ec 2ai c-ia Iuethoiia: F=ma Caeanue iana –
yoi eiyo. i?iii?oe-iinoe iaaeaeo ?acoeueoe?othuae neeie e aucuaaaiui ath
onei?aieai. Ii?aae. oaeei ia?cii iana oa?-coao eia?oiinoue oaea. Ii?aae.
oaeei ia?cii iana iac. eia?oiie.

A O. a?aaeoaoeee Iuethoiia iana aunooiaao eae enoi/iee iiey nee
oyaioaiey. Ia etha. oaei, iiiau. a yoi iiea, aeanoaoao neea,
i?iii?oeeiiaeueiay aai nianoaaiiie ianna, ianna enoi/ieea e iai?aaeaiay
e enoi/ieeo. C-i anaie?iiai oyaioaiey: F=G*M1*M2/r^2, aaea
G=6,670*10^(-11)i3/(ea(n2)- a?aa-iay iinoiyiiay. Ec yoie oi?ioeu iiaeii
iieo/eoue naycue iaaeaeo ianie oaea e aai aanii ? a iiea oyaioaiey
Caiee, if n/eoaoue, /oi m1 – iana oaea, m2=M – iana Caiee, a r=Rc –
?aaeeon Caiee: P=G*mM/(R3)^2=m*GM/(R3)^2=mg o.a. P=mg(7.2). Ii?aae.
oaeei ia?cii iana iac. a?aaeoaoeeiiiie. Oiuou iieacaee, /oi eia?oeeiiiay
e a?aa-iay ianu i?e auai?a iaeeiaeiaie nenoaiu aaeeieoe ?aaiu. Yoio
ooiaeaiaioaeueiue c-i i?e?iaeu iac. i?eioeeiii yeaeaaeaioiinoe iann.
Yenia?eiaioaeueii yoio i?eioeei aue i?iaa?ai a 1971 aiaeo n i/aiue
aunieie oi/iinoueth-10-12. A eeane/. oeceea n/eoaeinue, /oi iana oaea ia
iaiyaony ie a eaeeo i?ioeannao. Yoi ooa. oi?ioee?iaaeinue a aeaea c-ia
nio?aiaiey ianu. Iiiyoea ianu i?eia?aei > aeoaieee niune a ?aieao
?aeyoeaenoneie iaoaieee eee O. ioineo-oe, ?anniao?eaathuae aeaeaeaiea
oae n aieueoeie nei?inoyie. ?aeyoeaenoneay iaoaieea iieacuaaao, /oi ia
nou-aoao ii ioaeaeueiinoe caeiiia nio?aiaiey ianu e yia?aee. Iie neeou
aiaaeeii. Yoi anonoaaii, oae eae iaoa?ey (eie-ai eio. oa?-a?-aony ianie)
iaaiciiaeia aac aeaeaeaiey (eie-ai eio. oa?-a?-aony yia?aeae).

2.Iao/i. iaoiae iiciaiey. Niinia iieo/eoue /anoe/iua ioaaou ia aii?inu
i?eaeoiai ianeieueei nioai eao iacaae. Iaaethaeaiea, ?aciuoeaiea e iiuo
nino. oaeiacuaaaiue iao/iue iaoiae iiciaiey, eio. e iicaieyao aeaaaoue
ioaaou ia iiiaea eioa?anothuea ian aii?inu. Iniiaie iao/iiai iaoiaea
yae. iiuo – i?iaiue eaiaiue anao iaoeo ciaiee. Iiuo, yenia?eiaio – yoi
aaeeinoaaiiue noaeuey iao/i. enoeiu.I?iaiaey iaaethaeaiey eaeeo-eeai
i?e?iaeiuo yaeaiee, iaaiciiaeii ioaaoeoue ana i?ioeanu, n yoeie
yaeaieyie naycaiua. Iiyoiio ioaeii ioa?ineoue ana aoi?inoaiaiiua oaeou e
auaeaeeoue ini., o.a. nooue yae-y. Yoio i?ioean iac. aano?aae?iaaieai
eee iino?iaieai iiaeaee yae-y. A ?aciuoeaieyo nicae-ny iniiaa
iaaethaeaaiiai yae-y, aai iiaeaeue. *oi yae. nouanoaaiiui aeey aeaiiai
yae-y, a /oi ianouanoaaiiui, aii? iaiaeiicia/iue e neiaeiue. Ia anaaaea
ii ?aoaaony n?aco, ia ia?a. yoaiao iaaethaeaiey e ?aciuoeaiey. A
nicaeaaaaiie iiaeaee aeieaeiu auoue o/oaiu aeaaiua oa?-a?enoeee e ini.
ia?aiao?u eco/aaiiai yae-y. Iino?iaiiay iiaeaeue aeieaeia ia
oieueeiaa?ii iienuaaoue iaaethaeaaiia yoi yaeaiea, ii e oi?ioi
i?iaiice?iaaoue aai?acaeoea a iiauo one.. I?aaeneacaiey O. i?iaa?ythony
yenia?eiaioii eee iiuoii – aaaeiaeoae /anoueth iao/iiai iaoiaea
iiciaiey. N naiiai ia/aea iaiaoiaeeii aeiaiai?eony, /oi
iiae?acoiaaaoueny iiae oai eee eiui oa?ieiii. A iiiyoea “iiuo” aoaeai
aeeaaeuaaoue niune iaaethaeaiey ca yaeaieai i?e eiio?iee?oaiuo one.,
o.a. iaaethaeaiey n aiciiaeiinoueth eiio?iee?iaaoue, aini?iecaiaeeoue e
eciaiyoue aeaeaaiui ia?cii aiaoiea one-y. Nouanoaaiia aiciiaeiinoue
nicaeaaaoue eae iau/iua, oae e eneonnoaaiiua (o.a. a i?e?iaea ia
ano?a/athueany) one-y. Oeceea, oeiey, aeieiaey e ?yae ae?oaeo iaoe
iacuaathony anoanoaaiiuie eiaii iioiio, /oi a eo iniiaa eaaeeo iiuo.
Aeey iauyniaiey yenia?eiaioaeueiuo oaeoia i?eaeaeathony aeiioacu.
Aeiioaca – yoi i?aaeiieiaeaiea, iicaieythuaa iauynieoue e eiee/anoaaiii
iienaoue iaaethaeaaiia yaeaiea. Iienaoue /oi-eeai eiee/anoaaiii iiaeii
eeoue ia ycuea iaoaiaoeee. Iaaeaeo yaeaieyie i?e?iaeu nou. onoie/eaua,
iiaoi?ythueany nayce – i?iyaeaiey caeiiia i?e?iaeu. Ea/anoaaiiay
oi?ioee?iaea caeiiia iiaeao auoue eiiaaea aeaia aac i?eaea/aiey
iaoaiaoe/aneiai aiia?aoa. C-iu, caienaiiua ia ycuea oi?ioe iicaieytho
ia?aeoe e > aunieie nooiaie iiciaiey. Yoo nooiaiue iacuaatho O..O.a. i?e
ii?aaeaeaiiuo one. auaeaeiooay aeiioaca iiaeao ia?aeoe a O., a iniiaa
eio. eaaeao caeiiu. O. aeaao i?aaenoaaeaiea i caeiiiia?iinoyo e
nouanoaaiiuo naycyo a ii?aae. iaeoe. C-iu anoaaiuo iaoe onoaiaaeeaatho
eiee/anoaaiiua niioiioaiey iaaeaeo iaaethaeaaiuie yaeaieyie, o.a. eiatho
iaoaiaoe/aneoth oi?ioee?iaeo. Anoanoaiciaiea, eco/athuaa eiee/anoaaiiua
(o.a. oi/iua) niioiioaiey i?e?iaeiuo yaeaiee, ioi. e oi/iui iaoeai.
Iiiyoea “oi/iia” o?aaoao eiiiaioa?eaa. Oi/iua iaoee, eae i?aaeei
iia?e?otho ia n aaniethoii oi/iuie, a n i?eaeeaeaiiuie aaee/eiaie. I?e
eiee/anoaaiiii iienaiee ethaiaiiaaethaeaaiiai yae-y anaaaea
iaiaa?eaatho, n eaeie noaiaiueth oi/iinoe eiatho aeaei, o.a. i?eaiaeyo
iia?aoiinoe ecia?yaiuo aaee/ei. Aeiioacu aeieaeiu auoue i?iaa?aiu
oaeoaie, iiuoaie, cae?aaui niuneii. A naiae iaeoe iie aeieaeiu
iauyniyoue anth niaieoiiinoue eiathueony yaeaiee. Ii yoiai iaei. Aeey
oiai, /oiau noaoue O., aeiioaca aeieaeia noi?ioee?iaaoue eiee/anoaaiiua
ioiioaiey iaaeaeo iaaethaeaaiuie yaeaieyie. Oaeoe/anee yoi icia/aao
oi?ioee?iaeo caeiiia. Iai?aiaiiui one. i?aa?auaiey aeiioacu a O. yae.
i?aaeneacaiea iiauo, aei neo ii? ia iaaethaeaaoeony e ec ecaanoiuo
oai?ee ia neaaeothueo, yaeaiee, e iiaeoaa?aeaeaiea yoeo i?aaeneacaiee a
niaoeeaeueii iinoaaeaiiuo yenia?eiaioao. Ioaeii ?acee/aoue caeiiu
i?e?iaeu e caeiiu iaoee. 1aua i?iyaeythony a iniaaiiinoyo i?ioaeaiey
i?e?iaeiuo yaeaiee e i?ioeania e ai acaeiinayce iaeio. aaee/ei. Iie
iaeciaiiu e anaaaea auiieiythony. Iao/iua caeiiu – yoi iiiuoea iienaoue
caeiiu i?e?iaeu ia ycuea iao. oi?ioe e oi/iuo oi?ioee?iaie. A
aeaeueiaeoai ?a/ue aoaeao eaeoe oieueei i ieo. Iao/iua caeiiu ia oi/iu e
ia iinoiyiu. Ia ii?aaeaeaiiuo yoaiao ?acaeoey iaoee aicieeaao
iaiaoiaeeiinoue ooi/iaiey iaaethaeaaiuo a iiuoa yaeaiee e ia?aniio?a
caeiiia eee a?aieoe eo i?eiaieiinoe. Iinoiyiiay i?iaa?ea iiuoiuo oaeoia
ia aaca iiauo yenia?eiaioaeueiuo iaoiaeee, iicaieythueo oaae-oue
oi/iinoue i?iaaaeaiey yenia?eiaioa, iaiaoiaeeia anaaaea ia ethaii o?iaia
ciaiee. ?anoiaeaeaiea yenia?eiaioaeueiuo aeaiiuo e nouanoaothueo caeiiia
iicaieyao auaeaeaaoue iiaua aeiioacu e no?ieoue iiaua O..

3. Iinooeaoeaiinoue iniiaiuo c-iia anoanoaiciaiey. Aeey iienaiey
iiaaaeaiey i?inouo e neiaeiuo nenoai ioaeii ono-oue “i?aaeea ea?u”, o.a.
caeiiu eio iiae/eiythony oa eee eiua aeae aeaeaeaiey iaoa?ee. A iaeio.
iaoeao, eio. Ia ioiinyony e annaaiui, iai?eia? aaiiao?ey, iinooiatho
neaaeothuei ia?cii. Nia/aea oi?ioee?othony aeneiiu, a iioii ec ieo
aeaeathony auaiaeu (oai?aiu). Eiaeea iino?iaiey anoaaiuo iaoe ae?oaay,
iaeuecy n?aco aaanoe caeiiu e niio?aoue, /oi ec ieo neaae.. Oae
iinooieoue iaeuecy, iineieueeo enneaaeiaaoaeth iaecaanoiu ana caeiiu
anoanoaiciaiey. Iaeiie ec caaea/ yae. eiaii eo onoaiiaeaiea e
oi?ioee?iaaiea. Ii, ioaaoea ia eaaeae. aii?, enneaaeiaaoaeue iaecaaaeii
noaaeo ianeieueei iiauo. *ai aieueoa iiciaaony, oai oe?a noaiiayony
a?aieoeu iaiiciaiiiai. Onoaiiaeaiiua ia ii?aaeaeaiii yoaia ?acaeoey
iaoee caeiiu, anaaaea yae. i?eaeeaeaiiuie. Ii ia?a iaeiie. ciaiee, iiauo
yenia?eiaioaeueiuo oaeoia, yaeaiee e oaaee/aiey oi/iinoe ecia?aiee
iiyae-ny aeaiua, ia oeeaaeuaathueany a ?aiee eiathueony caeiiia e yoe
caeiiu ia?aniao?eaathony.Anoue e ae?oaay noi?iia yoiai aii?ina. Aeey
oi/iie oi?ioee?iaee caeiiia anoanoaiciaiey, a inia-oe oeceee, o?aaothony
iiaua ii?aaeaeaiey e iiiyoey, ciaiea niaoe. ?acaeaeia iaoaiaoeee. Enaaeo
Iuethoiio (1643-1727) aeey iienaiey caeiiia iaoaieee iio?aaiaaeinue
nicaeaoue nia?oaii iiaua aeey naiaai a?aiaie ?acaeaeu aunoae iaoaiaoeee:
aeeooa?aioeeaeueiia e eioaa?aeueiia en/eneaiea. Oeceee /anoi
noaeeeaaeenue n neooaoeeae, eiaaea eiaaoaainy iaoaiaoe/aneiai aiia?aoa
ieacuaaeinue iaaeinoaoi/ii aeey iieo/aiey eiee/anoaaiiuo oi?ioee?iaie
iieo/aiiiai c-ia e o?aaiaaeinue nicaeaaaoue niaoe. iaoaiaoe/anee aia?ao.
C-iu anoanoaiciaiey iinooee?othony ia iniiaaiee iaaethaeaaiuo iiuoiuo
oaeoia. Nia/aea eaeao i?ioean iaeiie. ciaiee a ii?aae. iaeoe. Yoe
?acoeueoaou aiaeece?othony e aeaeaaony iaeioi?ia i?aaeiieiaeaiea. Yoi
i?aaeiieiaeaiea ia auaiaeeony ec ae?oaeo caeiiia. Iii aicieeaao naii ii
naaa ia iniiaaiee iiuoa. Naeaeaiiia oiicaeeth/aiea, noi?ioee?iaaiiia a
aeaea iaoaiaoe/aneie oi?ioeu, noaiiaeony /anoueth aeiioacu. If
iineaaeothuea iiuou iiaeoaa?aeaeatho i?aaeeueiinoue yoiai
i?aaeiieiaeaiey, iii noaiiaeony c-iii. C-iu e O. ia aaniethoiu. Iie
?acaeaathony ii ia?a iaeiie. ciaiee. Ooiaeaiaioaeueiua caeiiu
anoanoaiciaiey iienuaatho ia?iiiia eie-ai yaeaiee a ?aciuo iaeanoyo. E
ana iie iiae/eiythony iaeioi?ui iauei i?aaeeai. ?anniio?ei eo. Ai ia?a.,
caeiiu naie ii naaa ia iaiythony. Eiaii iiyoiio iie e iacuaathony
ooiaeaiaioaeueiuie. Eia/a ieeaeay iaoea ia iiaea au ?acaeaaoueny. Ii,
iaaei iiiieoue i oii, /oi c-i iaienai aeey ii?aae. iaeoe yaeaiee. Anyeee
?ac, eiaaea n ii?aae. noaiaiueth oi/iinoe iiaeoaa?aeaeaaony eaeie-eeai
c-i, iiaeii ooaa?aeaeaoue, /oi c-i ieii/aoaeai e ie eaeie ?acoeueoao aai
ia ii?iaa?aiao a oie iaeoe, aeey eio. ii iaienai. Iaeiaei iiaeao oae
neo/eony, /oi iiyaeaiea iiauo yenia?eiaioaeueiuo aeaiiuo eee oai?ee
i?eaaaeao e oiio, /oi c-i ieaaeaony i?eaeeaeaiiui. Eia/a aiai?y, oaae.
oi/iinoe ecia?aiee iiaeao iaia?oaeeoue iaoi/iinoue aeaaea naiuo
iacuaeaiuo caeiiia. I?e oi?ioee?iaea caeiiia iaiaoiaeeii caaeaaaoue
a?aieoeu eo i?eiaieiinoe. C-iu e O. aeieaeiu iienuaaoue anth
niaieoiiinoue yaeaiee a oie iaeoe, aeey eio. Iie noi?ioee?iaaiu. Iie ia
aeieaeiu i?ioeai?a/eoue ecaanoiui oaeoai. Aieaa oiai, iie iaycaoaeueii
aeieaeiu i?aaeneacuaaoue iiaua, iaecaanoiua ?aiaa yae-y. Iaeiiaoe,
ieeaeie c-i ia aeieaeai ia?ooaoue i?eioeei i?e/eiiinoe. Yoi ci/eo,
/oiiaeuecy /oi-oi eciaieoue a niauoee eio. oaea neo/eeinue. Iiaeii
iiaeeyoue oieueei ia aoaeouaa, ii ieeae ia ia i?ioeia. A caeeth/aiea
ioiaoei, /oi iiaua ooiaeaiaioaeueiua caeiiu iaaiciiaeii auaanoe a ?aieao
noa?uo oai?ee. No?aieaiea iaeio. aaoi?ia naeaeaoue yoi ia eiaao iiae
niaie ieeaeiai iniiaaiey e ca/anooth naycaii eeoue n aieueoei aeaeaieai
aaoi?ia “iii?eaeiaeueie/aoue” e aianoe naie “aeeaae a iaoeo”.

