ÿþ<html> <head> <title>F¯'GÌ FH (G ¯'G4E'1 'Ì1'FÌ</title> <style> <!-- body { background : #FFFECB; /*font: normal 90% tahoma, Verdana, Sans-Serif; */ font: normal 105% Times New Roman; margin: 10 80 10 80; line-height: 1.7; } p { text-indent: 5%; } .h1main { color: darkblue; font: normal "Times New Roman"; } .formula { text-align: center; font-style: italic; direction: ltr; } li { line-height: 1.7; } table, td { border-color: black; border-style: solid; } --> </style> </head> <body dir="rtl"> <hr> <img src="http://aramis.obspm.fr/~heydari/dictionary/flower-border.gif" width="100%" align="middle"> <hr> <br /> <h1 class="h1main"> F¯'GÌ FH (G ¯'G4E'1 'Ì1'FÌ <br/> </h1> <p align="left"> E-E/ -Ì/1Ì ED'Ì1Ì<br/> '.*1AÌ2Ì©/'F  F~'G4¯'G ~'1Ì3  A1'F3G<br/> </p> <p align="left"> <a href="http://aramis.obspm.fr/~heydari/divers/ir-cal-eng.html" target="_blank">English version</a><br/> <a href="http://aramis.obspm.fr/~heydari/divers/ir-cal-fr.html" target="_blank">Version française</a><br/> </p> <h2>ñ) ~Ì4¯A*'1</h2> <p> ¯'G4E'1 'Ì1'FÌ .H14Ì/Ì 3*  H 'ÌF H̘¯Ì 1' /'1/ ©G /1 "F 3'D (' /H ¯01 ~Ì'~Ì ~/Ì/'1 .H14Ì/ '2 GEH¯'F (= '9*/'D &lArr; ~'FH4* ñ) (G'1Ì *91ÌA EÌ 4H/. ¯'G4E'1 'Ì1'FÌ (1 F~'G4 (= 15/ &lArr; ò)G'Ì '.*14F'.*Ì /BÌB '3*H'1 '3*  H A2HF (1 'ÌF /'1'Ì 1'˜E'F (= 3Ì3*E &lArr; ó) 'F/1GDÌ (= ©(Ì3G &lArr; ô) GH4EF/'FG 'Ì '3* ©G "F 1' '2 GE*'Ì '1H~'ÌÌ '4  ¯'G4E'1 ¯1¯H1Ì  (' 'ÌF©G ,H'F*1 '3*  /BÌB*1 EÌ ©F/. 'ÌF ¯'G4E'1 ~Ì4ÌFG 'Ì (3 /1'2 /'1/ /1 A1GF¯ 'Ì1'FÌ  H (H̘G ˜1A*1ÌF 1Ì4G G'Ì4 (G "ÌÌFG'Ì 21*4*Ì EÌ ~ÌHF/F/. 'ÌF EB'DG (1 "F FÌ3* ©G (G *'1Ì. EA5D ¯'G4E'1Ì /1 'Ì1'F (~1/'2/  2Ì1' ~13E'FG'Ì /̯1Ì 1' A1' 1'G /'1/. (' 'ÌF -'D (G ©H*'GÌ ©GF*1ÌF (FÌ'/G'Ì 'ÌF ¯'G4E'1 1' ('2 EÌ FE'Ì/. .H'FF/¯'F 9D'BG EF/ EÌ *H'FF/ (G '+1G'Ì /̯1Ì †HF *BÌ 2'/G (ñùóø)  (Ì14© (ñó÷ó)  /'F4F'EG Ì 'Ì1'FÌ©'  H 9(/ 'DDGÌ (ñó÷õ) 1,H9 ©FF/. ¯'G4E'1 'Ì1'FÌ ©FHFÌ 2'ÌÌ/G Ì '5D'-Ì '3* ©G (G 1G(1Ì '.*14F'3  1Ì'6Ì/'F  H 4'91 F'EH1 9E1 .Ì'E (ñðôø-ññóñ EÌD'/Ì) /1 Ì©E A1H1/ÌF ôõø G,1Ì .H14Ì/Ì (òñ E'13 ñð÷ù EÌD'/Ì &lArr; õ) 5H1* ¯1A*G '3*. '2 "F,' ©G 'ÌF '5D'- (G A1E'F ,D'D 'D/ÌF ED©4'G (H/G  "F 1' ¯'G4E'1 ,D'DÌ EÌ .H'F/F/. /Ì3G Ì ©FHFÌ "F  ©G (' *:ÌÌ1G' ÌÌ /1 ¯'G4E'1 ":'2ÌF ,D'DÌ ~/Ì/ "E/G  /1 ññ A1H1/ÌF ñóðô (óñ E'13 ñùòõ) (G 7H1 13EÌ /1 E,D3 4H1'Ì EDÌ (G *5HÌ( 13Ì/G '3*. </p> <p> ,4F FH1H2  ©G EÌ1'+Ì '3* 21*4*Ì (' (3Ì'1Ì ('1G'Ì A1GF¯Ì  FE'/ 4'/Ì "/EÌ '3* '2 (Ì/'1Ì Ì' FH¯4* 7(Ì9* ~3 '2 ¯04* 2E3*'F 3*1HF. FH1H2 1' 1H2 G' Ì' GA*G G' ~Ì4 '2 GEH¯'F (G'1Ì "ÌÌFG' H *1'/'/G'Ì 4'/Ì (.4Ì ©G '2 ¯04*G G'Ì ©GF (1 EÌ .Ì2F/ GE1'GÌ EÌ ©FF/. '2 "F EÌ'F EÌ *H'F .'FG *©'FÌ  3(2G 1Ì2Ì  H ,4F †G'14F(G 3H1Ì ~Ì4 '2 FH1H2 H GE†FÌF ,4F 3Ì2/G (/1 1' Ì'/ ©1/. G2'1'F 3'D '3* ©G FH1H2 1' E1/E'F ¯HF'¯HFÌ ©G /1 "3Ì'Ì ('.*1Ì H E1©2Ì 2F/¯Ì EÌ ©FF/ ,4F ¯1A*G 'F/  (' H,H/ /¯13'FÌG' Ì BHEÌ  /ÌFÌ  Ì' 2('FÌ. ¯04*G '2 ~Ì'E ˜1A FH1H2  'ÌF ©G 'ÌF "ÌÌF (G /ÌF Ì' BHE H̘G 'Ì *9DB F/'1/ /DÌDG'ÌÌ '5DÌ G3*F/ ©G "F 1' EÌ1'+ A1GF¯Ì E4*1© ED*G'Ì ¯HF'¯HF (' 2EÌFG G'Ì A1GF¯Ì ¯HF'¯HF ©1/G 'F/. </p> <p> ¯'G4E'1 'Ì1'FÌ (' H,H/ ~'̯'G H'D'Ì4  (H̘G /B* H .1/¯1'ÌÌ '4  /1 ('.*1 2EÌF †F/'F 4F'.*G FÌ3*. /1 H'B9 *' ©FHF ©E*1 E7'D9G 'Ì (G *-DÌD (F ~'1G'Ì 1'˜E'F '.*14F'.*Ì "F /1 ~1*H /3*'H1/G'Ì ,/Ì/ ~1/'.*G '3*. (H̘G  EAGHE 3'D H 7HD H'B9Ì "F /1 ¯'G4E'1 'Ì1'FÌ FÌ'2EF/ 1H4F 4/F 'F/  2Ì1' GE '©FHF /1 '.*14F'3Ì /H EAGHE 3'D GH1¯1/Ì (&lArr; ö) H 3'D GEH¯'F (G'1Ì (3'F ¯3*1/G 'Ì (' GE '4*('G EÌ 4HF/. '2 "F,' ©G 3'D GEH¯'F (G'1Ì ~'ÌG Ì ¯'G4E'1 'Ì1'FÌ '3*  'ÌF '4*('G EÌ *H'F/ (G 1'˜E'F 'F/1GDÌ "F "3Ì( 13'F/ H '2 /B*4 (©'G/. </p> <h2>ò) *H5ÌA ©DÌ</h2> <p> ":'2 FH1H2 GF¯'EÌ '3* ©G .H14Ì/ /1 3A1 ~/Ì/'1 .H/ /1 "3E'F (1 GEH¯'F (G'1Ì EF7(B EÌ 4H/. 'ÌF 1HÌ/'/ EÌ *H'F/ /1 G1 D-8G 'Ì '2 /H1G Ì 4('F1H2Ì òô 3'9*G ~Ì4 "Ì/. ¯1†G GEH¯'FG'Ì (G'1Ì H ~'ÌÌ2Ì G1/H 9('1*F/ '2 FB7G G'Ì (1.H1/ GH1~G (= /'Ì1G 'D(1H, &lArr; ÷) H GEH¯'1 (= '3*H' &lArr; ø) "3E'FÌ  GEH¯'F (G'1Ì *FG' FB7G 'Ì '3* ©G 1'3* 'A1'2 (&lArr; ù) H /1˜F' (&lArr; ñð) 1' '2 "F 'F/'2G EÌ ¯Ì1F/. GE†FÌF GEH¯'F (G'1Ì D-8G 'Ì '3* ©G .H14Ì/ /1 ,F(4 ~/Ì/'14 (G 3HÌ 4E'D GEH¯'1 1' B79 EÌ ©F/. G1†F/  'E1H2G *1,Ì- /'/G EÌ 4H/ ©G GEH¯'F (G'1Ì 1' D-8G 'Ì (/'FF/ ©G /1˜F'Ì GH1~GÌ .H14Ì/ (G 5A1 /1,G EÌ 13/. GE '©FHF /1 'Ì1'F 1HÌ/'/ FH1H2 (' /B*Ì (G*1 '2 Ì© G2'1E +'FÌG 'F/'2G ¯Ì1Ì EÌ 4H/ (ED© ~H1 ñóøó). (' (G ©'1 (1/F F*Ì,G G'Ì «~˜HG4©/G Ì E©'FÌ© "3E'FÌ H E-'3(G Ì 1H2Ì,G' (IMCCE)» (&lArr; ~'FH4* ññ) /1 ~'1Ì3 (1'Ì /H1G Ì EÌD'/Ì ñõøó-òõðð  ~Ì EÌ (1ÌE ©G (1'Ì FÌE1H2'F *G1'F õøô GEH¯'F  Ì' /1 -/H/ öôj GEG Ì 1HÌ/'/G'  /1 *'1Ì. òð E'13 1HÌ EÌ /GF/. (3'E/ 1HÌ/'/G' (1'Ì *'1Ì.G'Ì E,'H1 /1 ,/HD ñ FEH/G 4/G '3*. G1 3'D GEH¯'F (G'1Ì ©EÌ /Ì1*1 1HÌ EÌ /G/  (' /1F¯Ì ©E*1 '2 ö 3'9* F3(* (G 1HÌ/'/ ~Ì4ÌF. 'ÌF /1F¯ (1'(1 '3* (' ©31Ì '2 1H2 ©G (1 óöõ 1H2 ©'ED EÌ 'A2'Ì/ *' 3'D 1' ~/Ì/ "H1/. (' 'ÌF -'D  *'1Ì. 1HÌ/'/F GEH¯'F (G'1Ì '2 'ÌF ,'(,'ÌÌ GEÌ4¯Ì (3HÌ ,DH ~Ì1HÌ FEÌ ©F/ †HF /1 ¯'G4E'1 'Ì1'FÌ ~Ì41HÌG'Ì 'F('4*G G1 †G'1 Ì' ~F, 3'D Ì©('1 (' 'A2H/F Ì© 1H2 'F/1GDÌ ,0( EÌ 4HF/ (&lArr; (.4 õ). </p> <p> GE†FÌF  (' (G ©'1 (1/F /'/G G'Ì IMCCE 'F/'2G Ì ~Ì41HÌ 1' (1'Ì /H1G Ì 3'DG'Ì ñððð *' òõðð EÌD'/Ì -3'( EÌ ©FÌE:<br/> </p> <div class="formula"> dt = t(n+1) - t(n) </div> <br/> -1A <em>t</em> D-8G Ì GEH¯'F (G'1Ì ('4/ (1'Ì 3'D <em>n</em>. F*Ì,G Ì (1 "H1/ ,'(,'ÌÌ EÌ'F¯ÌF 9('1* '3* '2 õ.øñööò 3'9* ± ð.ððòôð +'FÌG ('F-1'A '3*'F/G)  Ì' õ 3'9* ôø /BÌBG õù.øó +'FÌG ± ø +'FÌG. /1F¯G'Ì ©EÌFG H (Ì4ÌFG (G *1*Ì( '2 "F 3'DG'Ì ñðùõ EÌD'/Ì (3'D ô÷ô 'Ì1'FÌ) H ñòñö EÌD'/Ì (3'D õùõ 'Ì1'FÌ) G3*F/. FEH/'1 *:ÌÌ1G'Ì /1F¯ /1 .D'D 3'DG' /1 4©D ñ F4'F /'/G 4/G '3*. '2 "F,' ©G /1'2'Ì 3'D GEH¯'F (G'1Ì Ì©3'F FÌ3* (&lArr; (.4 ó)  'F/'2G Ì ,'(,'ÌÌ EÌ'F¯ÌF (G /H1G Ì EH1/ F81 (3*¯Ì /'1/. ,/HD ò F4'F /GF/G Ì EÌ2'F ,'(,'ÌÌ (1'Ì †F/ /H1G Ì ¯HF'¯HF H FÌ2 7HD 3'D EÌ'F¯ÌF E1(H7 (G "FG' (1 -3( 2E'F .H14Ì/Ì 1'3*ÌF '3*. </p> <p align="center"> ,/HD ñ. *'1Ì.G'Ì 1HÌ/'/ GEH¯'F (G'1Ì /1 *G1'F <br/> (1'Ì /H1G Ì ñõøó *' òõðð EÌD'/Ì <br> <table border="2" cellpadding="2" cellspacing="5" align="center"> <tr> <td bgcolor="#ccccff">E'G E'13 </td> <td bgcolor="#ffcccc">(3'E/ 1HÌ/'/G'</td> <td bgcolor="#ccffcc">/1 3/ (j)</td> </tr> <tr> <td bgcolor="#ccccff">ñø</td> <td bgcolor="#ffcccc">ð</td> <td bgcolor="#ccffcc">ð</td> </tr> <tr> <td bgcolor="#ccccff">ñù</td> <td bgcolor="#ffcccc">óó</td> <td bgcolor="#ccffcc">ó.ö</td> </tr> <tr> <td bgcolor="#ccccff">òð</td> <td bgcolor="#ffcccc">õøô</td> <td bgcolor="#ccffcc">öó.ö</td> </tr> <tr> <td bgcolor="#ccccff">òñ</td> <td bgcolor="#ffcccc">óðñ</td> <td bgcolor="#ccffcc">óò.ø</td> </tr> <tr> <td bgcolor="#ccccff">òò</td> <td bgcolor="#ffcccc">ð</td> <td bgcolor="#ccffcc">ð</td> </tr> </table> </p> <p align="center"> <a href="http://aramis.obspm.fr/~heydari/divers/shift_hires.png" target="_blank"><img src="http://aramis.obspm.fr/~heydari/divers/shift_lowres.png" /></a> <br/> 4©D ñ- FEH/'1 *:ÌÌ1 /1F¯ GEH¯'F (G'1Ì F3(* (G 1HÌ/'/ ~Ì4ÌF <br/> (1'Ì /H1G Ì ñððð *' òõðð EÌD'/Ì. /1F¯ EÌ'F¯ÌF: õ 3'9* ôø /BÌBG õù.ø +'FÌG. (1'Ì /Ì/F F¯'1G 'Ì (' H'¯4H/ (G*1 ©DÌ© ©FÌ/. </p> <p> "4©'1 '3* ©G F.3*ÌF 1H2 3'D ¯'G4E'1 FEÌ *H'F/ '2 D-8G Ì /BÌB GEH¯'F (G'1Ì (Ì':'2/ H ('Ì/ '2 FÌE4(  ":'2 1H2 (F' (1 Ì© *1'/'/ ©GF 'Ì1'FÌ (&lArr; ñò)  41H9 4H/ (HB* 1'3*ÌF *G1'F). (F'(1 'ÌF  '¯1 GEH¯'F (G'1Ì ~Ì4 '2 FÌE1H2 1HÌ /G/ GE'F 1H2 ":'2 3'D ¯1A*G EÌ 4H/. '¯1 GEH¯'F (G'1Ì (G ~3 '2 FÌE1H2 'A*/ 1H2 (9/ 3'D ¯'G4E'1 1' .H'G/ ":'2Ì/. (G 3.FÌ /̯1  3'D ¯'G4E'1 '2 F2/Ì©*1ÌF FÌE4( (G GEH¯'F (G'1Ì 41H9 EÌ 4H/. /1 ¯04*G ":'2 3'D (' F~'G4 A1'2'Ì (&lArr; ñó) FÌE1H2ÌF .H14Ì/ *9ÌÌF EÌ 4/  (/ÌF E9F' ©G FH1H2 1H2Ì (H/ ©G A1'2'Ì .H14Ì/ '2 A1'2'Ì GEH¯'1 "3E'FÌ /1 EÌ ¯04*. ¯1†G 3'D ¯'G4E'1 EÌ *H'F/ *' ©E*1 '2 ñò 3'9* 2H/*1 Ì' /Ì1*1 '2 1HÌ/'/ GEH¯'F (G'1Ì ":'2 4H/  D-8G Ì /BÌB GEH¯'F (G'1Ì  Ì' *-HÌD 3'D  'GEÌ* A1GF¯Ì (3Ì'1 /'1/. G1 HB* ('4/ "F D-8G  4( Ì' 1H2  GEG Ì 96HG'Ì .'FH'/G  ~'©Ì2G H 1.* FH (1 *F  'ÌF 1HÌ/'/ '.*14F'.*Ì 1' (G ¯1/ 3A1G Ì GA* 3ÌF †4E (1 1'G EÌ E'FF/. 'E1H2G D-8G Ì FH1H2 1' 'Ì3*¯'GG'Ì 1'/ÌH H *DHÌ2ÌHF '9D'E EÌ ©FF/  -'D "F©G /1 ¯04*G 4DÌ© *H~  /GD  H 3'2G'Ì ('/Ì (1'Ì A1'¯HÌÌ 'ÌF 1HÌ/'/ (G ©'1 EÌ 1A*F/. (' 13Ì/F D-8G Ì FH1H2  GE¯Ì (G 4'/Ì (1 EÌ .Ì2F/ H FH1H2 1' (G GE .,3*G ('/ EÌ ¯HÌF/. </p> <p align="center"> ,/HD ò- /1F¯ EÌ'F¯ÌF (ÌF /H GEH¯'F (G'1Ì ~Ì'~Ì <br/> <table border="2" cellpadding="2" cellspacing="5" align="center"> <tr> <td bgcolor="#ccccff">/H1G Ì 2E'FÌ </td> <td bgcolor="#ffcccc"> /1F¯<br> (3'9*)<br> (3  /  +) </td> <td bgcolor="#ccffcc"> EÌ'F¯ÌF 3'D<br> (1H2 .H14Ì/Ì) </td> </tr> <tr> <td bgcolor="#ccccff">ôððð- *' òõðð+</td> <td bgcolor="#ffcccc">õ.øñôõø<br> õ 3. ôø /. õò.õ +</td> <td bgcolor="#ccffcc">óöõ.òôòò÷ô</td> </tr> <tr> <td bgcolor="#ccccff">ð *' òõðð+</td> <td bgcolor="#ffcccc">õ.øñöðó <br/> õ 3. ôø /. õ÷.÷ +</td> <td bgcolor="#ccffcc">óöõ.òôòóóõ</td> </tr> <tr> </tr> <td bgcolor="#ccccff">ñððð+ *' òõðð+</td> <td bgcolor="#ffcccc">õ.øñööò <br/> õ 3. ôø /. õù.ø +</td> <td bgcolor="#ccffcc">óöõ.òôòóõù</td> </tr> <tr> <td bgcolor="#ccccff">ñõðð+ *' òõðð+</td> <td bgcolor="#ffcccc">õ.øñööù <br> õ 3. ôù /. ð.ñ +</td> <td bgcolor="#ccffcc">óöõ.òôòóöò</td> </tr> <tr> <td bgcolor="#ccccff">ñøðð+ *' òòðð+</td> <td bgcolor="#ffcccc">õ.øñõó÷<br> õ 3. ôø /. õõ.ó +</td> <td bgcolor="#ccffcc">óöõ.òôòóð÷</td> </tr> <tr> <td bgcolor="#ccccff">øðð+ *' ñòðð+</td> <td bgcolor="#ffcccc">õ.øñöðù<br/> õ 3. ôø /. õ÷.ù +</td> <td bgcolor="#ccffcc">óöõ.òôòóó÷</td> </tr> <tr> <td bgcolor="#ccccff">ñùùõ+ *' òððõ+</td> <td bgcolor="#ffcccc">õ.øóðø÷<br> õ 3. ôù /. õñ.ñ +</td> <td bgcolor="#ccffcc">óöõ.