,,pap]s ,,( ,,! ,,peabody ,,museum ,,( ,,am]ican ,,ar*aeology ,,& ,,e?nology1 ,,h>v>d ,,univ]sity ,,vol4 ,,vi4--,,no4 #b ,a ,,possible ,,solution ,,( ,,! ,,numb] ,,s]ies ,,on ,,pages #ea ,,to #eh ,,( ,,! ,,dresd5 ,,codex ,,by ,,c>l ,e4 ,,gu! ,,cambridge1 ,,mass4 ,,publi%$ ,,by ,,! ,,museum #aiba ,,copyright1 #aiba ,,by ,,! ,,peabody ,,museum ,,( ,,am]ican ,,ar*aeology ,,& ,,e?nology1 ,,h>v>d ,,univ]sity ,,note ,! solution set =? 9 ?is pap] =m$ a "p ( a !sis = ! degree ( ,doctor ( ,philosophy1 tak5 9 ,an?ropology at ,h>v>d ,univ]sity4 ,?anks are due ,dr4 ,a4 ,m4 ,tozz] ( ,h>v>d ,univ]sity1 & ,mr4 ,s4 ,g4 ,morley ( ,! ,c>negie ,in/itution ( ,wa%+ton1 = ! int]e/ !y h tak5 9 my "w & ! valuable aid !y h giv54 ,i mu/ ?ank especially ,pr(essor ,r4 ,w4 ,willson ( ! ,a/ronomical ,dep>tm5t ( ,h>v>d = ! ine/imable help & unfail+ pati5ce he has contribut$ to my "w4 ,!re are _m /atem5ts ?r\gh\t ?is pap] :i* are ! direct result ( 8 tea*+s4 ,i wi% also to ?ank ,mr4 ,*>les ,p4 ,b[dit*1 )\t ^: inspiration & aid ?is "w w\ld n h be5 accompli%$4 ,,c>l ,e4 ,,gu! ,,&ov]1 ,,massa*usetts ,july1 #aiai ,a ,,possible ,,solution ,,( ,,! ,,numb] ,,s]ies ,,on ,,pages #ea ,,to #eh ,,( ,,! ,,dresd5 ,,codex ,,description ,9 ! ,dresd5 ,codex1 "o ( ! ?ree ,maya manuscripts 9 exi/5ce1 !re is f\nd a s]ies ( numb]s cov]+ eight pages1 #ea to #eh 7plate ,i74 ,z e>ly z #ahhf1 ,dr4 ,fr/emann recogniz$ ?is s]ies z an important "o1 & "o :i* probably ref]r$ to ! moon 9 "s way4 ,ea* page is divid$ into an upp] & a l[] half designat$1 respectively1 8a0 & 8b40 ,pages #ea;a & #eb;a =m a unit 9 !mselves1 b are cle>ly associat$ ) ! rema9+ pages4 ,! probable mean+ ( ?is gr\p is /ill s d\btful t x has be5 deem$ be/ to omit entirely a discussion ( x at ! pres5t "t4 ,! rema9+ sections ( ^! pages =m "o long s]ies ( numb]s :i* %\ld be read f left to "r1 beg9n+ at #ec;a1 read+ to #eh;a1 cont9u+ on #ea;b1 & end+ ! s]ies at #eh;b4 ,ea* half-page is divid$1 horizontally1 into f\r sections4 ,! upp] section consi/s ( two r[s ( hi]oglyphs4 ,! section j bel[ x conta9s a s]ies ( black numb]s :i* increase 9 value f left to "r4 ,! ?ird section consi/s ( ?ree r[s ( day glyphs ) r$ numb]s atta*$ to !m4 ,! int]val betwe5 ! glyphs 9 successive r[s c1 ( c\rse1 be ma!matically obta9$4 ,! la/1 & bottom1 division ( ! page is fill$ ) a s]ies ( black numb]s :i* are ( ?ree values only1 namely1 #agg1 #adh1 & #agh1 ( :i* ! fir/ is ! mo/ frequ5t4 ,at m or less regul> int]vals a v]tical /rip is run f ! top ( ! half-page to ! bottom4 ,?is /rip conta9s1 9 ! upp] "p1 eight or t5 glyphs4 ,bel[ !m 9 all b ! fir/ /rip is a con/ellation b&1 & bel[ t a figure ( "s k9d4 ,^! /rips divide ! numb] s]ies into gr\ps1 & are call$ 8pictures10 occurr+ on t5 ( ! f\rte5 half-pages4 ,consid]$ v]tically ! pages are compos$ ( columns4 ,ea* column conta9s1 beg9n+ at ! top1 two hi]oglyphs1 a long numb]1 ?ree day glyphs1 & _! numb]s1 & f9ally1 at ! bottom1 a %ort numb]4 ,! pictures occur betwe5 ^! columns4 ,! s]ies cov]s a p]iod ( #aa1ifj days1 al?\gh ! la/ numb] record$ 9 ! upp] s]ies is only #aa1ieh4 ,by means ( ! columns ?is p]iod ( #aa1ifj days is divid$ into #fi unequal p>ts4 ,let columns #b1 #c1 & #d on page #ed;b be tak5 z examples4 ,!n ea* column 9 ! s]ies %\ld be read 9 ! foll[+ mann]3#a ,! l[] numb] ( column #c is #h4ag or #agg4 ,add ?is numb] to ! upp] numb] ( column #b1 :i* is #a4 #b4 #aa4 #i or #hadi4 ,! result is #hcbf :i* is express$ correctly z #a4 #c4 #b4 #f 9 ! upp] numb] ( column #c4 ,! l[] numb] %\ld also be add$ to ! upp] day glyph ( column #b1 :i* is #aj ,caban1 giv+ #e ,ix1 :i* is ! day glyph & numb] appe>+ z ! fir/ 9 column #c4 ,! second day glyph & numb] is t ( ! day foll[+ #e ,ix1 namely #f ,m54 ,simil>ly1 #g ,cib is ! day aft] #f ,m54 ,go+ ?r\gh ! same process = column #d1 #adh1 t is1 ! l[] numb] #g4 #h ( t column1 %\ld be add$ to #hcbf to obta9 #hdgd1 :i* is express$ 9 ! upp] numb] ( column #d z #a4 #c4 #i4 #ad4 ,likewise1 #adh days aft] #e ,ix comes #aj ,ik1 :i* is ! upp] day glyph ( column #d1 & bel[ :i* are f\nd ! two days imm$iately foll[+1 namely1 #aa ,akbal & #ab ,kan4 #a ,= ^? unacqua9t$ ) ,maya ari?metic ! foll[+ po9ts w expla9 matt]s3 ! ,mayas us$ ! vigesimal sy/em ( enum]ation2 !y c\nt$ by tw5ties in/ead ( t5s4 ,a b> repres5t$ five1 & a dot /ood = "o4 ,!y repres5t$ numb]s l>g] ?an tw5ty by position1 j z we d4 ,h[ev]1 in/ead ( hav+ ! smalle/ d5om9ation at ! "r & ! l>ge/ at ! left ( a horizontal s]ies ( figures1 !y _h ! smalle/ at ! bottom & ! l>ge/ at ! top ( a column ( numb]s4 ,in/ead ( ea* unit 9 a giv5 position repres5t+ t5 times ! value ( t ( ! prec$+ position1 x repres5t$ tw5ty times ! value1 except 9 ! ?ird position :]e x 0 only eighte5 times z great4 ,?us ea* unit ( ! bottom numb] repres5t$ "o 7,k971 t ( ! numb] above x tw5ty 7,u9al71 t ( ! ?ird numb] #bj #ah or #cfj 7,tun71 t ( ! f\r? position #bj #cfj or #gbjj 7,katun71 etc4 ,= ease 9 h&l+1 ^! numb]s are writt5 9 our script ) arabic num]als1 ! bottom numb] on ! "r1 & sep>at$ by p]iods4 ,?us 9 column ?ree1 page #ec;a1 ! upp] numb] is #a4 #g4 #b1 :i* means t ! k9 ( ?is gr\p is #b1 ! ,u9al #g1 7#g #bj7 & ! ,tun #a 7#a #cfj71 mak+ 9 all #b #adj #cfj or #ejb4 ,! ,maya cal5d>1 l ours1 consi/$ ( a s]ies ( numb]s & a s]ies ( names = ea* day1 ea* s]ies repeat+ itself con/antly1 irrespective ( ! o!r4 ,!re 7 tw5ty diff]5t day names1 :i* rema9$ 9 an un*angeable ord]1 & ?irte5 numb]s4 ,9 ! pages "u discussion ^! day names appe> z glyphs prec$$ by ! necess>y numb]4 ,= fur!r details consult ,s4 ,g4 ,morley1 ,an ,introduction to ,maya ,hi]oglyphs1 ,bullet9 #eg1 ,bureau ( ,am]ican ,e?nology1 ,wa%+ton1 ,d4 ,c41 #aiae1 & ,c4 ,p4 ,b[dit*1 #aiaj4 ,9 %ort1 !n1 ! ideal arrangem5t ( ! s]ies is z foll[s3 ,ea* upp] numb] is ! sum ( all ! l[] numb]s ( ! prec$+ columns & its own column4 ,ea* l[] numb] expresses ! diff]5ce betwe5 ! upp] numb] ( its own column & t ( ! column imm$iately prec$+ x4 ,! day names & numb]s are ?ree horizontal s]ies1 ea* />t+ a day lat] ?an ! "o above x1 & record+ ?ree sets ( day names & numb]s :i* w\ld fit ! s]ies =m$ by ! upp] numb]s4 ,x %\ld be notic$ t ! ma!matical int]pretation ( ! s]ies does n appe> to dep5d 9 any way ^u ! hi]oglyphs appe>+ at ! top ( ! columns1 or ^u ! pictures4 ,?is s]ies deals q cle>ly ) synodical revolutions ( ! moon4 ,! entire s]ies records #aa1ifj days1 al?\gh ! la/ numb] 9 ! upp] s]ies is only #aa1ieh1 a condition t w be expla9$ lat]4 ,f\r hundr$ & five synodical revolutions ( ! moon consume1 accord+ to mod]n a/ronomy1 #aa1iei4hhi days1 or ab\t 4#aa ( a day less ?an ! l5g? ( ! s]ies4 ,moreov]1 ! diff]5ce gr\ps #adh1 #agg1 & #agh :i* sep>ate ! upp] numb]s1 also record synodical mon?s1 = five mon?s consume #adg4fe days1 & six mon?s #agg4ah days4 ,9 fact ! correspond5ce betwe5 ! numb]s 9 ! s]ies & ! synodical mon?s is s exact1 t n[h]e does an error ( m ?an "o day exi/4#b #b ,b[dit*1 #aiaj1 pp4 #bbb1 #bbc4 ,un=tunately ! ideal arrangem5t giv5 above is n foll[$ exactly4 ,! actual s]ies z x occurs 9 ! manuscript appe>s to be full ( errors1 a li/ ( :i* w be f\nd 9 ,table ,i1 p4 #d4 ,mo/ ( ^! errors h be5 po9t$ out & discuss$ repeat$ly4#c ,!re /ill exi/s "s d\bt z to :i* numb]s %\ld be consid]$ errors ( ! orig9al writ] & :i* %\ld be tak5 at _! face value4 ,= ?is reason ! errors are "h discuss$ 9 "s detail1 = 9 "s cases ! errors1 or suppos$ errors1 affect !ories 9 reg>d to ! s]ies4 #c ,by ,dr4 ,fr/emann1 ,dr4 ,?omas1 & ,mr4 ,b[dit*4 ,,table ,i ,,app>5t ,,irregul>ities ,l[] numb] s]ies3 ,abs5ce ( all #agh's t occur 9 upp] s]ies4 ,column #bc4 ,pres5ce ( #agh4 ,column #bf4 #agg in/ead ( #adh4 ,column #ej4 #aeg 8 8 #agg4 ,upp] numb] s]ies3 ,column #a4 #aeg in/ead ( #agg4 ,column #b4 #cec 8 8 #ced4 ,column #d4 #fgd 8 8 #fgi4 ,column #aj4 #agdh 8 8 #agdb4 ,column #ab4 #bjaf 8 8 #bjif4 ,column #ad4 #cadb4 8 8 #bdbb4 ,column #ae4 #beih 8 8 #beii4 ,column #bd4 #dafd 8 8 #dafc4 ,day s]ies3 ,column #e4 #d ,*ic*an in/ead ( #aa ,*ic*an4 ,column #aa4 ,omission ( #a_/b tonalamatl4 ,column #ag4 #a ,ik in/ead ( #b ,ik4 ,column #cf4 #d ,b5 in/ead ( #d ,ahau4 ,column #dg4 #aj ,eznab in/ead ( #aa ,eznab4 ,column #di4 #aa ,kan in/ead ( #ab ,kan4 ,columns3 ,columns #f & #g are rev]s$4 ,columns #eh & #ei are rev]s$4 ,totals3 ,upp] numb] s]ies totals #aa1ieh in/ead ( #aa1ifj4 ,day s]ies totals #aa1iei in/ead ( #aa1ifj4 ,9 ,table ,,ii1 pp4 #f1 #g1 bo? ! correct$ & ! uncorrect$ s]ies are giv54 ,9 ! c5tre ( ! table are ?ree columns conta9+ ! actual table4 ,! ?ird column conta9s ! uncorrect$ upp] numb]2 ! f\r? ! l[] numb]2 & ! fif? ! fir/ day sign & its numb]4 ,s9ce ! o!r two day s]ies agree1 except 9 a v few cases :i* w be m5tion$ lat]1 ) ! fir/ s]ies1 !y h be5 omitt$ f ! table4 ,! six? column conta9s ! day signs z !y probably %\ld occur1 & ! second conta9s ! correct$ upp] numb]4 ,! fir/ column gives ! pages ( ! manuscript & ! numb] ( ! columns on ea* 9 ord] to facilitate ref]5ce to ! manuscript4 ,ea* column ( ,table ,,ii1 ) ! exception ( ! fir/ & f\r?1 is compos$ ( two s]ies ( numb]s1 s9ce ea* int]val betwe5 ! numb]s ( ! manuscript has be5 plac$ 9 p>5!ses aft] ! la/ ( ! pair ( numb]s x deals )1 9 ord] to facilitate comp>ison ) ! l[] numb]s4 ,! names & numb]s 9 ! fif? column :i* h p>5!ses h be5 oblit]at$ 9 ! manuscript1 b are easily inf]r$ f ! o!r two r[s ( day signs & numb]s4 ,! mo/ prom95t irregul>ity is ! abs5ce ( ! numb] #agh 9 ! l[] numb]s :5 ! diff]5ces 9 bo? ! day s]ies & ! upp] numb]s %[ t #agh %\ld be ! diff]5ce4 ,?is occurs 9 columns #g1 #ad1 #bi1 #cg1 #eb & #fj ( ! manuscript4 ,! only place 9 :i* #agh does occur 9 ! l[] numb] is 9 column #bc1 :5 x agrees ) ! diff]5ce 9 ! day s]ies1 b n ) t ( ! upp] numb]4 ,9 o!r words1 ! six occurr5ces ( ! #agh-;day gr\p 9 ! upp] numb]s are neglect$ 9 ! l[] numb]s1 & ! only occurr5ce ( #agh 9 ! l[] numb]s does n agree ) ! upp] numb]s4 ,?is implies t x is ( deep] significance ?an a m]e error4 ,!re is ano!r disagreem5t betwe5 ! upp] & l[] numb]s :i* c\ld v well be ! result ( c>elessness4 ,9 column #bf1 ! l[] numb] is #agg1 :ile bo? ! upp] numb] & ! day s]ies give a diff]5ce ( #adh4 ,?is is ! only case 9 :i* ! diff]5ces ( #adh are n f\nd at ! same place 9 all s]ies1 &1 consequ5tly1 is probably an error ( ! scribe4 ,aga9 9 ! l[] numb] ( column #ej1 ! c>eless omission ( "o dot 9 ! ,u9al place has result$ 9 ! record ( #aeg in/ead ( ! correct numb]1 #agg4 ,) "o exception all ( ! errors 9 ! upp] numb]s occur 9 ! fir/ ?ird ( ! s]ies4 ,t exception1 i4e41 ! writ+ ( #dafd = #dafc 9 ! column #bd1 may be expla9$ by ! fact t ! writ] ( ! s]ies _h j add$ 9 column #bc ! extra day to ! day s]ies1 :i* ?rew x out ( agreem5t ) ! upp] numb]s4 ,= ! mom5t ?is fact slipp$ 8 m9d1 b he correct$ ! mi/ake by subtract+ "o day f ! diff]5ce betwe5 ! upp] numb]s ( columns #bd & #be4 ,,table ,,ii 7#a7 7#b7 7#c7 7#d7 7#e7 7#f7 ,page ,correct$ ,uncorrect$ & upp] upp] ,l[] ,uncorrect$ ,correct$ ,column numb] numb] numb] day signs day signs #j #aa ,manik #ec;a #a #agg 7#agg7 #aeg #agg #f ,kan #f ,kan 7#agg7 #b #ced 7#agg7 #cec 7#aif7 #agg #a ,imix 7#agg7 #a ,imix 7#agg7 #c #ejb 7#adh7 #ejb 7#adi7 #adh #f ,muluc 7#adh7 #f ,muluc 7#adh7 ,,picture #d #fgi 7#agg7 #fgd 7#agb7 #agg #a ,cimi 7#agg7 #a ,cimi 7#agg7 #e #hef 7#agg7 #hef 7#ahb7 #agg #i ,akbal 7#agg7 #i ,akbal 7#agg7 #f #ajcd 7#agh7 #ajcc 7#agg7 #agg #d 7,ahau7 7#agg7 #e ,imix 7#agh7 #ed;a #g #abaa 7#agg7 #abaa 7#agh7 #agg 7#ac7 ,enzab 7#agh7 #ac ,enzab 7#agg7 #h #achh 7#agg7 #achh 7#agg7 #agg #h ,m5 7#agg7 #h ,m5 7#agg7 #i #aefe 7#agg7 #aefe 7#agg7 #agg #c ,eb 7#agg7 #c ,eb 7#agg7 #aj #agdb 7#agg7 #agdh 7#ahc7 #agg #aa ,muluc 7#agg7 #aa ,muluc 7#agg7 #aa #aiai 7#agg7 #aiai 7#aga7 #agg #f ,cib 7 #dg7 #f ,cimi 7#agg7 #ab #bjif 7#agg7 #bjaf 7 #ig7 #agg #a ,akbal 7#cjg7 #a ,akbal 7#agg7 #ac #bbdd 7#adh7 #bbdd 7#bhh7 #adh #f ,*u5 7#adh7 #f ,*u5 7#adh7 #ee;a ,,picture #ad #bdbb 7#agh7 #cadb 7#hih7 #agg #b ,muluc 7#agh7 #b ,muluc 7#agh7 #ae #beii 7#agg7 #beih 7-#edd7 #agg #aj ,cimi 7#agg7 #aj ,cimi 7#agg7 #af #bggf 7#agg7 #bggf 7#agh7 #agg #e ,akbal 7#agg7 #e ,akbal 7#agg7 #ag #biec 7#agg7 #biec 7#agg7 #agg #ac ,ahau 7#agg7 #ac ,ahau 7#agg7 #ah #cacj 7#agg7 #cacj 7#agg7 #agg #h 8 8 #h ,caban 7#agg7 #ef;a #ai #cbgh 7#adh7 #cbgh 7#adh7 #adh 8 ,*ic*an 8 #ac ,*ic*an 7#adh7 ,,picture #bj #cdee 7#agg7 #cdee 7#agg7 #agg #h ,ik 7#agg7 #h ,ik 7#agg7 #ba #cfcb 7#agg7 #cfcb 7#agg7 #agg #c ,cauac 7#agg7 #c ,cauac 7#agg7 #bb #chji 7#agg7 #chji 7#agg7 #agg #aa ,cib 7#agg7 #aa ,cib 7#agg7 #eg;a #bc #cihf 7#agg7 #cihf 7#agg7 #agh #g ,ix 7#agh7 #g ,ix 7#agh7 #bd #dafc 7#agg7 #dafd 7#agh7 #agg #b ,*u5 7#agg7 #b ,*u5 7#agg7 #be #dcdj 7#agg7 #dcdj 7#agf7 #agg #aj ,lamat 7#agg7 #aj ,lamat 7#agg7 #bf #ddhh 7#adh7 #ddhh 7#adh7 #agg #b ,cib 7#adh7 #b ,cib 7#adh7 ,,picture #eh;a #bg #dffe 7#agg7 8 8 #agg #aj ,b5 7#agg7 #aj ,b5 7#agg7 #bh #dhdb 7#agg7 #dhdb 8 #agg #e ,oc 7#agg7 #e ,oc 7#agg7 #bi #ejbj 7#agh7 #ejbj 7#agh7 #agg #a ,lamat 7#agh7 #a ,lamat 7#agh7 #cj #eaig 7#agg7 #eaig 7#agg7 #agg #i ,*ic*an7#agg7 #i ,*ic*an 7#agg7 #ea;b #ca #ecgd 7#agg7 #ecgd 7#agg7 #agg #d ,ik 7#agg7 #d ,ik 7#agg7 #cb #eeea 7#agg7 #eeea 7#agg7 #agg #ab ,cauac 7#agg7 #ab ,cauac 7#agg7 #cc #egbh 7#agg7 #egbh 7#agg7 #agg #g ,cib 7#agg7 #g ,cib 7#agg7 #cd #eije 7#agg7 #eije 7#agg7 #agg #b ,b5 7#agg7 #b ,b5 7#agg7 #ce #fjhb 7#agg7 #fjhb 7#agg7 #agg #aj ,oc 7#agg7 #aj ,oc 7#agg7 #cf #fbcj 7#adh7 #fbcj 7#adh7 #adh #b ,enzab 7#adh7 #b ,enzab 7#adh7 #eb;b ,,picture #cg #fdjh 7#agh7 #fdjh 7#agh7 #agg #aa ,cib 7#agh7 #aa ,cib 7#agh7 #ch #fehe 7#agg7 #fehe 7#agg7 #agg #f ,b5 7#agg7 #f ,b5 7#agg7 #ci #fgfb 7#agg7 #fgfb 7#agg7 #agg #a ,oc 7#agg7 #a ,oc 7#agg7 #dj #fici 7#agg7 #fici 7#agg7 #agg #i ,manik 7#agg7 #i ,manik 7#agg7 #ec;b #da #gaaf 7#agg7 #gaaf 7#agg7 #agg #d ,kan 7#agg7 #d ,kan 7#agg7 #db #gbfd 7#adh7 #gbfd 7#adh7 #adh #i ,eb 7#adh7 #i ,eb 7#adh7 ,,picture #dc #gdda 7#agg7 #gdda 7#agg7 #agg #d ,muluc 7#agg7 #d ,muluc 7#agg7 #dd #gfah 7#agg7 #gfah 7#agg7 #agg #ab ,cimi 7#agg7 #ab ,cimi 7#agg7 #de #ggie 7#agg7 #ggie 7#agg7 #agg #g ,akbal 7#agg7 #g ,akbal 7#agg7 #ed;b #df #gigb 7#agg7 #gigb 7#agg7 #agg #b ,ahau 7#agg7 #b ,ahau 7#agg7 #dg #hadi 7#agg7 #hadi 7#agg7 #agg #aj ,caban 7#agg7 #aj ,caban 7#agg7 #dh #hcbf 7#agg7 #hcbf 7#agg7 #agg #e ,ix 7#agg7 #e ,ix 7#agg7 #di #hdgd 7#adh7 #hdgd 7#adh7 #adh #aj ,ik 7#adh7 #aj ,ik 7#adh7 ,,picture #ej #hfea 7#agg7 #hfea 7#agg7 #aeg #e ,cauac 7#agg7 #e ,cauac 7#agg7 #ee;b #ea #hhbh 7#agg7 #hhbh 7#agg7 #agg #ac ,cib 7#agg7 #ac ,cib 7#agg7 #eb #ijjf 7#agh7 #ijjf 7#agh7 #agg #i ,ix 7#agh7 #i ,ix 7#agh7 #ec #iahc 7#agg7 #iahc 7#agg7 #agg #d ,*u5 7#agg7 #d ,*u5 7#agg7 #ed #icfj 7#agg7 #icfj 7#agg7 #agg #ab ,lamat 7#agg7 #ab ,lamat 7#agg7 #ee #iecg 7#agg7 #iecg 7#agg7 #agg #g ,*ic*an 7#agg7 #g ,*ic*an 7#agg7 #ef #igad 7#agg7 #igad 7#agg7 #agg #b ,ik 7#agg7 #b ,ik 7#agg7 #eg #ihia 7#agg7 #ihia 7#agg7 #agg #aj ,cauac 7#agg7 #aj ,cauac 7#agg7 #eh #ajjci 7#adh7 #ajjci 7#adh7 #adh #b ,manik 7#adh7 #b ,manik 7#adh7 #ef;b ,,picture #ei #ajbaf 7#agg7 #ajbaf 7#agg7 #agg #aj ,kan 7#agg7 #aj ,kan 7#agg7 #fj #ajcid 7#agh7 #ajcid 7#agh7 #agg #f ,ik 7#agh7 #f ,ik 7#agh7 #fa #ajega 7#agg7 #ajega 7#agg7 #agg #a ,cauac 7#agg7 #a ,cauac 7#agg7 #fb #ajgdh 7#agg7 #ajgdh 7#agg7 #agg #i ,cib 7#agg7 #i ,cib 7#agg7 #eg;b #fc #ajibe 7#agg7 #ajibe 7#agg7 #agg #d ,b5 7#agg7 #d ,b5 7#agg7 #fd #aaajb 7#agg7 #aaajb 7#agg7 #agg #ab ,oc 7#agg7 #ab ,oc 7#agg7 #fe #aabej 7#adh7 #aabej 7#adh7 #adh #d ,eznab 7#adh7 #d ,eznab 7#adh7 ,,picture #ff #aadbg 7#agg7 #aadbg 7#agg7 #agg #ab ,m5 7#agg7 #ab ,m5 7#agg7 #fg #aafjd 7#agg7 #aafjd 7#agg7 #agg #g ,eb 7#agg7 #g ,eb 7#agg7 #eh;b #fh #aagha 7#agg7 #aagha 7#agg7 #agg #b ,muluc 7#agg7 #b ,muluc 7#agg7 #fi #aaieh 7#agg7 #aaieh 7#agg7 #agg #aj ,cimi 7#agg7 #aj ,cimi 7#agg7 ,,picture ,! app>5t error due to ! addition ( two dots 9 ! ,tun place 9 ! upp] numb] ( column #ad is m ! result ( an error ?an an error 9 itself4 ,?is numb] %[s a v cle> case ( erasure4 ,! writ] ( ?is section ( ! manuscript 9 copy+ f ! old] s\rce1 at fir/ ov]look$ column #ad1 & plac$ #g4c4ah1 ! upp] numb] 9 column #ae 9 ?is place4 ,realiz+ 8 mi/ake he eras$ ! ?ree dots 9 ! ,u9al place1 b utiliz$ two ( ! b>s & ! ?ree dots 9 ! ,k9 place z ! #ac ne$$ 9 ! ,u9al 9 column #ad1 & eras$ ! l[] b> ( ! orig9al #ah4 ,?is proc$ure ( ! writ]'s ?rew ! upp] numb] ( column #ad out ( alignm5t1 = ! two dots ( ! ,k9 appe> bel[ ! #ac1 some:at bel[ ! l9e ( ,k9s ( ! o!r columns4 ,! sev5 9 ! ,tun place %\ld h be5 a six1 s ! scribe ins]t$ an extra dot betwe5 ! two ( ! orig9al #g1 neglect+1 h[ev]1 to erase ! o!r two dots4 ,z a result ! upp] numb] ( column #ad records ! numb] #cadb1 :i* is #gbj great] ?an x %\ld be1 namely1 #bdbb4 ,9 column #aj1 #agdh 0 record$ in/ead ( #agdb1 = a b> & ?ree dots 7 writt5 9 ! ,k9 place in/ead ( only two dots4 ,?is is a v peculi> & unexpect$ =m ( c>elessness1 :i* is1 h[ev]1 correct$ 9 ! next column4 ,! rema9+ irregul>ities 9 ! upp] numb]s are all due to ! omission ( a "p ( ! numb]4 ,9 columns #b & #ae1 "o dot 0 omitt$ 9 ! ,k9 place1 ?us record+ #cec in/ead ( #ced 9 ! =m]1 & #beih in/ead ( #beii 9 ! latt]4 ,9 column #d "o b> 0 omitt$ 9 ! ,k9 place1 mak+ ! numb] #fgd1 five less ?an x %\ld be1 namely1 #fgi4 ,9 column #a1 "o dot 0 omitt$ 9 ! ,u9al place1 & 9 column #ab1 f\r dots ( ! same d5om9ation1 record+1 respectively1 #aeg & #bjaf in/ead ( #agg & #bjif4 ,!re is only "o decid$ error 9 ! day s]ies4 ,9 column #aa1 #f ,cib1 #g ,caban1 #h ,eznab 7 writt5 in/ead ( #f ,cimi1 #g ,manik1 #h ,lamat4 ,x %\ld be notic$ t ! numb] ( ! day 0 "r4 ,9 fact j "o-half a tonalamatl1 or #acj days1 0 dropp$ be=e ! day s]ies ( column #aa1 & add$ on aga9 imm$iately aft]w>ds4 ,?is is an extremely curi\s error to make 9 calculat+ & may %$ "s light on ! way 9 :i* ! ,mayas reckon$4 ,! five rema9+ irregul>ities 9 ! day s]ies are ( two k9ds4 ,9 column #e1 ! numb] prec$+ ! ?ird day1 ,*ic*an1 is #d in/ead ( #aa4 ,app>5tly ! writ] ( ! manuscript =got = ! mom5t t ! day 0 add$ to ! "o above x & n ! "o to ! left1 & wrote #d because ! numb] associat$ ) ! ?ird day sign ( column #d 0 #c4 ,! same mi/ake 0 made 9 ! ?ird day ( column #cf1 except t 9 ?is case x 0 ! day sign & n ! numb] :i* 0 confus$4 ,"h1 in/ead ( writ+ ,ahau1 :i* foll[$ ! ,cauac 9 ! second s]ies1 ,b5 0 record$ because ! sign to ! left 0 ,eb4 ,! o!r ?ree irregul>ities are all due to c>elessness 9 plac+ suffici5t dots 9 ! numb] associat$ ) ! day sign1 = 9 columns #ag1 #dg & #di1 #a ,ik1 #aj ,eznab & #aa ,kan 7 record$1 respectively1 in/ead ( ! necess>y #b ,ik1 #aa ,eznab & #ab ,kan4 ,!re are two places 9 :i* columns seem to be misplac$1 al?\gh ! ma!matics ( ! s]ies at ^! po9ts is correct z x /&s4 ,= ! sake ( uni=mity 9 ! arrangem5t ( ! diff]5ce gr\ps1 ! #agh-;day gr\p ( column #g %\ld occur 9 column #f1 & = ! same reason1 ! #adh-;day gr\p ( column #eh %\ld occur 9 column #ei4 ,pr(essor ,fr/emann calls bo? ( ^! v>iations errors1 & arranges 8 v]sion ( ! table s t ea* "p is j l ! o!r two4 ,he gives no reason = 8 op9ion o!r ?an ! phrase 8= ! au?or ( ! manuscript _h confus$ ! diff]5ces #agh & #adh44440d ,mr4 ,b[dit*1 on ! o!r h&1 all[s bo? ( ! v>iations to /& z !y appe> 9 ! manuscript1 & q rightly holds ! op9ion t1 8,x may possibly be t ^! numb]s ?us plac$ are errors ( ! scribe1 b ! m]e plea = uni=mity is n suffici5t to lead u to make ^! *anges40#e #d ,fr/emann1 #aija1 p4 #abc4 #e ,b[dit*1 #aiaj1 p4 #bag4 ,9 ,table ,,ii ! app>5t mi/ake 9 columns #eh & #ei rema9s z x occurs 9 ! manuscript1 = ! reason :i* ,mr4 ,b[dit* gives4 ,9 ! case ( columns #f & #g !re seems to be "s evid5ce t !re actually 0 an error made4 ,! la/ column on page #ec;a1 :i* is ! "o "u discussion1 conta9s no day glyph 9 ! fir/ day s]ies4 ,! glyph %\ld h be5 t ( ,ahau4 ,!re is di/9ct evid5ce1 al?o v fa9t1 t a glyph 0 once !re4 ,moreov]1 ! smoo? coat+ :i* cov]$ ! mat]ial ( ! manuscript page is n brok54 ,!re are o!r oblit]at$ glyphs 9 ^! pages ( ! manuscript1 b few 9 :i* ! surface1 al?\gh unbrok51 /ill conta9s a fa9t1 almo/ cont9u\s outl9e ( a glyph4 ,! glyph1 !n1 0 probably eras$4 ,! writ] ( ! manuscript _h probably completely f9i%$ column #f & />t$ column #g be=e he detect$ ! error4 ,he began to erase ! "p t 0 wrong1 !n realiz$ :at an am\nt ( alt]ation w\ld be necess>y1 & f9ally compromis$ by mak+ ! diff]5ce come betwe5 columns #f & #g in/ead ( columns #e & #f4 ,?is hypo!sis 9 reg>d to ! mann] 9 :i* ! erasure 0 done may be wrong1 b ! erasure /ill /&s z a /rong evid5ce to %[ t ! #agh %\ld h occurr$ 9 column #f r ?an aft] x4 ,f9ally !re appe>s to be an error 9 ! totals ( ! s]ies1 = ! upp] numb] s]ies records z a total #aa1ieh days & ! day s]ies #aa1iei days1 al?\gh !re is /rong reason = believ+ t ! s]ies %\ld record #aa1ifj days4 ,?is discrepancy 9 ! totals w be ref]r$ to aga94 ,9 g5]al1 !n1 ! app>5t irregul>ities 9 ! manuscript fall into two great classes1 ^? :i* are correct$ 9 ! next column or are easily detect$ because ( _! disagreem5t ) ! record 9 ! o!r two s]ies1 & ^? :i* are n obvi\sly due to c>elessness4 ,! latt] w be consid]$ "u ! solutions4 ,! =m] may be dismiss$ z cl]ical errors n affect+ ! solution4 ,9 ?is gr\p are two ( ! irregul>ities 9 ! l[] numb]s 7columns #bf & #ej71 & all eight 9 ! upp] numb]s1 sev5 ( :i* occur 9 ! fir/ ?ird ( ! manuscript4 ,! six errors 9 ! day s]ies1 & ! transposition ( columns #f & #g1 also belong 9 ?is class4 ,by ref]r+ to ,table ,,ii x w be notic$ t ! pictures occur aft] ! #adh-;day gr\ps 9 ea* case4 ,! upp] numb]s imm$iately prec$+ ! pictures are giv5 9 ,table ,,iii 7p4 #aa71 toge!r ) ! diff]5ces betwe5 !m4 ,by gr\p+ ^! diff]5ces1 x becomes app>5t t ! pictures may be divid$ into ?ree l>ge gr\ps ( #cihf days2 two out ( ! ?ree conta9+ ! same diff]5ce numb]s1 #agdb1 #ajcd1 & #abaj4 ,if1 9 ! la/ gr\p1 ! numb] #aj1jci 7 *ang$ to #aj1baf by add+ #agg1 ! diff]5ces = ?is gr\p w\ld also read z ! o!rs1 :5 ! end ( ! s]ies & ! beg9n+ ( ! s]ies are add$ toge!r 7#gjh #ejb #abaj71 = ! #aj? picture is1 9 a s5se1 out ( ! gr\p+ s9ce x occurs aft] ! la/ numb] 9 ! s]ies4 ,! #adh-;day gr\ps are arrang$ 9 ! same ord] = !y occur 9 ! same columns z ! numb]s us$ above4 ,by apply+ ! same process to ! #agh-;day gr\ps1 x is f\nd t !y also c be divid$ into gr\ps :i* conta9 #cihf days4 ,9 ?is case ! second & ?ird gr\ps conta9 ! same numb]s1 #beih & #achh 7,table ,,iv74 ,if ! numb] #abaa 9 ! fir/ gr\p is *ang$ to #ajcd by subtract+ #agg1 ! la/ numb] ( ?is gr\p w\ld be #achh2 & ! fir/ numb] #beih c\ld be =m$ by add+ ! rema9d] at bo? ends ( ! s]ies 7#aefd #ajcd #beih74 ,x %\ld be rememb]$ at ?is po9t t ! only column 9 :i* ! l[] numb]s conta9$ #agh is column #bc1 ( :i* ! upp] numb] is #cihf4 ,?is gives fur!r gr\nds = divid+ ! s]ies z x /&s into ?ree p>ts ( #cihf days1 ea* conta9+ #bc columns4 ,,table ,,iii ,,upp] ,,numb]s ,,( #adh-;,,day ,,gr\ps ,numb] ,diff]5ce ,gr\p 7#j7 #ejb #ejb #agdb #bbdd #ajcd #cihf #cbgh #abaj _/ #ddhh #agdb #fbcj #ajcd #cihf #gbfd #abaj _/ #hdgd #aefe #ajjci #abaa #aabej #cihf #gjh 7#aaieh7 7#ejb7 _/ ,,table ,,iv ,,upp] ,,numb]s ,,( #agh-;,,day ,,gr\ps ,numb] ,diff]5ce ,gr\p 7#aefd7 7#j7 #abaa #cihf #abaa #abaa _/ #bdbb #beih #ejbj #cihf #achh _/ #fdjh #beih #ijjf #cihf #achh _/ #ajcid #aefd 7#aaieh7 ,! ?ree p>ts are n exactly alike1 h[ev]1 z has already be5 po9t$ out 