4. Iaoa?ey, oi?iu aa nouanoaiaaiey.A iniiaa anao anoanoaaiiiiao/iuo
aeenoeeieei eaaeeo iiiyoea iaoa?ee, c-iu aeaeaeaiey e eciaiaiey eio.
eco/athony. A caaenei. io oiai, eae iu ii?aaeaeei yoi iiiyoea, iu e
aoaeai ?ani-aaoue i?iyaeaiea ?acee/i. oai?ee. Aeey iiieiaiey
anoanoaaiiiiao/iuo oai?ee, a /anoiinoe eiioeaioeee nia?aiai. oeceee,
i?eaieaiui yae. ii?aaeaeaiea, aeaiiia A.E. Eaieiui a iiiia?aoee
. “Iaoa?ey – anoue oeeinioneay
eaoaai?ey aeey iaicia/aiey iauaeoeaiie ?aaeueiinoe, eio. ioia?aaeaaony
iaoeie iuouaieyie, nou-aoao iacaaeneii io ieo. Iaoa?ey – yoi iniiaa
(noanoaioeey, noano?ao) anao ?aaeueii nouanoaothueo a ie?a na-a, naycae
e oi?i aeaeaeaiey, aaneiia/iia iiiaeanoai anao nouanoaothueo a ie?a
iauaeoia e nenoai”.A yoii ii?aaeaeaiee anoue 2 iniiaiuo iiiaioa.
Ai-ia?a., iaoa?ey nou-aoao iauaeoeaii, iacaaeneii io ian, io /ueaai-oi
noauaeoeaiiai niciaiey eee iuouaiey. Ai-aoi?uo, iaoa?ey eiie?oaony,
ioia?aaeaaony iaoeie iuouaieyie e, neaae., iiciaaaaia. Iu caeanue
enoiaeei ec iaoa?eaeenoe/aneiai aaeeinoaa ie?a ec ia?ae/iinoe iaoa?ee.
Iaoa?ey ianioai?eia e iaoie/oiaeaaiay. Iia aaneiia/ia. Iaiouaieaiui
ao?eaooii iaoa?ee yae. aa aeaeaeaiea, eae oi?ia nouanoaiaaiey iaoa?ee,
aa aaaeiaeoee ao?eaoo. Aeaeaeaiea a naiii iauai aeaea – yoi anyeia
eciaiaiea aiiaua. Aeaeaeaiea iaoa?ee aaniethoii, oaaea eae anyeee iieie
ioiineoaeai. Iiiyoue yoo iuneue i?iua anaai i?e ?anniio?aiee i?inoaeoeo
aeaeia aeaeaeaiey. Iai?eia?, oaei iieieony ioiineo. Caiee, ii ioiineo.
Nieioea iii aeaeaeaony. Oi?iaie nouanoaiaaiey iaoa?ee yae. i?ino?ainoai
e a?aiy. Iaoa?ey iaiouaieaia io ieo. Nia?aiaiiay iaoea iia?e?oao oaeeie
no?oeoo?iuie o?iaiyie, eae yeaiaioa?iua /anoeoeu e iiey, aoiiu e
iieaeoeu, iae?ineiie/aneea oaea, aaieiae/aneea nenoaiu, ieaiaou e
caacaeu, aaeaeoeee e iaoaaaeaeoeee; niaieoiiinoe i?aaieciia, niiniaiuo e
aini?iecaiaenoao e, iaeiiaoe, iau-ai. Iu aoaeai eco/aoue oieueei
ia?aua no?oeoo?iua o?iaie- iiey e /anoeoeu, iae?ineiie/aneea oaea.
?acee/atho ?yae iniiaiuo oi?i aeaeaeaiey iaoa?ee: iaoaie/aneoth,
oece/aneoth (aeeth/ay oaieiaoth, a?aaeoaoeeiiioth, yaea?ioth e o.ae.),
oeie/aneoth, aeieiae/aneoth, iauanoaaiioth. Aunoea oi?iu aeaeaeaiey
aeeth/atho a naay > iecoea, ii ia naiaeyony oieueei e iei. Oae, yaea?iua
i?ioeanu iaaiciiaeii iienaoue oieueei oi?ioeaie eeane/. iaoaieee. A
ianoiyuai eo?na aoaeoo ?anniio?aiu eeoue i?inoua oi?iu aeaeaeaiey
iaoa?ee – iaoaie/aneay, oece/aneay e oeie/aneay. Aeey iienaiey iaoa?ee e
aa aeaeaeaiey iaiaoiaeeii aaanoe eiee/anoaaiiua ia?u yoeo aaee/ei
enoiaey ec iinoaaeaiiuo caaea/. Ianna yae. eiee/anoaaiiie ia?ie iaoa?ee
e aaiaeeony eae aeey iee?i- e iae?iiauaeoia, oae e aeey iieae. Iaeiie
ec eiee/anoaaiiuo ia? aeaeaeaiey iaoa?ee yae. yi-y. Iia eiaao iiiai
oi?i: iaoaie/aneay, oaieiaay, yaea?iay, oeie/aneay e o.ae. Iineieueeo
iaoa?ey ia nou-aoao aac aeaeaeaiey, a aeaeaeaiea aac iaoa?ee iaaeaeo
eiee/anoaaiiuie oa?aeoa?enoeeaie ia?u e aeaeaeaiey iaoa?ee aeieaeia
nouanoaiaaoue naycue. Yoa naycue auea onoaiiaeaia a ia/aea iaoaai a. A.
Yeiooaeiii (1879-1955) a ?aaioao ii O. ioineo-oe. Iu aoaeai ?ani-aaoue 2
aeaea iaoa?ee – a-ai e iiea. E ia?aiio ioianai yeaiaioa?iua /anoeoeu,
aoiiu, iieaeoeu, anaiino?iaiiua ec ieo iae?inenoaiu. Ei aoi?iio ioianai
iniaoth oi?io iaoa?ee, oece/aneoth nenoaio n aaneiia/iui /eneii noaiaiae
naiaiaeu. I?eia?aie oece/aneeo iieae iiaoo neoaeeoue yeaeo?iiaaieoiua e
a?aa-iua iiey, iiey yaea?iuo nee, a oaeaea aieiiaua iiey.

5. ACAEIIAeAENOAEA. IIEA. I?EIOeEIU AEECEIAeAENOAEss E
AeAEUeIIAeAENOAEss. Ia?aia/. a eeane/. iaoaieea ooaa?aeeeanue eiioe-y,
/oi acaeiaeaenoaea iaaeaeo oaeaie i?ienoiaeeo /a?ac ionoia i?ino?ainoai,
eio. ia i?eieiaao o/anoey ai acaeiiaeaenoaee, ia?aaea/a acaeiaeaeno.
i?ienoiaeeo iaiiaaiii. Ii nooe aeaea ooaa?aeaeaeanue aiciiaeiinoue
iaiiaaiie ia?aaea/e eaeiai-eeai aicaeaenoaey io iaeiiai oaea ae?oaiio.
I?e yoii ia iaiaa?eaaeny iaoaieci yoie ia?aaea/e. Iaeiaei, aeaiua
i?aaenoaae. auee ioeeioou, eae ia niioaaonoaothuea ?aaeueiui, iinea
ioe?uoey e eneaae. yeaeo?e/. e iaaieoiuo iieae. Iiiyoea iiey a
i?eiaiaiee e yeaeo?e/aneiio e iaaieoiiio iieyi auei aaaaeaii a 30-o aa
19-ai a. I. Oa?aaeaai. Niaeanii eiioeaioeee aeeceiaeaenoaey,
acaeiiaeaenoaothuea oaea nicaeatho a eaaeae oi/ea ie?oaeathuaai eo
i?ino-aa iniaia nino.-iiea, eio. i?iyaeyaony a neeiaii aicaeaenoaee ia
ae?oa. oaea, a yoe iiey iiiauaiiua. Yenia?eiaioaeueii auei iieacaii, /oi
acaeiaeaenoaea yeaeo?e/anee ca?yaeaiiuo oae inou-aony ia iaiiaaiii.
Ia?aiauaiea 1ie ca?yaeaiiie /anoeoeu i?eaiaeeo e eciaiaieth nee,
aeaenoaothueo ia ae?oa. ca?yae. /anoeoeo ia a oio aea iiiaio, a nionoy
iaeioi?ia a?aiy. A ?acaeaeythuai /anoeoeu i?ino-aa i?ienoiaeeo iaeioi?ue
i?ioean, eio. ?ani?ino?aiyaony n eiia/iie, oioy e i/aiue aieueoie
nei?-oueth. Aue naeaeai auaiae, /oi eiaaony iin?aaeiee, inouanoaeythuee
acaeiaeaenoaea iaaeaeo ca?yaeaiiuie /anoeoeaie. Yoio iin?aaeiee aue
iacaai yeaeo?iiaaieoiui iieai. Eaaeaeay ca?yaeaiiay /anoeoea nicaeaao
aie?oa naay yeaeo?iiaaieoiia iiea, aeaenoaothuaa ia ae?oa. ca?yaeaiiua
/anoeoeu. Nei?inoue ?ani?ino?aiaiey yeaeo?iiaaieoiuo aiei ia i?aauoaao
nei?. eo ?ani?ino?aiaiey a aaeooia, =ie 3(108 i/n. Oeei ia?cii, aicieeea
iiaay eiioe-y – eiioe-y aeeceiaeaenoaey. Niaeanii yoie eiioeaioeee,
acaeiaeaenoaea oaeaie inou-aony iin?-aii oao eee eiuo iieae, iai?a?uaii
?ani?aaeaeaiiuo a i?ino-aa. Acaeiiaeaenoaea oae ia?aaeaaony ia
iaiiaaiii, a /a?ac iaeioi?ue i?iiaaeooie a?aiaie. Nei?inoue ia?aaea/e
acaeiaeaeno. ia?aie/aia nei?-oueth naaoa a aaeooia.A nia?aiai. oeceea
nou-aoao eaaioiaay O. iiey. Niaeanii yoie O., etha. iiea ia iai?a?uaii,
a aeene?aoii. Aeene?aoiinoue icia/aao iaee/ea iaeio. /anoeoe
iiey-eaaioia. Eaaeaeiio iieth niioa-otho naie /anoeoeu.4 aeaea
acaeiiaeaenoaee e iieae: A?aaeoaoeeiiiua acaeiaeaeno. iaania/eaatho
oyaioaiea oae ae?oa e ae?oao. Neaaua acaeiaeaeno. ioaaonoaaiiu ca
aieueoeinoai ?aniaaeia e i?aa?auaiee yeaiaioa?i. /anoeoe.
Yeaeo?iiaaieoiua acaeiaeaeno.-yoi acaeiaeaenoaea ca?yaeaiiuo oae.
Neeueiua acaeiaeaeno. naycuaathony i?ioiiu e iaeo?iiu (ioeeiiu) a
aoiiiii yae?a. Iineieueeo iiey caaeaiu a eaaeae oi/ea i?ino-aa, o.a. a
aaneiia/iii /enea oi/ae, aeey eo iienaiey o?aaoaony ia eiia/iia, a
aaneiia/iia /enei ia?aiao?ia (noaiaiae naiaiaeu). Neacaiiia ia icia/aao,
/oi aeey iienaiey iiey iaaei ?aaeueii caaeaaaoue aaneiia/iia /enei
ia?aiao?ia. Aeinoaoi/ii ono-oue c-i, iicaieythuee iaoiaeeoue iiea a
eaaeae oi/ea i?ino-aa. Oaeiauie yae.: c-i anaie?iiai oyaioaiey aeey
a?aaeoaoeeiiiuo iieae, c-i Eoeiia aeey yeaeo?e/. iieae e c-i
Aei-Naaa?a-Eaieana aeey iaaieoiuo iieae.Iniaie oi?iie nouanoaiaaiey
iaoa?ee yae. aieiu. Aieia i?aaenoaaeyao ec naay i?ioean ?ani?ino?aiaiey
aiciouaiey eaeiai-eeai oec. ia?aiao?a a i?ino-aa. aieiu a oi?oaeo
n?aaeao, eio. eieaeeciaaiu a naiie n?aaea, e aieiu (yeaeo?iiaaieoiua,
a?aa-iua), ia ia?aie/aiiua n?aaeie.

6. Nino. neno., aa eci. Ai a?aiaie. I?inoaeoay oi?iy aeaeaeaiey iaoa?ee
– iaoaie/aneia aeaeaeaiea (ia?aiauaiea oae a i?ino-aa e a?aiaie). A
anoanoaiciaiee aeey iienaiey nenoai aaiaeyony iiaeaee. I?inoaeoae
iiaeaeueth, ia eio. oaeiaii eco/aoue iaoaie/aneia aeaeaeaiea, yae.
iaoa?eaeueiay oi/ea, o.a. oaei, eiathuaa ianno, ii ia eiathuaa
aaiiao?e/aneeo ?acia?ia. Oaei iiaeii caiaieoue iao. oi/eie, if a ?aieao
iinoaaeaiiie caaea/e iiaeii i?aiaa?a/ue aai ?acia?aie e oi?iie. ?acaeae
iaoaieee, a eio. iienuaaaony aeaeaeaiea oaea, e ia ane?uaathony i?e/eiu,
aai aucuaathuea, iac. eeiaiaoeeie. Aeey iienaiey aeaeaeaiea oaea,
iaiaoiaeeii aaanoe nenoaio ion/., ioiineo. eio. caaeaoue aai
eii?aeeiaou, aaanoe aeeiaie/aneea ia?aiaiiua, iienuaathuea eciaiaiea
iieiaeaiey oaea ai a?aiaie e aaanoe caeiiu aeaeaeaiey oaea. Aiiaua
aiai?y, neno. ion/. aeieaeia a naay aeeth/aoue nenoaio oaea, eio. iu
n/eoaai iaiiaeaeaeiuie e /anu. N nenoaiie iaiiaeaeaeiuo oae iaiaoiaeeii
naycaoue nenoaio eii?ae., iai?eia? aeaea?oiauo. Iieiae-a o/ee a
eii?aeeiaoiii i?ino-aa caaeaaony ?aaeeonii-aaeoi?ii r(t). Iieiae-a o/ee
a i?ino-aa n oa/aieai a?aiaie iaiyaony, e eiiaoe ?aaeeona-aaeoi?a
au/a?/eaaao eeieth, eio. iac. o?aaeoi?eae aeaeaeaiey. O?aaeoi?eth iiaeii
?acaeoue ia aaneiia/ii iaeua o/anoee – dr. Iineieueeo ia?aiauaiea dr,
aaneiia/ii iaei, iii eaaeeo ia o?aaeoi?ee aeaeaeaiey. A?aiy dt, ca eio.
i?ienoiaeeo yoi ia?aiauaiea, oiaea aaneiia/ii iaei. Ia?aiauaiea dr e
a?aiy dt naycaiu ae?oa n ae?oaii i?e iiiiue aeeiaie/aneiai
ia?aiao?a-iaiiaaiie nei?., ii?aaeaeaiea eio.: ((t)=dr(t)/dt (9.1). O.i,
dr=(dt, neaae., iai?aae. iaiiaaiie nei?. niaiaaeaao n iai?aaeaieai
yeaiaioa?iiai ia?aiauaiey dr. Ii i?aaeeo neiaeaiey aaeoi?ia noiia anao
dr + r0 aeano iai aaeoi? r. Ii, iia?aoeey noiie?iaaiey ii aaneiia/ii
iaeui aaee/eiai iac. eioaa?e?iaaieai. au/eneaiea cia/aiey r(t), a etha.
iiiaio a?aiaie. r(t)=r0+ ‘eioaa?ae io t0 aei t'(((t)dt) (9.2).
onei?aiea, eio. oiaea yae. aaeoi?iie aaee/eiie e oiaea iiaeao caaenaoue
io a?aiaie e eii?ae.: a(t)=d((t)/dt (9.3). ==> d((t)=a(t)dt. If o-y a(t)
ecaanoia, oi n aa iiiiuueth iiaeii iaeoe nei?inoue oaea a etha. iiiaio
a?aiaie, a ciay aa, i?e iiiiue (9.2) iiaeii iaeoe iieiae. oaea a etha.
iiiaio a?aiaie. ((t)=(0+ ‘eioaa?ae io t0 aei t'(a(t)dt) (9.4), r(t) =
r0 +’eioaa?ae io t0 aei t'(((0 +’eioaa?ae io t0 aei t'(a(t)dt))dt) eee
r(t)=r0+(0(t-t)+ ‘eioaa?ae'(‘eioaa?ae io t0 aei t'( a(t)dt)dt) (9.5). A
yoeo oi?ioeao (0 – ia/aeueiay nei?inoue oaea, o.a. aai nei?inoue a
iiiaio a?aiaie t0. O.i, if iai ecaanoiu ia/aeueiia iieiae. iao. o/ee –
r0 e ia/aeueiay nei?inoue-(0, a oaeaea caaeneiinoue aaeoi?a nei?. eee
aaeoi?a onei?aiey io a?aiaie, iiaeii iaeoe eii?aeeiaou nenoaiu a etha.
iineaaeothuee iiiaio a?aiaie -r(t). A ?yaea neo/aaa o?aaoaony iaeoe ia
oieueei iieiae. oaea, ii e oio iooue, eio. iii i?ieaeao. I?ieaeaiiue
iooue anoue neaey?iay aaee/eia, iia iaicia/aaony S e /eneaiii =a aeeeia
o?aaeoi?ee. *oiau iaeoe i?ieaeaiiue iooue S iaiaoiaeeii i?inoiie?iaaoue
aeeeiu aaeoi?a dr, o.a. i?iaanoe eioaa?e?iaaiea ii iiaeoeth aaeoi?a dr:
S=’eioaa?ae io t0 aei t'(dr)= ‘eioaa?ae io t0 aei t'(v(t)dt) (9.6).

7. Ini. iieiaeaiey iaoaieee Aaeeeay. Ana O., nicaeaiiua aei noaiiaeaiey
nia?aiai. oeceee, aace?iaaeenue ia i?eioeeia, “I?e?iaea ia oa?ieo
?ac?uaia”. Eciaiaiea ninoiyiey nenoaiu i?ienoiaeeo ia iaiiaaiii, a
ieaaii. acaeiaeaenoaea oae i?ienoiaeeo iaiiaaiii. C-iu oeceee anaaaea
aace?othony ia iiuoao, yenia?eiaioao. Eiaii a ?aieao oaeiai iiaeoiaea
Aaeeeae nicaeae iniiau eeane/. iaoaieee. Iaiiiiei, /oi a iniiaa iaoaieee
A?enoioaey, aeiieie?iaaaoae a oio ia?eiae, eaaeaei ooa., /oi nei?inoue
oaea ~ i?eeiaeaiiie neea: v~F. Aaeeeae aeieacae iaaa?iinoue. Inouanoaee
yenia?eiaio a oiaea eio. ii ii?aaeaeye a?aiy, iaiaoiaeeiia aeey iaaeaiey
oae n aa?oeiu Iecaineie aaoie. Aicueiai ianeieueei oa?ia iaeeiaeiaiai
?acia?a, ecaioiaeaiiuo ec ?aciiai a-aa. Iie eiatho ?aciue aan. Aan oaea
oa?-coao neeo oyaioaiey, aeaenoaothuoth ia oaei ni noi?iiu Caiee. Neea
oyaioaiey, aeaenoaothuay ia oaei =a aai aano. If ni?aaaaeeeai ooa.
A?enoioaey, oi ?aciua oaea n ?aciui aanii aeieaeiu iaeaaeaoue ?aciuie
nei?inoyie iaaeaiey e, niioaaonoaaiii, aeinoeaaoue iia-oe caiee i?e
a?inaiee n aaoie ca ?aciua i?iiaaeooee a?aiaie. Iaeiaei, yenia?eiaiou,
i?iaaaeaiiua n ?aciuie oaeaie iieacaee, /oi iie aeinoeaaee iia-oe caiee
ca i?aeoe/anee iaeeiaeiaua i?iiaaeooee a?aiaie.Auaiae iaeiicia/ai.
Nei?inoue oaea ia ii?-ny i?eeiaeaiiie neeie. I?eeiaeaiiie neeie ii?-ny
eaeie-oi ae?oaie aeeiaie/aneee ia?aiao?. Aaeeeath iio?aaiaaeinue iiiai
eao e iiiai oneeee, /oiau auynieoue, /oi aea yoi ca ia?aiao?. A yoie
iaeoe iaeaieaa ecaanoiu aai yenia?eiaiou n aeaeaeaieai oa?ia ii
iaeeiiiie ieineinoe. Oa?u neaouaaeenue ii iaeeiiiie ieineinoe, aeeeia
eio. e aunioa auee caaeaiu. A oiaea iiuoa Aaeeeae ii?aaeaeye iooue S,
i?ioiaeeiue oaeii a caaenei. io a?aiaie t. Ei aue onoaiiaeai c-i,
yaeythueeny /anoiui neo/aai 2ai c-ia Iuethoiia. Iooue, i?ioiaeeiue oaeii
eaaae?aoe/ii caaeneo io a?aiaie: S=v0t + (at^2)/2, aaea eiinoaioa
a(onei?aiea) i?yii ~ aunioa h e ia?aoii ~ aeeeia iooe S. Ia/aeueiay
nei?inoue oaea – (0 a aai iiuoao iiaea iaiyoueny. A iiuoao Aaeeeay
onei?aiea ii?aaeaeyeinue onei?aieai naiaiae. iaaeaiey: a~gh/s.
Aiaeece?oy i?iaiaeeiua yenia?eiaiou, Aaeeeae i?eoae e auaiaeo i
nouanoaiaaiee c-ia eia?oeee. Aeaenoaeoaeueii, if ono?aieoue aeeeio
iniiaaiea iaeeiiiie ieineinoe e aaneiia/iinoe, onei?aiea aoaeao
no?aieoueny e ioeth, ci/eo, ca =ua i?iiaaeooee a?aiaie oaei aoaeao
i?ioiaeeoue =ua io?acee iooe e nei?inoue oaea aoaeao iino.. Oaei aoaeao
naii ii naaa aeaeaaoueny ii eia?oeee. E?iia yenia?eiaioia Aaeeeae thcae
oiic?eoaeueiua caeeth/aiey. Ii ?anniio?ae iiaaaeaiea oae e aeeauo
nouanoa aioo?e ei?aaey. Eo iiaaaeaiea ia caaeneo io oiai, noieo ei?aaeue
o i?e/aea eee aeaeaaaony ii niieieiie aiaea n iino. nei?-oueth. Auaiae:
if ei?aaeue aoaeao aeaeaaoueny n iino. nei?-oueth, oi iaoiaeynue aioo?e
ei?aaey iaaiciiaeii ii?aaeaeeoue, aeaeaeaony ii eee noieo.