òôòùõó</td> </tr> </table> </p> <p> FB7G Ì ":'2ÌF ¯'G4E'1 ©FHFÌ 'Ì1'FÌ GEH¯'F (G'1Ì "/ÌFG òò E'13 3'D öòò EÌD'/Ì '3* (&lArr; ñô). /1 òò 3~*'E(1 "F 3'D  (1'(1 (' GA*E E'G 91(Ì 1(Ì9 'D'HD  ~Ì'E(1 '3D'E '2 E©G (G E/ÌFG G,1* ©1/. 'E' .DÌAG Ì /HE 9E1 '(F .7'(  GF¯'E (1~'ÌÌ ¯'G4E'1 '3D'EÌ /1 -H'DÌ 3'D öóø EÌD'/Ì  *1,Ì- /'/ E(/# ¯'G4E'1 1' ":'2 E'G E-1E  ©G F2/ '91'( EB/3 4E1/G EÌ 4/  (¯Ì1/. /1 F*Ì,G  E(/# ¯'G4E'1 '3D'EÌ (G ñö ˜HÌÌG Ì ¯'G4E'1 ÌHDÌ'FÌ  (1'(1 (' ñù ˜HÌÌG Ì ¯'G4E'1 ¯1¯H1Ì 3'D öòò EÌD'/Ì 'A*'/  Ì9FÌ /H E'G H G4* 1H2 2H/*1 '2 G,1*. '2 3HÌ /̯1  †HF /1 ¯'G4E'1 BE1Ì E'GG' (G A5DG'Ì 7(Ì9Ì ~ÌHF/ F/'1F/ H (F' (1 'ÌF *'1Ì.G' F3(* (G †1.G Ì .H14Ì/Ì -1©* EÌ ©FF/  ¯'G4E'1 BE1Ì (1'Ì '/'1G Ì 'EH1 E/FÌ H ©4H1/'1Ì †F/'F ©'1 "E/ FÌ3* ((1'Ì FEHFG  (1'Ì 2E'F (F/Ì ©4'H12Ì  ¯1/ "H1Ì E'DÌ'* .1EF  H /̯1 (1F'EG 1Ì2ÌG'). /1 F*Ì,G  /4H'1ÌG'Ì ~/Ì/ "E/G (1 '+1 ¯'G4E'1 BE1Ì †F/ 3/G (9/  /1 2E'F ,D'D 'D/ÌF ED©4'G 3D,HBÌ  ©G (1 312EÌF ~GF'H1Ì A1E'F EÌ 1'F/  '5D'- ¯'G4E'1 1' ('Ì3*G 3'.*F/. A2HF (1 'ÌF  ,4F FH1H2 (G EÌ'FG Ì (1, E'GÌ (-H*) D:2Ì/G (H/  †HF 'F/1GD4G' (&lArr; ô) 1' (G ,' FÌ'H1/G (H/F/. /1 H'B9  (F' (1 *'1Ì.FHÌ3'F H '.*14F'3'F F2/Ì© (G /H1'F '5D'-  '5DÌ *1ÌF 'F¯Ì2G Ì ('2/Ì3Ì ¯'G4E'1 'ÌF (H/ ©G FH1H2 (G GEH¯'F (G'1Ì ~ÌHF/ /'/G 4H/ (/'F4F'EG Ì 'Ì1'FÌ©'). </p> <p align="center"> ,/HD ó. E'GG' H A5DG'Ì ¯'G4E'1 'Ì1'FÌ <table border="2" cellpadding="2" cellspacing="5" align="center"> <tr> <td bgcolor="silver">*1*Ì(</td> <td bgcolor="khaki">'H3*'ÌÌ<br/> (A.D. c. -2000 to -300)</td> <td bgcolor="#ffcccc">A'13Ì EÌ'FG <br/> (A.D. c. -300 to +700)</td> <td bgcolor="#ccffcc">A'13Ì FHÌF</td> <td>1H2G'</td> <td bgcolor="snow">A5DG'</td> </tr> <tr> <td bgcolor="silver">ñ</td> <td bgcolor="khaki">Fravashi/Fravarti <br /> ¯HG1 'Ì2/Ì</td> <td bgcolor="#ffcccc">Fraward&icirc;n</td> <td bgcolor="#ccffcc">A1H1/ÌF</td> <td>óñ </td> <td bgcolor="snow">(G'1</td> </tr> <tr> <td bgcolor="silver">ò</td> <td bgcolor="khaki">Asha Vahishta <br />(G*1ÌF 1'3*©'1Ì </td> <td bgcolor="#ffcccc">Ardawahisht</td> <td bgcolor="#ccffcc">'1/Ì(G4*</td> <td>óñ</td> <td bgcolor="snow">(G'1</td> </tr> <tr> <td bgcolor="silver">ó</td> <td bgcolor="khaki">Haurvat&acirc;t <br/> /13*Ì  13'ÌÌ</td> <td bgcolor="#ffcccc">Khord&acirc;d</td> <td bgcolor="#ccffcc">.1/'/</td> <td>óñ</td> <td bgcolor="snow">(G'1</td> </tr> <tr> <td bgcolor="silver">ô</td> <td bgcolor="khaki">Tishtrya <br/> *Ì4*1  3*'1G Ì ('1'F </td> <td bgcolor="#ffcccc">T&icirc;r</td> <td bgcolor="#ccffcc">*Ì1</td> <td>óñ</td> <td bgcolor="snow">*'(3*'F</td> </tr> <tr> <td bgcolor="silver">õ</td> <td bgcolor="khaki">Am&eacute;r&eacute;t&acirc;t<br> ,'H/'F¯Ì</td> <td bgcolor="#ffcccc">Amurd&acirc;d</td> <td bgcolor="#ccffcc">'E1/'/  E1/'/</td> <td>óñ</td> <td bgcolor="snow">*'(3*'F</td> </tr> <tr> <td bgcolor="silver">ö</td> <td bgcolor="khaki">Khshathra Vairya<br>¯2ÌF4 FÌ©</td> <td bgcolor="#ffcccc">Shahrewar</td> <td bgcolor="#ccffcc">4G1ÌH1</td> <td>óñ</td> <td bgcolor="snow">*'(3*'F</td> </tr> <tr> <td bgcolor="silver">÷</td> <td bgcolor="khaki">Mithra<br> EÌ*1'  EG1  .H14Ì/</td> <td bgcolor="#ffcccc">Mihr</td> <td bgcolor="#ccffcc">EG1</td> <td>óð</td> <td bgcolor="snow">~'ÌÌ2</td> </tr> <tr> <td bgcolor="silver">ø</td> <td bgcolor="khaki">Ap<br>"(</td> <td bgcolor="#ffcccc">&Acirc;b&acirc;n</td> <td bgcolor="#ccffcc">"('F</td> <td>óð</td> <td bgcolor="snow">~'ÌÌ2</td> </tr> <tr> <td bgcolor="silver">ù</td> <td bgcolor="khaki">&Acirc;thra<br>"*4</td> <td bgcolor="#ffcccc">&Acirc;dur</td> <td bgcolor="#ccffcc">"01</td> <td>óð</td> <td bgcolor="snow">~'ÌÌ2</td> </tr> <tr> <td bgcolor="silver">ñð</td> <td bgcolor="khaki">Dathush&ocirc;<br>"A1Ì/¯'1</td> <td bgcolor="#ffcccc">Day</td> <td bgcolor="#ccffcc">/Ì</td> <td>óð</td> <td bgcolor="snow">2E3*'F</td> </tr> <tr> <td bgcolor="silver">ññ</td> <td bgcolor="khaki">Vohu Manah<br>EF4 FÌ©</td> <td bgcolor="#ffcccc">Wahman</td> <td bgcolor="#ccffcc">(GEF</td> <td>óð</td> <td bgcolor="snow">2E3*'F</td> </tr> <tr> <td bgcolor="silver">ñò</td> <td bgcolor="khaki">Sp&eacute;nt&acirc; &Acirc;rmaiti<br>"1'E4 H1,'HF/</td> <td bgcolor="#ffcccc">Spandarmad</td> <td bgcolor="#ccffcc">'3AF/</td> <td>òù Ì' óð</td> <td bgcolor="snow">2E3*'F</td> </tr> </table> </p> <p> (G /DÌDG'ÌÌ ©G /1 ('D' Ì'/ 4/F/  .H',G F8'E 'DED©  H2Ì1 ('*/(Ì1 H 3Ì'3*E/'1  ED©4'G 1' E*B'9/ ©1/ ©G (G '5D'- ¯'G4E'1 A1E'F /G/. .H',G F8'E 'DED© ¯1HGÌ '.*14F'3 (1¯2Ì/ H 1G(1Ì 'Ì4'F 1' (G 9E1 .Ì'E ¯E'4*. HÌ F~'G4¯'GÌ (&lArr; ò) /1 ~'Ì*.*  '5AG'F  (1~' ©1/ ((1.Ì EF(9G' 1Ì Ì' FÌ4'~H1 1' F'E (1/G 'F/). ~3 '2 F~'G4G' H E-'3(G G'  ¯1HG '.*14F'3'F GEH¯'F (G'1Ì 3'D öòò EÌD'/Ì 1' (1¯2Ì/. /1 F*Ì,G  ":'2 ¯'G4E'1 'Ì1'FÌ (G 44 E'G ~Ì4 '2 G,1* FG'/G 4/. GE†FÌF  ¯1HG .Ì'E 1'˜E'FÌ (1'Ì 'F/1GD4G' '(/'9 ©1/ ©G /1 ,G'F (Ì GE*'3*. 'ÌF 1'˜E'F (1 †1.G Ì óó 3'DG 'Ì '3*H'1 '3* ©G /1 ~'ÌÌF (&lArr; (.4 õ) (G 41-4 .H'GÌE ~1/'.*. '2 'ÌFG' ¯04*G  3'D (G ñò E'G óð 1H2G (.4 4/  H õ Ì' ö 1H2 ('2E'F/G  ©G «~F,G Ì /2/Ì/G» Ì' 'F/1¯'G .H'F/G EÌ 4/F/  (G ~'Ì'F E'G '3~F/'1E/ ('3AF/)  ~Ì4 '2 FH1H2  'A2H/G 4/F/  /13* GE'F¯HFG ©G /1 'Ì1'F ~Ì4 '2 '3D'E 13E (H/. H ,'D( 'ÌF©G ¯1HG .Ì'E F'EG'Ì 'H3*'ÌÌ E'GG'Ì 'Ì1'FÌ 1' 2F/G ©1/ (,/HD ó)  G1†F/ ©G 'E©'FG'Ì /̯1Ì FÌ2 (113Ì 4/F/ H '2 ,EDG F'EG'Ì 4'91'FG Ì *'2G 'Ì (1'Ì E'GG' ~Ì4FG'/ 4/F/. </p> <p> ~3 EÌ (ÌFÌE ©G G/A '5D'- *FG' '2 EÌ'F (1/'4*F /4H'1ÌG'Ì '/'1Ì H 'B*5'/Ì F(H/  (D©G ~'3/'1Ì '2 FH1H2  Ì©Ì '2 '5DÌ*1ÌF FE'/G'Ì GHÌ* 'Ì1'FÌ  FÌ2 /1 /3*H1 ©'1 B1'1 /'4*. ©H*'G "F©G '5D'- ¯'G4E'1 ~Ì'E/Ì 3*1¯ /'4*  ©G 4'Ì/ /1 *'1Ì. 'Ì1'F (Ì GE'FF/ (H/G ('4/. 'ÌF ('2/Ì3Ì FH1H2 1' (G GEH¯'F (G'1Ì †3~'F/  H 'ÌF †Ì2Ì (H/ ©G /1 ¯'G4E'1 3'3'FÌ H,H/ F/'4*  2Ì1' †FÌF EÌ FE'Ì/ ©G 'ÌF ¯'G4E'1 /'1'Ì 'F/1GD4 ô 3'DG F(H/  H /1 9H6 G1 ñòð 3'D Ì© ('1 Ì© E'G (G ¯'G4E'1 EÌ 'A2H/ (de Blois 1996). </p> <p> (1 9©3 ¯'G4E'1 '3D'EÌ  ©G ~'ÌG '4 (1 E'G BE1Ì GD'DÌ òù.õóðö 1H2G H 3'D BE1Ì óõô 1H2G FG'/G 4/G  /H'2/G E'G 3'D 'Ì1'FÌ 3.* (G A5DG'Ì 3'D ~ÌHF/ .H1/G 'F/. 44 E'G F.3*ÌF ¯'G4E'1 FHÌF  ©G /1 ññ A1H1/ÌF ñóðô (G *5HÌ( E,D3 4H1'Ì EDÌ 13Ì/  G1 Ì© óñ 1H2 /'1F/  H ~F, E'G /̯1 G1Ì© óð 1H2 H H'~3ÌF E'G òù Ì' óð 1H2. 'ÌF¯HFG *B3ÌE 3'D (G E'GG'ÌÌ (' 7HDG'Ì ¯HF'¯HF *H'AB ©'ED /'1/ (' 'ÌF H'B9Ì* ©G A5DG'Ì '.*14F'.*Ì /1'2'Ì Ì©3'FÌ F/'1F/ (G'1 H *'(3*'F '2 ~'ÌÌ2 H 2E3*'F /1'2*1F/ (&lArr; ñõ). F'E E'GG'  (G /Ì3G Ì 'H3*'ÌÌ (FÌ'/ÌF "FG'  E9F'G'Ì "FG'  H A1¯4* 2('FÌ©4'F /1 ¯01 2E'F /1 ,/HD ó FE'Ì'F/G 4/G 'F/. </p> <h2>ó) /1'2'Ì 3'D</h2> <p> 3'D 'Ì1'FÌ 3'DÌ '3* «GH1¯1/Ì» ©G /1 "F FB7G Ì ('2(1/ (= E1,9) GEH¯'F (G'1Ì '3*. (' 'ÌF-'D F('Ì/ "F 1' (' 3'D GH1¯1/Ì ©G '.*14F'3'F FHÌF H69 ©1/G 'F/ '4*('G ©1/. GE '©FHF  3'D GH1¯1/Ì (/ÌF 3'F *91ÌA EÌ 4H/ ©G 9('1* '3* '2 E/* 2E'FÌ ©G /1 "F /1˜F'Ì EÌ'F¯ÌF .H14Ì/  F3(* (G GEH¯'F EÌ'F¯ÌF 2ÌEG (&lArr; ñö)  óöð /1,G 'A2'Ì4 EÌ Ì'(/. 'ÌF *91ÌA (G *5HÌ( GE'Ì4 9EHEÌ '*-'/ÌG Ì ,G'FÌ '.*14F'3Ì /1 /H(DÌF /1 3~*'E(1 ñùùõ 13Ì/G '3* (Seidelmann et al. 1992). 4E'1Ì ~˜HG4¯1  (H̘G Meeus & Savoie 1992 H Cassidy 1996 H Meeus 2002 (G ,/'3'FÌ EÌ'F 3'D GEH¯'F (G'1Ì H 'ÌF 3'D GH1¯1/Ì FHÌF *#©Ì/ ©1/G 'F/. (' 'ÌF -'D  ¯1A*F Ì©Ì (G ,'Ì /̯1Ì '4*('GÌ '3* (3Ì'1 1'Ì,. /1 H'B9  (Ì4*1 '.*14F'3'F H /3* 'F/1 ©'1'F ¯'G4E'1Ì 3'D GH1¯1/Ì 1' 'ÌF 7H1 *91ÌA EÌ ©FF/ ©G '2 GEH¯'F (G'1Ì ":'2 EÌ 4H/  HDÌ 7HD 3'D GH1¯1/Ì FHÌF 1' (G "F F3(* EÌ /GF/ (&lArr; ñ÷). H E*#3A'FG (1.Ì '2 '.*14F'3'F H ¯'G4E'1¯1'F 'Ì1'FÌ '2 'ÌF "4A*¯Ì /1 'E'F FÌ3*F/. ('Ì/ *#©Ì/ ©1/ ©G 'ÌF EAGHE FHÌF 3'D GH1¯1/Ì  ©G (1'Ì E7'D9G G'Ì E©'FÌ© "3E'FÌ H69 4/G '3*  ~'ÌG '4 (1 /1˜F'Ì EÌ'F¯ÌF .H14Ì/ '3* H /1 H'B9 (G Ğ FB7G Ì H̘G 'Ì '2 E/'1 ,F(4 ~/Ì/'1 3'D'FG Ì .H14Ì/ (3*¯Ì F/'1/. G/A '2 'ÌF EAGHE E7'D9G Ì 1A*'1 /1'2 /H1G Ì 3'D (' (G -3'( "H1/F ~Ì4'Ì'F (&lArr; ñø) H †4E~H4Ì '2 "4A*¯ÌG' Ì ¯1'F4Ì ©H*'G /H1G '3*. G1†G ('4/ 3H/EF/Ì 'ÌF EAGHE (1'Ì ~˜HG4G'Ì E©'FÌ© "3E'FÌ  ¯'G4E'1G'Ì .H14Ì/Ì *1'/'/Ì  'Ì1'FÌ Ì' ¯1¯H1Ì (&lArr; ñù)  (1 ~'ÌG Ì 7HD EÌ'F¯ÌF 3'D GEH¯'F (G'1Ì 1'3*ÌF FG'/G 4/G 'F/. ('Ì/ ¯A* ©G F'E¯0'1Ì ©FHFÌ '4*('G (1 'F¯Ì2 '3*  2Ì1' Ì© '57D'- (3'D GH1¯1/Ì) (1'Ì /H EAGHE E*A'H* HDÌ (3Ì'1 F2/Ì© (G ©'1 (1/G EÌ 4H/. (F' (1 'ÌF  (1 '*-'/ÌG Ì ,G'FÌ '.*14F'3Ì '3* ©G (G 1A9 'ÌF '(G'E (~1/'2/  (' ¯2ÌF4 /H '57D'- E4.5 (1'Ì 'ÌF /H EAGHE. EF7BÌ EÌ FE'Ì/ ©G '57D'- 3'D GH1¯1/Ì (1'Ì E©'FÌ© "3E'FÌ (G ©'1 1H/ H 3'D GEH¯'F (G'1Ì (1'Ì A'5DG Ì 2E'FÌ EÌ'F /H ¯01 ~Ì'~Ì .H14Ì/ '2 GEH¯'F (G'1Ì. H .1/EF/'FG EÌ FE'Ì/ ©G 'Ì1'FÌ'F "F 3'D 1' <b>3'D FH1H2</b> (F'EF/. </p> <p> /1 'ÌF,' F¯'G F2/Ì©*1Ì (G /¯13'FÌ 3'DG'Ì GH1¯1/Ì H GEH¯'F (G'1Ì EÌ 'F/'2ÌE. Bretagnon & Rocher 2001 GEH¯4 (E9'/DG  &lArr; òð) 2Ì1 1' (1'Ì /1'2'Ì 3'D GH1¯1/Ì (G /3* EÌ /GF/: </p> <div class="formula"> 365.24219052 - 61.56 10<sup>-6</sup> T - 68.4 10<sup>-9</sup> T<sup>2</sup> + 263.0 10<sup>-9</sup> T<sup>3</sup> + 3.2 10<sup>-9</sup> T<sup>4</sup> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1) </div> <br/> 3'/G ¯A*G ('4ÌE  <em>T</em> 9('1* '3* '2 *9/'/ 1H2G'Ì Ì©3'F øöôðð +'FÌG 'Ì (2E'F ,G'FÌ '*EÌ) (1 -3( G2'1G G'Ì ÌHDÌ'FÌ (óöõòõð 1H2G) F3(* (G 2ÌEG Ì ©FHFÌ. 'ÌF 9('1* 1Ì'6Ì E9*(1 '3* (1'Ì ('2G Ì ñðððð± 3'D F3(* (G *'1Ì. ÌHDÌ'FÌ J2000.0. 3'D GH1¯1/Ì (1 -3( 2E'F ,G'FÌ  ©G (G †1.4 2EÌF (G ¯1/ "3G '4 (3*¯Ì /'1/  *H37 E$DA'F F'E(1/G (' GEH¯4 2Ì1 (Ì'F EÌ 4H/: </p> <div class="formula"> 365.2421789 - 135.63 10<sup>-6</sup> T - 68.4 10<sup>-9</sup> T<sup>2</sup> + 263.0 10<sup>-9</sup> T<sup>3</sup> + 3.2 10<sup>-9</sup> T<sup>4</sup> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2) </div> <br/> /1 'ÌF,' <em>T</em> (1 -3( 2E'F ,G'FÌ '3*. (F' (1 'ÌF  EÌ (ÌFÌE ©G (1'Ì 2ÌEG Ì J2000 7HD 3'D GH1¯1/Ì óöõ.