9 consid]+ ! probable errors4 ,if ! upp] numb]s & day numb]s 9 column #f %\ld be alt]$1 s t ! diff]5ce #agh might occur 9 t column in/ead ( column #g1 & if1 by ! same process1 ! diff]5ce ( #adh c\ld occur 9 column #ei in/ead ( #eh1 !n ! ?ree p>ts ( ! s]ies w\ld be entirely alike4 ,! ?ree facts m5tion$ are1 h[ev]1 v /rong evid5ce = suppos+ t ! p :o us$ ?is table consid]$ x z consi/+ ( ?ree equal p>ts4 ,?is s]ies 9 ! ,dresd5 is v simil> to o!r pages ( ! ,dresd5 & o!r manuscripts1 two examples ( :i* are giv5 z illu/rations4 ,"o ( ! mo/ int]e/+ p>allels is ! s]ies on pages #df-ej ( ?is same manuscript4 ,?is s]ies cov]s a p]iod ( #bibj days :i* is divid$ into #bj unequal subdivisions4 ,on page #bd1 :i* j prec$es page #df1 ?is numb] is us$ z a unit 9 multiplication1 t is1 ! numb]s occurr+ on page #bd are sep>at$ f ea* o!r by #bibj or multiples ( ?is numb]4 ,on pages #dd;b & #de;b ! numb] #gh is divid$ into f\r unequal p>ts1 & on pages #dc;b & #dd;b x is us$ z a unit 9 a s]ies :i* f9ally rea*es ! numb] #aidj #gh4 ,,solutions ,! fir/ ref]5ces to ^! pages 9 ! manuscript 7 conc]n$ *iefly ) ! read+ ( ! numb]s )\t any !ories 9 reg>d to ! probable mean+ ( ! s]ies4 ,dr4 ,fr/emann1 9 #ahhf1 0 probably ! fir/ to m5tion ^! pages specifically4 ,at ?is "t he correct$ _m ( ! errors 9 ! s]ies1 & relat$ ! r[s ( days to ! numb] s]ies4#f ,he _h already recogniz$ a close relation betwe5 ! diff]5ce betwe5 ! #a/ & #i? pictures1 i4e41 #aj1gdh1 & ! ,saturn sid]eal p]iod ( #aj1gec days4 ,( c\rse1 9 ord] to d ?is he _h also id5tifi$ ! v>i\s signs 9 ! 8con/ellation b&s10 assign+ !m to v>i\s planets4#g ,^! id5tifications are bas$ on little m ?an ! wi% he _h t !y might be ^? planets1 & = t reason !y are s]i\sly op5 to d\bt4 #f ,fr/emann1 #ahhf1 p4 #cd4 #g ,ibid41 pp4 #fh-ga4 ,cyrus ,?omas1 two ye>s lat]1 also discuss$ ?is s]ies at "s l5g?1 b conf9$ 8 consid]ations entirely to ! ma!matical side ( ! "w4 ,he also po9t$ out mo/ ( ! errors1 agree+ 9 ! ma9 ) ,fr/emann4 ,he consid]$ t ! s]ies conta9$ #aa1ifj days4 ,9 8 conclusion he said 8! sum ( ! s]ies z %[n by ! numb]s ov] ! second column ( ,plate #eh;b is #cc ye>s1 #c mon?s1 & #ah days4 ,z ?is includes only ! top day ( ?is column 7#aj ,cimi71 we mu/ add two days to complete ! s]ies1 :i* ends ) #ab ,lamat40#h #h ,?omas1 #ahhh1 p1 #cbe4 ,dur+ ! foll[+ ye>s1 ,dr4 ,fr/emann repeat$ly ref]r$ to ^! pages 9 8 publications &1 9 #ahih1 publi%$ an article devot$ to ^! pages alone4#i ,! mo/ detail$ z well z ! f9al discussion ( ^! pages is t giv5 9 8 book on ! ,dresd5 ,codex4#aj ,9 pages #ec-eh1 & #ea;b & #eb;b he recognizes ! simil>ity to pages #df-ej1 & rem>ks t ! ,mayas n only comb9$ ! tonalamatl & ! ,m]cury ye>1 b also attempt$ to br+ ! lun> revolution into accord ) ^! two4 ,9 o!r words1 ,fr/emann seems to imply t ! prim>y purpose ( ! s]ies 0 ! c\nt+ ( ! ,m]cury ye>s1 & t ! lun> "p ( ! problem 0 second>y4 #i ,fr/emann1 #ahih4 #aj ,ibid41 #aija1 pp4 #aah-acc4 ,he expla9s ! numb] #aa1ieh z ! result ( attempts to make ! lun> c\nt agree ) #aa1ifj4 8,!y ! ,mayas f\nd t #dje lun> revolutions am\nt$ approximately to #aa1ieh days1 :i* is1 9 fact1 ! l>ge/ numb] on ! second half page ( page #eh40aa ,?is w n /& at all z ! reason = ! #aa1ieh s9ce #dje lun> revolutions come to #aa1iei4hhi days1 & if ! ,mayas knew ! revolutions accurately en\gh to "k :5 to int]calate a day1 !y mo/ c]ta9ly w\ld n h int5tionally =m$ ! numb] #aa1ieh1 :5 !y 7 p]fectly well aw>e ( ! fact t ! "t 0 m ?an #aa1iei days4 ,he recognizes 9 ! numb]s #agg1 #adh & #agh multiples ( lun> mon?s ( #bi & #cj days4 #aa ,fr/emann1 #aija1 p4 #aba4 ,dr4 ,fr/emann at ?is "t divides ! s]ies into ! ?ree equal divisions 9 :i* x has s9ce be5 consid]$4 ,^! are ( #cihf days1 ?us caus+ ! int]calat$ days to come at ! same "t 9 all ?ree4#ab ,he also divid$ ea* ( ^! ?ree divisions into ?ree unequal gr\ps ( #agdb1 #ajcd1 & #abaj days ea*4 ,he advances !ories1 bas$ on ! positions ( ! pictures 9 ! s]ies1 to %[ t ! s]ies also ref]r$ to ! sid]ial p]iods ( ,saturn & ,jupit]1 & discusses ! mean+ ( ! glyphs f\nd on ^! pages4 #ab ,ibid41 p4 #abc4 ,?is detail$ discussion by ,dr4 ,fr/emann ( pages #ea-eh ( ! ,dresd5 has be5 us$ z a f\ndation by _m 9 fur!r /udies ( ^! pages4 ,x is highly probable1 h[ev]1 t a c>eful /udy ( 8 int]pretations w h to be made1 9 :i* ! prov$ assumptions mu/ be cle>ly diff]5tiat$ f ^? 9 :i* ! 8wi% is fa!r to ! ?\ght40 ,mr4 ,b[dit*1 9 #aiaj1ac discuss$ ^! pages & _! relation to ! a/ronomical k ( ! ,mayas4 ,he divid$ ! s]ies into ! same gr\ps z ,dr4 ,fr/emann1 bas+ 8 division ^u ! pictures :i* occur 9 e case imm$iately aft] ! numb] #adh4ad ,mr4 ,b[dit* br\ght out v cle>ly t ?is s]ies is a lun> s]ies1 by means ( a table :i* comp>es ! numb]s record$ 9 ! manuscript & ! multiples ( true lunations4#ae ,!re c be no "q on ?is po9t1 = ! diff]5ce betwe5 ! record$ days & ! true lunations is nev] m ?an 4#i ( a day4 ,he also po9t$ out a way 9 :i* ?is s]ies c\ld be us$ ov] & ov] aga9 9 ! =m ( a cycle1#af & !n discuss$ ! relation ( ?is s]ies to ! ,saturn & ,m]cury p]iods1 disagree+ ) ,fr/emann on sev]al po9ts4 #ac ,b[dit*1 #aiaj1 pp4 #baa-bca4 #ad ,ibid41 p4 #bah4 #ae ,b[dit*1 #aiaj1 pp4 #bbb1 #bbc4 #af ,ibid41 p4 #bbd4 ,mr4 ,b[dit* also po9t$ out a peculi> co9cid5ce betwe5 ! synodical revolutions ( ,jupit] & ! numb]s 9 ! s]ies1 b bas$ 8 argum5t on q diff]5t mat]ial f ! simil> !ory ( ,dr4 ,fr/emann's4 ,! important fact br\ght out is t ! ?ree p>ts ( ! s]ies "u discussion are almo/ exactly equal to #aj revolutions ( ,jupit]1 = "o revolution ( ,jupit] consumes #cih4hfg days4#ag 8,?is w\ld give a reason = ! selection ( #aa1ieh to #aa1ifj days or #dje revolutions1 & = ! division ( ?is numb] into ?ree sections ( #cihf days ea*40#ah #ag ,ibid41 pp4 #bbi1 #bcj4 #ah ,ibid41 p4 #bca4 ,dr4 ,fr/emann & ,mr4 ,b[dit* diff] 9 reg>d to "s ( ! corrections :i* %\ld be made 9 ! manuscript1 b on ! :ole ! two discussions ( ^! pages supplem5t "o ano!r4 ,! g5]al conclusion to be drawn f !m is t ^! pages ( ! ,dresd5 are closely associat$ ) ! synodical lun> mon?1 & possibly1 ) ! synodical revolution ( ,jupit]4 ,?ree ye>s aft] ,mr4 ,b[dit*'s discussion1 ,mr4 ,me9%aus5 publi%$ an article 9 :i* ! relation ( ?is s]ies to eclipses 0 fir/ br\ght out4#ai ,he comp>$1 by means ( two tables1 record$ eclipses ( ! #ah? & #ai? c5turies ) ! numb]s 9 ! ,dresd5 ,codex4 ,out ( ! #fi dates 9 ! manuscript all b #ae dates agre$ ) ! fir/ case1 &1 9 ! second1 all b #ac1 due to ! fact t all ! eclipses are n visible at "o place on ! e>?'s surface4 8,ano!r indication t ! numb]s 9 ! codex h aris5 f ! obs]vation ( eclipses lies 9 ! fact t ! exact gr\p+ ( ! numb]s :i* is induc$ by ! ins]tion ( pictures 9 ! numb] p]iods is also possible 9 lun> eclipses :i* are visible at "o p>ticul> po9t40#bj ,9 ! table giv5 to uphold ?is /atem5t1 ! numb]s1 to be sure1 c be gr\p$ 9 ! mann] :i* he sugge/s2 b !y c also be gr\p$ 9 o!r s]ies4 ,9 8 op9ion ! reason = ! gr\p+ 8lies 9 ! close proximity ( a sol> eclipse to a lun> eclipse10#ba t is1 t at ! date at :i* ! pictures are ins]t$ a sol> eclipse occurr$ #ae days ei!r be=e or aft] a lun> eclipse4 ,!re are two facts :i* t5d to uphold ?is !ory4 ,"o is ! occurr5ce ( ! sun & ! moon 9 %ields ov] ne>ly all pictures1 :i* he int]prets z 8signs ( sol> & lun> eclipses02 ! o!r is ! s]ies ( dates on pages #ea;a & #eb;a1 :i* are #ae days ap>t4 ,9 a table ( record$ eclipses pro( is giv5 t su* d\ble eclipses c occur at ! int]vals :i* sep>ate ! pictures 9 ! manuscript4 ,s9ce ^! int]vals v>y a great deal1 ,me9%aus5 believes t !y w =m ! means ( id5tify+ ! specific eclipses record$ 9 ! manuscript4 #ai ,me9%aus51 #aiac1 pp4 #bba-bbg4 #bj ,ibid41 p4 #bbe4 #ba ,me9%aus51 #aiac1 p4 #bbe4 ,8 g5]al conclusion is t 8! mat]ial advanc$ w