8.I?eioeei ioineo-oe Aaeeeay. I?aia?aciaaiey Aaeeeay. Aaeeeae aaae
iiiyoea eia?oe. nenoaiu ion/., a eio. oaei nio?aiyao nino. iieiy eee
=ia?iiai i?yiieeiaeiiai aeaeaeaiey, if ia iaai ia aeaenoaotho ae?oa.
oaea (neeu).I?eioeei ioineo-oe Aaeeeay: ana oece/aneea caeiiu ia
iaiythony (eiaa?eaioiu) a ?aciuo eia?oe. neno. ion/.. Eee ana caeiiu
iaoaieee eiaa?eaioiu i?e i?eiaiaiee e iei i?aia?. Aaeeeay. Aeey
ia?aoiaea ec 1ie eia?oe. nenoaiu ion/. a ae?oa. Aaeeeae aaae i?aia?..
Ionoue eiaaony eia?oeeaeueiay neno. ion/., iieiae. oae a eio. caaeaaony
aeaea?oiauie eii?aeeiaoaie. Iai?eia?, oi/ea A ia ?en. 10.3. E?iia
nenoaiu eii?ae. XYZ (iaicia/atho E), iiaeao auoue e ae?oaay
eia?oeeaeueiay neno. eii?ae., iai?eia?, X’Y’Z’ (iaciaai aa E’).
Eia?oeeaeueiay neno. eii?ae. E’ aeaeaeaony n iino. nei?-oueth u ioiineo.
nenoaiu E. I?ino?ainoai ecio?iiiia, a iai ia nou-aoao auaeaeaiiiai
iai?aae-y, iiyoiio oaeiaii aua?aoue iai?aae. ine OX niaiaaeathuei n
iai?aaeaieai nei?. u. O.a. neno. E’ aeaeaeaony aaeieue ine OX nenoaiu
ion/. E. Iieiae-a o/ee A a neno-a E caaeaaony aaeoi?ii r(x,y,z) eee aai
i?iaeoeeyie ia ine OX, OY e OZ, eio. ?aaiu, niioaaonoaaiii, x, y e z.
Iieiae-a oie aea o/ee a neno-a E’ caaeathony eii?aeeiaoaie x’, y’ e z’.
Naycue iaaeaeo x, y, z e x’, y’, z’ aeaaony i?aia?aciaaieyie Aaeeeay:
x’=x+ut; y’=y;z’=z; t’=t. Aeiiieieoaeueii e i?aia?aciaaieyi eii?ae.
aaaaeaii i?aia?aciaaiea a?aiaie (eiioe-y aeaeueiiaeaenoaey).
Eiaa?eaioiinoue icia/aao iacaaeneiinoue, iaeciaiiinoue ioiineo.
eaeeo-eeai oece/aneeo one-ee. A iaoaiaoeea iiae eiaa?eaioiinoueth
iiieiaaony iaeciaiiinoue aaee/eiu ioiineo. eaeeo-eeai i?aia?..
?anniio?ei, eaeea ia?aiao?u ia iaiythony i?e i?aia?aciaaieyo Aaeeeay,
o.a. yae. eiaa?eaioaie yoeo i?aia?.. Ia?aue-a?aiy. I?e ia?aoiaea io 1ie
eia?oe. nenoaiu ion/. e ae?oaie ia iaiyaony eae naii a?aiy t=t’, oae e
aeeeoaeueiinoue eaeiai-eeai niauoey ‘aeaeueoa’t : ‘aeaeueoa’t’= t’2 -t’1
= t2 -t1 = ‘aeaeueoa’t (10.2) Iiieii a?aiaie, iaeciaiiui inoaaony
?annoiyiea iaaeaeo aeaoiy oi/eaie. Iaicia/ei ?annoiyiea iaaeaeo oi/eaie
A e A /a?ac l a neno-a K e l’ a neno-a K’. Eii?aeeiaou yoeo oi/ae,
niioaaonoaaiii, xA, yA, zA, xB, yB, zB a neno-a K e x’A, y’A, z’A, x’B,
y’B, z’B a neno-a E’. ?annoiyiea iaaeaeo oi/eaie ii?-ny eo eii?aeeiaoai
ii oai?aia Ieoaai?a: l’ = ‘ei?aiue'( (x’A-x’B)^2 + (y’A-y’B)^2 +
(z’A-z’B)^2 ) = ‘ei?aiue'( (xA + vt – xB -vt)^2 + (yA-yB)^2 + (zA-zB)^2
) =l. (10.3) I?iaeeooa?aioee?oai ii a?aiaie niioiioaiey (10.1) e iieo/ei
i?aia?. Aaeeeay aeey nei?inoae: V’x=dx’/dt=dx/dt + u=Vx+u;
V’y=dy’/dt=dy/dt=Vy; V’z=dz’/dt=dz/dt=Vz; (10.4) I?iaeeooa?aioee?oai ii
a?aiaie e iieo/ei c-i i?aia?. onei?aiee i?e ia?aoiaea ec 1ie eia?oe.
nenoaiu ion/. a ae?oa.: a’x=dV’x/dt=dVx/dt + du/dt=dVx/dt=ax;
a’y=dV’y/dt=dVy/dt=ay; a’z=dV’z/dt=dVx/dt=ax; (10.5). Ec yoeo au?aaeaiee
aeaeii, /oi ana 3 i?iaeoeee onei?aiey ia ine eii?ae. inoathony iaeciai.
i?e ia?aoiaea ec nenoaiu ion/. E a E’. Oeei ia?cii, onei?aiea oiaea yae.
eiaa?eaioii i?aia?. Aaeeeay. C-i nio?aiaiey ianu aue noi?ioee?iaai oaea
iinea Aaeeeay e Iuethoiia. Ii, aeiaaaei, /oi a eeane/. iaoaieea iana
oaea ia caaeneo io auai?a nenoaiu ion/. e oaeaea yae. eiaa?eaioii
i?aia?. Aaeeeay.

9. C-iu eeane/. iaoaieee e eo eiaa?eaioiinoue ioiineo. i?aia?. Aaeeeay.
Ia?aue c-i Iuethoiia. Anyeia oaei a eia?oe. neno-a ion/. nio?aiyao nino.
iieiy eee =ia?iiai i?yiieeiaeiiai aeaeaeaiey, iiea aicaeaenoaea ni
noi?iiu ae?oaeo oae ia canoaaeo aai eciaieoue yoi nino.. 2e c-i
Iuethoiia. Onei?aiea oaea i?yii i?iii?oeeiiaeueii noiia nee,
aeaenoaothueo ia iaai e ia?aoii i?iii?oeeiiaeueii aai ianna. Caieoai
yoio c-i a aaeoi?iie oi?ia n o/aoii eeiaiaoe/aneeo niioiioaiee:
‘noiia’F(aaeoi?)(t)=ma(aaeoi?)(t)=mdv(aaeoi?)(t)/dt=m(d^2)r(aaeoi?)(t)/d
(t^2 ) (10.6.a); ‘noiia’F(aaeoi?)(t)=
mdv(aaeoi?)(t)/dt=d(mv(aaeoi?)(t))/dt=dP(aaeoi?)(t)/dt (10.6.a). C-i
Iuethoiia, caienaiiue a aeaea (10.6.a) eee (10.6.a) n iao. o/ee c?aiey
eiaao aeae AeO. Ethaay ec oi?ioee?iaie (10.6.a,a) 2ai c-ia Iuethoiia
iac. iniiaiui o?aaiaieai aeeiaieee. ?aoaiea yoiai o?aaiaiey yae. ini.
caaea/ae aeeiaieee (ii ecaanoiiio caeiio aeaeaeaiey oaea r(t) iaeoe
aeaenoaothuea ia yoi oaei neeu, a ia?aoiie caaea/a ii ecaanoiie caaenei.
aeaenoaothueo nee io a?aiaie ‘noiia’F(t) o?aaoaony iaeoe c-i aeaeaeaiey
oaea r(t)). 3e c-i Iuethoiia. Neeu, n eioi?uie acaeiiaeaenoaotho oaea
?aaiu ii aaee/eia, i?ioeaiiieiaeiu ii iai?aae-y e iai?aaeaiu aaeieue
eeiee acaeiaeaeno.. Yoio c-i ooaa?aeaeaao, /oi neeiaia aicaeaenoaea ia
oaei iineo oa?-a? acaeiaeaeno.. Yoio aea c-i ooaa?aeaeaao, /oi
acaeiaeaeno. anao oae yae. oeaio?aeueiuie. C-i anaie?iiai oyaioaiey,
ioe?uoue Iuethoiiii, eiiaaea iacuaatho /aoaa?oui c-iii Iuethoiia.
F(aaeoi?)=G(m1)(m2)/r^2 * r(aaeoi?)/r (10.7), aaea (r(aaeoi?)/r )
aaeeie/iue aaeoi?, iai?aaeaiiue aaeieue eeiee acaeiaeaeno.,
ii?aaeaeythuee iai?aae. a?aaeoaoeeiiiie neeu F(aaeoi?). Oaei,
aeaeaathuaany i?yiieeiaeii e =ia?ii ioiineo. nenoaiu ion/. E,
aneaaenoaea o?aaiaiee (10.4) aeaeaeaony oaeaea i?yiieeiaeii e =ia?ii
ioiineo. nenoaiu ion/. E’. Yoi iaicia/aao, /oi ia?aue c-i Iuethoiia
ni?aaaaeeea ai anao eia?oe. neno. ion/.. A neno-a eii?ae. E oi?ia caiene
2ai c-ia Iuethoiia ii?-ny o?aaiaieyie (10.6). Iineieueeo, onei?aiea e
iana eiaa?eaioiu ioiineo. i?aia?. Aaeeeay, o?-a (10.6) iaeeiaeiai
caienuaaaony a ?acee/i. eia?oe. neno. ion/.. Iineieueeo, aaee/eia neeu
ia iaiyaony i?e ia?aoiaea io 1ie eia?oe. nenoaiu ion/. e ae?oaie, o?aoee
c-i Iuethoiia oiaea eiaa?eaioai ioiineo. i?aia?. Aaeeeay. 4e c-i ia
ioaeaeaaony a aeieacaoaeuenoaa eiaa?eaioiinoe ioiineo. i?aia?. Aaeeeay,
iineieueeo ?annoiyiey, ianu e neeu ia iaiythony i?e ia?aoiaea ec 1ie
eia?oe. nenoaiu ion/. a ae?oa.. OI., ana caeiiu Iuethoiia eiaa?eaioiu
ioiineo. i?aia?. Aaeeeay. Yoi ci/eo, /oi iie ni?aaaaeeeau e
caienuaathony iaeeiaeiaui ia?cii ai anao eia?oe. neno. ion/..

(28) *anoi, e?iia e?oaiaie /anoiou eieaaaiee ‘aiaaa’=2’Ie’/T
eniieuecotho oeeeee/aneoth /anoioo ‘ith’=1/T. *anoioa ecia?yaony a
Aa?oeao, 1 Aoe – yoi 1 eieaaaiea a naeoiaeo. A iauai neo/aa aianoi
niauaiey o/ee n?aaeu ec iieiaeaiey ?aaiiaaney iiaeii aaanoe etha.
“eieaaethueeny” ia?aiao?. Aeey caoeiauo aiei oaeei ia?aiao?ii yae.
aeaaeaiea aaca a aeaiie oi/ea i?ino-aa. Caoeiaua aieiu – i?iaeieueiua
aieiu e oece/anee naiaeyony e i?ioeanno ?ani?ino?aiaiey a aaca eieaaaiee
aeaaeaiey. Yoe eieaaaiey iau/ii nicaeatho iooai eieaaaiee iaia?aiu
ia?iaiaeeeoey?ii aa ieineinoe. Aicieeathuea ia?aiaaeu aeaaeaiey e
i?aaenoaae. niaie caoeiaoth aieio. Iaeanoue /anoio, eio. neuoeo
/aeiaa/aneia ooi eaaeeo a aeeaiaciia 20-20000 Aoe. Ae?oaei /?acau/aeii
aaaeiui aeaeii aiei yae. yeaeo?iiaaieoiua aieiu. Yeaeo?iiaaieoiua aieiu
iiaoo aicieeaoue e ?ani?ino?aiyony a ionoii i?ino-aa, o.a. a aaeooia. Ec
o?aaiaiee Iaenaaeea neaae., /oi ia?aiaiiia iaaieoiia iiea nicaeaao
aie?oa naay a i?ino-aa ia?aiaiiia yeaeo?e/aneia iiea. A naith i/a?aaeue,
ia?aiaiiia yeaeo?e/aneia iiea nicaeaao aie?oa naay a i?ino-aa
ia?aiaiiia iaaieoiia iiea. Yoio i?ioean i?eaiaeeo e iiyaeaieth a
i?ino-aa iaeioi?ie aieiu – yeaeo?iiaaieoiie aieiu. Yoa aieia yae.
iiia?a/iie. Iai?yaeaiiinoe yeaeo?e/aneiai e iaaieoiiai iieae aieiu
ia?iaiaeeeoey?iu ae?oa ae?oao e iai?aae. ?ani?ino?aiaiey aieiu. Ia
?en.18.5 iieacaiu iai?yaeaiiinoe yeaeo?e/aneiai e iaaieoiiai iieae a
aaaouae aieia.Iniaaiiinoueth yeaeo?iiaaieoiuo aiei yae. oi, /oi aeey eo
?ani?ino?aiaiey ia o?aaoaony ieeaeie n?aaeu. Ia?aiaiiua yeaeo?iiaaieoiua
iiey iiaoo ?ani?ino?aiyoueny a aaeooia. Aeey eiee/anoaaiiiai iienaiey
aiei aaiaeyo 2 iiiyoey: eioaineaiinoue aieiu e iauaiioth ieioiinoue
yia?aee aieiu. Eioaineaiinoue aieiu – yoi n?aaeiyy ii a?aiaie yi-y,
ia?aiineiay aieiaie /a?ac aaeeie/ioth ie-aeue, ia?aeeaeueioth aieiiaiio
o?iioo, ca aaeeieoeo a?aiaie. Iauaiiay ieioiinoue yia?aee – yoi yi-y
aiei, i?eoiaeyuayny ia aaeeieoeo iauaia. Aieia – yoi i?ioean
?ani?ino?aiaiey eieaaaiee a i?ino-aa (a oi?oaie n?aaea , eae yoi eiaao
ianoi aeey caoeiauo aiei, eee a aaeooia, eae yoi eiaao ianoi aeey
yeaeo?iiaaieoiuo aiei). Yia?aey eieaaaiee ii?-ny aiieeooaeie e /anoioie.
Iia ~ eaaae?aoo aiieeooaeu eieaaaiee. A neno-a NE eioaineaiinoue aieiu
au?aaeaaony a Ao/i2. Aac auaiaea i?eaaaeai au?aaeaiey aeey eioaineaiinoe
e nei?. caoeiaie e yeaeo?iiaaieoiie aiei. Aeey caoeiaie aieiu: J = 1/2 *
pvA^2w^2 Vii=sqrt(E/p); Vi=sqrt(G/p) aaea A – aiieeooaea eieaaaiee
n?aaeu, ‘aiaaa’ – /anoioa, (, (//, (( – nei?inoue aieiu, i?iaeieueiie e
iiia?a/iie, ‘?i’ – ieioiinoue n?aaeu, a eio. ?ani?ino?aiyaony caoeiaay
aieia, E – eiooeoeeaio THiaa, G – eiyo. naeaeaa. ?ani?ino?aiaiea caoea a
oi?oaie n?aaea naycaii n iauaiiie aeaoi?iaoeeae. Iiyoiio aeaaeaiea a
eaaeae oi/ea n?aaeu iai?a?uaii eieaaeaony n /anoioie ‘aiaaa’ aie?oa
iaeioi?iai n?aaeiaai cia/aiey. Aeaaeaiea, aucaaiiia caoeiaie
aeaoi?iaoeeae n?aaeu iac. caoeiaui aeaaeaieai. Iaoa ooi aini?eieiaao
caoeiaua aeaaeaiey iaiaeeiaeiai ia ?aciuo /anoioao. Iaeanoue /anoio
,eio. aini?eieiaao ooi eaaeeo a aeeaiaciia 20 – 20000 Aoe. Iaeaieueoae
/oanoaeoaeueiinoueth ooi iaeaaeaao a aeeaiaciia /anoio ieiei 1000 Aoe.
Ia yoeo /anoioao ooi niiniaii aini?eieiaoue caoee, caoeiaia aeaaeaiea a
eio. ioe-ny ia 7 ii?yaeeia. Aeey eioaineaiinoe yeaeo?iiaaieoiie aieiu
ni?aaaaeeeai:
J=1/2*EoHo=1/2*sqrt(E*Eo/M*Mo)*Eo^2=1/2*sqrt(M*Mo/E*Eo)*Ho^2; aaea Ei e
Hi aiieeooaeu iai?yaeaiiinoe yeaeo?e/aneiai e iaaieoiiai iieae,
‘yineeiio'(E) e ‘ith'(M) aeeyeaeo?e/aneay e iaaieoiay i?iieoeaaiinoe
n?aaeu, ‘yineeiio’i (Eo) e ‘ith’i (Mo) aeeyeaeo?e/aneay e iaaieoiay
i?iieoeaaiinoe aaeooia – iinoiyiiua, aaaaeaiiua a neno-a NE. Nei?inoue
?ani?ino?aiaiey yeaeo?iiaaieoiuo aiei a n?aaea =a V=1/sqrt(EMEoMo);, A
aaeooia E=M=1, iiyoiio nei?inoue yeaeo?iiaaieoiie aieiu a aaeooia
aoaeao =a c=1/sqrt(EoMo) = 3*10^8 m/c. Eae aeaeii, iia ?ania nei?.
naaoa a aaeooia – n, /oi ia oaeeaeoaeueii, iineieueeo naao yae.
yeaeo?iiaaieoiuie aieiaie.