òôòñùðõò 1H2 Ì©3'F øöôðð +'FÌG 'Ì (H/  ©G (1'(1 EÌ 4H/ (' óöõ.òôòñ÷øù 1H2 .H14Ì/Ì H'B9Ì  H EÌ *H'F "F 1' (G 1BE *B1Ì(Ì óöõ.òôòò 1H2 ¯1/ ©1/. GEH¯4G'Ì (ñ) H (ò) GE†FÌF F4'F EÌ /GF/ ©G /1'2'Ì 3'D GH1¯1/Ì +'(* FÌ3*. </p> <p> '2 3HÌ /̯1  A'5DG Ì 2E'FÌ EÌ'F¯ÌF (ÌF /H ¯01 ~Ì'~Ì .H14Ì/ '2 GEH¯'F (G'1Ì  †F'F©G Meeus 2002 (G /3* "H1/G  (1'Ì /1˜F'Ì 1'3*ÌF .H14Ì/  (1 ~'ÌG Ì (F ~'1G'Ì E/'1Ì 2EÌF Simon et al. 1994 H -D /BÌB GEH¯4 ©~D1 †FÌF '3*: <div class="formula"> 365.2423748 + 10.34 10<sup>-5</sup> T - 12.43 10<sup>-6</sup> T<sup>2</sup> - 22.63 10<sup>-7</sup> T<sup>3</sup> + 1.31 10<sup>-7</sup> T<sup>4</sup> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3) </div> <br/> <em>T</em> (1 -3( G2'1G G'Ì ÌHDÌ'FÌ (óöõòõð 1H2 Ì©3'F) '2 2ÌEG Ì J2000.0 -3'( EÌ 4H/. /H1G Ì '9*('1 'ÌF GEH¯4 '2 õðð ~Ì4 '2 EÌD'/ *' ôõðð EÌD'/Ì '3*. GE†FÌF *#©Ì/ EÌ 4H/ ©G 'ÌF GEH¯4 A1¯4* ©DÌ 3'D 1'3*ÌF GEH¯'F (G'1Ì 1' EÌ FE'Ì/ /1 /1'2 E/*. ,F(4 F'Ì©FH'.* ©~D1Ì 2EÌF 1' (G -3'( EÌ "H1/  HDÌ '2 'A*'.Ì2G'Ì 7HD 3'D  ©G 2'ÌÌ/G Ì "4A*¯ÌG'Ì ¯1'F4Ì /H1G 'Ì G3*F/  †4E EÌ ~H4/. -D ©'ED E3#DG /1 1H2Ì, IMCCE (' GEH¯4Ì (G /3* EÌ "Ì/ ©G '2 ùö ,EDG 3'.*G 4/G '3*. GEH¯4 (ó) 1' EÌ *H'F (1 -3( 1H2G'Ì .H14Ì/Ì (G /Ì3G Ì 2Ì1 FH4*: </p> <div class="formula"> 365.2423632 + 2.93 10<sup>-5</sup> T - 12.43 10<sup>-6</sup> T<sup>2</sup> - 22.63 10 <sup>-7</sup> T<sup>3</sup> + 1.31 10<sup>-7</sup> T<sup>4</sup> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(4) </div> <p> EB'Ì3G Ì EÌ'F GEH¯4G'Ì (ñ) H (ó) Ì' (ò) H (ô) (G 1H4FÌ F4'F EÌ /G/ ©G 3'DG'Ì EÌ'F¯ÌF GEH¯4 (G'1Ì H GH1¯1/Ì Ì©Ì FÌ3*F/. (1'Ì FEHFG  /1 2ÌEG Ì J2000.0  3'D GH1¯1/Ì EÌ'F¯ÌF óöõ.òôòñ÷øù 1H2 '3*  -'D "F©G 3'D EÌ'F¯ÌF GEH¯'F (G'1Ì óöõ.òôòóöò 1H2  Ì9FÌ ñõ.øò +'FÌG /1'2*1. "F3'F ©G 3'D GH1¯1/Ì (G óöõ.òôòò 1H2 *B1Ì( 4/  3'D GEH¯'F (G'1Ì 1' GE EÌ *H'F -/H/ óöõ.òôòô 1H2 /'F3*. GE†FÌF '2 GEH¯4 (ó) "4©'1 '3* ©G 3'D GEH¯'F (G'1Ì GE (' 2E'F *:ÌÌ1 EÌ ©F/ (4©D ò). /1 -H'DÌ 2ÌEG Ì óððð- 7HD "F óöõ.òôñø÷ò 1H2 Ì©3'F (H/  -'D "F©G /1 /1 ":'2 951 E3Ì-Ì* (G óöõ.òôòñóø 1H2 Ì©3'F 'A2'Ì4 Ì'A*. GFH2 GE /1 -'D 'A2'Ì4 '3*  H /1 2ÌEG Ì õððð+ (G 7HD (Ì4ÌFG Ì .H/  óöõ.òôòõòõ 1H2 Ì©3'F  .H'G/ 13Ì/. (F' (1 'ÌF  /¯13'FÌ EÌ'F 3'DG'Ì GEH¯'F (G'1Ì H GH1¯1/Ì (G /1'2'Ì "FG' E-/H/ FEÌ 4H/  2Ì1' A1¯4*G'Ì /1'2 /H1G Ì "FG' FÌ2 F'GE'FF/F/. (1 9©3 3'D GEH¯'F (G'1Ì  3'D GH1¯1/Ì *' /3* ©E 2ÌEG Ì øððð+ GEH'1G (G ©'G4 '/'EG .H'G/ /'/. </p> <p> 4©D ò GE†FÌF F4'F EÌ /G/ *:ÌÌ1 3'D 1'3*ÌF GEH¯'F (G'1Ì 1' (1 -3( 1H2 .H14Ì/Ì  "F†F'F©G E-'3(G G'Ì IMCCE (G /3* "H1/G 'F/. (1'Ì 1H4FÌ  F*Ì,G Ì "F E-'3(G G' (G /H 5H1* FEH/G 4/G 'F/  †HF /1'2'Ì 3'D 1'3*ÌF 'A*'.Ì2G'Ì EGEÌ EÌ ©F/ /1 /H1G G'Ì F3(*# ©H*'G. FB7G G'ÌÌ ©G /1 E1©2 .7G'Ì 9EH/Ì B1'1 /'1F/  FE'ÌF/G Ì 7HD 3'D EÌ'F¯ÌF /1 /H1G G'Ì õðð 3'DG G3*F/. .H/ .7G'Ì 9EH/Ì 'F-1'AG'Ì '3*'F/G 1' (1'Ì "F /H1G G' F4'F EÌ /GF/. .E (= EF-FÌ) /F/'FG /'1 FÌ2 /'/G G'Ì IMCCE 1' EÌ FE'Ì/  (' 'ÌF *A'H* ©G (' (G ©'1 (1/F ~'D'ÌG 'Ì GEG Ì FH3'FG'ÌÌ ©G /H1G 'Ì ©E*1 '2 ñðð 3'D /4*G 'F/ 5'A 4/G 'F/. 'ÌF /1 6EF -'©Ì '2 "F '3* ©G EGE*1ÌF 'A*'.Ì2G'Ì 7HD 3'D GEH¯'F (G'1Ì 2'ÌÌ/G Ì "4A*¯ÌG'Ì ©H*'G /H1G 'F/. '¯1 ~'D'ÌG Ì ~12H1*1Ì (G ©'1 (1ÌE  4©D ©DÌ .E 3'D GEH¯'F (G'1Ì 1'3*ÌF (G 4©D 3'D GEH¯'F (G'1Ì EÌ'F¯ÌF F2/Ì© EÌ 4H/. (G ©H*'GÌ  E' 7HD 3'D GEH¯'F (G'1Ì EÌ'F¯ÌF 1' óöõ.òôòóöò 1H2 .H14Ì/Ì EÌ ¯Ì1ÌE ©G (1'Ì /H1G 'Ì ñððð 3'DG E*E1©2 (1 2E'F ©FHFÌ  ñõðð+ *' òõðð+ E-'3(G 4/G '3*. </p> <p> /'F3*FÌ '3* ©G /1 2E'F .Ì'E 7HD EÌ'F¯ÌF 3'D GEH¯'F (G'1Ì óöõ.òôòóó÷ 1H2 .H14Ì/Ì (H/. 'ÌF 1BE EÌ'F¯ÌFÌ '3* (1'Ì /H1G 'Ì ôðð 3'DG  '2 øðð *' ñòðð EÌD'/Ì. '2 3HÌ /̯1  7HD 3'D /1 ¯'G4E'1 'Ì1'FÌ  Ì9FÌ "F†G '2 1'˜E'F 'F/1GDÌ "F (1 EÌ "Ì/  9('1* '3* '2 ..óöõ.òôòô 1H2: </p> <div class="formula"> 365 + 8/33 = 365.2424.. </div> <br/> (&lArr; (.4 õ). 'ÌF 1BE (' 7HD 3'D /1 2E'F .Ì'E (óöõ.òôòóó÷ 1H2 .H14Ì/Ì) 3'2¯'1Ì /'1/  H -*' (' 7HD 3'D /1 951 ©FHFÌ (óöõ.òôòô 1H2) 3'2¯'1*1 '3*. /1 EB'Ì3G (' /1'2'Ì 3'D /1 ¯'G4E'1 ¯1¯H1Ì  (1 -3( 1H2 .H14Ì/Ì: </p> <div class="formula"> 365 + 1/4 - 1/100 + 1/400 = 365 + 97/400 = 365.2425 </div> <br/> EÌ *H'F ¯A* ©G /3*'H1/ .Ì'E (1 4F'.* /BÌB*1Ì '2 ,F(4 3'D'FG Ì .H14Ì/ '3*H'1 '3*. <br/> <p> †F/Ì ~Ì4 ~˜HG4¯1'FÌ 7HD 3'D (Ì4 '2 -/ /BÌBÌ 1' (G .Ì'E F3(* /'/G 'F/: óöõ.òôòñùøõøñõö 1H2 (O'Connor & Robertson 1999). *' "F,' ©G E' EÌ /'FÌE  Ğ EF(9 *'1Ì.Ì †FÌF 1BEÌ 1' *#ÌÌ/ FEÌ ©F/. (G *5H1 E'  'ÌF 9// 3'.*¯Ì '3*  H '2 /H1G Ì ~Ì4FG'/Ì òøòð 3'DG F'4Ì EÌ 4H/ (&lArr; (.4 ÷). </p> <p align="center"> <a href="http://aramis.obspm.fr/~heydari/divers/year_length_hires.png"><img src="http://aramis.obspm.fr/~heydari/divers/year_length.png"></a> </p> <div style="margin: 5 100 5 100; line-height: 1.7;"> 4©D ò - /1'2'Ì 3'DG'Ì GH1¯1/Ì H GEH¯'F (G'1Ì (' ¯01 G2'1G G' (G *1*Ì( (' .EG'Ì (= EF-FÌ) ~1 H FB7G †ÌF F4'F /'/G 4/G '3*  G1 /H (1 -3( 1H2G'Ì Ì©3'F. 3'D GEH¯'F (G'1Ì 1'3*ÌF  (1 -3( 1H2 .H14Ì/Ì  Ì' (G 3.FÌ /̯1 3'D FH1H2  ©G '2 E-'3(G G'Ì IMCCE (G /3* EÌ "Ì/  FÌ2 (G /H 4ÌHG F4'F /'/G 4/G '3*: FB7G G'ÌÌ ©G /1 E1©2 .7G'Ì 9EH/Ì B1'1 /'1F/  FE'ÌF/G Ì 7HD 3'D EÌ'F¯ÌF /1 /H1G G'Ì õðð 3'DG G3*F/. .H/ .7G'Ì 9EH/Ì 'F-1'AG'Ì '3*'F/G 1' (1'Ì "F /H1G G' F4'F EÌ /GF/. .E /F/'FG /'1 FÌ2 '2 /'/G G'Ì IMCCE (1EÌ "Ì/  (' 'ÌF *A'H* ©G (' (G ©'1 (1/F ~'D'ÌG 'Ì GEG Ì FH3'FG'ÌÌ ©G /H1G 'Ì ©E*1 '2 ñðð 3'D /4*G 'F/ 5'A 4/G 'F/. .7G'Ì 'ABÌ (G *1*Ì( F4'F¯1 7HD 3'D (F' (1 .Ì'E H ¯'G4E'1 ¯1¯H1Ì G3*F/. "FG' 1' ('Ì/ (' 7HD 3'D GEH¯'F (G'1Ì  (1 -3( 1H2 .H14Ì/Ì  ©G E-'3(G G'Ì IMCCE (G /3* EÌ /GF/  EB'Ì3G ©1/. (1'Ì /Ì/F F¯'1G 'Ì (' H'¯4H/ (G*1 ©DÌ© ©FÌ/. </div> <h2>ô) /¯13'FÌ 3'DG'Ì «GH1¯1/Ì» H FH1H2</h2> <p> '2 "F,' ©G E/'1 ¯1/4 2EÌF (G ¯1/ .H14Ì/ (Ì6Ì '3*  319* E/'1Ì 2EÌF Ì©FH'.* FÌ3*. /1 FB7G Ì ~Ì1'GH1 (&lArr; òñ) 2EÌF ©H*'G*1ÌF /H1Ì 1' '2 .H14Ì/ /'1/  H (F' (1 'ÌF *F/*1 '2 'F/'2G Ì EÌ'F¯ÌF -1©* EÌ ©F/. -'D "F©G /1 '~'GH1 (&lArr; òò)  ©G /1 /H1*1ÌF A'5DG '4 '2 .H14Ì/ '3*  "G3*G *1 EÌ 1H/. GE†FÌF  (G 3(( ~/Ì/G Ì ~Ì4'Ì'F  GEH¯'F (G'1Ì 3'DÌ õð.ó +'FÌG Ì ©E'FÌ F3(* (G 3*'1¯'F /1 3HÌ H'1HFG Ì ,F(4 .H14Ì/ ,' (G ,' EÌ 4H/  /1 GE'F -'D ©G "3G Ì (21¯ E/'1 2EÌF (G 'F/'2G Ì ññ.ö +'FÌG /1 3'D /1 3HÌ E3*ÌBÌE *:ÌÌ1 ,' EÌ /G/. /1 F*Ì,G  HB*Ì ©G .H14Ì/  ~3 '2 3A1 Ì©3'DG Ì ~/Ì/'1 .H/ /1 7HD GH1~G  '2 FB7G Ì GEH¯'F (G'1Ì EÌ ¯01/  2EÌF Ì© /H1 ©'ED (G ¯1/ .H14Ì/ F¯1/Ì/G '3*. /1 H'B9 2EÌF Ì© /H1 ©'ED EFG'Ì ©E'F ©H†©Ì 1' ~ÌEH/G '3*. 2EÌF 'ÌF ©E'F ©H†© 1' GEÌ4G (' 319* Ì©3'FÌ FEÌ ~ÌE'Ì/  2Ì1' 319*4 (3*¯Ì /'1/ (G ,'Ì4 F3(* (G FB7G Ì ~Ì1'GH1. /1 F*Ì,G  (3*G (G 'ÌF©G †G FB7G 'Ì '2 E/'1 2EÌF (1'Ì ":'2 3'D (1¯2Ì/G 4H/  ~ÌE'Ì4 ©'ED E/'1 /1 E/*G'Ì F'(1'(1 'F,'E EÌ ¯Ì1/. 'ÌF F©*G (/ÌF E9F' '3* ©G /1'2'Ì 3'D GH1¯1/Ì «1'3*ÌF» (3*¯Ì /'1/ (G FB7G Ì E1,9 (1¯2Ì/G Ì 1HÌ GH1~G. </p> <p> (G ©'1 ¯1A*F /Ì3HD (&lArr; òó) 1Ì'6Ì 3'/G 'Ì ('2FEH/ 1' "3'F*1 EÌ ©F/. EÌ *H'F 7HD 3'D 1' (' <em> Y = T - t </em> F4'F /'/  ©G <em>T</em> 2E'F D'2E (1'Ì 'ÌF '3* ©G .H14Ì/ F3(* (G ~Ì1'GH1 Ì© /H1 ©'ED (2F/ H <em>t</em> E/*Ì '3* ©G .H14Ì/ 51AG ,HÌÌ EÌ ©F/ †HF FB7G Ì E1,9 (G "F F2/Ì© EÌ 4H/. 'ÌF 2E'F 51AG ,HÌÌ 4/G 1' EÌ *H'F (' F3(3* <em> t = S/V </em> F4'F /'/  ©G <em>S</em> /1'2'Ì ©E'F ©H†© E3Ì1 '3* H <em>V</em> 319* ~/Ì/'1 .H14Ì/. '2 "F,' ©G /1'2'Ì ©E'F +'(* '3*  <em>t</em> *FG' (G 319* (3*¯Ì /'1/. (1'Ì FEHFG  GF¯'E .H1Ì3*'F 2E3*'FÌ (&lArr; òô)  /1 FÌEG Ì /Ì E'G  2EÌF (G ~Ì1'GH1 (3Ì'1 F2/Ì© '3* H .H14Ì/ (' 319*Ì (Ì4 '2 EÌ2'F EÌ'F¯ÌF (G 3HÌ ~Ì1'GH1 EÌ 1H/. (F' (1 'ÌF  HB* 51AG ,HÌÌ 4/G ©E*1 '2 2E'FÌ '3* ©G .H14Ì/ (G GEH¯'F (G'1Ì F2/Ì© EÌ 4H/. (F' (1 'ÌF  "F 3'D GH1¯1/Ì ©G ":'24 FB7G Ì .H1Ì3*'F 2E3*'FÌ '3* FG *FG' '2 3'D GH1¯1/Ì F3(* (G FB7G Ì GEH¯'F (G'1Ì 7HD'FÌ*1 .H'G/ (H/  (D©G '2 GEG Ì 3'DG'Ì GH1¯1/Ì /̯1 GEE /1'2*1 .H'G/ (H/. Meeus 2000  (1 ~'ÌG Ì E-'3(G G'Ì 1H2Ì, 3Ì'1G 'Ì Simon et al. 1994  A'5DG G'Ì 2E'FÌ EÌ'F¯ÌF (ÌF /H ¯01 ~Ì'~Ì .H14Ì/ '2 FB7G G'Ì ":'2 A5DG' (1'Ì 2ÌEG G'Ì ¯HF'¯HF 1' (G /3* EÌ /G/. F*Ì,G G'  ©G /1 ,/HD ô FE'Ì'F/G 4/G 'F/  (G 1H4FÌ F4'F EÌ /GF/ ©G 3'DG'Ì GH1¯1/Ì ¯HF'¯HF /1'2'Ì Ì©3'FÌ F/'1F/. (1'Ì FEHFG  EÌ (ÌFÌE ©G /1 2ÌEG Ì òððð  3'D GH1¯1/Ì .H1Ì3*'F 2E3*'FÌ /1'2*1ÌF '3* (' 7HD óöõ.òôò÷ôñ 1H2 Ì©3'F  H ©H*'G*1ÌF 3'D .H1Ì3*'F *'(3*'FÌ '3*  ©G óöõ.òôñöò÷ 1H2 EÌ 4H/. /1 H'B9  3'D GH1¯1/Ì ~˜HG4¯1'F E©'FÌ© "3E'FÌ †Ì2Ì '3* EÌ'F¯ÌF †G'1 ¯HFG 3'DÌ ©G ":'24'F †G'1 A5D G3*F/. (F' (1 'ÌF  3'D 'Ì1'FÌ FH1H2  ©G «GH1¯1/Ì» '3*  F('Ì/ (' "F 3'DG'Ì GH1¯1/Ì /̯1 '4*('G 4H/. </p> <p align="center"> ,/HD ô. †F/¯'F¯Ì 3'DG'Ì GH1¯1/Ìm <table border="2" cellpadding="2" cellspacing="5" align="center"> <tr> <td bgcolor="#ccccff">2ÌEG<br/> (&lArr; ~'FH4* ñö) </td> <td bgcolor="yellow"> GEH¯'F (G'1Ì <br/> 3'D FH1H2 </td> <td bgcolor="snow"> 3'D <br/> .H1Ì3*'F *'(3*'FÌ </td> <td bgcolor="#ccffcc"> 3'D <br/> GEH¯'F ~'ÌÌ2Ì </td> <td bgcolor="tan"> 3'D <br/> .H1Ì3*'F 2E3*'FÌ </td> </tr> <tr> <td bgcolor="#ccccff">ñððð-</td> <td bgcolor="yellow">óöõ.òôòðòò <br/> óöõ.òôòòó </td> <td bgcolor="snow"> óöõ.òôñøõù </td> <td bgcolor="#ccffcc"> óöõ.òôò÷ñø </td> <td bgcolor="tan"> óöõ.òôòø÷ñ </td> </tr> <tr> <td bgcolor="#ccccff">ð</td> <td bgcolor="yellow">óöõ.òôòñóø <br/> óöõ.òôòò÷</td> <td bgcolor="snow"> óöõ.òôñ÷òö </td> <td bgcolor="#ccffcc"> óöõ.òôòôùö </td> <td bgcolor="tan"> óöõ.òôòøøó </td> </tr> <tr> <td bgcolor="#ccccff">ñððð+</td> <td bgcolor="yellow">óöõ.òôòòöñ <br/> óöõ.òôòóò</td> <td bgcolor="snow">óöõ.òôñöôø </td> <td bgcolor="#ccffcc"> óöõ.òôòòõ÷ </td> <td bgcolor="tan"> óöõ.òôòøôð </td> </tr> <tr> <td bgcolor="#ccccff">òððð+</td> <td bgcolor="yellow"> óöõ.òôòó÷õ <br/> óöõ.òôòóö</td> <td bgcolor="snow"> óöõ.òôñöò÷ </td> <td bgcolor="#ccffcc"> óöõ.òôòðñø </td> <td bgcolor="tan"> óöõ.