prove suffici5tly t ^! numb]s are associat$ 9 "s way ) sol> & lun> eclipses1 & ?is explanation mu/ rema9 /&+ at lea/ until o!r numb]s1 correspond+ equally rem>kably1 are f\nd40#bb #bb ,ibid41 pp4 #bbf1 #bbg4 ,pr(essor ,r4 ,w4 ,willson ( ! ,a/ronomical ,dep>tm5t ( ,h>v>d ,univ]sity1 work+ on a simil> !ory at ab\t ! same "t1 _h f\nd1 h[ev]1 t no s]ies ( sol> eclipses correspond+ to ! int]vals ( ! pictures 9 ! text 0 visible 9 ,yucatan betwe5 ! ,*ri/ian era & ! "t ( ! ,spani% conque/4#bc ,?is app>5tly invalidates ,me9%aus5's !ory4 #bc ,pr(essor ,willson's "w on ! ,dresd5 manuscript has n yet be5 publi%$4 ,x is ref]r$ to "h only ?r\gh 8 k9d p]mission4 ,pr(essor ,willson believes t ! table 9 ! manuscript indicates ! days ( ecliptic conjunction 7t is1 ,new ,moon occurr+ s ne> ! moon's node t eclipses may occur7 &1 z ,mr4 ,b[dit* has %[n1 ) a high degree ( accuracy4 ,suffici5t pro( ( ?is1 9 ,pr(essor ,willson's op9ion1 is ! close correspond5ce ( ! int]vals ( ! codex ) ! int]vals ( ,s*ram's lun> table4#bd #bd ,s*ram1 #aijh1 pp4 #ceh1 #cei4 ,! simil>ity betwe5 ! numb]s 9 ! ,dresd5 & ,s*ram's table is s rem>kable t x seems advisable to po9t out "s ( ! mo/ out/&+ features4 ,9 addition to giv+ ! days ( multiples ( ! lun> synodic mon?s1 ?is table also gives ! "t ( possible occurr5ces ( bo? sol> & lun> eclipses4 ,eclipses occur 9 cycles1 ! be/ kn[n ( :i* is ! ,s>os1 al?\gh !re are also small] cycles :i* are n s accurate4 ,table ,v 7p4 #ag7 gives ! occurr5ces ( c5tral sol> eclipses accord+ to ,s*ram4 ,x %\ld be notic$ t !y occur 9 gr\ps ( ?rees & f\rs1 ea* set be+ sep>at$ f ! prec$+ "o by #bi synodical mon?s4 ,! numb]s 9 ea* gr\p are only six mon?s ap>t4 ,table ,,vi 7p4 #ag7 is a correspond+ s]ies ( lun> eclipses1 :i* also occur 9 a gr\p+ simil> to t ( ! sol> eclipses4 ,x %\ld be notic$ 9 pass+ t ! fir/ numb]s ( ^! gr\ps1 9 bo? ! sol> & lun> eclipses are sep>at$ by #dg & #da lunations1 ! latt] occurr+ aft] e ?ird gr\p 9 ,table ,v4 ,table ,,vii 7p4 #ag7 conta9s ! numb]s :i* are 9 ! same columns z ! #agh-;day gr\ps 9 ! ,dresd54 ,by comp>+ ,table ,v & ,table ,,vii1 x w be f\nd t ! numb]s 9 ! ,dresd5 are ! same z ! fir/ numb]s 9 gr\ps #a1 #b1 #d1 #e1 #g & #h ( ! sol> eclipses4 ,9 ! la/ two numb]s !re is a diff]5ce ( "o day1 :i* is expla9$ by recall+ ! addition ( an extra day 9 ! day s]ies b n 9 ! upp] numb]s ( ! ,dresd54 ,if #fgi days are add$ to ea* numb] 9 ,table ,,vii1 :i* am\nts to ! same ?+ z advanc+ ! ,dresd5 table #fgi days ) respect to ,s*ram's table1 x w be f\nd t ^! numb]s w also agree ) ! fir/ numb]s 9 gr\ps #b1 #c1 #e1 #f & #h & ) ! second numb] 9 gr\p #i ( ! lun> eclipses1 9 ,table ,,vi4 ,a simil> agreem5t may be obs]v$ = ! #adh-;day gr\ps 7see ,table ,,iii74 ,?is rem>kable agreem5t betwe5 ! #agh-;day gr\ps 9 ! ,dresd5 & ! occurr5ces ( eclipses may h sev]al mean+s4 7#a7 ,"o possibility1 & "o :i* %\ld always be kept 9 m9d1 is t ?is agreem5t is simply ano!r co9cid5ce1 ( :i* !re are always _m 9 *ronological "w4 7#b7 ,x may be t ! numb]s ref] to dates ( prophesi$ eclipses :i* ! ,mayas _h le>n$ occurr$ at m or less regul> int]vals4 7#c7 ,s9ce ?is table has a place 9 ! cal5d> ( ! ,mayas 7= a date probably occurs on page #eb;a71 x may be t ^! numb]s ref] to def9ite hi/orical eclipses4 ,if !y d1 !y w af=d a means by :i* an absolute correlation betwe5 ! ,maya & ! ,julian cal5d>s may be obta9$4 ,pr(essor ,willson is at pres5t work+ on ?is problem4 ,,table ,v ,,sol> ,,eclipses ,gr\p ,eclipse ,mon? _/ #ajcd #ce #a #abaa #da #achh #dg #aefe #ec _/ #bdbb #hb #b #beii #hh #bggf #id #biec #ajj _/ #cfcb #abc #c #chji #abi #cihg #ace #dafd #ada _/ #ejbj #agj #d #eaig #agf #ecge #ahb #eeeb #ahh _/ #fdjh #bag #e #fehe #bbc #fgfb #bbi _/ #gfai #beh #f #ggif #bfd #gigc #bgj #haej #bgf _/ #ijjg #cje #g #iahd #caa #icfa #cag #iech #cbc _/ #ajcie #ceb #h #ajegb #ceh #ajgej #cfd _/ #aafjf #cic #i #aaghc #cii #aaifj #dje ,,table ,,vi ,,lun> ,,eclipses ,gr\p ,eclipse ,mon? _/ #ejb #ag #a #fgi #bc #hef #bi _/ #agac #eh #b #ahij #fd #bjfg #gj #bbdd #gf _/ #caja #aje #c #cbgh #aaa #cdee #aag _/ #dcaa #adf #d #ddhi #aeb #dfff #aeh #dhdc #afd _/ #efii #aic #e #ehgg #aii #fjed #bje #fbca #baa _/ #gjhg #bdj #f #gbfd #bdf #gddb #beb _/ #hbih #bha #g #hdge #bhg #hfeb #bic #hhcj #bii _/ #ifhf #cbh #h #ihfc #ccd #ajjdj #cdj _/ #ajhif #cfi #i #aajgd #cge #aabea #cha #aadbh #chg ,,table ,,vii #agh-;,,day ,,gr\ps ,numb] ,mon? #ajcd #ce #bdbb #hb #ejbj #agj #fdjh #bag #ijjf #cje #ajcid #ceb ,9 ord] to det]m9e ! exact ext5t to :i* ! eclipse seasons affect ^! pages 9 ! ,dresd5 ,codex x is necess>y to "w out 9 z great detail z possible ! cal5d> repres5t$4 ,mod]n a/ronomy %[s t ! synodical revolution ( ! moon consumes #bi4ecjei days1 ab\t 4#jc days m ?an #bi-a_/b days4 ,s9ce a cal5d> mu/ be bas$ on :ole days ! natural me?od ( comb9+ ! mon?s w\ld be to alt]nate "o ( #bi days ) "o ( #cj days4 ,at ! end ( two mon?s or #ei days ! true synodical mon? w\ld be 9 advance ( ! cal5drical mon? by 4#jfaah days4 ,e two mon?s ?is error is d\bl$ s t at ! end ( #cd mon?s ! cal5d> w\ld h complet$ #ajjc days & ! synodical mon? #ajjd4jd days4 7,see ,table ,,viii1 p4 #ai47 ,"o me?od ( correct+ ?is w\ld be to make ! la/ mon? a #cj-;day mon? in/ead ( "o ( #bi days z x w\ld be by simple alt]nation4 ,?is #cd-mon? p]iod c\ld !n be repeat$ z a cycle ) an accumulat+ error ( 4#jd days at e repetition4 ,su* a s]ies utt]ly disreg>ds1 h[ev]1 all o!r ph5om5a su* z eclipses1 seasons1 etc4 ,z soon z eclipses are consid]$ ! arrangem5t ( ! mon?s mu/ be alt]$ 9 ord] to use ! p]iodicity ( eclipses 9 ! cal5d>4 ,eclipses occur at regul> seasons1 approximately six mon?s ap>t4 ,! av]age int]val betwe5 eclipse seasons is #agc4caj days1 #c4hgd days less ?an six synodical lun> mon?s4 ,9 ,table ,,ix 7p4 #bj7 ! eclipse season is comp>$ ) ! ne>e/ synodical lun> mon?4 ,x w be notic$ t ! diff]5ce increases betwe5 ! two s]ies until x is necess>y to use five synodical mon?s = "o int]val in/ead ( six to keep ! diff]5ce less ?an half a mon?4 ,x is necess>y to d ?is ?ree times 9 #ace synodical mon?s1 or #cihf4fcj days1 :i* exce$ #bc eclipse seasons1 or #cihf4aca days1 by practically "o half-day4 ,x w\ld be mo/ logical to drop ^! extra mon?s out ( ! set ( six1 dur+ t gr\p 9 :i* ! diff]5ce t5ds to become mo/ ne>ly half a mon?4 ,t w\ld be j be=e ! #bc;d1 #gj?1 & #aag? mon?1 t is1 #dg mon?s ap>t1 requir+ #da mon?s to complete ! #ace-mon? p]iod4 ,,table ,,viii ,numb] ( ,numb] ( ,elaps$ days ,elaps$ days mon? days 9 mon? cal5d> mon? synodical mon? ,error #a #cj #cj #bi4ec -4#dg #b #bi #ei #ei4jf 4#jf #c #cj #hi #hh4ei -4#da #d #bi #aah #aah4ab 4#ab #e #cj #adh #adg4fe -4#ce #f #bi #agg #agg4ah 4#ah #g #cj #bjg #bjf4ga -4#bi #h #bi #bcf #bcf4bd 4#bd #i #cj #bff #bfe4gh -4#bb #aj #bi #bie #bie4ca 4#ca #aa #cj #cbe #cbd4hd -4#af #ab #bi #ced #ced4cg 4#cg #ac #cj #chd #chc4ij -4#aj #ad #bi #dac #dac4dc 4#dc #ae #cj #ddc #ddb4if -4#jd #af #bi #dgb #dgb4di 4#di #ag #cj #ejb #ejb4jb 4#jb #ah #bi #eca #eca4ee 4#ee #ai #cj #efa #efa4jh 4#jh #bj #bi #eij #eij4fa 4#fa #ba #cj #fbj #fbj4ad 4#ad #bb #bi #fdi #fdi4fg 4#fg #bc #cj #fgi #fgi4bj 4#bj #bd #bi #gjh #gjh4gc 4#gc #be #cj #gch #gch4bf 4#bf #bf #bi #gfg #gfg4hj 4#hj #bg #cj #gig #gig4cc 4#cc #bh #bi #hbf #hbf4hf 4#hf #bi #cj #hef #hef4ci 4#ci #cj #bi #hhe #hhe4ib 4#ib #ca #cj #iae #iae4de 4#de #cb #bi #idd #idd4ih 4#ih #cc #cj #igd #igd4ea 4#ea #cd #bi #ajjc #ajjd4jd #a4jd ,?is s]ies ( #ace lun> mon?s1 or #bc eclipse seasons1 c be repeat$ almo/ indef9itely1 alt]nat+ #cihf & #cihg days to ! s]ies & /ill keep ! synodical mon? 9 accord ) ! eclipse season4 ,b ano!r factor mu/ also be consid]$4 ,mon?s ( #bi & #cj days _c be simply alt]nat$ & ei!r con=m ) ! true synodical mon? or complete ! ecliptic s]ies