䊐䉳䉺ᛛⴚ⎇ⓥႎ๔㩷╙ 㪋㪍 ภ㩷 㩷 㪉㪇㪈㪇 ᐕ㩷㩷ᴉ᳓ᬀ‛䈱ౣ↢䈮䉋䉎ḓᴧ䈱᳓⾰ᡷༀ䈮㑐䈜䉎੍᷹ᚻᴺ㩷ખ ᴛ ᱞ ᔒ㩷 㩷ፉ ᄙ ⟵ ᒾᱞ ↰ ᢥ ᒾ 䋪䋱ⴼ 㩷 ᤘ ᄥ㩷㩷ਛ ㊁ ๺ ౖ㩷 䋪㪉㩷㩷᭎ⷐḓᴧ䈭䈬䈱㐽㎮᳓ၞ䈪䈲䇮ንᩕ㙃ൻ䈮䉋䉎ᬀ‛䊒䊤䊮䉪䊃䊮䈱⊒↢䈏᳓⾰ᳪỘ䈱໧㗴䉕↢䈛䈘䈞䉎䈖䈫䈏䈅䉎䇯ንᩕ㙃ൻ䈮䉋䉍ᳪỘ䈚䈢ḓᴧ䈱᳓⾰ᡷༀ䈻䈱ኻᔕᣇᴺ䈲⒳䇱⠨䈋䉌䉏䉎䈏䇮᳓↢ᬀ‛⟲⪭䉕ౣ↢䈜䉎䈭䈬䈱䉋䈉䈭⥄ὼ䈱↢ᘒ♽䈏ᜬ䈧ᵺൻᯏ⢻䉕↪䈇䉎ᚻᴺ䈏๟࿐䈻䈱ᖡᓇ㗀䉅ዋ䈭䈒቟ో䈮ታᣉ䈪䈐䇮䉁䈢⋭䉣䊈䊦䉩䊷䈱ⷰὐ䈎䉌䉅ఝ૏ᕈ䈏㜞䈇䉅䈱䈫⠨䈋䉌䉏䉎䇯䈖䉏䈮ኻ䈚䈩䇮╩⠪䉌䈲ᴉ᳓ᬀ‛䈱ౣ↢䈫䈠䈱ᵺൻᯏ⢻䉕ᵴ↪䈚䈢ḓᴧ䈱᳓⾰ᡷༀ䉕⹜䉂䈩䈐䈩䈇䉎䇯ᴉ᳓ᬀ‛䈮䉋䉎᳓⾰ᡷༀ䉕ലᨐ⊛䈎䈧วℂ⊛䈮ㆡ↪䈜䉎䈢䉄䈮䈲䇮䈠䈱᜼േ䉕੐೨䈮੍᷹䈜䉎ᚻᴺ䈏ᔅⷐ䈫䈭䉎䇯ᧄႎ๔䈪䈲䇮ᴉ᳓ᬀ‛䈏ḓᴧ䈱᳓⾰䈮෸䈿䈜ᓇ㗀䉕੍᷹䉁䈢䈲⹏ଔ䈪䈐䉎⸘▚ᚻᴺ䉕⠨᩺䈚䇮䈠䈱᳓⾰ᡷༀ䈱⹏ଔ䉕⹜䉂䈢䇯㩷

Method for predicting water quality improvement in enclosed waters
by using spontaneous regeneration functions of submerged plants
Abstract
Enclosed bodies of water, such as lake and ponds can have problems of water quality due to eutrophication.
There are many methods that can be used to counteract eutrophication in these bodies of water. Spontaneous
regeneration using submerged plants function is a very safe and low-energy method of remediating eutrophicatedwater. Although some authors have previously studied remediation using submerged plants empirically, nomethods for predicting their effects had been developed. This study proposes a method for calculating the effects
on water quality of sub merged plants and considers its applicability.

䉨䊷䊪䊷䊄䋺 ḓᴧ㩷 ᳓⾰㩷 ᴉ᳓ᬀ‛ᵺൻ㩷 ੍᷹㩷 ⸃ᨆ㪁䋱㩷 ᧲ർᄢቇᄢቇ㒮Ꮏቇ⎇ⓥ⑼㩷 ⎇ⓥຬ㩷㪁㪉㩷 ᧲ർᄢቇᄢቇ㒮Ꮏቇ⎇ⓥ⑼㩷 ಎᢎ᝼㩷䋭㪍㪌䋭䊐䉳䉺ᛛⴚ⎇ⓥႎ๔㩷 ╙ 㪋㪍 ภ䊂䊦䈫䈚䈩⸘▚䈮⚵䉂ㄟ䉁䉏䉎䇯䈖䉏䉌䈱ᡰ㈩ᣇ⒟ᑼ䉕એ§䋱䋮䈲䈛䉄䈮㩷
㩷ਅ䈮␜䈜䇯㩷ḓᴧౝ䈱ᵹ䉏䈱ಽᏓ䈲એਅ䈱⸘▚ᑼ䈎䉌ᓧ䉌䉏䉎䇯㩷ᓥ᧪䈎䉌䇮ⅣႺ໧㗴䈲䇮ᄢ᳇䉇᳓⾰䇮䉁䈢࿯ფ䊶࿾ਅ᳓䈮䈍䈔䉎ൻቇ⊛䈭ᳪᨴ䈮䈲ᄢ䈐䈭㑐ᔃ䈏ነ䈞䉌䋨㪥㪸㫍㫀㪼㫉㪄㪪㫋㫆㫂㪼㫊㩷 ᣇ⒟ᑼ䋩㩷䉏䇮ᴺᓞ䉇᧦଀䈏೙ቯ䈘䉏䉎䈖䈫䈪䇮ⴕ᡽⊛䈮ኻᔕ䈘㩷

wPw 2vi Q kl f i (1)wxi
wxk wxl

wviwv
 vk iwtwx k㩷䉏䈩䈇䉎䇯৻ᣇ䇮ᴡᎹ䇮⾂᳓ᳰ䉇ḓᴧ䈪䈲䇮ੱὑ⊛䈭ൻቇ⊛㩷ᳪᨴ䈣䈔䈪䈭䈒䇮ንᩕ㙃ൻ䈮䉋䉎᳓⾰ᖡൻ䈱໧㗴䈏↢㩷䈛䈩䈇䉎䇯․䈮䇮㐽㎮ᕈ᳓ၞ䈮䈍䈇䈩䈲䈠䈱௑ะ䈏ᒝ䈢䈣䈚䇮㩷䈇䈖䈫䈏ᜰ៰䈘䉏䈩䈇䉎䇯᳓ⅣႺ䈱ንᩕ㙃ൻ䈲䇮ᬀ‛㩷

