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Flotacion: Teoria Y Balance Metalúrgico

Descripción: FLOTACION: TEORIA, REACTIVOS, BALANCE METALURGICO Y EJEMPLOS DE APLICACIÓN

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Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG JNKWEHBKC B# [email protected] GFN TQKHFXK GF JNKWEHBØC Ne gfjbcbhbøc wqegbhbkcen gf jnkwehbøc gbhf uvf fx vce wâhcbhe gf hkchfcwqehbøc gf `bcfqenfx fc lÿ`fgk. fc ne uvf xf etqkzfhlec nex tqktbfgegfx jàxbhk-uvà`bhex xvtfqjbhbenfx gf nex teqwàhvnex teqe fjfhwveq ne xfnfhhbøc# Fc kwqex teneaqex. xf wqewe gf vc tqkhfxk gf xfteqehbøc gf `ewfqbex gf gbxwbcwk kqbmfc uvf xf fjfhwÿe gfxgf xvx tvntex ehvkxex tkq `fgbk gf avqavoex gf mex r e aexf gf xvx tqktbfgegfx lbgqkjànbhex f lbgqkjøabhex# Xfmÿc ne gfjbcbhbøc. ne jnkwehbøc hkcwf`tne ne tqfxfchbe gf wqfx jexfx? xønbge. nàuvbge r mexfkxe# Ne jexf xønbge fxwå qftqfxfcwege tkq nex `ewfqbex e xfteqeq. ne jexf nàuvbge fx fn emve r ne jexf mex fx fn ebqf# Nkx xønbgkx jbckx r nbafqegkx r fn emve. ecwfx gf ne etnbhehbøc gfn tqkhfxk. xf tqfteqec fc jkq`e gf tvnte hkc tkqhfcweof gf xønbgkx zeqbeanfx tfqk ckq`en`fcwf ck xvtfqbkq e 74& gf xønbgkx# Vce zf bcmqfxege ne tvnte en tqkhfxk. xf bcrfhwe fn ebqf teqe tkgfq jkq`eq nex avqavoex. uvf xkc nkx hfcwqkx xkaqf nkx hvenfx xf eglbfqfc nex teqwàhvnex xønbgex# Teqe nkmqeq vce avfce hkchfcwqehbøc xf qfuvbfqf uvf nex fxtfhbfx uvf hkcxwbwvrfc ne `fce fxwâc xfteqegex k nbafqegex# Fxwk xf nkmqe fc nex fwetex tqfzbex gf hlechegk r `knbfcge# Teqe ne `erkqàe gf nkx `bcfqenfx. xf nkmqe vc egfhvegk mqegk gf nbafqehbøc `knbfcgk e we`eõkx hfqheckx e nkx 544 `bhqkcfx ,4.5 ``"# En ev`fcweq fn we`eõk gf ne teqwàhvne. hqfhfc nex tkxbabnbgegfx gf `ene eglfqfchbe e ne avqavoe9 fc wecwk uvf nex teqwàhvnex `vr jbcex ck wbfcfc fn xvjbhbfcwf b`tvnxk teqe tqkgvhbq vc fchvfcwqk fjfhwbzk teqwàhvne avqavoe# JNKWEHBØC AVNI? Qfhvtfqehbøc gf wkgex nex fxtfhbfx zenbkxex ,kqk. tnk`k. tnewe. bch. hkaqf. fwh#" fc vc xknk tqkgvhwk nne`egk Hkchfcwqegk Avni# QFEHWBZKX GF JNKWEHBKC? Nkx qfehwbzkx gf jnkwehbøc xf gbzbgfc fc? hknfhwkqfx. fxtv`ecwfx r `kgbjbhegkqfx# Hknfhwkq? Hk`tvfxwk kqmåcbhk lfwfqktkneq uvf xf eaxkqaf xfnfhwbze`fcwf xkaqf ne ‡ xvtfqjbhbf gf nex teqwàhvnex. lehbfcgk uvf fxwex xf zvfnzec lbgqøjkaex ,efqøjbnex"# Fof`tnk? |ecwewkx uvf xf vwbnbec fc ne jnkwehbøc gf xvnjvqkx# Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 5 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG Nkx hknfhwkqfx vxegkx hkc `erkq jqfhvfchbe xkc nkx |ecwewkx r nkx efqkjnkewx# Xbc nkx hknfhwkqfx nkx xvnjvqkx ck tkgqàec tfmeqxf e nex avqavoex r âxwex xvabqàec e ne xvtfqjbhbf xbc nkx `bcfqenfx r nkx xvnjvqkx zenbkxkx xf bqàec e nex hknex# Vce hecwbgeg f|hfxbze gf hknfhwkq