(29) Iniiau eaaioiaie iaoaieee auee caeiaeaiu a ?aaioao eiioea 19-ai,
ia/aea 20-ai aaeia. A yoeo ?aaioao ane?uaaeenue iai?eie?eiua
i?ioeai?a/ey iaaeaeo i?eioeeiaie e caeiiaie eeane/. oeceee e
iaeiieaiiuie e oiio a?aiaie yenia?eiaioaeueiuie oaeoaie. Nia/aea
?anniio?ei yenia?eiaiou ii eceo/aieth e iiaeiuaieth naaoa. A ?aieao
eeane/. oeceee e yeaeo?iaeeiaieee Iaenaaeea eceo/aoue yeaeo?iiaaieoiua
aieiu iiaee eeoue ca?yaeaiiua /anoeoeu (iai?eia? yeaeo?iiu),
aeaeaeoueany n onei?aieai. If onei?aiea ca?yaeaiiie /anoeoeu eciaiyaony
ii aa?iiie/aneiio caeiio n /anoioie ‘aiaaa’ (ni. oi?ioeo (18.3)), oi
eceo/aoue oaeay /anoeoea aoaeao ia oie aea /anoioa ‘aiaaa’, o.a. a aa
niaeo?a aoaeao i?enoonoaiaaoue eeoue iaeia aeeeia aieiu (eee /anoioa).
Oaeea niaeo?u iacuaathony eeiae/aouie. If aea onei?aiea /anoeoeu
eciaiyaony ii ethaiio caeiio, ioee/iiio io (18.3), eee ia iaiyaony
aiana, oi niaeo?u eceo/aiea oaeeo /anoeoe aoaeoo nieioiuie eee
iai?a?uaiuie, o.a. a ieo aoaeoo i?enoonoaiaaoue aieiu ni anaie aeeeiaie
(eee /anoioaie) a iaeioi?ii aeeaiaciia. Ia ?en.19.1iieacaiu
yenia?eiaioaeueii iaaethaeaaiua niaeo?u eceo/aiey iaa?aoiai oaa?aeiai
oaea e ?ac?aaeaiiiai aaca. Ia ?en.19.1 ii ai?eciioaee ioeiaeaiu aeeeiu
aiei, ia eio. eceo/aaony naao, a ii aa?oeeaee – ioiineoaeueiua
eioaineaiinoe eceo/aiey a oneiaiuo aaeeieoeao. If niaeo? eceo/aiey
iaa?aoiai oaea ia ia?aue acaeyae ia i?ioeai?a/eo eeane/. O. eceo/aiey,
oi niaeo? eceo/aiey ?ac?aaeaiiuo aacia ia iiaeao auoue iauyniai n
iiceoeee eeane/. yeaeo?iaeeiaieee. Enneaaeiaaiea niaeo?a eceo/aiey
aiaei?iaea iieacaee, /oi aeeeiu aiei eceo/aiey iiae/eiythony i?inoie
caeiiiia?iinoe: 1/lambda=R(1/n1^2-1/n2^2), aaea R(((10967776(((5(i-1) –
iinoiyiiay ?eaeaa?aa, iacaaiiay a /anoue oaaaeneiai oeceea
TH.?.?eaeaa?aa((1854-1919), eiathuay niune a?aie/iie aeeeiu aieiu
iaaeaeo nieioiui e eeiae/aoui niaeo?ii a ieion 1ie noaiaie, n1 e n2(((
iaoo?. /enea, i?e/ai n1(((n2. Ioiaoei aaaeiue iiiaio. Oi?ioea,
iienuaathuay niaeo? eceo/aiey aiaei?iaea niaea?aeeo iaai? oeaeuo /enae.
A eaaioiaie oeceea eiaii oeaeua /enea ea?atho aaaeioth ?ieue i?e
iienaiee iiaaaeaiey iee?inenoai. Iiiuoee iieo/eoue /oi-eeai iiaeiaiia n
iiceoeee eeane/. oeceee auee i?inoi aanniuneaiiu. A eiioea i?ioeiai a.
?yae o/aiuo naeaeaee iiiuoee iieo/eoue oi?ioeu, iienuaathuea eceo/aiea
iaa?aouo oaa?aeuo oae. Ancii, /oi a iniiaa anae oai?e eaaeaee
eeanne/aneea i?aaenoaae.. ?yeath a 1900-ii aiaeo e Aeaeeino a 1904-ii
aiaeo oaeaeinue auaanoe oaeoth oi?ioeo, aa a?aoee i?eaaaeai ia ?en.19.1
ioieoe?ii. A eio?ae?aniie iaeoe niaeo?a yoa caaeneiinoue oi?ioi
niaeanoaony n yenia?eiaioii, a iaeoe aeaeeiiai naaoa iia ?anoiaeeony n
yenia?eiaioii i/aiue neeueii, a a oeueo?aoeieaoiaie iaeoe –
eaoano?ioe/anee. Auaiae oi?ioeu ?aeay-Aeaeeina aue i?iaaaeai a ?aieao
eeane/. oeceee aacoi?a/ii, a ?acoeueoao iieo/eeny aano?aeiui, iineieueeo
eceo/aaiay iaa?aoui oaeii yi-y aeieaeia auea ii yoie oi?ioea no?aieony e
aaneiia/iinoe. Ianiiniaiinoue eeane/. oeceee iauynieoue eceo/aiea
iaa?aoiai oaea iacaaee “oeueo?aoeieaoiaie eaoano?ioie”. Nouanoaiaaee aua
ae?oa. yenia?eiaiou ii oioiyooaeoo, i?iaaaeaiiua a 1888-1890 aa iaoei
niioa/anoaaiieeii A.A.Noieaoiaui (1839-1896). Eaeay yenia?eiaioa
caeeth/aeanue a neaae-i: naaoiaia eceo/aiea iai?aaeyeinue ia ieanoeio
iaoaea – eaoiae, iaoiaeyuothny a noaeeyiiie ioea/aiiie eieaa (?en.19.2).
A yoie aea eieaa aiiae. Iaaeaeo yeaeo?iaeaie i?eeeaaeuaaeinue
iai?yaeaiea o?aaoaiie iiey?iinoe. Naao au?uaae ec eaaeiaea yeaeo?iiu,
eio. caoai iiiaaeaee ia aiiae. Iaiyy ?aciinoue iioaioeeaeia iaaeaeo
eaoiaeii e aiiaeii iiaeii auei ii?aaeaeeoue yia?aeth au?aaiiuo
yeaeo?iiia e enneaaeiaaoue caaeneiinoue yoie yia?aee io ia?aiao?ia
yeaeo?iiaaieoiiai eceo/aiey. Aeey ii?aaeaeaiey eei. yia?aee au?aaiiuo
yeaeo?iiia iaiaoiaeeii auei i?eeiaeeoue iaaeaeo aiiaeii e eaoiaeii
io?eoeaoaeueiia iai?yaeaiea U. Eiaaea noiia eei. e iio. yia?aee
yeaeo?iia ieacuaaeanue io?eoeaoaeueiie, yeaeo?e/aneee oie, nicaeaaaaiue
eaoyueie yeaeo?iiaie i?ae?auaeny. mv^2/2-eU mv^2/2=eUmin. Oeei
ia?cii, ecia?yy ieieiaeueiia caaea?aeeaathuaa iai?yaeaiea iaaeaeo
aiiaeii e eaoiaeii, iiaeii auei iaeoe eeiaoe/aneoth yia?aeth aueaoaaoeo
yeaeo?iiia. Iiuou Noieaoiaa iieacaee, /oi yi-y au?aaiiuo ec eaoiaea
yeaeo?iiia eeiaeii naycaia n /anoioie iaaeathuaai naaoa. Ec eeane/. aea
O. neaaeiaaei, /oi eo yi-y aeieaeia auoue i?iii?oeeiiaeueiie eaaae?aoo
aiieeooaeu iai?yaeaiiinoe yeaeo?e/aneiai iiey iaaeathuae
yeaeo?iiaaieoiie aieiu eee eioaineaiinoe yoie aieiu. Oeei ia?cii,
iaaethaeaeinue yaiia ?anoiaeaeaiea eeane/. O. n yenia?eiaioii. A iniiaa
“eeanne/a neeo” oai?ee oaieiaiai eceo/aiey e oioiyooaeoa eaaeaei
i?aaeiieiaeaiea i iai?a?uaiinoe i?ioeana eceo/aiey e iiaeiuaiey
yeaeo?iiaaieoiuo aiei, o.a. n/eoaeinue, /oi iiaoo iiaeiuaoueny e
enioneaoueny ethaua ii?oeee yia?aee. Iaieoe “oeueo?aoeieaoiaoth
eaoano?ioo” oaeaeinue I.Ieaieo (1858-1947). A 1905 aiaeo ei aue naeaeai
aeieeaae ia canaaeaiee Aa?eeineie Aeaaeaiee iaoe, a eio. ii i?aaeeiaeee
i?aaeeueioth oi?ioeo, ea/anoaaiii e eiee/anoaaiii iauyniythuoth
eceo/aiea iaa?aouo oae. I.Ieaie iie?aeny ia aeiioaco, /oi naao
enioneaaony ii?oeeyie – eaaioaie n yia?aeae, =ie E=hV aaea
h((((6,6254(((0,0002)(10-34 Aeae(n – iinoiyiiay Ieaiea, a v – /anoioa
yeaeo?iiaaieoiiai eceo/aiey. Ancii, /oi aeiioaca Ieaiea i?ioeai?a/eea
eeanne/aneei i?aaenoaaeaieyi O. yeaeo?iiaaieoiiai eceo/aiey –
yeaeo?iaeeiaieee Iaenaaeea e ia?aiia/aeueii i?eieiaeanue eae aano?aeoiay
aeiioaca. Aeiioaco Ieaiea ?acaee A.Yeiooaei. Ii i?aaeiieiaeee, /oi
yeaeo?iiaaieoiia eceo/aiea ia oieueei enioneaaony, ii e iiaeiuaaony
ii?oeeyie – eaaioaie. A ?aieao yoiai i?aaeiieiaeaiey Yeiooaei niia eaaei
iauynieoue iiuou ii oioiyooaeoo. Aeaenoaeoaeueii, ec c-ia nio?aiaiaey
yia?aee neaae., /oi iiaeiuaiiue eaaio naaoa n yia?aeae E=hv o?aoeony,
ai-ia?a., ia ?aaioo auoiaea Aa, iaiaoiaeeioth aeey au?uaaiey yeaeo?iia
ec iaoaea, e, ai-aoi?uo, ia niiauaiea yeaeo?iio eei. yia?aee. A
i?aaeiieiaeaiee, /oi 1 eaaio yia?aee iiaeao auaeoue ec iaoaeeea oieueei
1 yeaeo?ii, c-i nio?aiaiey yia?aee caienuaaaony: Hv=As+mv^2/2; Yoi o?-a
naaiaeiy iac. o?aaiaieai Yeiooaeia aeey oioiyooaeoa. Ec iaai iaeiicia/ii
neaae., /oi yi-y oioiyeaeo?iiia naycaia eeiaeiie caaeneiinoueth n
/anoioie iaaeathuaai naaoa. Iicaeiaa A.Yeiooaei a ?aieao yoie aeiioacu
nicaeae eaaioiaoth O. eceo/aiey e iiaeiuaiey naaoa, eio. yae. iniiaie
eaaioiaie yeaeo?iaeeiaieee e eaaioiaie yeaeo?iieee.

(30) No?iaiea aoiia, iiuo ?aca?oi?aea A ia/aea iaoaai a. auei ecaanoii,
/oi nou-aoao ?aaeeiaeoeaiue ?aniaae aoiiia, a oiaea eio. ec aoiia
aueaoatho iieiaeeoaeueii e io?eoe-ii ca?yaeaiiua /anoeoeu (a oii /enea
yeaeo?iiu). Ia iniiaaiee yoeo yenia?eiaioia i?aaeiieaaaeinue, /oi
iieiaeeoaeueiue ca?yae ?ani?aaeaeai =ia?ii a i?aaeaeao oa?a, ?aaeeonii
ii?yaeea a ~ 10-10 i, a yeaeo?iiu iaoiaeyony aioo?e yoiai oa?a e
acaeiiaeaenoaotho n ioaeaeueiuie aai /anoyie e ae?oa n ae?oaii ii caeiio
Eoeiia. Yoa iiaeaeue aoiia auea i?aaeeiaeaia a 1903 a. aiaeeeneei
oeceeii Ae.Ae.Oiiniiii (1856-1940) e /anoi iacuaaeanue iiaeaeueth
“ioaeeia n ecthiii”. Iaeiaei, aieioue aei 1911 a., aei iiuoa
Y.?aca?oi?aea (1871-1937), ia auei ieeaeeo aeiioac, iauyniythueo
eeiae/aoua niaeo?u eceo/aiey ?ac?aaeaiiuo aacia. ?aca?oi?ae iinoaaee
iiuo ii ?annaeaaieth ‘aeueoa'(((/anoeoe (yaea? aoiia aaeey), eio.
?iaeaeaeenue i?e ?aaeeiaeoeaiii ?aniaaea iaeio. ye-oia. Ana
‘aeueoa'(((/anoeoeu aueaoaee n i?aeoe/anee iaeeiaeiauie nei?inoyie
ii?yaeea 107 i/n, i?ioiaeeee neaicue oiieoth iaoaeee/aneoth oieueao
(ni.?en.19.3), ioeeiiyeenue io naiaai ia?aiia/aeueiiai iai?aae-y e
?aaeno?e?iaaeenue ia ye?aia ec na?ienoiai oeeiea a aeaea naaoiauo
aniuoae, aeaeiuo iiae iee?ineiiii. A niioaaonoaee n iiaeaeueth aoiia
Oiiniia ‘aeueoa'(((/anoeoeu aeieaeiu auee i?e eaaeaeii noieeiiaaiee n
aoiiii ioeeiiyoueny ia i/aiue iaaieueoea oaeu, ii?yaeea 0,01I(0,1I. A
?acoeueoaoa iiiai/eneaiiuo noieeiiaaiee n aoiiaie i?e i?ieaoa neaicue
oieueao ‘aeueoa'(((/anoeoeu aeieaeiu auee ioeeiieoueny ia oaeu ii?yaeea
1I(10I. *anoeoe, ioeeiieaoeony ia aieueoea oaeu auoue ia iiaei, /anoeoe,
nianai ia ioeeiieaoeony aeieaeii auei auoue i/aiue iaei. *oi aea
iaaethaeaeinue a aeaenoaeo-oe? Ia iiuoa ieacaeinue, /oi (99(( /anoeoe
aiiaua ia ioeeiieeenue io naiaai iai?aae-y, o.a. ia noaeeeaaeenue n
aoiiaie, i?ieaoay neaicue oieueao. Yoi cia/eei, /oi ((99(( ec /enea
ioeeiieaoeony /anoeoe i?e i?ieaoa neaicue oieueao eniuoaee eeoue
iaeiie?aoiia noieeiiaaiea n aoiiaie. Oeei ia?cii, a iiuoa ?aca?oi?aea
oaeoe/anee iaaethaeaeinue noieeiiaaiea ‘aeueoa'(((/anoeoeu n iaeeii/iui
aoiiii. Ieacaeinue, /oi ‘aeueoa'(((/anoeoeu, noieeioaoeany n aoiiii
ioeeiiyeenue a n?aaeiai ia ai?acaei aieueoea oaeu, /ai iaeeaeaeinue.
N?aaee ?annayiiuo /anoeoe auee ioeeiieaoeany ia i/aiue aieueoea oaeu,
aieioue aei 180I. Oaie ?annayiey caaeneo io neeu acaeiaeaeno.
‘aeueoa'(((/anoeoeu n aoiiii. Yoa neea – neea Eoeiia i/aiue neeueii
caaeneo io ?annoiyiey: Fmax=kq’aeueoa’Qr^-2. A yoie oi?ioea k –
eiinoaioa, caaenyuay io auai?a nenoaiu aaeeieoe, q’aeueoa’ – ca?yae
‘aeueoa'(((/anoeoeu, Q – iieiaeeoaeueiue ca?yae, eiathueeny a aoiia. A
?aieao iiaeaee Oiiniia ‘aeueoa'(((/anoeoeu aeieaeiu i?ieaoaoue neaicue
aoiiu. Iaeneiaeueiay neea eo acaeiaeaeno. n aoiiii aoaeao ia a?aieoea
aoiia i?e r=a, o.a. Fmax=kq’aeueoa’Qa^-2 (ia iaiueoeo ?annoiyieyo
acaeiaeaenoaea aoaeao i?ienoiaeeoue ia ni anai ca?yaeii Q, a eeoue n aai
/anoueth, oiaiueoathuaeny auno?aa, /ai r2. Oeei ia?cii, i/aiue aieueo
cia/. neeu Eoeiia iiaeao auoue aeinoeaiooi eeoue a oii neo/aa, eiaaea
iieiaeeoaeueiue ca?yae aoiia aoaeao nin?aaeioi/ai a i/aiue iaeaiueeii
yae?a ?acia?ii Rss~10-14 i, o.a. a 10000 ?ac iaiueoa ?acia?ia aoiia. If
a yoii yae?a aoaeao nin?aaeioi/aia i?aeoe/anee any iana aoiia, oi i?e
noieeiiaaiee n oaeei yae?ii ‘aeueoa'(-((/anoeoeu aoaeoo iaiyoue
o?aaeoi?eth ca n/ao eoeiiianeeo nee acaeiaeaeno.. Ec iiuoa ?aca?oi?aea
neaaeiaaei, /oi aoii eiaao eioth no?oeoo?o, /ai ii Oiiniio. A aoiia
eiaaony i/aiue iaeaiueeia iieiaeeoaeueii ca?yaeaiiia yae?i, aie?oa eio.
a?auathony yeaeo?iiu. Ianna yeaeo?iiia iaea ii n?aaiaieth n ianie yae?a.
Iaeiaei, yoa iiaeaeue aoiia i?ioeai?a/eea eeane/. yeaeo?iaeeiaieea. A
/ai aea nino. yoi i?ioeai?a/ea? *oiau yeaeo?iiu ia oiaee ia yae?i, iie
aeieaeiu a?auyoueny aie?oa iaai iiaeiaii ieaiaoai a Nieia/iie neno-a.
Iaeiaei a?auaynue, iie eniuouaatho onei?aiea, e, a niioaaonoaee n
caeiiaie eeane/. yeaeo?iaeeiaieee, aeieaeiu eceo/aoue yia?aeth a aeaea
yeaeo?iiaaieoiuo aiei. Eceo/ay yia?aeth yeaeo?ii nai aeieaeai aue aa
oa?youe e i?eaeeaeaoueny e yae?o. *a?ac i/aiue ei?ioeia a?aiy ~ 10-8 n
yeaeo?ii aeieaeai aue au oianoue ia yae?i e aoii, niioaaonoaaiii,
i?ae?aoeoue naia nou-iea. (31) Ei?ioneoey?ii – aieiiaie aeoaeeci.
Oeceeaie auee i?aaei?eiyou iiiuoee nicaeaiey oai?ee, eio. iiaee au
iauynieoue yenia?eiaiou Y. ?aca?oi?aea. Iaeaieueoee neaae inoaaeea O. I.
Ai?a, nicaeaiiay a 1913 a. A aa iniiaa eaaeao 2 iinooeaoa. Ia?aue
iinooeao. Ec anao aiciiaeiuo i?aeo yeaeo?iia a aoiia inouanoaeythony
oieueei oa, eio. iiae/eiythony o?aaiaaieyi aeene?aoiinoe, o.a. ia
iai?a?uaiiio ?ani?aaeaeaieth yia?aee, a aeene?aoiiio, ?ac?uaiiio.
Yeaeo?ii, iaoiaeyueeny ia oaeie i?aeoa ia eceo/aao, ianiio?y ia oi, /oi
ii aeaeaaaony n onei?aieai e n o/ee c?aiey eeane/. yeaeo?iaeeiaieee
aeieaeai eceo/aoue yeaeo?iiaaieoiua aieiu. I?aeou, aeaeaaynue ii eio ,
yeaeo?ii ia eceo/aao , iacuaatho noaoeeiia?iuie. Oneiaea aeey
noaoeeiia?iuo i?aeo I.Ai? iieo/ee enoiaey ec iinooeaoa I.Ieaiea i
eaaioiaaiiinoe yia?aee yeaeo?iiaaieoiiai eceo/aiey. Niaeanii yoiio
iinooeaoo, yi-y nenoaiu (aa?iiie/aneiai inoeeeeyoi?a o I.Ieaiea e
yeaeo?iia a aoiia o I.Ai?a) =a: En=nhw/2I=nhv (ci. Oi?ioeo 19.3 ). Yoio
iinooeao ii?aaeaeyao i?aaeei eaaioiaaiey iiiaioa eie-aa aeaeaeaiey
yeaeo?iia Ln a niioaaonoaee n oi?ioeie 19.3. Aai cia/. aeieaeii auoue
?aaiui: Ln = mvr = nh/2i, aaea m, v e r- iana, nei?inoue e ?aaeeon
i?aeou yeaeo?iia, h – iinoiyiiay Ieaiea, a n iaoo?. /enei, i?eieiathuaa
cia/aiey 1,2,3… Ia?aue iinooeao ii?aaeaeee aaaeiia iai?aae. ai anae
eaaioiaie oeceea. Ii aaae iiiyoea eaaioiaaiiinoe ia?aiao?ia,
iienuaathueo aeaeaeaiea /anoeoeu. Yoe ia?aiao?u : nei?inoue, eiioeuen
eee eie-ai aeaeaeaiey, iiiaio eie-aa aeaeaeaiey, ?aaeeon i?aeou e,
eiia/ii, yi-y ia iiaoo i?eieiaoue iai?a?uaiue iaai? cia/aiee, eae yoi
eiaei ianoi a eeane/. oeceea. Iie iiaoo i?eieiaoue oieueei iaeioi?ue
iaai? aeene?aoiuo cia/aiee. 2e iinooeao ooaa?aeaeae: i?e ia?aoiaea
yeaeo?iia n 1ie noaoeeiia?iie i?aeou ia ae?oa. eceo/aaony eee
iiaeiuaaony eaaio yia?aee. Yia?aey eaaioa =a ?aciinoe yia?aee oao
noaoeeiia?iuo ninoiyiee iaaeaeo eioi?uie i?iecioae ia?aoiae. If
yia?aeth iaeiiai ninoiyiey iaicia/eoue /a?ac En, a ae?oaiai /a?ac Em, oi
eceo/aaony eaaio n /anoioie Wnm, aaea Wnm oaeiaeaoai?yao oneiaeth:
2IhWnm =En-Em.(w-iiaaa,I – ie). Aaaaeaiiua iinooeaou iicaieeee I.Ai?o
iieo/eoue aeene?aoiue niaeo? eceo/aiey aoiia e aeey aiaei?iaea auaanoe
oi?ioeo 19.1. Neaaie noi?iiie O. I.Ai?a auea aa aioo?aiiyy
i?ioeai?a/eainoue. Iia ia auea ie iineaaeiaaoaeueii eeane/., ie
iineaaeiaaoaeueii eaaioiaie O.. A neeo yoiai, iia ia iicaieyea
iauyniyoue niaeo?u > neiaeiuo, /ai aiaei?iae aoiiia. Iia yae. oieueei
ia?aoiaeiui oaaii ia iooe e nicaeaieth iineaaeiaaoaeueiie O.,
iauyniythuae iiaaaeaiea iee?inenoai. O. Ai?a auea e?oiiui oaaii a
?acaeoee aoiiiie e anae eaaioiaie oeceee. A ia?aoth i/a?aaeue iia
iieacaea iai?eiaieiinoue i?aaenoaaeaiee eeane/. oeceee e iee?inenoaiai,
a oii /enea e aoiio e iaiaoiaeeiinoue aaaaeaiey eaaioiaaiiinoe
ia?aiao?ia iee?inenoaiu. Ia?aie/aiey O. Ai?a iieacaee iai?eaieeiinoue
eeanne/aneiai iiaeoiaea e iienaieth iee?inenoai. O?aaiaaeinue
auaeaeiooue iiaoth, aeiaaeueioth eaeath, ia iniiaa eio. iiaeii auei au
iieo/eoue oeaeinoioth, iai?ioeai?a/eaoth O. iee?iie?a. Oaeay eaeay auea
auaeaeiooa oieueei /a?ac 11 eao iinea nicaeaiey O. Ai?a. A 1924 aiaeo
o?aioe. o/aiue Eoe aea A?ieeue auaeaeioe aeiioaco i aeaienoaaiiinoe
i?e?iaeu iee?iie?a. Ii i?aaeiieiaeee, /oi iee?i/anoeoeu iaeaaeatho
iaeiia?aiaii naienoaaie /anoeoe e aiei. Yoi iieiae., iai?eaieaiia n o/ee
c?aiey eeane/. oeceee, ieacaeinue oieaa?naeueiui i?e iienaiee ia oieueei
iee?i, ii e iae?iie?a. E.ae.A?ieeue i?aaeiieiaeee /oi ana nenoaiu, a oii
/enea e iee?i/anoeoeu, iaeaaeatho eae aieiiauie, oae e ei?ioneoey?iuie
naienoaaie. Niaeanii i?aaeiieiaeaieth, ethaiio oaeo, n ianie m,
aeaeaeouaiony ni nei?-oueth v , niioa. aieia: lambda=h/mv (19.4) Oi?ioeo
19.4 eaaei iieo/eoue i?eiaieoaeueii e eaaioai naaoa. Yia?aey eaaioa, eio
iiaeii i?eienaoue ianno m, ii?-ny n 1ie noi?iiu eae A=mc2 , n ae?oaie
noi?iiu iia =a E=hv-hc/lambda. I?e?aaieaay i?aaua /anoe yoeo oi?ioe e
o/eouaay, /oi aeey oioiia nei?inoue ?ani?ino?aiaiey v =a nei?. naaoa n,
iieo/aai oi?ioeo 19.4. Aeaeaeaiea oaea a i?ino-aa e a?aiaie i?ienoiaeeo
oaeaea, eae ?ani?ino?ai aieiu n aeeeiie lambda. Aii?in i
ei?ioneoey?ii-aieiiaii aeoaeecia aue i?aaeiaoii aeeneonnee a oa/aiee
ianeieueeeo aeanyoeia eao. Ia?aia/. aieiu E.aea A?ieey i?aaeiieaaaeenue
eae iaaeyaeii – ?aaeueiua aieiiaua i?ioeanu oeia yeaeo?iiaaieoiuo aiei.
Iicaeiaa aieiu E.aea A?ieey o?aeoiaaeenue eae iaeioi?ua aa?iyoiinoiua
aieiu, iienuaathuea aeaeaeaiea /anoeoe. A ianoiyuaa a?aiy iiaeii
i?aaeeiaeeoue neaaeothuoth o?aeoiaeo ei?ioneoey?ii-aieiiaiai aeoaeecia.
I?e ?ani?ino?aiaiee /anoeoeu a i?ino-aa aa aeaeaeaiea iienuaaaony
aieiie. I?e acaeiiaeaenoaee /anoeoeu n ae?oaeie nenoaiaie iia
i?iyaeyaony eae ei?ioneoea – /anoeoea. I?iua anaai yoi i?ineaaeeoue ia
i?eia?a oioiiia. Yeaeo?iiaaieoiua aieiu ?ani?ino?aiythony a i?ino-aa ii
caeiiai ?ani?ino?aiaiey aiei. Eiaaea yeaeo?iiaaieoiua aieiu
acaeiiaeaenoaotho n oaeaie (i?eia?ii iiaeao neoaeeo oioiyooaeo), oi
n?aco aea i?iyaeythony /enoi ei?ioneoey?iua na-aa. Yeaeo?iiaaieoiua
aieiu iiaeiuathony eae /anoeoeu n ii?aae. yia?aeae.