wviwxi(2)0䋨ᵻ᳓ᣇ⒟ᑼ䋩㩷䊒䊤䊮䊃䊮䈱⇣Ᏹ⊒↢䈮䉋䉍ᳪỘ䈚⇣⥇䉕↢䈛䈢䉍䇮㘶㩷wviᢱ䈮ଏ䈜䉎႐ว䈮䈲䇮䈠䈱Ქᕈ䉅 ᔨ䈘䉏䈩䈇䉎䇯䉁䈢䇮㩷 wt㐽㎮ᕈ᳓ၞ䈏䈢䉄ᳰ䈱䉋䈉䈭႐ว䈮䈲䇮ንᩕ㙃ൻ䈮䉋

 vk

㩷

䉎᳓⾰ᖡൻ䈮䉋䉍ㄘᬺ↪᳓䈫䈚䈩೑↪䈪䈐䈭䈇䈫䈇䈉ⵍ

wvi
wxk

gw 2vi
w]
 fi
 vkl
wxk wxl
wxi(3)(4)w]
wv
H i 0wxi
wt㩷䈖䈖䈮䇮 vi 䋺ᵹㅦ䇮 P 䋺࿶ജ䇮 vkl 䋺ᵹ૕‛ᕈ䇮 ] 䋺᳓૏䇮H 䋺᳓ᷓ䇮 f i 䋺ᄖജ䉕⴫䈚䈩䈇䉎䇯䈢䈣䈚䇮㩷ኂ䉅⊒↢䈚䈩䈍䉍䇮䈠䈱ኻᔕ䈏᳞䉄䉌䉏䉎䇯᳓ㄝⅣႺ䈲䇮㘶ᢱ䉇↥ᬺ೑᳓䈣䈔䈪䈭䈒䇮↢‛䈱↢⢒䉇䊧䉪䊥䉣䊷䉲䊢䊮䈱႐䈫䈚䈩䈱ᓎഀ䉅䈅䉍䇮ᦨㄭ਎⇇⊛䈮ኻᔕ䈏᳞䉄䉌䉏䈩䈇䉎䇸↢‛ᄙ᭽ᕈ䇹䈮䉅㑐ㅪ䈚䈢໧㗴䈪䈅䉍䇮᳓ၞ䈱⥄ὼౣ↢䈲ᕆോ䈪䈅䉎஥㕙䉅ᜬ䈦䉁䈢䇮ḓᴧౝ䈱ኻ⽎‛⾰䈱ᤨ㑆ᄌൻ䈲એਅ䈱‛⾰⒖ⴕ

䈩䈇䉎䇯

᜛ᢔᣇ⒟ᑼ䈎䉌ၮᧄ⊛䈮ᓧ䉌䉏䉎䇯㩷㐽㎮ᕈ᳓ၞ䈮䈍䈔䉎ንᩕ㙃ൻ䈻䈱ኻᔕ╷䈮䈲䇮ᦑ

㩷 wC ( i )᳇䉇ᵾ᷸䊶ⷒ࿯䇮᳓↢ᬀ‛╬䈱↢ᘒ♽䉕ᵴ↪䈜䉎ᣇ

㩷

wt

 vk

wC ( i )wxk

Dkl( i )w 2C (i ) * (i )wxk wxl(5)ᴺ䈭䈬䈏⠨䈋䉌䉏䉎䇯ᒰ␠䈲䇮ᓥ᧪䈎䉌䈖䈱໧㗴䈮ኻ䈚㩷䈩䇮䊐䉢䉴䉺Ꮏᴺ䉕ឭ᩺䈚䇮᛽᳓䊶ᴉ᳓ᬀ‛䈱․ᕈ䉕วฝ⢋਄䈱䉦䉾䉮ౝ䈱 (i ) 䈲ḓᴧౝ䈱ኻ⽎᭴ᚑ‛⾰䈱⋧䉕ℂ⊛䈮ᵴ䈎䈚䈢ᚻᴺ䈪䈠䈱ኻᔕ䉕⹜䉂䈩䈇䈩䇮ታ⸽⹜⴫䈜䉅䈱䈫䈜䉎䇯䉁䈢䇮 * 䈲‛⾰ᓴⅣ䈮䉋䉎↢ᚑ㗄䈪䈅䉎㛎䈱ታ❣䉕㊀䈰䈩䈇䉎䇯㩷䈏䇮ታ㓙䈱⸃ᨆ䊝䊂䊦䈪䈲䋱㓏䈱ᤨ㑆ᓸಽ䈱ᒻ䈫䈭䉎䇯㩷ᧄᢥߢߪ‫ޔ‬᳓ၞߩንᩕ㙃ൻߦኻߔࠆᴉ᳓ᬀ‛ߩౣ↢㩷ߦࠃࠆᡷༀㆊ⒟ࠍ⹏ଔ࡮੍᷹ߒᓧࠆ⸃ᨆᚻᴺࠍ⏕┙ߔ㩷ࠆߎߣࠍ⋡⊛ߣߒߚ‫ߩߘޔߦࠄߐޕ‬ㆡ↪ᕈࠍ⸘▚଀ߢ§䋳䋮‛⾰ᓴⅣ䊝䊂䊦㩷㩷␜ߒ‫⃻ޔ‬࿾ߩታᣉ᧦ઙߦᔕߓߚല₸⊛ߥ⸘↹ࠍⴕ߁╬‫ޔ‬ḓᴧౝ䈱‛⾰ᓴⅣ䉕᭴ᚑ䈜䉎ኻ⽎‛⾰䈱Ớᐲᄌൻ䉕ታ੹ᓟߩዷ㐿ࠍวℂ⊛ߦታᣉߔࠆߚ߼ߩၮ␆ࠍឭଏߔࠆ‫ޕ‬㓙䈮⸘▚䈜䉎䈢䉄䈮䈲䇮ᑼ㩿㪌㪀䈱‛⾰ᓴⅣ䈮䉋䉎↢ᚑ㗄㩷* (i ) 䉕᭴ᚑ‛⾰䈗䈫䈮᳿䉄䉎ᔅⷐ䈏䈅䉎䇯ᧄᢥ䈮䈍䈇䈩䈲䇮㩷⚦੗╬ 㪈䋩䈏ℚℛḓ䈮ㆡ↪䈚䈢䊝䊂䊦䉕ၮ␆䈫䈚䈩⧯ᐓ䈱ᡷ§䋲䋮੍᷹䈮䈍䈔䉎ᡰ㈩ᣇ⒟ᑼ㩷㩷⦟䉕ᣉ䈚䈢䊝䊂䊦䈪⸃ᨆ䈜䉎䇯㩷