leqàe uvf jnkweqåc bchnvxk nkx `ewfqbenfx ck gfxfegkx ,tbqbwex r qkhex" k nkx xvnjvqkx uvf gfafqàec jnkweq fc hbqhvbwkx xbmvbfcwfx# Exà tkq fof`tnk. fc fn hexk gf ne jnkwehbøc gf `bcfqenfx gf tnk`k-bch-tbqbwe. fc fn hbqhvbwk gf tnk`k xf `ecwbfcf gftqb`bgk fn bch. teqe jnkweqnk tkxwfqbkq`fcwf fc xv qfxtfhwbzk hbqhvbwk9 tfqk vc f|hfxk gf hknfhwkq tkgqàe lehfq jnkweq fn bch ovcwk hkc fn tnk`k# Vce hkxe xb`bneq xvhfgfqàe fc fn hbqhvbwk gf bch hkc vc f|hfxk gf hknfhwkq. lehbfcgk jnkweq ne tbqbwe uvf xf fchvfcwqe gftqb`bge tkq fn fjfhwk gf ne n e hen egbhbkcege# Fxtv`ecwf? Xkc emfcwfx wfcxkehwbzkx uvf xf egbhbkcec e kaofwk gf? ‡ 5# Fxweabnbeq ne fxtv`e 1# Gbx`bcvbq ne wfcxbøc xvtfqjbhben gfn emve 8# @fokqeq ne hbcâwbhe gf bcwfqehhbøc avqavoe  ‘  teqwàhvne 7# Gbx`bcvbq fn jfcø`fck gf vcbøc gf gkx k `åx avqavoex ,hkenfxhfchbe" @kgbjbhegkqfx? Fxwkx qfehwbzkx tvfgfc xfq gf wqfx wbtkx? `kgbjbhegkqfx gf tL. ‡ ehwbzegkqfx r gftqfxkqfx#  @kgbjbhegkqfx gf tL ? Fn tL bcgbhe b cgbhe fn mqegk gf ehbgf k gf enhenbcbgeg gf ne tvnte# Fn tL = fx cfvwqk ,cb enhenbck cb åhbgk" r hkqqfxtkcgf en emve tvqe# Gf 4 e : fx åhbgk r gf < e 57 fx enhenbck# Fn tL xf `bgf hkc vc eteqewk nne`egk tkwfchbø`fwqk k hkc vc tetfn wkqcexkn# Hege xvnjvqk wbfcf xv tqktbk tL gf jnkwehbøc. gkcgf tvfgf jnkweq `fokq# Fxwe tqktbfgeg zeqàe xfmÿc fn `bcfqen r xv tqkhfgfchbe# Nkx qfmvnegkqfx gf tL wbfcfc ne `bxbøc gf geq e hege tvnte fn tL `åx egfhvegk teqe vce jnkwehbøc øtwb`e# Ne hen fx vc qfehwbzk etqktbegk teqe qfmvneq fn tL. tvfx gftqb`f nex mecmex r tqfhbtbwe nex xenfx gbxvfnwex fc fn emve# Ne hen xf tvfgf enb`fcweq e ne fcwqege gfn `knbck e aknex# Fx b`tkqwecwf vxeq gkxbjbhegkqfx evwk`åwbhkx teqe fxweq xfmvqkx gf ne hecwbgeg gf qfehwbzk gkxbjbhegk e nex tvntex ,Jbm# 8"# Ler qfehwbzkx xønbgkx r nàuvbgkx#  Ehwbzegkqfx? Xkc qfehwbzkx uvà`bhkx kqmåcbhkx k bckqmåcbhkx uvf ervgec en hknfhwkq e egxkqafqxf egxkqafqxf fc ne xvtfqjbhbf gfn `bcfqen e jnkweq# jnkweq# Xvnjewk gf Hkaqf Hkaqf ,HvXK7"? ,HvXK7"? Fn HvXK7 6 L1K. xvnjewk xvnjewk gf hkaqf hkc 6 `knâhvnex gf emve. jkq`e hqbxwenfx evnfx evnfx aqbnnecwfx exb`âwqbhkx gfn xbxwf`e wqbhnàcbhk hkc vce gfcxbgeg gf 1#1< m+`n# Fx vc ehwbzegkq gf ne fxjenfqbwe. we`abâc tbqbwe. henhktbqbwe. tbqkwbwe. tbqkwbwe. eqxfcktbqbwe r hveqk# Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 1 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG  Gftqfxkqfx? Xkc qfehwbzkx uvà`bhkx kqmåcbhkx k bckqmåcbhkx uvf b`tbgfc ne ehhbøc gfn hknfhwkq fc ne xvtfqjbhbf gfn `bcfqen# Hbecvqk gf Xkgbk ,CeHC"? Xkc hqbxwenfx fc jkq`e gf tfnnfwx gf hknkq anecuvfhbck. xf vxec teqe fn qfhvaqb`bfcwk r gftqfxbøc gf `bcfqenfx xvnjvqegkx gf jbfqqk. hkaqf r bch Abxvnjbwk gf Xkgbk ,CeLXK8"? Fx vc gftqfxkq teqe xvnjvqkx gf bch r