(32) IOAAO IONOONOAOAO! (Aieiiaay o-y; o?-a O?aaeeiaa?a).

(33) IOAAO IONOONOAOAO! (Niioiioaiea iaii?aaeaeaiiinoae Aaecaiaa?aa).

Aieiaiea! A neaae-i ?acaeaea iaeioi?ua aii?inu ia?ae?uaathony. Aeey
aa?aioe?iaaiii-oi?ioaai ioaaoa ia yecaiaia neaae. iciaeiieony n anaie 3
aii?naie (? 34, ? 35, ? 36).

(34) A ianoiyuaa a?aiy eiioe-y naiii?aaiecaoeee iieo/aao ana aieueoaa
?ani?ino?ai ia oieueei a anoanoaiciaiee, ii e a nioe-ii aoiaieoa?iuo
?acaeaeao iaoe. Aieueoeinoai iaoe eco/aao i?ioeanu yaiethoeee nenoai e
iie auioaeaeaiu aiaeece?iaaoue iaoaieciu eo naiii?aaiecaoeee. Iu iiae
naiii?aaiecaoeeae aoaeai iiae?acoiaaaoue yae-y, i?ioeanu , i?e eio.
nenoaiu (iaoaie/aneea, oeie/aneea, aeieiae/aneea e o.ae.) ia?aoiaeyo ia
ana > neiaeiua o?iaie, oa?aeoa?ecoaiua naieie caeiiaie, eio. ia
naiaeyony oieueei e caeiiai i?aaeuaeouaai o-iy. Oaeea i?eia?u iu
?aniao?eaaee a i?aaeuaeoueo ?acaeaeao. Eiioeaioeey naiii?aaiecaoeee a
ianoiyuaa a?aiy noaiiaeony ia?aaeeaiie. Iau/ii iiae ia?aaeeaiie a iaoea
iiae?acoiaaatho ooiaeaiaioaeueioth O., eio. i?eiaiyaony aeey iauyniaiey
oe?ieiai e?oaa yaeaiee, ioiinyueony e niioaaonoaothuae iaeoe eneaae..
I?eia?aie oaeeo oai?ee iiaoo neoaeeoue eeanne/aneay iaoaieea Iuethoiia,
yaiethoeeiiiia o/aiea Aea?aeia eee eaaioiaay oeceea. Nae/an cia/.
iiiyoey ia?aaeeaiu aua aieueoa ?anoe?eeinue, iineieueeo iii i?eiaiyaony
ia oieueei e ioaeaeueiui iaoeai, ii e e iaaeaeenoeeieeia?iui iai?aae-yi
eneaae..

(35) I?eioeei Ia?aoiie Nayce. Oeie/iui i?eia?ii oaeeo
iaaeaeenoeeieeia?iuo ia?aaeeai yae. aicieeoay iieaaea iacaae eeaa?iaoeea
e iiyaeaoaany /aoaa?oue a. nionoy neia?aaoeea. Iiae neia?aaoeeie a
ianoiyuaa a?aiy iiae?acoiaaatho iaeanoue iao/iuo eneaae., oeaeueth eio.
yae. auyaeaiea iaueo caeiii?iinoae a i?ioeannao ia?aciaaiey ,
onoie/eainoe e ?ac?ooaiey oii?yaei/aiiuo a?aiaiiuo e i?ino?ainoaaiiuo
no?oeoo? a neiaeiuo ia?aaiiaaniuo neno. ?acee/iie i?e?iaeu (oece/aneeo,
oeie/aneeo aeieiae/aneeo , yeieiae/aneeo, nioeeaeueiuo).

(36) Neia?aaoeea e Eeaa?iaoeea. Ii?aaeaeei, /oi eaaeeo a iniiaa
eeaa?iaoeee e neia?aaoeee. Eeaa?iaoeea a iniiaiii caieiaeanue aiaeecii
aeeiaie/aneiai ?aaiiaaney a naiii?aaiecothueony neno.. Iia iie?aeanue ia
i?eioeei io?eoeaoaeueiie ia?aoiie nayce , naenii eio anyeia ioeeiiaiea
nenoaiu ei??aeoe?oaony oi?aaeythuai ono?ienoaii iinea iieo/aiey neaiaea
eioi?iaoeee ia yoii. Iu n aaie noaeeeaaeenue n oaeei i?eia?ii, eiaaea
?aniao?eaaee ciaee a o?aaiaieyo Iaenaaeea, naycuaathueo iaaieoiua e
yeaeo?e/aneea iiey. Io?eoeaoaeueiue ciae a caeiia Oa?aaeay e icia/ae,
/oi aicaeaenoaea ei??aeoe?oaony a noi?iio aai oiaiueoaiey. Ae?oaie
i?eia?. Nai ioaoe eeaa?iaoeee I.Aeia? ?anneacuaae, eae aicieeea yoa
iaoea. Iia aicieeea, eiaaea noaee ecia?aoaoue naiiiaaiaeyueany caieoiua
nenoaiu. A yoeo neno. ano?aoeeenue n oaeie neooaoeeae, eiaaea
iai?aaeeueii iiaeaiiue ei??aeoe?othuee neaiae i?eaiaeee e auoiaeo ec
no?iy anae nenoaiu iaaaaeaiey. A iauai ?a/ue oea i oii, /oi a neno-a,
?acaeaathuaeny ii caaeaiiui caeiiai, naycue aeieaeia auoue
io?eoeaoaeueiie. Iiyniaiea auoaneacaiiiio aeaaony ?en. 5.1. A
neia?aaoeea enneaaeothony iaoaieciu aicieeiiaaiey iiauo ninoiyiee,
no?oeoo? e oi?i a i?ioeana naiii?aaiecaoeee, a ia nio?aiaiey eee
iiaeaea?aeaiey noa?uo oi?i. Iia iie?aaony ia i?eioeei iieiaeeoaeueiie
ia?aoiie nayce, eiaaea eciaiaiea, aicieeoaa a neno-a, ia iiaeaaeyaony
eee ei??aeoe?oaony, a iaiai?io, iaeaieeaathony e i?eaiaeyo e ?ac?ooaieth
noa?ie e aicieeiiaaieth iiaie nenoaiu. N o/ee c?aiey i?eaaaeaiiiai
I.Aeia?ii i?eia?a i?ioean naii?ac?ooaiey caieoiiai eiiieaena iia auoue
iienai n neia?aaoe/aneeo iiceoeee. A oi a?aiy yoio i?ioean n/eoaeny
noaoai io?eoeaoaeueiui e aai noa?aeenue iiaeaaeoue. Aeey oa?-a?enoeee
naiii?aaiecothueony i?ioeania i?eiaiytho ?acee/i. oa?ieiu, ia/eiay io
neia?aaoe/aneeo e eii/ay ia?aaiiaaniuie e aeaaea aaoiiiyoe/aneeie eee
naiiiaiiaeythueieny. Iaeiaei, ana iie au?aaeatho 1 e ooaea eaeath. A
aeaeueiaeoai o ian ?a/ue iieaeao i naiii?aaiecothueony neno., eio. yae.
ioe?uouie nenoaiaie , iaoiaeyueieny aaeaee io o/ee oa?iiaeeiaie/aneiai
?aaiiaaney. Eaeae yaiethoeee nenoai (einiiaiie/aneea, aeieiae/aneea,
oece/aneea) iieo/eee oe?ieia i?eciaiea a iaoea. Iaeiaei,aieioue aei
ianoiyuaai a?aiaie, iie oi?ioee?iaaeenue eiooeoeaiuie iiiyoeyie.
Oa?ieiieiae/aneee e iao/iue iiaeoiae ?acaeaaaony oieueei a ianoiyuaa
a?aiy. A ?aieo oai?eyo yaiethoeee iniiaiia aieiaiea ia?auaeinue ia
aicaeaenoaea ie?oaeathuae n?aaeu ia nenoaio. Iu > iiae?iaii yoi
?anniio?ei a O. yaiethoeee Aea?aeia. A aea?aeineie O. O. i?ienoiaeaeaiey
iiauo aeaeia ?anoaiee e aeeaioiuo iooai anoaaiiai ioai?a aeaaiue aeoeaio
aeaeaeny ia n?aaeo, eio. aunooiaea a ea/. ii?aaeaeythuaai oaeoi?a.
?acoiaaony, aiaoiea one-y n?aaeu ieacuaatho ia?iiiia aeeyiea ia
yaiethoeeth, ii yoi aeeyiea ia a iaiueoae noaiaiecaaeneo oaeaea e io
naiie nenoaiu, aa ninoiyiey e aioo. i?aae?aniieiaeaiiinoe. I?eaaaeai 2
i?eia?a. O ian anoue aiaeyiie ia?, i?e aai ioeaaeaeaiee ii ia?aoiaeeo a
iiaoth no?oeoo?o a aeaea e?enoaeeia.Nenoai > i?aaieciaaiiuo, /ai
oaioe/anee aeaeaathueany iieaeoeu aiaeu. Ii, yoio i?ioean eae
auyniyaony, iiaeao i?ienoiaeeoue oieueei oaaea, eiaaea a naiie n?aaea
anoue aeiiieieoaeueiua oeaio?u e?enoaeeiia?aciaaiey. O. a. iaiaoiaeeiui
one. yae. naia n?aaea e aa acaeiinayce. Ae?oaie i?eia?. Eaca?u. A
eaca?ao oaioe/aneia niiioaiiia eceo/aiea i?aa?auaaony a no?iai
i?aaieciaaiiia eiaeooee?iaaiiia, neaaenoaeai /aai e iiyae.
iiiio?iiaoe/aneia eceo/aiey. A yoeo i?eia?ao iu ia eniieueciaaee oi/iua
oa?-a?enoeee oii?yaei/aiiinoe eee naiii?aaieciaaiiinoe no?oeoo?u. A
neaae-i ?acaeaea iu aaaaeai ia?o oii?yaei/aiiinoe no?oeoo?u yio?iieth e
nayaeai n iae i?ioaeaiea i?ioeania. N o/ee c?aiey ia?aaeeaiu
naiii?aaiecaoeee noaei yniui, /oi one. ?acaeoey ia oieueei aeeauo, ii e
aeeiaie/aneeo nenoai aiiaua yae. acaeiaeaenoaea nenoaiu e ie?oaeathuae
n?aaeu. Oieueei a ?acoeueoaoa oaeiai acaeiaeaeno. i?ienoiaeeo iaiai
aauanoaii, yia?aeae e eioi?iaoeeae iaaeaeo nenoaiie e aa ie?oaeaieai.
Aeaaiaea?y yoiio aicieeaao e iiaeaea?aeeaaaony ia?aaiiaaniinoue, a yoi a
naith i/a?aaeue i?eaiaeeo e niiioaiiiio aicieeiiaaieth iiauo no?oeoo?.
Oaeeo eae e?enoaeeu eee eaca?iia eceo/aiea.

(34) Naiii?aaiecaoeey eae iniiaa yaiethoeee. Oeei ia?cii ,
naiii?aaiecaoeey aicieeaao eae enoi/iee yaiethoeee nenoai, oae eae iia
neoaeeo ia/aeii i?ioeana aicieeiiaaiey ea/anoaaiii iiauo e > neiaeiuo
no?oeoo? a ?acaeoee nenoaiu. *oiau iiiyoue, ii/aio naiii?aaiecaoeey
aunooiaao a iniiaa yaiethoeee, iaiaoiaeeii neacaoue ianeieueei neia i
oeoeooaoeeyo e oaina. ?anniio?ei oaeoth nenoaio, eae aac. Iieaeoeu aaca
aeaeaathony neo/aeii, oaioe/ii. Iaeiaei, a iiuoao n a?ioiianeei
aeaeaeaieai iu aeaeei, /oi neo/aeiua, oaioe/iua aeaeaeaiey iieaeoe
(iee?inenoai) iiaoo i?eaanoe e e eieeaeoeaiiio aeaeaeaieth
iae?ineiie/aneeo /anoeoe. Oeoeooaoeee i?aaenoaae. niaie neo/aeiua
ioeeiiaiey nenoaiu ia iee?i o?iaia. Ii ?acoeueoao eo aeaenoaey iiaeao
neacaoueny e ia iae?i o?iaia, i?e/ai iai?aaeneacoaiui ia?cii. A e?eoe/.
oi/ea yaiethoeee ,eae i?aaeei, ioe?uaaaony ianeieueei aiciiaeiinoae.
Eaeie iooue i?e yoii auaa?ao neno., a cia/eo. noaiaie caaeneo io
neo/aeiuo oaeoi?ia. E a oeaeii iiaaaeaiea nenoaiu iaeuecy i?aaeneacaoue
n iieiie aeinoiaa?iinoueth. Iu n aaie ?aniao?eaaee yoio aii? a ?acaeaea
Oeceea aiciiaeiiai. Iu aeaaea oeacaee a?aieoeu neo/aeiinoe a iiaaaeaiee
nenoaiu. A iee?iie?a auai? iiaaaeaiey nenoaiu ii?aaeaeai oieueei n
oi/iinoueth aei niioiioaiey iaii?aaeaeaiiinoae Aaecaiaa?aa. Oaeoe/anee
iu iieacaee, /oi a naiie neno-a caeiaeai oain, iaii?aaeaeaiiinoue. E yoa
iaii?aaeaeaiiinoue a e?eoe/aneeo oi/eao iiaaaeaiey nenoaiu iiaeao
i?eaanoe e ?acaeoeth iiaie no?oeoo?u n ia i?aaeneacaiiuie naienoaaie.