ᧄ੍᷹ᚻᴺ䈲䇮ḓᴧౝ䈱ᵹേ䉕᳞䉄䉎䈢䉄䈱ᵹ૕⸃ᨆ䈭䈍䇮ᧄᢥ䈪䈲䇮⸘▚䊝䊂䊦䈱ኻ⽎䈫䈭䉎‛⾰䉕એਅ䈱䉋䈉䈮⸳ቯ䈚䈩⠨䈋䉎䉅䈱䈫䈜䉎䇯䋨ᧄᢥਛ⸥ภ૬⸥䋩㩷䈫ኻ⽎‛⾰䈱Ớᐲ䉕᳞䉄䉎‛⾰⒖ⴕ᜛ᢔᣇ⒟ᑼ䈎䉌᭴ᚑ䋨䋱䋩 ᬀ‛䊒䊤䊮䉪䊃䊮㩷 (P ) 㩷䈘䉏䉎䇯㩷䋨䋲䋩 䊂䊃䊥䉺䉴㩷 ( PD ) 㩷ᵹേ⸘▚䈮䈲䇮ㅢᏱ䈱ᵹ૕⸃ᨆ䈪૶䉒䉏䈩䈇䉎䋨䋳䋩 ήᯏᘒ⓸⚛㩷 (CDIN) 㩷㪥㪸㫍㫀㪼㫉㪄㪪㫋㫆㫂㪼㫊 䈱ᣇ⒟ᑼ䉇 㪥㪄㪪 ᣇ⒟ᑼ䈮䈍䈇䈩ᷓ䈘ᣇะ䈱䋨䋴䋩 ၸⓍጀ⓸⚛ (N ) 㩷ᵹㅦ䉕৻᭽䈫઒ቯ䈚䈢ᵻ᳓ᣇ⒟ᑼ䈏↪䈇䉌䉏䉎䇯䉁䈢䇮䉪䊨䋨䋵䋩 ήᯏᘒ䊥䊮㩷 (C P ) 㩷䊨䊐䉞䊦䉇ᩕ㙃Ⴎ䈱Ớᐲ䈏ᤨ㑆⊛䈮ᄌൻ䈜䉎᭽ሶ䈲‛⾰䋨䋶䋩 ၸⓍጀ䊥䊮㩷 (F ) 㩷⒖ⴕ᜛ᢔᣇ⒟ᑼ䉕ၮᧄ䈫䈜䉎䇯䈭䈍䇮ḓᴧౝ䈪䈲䇮⸘▚ኻ⽎䈫䈜䉎‛⾰䈱Ớᐲ䈲䇮⒳䇱䈱᧦ઙ䈱䉅䈫䈮⋧ᄌൻ䈏⊒↢䈖䈖䈮䇮ᬀ‛䊒䊤䊮䉪䊃䊮䈮䈍䈇䈩䈲䇮න⋧䊝䊂䊦䈫⮣⮺䇮㩷䈜䉎䇯䈠䈱䈢䉄䇮䈖䈱䉋䈉䈭‛⾰⋧ᄌൻ䈱䉅䈫䈪䈱෼ᡰ䉕↢✛⮺䇮⃯⮺䈫ಽ㔌䈚䈢 㪊 ⋧䊝䊂䊦䈫䉕⠨䈋䈩䈇䉎䇯䈖䉏䉌䈱ᚑ㗄䈫䈚䈩⠨ᘦ䈜䉎ᔅⷐ䈏䈅䉎䇯䈖䈱᜼േ䈲䇮‛⾰ᓴⅣ䊝㑐ㅪ䈱᭽ሶ䉕࿑䋱䈮␜䈜䇯䉁䈢䇮਄⸥‛⾰䈱ౝ䇮ၸⓍጀ䈪㩷䋭㪍㪍䋭ᴉ᳓ᬀ‛䈮䉋䉎⥄ὼౣ↢ᯏ⢻䉕↪䈇䈢ḓᴧ䈱᳓⾰ᵺൻ䈮㑐䈜䉎੍᷹ᚻᴺ㩷㩷㩷䈠䈱䉅䈱䇮㪊 ⋧䊝䊂䊦䈪䈲ోᬀ‛䊒䊤䊮䉪䊃䊮䈱✚⸘䈫䈚䈩㩷ᛒ䈉䇯㩷㩿㪊㪀ήᯏᘒ⓸⚛㩷㩷㩷㩷 ήᯏᘒ⓸⚛䈱↢ᚑ㗄䈲એਅ䈮␜䈜ᑼ䈪ᛒ䈉䇯㩷㩷㩷㩷㩷㩷ᑼ㩿㪏㪀ᦨฝㄝ╙ 㪈 㗄䈲ᬀ‛䊒䊤䊮䉪䊃䊮䈮䉋䉎ๆ෼䇮╙ 㪉 㗄䈲㩷ၸⓍጀ⓸⚛䈱ήᯏൻ䇮╙ 㪊 㗄䈲䊂䊃䊥䉺䉴䈱ήᯏൻ䉕⴫䈚㩷䈩䈇䉎䇯䈭䈍䇮ᑼ㩿㪏㪀ᦨฝㄝ╙ 㪈 㗄䈱 G p P 䈲ᬀ‛䊒䊤䊮䉪䊃㩷䊮䈏න⋧䈱႐ว䈲୯䈠䈱䉅䈱䇮㪊 ⋧䈱႐ว䈲ฦ⋧䈪 G p 䉕㩷wCDINwt

E N GP P Q N N u f 'T Q ' E N PD u f 'T䈜䉎䉅䈱䈫䈚䈩ᛒ䈉䇯㩷䈱⓸⚛䈫䊥䊮䈮㑐䈚䈩䈲ᑼ㩿㪌㪀Ꮐㄝ╙ 㪉 㗄䈱⒖ᵹ㗄䈲⠨䈋䈭㩿㪋㪀ၸⓍጀ⓸⚛㩷䈒䈩䉋䈇䈖䈫䈫䈭䉎䇯㩷

ၸⓍጀ⓸⚛䈮㑐䈚䈩䈲એਅ䈱↢ᚑ㗄䉕↪䈇䉎䇯㩷ฦ⋧䈱⸘▚䈮↪䈇䉎↢ᚑ㗄䉕એਅ䈮␜䈜䇯㩷㩷 䋨䋱䋩ᬀ‛䊒䊤䊮䉪䊃䊮㩷*㩷(8)⸘▚䈚䇮ኻᔕ䈚䈢ᬀ‛䊒䊤䊮䉪䊃䊮Ớᐲ䈮ਸ਼▚䈚䈢਄䈪✚⸘࿑㧝 ‛⾰ᓴⅣ᭎ᔨ࿑㩷*㩷