òôò÷ôñ </td> </tr> <tr> <td bgcolor="#ccccff">óððð+</td> <td bgcolor="yellow"> óöõ.òôòôöô <br/> óöõ.òôòó÷ </td> <td bgcolor="snow"> óöõ.òôñöõù </td> <td bgcolor="#ccffcc"> óöõ.òôñøðð </td> <td bgcolor="tan"> óöõ.òôòõùô </td> </tr> <tr> <td bgcolor="#ccccff">ôððð+</td> <td bgcolor="yellow"> óöõ.òôòõñö <br/> óöõ.òôòóõ </td> <td bgcolor="snow"> óöõ.òôñ÷óô </td> <td bgcolor="#ccffcc"> óöõ.òôñöòð </td> <td bgcolor="tan"> óöõ.òôòôð÷ </td> </tr> </table> m 3'DG' (1 -3( 1H2G'Ì Ì©3'F 'F/  (,2 3'D GEH¯'F (G'1Ì ©G GE†FÌF (1 -3( 1H2G'Ì .H14Ì/Ì /'/G 4/G '3*. </p> <h2>õ) 1'˜E'F 'F/1GD4 </h2> <p> ,' (G ,'ÌÌ 2E'FÌ dt EÌ'F /H GEH¯'F (G'1Ì ~Ì'~Ì  ©G /1 ,/HD ò F4'F /'/G 4/G '3*  †F'F©G ¯A*ÌE  FE'ÌF/G Ì ©31Ì '2 1H2 '3* ©G (1 óöõ 1H2 ©'ED 'A2HF EÌ 4H/. (G 3.FÌ /̯1  G1 3'DG 2E'F .H14Ì/Ì (G 'F/'2G Ì ©31 dt/24 1H2 F3(* (G ¯'G4E'1 ~Ì4 EÌ 'A*/. (' ¯1A*F dt (1'(1 (' õ.øñööò 3'9* ((G /3* "E/G (1'Ì /H1G Ì ñððð *' òõðð EÌD'/Ì)  EÌ (ÌFÌE ©G 'ÌF ~Ì41HÌ 9('1* EÌ 4H/ '2 </p> <div class="formula"> 5.81662 / 24 = 0.242359 </div> <br/> 1H2 /1 3'D  Ì' (G *B1Ì( ð.òôòô 1H2. (F' (1 'ÌF  ~3 '2 ¯04* †G'1 3'D 'ÌF ~Ì41A*G' 1HÌ GE EÌ 4HF/ ð.ùöùôô 1H2 <br/> <div class="formula"> 4 x 0.24236 = 0.96944 </div> <br/> ©G EÌ *H'F "F 1' Ì© 1H2 ©'ED ¯1A*  H /1 F*Ì,G Ì© 1H2 'F/1GDÌ (G ¯'G4E'1 'A2H/. HDÌ 'ÌF *5-Ì- Ì© 1H2 G1 †G'1 3'D 3.'H* EF/'FG '3* H ('9+ EÌ 4H/ ©G ¯'G4E'1 '2 2E'F .H14Ì/Ì ,DH (ÌA*/. 'ÌF F©*G E3#DG Ì (FÌ'/ÌF ¯'G4E'1G'Ì .H14Ì/Ì '3*. (G GEÌF /DÌD '3* ©G /1 ¯'G4E'1 'Ì1'FÌ 'F/1GD4 (&lArr; ô) (G 7H1 EF8E G1 †G'1 3'D Ì©('1 'F,'E FEÌ ¯Ì1/. '2 3HÌ /̯1  '¯1 'F/1GD4 19'Ì* F4H/  D-8G Ì FH1H2 F3(* (G FB7G Ì GEH¯'F (G'1Ì (G /1HF 2E3*'F EÌ D:2/ H G1 3'D '2 "F /H1*1 EÌ 4H/ *' ~3 '2 /1 -/H/ ñõð÷ 3'D  (' 3Ì1Ì ©'ED /1 *E'E A5DG'  /H('1G (G FB7G Ì ":'2ÌF ('2 ¯1//. (G 3.FÌ /̯1  ~3 '2 †G'1 3'D GEH¯'F (G'1Ì /1 ò A1H1/ÌF H ~3 '2 G4* 3'D /1 ó A1H1/ÌF 1HÌ .H'G/ /'/  H (/ÌF3'F. </p> <p> 1'˜E'F 'F/1GDÌ ¯'G4E'1 'Ì1'FÌ (1 ~'ÌG Ì †1.G 'Ì óó 3'DG '3*H'1 '3*. 'ÌF †1.G *4©ÌD 4/G '3* '2 ø </p> <div class="formula"> 33 x 0.2424 = 7.9992 = 8 </div> <p> 3'D 'F/1GDÌ óöö 1H2G H òõ 3'D 9'/Ì óöõ 1H2G. (F' (1 'ÌF  /H¯HFG 3'D 'F/1GDÌ /'1ÌE: ñ) 3'D 'F/1GDÌ ~3 '2 ó 3'D 9'/Ì (1('9Ì)  H ò) 3'D 'F/1GDÌ ~3 '2 ô 3'D 9'/Ì (.E'3Ì). /1 /H1G Ì †G'1 3'DG  GEH¯'F (G'1Ì GEH'1G (G 7H1 2H, /H ('1 ~3 '2 FÌE1H2 H /H1 ('1 ~Ì4 '2 FÌE1H2 1HÌ EÌ /G/. (' 'ÌF -'D  /1 -/H/ G1 óó 3'D Ì© ('1 GEH¯'F (G'1Ì (3Ì'1 F2/Ì© (G FÌE4( EÌ 'A*/  H /H1G Ì ~F,3'DG 1' ~/Ì/ EÌ "H1/. /13**1 ¯A*G ('4ÌE  'ÌF H69 (G 3'F †Ì1G G1 óó 3'D 1HÌ EÌ /G/  H ¯'G  'D(*G (3Ì'1 ©EÌ'(*1  G1 òù 3'D. </p> <p> F.3*ÌF 3'D 'F/1GDÌ †1.G Ì óó 3'DG .E'3Ì '3* H GA* *'Ì /̯1 1('9Ì. (F' (1 'ÌF 'F/1GD4 G' (G 3'DG'Ì 2Ì1 '9E'D EÌ 4HF/: õ  ù  ñó  ñ÷  òñ  òõ  òù  óó. /1'2'Ì †1.G Ì ©'ED (G: </p> <div class="formula"> 25 x 365 + 8 x 366 = 12053 </div> <br/> 1H2 ¯'G4E'1 31 EÌ 2F/. /1 EB'Ì3G  E/* 2E'F .H14Ì/Ì .H'G/ (H/: <br/> <div class="formula"> 33 x 365.242362 = 12052.99795 </div> <br/> 1H2. 'ÌF (/ÌF E9F' '3* ©G †1.G Ì óó 3'DG (G 'F/'2G Ì ð.ððòðõ 1H2 Ì' /1 -/H/ ó /BÌBG '2 2E'F .H14Ì/Ì ,DH EÌ 'A*/. (G GEÌF /DÌD '3* ©G †1.G Ì óó 3'DG GE FÌ'2 (G *F8ÌE /'1/. (' A16 +'(* (H/F 7HD 3'D  ~3 '2 õðð †1.G  Ì' -/H/ ñöððð 3'D  ¯'G4E'1 'Ì1'FÌ Ì© 1H2 '2 2E'F .H14Ì/Ì ~Ì4*1 .H'G/ (H/. HDÌ '2 "F,' ©G 7HD 3'D ~3 '2 2ÌEG Ì óððð ©'G4 .H'G/ Ì'A* H /1 -H'DÌ øððð (G -/H/ óöõ.òôñøò 1H2 .H'G/ 13Ì/  'ÌF ,DH (H/F Ì© 1H2G ~3 '2 /H1G Ì ©H*'G*1Ì 1HÌ .H'G/ /'/. (G G1 -'D  EF7BÌ EÌ FE'Ì/ ©G HB*Ì .7' (G ñ/óó 1H2 13Ì/ †1.G Ì óó 3'DG ,'Ì .H/ 1' (G †1.G Ì òù 3'DG (/G/ *' ¯'G4E'1 (' 2E'F .H14Ì/Ì GE'GF¯ (E'F/. ('Ì/ ¯A* ©G (ÌGH/G EÌ FE'Ì/ ©G (1HFÌ'(4 1' (1'Ì /H1G G'Ì (3Ì'1 /H1 "ÌF/G (G ©'1 (1/  †HF /1'2'Ì 3'D Ì©3'F FEÌ E'F/  H 'A2HF (1 'ÌF EE©F '3* "4A*¯ÌG'Ì F'4F'.*G (1 GE (ÌA2'ÌF/ "F3'F ©G (*H'FF/ *#+Ì1 EGEÌ (1 7HD 3'D (¯0'1F/. </p> <p> /1 ¯04*G ©G FÌH*F GFH2 F¯1G Ì ¯1'F4 .H/ 1' ~Ì4 FFG'/G (H/ H D'~D'3  D'¯1'F˜  'HD1  G'EÌD*HF H /̯1'F GFH2 E©'FÌ© "3E'FÌ 1' ~/Ì/ FÌ'H1/G (H/F/  D-8G Ì GEH¯'F (G'1Ì 1' (' (1HFÌ'(4 F~'G4G'Ì /BÌB ~Ì4 (ÌFÌ EÌ ©1/F/. 'E1H2G  /1 3'ÌG Ì ~Ì41A*G'ÌÌ ©G /1 E©'FÌ© "3E'FÌ H (H̘G /1 1'Ì'F¯1G' H 1H4G'Ì 9//Ì -'5D 4/G 'F/  D-8G Ì GEH¯'F (G'1Ì 1' EÌ *H'F (3Ì'1 /BÌB*1 ~Ì4 (ÌFÌ ©1/. (' 'ÌF -'D  'F/'2G ¯Ì1ÌG'Ì E(*FÌ (1 F~'G4 61H1Ì G3*F/ (1'Ì ('2(ÌFÌ GE'GF¯Ì EÌ'F E/D 1Ì'6Ì H H'B9Ì*. GE†FÌF  F~'G4 (.4 EGEÌ '3* '2 A1GF¯ ¯'G4E'1Ì 'Ì1'FÌ  H .1/EF/'FG EÌ FE'Ì/ ©G ~'3 /'4*G 4H/. A2HF (1 'ÌF  GE '©FHF ©G '.*14F'3Ì /H3*©'1 (&lArr; òõ) ~Ì41A*G'Ì AFÌ EGE ©1/G '3*  E1/E (Ì4*1Ì EÌ *H'FF/ /1 F~'G4 -1©* .H14Ì/ /1 -H'DÌ FH1H2 41©* ©FF/. '2 "F,' ©G FH1H2 †F/ÌF "ÌÌF H ,4F GE¯'FÌ 1' (G GE1'G EÌ "H1/  F~'G4 ¯3*1/G Ì .H14Ì/ /1 -H'DÌ GEH¯'F (G'1Ì EÌ *H'F/ FH "H1Ì 4'/Ì (.4Ì ('4/ /1 ',1' H ~'3/'4* 'ÌF "ÌÌF ©GF. /1 6EF  †FÌF ,4F F~'G4 .H14Ì/ A15* .H(Ì .H'G/ (H/ (1'Ì "EH24 '.*14F'3Ì H ¯'G4E'1Ì (G GE¯'F. GE†FÌF  EÌ *H'F †FÌF F~'G4 G' 1' (1'Ì -H'DÌ EG1¯'F FÌ2  ©G ,4FH'1G Ì GEH¯'F ~'ÌÌ2Ì '3*  *H5ÌG ©1/. </p> <h2>ö) 31'F,'E '5D'- ¯'G4E'1</h2> <p> /'F3*G G'Ì E' /1 ('1G Ì ('2/Ì3Ì ¯'G4E'1 '2 .H/ .Ì'E FEÌ "ÌF/  (D©G (G 7H1 F'E3*BÌE '2 1H'Ì*G'Ì E.*51 '.*14F'3'F /H1G G'Ì (9/ '3*F('7 EÌ 4HF/. /1 H'B9  ñó 3'D ~3 '2 ~Ì 1Ì2Ì '5D'- (1 .Ì'E .4E ¯1A*G 4/. ~3 '2 E1¯ ED©4'G H B*D F8'E 'DED© (G /3* Ì'1'F -3F 5('-  GE31 /HE ED©4'G  *H1'F .'*HF  (G E/* /H 3'D FÌ'(* 3D7F* 1' (G /3* ¯1A*. '2 "F,' ©G 'H (1 31 E3#DG Ì ,'F4ÌFÌ (' F8'E 'DED© F2'9 ©1/G (H/  .4E .H/ 1' (1 31 GE©'1'F H2Ì1  '2 ,EDG .Ì'E  A1H1Ì.*. A2HF (1 'ÌF  (FÌ'/¯1'Ì'F E0G(Ì  ©G .Ì'E 1' /H3* F/'4*F/  (G 3(( "2'/F/Ì4Ì 'H ©G /1 1('9Ì G'Ì4 FE'Ì'F 'F/  /1 /1('1 B/1* ¯1A*F/. GE†FÌF (9Ì/ FÌ3* ©G '2 ©H44G'Ì .Ì'E (1'Ì ~'3/'1Ì '2 A1GF¯ H GHÌ* 'Ì1'FÌ F'.4FH/ (H/F/. EB11Ì E'DÌ F~'G4¯'G 1' (1Ì/F/ H (G A9'DÌ*G'Ì "F  '2 ,EDG '5D'- ¯'G4E'1  ~'Ì'F /'/F/ (Youschkevitch & Rosenfeld 1973). </p> <p> (' 'ÌF -'D 4© FÌ3* ©G 1'˜E'F 'F/1GDÌ †G'13'DG H ~F,3'DG 1' .Ì'E H ¯1HG4 "A1Ì/G 'F/. '.*14F'3 .'2FÌ  ©G (G '-*E'D 96HÌ '2 ¯1HG .Ì'E (H/  H (9/G' /1 2E'F 3F,1  ~31 ED©4'G  2Ì, 3F,1Ì 1' ~/Ì/ "H1/  'F/1GD4G'Ì †G'13'DG H ~F,3'DG 1' (G ©'1 EÌ (1/. (G '-*E'D (3Ì'1 'H '2 /3*'H1/ ¯1HG .Ì'E (G1G (1/G '3*. F2/Ì© (G /H 3/G (9/ '.*14F'3 H 1Ì'6Ì/'F F'EH1 F5Ì1 'D/ÌF *H3Ì (ñòðñ *' ñò÷ô EÌD'/Ì)  31~13* F~'G4¯'G E1':G  ©G 2Ì, 'ÌD.'FÌ 1' ~/Ì/ "H1/  '7D'9G'Ì ©H*'G HDÌ EGEÌ '2 '5D'- ¯'G4E'1 /1 2E'F ED©4'G (G /3* EÌ /G/. /1 2Ì, 'ÌD.'FÌ .H/ (G 1H4FÌ (Ì'F EÌ /'1/: «... H ~F,G Ì E3*1BG /1 ".1 '3AF/'1E0 E'G ¯Ì1F/ H (G G1 †G'1 3'D Ì© 1H2 ©(Ì3G ('40 H 3'D 3Ì5/ H 45* H 44 1H2 4H0 H †HF GA* ('1 Ì' G4* ('1 (G †G'1 3'D ©(Ì3G "E0 Ì© ('1 (G ~F, 3'D ©(Ì3G 'A*0 H E91A* 'H'ÌD 3'DG' H ©('Ì3 (G '3*B1'! E9DHE 4H0 ...». EÌ (ÌFÌE 71- 'F/1GD4G'Ì †G'13'DG H ~F,3'DG 1' H '4'1G 'Ì 6EFÌ (G †1.G G'Ì òù H óó 3'DG. (1'Ì '7D'9 (Ì4*1 /1('1G Ì ©H44G'Ì ¯HF'¯HF /1 EH1/ 'F/1GD4 (1 ~'ÌG Ì 71- †G'13'DG/~F,3'DG /1 7Ì *'1Ì. 1,H9 ©FÌ/ (G 5Ì'/ (ñóöð) H GE†FÌF (G '+1 .H'F/FÌ 9(/ 'DDGÌ (ñó÷õ)  ©G (G *'1Ì. 31'31Ì ¯'G4E'1 'Ì1'FÌ EÌ ~1/'2/. </p> <h2>÷) †1.G Ì òøòð 3'DG</h2> <p> /1 ¯04*G 'Ì FG †F/'F /H1  (1.Ì ~˜HG4¯1'F ¯'G4E'1Ì /1 'Ì1'F ((H̘G 4'/1H'F (G1H2  ñóóñ  H 4'/1H'F (Ì14©  ñó÷ó) H,H/ †1.G 'Ì 1' /1 ¯'G4E'1 'Ì1'FÌ ~Ì4 FG'/G 'F/ ©G *' ©FHF F'4F'.*G (H/G '3*. 'Ì4'F ¯'G4E'1 1' (G †1.G G'Ì òøòð 3'DG (.4 EÌ ©FF/  ©G .H/ (G òñ 2Ì1†1.G Ì ñòø 3'DG H Ì© 2Ì1†1.G ñóò 3'DG *B3ÌE EÌ 4H/. </p> <div class="formula"> 2820 = 21 x 128 + 132 </div> <br/> 2Ì1†1.G G'Ì ñòø H ñóò 3'DG FÌ2 .H/ '2 /H1G G'Ì òù  óó  H ó÷ 3'DG ~/Ì/ "E/G 'F/ <br/> <div class="formula"> 128 = 29 + 3 x 33 <br/> 132 = 29 + 2 x 33 + 37 </div> <br/> (G ©H*'GÌ  'ÌF †1.G '2 òñó÷ 3'D 9'/Ì H öøó 3'D 'F/1GDÌ *4©ÌD 4/G '3*. <br/> <p> 'ÌF 71- /'1'Ì †F/ '4©'D '3*. '/9' EÌ ©F/ ©G †1.G Ì òøòð 3'DG FE'Ì'F¯1 E/*Ì '3* ©G ~3 '2 3~1Ì 4/F "F GEH¯'FG'Ì (G'1Ì /1 GE'F D-8G '2 1H2 *©1'1 EÌ 4HF/. E7'D9G Ì /'/G G'Ì 1H2Ì, IMCCE (G E' 'E©'F *#ÌÌ/ 'ÌF E7D( 1' FEÌ /G/. 'ÌF F©*G 1' /1 ¯04*G ~˜HG4¯1'F  '2 "F EÌ'F ED© ~H1 (ñóøó) H 5Ì'/ (ñó÷ø)  ¯H42/ ©1/G 'F/. A2HF (1 'ÌF  †1.G Ì òøòð 3'DG F2/Ì© (G ð.õ 1H2 '2 2E'F .H14Ì/Ì ~Ì4 EÌ 'A*/. (' A16 /1'2'Ì ©FHFÌ (1'Ì 3'D GEH¯'FÌ  †1.G '2 </p> <div class="formula"> 2820 x 365.242362 = 1029983.461 </div> <br/> 1H2 *4©ÌD EÌ 4H/  -'D "F©G ¯'G4E'1 /'1'Ì <br/> <div class="formula"> 2137 x 365 + 683 x 366 = 1029983 </div> <br/> 1H2 '3*. (1'Ì 'ÌF©G †1.G (' 2E'F .H14Ì/Ì GE¯'E (E'F/  /1'2'Ì 3'D ('Ì/ óöõ.òôòñùøö 1H2  Ì' (G *B1Ì( óöõ.òôòò 1H2  ('4/. 'ÌF 1BE  ©G '2 ©31 öøó/òøòð FÌ2 (1EÌ "Ì/  (G 8'G1 /1'2'Ì 3'D GH1¯1/Ì '3* (/1 ('1G '4 EA5D (-+ ©1/G 'ÌE) ©G (G '4*('G (1'Ì 3'D 'Ì1'FÌ ¯1A*G 4/G '3*. /1 F*Ì,G  71- òøòð 3'DG †F/ ('1 /†'1 /4H'1Ì EÌ 4H/  (1'Ì FEHFG òñ E'13 ñ- EÌD'/Ì  òñ E'13 ñöðð H òñ E'13 òðòõ. </p> <p> †1.G Ì òøòð 3'DG EE©F '3* EF4# 7HD 3'D (Ì4 '2 -/ /BÌBÌ ('4/ (óöõ.òôòñùøõøñõö 1H2) ©G (G .Ì'E F3(* /'/G 4/G '3* ((.4 ô). /1 H'B9 ©31 öøó/òøòð E*1'/A '3* (' 3'DÌ óöõ.òôòñùøõøñõöðó 1H2G  ©G (G 3'F 4¯A* 'F¯Ì2Ì (' 1BE ~Ì4FG'/ 4/G GE'FF/Ì /'1/  H 'ÌF F©*G (1'F¯Ì2'FF/G Ì 4© /1 '9*('1 "F 1BE '3*. 'ÌF 1BE /1 H'B9 3'.*¯Ì EE©F '3* '2 'ÌF '4*('G 1Ì4G ¯1A*G ('4/ ©G .Ì'E .H/ †1.G Ì òøòð 3'D 1' H69 ©1/G '3*. HDÌ Ğ 3F/ *'1Ì.Ì †FÌF (1 "H1/Ì 1' (G .Ì'E ~ÌHF/ FEÌ /G/ (5Ì'/ ñó÷ø). 'ÌF '4*('G EE©F '3* '2 'ÌF,' F'4Ì 4/G ('4/ ©G 4'/1H'F (G1H2 (ñóóñ) 71- .H/ 1' (G 5H1* ,/HDG'ÌÌ ©G «.Ì'EÌ» EÌ F'EÌ/ 916G ©1/  H GEÌF /1 1' (1'Ì *9(Ì1 :D7 ('2 FG'/G '3*. </p> <p> ~3 †FÌF (G F81 EÌ 13/ ©G ~'ÌG Ì †1.G Ì òøòð 3'DG '2 /1 "EÌ.