(37) ANOANOAAIII – IAO*IAss E AOIAIEOA?IAss EOEUeOO?U O/aiua e
niaoeeaeenou ian/eouaatho > 170 ii?aaeaeaiee iiiyoey eoeueoo?a. Yoi
naeaeaoaeuenoaoao i oieaa?naeueiinoe aeaiiai yae-y /aeianeiai iaunoaa.
Iiiyoeai eoeueoo?a iaicia/atho e iau/iua yae-y, e ni?oa ?anoaiee e
oinoaaiiua ea/-aa /aea, e ia?ac aeecie, e nenoaio iieiaeeoaeueiuo
oeaiiinoae e oae aeaeaa. A oaeii eiioaenoa ana nicaeaiiia /aeii anoue
eoeueoo?a. Iu eniieuecoai iaeii ec ii?aaeaeaiee eoeueoo?u, eio. naycaii
n aa eino?oiaioaeueiie o?aeoiaeie. Eoeueoo?a – yoi neno. n?-a /aeianeie
aeayo-oe, aeaaiaea?y eio. ?aaeecothony aeaenoaey eiaeeaeaea, a?oii,
/aeiaa/anoaa a eo acaeiiaeaenoaee n i?e?iaeie e iaaeaeo niaie. Yoe n?-aa
nicaeathony ethaeueie , iinoiyiii iaiythony e niaa?oainoaothony. I?eiyoi
auaeaeyoue 3 oeia eoeueoo?u: iaoa?eaeueioth, nioeeaeueioth e aeooiaioth.
Iaoa?eaeueiay eoeueoo?a -niaieoiiinoue n?-a auoey /aea e iaunoaa. Iia
aee ?aciiia?aciua oaeoi?u: i?oaeey o?oaea, oaoieeo, aeaanino-a /aea e
iaunoaa. Nioeeaeueiay eoeueoo?a – yoi neno. i?aaee iiaaaeaiey ethaeae a
?acee/i. aeaeao iauaiey. Iia aee yoeeao, i?ioanneiiaeueioth, i?aaiaoth,
?aeeaeicioth e o. ae. ?aciiaeaeiinoe aeayo-oe /aea. Aieaa iiae?iaii
niaea?aeaoaeueiay /anoue 1ie e 2e eoeueoo? eco/aaony a ae?oaeo
aeenoeeieeiao. Aeooiaiay eoeueoo?a – yoi ninoaaiay /anoue eoeueoo?iuo
aeinoeaeaiee /aeiaa/anoaa. Ini. aeaeu aeooiaiie eoeueoo?u – ii?aeue,
i?aai, ie?iaicc?aiea, eaeaieiaey, ene-ai, iaoea e o.ae. Eaaeae ec yoeo
aeaeia aeooiaiie eoeueoo?u nino. ec ioiineo. naiinoiyoaeueiuo /anoae.
Yoe /anoe acaeiinaycaiu e ioiinyony e aeooiaiie eoeueoo?a /aeiaa/anoaa.
Iiae iaoeie a ianoiyuaa a?aiy iiieiatho oo noa?o /aeianeie aeayo-oe, o-y
eio. – au?aaioea e oai?aoe/ nenoaiaoecaoeey iauaeoeai. ciaiee i
aeaenoaeo-oe. Neno. iaoe oneiaii aeaeeony ia anoaaiua, iauanoaaiiua e
oaoie/aneea iaoee. A iaoea i?eiyoi auaeaeyoue nenoaio ciaiee i i?e?iaea
– anoanoaiciaiea, eio. yae. i?aaeiaoii anoanoaaiiiiao/iie eoeueoo?u e
nenoaio ciaiee i iiceoeaii cia/eiuo oeaiiinoyo auoey eiaeeaeaea, a?oii
, ain-aa, /aeiaa/anoaa – aoiaieoa?iua iaoee eee aoiaieoa?ioth
eoeueoo?o. Aei oiai, eae iaoea ioi?ieeanue a naiinoiyoaeueioth /anoue
eoeueoo?u /aeiaa/anoaa, ciaiey i i?e?iaea e oeaiiinoyo iau-aaiie aeecie
aoiaeeee a eiua ninoiyiey aeooiaiie eoeueoo?u : i?aeo. iiuo, ioae?inoue,
ia?iaeiay iaaeeoeeia, iaoo?oeeinioey e o.ae. Acaeiinaycue
anoanoaaiiiiao/iie e aoiaieoa?iie eoeueoo? caee. a neaae-i: * iie eiatho
aaeeioth iniiao, au?aaeaiioth a iio?aaiinoyo e eioa?anao /aea e
/aeiaa/anoaa, a nicaeaiee iioeiaeueiuo one-ee aeey naiinio?aiaiey e
naiiniaa?oainoaiaaiey; * inouanoaeytho acaeiiiaiai aeinoeaioouie
?acoeueoaoaie; * acaeiii eii?aeeie?otho a i?ioeana ?acaeoey
/aeiaa/anoaa; * yae. naiinoiyoaeueiuie aaoayie aaeeiie nenoaiu ciaiee
iaoee e aeooiaiie eoeueoo?u a oeaeii. Iu yaeyainy naeaeaoaeyie oiai, eae
nioeeieiae, th?enou, yeiiiienou, iaiaaeaea?u e ae?oa. niaoeeaeenou –
aoiaieoa?ee ia/eiatho i?eiaiyoue a naiae ?aaioa nenoaiiue iiaeoiae,
eaeae e iaoiaeu eeaa?iaoeee e O. eioi?iaoeee, ciaiea ooiaeaiaioaeueiuo
caeiiia anoanoaiciaiey e a /anoiinoe oeceee. Iiyniei auoaneacaiiia
i?eia?aie ec i?aeoeee. TH?eno ?acae?aao aeaei i noieeiiaaiee noaeia.
Eiia/ii, aio ioaeii ciaoue caeiiu, i?eiyou a ie?iaie i?aeoeea
noaeiaiaeaeaiey. Ii, n ae?oaie noi?iiu, if ii ia ciaao, /oi oaeia iana,
?aaeeon iiai?ioa, nei?inoue, onei?aiea e o. ae. , ii ia niiaeao
?aaeueii i?eiaieoue naie i?ioanneiiaeueiua ciaiey. Nioeeieia eco/aao
iau-iia iiaiea iooai ii?ina. Ii eae ii niiaeao ioeaieoue noaiaiue
aeinoiaa?iinoe ?acoeueoaoia, if ia eiaao i?aaenoaaeaiea i O. aa?iyoiinoe
e O. iia?aoiinoae. Aac ciaiey yoeo ?acaeaeia anoaaiuo iaoe, ?acoeueoaou
aai i?aaeneacaiee ia aoaeoo i?aaenoaaeyoue i?aeoe/aneie oeaiinoe.
Iaiaaeaea? ?aeeaie?oao ecaeaeea eaeiai – oi i?aaei?eyoey. Oi?ioi
ecaanoii, /oi ia aunoaaeao eee i?iniio?ao ia?aua aii?inu anaaaea
eanathony oaoi. noi?ii ecaeaeey. Eiia/ii, iieiinoueth ioaaoeoue ia oaeea
aii?inu iiaeao oieueei niaoeeaeeno, eiathuee oi?iooth ooiaeaiaioaeueioth
anoanoaaiiiiao/ioth iiaeaioiaeo. Iaeiaei ?acae?aoueny a yoeo aii?inao
aeieaeai e iaiaaeaea?. Nouanoaoao e ae?oaay noi?iia ?anniao?eaaaiiai
aii?ina. Iaoea /anoi iaaeiyaony a oao a?aoao, a eio. iiaeiia ia noieueei
iia naia, neieueei oa neno. einoeoooia, a ?aieao eio. iia ooieoeeiie?oao
e ?acaeaaaony. A ianoiyuaa a?aiy i/aaeaeii, /oi ?acaeoea iaoee iiaeao
i?eaiaeeoue e io?eoeaoaeueiui iineaaenoaeyi aeeythuai ia ana /aeinoai a
oeaeii. Aeooaeueiui noaiiaeony aii? i nioe. ioaaonoaaiiinoe anao
ethaeae, a ia oieueei o/aiuo ca aiciiaeiinoue thcaiey ec ioe?uoee e
aeinoeaeaiee. A ianoiyuaa a?aiy noi?ie?iaaeanue iai?aae., iacuaaaiia
yoeeie iaoee, aeenoeeieeia, eco/athuae i?aanoaaiiua iniiau iao/i.
aeayo-oe. A ea/. i?eia?a iiaeii i?eaanoe i?eia? ec enoi?. 2e ie?iaie
aieiu. ?.Iiiaiaaeia?a iacuaatho iooeii aoiiiie aiiau. Ii yaeyeny
eii?aeeiaoi?ii e ?oeiaiaeeoaeai i?iaeoa nicaeaiey aoiiiie aiiau. Iia
auea nicaeaia e eniuoaia nia/aea a Iaaaaea, a iioii e a Oe?ineia e
Iaaanaea. Iicaeiaa Iiiaiaaeia?, iniciaaay oyaeanoue ioaaonoaaiiinoe,
ooae ec i?iaeoa e noae caieiaoueny aeayoaeueiinoueth, iai?aaeaiiie ia
i?aaeioa?auaiea thcaiey aoiiiuo aiia. Auoaneacaiiia ooaa?aeaeaao ian a
iunee, /oi i?aaenoaaeyaony aanueia aaaeiui iiciaeiieony n ini.
eiioeaioeeyie anoanoaiciaiey. Yoi iaiaoiaeeii aeey oiai, /oiau: ai
ia?a., niciaoaeueii i?eiaiyoue eo a naiae aeayo-oe, ai aoi?uo, /oiau
iieo/eoue > yniia e oi/iia i?aaenoaaeaiea i nia?aiai. iao/i. ea?oeia
ie?a, eio. aeaao anoanoaiciaiea. Iaiaoiaeeiinoue i?eiaiaiey anonoaaii
iao/iuo iaoiaeia e caeiiia a i?aeoe/aneie aeayo-oe aoiaieoa?iuo
niaoeeaeueiinoae e i?eaaei e iinoaiiaea oiai eo?na, eio. iu aoaeai
eco/aoue: Oeceea aeey aoiaieoa?eaa.

Naycue iaaeaeo ?acaeaeaie anoanoaiciaiey. Neiai anoanoaiciaiea
i?aaenoaaeyao ec naay ni/aoaiea 2o neia: anoanoai (i?e?iaea) e ciaiea. A
ianoiyuaa a?aiy iiae anoanoaiciaieai iiae?acoiaaaaony a iniiaiii oi/iia
ciaiea i oii, /oi a i?e?iaea, ai Anaeaiiie aeaenoaeoaeueii anoue eee ii
e?aeiae ia?a aiciiaeii. Ia?aia/. e oeceea A?enoioaeue ioiinee i?iaeaiu
ono?-aa, i?ienoiaeaeaiey, i?aaiecaoeee anaai, /oi anoue ai Anaeaiiie,
aeaaea aeecie. Naii neiai oeceea, a?a/aneia ii i?ienoiaeaeaieth, aeecei
e ?onneiio neiao i?e?iaea. Oeei ia?cii, ia?aiia/aeueii anoanoaiciaiea
iacuaaeinue oeceeie. A naiai ?acaeoee iaoea i?ioea 4 noaaeee ?acaeoey.
Ia 1ie noaaeee oi?ioee?iaaeenue iau. i?aaenoaae. i i?e?iaea,
ie?oaeathuai ie?a eae i /ai-oi oeaeii. A yoie noaaeee i?iecioei ?acaeoea
iaoo?oeeinioee (oeeinioee i?e?iaeu) noaaoae aianoeeeuai eaeae e
aeiaaaeie, eio. e 13-15 aaeai noaee ca/aoeaie anoaaiuo iaoe. A 15-17
aaeao iineaaeiaaea aiaeeoe/aneay noaaeey – iuneaiiia ?an/eaiaiea e
auaeaeaiea /anoiinoae, i?aa?aoeaoay oeceeo, ano?iiiieth, oeieth,
aeieiaeth aeaenoaeoaeueii a iaoee. Iicaeiaa, aeeaea e iaoaio a?aiaie,
ianooieea neioaoe/aneay noaaeey eco/aiey i?e?iaeu, oa?aeoa?ecoaiay
ainnicaeaieai oeaeinoiie ea?oeiu ie?a ia iniiaa ?aiaa iiciaiiuo
/anoiinoae. Naaiaeiy i?eoei a?aiy iainiiaaoue ia oieueei
i?eioeeieaeueioth oeaeinoiinoue anaai anoanoaiciaiey, ii iiynieoue,
ii/aio eiaii oeceea, oeiey e aeieiaey noaee ini. e naiinoiyoaeueiuie
?acaeaeaie iaoee i i?e?iaea. O.a. a ianoiyuaa a?aiy inou-aony oeaeinoiay
eioaa?aeueii – aeeooa?aioeeaeueiay noaaeey ?acaeoey anoanoaiciaiey,
eae aaeeiie iaoee i i?e?iaea. Ana iienaiiua noaaeee eco/aiey i?e?iaeu ii
nou-ao i?aaenoaae. caaiuey 1ie oeaie. Eaaeae ec ?acaeaeia anoanoaiciaiey
i?iuae /a?ac yoe noaaeee. ?anniio?aa a neaaeothuae /anoe ei?ioei eno-th
?acaeoey oeceee iu aeaeei, /oi iia oiaea i?ioea ana iienaiiua noaaeee.
Ioee/ea eiaaony eeoue a oii, /oi iienaiea yoaiia ?acaeoey oeceee iu
aoaeai aeaaaoue n o/ee c?aiey ?acaeoey iaoiaeia iiaeoiaea e eco/aaiui
yaeaieyi. A oeceea nae/an oaeaea ianooiaao eioaa?aoeeiiiay noaaeey,
oa?aeoa?ecoaiay oai, /oi i?iaiaeyony iiiuoee nicaeaoue aaeeiua O.,
iauaaeeiythuea ?acee/i. ?acaeaeu. I?eia?ii oiio iiaeao neoaeeoue iiiuoea
nicaeaoue aaeeioth O. iiey. ?anniio?ei aeaaiua ?acaeaeu anoanoaiciaiey e
naycue iaaeaeo ieie. Iu oaea aiai?eee i aeaeaeaiee iaoa?ee. A ii?yaeea
aic?anoaiey neiaeiinoe iu i?eaiaeeee neaaeothuea oi?iu aeaeaeaiey:
iaoaie/aneoth, oece/aneoth, oeie/aneoth, aeieiae/aneoth, iauanoaaiioth.
Ana oi?iu aeaeaeaiey naycaiu iaaeaeo niaie. Aunoea niaea?aeao a naaa
iecoea, ninoaaiuie /anoe, ii ie a eiai neo/aa ia naiaeyony oieueei e
iei. Iai?eia?, iaeuecy yaea?iua neeu naanoe e iaoaie/aneei. ?acee/iua
aeaeu aeaeaeaiee, nouanoaothueo a i?e?iaea eco/atho ?acee/i. ?acaeaeu
anoanoaiciaiey: OECEEA, OEIEss, AEIEIAEss, INEOIEIAEss e ae?oa.
?acaeaeu. A eaaeaeii ec ?acaeaeia anoanoaiciaiey eiathony naie caeiiu,
eio. ia iiaoo auoue naaaeaiu e caeiiai ae?oaeo ?acaeaeia, iaeiaei, O.,
iienuaathuea neiaeiua no?oeoo?u, iie?athony ia O. e caeiiu aeey i?inouo
no?oeoo?. I?e yoii, eae i?aaeei, ii ia?a oneiaeiaiey no?oeoo? e
?acaeaeia anoanoaiciaiey eo caeiiu noaiiayony iaiaa oi/iuie,
oi?ioee?iaee i?eaeeaeathony e ea/-aaiui. *ai ieaea o?iaaiue ?acaeaea
anoanoaiciaiey, oai neiaeiaa e oi/iaa iaoaiaoe/aneea oi?ioee?iaee aai
caeiiia. Iaeaieaa neiaeiu aeey iiieiaiey caeiiu oeceee – ooiaeaiaioa
anao anoaaiuo iaoe. A yoii ?acaeaea iu iiiuoaainy iieacaoue naycue
oeceee n ae?oaeie iaoeaie, i/a?oe i e?oa ooiaeaiaioaeueiuo caaea/,
aicieeathueo a iia?aie/iuo iaeanoyo e ia nouea iaoe. Iaeiaei, iu
einiainy naycae oeceee n oaoieeie, oeceee n i?ii-oueth, oeceee n
iau-aaiie aeeciueth e oeceee n eneonnoaii. Naycue n iineaaeiai
i?ineaaeeaaaony ia iiiaeo eno-eeo i?eia?ao, eiaaea auaeathueany
neoeueioi?u, a?oeoaeoi?u e aeeaiienoeu i?ioeiai auee iaeiia?aiaii e
e?oiiuie o/aiuie. Oeiey eniuouaaao ia naaa aeeyiea oeceee, iiaeaeoe
neeueiaa, /ai ethaay ae?oaay iaoea. Ia ca?a naiaai ?acaeoey iia ea?aea
aaaeioth ?ieue a noaiiaeaiee oeceee. Yoe iaoee acaeiiaeaenoaiaaee i/aiue
neeueii, iie auee i?aeoe/anee ia?acaeaeeiu. O. aoiiiiai no?iaiey a-aa
iieo/eea iniiaaoaeueiia iiaeoaa?aeaeaiea eiaii a oeie/aneeo iiuoao. Iiae
O. iai?aaie/aneie oeiee iiaeaae /a?oo Ae.E.Iaiaeaeaaa (1834-1907),
nicaeaa naith ia?eiaee/aneoth nenoaio oeie/aneeo ye-oia. Yoa neno.
auyaeea iaiaei oaeeaeoaeueiuo naycae iaaeaeo ?acee/iuie yeaiaioaie. Iia
i?aaeneacaea nou-iea iiiaeo oaaea aua iaecaanoiuo oeie/aneeo ye-oia.
Iaeiaei, iauyniaiea nenoaiu Iaiaeaeaaaa aiciiaeii oieueei n iii?ie ia O.
no?iaiey aoiia, o.a. ia oece/aneoth O.. A ianoiyuaa a?aiy a
iai?aaie/aneie oeiee inoaeenue 2 ?acaeaea: oece/aneay oeiey e eaaioiaay
oeiey. Naie iacaaiey yoeo ?acaeaeia aiai?yo i oaniie nayce n oeceeie.
Ae?oaay aaoaue oeiee – i?aaie/aneay oeiey, oeiey aauanoa, naycaiuo n
aeeciaiiuie i?ioeannaie. Iaeii a?aiy i?aaeiieaaaee, /oi i?aaie/aneea
a-aa noieue neiaeiu, /oi eo iaeuecy neioace?iaaoue. Iaeiaei, ?acaeoea
oeceee e iai?aaie/aneie oeiee eciaieei neooaoeeth. A ianoiyuaa a?aiy
iao/eeenue neioace?iaaoue neiaeiua i?aaie/aneea niaaeeiaiey,
iaiaoiaeeiua a aeeciaiuo i?ioeannao. Aeaaiie caaea/ae i?aaie/aneie
oeiee yae. aiaeec e neioac aauanoa, ia?acothueony a aeieiae/aneeo neno.,
aeeauo i?aaieciao. Ionthaea auoaeaao oaniay naycue oeiee e oeceee n
ae?oaei ?acaeaeii anoanoaiciaiey, n aeieiaeae. Eco/aiea aeeauo
i?aaieciia iicaieyao oaeaeaoue iiiaeanoai /enoi oece/aneeo yaeaiee:
oee?eoeyoeeth e aeae?iaeeiaieeo i?ioaeaiey e?iae, aeaaeaiea a ninoaeao e
o.ae. Aeieiaey – i/aiue oe?ieia iiea aeayo-oe aeey i?eeiaeaiey
oece/aneeo e oeie/aneeo oai?ee. Iai?eia?, eae inou-aony c?aiea, /oi
i?ienoiaeeo a aeaca. Eae eaaio naaoa acaeiiaeaenoaoao n nao/aoeie.
Iaeiaei, yoe aii?inu ia ini. a aeieiaee, ia iie eaaeao a nouiinoe anaai
aeeaiai. Ooiaeaiaioaeueiua i?ioeanu, eco/aaiua a aeieiaee eaaeao
aeoaaea, a iiieiaiee ooieoeeiie?iaaiey eeaoie, eo aeioeie/aneeo oeeeeia.
A eiia/iii eoiaa, a iiieiaiee oiai, /oi anoue aeeciue. Iiiyoea aeecie ia
oaeaaony naanoe oieueei e oei eee oec. i?ioeanai. Ineoieiaey eco/aao
io?aaeaiea aeaenoaeo-oe a i?ioeannao aeayo-oe /aea e aeeaioiuo. Yoa
iaoea eaaeeo ia a?aie anoaaiuo e iau-aaiuo iaoe. Eacaeinue au, eaeay
naycue iiaeao auoue o iaa n oeceeie. Aeaaaeoa ?anniio?ei ia?o i?eia?ia.
Iaeiie ec aaoaueth ineoieiaee yae. oeceieiaey iuouaiee. Iia ?ani.
acaeiinaycue iaaeaeo iiaaaeaieai /aea e aai iuouaieyie. Ii/aio e?aniue
oeaao aucuaaao o?aaiaeiua iuouaiey, a caeaiue iaiai?io. Iaaea?ii
cai?auathuee oeaao naaoioi?a – e?aniue, a ?ac?aoathuee – caeaiue. Ioaao
iiaeao aeaoue oeceea. Aeiai max eceo/aiey nieioea i?eoiaeeony ia caeaiue
oeaao. Aeaiue – naiia aaciianiia a?aiy nooie, e a i?ioeana yaiethoeee o
aeeauo i?aaieciia au?aaioaeanue iieiaeeoaeueiay ?aaeoeey ia caeaiue
oeaao. A noia?eao max eceo/aiey nieioea naeaeioo a e?anioth iaeanoue.
Noia?ee – naiia iianiia a?aiy nooie, eiaaea oeuiua aeeaioiua auoiaeyo ia
ioioo. Ancii, /oi a i?ioeana yaiethoeee au?aaioaeinue io?eoeaoaeueiay
?aaeoeey ia yoio oeaao. Ae?oaie i?eia? ec iaeoe e?eieiaeenoeee, eio.
oneiaii oaeaea iiaeii ioianoe e aaoae ineoieiaee, iineieueeo iia ?ani.
iiaaaeaiey ethaeae a neiaeiuo neooaoeeyo, i?eaiaeyueo e e?eieiaeueiui
neo/ayi. Eiaaea aeieoi? Aaonii ni?inee, ciaao ee Oa?eie Oiein i O.
Eiia?ieea e i no?iaiee niei. nenoaiu, Oiein ioaaoee, /oi iaaa?ii ciae,
ii iinoa?aeny ia yoii caauoue. Oai ia iaiaa, aeieoi?ii Aaoniiii auei
onoaiiaeaii, /oi Oiein iaeaaeaao aeoaieeie ciaieyie a iaeoe oeiee e
?yaea ?acaeaeia oeceee. Aeaenoaeoaeueii, nae/an ie 1 e?eieiaeeno ia
iiaeao iaieoenue aac oaeiai ?acaeaea oeceee, eae iaoaieea, oi/iaa aa
i?eeeaaeiiai ?acaeaea – aaeeenoeee, a oaeaea ?yaea ae?oaeo. A
caeeth/aiee yoiai ?acaeaea oiiiyiai aua 1 iiiaio, auyaeythuee naycue
oeceee n ae?oaeie ?acaeaeaie anoanoaiciaiey. Ana i?eai?u, eniieuecoaiua
a iiuoao e yenia?eiaioao nicaeaiu niaoeeaeenoaie n oaoie/aneei (o.a.
oec.) ia?aciaaieai. I?eioeei aeaenoaey yoeo i?eai?ia iniiaai ia
oece/aneeo caeiiao. A eiia/iii eoiaa, oanoa? aeey ecia?aiey iai?yaeaiey
eee oiea , oiiia?ao, iieo/athuee i?ino?ainoaaiioth ea?oeio aioo?aiieo
i?aaiia, iee?iaiaeecaoi?, ii?aaeaeythuee o?iaaiue caa?yciaiiinoe
ie?oaeathuae n?aaeu eee iio?aaeyaiie ieue, o?aaotho io ?aaioathueo
ii?aaeaeaiiuo ciaiee. N 1ie noi?iiu – yoi ciaiea iniiaiuo i?eioeeiia
?aaiou i?eai?a, n ae?oaie noi?iiu – oiaiea ioeaieaaoue noaiaiue oi/iinoe
ia?aiao?ia, eio. ecia?yao aeaiiue i?eai?.