㩷 wN Q N u f ' J (1  k W ) u E P  E J ' (1 k W )P  k WNTSDNNSD
DRN*wt(9)ᬀ‛䊒䊤䊮䉪䊃䊮䈮ኻ䈜䉎↢ᚑ㗄 * 䉕ᰴᑼ䈮␜䈜䇯㩷ᑼ㩿㪐㪀ᦨฝㄝ╙ 㪈 㗄䈲ၸⓍጀ䈱ήᯏൻ䇮╙ 㪉 㗄䈲ᬀ‛䊒䊤㩷䊮䉪䊃䊮䈱ᴉ㒠䇮╙㪊 㗄䈲䊂䊃䊥䉺䉴䈱ᴉ㒠䇮╙㪋 㗄䈲ᴉ᳓ᬀwPwt(G p  D p ) P  J (1  k SDW ) P (6)‛䈱ᩮ䈮䉋䉎ၸⓍጀ⓸⚛䈱ๆ෼䉕⴫䈚䈩䈇䉎䇯䈭䈍䇮䊂䊃䊥䉺䉴䉇ήᯏᘒ⓸⚛䈫ห᭽䈮䇮ᑼ㩿㪐㪀䈱ᦨฝㄝ╙ 㪉 㗄䈮䈍䈔䉎䈖䈖䈮䇮㩷CDIN
LAVG
CDIP
㩷Gp Pmax u f s uuuu fT  kASKN  CDIN KP CDIP KI  LAVG
㩷K PP
R CP  C g uu Z (1  k Z W )㩷 Dp
K PP  P㩷
W㩷k AS1 . 10 u㩷W  4 . 91>

exp  7 . 75 u 10  3 u PD㩷L AVG D³ L0 exp(kt )dt0㩷k㩷

TP  T 'uWᬀ‛䊒䊤䊮䉪䊃䊮䈮㑐䈜䉎㗄䈲䇮න⋧䈱႐ว䈲䈠䈱䉅䈱䉕䇮㪊 ⋧䊝䊂䊦䈱႐ว䈲ฦᬀ‛䊒䊤䊮䉪䊃䊮䈱✚⸘䉕↪䈇䉎䇯㩷㩿㪌㪀ήᯏᘒ䊥䊮㩷ήᯏᘒ䊥䊮䈱↢ᚑ㗄䈲ၮᧄ⊛䈮ήᯏ⓸⚛䈫ห䈛ᒻ䈱ቯ@ᑼൻ䈪ᛒ䈉䇯㩷
㩷

L0[exp(kD)  1]
k㩷

*wCDIPwt

E N GP P Q N F u f 'T2 Q ' E N PD u f 'T2 (10)ᬀ‛䊒䊤䊮䉪䊃䊮䈲ήᯏᘒ⓸⚛䈫ห᭽䈭ᛒ䈇ᣇ䈫䈭䉎䇯ฦ㗄䈱ౝኈ䈲ήᯏᘒ⓸⚛䈫ห䈛ᗧ๧䉕⴫䈚䈩䈇䉎䇯㩷㩿㪍㪀ၸⓍጀ䊥䊮㩷ᧄᢥ䈪䈲䇮න⋧䊝䊂䊦䈪䉅 㪊 ⋧䊝䊂䊦䈪䉅ᬀ‛䊒䊤䊮䉪䊃䊮ၸⓍጀ䊥䊮䈱↢ᚑ㗄䉅䉁䈢ၮᧄ⊛䈮ၸⓍጀ⓸⚛䈫ห᭽䈮ኻ䈜䉎↢ᚑ㗄䈱ᒻ䈲ห䈛ᑼ㩿㪍㪀䈪⠨䈋䉎䇯⮣⮺䇮✛⮺䈍䉋䈶⃯⮺䈱㆑䈇䈲䈠䈱ਛ䈱ଥᢙ䈏ᄌ䉒䉎䉅䈱䈫䈚䈩ᛒ䈉䉅䈱䈮એਅ䈱ᑼ䈪⸘▚䈜䉎䇯㩷䈫䈜䉎䇯㩷*㩷 wF㩷ᑼ㩿㪍㪀䈱ᦨฝㄝ䈲䇮 G p 䈏ᬀ‛䊒䊤䊮䉪䊃䊮䈱Ⴧᱺ䈮㑐䈜wt

Q N F u f 'T2 J (1  kSDW ) u EN P  ENJ ' (1  kSDW )PD  kRNW(11)䉎ଥᢙ䇮 D p 䈏ᱫṌ䈮㑐䈜䉎ଥᢙ䈪䈅䉍䇮╙ 㪉 㗄䈏⥄ὼᴉᬀ‛䊒䊤䊮䉪䊃䊮䈲ၸⓍጀ⓸⚛䈫ห᭽䈭ᛒ䈇ᣇ䈫䈭䉎䇯ฦ㩷㒠䈫ᬀ‛⟲⪭䈮䉋䉎ᴉ㒠䈱ଦㅴ䉕⴫䈚䈩䈇䉎䇯㩷㗄䈱ౝኈ䈲䇮ήᯏᘒ䊥䊮䈫ห᭽䇮ήᯏ⓸⚛䈫ห䈛ᗧ๧䉕⴫䈚䈩䈇䉎䇯ᑼ㩿㪍㪀䈎䉌ᑼ㩿㪈㪈㪀䈮䈍䈔䉎⸥ภ䉕䉁䈫䉄䈩⴫䋱䈭䈍䇮㪊 ⋧䊝䊂䊦䉕⠨䈋䉎႐ว䈮䈲䇮ᑼ㩿㪍㪀䈏ฦᬀ‛䊒䊤䊮䉪䊃䊮䈮ኻ䈚䈩↪䈇䉌䉏䉎䈖䈫䈮䈭䉍䇮ᬀ‛䊒䊤䊮䉪䊃䊮䈣䈔䈮␜䈜䇯㩷䈪䉅 㪊 ర䈱ㅪ┙ᓸಽᣇ⒟ᑼ䈮䈭䉎䈖䈫䈮ᵈᗧ䈜䉎䇯㩷㩷㩷 㩿㪉㪀䊂䊃䊥䉺䉴㩷㩷㩷 䊂䊃䊥䉺䉴䈮ኻ䈜䉎↢ᚑ㗄䈲એਅ䈮␜䈜ᑼ䈪ᛒ䈉䇯㩷§䋴䋮⸘▚ᣇᴺ㩷㩷㩷 㫝㪉㪅䈍䉋䈶㫝㪊㪅䈪ᧄᢥ䈮䈍䈔䉎ᡰ㈩ᣇ⒟ᑼ䉕␜䈚䈢䇯ታ㩷* wPDwt
㩷