jbfqqk# Xf vxe fc qff`tnek gfn hbecvqk gf xkgbk teqwbhvneq`fcwf fc `bcfqenfx hkc hkcwfcbgk hkcwfcbgk gf tnewe. ne egbhbøc gfn emfcwf qfgvhwkq xvnjbwk gf xkgbk k abxvnjbwk gf xkgbk tqfzbfcf ne k|bgehbøc r tkq hkcxbmvbfcwf. ne ehwbzehbøc qfxvnwecwf gf ne fxjenfqbwe Xvnjewk gf _bch ,_cXK7"? Fn _cXK7 = L14. xkc hqbxwenfx bchknkqkx9 fx vck gf nkx qfehwbzkx qfmvnegkqfx tqbchbtenfx gf ehhbøc gftqfxkqex. vwbnbege teqe ne jnkwehbøc xfnfhwbze gf `bcfqenfx gf hkaqf r tnk`k gf ne fxjenfqbwe# Fc fn hvegqk tkgf`kx zfq enmvckx qfehwbzkx etnbhegkx e `bcfqenfx fxtfhàjbhkx Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 8 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG Fc fn xbmvbfcwf gbemqe`e tkgf`kx zfq nex fwetex fc nex uvf xf ze egbhbkcecgk nkx qfehwbzkx e ne tvnte fc vc hbqhvbwk gf `knbfcge Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 7 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG @fhecbx`kx gf Jnkwehbøc Teqe fxwvgbeq fn `fhecbx`k gf ne jnkwehbøc fx cfhfxeqbk hkckhfq nk uvf xvhfgf hkc ne teqwàhvne gf `bcfqen r vce avqavoe gf ebqf teqe uvf fnnkx jkq`fc vce vcbøc fxweanf# Fn tqkhfxk gf jnkwehbøc fxwå aexegk xkaqf nex tqktbfgegfx lbgqkjànbhex f lbgqkjøabhex gf nkx xønbgkx e xfteqeq# Xf wqewe jvcge`fcwen`fcwf gf vc jfcø`fck gf hk`tkqwe`bfcwk gf xønbgkx jqfcwf en emve. k xfe. gf `koeabnbgeg gf nkx xønbgkx# Nkx `fwenfx cewbzkx. xvnjvqkx gf `fwenfx k fxtfhbfx wenfx hk`k mqejbwk. heqaøc abwv`bckxk. wenhk r kwqkx. xkc tkhk `koeanfx Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 6 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG tkq fn emve r xf nne`ec `bcfqenfx lbgqkjøabhkx# Tkq kwqe teqwf. nkx `bcfqenfx uvf xkc ø|bgkx. xvnjewkx. xbnbhewkx. heqakcewkx r kwqkx xkc lbgqkjànbhkx. k xfe. `koeanfx tkq fn emve# Xf tvfgf kaxfqzeq egf`åx uvf nkx `bcfqenfx lbgqkjøabhkx xkc efqkjànbhkx. fx gfhbq. wbfcfc mqec ejbcbgeg tkq nex avqavoex gf ebqf. `bfcwqex uvf nkx `bcfqenfx lbgqkjànbhkx xkc efqkjøabhkx. k xfe. ck xf eglbfqfc ckq`en`fcwf e fnnex# Fc qfxv`fc. fx cfhfxeqbk bchqf`fcweq ne tqktbfgeg lbgqøjkae fc nex teqwàhvnex `bcfqenfx gf vce tvnte teqe jehbnbweq ne jnkweabnbgeg# Fxwk xf fjfhwÿe hkc nkx qfehwbzkx nne`egkx hknfhwkqfx. uvf xkc mfcfqen`fcwf hk`tvfxwkx kqmåcbhkx gf heqåhwfq lfwfqktkneq. k xfe. vce teqwf gf ne `knâhvne fx vc hk`tvfxwk fzbgfcwf`fcwf etkneq ,lbgqkheqavqk" r ne kwqe fx vc mqvtk tkneq hkc nex tqktbfgegfx bøcbhex. fx gfhbq. hkc heqme fnâhwqbhe gfjbcbge# Ne teqwàhvne uvfge hvabfqwe tkq fn hknfhwkq uvf xf eglbfqf e xv xvtfqjbhbf tkq `fgbk gf xv teqwf tkneq. tqktkqhbkcåcgknf hkc ne teqwf tkneq tqktbfgegfx lbgqkjøabhex# Fn emqfmegk gf fxtv`ecwfx. hk`k xf le gbhlk. tfq`bwf ne jkq`ehbøc gf avqavoex gf w e`eõk r henbgeg egfhvege teqe fn tqkhfxk# Tvfx abfc. fn hkcwehwk fcwqf nex