*F 3'DG'Ì GEH¯'F (G'1Ì H GH1¯1/Ì EÌ "Ì/  †F'F©G /1 ('D' 41- /'/ÌE. GE†FÌF /1 71- †1.G (G *:ÌÌ1 7HD 3'D (' ¯04* 2E'F *H,G F4/G '3*. A2HF (1 'ÌFG'  'ÌF 71- ~̆Ì/G ¯'G4E'1 'Ì1'FÌ 1' /BÌB*1 FEÌ ©F/  2Ì1' †1.G Ì óó 3'DG Ì ©FHFÌ GE 3'/G *1 '3* H GE ©'1 "E/*1. </p> <h2>ø) Ì'//'4*Ì ©H*'G /1('1G Ì 1Ì4G Ì ©GF ¯'G4E'1 'Ì1'FÌ </h2> <p> F.3*ÌF /HD*G'Ì 'Ì1'FÌ 1' E'/G' (÷òø *' õõð ~Ì4 '2 EÌD'/) H G.'EF4Ì'F (õõð *' óóð ~Ì4 '2 EÌD'/) (F' FG'/F/. '2 ¯'G4E'1Ì /H1'F G.'EF4Ì'F "¯'GÌG'ÌÌ (G E' 13Ì/G 'F/  HDÌ E/1©G'Ì E1(H7 (G 951 ~Ì4 '2 G.'EF4Ì'F FG *FG' (3Ì'1 F'/1F/  '2 ¯'G4E'1Ì †Ì2Ì FEÌ ¯HÌF/. </p> <p> 4E'1Ì F4'FG G'Ì *'1Ì.Ì H ('3*'F4F'3Ì -'©Ì '2 "F 'F/ ©G ¯'G4E'1 13EÌ 951 G.'EF4Ì E'GÌ-.H14Ì/Ì (H/G H '2 ('(DÌ'F 'B*('3 4/G '3*. /1 6EF  ¯'G4E'1 .H14Ì/Ì /̯1Ì H,H/ /'4*G ©G *H/G Ì E1/E "F 1' (G ¯3*1/¯Ì (G ©'1 EÌ (1/G 'F/. /DÌD ~0Ì14 ¯'G4E'1 ('(DÌ 3Ì'3Ì (H/G '3*. ('(DÌ'F *,1(G Ì (Ì4*1Ì /1 ©4H1/'1Ì /'4*F/ H G.'EF4Ì'F EÌ *H'F3*F/ '2 "F'F /F('DG 1HÌ ©FF/ H '2 13EG'Ì 9EDÌ '/'1Ì "F'F (G1G ¯Ì1F/. ~0Ì14 'ÌF ¯'G4E'1 GE†FÌF F4'FG Ì '-*1'E G.'EF4Ì'F (G Ì©Ì '2 E1/E'FÌ (H/ ©G 'E~1'*H1Ì 1' *4©ÌD EÌ /'/F/. EÌ /'FÌE ©G G.'EF4Ì'F (G "ÌÌFG' H /ÌFG'Ì BHEG'Ì /̯1 '1, EÌ ¯0'4*F/  H ©H14 (21¯ /1 E1'3E *',¯0'1Ì .H/ ./'Ì (21¯ ('(DÌ'F E1/H© 1' 3*'Ì4 ©1/. 9(/ 'DDGÌ (ñó÷õ) †F/ /DÌD B'F9 ©FF/G /'Ì1 (1 ~0Ì14 ¯'G4E'1 E'GÌ-.H14Ì/Ì ('(DÌ EÌ /G/  -'D "F©G F81 (1.Ì ~˜HG4¯1'F 1' ©G ¯'G4E'1 /HD*Ì G.'EF4Ì 1' *BDÌ/Ì '2 E/D E51Ì /'F3*G 'F/  B'79'FG 1/ EÌ ©F/. </p> <p> (1Ì'F (Briant)  H̘3*G ¯1 951 G.'EF4Ì  (' '3*F'/ (G *'1Ì.FHÌ3'F ('3*'F (~DH*'1©  /ÌH/1H3  ©$ÌF*H3  ©H1*ÌH3  /Ì3G "1©H3)  (1 'ÌF ('H1 '3* ©G G.'EF4Ì'F /1 ©F'1 ¯'G4E'1 ('(DÌ /'1'Ì ¯'G4E'1Ì .H14Ì/Ì (H/F/ ©G /1 "F 3'D '2 óöð 1H2 H õ 1H2 'F/1¯'GÌ *4©ÌD 4/G (H/. H'B9Ì*Ì *'1Ì.Ì G3*Ì ¯'G4E'1 .H14Ì/Ì ©GFÌ /1 'Ì1'F "F 951 1' *#ÌÌ/ EÌ ©F/. H "F 'ÌF '3* ©G ~3 '2 A*- "3Ì'Ì ©H†© *H37 ©H14 (21¯ H H1H/4 (G 4G1 3'1/  /1 õôö ~Ì4 '2 EÌD'/  ¯'G4E'1 .H14Ì/Ì 21*4*Ì (G ©'~'/H3 (/1 *1©ÌG ©FHFÌ) 1'G Ì'A* H (G ~0Ì14 ©'~'/H3ÌÌ'F /1 "E/. ¯'G4E'1 .H14Ì/Ì ©'~'/H3Ì  ©G ñò E'G óð 1H2G /'4* (G '6'AG Ì õ 1H2 'F/1¯'GÌ  *BDÌ/Ì (H/ '2 ¯'G4E'1 21*4*Ì. E'GG'Ì "F F'E 'Ì1'FÌ /'4*F/ H '2 *1*Ì( ¯'G4E'1 21*4*Ì ~Ì1HÌ EÌ ©1/F/ (/'F4F'EG Ì 'Ì1'FÌ©'). A1'EH4 F©FÌE  /1 7HD 3/G G'ÌÌ ©G "3Ì'Ì ©H†© (.4Ì '2 'E~1'*H1Ì 'Ì1'F (H/  'Ì1'FÌ'F (G 'ÌF F'-ÌG EG',1* ©1/F/. -*' /1 3/G Ì †G'1E EÌD'/Ì  Ì9FÌ F2/Ì© (G ÷ðð 3'D ~3 '2 ~Ì1H2Ì '3©F/1  F3DG'Ì (9/Ì F.3*ÌF EG',1'F 'Ì1'FÌ /1 /G©/G G'Ì ©'~'/H3 EÌ 2Ì3*F/. 'ÌF H'B9Ì*G' '2 (113Ì E/1©G'Ì ('3*'F4F'.*Ì  1H'Ì*G'Ì ÌHF'FÌ'F  3F¯FH4*G G'Ì ¯H1G'  H 3©G G'Ì ('2E'F/G (G /3* "E/G 'F/. GE†FÌF "¯'GÌG'Ì (3Ì'1 /'1ÌE /1 ('1G Ì ~13*4¯'GG'Ì 21*4*Ì /1 "3Ì'Ì ©H†©. ©GF*1ÌF "FG' 1' ©H14 (21¯ Ì' 31/'1'F4 /1 3/G Ì 44E ~Ì4 '2 EÌD'/ (1 ~' ©1/G (H/F/. 'ÌF H'B9Ì* ©G /1 /H1G Ì A1E'F1H'ÌÌ G.'EF4Ì'F  ©'~'/H3Ì'F ¯'G4E'1 21*4*Ì 1' 'B*('3 ©1/F/ H FG ¯'G4E'1 /HD*Ì 1'  FE'Ì'F¯1 1Ì4G /'1 (H/F ¯'G4E'1 21*4*Ì /1 EÌ'F 'Ì1'FÌ'F  (H̘G (1'Ì (G ,' "H1/F 'EH1 /ÌFÌ H A1GF¯Ì 1H2'FG  (H/G '3*. H 'ÌF F©*G /DÌD ©GF*1 (H/F ¯'G4E'1 21*4*Ì '2 ¯'G4E'1 /HD*Ì G.'EF4Ì '3*. </p> <p> E/1©G'Ì *'1Ì.Ì E1(H7 (G ¯'G4E'1Ì /1 /H1'FG'Ì ©GF 'Ì1'F †F'F F'Ì'( 'F/ ©G Ğ '7D'9Ì 1' F('Ì/ F'/Ì/G ¯1A*  (H̘G FH4*G G'Ì '(H1Ì-'F (Ì1HFÌ 1'. 'ÌF H'B9ÌÌ*Ì '3* ©G /13*Ì "¯'GÌG'ÌÌ ©G (Ì1HFÌ '2 ¯'G4E'1 ~Ì4 '2 '3D'E 'Ì1'F /'/G ('1G' (G '+('* 13Ì/G '3* (9(/ 'DDGÌ ñó÷õ). (Ì1HFÌ /1 "+'1 'D('BÌG Ì .H/ /1('1G Ì ~Ì4/'/Ì'F  ©GF*1ÌF /H/E'F 'Ì1'FÌ (F' (1 *'1Ì. *1'/'/Ì  3.F EÌ ¯HÌ/. F.3*ÌF 4'G 'ÌF /H/E'F ©ÌHE1+ '3'7Ì1Ì (H/. ~3 '2 ~Ì4/'/Ì'F ©Ì'FÌ'F (G A1E'F1H'ÌÌ 13Ì/F/  H H'~3ÌF 4'G "F'F /'1' (/'1ÌH4 3HE) /1 -EDG Ì '3©F/1 ©4*G 4/. '2 "F,' ©G (Ì1HFÌ ©H14 H '1/4Ì1 Ì©E (/1'2 /3*) 1' ,2H ©Ì'FÌ'F EÌ /'F/ H ©Ì'FÌ'F 1' (' G.'EF4Ì'F Ì©Ì EÌ ¯Ì1/  ~Ì4/'/Ì'F ('Ì/ ©GF*1 '2 G.'EF4Ì'F ('4F/. H (F' (1 'A3'FG G' FH1H2 1' ,E4Ì/ ~Ì4/'/Ì (Yima Ì' Yama /1 'A3'FG G'Ì GF/H 'Ì1'FÌ) (1~' ©1/G ©G 2E'F4 (G ":'2 /H1'F 4G1F4ÌFÌ GF/H 'Ì1'FÌ'F H ¯01 '2 4©'1 (G /'E/'1Ì H ©4'H12Ì (1 EÌ ¯1/  2E'FÌ (3Ì'1 ©GF ©G (G 8'G1 (G 951Ì ©G /1 "F Ì.(F/'F (21¯Ì 1HÌ /'/G  ~ÌHF/ EÌ .H1/. (G G1 -'D  'ÌF 'A3'FG G' (1 ©GF3'DÌ (3Ì'1 FH1H2 H 'GEÌ* A1GF¯Ì "F *#©Ì/ /'1F/. </p> <p> (F' (1 (Ì1HFÌ  ~Ì4/'/Ì'F 3'D 1' óöð 1H2 EÌ ¯1A*F/ H E'G 1' óð 1H2. G1 ö 3'D Ì© E'G 'F/1GDÌ /'4*F/ H G1 ñòð 3'D /H E'G 'F/1GDÌ  Ì©Ì (1'Ì õ 1H2G'Ì 1G' ©1/G H /̯1Ì (1'Ì Ì©†G'1E 1H2G'Ì A1HG4*G. /1'2'Ì 3'D /1 "F ¯'G4E'1 †FÌF E-'3(G EÌ 4H/ (9(/ 'DDGÌ ñó÷õ): <br/> Ì© 3'D: <br/> <div class="formula"> 12 x 30 = 360 </div> <br/> 1H2. /1 ö 3'D: <br/> <div class="formula"> 6 x 360 + 30 = 2190 </div> <br/> 1H2. /1 ñòð 3'D: <br/> <div class="formula"> 20 x 2190 + 30 = 43830 </div> <br/> 1H2. ~3 7HD EÌ'F¯ÌF 3'D /1 /H1G Ì ñòð 3'D EÌ 4H/: <br/> <div class="formula"> 43830 / 120 = 365.25 </div> <br/> 1H2. Ì9FÌ óöõ 1H2 H Ì©†G'1E 1H2. (F' (1 'ÌF  '¯1 ¯A*G Ì (Ì1HFÌ 1' (~0Ì1ÌE  ¯'G4E'1 'Ì1'FÌ'F ~Ì4 '2 951 G.'EF4Ì .H14Ì/Ì (H/G '3*  H H̘¯ÌG'Ì ¯'G4E'1 21*4*Ì 1' /'4*G '3*. ~3 /1 EÌ'F *E/FG'Ì ©GF *FG' E51Ì'F F(H/F/ ©G ¯'G4E'1 .H14Ì/Ì /'4*F/. 'ÌF©G 'ÌF ¯'G4E'1 '2 ©Ì ":'2 4/G '3* /'F3*G FÌ3*  G1†F/ ©G (Ì1HFÌ '(/'9 'F/1GD4 Ì© E'GG 1' '2 .H/ 21*4* EÌ /'F/. ¯1†G /13* FEÌ /'FÌE ©G 21*4* ©Ì EÌ 2Ì3*G '3* ((1.Ì EF(9G'Ì ÌHF'FÌ 2E'F 'H 1' (G öððð 3'D ~Ì4 '2 E3Ì- EÌ 13'FF/  -'D "F©G *1'/'/ "F 1' öðð ~Ì4 '2 EÌD'/ EÌ ¯Ì1/)  ~˜HG4G'Ì '.Ì1 /1('1G Ì H̘¯ÌG'Ì 2('FÌ© ¯'G'F (©GF*1ÌF (.4 'H3*' ©G (G .H/ 21*4* F3(* /'/G EÌ 4H/) (G -H'DÌ ñõðð ~Ì4 '2 EÌD'/ '4'1G /'1F/ (/'F4F'EG Ì 'Ì1'FÌ©'). ,'D( '3* ©G (G *'2¯Ì Mary Settegast  (1 ~'ÌG Ì /'/G G'Ì ('3*'F4F'.*Ì 951 FH3F¯Ì  2E'F 21*4* 1' (G G2'1G Ì GA*E ~Ì4 '2 EÌD'/ ('2 EÌ ¯1/'F/. </p> <p> 'ÌF ¯'G4E'1 ©GF 2E'FÌ '5D'- 4/: (G ,'Ì 'F/1GDÌ/F Ì© E'G ©'ED G1 ö 3'D  õ 1H2 'F/1¯'G 1' (G ~3 '2 3Ì5/ H 43*EÌF 1H2 3'D 'A2H/F/. *'1Ì. G3* 4/F 'ÌF ¯'G4E'1 óöõ 1H2G EH6H9 (-+ '3*. West 3'D õðò ~Ì4 '2 EÌD'/ 1' ~Ì4FG'/ ©1/  Boyce F.3* /H1'F 3'3'FÌ'F 1' ~Ì4 FG'/  HDÌ (*'2¯Ì (1 "H1/ .H/ 1' ('2F¯1Ì3*G H /H1'F G.'EF4Ì'F 1' ~Ì4FG'/ EÌ ©F/ (/'F4F'EG Ì 'Ì1'FÌ©'). E3#DG GFH2 E71- '3*. </p> <p> H̘¯Ì (1,3*G Ì ¯'G4E'1 'Ì1'FÌ FH1H2 '3* ©G /1 ('H1G'Ì 21*4*Ì (' "*4  GA*EÌF "A1Ì/G Ì 'GH1'E2/'  ~ÌHF/ /'1/. /1 H'B9  FH1H2 EGE*1ÌF ,4FH'1G /1 ¯'G4E'1 .H14Ì/Ì 21*4*Ì (G 4E'1 EÌ 1H/. (F' (1 Boyce (GE'F,'  /1 "ÌG Ì ¯'GF('1G')  /1 EÌ'F GA* "ÌÌF ©GF 21*4*Ì «*FG' FH1H2 '3* ©G (G 8'G1 *H,ÌG ©Ì4 EF/'FG /'1/  2Ì1' ,4F FH1H2 /1 GEH¯'F (G'1Ì '3*  GF¯'EÌ ©G .H14Ì/  FÌ1HEF/*1ÌF FE'/ "A1ÌF4 "*4  '2 FH (G ,G'F ¯1E' H 2F/¯Ì EÌ (.4/. ... (3Ì'1 E-*ED EÌ FE'Ì/ ©G FH1H2 1'  ©G /'1'Ì ~Ì'E FE'/ÌF E9FHÌ '3*  .H/ 21*4* (FÌ'/ FG'/G ('4/.» </p> <h2>3~'3¯2'1Ì </h2> <div dir="ltr"> <h2>Acknowledgements</h2> <p> It is a pleasure to thank the French <em> Institut de M&eacute;canique C&eacute;leste et de Calcul des Eph&eacute;m&eacute;rides</em> (IMCCE), Director Dr. William Thuillot, and Dr. Patrick Rocher for providing the ephemeris which was essential for this study and also for helpful discussions. My field of research in astrophysics being well outside that of calendars and time reckoning, I learned a lot in the process of writing this paper and would like to thank all the people who took part in this project. I am particularly indebted to the calendar expert Mr. Simon Cassidy, Emeryville Ca. U.S.A., for numerous e-mail exchanges and for a critical reading of the paper which contributed to improve its content. I express my deep gratitude to him. I benefited also from discussions and comments by several colleagues at Paris Observatory, in particular Dr. Thibaut Le Bertre, Dr. Jean-François Lestrade, and Dr. James Lequeux. I would like to thank them. I am grateful also to Dr. Vassilis Charmandaris, Cornell University, USA, for comments. My thanks are also directed to Mr. Fr&eacute;d&eacute;ric Meynadier, Paris Observatory/Paris VI University, for his valuable and efficient cooperation. I am also thankful to Mr. Jean Meeus, Brussels, and Dr. Iraj Malakpour, Geophysics Institute, Tehran, for replying to my questions. I would like also to acknowledge Drs. Edward M. Reingold & Nachum Dershowitz as well as Dr. Hossein B&acirc;gher-Z&acirc;deh (/©*1 -3ÌF ('B1 2'/G) for using their calendar conversion codes. I am also grateful to Dr. Kazimierz M. Borkowski, Torun Radio Astronomy Observatory, Nicolaus Copernicus University, Poland, who read the paper and made several interesting comments. I want also to thank Dr. Jafar &Acirc;gh&acirc;y&acirc;ni-Ch&acirc;voshi (/©*1 ,9A1 "B'Ì'FÌ †'H4Ì), Sharif University, Tehran, for providing several historical documents. I am also grateful to Dr. M.Sch. Adib-Solt&acirc;ni (/©*1 EÌ1 4E3 'D/ÌF '/Ì( 3D7'FÌ), Tehran, for his remarks, in particular regarding etymology. The first Persian version of this paper was made possible thanks to the software <a href="http://www.mathstat.dal.ca/~selinger/farsiweb" target="_blank">Farsiweb</a> kindly provided by Prof. Peter Selinger, Department of Mathematics and Statistics, University of Ottawa, Canada. I would like to express my thanks to him. Finally, I would like to dedicate this paper to the memory of the late scholars Zabih Behruz ('3*'/ 0(Ì- (G1H2) and Ahmad Birashk ('3*'/ '-E/ (Ì14©), who initiated the modern research on the Iranian calendar. </p> </div> <hr/> <h3>~'FH4*G'</h3> <p> GE†FÌF H'˜G F'EG Ì ~'Ì'F 'ÌF EB'DG 1' ((ÌFÌ/. </p> <p> ñ) <b><u>GEH¯'F </u></b> (hamug&acirc;n) (1'(1 (' equinox /1 2('FG'Ì '1H~'ÌÌ  '2 H'˜G Ì D'*ÌF æquinoctium  '2 -æqui «(1'(1  E3'HÌ» + -noct  '2 nox «4(». GEH¯'F '2 ~GDHÌ GEH¯ «(1'(1  E3'HÌ» + -"F  ~3HF/ 2E'F H ,'  GE†HF /1 (G'1'F  (1¯1Ì2'F  .'H1'F. FEHFG Ì ©'1(1/ /1 ~GDHÌ hamog drahn&acirc;d = GEH¯ /1'2' = E*3'HÌ 'D7HD. &lArr; GEH¯'1 (~'FH4* ø)  &lArr; GEH¯4 (~'FH4* òð). </p> <p> ò) <b><u>F~'G4 </u></b> (nep&acirc;he&#353;) (1'(1 15/ H observation. H'˜G Ì '1H~'ÌÌ '2 D'*ÌF observationem «~'3/'1Ì  ~'3  F¯'G/'1Ì»  '2 observare «~'3 /'4*F  ~'ÌÌ/F  F¯'G /'4*F»  '2 -ob «(1  (G» + servare «~'ÌÌ/F  F¯'G /'4*F». F~'G4 '2 ~Ì4HF/ -ne H 3*'© A9DÌ ~'G-. ~Ì4HF/ -ne  ©G /1 H'˜G G'Ì A'13Ì F¯'G  F43*F  FGA*F  FA1ÌF (1,' E'F/G '2 A'13Ì ('3*'F H 'H3*'ÌÌ -ni EÌ "Ì/ ( '1EFÌ -ni  'Ì1DF/Ì ©GF -ne  'Ì3DF/Ì ©GF -nidhr  "DE'FÌ -nieder  ~H1H'-GF/-H- '1H~'ÌÌ -ni*  (G E9F'Ì «(G 3HÌ  (G ~'ÌÌF  ~'ÌÌF»). ~'G ©G /Ì3G G'Ì /̯14 ~'Ì- (~'ÌÌ/F) H ~'3 (/1 ¯ÌD©Ì A9D ~'3*F) G3*F/ (G E9F'Ì «F¯'G ©1/F  -1'3* ©1/F» '3*. '2 A'13Ì ('3*'F H 'H3*'ÌÌ -p&acirc; Ì' -p&acirc;y «F¯G('FÌ ©1/F  ~'3 /'4*F». GE†FÌF  F~'G4¯'G /1 (1'(1 observatory H 15/.'FG. </p> <p> ó) <b><u>1'˜E'F </u></b> (r&acirc;~m&acirc;n) (1'(1 system /1 2('FG'Ì '1H~'ÌÌ. H'˜G Ì '1H~'ÌÌ ¯1A*G 4/G '3* '2 D'*ÌF systema «"1'3*  *1*Ì(» '2 ÌHF'FÌ systema «(' GE "1'3*G»  '2 -syn (GE1Ì4G (') «GE-» + 3*'© histanai (GE1Ì4G (') «'Ì3*'F/F»  1Ì4G Ì ~H1H'-GF/-H- '1H~'ÌÌ -sta* «'Ì3*'/F». 