Dp P  J ' (1 kSDW) Q ' PD u f 'T(7)ᑼ㩿㪎㪀ᦨฝㄝ╙ 㪈 㗄䈲ᬀ‛䊒䊤䊮䉪䊃䊮䈱ᱫṌ䇮╙ 㪉 㗄䈲䊂䊃㓙䈱⸘▚䈪䈲䇮ᬀ‛䊒䊤䊮䉪䊃䊮䈏න⋧䈱႐ว 㪍 ర䈱ㅪ┙㩷䊥䉺䉴䈱ᴉ㒠䇮╙ 㪊 㗄䈲䊂䊃䊥䉺䉴䈱ήᯏൻ䉕⴫䈚䈩䈇䉎䇯㩷

ᓸಽᣇ⒟ᑼ䈫䈭䉍䇮㪊 ⋧䈱႐ว䈮䈲 㪏 ర䈱ㅪ┙ᓸಽᣇ⒟ᑼ㩷䈭䈍䇮ᑼ䋨䋷䋩ਛ䈱ᬀ‛䊒䊤䊮䉪䊃䊮 P 䈲න⋧䊝䊂䊦䈪䈲䈫䈭䉎䇯㩷䋭㪍㪎䋭䊐䉳䉺ᛛⴚ⎇ⓥႎ๔㩷 ╙ 㪋㪍 ภ⴫㧝 ⸥ภ⺑᣿㩷ᤋ䈘䈞䈩ḓᴧౝ䈱ᵹㅦ䉕᳞䉄䈩䇮ᑼ㩿㪌㪀䈮ઍ౉䈜䉎䈖䈫䈪䇮㩷‛⾰Ớᐲᄌൻ䉕⸘▚䈜䉎䈖䈫䈫䈭䉎䇯㩷㩷䉁䈢䇮᳓⨲䈏ሽ࿷䈜䉎䈖䈫䈪䇮䈠䈱㗔ၞ䈮䈲৻⒳䈱ᵹㅦ㩷䈮㑐䈜䉎ᛶ᛫䈏⊒↢䈜䉎䈖䈫䈏⠨䈋䉌䉏䉎䇯ᵹㅦᛶ᛫䈮㑐㩷䈚䈩䈲䇮એਅ䈱 㪉 ⒳㘃䈱䈬䈤䉌䈎䈪⴫⃻䈪䈐䉎䇯㩷D vi(13)

Dvi vk vk(14)㩷㩷㩷䈅䉎䈇䈲䇮㩷㩷㩷㩷㩷㩷ᧄ⸘▚଀䈪䈲䇮ḓᴧౝ䈱‛⾰ᓴⅣ䉕䈖䈖䈪䈱ቯᑼൻ䈏㩷ㆡಾ䈮⴫⃻䈪䈐䉎䈎䋿䈠䈱㓙䈮ḓᴧౝ䈱ᵹേ䈏‛⾰ᓴⅣ㩷䈮䈬䈱⒟ᐲ䈬䈱䉋䈉䈮ᓇ㗀䈜䉎䈎䋿䉕ᬌ⸛䈜䉎䈖䈫䈫䈚䈩䇮㩷න⚐䈮৻ᣇะ䈎䉌䈱㘑䈱ᓇ㗀䈮䈧䈇䈩⠨䈋䇮䉁䈢ᵹㅦᛶ㩷᛫䈮㑐䈚䈩䈲න⚐䈮ᑼ㩿㪈㪊㪀䉕↪䈇䉎䈖䈫䈫䈜䉎䇯㩷㩷fi Rfi R䉋䈦䈩䇮ḓᴧౝ䈮ᵹേ䈏䈭䈇႐ว䇮ᵹേ䈏Ყセ⊛න⚐䈮㩷 䈖䈱䉋䈉䈮ᓧ䉌䉏䈢䋶ర䈅䉎䈇䈲䋸ర䈱ᓸಽᣇ⒟ᑼ䉕᳢↪