teqwàhvnex r nex avqavoex qfuvbfqf uvf nex tqb`fqex fxwâc fc hkcxwecwf embwehbøc. ne hven ne kwkqme fn qkwkq gf ne `åuvbce gf jnkwehbøc. gf `kgk uvf teqe qfenbeq ne vcbøc hkc nex avqavoex xkc cfhfxeqbkx? e" xv fchvfcwqk r a" hkcgbhbkcfx jezkqeanfx teqe jkq`eq fn emqfmegk# Fn hkcwehwk teqwàhvne-avqavoe xf ehfqhe lexwe fn tvcwk fc uvf ne tfnàhvne gf emve uvf nex xfteqe fx `vr jbce# Fc fxwf `k`fcwk teqe uvf ne teqwàhvne tvfge ehfqheqxf `åx e ne avqavoe wbfcf uvf xvtfqeq nk uvf xf hkcxbgfqe vce aeqqfqe fcfqmâwbhe# Teqe nex teqwàhvnex lbgqkjànbhex. fc uvf ne exkhbehbøc gf ne teqwàhvne hkc nex `knâhvnex gf emve fx `vr jbq`f. fxwe aeqqfqe cvche xf xvtfqe r nex n ex teqwàhvnex ck jnkwec# Teqe nex teqwàhvnex lbgqkjøabhex. ne aeqqfqe uvfge qftfcwbce`fcwf qkwe tkq jvfqex ck abfc hkckhbgex. tfq`bwbfcgk vc hkcwehwk wqbjåxbhk ,xønbgk-nàuvbgk-mex"# , xønbgk-nàuvbgk-mex"# Zeqbeanfx Ktfqehbkcenfx Qfnfzecwfx fc fn Tqkhfxk Enmvcex gf nex zeqbeanfx gf `erkq b`tkqwechbe b `tkqwechbe teqe fn tqkhfxk gf jnkwehbøc xkc?  Mqecvnk`fwqàe? Eguvbfqf mqec b`tkqwechbe gegk uvf ne jnkwehbøc qfuvbfqf uvf nex fxtfhbfx `bcfqenfx ÿwbnfx wfcmec vc mqegk gf nbafqehbøc egfhvegk teqe xv hkchfcwqehbøc#  Wbtk gf Qfehwbzkx? Nkx qfehwbzkx tvfgfc hnexbjbheqxf fc hknfhwkqfx. fxtv`ecwfx r `kgbjbhegkqfx# Ne fjbhbfchbe gfn tqkhfxk gftfcgfqå gf ne xfnfhhbøc gf ne `fokq jøq`vne gf qfehwbzkx#  Gkxbx gf Qfehwbzk? Ne hecwbgeg gf qfehwbzkx qfuvfqbge fc fn tqkhfxk gftfcgfqå gf nex tqvfaex `fwenÿqmbhex tqfnb`bceqfx r gfn aenechf fhkcø`bhk gfxtqfcgbgk gf ne fzenvehbøc gf nkx hkcxv`kx  Gfcxbgeg gf Tvnte? F|bxwf vc tkqhfcweof gf xønbgkx øtwb`k teqe fn tqkhfxk uvf wbfcf bcjnvfchbe fc fn wbf`tk gf qfxbgfchbe gfn `bcfqen fc nkx hbqhvbwkx# Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce : Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG  Ebqfehbøc? Ne ebqfehbøc tfq`bwbqå ev`fcweq k qfweqgeq ne jnkwehbøc fcafcfjbhbk gf ne qfhvtfqehbøc k gf ne nfr. qfxtfhwbze`fcwf# Fn ebqf fx vck gf nkx wqfx fnf`fcwkx b`tqfxhbcgbanfx fc fn tqkhfxk gf jnkwehbøc. ovcwk hkc fn `bcfqen r fn emve#  Qfmvnehbøc gfn tL? Ne jnkwehbøc fx xv`e`fcwf xfcxbanf en tL.fxtfhben`fcwf hvecgk xf wqewe gf jnkwehbøc xfnfhwbze# Hege jøq`vne gf qfehwbzkx wbfcf vc tL øtwb`k e`abfcwf fc fn hven xf kawfcgqàe fn `fokq qqfxvnwegk fxvnwegk ktfqehbkcen#  Wbf`tk gf Qfxbgfchbe? Fn wbf`tk gf qfxbgfchbe gftfcgfqå gf ne hbcâwbhe gf jnkwehbøc gf nkx `bcfqenfx gf ne hbcâwbhe gf ehhbøc gf qfehwbzkx. gfn zknv`fc gf nex hfngex. gfn tkqhfcweof gf xønbgkx gf nex tvntex fc nex hfngex r gf nex heqmex hbqhvnecwfx#  Henbgeg gfn Emve? Fc nex Tnecwex ne gbxtkcbabnbgeg gf emve fx vc tqkanf`e# Ckq`en`fcwf xf vwbnbe fn emve gf qfhbqhvnehbøc gf fxtfxegkqfx uvf hkcwbfcf hecwbgegfx qfxbgvenfx gf qfehwbzkx r xønbgkx fc xvxtfcxbøc. hkc nex hkcxfhvfchbex qfxtfhwbzex gfqbzegex tkq fxwf jnvok gf qfhbqhvnehbøc# HFNGEX GF JNKWEHBKC? Jvchbkcfx? 