1'˜E'F '2 1'˜  '2 'H3*'ÌÌ -raz  A'13Ì ('3*'F -rad «"1'3*F  F8E /'/F» + ~3HF/ '3E 3'2 -E'F ©G /1 H'˜G G'Ì 3'2E'F  3'.*E'F  2'ÌE'F  †'ÌE'F H /̯1G' (G ©'1 1A*G. 'ÌF H'˜G'Ì 'H3*'ÌÌ H A'13Ì ('3*'F GE1Ì4G 'F/ (' 3'F3©1Ì* -raj «A1E'F 1'F/F  '/'1G ©1/F  G/'Ì* ©1/F»  ÌHF'FÌ oregein «¯3*1/F»  D'*ÌF rego «1'G (1/F»  ~H1H'-GF/-H- '1H~'ÌÌ -reg* «1'3* 1A*F  1'3* ©1/F». /1 A'13Ì FHÌF 4E'1 (3Ì'1Ì H'˜G '2 -raz H -rad EÌ "ÌF/: 1'3*  "1'3*F  1'4* ('A1'4*F)  1,  1˜  1˜G  1/G  1'/G  1/ÌA  (/1 BEÌ) 1† rec «1/ÌA  1/G » (/1 D1Ì) 12¯ rezg «1/ÌA  5A»  1Ì3  1Ì3G  13*G  1'Ì (/1 "1'Ì4  1'Ì'FG  1'Ì'F¯1)  H /̯1G'. </p> <p> ô) <b><u>'F/1GDÌ </u></b> (andarheli) 5A* 'F/1GD  A9D 'F/1GDÌ/F  '3E A9DÌ 'F/1GD4. 'F/1GDÌ (1'(1 intercalatory  'F/1GDÌ/F /1 (1'(1 to intercalate H 'F/1GD4 intercalation. A9D intercalate (G E9F'Ì «,' /'/'F  /1HF FG'/F  /1 EÌ'F ¯0'4*F» /1 ¯'G4E'1Ì «'A2H/F 1H2 Ì' E'GÌ (G ,'ÌÌ '2 ¯'G4E'1». H'˜G Ì 'F¯DÌ3Ì '2 D'*ÌF intercalatus 5A* EA9HDÌ intercalare '2 -inter «'F/1-» + calare «'9D'E ©1/F». 'F/1GD  'F/1GDÌ/F  '2 'F/1G4*F /1 ~GDHÌ  (G E9F'Ì «/1 EÌ'F †Ì2Ì Ì' ,E9Ì FG'/F»  '2 ~Ì4HF/ 'F/1-  '2 A'13Ì ('3*'F H 'H3*'ÌÌ -antar «EÌ'F /H Ì' †F/ †Ì2 /1HF»  (3F,Ì/ (' 3'F3©1Ì* -antar  D'*ÌF -inter  ¯H*Ì© -undar  ~H1H'-GF/-H -'1H~'ÌÌ -enter* «EÌ'F  (ÌF» + GDÌ/F  G4*F  /1 ~GDHÌ ~'1*Ì hyrz  'H3*'ÌÌ -harez «GDÌ/F  G4*F  1G'©1/F». </p> <p> õ) (F' (1 ¯'G4E'1 ¯1¯H1Ì ñõ E'13 /1 ¯'G4E'1 ÌHDÌ'FÌ. </p> <p> ö) <b><u>GH1¯1/Ì </u></b> (hurgardi) /1 (1'(1 tropical  '2 tropic  '2 D'*ÌF tropicus '2 ÌHF'FÌ tropikos «E1(H7 (G ¯1/Ì/F  ¯4*F Ì' /¯1¯HFÌ (/1 ,F(4 .H14Ì/)  E1(H7 (G .H1Ì3*'F ('FBD'()»  '2 tropos «¯4*  ¯1/  1H4»  tropein «¯1/Ì/F » 1Ì4G Ì GF/-H -'1H~'ÌÌ -trep* «¯1/Ì/F». GH1¯1/ '2 GH1 «.H14Ì/» '2 ~GDHÌ GH1  .H1  'H3*'ÌÌ -hvar. (3F,Ì/ (' 3'F3©1Ì* -surya  ÌHF'FÌ helios  D'*ÌF sol  "DE'FÌ Sonne  'F¯DÌ3Ì sun  '2 ~H1H'-GF/-H- '1H~'ÌÌ -sawel* «.H14Ì/». ¯1/  ¯1/Ì/F  ¯4*F '2 ~GDHÌ gardidan H va&#353;tan  'H3*'ÌÌ -varet  3'F3©1Ì* -vrt  D'*ÌF vertere «¯1/Ì/F»  ~H1H'-GF/-H- '1H~'ÌÌ -wert*. </p> <p> ÷) <b><u>GH1~G</u></b> (hurpeh) (1'(1 ecliptic H /'Ì1G 'D(1H,. ecliptic '2 D'*ÌF ecliptica linea «.7 .H1¯1A*G'»  '2 eclipsis «.H1¯1A*»  '2 ÌHF'FÌ ekleipsis «1G' ©1/ .H1¯1A*»  '2 ekleipein «1G' ©1/F ,'ÌÌ E9EHD  '2 ~/Ì/'1 4/'F /1E'F/F»  '2 -ek Ì' -ex «(1HF» + leipein «1G' ©1/F». GH1~G «1'G .H14Ì/»  '2 GH1 «.H14Ì/» (&lArr; ~'FH4* ö /1 ('D') + ~G (peh) «1'G»  '2 'H3*'ÌÌ -pa¸ «1'G»  ©G /Ì3G G'Ì /̯14 G3*F/: -pa¸i H -pa¸&acirc; H -pantay  «~F/» /1 A'13Ì  3'F3©1Ì* pathi H panthah  ÌHF'FÌ pontos «/1Ì'Ì ('2»  patos «1'G»  D'*ÌF pons «~D»  ~H1H'-˜1E'FÌ© * «Ì'A*F » 'F¯DÌ3Ì find ~H1H'-GF/-H-'1H~'ÌÌ -pent* «¯04*F  1A*F  ~D». (F' (1 ~H©H1FÌ  H'˜G Ì ˜1E'FÌ© -patha* «1'G  ¯01¯'G» '2 'Ì1'FÌ -path* (G H'E ¯1A*G 4/G  *H'F/ (H/ '2 1'G 3©'G'. </p> <p> ø) <b><u>GEH¯'1</u></b> (hamug&acirc;r) (1'(1 '1H~'ÌÌ equator  91(Ì '3*H'! «(1'(1 4/F». H'˜G Ì '1H~'ÌÌ '2 D'*ÌF æquator diei et noctis «(1'(1 ©FF/G Ì 1H2 H 4(»  '2 æquare «(1'(1 ©FF/G  GEH¯'FF/G» '2 æquus «(1'(1  E3'HÌ». GEH¯'1 «(1'(1 ©FF/G» '2 ~GDHÌ GEH¯ "(1'(1  E3'HÌ" + -"1 «"H1F/G» '2 «"H1/F» /1 E9F'Ì «©1/F». &lArr; GEH¯'F (~'FH4* ñ)  &lArr; GEH¯4 (~'FH4* òð). </p> <p> ù) <b><u>1'3* 'A1'2 </u></b> (1'(1 right ascension  (G E9F'Ì: «A'5DG Ì 2'HÌG 'Ì EÌ'F '.*1 Ì' FB7G 'Ì /1 "3E'F ©G '2 GEH¯'F (G'1Ì 'F/'2G ¯Ì1Ì EÌ 4H/ (G 3HÌ .'H1  /1 7HD GEH¯'1 "3E'FÌ  *' "F,' ©G /'Ì1G 'Ì ©G '2 '.*1 H B7(G'Ì 4E'D H ,FH( EÌ ¯01/ GEH¯'1 "3E'FÌ 1' B79 EÌ ©F/.» </p> <p> ñð) <b><u>/1˜F' </u></b> (dere~n&acirc;) /1 (1'(1 longitude  91(Ì 7HD  7HD ,:1'AÌ'ÌÌ. H'˜G Ì '1H~'ÌÌ '2 D'*ÌF longitudo «/1'2'»  '2 longus «/1'2» + tudo- ~3HF/ 3'2F/G Ì '3EG'Ì F'(3H/FÌ. longus GE1Ì4G ('4/ (' 'H3*'ÌÌ -darega H -dr&acirc;jah «/1'2'  E3'A*»  -dr&acirc;jyo «/1'2»  A'13Ì ('3*'F -darga  A'13Ì EÌ'FG draz  A'13Ì FHÌF der&acirc;z. (3F,Ì/ (' H'˜G Ì 3'F3©1Ì* -dirgha  ÌHF'FÌ dolikhos  «©4Ì/G»  ¯H*Ì© tulgus  ~H1H'-GF/-H- '1H~'ÌÌ -del*. /1˜F' '2 /1˜ «/1'2»  /Ì3G Ì /̯1Ì '2 «/1'2» (GE†HF /1 D1Ì D©Ì dere~ «/1'2»  dere~i «/1'2'») + ~3HF/ '3E 3'2 F'- (GE†HF /1 ~GF'  /1'2F'  A1'.F'  *Ì2F'). </p> <p> ññ) <b><u>1H2Ì, </u></b> (1'(1 (' ephemeris «,/HDÌ ©G ,'  B/1  H (1.Ì /'/G G'Ì /̯1 '.*1'F  (H̘G .H14Ì/  E'G  3Ì'1G G'  H /F('DG /'1G'  1' (1'Ì G1 1H2 3'D (G /3* EÌ /G/. GE†FÌF ©*'(Ì ©G /1 (1 ¯Ì1F/G Ì E,EH9G 'Ì '2 'ÌF ,/HDG'3*.» ephemeris '2 D'*ÌF  '2 ÌHF'FÌ ephemeros «1H2'FG  /A*1 Ì'//'4* 1H2'FG»  '2 -epi «(1» + hemerai -'D* EA9HDÌ hemera «1H2». 1H2Ì, '2 1H2 + 2Ì,. 1H2 '2 A'13Ì EÌ'FG roc  A'13Ì ('3*'F -raucah «1H2»  'H3*'ÌÌ -raocah «FH1»  3'F3©1Ì* -rocas «FH1»  ÌHF'FÌ leukos «3AÌ/  1H4F»  D'*ÌF lux «FH1»  ~H1H'-GF/-H- '1H~'ÌÌ -leuk* «FH1  1H4F'ÌÌ». H'˜G G'Ì A'13Ì «1H4F»  «A1H:»  H «'A1H.*F» '2 'ÌF .'FH'/G G3*F/  GE†HF 'F¯DÌ3Ì light  "DE'FÌ Licht  H A1'F3G lumière. 2̯  ©G (G 2Ì, 91(Ì/G 4/G '3*  /1 A'13Ì EÌ'FG (G E9F'Ì «,/HD '.*1Ì  3'DF'EG» '3*. 2̯ /1 '5D (G E9F'Ì «1Ì3E'F  14*G» (H/G '3*. †1'ÌÌ (G ©'1 (1/F "F (1'Ì ,/HD '2 'ÌF,'3* ©G .7G'Ì ,/HD 1' (G 14*G *'1G'ÌÌ ©G /1 ©'1¯'G ('AF/¯Ì (G ©'1 EÌ 1HF/ GE'FF/ ©1/G 'F/. GE†FÌF  1H2Ì,G' = ephemerides. </p> <p> ñò) FG'/F ":'2 1H2 (1 FÌE4( *1'/'/Ì ©GF '3* /1 'Ì1'F 2EÌF †F'F©G '(H 1Ì-'F (Ì1HFÌ /1 "+'1 'D('BÌG (/'F '4'1G EÌ ©F/. (Ì1HFÌ *#©Ì/ /'1/ ©G 2Ì, 4G1Ì'1  ,/HDG'Ì '.*1Ì ©G /1 2E'F .31H 'FH4Ì1H'F (-/H/ õõõ EÌD'/Ì) A1'GE "E/F/  (1 'ÌF ~'ÌG (H/F/ ©G ":'2 1H2 1' '2 FÌE4( -3'( EÌ ©1/F/. 'ÌF©G /1 '.*14F'3Ì ('.*1 2EÌF ":'2 1H2 1' FÌE4( (¯Ì1F/ (G †F/'F /H1 (1FEÌ ¯1//. /1 H'B9  *' 3'D ñùòõ '.*14F'3'F 1H2 .H/ 1' '2 FÌE1H2 ":'2 EÌ ©1/F/ H /1 FÌE1H2 (G ~'Ì'F EÌ 13'F/F/. 2E'F EÌ'F¯ÌF ¯1ÌF̆ (Greenwich Mean Time) (1 ~'ÌG Ì FÌE1H2 EÌ'F¯ÌF .H14Ì/Ì /1 ¯1ÌF̆ B1'1 /'4*  -'D "F©G 2E'F 4'1EF/ ¯1ÌF̆ (Greenwich Civil Time) '2 FÌE4( ":'2 EÌ 4/. GFH2 GE /1 1'˜E'F ÌHDÌ'FÌ  ©G /1 '.*14F'3Ì A1'H'F (G ©'1 EÌ 1H/  1H2 '2 FÌE1H2 ":'2 EÌ 4H/. </p> <p> ñó) <b><u>A1'2' </u></b> (1'(1 altitude  (G E9F'Ì «2'HÌG Ì EÌ'F ,'Ì '.*1 (1 3~G1 "3E'FÌ H 'AB». A1'2' '2 A1'2 «('D'  (1» '2 ~GDHÌ fr&acirc;c «"F 3HÌ  ~Ì4  ,DH  1HÌ» + ~3HF/ -" (GE†HF ~GF'  /1'2'  H /̯1G'). </p> <p> ñô) (F' (1 ¯'G4E'1 ¯1¯H1Ì  ©G EÌ 4H/ ñù E'13 /1 ¯'G4E'1 ÌHDÌ'FÌ. *'1Ì. ñ÷ E'13 öòò EÌD'/Ì  ©G *BÌ 2'/G EÌ /G/  /13* FÌ3*  †F'F©G (Ì14© (/'F '4'1G ©1/G '3*. </p> <p> ñõ) /1'2'Ì A5DG'Ì '.*14F'.*Ì /1 2E'F ©FHFÌ 9('1*F/ '2: (G'1 ùò.÷ö 1H2  *'(3*'F ùó.öõ 1H2  ~'ÌÌ2 øù.øô 1H2  H 2E3*'F øø.ùù 1H2. A5DG' Ì©3'F FÌ3*F/ 2Ì1' E/'1 2EÌF (G ¯1/ .H14Ì/ ©EÌ (Ì6Ì 4©D '3* H .H14Ì/ /13* /1 E1©2 E/'1 B1'1 F/'1/. (F' (1 B'FHF /HE ©~D1  2EÌF HB*Ì (G .H14Ì/ F2/Ì©*1 '3* *F/*1 '2 2E'FÌ -1©* EÌ ©F/ ©G '2 "F /H1 '3*. (F' (1 'ÌF  A5DG'ÌÌ ©G GF¯'E F2/Ì© (H/F 2EÌF (G .H14Ì/ 1HÌ EÌ /GF/ 2H/*1 3~1Ì EÌ 4HF/. 2EÌF /1 FÌEG Ì /Ì E'G (G ~Ì1'GH1 (&lArr; òñ)  F2/Ì©*1ÌF FB7G (G .H14Ì/  EÌ 13/  H /1 FÌEG Ì *Ì1 E'G '2 '~'GH1 (&lArr; òò)  /H1*1ÌF FB7G Ì E/'14  EÌ ¯01/. (F' (1 'ÌF  /1 FÌE©1G Ì 4E'DÌ  *'(3*'F /1'2*1 '2 2E3*'F '3*. /1 FÌE©1G Ì ,FH(Ì 2E3*'F /1'2*1 '3*. 'E' 'ÌF H69 ,'H/'FG FÌ3*  H /1'2'Ì A5DG' (' ¯04* 2E'F *:ÌÌ1 EÌ ©F/  2Ì1' (F ~'1G'Ì E/'1Ì 2EÌF ~'Ì' FÌ3*F/. ~Ì4'Ì'F (&lArr; ñø)  Ì' ,F(4 3HÌ "3G Ì †1.4 2EÌF  ,'Ì .H1Ì3*'F G' (&lArr; òñ) H GEH¯'F G' 1'  F3(* (G ~Ì1'GH1  /¯1¯HF EÌ ©F/. F2/Ì© (G òñððð 3'D 7HD EÌ ©4/ *' 'ÌF FB7G G' F3(* (G ~Ì1'GH1 Ì© /H1 ©'ED (2FF/. GE†FÌF  *:ÌÌ1G'Ì 4©D Ì' '3E1©2Ì (osmarkazi  (G 'F¯DÌ3Ì eccentricity) E/'1 2EÌF  ©G /H1G '4 -/H/ ñððððð 3'D '3*  7HD A5DG' 1' /¯1¯HF EÌ ©F/. </p> <p> ñö) <b><u>2ÌEG </u></b> (zim&eacute;) /1 (1'(1 H'˜G Ì '1H~'ÌÌ epoch (' *91ÌA: D-8G Ì' *'1Ì.Ì ©G /1 "F (F ~'1G'Ì E/'1Ì Ì' ,'Ì '.*1'F E-'3(G 4/G 'F/. (G /3* /'/F 2ÌEG EGE '3* †HF ,'G'Ì ~/Ì/'1 '.*1'F *:ÌÌ1 EÌ ©FF/ (1 '+1 ~/Ì/G Ì ~Ì4'Ì'F (&lArr; ñø)  H (F ~'1G'Ì E/'1Ì /¯1¯HF EÌ 4HF/ (G 3(( *#+Ì1G'Ì ¯1'F4Ì 3Ì'1G G'. H'˜G Ì '1H~'ÌÌ '2 D'*ÌF epocha  '2 ÌHF'FÌ epokhe «'Ì3*  'Ì3*¯'G  FB7G Ì E9ÌF 2E'F»  '2 epekhein «E©+ ©1/F  ,'Ì ¯1A*F»  '2 -epi «1H  (G  ('D'» + ekhein «¯1A*F  F¯G/'4*F.» 2ÌEG '2 2ÌE /1 ~GDHÌ «2E'F  3'D  E/*  2E3*'F» + ~3HF/ e- ©G /1 A'13Ì A1'H'F (G ©'1 EÌ 1H/ (1'Ì 3'.*F ,/'4/G G' (2E'F  2E'FG  'F/Ì4  'F/Ì4G  1H2  1H2G). 2ÌE  ©G (G 'H3*'ÌÌ -zyam H -zayan «2E3*'F» (1EÌ ¯1//  (G '-*E'D GE1Ì4G '3* (' H'˜G Ì 2E'F. </p> <p> ñ÷) (1'Ì FEHFG  /1 *'13Ì* (website) EH2G Ì EDÌ /1Ì'ÌÌ 'F¯D3*'F  H'(3*G (G F~'G4¯'G 3D7F*Ì ¯1ÌF̆ ~Ì4ÌF  †FÌF "E/G '3*: </p> <blockquote> «3'D 9('1* '3* '2 A'5DG Ì 2E'FÌ EÌ'F /H ¯01 ~Ì'~Ì .H14Ì/ '2 GEH¯'F (G'1Ì. 'D(*G "F†G /1 H'B9 1HÌ EÌ /G/ 'ÌF '3* ©G 2EÌF (G ¯1/ .H14Ì/ EÌ ¯1//  HDÌ (1'Ì "3'F*1 4/F AGE E7D( -1©* ~/Ì/'1 .H14Ì/ 1' /1 F81 EÌ ¯Ì1ÌE. GEH¯'F (G'1Ì D-8G 'Ì '3* ©G .H14Ì/ /1 -1©*4 '2 ,FH( (G 4E'D (1 A1'2 GEH¯'1 2EÌF B1'1 EÌ ¯Ì1/. 3'D (F' (1 *91ÌA ('D' GH1¯1/Ì F'EÌ/G EÌ 4H/  H 7HD 3'D '3* ©G A5DG' 1' *9ÌÌF EÌ ©F/. 