↢䈛䈩䈇䉎႐ว䇮ᵹേ䈏䈅䉎႐ว䈮䈲䇮ᬀ‛⟲⪭䈱㈩⟎䈱ᕈ䈱䈅䉎ᒻ䈪⸘▚䈜䉎䈢䉄䈮䈲䇮૗䉌䈎䈱ᚻᴺ䈮䉋䉍㔌ᢔᓇ㗀䈮䈧䈇䈩ᐞ䈧䈎䈱⸘▚଀䉕␜䈜䇯䈭䈍䇮⸘▚଀䈲ၯൻ䈚䈩ᢙ୯⸃ᨆ䈪⸘▚䈜䉎䈖䈫䈫䈭䉎䇯ᧄᢥ䈪䈲䇮ⓨ㑆䉕᦭₹⋵䈘䈇䈢䉁Ꮢ䈮䈅䉎೎ᚲᴧ䈪ታᣉ䈜䉎䇯㩷㒢ⷐ⚛ᴺ䈪䉁䈢ᤨ㑆㗔ၞ䉕೨ㅴᏅಽ䈪㔌ᢔൻ䈚䈩⸘▚䈜㩷䉎䇯㩷 䈭䈍䇮ᑼ㩿㪈㪀䈅䉎䈇䈲ᑼ㩿㪊㪀䈪䈱ᵹേ⸘▚䈍䉋䈶ᑼ㩿㪌㪀䈮㪌㪅㪈㩷 ᵹേ⸘▚㩷䉋䉎ฦ⋧䈱Ớᐲᄌൻ䈱⸘▚䈲䇮ᤨ㑆䈮㑐䈜䉎ታ⾰ዉ㑐ᢙ㩷 ⸘▚ኻ⽎䈫䈜䉎೎ᚲᴧ䈱᭎ⷐ䉕᦭㒢ⷐ⚛䊜䉾䉲䊠䈭䉌䈶䈱ᕈ⾰䈎䉌⸘▚䈮䈍䈔䉎቟ቯൻ䉕ᔅⷐ䈫䈜䉎႐ว䈏↢䈛䉎䇯䈮ᵹㅦಽᏓ䈫䈫䉅䈮࿑ 㪉 䈮␜䈜䇯㩷ᧄᢥ䈪䉅 㪧㪪㪧㪞㪆㪧㪬㪧㪞 ╬䈱቟ቯൻ䉕ᔅⷐ䈮ᔕ䈛䈩ᣉ䈜䈖䈫㩷 ⸘▚᧦ઙ䈫䈚䈩䈲䇮਄㕙䈎䉌䈱ᐔ㕙 㪉 ᰴర䊝䊂䊦䈫䈚䇮ᴧ䈫䈚䈩䈇䉎䇯㩷๟࿐䈪䈱ᵹㅦ䉕䉷䊨䈫䈚䈢Ⴚ⇇᧦ઙ䉕⸳ቯ䈚䈩䈇䉎䇯䈖䈖䈪㩷㩷§䋵䋮⸘▚଀㩷㩷䈋䉌䉏䈢ᵹㅦಽᏓ䉕એ㒠䈱Ớᐲ⸘▚䈮↪䈇䈩䈇䉎䇯㩷㩷㪌㪅㪉 ‛⾰ᓴⅣ⸃ᨆ㩷‛⾰䈱ᓴⅣ䈮઻䈉Ớᐲᄌൻ䈱⸘▚䈲䇮ḓᴧౝ䈱ᵹㅦಽ㩷ᧄᢥ䈪␜䈚䈢⸘▚ᚻᴺ䈲䉁䈫䉄䈩᳓⾰੍᷹䊝䊂䊦䈫⸒䉒㩷䉏䈩䈇䉎䇯ᧄ┨䈪䈲䇮䈖䈖䉁䈪⺑᣿䈚䈢᳓⾰੍᷹䊝䊂䊦䈱㩷ㆡ↪ᕈ䉕⸘▚଀䈪␜䈜䇯㩷㩷ᧄᢥ䈪䈲䇮ḓᴧౝ䈮ሽ࿷䈜䉎ኻ⽎‛⾰䈱Ớᐲᄌൻ䈮ਥ㩷⌒䉕䈍䈇䈩䈇䉎䈢䉄䇮‛⾰ᓴⅣ䈮㑐䈚䈩䈲⹦⚦䈮⸥ㅀ䈚䈢䇯㩷䈚䈎䈚䈭䈏䉌䇮ᵹേ⸘▚䈮䈍䈇䈩䈲㫝㪉㪅䈪ᑼ㩿㪈㪀䈅䉎䈇䈲ᑼ㩷㩿㪊㪀䉕↪䈇䉎䈖䈫䉕␜䈚䈢䈣䈔䈪䇮ᵹേ⃻⽎䈏↢䈛䉎ේേജ䉕㩷᣿⸥䈚䈩䈇䈭䈇䇯ᵹേ⃻⽎䉕↢䈛䈘䈞䉎ⷐ࿃䈲䇮ᵹ౉䊶ᵹ಴䇮㩷㘑ᔕജ䈮䉋䉎ᵹ䉏䈭䈬⒳䇱⠨䈋䉌䉏䉎䈏䇮䈖䈖䈪䈲㘑䈮䉋䉎㩷ḓᴧౝ䈱ᵹേ⃻⽎䉕⠨䈋䈩ኻ⽎‛⾰Ớᐲ䈱ᤨ㑆ᄌൻ䈻䈱㩷ᓇ㗀䉕⠨䈋䉎䉅䈱䈫䈜䉎䇯㩷㩷㘑ᔕജ䈲ᑼ㩿㪈㪀䈅䉎䈇䈲ᑼ㩿㪊㪀䈱ᄖജ㗄 f i 䈪⠨ᘦ䈘䉏䉎䈏䇮㪉㪀㩷㩷fi1UWi1UJ a2Wi WkWk᳓⨲⟲⪭㩷㩷䈖䈖䈪䈲䈠䈱ౕ૕⊛䈭ᒻ䈮ᰴᑼ䉕↪䈇䉎 䇯㩷㩷㘑ㅦ㧦3m/sec㩷㧔12㧕㩷㩷㩷