5# @ecwfcfq wkgex nex teqwàhvnex fc xvxtfcxbøc gfcwqk gf nex tvntex fc jkq`e fjfhwbze. hkc fn jbc gf tqfzfcbq ne xfgb`fcwehbøc gf âxwex# 1# Tqkgvhbq vce avfce ebqfehbøc. uvf tfq`bwe ne gbxf`bcehbøc gf avqavoex gf ebqf e wqezâx gf ne hfnge# 8# Tqk`kzfq nex hknbxbkcfx r eglfxbkcfx gf teqwàhvne-avqavoe# 7# @ecwfcfq uvbfwvg fc ne tvnte bc`fgbewe`fcwf aeok ne hknv`ce gf fxtv`e# 6# Tqkzffq vc fjbhbfcwf wqecxtkqwf gf ne tvnte enb`fcwege e ne hfnge. gfn hkchfcwqegk r gfn qfnezf# :# Tqkzffq vc `fhecbx`k gf hkcwqkn gf ne enwvqe gf ne tvnte r gf ne fxtv`e. ne ebqfehbøc gf ne tvnte r gfn mqegk gf embwehbøc# Heqehwfqàxwbhex? 5# Jehbnbgeg teqe ne enb`fcwehbøc gf ne tvnte fc jkq`ex hkcwbcÿe# 1# @ecwfcfq ne tvnte fc fxwegk gf xvxtfcxbøc# 8# Ck gfaf khvqqbq ne n e xfgb`fcwehbøc gf nex teqwàhvnex# 7# Xfteqehbøc egfhvege gfn hkchfcwqegk r gfn qfnezf Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce = Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG Fjbhbfchbe Ne fjbhbfchbe gf vce hfnge gf jnkwehbøc xf gfwfq`bce tkq nkx xbmvbfcwfx extfhwkx? 5# Wkcfneof uvf xf tvfgf wqeweq tkq vcbgeg gf zknv`fc# 1# Henbgeg gf nkx tqkgvhwkx kawfcbgkx r qfhvtfqehbkcfx# qfhvtfqehbkcfx# 8# Hkcxv`k gf fcfqmàe fnâhwqbhe. qfehwbzkx. fxtv`ecwfx r kwqkx qfehwbzkx. hkc fn jbc gf kawfcfq nkx qfxvnwegkx øtwb`kx# 7# Mexwkx gf ktfqehbøc r `ecwfchbøc tkq wkcfnege gf `bcfqen wqewegk# HFNGEX GF JNKWEHBØC @FHÅCBHEX Nex hfngex gf jnkwehbøc `fhåcbhex wbfcfc wqfx kcex wàtbhex?    Ne kce gf embwehbøc fx euvfnne gkcgf xf tqkgvhf ne eglfxbøc teqwàhvne-avqavoe# Fc fxwe kce gfafc f|bxwbq hkcgbhbkcfx lbgqkgbcå`bhex r jbxbhkuvà`bhex uvf jezkqfhec fxwf hkcwehwk Ne kce bcwfq`fgbe xf heqehwfqbe tkq xfq vce kce gf qfnewbze hen`e. nk uvf jezkqfhf ne `bmqehbøc gf nex avqavoex lehbe ne xvtfqjbhbf gf ne hfnge# Ne kce xvtfqbkq hkqqfxtkcgf e ne jexf ehvkxe. jkq`ege tkq avqavoex# Ne fxtv`e gfxheqme tkq qfaenxf cewvqen. k hkc ervge gf tenfwex `fhåcbhex# Hvecgk ne wvqavnfchbe fc ne bcwfqjexf tvnte -fxtv`e fx enwe xf tqkgvhf hkcwe`bcehbøc gfn hkchfcwqegk gfabgk en eqqexwqf xbmcbjbhewbzk gf tvnte lehbe ne fxtv`e# Qfehwbzkx gf Jnkwehbøc Vwbnbegkx fc neakqewkqbk n eakqewkqbk  Hknfhwkq \ECWEWK _6 Tqktbfgegfx uvà`bhex r vxkx Fx vc tqkgvhwk uvf xf etnbhe mfcfqen`fcwf fc euvfnnex ktfqehbkcfx uvf qfuvbfqfc fn `åx enwk mqegk gf tkgfq hknfhwkq# Xf vxe fc ne jnkwehbøc gf `bcfqenfx xvnjvqkxkx gf Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce < Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG hkaqf# Nkx |ecwewkx wbfcgfc e gfxhk`tkcfqxf fc xknvhbkcfx hkc vc tL bcjfqbkq e :#4# Xf etnbhe hkc fxtfhben â|bwk fc ne jnkwehbøc gf ne tbqbwe uvf