10. Aeaoa?ieieci eeane/. iaoaieee. Iiae aeaoa?ieieciii iiieiaaony
oeeinioneia o/aiea ia iauaeoeaiie caeiiiia?iinoe, acaeiinayce e
i?e/eiiie iaoneiaeaiiinoe anao yaeaiee iao. e aeooiaiiai ie?a.
Oeaio?aeueiui yae?ii aeaoa?ieiecia yae. iieiae. i i?e/eiiinoe. Eaeay
aeaoa?ieiecia nino. a oii, /oi ana yae-y e niauoey a ie?a ia
i?iecaieueiu, a iiae/eiythony iauaeoeaiui caeiiiia?iinoyi, iacaaeneii io
iaoeo ciaiee i i?e?iaea yaeaiee. Anyeia neaaenoaea eiaao naith i?e/eio.
aeaoa?ieieci Eaieana(1749 – 1827). Niaeanii eeanne/aneiio
iaoaienoe/aneiio aeaoa?ieiecio nou-aoao no?iai iaeiicia/iay naycue
iaaeaeo oece/aneeie aaee/eiaie, oa?-a?ecothu. nino. nenoaiu a eaeie-oi
iiiaio a?aiaie (eii?aeeiaou e eiioeuenu) e cia/aieyie yoeo aaee/ei a
etha. iineaaeothuee eee i?aaeuaeouee iiiaiou a?aiaie. I?eioeei
iaoaie/aneiai aeaoa?ieiecia. If ecaanoiu ia/aeueiua eii?aeeiaou e nei?.
oae nenoaiu, a oaeaea caeiiu acaeiaeaeno. oae, oi iiaeii ii?aaeaeeoue
nino. nenoaiu a etha. iineaaeothuee iiiaio a?aiaie. Ioiaoei, /oi aeey
oniaoiiai i?aeoe/aneiai ?aoaiey iiaeiaiuo caaea/ caeiiu acaeiaeaeno. oae
ioaeii ciaoue i/aiue oi/ii, eeai ioaeii nie?eoueny n oai, /oi ?an/ao
aoaeao aaeaeaaoii iienuaaoue iiaaaeaiea nenoaiu eeoue a ia?aie/aiiii
a?aiaiiii eioa?aaea. Naycaii yoi n oai, /oi iaoi/iinoe ?an/aoa eiatho
naienoai iaeaieeaaoueny e eneaaeaoue iieo/athuothny ea?oeio, – /ai
aeaeueoa, oai aieueoa. E?iia oiai ioaeii eiaoue aaeaeo, /oi aeey ?aoaiey
caaea/e i aeaeaeaiee aieueoiai eie-aa acaeiiaeaenoaothueo oae ioaeii
caaeaoue i/aiue aieueo eie-ai ia/aeueiuo aeaiiuo, caeiiia acaeiaeaeno. e
?aoaoue i/aiue a?iiicaeeoth nenoaio aeeooa?aioeeaeueiuo o?aaiaiee. N
iiceoeee naaiaeiyoieo ciaiee i i?e?iaea iiaeii ooaa?aeaeaoue, /oi
iaoaienoe/aneee aeaoa?ieieci Eaieana ia ?aaioaao a iee?iia?a, aaea
i?ioeanu acaeiaeaeno. /anoeoe ii naiae i?e?iaea yae. aa?iyoiinoiuie. I?e
noieeiiaaiee 2o aoiiia 1 ec ieo iiaeao aicaoaeeoueny (ia?aeoe a
aicaoaeaeaiiia nino.), a iiaeao e inoaoueny a iniiaiii, iaaicaoaeaeaiiii
nino.. A iineaaeiai neo/aa aoiiu aoaeoo noaeeeaaoueny eae eaeaaeueii
oi?oaea oa?u, a ia?aii neo/aa eae iaoi?oaea oa?u. ?acoeueoaou
noieeiiaaiey a yoeo neo/ayo aoaeoo neeueii ?acee/aoueny, a ?aoeoue, eae
aoaeao i?ienoiaeeoue acaeiaeaenoaea, aei oiai eae iii i?iecieaeao, a
i?eioeeia iaaiciiaeii. A iee?iie?a iiaoo iaeiia?aiaii i?ioaeaoue
i?ioeanu, eio. aaniethoii ianiaianoeiu a iae?iie?a. Eiaaea iienuaaaony
eaaioiaay iee?inenoaia, i?aaeneacuaaaony aa iiaaaeaiea a ?aieao
aa?iyoiinoiiai iienaiey, ii ia aeaaony iaeiicia/iiai ioaaoa, eae
eiie?aoii iia aoaeao naay aanoe. I?e yoii anaaaea inoathony a neea
i?e/eiii-neaaenoaaiiua nayce.

11. ?AAIOA, eeiaoe/aneay yi-y.Yia?aey- iaeaieaa iauay eiee/anoaaiiay
ia?a aeaeaeaiey e acaeiaeaeno. iaoa?ee. Aeey eciee?iaaiiie nenoaiu yi-y
inoaaony iino., iia iiaeao ia?aoiaeeoue ec 1ie oi?iu a ae?oa., ii aa
eie-ai inoaaony iaeciaiiui. If neno. ia eciee?iaaia, oi yi-y iiaeao
eciaiyony i?e iaeiia?aiaiiii eciaiaiee yia?aee ie?oaeathueo oae ia
oaeoth aea aaee/eio eee ca n/ao yia?aee acaeiaeaeno. oae aioo?e nenoaiu.
I?e ia?aoiaea nenoaiu ec iaeiiai ninoiyiey a ae?oaia aa yi-y ia caaeneo
io oiai, eaeei iooai i?iecioae yoio ia?aoiae. Yia?aey nenoaiu a iauai
neo/aa iiaeao ia?aoiaeeoue a ae?oa. oi?iu iaoa?ee. Iineieueeo nou-aoao
iiiaiia?acea oi?i aeaeaeaiey iaoa?ee, nou-aoao e iiiaiia?acea aeaeia
yia?aee: eeiaoe/aneoth, iioaioeeaeueioth e iiei iaoaie/aneoth yia?aeth.
?aaioa neeu- ia?a aeaenoaey neeu, eio. caaeneo io /eneaiiie aaee/eiu
neeu e aa iai?aae-y, io ia?aiauaiey o/ee i?eeiaeaiey neeu. If neea F
iinoiyia ii aaee/eia e iai?aae., a ia?aiauaiea i?ienoiaeeo aaeieue
i?yiie, oi ?aaioa =a i?iecaaaeaieth neeu ia aaee/eio ia?aiauaiey e
eineion oaea iaaeaeo iai?aaeaieai neeu e ia?aiauaieai. ?aaioa – aaee/eia
neaey?iay. Aaeeieoeae ecia?aiey Aeaeioeue (Aeae). A iauai neo/aa aeey
au/eneaiey ?aaiou iiae aeaenoaeai ia?aiaiiie neeu ia e?eaieeiaeiii
o/anoea o?aaeoi?ee aaiaeyo yeaiaioa?ioth ?aaioo dA. N/eoaai, /oi ia
aaneiia/ii iaeii o/anoea iooe dr neea ia iaiyaony e yeaiaioa?iay ?aaioa
dA ii?-ny eae: dA=F*dr*cos’aeueoa’=(F’aaeoi?’dr’aaeoi?’) (11.2). ?aaioa
– aaee/eia aaeaeeoeaiay; ?aaioa neeu ia eiia/iii o/anoea iooe (1)R(2)
ii?-ny eae noiia yeaiaioa?i. ?aaio. Noiie?iaaiea ii aaneiia/ii iaeui
aaee/eiai dA anoue iia?aoeey eioaa?e?iaaiey: A12=’eioaa?ae io 1 aei
2′(F(aaeoi?)dr(aaeoi?)) (11.3), aaea eioaa?e?iaaiea aaaeaony aaeieue
o?aaeoi?ee. A aaeoi?iii aiaeeca oaeie eioaa?ae iac. oee?eoeyoeeae
aaeoi?a neeu. Caiaoei, /oi a yoii au?aaeaiee eaaei ia?aeoe e ae?oaie
ia?aiaiiie eioaa?e?iaaiey, ei a?aiaie. A12=’eioaa?ae io 1 aei
2′(F(aaeoi?)dr(aaeoi?)) = ‘eioaa?ae io t1 aei
t2′((F(aaeoi?)V(aaeoi?))dt)= ‘eioaa?ae io t1 aei t2′(Ndt) (11.4).
Aaaaeaiiay caeanue aaee/eia N iac. iaiiaaiie iaoaie/aneie iiuiinoueth
eee i?inoi iiuiinoueth oaea.
N=dA/dt=(F(aaeoi?)dr(aaeoi?)/dt)=(F(aaeoi?)v(aaeoi?)) (11.5). *oi aoaeao
i?ienoiaeeoue n nenoaiie (a i?inoaeoai neo/aa -n iao. oi/eie) i?e
niaa?oaiee ?aaiou iaae iae. Caieoai yeaiaioa?ioth ?aaioo e au?acei neeo
a iai i?e iiiiue 2ai c-ia Iuethoiia.
dA=(F(aaeoi?)dr(aaeoi?))=m(a(aaeoi?)dr(aaeoi?))=m(dv(aaeoi?)dr(aaeoi?))/
dt=m (dv(aaeoi?)v(aaeoi?))=md(v(aaeoi?)v(aaeoi?))/2=md(v^2)/2=d(mv^2/2)
(11.6) Neaaa noieo yeaiaioa?iay ?aaioa, a ni?aaa aeeooa?aioeeae
iaeioi?ie o-e ,eiathuee ?acia?iinoue ?aaiou e caaenyuee io nei?.:
aeeooa?aioeeae o-e nei?., ii?aae-iie niaa?oaiie ?aaioie. Ionoue a
ia/aeueiue iiiaio a?aiaie t0 nei?inoue oaea ?aaiyeanue (0. Iieioth
?aaioo ca i?iiaaeooie a?aiaie io t0 aei t1 iieo/ei iinea eioaa?e?iaaiey
dA, eae yoi naeaeaii a oi?ioea (11.4). Niaa?oaaiay iaae oaeii ?aaioa
i?eaaea e oaaee/aieth aai nei?..Oaia?ue iiaeii aaanoe iiiyoea eei.
yia?aee: A01=m(v1)^2/2 – m(v0)^2/2 = Ek1-Ek0. (11.7) Eeiaoe/aneay yi-y
ii?-ny ?aaioie, eio. niaa?oaia iaae oaeii. Iieiaeeoaeueiay ?aaioa
i?eaiaeeo e oaaee/aieth nei?. oaea e e oaaee/aieth eei. yia?aee,
io?eoeaoaeueiay – e oiaiueoaieth oiai e ae?oaiai. If neno. nino. ec
iiiaeo oae, oi aa eeiaoe/aneay yi-y neeaaeuaaaony ec eeiaoe/aneeo
yia?aee anao oae.

12. Iiey eiina?aaoeaiuo nee. Iioaioeeaeueiay yia?aee . 13. C-i
nio?aiaiey iaoaie/aneie yia?aee. E?iia eei. yia?aee anoue aua
iioaioeeaeueiay yi-y, aeey eio. ia nou-aoao iauae oi?ioeu. Yoi iiiyoea
iiaeii aaanoe eeoue aeey ia?aie/. eeana nee – aeey eiina?aaoeaiuo nee.
Yoi neeu, ?aaioa eio. ii caieiooie o?aaeoi?ee =a ioeth. Nouanoaoao
ae?oaia ii?aaeaeaiea eiina?aaoeaiuo nee. Eiina?aaoeaiuie neeaie
iacuaathony oaeea neeu, ?aaioa a iiea eio. ia caaeneo io o?aaeoi?ee e
ii?-ny oieueei ia/aeueiui e eiia/iui iieiaeaieai nenoaiu. Iao?oaeii
iieacaoue, /oi yoe ii?aaeaeaiey ?aaiicia/iu. Aeaenoaeoaeueii, if ?aaioa
ia caaeneo io o?aaeoi?ee, oi i?e ia?aoiii aeaeaeaiee aaeieue o?aaeoi?ee
iia aoaeao oaeay aea, ii n ia?aoiui ciaeii. I?inoiie?iaaa aeaeaeaiea ii
caieiooie o?aaeoi?ee, ninoiyuae ec 2o e?eauo, iieo/aai a noiia 0.
Eiina?aaoeaiua neeu, eae i?aaeei, caaenyo oieueei io iieiaeaiey oaea, a
iaeiina?aaoeaiua – io aai nei?.. ?anniio?ei i?eia?u iieae eiina?aaoeaiuo
e iaeiina?aaoeaiuo nee. Neeu o?aiey eee nii?ioeaeaiey yae.
iaeiina?aaoeaiuie. Eo iai?aae. ii?-ny nei?-oueth ia?aiauaiey oae. Neeu
o?aiey anaaaea iai?aaeaiu a noi?iio, i?ioeaiiieiaeioth iai?aae.
aeaeaeaiey, o.a.: F(aaeoi?)o?=-(v(aaeoi?)/v)Fo?. Caeanue v(aaeoi?)/v –
aaeeie/iue aaeoi?, iai?aaeaiiue aaeieue nei?. oaea. ?aaioa neeu o?aiey
ii caieiooie o?aaeoi?ee l =a: A(l)= ‘eioaa?ae c e?oaeeii io
(l)'(-Fo?((v(aaeoi?)/v)dr(aaeoi?)))= -‘eioaa?ae io t1 aei
t2′(Fo?((v(aaeoi?)/v)dr(aaeoi?)/dt)dt)= -‘eioaa?ae io t1 aei
t2′(Fo?((v(aaeoi?)v(aaeoi?))/v)dt)= -‘eioaa?ae io t1 aei t2′(Fo?*vdt)=-
‘eioaa?ae c e?oaeeii io (l)'(Fo?*dl). E?oaeie o eioaa?aea –
eioaa?e?iaaiea ii caieiooie o?aaeoi?ee. Iineaaeiaa iiaeuioaa?aeueiia
au?aaeaiea neaey?iia, iii anaaaea iieiaeeoaeueii, neaae., ?aaioa neeu
o?aiey ia caieiooie o?aaeoi?ee anaaaea io?eoeaoaeueia. Yoa ?aaioa oai
aieueoa ii iiaeoeth, /ai aeeeiaa iooue. Auaiae: neeu o?aiey –
iaeiina?aaoeaiua neeu. I?eia?ii iiey eiina?aaoeaiuo nee yae. iiea
oyaioaiey aaeece iia-oe Caiee. ?aaioa, eio. cao?a/eaaaony ia ia?aiauaiea
oaea ec iieiaeaiey r1 a iieiae. r2 =a: A12=’eioaa?ae io r1 aei
r2′(mg(aaeoi?)dr(aaeoi?))=’eioaa?ae io r1 aei r2′(mg dr(g))=-mg’eioaa?ae
io h1 aei h2′(dh)=mg(h1-h2). Ec yoie oi?ioeu aeaeii, /oi ?aaioa neeu
oyaeanoe caaeneo io aaee/eiu yoie neeu e io ?aciinoe ia/aeueiie e
eiia/iie aunio oaea. Ieeaeie caaenei. io oi?iu o?aaeoi?ee iao, a ci/eo,
neea oyaeanoe eiina?aaoeaia. Oaeaea i?inoi iiaeii aeieacaoue, /oi
eiina?aaoeaiuie yae. neeu, nicaeathuea iaeii?iaeiia iiea. Iiea nee iac.
iaeii?iaeiui, if a etha. oi/ea yoiai iiey neea, aeaenoaothuay ia oaei
iaeeiaeiaa ii aaee/eia e iai?aae.. Eiina?aaoeaiuie yae. oaeaea iiey
oeaio?aeueiuo nee. Oeaio?aeueiuie iacuaathony neeu, iai?aaeaiiua aaeieue
eeiee acaeiaeaeno. oae, aaee/eia eio. caaeneo oieueei io ?annoiyiey
iaaeaeo oaeaie. Oaeiio oneiaeth oaeiaeaoai?ytho, iai?eia?, eoeiiianeea
neeu e neeu oyaioaiey. A iiea eiina?aaoeaiuo nee iiaeii aaanoe aua 1
aeae iaoaie/aneie yia?aee – iioaioeeaeueioth yia?aeth. I?aaeaea /ai aa
aaiaeeoue, auae?atho o/eo, a eio. iia =a ioeth. Iioaioeeaeueiay yi-y
oaea a etha. oi/ea i?ino-aa ii?-ny ?aaioie, eio. ioaeii niaa?oeoue,
/oiau ia?aianoeoue oaei ec yoie o/ee a o/eo n ioeaaie iio. yia?aeae.
Ioiaoei 2 nouanoaaiiuo iiiaioa, auoaeathueo ec yoiai ii?aaeaeaiey.
Ai-ia?a., iineieueeo ?ani-aony iiea eiina?aaoeaiuo nee, cia/. iio.
yia?aee oaea caaeneo io iieiaeaiey oaea e auai?a o/ee ioeaaie iio.
yia?aee e ia caaeneo io oi?iu iooe, ii eio oaei ia?aiauaaony. Ai-aoi?uo,
iineieueeo auai? ioey iio. yia?aee i?iecaieai, cia/. iio. yia?aee ii?-ny
n oi/iinoueth aei aaeaeeoeaiie iino., neaae. oec. niune eiaao eeoue
?aciinoue iioaioeeaeueiuo yia?aee eee i?e?auaiea iio. yia?aee, ii ia
naia yi-y. Ia ?en.11.3 iu i?aaenoaaeee 3 o/ee a i?ino-aa iiey
eiina?aaoeaiuo nee: o/eo (b), o/eo (n) e o/eo (i), iioaioeeaeueioth
yia?aeth a eio. aoaeai n/eoaoue =ie 0. Iaicia/ei /a?ac Abo ?aaioo, eio.
niaa?oaaony i?e ia?aiina oaea ec o/ee (b) a o/eo (o). If ia?aiauaoue
oaei ec o/ee (o) a o/eo (b), oi niaa?oaaiay i?e yoii ?aaioa aoaeao =a
Aob=-Abo, iineieueeo iaiyaony iai?aae. aeaeaeaiey, ii ia iaiythony
aeaenoaothuea ia oaei neeu. ?aaioo ii ia?aiauaieth oaea ec o/ee (c) a
o/eo (o) aoaeai iaicia/aoue, eae Ano. Oi/ii oaeaea Ani=-Ain. I?e
ia?aiauaiee oaea ec o/ee (b) a o/eo (c) niaa?oaaony ?aaioa Abc=-Acb.
Niaeanii ii?aaeaeaieth iio. yia?aee e oi?ioea (11.3) aeey au/eneaiey
?aaiou eiaai: Ei(b)=A(b0)= ‘eioaa?ae io b aei 0′(F(aaeoi?)dr(aaeoi?));
Ei(n)=A(n0)= ‘eioaa?ae io n aei 0′(F(aaeoi?)dr(aaeoi?)); (11.8). Ei(b)-
Ei(c)= ‘eioaa?ae io b aei 0′(F(aaeoi?)dr(aaeoi?))- ‘eioaa?ae io n aei
0′(F(aaeoi?)dr(aaeoi?))= ‘eioaa?ae io b aei 0′(F(aaeoi?)dr(aaeoi?))+
‘eioaa?ae io 0 aei c'(F(aaeoi?)dr(aaeoi?))= ‘eioaa?ae io b aei
c'(F(aaeoi?)dr(aaeoi?))=A(bc) (11.9) Ieacaeinue aeieacaiiui neaaeothuaa
ooa.: ?aaioa, niaa?oaaiay i?e ia?aiauaiee oaea a iiea eiina?aaoeaiuo nee
ec o/ee (b) a o/eo (c), =a ?aciinoe iioaioeeaeueiuo yia?aee oaea a
oi/eao (b) e (c). Iaeiaei, yoa aea ?aaioa =a ?aciinoe eeiaoe/aneeo
yia?aee a oi/ea (n) e (b). A(bc)=Ee(b)-Ee(n)=Ei(n)-Ei(b) =>
Ee(b)+Ei(b)=Ee(n)+Ei(n) (11.10) Iieo/eeinue, /oi noiia eei. e iio.
yia?aee oaea, eio. iac. iieiie iaoaie/aneie yia?aeae oaea, ieacaeanue
iaeciaiiie. Oiaea naiia ni?aaaaeeeai e aeey nenoaiu iaoaie/aneeo oae.
Iieo/eaoaany ooa. iineo iac. c-ia nio?aiaiey iaoaie/aneie yia?aee:
iieiay iaoaie/aneay yi-y eciee?iaaiiie nenoaiu a eio. aeaenoaotho
eiina?aaoeaiua neeu inoaaony iaeciaiiie. Iaaeaeo eiina?aaoeaiuie neeaie
e iio. yia?aeae aeieaeia auoue naycue, iineieueeo iioaioeeaeueiay yi-y
aaiaeeony oieueei a iiea eiina?aaoeaiuo nee. Iaeaeai yoo naycue aeey
i?inoaeoaai neo/ay, eiaaea iioaioeeaeueiay yi-y caaeneo oieueei io 1ie
eii?aeeiaou. I?eia?ii iiaeao neoaeeo iioaioeeaeueiay yi-y aaeece iia-oe
Caiee, e iaio e ia?aoeiny. Ionoue inue (oy) iai?aaeaia aa?oeeaeueii
aaa?o e eiaao iieue ia iia-oe Caiee. Oiaaea iioaioeeaeueiay yi-y caaeneo
oieueei io eii?aeeiaou y e =a: Ei=mgy. Aicueiai /anoioth i?iecaiaeioth
ii eii?aeeiaoa y io eaaie e i?aaie /anoae =noaa: dEi/dy=mg. Ni?aaa noieo
neea oyaeanoe, eio. iai?aaeaia aaa?o, o.a. i?ioea ine (oy).
Ii-aeaeeiiio, i?iecaiaeiie, noiyuae a eaaie /anoe =noaa oiaea iiaeii
i?eienaoue iai?aae.; aa i?iaeoeey ia inue (oy) aoaeao =a
(dEi/dy)’subscript y’=-mg=-F’subscript y’. A neo/aa, eiaaea
aeaenoaothuay neea eiaao i?iaeoeee ia ana eii?aeeiaoiua ine, iiaeii
caienaoue aiaeiae/iua au?aaeaiey e aeey i?iaeoeee ia ae?oa. ine.
Fx=-dEi/dx; Fy=-dEi/dy; Fz=-dEi/dz (11.11) Aeey neeu, oaeei ia?cii,
ni?aaaaeeeai au?aaeaiea: F(aaeoi?)=-(e(aaeoi?)x(dEi/dx)+
e(aaeoi?)y(dEi/dy)+ (aaeoi?)z(dEi/dz))=-(
e(aaeoi?)x(d/dx)+e(aaeoi?)y(d/dy)+e(aaeoi?)z(d/dz))Ei= -grad Ei
(11.12). A?aaeeaio iio. yia?aee. Ioiaoei iaeioi?ua na-aa yoiai aaeoi?a.
Iniaaiiinoue aai nino. a oii, /oi aaeieue eii?aeeiaoiuo inae ioaeii
ioeeaaeuaaoue ia /enea, a iaoaiaoe/aneea iia?aoeee aeeooa?aioee?iaaiey
ii niioaaonoaothuae eii?aeeiaoa. Ca a?aaeeaioii iaycaoaeueii aeieaeia
noiyoue neaey?iay o-y, e eio. ii i?eiaiyaony. A?aaeeaio iio. yia?aee
eiaao iai?aae., a eio. iioaioeeaeueiay yi-y oaaee/eaaaony auno?aa anaai,
e aaee/eio, ?aaioth nei?. yoiai oaaee/aiey, if aeaeaaoueny a yoii
iai?aaeaiee. Ec neacaiiiai neaae., /oi neeu iiey canoaaeytho oaei
aeaeaaoueny a iai?aaeaiee ieieioia iio. yia?aee. Ana anoaaiua i?ioeanu
no?aiyony i?eaanoe nenoaio e ieieioio iio. yia?aee. Yoio auaiae
ni?aaaaeeea ia oieueei aeey iaoaieee, ii e aeey ae?oaeo ?acaeaeia oeceee
e anoanoaiciaiey.