䈭䈍䇮䈖䈖䈮 Wi 䈲㘑ㅦ䊔䉪䊃䊦䉕␜䈚䈩䈇䉎䇯㩷ᧄ᧪䈲䇮ኻ⽎඙ၞ䈱㘑䊂䊷䉺䉕⸘᷹䈚䈢਄䈪ᑼ㩿㪈㪉㪀䈮෻䋭㪍㪏䋭㩷㧔࿖࿯࿾ℂ㒮᠟ᓇߩⓨਛ౮⌀ࠍ૶↪㧕࿑ 2 ⸃ᨆኻ⽎ߣᵹㅦಽᏓᴉ᳓ᬀ‛䈮䉋䉎⥄ὼౣ↢ᯏ⢻䉕↪䈇䈢ḓᴧ䈱᳓⾰ᵺൻ䈮㑐䈜䉎੍᷹ᚻᴺ㩷㩷㪈㪉㪇Ꮣ䈏䈭䈇⁁ᘒ䈫㘑䈮䉋䈦䈩⊒↢䈜䉎ᵹㅦಽᏓ䉕⠨ᘦ䈜䉎䉅䈱䈫䉕⸘▚䈜䉎䇯䈭䈍䇮Ყセ䈱䈢䉄䈮ḓᴧౝ䈮ᴉ᳓ᬀ‛䈏⹦⚦䈲ᢥ₂ 㪊㪀䉕ෳᾖ䈘䉏䈢䈇䇯䈖䉏䉌䈲䇮⃻࿾䈪೎ㅜ㓒㔌᳓⇇䉕૶䈦䈩ಣℂ඙䈫ኻ⽎඙䉕⸳⟎䈚䈢䈫䈐䈱ታ᷹୯䉕ᣢỚᐲ㩿㱘㪾㪆㪣㪀㩷䈭䈇⁁ᘒ䈱⸘▚䉅ታᣉ䈜䉎䇯ᧄ⸘▚䈮↪䈇䉎䊌䊤䊜䊷䉺䈱㪊㪀㪏㪇㩷㪍㪇㩷㪋㪇㩷ᓔ䈱⒳䇱䈱ႎ๔䉕ෳᾖ䈚䈭䈏䉌䈱หቯ䈎䉌᳿䉄䈩䈇䉎 䇯䉁㪉㪇㩷䈢䇮ᧄ⸘▚଀䈪䈲ᬀ‛䊒䊤䊮䉪䊃䊮䈱 㪊 ⋧䊝䊂䊦䈱⚿ᨐ䉕㩷㪇␜䈜䈖䈫䈫䈜䉎䇯㩷㩷㪈㪌㪇㪉㪇㪇ᣣᢙ㩿㪻㪸㫐㪀㪉㪌㪇㪊㪇㪇⮣⮺✛⮺⃯⮺㩷䈜䇯㩷Ớᐲ㩿㱘㪾㪆㪣㪀䈖䈱䈫䈐䈱䉪䊨䊨䊐䉞䊦䈱ᤨ♽೉⊛䈭Ớᐲᄌൻ䉕࿑ 㪊 䈮␜㪏㪇㩷㪍㪇㩷㪋㪇㩷㪉㪇㩷㩿㪉㪀ḓᴧౝ䈱ᵹㅦಽᏓ䈏䈭䈇႐ว㩷ḓᴧౝ䈱ᵹㅦಽᏓ䉕⠨ᘦ䈚䈭䈇႐ว䈱䉪䊨䊨䊐䉞䊦Ớᐲ㩷㪇䈱ᤨ㑆ᄌൻ䉕࿑ 㪋 ␜䈜䇯䈭䈍䇮ᐔ㕙⊛䈭ỚᐲಽᏓ䉕࿑ 㪌 䈮㩷␜䈜䇯࿑㪋 䈮䈍䈔䉎䉫䊤䊐⴫␜▎ᚲ䉕࿑㪌 䈮⸥タ䈜䉎䇯ᴉ᳓㩷㪇㪌㪇㪈㪇㪇㪈㪌㪇㪉㪇㪇ᣣᢙ㩿㪻㪸㫐㪀㪉㪌㪇㪊㪇㪇㧔ᵹㅦߥߒ㧦B ὐ㧕㩷㩷⮣⮺✛⮺⃯⮺㪈㪇㪇㩷㪏㪇Ớᐲ㩿㱘㪾㪆㪣㪀⮣⮺✛⮺⃯⮺㩷㪈㪇㪇㩷 㪍㪇㪏㪇㩷㪍㪇㩷㪋㪇㩷㩷 㪋㪇㩷㪉㪇㩷 㪉㪇㩷㪇㩷㪇㩷㪈㪇㪇㪈㪌㪇㪉㪇㪇ᣣᢙ㩿㪻㪸㫐㪀㪉㪌㪇㪊㪇㪇㪋㪇㪇㪈㪉㪇㪈㪉㪇㩷㪊㪌㪇࿑ 4(b) ᴉ᳓ᬀ‛ߦࠃࠆࠢࡠࡠࡈࠖ࡞ᄌൻ㩷ᬀ‛䈱ലᨐ䈲䈠䈱㓸⪭⟲䈮ዪᚲൻ䈚䈩䈇䉎䇯㩷㪌㪇㪋㪇㪇㧔ᵹㅦߥߒ㧦A ὐ㧕㩷⊒↢䈚䈭䈇䈱䈪䇮ᵹㅦ䈏䈅䈦䈩䉅䈭䈒䈩䉅ห䈛⚿ᨐ䉕ᓧ䉎䇯㪇㪊㪌㪇࿑ 4(a) ᴉ᳓ᬀ‛ߦࠃࠆࠢࡠࡠࡈࠖ࡞ᄌൻ㪈㪇㪇㩷 ḓᴧ䈮ᴉ᳓ᬀ‛䈏䈭䈇႐ว䈮䈲䇮ḓᴧౝ䈮Ớᐲ൨㈩䈏Ớᐲ㩿㱘㪾㪆㪣㪀㪈㪇㪇㪈㪉㪇㩿㪈㪀ḓᴧౝ䈮ᴉ᳓ᬀ‛䈏䈭䈇႐ว㩷㩷㪌㪇㩷ᣣ䉁䈪䈱䋱ᐕ㑆䈪ታᣉ䈚䈩䈇䉎䇯㩷㩷㪇㩷䈜䈼䈩䈱ᤨ♽೉⸘▚⚿ᨐ䈲 㪋 ᦬ 㪈 ᣣ䈎䉌⠉ᐕ䈱 㪊 ᦬ 㪊䋱㩷⮣⮺✛⮺⃯⮺㪈㪇㪇㪊㪌㪇㪋㪇㪇㩷㩷࿑ 3 ᴉ᳓ᬀ‛ߥߒߩࠢࡠࡠࡈࠖ࡞ᄌൻ㪇㪌㪇㪈㪇㪇㪈㪌㪇㪉㪇㪇ᣣᢙ㩿㪻㪸㫐㪀㪉㪌㪇㪊㪇㪇㪊㪌㪇࿑ 4(c) ᴉ᳓ᬀ‛ߦࠃࠆࠢࡠࡠࡈࠖ࡞ᄌൻ㧔ᵹㅦߥߒ㧦C ὐ㧕㩷㩷㩷㩿㪊㪀ḓᴧౝ䈱ᵹㅦಽᏓ䉕⠨ᘦ䈚䈢႐ว㩷೨⸘▚଀䈫ห᭽䈮䇮䉪䊨䊨䊐䉞䊦Ớᐲ䈱ᤨ㑆ᄌൻ䉕࿑㪍 䈮䇮㩷ḓᴧౝ䈱ᵹㅦಽᏓ䉕⠨ᘦ䈚䈢႐ว䈱ᐔ㕙⊛䈭ỚᐲಽᏓ䉕㩷⮣⮺䈮䈧䈇䈩࿑ 㪎 䈮␜䈜䇯䈭䈍䇮Ớᐲ䉕䉫䊤䊐ൻ䈚䈩䈇䉎㩷႐ᚲ䈲࿑ 㪎 䈮⸥䈚䈩䈅䉎䇯ᵹㅦಽᏓ䈏䈭䈇႐ว䈮Ყ䈼䈩ḓ㩷ᴧౝ䈱ỚᐲಽᏓ䈏ᐔṖൻ䈚䈩䈇䉎⚿ᨐ䈏ᓧ䉌䉏䈩䈇䉎䇯㩷㩷㩷㩷㩷㩷AB§䋶䋮䉁䈫䉄㩷㩷 ᧄᢥߢᴉ᳓ᬀ‛ߦࠃࠆ⥄ὼౣ↢ᯏ⢻ࠍ↪޿ߚḓᴧߩ㩷᳓⾰ᵺൻ੍᷹ᚻᴺࠍ⠨᩺ߒ‫⧯ޔ‬ᐓߩ଀㗴ࠍ␜ߒߚ‫ޕ‬ḓᴧ㩷ౝߩᵹേ߇ߥ޿႐วߢ߽‫ޔ‬ᴉ᳓ᬀ‛⟲⪭ౝߢ᳓⾰ᡷༀല㩷ᨐ߇޽ࠆߎߣ‫ޔ‬ḓᴧౝߩᵹേ߇޽ࠆ႐วߢߪ‫ޔ‬ᴉ᳓ᬀ‛㩷⟲⪭ౝ߅ࠃ߮ᵹࠇߩਅᵹᣇะߦߪ᳓⾰ᡷༀലᨐ߇⷗ࠄ