hkcwbfcf kqk# Tqfhevhbkcfx Tqfhevhbkcfx gf @ecfok Nkx |ecwewkx xkc fxweanfx gvqecwf neqmkx tfqàkgkx gf wbf`tk. xbf`tqf r hvecgk xf en`ehfcfc fc vc nvmeq xfhk r jqfxhk# Nex tfqxkcex uvf `ecfoec nex |ecwewkx gfafc wk`eq hbfqwex tqfhevhbkcfx# Gfaf fzbweqxf ne nne`e zbze k fn jvfmk. tvfxwk uvf nex |ecwewkx r enmvcex gf xvx tqkgvhwkx gf gfxhk`tkxbhbøc xkc hk`avxwbanfx# Nkx |ecwewkx. fc wâq`bckx mfcfqenfx. gfafc `ecbtvneqxf hkc fn `bx`k mqegk gf tqfhevhbøc uvf xf ehkcxfoe teqe kwqkx tqkgvhwkx uvà`bhkx kqmåcbhkx »Uvâ xf tvfgf lehfq gfxtvâx gf uvf lere khvqqbgk ne hkcwe`bcehbøc; Ne hkcwe`bcehbøc uvf khvqqf tkhk e tkhk mfcfqen`fcwf ck xf tvfgf gfwfhweq lexwe uvf fn tqkanf`e le enhecegk vce `fgbge mqezf# Fn qfxvnwegk fx uvf ne nb`tbfe gf ne hkcwe`bcehbøc xfe vc tqkhfxk hk`tnbhegk. heqk. r e zfhfx b`tkxbanf# Fc mfcfqen. vce hk`vcbgeg hvrex emvex xvawfqqåcfex lec xbgk hkcwe`bcegex wbfcf hbchk kthbkcfx?  Qfwfcfq nkx hkcwe`bcecwfx teqe tqfzfcbq xv `bmqehbøc gfxgf fn tvcwk gf kqbmfc#  F|wqefq nkx hkcwe`bcecwfx gfn ehvàjfqk#  Wqeweq nex emvex xvawfqqåcfex fc fn nvmeq gf f|wqehhbøc k ecwfx gf vxeqnex#   Qfleabnbweq fn ehvàjfqk tkq `fgbk gf bc`kzbnbehbøc k gfwk|bjbhehbøc gf nkx hkcwe`bcecwfx. hkcwe`bcecwfx. `bfcwqex uvf fxwkx wkgezàe xf fchvfcwqfc fc fn ehvàjfqk# Eaecgkceq fn vxk gfn ehvàjfqk r avxheq `ececwbenfx enwfqcewbzkx teqe emve tkweanf# Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 2 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG Zeqbkx jehwkqfx gfwfq`bcec hvån fx ne `fokq kthbøc. bchnvrfcgk fn wbtk r `emcbwvg gf hkcwe`bcehbøc. nex hkcgbhbkcfx mfknømbhex. xb nex nfrfx qfuvbfqfc hbfqwex ehhbkcfx fxtfhàjbhex. r hvecwk gbcfqk fx gbxtkcbanf teqe fn tqkrfhwk# Wkgex fxwex kthbkcfx xkc heqex# Nkx zeqbkx `âwkgkx gf wqewe`bfcwk wbfcfc hkxwkx `vr enwkx r `vhlex gbjbhvnwegfx wâhcbhex. r gf `ecfqe uvf `vhlex hk`vcbgegfx ktwec tkq eaecgkceq fn ehvàjfqk hvecgk xf fcjqfcwec hkc hkcwe`bcehbøc gf xv emve xvawfqqåcfe# Ne hk`vcbgeg fcwkchfx wbfcf uvf fchkcwqeq kwqk eaexwfhb`bfcwk gf emve. k wenegqeq cvfzkx tkkx `åx nfokx gfn åqfe hkcwe`bcege# Ne gftvqehbøc gf nex emvex? ,Nkx gfxfhlkx wqecxtkqwegkx tkq fn emve qfuvbfqfc gf vc wqewe`bfcwk fjbhe fc tnecwex gftvqegkqex teqe gfxwqvbq nkx fnf`fcwkx hkcwe`bcecwfx. ecwfx gf xfq zfqwbgex e nkx qàkx r en `eq# @bcfqen tknb`fwånbhk Hexk ? @bcfqen @bcfqen hkc nfrfx nfrfx ? 5 & Ta . 5&Hv . 5& _c. 54 k [email protected] r mecme Vc `bcfqen tknb`fwånbhk hk`k hk`k fn uvf xf `vfxwqe. xf xf jnkwe teqe kawfcfq hkchfcwqegkx hkchfcwqegkx gf hkaqf. tnk`k r bch tkq xfteqegk. teqe nk hven xf wbfcfc nex xbmvbfcwfx tevwex?      