m5tion$1 = #cihf conta9s ?ree m days ?an sixty-eight #cj-;day mon?s1 & sixty-sev5 #bi-;day mon?s4 ,!re=e 9 ! #cihf s]ies ?ree ( ! #bi-;day mon?s mu/ be *ang$ to #cj-;day mon?s1 & 9 ! #cihg s]ies f\r mu/ be *ang$4 ,! position ( ^! *anges is arbitr>y4 ,!y c1 = example1 be ! #cd?1 #fh?1 & #ajb;d mon?s1 & :5 necess>y1 ! #acd?4 ,,table ,,ix ,,comp>ison ,,( ,,synodic ,,mon?s ,,& ,,eclipses ,eclipse season ,synodic mon? ,numb] ,days ,numb] ,days ,diff]5ce #a #agc4caj #f #agg4ahd #c4hgd #b #cdf4fbj #ab #ced4cfg #g4gdg #c #eai4icj #ah #eca4eea #aa4fba #d #fic4bdj #bc #fgi4bjd -#ad4jcf #e #hff4eej #bi #hef4chg -#aj4afc #f #ajci4hfj #ce #ajcc4ega -#f4bhi #g #abac4agj #da #abaj4ged -#b4daf #h #achf4dhj #dg #achg4ich #a4deh #i #aeei4gij #ec #aefe4aba #e4cca #aj #agcc4ajj #ei #agdb4cje #i4bje #aa #aijf4daa #fe #aiai4dhi #ac4jgh #ab #bjgi4gba #gj #bjfg4ada -#ab4ehj #ac #bbec4jca #gf #bbdd4cbe -#h4gjf #ad #bdbf4cda #hb #bdba4ejh -#d4hcc #ae #beii4fea #hh #beih4fib -4#iei #af #bggb4ifa #id #bgge4hge #b4iad #ag #bidf4bga #ajj #biec4jei #f4ghh #ah #caai4eha #ajf #cacj4bdc #aj4ffb #ai #cbib4hia #aab #ccjg4dbf #ad4ece #bj #cdff4bja #aag #cdee4jgi -#aa4abb #ba #cfci4eaa #abc #cfcb4bfc -#g4bdh #bb #chab4hba #abi #chji4ddf -#c4cge #bc #cihf4aca #ace #cihf4fcj 4#dii ,,table ,x #adh-;,,day ,,gr\ps ,upp] ,mon? numb] numb] ,int]val ,gr\ps #ejb #ag #ei #bbdd #gf #id7dg #dg7 #ce _/ #cbgh #aaa #da #da #ddhh #aeb #ei #fbcj #baa #id7dg #dg7 #ce _/ #gbfd #bdf #da #da #hdgd #bhg #ec #ajjci #cdj #id7dg #dg7 #da _/ #aabej #cha ,! next logical /ep is a comp>ison betwe5 ! !oretical cal5d>s j describ$ & ! manuscript4 ,a /udy ( ! manuscript reveals t3 7#a7 ! s]ies record$ repres5ts #dje lun> mon?s or ?ree times #ace mon?s1 & t ! s]ies naturally falls into ?ree great subdivisions ( #cihf days ea*2 7#b7 ea* ?ird consi/s ( #bc columns or unequal subdivisions2 7#c7 ! int]vals betwe5 ! #agh-;day gr\ps are #dg & #hh mon?s2 7#d7 ! #adh-;day gr\ps fall approximately at #dg & #da mon? int]vals 7see ,table ,x72 7#e7 ! fir/ #agh-;day gr\p 9 ea* ?ird occurs betwe5 ! #cj? & #ce? mon? inclusive1 & ! o!r #agh-;day gr\p ( ! ?ird comes #dg mon?s lat]4 ,s9ce ! numb] #agh is compos$ ( f\r #cj-;& two #bi-;day mon?s1 an extra day mu/ h be5 add$1 t is1 a #cj-;day mon? 0 sub/itut$ = "o ( ! #bi-;day mon?s1 if ! manuscript repres5ts a regul> alt]nat+ s]ies4 ,! obvi\s conclusions to be drawn f ^! facts are3 7#a7 t ! s]ies 0 divid$ into ?ree gr\ps ( #cihf days ea* 9 ord] to associate ! lun> cal5d> closely ) ! ecliptic cycle ( ! same l5g?2 7#b7 t ! #bc columns 9 ea* ?ird may repres5t ! tw5ty-?ree eclipse seasons 9 ea* eclipse p]iod ( #cihf days2 7#c7 t gr\ps ( #dg & #da mon?s 7 us$ 9 "s way 9 ! s]ies1 = ! #agh-;day gr\ps are sep>at$ by #dg & #hh mon?s & #hh is compos$ ( #dg & #da1 ! two p]iods s closely associat$ ) ! recurr5ce ( eclipses2 7#d7 t ! six mon?s p]iod 0 *ang$ to "o ( five mon?s ( #adh days approximately e #dg & #da mon?s1 :i* is ! me?od already advanc$ 9 ! !oretical ecliptic lun> s]ies = keep+ ! synodical mon?s & ecliptic seasons toge!r2 7#e7 t "o extra day 0 add$ to ! alt]nat+ #bi-;& #cj-;day mon?s1 betwe5 ! #cj? & #ce? mon? inclusive ( ea* ?ird1 9 accordance ) ! !oretical necessity = s do+ already br\ght out1 & t ano!r ( ! ?ree extra days 0 add$ #dg mon?s lat]4 ,:5 ! diff]5ce gr\ps#be are divid$ into mon?s x is f\nd t x is an easy matt] to arrange ! mon?s 9 an alt]nat+ s]ies4 ,! gr\p ( #agg days is compos$ ( ?ree #cj-;& ?ree #bi-;day mon?s1 ei!r ( :i* :5 alt]nat$ c beg9 ! gr\p1 :i* !n ends ) ! o!r1 i4e41 #bi1 #cj1 #bi1 #cj1 #bi1 #cj1 or #cj1 #bi1 #cj1 #bi1 #cj1 #bi4 ,! gr\p ( #adh days consi/s ( ?ree #cj-;& two #bi-;day mon?s1 necessitat+ t x beg9 & end ) a #cj-;day mon? :5 alt]nat$1 ?us1 #cj1 #bi1 #cj1 #bi1 #cj4 ,9 ! #agh-;day gr\p "o ( ! #bi-;day mon?s is replac$ by a #cj-;day mon?1 o!rwise ! gr\p is exactly l t ( #agg days1 :i* x exce$s by "o day4 ,x is evid5t t !re w always be ?ree #cj-;day mon?s 9 succession 9 ! #agh-;day gr\p1 & t c>e mu/ be tak5 9 *oos+ ! "r sequ5ce ( ! #agg-;day gr\ps :i* fall ne> ^? ( #adh days 9 ord] to avoid hav+ two #cj-;day mon?s 9 succession4 #be ,t is1 ! #agg-;day1 #adh-;day & #agh-;day gr\ps4 ,!re rema9s simply ! sub/itution ( ! six or five mon?s1 z ! case may be1 9 place ( ! diff]5ce gr\ps 9 ! manuscript4 ,h[ev]1 if ! ,mayas consid]$ ea* ?ird ( ! table z a unit1 x is reasonable to assume t ! sequ5ce ( ! mon?s 9 ea* ?ird is id5tical4 ,!re=e x is necess>y to arrange a sequ5ce = only "o-?ird1 t is1 #ace mon?s1 & !n1 if ! assumption is correct1 ?is sequ5ce w fit ! o!r two-?irds ( ! s]ies4 ,ea* ?ird ( ! table consi/s ( #ace mon?s cov]+ ?ree m days ?an w\ld be cov]$ by a simple alt]nation ( #cj-;& #bi-;day mon?s4 ,^! ?ree int]cal>y days 7 ins]t$ at def9ite int]vals4 ,a clue to ! position ( two ( !m is giv5 by ! #agh-;day gr\ps4 ,"o 0 ins]t$ betwe5 ! #cj? & #ce? mon?s1 ano!r #dg mon?s lat]1 betwe5 ! #gg? & #hb;d mon?s4 ,!oretically ! extra day %\ld be ins]t$ 9 ! #cd? mon? aft] ! beg9n+ ( a s]ies ( alt]nat+ #bi-;& #cj-;day mon?s1 = !n ! error betwe5 ! synodical revolution ( ! moon & ! cal5drical mon?s becomes m ?an "o day4 ,9 ! #bi-;day mon? prec$+ ! #cd?1 namely ! #cb;d mon?1 ! error at ! end is also practically "o day1 i4e41 4#ih days4 ,! #bi-;day mon? mo/ ne>ly ! c5tre ( ! fir/ #agh-;day gr\p is ! #cb;d mon? ( ! s]ies1 ! ?ird 9 ! gr\p4 ,! ,mayas may h *os5 ?is mon? because ( its position 9 ! #agh-;day gr\p1 mak+ ! sequ5ce ( ! mon?s #bi1 #cj1 #cj1 #cj1 #bi1 #cj1 if ! #cj? mon? 0 a #bi-;day mon? z x w\ld be by simple alt]nation4 ,! second "t ?is int]cal>y day occurs 9 ea* ?ird is #dg mon?s lat]4 ,obvi\sly1 ?is may be ! recurr5ce ( ?is int]calation 9 a repetition ( a small] gr\p ( mon?s ?an ! #ace-mon? gr\p4 ,if #dg mon?s are subtract$ f ! #gi? mon? :i* is ! ?ird 9 ! second #agh-;day gr\p ! result is #cb1 :i* implies t ! small] division is #dg mon?s4 ,two #dg-mon? p]iods complete all b #da ( ! #ace mon?s 9 ea* ?ird4 ,!n1 ( necessity1 if ea* ?ird ( ! manuscript is a unit1 a #da-mon? gr\p foll[s two #dg-mon? gr\ps1 an arrangem5t :i* also agrees ) ! eclipse gr\ps 9 ,tables ,v4 ,! two #agh-;day gr\ps acc\nt = only two ( ! ?ree int]calat$ days1 & s9ce no #agh-;day gr\p occurs 9 ! #da-mon? division1 ! addition ( ?is day mu/ h be5 accompli%$ 9 "s m obscure mann]4 ,s9ce bo? #dg & #da are odd numb]s1 ea* gr\p mu/ conta9 at lea/ "o m mon? ( "o k9d ?an ! o!r4 ,s9ce two synodical revolutions ( ! moon are slightly long] ?an two cal5drical mon?s x is wise/ to />t & end ea* gr\p ) a #cj-;day mon?4 ,if ?is is done1 ! #dg-mon? gr\p w conta9 tw5ty-five #cj-;day & tw5ty-two #bi-;day mon?s1 & ! #da-mon? gr\p tw5ty-"o #cj-;day & tw5ty #bi-;day mon?s1 mak+ = ! composition ( ! #ace mon?s1 sev5ty-"o #cj-;day & sixty-f\r #bi-;day mon?s1 t is1 sev5 m ( ! #cj-;day mon?s ?an ( ^? ( #bi days1 %[+ t actually ?ree ( ! sixty-sev5 #bi-;day mon?s expect$ 9 a normal repetition h become #cj-;day mon?s4 ,?is is caus$ by ! occurr5ce ( two #cj-;day mon?s 9 succession at ! end ( "o s]ies & ! beg9n+ ( ! next4 ,if ! #ace mon?s 9 ea* ?ird are numb]$ 9 succession x w be se5 t 9 ! fir/ #dg-mon? gr\p & 9 ! #da-mon? gr\p1 ! #cj-;day mon?s are ! odd numb]s4 ,9 ! second #dg-mon? gr\p !y are ! ev5 numb]s1 ( :i* !re is "o m 9 ?is division ?an odd numb]s1 ?us acc\nt+ = ! additional "o ( ! ?ree days4 ,if ! p]iod ( #cihf days 7 consid]$ by itself1 ! arrangem5t giv5 w\ld be suffici5t4 ,z soon1 h[ev]1 z ?is p]iod is repeat$ a numb] ( times an error develops1 s9ce #ace synodical revolutions ( ! moon are complet$ 9 #cihf4fc days4 ,twice ?is numb] gives #gigc4bf1 or #a4bf days m ?an twice #cihf4 ,9 ord] to keep ! sequ5ce ( mon?s 9 ! arrangem5t giv5 above 9 accordance ) ! moon1 x becomes necess>y to int]calate "o m day