7HD 3'D GH1¯1/Ì óöõ.òôòñù 1H2 '3*.» </blockquote> <p> /1 'ÌF,'  /1 GE "EÌ.*F EAGHEG'Ì 3'DG'Ì GH1¯1/Ì H GEH¯'F (G'1Ì ('9+ '4*('G A'5DG 2E'FÌ EÌ'F /H ¯01 ~Ì'~Ì .H14Ì/ '2 GEH¯'F (G'1Ì 4/G '3*. 7HD 5-Ì- 3'D GEH¯'F (G'1Ì óöõ.òôòóöò 1H2 Ì' óöõ.òôòô 1H2 '3*. <br/> FEHFG G'Ì /̯1 'ÌF "4A*¯Ì: <blockquote> «3'D GH1¯1/Ì: 3'DÌ ©G (' /H ¯01 ~Ì'~Ì .H14Ì/ '2 GEH¯'F (G'1Ì *91ÌA EÌ 4H/: óöõ.òôòñù 1H2.» <br/> (Dictionary of Science and Technology, 1992, Academic Press, Inc.) </blockquote> <blockquote> «3'D GH1¯1/Ì: A'5DG Ì 2E'FÌ EÌ'F /H ¯01 ~Ì'~Ì .H14Ì/ '2 GEH¯'F (G'1Ì. 7HD4 óöõ.òôòò 1H2 EÌ'F¯ÌF .H14Ì/Ì.» <br/> (Encyclopedia of Astronomy and Astrophysics, 2001, Institute of Physics Publishing). </blockquote> </p> <p> ñø) <b><u>~Ì4'Ì'F </u></b> (pi&#353;&acirc;y&acirc;n) /1 (1'(1 precession. .H14Ì/ /1 ,F(4 ~/Ì/'1 3'D'FG Ì .H/ (G 3HÌ .'H1 EÌ 1H/. E3Ì1 .H14Ì/  ©G GH1~G F'EÌ/G EÌ 4H/  GEH¯'1 1' /1 /H FB7G B79 EÌ ©F/: GEH¯'F (G'1Ì H GEH¯'F ~'ÌÌ2Ì. (' 13Ì/F .H14Ì/ (G 'ÌF /H FB7G  4( H 1H2 Ì©3'F EÌ 4HF/. GEH¯'F (G'1Ì G1 3'D F3(* (G 3'D ~Ì4 ©EÌ 2H/*1 1HÌ EÌ /G/  (G 3.FÌ /̯1  GEH¯'F (G'1Ì G1 3'D ©EÌ ©E*1 '2 Ì© /BÌBG Ì ©E'F (õð.ó +'FÌG) (G 3HÌ ('.*1 Ì' (G 3HÌ .H14Ì/ ,' (G ,' EÌ 4H/  H /1 F*Ì,G .H14Ì/ E/'14 1' (G 7H1 ©'ED FEÌ ~ÌE'Ì/. 'ÌF ~/Ì/G Ì precession 2'ÌÌ/G Ì FÌ1HG'ÌÌ ¯1'F4Ì '3* ©G E'G (F2/Ì© (G öðj)  .H14Ì/  H 3Ì'1G G' (1 (1 "E/¯Ì GEH¯'1 2EÌF H'1/ EÌ ©FF/ H 1'3*'Ì "3G Ì †1.4 2EÌF 1' *:ÌÌ1 EÌ /G/. precession '2 D'*ÌF præcissionem «~Ì4 (B(D) "E/F»  '2 præcessus 5A* EA9HDÌ præcedere  '2 -præ «~Ì4» + cedere «1A*F». ~Ì4'Ì'F '2 ~Ì4 + "Ì'F '2 "Ì- 3*'© "E/F  '2 A'13Ì ('3*'F H 'H3*'ÌÌ -ay «1A*F»  A'13Ì ('3*'F aitiy  'H3*'ÌÌ aeiti «EÌ 1H/» + -"F ~3HF/ 2E'F H ,'. </p> <p> ñù) 3'D ¯'G4E'1 ¯1¯H1Ì GE (' 3'D GEH¯'F (G'1Ì EB'Ì3G ~0Ì1 '3*  (/ÌF E9F' ©G G/A '5DÌ H '9D'E 4/G Ì ¯'G4E'1 ¯1¯H1Ì 'ÌF (H/ ©G D-8G Ì GEH¯'F (G'1Ì 1' (G *'1Ì. òñ E'13 ~ÌHF/ /G/. ©DÌ3'  /1 F.3*ÌF 4H1'Ì .H/ /1 Nicaea (G 3'D óòõ EÌD'/Ì  òñ E'13 1' (G 9FH'F *'1Ì. 419Ì GEH¯'F (G'1Ì (1'Ì (G ,' "H1/F 9Ì/ ~'© (P&acirc;ques) *5HÌ( ©1/G (H/. 1H2 (1¯2'1Ì 9Ì/ ~'© 9('1* '3* '2 F.3*ÌF Ì©4F(G ~3 '2 F.3*ÌF ~1E'G ©DÌ3'ÌÌ ©G /1 1H2 GEH¯'F (G'1Ì Ì' ~3 '2 "F 1HÌ EÌ /G/. (-+ /1 ('1G Ì 'ÌF©G ¯'G4E'1 ¯1¯H1Ì (' †G /B*Ì EÌ *H'F/ GEH¯'F (G'1Ì 1' /1 òñ E'13 F¯'G /'1/ (Ì1HF '2 -Ì7G Ì 'ÌF Ì'//'4* '3*. </p> <p> òð) <b><u>GEH¯4 </u></b> (hamuge&#353;) (1'(1 91(Ì «E9'/DG» H equation. H'˜G Ì '1H~'ÌÌ '2 D'*ÌF æquatus 5A* EA9HDÌ æquare «(1'(1 ©1/F  GEH'1 ©1/F»  '2 æquus «(1'(1  E3'HÌ» + tion- ~3HF/ '3E 3'2 '2 D'*ÌF tio-. GEH¯4 '2 GEH¯Ì/F  '2 ~GDHÌ GEH¯ «(1'(1  E3'HÌ» + ~3HF/ '3E 3'2 -4. &lArr; GEH¯'F (~'FH4* ñ)  H &lArr; GEH¯'1 (~'FH4* ø). </p> <p> òñ) <b><u>~Ì1'GH1 </u></b> (pir&acirc;hur) /1 (1'(1 perihelion: «FB7G 'Ì '2 E/'1 ,3EÌ ©G (G ¯1/ .H14Ì/ EÌ ¯1// GF¯'EÌ ©G ©E*1ÌF A'5DG 1' '2 .H14Ì/ /'1/.» perihelion '2 H'˜G Ì D'*ÌF perihelium (©~D1  1596)  '2 ÌHF'FÌ -peri «F2/Ì©  '71'A» + helion '2 helios «.H14Ì/». -peri GE1Ì4G '3* (' A'13Ì ('3*'F -pariy  'H3*'ÌÌ -pairi «F2/Ì©  '71'A»  3'F3©1Ì* -pari (G GE'F E9F'G'  A'13Ì FHÌF ~Ì1'-  1Ì4G Ì ~H1H'-GF/-H- '1H~'ÌÌ -per*. H'˜G Ì helios «.H14Ì/»  GE1Ì4G (' .H1 (.H14Ì/)  GH1  'H3*'ÌÌ -hvar  3'F3©1Ì* -surya  D'*ÌF sol  "DE'FÌ Sonne  'F¯DÌ3Ì sun  1Ì4G Ì ~H1H'-GF/-H- '1H~'ÌÌ -sawel* «.H14Ì/». ~Ì1'GH1 '2 ~Ì4HF/ ~Ì1'- (A'13Ì EÌ'FG -p&eacute;r&acirc;  A'13Ì ('3*'F H 'H3*'ÌÌ "F /1 ('D' /'/G 4/G 'F/) + GH1  †F'F©G /1 ('D' FEH/G 4/. </p> <p> òò) <b><u>'~'GH1 </u></b> (ap&acirc;hur) /1 (1'(1 aphelion  (G E9F'Ì «FB7G 'Ì '2 E/'1 ,3EÌ ©G (G ¯1/ .H14Ì/ EÌ ¯1// GF¯'EÌ ©G (Ì4*1ÌF A'5DG 1' '2 .H14Ì/ /'1/.» aphelion '2 D'*ÌF aphelium  '2 ÌHF'FÌ -apo «/H1 '2  /H1  '2». 'ÌF H'˜G GE1Ì4G '3* (' A'13Ì ('3*'F H 'H3*'ÌÌ -ap&acirc; «/H1  /H1 '2»  3'F3©1Ì* -apa  D'*ÌF -ab  "DE'FÌ -af  'F¯DÌ3Ì of, off  1Ì4G Ì ~H1H'-GF/-H-'1H~'ÌÌ -apo*. (.4 /HE 'ÌF H'˜G  helios GE E9F' H GE1Ì4G '3* (' «.H1» /1 «.H14Ì/»  &lArr; ~Ì1'GH1 (~'FH4* òñ). '~'GH1 '2 '~'- (-ap&acirc;) «/H1  /H1 '2» '2 A'13Ì ('3*'F H 'H3*'ÌÌ  †F'F©G /1 ('D' ¯A*G 4/ + GH1 «.H14Ì/». &lArr; ~Ì1'GH1 (~'FH4* òñ). </p> <p> òñ) <b><u>/Ì3HD </u></b> (disul)  /1 (1'(1 formula  '2 D'*ÌF (G E9F'Ì «5H1* ©H†©  4©D ©H†©  B'D( ©H†©»  '2 forma «5H1*  4©D  B'D(» + ~3HF/ ©G4 ulus- (E$F+ ula-  .F+' ulum-). /Ì3HD '2 /Ì3 «5H1*  4©D»  '2 ~GDHÌ dês, dêsag «5H1*  4©D  A1E  3'.*E'F»  E5/1 dêsidan «4©D /'/F  E*4©D ©1/F  3'.*F» + ~3HF/ A'13Ì -'HD  -'HDG ©G E'FF/ ~3HF/ D'*ÌF ©G4 H ©H†©Ì 1' EÌ 13'F/. FEHFG G': 2F¯HDG  ©H*HDG  EN4©HDG (EN4© ©H†©)  *OF¯HDG (*OF¯ ©H†©)  ¯DHDG  ¯HDG (¯HÌ ©H†©)  ,'4HDG (/1 ©1/Ì .1 ©H†©)  H /̯1G'. </p> <p> òô) <b><u>.H1Ì3*'F </u></b> (xorist&acirc;n) /1 (1'(1 solstice H 'FBD'(. H'˜G Ì '1H~'ÌÌ '2 D'*ÌF solstitium  '2 sol «.H14Ì/» + -stit- '2 stes «'Ì3*'F»  GE1Ì4G (' stare «'Ì3*'/F»  ÌHF'FÌ histanai «'Ì3*'F/F»  3'F3©1Ì* -sth&acirc; «'Ì3*'/F»  'H3*'ÌÌ -st&acirc; «'Ì3*'/F»  A'13Ì FHÌF ist&acirc;dan ~H1H'-GF/-H- '1H~'ÌÌ -st&acirc;* «'Ì3*'/F». D'*ÌF sol GE (' .H1  GH1  .H14Ì/ A'13Ì GE1Ì4G '3*. &lArr; GH1¯1/Ì. 3(( 'ÌF F'E¯0'1Ì 'ÌF '3* ©G .H14Ì/ GF¯'E 13Ì/F (G 4E'DÌ *1ÌF (Ì' ,FH(Ì *1ÌF) FB7G Ì E/'14 /1 "3E'F  H ~Ì4 '2 "F©G ('2¯1//  2E'FÌ (G 8'G1 (Ì -1©* EÌ E'F/. &lArr; GH1¯1/Ì (~'FH4* ö). </p> <p> òõ) <b><u>/H3*©'1 </u></b> (dustk&acirc;r) /1 (1'(1 amateur «©3Ì ©G ©'1  A9'DÌ*  GF1  /'F4  Ì' H124Ì 1' (G .'71 31¯1EÌ EÌ ©F/ FG (G 9FH'F ~Ì4G  GE†HF '.*14F'3 /H3*©'1.» amateur '2 D'*ÌF amator «/H3*/'1  9D'BG EF/  9'4B»  '2 amare «/H3* /'4*F». /H3*©'1 '2 /H3* + ©'1. (G BÌ'3 '.*14F'3 /H3*©'1  '.*14F'3 ~Ì4G ©'1 (professional). </p> <h3>('2(1/G' / References </h3> <ul> <li> 9(/ 'DDGÌ  16'  ñó÷õ  *'1Ì. *'1Ì. /1 'Ì1'F  *G1'F  'EÌ1 ©(Ì1 </li> <li> (G1H2  0(Ì-  ñóóñ  *BHÌE H *'1Ì. /1 'Ì1'F  *G1'F  'Ì1'F ©H/G  4E'1G Ì ñõ </li> <li> (Ì14©  '-E/  ñó÷ó  ¯'GF'EG Ì *7(ÌBÌ 3G G2'1 3'DG  (FÌ'/ /'F4FEG Ì (21¯ 'Ì1'FÌ </li> <li> (Ì1HFÌ  '(H 1Ì-'F  óùð G,1Ì BE1Ì  "+'1 'D('BÌG 9F 'DB1HF 'D.'DÌG  *1,EG Ì 9DÌ '©(1 /'F' 314*  *G1'F  ñóõò  'F*4'1* '(F 3ÌF' </li> <li> *BÌ 2'/G  3Ì/ -3F  ñùóø EÌD'/Ì  ¯'G4E'1G'Ì ©GF 'Ì1'FÌ  '+1 (G 2('F 'F¯DÌ3Ì  /'/G 4/G /1 ~'ÌÌF. </li> <li> ED© ~H1  'Ì1,  ñóøó  ~Ì'E 4.5Ì </li> <li> 5Ì'/  E-E/ 16'  ñóöð  *1*Ì( H *B3ÌE ©('!3 1('9Ì H .E'3Ì /1 *'1Ì. ,D'DÌ  ¯2'14 /H'2/GEÌF ©FA1'F3 1Ì'6Ì ©4H1  /'F4¯'G 5F9*Ì '5AG'F  5. óó </li> <li> 5Ì'/  E-E/ 16'  ñó÷ø  /3*'H1/ (113ÌG'Ì 1H4 E-'3('* *BHÌE 15/ FÌE1H2Ì H ,/HD .Ì'EÌ  A1G(¯  H̘G Ì (21¯/'4* .Ì'E  A5DF'EG Ì 9DEÌ-~˜HG4Ì  3'D /H'2/GE  4E'1G G'Ì 'HD-†G'1E  ~Ì'~Ì òù-óò  (G'1-2E3*'F ñó÷ø  'F*4'1 ñó÷ù  5. õó </li> </ul> <div dir="ltr"> <ul> <li> de Bloy, François, 1996, The Persian Calendar, J. Brit. Inst. Persian Studies 34, 39 </li> <li> Borkowski, Kazimierz M., 1996/1997, <a href="http://www.astro.uni.torun.pl/~kb/Papers/EMP/PersianC-EMP.htm" target="_blank">The Persian calendar for 3000 years</a>, Earth, Moon and Planets 74, No 3, 223 </li> <li> Bretagnon, Pierre, Rocher, Patrick, 2001, Du Temps universel au Temps coordonn&eacute;e barycentrique, Revue du Palais de la D&eacute;couverte 285, f&eacute;vrier, p. 39 </li> <li> Briant, Pierre, Histoire de l'Empire Perse, 1996, Fayard, p. 292 </li> <li> Cassidy, Simon, 1996, <a href="http://www.angelfire.com/dc2/calendrics/index.html#top" target="_blank">Error in Statement of Tropical Year</a> </li> <li> <a href="http://www.iranica.com/" target="_blank">Encyclopedia Iranica</a>, ed. Ehsan Yarshater, Columbia University, Eisenbrauns, Inc., Winona Lake, Indiana </li> <li> Meeus, Jean, 2002, More Mathematical Astronomy Morsels, William-Bell Inc., Richmond, Virginia, Ch. 63 </li> <li> Meeus, Jean, Savoie, Denis, 1992, The history of the tropical year, J. Br. Astron. Assoc. 102, 1 </li> <li> Morrison, L.V., Stephenson, F.R., 1982, Sun and Planetary System 96, 73, Reidel, Dordrecht </li> <li> O'Connor, John J., Robertson, Edmund F., 1999, <a href="http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Khayyam.html" target="_blank">The MacTutor History of Mathematics archive, Omar Khayyam</a> </li> <li> Seidelmann, P. K., Guinot, B., Doggett, L.E., 1992, in Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, Californian, ed. P. K. Seidelmann, p. 80 </li> <li> Settegast, Mary, 2005, When Zarathustra Spoke: The Reformation of Neolithic Culture and Religion, Bibliotheca Iranica: Zoroastrian Studies </li> <li> Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touz&eacute;, M., Francou, G., Laskar, J., 1994, Astron. & Astrophy. 282, 663 </li> <li> Stephenson, F. Richard, 2003, Historical eclipses and Earth's rotation, <a href="http://www.ras.org.uk/pdfs/Stephenson.pdf" target="_blank">Astronomy & Geophysics 44 (2)</a>, 2.22 </li> <li> Stephenson, F.R., Houlden, M.A., 1986, Atlas of Historical Eclipse Maps, page x, Cambridge University Press </li> <li> Taqiz&acirc;deh, S. H., 1938, <a href="http://www.avesta.org/taqizad.htm" target="_blank">Old Iranian Calendars</a>, Royal Asiatic Society </li> <li> Youschkevitch, A.P., Rosenfeld, B.A., 1973, "al-Khayyami", Dictionary of Scientific Biography VIII, p. 323 </ul> </div> <h3>AG13* '57DD'-G'Ì (G ©'1 1A*G /1 'ÌF EB'DG (' (1'(1G'Ì 'F¯DÌ3Ì "FG'</h3> <table border="2" cellpadding="2" cellspacing="5" align="center"> <tr> <td bgcolor="#ffcccc" align="center" width="250"><b>A'13Ì</b></td> <td bgcolor="#ccccff" align="center" width="120"><b>'F¯DÌ3Ì</b></td> </tr> <tr> <td bgcolor="#ffcccc" align="center"> "3G <br/>(&acirc;s&eacute;) </td> <td bgcolor="#ccccff" align="center">axis</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">'~'GH1 <br/>(ap&acirc;hur)</td> <td bgcolor="#ccccff" align="center">aphelion</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">'.