tL gf ne tvnte enqfgfgkq gf < fc ne tqb`fqe jnkwehbøc , avni" gftqb`bq fn `bcfqen gf bch fc fn `knbck. hkc ne egbhbøc gf enmvck gf nkx gftqfxkqfx teqe anfcge. fc fxwf hexk vxeqf`kx ne `fhne gf hbecvqk gf xkgbk r xvnjewk gf bch , fc tqktkqhbøc vck gf hbecvqk r wqfx wq fx gf xvnjewk" ehkcgbhbkceq ehkcgbhbkceq ne tvnte hkc hkc vc gbwbkjkxjewk hk`k hk`k hknfhwkq hknfhwkq tqbchbten tqbchbten , E-14< ø E747" r hk`k hknfhwkq xfhvcgeqbk vc |ecwewk , _-: " xf kawbfcf kawbfcf vc hkchfcwqegk avni ,tnk`k-hkaqf-tnewe" . fn uvf nvfmk xfqå nb`tbegk r gfxtvâx ehkcgbhbkcegk hkc vc gftqfxkq ,fc fxwf hexk teqe fn hkaqf" fn gftqfxkq gf hkaqf e vxeq fx vce xknvhbøc gf hbecvqk gf xkgbk uvf xf emqfmeqå fc f|hfxk . lexwe uvf xf ckwf uvf re ne henhktbqbwe ck jnkwe fc nex hfngex gf xfteqehbøc Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 54 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG    gf fxwe `ecfqe wfcgqf`kx vc hkchfcwqegk gf hkaqf uvf xengqå tkq gkcgf hkqqbfcwf`fcwf xenf fn qfnezf r kwqk hkchfcwqegk uvf hkcwbcvø jnkwecgk ,tnk`ktnewe" fn qfnezf gf fxwf tqb`fq hbqhvbwk gf jnkwehbøc avni fx nvfmk ehkcgbhbkcegk ehkcgbhbkcegk hkc xvnjewk gf hkaqf teqe ehwbzeq e ne fxjenfqbwe , uvf xf gftqb`bø fc ne `knbfcge " xf xvaf fn fn tL gf ne tvnte hkc hkc nfhlege gf hen lexwe 54 r xf egbhbkce fc fn fn ehkcgbhbkcegkq ehkcgbhbkcegkq fn hknfhwkq , _-55" r vc fxtv`ecwf fxtv`ecwf ,G-164"  xf jnkwe ne fxjenfqbwe  fc fn qfnezf bqec bqec nex tbqbwex. mecmex mecmex r kwqkx hk`tkcfcwfx gfn qfnezf Ne gkxbjbhehbøc gf nkx qfehwbzkx fx fn qfxvnwegk gf ne fzenvehbøc gf zeqbeanfx gf jnkwehbøc lfhle hkc fn `bcfqen fc fn neakqewkqbk `fwenÿqmbhk Fof`tnk gf egbhbøc gf gf |ecwewk fc xknvhbøc xknvhbøc en 54 & ? Xb ne `fokq `fokq gkxbx fx fx 64 m tkq wkcfnege wkcfnege gf `bcfqen `bcfqen ? e" Teqe vce tqvfae fc neakqewkqbk. neakqewkqb k. hkc `fgbk ibnkmqe`k gf `vfxwqe. `vfxwqe. fn tfxk gf |ecwewk xfqå ? 64 `m tkq im r teqe ne `vfxwqe `vfxwqe gf ° im xfqå 4.416 m a" Teqe tqfteqeq tqfteqeq ne xknvhbøc gf |ecwewk en 54 & tfxe`kx 54 mqe`kx gf |ecwewk |ecwewk r egbhbkce`kx e 24 `n gf emve. uvfgecgk vce xknvhbøc hkc vce gfcxbgeg etqk|b`ege e 5 m+hh h" Gf ne xknvhbøc ecwfqbkq. wk`e`kx 4.16 `n r eõegb`kx en `knbck uvf tqfzbe`fcwf le xbgk heqmegk hkc ne `vfxwqe `bcfqen r fn emve Fof`tnk gf egbhbøc gf E-14< tvqk Xb ne gkxbx fchkcwqege fx ? 4.416 m + [email protected]      Teqe ne `vfxwqe gf `bcfqen gf ° im 0 4.4516 m Ne gfcxbgeg gfn E-14< fx 5.56 m + hh Zknv`fc gf E-14< 0 4.4516 4.4516 + 5.56 5.56 0 4.454<= hh 14 mkwbwex gf fxwf hknfhwkq lehfc vc hh R teqe fxwf hexk hexk xf eõegbqå eõegbqå ,14",4.454<=" ,14",4.454<=" + ,5" 0 4.15= mkwbwex Fof`tnk gf egbhbøc gf gf E-14< fc xknvhbøc en 54 &  Teqe ne `vfxwqe gf `bcfqen gf ° im xf qfuvbfqf 4.4516 mqe`kx gf E-14< Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 55 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG     Teqe tqfteqeq vce xknvhbøc gf E-14< en 54 & ? wk`e`kx 4.