e two repetitions ( ! #cihf p]iod4 ,?is may be done by *ang+ ! la/ #bi-;day mon? 9 ! #da-mon? gr\p to a #cj-;day mon?1 mak+ ! la/ #agg-;day gr\p 9 ! ?ird "o ( #agh days4 ,! ,mayas c]ta9ly did ?is 9 ! fir/ ?ird ( ! s]ies giv5 & arrang$ = x 9 ! la/ ?ird 9 a mann] :i* w be demon/rat$ lat]4 ,tabulat+ ! solution "h advanc$ w =m ,table ,,xi 7p4 #be71 9 :i* ! #cj-;& #bi-;day mon?s 9 "o-?ird ( ! manuscript h be5 arrang$ 9 ?ree columns1 ! fir/ two ( :i* repres5t ! #dg-mon? gr\ps & ! la/ "o ! #da-mon? gr\p4 ,be=e ! fir/ column ( mon?s are numb]s to facilitate locat+ any giv5 mon? 9 ! gr\p4 ,! two k9ds ( mon?s occur 9 direct alt]nation 9 ea* gr\p1 ) ?ree exceptions4 ,! #cb;d mon? 9 bo? ( ! #dg-mon? gr\ps is "o ( #cj days in/ead ( #bi1 because ( ! addition ( ! int]cal>y day4 ,! #dj? mon? 9 ! #da-mon? gr\p is giv5 z "o ( #bi days ) a #cj 9 p>5!ses be=e x1 repres5t+ ! fact t e o!r ?ird an extra int]cal>y day %\ld be ins]t$ 9 ?is mon?4 ,to ! "r ( ! mon? columns are ?ree columns giv+ ! diff]5ce gr\ps z f\nd 9 ! manuscript 7see ,table ,,ii71 ea* column giv+ ^? numb]s f\nd 9 ea* ?ird ( ! manuscript1 ! fir/ ?ird be+ ! left "o ( ! ?ree4 ,x %\ld be notic$ t ! misplac$ 787 #adh-;day gr\p 9 ! la/ ?ird does n int]f]e ) ! sequ5ce ( ! mon?s4 ,f9ally x only rema9s to review ! irregul>ities ( ! manuscript 9 ! light ( ! solution j advanc$4 ,^? irregul>ities :i* are correct$ imm$iately aft]w>ds1 or are at v>iance ) ! re/ ( ! column 9 :i* !y occur1 are1 9 all probability1 errors on ! "p ( ! writ] ( ! s]ies1 su* z might h be5 caus$ by c>eless transcription f ano!r copy ( ! table1 & correction 9 ! foll[+ column to avoid ! task ( erasure4 ,elim9at+ ^! irregul>ities1 !re rema9 ?ree to be inve/igat$1 namely1 7#a7 ! abs5ce ( ! #agh numb]s 9 ! l[] numb] s]ies1 ) "o conspicu\s exception2 7#b7 ! occurr5ce ( #agh 9 column #g in/ead ( #f1 & ( #adh 9 column #eh in/ead ( #ei2 & 7#c7 ! discrepancies 9 ! totals ( ! s]ies4 ,,table ,,xi4--,,! ,,arrangem5t ,,( ,,lun> ,,mon?s ,,9 ,,! ,,dresd5 ,,table ,no4 ,days ,days ,days ( 9 ,dresd5 gr\ps 9 ,dresd5 gr\ps 9 ,dresd5 gr\ps mon? mon? #a #b #c mon? #a #b #c mon? #a #b #c #a #cj #cj #cj #b #bi #bi #bi #c #cj #cj #cj #d #bi #agg #agg #agg #bi #agg #agg #agg #bi #agg #agg #agg #e #cj #cj #cj #f #bi _/ #bi _/ #bi _/ #g #cj #cj #cj #h #bi #bi #bi #i #cj #cj #cj #aj #bi #agg #agg #agg #bi #agg #agg #agg #bi #agg #agg #agg #aa #cj #cj #cj #ab #bi _/ #bi _/ #bi _/ #ac #cj #cj #cj #ad #bi #bi #bi #ae #cj #adh #adh #adh #cj #cj #adh #adh #adh #af #bi #bi #agg #agg #agg #bi #ag #cj _/ #cj #cj _/ #ah #bi #bi _/ #bi #ai #cj #cj #cj #bj #bi #bi #adh #bi #ba #cj #agg #agg #agg #cj #agg #agg #cj #agg #agg #agg #bb #bi #bi #bi #bc #cj _/ #cj _/ #cj _/ #bd #bi #bi _/ #bi #be #cj #cj #cj #bf #bi #bi #agg #bi #bg #cj #agg #agg #agg #cj #adh #adh #cj #agg #agg #agg #bh #bi #bi #bi #bi #cj _/ #cj _/ _/ #cj #cj #bi #bi #bi _/ #ca #cj #cj #cj 99#cb #cj #cj #bi #cc #cj #agh #agh #agh #cj #agh #agh #agh #cj #agg #agg #agg #cd #bi #bi #bi #ce #cj _/ #cj _/ #cj _/ #cf #bi #bi #bi #cg #cj #cj #cj #ch #bi #agg #agg #agg #bi #agg #agg #agg #bi #agh #agg #agg #ci #cj #cj #cj 7#agh7 #dj #bi #bi 7#cj7bi #da #cj _/ #cj _/ -#cj _/ #db #bi #bi #dc #cj #cj #dd #bi #bi #de #cj #agg #agg #agg #cj #agg #agg #agg #df #bi #bi #dg #cj _/ #cj _/ ,! great bulk ( ! diff]5ce gr\ps z express$ by ! l[] numb] s]ies are #agg1 ! only dep>ture f ^! be+ ! designation ( ! #adh-;day gr\ps & ! extra #agh-;day gr\p at ! end ( ! fir/ ?ird4 ,! complete disreg>d ( all ( ! six normal #agh-;day gr\ps by ! l[] numb]s seems to imply t no attempt 0 made to h ! latt] agree ) ! actual diff]5ces 9 ! upp] numb]s1 a conclusion :i* is /r5g!n$ by ! fact t none ( ! l[] numb]s %[s evid5ce ( ! cl]ical errors 9 ! diff]5ces ( ! upp] numb]s4 ,x seems mo/ probable t ! l[] numb] s]ies 0 int5d$ m]ely z a guide to indicate ! position ( ! five mon? p]iods & to place emphasis on ! extra int]cal>y day add$ 9 ! #bc;d column1 )\t attempt+ to h ?is s]ies accurate4 ,! pres5ce ( ! #agh-;day gr\p 9 column #g in/ead ( #f has be5 discuss$ at "s l5g? "u ! description ( ! errors4 ,! scribe1 realiz+ t 9 neglect+ to put 9 ?is #agh-;day gr\p1 ! fir/ "o ( ! s]ies1 a s]i\s error _h be5 committ$1 may h attempt$ to erase ! incorrect record 9 column #f2 !n1 realiz+ t f\r numb]s & ?ree glyphs w\ld h to be alt]$1 decid$ to correct ?is mi/ake--al?\gh x 0 ( m importance ?an ! o!r two errors--z he _h ! =m] ones1 i4e41 by mak+ ! correction 9 ! next column4 ,! v simil> irregul>ity 9 ! la/ ?ird ( ! manuscript1 ! plac+ ( ! #adh-;day gr\p "o column ahead ( its expect$ position1 _c be expla9$ 9 ! same mann]4 ,x is v evid5t t ?is column has be5 delib]ately plac$ :]e x is4 ,t x does n h to d ) ! mon? sequ5ce is evid5t1 s9ce x does n affect x4 ,x mu/ !n affect ! ecliptic "p ( ! s]ies1 = x causes a %ort season to occur six mon?s e>li] ?an expect$4 ,^u comp>ison ( ,tables ,,vi & ,x1 x w be se5 t all ( ! dates ( ! #adh-;day gr\p occur dur+ "o ( ! eclipse gr\ps giv5 9 ,s*ram's table4 ,h[ev]1 _h ! #adh-;day gr\p "u discussion be5 plac$ 9 ! #ei? column1 z uni=mity dem&s1 ?is numb]1 #aj1baf1 w\ld n h fall5 9 "o ( ! eclipse gr\ps giv5 9 ,table ,,vi4 ,?is t5ds to %[ t !re 0 "s reason o!r ?an regulat+ ! diff]5ce gr\ps to agree ) ! eclipse seasons1 = ! position ( ! #adh-;day gr\ps4 ,?is reason1 z yet undet]m9$1 is possibly associat$ ) ! pictures1 :i* imm$iately foll[ ! #adh-;day gr\ps4 ,f9ally !re rema9 only ! totals ( ! s]ies to be consid]$4 ,! total ( ! upp] numb] s]ies records #aa1ieh days4 ,sixty-n9e eclipse seasons complete #aa1ieh4ci days1 less ?an half a day m ?an ! record$ numb]4 ,?is close agreem5t & ! failure to add ! extra int]cal>y day to ! upp] numb] s]ies at ! end ( ! fir/ ?ird1 give rise to ! belief t ! upp] numb] s]ies is a cal5d> 9 itself1 & records a means by :i* dates ( probable eclipses may be reckon$4 ,! units ( ! c\nt 7 eclipse seasons express$ z lun> mon?s1 #fi ( :i* are repres5t$ 9 ! cal5d> record$ on ^! pages4 ,! ,mayas und\bt$ly knew ! relation ( ! eclipses to ! moon1 at lea/ 9 a vague way1 & felt t x 0 necess>y to associate ?is eclipse cal5d> 9 "s way ) ! lun> cal5d>1 compos$ ( #bi-;& #cj-;day mon?s4 ,!re=e ! day s]ies is f\nd imm$iately bel[ ! upp] numb] s]ies4 ,?is s]ies ( days con/itutes a lun> cal5d> :i* co9cides z closely z possible ) ! eclipse cal5d>4 ,x may be ! =mal lun> cal5d> ( ! ,mayas1 b x may also be an adaptation ( ! =mal cal5d> to ! eclipse p]iods4 ,! day s]ies v>ies f ! eclipse s]ies 9 two places only4 ,at ! end ( ! fir/ ?ird ( ! s]ies1 x 0 necess>y to add "o day to ! lun> cal5d>1 an addition /rongly po9t$ out 9 ! record1 b n to ! eclipse cal5d>1 because ( ! increas+ error betwe5 ! revolutions ( ! moon & ! cal5drical lun> mon?s4 ,!re=e1 ?r\gh\t ! rema9+ two-?irds ( ! s]ies1 ! lun> cal5d> 0 "o day 9 advance ( ! eclipse cal5d>4 ,at ! end ( ! s]ies1 s9ce #dje ( ! moon's revolutions complete #aa1iei4hi days1 & ! day s]ies only #aa1iei1 "o m day %\ld be add$1 9 ord] to keep ! error z small z possible4 ,?is 0 accompli%$ by *ang+ f ! middle to ! l[] l9e ( days4 ,on page #eb;a1 imm$iately prec$+ ! cal5d>1 are f\r day signs ) numb]s4 ,"o ( ^!1 #ab ,lamat1 is ! z]o day ( ! day s]ies1 b is associat$ ) ! middle l9e ( day glyphs & n ! upp] l9e1 z might be expect$4 ,! s]ies ( days :i* come1 cal5drically speak+1 j be=e & aft] ! actual s]ies1 may h be5 plac$ 9 ! record to %[ t slight v>iations f ! av]age 7 to be expect$4 ,! entire record is bas$ on ! middle l9e ( days until ! end ( ! s]ies4 ,"h ! day j bel[ ! la/ day ( ! middle l9e is #ab ,lamat1 ! end ( #df tonalamatls 7#bfj-;day cycle71 & ! z]o day ( ! record$ s]ies4 ,! tonalamatl 0 probably z easily us$ by ! ,mayas z 8#fj days0 & 8#ij days0 are us$ n[4 ,! entire cal5drical sy/em ( ! ,mayas is bas$ on ! cycle pr9ciple4 ,! s]ies record$ 9 ^! pages 0 probably also a cycle1 & 9 ord] to repeat x1 #ab ,lamat mu/ aga9 be us$ z ! z]o date4 ,if to ^! argum5ts is add$ ! fact t an additional day is necess>y to keep ! cal5d> 9 accord ) ! synodic revolution ( ! moon1 !re rema9s little d\bt b t ! us]s ( ?is cal5d> add$ ! extra day by go+ f ! middle to ! l[] l9e ( day glyphs1 !reby keep+ ! error betwe5 ! moon & ! cal5d> z l[ z possible1 complet+ ! #df? tonalamatl1 & at ! same "t mak+ x possible to repeat ! record$ s]ies z a cycle4 ,if ! s]ies is repeat$ once1 at ! end ( #haj mon?s1 or ab\t #ff-a_/b ye>s1 ! eclipse cal5d> w be beh9d ! av]age eclipse season 4#gh days1 & ! lun> cal5d> w be 9 advance ( ! synodical revolutions ( ! moon only 4#bb days4 ,9 g5]al1 !n1 ! irregul>ities 9 ! cal5d> record$ on ^! pages fall into two gr\ps1 ^? :i* are cl]ical errors ( ! scribe & d n !re=e affect ! solution advanc$1 & ^? :i* d n appe> to be ( ! cl]ical type4 ,9 ! light ( ! solution advanc$1 x has be5 %[n t !re are p]fectly logical reasons = ! latt] gr\p ( app>5t irregul>ities4 ,,conclusion ,on pages #ea to #eh ( ! ,dresd5 ,codex occurs a s]ies ( numb]s1 runn+ cont9u\sly ?r\gh all ! pages except ! upp] halves ( ! fir/ two4 ,?is s]ies records a p]iod ( #aa1ifj days1 divid$ by means ( columns into sixty-n9e unequal subdivisions1 ( #agg1 #adh1 & #agh days1 ( :i* ! fir/ is ! mo/ frequ5t4 ,!re are ?ree di/9ct s]ies4 ,"o s]ies ( numb]s is 9 ! upp] "p ( ! record1 & consi/s ( totals increas$ /ep by /ep until ! f9al total rea*$ records #aa1ieh days4 ,j bel[ ?is s]ies are ?ree s]ies ( day signs & numb]s1 ! middle "o ( :i* is ! actual s]ies4 ,^! dates are sep>at$ by ! same numb] ( days z ! upp] numb] s]ies1 except 9 ! #bc;d gr\p1 at :i* place "o extra day is add$ to ! day s]ies & n to ! upp] numb] s]ies1 caus+ ! =m] to be 9 advance ( ! latt] "o day ?r\gh\t ! rema9d] ( ! record4 ,at ! end ( ! day s]ies ano!r extra day is add$ by c\nt+ 9 ! la/ day 9 ! l[] r[ ( days1 ?us complet+ ! #aa1ifj-;day p]iod4 ,bel[ ?is day s]ies is ano!r numb] s]ies no t]m ( :i* exce$s #agh4 ,9 a g5]al way x records ! diff]5ces betwe5 ! dates appe>+ above ea* ( its numb]s4 ,! agreem5t is h[ev] s inaccurate t ?is l[] numb] s]ies c\ld1 at be/1 h be5 us$ only z a g5]al guide to ! us] ( ! manuscript1 9 t x calls att5tion to ! int]vals ( unusual l5g?4 ,! s]ies record$ is compos$ ( ?ree equal p>ts1 ea* compos$ ( #bc subdivisions & cov]+ #cihf days4 ,! numb] s]ies on ^! pages record an eclipse cal5d>1 t is1 a s]ies ( dates by means ( :i* ! occurr5ce ( eclipses 0 =etold4 ,?is cal5d> is compos$ ( ?ree id5tical p>ts1 ) ! exception ( "o #adh-;day gr\p :i* occurs six mon?s e>li] 9 ! la/ ?ird ?an 9 ! o!r two4 ,ea* ?ird is compos$ ( #bc unequal subdivisions :i* repres5t ! tw5ty-?ree eclipse seasons1 express$ 9 lun> mon?s1 9 #cihf days4 ,! upp] numb] s]ies records ?is cal5d>1 & its total ( #aa1ieh days is only 4#ci days less ?an #fi eclipse seasons4 ,9 ord] to make x m intelligible ?is eclipse cal5d> is accompani$ by a probably m g5]ally kn[n lun> cal5d>1 :i* may h be5 alt]$ slightly to con=m to ! requirem5ts ( ! eclipse cal5d> x accompanies4 ,?is lun> cal5d> is conta9$ 9 ! day s]ies j bel[ ! eclipse cal5d>4 ,x also is record$ 9 ?ree divisions agree+ closely ) ! eclipse cal5d>4 ,"o hundr$ & ?irty-five lun> mon?s ( #cj & #bi days complete #cihf days1 4#fc days less ?an #ace synodical revolutions ( ! moon4 ,?is error :i* am\nts to m ?an "o day :5 repeat$ once1 necessitates ! addition ( an extra day 9 ! lun> cal5d> e o!r ?ird1 :i* 0 done 9 ! manuscript 9 ! fir/ & la/ ?ird1 mak+ ! total record$ by ! lun> cal5d> #aa1ifj1 two days m ?an ! eclipse cal5d>1 & 4#aa days m ?an #dje synodical revolutions ( ! moon4 ,?is p]iod ( #aa1ifj days may h be5 us$ z a cycle1 ! z]o day ( :i* is #ab ,lamat4 ,ea* ?ird ( ! lun> cal5d> consi/s ( #cj-;& #bi-;day mon?s arrang$ 9 alt]nat+ sequ5ce1 ) int]cal>y days add$ by ! sub/itution ( a #cj-;day = a #bi-;day mon? :5 ! error aris+ f ! noncon=mity ( ! moon's revolution rea*es m ?an "o day4 ,9 ord] t ! lun> cal5d> might agree ) ! eclipse cal5d> m closely1 ^! mon?s 7 record$ 9 gr\ps ( five & six4 ,! mon?s 9 ea* ?ird ( ! s]ies 7 divid$ into ?ree gr\ps1 :i* are ! same 9 ea* ?ird4 ,! fir/ two gr\ps conta9$ #dg mon?s ea*1 & complet$ ! fir/ sixte5 dates ( ! ?ird4 ,! la/ gr\p 0 "o ( #da mon?s1 :i* 0 repres5t$ by ! la/ sev5 dates ( ! ?ird4 ,an int]cal>y day 0 add$ 9 ! #cb;d mon? ( ea* ( ! #dg-mon? gr\ps to correct ! accumulat+ error1 !reby caus+ ! #f? & #ad? subdivisions ( ! ?ird to be ( #agh days4 ,9 ! fir/ & la/ ?ird ! #dj? mon? ( ! #da-mon? gr\p also conta9$ an int]cal>y day = ! same reason1 mak+ ! #bc;d subdivision #agh days1 b 9 ! la/ column ( ! record ?is extra day is add$ by go+ f ! middle to ! l[] l9e ( day signs4 ,ea* ( ! #dg-;& #da-mon? divisions began & end$ ) a mon? ( ?irty days4 ,! num]ical s]ies ( ^! pages ( ! ,dresd5 record1 !n1 an eclipse cal5d> :i* is ref]r$ to a lun> cal5d>4 ,?is solution expla9s all ! irregul>ities ( ! s]ies except ^? :i* seem cle>ly to be cl]ical errors ( ! scribe4 ,only ! num]ical & cal5drical s]ies on ^! pages h be5 consid]$4 ,no attempt has be5 made to expla9 ! hi]oglyphs1 ! pictures1 or ! fir/ two pages1 :i*1 al?\gh %[+ a close association to ! long s]ies1 are nev]!less a unit 9 !mselves4 ,,bibliography ,,b[dit*1 ,c4 ,p4 #aiaj4 ,! ,num]ation1 ,cal5d> ,sy/ems & ,a/ronomical ,k ( ! ,mayas4 ,cambridge4 ,f,,r/emann1 ,e4 #ahhf4 ,erlut]ung5 zur ,mayah&s*rift d] ,knigli*5 ff5tli*5 ,biblio!k zu ,dresd54 ,dresd54 #ahih4 ,zur ,entziff]ung d] ,mayah&s*rift1 ,,vii4 ,dresd54 7,trans4 9 ,bull4 #bh1 ,bur4 ,am4 ,e?nol41 pp4 #dfc-gb47 #aija4 ,comm5t> zur ,mayah&s*rift d] ,knigli*5 ff5tli*5 ,biblio!k zu ,dresd54 ,dresd54 7,trans4 9 ,pap]s ( ! ,peabody ,museum1 ,vol4 ,,iv1 ,no4 #b47 ,,me9%aus51 ,,m>t94 #aiac4 b] ,sonn5- und ,mondf9/]nisse 9 d] ,dresd5] ,mayah&s*rift4 ,zeit4 fr ,e?nol41 ,bd4 ,,xlv1 pp4 #bba-bbg4 ,,s*ram1 ,r4 #aijh4 ,kal5d>iographis*e und ,*ronologis*e ,tafeln4 ,leipzig4 ,,?omas1 ,,cyrus4 #ahhh4 ,aids to ! ,/udy ( ! ,maya ,codices4 #f? ,ann4 ,rep41 ,bur4 ,am4 ,e?nol41 pp4 #bec-cga4 ,,pr9t$ ,,at ,,! ,,h>v>d ,,univ]sity ,,press ,,cambridge1 ,,mass41 ,u4 ,s4 ,a4 ,,peabody ,,museum ,,pap]s4 ,,vol4 ,,vi1 ,,no4 #b1 ,,plate #a ,illu/ration3 ,,dresd5 ,,codex1 ,,pages #ea ,,to #eh4 ,,transcrib]',s ,,notes 99 ,?is text has be5 pres]v$ z 9 ! orig9al1 includ+ ar*aic & inconsi/5t spell+1 punctuation & gramm>1 except z not$ bel[4 99 ,:]e ! orig9al "w uses text 9 italics1 ?is e-text uses text4 ,small capitals 9 ! orig9al "w are repres5t$ "h 9 all capitals4 99 ,footnotes h be5 r5umb]$ & !n mov$ to directly bel[ ! p>agraph to :i* !y belong4 99 ,obvi\s pr9t]'s errors h be5 sil5tly correct$4 99 ,page #c3 ,table ,i 0 relocat$ f mid-p>agraph 7page #d7 to imm$iately prior to ! beg9n+ ( ! p>agraph4 99 ,page #e3 ,table ,,ii 0 relocat$ f mid-p>agraph 7pages #f & #g7 to imm$iately prior to ! beg9n+ ( ! p>agraph4 99 ,page #h3 u9al *ang$ to ,u9al4 99 ,page #aa3 ,tables ,,iii & ,,iv 7 relocat$ f )9 ! p>agraph to imm$iately prior to ! p>agraph4 99 ,page #aa3 ,table ,,iii & ,table ,,iv 7 side-by-side4 ,table ,,iv 0 relocat$ to bel[ ,table ,,iii4 99 ,page #ag3 ,tables ,v1 ,,vi & ,,vii 7 side-by-side & ,table ,,vii 0 relocat$ to bel[ ,tables ,v & ,,vi4 99 ,page #ah3 ,table ,,viii 0 relocat$ f mid-p>agraph 7page #ai7 to imm$iately prior to ! beg9n+ ( ! p>agraph4 99 ,page #ai3 ,table ,,ix & ,table ,x 7 relocat$ f mid-p>agraph 7page #bj7 to imm$iately prior to ! beg9n+ ( ! p>agraph4 99 ,page #bd3 ,table ,,xi 0 relocat$ f mid-p>agraph 7page #be7to imm$iately prior to ! relevant p>agraph on page #bd4 99 ,page #bd1 ,table ,,xi3 ,! ref]5ce = ! a/]isk at ,no4 ( ,mon? #cb 0 n f\nd4