14. Aioo?. yi-y nenoaiu. C-i nio?-y yia?aee. Iu ?anniio?aee
acaeiii?aa?auaiea eei. e iio. yia?aee a iiea eiina?aaoeaiuo nee. *oi
i?ienoiaeeo, if aeaenoaotho iaeiina?aaoeaiua neeu. Iu ciaai, /oi, if
oaeo niiaueo nei?inoue (niiaueoue eeiaoe/aneoth yia?aeth)e ionoeoue
aeaeaaoueny, iai?eia?, ii iia-oe caiee, iii inoaiiaeoueny ca n/ao nee
o?aiey. Aai iioaioeeaeueiay yi-y ia eciaieony, a eeiaoe/aneay noaiao =ie
ioeth, eiaaea iii inoaiiaeoueny. Aeey ioaaoa ia aii?, ai /oi ia?aoea
eeiaoe/aneay yi-y, iaiaoiaeeii aaanoe aua 1 aeae yia?aee- aioo?aiithth
yia?aeth. Ii?aaeaeei aioo?aiithth yia?aeth Aai eae noiio eeiaoe/aneeo e
iioaioeeaeueiuo yia?aee /anoeoe (aoiiia), ninoaaeythueo oaei:
Aai=S((A^i)iio+(A^i)eei) (11.13) Caeanue N -/enei /anoeoe, i -iiia?
/anoeoeu. Ia?aiao?ii, oa?aeoa?ecothuei aioo?aiithth yia?aeth yae.
oaiia?aoo?a oaea O0E, au?aaeaiiay a a?aaeonao Eaeueaeia. *ai aieueoa
oaiia?aoo?a oaea, oai n aieueoae nei?-oueth aeaeaathony aoiiu e oai
naiui aieueoa aioo?aiiyy yi-y. *eneaiii aioo?aiiyy yi-y =a:
Aai=(I/’ith’)C O^0 (11.14) I – iana oaea, ??????iiey?iay iana (/eneaiii
?aaiay aoiiiiio eee iieaeoey?iiio aano ninoaaeythueo aoiiia),N
-oaieiaieinoue, ?aaiay yia?aee, eio. ioaeii ia?aaeaoue 1io
eeeia?aiio-iieth, /oiau iaa?aoue aai ia 1 a?aaeon Oeaeueney eee
Eaeueaeia. Eciaiaiea aioo. yia?aee i?e ia?aoiaea nenoaiu ec ninoiyiey 1
a nino. 2 i?iii?oeeiiaeueii eciaiaieth oaiia?aoo?u oaea: Aai(2)-Aai(1) =
‘aeaeueoa’U = (M/m)C ‘aeaeueoa T^0. Noiio eei., iio. e aioo. yia?aee
nenoaiu i?eiyoi iacuaaoue iieiie yia?aeae A. A ?anniio?aiiii iaie
i?eia?a n inoaiaaeeaathuainy oaeii eeiaoe/aneay yi-y oaea ia?aoiaeeo ai
aioo?aiithth yia?aeth, o.a. eaeao ia iaa?aaaiea nenoaiu. N o/aoii
auoaneacaiiiai iu iiaeai noi?ioee?iaaoue c-i nio?aiaiey iieiie yia?aee
nenoaiu: Iieiay yi-y eciee?iaaiiie nenoaiu inoaaony iino.. Iu oaia?ue ia
eiie?aoece?oai, eaeea neeu (eiina?aaoeaiua eee iaeiina?aaoeaiua)
aeaenoaotho a yoie neno-a. ?aaioa a neno-a, niaa?oaaiay ca n/ao iio.
yia?aee, iiaeao ia?aoiaeeoue e a eeiaoe/aneoth yia?aeth nenoaiu, e ai
aioo?aiithth yia?aeth. I?e oaaee/aiee aioo. yia?aee neno. iaa?aaaaony.

12.1 Iinooeaou O. ioineo-oe. E eiioeo i?ioeiai a. Ae.E.Iaenaaeeii
(1831-1879) auee noi?ioee?iaaiu ini. caeiiu yeaeo?e/anoaa e iaaiaoecia a
aeaea nenoaiu aeeooa?aioeeaeueiuo o?aaiaiee, eio. iienuaaee iinoiyiiua e
ia?aiaiiua yeaeo?e/aneea e iaaieoiua iiey. ?aoaiey nenoaiu o?aaiaiee
Iaenaaeea iienuaaee anth aaiio iiaaaeaiee yeaeo?iiaaieoiuo iieae a
i?ino-aa e a?aiaie. Ec nenoaiu o?aaiaiee Iaenaaeea neaaeiaaei, /oi
ia?aiaiiua yeaeo?e/aneea e iaaieoiua iiey iiaoo nouanoaiaaoue oieueei a
oi?ia aaeeiiai yeaeo?iiaaieoiiai iiey, eio. ?ani?ino?aiythony a i?ino-aa
iinea aicieeiiaaiey n iino. nei?-oueth, =ie nei?. naaoa a aaeooia – n.
Ia aii? i oii, a eaeie n?aaea ?ani?ino?aiyaony yoi iiea, O. Iaenaaeea
ioaaoa ia aeaaaea. Eeth/aaui iiiaioii O. Iaenaaeea yaeyeinue oi, /oi
o?aaiaiey Iaenaaeea auee iaeiaa?eaioiu ioiineo. i?aia?. Aaeeeay. Yoi
icia/aei, /oi i?e ia?aoiaea n iiiiuueth i?aia?. Aaeeeay ec 1ie eia?oe.
nenoaiu ion/. a ae?oa., o?aaiaiey iaiyee naie aeae. Yoi iaicia/aei, /oi
i?aia?. Aaeeeay iaeuecy auei i?eiaiyoue i?e iienaiee yeaeo?e/. e
iaaieoiuo yaeaiee. No?iaia iaoaiaoe/aneia aeieacaoaeuenoai
iaeiaa?eaioiinoe o?aaiaiee Iaenaaeea ioiineo. i?aia?. Aaeeeay
aeinoaoi/ii neiaeii. Iiyoiio, i?ieeethno?e?oai yoio oaeo ia i?inoii e
iaaeyaeiii i?eia?a. Aeey yoiai iio?aaoaony aniiiieoue, eaeea neeu
aeaenoaotho ia aeaeaeoueany ca?yaeu a yeaeo?e/. e iaaieoiuo iieyo.
Ionoue 2 iaeiieiaiiuo ca?yaea eaoyo n iaeeiaeiaie nei?-oueth a
iai?aaeaiee ine (ox), eae yoi iieacaii ia ?en.12.1. A iaiiaeaeaeiie
neno-a ion/. ca?yaeu aoaeoo nicaeaaaoue yeaeo?e/aneea e iaaieoiua iiey,
e, neaae., aoaeoo iaoiaeeoueny a iieyo ae?oa ae?oaa. Yeaeo?e/aneia iiea
aicaeaenoaoao ia ca?yae neeie Eoeiia, iaaieoiia – neeie Ei?aioea.
Iaiiiiei oi?ioeu aeey au/eneaiey yoeo nee aeey neo/ay, i?eaaaeaiiiai ia
?enoiea. Fe=1/4Ie’yineeiio ioeaaia’*q1q2/l^2; Fa=q2*v*B1, aaea
B1=4*Ie*q1*v/’ith ioeaaia’*l^2. Caeanue B1 – iaaieoiay eiaeoeoeey,
nicaeaaaaiay ia?aui ca?yaeii a oi/ea, aaea iaoiaeeony 2e. Neea Eoeiia
aeey iaeiieiaiiuo ca?yaeia anaaaea yae. neeie iooaeeeaaiey, a neea
Ei?aioea a aeaiiii neo/aa yae. neeie i?eoyaeaiey. Oeei ia?cii, a
iaiiaeaeaeiie neno-a ion/. aaee/eia neeu acaeiaeaeno. =a: F = FK – FE.
If ia?aeoe e neno-a ion/., aeaeaeouaeny aaeieue ine (io) ni nei?-oueth (
aianoa n ca?yaeaie, oi a iae ca?yaeu ieaaeoony iaiiaeaeaeiuie, e neea
Ei?aioea ia aicieeiao. Oeei ia?cii, neeu acaeiaeaeno. ca?yaeia a
?acee/i. eia?oe. neno. ion/. ieaaeoony ?aciuie. Neaae. e iiaaaeaiea
/anoeoe ,eo aeaeaeaiea ai a?aiaie, aoaeao ?aciui a caaenei. io oiai, a
eaeie eia?oe. neno-a eii?ae. iu ?anniao?eaaai yoi aeaeaeaiea. Ancii, /oi
yoi aano?ae e ionthaea naeaeaai auaiae, /oi e aeaeaeoueiny ca?yaeai,
caeiiu aeaeaeaiey e acaeiaeaeno. eio. iienuaathony o?aaiaieyie
Iaenaaeea, iaeuecy i?eiaiyoue i?eioeei ioineo-oe Aaeeeay, o.a. i?aia?.
Aaeeeay. Aoi?ui yoaiii a noaiiaeaiee niaoeeaeueiie O. ioineo-oe noae
iiuo A.A.Iaeeaeueniia (1852-1931), i?iaaaeaiiue a 1881 aiaeo. A iiuoa
ii?aaeaeyeanue nei?inoue naaoa a ?acee/i. aeaeaeoueony neno. ion/.. Oaea
aiai?eeinue, /oi ii O. Iaenaaeea yeaeo?iiaaieoiua aieiu aeieaeiu
?ani?ino?aiyoueny ni nei?-oueth a aaeooia – n. Anoae aii?, a eaeie
eia?oe. neno-a ion/. yoi i?ienoiaeeo. If oaeiaie n/eoaoue nenoaio ion/.,
naycaiioth n iaiiaeaeaeiuie caacaeaie, oi nei?inoue iaoae ieaiaou
ioiineo. ieo ( = 30 ei/n. Yoa nei?inoue aieueoay e n?aaieiay ni
nei?-oueth naaoa n. Iaeeaeuenii yenia?eiaioaeueii ii?aaeaeye nei?inoue
naaoa a ?aciuo neno. ion/., a eiaii, ii ecia?ye nei?inoue naaoa,
eaeouaai a 2o i?ioeaiiieiaeiuo ioiineo. Caiee iai?-yo. A niioaaonoaee n
i?aia?aciaaieyie Aaeeeay e iieiaeaieyie eeane/. iaoaieee, nei?. naaoa a
yoeo neno. ion/. aeieaeiu auee au ioee/aony ia aaee/eio 2v. ?acoeueoaou
yenia?eiaioa Iaeeaeueniia iaeiicia/ii iieacaee, /oi nei?inoue naaoa ia
caaeneo io auai?a nenoaiu ion/. e anaaaea =a n. O.a. auei onoaiiaeaii,
/oi yeaeo?iiaaieoiua aieiu ai anao eia?oe. neno. ion/. ?ani?ino?aiythony
n iaeeiaeiaie nei?-oueth n(3(108 i/n. Yenia?eiaiou, iiaeiaiua iiuoo
Iaeeaeueniia iiaoi?yeenue iaiaeiie?aoii ni ana aic?anoathuae
oi/iinoueth. Ia naaiaeiyoiee aeaiue iiaeii ooaa?aeaeaoue, /oi nei?inoue
a ?acee/i. neno. ion/. iaeeiaeiaa n oi/iinoueth ii?yaeea ianeieueeeo
ii/n.

16. I?aia?aciaaiey Ei?aioea. A 1904-i aiaeo aieeaiaeneee oecee
O.A.Ei?aioe (1853-1928) auaae i?aia?. aeey ia?aoiaea ec 1ie eia?oe.
nenoaiu ion/. a ae?oa., ioee/iua io i?aia?. Aaeeeay. Neno. o?aaiaiee
Iaenaaeea auea eiaa?eaioia ioiineo. yoeo i?aia?.. I?aia?aciaaiey
eanaeenue e eii?ae., e a?aiaie. Iaicia/ei eii?aeeiaou e a?aiy iaeioi?iai
niauoey (iai?eia? iieiaeaiey iao. o/ee a i?ino-aa) a eia?oe. neno-a
ion/. E /a?ac x, y, z, t, a a ae?oaie eia?oe. neno-a ion/. E’ /a?ac
x’,y’,z’,t’. Nenoaiu ion/. aua?aiu oae, /oiau eo eii?aeeiaoiua naoee
ia/aeueiue iiiaio a?aiaie t=t’=0 niaiaaeaee, a a aeaeueiaeoai neno. E’
aeaeaaeanue ioiineo. nenoaiu E ni nei?-oueth u aaeieue aa ine (ox).
I?aia?aciaaiey Ei?aioea eiatho aeae: x’=x-ut/’ei?aiue'(1-(u/c)^2); y’=y;
z’=z; t’=(t-ux/c^2)/’ei?aiue'(1-(u/c)^2) (12.1). N?aco iiaeii neacaoue,
/oi i?e u/c ‘no?aieony’ 0 i?aia?. Ei?aioea ia?aoiaeyo a i?aia?. Aaeeeay.
O.a. i?aia?. Aaeeeay yae. /anoiui neo/aai i?aia?. Ei?aioea i?e iaeuo
nei?inoyo aeaeaeaiey. Aiaeece?oy neiaeeaoaany iieiae. A.Yeiooaei
?ac?aaioae iiaoth iaoaieeo aieueoeo nei?inoae, iacuaaaioth nae/an
?aeyoeaenoneie iaoaieeie eee niaoeeaeueiie O. ioineo-oe. A iniiaa yoie
O. eaaeao 2 iinooeaoa. Niaeanii ia?aiio iinooeaoo nei?inoue
?ani?ino?aiaiey naaoa ai anao eia?oe. neno. eii?ae. iaeeiaeiaa e =a
nei?. ?ani?ino?aiaiey naaoa a aaeooia – n. Yoio iinooeao ooaa?aeaeaao
yeaeaaeaioiinoue eia?oe. nenoai ion/. ioiineo. nei?. naaoa. 2e iinooeao
caee. a oii, /oi ana oece/aneea caeiiu e yae-y oi?ioee?othony e
i?ioaeatho iaeeiaeiai ai anao eia?oe. neno. ion/., o.a. eiaa?eaioiu
ioiineo. i?aia?. Ei?aioea. Aace?oynue ia yoeo iinooeaoao, Yeiooaei
?ac?aaioae O. aeaeaeaiey nenoai i?e ethauo nei?inoyo, aieioue aei
nei?inoae naaoa. A ?aieao O. ioineo-oe iieo/aiu auaiaeu, eacaeinue au
i?ioeai?a/auea caeiiai eeane/. iaoaieee. Iaeiaei, ana auaiaeu yoie O.
iiaeoaa?aeaeaiu yenia?eiaioaeueii n aunieie oi/iinoueth. Niaeanii
i?eioeeio niioaaonoaey noa?ay O. (eeanne/aneay iaoaieea eee iaoaieea
aeaeaeaiey oae i?e iaeuo nei?inoyo) yae. /anoiui neo/aai iiaie. E
iaiai?io, iiaay O. ioineo-oe ia?aoiaeeo a noa?oth eeanne/aneoth iaoaieeo
i?e nei?inoyo aeaeaeaiey v

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