*14F'3<br/>(axtar&#353;en&acirc;s)</td> <td bgcolor="#ccccff" align="center">astronomer</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">'.*14F'3 ~Ì4G ©'1<br/>(axtar&#353;en&acirc;s-e pi&#353;ek&acirc;r)</td> <td bgcolor="#ccccff" align="center">professional astronomer</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">'.*14F'3 /H3*©'1<br/>(axtar&#353;en&acirc;s-e dustk&acirc;r)</td> <td bgcolor="#ccccff" align="center">amateur astronomer</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">'.*14F'3Ì<br/>(axtar&#353;en&acirc;si)</td> <td bgcolor="#ccccff" align="center">astronomy</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">'.*1AÌ2Ì©<br/>(axtarfizik) </td> <td bgcolor="#ccccff" align="center">astrophysics</td> </tr> <tr> <td bgcolor="#ffcccc" align="center"> 'F/1¯'G  *1HA*G  /2/Ì/G <br/>(andarg&acirc;h, taruft&eacute;, dozdid&eacute;)</td> <td bgcolor="#ccccff" align="center">epagomena</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">'F/1¯'G'F  1H2 G'Ì *1HA*G  1H2 G'Ì /2/Ì/G<br/>(andarg&acirc;h&acirc;n ruzh&acirc;-ye taruft&eacute;, ruzh&acirc;-ye dozdid&eacute;)</td> <td bgcolor="#ccccff" align="center">epagomenae<br/>epagomenal days</td> </tr> <tr> <td bgcolor="#ffcccc" align="center"> 'F/1GD4<br/>(andarhele&#353;)</td> <td bgcolor="#ccccff" align="center">intercalation</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">'F/1GDÌ<br/>(andarheli)</td> <td bgcolor="#ccccff" align="center">intercalary, leap</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">'F/1GDÌ/F<br/>(andarhelidan)</td> <td bgcolor="#ccccff" align="center">to intercalate</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">('2(1/<br/>(b&acirc;zbord)</td> <td bgcolor="#ccccff" align="center">reference</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">('2/Ì3Ì<br/>(b&acirc;zdisi)</td> <td bgcolor="#ccccff" align="center">reform</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">(F ~'1<br/>(bonp&acirc;r)</td> <td bgcolor="#ccccff" align="center">element</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">~Ì1'GH1<br/>(pir&acirc;hur)</td> <td bgcolor="#ccccff" align="center">perihelion</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">~Ì4'Ì'F<br/>(pi&#353;&acirc;y&acirc;n)</td> <td bgcolor="#ccccff" align="center">precession</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">*'13Ì*<br/>(t&acirc;rsit)</td> <td bgcolor="#ccccff" align="center">website</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">*1'/'/<br/>(tar&acirc;d&acirc;d)</td> <td bgcolor="#ccccff" align="center">tradition</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">†1.G<br/>(carx&eacute;)</td> <td bgcolor="#ccccff" align="center">cycle</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">.E<br/>(xam)</td> <td bgcolor="#ccccff" align="center">curve</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">.H1Ì3*'F<br/>(xorist&acirc;n)</td> <td bgcolor="#ccccff" align="center">solstice</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">.H1Ì3*'F *'(3*'FÌ<br/>(xorist&acirc;n-e t&acirc;best&acirc;ni)</td> <td bgcolor="#ccccff" align="center">summer solstice</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">.H1Ì3*'F 2E3*'FÌ<br/>(xorist&acirc;n-e zemest&acirc;ni)</td> <td bgcolor="#ccccff" align="center">winter solstice</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">/1'2'<br/>(der&acirc;z&acirc;)</td> <td bgcolor="#ccccff" align="center">length</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">/1˜F'<br/>(dere n&acirc;)</td> <td bgcolor="#ccccff" align="center">longitude</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">/H3*©'1<br/>(dustk&acirc;r)</td> <td bgcolor="#ccccff" align="center">amateur</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">/Ì3HD<br/>(disul)</td> <td bgcolor="#ccccff" align="center">formula</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">/Ì3G<br/>(dis&eacute;)</td> <td bgcolor="#ccccff" align="center">form</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">1'3* 'A1'2<br/>(r&acirc;st afr&acirc;z)</td> <td bgcolor="#ccccff" align="center">right ascension</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">1'˜E'F<br/>(r&acirc;~m&acirc;n)</td> <td bgcolor="#ccccff" align="center">system</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">1'Ì'F¯1<br/>(r&acirc;y&acirc;ngar)</td> <td bgcolor="#ccccff" align="center">computer</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">1H2Ì,<br/>(ruzij)</td> <td bgcolor="#ccccff" align="center">ephemeris</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">2E'F 4'1EF/<br/>(zam&acirc;n-e &#353;&acirc;rmand)</td> <td bgcolor="#ccccff" align="center">civil time</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">2ÌEG<br/>(zim&eacute;)</td> <td bgcolor="#ccccff" align="center">epoch</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">3'D .H1Ì3*'FÌ<br/>(s&acirc;l-e xorist&acirc;ni)</td> <td bgcolor="#ccccff" align="center">solstitial year</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">3'D GEH¯'FÌ<br/>(s&acirc;l-e hamug&acirc;ni)</td> <td bgcolor="#ccccff" align="center">equinoctial year</td> </tr> <tr> <td bgcolor="#ffcccc" align="center"> 3'D GEH¯'F (G'1Ì <br/> (s&acirc;l-e hamug&acirc;n-e bah&acirc;ri)<br/> 3'D FH1H2 <br/> (s&acirc;l-e nowruz) </td> <td bgcolor="#ccccff" align="center">vernal-equinox year</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">3'D GH1¯1/Ì<br/>(s&acirc;l-e hurgardi)</td> <td bgcolor="#ccccff" align="center">tropical year</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">4'1EF/<br/>(&#353;&acirc;rmand)</td> <td bgcolor="#ccccff" align="center">civil</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">A1'2'<br/>(far&acirc;z&acirc;)</td> <td bgcolor="#ccccff" align="center">altitude</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">¯'G4E'1<br/>(g&acirc;h&#353;om&acirc;r)</td> <td bgcolor="#ccccff" align="center">calendar</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">¯'G4E'1Ì<br/>(g&acirc;h&#353;om&acirc;ri)</td> <td bgcolor="#ccccff" align="center">time reckoning</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">¯1'F4<br/>(ger&acirc;ne&#353;)</td> <td bgcolor="#ccccff" align="center">gravitation</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">E/'1<br/>(mad&acirc;r)</td> <td bgcolor="#ccccff" align="center">orbit</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">F~'G4<br/>(nep&acirc;he&#353;)</td> <td bgcolor="#ccccff" align="center">observation</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">F~'G4¯'G<br/>(nep&acirc;he&#353;g&acirc;h)</td> <td bgcolor="#ccccff" align="center">observatory</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">F~'G¯1  F~'GF/G<br/>(nep&acirc;hgar, nep&acirc;hand&eacute;)</td> <td bgcolor="#ccccff" align="center">observer</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">F~'GÌ/F<br/>(nep&acirc;hidan)</td> <td bgcolor="#ccccff" align="center">to observe</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">F¯1G<br/>(negar&eacute;)</td> <td bgcolor="#ccccff" align="center">theory</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">FÌE1H2'F<br/>(nimruz&acirc;n)</td> <td bgcolor="#ccccff" align="center">meridian</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">H'¯4H/<br/>(v&acirc;go&#353;ud)</td> <td bgcolor="#ccccff" align="center">resolution</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">GEH¯'1<br/>(hamug&acirc;r)</td> <td bgcolor="#ccccff" align="center">equator</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">GEH¯'F<br/>(hamug&acirc;n)</td> <td bgcolor="#ccccff" align="center">equinox</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">GEH¯'F (G'1Ì<br/>(hamug&acirc;n-e bah&acirc;ri)</td> <td bgcolor="#ccccff" align="center">vernal (spring) equinox</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">GEH¯'F ~'ÌÌ2Ì<br/>(hamug&acirc;n-e p&acirc;yizi)</td> <td bgcolor="#ccccff" align="center">autumnal equinox</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">GEH¯4<br/>(hamuge#353;)</td> <td bgcolor="#ccccff" align="center">equation</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">GEH¯Ì/F<br/>(hamugidan)</td> <td bgcolor="#ccccff" align="center">to equate</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">GH1~G<br/>(hurpeh)</td> <td bgcolor="#ccccff" align="center">ecliptic</td> </tr> <tr> <td bgcolor="#ffcccc" align="center">GH1¯1/Ì<br/>(hurgardi)</td> <td bgcolor="#ccccff" align="center">tropical</td> </tr> </table> <p>&nbsp;</p> <p>&nbsp;</p> <hr> <img src="http://aramis.obspm.fr/~heydari/dictionary/flower-border.gif" width="100%" align="middle"> <hr> <br /> <div dir="ltr"> <font size="-1"> &copy; Copyright 2004-2008 by <a href="../contact.html">M. Heydari-Malayeri</a> <br> <a href="../"><img src="../images/home2.gif" alt="[calvin]" width="35" align="left"></a> <img src="../images/perroquet.gif" width="17"> <a href="http://www.obspm.fr/obsparis.fr.shtml">Observatoire de Paris</a> <img src="../images/perroquet.gif" width="17"> <a href="http://aramis.obspm.fr/lerma.shtml">LERMA</a> <img src="../images/perroquet.gif" width="17"> <br/> Last updated: 01 August 2008 </font> </div> <p>&nbsp;</p> </body> </html>