㩷 ࿑ 5 ᴉ᳓ᬀ‛ߩᐔ㕙⊛ߥലᨐ㧔ᵹㅦߥߒ㧕䋭㪍㪐䋭㩷㩷C㪋㪇㪇䊐䉳䉺ᛛⴚ⎇ⓥႎ๔㩷 ╙ 㪋㪍 ภࠇࠆߎߣ߇⏕⹺ߐࠇߚ‫੹ޕ‬ᓟ‫ޔ‬⒳‫ࠍ▚⸘ߩޘ‬ታᣉߒ‫ޔ‬ᴉ㪈㪉㪇㩷⮣⮺✛⮺⃯⮺㩷㪈㪇㪇Ớᐲ㩿㱘㪾㪆㪣㪀㪏㪇᳓ᬀ‛⟲⪭ߩല₸⊛ߥ㈩⟎ߥߤߩᬌ⸛ࠍⴕ߁‫ޕ‬㪍㪇ෳ ⠨ ᢥ ₂㩷㪋㪇㩷㪉㪇㪇㪈㪀㩷 㩷 ⚦↰ዏ䇮⚦⷗⍮ᒾ䋺ℚℛḓർḓ䈱᳓⾰㋦⋥ಽᏓ䈱ቄ㪇㪌㪇㪈㪇㪇㪈㪌㪇㪉㪇㪇ᣣᢙ㩿㪻㪸㫐㪀㪉㪌㪇㪊㪇㪇㪊㪌㪇▵ᄌൻ䈮㑐䈜䉎◲ᤃ䊝䊂䊦䈫᷷ᥦൻ䈱ᓇ㗀䈻䈱ㆡ↪䇮㪋㪇㪇ᴡᎹᛛⴚ⺰ᢥ㓸䇮╙ 㪏 Ꮞ䇮㪉㪇㪇㪉 ᐕ 㪍 ᦬㩷࿑㧢(a) ᴉ᳓ᬀ‛ߦࠃࠆࠢࡠࡠࡈࠖ࡞ᄌൻ㪉㪀㩷 㩷 ᧻᪸㗅ਃ㇢✬⪺䋺ⅣႺᵹ૕ᳪᨴ䇮᫪ർ಴㧔ᵹㅦ޽ࠅ㧦A ὐ㧕㪊㪀㩷 ⅣႺ⋭✚ว᡽╷ⅣႺዪ✚ോ⺖ⅣႺ⎇ⓥᛛⴚቶ䋺↢ᘒᎿ㪈㪉㪇ቇᛛᴺ䈫䈚䈩䈱ᴉ᳓ᬀ‛ౣ↢䈮䉋䉎ḓᴧ䈱᳓ⅣႺ࿁ᓳ㪈㪇㪇䈫ᵷ↢䊋䉟䉥䊙䉴䊥䉰䉟䉪䊦⛔ว䉲䉴䊁䊛䈱㐿⊒䈮㑐䈜䉎⮣⮺✛⮺⃯⮺㪏㪇⎇ⓥ䇮ⅣႺ⋭ⅣႺ⎇ⓥ䊶ᛛⴚ㐿⊒ផㅴ⾌⚳ੌ⎇ⓥᚑᨐႎ๔䇮ᐔᚑ 㪈㪐 ᐕᐲ䌾ᐔᚑ 㪉㪈 ᐕᐲ㩷㪍㪇㪋㪇㪉㪇㪇⻢㩷 ㄉ㩷㪇㪌㪇㪈㪇㪇㪈㪌㪇㪉㪇㪇ᣣᢙ㩿㪻㪸㫐㪀㪉㪌㪇㪊㪇㪇㪊㪌㪇㪋㪇㪇ᧄᢥߩౝኈߪ‫ޔ‬ⅣႺ⋭ߩⅣႺ⎇ⓥ࡮ᛛⴚ㐿⊒ផㅴ⾌࿑㧢(b) ᴉ᳓ᬀ‛ߦࠃࠆࠢࡠࡠࡈࠖ࡞ᄌൻߢታᣉߒߚ‫↢ޟ‬ᘒᎿቇᛛᴺߣߒߡߩᴉ᳓ᬀ‛ౣ↢ߦࠃ㧔ᵹㅦ޽ࠅ㧦B ὐ㧕ࠆḓᴧߩ᳓ⅣႺ࿁ᓳߣᵷ↢ࡃࠗࠝࡑࠬ࡝ࠨࠗࠢ࡞⛔

㪈㪉㪇㪈㪇㪇Ớᐲ㩿㱘㪾㪆㪣㪀Ớᐲ㩿㱘㪾㪆㪣㪀ᩣᑼળ␠㩷วࠪࠬ࠹ࡓߩ㐿⊒ߦ㑐ߔࠆ⎇ⓥ‫৻ߩޠ‬Ⅳߣߒߡታᣉߒ

⮣⮺✛⮺⃯⮺㪏㪇ߚ‫╩ޕ‬㗡⎇ⓥ⠪ߩ⑔ፉᄢቇℂᎿቇ⎇ⓥ⟲౒↢ࠪࠬ࠹ࡓℂᎿቇ㘃ⅣႺࠪࠬ࠹ࡓࡑࡀࠫࡔࡦ࠻ኾ᡹ߩⒷ᫪ᖘᐔ㪍㪇ᢎ᝼ߦ⸥ߒߡ⻢ᗧࠍ⴫ߒ߹ߔ‫ޕ‬㪋㪇㪉㪇㪇䈵 䈫 䈖 䈫 㩷㪇㪌㪇㪈㪇㪇㪈㪌㪇㪉㪇㪇ᣣᢙ㩿㪻㪸㫐㪀㪉㪌㪇㪊㪇㪇㪊㪌㪇㩷 ⥄ ὼ ౣ↢ ᯏ ⢻ 䉕↪ 䈇 䈢 ᳓ ⾰䈱 ᡷ㪋㪇㪇ༀ䊶࿁ᓳ䈮ኻ䈜䉎ឭ᩺䈲䇮䈖䉏䉁䈪ᒰ࿑㧢(c) ᴉ᳓ᬀ‛ߦࠃࠆࠢࡠࡠࡈࠖ࡞ᄌൻ␠䈮䈍䈇䈩ታᣉ䈚䈩䈐䈩䈇䉎䈏䇮䈠䈱㧔ᵹㅦ޽ࠅ㧦C ὐ㧕੍᷹⸃ᨆ䈮㑐䈚䈩䈲㐿ᆎ䈚ᆎ䉄䈢Ბ㓏䈪䈜䇯੹ᓟ䇮ᬀ↢ᶋፉ䈭䈬䈱⒳䇱
䈱ᯏ⢻䈮ᚻᴺ䉕ዷ㐿䈚䇮᳓ⅣႺ䈱ᡷખᴛ㩷 ᱞᔒ㩷㩷㩷࿑ 7 ᴉ᳓ᬀ‛ߩᐔ㕙⊛ߥലᨐ㧔ᵹㅦ޽ࠅ㧕䋭㪎㪇䋭ༀ䈮ነਈ䈪䈐䉏䈳䈫⠨䈋䈩䈇䉁䈜䇯㩷㩷㩷