<= hh gf E-14< tvqk , 5 mqe`k " r nk eõegb`kx e 2 `n gf emve , 2 mqe`kx" Fxwe xknvhbøc hkcwbfcf 5 m gf E-14< tkq hege 2.<= hh Fcwkchfx ne gkxbx xfqå 4.518 hh hh gf xknvhbøc en 54 & ,14",4.518" + ,5" 0 1.7: mkwbwex & Hv Heafe Hkchfcwqegk Hv Hkchfcwqegk Ta Hkchfcwqegk _c Qfnezf 5 84 4.2 5 4.4< & Ta 5.5 5 :< 4.2 4.42 & _c 5.1 5.5 4.2 :5 4.42 K Em + [email protected] 54 <.: 8<4 =.2 8.: Aenechf gf `ewfqbenfx? J 5J 0 E ) A 0 84 E ) 4.2 A ) H ) W ) 5H ) 4.4< W ) :< A ) 4.2 H ) 4.42 W 5.1J 0 5.5 E ) 4.2 A ) :5 H ) 4.42 W 5.5J 0 5 E E? Hkchfcwqegk gf hkaqf A? Hkchfcwqegk gf tnk`k H? Hkchfcwqegk gf bch Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 51 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG  TEQE FN HÅNHVNK GFN HKCHFCWQEGK GF HKAQF ,E" ? E 0 ,J" 5 5 5 5 5 4.2 5 4.4< 5.5 :< 4.2 4.42 5.1 4.2 :5 4.42 5 5 5 5 84 4.2 5 4.4< 5 :< 4.2 4.42 5.5 4.2 :5 4.42 Xf qfxwe hknv`ce e hknv`ce. uvfgecgk gfwfq`bcecwfx gf 8|8 E0 ,J" E 0 ,J" 4 4 4 -4.5 4.5 -4.21 ::.2 -:=.5 -4.<5 -4.8 :4.5 -:4.25 4 4 4 -12.5 4.5 -4.21 := -:=.5 -4.<5 -4.1 :4.5 -:4.25 -4.5 4.5 -4.21 ::.2 -:=.5 -4.<5 -4.8 :4.5 -:4.25 -12.5 4.5 -4.21 := -:=.5 -4.<5 -4.1 :4.5 -:4.25 @vnwbtnbhe`kx fc fuvbx …## Qfxwåcgknkx ? fo` ? ,-4.5" ,:4.5" - ,-4.8" ,4.5" 0 -6.2< ,-4.5" ,-:=.5" - ,::.2" ,4.5" 0 4.41 Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` r exà fn qfxwk … Tåmbce 58 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG E0J -6.2< 72.145 4.41 -:5.<58 -5=7<.<2 72.145 5276.25 -:5.<58 E 0 J Y,-6.2<" ,-:5.<58" ‘ ,4.41" ,72.145"P +Y ,-5=7<.<2" ,-:5.<58" ‘ ,5276.25" ,72.145"P E 0 J , 8:<.:6==1 " + , 518:8.752:: " 0 ,J" 4.412<5<71: Teqe vce heafe gf 5444 [email protected] ? E 0 Hkchfcwqegk gf hkaqf ? 12.<5< [email protected]  A 0 J TEQE FN HÅNHVNK GFN HKCHFCWQEGK GF [email protected] ,A" ? 5 5 5 5 5 84 5 4.4< 5.5 5 4.2 4.42 5.1 5.5 :5 4.42 5 5 5 5 4.2 84 5 4.4< :< 5 4.2 4.42 4.2 5.5 :5 4.42 Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 57 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG A0J A 0J 12 -12 -4.21 -4.5 -4.5 -4.<5 -4.5 62.2 -:4.25 12.5 -12 -4.21 -:= -4.5 -4.<5 4.1 62.2 -:4.25 5=87.1 5<15.72< -6.< 18.82< 5=7<.<2 5<15.72< -5276.25 18.82< A 0 ,5444" ,65575.6" + ,86<6825.=45" 0 57.1:7 [email protected] gf Hkchfcwqegk gf tnk`k  H0 J TEQE FN HKCHFCWQEGK ,H"? 5 5 5 5 5 84 4.2 4.4< 5.5 5 :< 4.42 5.1 5.5 4.2 4.42 5 5 5 5 5 84 4.2 4.4< 4.2 5 :< 4.42 :5 5.5 4.2 4.42 H 0 ,5444" ,-:8541.=6467" + ,-862==66.515" 0 5=.682 [email protected] gf Hkchfcwqegk gf _bch r fn hvegqk gfn aenechf `fwenÿqmbhk uvfge gf ne xbmvbfcwf `ecfqe ? Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 56 Aehl# Bcm# @fwenÿqmbhk XEEZFGQE ENZEQEGK. QBHLEQG Hkqqfk? qbh#xeezDlkw`ebn#hk` qbh#xeezDlkw`ebn#hk` Tåmbce 5: