,,our ,,cal5d>4 ,! ,julian ,cal5d> & ,its ,errors4 ,,h[ ,,correct$ ,,by ,,! ,,gregorian4 ,rules ,= ,f9d+ ! ,dom9ical ,lett]1 ,,& ,,! ,,day ,,( ,,! ,,week ,,( ,,any ,,ev5t ,,f ,,! ,,days ,,( ,,julius ,,caes> #df ,b4 ,c4 ,,to ,,! ,,ye> ,,( ,,our ,,"l ,,f\r ,,?\s&--,a ,,new ,,& ,,easy ,,me?od ,,( ,,fix+ ,,! ,,date ,,( ,,ea/]4 ,,hebrew ,,cal5d>2 ,,%[+ ,,! ,,correspond5ce ,,9 ,,! ,,date ,,( ,,ev5ts ,,record$ ,,9 ,,! ,,bible ,,) ,,our ,,pres5t ,,gregorian ,,cal5d>4 ,,illu/rat$ ,,by ,,valuable ,,tables ,,& ,,*>ts4 ,,by ,,rev4 ,,george ,,ni*ols ,,pack]1 ,,corn+1 ,n4 ,y4 ,ent]$ accord+ to ,act ( ,congress1 9 #ahij1 #ahib & #ahic1 ,,by ,,rev4 ,,george ,,ni*ols ,,pack]1 ,9 ! ,(fice ( ! ,libr>ian ( ,congress1 ,wa%+ton1 ,d4 ,c4 ,,all ,,rights ,,res]v$4 ,,williamsport1 ,,pa43 ,,fr$ ,r4 ,,mill] ,,blank ,,book ,,co4 #ahic4 ,,to ,,hon4 ,,h5ry ,w4 ,,williams1 ,,ju/ice ,,( ,,! ,,supreme ,,c\rt ,,( ,,p5nsylvania ,,:om ,i ,,h ,,f\nd ,a ,,true ,,fri5d ,,9 ,,pov]ty ,,& ,,9 ,,sickness1 ,,& ,,f ,,:om ,i ,,h ,,receiv$ ,,words ,,( ,,enc\ragem5t ,,& ,,com=t ,,dur+ ,,_m ,,ye>s ,,( ,,adv]sity1 ,,& ,,at ,,^: ,,sugge/ion ,,?is ,,little ,,volume ,,has ,,be5 ,,writt51 ,,& ,,by ,,^: ,,assi/ance ,,x ,,is ,,n[ ,,publi%$1 ,,?is ,,humble ,,volume ,,is ,,d$icat$ ,,z ,a ,,tribute ,,( ,,respect ,,by ,,! ,,au?or4 ,,preface4 ,_m ye>s ago1 :ile engag$ 9 tea*+1 ! writ] ( ?is little volume 0 9 ! habit ( br++ to ! att5tion ( 8 pupils a few simple rules = f9d+ ! dom9ical lett] & ! day ( ! week ( any giv5 ev5t )9 ! pa/ & ! pres5t c5turies2 fur!r ?an ?is he gave ! subject no special att5tion4 ,a few ye>s ago1 hav+ occasion to le>n ! day ( ! week ( c]ta9 ev5ts t 7 transpir+ at regul> int]vals on ! same day ( ! same mon?1 b 9 diff]5t ye>s1 he 0 l$ to inve/igate ! subject m ?or\ghly1 s t he is n[ able to give rules = f9d+ ! dom9ical lett] & ! day ( ! week ( any ev5t t has transpir$ or w transpire1 f ! comm5cem5t ( ! ,*ri/ian era to ! ye> ( our ,"l #d1jjj1 & to expla9 ! pr9ciples on :i* ^! rules re/4 ,:5 ! inve/igations 7 ent]$ ^u he _h no ?\ght ( writ+ a book2 b hav+ be5 laid aside f active labor by ill heal?1 he f\nd relief f ! despond5cy 9 :i* sickness & pov]ty plung$ him by pursu+ ! /udy ( ! cal5d>1 its hi/ory1 & ! me?od ( dispos+ ( ! fraction ( a day f\nd 9 ! "t requir$ = ! revolution ( ! ,e>? 9 its orbit ab\t ! ,sun4 ,he became s mu* int]e/$ 9 ! /udy ( ?is subject t he frequ5tly spoke ( x to fri5ds & acqua9tances :om he met4 ,on "o occasion1 :ile speak+ to ,hon4 ,h4 ,w4 ,williams ab\t "s ( ! curi\s results ( ! process by :i* ! co9cid5ce ( ! sol> & ! civil ye> is pres]v$1 x 0 sugge/$ to him t he %\ld put ! /ory ( ! cal5d>1 its correction by ,gregory1 & ! !ory & results ( int]calation1 9 writ+4 ,x 0 urg$ t ?is w\ld give increas$ int]e/ to ! /udy1 help ! writ] to =get 8 pa9s1 & probably enable him to realize a little money f ! sale ( 8 "w to meet press+ wants4 ,act+ ^u ?is sugge/ion1 an ef=t has be5 made to put into ?is little volume "s ( ! mo/ int]e/+ facts relat+ to ! orig91 condition1 & practical op]ation ( ! cal5d> n[ 9 use2 toge!r ) rules = f9d+ ! day ( ! week on :i* any giv5 day ( any mon? has fall5 or w fall dur+ f\r ?\s& ye>s f ! beg9n+ ( our era4 ,! writ] does n claim absolute orig9ality = all t appe>s 9 ! foll[+ pages2 on ! contr>y1 he has made free use ( all ! mat]ials t came )9 8 rea* relat+ to ! hi/ory ( ! cal5d> & ! "w ( its correction by ,gregory4 ,^! mat]ials1 toge!r ) 8 own calculations1 he has arrang$ 9 accordance ) a plan ( 8 own devis+1 s t ! outl9e & ! execution ( ! "w may be truly said to be orig9al4 ,( its value ! _w mu/ judge4 ,x has be5 prep>$ 9 weakness ( body & 9 suff]+1 :i* h be5 to "s ext5t reliev$ by ! m5tal occupation ?us af=d$1 b :i* may h nev]!less left _! impress on ! "w4 ,b let x be read be=e pron\nc+ judgm5t ^u x4 ,cic]o c\ld inf] ! littl5ess ( ! ,hebrew ,god f ! smallness ( ! t]ritory he _h giv5 8 p4 ,to :om ,kitto replies3 ,! int]e/ & importance ( a c\ntry arise1 n f its t]ritorial ext5t1 b f ! m5 :o =m its liv+ s\l2 f its in/itutions be>+ ! impress ( m9d & _s1 & f ! ev5ts :i* gr[ out ( ! "* & condition ( its inhabitants4 ,s ! value ( a book does n consi/ 9 ! size & numb] ( its pages1 b f ! k t may be ga9$ by its p]usal4 ,,! ,,au?or4 ,,preface ,,to ,,! ,,revis$ ,,edition4 ,soon aft] ! publication ( ! =m] edition ( ?is "w1 x 0 sugge/$ t a *apt] be add$ on ,ea/]2 rules = fix+ its date1 & also *ur* fe/ivals t dep5d$ ^u ! date ( ,ea/]4 ,x 0 sugge/$ t ?is w\ld add v mu* to ! value ( ! "w1 if s pres5t$ z to be br\ght )9 ! compreh5sion ( ord9>y m9ds4 ,kn[+ t ! det]m9ation ( ,ea/] 0 an affair ( consid]able nicety & complication1 & _h _h ! att5tion ( our be/ m9ds1 & !y _h fail$ s to pres5t x1 t ev5 among s*ol>ly m51 probably n "o 9 a hundr$ 0 able to det]m9e its date )\t ref]r+ to tables prep>$ = t purpose ! au?or ( ?is "w felt z ?\gh he 0 h>dly compet5t = ! task4 ,nev]!less x 0 und]tak51 & ! "w has be5 revis$ & enl>g$ by a ,*apt] on ! ,peculi>ities ( ! ,roman ,cal5d>1 ano!r on fix+ ! date ( ev5ts prior to ! ,*ri/ian era1 & a ?ird "p on ,ea/]1 *ur* fe/ivals1 & ! ,hebrew ,cal5d>4 ,9 ! op9ion ( ! au?or1 ! rules = det]m9+ ! date ( ,ea/] are s simplifi$ by 8 new me?od t any p]son ( ord9>y intellig5ce may und]/& !m4 ,h[ well he has succe$$ ! public w decide4 ,g4 ,n4 ,p4 ,,cont5ts4 ,,"p ,,fir/4 ,,def9itions--,,hi/ory4 ,pages4 ,,*apt] ,i4--,def9itions #aa ,,*apt] ,,ii4--,hi/ory ( ! divisions ( "t1 & ! old ,roman ,cal5d> #ab ,,*apt] ,,iii--,hi/ory ( ! re=mation ( ! ,cal5d> by ,julius ,caes> #ah ,,*apt] ,,iv4--,hi/ory ( ! re=mation ( ! ,julian ,cal5d> by ,pope ,gregory ,,xiii #bj ,,*apt] ,v4--,peculi>ities ( ! ,roman ,cal5d> #bf ,,"p ,,second4 ,,ma!matical4 ,,*apt] ,i4--,errors ( ! ,julian ,cal5d> #cf ,,*apt] ,,ii4--,errors ( ! ,gregorian ,cal5d> #ch ,,*apt] ,,iii4--,dom9ical ,lett] #ci ,,*apt] ,,iv4--,rule = f9d+ ! ,dom9ical ,lett] #dd ,,*apt] ,v4--,rule = f9d+ ! day ( ! week ( any giv5 date1 = bo? ,old & ,new ,/yles #ej ,,*apt] ,,vi4--,a simple me?od ( f9d+ ! day ( ! week ( ev5ts1 :i* occur quadr5nially2 ! inaugural ( ! ,presid5ts1 ! day ( ! week on :i* !y h occurr$ & on :i* !y w occur = ! next "o hundr$ ye>s #fa ,"s peculi>ities conc]n+ ev5ts :i* fall on ! #bi? ( ,febru>y #fd ,,*apt] ,,vii4--,rule = f9d+ ! day ( ! week ( ev5ts prior to ! ,*ri/ian era #fh ,,"p ,,?ird4 ,,cycles--,,julian ,,p]iod--,,ea/]4 ,,*apt] ,i4--,! ,sol> ,cycle #gc ,,*apt] ,,ii4--,! ,lun> ,cycle #ge ,,*apt] ,,iii4--,! ,lun> ,cycle & ,gold5 ,numb] #gg ,,*apt] ,,iv4--,cycle ( ,indiction1 & ! ,julian ,p]iod #gi ,,*apt] ,v4--,ea/] #hb ,,*apt] ,,vi4--,a new & easy me?od ( fix+ ! date ( ,ea/] #hh ,,*apt] ,,vii4--,*ur* fea/s & fa/s ^: date dep5d on ! date ( ,ea/] #ajh ,,*apt] ,,viii4--,hebrew ,cal5d> #abd ,,app5dix #acd ,,errata #adi ,,our ,,cal5d>4 ,,"p ,,fir/4 ,,def9itions4 ,,hi/ory4 ,,*apt] ,i4 ,,def9itions4 a--,a ,cal5d> is a me?od ( di/ribut+ "t into c]ta9 p]iods adapt$ to ! purposes ( civil life1 z h\rs1 days1 weeks1 mon?s1 ye>s1 etc4 b--,! only natural divisions ( "t are ! sol> day1 ! sol> ye>1 & ! lun> mon?4 c--,an h\r is "o ( ! subdivisions ( ! day into tw5ty-f\r equal p>ts4 d--,! true sol> day is ! int]val ( "t :i* elapses betwe5 two consecutive returns ( ! same t]re/rial m]idian to ! ,sun1 ! mean l5g? ( :i* is tw5ty-f\r h\rs4 e--,! week is a p]iod ( sev5 days1 hav+ no ref]5ce :atev] to ! cele/ial motions1 a circum/ance to :i* x owes its unalt]able uni=mity4 f--,! lun> mon? is ! "t :i* elapses betwe5 two consecutive new or full moons1 & 0 us$ 9 ! ,roman cal5d> until ! "t ( ,julius ,caes>1 & consi/s ( #bi;d1 #ab;h1 #ddm1 #b4hgs4 g--,! cal5d> mon? is usually employ$ to d5ote an arbitr>y numb] ( days approa*+ a twelf? "p ( a ye>1 & has n[ its place 9 ! cal5d> ( ne>ly all nations4 h--,! ye> is ei!r a/ronomical or civil4 ,! sol> a/ronomical ye> is ! p]iod ( "t 9 :i* ! ,e>? p]=ms a revolution 9 its orbit ab\t ! sun or passes f any po9t ( ! ecliptic to ! same po9t aga91 & consi/s ( #cfe days1 #e h\rs1 #dh m9utes & #di4fb seconds ( mean sol> "t4 ,app5dix ,a4 i--,! civil ye> is t :i* is employ$ 9 *ronology1 & v>ies among diff]5t nations1 bo? 9 respect ( ! seasons at :i* x comm5ces & ( its subdivisions4 ,,*apt] ,,ii4 ,,hi/ory ,,( ,,! ,,divisions ,,( ,,"t ,,& ,,! ,,old ,,roman ,,cal5d>4 ,day--,! subdivision ( ! day into tw5ty-f\r p>ts or h\rs has prevail$ s9ce ! remote/ ages1 ?\gh diff]5t nations h n agre$ ei!r ) respect to ! epo* ( its comm5cem5t or ! mann] ( di/ribut+ ! h\rs4 ,europeans 9 g5]al1 l ! anci5t ,egyptians1 place ! comm5cem5t ( ! civil day at midnight2 & reckon twelve morn+ h\rs f midnight to midday & twelve ev5+ h\rs f midday to midnight4 ,a/ronom]s1 aft] ! example ( ,ptolemy1 reg>d$ ! day z comm5c+ ) ! ,sun's culm9ation1 or noon1 & f9d x mo/ conv5i5t = ! purpose ( computation to reckon ?r\gh ! :ole tw5ty-f\r h\rs4 ,hipp>*us reckon$ ! tw5ty-f\r h\rs f midnight to midnight4 ,! ,roman day1 f sunrise to sunset1 & ! night1 f sunset to sunrise1 7 ea* divid$ at all seasons ( ! ye> into twelve h\rs1 ! h\r be+ uni=mly "o-twelf? ( ! day or ! night1 ( c\rse1 v>i$ 9 l5g? ) ! l5g? ( ! day or night at diff]5t seasons ( ! ye>4 ,week--,al?\gh ! week did n ent] into ! cal5d> ( ! ,greeks1 & 0 n introduc$ at ,rome till aft] ! reign ( ,!odosius1 ,a4 ,d4 #bib1 x has be5 employ$ f "t immemorial 9 almo/ all ,ea/]n c\ntries2 & z x =ms nei!r an aliquot "p ( a ye> nor ( ! lun> mon?s1 ^? :o reject ! ,mosaic recital w be at a loss to assign to x an orig9 hav+ mu* semblance ( probability4 ,9 ! ,egyptian a/ronomy ! ord] ( ! planets1 beg9n+ ) ! mo/ remote1 is ,saturn1 ,jupit]1 ,m>s1 ! ,sun1 ,v5us1 ,m]cury1 ! ,moon4 ,n[1 ! day be+ divid$ into tw5ty-f\r h\rs1 ea* h\r 0 consecrat$ to a p>ticul> planet1 namely3 ,"o to ,saturn1 ! foll[+ to ,jupit]1 ?ird to ,m>s1 & s on accord+ to ! above ord]2 & ! day receiv$ ! "n ( ! planet :i* presid$ ov] its fir/ h\r4 ,if1 !n1 ! fir/ h\r ( a day 0 consecrat$ to ,saturn1 t planet w\ld also h ! #h?1 ! #e? & ! #bb;d h\rs2 ! #bc;d w\ld fall to ,jupit]1 ! #bd? to ,m>s1 & ! #be? or ! fir/ h\r ( ! second day w\ld belong to ! ,sun4 ,9 l mann] ! fir/ h\r ( ! ?ird day w\ld fall to ! ,moon1 ! fir/ h\r ( ! f\r? to ,m>s1 ( ! fif? to ,m]cury1 ( ! six? to ,jupit] & ! sev5? to ,v5us4 ,! cycle be+ complet$1 ! fir/ h\r ( ! eigh? day w\ld aga9 return to ,saturn & all ! o!rs succe$ 9 ! same ord]4 ,see table on ! #ag? page4 ,x w be se5 by ! table1 & x is also record$ by ,dio ,cassius1 ( ! second ,c5tury1 t ! ,egyptian week comm5c$ ) ,saturday4 ,on _! flight f ,egypt ! ,jews1 f hatr$ to _! anci5t oppressors1 made ,saturday ! la/ day ( ! week4 ,x is /at$ t ! anci5t ,saxons borr[$ ! week f "s ,ea/]n nation1 & sub/itut$ ! names ( _! own div9ities = ^? ( ! gods ( ,greece4 ,! names ( ! days are "h giv5 9 ,lat91 ,saxon & ,engli%4 ,x w be se5 t ! ,engli% names ( ! days are d]iv$ f ! ,saxon4 ,,lat94 ,,saxon4 ,,engli%4 ,dies ,solis4 ,sun's ,day4 ,,sunday4 ,dies ,lunae4 ,moon's ,day4 ,,monday4 ,dies ,m>tis4 ,tiw's ,day4 ,,tuesday4 ,dies ,m]curii4 ,wod5's ,day4 ,,w$nesday4 ,dies ,jovis4 ,?or's ,day4 ,,?ursday4 ,dies ,v5]is4 ,friga's ,day4 ,,friday4 ,dies ,saturni4 ,set]ne's ,day4 ,,saturday4 ,mon?--,! anci5t ,roman ye> conta9$ b t5 mon?s & is indicat$ by ! names ( ! la/ f\r4 ,septemb] f ,septem1 sev52 ,octob] f ,octo1 eight2 ,novemb] f ,novem1 n9e1 & ,decemb] f ,decem1 t52 ,july & ,augu/ 7 also d5om9at$ ,qu9tilis & ,sextilis1 f ,qu9tus five1 & ,sex1 six4 ,qu9tilis 0 *ang$ to ,july 9 honor ( ,julius ,caes>1 :o 0 born on ! #ab? ( t mon? #ih ,b4 ,c4 ,sextilis 0 *ang$ to ,augu/ by ! ,roman ,s5ate to flatt] ,augu/us on 8 victories ab\t #h ,b4 ,c4 ,9 ! reign ( ,numa ,pompilius1 ab\t #gjj ,b4 ,c41 two mon?s 7 add$ to ! ye>1 ,janu>y at ! beg9n+1 & ,febru>y at ! end ( ! ye>4 ,?is arrangem5t cont9u$ till #dej ,b4 ,c41 :5 ! ,decemvirs 7t5 magi/rates7 *ang$ ! ord]1 plac+ ,febru>y aft] ,janu>y1 mak+ ,m>* ! ?ird in/ead ( ! fir/ mon? ( ! ,roman ye>4 ,ye>--,if ! civil ye> correspond ) ! sol> ! seasons ( ! ye> w always come at ! same p]iod4 ,b if ! civil ye> is suppos$ to be too long 7z is ! case 9 ! ,julian ye>7 ! seasons w g back proportionately2 b if too %ort !y w advance 9 ! same proportion4 ,n[1 z ! anci5t ,egyptians reckon$ ?irty days to ! mon? inv>iably1 & to complete ! ye>1 add$ five days1 call$ supplem5t>y days1 _! ye> consi/$ ( #cfe days4 ,!y made use ( no int]calation1 & by los+ "o-f\r? ( a day e ye>1 ! comm5cem5t ( ! ye> w5t back "o day 9 e p]iod ( f\r ye>s1 & consequ5tly made a revolution ( ! seasons 9 #adfj ye>s4 ,h5ce ! ,egyptian ye> 0 call$ a vague or erratic ye> because ! fir/ day ( ! ye> 9 ! c\rse ( #adfj ye>s w&]$1 z x 71 ov] all ! seasons4 ,!re=e #adfj ,julian ye>s ( #cfe-a_/d days ea* are equal to #adfa ,egyptian ye>s ( #cfe days ea*4 ,! anci5t ,roman ye> consi/$ ( twelve lun> mon?s1 ( tw5ty-n9e & ?irty days alt]nately1 :i* equals #ced days2 b a day 0 add$ to make ! numb] odd1 :i* 0 consid]$ m =tunate1 s t ! ye> consi/$ ( #cee days4 ,?is diff]$ f ! sol> ye> by t5 :ole days & a fraction2 b to re/ore ! co9cid5ce1 ,numa ord]$ an additional or int]cal>y mon? to be ins]t$ e second ye> betwe5 ! #bc;d & #bd? ( ,febru>y1 consi/+ ( tw5ty-two & tw5ty-?ree days alt]nately1 s t f\r ye>s conta9$ #adfe days1 & ! mean l5g? ( ! ye> 0 consequ5tly #cff-a_/d days1 s t ! ye> 0 !n too long by "o day4 ,z ! error am\nt$ to tw5ty-f\r days 9 z _m ye>s1 x 0 ord]$ t e ?ird p]iod ( eight ye>s1 in/ead ( conta9+ f\r int]cal>y mon?s1 two ( tw5ty-two & two ( tw5ty-?ree days1 am\nt+ 9 all to n9ety days1 %\ld conta9 only ?ree ( ^? mon?s ( tw5ty-two days ea*1 am\nt+ to sixty-six days1 !reby suppress+ tw5ty-f\r days 9 z _m ye>s1 r$uc+ ! mean l5g? ( ! ye> to #cfe-a_/d days4 ,_h ! int]calations be5 regul>ly made ! concurr5ce ( ! sol> & ! civil ye> w\ld h be5 pres]v$ v ne>ly4 ,b its regulation 0 left to ! pontiffs1 :o1 to prolong ! t]m ( a magi/racy or ha/5 an annual election1 w\ld give to ! int]cal>y mon? a great] or less numb] ( days1 & consequ5tly ! cal5d> 0 ?r[n into confusion1 s t 9 ! "t ( ,julius ,caes> !re 0 a discrepancy betwe5 ! sol> & ! civil ye> ( ab\t ?ree mon?s2 ! w9t] mon?s be+ c>ri$ back into autumn & ! autumnal into summ]4 ,a table ( ! ord] & ! names ( ! planets 9 ! ,egyptian a/ronomy illu/rat+ ! orig9 ( ! names ( ! days ( ! week3 ---------------------------------------- ----------------- ,saturn1 ,jupit]1 ,m>s1 ,sun1 ,v5us1 ,m]cury1 ,moon1 ,saturday4,?ursday4,tuesday4,sunday4,fri day4,w$nesday4,monday4 ---------------------------------------- ----------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd ---------------------------------------- ----------------- ,,*apt] ,,iii4 ,,hi/ory ,,( ,,! ,,re=mation ,,( ,,! ,,cal5d> ,,by ,,julius ,,caes>4 ,9 ord] to put an end to ! disord]s aris+ f ! neglig5ce or ignorance ( ! pontiffs1 ,julius ,caes>1 #df ,b4 ,c41 aboli%$ ! use ( ! lun> ye> & ! int]cal>y mon?1 & regulat$ ! civil ye> entirely by ! ,sun4 ,) ! advice & assi/ance ( ! a/ronom]s1 especially ,sosig5es ( ,alex&ria1 he fix$ ! mean l5g? ( ! ye> at #cfe-a_/d days1 & decid$ t !re %\ld be ?ree consecutive ye>s ( #cfe days1 & a f\r? ( #cff4 ,9 ord] to re/ore ! v]nal equ9ox to ! #bd? ( ,m>*1 ! place x occupi$ 9 ! "t ( ,numa1 two mon?s1 toge!r consi/+ ( #fg days1 7 ins]t$ betwe5 ! la/ day ( ,novemb] & ! fir/ day ( ,decemb] ( t ye>4 ,an int]cal>y mon? ( #bc days _h already be5 add$ to ,febru>y ( ! same ye> accord+ to ! old me?od1 s t ! fir/ ,julian ye> comm5c$ ) ! fir/ day ( ,janu>y1 #de ye>s be=e ,*ri/1 & #gji f ! f\ndation ( ,rome1 mak+ ! ye> ,a4 ,u4 ,c4 #gjh to consi/ ( ! prodigi\s numb] ( #dde days1 7i4 e4 #cee #bc #fg #dde74 ,h5ce x 0 call$ by "s ! ye> ( confusion2 ,macrobius said x %\ld be nam$ ! la/ ye> ( confusion4 ,!re 0 also adopt$ at ! same "t a m commodi\s arrangem5t 9 ! di/ribution ( ! days ?r\gh\t ! sev]al mon?s4 ,x 0 decid$ to give to ,janu>y1 ,m>*1 ,may1 ,july1 ,septemb] & ,novemb] ea* ?irty-"o days2 & ! o!r mon?s ?irty1 except+ ,febru>y1 :i* 9 common ye>s %\ld h b tw5ty-n9e days1 b e f\r? ye> ?irty2 s t ! av]age l5g? ( ! ,julian ye> 0 #cfe-a_/d days4 ,augu/us ,caes> int]rupt$ ?is ord] by tak+ "o day f ,febru>y1 r$uc+ x to tw5ty-eight & giv+ x to ,augu/1 t ! mon? be>+ 8 "n %\ld h z _m days z ,july1 :i* 0 nam$ 9 honor ( 8 great-uncle1 ,julius4 ,9 ord] t ?ree mon?s ( ?irty-"o days might n come toge!r1 ,septemb] & ,novemb] 7 r$uc$ to ?irty days1 & ?irty-"o giv5 to ,octob] & ,decemb]4 ,9 ! ,julian cal5d> a day 0 add$ to ,febru>y e f\r? ye>1 x be+ ! %orte/ mon?1 :i* 0 call$ ! additional or int]cal>y day1 & 0 ins]t$ 9 ! cal5d> betwe5 ! #bc;d & #bd? ( t mon?4 ,9 ! anci5t ,roman cal5d> ! fir/ day ( e mon? 0 inv>iably call$ ! cal5ds4 ,! #bd? ( ,febru>y !n 0 ! #f? ( ! cal5ds ( ,m>*--,sexto cal5das2 ! prec$+1 :i* 0 ! additional or int]cal>y day1 0 call$ bis-sexto cal5das 7f bis1 twice1 & sextus1 six71 twice ! six? day4 ,h5ce ! t]m bis-sextile z appli$ to e f\r? ye>1 commonly call$ leap-ye>4 ,app5dix ,b4 ,,*apt] ,,iv4 ,,hi/ory ,,( ,,! ,,re=mation ,,( ,,! ,,julian ,,cal5d> ,,by ,,pope ,,gregory ,,xiii4 ,true en\gh1 ! ye> 9 :i* ,julius ,caes> re=m$ ! anci5t ,roman cal5d> 0 ! la/ ye> ( confusion1 & ! me?od adopt$ by him a commodi\s "o1 & answ]$ a v good purpose = a %ort "t2 b z ! ye>s roll$ on & c5tury aft] c5tury _h pass$ away1 a/ronom]s began to discov] ! discrepancy betwe5 ! sol> & ! civil ye>2 t ! v]nal equ9ox did n occupy ! place x occupi$ 9 ! "t ( ,caes>1 namely1 ! #bd? ( ,m>*1 b 0 gradually retrograd+ t[>ds ! beg9n+ ( ! ye>1 s t at ! meet+ ( ! ,c\ncil ( ,nice 9 #cbe x fell on ! #ba/4 ,app5dix ,c4 ,! v5]able ,b$e1 9 ! #h? c5tury1 obs]v$ t ^! ph5om5a took place ?ree or f\r days e>li] ?an at ! meet+ ( t c\ncil4 ,rog] ,bacon1 9 ! #ac? c5tury1 wrote a treatise on ?is subject & s5t x to ! ,pope1 sett+ =? ! errors ( ! ,julian cal5d>4 ,! discrepancy at t "t am\nt$ to sev5 or eight days4 ,?us ! errors ( ! cal5d> cont9u$ to increase until #aehb1 :5 ! v]nal equ9ox fell on ! #aa? in/ead ( ! #ba/ ( ,m>*4 ,gregory1 p]ceiv+ t ! measure 7( re=m+ ! cal5d>7 0 likely to conf] great eclat on 8 pontificate1 und]took ! long desir$ re=mation2 & hav+ f\nd ! gov]nm5ts ( ! pr9cipal ,ca?olic /ates ready to adopt 8 views1 he issu$ a brief 9 ! mon? ( ,m>*1 #aehb1 9 :i* he aboli%$ ! use ( ! anci5t cal5d>1 & sub/itut$ t :i* has s9ce be5 receiv$ 9 almo/ all ,*ri/ian c\ntries "u ! "n ( ! ,gregorian cal5d> or ,new ,/yle4 ,! edict ( ! ,pope took effect 9 ,octob] ( t ye>1 caus+ ! #e? to be call$ ! #ae? ( t mon?1 ?us suppress+ t5 days & mak+ ! ye> #aehb to consi/ ( only #cee days4 ,s we see t ! t5 days t _h be5 ga9$ by incorrect computation dur+ ! pa/ #abeg ye>s1 7 d$uct$ f #aehb1 re/or+ ! concurr5ce ( ! sol> & ! civil ye>1 & consequ5tly ! v]nal equ9ox to ! place x occupi$ 9 #cbe1 namely1 ! #ba/ ( ,m>*4 ,! ,pope 0 promptly obey$ 9 ,spa91 ,portugal1 & ,italy4 ,! *ange took place ! same ye> 9 ,france1 by call+ ! #aj? ! #bj? ( ,decemb]4 ,_m o!r ,ca?olic c\ntries made ! *ange ! same ye>1 & ! ,ca?olic /ates ( ,g]many ! ye> foll[+2 b mo/ ( ! ,prote/ant c\ntries adh]$ to ! ,old ,/yle until aft] ! ye> #agjj4 ,among ! la/ 0 ,great ,brita92 %e1 aft] hav+ suff]$ a great deal ( inconv5i5ce = ne>ly two hundr$ ye>s by us+ a diff]5t date f ! mo/ ( ,europe1 at l5g?1 by an act ( ,p>liam5t1 fix$ on ,septemb]1 #ageb1 z ! "t = mak+ ! mu* desir$ *ange1 :i* 0 done by call+ ! #c;d ( t mon? ! #ad? 7z ! error n[ am\nt$ to elev5 days71 adopt+ at ! same "t ! ,gregorian rule ( int]calation4 ,russia is ! only ,*ri/ian c\ntry t /ill adh]es to ! ,old ,/yle1 & by us+ a diff]5t date f ! re/ ( ,europe is n[ twelve days beh9d ! true "t4 ,! discrepancy betwe5 sol> & civil "t does n effect ! day1 =1 z has already be5 %[n1 ! mean l5g? ( ! day is tw5ty-f\r h\rs1 & is m>k$ by "o revolution ( ! e>? ^u its axis4 ,nor does x effect ! week1 = ! week is uni=mly sev5 ( ^? days4 ,b x effects ! ye>1 ! mon? & ! day ( ! mon?4 ,russia1 by adh]+ to ! ,old ,/yle1 has reckon$ z _m days & z _m weeks1 & ev5ts h transpir$ on ! same day ( ! week z !y h ) u :o h adopt$ ! ,new ,/yle2 z ,*ri/ian nations we are obs]v+ ! same day z ! ,sabba?4 ,:5 x 0 ,tuesday1 ! #bj? day ( ,decemb]1 #ahhh1 9 ,russia1 x 0 ,tuesday1 ! #a/ day ( ,janu>y1 #ahhi1 9 ^? c\ntries :i* h adopt$ ! ,new ,/yle4 ,columbus sail$ f ,palos1 9 ,spa91 on ,friday1 ,augu/ #c;d1 #adib1 ,old ,/yle1 :i* 0 ,friday1 ,augu/ #ab?1 ,new ,/yle4 ,wa%+ton 0 born on ,friday1 ,febru>y #aa?1 #agcb1 ,old ,/yle1 :i* 0 ,friday1 ,febru>y #bb;d1 ,new ,/yle4 ,n[1 ! diff]5ce 9 /yles dur+ ! #ae? c5tury is n9e days2 dur+ ! #af? & #ag? c5turies1 t5 days2 ! #ah? c5tury1 elev5 days1 & ! #ai?1 twelve days4 ,9 reg>d to ! sail+ ( ,columbus1 ! *ange is made by suppress+ n9e days1 call+ ! #c;d ! #ab? ( ,augu/4 ,9 reg>d to ! bir? ( ,wa%+ton1 ! *ange is effect$ by suppress+ elev5 days1 call+ ! #aa? ( ,febru>y ! #bb;d4 ,z reg>ds ,russia1 %e c\ld h made ! *ange la/ ye> by call+ ! #bj? ( ,decemb]1 #ahhh1 ! #a/ day ( ,janu>y1 #ahhi1 !reby suppress+ twelve days1 & mak+ ! ye> #ahhh to consi/ ( only #ced days1 & ! mon? ( ,decemb] tw5ty days4 ,! me?ods ( computation1 bo? ,old & ,new ,/yles1 w be expla9$ 9 ano!r *apt]4 ,to p]sons unacqua9t$ ) a/ronomy1 ! diff]5ce betwe5 ,old & ,new ,/yles w\ld probably be bett] und]/ood by ! diagram on ! #be? page4 ,! figures repres5t ! ecliptic1 :i* is ! app>5t pa? ( ! ,sun1 or ! real pa? ( ! ,e>? z se5 f ! ,sun1 9 h] annual or ye>ly revolution ar\nd ! ,sun 9 ! ord] ( ! mon?s1 z m>k$ on ! ecliptic4 ,att5tion is call$ to f\r po9ts on ! ecliptic1 namely1 ! v]nal equ9ox1 ! autumnal equ9ox1 ! w9t] sol/ice1 & ! summ] sol/ice4 ,^! occur1 9 ! ord] giv5 above1 on ! #ba/ ( ,m>*1 ! #ba/ ( ,septemb]1 ! #ba/ ( ,decemb] & ! #ba/ ( ,june4 ,x has already be5 /at$ t if ! civil ye> correspond ) ! sol>1 ! seasons ( ! ye> w always come at ! same p]iod4 ,julius ,caes> f\nd ! anci5t ,roman ye> 9 advance ( ! sol>2 ,gregory f\nd ! ,julian beh9d ! sol> ye>2 s "o re=ms ! cal5d> by int]calation1 ! o!r by suppression4 ,app5dix ,d4 ,caes> re/or$ ! co9cid5ce ( ! sol> & ! civil ye>1 b fail$ to reta9 x by all[+ :at probably appe>$ to him at ! "t a trifl+ error 9 8 cal5d>4 ,! error1 :i* 0 #aa m9utes & #aj4ch seconds e ye>1 0 h>dly p]ceptable = a %ort p]iod1 b /ill am\nt$ to ?ree days e #djj ye>s4 ,h5ce ! necessity 9 #aehb ( re=m+ ! re=m$ cal5d> ( ,julius ,caes> to re/ore ! co9cid5ce4 ,app5dix ,e4 ,f ! meet+ ( ! ,c\ncil ( ,nice1 9 #cbe1 to #aehb1 a p]iod ( #abeg ye>s1 !re 0 f\nd to be an error 9 ! ,julian cal5d> ( t5 days4 ,n[1 9 #abeg ye>s ! ,e>? p]=ms #abeg annual & #dei1aji daily revolutions1 aft] :i* ! v]nal equ9ox 0 f\nd to occur on ! #ba/ ( ,m>*1 true or sol> "t2 ?us concurr+ ) ! v]nal equ9ox ( #cbe4 ,b ! errone\s ,julian cal5d> w\ld make ! ,e>? p]=m #dei1aai daily revolutions to complete ! #abeg ye>s1 a discrepancy ( t5 days1 mak+ ! v]nal equ9ox to fall on ! #aa? in/ead ( ! #ba/4 ,x w be se5 by ! diagram t ! t5 days 7 d$uct$ f ,octob]1 9 #aehb1 mak+ x a %ort mon?1 consi/+ ( only tw5ty-"o days4 ,! discrepancy betwe5 ! ,julian & ,gregorian cal5d> am\nts to ?irty days 9 #djjj ye>s2 ?ree mon?s 9 #ab1age ye>s4 ,h5ce1 9 #ab1age ye>s ! equ9oxes w\ld take ! place ( ! sol/ices1 & ! sol/ices ! place ( ! equ9oxes4 ,9 #bd1cej ye>s1 ! v]nal equ9ox w\ld take ! place ( ! autumnal equ9ox1 & ! w9t] sol/ice ! place ( ! summ] sol/ice4 ,& 9 #dh1gjj ye>s1 accord+ to ! ,julian rule ( int]calation1 !re w\ld be ga9$ ne>ly #cfe-a_/d days1 or "o entire revolution ( ! ,e>?4 ,s1 to re/ore ! concurr5ce ( ! ,julian & ,gregorian ye>s1 !re w\ld h to be suppress$ #cfe-a_/d days1 call+ ! #a/ day ( ,janu>y1 #dh1fii1 ! #a/ day ( ,janu>y1 #dh1gjj4 ,?us w\ld disappe> f ! ,julian cal5d> twelve mon?s1 or "o :ole ye>1 x hav+ be5 divid$ among ! ?\s&s ( ! prec$+ ye>s4 ,illu/ration3 ,! ,julian cal5d>1 re=m$ by ,gregory ,,xiii1 ,oct4 #e?1 #aehb1 by suppress+ t5 days1 call+ ! #e? ( ,oct4 ! #ae?1 mak+ x a %ort mon? ( #ba days1 & ! ye> to consi/ ( #cee days4 ,! ,roman cal5d>1 re=m$ by ,julius ,caes>1 #df ,b4 ,c41 by int]calat+ #ij days1 mak+ t ye> to consi/ ( #dde days1 t is1 #cee #bc #fg #dde days1 & ! la/ ye> ( confusion4 ,to make ?is subject bett] und]/ood1 let u suppose ! sol> ye> to consi/ 9 r\nd numb]s ( #cfe days1 & ! civil ye> #cff4 ,x is evid5t t at ! end ( ! ye> ( #cfe days1 !re w\ld /ill be want+ "o day to complete ! civil ye> ( #cff days1 s "o day mu/ be add$ to t ye>1 & to e succe$+ ye>1 to complete ! ye>s ( #cff days ea*1 :i* w\ld be ! loss ( "o ye> ( #cfe days 9 #cfe ye>s4 ,h5ce1 #cfd ye>s ( #cff days ea* are equal to #cfe ye>s ( #cfe days ea*1 want+ "o day4 ,aga91 let u suppose ! civil ye> to consi/ ( #cfd days4 ,x is evid5t t at ! end ( ! suppos$ sol> ye> ( #cfe days1 !re w\ld be an advance or ga9 ( "o day 9 t ye> & e succe$+ ye>1 s t 9 #cfe ye>s !re w\ld be a ga9 ( #cfe days or "o :ole ye>4 ,h5ce1 #cff ye>s ( #cfd days ea* are equal to #cfe ye>s ( #cfe days ea*1 want+ "o day4 ,app5dix ,f4 ,,*apt] ,v4 ,,peculi>ities ,,( ,,! ,,roman ,,cal5d>4 ,! ,romans1 in/ead ( di/+ui%+ ! days ( ! mon? by ! ord9al numb]s1 fir/1 second1 ?ird1 etc41 c\nt$ backw>ds f ?ree fix$ po9ts1 namely1 ! ,cal5ds1 ! ,nones1 & ! ,ides4 ,cal5ds 7,lat9 ,cal&ae1 f ,cal>e1 to call17 0 s d5om9at$ because x _h be5 an anci5t cu/om ( ! pontiffs to call ! p toge!r on t day to apprise !m ( ! fe/ivals1 or days t 7 to be kept sacr$ dur+ ! mon?4 ,nones 7,lat9 nonae1 f nonus1 ! n9?17 ! n9? day be=e ! ,ides4 ,ides 7,lat9 idus1 suppos$ to be d]iv$ f an obsolete v]b idu>e1 to divide17 0 ne> ! middle ( ! mon?1 ei!r ! #ac? or ! #ae? day4 ,! fir/ day ( ea* mon? 0 inv>iably call$ ! ,cal5ds4 ,! ,nones 7 ! fif?1 & ! ,ides ! ?irte5?1 except 9 ,m>*1 ,may1 ,july1 & ,octob]1 9 :i* ! ,nones occurr$ on ! sev5? day & ! ,ides on ! fifte5?4 ,f ^! ?ree po9ts ! days ( ! mon? 7 numb]$--n =w>d1 b backw>d--z s _m days be=e ! ,nones1 ! ,ides1 or ! ,cal5ds1 ! po9t ( dep>ture be+ c\nt$ 9 ! reckon+1 s t ! la/ day ( e mon? 0 ! second ( ! ,cal5ds ( ! foll[+ mon?4 ,x w be se5 by ! ,roman & ,engli% cal5d> f\nd on ! foll[+ pages1 t !re are six days ( ,nones 9 ,m>*1 ,may1 ,july & ,octob]1 & f\r ( all ! o!r mon?s2 also t all ! mon?s h eight days ( ,ides4 ,! numb] ( days ( ,cal5ds dep5d ^u ! numb] ( days 9 ! mon?1 & ! day ( ! mon? on :i* ! ,ides fall4 ,if ! mon? has ?irty-"o days & ! ,ides fall on ! ?irte5?1 !re are n9ete5 days ( ,cal5ds2 b if ! ,ides fall on ! fifte5?1 !re are only sev5te5 days ( ,cal5ds4 ,z ! ,ides fall on ! ?irte5? ( all ! mon?s ( ?irty days1 !y h eighte5 days ( ,cal5ds4 ,febru>y1 ! mon? ( tw5ty-eight days1 has only sixte51 except 9 leap-ye>1 :5 ! six? ( ! ,cal5ds is reckon$ twice4 ,x may also be se5 f ! cal5d> t ! ,romans1 aft] ! fir/ day ( ! mon?1 began to reckon s _m days be=e ! ,nones1 z #d?1 #c;d1 #b;d1 !n ,nones2 aft] ! ,nones1 s _m days be=e ! ,ides1 z #h?1 #g?1 #f?1 etc41 & aft] ! ,ides1 s _m be=e ! ,cal5ds ( ! next mon?1 ! highe/ numb]s be+ reckon$ fir/4 ,9 r$uc+ ! ,roman cal5d> to our own1 x %\ld be rememb]$ t 9 reckon+ backw>d f a fix$ po9t1 t ! po9t ( dep>ture is c\nt$2 also1 t ! la/ day ( ! mon? is n ! po9t f :i* ! ,cal5ds are reckon$1 b ! fir/ day ( ! foll[+ mon?4 ,we h !n ?is rule = f9d+ ! ,engli% expression = any ,lat9 date3 ,,rule4 ,if ! giv5 date be ,cal5ds1 add two to ! numb] ( days 9 ! mon?1 f :i* subtract ! giv5 date2 if ! date be ,nones1 or ,ides1 add "o to t ( ! day on :i* ! ,nones or ,ides fall1 f :i* subtract ! giv5 date1 & y w h ! day ( ! mon? 9 our cal5d>4 ,to f9d ! ,lat9 expression = any ,engli% date1 ! prec$+ me?od is to be rev]s$1 ^u ! pr9ciple t if #e - #c #b1 !n #e - #b #c4 ,b 9 r$uc+ a ,roman date to a date ( ,febru>y 9 leap-ye>1 = ! fir/ tw5ty-f\r days1 proce$ accord+ to ! prec$+ rule z if ! mon? _h only tw5ty-eight days1 & to obta9 ! prop] expression = ! rema9+ five days1 reg>d ! mon? z hav+ tw5ty-n9e days1 tak+ ! ,roman date f #ca in/ead ( #cj4 ,?us #ca - #f #be1 :ile #cj -#f #bd2 ! =m] correspond+ ) sexto cal5das1 ! latt] ) bis-sexto cal5das ( ! ,julian cal5d>4 ,by ref]r+ to ! table on ! #ce? page1 "o may easily le>n h[ to f9d ! ,engli% expression = any ,lat9 date1 or ! ,lat9 expression = any ,engli% date4 ,x has already be5 /at$ t 9 ,janu>y ! ,nones fall on ! #e?1 & ! ,ides on ! #ac?1 ,janu>y !n hav+ ?irty "o days1 ! numb] f :i* to subtract ! ,roman date to obta9 ! correspond+ day ( ! mon? is1 = ,nones1 #e #a #f2 = ,ides1 #ac #a #ad2 = ,cal5ds1 #ca #b #cc4 ,h5ce ! fir/ column 9 ! table "u ,janu>y are ! numb]s #f1 #ad & #cc4 ,febru>y is ! same z ,janu>y = ,nones & ,ides4 ,= ,cal5ds 9 leap-ye>1 = ! fir/ #bd days1 x is #bh #b #cj2 = ! rema9+ #e days x is #bi #b #ca4 ,h5ce = ! fir/ column "u ,febru>y are ! numb]s #f1 #ad1 #cj & #ca4 ,m>* is ! same z ,janu>y1 except t ! ,nones fall on ! #g? & ! ,ides on ! #ae?1 consequ5tly we h = ,nones1 #g #a #h1 & = ,ides1 #ae #a #af2 h5ce1 = ! fir/ column "u ,m>* we h ! numb]s #h1 #af1 & #cc4 ,9 ! table ! ?ree mon?s are tak5 to illu/rate h[ easily ! *ange may be made f ,roman to ,engli%1 or f ,engli% to ,roman date4 ,a complete cal5d> = #ahib1 bo? 9 ,roman & ,engli%1 :i* w be v conv5i5t = ref]5ce1 may be f\nd on ! f\r foll[+ pages4 ,! fir/ sev5 lett]s ( ! alphabet1 us$ to repres5t ! days ( ! week1 are plac$ 9 ! cal5d> beside ! days ( ! week4 ,! lett] t repres5ts ,sunday is call$ ! dom9ical or ,sunday lett]4 ,! lett] t repres5ts ! fir/ ,sunday 9 any giv5 ye> repres5ts all ! ,sundays 9 t ye>1 unless x be leap-ye>1 :5 two ,sunday lett]s are us$4 ,! fir/ repres5ts all ! ,sundays 9 ,janu>y & ,febru>y1 :ile ! lett] t prec$es x repres5ts all ! ,sundays = ! re/ ( ! ye>4 ,! reason ( ?is is1 ! day int]calat$1 or ?ru/ 91 betwe5 ! #bh? day ( ,febru>y & ! #a/ day ( ,m>* s int]rupts ! ord] ( ! lett]s t ,d1 :i* always repres5ts ! #a/ day ( ,m>*1 n[ repres5ts ! #bi? day ( ,febru>y1 s t 9 #ahib x repres5ts ,monday1 ! #bi? day ( ,febru>y1 also ,tuesday ! #a/ day ( ,m>*4 ,z x repres5t$ all ! ,mondays 9 ,janu>y & ,febru>y1 x w n[ repres5t all ! ,tuesdays = ! re/ ( ! ye>1 :ile ,c1 ! lett] prec$+1 repres5t$ all ! ,sundays1 w n[ repres5t all ! ,mondays1 & ,b all ! ,sundays4 ,= ,janu>y & ,febru>y we h !n ,c1 ,sunday2 ,d1 ,monday2 ,e1 ,tuesday2 ,f1 ,w$nesday2 ,g1 ,?ursday2 ,a1 ,friday1 & ,b1 ,saturday4 ,= ! re/ ( ! ye> we h ,b1 ,sunday2 ,c1 ,monday2 ,d1 ,tuesday2 ,e1 ,w$nesday2 ,f1 ,?ursday2 ,g1 ,friday1 & ,a1 ,saturday4 ,see ,"p ,second1 *apt]s ,,iv & ,v4 ---------------------------------------- -------------- ,,jan41 #ahib4 ,,feb41 #ahib4 ,,m>*1 #ahib4 ---------------------------------------- -------------- #a;,cal4 a,fri4 #a;,cal4 d,mon4 #a;,cal4 d,tues4 #b #d b,sat4 #b #d e,tues4 #b #f e,w$4 #c #c c,sun4 #c #c f,w$4 #c #e f,?ur4 #d #b d,mon4 #d #b g,?ur4 #d #d g,fri4 #e,non4 e,tues4 #e,non4 a,fri4 #e #c a,sat4 #f #h f,w$4 #f #h b,sat4 #f #b b,sun4 #g #g g,?ur4 #g #g c,sun4 #g,non4 c,mon4 #h #f a,fri4 #h #f d,mon4 #h #h d,tues4 #i #e b,sat4 #i #e e,tues4 #i #g e,w$4 #aj #d c,sun4 #aj #d f,w$4 #aj #f f,?ur4 #aa #c d,mon4 #aa #c g,?ur4#aa #e g,fri4 #ab #b e,tues4#ab #b a,fri4 #ab #d a,sat4 #ac;,ides4f,w$4 #ac;,ides4b,sat4 #ac #c b,sun4 #ad #ai g,?ur4#ad #af c,sun4 #ad #b c,mon4 #ae #ah a,fri4 #ae #ae d,mon4 #ae;,ides4d,tues4 #af #ag b,sat4 #af #ad e,tues4#af #ag e,w$4 #ag #af c,sun4 #ag #ac f,w$4 #ag #af f,?ur4 #ah #ae d,mon4 #ah #ab g,?ur4#ah #ae g,fri4 #ai #ad e,tues4#ai #aa a,fri4 #ai #ad a,sat4 #bj #ac f,w$4 #bj #aj b,sat4 #bj #ac b,sun4 #ba #ab g,?ur4#ba #i c,sun4 #ba #ab c,mon4 #bb #aa a,fri4 #bb #h d,mon4 #bb #aa d,tues4 #bc #aj b,sat4 #bc #g e,tues4#bc #aj e,w$4 #bd #i c,sun4 #bd #f f,w$4 #bd #i f,?ur4 #be #h d,mon4 #be #f g,?ur4#be #h g,fri4 #bf #g e,tues4#bf #e a,fri4 #bf #g a,sat4 #bg #f f,w$4 #bg #d b,sat4 #bg #f b,sun4 #bh #e g,?ur4#bh #c c,sun4 #bh #e c,mon4 #bi #d a,fri4 #bi #b d,mon4 #bi #d d,tues4 #cj #c b,sat4 #cj #c e,w$4 #ca #b c,sun4 #ca #b f,?ur4 ---------------------------------------- ----- ---------------------------------------- -------------- ,,april1 #ahib4 ,,may1 #ahib4 ,,june1 #ahib4 ---------------------------------------- ----- #a;,cal4 g,fri4 #a;,cal4 b,sun4 #a;,cal4 e,w$4 #b #d a,sat4 #b #f c,mon4 #b #d f,?ur4 #c #c b,sun4 #c #e d,tues4 #c #c g,fri4 #d #b c,mon4 #d #d e,w$4 #d #b a,sat4 #e,non4 d,tues4 #e #c f,?ur4 #e,non4 b,sun4 #f #h e,w$4 #f #b g,fri4 #f #h c,mon4 #g #g f,?ur4 #g,non4 a,sat4 #g #g d,tues4 #h #f g,fri4 #h #h b,sun4 #h #f e,w$4 #i #e a,sat4 #i #g c,mon4 #i #e f,?ur4 #aj #d b,sun4 #aj #f d,tues4#aj #d g,fri4 #aa #c c,mon4 #aa #e e,w$4 #aa #c a,sat4 #ab #b d,tues4#ab #d f,?ur4#ab #b b,sun4 #ac;,ides4e,w$4 #ac #c g,fri4 #ac;,ides4c,mon4 #ad #ah f,?ur4#ad #b a,sat4 #ad #ah d,tues4 #ae #ag g,fri4 #ae;,ides4b,sun4 #ae #ag e,w$4 #af #af a,sat4 #af #ag c,mon4 #af #af f,?ur4 #ag #ae b,sun4 #ag #af d,tues4#ag #ae g,fri4 #ah #ad c,mon4 #ah #ae e,w$4 #ah #ad a,sat4 #ai #ac d,tues4#ai #ad f,?ur4#ai #ac b,sun4 #bj #ab e,w$4 #bj #ac g,fri4 #bj #ab c,mon4 #ba #aa f,?ur4#ba #ab a,sat4 #ba #aa d,tues4 #bb #aj g,fri4 #bb #aa b,sun4 #bb #aj e,w$4 #bc #i a,sat4 #bc #aj c,mon4 #bc #i f,?ur4 #bd #h b,sun4 #bd #i d,tues4#bd #h g,fri4 #be #g c,mon4 #be #h e,w$4 #be #g a,sat4 #bf #f d,tues4#bf #g f,?ur4#bf #f b,sun4 #bg #e e,w$4 #bg #f g,fri4 #bg #e c,mon4 #bh #d f,?ur4#bh #e a,sat4 #bh #d d,tues4 #bi #c g,fri4 #bi #d b,sun4 #bi #c e,w$4 #cj #b a,sat4 #cj #c c,mon4 #cj #b f,?ur4 #ca #b d,tues4 ---------------------------------------- ----- ---------------------------------------- ------------- ,,july1 #ahib4 ,,aug41 #ahib4 ,,sept41 #ahib4 ---------------------------------------- ----- #a;,cal4 g,fri4 #a;,cal4 c,mon4 #a;,cal4 f,?ur4 #b #f a,sat4 #b #d d,tues4 #b #d g,fri4 #c #e b,sun4 #c #c e,w$4 #c #c a,sat4 #d #d c,mon4 #d #b f,?ur4 #d #b b,sun4 #e #c d,tues4 #e,non4 g,fri4 #e,non4 c,mon4 #f #b e,w$4 #f #h a,sat4 #f #h d,tues4 #g,non4 f,?ur4 #g #g b,sun4 #g #g e,w$4 #h #h g,fri4 #h #f c,mon4 #h #f f,?ur4 #i #g a,sat4 #i #e d,tues4 #i #e g,fri4 #aj #f b,sun4 #aj #d e,w$4 #aj #d a,sat4 #aa #e c,mon4 #aa #c f,?ur4#aa #c b,sun4 #ab #d d,tues4#ab #b g,fri4 #ab #b c,mon4 #ac #c e,w$4 #ac;,ides4a,sat4 #ac;,ides4d,tues4 #ad #b f,?ur4#ad #ai b,sun4 #ad #ah e,w$4 #ae;,ides4g,fri4 #ae #ah c,mon4 #ae #ag f,?ur4 #af #ag a,sat4 #af #ag d,tues4#af #af g,fri4 #ag #af b,sun4 #ag #af e,w$4 #ag #ae a,sat4 #ah #ae c,mon4 #ah #ae f,?ur4#ah #ad b,sun4 #ai #ad d,tues4#ai #ad g,fri4 #ai #ac c,mon4 #bj #ac e,w$4 #bj #ac a,sat4 #bj #ab d,tues4 #ba #ab f,?ur4#ba #ab b,sun4 #ba #aa e,w$4 #bb #aa g,fri4 #bb #aa c,mon4 #bb #aj f,?ur4 #bc #aj a,sat4 #bc #aj d,tues4#bc #i g,fri4 #bd #i b,sun4 #bd #i e,w$4 #bd #h a,sat4 #be #h c,mon4 #be #h f,?ur4#be #g b,sun4 #bf #g d,tues4#bf #g g,fri4 #bf #f c,mon4 #bg #f e,w$4 #bg #f a,sat4 #bg #e d,tues4 #bh #e f,?ur4#bh #e b,sun4 #bh #d e,w$4 #bi #d g,fri4 #bi #d c,mon4 #bi #c f,?ur4 #cj #c a,sat4 #cj #c d,tues4#cj #b g,fri4 #ca #b b,sun4 #ca #b e,w$4 ---------------------------------------- ----- ---------------------------------------- -------------- ,,oct41 #ahib4 ,,nov41 #ahib4 ,,dec41 #ahib4 ---------------------------------------- ----- #a;,cal4 a,sat4 #a;,cal4 d,tues4 #a;,cal4 f,?ur4 #b #f b,sun4 #b #d e,w$4 #b #d g,fri4 #c #e c,mon4 #c #c f,?ur4 #c #c a,sat4 #d #d d,tues4 #d #b g,fri4 #d #b b,sun4 #e #c e,w$4 #e,non4 a,sat4 #e,non4 c,mon4 #f #b f,?ur4 #f #h b,sun4 #f #h d,tues4 #g,non4 g,fri4 #g #g c,mon4 #g #g e,w$4 #h #h a,sat4 #h #f d,tues4 #h #f f,?ur4 #i #g b,sun4 #i #e e,w$4 #i #e g,fri4 #aj #f c,mon4 #aj #d f,?ur4#aj #d a,sat4 #aa #e d,tues4#aa #c g,fri4 #aa #c b,sun4 #ab #d e,w$4 #ab #b a,sat4 #ab #b c,mon4 #ac #c f,?ur4#ac;,ides4b,sun4 #ac;,ides4d,tues4 #ad #b g,fri4 #ad #ah c,mon4 #ad #ai e,w$4 #ae;,ides4a,sat4 #ae #ag d,tues4#ae #ah f,?ur4 #af #ag b,sun4 #af #af e,w$4 #af #ag g,fri4 #ag #af c,mon4 #ag #ae f,?ur4#ag #af a,sat4 #ah #ae d,tues4#ah #ad g,fri4 #ah #ae b,sun4 #ai #ad e,w$4 #ai #ac a,sat4 #ai #ad c,mon4 #bj #ac f,?ur4#bj #ab b,sun4 #bj #ac d,tues4 #ba #ab g,fri4 #ba #aa c,mon4 #ba #ab e,w$4 #bb #aa a,sat4 #bb #aj d,tues4#bb #aa f,?ur4 #bc #aj b,sun4 #bc #i e,w$4 #bc #aj g,fri4 #bd #i c,mon4 #bd #h f,?ur4#bd #i a,sat4 #be #h d,tues4#be #g g,fri4 #be #h b,sun4 #bf #g e,w$4 #bf #f a,sat4 #bf #g c,mon4 #bg #f f,?ur4#bg #e b,sun4 #bg #f d,tues4 #bh #e g,fri4 #bh #d c,mon4 #bh #e e,w$4 #bi #d a,sat4 #bi #c d,tues4#bi #d f,?ur4 #cj #c b,sun4 #cj #b e,w$4 #cj #c g,fri4 #ca #b c,mon4 #ca #b a,sat4 ---------------------------------------- ----- ---------------------------------------- ------ ,,janu>y4 ,,febru>y4 ,,m>*4 ---------------------------------------- ------ ,cal4 #a ,cal4 #a ,cal4 #a #f - #d #b #f - #d #b #h - #f #b #f - #c #c #f - #c #c #h - #e #c #f - #b #d #f - #b #d #h - #d #d ,nones #e ,nones #e #h - #c #e #ad - #h #f #ad - #h #f #h - #b #f #ad - #g #g #ad - #g #g ,nones #g #ad - #f #h #ad - #f #h #af - #h #h #ad - #e #i #ad - #e #i #af - #g #i #ad - #d #aj #ad - #d #aj #af - #f #aj #ad - #c #aa #ad - #c #aa #af - #e #aa #ad - #b #ab #ad - #b #ab #af - #d #ab ,ides #ac ,ides #ac #af - #c #ac #cc - #ai #ad #cj - #af #ad #af - #b #ad #cc - #ah #ae #cj - #ae #ae ,ides #ae #cc - #ag #af #cj - #ad #af #cc - #ag #af #cc - #af #ag #cj - #ac #ag #cc - #af #ag #cc - #ae #ah #cj - #ab #ah #cc - #ae #ah #cc - #ad #ai #cj - #aa #ai #cc - #ad #ai #cc - #ac #bj #cj - #aj #bj #cc - #ac #bj #cc - #ab #ba #cj - #i #ba #cc - #ab #ba #cc - #aa #bb #cj - #h #bb #cc - #aa #bb #cc - #aj #bc #cj - #g #bc #cc - #aj #bc #cc - #i #bd #cj - #f #bd #cc - #i #bd #cc - #h #be #ca - #f #be #cc - #h #be #cc - #g #bf #ca - #e #bf #cc - #g #bf #cc - #f #bg #ca - #d #bg #cc - #f #bg #cc - #e #bh #ca - #c #bh #cc - #e #bh #cc - #d #bi #ca - #b #bi #cc - #d #bi #cc - #c #cj #cc - #c #cj #cc - #b #ca #cc - #b #ca ---------------------------------------- ------ ,,"p ,,second4 ,,ma!matical4 ,,*apt] ,i4 ,,errors ,,( ,,! ,,julian ,,cal5d>4 ,x w be necess>y 9 ! fir/ place to und]/& ! diff]5ce betwe5 ! ,julian & ,gregorian rule ( int]calation4 ,if ! numb] ( any ye> be exactly divisible by f\r x is leap ye>2 if ! rema9d] be #a1 x is ! fir/ ye> aft] leap-ye>2 if #b1 ! second2 if #c1 ! ?ird2 ?us3 #ahhh _/ #d #dgb1 no rema9d]4 #ahhi _/ #d #dgb1 rema9d]1 #a4 #ahij _/ #d #dgb1 rema9d]1 #b4 #ahia _/ #d #dgb1 rema9d]1 #c4 #ahib _/ #d #dgc1 no rema9d]4 ,& s on1 e f\r? ye> be+ leap-ye> ( #cff days4 ,?is is ! ,julian rule ( int]calation1 :i* is correct$ by ! ,gregorian by mak+ e c5turial ye>1 or ! ye> t completes ! c5tury1 a common ye>1 if n exactly divisible by #djj2 s t only e f\r? c5turial ye> is leap-ye>2 ?us1 #a1gjj1 #a1hjj1 & #a1ijj are common ye>s1 b #b1jjj1 ! f\r? c5turial ye>1 is leap ye>1 & s on4 ,by ! ,julian rule ?ree-f\r?s ( a day is ga9$ e c5tury1 :i* 9 #djj ye>s am\nts to ?ree days4 ,?is is correct$ by ! ,gregorian1 by mak+ ?ree consecutive c5turial ye>s common ye>s1 ?us suppress+ ?ree days 9 #djj ye>s4 ,,rule4 ,multiply ! diff]5ce betwe5 ! ,julian & ! sol> ye> by #ajj1 & we h ! error 9 #ajj ye>s4 ,multiply ?is product by #d & we h ! error 9 #djj ye>s4 ,n[1 #djj is ! t5? ( #d1jjj2 !re=e1 multiply ! la/ product by #aj1 & we h ! error 9 #d1jjj ye>s4 ,n[1 z ! discrepancy betwe5 ! ,julian & ,gregorian ye> is ?ree days 9 #djj ye>s1 mak+ #c-djj ( a day e ye>1 s by divid+ #cfe-a_/d1 ! numb] ( days 9 a ye>1 by #c-djj1 we h ! "t x w\ld take to make a revolution ( ! seasons4 ,,solution4 7#cfe d1 #f h47 - 7#cfe d1 #e h1 #dh m1 #di4fb s47 7#aa m1 #aj4ch s47 ,n[1 7#aa m1 #aj4ch s47 x #ajj #ah h1 #cg4c m1 ! ga9 9 #ajj ye>s4 ,?is is1 reckon$ 9 r\nd numb]s1 #ah h\rs1 or ?ree-f\r?s ( a day4 ,n[1 7#c_/d x #d7 7#a x #c7 #c3 ! ,julian rule ga9+ ?ree days1 ! ,gregorian suppress+ ?ree days 9 #djj ye>s4 7#c x #aj7 #cj1 ! numb] ( days ga9$ by ! ,julian rule 9 #d1jjj ye>s4 #cfe-a_/d _/ #c #djj #dh1gjj1 s t 9 ?is long p]iod ( "t1 ?is fall+ back #c_/d ( a day e c5tury w\ld am\nt to #cfe-a_/d days2 !re=e1 #dh1fii ,julian ye>s are equal to #dh1gjj ,gregorian ye>s4 ,,*apt] ,,ii4 ,,errors ,,( ,,! ,,gregorian ,,cal5d>4 ,by ref]5ce to ! prec$+ *apt] x w be se5 t !re is an error ( #cg4c m9utes 9 e #ajj ye>s n correct$ by ! ,gregorian cal5d>2 ?is am\nts to only 4#cgc ( a m9ute a ye>1 or "o day 9 #c1hfa ye>s1 & "o day & fifty-two m9utes 9 #d1jjj ye>s4 ,,rule4 ,to f9d h[ long x w\ld take to ga9 "o day3 ,divide ! numb] ( m9utes 9 a day by ! decimal 4#cgc1 t be+ ! fraction ( a m9ute ga9$ e ye>4 ,to f9d h[ mu* "t w\ld be ga9$ 9 #d1jjj ye>s1 multiply ! decimal 4#cgc by #d1jjj1 & y w h ! answ] 9 m9utes1 :i* mu/ be r$uc$ to h\rs4 ,,solution4 7#bd x #fj7 _/ 4#cgc #c1hfa1 ne>ly2 h5ce ! error w\ld am\nt to only "o day 9 #c1hfa ye>s4 74#cgc x #d1jjj7 _/ #fj 7#bd h1 #eb m17 7#a d1 #j h1 #eb m71 ! error 9 #d1jjj ye>s4 ,?is trifl+ error 9 ! ,gregorian cal5d> may be correct$ by suppress+ ! int]calations 9 ! ye> #d1jjj1 & its multiples1 #h1jjj1 #ab1jjj1 #af1jjj1 etc41 s t x w n am\nt to a day 9 #ajj1jjj ye>s4 ,,rule4 ,divide #ajj1jjj by #d1jjj & y w h ! numb] ( int]calations suppress$ 9 #ajj1jjj ye>s4 ,multiply #a d1 #eb m1 7t be+ ! error 9 #d1jjj ye>s7 by ?is quoti5t1 & y w h ! discrepancy betwe5 ! ,gregorian & sol> ye> = #ajj1jjj ye>s4 ,by ?is improv$ me?od we suppress #be days1 s t ! error w only am\nt to #be times #eb m9utes4 ,,solution4 #ajj1jjj _/ #d1jjj x 7#a d1 #eb m17 7#be;d1 #ba h1 #dj m47 ,n[1 7#be;d1 #ba h1 #dj m17 - #be d 7#ba h1 #dj m17 ! error 9 #ajj1jjj4 ,,*apt] ,,iii4 ,,dom9ical ,,lett]4 ,dom9ical 7f ! ,lat9 ,dom9us1 ,"l17 indicat+ ! ,"l's day or ,sunday4 ,dom9ical lett]1 "o ( ! fir/ sev5 lett]s ( ! alphabet us$ to d5ote ! ,sabba? or ,"l's day4 ,= ! sake ( great] g5]ality1 ! days ( ! week are d5ot$ by ! fir/ sev5 lett]s ( ! alphabet1 ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 ,g1 :i* are plac$ 9 ! cal5d> beside ! days ( ! ye>1 s t ,a /&s opposite ! fir/ day ( ,janu>y1 ,b opposite ! second1 ,c opposite ! ?ird1 & s on to ,g1 :i* /&s opposite ! sev5?2 aft] :i* ,a returns to ! eigh?1 & s on ?r\gh ! #cfe days ( ! ye>4 ,n[1 if "o ( ! days ( ! week1 ,sunday = example1 is repres5t$ by ,f1 ,monday w be repres5t$ by ,g1 ,tuesday by ,a1 ,w$nesday by ,b1 ,?ursday by ,c1 ,friday by ,d1 & ,saturday by ,e2 & e ,sunday ?r\gh\t ! ye> w h ! same "*1 ,f1 e ,monday ,g1 e ,tuesday ,a1 & s ) reg>d to ! re/4 ,! lett] :i* d5otes ,sunday is call$ ! ,dom9ical or ,sunday lett] = t ye>2 & :5 ! dom9ical lett] ( ! ye> is kn[n1 ! lett]s :i* respectively correspond to ! o!r days ( ! week become kn[n also4 ,did ! ye> consi/ ( #cfd days1 or #eb weeks inv>iably1 ! fir/ day ( ! ye> & ! fir/ day ( ! mon?1 & 9 fact any day ( any ye>1 or any mon?1 w\ld always comm5ce on ! same day ( ! week4 ,b e common ye> consi/s ( #cfe days1 or #eb weeks & #a day1 s t ! foll[+ ye> w beg9 "o day lat] 9 ! week ?an ! ye> prec$+4 ,?us ! ye> #ahcg comm5c$ on ,sunday1 ! foll[+ ye>1 #ahch1 on ,monday1 #ahci on ,tuesday1 & s on4 ,z ! ye> consi/s ( #eb weeks & #a day1 x is evid5t t ! day :i* beg9s & ends ! ye> mu/ occur #ec times2 ?us ! ye> #ahcg beg9s on ,sunday & ends on ,sunday2 s ! foll[+ ye>1 #ahch1 mu/ beg9 on ,monday4 ,z ,a repres5t$ all ! ,sundays 9 #ahcg & z ,a always /&s = ! fir/ day ( ,janu>y1 s 9 #ahch x w repres5t all ! ,mondays1 & ! dom9ical lett] goes back f ,a to ,g2 s t ,g repres5ts all ! ,sundays 9 #ahch1 ,a all ! ,mondays1 ,b all ! ,tuesdays1 & s on1 ! dom9ical lett] go+ back "o place 9 e ye> ( #cfe days4 ,:ile ! foll[+ ye> comm5ces "o day lat] 9 ! week ?an ! ye> prec$+1 ! dom9ical lett] goes back "o place f ! prec$+ ye>2 ?us :ile ! ye> #ahfe comm5c$ on ,sunday1 #ahff on ,monday1 #ahfg on ,tuesday1 ! dom9ical lett]s are ,a1 ,g & ,f1 respectively4 ,!re=e1 if e ye> consi/$ ( #cfe days1 ! dom9ical cycle w\ld be complet$ 9 sev5 ye>s1 s t aft] sev5 ye>s ! fir/ day ( ! ye> w\ld aga9 occur on ! same day ( ! week4 ,b ?is ord] is int]rupt$ e f\r ye>s by giv+ ,febru>y #bi days1 !reby mak+ ! ye> to consi/ ( #cff days1 :i* is #eb weeks & two days1 s t ! foll[+ ye> w\ld comm5ce two days lat] 9 ! week ?an ! ye> prec$+1 ?us ! ye> #ahhh be+ leap-ye>1 _h two dom9ical lett]s1 ,a & ,g2 ,a = ,janu>y & ,febru>y1 & ,g = ! re/ ( ! ye>4 ,! ye> comm5c$ on ,sunday & end$ on ,monday1 mak+ #ec ,sundays & #ec ,mondays1 & ! foll[+ ye>1 #ahhi1 to comm5ce on ,tuesday4 ,x n[ becomes evid5t t if ! ye>s all consi/$ ( #cfd days1 or #eb weeks1 !y w\ld all comm5ce on ! same day ( ! week2 if !y all consi/$ ( #cfe days1 or #eb weeks & "o day1 !y w\ld all comm5ce "o day lat] 9 ! week ?an ! ye> prec$+2 if !y all consi/$ ( #cff days1 or #eb weeks & two days1 !y w\ld comm5ce two days lat] 9 ! week2 if #cfg days or #eb weeks & ?ree days1 !n ?ree days lat]1 & s on1 "o day lat] = e additional day4 ,x is also evid5t t e additional day causes ! dom9ical lett] to g back "o place4 ,n[ 9 leap-ye> ! #bi? day ( ,febru>y is ! additional or int]cal>y day4 ,s "o lett] = ,janu>y & ,febru>y1 & ano!r = ! re/ ( ! ye>4 ,if ! numb] ( ye>s 9 ! int]cal>y p]iod 7 two1 & sev5 be+ ! numb] ( days 9 ! week1 _! product w\ld be #b x #g #ad2 f\rte51 !n1 w\ld be ! numb] ( ye>s 9 ! cycle4 ,aga91 if ! numb] ( ye>s 9 ! int]cal>y p]iod 7 ?ree1 & ! numb] ( days 9 ! week be+ sev51 _! product w\ld be #c x #g #ba2 tw5ty-"o w\ld !n be ! numb] ( ye>s 9 ! cycle4 ,b ! numb] ( ye>s 9 ! int]cal>y p]iod is f\r1 & ! numb] ( days 9 ! week is sev51 !re=e _! product is #d x #g #bh2 tw5ty-eight is !n ! numb] ( ye>s 9 ! cycle4 ,?is p]iod is call$ ! dom9ical or sol> cycle1 & re/ores ! fir/ day ( ! ye> to ! same day ( ! week4 ,at ! end ( ! cycle ! dom9ical lett]s return aga9 9 ! same ord]1 on ! same days ( ! mon?4 ,?us1 = ! ye> #ahja1 ! dom9ical lett] is ,d2 #ahjb1 ,c2 #ahjc1 ,b2 #ahjd1 ,a & ,g2 & s on1 go+ back five places e f\r ye>s = tw5ty-eight ye>s1 :5 ! cycle1 be+ end$1 ,d is aga9 dom9ical lett] = #ahbi1 ,c = #ahcj1 & s on e #bh ye>s =ev]1 accord+ to ! ,julian rule ( int]calation4 ,b ?is ord] is int]rupt$ 9 ! ,gregorian cal5d> at ! end ( ! c5tury by ! secul> suppression ( ! leap-ye>4 ,x is n int]rupt$1 h[ev]1 at ! end ( e c5tury1 = ! leap-ye> is n suppress$ 9 e f\r? c5turial ye>2 consequ5tly ! cycle w !n be cont9u$ = two hundr$ ye>s4 ,x %\ld be "h /at$ t ?is ord] cont9u$ )\t int]ruption f ! comm5cem5t ( ! era until ! re=mation ( ! cal5d> 9 #aehb1 dur+ :i* "t ! ,julian cal5d>1 or ,old ,/yle 0 us$4 ,x has already be5 %[n t if ! numb] ( ye>s 9 ! int]cal>y p]iod be multipli$ by sev51 ! numb] ( days 9 ! week1 _! product w be ! numb] ( ye>s 9 ! cycle4 ,n[1 9 ! ,gregorian cal5d>1 ! int]cal>y p]iod is #djj ye>s2 ?is numb] be+ multipli$ by sev51 _! product w\ld be #b1hjj ye>s1 z ! int]val 9 :i* ! co9cid5ce is re/or$ betwe5 ! days ( ! ye> & ! days ( ! week4 ,?is long p]iod1 h[ev]1 may be r$uc$ to #djj ye>s2 = s9ce ! dom9ical lett] goes back five places e f\r ye>s1 9 #djj ye>s x w g back #ejj places 9 ! ,julian & #dig 9 ! ,gregorian cal5d>1 ?ree int]calations be+ suppress$ 9 ! ,gregorian e #djj ye>s4 ,n[ #dig is exactly divisible by sev51 ! numb] ( days 9 ! week1 !re=e1 aft] #djj ye>s ! cycle w be complet$1 & ! dom9ical lett]s w return aga9 9 ! same ord]1 on ! same days ( ! mon?4 ,9 answ] to ! "q1 ,:y two dom9ical lett]s = leap-ye>8 we reply1 because ( ! additional or int]cal>y day aft] ! #bh? ( ,febru>y4 ,x has already be5 %[n t e additional day causes ! dom9ical lett] to g back "o place4 ,z !re are #cff days 9 leap-ye>1 ! lett] mu/ g back two places1 "o be+ us$ = ,janu>y & ,febru>y1 & ! o!r = ! re/ ( ! ye>4 ,did we cont9ue "o lett] ?r\gh ! ye> & !n g back two places1 x w\ld cause confusion 9 computation1 unless ! int]calation be made at ! end ( ! ye>4 ,:5ev] ! int]calation is made !re mu/ necess>ily be a *ange 9 ! dom9ical lett]4 ,_h x be5 s arrang$ t ! additional day 0 plac$ aft] ! #cj? ( ,june or ,septemb]1 !n ! fir/ lett] w\ld be us$ until ! int]calation is made 9 ,june or ,septemb]1 & ! second to ! end ( ! ye>4 ,or suppose t ! end ( ! ye> _h be5 fix$ z ! "t & place = ! int]calation1 7:i* w\ld h be5 mu* m conv5i5t = computation17 !n !re w\ld h be5 no use :atev] = ! second dom9ical lett]1 b at ! end ( ! ye> we w\ld g back two places2 ?us1 9 ! ye> #ahhh1 in/ead ( ,a be+ dom9ical lett] = two mon?s m]ely1 x w\ld be cont9u$ ?r\gh ! ye>1 & !n pass+ back to ,f1 no use :atev] be+ made ( ,g1 & s on at ! end ( e leap-ye>4 ,h5ce x is evid5t t ?is arrangem5t w\ld h be5 mu* m conv5i5t1 b we h ?is ord] ( ! mon?s1 & ! numb] ( days 9 ! mon?s z ,augu/us ,caes> left !m eight ye>s be=e ,*ri/4 ,! dom9ical lett] probably 0 n kn[n until ! ,c\ncil ( ,nice1 9 ! ye> ( our ,"l #cbe1 :]e1 9 all probability1 x _h its orig94 ,,*apt] ,,iv4 ,,rule ,,= ,,f9d+ ,,! ,,dom9ical ,,lett]4 ,divide ! numb] ( ! giv5 ye> by #d1 neglect+ ! rema9d]s1 & add ! quoti5t to ! giv5 numb]4 ,divide ?is am\nt by #g1 & if ! rema9d] be less ?an ?ree1 take x f #c2 b if x be #c or m ?an #c1 take x f #aj & ! rema9d] w be ! numb] ( ! lett] call+ ,a1 #a2 ,b1 #b2 ,c1 #c1 etc4 ,by ?is rule ! dom9ical lett] is f\nd f ! comm5cem5t ( ! era to ,octob] #e?1 #aehb4 ,o4 ,s4 ,f ,octob] #ae?1 #aehb1 till ! ye> #agjj1 take ! rema9d] z f\nd by ! rule f #f1 if x be less ?an #f1 b if ! rema9d] be #f1 take x f #ac1 & s on accord+ to in/ructions giv5 9 ! table on #di? page4 ,x %\ld be und]/ood "h1 t 9 leap-ye>s ! lett] f\nd by ! prec$+ rule w be ! dom9ical lett] = t "p ( ! ye> t foll[s ! #bi? ( ,febru>y1 :ile ! lett] :i* foll[s x w be ! "o = ,janu>y & ,febru>y4 ,,examples4 ,to f9d ! dom9ical lett] = #acfe1 we h #acfe _/ #d #cda 2 #acfe #cda #agjf2 #agjf _/ #g #bdc1 rema9d] #e4 ,!n #aj - #e #e2 !re=e ,e be+ ! fif? lett] is ! dom9ical lett] = #acfe4 ,to f9d ! dom9ical lett] = #afbj1 we h #afbj _/ #d #dje2 #afbj #dje #bjbe2 #bjbe _/ #g #bhi1 rema9d] #b4 ,!n #f - #b #d2 !re=e1 ,d & ,e are ! dom9ical lett]s = #afbj2 ,e = ,janu>y & ,febru>y1 & ,d = ! re/ ( ! ye>4 ,! process ( f9d+ ! dom9ical lett] is v simple & easily und]/ood1 if we obs]ve ! foll[+ ord]3 #a/4 ,divide by #d4 #b;d4 ,add to ! giv5 numb]4 #c;d4 ,divide by #g4 #d?4 ,take ! rema9d] f #c or #aj1 f ! comm5cem5t ( ! era to ,octob] #e?1 #aehb4 ,f ,octob] #ae?1 #aehb to #agjj1 f #f or #ac4 ,f #agjj to #ahjj1 f #g1 & s on4 ,see table on #di? page4 ,we divide by #d because ! int]cal>y p]iod is f\r ye>s2 & z e f\r? ye> conta9s ! divisor #d once m ?an any ( ! ?ree prec$+ ye>s1 s !re is "o m add$ to ! f\r? ye> ?an !re is to any ( ! ?ree prec$+ ye>s2 & z e ye> consi/s ( #eb weeks & "o day1 ?is additional ye> gives an additional day to ! rema9d] aft] divid+ by #g4 ,= example1 ! ye> #a ( ! era consi/s ( #eb w4 #a d4 #b ye>s consi/ ( #ajd w4 #b d4 #c ye>s consi/ ( #aef w4 #c d4 7#d _/ #d7 #d #e ye>s consi/ ( #bfj w4 #e d4 ,h5ce ! numb]s ?us =m$ w be #a1 #b1 #c1 #e1 #f1 #g1 #h1 #aj1 #aa1 #ab1 #ac1 #ae1 & s on4 ,we divide by #g1 because !re are sev5 days 9 ! week1 & ! rema9d]s %[ h[ _m days m ?an an ev5 numb] ( weeks !re are 9 ! giv5 ye>4 ,take1 = example1 ! fir/ twelve ye>s ( ! era aft] be+ increas$ by "o-f\r?1 & we h #a _/ #g #j rema9d] #a ,!n #c - #a #b ,b #b _/ #g #j #b #c - #b #a ,a #c _/ #g #j #c #aj - #c #g ,g #e _/ #g #j #e #aj - #e #e ,f ,e #f _/ #g #j #f #aj - #f #d ,d #g _/ #g #a #j #c - #j #c ,c #h _/ #g #a #a #c - #a #b ,b #aj _/ #g #a #c #aj - #c #g ,a ,g #aa _/ #g #a #d #aj - #d #f ,f #ab _/ #g #a #e #aj - #e #e ,e #ac _/ #g #a #f #aj - #f #d ,d #ae _/ #g #b #a #c - #a #b ,c ,b ,f ?is table x may be se5 t x is ^! rema9d]s repres5t+ ! numb] ( days m ?an an ev5 numb] ( weeks 9 ! giv5 ye>1 t we h to deal ) 9 f9d+ ! dom9ical lett]4 ,did ! ye> consi/ ( #cfd days1 or #eb weeks1 inv>iably1 !re w\ld be no *ange 9 ! dom9ical lett] f ye> to ye>1 b ! lett] t repres5ts ,sunday 9 any giv5 ye> w\ld repres5t ,sunday 9 e ye>4 ,did ! ye> consi/ ( only #cfc days1 ?us want+ "o day ( an ev5 numb] ( weeks1 !n ^! rema9d]s1 in/ead ( be+ tak5 f a giv5 rema9d]1 w\ld be add$ to t numb]1 ?us remov+ ! dom9ical lett] =w>d "o place1 & ! beg9n+ ( ! ye>1 in/ead ( be+ "o day lat]1 w\ld be "o day e>li] 9 ! week ?an 9 ! prec$+ ye>4 ,?us1 if ! ye> #a ( ! era be tak5 f #c1 we w\ld h #c - #a #b2 !re=e1 ,b be+ ! second lett]1 is dom9ical lett] = ! ye> #a4 ,b if ! ye> consi/ ( only #cfc days1 !n ! #a in/ead ( be+ tak5 f #c w\ld be add$ to #c2 !n we w\ld h #c #a #d2 !re=e1 ,d be+ ! f\r? lett] w\ld be dom9ical lett] = ! ye> #a4 ,! =m] go+ back f ,c to ,b1 ! latt] =w>d f ,c to ,d2 or :i* am\nts to ! same ?+1 make ! ye> to consi/ ( #ea weeks & #f days2 !n #aj - #f #d1 mak+ ,d ! dom9ical lett] z be=e4 ,z sev5 is ! numb] ( days 9 ! week1 & ! object ( ^! subtractions is to remove ! dom9ical lett] back "o place e common ye>1 & two 9 leap-ye>1 :y n take ^! rema9d]s f #g8 ,we answ]1 all dep5ds ^u ! day ( ! week on :i* ! era comm5c$4 ,_h ,g1 ! sev5? lett] be5 dom9ical lett] = ! ye> prec$+ ! era1 !n ^! rema9d]s w\ld be tak5 f #g2 & #g w\ld be us$ until *ange ( /yle 9 #aehb4 ,b we "k f computation t ,c1 ! ?ird lett]1 is dom9ical lett] = ! ye> prec$+ ! era2 s we comm5ce ) ?ree1 & take ! small] rema9d]s1 #a & #b f #c2 t br+s u to ,a4 ,we take ! l>g] rema9d]s1 f #c to #f1 f #c #g #aj4 ,we add ! #g because !re are sev5 days 9 ! week4 ,we use ! numb] #aj until we get back to ,c1 ! ?ird lett]1 ! place f :5ce we />t$4 ,= example1 we h #c - #a #b ,b #c - #b #a ,a #aj - #c #g ,g #aj - #d #f ,f #aj - #e #e ,e #aj - #f #d ,d #c - #j #c ,c ,! cycle ( sev5 days be+ complet$1 we comm5ce ) ! numb] ?ree aga91 & s on until #aehb1 :5 on acc\nt ( ! errors ( ! ,julian cal5d>1 t5 days 7 suppress$ to re/ore ! co9cid5ce ( ! sol> & civil ye>4 ,n[ e day suppress$ removes ! dom9ical lett] =w>d "o place2 s c\nt+ f ,c to ,c aga9 is sev51 ,d is eight1 ,e is n9e1 & ,f is t54 ,z ,f is ! six? lett]1 we take ! rema9d]s f #a to #e1 f #f2 if ! rema9d] be #f1 take x f #f #g #ac4 ,!n #f or #ac is us$ till #agjj1 :51 ano!r day be+ suppress$1 ! numb] is increas$ to #g4 ,& aga9 9 #ahjj1 = ! same reason1 a *ange is made to #a or #h2 9 #aijj to #b or #i1 & s on4 ,x w be se5 by ! table on ! #di? page t ! small] numb]s run f #a to #g2 ! l>g] ones f #h to #ac4 ,f ! comm5cem5t ( ! ,*ri/ian era to ,octob] #e?1 #aehb1 take ! rema9d]s1 aft] divid+ by #g1 f #c or #aj2 f ,octob] #ae?1 #aehb to #agjj f #f or #ac #agjj to #ahjj #g #ahjj to #aijj #a or #h #aijj to #bajj #b or #i #bajj to #bbjj #c or #aj #bbjj to #bcjj #d or #aa #bcjj to #bejj #e or #ab #bejj to #bfjj #f or #ac #bfjj to #bgjj #g #bgjj to #bijj #a or #h #bijj to #cjjj #b or #i #cjjj to #cajj #c or #aj #cajj to #ccjj #d or #aa #ccjj to #cdjj #e or #ab #cdjj to #cejj #f or #ac #cejj to #cgjj #g #cgjj to #chjj #a or #h #chjj to #cijj #b or #i #cijj to #djjj #c or #aj #djjj to #dajj #d or #aa #dajj to #dbjj #e or #ab #dbjj to #dcjj #f or #ac #dcjj to #dejj #g #dejj to #dfjj #a or #h #dfjj to #dgjj #b or #i #dgjj to #dijj #c or #aj #dijj to #ejjj #d or #aa #ejjj to #eajj #e or #ab ,,*apt] ,v4 ,,rule ,,= ,,f9d+ ,,! ,,day ,,( ,,! ,,week ,,( ,,any ,,giv5 ,,date1 ,,= ,,bo? ,,old ,,& ,,new ,,/yles4 ,by arrang+ ! dom9ical lett]s 9 ! ord] 9 :i* ! diff]5t mon?s comm5ce1 ! day ( ! week on :i* any mon? ( any ye>1 or day ( ! mon? has fall5 or w fall1 f ! comm5cem5t ( ! ,*ri/ian era to ! ye> ( our ,"l #djjj1 may be calculat$4 7,app5dix ,g47 ,!y h be5 arrang$ ?us 9 ! foll[+ c\plet1 9 :i* ,at /&s = ,janu>y1 ,dov] = ,febru>y1 ,dwells = ,m>*1 etc4 ,at ,dov] ,dwells ,george ,br[n1 ,esquire1 ,good ,c>los ,f9*1 & ,david ,fry]4 ,n[ if ,a be dom9ical or ,sunday lett] = a giv5 ye>1 !n ,janu>y & ,octob] be+ repres5t$ by ! same lett]1 beg9 on ,sunday2 ,febru>y1 ,m>* & ,novemb]1 = ! same reason1 beg9 on ,w$nesday2 ,april & ,july on ,saturday2 ,may on ,monday1 ,june on ,?ursday1 ,augu/ on ,tuesday1 ,septemb] & ,decemb] on ,friday4 ,x is evid5t t e mon? 9 ! ye> mu/ comm5ce on "s "o day ( ! week repres5t$ by "o ( ! fir/ sev5 lett]s ( ! alphabet4 ,n[ let ,janu>y #a/ be repres5t$ by ,a1 ,sun4 ,feb4 #a/ 7#d w4 #c d4 f ! prec$+ date7 by ,d1 ,w$4 ,m>4 #a/ #d w4 #j d4 by ,d1 ,w$4 ,apr4 #a/ #d w4 #c d4 by ,g1 ,sat4 ,may #a/ #d w4 #b d4 by ,b1 ,mon4 ,june #a/ #d w4 #c d4 by ,e1 ,?ur4 ,july #a/ #d w4 #b d4 by ,g1 ,sat4 ,aug4 #a/ #d w4 #c d4 by ,c1 ,tues4 ,sept4 #a/ #d w4 #c d4 by ,f1 ,fri4 ,oct4 #a/ #d w4 #b d4 by ,a1 ,sun4 ,nov4 #a/ #d w4 #c d4 by ,d1 ,w$4 ,dec4 #a/ #d w4 #b d4 by ,f1 ,fri4 ,n[ ea* ( ^! lett]s plac$ opposite ! mon?s respectively repres5ts ! day ( ! week on :i* ! mon? comm5ces1 & !y are ! fir/ lett]s ( ea* ^w 9 ! prec$+ c\plet4 ,to f9d ! day ( ! week on :i* a giv5 day ( any ye> w occur1 we h ! foll[+ ,,rule4 ,f9d ! dom9ical lett] = ! ye>4 ,read f ?is to ! lett] :i* beg9s ! giv5 mon?1 always read+ f ,a t[>d ,g1 call+ ! dom9ical lett] ,sunday1 ! next ,monday1 etc4 ,?is w %[ on :at day ( ! week ! mon? comm5c$2 !n reckon+ ! numb] ( days f ?is w give ! day requir$4 ,,examples4 ,hi/ory records ! fall ( ,con/ant9ople on ,may #bi?1 #adec4 ,on :at day ( ! week did x occur8 ,we h !n #adec _/ #d #cfc 2 #adec #cfc #ahaf2 #ahaf _/ #g #bei1 rema9d] #c4 ,!n #aj - #c #g2 !re=e1 ,g be+ ! sev5? lett] is dom9ical lett] = #adec4 ,n[ read+ f ,g to ,b1 ! lett] = ,may1 we h ,g ,sunday1 ,a ,monday1 & ,b ,tuesday2 h5ce ,may comm5c$ on ,tuesday & ! #bi? 0 ,tuesday4 ,! *ange f ,old to ,new ,/yle 0 made by ,pope ,gregory ,,xiii1 ,octob] #e?1 #aehb4 ,on :at day ( ! week did x occur8 ,we h !n #aehb _/ #d #cie2 #aehb #cie #aigg2 #aigg _/ #g #bhb1 rema9d] #c4 ,!n #aj - #c #g2 !re=e1 ,g be+ ! sev5? lett]1 is dom9ical lett] = #aehb4 ,n[ read+ f ,g to ,a1 ! lett] = ,octob]1 we h ,g ,sunday1 ,a ,monday1 etc4 ,h5ce ,octob] comm5c$ on ,monday1 & ! #e? 0 ,friday4 ,on :at day ( ! week did ! #ae? ( ! same mon? fall 9 #aehb8 ,we h !n #aehb _/ #d #cie2 #aehb #cie #aigg2 #aigg _/ #g #bhb1 rema9d] #c4 ,!n #f - #c #c2 !re=e1 ,c be+ ! ?ird lett]1 is ! dom9ical lett] = #aehb4 ,n[ read+ f ,c to ,a1 ! lett] = ,octob]1 we h ,c ,sunday1 ,d ,monday1 ,e ,tuesday1 etc4 ,h5ce ,octob] comm5c$ on ,friday1 & ! #ae? 0 ,friday4 ,h[ is ?is1 says "o8 ,y h j %[n by computation t ,octob]1 #aehb1 comm5c$ on ,monday1 y n[ say t x occurr$ on ,friday4 ,y also /at$ t ! #e? 0 ,friday2 y n[ say t ! #ae? 0 ,friday4 ,?is is absurd2 t5 is n a multiple ( sev54 ,!re is no?+ absurd ab\t x4 ,! =m] computation 0 ,old ,/yle1 ! latt] ,new ,/yle1 ! ,old be+ t5 days beh9d ! new4 ,z reg>ds an int]val ( t5 days betwe5 ! two ,fridays1 !re 0 none2 ,friday1 ! #e?1 & ,friday1 ! #ae?1 0 "o & ! same day2 !re 0 no int]val1 no?+ ev] occurr$1 !re 0 no "t = any?+ to occur2 ! edict ( ! ,pope decid$ x2 he said ! #e? %\ld be call$ ! #ae?1 & x 0 s4 ,h5ce to ,octob] ! #e?1 #aehb1 ! computation %\ld be ,old ,/yle2 f ! #ae? to ! end ( ! ye> ,new ,/yle4 ,on :at day ( ! week did ! ye>s #a1 #b & #c1 ( ! era comm5ce8 ,none ( ^! numb]s c be divid$ by #d2 nei!r are !y divisible by #g2 b !y may be treat$ z rema9d]s aft] divid+ by #g4 ,n[ ea* ( ^! numb]s ( ye>s consi/s ( an ev5 numb] ( weeks ) rema9d]s ( #a1 #b & #c days respectively4 ,h5ce we h !n = ! ye> #a1 #c - #a #b2 !re=e1 ,b be+ ! second lett]1 is ! dom9ical lett] = ! ye> #a4 ,n[ read+ f ,b to ,a1 ! lett] = ,janu>y1 we h ,b ,sunday1 ,c ,monday1 ,d ,tuesday1 etc4 ,h5ce ,janu>y comm5c$ on ,saturday4 ,!n we h = ! ye> #b1 #c - #b #a2 !re=e ,a be+ ! fir/ lett]1 is dom9ical lett] = ! ye> #b2 h5ce x is evid5t t ,janu>y comm5c$ on ,sunday4 ,aga9 we h = ! ye> #c1 #aj - #c #g2 !re=e1 ,g be+ ! sev5? lett]1 is dom9ical lett] = ! ye> #c4 ,n[ read+ f ,g to ,a1 ! lett] = ,janu>y1 we h ,g ,sunday1 ,a ,monday2 h5ce ,janu>y comm5c$ on ,monday4 ,on :at day ( ! week did ! ye> #d comm5ce8 ,n[ we h a numb] t is divisible by #d1 x be+ ! fir/ leap-ye> 9 ! era1 s we h #d _/ #d #a2 #d #a #e2 #e _/ #g #j1 rema9d] #e4 ,!n #aj - #e #e2 !re=e1 ,e be+ ! #e? lett]1 is dom9ical lett] = t "p ( ! ye> :i* foll[s ! #bi? ( ,febru>y1 :ile ,f1 ! lett] t foll[s x1 is dom9ical lett] = ,janu>y & ,febru>y4 ,n[ read+ f ,f to ,a1 ! lett] = ,janu>y1 we h ,f ,sunday1 ,g ,monday1 ,a ,tuesday2 h5ce ,janu>y comm5c$ on ,tuesday4 ,n[ we h dispos$ ( ! fir/ f\r ye>s ( ! era2 ! dom9ical lett]s be+ ,b1 ,a1 ,g1 & ,f1 ,e4 ,h5ce x is evid5t1 :ile "o ye> consi/s ( an ev5 numb] ( weeks & "o day1 two ye>s ( an ev5 numb] ( weeks & two days1 ?ree ye>s ( an ev5 numb] ( weeks & ?ree days1 t e f\r? ye>1 by int]calation1 is made to consi/ ( #cff days2 s t f\r ye>s consi/ ( an ev5 numb] ( weeks & five days2 = we h 7#d _/ #d7 #d #e1 ! dom9ical lett] go+ back f ,g 9 ! ye> #c1 to ,f1 = ,janu>y & ,febru>y 9 ! ye> #d1 & f ,f to ,e = ! re/ ( ! ye>1 caus+ ! foll[+ ye> to comm5ce two days lat] 9 ! week ?an ! ye> prec$+4 ,! ye> #a _h #ec ,saturdays2 ! ye> #b1 #ec ,sundays2 ! ye> #c1 #ec ,mondays1 & ! ye> #d1 #ec ,tuesdays & #ec ,w$nesdays1 caus+ ! ye> #e to comm5ce on ,?ursday1 two days lat] 9 ! week ?an ! prec$+ ye>4 ,n[ :at is true conc]n+ ! fir/ f\r ye>s ( ! era1 is true conc]n+ all ! future ye>s1 & ! reason = ! divisions1 additions & subtractions 9 f9d+ ! dom9ical lett] is evid5t4 ,! ,decl>ation ( ,indep5d5ce 0 sign$ ,july #d1 #aggf4 ,on :at day ( ! week did x occur8 ,we h !n #aggf _/ #d #ddd2 #aggf #ddd #bbbj2 #bbbj _/ #g #cag1 rema9d] #a4 ,!n #g - #a #f1 !re=e ,f & ,g are ! dom9ical lett]s = #aggf1 ,g = ,janu>y & ,febru>y1 & ,f = ! re/ ( ! ye>4 ,n[ read+ f ,f to ,g1 ! lett] = ,july1 we h ,f ,sunday1 ,g ,monday2 h5ce ,july comm5c$ on ,monday1 & ! f\r? 0 ,?ursday4 ,on :at day ( ! week did ,lee surr5d] to ,grant1 :i* occurr$ on ,april #i?1 #ahfe8 ,we h !n #ahfe _/ #d #dff2 #ahfe #dff #bcca2 #bcca _/ #g #ccc1 rema9d] #j4 ,!n #a - #j #a2 !re=e1 ,a be+ ! fir/ lett]1 is dom9ical lett] = #ahfe4 ,n[ read+ f ,a to ,g1 ! lett] = ,april1 we h ,a ,sunday1 ,b ,monday1 ,c ,tuesday1 etc4 ,h5ce ,april comm5c$ on ,saturday1 & ! #i? 0 ,sunday4 ,b5jam9 ,h>rison 0 inaugurat$ ,presid5t ( ! ,unit$ ,/ates on ,monday1 ,m>* #d1 #ahhi4 ,on :at day ( ! week w ! #d? ( ,m>* fall 9 #aihi8 ,we h !n #aihi _/ #d #dig2 #aihi #dig #bdhf2 #bdhf _/ #g #cee1 rema9d] #a4 ,!n #b - #a #a2 !re=e1 ,a be+ ! fir/ lett]1 is dom9ical lett] = #aihi4 ,n[1 read+ f ,a to ,d1 ! lett] = ,m>*1 we h ,a ,sunday1 ,b ,monday1 ,c ,tuesday1 & ,d ,w$nesday2 h5ce ,m>* w comm5ce on ,w$nesday1 & ! #d? w fall on ,saturday4 ,columbus l&$ on ! isl& ( ,san ,salvador on ,friday1 ,octob] #ab1 #adib4 ,on :at day ( ! mon? & on :at day ( ! week w ! f\r hundr$? anniv]s>y fall 9 #ahib8 ,! day ( ! mon? on :i* ,columbus l&$ is1 ( c\rse1 ! day to be obs]v$ 9 commemoration ( t ev5t4 ,! ,julian cal5d>1 :i* 0 !n 9 use ?r\gh\t ,europe1 & ! v be/ t _h ev] be5 giv5 to ! _w1 made ! ye> too long by m ?an elev5 m9utes4 ,^? elev5 m9utes a ye> _h accumulat$1 f ! c\ncil ( ,nice1 9 #cbe1 to ! discov]y ( ,am]ica1 9 #adib1 to n9e days1 s t ! civil ye> 0 n9e days beh9d ! true or sol> "t2 t is1 :5 ! ,e>?1 9 h] annual revolution1 _h arriv$ at t po9t ( ! ecliptic co9cid+ ) ! #ba/ ( ,octob]1 ! civil ye>1 accord+ to ! ,julian cal5d>1 0 ! #ab?4 ,n[1 to re/ore ! co9cid5ce1 ! n9e days mu/ be dropp$1 or suppress$1 call+ :at 0 errone\sly call$ ! #ab? ( ,octob]1 ! #ba/4 ,s9ce ! ,julian cal5d> 0 correct$ by ,gregory1 9 #aehb1 we h s int]calat$ z to reta91 v ne>ly1 ! co9cid5ce ( ! sol> & ! civil ye>4 ,x has already be5 %[n 9 ,*apt] ,,iii1 7q4 v47 t 9 ! ,gregorian cal5d>1 ! cycle :i* re/ores ! co9cid5ce ( ! day ( ! mon? & ! day ( ! week1 is complet$ 9 #djj ye>s2 s t aft] #djj ye>s1 ev5ts w aga9 transpire 9 ! same ord]1 on ! same day ( ! week4 ,n[1 z ,columbus l&$ on ,friday1 ,octob] #ba/1 #adib1 s ,friday1 ,octob] #ba/1 #ahib1 is ! day ( ! mon? & also ! day ( ! week to be obs]v$ 9 commemoration ( t ev5t4 ,we h !n #ahib _/ #d #dgc2 #ahib #dgc #bcfe2 #bcfe _/ #g #ccg1 rema9d] #f4 ,!n #h - #f #b2 !re=e1 ,b & ,c are dom9ical lett]s = #ahib1 ,c = ,janu>y & ,febru>y1 & ,b = ! re/ ( ! ye>4 ,n[1 read+ f ,b to ,a1 ! lett] = ,octob]1 we h ,b ,sunday1 ,c ,monday1 etc4 ,h5ce ,octob] w comm5ce on ,saturday & ! #ba/ w be ,friday4 ,al?\gh !re 0 an error ( ?irte5 days 9 ! ,julian cal5d> :5 x 0 re=m$ by ,gregory1 9 #aehb1 !re 0 a correction made ( only t5 days4 ,!re 0 /ill an error ( ?ree days f ! "t ( ,julius ,caes> to ! ,c\ncil ( ,nice1 :i* rema9$ uncorrect$4 ,gregory re/or$ ! v]nal equ9ox to ! #ba/ ( ,m>*1 its date at ! meet+ ( t c\ncil1 n to ! place x occupi$ 9 ! "t ( ,caes>1 namely1 ! #bd? ( ,m>*4 ,_h he done s x w\ld n[ fall on ! #bd?1 by adopt+ ! ,gregorian rule ( int]calation4 ,app5dix ,h4 ,if desirable calculations may be made 9 bo? ,old & ,new ,/yles f ! ye> ( our ,"l #cjj4 ,!re is no p]ceptible discrepancy 9 ! cal5d>s1 h[ev]1 until ! close ( ! #d? c5tury1 :5 x am\nts to ne>ly "o day1 reckon$ 9 r\nd numb]s "o day4 ,n[ 9 ord] to make ! calculation1 proce$ accord+ to rule already giv5 = f9d+ ! dom9ical lett]1 & = ,new ,/yle take ! rema9d]s aft] divid+ by sev5 f ! numb]s 9 ! foll[+ table3 ,f #djj to #ejj ,f #d or #aa #ejj #fjj #e #ab #fjj #gjj #f #ac #gjj #ijj #g #ijj #ajjj #a #h #ajjj #aajj #b #i #aajj #acjj #c #aj #acjj #adjj #d #aa #adjj #aejj #e #ab #aejj #agjj #f #ac ,x w be f\nd by calculation t f ! ye> #djj to #ejj ! discrepancy is #a day #ejj #fjj #b #fjj #gjj #c #gjj #ijj #d #ijj #ajjj #e #ajjj #aajj #f #aajj #acjj #g #acjj #adjj #h #adjj #aejj #i #aejj #agjj #aj ,h5ce ! necessity1 9 re=m+ ! cal5d> 9 #aehb1 ( suppress+ t5 days4 7,see table on #ei? page47 ,on :at day ( ! week did ,janu>y comm5ce 9 #dej8 ,we h !n #dej _/ #d #aab2 #dej #aab #efb2 #efb _/ #g #hj1 rema9d] #b4 ,!n #c - #b #a2 !re=e1 ,a be+ ! fir/ lett]1 is dom9ical lett] = #dej1 ,old ,/yle1 & ,janu>y comm5c$ on ,sunday4 ,= ,new ,/yle we h #d - #b #b2 !re=e1 ,b be+ ! second lett]1 is dom9ical lett] = ! ye> #dej4 ,n[ read+ f ,b to ,a1 ! lett] = ,janu>y1 we h ,b ,sunday1 ,c ,monday1 ,d ,tuesday1 etc4 ,h5ce1 ,janu>y comm5c$ on ,saturday4 ,old ,/yle makes ,sunday ! fir/ day2 ,new ,/yle makes ,saturday ! fir/ & ,sunday ! second4 ,on :at day ( ! week did ,janu>y comm5ce 9 ! ye> #abej8 ,we h !n #abej _/ #d #cab2 #abej #cab #aefb2 #aefb _/ #g #bbc1 rema9d] #a4 ,!n #c - #a #b2 !re=e1 ,b be+ ! second lett]1 is dom9ical lett] = ! ye> #abej1 ,old ,/yle4 ,n[1 read+ f ,b to ,a1 ! lett] = ,janu>y1 we h ,b ,sunday1 ,c ,monday1 etc4 ,h5ce ,janu>y comm5c$ on ,saturday4 ,b is also dom9ical lett]1 ,new ,/yle2 = we take ! rema9d] aft] divid+ by #g1 f ! same numb]4 ,z bo? ,old & ,new ,/yles h ! same dom9ical lett]1 s bo? make ,janu>y to comm5ce on ! same day ( ! week2 b ,old ,/yle1 dur+ ?is c5tury1 is sev5 days beh9d ! true "t1 s t :5 x is ! fir/ day ( ,janu>y by ! ,old1 x is ! eigh? by ! ,new4 ,v]nal equ9ox 9 ! "t ( ,numa1 ab\t #gjj ,b4 ,c4 ,x is "h se5 by ! errors ( ! ,julian ,cal5d> ! ,v]nal ,equ9ox is made to occur ?ree days e>li] e #djj ye>s1 s t 9 #aehb x fell on ! #aa? in/ead ( ! #ba/ ( ,m>*4 #ah #ag #af #ae #ad #ac #ab #aa ,by suppress+ #aj d ,h\ ,h\ ,by ! ,gregorian rule ( int]calation ! co9cid5ce ( ye>s4 ,m>* #bd1 #df ,b4 ,c4 #bc #a ,a4 ,d4 ,re/or$ #bb #ajj by #ba #cjj ,julius #bj #djj ,caes>1 #ai ,v]nal #ejj equ9ox #df ,b4 ,c41 at ! #fjj ,c\ncil to ! ( #hjj ,nice1 place x #cbe #ijj ,a4 ,d4 occupi$ #ajjj 9 ! #abjj "t ( #acjj ,numa4 #adjj ays1 ,co9cid5ce #j ,re/or$ 9 #afjj rs beh9d "t1 #ah #f 9 advance4 #agjj #ab #ab #ahjj #f #ah #aijj ,co9cid5ce #j ,re/or$4 #bjjj rs beh9d "t1 #ah #f 9 advance4 #bajj #ab #ab #bbjj #f #ah #bcjj ,co9cid5ce #j ,re/or$4 #bdjj ! sol> & civil ye> is re/or$ v ne>ly e #djj ,app5dix ,i4 ,,*apt] ,,vi4 ,a ,,simple ,,me?od ,,= ,,f9d+ ,,! ,,day ,,( ,,! ,,week ,,( ,,ev5ts ,,:i* ,,occur ,,quadr5nially4 ,! inaugural ( ! ,presid5ts4 ,! day ( ! week on :i* !y h occurr$1 & on :i* !y w occur = ! next "o hundr$ ye>s3 ,april #cj?1 #aghi1 ,?ursday1 ,george ,wa%+ton4 ,m>* #d?1 #agic1 ,monday1 #agig1 ,saturday1 ,john ,adams #ahja1 ,w$nesday1 ,?omas ,jeff]son4 #ahje1 ,monday1 #ahji1 ,saturday1 ,james ,madison4 #ahac1 ,?ursday1 #ahag1 ,tuesday1 ,james ,monroe4 #ahba1 ,sunday1 #ahbe1 ,friday1 ,john ,q4 ,adams4 #ahbi1 ,w$nesday1 ,&rew ,jackson4 #ahcc1 ,monday1 #ahcg1 ,saturday1 ,m>t9 ,van ,bur54 #ahda1 ,?ursday1 ,wm4 ,h4 ,h>rison4 #ahde1 ,tuesday1 ,james ,k4 ,polk4 #ahdi1 ,sunday1 ,za*>y ,taylor4 #ahec1 ,friday1 ,frankl9 ,pi]ce4 #aheg1 ,w$nesday1 ,james ,bu*anan4 #ahfa1 ,monday1 ,abraham ,l9coln4 #ahfe1 ,saturday1 #ahfi1 ,?ursday1 ,ulysses ,s4 ,grant4 #ahgc1 ,tuesday1 #ahgg1 ,sunday1 ,ru!r=d ,b4 ,hays4 #ahha1 ,friday1 ,james ,a4 ,g>field4 #ahhe1 ,w$nesday1 ,grov] ,clevel&4 #ahhi1 ,monday1 ,b5jam9 ,h>rison4 #ahic1 ,saturday1 ,grov] ,clevel&4 #ahig1 ,?ursday1 #aija1 ,monday1 #aije1 ,saturday1 #aiji1 ,?ursday1 #aiac1 ,tuesday1 #aiag1 ,sunday1 #aiba1 ,friday1 #aibe1 ,w$nesday1 #aibi1 ,monday1 #aicc1 ,saturday1 #aicg1 ,?ursday1 #aida1 ,tuesday1 #aide1 ,sunday1 #aidi1 ,friday1 #aiec1 ,w$nesday1 #aieg1 ,monday1 #aifa1 ,saturday1 #aife1 ,?ursday1 #aifi1 ,tuesday1 #aigc1 ,sunday1 #aigg1 ,friday1 #aiha1 ,w$nesday1 #aihe1 ,monday1 #aihi1 ,saturday1 #aiic1 ,?ursday4 ,any "o und]/&+ :at has be5 said 9 a prec$+ *apt] conc]n+ ! dom9ical lett]1 c v easily make out su* a table )\t go+ ?r\gh ! process ( mak+ calculations = e ye>4 ,z e succe$+ ye>1 or any day ( ! ye>1 comm5ces "o day lat] 9 ! week ?an ! ye> prec$+1 & two days lat] 9 leap-ye>1 :i* makes five days e f\r ye>s1 & z ! ,presid5tial t]m is f\r ye>s1 s e inaugural occurs five days lat] 9 ! week ?an x did 9 ! prec$+ t]m4 ,n[1 z c\nt+ =w>d five days is equival5t to c\nt+ back two1 x w be mu* m conv5i5t to c\nt back two days e t]m4 ,!re is "o exception1 h[ev]1 to ?is rule2 ! ye> :i* completes ! c5tury is reckon$ z a common ye> 7t is1 ?ree c5turies out ( f\r71 consequ5tly we c\nt =w>d only f\r days or back ?ree4 ,comm5c+1 !n1 ) ! second inaugural ( ,wa%+ton1 :i* occurr$ on ,monday1 ,m>* #d1 #agic1 & c\nt+ back two days to ,saturday 9 #agig1 ?ree days to ,w$nesday 9 #ahja & two days to #ahje1 & s on two days e t]m till #aija1 :51 = reasons already giv51 we c\nt back ?ree days aga9 = "o t]m only1 aft] :i* x w be two days = ! next two hundr$ ye>s2 h5ce anyone c make 8 calculations z he writes1 & z fa/ z he c write4 ,see table on #fa/ page4 ,,"s ,,peculi>ities ,,conc]n+ ,,ev5ts ,,:i* ,,fall ,,on ,,! ,,tw5ty-,,n9? ,,day ,,( ,,febru>y4 ,! civil ye> & ! day mu/ be reg>d$ z comm5c+ at ! same in/ant4 ,we _c well reckon a fraction ( a day1 giv+ to ,febru>y #bh days & #f h\rs1 mak+ ! foll[+ mon? to comm5ce six h\rs lat] e ye>2 if s1 !n ,m>*1 = example1 9 #ahhh w\ld comm5ce at #ab m4 night4 #ahhi #f a4 m4 #ahij #ab m4 #ahia #f p4 m4 #ahib #ab m4 night1 aga91 & s on4 ,in/ead ( do+ s1 we wait until ! fraction accumulates to a :ole day2 !n give to ,febru>y #bi days1 & ! ye> #cff4 ,!re=e1 ev5ts :i* fall on ! #bi? ( ,febru>y _c be celebrat$ annually1 b only quadr5nially2 & at ! close ( ^? c5turies 9 :i* ! int]calations are suppress$ only oct5nially4 ,= example3 ,f ! ye> #afif to #agjd1 #agif to #ahjd1 & #ahif to #aijd1 !re is no #bi? day ( ,febru>y2 consequ5tly no day ( ! mon? 9 ! civil ye> on :i* an ev5t fall+ on ! #bi? ( ,febru>y c\ld be celebrat$4 ,!re=e1 a p]son born on ! #bi? ( ,febru>y1 #ahif1 c\ld celebrate no bir?day till #aijd1 a p]iod ( eight ye>s4 ,9 e common ye> ,febru>y has #bh days1 ea* day ( ! week be+ conta9$ 9 ! numb] ( days 9 ! mon? f\r times2 b 9 leap-ye>1 :5 ,febru>y has #bi days1 ! day :i* beg9s & ends ! mon? is conta9$ five times4 ,let u suppose t 9 a c]ta9 ye>1 :5 ,febru>y has #bi days1 ! mon? comes 9 on ,friday2 x also mu/ necess>ily end on ,friday4 ,aft] f\r ye>s x w comm5ce on ,w$nesday1 & end on ,w$nesday1 & s on1 go+ back two days 9 ! week e f\r ye>s1 until aft] #bh ye>s we come back to ,friday aga94 ,?is1 z has already be5 expla9$1 is ! dom9ical or sol> cycle4 ,= example3 ,febru>y 9 ,! ye> #d has five ,fridays4 #h ,w$nesdays4 #ab ,mondays4 #af ,saturdays4 #bj ,?ursdays4 #bd ,tuesdays4 #bh ,sundays4 #cb ,fridays4 ,s t aft] #bh ye>s we come back to ,friday aga92 & s on e #bh ye>s1 until *ange ( /yle 9 #aehb1 :5 ! ,gregorian rule ( int]calation be+ adopt$ by suppress+ ! int]calations 9 ?ree c5turial ye>s out ( f\r int]rupts ?is ord] at ! close ( ^! ?ree c5turies4 ,= example--#agjj1 #ahjj & #aijj1 aft] :i* ! cycle ( #bh ye>s w be cont9u$ until #bajj1 & s on4 ,! cycle be+ int]rupt$ by ! ,gregorian rule ( int]calation1 causes all ev5ts :i* occur betwe5 #bh & #ab ye>s ( ! close ( ! c5turies to fall on ! same day ( ! week aga9 9 #dj ye>s2 & ^? ev5ts t fall )9 #ab ye>s ( ! close ( ^! c5turies1 to fall on ! same day ( ! week aga9 9 #ab ye>s2 aft] :i* ! cycle ( #bh ye>s w be cont9u$ dur+ ! c5tury4 ,see foll[+ table3 #ahjd ,febru>y has five ,w$nesdays4 #ahjh ,mondays4 #ahab ,saturdays4 #ahaf ,?ursdays4 #ahbj ,tuesdays4 #ahbd ,sundays4 #ahbh ,fridays4 #ahcb ,w$nesdays4 #ahcf ,mondays4 #ahdj ,saturdays4 #ahdd ,?ursdays4 #ahdh ,tuesdays4 #aheb ,sundays4 #ahef ,fridays4 #ahfj ,w$nesdays4 #ahfd ,mondays4 #ahfh ,saturdays4 #ahgb ,?ursdays4 #ahgf ,tuesdays4 #ahhj ,sundays4 #ahhd ,fridays4 #ahhh ,w$nesdays4 #ahib ,mondays4 #ahif ,saturdays4 #aijj #aijd ,mondays4 #aijh ,saturdays4 #aiab ,?ursdays4 #aiaf ,tuesdays4 #aibj ,sundays4 #aibd ,fridays4 #aibh ,w$nesdays4 ,x w be se5 f ?is table t 9 #ahjd ,febru>y _h five ,w$nesdays2 & !n aga9 9 #ahcb1 #ahfj & #ahhh2 !n suppress+ ! int]calation 9 ! ye> #aijj suppresses ! #bi? ( ,febru>y2 s opposite #aijj 9 ! table is blank1 & ! #bi? ( ,febru>y does n occur aga9 till #aijd1 & ! five ,w$nesdays d n occur aga9 till #aibh--t is1 #dj ye>s f #ahhh1 :5 x la/ occurr$4 ,aga9 tak+ ! five ,mondays :i* occurr$ fir/ 9 ?is c5tury1 9 #ahjh1 & !n aga9 9 #ahcf1 #ahfd & 9 #ahib1 y w see1 = reasons already giv51 t x w occur aga9 9 #ab ye>s1 t is1 9 #aijd2 & s on ) all ! days ( ! week1 :5 x w be se5 :at is peculi> conc]n+ ! #bi? ( ,febru>y4 ,b att5tion is p>ticul>ly call$ to ! five ,?ursdays1 :i* occur fir/ 9 ?is c5tury #ahaf1 & !n aga9 9 #ahdd & #ahgb1 ! la/ date be+ )9 #bh ye>s ( ! close ( ! c5tury4 ,suppress+ ! int]calation suppresses ! #bi? ( ,febru>y2 consequ5tly ! five ,?ursdays d n occur aga9 till #aiab1 t is #dj ye>s f ! prec$+ date1 aft] :i* ! cycle w be cont9u$ = two hundr$ ye>s4 ,h5ce x may be se5 t ! dom9ical or sol> cycle ( #bh ye>s is s int]rupt$ at ! close ( ^! c5turies by ! suppression ( ! leap-ye>1 t c]ta9 ev5ts d n occur aga9 on ! same day ( ! week "u #dj ye>s1 :ile o!rs are repeat$ aga9 on ! same day ( ! week 9 #ab ye>s2 also ! numb] ( ye>s 9 ! cycle1 t is #bh #ab #dj4 ,& aga9 ! *ange ( /yle 9 #aehb1 causes all ev5ts :i* occur betwe5 #bh & #h ye>s ( t *ange1 to fall aga9 on ! same day ( ! week 9 #cf ye>s1 & all t occur )9 #h ye>s ( t *ange to be repeat$ aga9 on ! same day ( ! week 9 #h ye>s1 aft] :i* ! cycle ( #bh ye>s is cont9u$ = #ajj ye>s2 also t ! numb] ( ye>s 9 ! cycle1 t is1 #bh #h #cf4 ,,*apt] ,,vii4 ,,rules ,,= ,,f9d+ ,,! ,,day ,,( ,,! ,,week ,,( ,,ev5ts ,,t ,,transpir$ ,,prior ,,to ,,! ,,*ri/ian ,,era4 ,fir/1 x %\ld be und]/ood t ! ye> #d is ! fir/ leap ye> 9 our era1 reckon+ f ! ye> #a ,b4 ,c41 :i* mu/ necess>ily be leap ye>2 s t ! odd numb]s #a1 #e1 #i1 #ac1 etc41 are leap ye>s4 ,h5ce e ye> t is divisible by f\r & "o rema9d]1 is leap ye>2 if no rema9d]1 x is ! fir/ ye> aft] leap-ye>2 if #c1 ! second2 if #b1 ! ?ird1 ?us3 #de _/ #d #aa1 rema9d]1 #a1 #dd _/ #d #aa1 no rema9d]1 #dc _/ #d #aj1 rema9d]1 #c1 #db _/ #d #aj1 rema9d]1 #b1 #da _/ #d #aj1 rema9d]1 #a1 & s on1 e ye> be+ divid$ by f\r & #a rema9d] is leap-ye> ( #cff days4 ,x %\ld be borne 9 m9d t ! same cal5d> 0 9 use )\t any correction f ! days ( ,julius ,caes> #df ,b4 ,c4 to ,pope ,gregory ,,xiii 9 #aehb2 consequ5tly ! me?od ( f9d+ ! dom9ical lett] is1 9 "s respects1 simil> to ! "o already giv5 on ! #dd? page4 ,b 9 "s respects ! "o is ! rev]se ( ! o!r1 = we reckon backw>d & =w>d f a fix$ po9t--! era2 t is ! numb]s increase ea* way f ! era4 ,also ! dom9ical lett]s occur 9 ! natural ord] ( ! lett]s 9 reckon+ backw>d1 b exactly ! rev]se 9 reckon+ =w>d4 ,see table on ! #gc;d page1 :]e ! dom9ical lett] is plac$ opposite ea* ye> f #de ,b4 ,c4 to #de ,a4 ,d4 ,n[ we use ! same numb] #c1 because ,c1 ! ?ird lett] is dom9ical lett] = ! ye> #a ,b4 ,c41 ! po9t f :i* we reckon4 ,b in/ead ( tak+ ! rema9d]1 aft] divid+ by #g1 f #c or #aj1 to f9d ! numb] ( ! lett]1 z 9 ,"p ,second1 ,*apt] ,,iv1 7q4 v47 we add ! rema9d] to #c2 h5ce we h ! foll[+3 ,,rule4 ,divide ! numb] ( ! giv5 ye> by #d1 neglect+ ! rema9d]s1 & add ! quoti5t to ! giv5 numb]1 divide ?is am\nt by #g1 & add ! rema9d] to #c1 & t am\nt w give ! numb] ( ! lett]1 call+ ,a1 #a2 ,b1 #b2 ,c1 #c1 etc42 except ! fir/ ye> aft] leap-ye>1 7:i* is ! ye> exactly divisible by #d71 ! numb] ( ! lett] is "o less ?an is indicat$ by ! rule4 ,?is rule gives ! dom9ical lett] = ,janu>y & ,febru>y only1 9 leap-ye>1 :ile ! lett] t prec$es x1 is ! lett] = ! re/ ( ! ye>4 ,if ! am\nt be great] ?an sev51 we %\ld reckon f ,a to ,a or ,b aga94 ,x has already be5 /at$ 9 ,"p ,fir/1 ,*apt] ,,iii1 7q4 v471 t a *ange 0 made by ,augu/us ,caes> ab\t #h ,b4 ,c41 9 ! numb] ( days 9 ! mon?2 &1 z ?is *ange effects ! day ( ! week on :i* c]ta9 ev5ts fall1 x becomes necess>y t !y %\ld be pres5t$ z !y 7 arrang$ by ,julius ,caes>1 & z correct$ by ,augu/us4 ,julius ,caes> gave to ,febru>y #bi days 9 common ye>s1 & 9 leap-ye> #cj4 ,?is arrangem5t 0 ! v be/ t c\ld possibly be made1 b1 z has already be5 %[n1 x 0 int]rupt$ to gratify ! vanity ( ,augu/us4 ,! left h& column 9 ! table on ! #gb;d page repres5ts ! numb] ( days 9 ea* mon? f ! days ( ,julius ,caes> to ,augu/us1 a p]iod ( #cg ye>s4 ,! "r h& column repres5ts ! numb] ( days 9 ! mon?s z !y n[ are1 & h be5 s9ce ! *ange 0 made by ,augu/us1 #h ,b4 ,c4 ,consequ5tly ! rule = f9d+ ! day ( ! week on :i* ev5ts h fall5 = ! #cg ye>s prior to ! la/ m5tion$ date1 is n p]fectly exact1 & ne$s a little explanation "h4 ,! rule itself is giv51 & fully expla9$ 9 ,"p ,second1 ,*apt] ,v1 7q4 v47 b _c be appli$ to ! #cg ye>s )\t "s correction4 ,9 all ! mon?s m>k$ ) a />1 ev5ts fall "o day lat] 9 ! week ?an t :i* is indicat$ by ! rule4 ,?is %\ld be borne 9 m9d1 & make ! ev5t "o day lat] 9 ! week ?an t :i* is f\nd by ! rule4 ,= example1 ,julius ,caes> 0 assass9at$ on ! #ae? ( ,m>*1 #dd ,b4 ,c4 ,by giv+ to ,febru>y #bh days ! fir/ day ( ,m>* w\ld fall on ,w$nesday1 &1 ( c\rse1 ! #ae? w\ld be ,w$nesday4 ,b ,caes> gave to ,febru>y #bi days1 s t ! fir/ day ( ,m>* fell on ,?ursday1 & ! #ae? 0 ,?ursday4 ,h5ce1 e ev5t f ,m>* to ,septemb] w fall "o day lat] 9 ! week ?an ! rule indicates4 ,b ! rule is applicable to ,septemb]1 = x w make no diff]5ce :e!r !re are #bi days 9 ,febru>y or #ca 9 ,augu/1 !re are ! same numb] ( days f ,febru>y to ,septemb]4 ,b ! #ca days 9 ,septemb] w cause all ev5ts to fall "o day lat] 9 ! week dur+ ! mon? ( ,octob]1 b !y co9cide aga9 dur+ ! mon? ( ,novemb]4 ,! ord] is int]rupt$ aga9 9 ,decemb] by giv+ #ca days to ,novemb]4 ,see foll[+ table3 ,z ,arrang$ by ,julius ,z ,correct$ by ,augu/us1 ,caes>4 #h ,b4 ,c4 ,janu>y1 #ca ,janu>y1 #ca ,febru>y1 #bi ,febru>y1 #bh ,m>*1 #ca99 ,m>*1 #ca ,april1 #cj99 ,april1 #cj ,may1 #ca99 ,may1 #ca ,june1 #cj99 ,june1 #cj ,july1 #ca99 ,july1 #ca ,augu/1 #cj99 ,augu/1 #ca ,septemb]1 #ca ,septemb]1 #cj ,octob]1 #cj99 ,octob]1 #ca ,novemb]1 #ca ,novemb]1 #cj ,decemb]1 #cj99 ,decemb]1 #ca ---------------------------------------- ---------------- ,dom9ical,ye>4,dom9ical,ye>4,dom9ical,ye >4,dom9ical,ye>4 ,lett]4 ,lett]4 ,lett]4 ,lett]4 ---------------------------------------- ---------------- ,b4 ,c4 ,b4 ,c4 ,a4 ,d4 ,a4 ,d4 cb #de b #bb b #a c #bc a #dd ag #ba a #b ba #bd g #dc f #bj g #c g #be f #db e #ai fe #d f #bf ed #da d #ah d #e e #bg c #dj cb #ag c #f dc #bh b #ci a #af b #g b #bi a #ch g #ae ag #h a #cj gf #cg f #ad f #i g #ca e #cf ed #ac e #aj fe #cb d #ce c #ab d #aa d #cc c #cd b #aa cb #ab c #cd ba #cc a #aj a #ac b #ce g #cb gf #i g #ad ag #cf f #ca e #h f #ae f #cg e #cj d #g ed #af e #ch dc #bi c #f c #ag d #ci b #bh ba #e b #ah cb #dj a #bg g #d a #ai a #da g #bf f #c gf #bj g #db fe #be e #b e #ba f #dc d #bd dc #a d #bb ed #dd c #bc c #de ---------------------------------------- ---------------- ,,"p ,,?ird4 ,,cycles--,,julian ,,p]iod--,,ea/]4 ,,hebrew ,,cal5d>4 ,,*apt] ,i4 ,,! ,,sol> ,,cycle4 ,cycle1 7,lat9 ,cyclus1 r+ or circle74 ,! revolution ( a c]ta9 p]iod ( "t :i* f9i%es & re-comm5ces p]petually4 ,cycles 7 inv5t$ = ! purpose ( *ronology1 & = m>k+ ! int]vals 9 :i* two or m p]iods ( unequal l5g? are ea* complet$ a c]ta9 numb] ( times1 s t bo? beg9 exactly 9 ! same circum/ance z at fir/4 ,cycles us$ 9 *ronology are ?ree3 ,! sol> cycle1 ! lun> cycle1 & ! cycle ( indiction4 ,! sol> cycle is a p]iod ( "t aft] :i* ! same days ( ! ye> recur on ! same days ( ! week4 ,if e ye> conta9$ #cfe days1 !n e ye> w\ld comm5ce "o day lat] 9 ! week ?an ! ye> prec$+1 & ! cycle w\ld be complet$ 9 sev5 ye>s4 ,= if ! fir/ day ( ,janu>y1 9 any giv5 ye>1 fall on ,sunday1 !n ! foll[+ ye> on ,monday1 ! ?ird on ,tuesday1 & s on to ,sunday aga9 9 sev5 ye>s4 ,b ?is ord] is int]rupt$ 9 ! ,julian cal5d> e f\r ye>s by giv+ to ,febru>y #bi days1 & consequ5tly ! ye> #cff4 ,n[ ! numb] ( ye>s 9 ! int]cal>y p]iod be+ f\r & ! days ( ! week be+ sev51 _! product is #d x #g #bh2 tw5ty-eight ye>s !n is a p]iod aft] :i* ! fir/ day ( ! ye> & ! fir/ day ( e mon? recur aga9 9 ! same ord] on ! same day ( ! week4 ,?is p]iod is call$ ! sol> cycle or ! cycle ( ! sun1 ! orig9 ( :i* is unkn[n2 b is suppos$ to h be5 inv5t$ ab\t ! "t ( ! ,c\ncil ( ,nice1 9 ! ye> ( our ,"l #cbe2 b ! fir/ ye> ( ! cycle is plac$ by *ronologi/s n9e ye>s be=e ! comm5cem5t ( ! ,*ri/ian era4 ,h5ce ! ye> ( ! cycle correspond+ to any giv5 ye> 9 ! ,julian cal5d> is f\nd by ! foll[+ rule3 ,add n9e to ! date & divide ! sum by tw5ty-eight2 ! quoti5t is ! numb] ( cycles elaps$1 & ! rema9d] is ! ye> ( ! cycle4 ,%\ld !re be no rema9d]1 ! propos$ ye> is ! tw5ty-eigh?1 or la/ ( ! cycle4 ,?us1 = ! ye> #ahib1 we h 7#ahib #i7 _/ #bh #fg1 rema9d] #be4 ,!re=e1 #fg is ! numb] ( cycles1 & #be ! numb] 9 ! cycle4 ,,*apt] ,,ii4 ,,! ,,lun> ,,cycle4 ,! ,lun> cycle1 or ! cycle ( ! moon1 is a p]iod ( n9ete5 ye>s1 aft] :i* ! new & full moons fall on ! same days ( ! ye> z !y did n9ete5 ye>s be=e4 ,?is cycle 0 inv5t$ by ,meton1 a celebrat$ a/ronom] ( ,a!ns1 & may be reg>d$ z ! ma/]piece ( anci5t a/ronomy4 ,9 n9ete5 sol> ye>s !re are #bce lunations1 a numb] :i*1 on be+ divid$ by n9ete51 gives twelve lunations1 ) sev5 ( a rema9d]1 to be di/ribut$ among ! ye>s ( ! p]iod4 ,! p]iod ( ,meton1 !re=e1 consi/$ ( twelve ye>s conta9+ twelve mon?s ea*1 & sev5 ye>s conta9+ ?irte5 m\?s ea*1 & ^! la/ =m$ ! ?ird1 fif?1 eigh?1 elev5?1 ?irte5?1 sixte5?1 & n9ete5? ye>s ( ! cycle4 ,z x _h n[ be5 discov]$ t ! exact l5g? ( ! lunation is a little m ?an tw5ty-n9e & a half days1 x became necess>y to ab&on ! alt]nate succession ( full & defici5t mon?s2 &1 9 ord] to pres]ve a m accurate correspond5ce betwe5 ! civil mon? & ! lunation1 ,meton divid$ ! cycle into #abe full mon?s ( #cj days1 & #aaj defici5t mon?s ( #bi days ea*4 ,! numb] ( days 9 ! p]iod 01 !re=e1 #fidj2 = 7#abe x #cj7 7#aaj x #bi7 #fidj4 ,9 ord] to di/ribute ! defici5t mon?s ?r\gh ! p]iod 9 ! mo/ equable mann]1 ! :ole p]iod may be reg>d$ z consi/+ ( #bce full mon?s ( ?irty days1 or #gjej days1 f :i* #aaj days are to be d$uct$2 = 7#bce x #cj7 #gjej2 #gjej - #aaj #fidj1 z be=e4 ,?is gives "o day to be suppress$ 9 sixty-f\r1 s t if we suppose ! mon?s to conta9 ea* ?irty days1 & !n omit e sixty-f\r? day 9 reckon+ f ! beg9n+ ( ! p]iod1 ^? mon?s 9 :i* ! omission takes place w1 ( c\rse1 be ! defici5t mon?s4 ,! numb] ( days 9 ! p]iod be+ kn[n1 x is easy to asc]ta9 its accuracy bo? 9 respect ( ! sol> & lun> motions4 ,! exact l5g? ( n9ete5 sol> ye>s is 7#cfe;d1 #e;h1 #dhm1 #di4fbs47 x #ai #fici;d1 #ad;h1 #bgm1 #db4ghs42 h5ce1 ! p]iod1 :i* is exactly #fidj days1 exce$s n9ete5 annual revolutions ( ! e>? by a little m ?an n9e & a half h\rs4 ,on ! o!r h&1 ! exact "t ( ! synodic revolution ( ! moon is #bi;d1 #ab;h1 #ddm1 #b4hgs42 #bce lunations1 !re=e1 conta9 #bce x 7#bi;d1 #ab;h1 #ddm1 #b4hgs47 7#fici;d1 #af;h1 #cam1 #ad4des471 s t ! p]iod exce$s #bce lunations by ne>ly sev5 & a half h\rs4 ,at ! end ( f\r cycles1 or sev5ty-six ye>s1 ! accumulation ( ! sev5 & a half h\rs ( diff]5ce betwe5 ! cycle & #bce lunations am\nts to ?irty h\rs1 or "o :ole day & six h\rs4 ,calippus1 !re=e1 9 ord] to make a correction ( ! ,metonic cycle1 propos$ to quadruple ! p]iod ( ,meton1 & d$uct "o day at ! end ( t "t by *ang+ "o ( ! full mon?s into a defici5t mon?4 ,! p]iod ( ,calippus1 !re=e1 consi/$ ( ?ree ,metonic cycles ( #fidj days ea*1 & a p]iod ( #fici days2 & its error 9 respect to ! moon1 consequ5tly1 am\nt$ to only six h\rs1 or to "o day 9 #cjd ye>s4 ,?is p]iod exce$s sev5ty-six true sol> ye>s by #ad;h1 #im1 #h4hhs41 b co9cides exactly ) sev5ty-six ,julian ye>s2 & 9 ! "t ( ,calippus ! l5g? ( ! sol> ye> 0 almo/ univ]sally suppos$ to be exactly #cfe-a_/d days4 ,,*apt] ,,iii4 ,,! ,,lun> ,,cycle ,,& ,,gold5 ,,numb]4 ,9 connect+ ! lun> mon? ) ! sol> ye>1 ! fram]s ( ! ecclesia/ical cal5d> adopt$ ! p]iod ( ,meton1 or lun> cycle1 :i* !y suppos$ to be exact4 ,a diff]5t arrangem5t has1 h[ev]1 be5 foll[$ ) respect to ! di/ribution ( ! mon?s4 ,! lunations are suppos$ to consi/ ( tw5ty-n9e & ?irty days alt]nately1 or ! lun> ye> ( #ced days2 & 9 ord] to make up n9ete5 sol> ye>s1 six embolismic or int]cal>y mon?s1 ( ?irty days ea*1 are introduc$ 9 ! c\rse ( ! cycle1 & "o ( tw5ty-n9e days is add$ at ! end4 ,?is gives 7#ai x #ced7 7#f x #cj7 #bi #fice days1 to be di/ribut$ among #bce lun> mon?s4 ,b e leap-ye> "o day mu/ be add$ to ! lun> mon? 9 :i* ! #bi? ( ,febru>y is includ$4 ,n[ if leap-ye> happ5$ on ! fir/1 second or ?ird ye> ( ! p]iod1 !re w be five leap-ye>s 9 ! p]iod1 b only f\r :5 ! fir/ leap-ye> falls on ! f\r?4 ,9 ! =m] case ! numb] ( days 9 ! p]iod becomes #fidj1 & 9 ! latt] #fici4 ,! mean l5g? ( ! cycle is1 !re=e1 #fici-c_/d days1 agree+ exactly ) n9ete5 ,julian ye>s4 ,by means ( ! lun> cycle ! new moons ( ! cal5d> 7 indicat$ be=e ! re=mation 9 #aehb4 ,z ! cycle re/ores ^! ph5om5a to ! same days ( ! civil mon?1 !y w fall on ! same days 9 any two ye>s :i* occupy ! same place 9 ! cycle2 consequ5tly a table ( ! moon's phases = n9ete5 ye>s w s]ve = any ye> :atev] :5 we "k its numb] 9 ! cycle4 ,! numb] ( ! ye> 9 ! cycle is call$ ! ,gold5 ,numb]2 ei!r because x 0 s t]m$ by ! ,greeks1 :o1 on acc\nt ( its utility1 ord]$ x to be inscrib$ 9 lett]s ( gold 9 _! temples1 or m probably because x 0 usual to di/+ui% x by r$ lett]s 9 ! cal5d>4 ,! ,gold5 ,numb]s 7 introduc$ into ! cal5d> ab\t ! ye> #ecj1 b dispos$ z !y w\ld h be5 if !y _h be5 ins]t$ at ! "t ( ! ,c\ncil ( ,nice4 ,! cycle is suppos$ to comm5ce ) ! ye> 9 :i* ! new moon falls on ! fir/ day ( ,janu>y1 :i* took place ! ye> prec$+ ! comm5cem5t ( our era4 ,h5ce to f9d ! ,gold5 ,numb] = any ye>1 we h ! foll[+ rule3 ,add "o to ! date1 divide ! sum by n9ete52 ! quoti5t is ! numb] ( cycles elaps$1 & ! rema9d] is ! ,gold5 ,numb]4 ,%\ld !re be no rema9d]1 ! propos$ ye> is1 ( c\rse1 ! la/ or n9ete5? ( ! cycle4 ,?us1 = ! ye> #ahib1 we h 7#ahib #a7 _/ #ai #ii1 rema9d] #ab2 !re=e1 #ii is ! numb] ( cycles1 & #ab ! numb] 9 ! cycle1 or ! ,gold5 numb]4 ,x ought to be rem>k$ t ! new moons det]m9$ 9 ?is mann]1 may diff] f ! a/ronomical new moons sometimes z mu* z two days4 ,! reason is1 t ! sum ( ! sol> & lun> inequalities :i* are comp5sat$ 9 ! :ole p]iod1 may am\nt 9 c]ta9 cases to #aj degrees & !reby cause ! new moon to arrive on ! second day be=e or aft] its mean "t4 ,! cycle ( ! sun br+s back ! days ( ! mon? to ! same day ( ! week2 ! cycle ( ! moon re/ores ! new moons to ! same day ( ! mon?2 !re=e1 #bh x #ai #ecb ye>s1 includes all ! v>iations 9 respect ( ! new moons & ! dom9ical lett]1 & is consequ5tly a p]iod aft] :i* ! new moons aga9 occur on ! same day ( ! mon? & ! same day ( ! week4 ,?is is call$ ! ,dionysian or ,great ,pas*al ,p]iod1 f its hav+ be5 employ$ by ,dionysius ,exiguus 9 det]m9+ ,ea/] ,sunday4 ,,*apt] ,,iv4 ,,cycle ,,( ,,indiction1 ,,& ,,! ,,julian ,,p]iod4 ,! cycle ( ,indiction or ,roman ,indiction1 is a p]iod ( fifte5 ye>s2 n a/ronomical l ! two =m]1 b entirely arbitr>y4 ,its orig9 & ! purpose = :i* x 0 e/abli%$ are alike unc]ta92 b x is conjectur$ t x 0 introduc$ by ,con/ant9e ! ,great1 ab\t ! ye> #cab ( ! common era1 & _h ref]5ce to c]ta9 judicial acts t took place "u ! ,greek emp]ors at /at$ int]vals ( fifte5 ye>s4 ,9 *ronological reckon+1 x is consid]$ z hav+ comm5c$ on ! fir/ day ( ,janu>y ( ! ye> #cac4 ,by ext5d+ x backw>d1 x w be f\nd t ! cycle comm5c$ ?ree ye>s be=e ! beg9n+ ( our era4 ,9 ord]1 !re=e1 to f9d ! numb] ( any ye> 9 ! cycle ( indiction1 we h ?is rule3 ,add ?ree to ! date1 divide ! numb] by fifte52 & ! rema9d] is ! ye> ( ! indiction4 ,%\ld !re be no rema9d]1 ! propos$ ye> is ! fifte5? or la/ ( ! cycle4 ,?us1 = ! ye> #ahib1 we h 7#ahib #c7 _/ #ae #abf1 rema9d] #e4 ,!re=e1 #e is ! numb] 9 ! cycle4 ,! ,julian p]iod1 propos$ by ! celebrat$ ,joseph ,scalig]1 z an univ]sal measure ( *ronology1 is a p]iod ( #gihj ye>s1 & is =m$ by ! cont9ual multiplication ( ! ?ree numb]s1 #bh1 #ai & #ae2 t is1 ( ! cycle ( ! sun1 ! cycle ( ! moon1 & ! cycle ( indiction4 ,?us1 7#bh x #ai x #ae7 #gihj4 ,9 ! c\rse ( ?is long p]iod no two ye>s c be express$ by ! same numb]s 9 all ! ?ree cycles4 ,! fir/ ye> ( ! ,*ri/ian era _h #aj = its numb] 9 ! cycle ( ! sun1 #b 9 ! cycle ( ! moon1 & #d 9 ! cycle ( ! indiction4 ,n[1 x is f\nd by actual calculation1 t ! only numb] less ?an #gihj :i*1 on be+ divid$ successively by #bh1 #ai1 & #ae1 leaves ! respective rema9d]s #aj1 #b & #d1 is #dgad4 ,h5ce1 ! fir/ ye> ( ! ,*ri/ian era correspond$ ) ! ye> #dgad ( ! ,julian p]iod1 :i* p]iod co9cides ) ! #gaj? be=e ! common mundane era #djjd ,b4 ,c42 = #djjd #gaj #dgad4 ,h5ce1 also1 ! ye> ( our era correspond+ to any o!r ye> ( ! p]iod1 or vice v]sa1 is f\nd by ! foll[+ rule3 ,:5 ! giv5 ye> is ant]ior to ! comm5cem5t ( ! era1 subtract ! numb] ( ! ye> ( ! ,julian p]iod f #dgad1 & ! rema9d] is ! ye> be=e ,*ri/2 or1 subtract ! ye> be=e ,*ri/ f #dgad1 & ! rema9d] is ! correspond+ ye> 9 ! ,julian p]iod4 ,?us1 ,rome 0 f\nd$ 9 ! ye> #cifj ( ! ,julian p]iod4 ,:at 0 ! ye> be=e ,*ri/8 ,we h !n #dgad - #cifj #ged4 ,julius ,caes> 0 assass9at$ #dd ye>s be=e ,*ri/1 :at 0 ! correspond+ ye> ( ! ,julian p]iod8 ,we h !n1 #dgad - #dd #dfgj4 ,:5 ! giv5 ye> is aft] ,*ri/1 subtract #dgac f ! ye> ( ! p]iod1 & ! rema9d] is ! ye> ( ! era2 or add #dgac to ! ye> ( ! era1 & ! sum is ! correspond+ ye> 9 ! ,julian p]iod4 ,?us1 ! ,c\ncil ( ,nice 0 conv5$ 9 ! ye> #ejch ( ! ,julian p]iod1 :at 0 ! ye> ( our era8 ,we h !n1 #ejch - #dgac #cbe4 ,:at ye> ( ! ,julian p]iod corresponds ) ! pres5t ye>1 #ahib8 ,we h !n1 #dgac #ahib #ffje4 ,,*apt] ,v4 ,,ea/]4 ,ea/] 7,g]m4 ,o/]n1 ,old ,saxon ,o/]1 f ,o/51 signify+ ris+74 ,! ,engli% "n is probably d]iv$ f ,o/]a or ,eo/re1 ! ,teutonic goddess ( spr+1 ^: fe/ival occurr$ ab\t ! same "t ( ! ye> z ! celebration ( ,ea/]4 ,! ,hebrew-,greek ^w ,pas*a has pass$ into ! "n giv5 to ?is fea/ by mo/ ,*ri/ian nations4 ,?is fe/ival is held 9 commemoration ( our ,"l's resurrection4 ,! ,jews celebrat$ _! passov]1 9 con=mity ) ! directions giv5 !m by ,moses1 on ! #ad? day ( ! mon? ,nisan1 be+ ! lun> mon? ( :i* ! #ad? day ei!r falls on or next foll[s ! day ( ! v]nal equ9ox4 ,9 ! ye> ( our ,"l's crucifixion ?is fell on a ,friday2 ! resurrection1 !re=e1 took place on ! fir/ day ( ! week1 :i* f !nce is d5om9at$ ! ,"l's ,day4 ,! primitive ,*ri/ians1 9 celebrat+ ?is anniv]s>y1 fell into two diff]5t sy/ems4 ,! ,we/]n *ur*es obs]v$ ! ne>e/ ,sunday to ! full moon ( ,nisan1 tak+ no acc\nt ( ! day on :i* ! passov] w\ld be celebrat$4 ,! ,asiatics1 on ! o!r h&1 foll[+ ! ,jewi% cal5d>1 adopt$ ! #ad? ( ,nisan ^u :i* to commemorate ! crucifixion1 & obs]v$ ! fe/ival ( ,ea/] on ! ?ird day foll[+1 ^u :atev] day ( ! week t might fall1 h5ce !y obta9$ ! "n ( ,qu>todecimans1 7f qu>to1 f\r1 & decem1 t517 ! f\rte5? day m54 ,! =m] appeal$ to ! au?ority ( ,/4 ,pet] & ,/4 ,paul1 ! latt] to t ( ,/4 ,john4 ,! dispute :i* took place ^u ?is po9t 9 ! second & ?ird c5turies ( our era is rem>kable1 z connect$ ) p]haps ! fir/ ev5t :i* c be br\ght to be> ^u ! "q ( ! primacy ( ! ,roman bi%op2 & x is ! m int]e/+ z bo? p>ties are accu/om$ to claim x z a te/imony 9 favor ( _! own views4 ,victor1 bi%op ( ,rome1 wrote an imp]i\s lett] to ! ,asiatic bi%ops1 requir+ _! con=mity to ! ,we/]n rule2 :i* 0 answ]$ by ,polycrates1 bi%op ( ,ephesus1 9 ! "n ( ! re/1 express+ _! resolution to ma9ta9 ! cu/om h&$ d[n to !m by _! ance/ors4 ,! ,roman bi%op !reupon broke (f communion ) !m2 b he 0 rebuk$ by ,ir5aeus1 ( ,lyons1 & x 0 agre$ by 8 m$iation t ea* p>ty %\ld reta9 its cu/oms4 ,su* cont9u$ to be ! practice till ! "t ( ,con/ant9e1 :5 ! ,c\ncil ( ,nice det]m9$ ! matt] by ! foll[+ ,canons3 a--,ea/] mu/ be celebrat$ on a ,sunday4 b--,?is ,sunday mu/ foll[ ! #ad? day ( ! pas*al moon1 s t if ! #ad? day ( ! pas*al moon fall on a ,sunday1 !n ,ea/] mu/ be celebrat$ on ! ,sunday foll[+4 c--,! pas*al moon is t moon ( :i* ! #ad? day ei!r falls on or next foll[s ! day ( ! v]nal equ9ox4 d--,! #ba/ ( ,m>* is to be acc\nt$ ! day ( ! v]nal equ9ox4 7,app5dix ,l47 ,sometimes a misund]/&+ has aris5 f n obs]v+ t ?is regulation is to be con/ru$ accord+ to ! tabul> full moon z det]m9$ f ! epact1 & n by ! true full moon1 :i* 9 g5]al1 occurs "o or two days e>li]4 ,f ^! conditions x foll[s1 t if ! pas*al full moon fall on ,saturday1 ! #ba/ ( ,m>*1 !n ,ea/] w happ5 on ! #bb;d1 its e>lie/ possible date4 ,= if ! full moon arrive on ! #bj?1 x w\ld n be ! pas*al full moon1 :i* _c happ5 be=e ! #ba/1 consequ5tly ! foll[+ moon is ! pas*al full moon1 :i* happ5s #cj days aft] ! #bj? ( ,m>*1 :i* is ! #ai? ( ,april4 ,n[1 if 9 ?is case ! #ai? ( ,april is ,sunday1 !n ,ea/] mu/ be celebrat$ ! foll[+ ,sunday1 or ! #bf? ( ,april4 ,h5ce1 ,ea/] ,sunday _c happ5 e>li] ?an ! #bb;d ( ,m>*1 or lat] ?an ! #bf? ( ,april4 ,! obs]vance ( ^! rules r5d]s x necess>y to reconcile ?ree p]iods :i* h no common measure1 namely1 ! week1 ! lun> mon?1 & ! sol> ye>2 & z ?is c be done only approximately1 & )9 c]ta9 limits1 ! det]m9ation ( ,ea/] is an affair ( consid]able nicety & complication4 ,x has already be5 %[n t ! lun> cycle conta9$ #fici days & #ah h\rs2 also1 t ! exact "t ( #bce lunations is #fici;d1 #af;h1 #cam1 #ad4des4 ,! diff]5ce1 :i* is #a;h1 #bhm1 #de4ees41 am\nts to a day 9 #cjh ye>s1 s t at ! end ( ?is "t ! new moons occur "o day e>li] ?an !y are indicat$ by ! ,gold5 ,numb]s4 ,dur+ ! #abeg ye>s t elaps$ betwe5 ! ,c\ncil ( ,nice & ! re=mation1 ! error _h accumulat$ to f\r days1 s t ! new moons1 :i* 7 m>k$ 9 ! cal5d> z happ5+1 = example1 on ! #e? ( ! mon?1 actually fell on ! #a/4 ,x w\ld h be5 easy to correct ?is error by plac+ ! ,gold5 ,numb]s f\r l9es high] 9 ! new cal5d>1 b ! suppression ( t5 days _h already r5d]$ x necess>y to place !m t5 l9es l[]1 & to c>ry ^? :i* belong$1 = example1 to ! #e? & #f? ( ! mon?1 to ! #ae? & #af?4 ,b suppos+ ?is correction to h be5 made1 x w\ld h become necess>y1 at ! end ( #cjh ye>s1 to place !m "o l9e high]1 9 consequ5ce ( ! accumulation ( ! error ( ! cycle to a :ole day4 ,on ! o!r h&1 z ! ,gold5 ,numb]s 7 only adapt$ to ! ,julian cal5d>1 e omission ( ! c5t5>y int]calation w\ld require !m to be plac$ "o l9e l[]1 opposite ! #f?1 = example1 in/ead ( ! #e? ( ! mon?1 s t1 g5]ally speak+1 ! places ( ! ,gold5 ,numb]s w\ld h to be *ang$ e c5tury4 ,on ?is acc\nt ,lilius ?\ght fit to reject ! ,gold5 ,numb]s f ! ,cal5d>1 & supply _! places by ano!r set ( numb]s call$ ,epacts1 ! use ( :i* we %all n[ proce$ to expla94 ,epact1 7,greek epaktos1 add$ or introduc$74 ,! excess ( ! sol> ye> beyond ! lun>1 employ$ 9 ! cal5d> to signify ! moon's age at ! beg9n+ ( ! ye>4 ,! common sol> ye> consi/$ ( #cfe days & ! lun> ye> only #ced days1 ! diff]5ce is elev52 :5ce1 if a new moon fall on ! fir/ day ( ,janu>y 9 any ye>1 ! moon w be elev5 days old on ! fir/ day ( ! foll[+ ye>1 & tw5ty-two days old on ! fir/ ( ! ?ird ye>4 ,! numb]s elev5 & tw5ty-two are !re=e ! epacts ( ^? ye>s respectively4 ,ano!r addition ( elev5 gives ?irty-?ree = ! epact ( ! f\r? ye>2 b 9 consequ5ce ( ! ins]tion ( ! int]cal>y mon? 9 ea* ?ird ye> ( ! lun> cycle1 ?is epact is r$uc$ to ?ree2 = #cc - #cj #c4 ,9 l mann] ! epacts ( all ! foll[+ ye>s ( ! cycle are obta9$ by successively add+ elev5 to ! epact ( ! =m] ye>1 & reject+ ?irty z (t5 z ! sum exce$s or equals t numb]4 ,9 ord] to %[ h[ ! epacts are connect$ ) ! ,gold5 ,numb]s1 let a cyph] repres5t ! new moon on ! fir/ day ( ,janu>y 9 any ye>1 !n ! epacts & ,gold5 ,numb]s = a :ole lun> cycle w\ld be repres5t$ ?us3 #a #b #c #d #e #f #g #h #i #j #aa #bb #c #ad #be #f #ag #bh #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #i #bj #a #ab #bc #d #ae #bf #g #ah ,b ! ord] is int]rupt$ at ! end ( ! cycle2 = ! epact ( ! foll[+ ye> f\nd 9 ! same mann] w\ld be #ah #aa #bi1 :]eas x ought to be a ciph] to correspond ) ! moon's age & ! ,gold5 ,numb] #a4 ,! reason = ?is is1 t ! int]cal>y mon?1 ins]t$ at ! end ( ! cycle1 conta9s only tw5ty-n9e days in/ead ( ?irty2 :5ce1 aft] #aa has be5 add$ to ! epact ( ! ye> correspond+ to ! ,gold5 ,numb] #ai1 we mu/ reject tw5ty-n9e in/ead ( ?irty1 9 ord] to h ! epact ( ! succe$+ ye>2 or1 :i* comes to ! same ?+1 we mu/ add twelve to ! epact ( ! la/ ye> ( ! cycle1 & !n reject ?irty z be=e4 ,?us1 #ah #ab #cj2 #cj - #cj #j2 ! ciph] correspond+ ) ! ,gold5 ,numb] #a4 ,?is me?od ( =m+ ! epacts might h be5 cont9u$ indef9itely if ! ,julian int]calation _h be5 foll[$ )\t correction & ! cycle _h be5 p]fectly exact2 b z nei!r ( ^! suppositions is true1 two equations or corrections mu/ be appli$1 "o dep5d+ on ! error ( ! ,julian ye>1 :i* is call$ ! sol> equation2 ! o!r on ! errors ( ! lun> cycle1 :i* is call$ ! lun> equation4 ,! sol> equation occurs ?ree times 9 #djj ye>s1 namely1 9 e secul> ye> :i* is n a leap-ye>2 = 9 ?is case ! omission ( ! int]cal>y day causes ! new moons to arrive "o day lat] 9 all ! foll[+ mon?s1 s t ! moon's age at ! end ( ! mon? is "o day less ?an x w\ld h be5 if ! int]calation _h be5 made1 & ! epacts mu/ accord+ly be all dim9i%$ by unity4 ,?us1 ! epacts #aa1 #bb1 #c1 #ad1 etc41 become #aj1 #ba1 #b1 #ac1 etc4 ,on ! o!r h&1 :5 ! "t by :i* ! new moons anticipate ! lun> cycle am\nts to a :ole day1 :i*1 z we h se51 x does 9 #cjh ye>s1 ! new moons w arrive "o day e>li] & ! epacts mu/1 consequ5tly1 be increas$ by unity4 ,?us1 ! epacts #aa1 #bb1 #c1 #ad1 etc41 9 consequ5ce ( ! lun> equation1 becomes #ab1 #bc1 #d1 #ae1 etc4 ,9 ord] to pres]ve ! uni=mity ( ! cal5d>1 ! epacts are *ang$ only at ! comm5cem5t ( ! c5tury2 ! correction ( ! error ( ! lun> cycle is !re=e made at ! end ( #cjj ye>s4 ,9 ! ,gregorian cal5d> ?is error is assum$ to am\nt to a day 9 #cab-a_/b ye>s1 or eight days 9 #bejj ye>s1 an assumption :i* requires ! l9e ( epacts to be *ang$ sev5 times successively at ! end ( ea* p]iod ( #cjj ye>s1 & once at ! end ( #djj ye>s2 & f ! mann] 9 :i* ! epacts 7 dispos$ at ! re=mation1 x 0 f\nd mo/ correct to suppose "o ( ! p]iods ( #bejj ye>s to t]m9ate ) ! ye> #ahjj4 ,! ye>s 9 :i* ! sol> equation occurs1 c\nt+ f ! re=mation1 are #agjj1 #ahjj1 #aijj1 #bajj1 #bbjj1 #bcjj1 #bejj1 etc4 ,^? 9 :i* ! lun> equation occurs are #ahjj1 #bajj1 #bdjj1 #bgjj1 #cjjj1 #ccjj1 #cfjj1 #cijj1 aft] :i* #dcjj1 #dfjj1 & s on4 ,:5 ! sol> equation occurs1 ! epacts are dim9i%$ by unity2 :5 ! lun> equation occurs1 ! epacts are augm5t$ by unity2 & :5 bo? equations occur toge!r1 z 9 #ahjj1 #bajj1 #bgjj1 etc41 !y comp5sate ea* o!r1 & ! epacts are n *ang$4 ,,*apt] ,,vi4 ,a ,,new ,,& ,,easy ,,me?od ,,( ,,fix+ ,,! ,,date ,,( ,,ea/]4 ,9 det]m9+ ! date ( ,ea/]1 we make use ( ! numb]s call$ epacts2 &1 z ^! numb]s h already be5 expla9$ 9 ! prec$+ *apt]1 7q4 v47 x w be necess>y to give !m only a brief notice "h4 ,epact1 z has already be5 def9$1 is ! excess ( ! sol> ye> beyond ! lun>1 employ$ 9 ! cal5d> to signify ! moon's age at ! beg9n+ ( ! ye>2 t is1 if a new moon fall on ! fir/ day ( ,janu>y 9 any ye>1 x w be elev5 days old on ! fir/ day ( ! foll[+ ye>1 & tw5ty-two days old on ! fir/ day ( ! ?ird ye>1 & s on4 ,n[1 9 ?is "w1 9 fix+ ! date ( ,ea/]1 we ab&on ! use ( ! new moons altoge!r1 & make calculations :olly f ! pas*al full moons1 :i* _c happ5 e>li] ?an ! #ba/ ( ,m>*1 nor lat] ?an ! #ai? ( ,april4 ,app5dix ,j4 ,! epacts are "h us$ to %[ ! day ( ! mon? on :i* ! pas*al full moons fall2 t is1 if ! pas*al moon fall on a giv5 day ( ! mon? 9 any ye>1 x w happ5 elev5 days e>li] ! foll[+ ye>1 & tw5ty-two days e>li] ! ?ird ye>1 & s on4 ,to illu/rate1 suppose ! pas*al moon fall on ! #ah? ( ,april 9 any giv5 ye>1 on ! foll[+ ye> x w\ld fall on ! #g?1 9 ! ?ird ye> on ! #bg? ( ,m>*2 & 9 ! f\r? ye> ! moon w\ld full on ! #af? ( ,m>*1 b t w\ld n be ! pas*al moon1 :i* _c happ5 e>li] ?an ! #ba/2 s ! foll[+ moon w\ld be ! pas*al moon1 :i* happ5s ?irty days lat]1 or ! #ae? ( ,april2 !n ! fif? ye> x w\ld fall on ! #d? ( ,april1 & s on4 ,! sol> & lun> equations or corrections are n made by *ange ( epacts1 = only "o l9e ( epacts is us$ 9 ?is "w1 b ^! corrections are made by a *ange ( ! day ( ! mon? on :i* ! cycle comm5ces4 ,?is *ange is made at ! beg9n+ ( a c5tury1 &1 ( c\rse1 does n occur b once 9 a hundr$ ye>s1 & frequ5tly no *ange is made = two1 & ev5 ?ree hundr$ ye>s4 ,! reason = mak+ ^! *anges has be5 giv5 9 ! prec$+ *apt]1 7q4 v471 & w aga9 be notic$ 9 ! prop] place4 ,! l9e ( epacts us$ are ?us repres5t$1 comm5c+ ) a ciph] z ! po9t ( dep>ture3 #j1 #aa1 #bb1 #c1 #ad1 #be1 #f1 #ag1 #bh1 #i1 #bj1 #a1 #ab1 #bc1 #d1 #ae1 #bf1 #g1 #ah4 ,x %\ld be borne 9 m9d t ! epacts are obta9$ by successively add+ elev5 to ! epact ( ! =m] ye>1 & reject+ ?irty z (t5 z ! sum exce$s or equals t numb]4 ,b1 z ! int]cal>y mon? ins]t$ at ! end ( ! cycle conta9s only #bi days1 add twelve in/ead ( elev51 to eighte51 ! la/ ( ! cycle1 & !n reject ?irty z be=e2 ?us1 #ah #ab #cj2 !n #cj - #cj #j4 ,! cycle be+ complet$1 we aga9 comm5ce ) ! ciph] z ! po9t ( dep>ture4 ,aft] hav+ f\nd ! pas*al full moons = "o lun> cycle1 a p]iod ( n9ete5 ye>s1 !n ! pas*al moons aga9 occur 9 ! same ord]1 on ! same days ( ! mon?1 z !y did n9ete5 ye>s be=e4 ,n[1 z has also be5 %[n 9 ! prec$+ *apt]1 ?is cycle might h be5 cont9u$ indef9itely _h ! ,julian int]calation be5 foll[$ )\t correction1 & ! cycle be5 p]fectly exact2 b nei!r ( ^! be+ true1 two equations or corrections mu/ be made1 "o dep5d+ on ! error ( ! ,julian cal5d>1 :i* is call$ ! sol>-equation2 ! o!r on ! error ( ! lun> cycle1 :i* is call$ ! lun> equation4 ,e omission ( ! int]cal>y day1 :i* occurs ?ree times 9 #djj ye>s1 w cause ! full moons to fall "o day lat]2 = example1 on ! #ac? ( ! mon? in/ead ( ! #ab?4 ,on ! o!r h&1 z has also be5 %[n 9 ! prec$+ *apt]1 ! error ( ! lun> cycle is "o day 9 #cjj ye>s2 s t at ! end ( e #cjj ye>s ! full moons w fall "o day e>li]1 = example1 on ! #aa? ( ! mon? in/ead ( ! #ab?4 ,n[1 :5 bo? equations occur toge!r1 !y comp5sate ea* o!r2 t is1 :ile ! sol> equation w\ld cause ! full moon to fall on ! #ac?1 ! lun> equation w\ld make x fall on ! #aa?2 !re=e1 no correction is to be made--!re is no?+ to correct4 ,_h !y occurr$ s+ly1 ! full moon1 at ! beg9n+ ( ! cycle1 w\ld h fall5 ei!r on ! #ac? or ! #aa?2 b z !y occur toge!r1 no *ange is made2 & ! full moons ( ! cal5d> w rema9 z !y are = ! next "o hundr$ ye>s4 ,h5ce1 ! date ( ,ea/] may v easily be det]m9$1 z indicat$ 9 ! foll[+ tables 7q4 v474 ,x is kn[n by actual calculation t ! pas*al full moon fell on ! #ab? ( ,april 9 ! ye> #aeif1 :i* moon 0 ! fir/ ( a cycle aft] ! re=mation ( ! cal5d> by ,gregory4 ,n[1 by tak+ ! epact ( ! foll[+ ye>s ( ! cycle1 :i* are #aa1 #bb1 #c1 #ad1 #be1 etc41 f #ab1 ! date ( ! fir/ pas*al moon1 & y w h all ! moons ( ! cycle4 ,( c\rse1 ! epacts #bb1 #be1 etc41 _c be tak5 f #ab1 b be+ c>ri$ back f ! #ab? ( ,april1 !y w %[ on :at day 9 ,m>* ! full moons fall4 ,:5 ! epacts are great] ?an #ab1 x w\ld be m conv5i5t to take !m f #dc1 z ! numb] ( days 9 ,m>* be+ #ca1 s #ab #ca #dc4 ,to f9d ! pas*al moons ( ! cycle1 we h !n ?is rule3 ,if ! epact is less ?an #ab1 take x f #ab2 if great]1 take x f #dc1 & ! rema9d] w be ! date ( ! pas*al moon2 unless ! full moon fall be=e ! #ba/ ( ,m>*1 9 :i* case ! foll[+ moon w be ! pas*al moon1 :i* happ5s ?irty days lat]4 ,b :5 ! sol> equation occurs 9 #agaj1 caus+ ! cycle to comm5ce ) ! #ac? ( ,april1 !n ! epacts mu/ be tak5 f #ac1 or #ac #ca #dd4 ,& aga9 9 #aijj1 ! correction makes ! cycle comm5ce on ! #ad? ( ,april2 s ! numb] f :i* ! epacts are tak5 is #ad1 or #ad #ca #de1 & s on4 ,:5ev] !re is a *ange ( date ( ! pas*al moon 9 ! beg9n+ ( ! cycle1 z !re is aga9 9 #bbjd1 #bcah & #bdac1 etc41 z may be se5 9 ! foll[+ tables1 !n ! epacts mu/ be tak5 f t date1 or t date plus #ca1 ! numb] ( days 9 ,m>*4 ,or ! date ( ! pas*al moons may v easily be det]m9$ by tak+ elev5 successively f ! date ( e prec$+ full moon1 & t w give ! date ( ! pas*al moons2 only x %\ld be borne 9 m9d t1 :5ev] ! full moon falls be=e ! #ba/ ( ,m>*1 ! foll[+ moon is ! pas*al moon1 :i* happ5s ?irty days lat]4 ,z ,ea/] ,sunday is ! fir/ ,sunday aft] ! pas*al full moon1 s all t rema9s to be done 9 fix+ ! date ( ,ea/]1 is to f9d ! day ( ! mon? on :i* t ,sunday falls2 & z ?is c easily be done by ! use ( ! dom9ical lett]1 :i* lett] & its use 9 fix+ dates hav+ be5 fully expla9$ 9 ,"p ,second1 ,*apt]s ,,iv & ,v1 7q4 v471 a repetition seems to be unnecess>y "h4 ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- gf #aeif ,april #ab #ad #j #a e #aeig #a #f #aa #b d #aeih ,m>* #ba #bb #bb #c c #aeii ,april #i #aa #c #d ba #afjj ,m>* #bi #b #ad #e g #afja ,april #ag #bb #be #f f #afjb #f #g #f #g e #afjc ,m>* #bf #cj #ag #h dc #afjd ,april #ad #ah #bh #i b #afje #c #aj #i #aj a #afjf ,m>* #bc #bf #bj #aa g #afjg ,april #aa #ae #a #ab fe #afjh ,m>* #ca #f #ab #ac d #afji ,april #ai #bf #bc #ad c #afaj #h #aa #d #ae b #afaa ,m>* #bh #c #ae #af ag #afab ,april #af #bb #bf #ag f #afac #e #g #g #ah e #afad ,m>* #be #cj #ah #ai d #afae ,april #ab #ai #j #a cb #afaf #a #c #aa #b a #afag ,m>* #ba #bf #bb #c g #afah ,april #i #ae #c #d f #afai ,m>* #bi #ca #ad #e ed #afbj ,april #ag #ai #be #f c #afba #f #aa #f #g b #afbb ,m>* #bf #bg #ag #h a #afbc ,april #ad #af #bh #i gf #afbd #c #g #i #aj e #afbe ,m>* #bc #cj #bj #aa d #afbf ,april #aa #ab #a #ab c #afbg ,m>* #ca #d #ab #ac ba #afbh ,april #ai #bc #bc #ad g #afbi #h #ae #d #ae f #afcj ,m>* #bh #ca #ae #af e #afca ,april #af #bj #bf #ag dc #afcb #e #aa #g #ah b #afcc ,m>* #be #bg #ah #ai ---------------------------------------- -------------- ,by close exam9ation ( ! above tables1 x w be se5 t !re is j elev5 days diff]5ce 9 ! date ( ^! pas*al moons1 f ye> to ye>1 ?r\gh ! :ole lun> cycle1 & ?r\gh all lun> cycles4 ,9 det]m9+ ! date ( ,ea/]1 x w also be se51 t :5ev] ! full moon falls be=e ! #ba/ ( ,m>*1 !n ! foll[+ moon1 :i* happ5s ?irty days lat]1 is ! pas*al moon1 z ! #ba/ ( ,m>* is its e>lie/ possible date4 ,also :5 ! cycle is ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- a #afcd ,april #ab #af #j #a g #afce #a #h #aa #b fe #afcf ,m>* #ba #bc #bb #c d #afcg ,april #i #ab #c #d c #afch ,m>* #bi #d #ad #e b #afci ,april #ag #bd #be #f ag #afdj #f #h #f #g f #afda ,m>* #bf #ca #ag #h e #afdb ,april #bd #bj #bh #i d #afdc #c #e #i #aj cb #afdd ,m>* #bc #bg #bj #aa a #afde ,april #aa #af #a #ab g #afdf ,m>* #ca #a #ab #ac f #afdg ,april #ai #ba #bc #ad ed #afdh #h #ab #d #ae c #afdi ,m>* #bh #d #ae #af b #afej ,april #af #ag #bf #ag a #afea #e #i #g #ah gf #afeb ,m>* #be #ca #ah #ai e #afec ,april #ab #ac #j #a d #afed #a #e #aa #b c #afee ,m>* #ba #bh #bb #c ba #afef ,april #i #af #c #d g #afeg ,m>* #bi #a #ad #e f #afeh ,april #ag #ba #be #f e #afei #f #ac #f #g dc #affj ,m>* #bf #bh #ag #h b #affa ,april #ad #ag #bh #i a #affb #c #i #i #aj g #affc ,m>* #bc #be #bj #aa fe #affd ,april #aa #ac #a #ab d #affe ,m>* #ca #e #ab #ac c #afff ,april #ai #be #bc #ad b #affg #h #aj #d #ae ag #affh ,m>* #bh #a #ae #af f #affi ,april #af #ba #bf #ag e #afgj #e #f #g #ah d #afga ,m>* #be #bi #ah #ai ---------------------------------------- -------------- complet$1 !n ! pas*al moons aga9 occur 9 ! same ord]1 on ! same day ( ! mon? z !y did n9ete5 ye>s be=e4 ,n[ ?is cycle is six times repeat$ 9 a p]iod ( #aad ye>s1 :5 ! int]cal>y day be+ suppress$ 9 #agjj1 causes ! fir/ pas*al moon ( ! cycle to fall on ! #ac? ( ,april in/ead ( ! #ab?1 & all ! moons ( ! cycle to fall "o day lat] ?an !y w\ld _h ! correction n be5 made4 ,! cycle is n[ repeat$ t5 times )\t ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- cb #afgb ,april #ab #ag #j #a a #afgc #a #b #aa #b g #afgd ,m>* #ba #be #bb #c f #afge ,april #i #ad #c #d ed #afgf ,m>* #bi #e #ad #e c #afgg ,april #ag #ah #be #f b #afgh #f #aj #f #g a #afgi ,m>* #bf #b #ag #h gf #afhj ,april #bd #ba #bh #i e #afha #c #f #i #aj d #afhb ,m>* #bc #bi #bj #aa c #afhc ,april #aa #ah #a #ab ba #afhd ,m>* #ca #b #ab #ac g #afhe ,april #ai #bb #bc #ad f #afhf #h #ad #d #ae e #afhg ,m>* #bh #cj #ae #af dc #afhh ,april #af #ah #bf #ag b #afhi #e #aj #g #ah a #afij ,m>* #be #bf #ah #ai g #afia ,april #ab #ae #j #a fe #afib #a #f #aa #b d #afic ,m>* #ba #bb #bb #c c #afid ,april #i #aa #c #d b #afie ,m>* #bi #c #ad #e ag #afif ,april #ag #bb #be #f f #afig #f #g #f #g e #afih ,m>* #bf #cj #ag #h d #afii ,april #ad #ai #bh #i c #agjj #c #d #i #aj b #agja ,m>* #bc #bg #bj #aa a #agjb ,april #aa #af #a #ab g #agjc ,m>* #ca #a #ab #ac fe #agjd ,april #ai #bj #bc #ad d #agje #h #ab #d #ae c #agjf ,m>* #bh #d #ae #af b #agjg ,april #af #ag #bf #ag ag #agjh #e #h #g #ah f #agji ,m>* #be #ca #ah #ai ---------------------------------------- -------------- correction1 t is1 till ! ye> #aijj1 a p]iod ( #aij ye>s1 :5 ! int]calation be+ aga9 suppress$1 causes ! fir/ pas*al moon ( ! cycle to fall on ! #ad? ( ,april1 &1 ( c\rse1 all ! o!r moons ( ! cycle to fall "o day lat]4 ,! reason ! correction is n made ! fir/ ye> ( ! c5tury is1 ! lun> cycle mu/ fir/ be complet$1 & t did n occur until #agaj4 ,z #ajj is n a multiple ( #ai1 ! numb] ( ye>s 9 ! cycle1 &1 z ! corrections ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- e #agaj ,april #ac #bj #j #a d #agaa #b #e #aa #b cb #agab ,m>* #bb #bg #bb #c a #agac ,april #aj #af #c #d g #agad ,m>* #cj #a #ad #e f #agae ,april #ah #ba #be #f ed #agaf #g #ab #f #g c #agag ,m>* #bg #bh #ag #h b #agah ,april #ae #ag #bh #i a #agai #d #i #i #aj gf #agbj ,m>* #bd #ca #bj #aa e #agba ,april #ab #ac #a #ab d #agbb #a #e #ab #ac c #agbc ,m>* #ba #bh #bc #ad ba #agbd ,april #i #af #d #ae g #agbe ,m>* #bi #a #ae #af f #agbf ,april #ag #ba #bf #ag e #agbg #f #ac #g #ah dc #agbh ,m>* #bf #bh #ah #ai b #agbi ,april #ac #ag #j #a a #agcj #b #i #aa #b g #agca ,m>* #bb #be #bb #c fe #agcb ,april #aj #ac #c #d d #agcc ,m>* #cj #e #ad #e c #agcd ,april #ah #be #be #f b #agce #g #aj #f #g ag #agcf ,m>* #bg #a #ag #h f #agcg ,april #ae #ba #bh #i e #agch #d #f #i #aj d #agci ,m>* #bd #bi #bj #aa cb #agdj ,april #ab #ag #a #ab a #agda #a #b #ab #ac g #agdb ,m>* #ba #be #bc #ad f #agdc ,april #i #ad #d #ae ed #agdd ,m>* #bi #e #ae #af c #agde ,april #ag #ah #bf #ag b #agdf #f #aj #g #ah a #agdg ,m>* #bf #b #ah #ai ---------------------------------------- -------------- _c be made only at ! beg9n+ ( ! cycle1 s !y _c be made ! fir/ ye> ( ! c5tury only once 9 #aijj ye>s4 ,x may be se5 f "o ( ! above tables t ! correction is made 9 ! ye> #aijj1 = ! reason t t is ! fir/ c5tury :i* is a multiple ( #ai4 ,! next c5turial ye> t is exactly divisible by #ai1 is #chjj4 ,!re=e1 none ( ! corrections = ! next #aijj ye>s1 w occur on ! fir/ ye> ( ! c5tury4 ,x may also be se5 f ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- gf #agdh ,april #ac #ad #j #a e #agdi #b #f #aa #b d #agej ,m>* #bb #bi #bb #c c #agea ,april #aj #aa #c #d ba #ageb ,m>* #cj #b #ad #e g #agec ,april #ah #bb #be #f f #aged #g #ad #f #g e #agee ,m>* #bg #cj #ag #h dc #agef ,april #ae #ah #bh #i b #ageg #d #aj #i #aj a #ageh ,m>* #bd #bf #bj #aa g #agei ,april #ab #ae #a #ab fe #agfj #a #f #ab #ac d #agfa ,m>* #ba #bb #bc #ad c #agfb ,april #i #aa #d #ae b #agfc ,m>* #bi #c #ae #af ag #agfd ,april #ag #bb #bf #ag f #agfe #f #g #g #ah e #agff ,m>* #bf #cj #ah #ai d #agfg ,april #ac #ai #j #a cb #agfh #b #c #aa #b a #agfi ,m>* #bb #bf #bb #c g #aggj ,april #aj #ae #c #d f #agga ,m>* #cj #ca #ad #e ed #aggb ,april #ah #ai #be #f c #aggc #g #aa #f #g b #aggd ,m>* #bg #c #ag #h a #agge ,april #ae #af #bh #i gf #aggf #d #g #i #aj e #aggg ,m>* #bd #cj #bj #aa d #aggh ,april #ab #ai #a #ab c #aggi #a #d #ab #ac ba #aghj ,m>* #ba #bf #bc #ad g #agha ,april #i #ae #d #ae f #aghb ,m>* #bi #ca #ae #af e #aghc ,april #ag #bj #bf #ag dc #aghd #f #aa #g #ah b #aghe ,m>* #bf #bg #ah #ai ---------------------------------------- -------------- ! above tables1 t1 ?\gh ! int]cal>y day 0 suppress$ 9 ! ye> #ahjj1 no *ange is made 9 ! date ( ! pas*al moon4 ,! reason is1 ! lun> equation also occurr$2 :ile ! =m] correction w\ld cause ! pas*al moon to fall "o day lat]1 t is on ! #ad? day ( ,april1 ! latt] w\ld make x fall "o day e>li]1 t is on ! #ab?2 s !y comp5sate ea* o!r1 & !re is no correction to be made until ! ye> #aijj1 :5 ! sol> equation ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- a #aghf ,april #ac #af #j #a g #aghg #b #h #aa #b fe #aghh ,m>* #bb #bc #bb #c d #aghi ,april #aj #ab #c #d c #agij ,m>* #cj #d #ad #e b #agia ,april #ah #bd #be #f ag #agib #g #h #f #g f #agic ,m>* #bg #ca #ag #h e #agid ,april #ae #bj #bh #i d #agie #d #e #i #aj cb #agif ,m>* #bd #bg #bj #aa a #agig ,april #ab #af #a #ab g #agih #a #h #ab #ac f #agii ,m>* #ba #bd #bc #ad e #ahjj ,april #i #ac #d #ae d #ahja ,m>* #bi #e #ae #af c #ahjb ,april #ag #ah #bf #ag b #ahjc #f #aj #g #ah ag #ahjd ,m>* #bf #a #ah #ai f #ahje ,april #ac #ad #j #a e #ahjf #b #f #aa #b d #ahjg ,m>* #bb #bi #bb #c cb #ahjh ,april #aj #ag #c #d a #ahji ,m>* #cj #b #ad #e g #ahaj ,april #ah #bb #be #f f #ahaa #g #ad #f #g ed #ahab ,m>* #bg #bi #ag #h c #ahac ,april #ae #ah #bh #i b #ahad #d #aj #i #aj a #ahae ,m>* #bd #bf #bj #aa gf #ahaf ,april #ab #ad #a #ab e #ahag #a #f #ab #ac d #ahah ,m>* #ba #bb #bc #ad c #ahai ,april #i #aa #d #ae ba #ahbj ,m>* #bi #b #ae #af g #ahba ,april #ag #bb #bf #ag f #ahbb #f #g #g #ah e #ahbc ,m>* #bf #cj #ah #ai ---------------------------------------- -------------- aga9 occurs1 & ! fir/ pas*al moon ( ! cycle falls on ! #ad?2 :i* cycle is repeat$ sixte5 times 9 a p]iod ( #cjd ye>s1 aft] :i*1 9 #bbjd1 ! date ( ! fir/ pas*al moon is ! #ae? ( ,april4 ,! reason !re is no correction to make 9 ?is long p]iod is1 fir/1 ! ye> #bjjj is a common ye> 9 ! ,gregorian cal5d>2 second1 9 ! ye> #bajj bo? ! sol> & ! lun> equations aga9 occur1 & occurr+ toge!r1 !y comp5sate ea* o!r2 consequ5tly ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- dc #ahbd ,april #ac #ag #j #a b #ahbe #b #b #aa #b a #ahbf ,m>* #bb #be #bb #c g #ahbg ,april #aj #ad #c #d fe #ahbh ,m>* #cj #e #ad #e d #ahbi ,april #ah #ah #be #f c #ahcj #g #aj #f #g b #ahca ,m>* #bg #b #ag #h ag #ahcb ,april #ae #ba #bh #i f #ahcc #d #f #i #aj e #ahcd ,m>* #bd #bi #bj #aa d #ahce ,april #ab #ah #a #ab cb #ahcf #a #b #ab #ac a #ahcg ,m>* #ba #bb #bc #ad g #ahch #i #ad #d #ae f #ahci ,m>* #bi #cj #ae #af ed #ahdj ,april #ag #ah #bf #ag c #ahda #f #aj #g #ah b #ahdb ,m>* #bf #bf #ah #ai a #ahdc ,april #ac #ae #j #a gf #ahdd #b #f #aa #b e #ahde ,m>* #bb #bb #bb #c d #ahdf ,april #aj #aa #c #d c #ahdg ,m>* #cj #c #ad #e ba #ahdh ,april #ah #bb #be #f g #ahdi #g #g #f #g f #ahej ,m>* #bg #cj #ag #h e #ahea ,april #ae #ai #bh #i dc #aheb #d #d #i #aj b #ahec ,m>* #bd #bg #bj #aa a #ahed ,april #ab #af #a #ab g #ahee #a #a #ab #ac fe #ahef ,m>* #ba #bj #bc #ad d #aheg #i #ab #d #ae c #aheh ,m>* #bi #d #ae #af b #ahei ,april #ag #ag #bf #ag ag #ahfj #f #h #g #ah f #ahfa ,m>* #bf #ca #ah #ai ---------------------------------------- -------------- ! cycle is cont9u$ until #bbjd1 aft] :i*1 z has already be5 /at$1 ! date ( ! fir/ pas*al moon is ! #ae? ( ,april4 ,?is cycle is repeat$ six times 9 a p]iod ( #aad ye>s1 :5 9 #bcah1 = reasons already giv51 ! date ( ! fir/ pas*al moon ( ! next cycle falls on ! #af?1 & is repeat$ five times 9 a p]iod ( #ie ye>s1 :51 9 #bdac1 ! lun> equation occurs alone1 & ! date ( ! fir/ pas*al moon = ! next #ie ye>s1 t is till ! ye> #bejh1 ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- e #ahfb ,april #ac #bj #j #a d #ahfc #b #e #aa #b cb #ahfd ,m>* #bb #bg #bb #c a #ahfe ,april #aj #af #c #d g #ahff ,m>* #cj #a #ad #e f #ahfg ,april #ah #ba #be #f ed #ahfh #g #ab #f #g c #ahfi ,m>* #bg #bh #ag #h b #ahgj ,april #ae #ag #bh #i a #ahga #d #i #i #aj gf #ahgb ,m>* #bd #ca #bj #aa e #ahgc ,april #ab #ac #a #ab d #ahgd #a #e #ab #ac c #ahge ,m>* #ba #bh #bc #ad ba #ahgf ,april #i #af #d #ae g #ahgg ,m>* #bi #a #ae #af f #ahgh ,april #ag #ba #bf #ag e #ahgi #f #ac #g #ah dc #ahhj ,m>* #bf #bh #ah #ai b #ahha ,april #ac #ag #j #a a #ahhb #b #i #aa #b g #ahhc ,m>* #bb #be #bb #c fe #ahhd ,april #aj #ac #c #d d #ahhe ,m>* #cj #e #ad #e c #ahhf ,april #ah #be #be #f b #ahhg #g #aj #f #g ag #ahhh ,m>* #bg #a #ag #h f #ahhi ,april #ae #ba #bh #i e #ahij #d #f #i #aj d #ahia ,m>* #bd #bi #bj #aa cb #ahib ,april #ab #ag #a #ab a #ahic #a #b #ab #ac g #ahid ,m>* #ba #be #bc #ad f #ahie ,april #i #ad #d #ae ed #ahif ,m>* #bi #e #ae #af c #ahig ,april #ag #ah #bf #ag b #ahih #f #aj #g #ah a #ahii ,m>* #bf #b #ah #ai ---------------------------------------- -------------- falls back to ! #ae? ( ,april4 ,aft] :i* ! #af?1 on acc\nt ( ! sol> equation1 is aga9 ! date ( ! fir/ pas*al moon ( ! cycle = ano!r p]iod ( #ie ye>s2 t is till ! ye> #bfjc1 :5 ! sol> equation causes ! fir/ pas*al moon to fall on ! #ag?1 :i* cycle is repeat$ sixte5 times dur+ ano!r p]iod ( #cjd ye>s1 aft] :i*1 9 #bijg1 ! correction makes ! date ( ! fir/ pas*al moon ( ! ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- g #aijj ,april #ad #ae #j #a f #aija #c #g #aa #b e #aijb ,m>* #bc #cj #bb #c d #aijc ,april #aa #ab #c #d cb #aijd ,m>* #ca #c #ad #e a #aije ,april #ai #bc #be #f g #aijf #h #ae #f #g f #aijg ,m>* #bh #ca #ag #h ed #aijh ,april #af #ai #bh #i c #aiji #e #aa #i #aj b #aiaj ,m>* #be #bg #bj #aa a #aiaa ,april #ac #af #a #ab gf #aiab #b #g #ab #ac e #aiac ,m>* #bb #bc #bc #ad d #aiad ,april #aj #ab #d #ae c #aiae ,m>* #cj #d #ae #af ba #aiaf ,april #ah #bc #bf #ag g #aiag #g #h #g #ah f #aiah ,m>* #bg #ca #ah #ai e #aiai ,april #ad #bj #j #a dc #aibj #c #d #aa #b b #aiba ,m>* #bc #bg #bb #c a #aibb ,april #aa #af #c #d g #aibc ,m>* #ca #a #ad #e fe #aibd ,april #ai #bj #be #f d #aibe #h #ab #f #g c #aibf ,m>* #bh #d #ag #h b #aibg ,april #af #ag #bh #i ag #aibh #e #h #i #aj f #aibi ,m>* #be #ca #bj #aa e #aicj ,april #ac #bj #a #ab d #aica #b #e #ab #ac cb #aicb ,m>* #bb #bg #bc #ad a #aicc ,april #aj #af #d #ae g #aicd ,m>* #cj #a #ae #af f #aice ,april #ah #ba #bf #ag ed #aicf #g #ab #g #ah c #aicg ,m>* #bg #bh #ah #ai ---------------------------------------- -------------- cycle1 ! #ah? ( ,april1 :i* cycle is cont9u$ )\t correction till ! ye> #caaf1 a p]iod ( #bji ye>s4 ,by ref]5ce to ! above tables1 x w be se5 t ! sol> & lun> equations occur toge!r 9 ! ye> #bgjj & comp5sate ea* o!r2 also1 t ! ye> #bhjj is a common ye> 9 ! ,gregorian cal5d>2 consequ5tly !re is no correction to make f #bfjc to #bijg2 also ! two equations occur toge!r ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- b #aich ,april #ad #ag #j #a a #aici #c #i #aa #b gf #aidj ,m>* #bc #bd #bb #c e #aida ,april #aa #ac #c #d d #aidb ,m>* #ca #e #ad #e c #aidc ,april #ai #be #be #f ba #aidd #h #i #f #g g #aide ,m>* #bh #a #ag #h f #aidf ,april #af #ba #bh #i e #aidg #e #f #i #aj dc #aidh ,m>* #be #bh #bj #aa b #aidi ,april #ac #ag #a #ab a #aiej #b #i #ab #ac g #aiea ,m>* #bb #be #bc #ad fe #aieb ,april #aj #ac #d #ae d #aiec ,m>* #cj #e #ae #af c #aied ,april #ah #be #bf #ag b #aiee #g #aj #g #ah ag #aief ,m>* #bg #a #ah #ai f #aieg ,april #ad #ba #j #a e #aieh #c #f #aa #b d #aiei ,m>* #bc #bi #bb #c cb #aifj ,april #aa #ag #c #d a #aifa ,m>* #ca #b #ad #e g #aifb ,april #ai #bb #be #f f #aifc #h #ad #f #g ed #aifd ,m>* #bh #bi #ag #h c #aife ,april #af #ah #bh #i b #aiff #e #aj #i #aj a #aifg ,m>* #be #bf #bj #aa gf #aifh ,april #ac #ad #a #ab e #aifi #b #f #ab #ac d #aigj ,m>* #bb #bi #bc #ad c #aiga ,april #aj #aa #d #ae ba #aigb ,m>* #cj #b #ae #af g #aigc ,april #ah #bb #bf #ag f #aigd #g #ad #g #ah e #aige ,m>* #bg #cj #ah #ai ---------------------------------------- -------------- aga9 9 ! ye> #cjjj & comp5sate ea* o!r1 is ! reason !re is no correction to make f #bijg to #caaf1 aft] :i* ! fir/ pas*al moon falls on ! #ai?1 & is repeat$ fifte5 times 9 a p]iod ( #bhe ye>s1 t is till ! ye> #cdja1 :5 ! correction makes ! #bj? ( ,april1 ! date ( ! full moon1 b t _c be ! pas*al moon1 :i* _c happ5 lat] ?an ! #ai?2 consequ5tly ! ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- dc #aigf ,april #ad #ah #j #a b #aigg #c #aj #aa #b a #aigh ,m>* #bc #bf #bb #c g #aigi ,april #aa #ae #c #d fe #aihj ,m>* #ca #f #ad #e d #aiha ,april #ai #bf #be #f c #aihb #h #aa #f #g b #aihc ,m>* #bh #c #ag #h ag #aihd ,april #af #bb #bh #i f #aihe #e #g #i #aj e #aihf ,m>* #be #cj #bj #aa d #aihg ,april #ac #ai #a #ab cb #aihh #b #c #ab #ac a #aihi ,m>* #bb #bf #bc #ad g #aiij ,april #aj #ae #d #ae f #aiia ,m>* #cj #ca #ae #af ed #aiib ,april #ah #ai #bf #ag c #aiic #g #aa #g #ah b #aiid ,m>* #bg #c #ah #ai a #aiie ,april #ad #af #j #a gf #aiif #c #g #aa #b e #aiig ,m>* #bc #cj #bb #c d #aiih ,april #aa #ab #c #d c #aiii ,m>* #ca #d #ad #e ba #bjjj ,april #ai #bc #be #f g #bjja #h #ae #f #g f #bjjb ,m>* #bh #ca #ag #h e #bjjc ,april #af #bj #bh #i dc #bjjd #e #aa #i #aj b #bjje ,m>* #be #bg #bj #aa a #bjjf ,april #ac #af #a #ab g #bjjg #b #h #ab #ac fe #bjjh ,m>* #bb #bc #bc #ad d #bjji ,april #aj #ab #d #ae c #bjaj ,m>* #cj #d #ae #af b #bjaa ,april #ah #bd #bf #ag ag #bjab #g #h #g #ah f #bjac ,m>* #bg #ca #ah #ai ---------------------------------------- -------------- moon t prec$es x by ?irty days1 & :i* falls on ! #ba/ ( ,m>*1 is ! date ( ! fir/ pas*al moon ( ! cycle :i* comm5ces ) ! ye> #cdja4 ,! day ( ! mon? on :i* ,ea/] ,sunday has fall5 or w fall1 f ! ye> #aeif to #bjac1 is already det]m9$1 & may be se5 by ref]5ce to ! above tables4 ,f #bjac to #cdja1 ! date ( ,ea/] is det]m9$ = "o lun> cycle only1 at ! ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- ag #bbjd ,april #ae #bb #j #a f #bbje #d #g #aa #b e #bbjf ,m>* #bd #cj #bb #c d #bbjg ,april #ab #ai #c #d cb #bbjh #a #c #ad #e a #bbji ,m>* #ba #bf #be #f g #bbaj ,april #i #ae #f #g f #bbaa ,m>* #bi #ca #ag #h ed #bbab ,april #ag #ai #bh #i c #bbac #f #aa #i #aj b #bbad ,m>* #bf #bg #bj #aa a #bbae ,april #ad #af #a #ab gf #bbaf #c #g #ab #ac e #bbag ,m>* #bc #cj #bc #ad d #bbah ,april #aa #ab #d #ae c #bbai ,m>* #ca #d #ae #af ba #bbbj ,april #ai #bc #bf #ag g #bbba #h #ae #g #ah f #bbbb ,m>* #bh #ca #ah #ai f #bcah ,april #af #ba #j #a e #bcai #e #f #aa #b dc #bcbj ,m>* #be #bh #bb #c b #bcba ,april #ac #ag #c #d a #bcbb #b #i #ad #e g #bcbc ,m>* #bb #be #be #f fe #bcbd ,april #aj #ac #f #g d #bcbe ,m>* #cj #e #ag #h c #bcbf ,april #ah #be #bh #i b #bcbg #g #aj #i #aj ag #bcbh ,m>* #bg #a #bj #aa f #bcbi ,april #ae #ba #a #ab e #bccj #d #f #ab #ac d #bcca ,m>* #bd #bi #bc #ad cb #bccb ,april #ab #ag #d #ae a #bccc #a #b #ae #af g #bccd ,m>* #ba #be #bf #ag f #bcce ,april #i #ad #g #ah ed #bccf ,m>* #bi #e #ah #ai ---------------------------------------- -------------- beg9n+ ( ea* p]iod2 = ! reason t x 0 deem$ unnecess>y1 because ! pas*al moons1 ! epacts1 & ! ,gold5 ,numb]s are ! same = e cycle 9 ! p]iod4 ,!re=e1 all t rema9s to be done is to f9d ! day ( ! mon? on :i* ! fir/ ,sunday1 aft] ! pas*al moon1 falls4 ,! dom9ical lett]s = any p]iod may v easily be f\nd by c\nt+ backw>ds "o lett] ea* ye> = e common ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- f #bdac ,april #ae #ba #j #a e #bdad #d #f #aa #b d #bdae ,m>* #bd #bi #bb #c cb #bdaf ,april #ab #ag #c #d a #bdag #a #b #ad #e g #bdah ,m>* #ba #be #be #f f #bdai ,april #i #ad #f #g ed #bdbj ,m>* #bi #e #ag #h c #bdba ,april #ag #ah #bh #i b #bdbb #f #aj #i #aj a #bdbc ,m>* #bf #b #bj #aa gf #bdbd ,april #ad #ba #a #ab e #bdbe #c #f #ab #ac d #bdbf ,m>* #bc #bi #bc #ad c #bdbg ,april #aa #ah #d #ae ba #bdbh ,m>* #ca #b #ae #af g #bdbi ,april #ai #bb #bf #ag f #bdcj #h #ad #g #ah e #bdca ,m>* #bh #cj #ah #ai ag #bejh ,april #af #bb #j #a f #beji #e #g #aa #b e #beaj ,m>* #be #cj #bb #c d #beaa ,april #ac #ai #c #d cb #beab #b #c #ad #e a #beac ,m>* #bb #bf #be #f g #bead ,april #aj #ae #f #g f #beae ,m>* #cj #ca #ag #h ed #beaf ,april #ah #ai #bh #i c #bfag #g #aa #i #aj b #beah ,m>* #bg #c #bj #aa a #beai ,april #ae #af #a #ab gf #bebj #d #g #ab #ac e #beba ,m>* #bd #cj #bc #ad d #bebb ,april #ab #ai #d #ae c #bebc #a #d #ae #af ba #bebd ,m>* #ba #bf #bf #ag g #bebe ,april #i #ae #g #ah f #bebf ,m>* #bi #ca #ah #ai ---------------------------------------- -------------- ye>1 & two = leap-ye>1 ! f\r? lett] be+ dom9ical lett] = ,janu>y & ,febru>y & ! fif? = ! re/ ( ! ye>2 ?us1 if ,g be dom9ical lett] = any giv5 ye>1 we w\ld h !n1 ,g1 ,f1 ,e1 ,,dc2 ,b1 ,a1 ,g1 ,,fe2 ,d1 ,c1 ,b1 ,,ag2 ,f1 ,e1 ,d1 ,,cb1 etc4 ,by c\nt+ ^! lett]s backw>ds1 or 9 ! tables1 f ! bottom ( ! column upw>ds1 !y w occur 9 alphabetical ord]4 ,aga9 x may be se5 by ref]5ce ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- b #bfjc ,april #ag #bd #j #a ag #bfjd #f #h #aa #b f #bfje ,m>* #bf #ca #bb #c e #bfjf ,april #ad #bj #c #d d #bfjg #c #e #ad #e cb #bfjh ,m>* #bc #bg #be #f a #bfji ,april #aa #af #f #g g #bfaj ,m>* #ca #a #ag #h f #bfaa ,april #ai #ba #bh #i ed #bfab #h #ab #i #aj c #bfac ,m>* #bh #d #bj #aa b #bfad ,april #af #ag #a #ab a #bfae #e #i #ab #ac gf #bfaf ,m>* #be #ca #bc #ad e #bfag ,april #ac #bj #d #ae d #bfah #b #e #ae #af c #bfai ,m>* #bb #bh #bf #ag ba #bfbj ,april #aj #af #g #ah g #bfba ,m>* #cj #a #ah #ai b #bijg ,april #ah #bd #j #a ag #bijh #g #h #aa #b f #biji ,m>* #bg #ca #bb #c e #biaj ,april #ae #bj #c #d d #biaa #d #e #ad #e cb #biab ,m>* #bd #bg #be #f a #biac ,april #ab #af #f #g g #biad #a #h #ag #h f #biae ,m>* #ba #bd #bh #i ed #biaf ,april #i #ab #i #aj c #biag ,m>* #bi #d #bj #aa b #biah ,april #ag #bd #a #ab a #biai #f #i #ab #ac gf #bibj ,m>* #bf #ca #bc #ad e #biba ,april #ad #bj #d #ae d #bibb #c #e #ae #af c #bibc ,m>* #bc #bh #bf #ag ba #bibd ,april #aa #af #g #ah g #bibe ,m>* #ca #a #ah #ai ---------------------------------------- -------------- to ^! tables1 t ,ea/] occurs less frequ5tly on ! #bb;d ( ,m>*1 its e>lie/ possible date1 & ! #be? ( ,april1 :i* has hi!rto be5 consid]$ its late/ possible date1 ?an any ( ! days int]v5+4 ,x _c happ5 on ! #bb;d1 only :5 ! pas*al moon falls on ! #ba/1 & t day mu/ be ,saturday4 ,x fell on ! #bb;d1 fir/1 aft] ! re=mation ( ! cal5d> by ,gregory 9 #aeih2 aga9 9 #afic1 #agfa1 ---------------------------------------- -------------- ,dom9ical,ye>4 ,pas*al,ea/]4,epact4,gold5 ,lett]4 ,full ,numb]4 ,moon4 ---------------------------------------- -------------- ba #caaf ,april #ai #bc #j #a g #caag #h #ae #aa #b f #caah ,m>* #bh #ca #bb #c e #caai ,april #af #bj #c #d dc #cabj #e #aa #ad #e b #caba ,m>* #be #bg #be #f a #cabb ,april #ac #af #f #g g #cabc #b #h #ag #h fe #cabd ,m>* #bb #bc #bh #i d #cabe ,april #aj #ab #i #aj c #cabf ,m>* #cj #d #bj #aa b #cabg ,april #ah #bd #a #ab ag #cabh #g #h #ab #ac f #cabi ,m>* #bg #ca #bc #ad e #cacj ,april #ae #bj #d #ae d #caca #d #e #ae #af cb #cacb ,m>* #bd #bg #bf #ag a #cacc ,april #ab #af #g #ah g #cacd #a #h #ah #ai d #cdja ,m>* #ba #bb #j #a c #cdjb ,april #i #aa #aa #b b #cdjc ,m>* #bi #c #bb #c ag #cdjd ,april #ag #bb #c #d f #cdje #f #g #ad #e e #cdjf ,m>* #bf #cj #be #f d #cdjg ,april #ad #ai #f #g cb #cdjh #c #aj #ag #h a #cdji ,m>* #bc #bf #bh #i g #cdaj ,april #aa #ae #i #aj f #cdaa ,m>* #ca #g #bj #aa ed #cdab ,april #ai #bf #a #ab c #cdac #h #aa #ab #ac b #cdad ,m>* #bh #c #bc #ad a #cdae ,april #af #bc #d #ae gf #cdaf #e #g #ae #af e #cdag ,m>* #be #cj #bf #ag d #cdah ,april #ac #ai #g #ah c #cdai #b #d #ah #ai ---------------------------------------- -------------- & 9 #ahah4 ,x has n occurr$ s9ce1 nor w n aga9 till #bbhe1 a p]iod ( #dfg ye>s4 ,! reason t x does n occur on ! #bb;d ( ,m>* 9 ?is long p]iod is1 ! pas*al moon does n fall on ! #ba/1 f ! ye> #aijj to #bbjd1 a p]iod ( #cjd ye>s4 ,we ref] to ! tabul> moon1 n to ! true or a/ronomical moon1 :i* may occur on ! #ba/ m ?an once 9 ?is long p]iod4 ,,*apt] ,,vii4 ,,*ur* ,,fea/s ,,& ,,fa/s ,,^: ,,date ,,dep5d ,,on ,,! ,,date ,,( ,,ea/]4 ,fea/s1 or ,fe/ivals1 are days set ap>t by ! *ur*1 ei!r = ! grateful memorial ( ! mo/ rem>kable ev5ts connect$ ) ! plan ( r$emption1 or ^u :i* to commemorate ! actions & suff]+s ( su* p]sons z h be5 mo/ in/rum5tal 9 c>ry+ =w>d ! designs ( ,god = ! salvation ( mank9d4 ,! ecclesia/ical ye> is divid$ into eight seasons1 namely3 ,adv5t-tide1 ,*ri/mas-tide1 ,epiphany-tide1 ,l5t5-tide1 ,ea/]-tide1 ,asc5sion-tide1 ,:itsun-tide1 & ,tr9ity-tide4 ,! fir/ day ( ea* ( ^! seasons has be51 & is n[ obs]v$ by ! *ur* 9 commemoration ( "s ( ! mo/ rem>kable ev5ts connect$ ) ! plan ( r$emption4 ,all ^! w be notic$ 9 ! ord] 9 :i* !y occur 9 ! ecclesia/ical ye>1 :ile _m o!r days int]v5+1 :i* are obs]v$ z fea/s or fa/s1 w be giv5 a pass+ notice4 a--,adv5t ,sunday1 :i* is ! day ne>e/ ,/4 ,&rew's ,day 7,nov4 #cj71 or ! fir/ ,sunday aft] ! #bf? ( ,novemb]1 has be5 recogniz$ s9ce ! six? c5tury z ! fir/ day ( ! ecclesia/ical ye>4 ,adv5t 7,lat9 ,adv5tus1 ! com+17 signifies ! com+ ( our ,savi\r1 ! p]iod ( ! approa* ( ! nativity4 ,z ,adv5t-tide la/s f ,adv5t ,sunday to ,*ri/mas1 ! l5g? ( ! season dep5ds ^u ! day ( ! mon? on :i* ,adv5t ,sunday falls4 ,z x may happ5 z e>ly z ! #bg? ( ,novemb] or z late z ! #c;d ( ,decemb]1 s ,adv5t-tide w conta9 no m ?an tw5ty-eight days nor less ?an tw5ty-two4 ,x %\ld be borne 9 m9d t1 ?\gh ?is fe/ival is class$ among ! movable fea/s1 x does n dep5d ^u ! date ( ,ea/]1 b ^u ! day ( ! mon? on :i* ,adv5t ,sunday falls4 ,! f\r ,sundays be=e ,*ri/mas 7 made prep>ation days = ! fe/ival ( ,*ri/mas1 & 7 call$ ! fir/1 second1 ?ird1 & f\r? ,sundays 9 ,adv5t4 ,emb] days & ,emb] weeks are ! f\r seasons set ap>t by ! ,we/]n *ur* = special pray] & fa/+1 & ! ord9ation ( cl]gy2 kn[n 9 ! *ur* z quatuor tempora1 7! f\r seasons47 ,! ,emb] weeks are ! weeks next foll[+ ,/4 ,lucy's ,day 7,dec4 #ac?71 ! fir/ ,sunday 9 ,l5t1 ,:itsun ,day1 & ,holy ,cross ,day 7,sept4 #ad?74 ,! ,w$nesdays1 ,fridays & ,saturdays ( ^! weeks are ! ,emb] days di/9ctively4 ,! "n by "s is suppos$ to be d]iv$ f a ,g]man ^w signify+ ,ab/95ce2 by o!rs x is suppos$ to signify ,a%es4 b--,*ri/mas 7f ,*ri/ & ! ,saxon maess1 signify+ ! mass & a fea/71 is a fe/ival held 9 commemoration ( ! nativity ( our ,savi\r ?r\gh\t ne>ly ! :ole ( ,*ri/5dom4 ,x is occupi$1 !re=e1 ) ! ev5t 7! inc>nation7 :i* =ms ! c5t] & turn+ po9t ( ! hi/ory ( ! _w4 ,?\gh ! day ( ,*ri/'s bir? _c be asc]ta9$ f ! ,new ,te/am5t1 nor f any o!r s\rce1 yet ! :ole ,*ri/ian _w = m ?an #acjj ye>s h concurr$ 9 celebrat+ ! nativity on ! #be? ( ,decemb]4 ,?is is ! fir/ ( ! f\r great fea/s 9 ! ecclesia/ical ye>2 ! o!r ?ree are ,ea/]1 ,asc5sion1 & ,:itsun ,day4 ,! l5g? ( ,*ri/mas-tide or season is twelve days1 la/+ f ! #be? ( ,decemb] to ,epiphany4 c--,epiphany 7,greek ,epiphania1 ,!ophania or ,*ri/ophania17 is a fe/ival 9 commemoration ( ! manife/ation ( ,jesus ,*ri/ to ! _w z ! ,son ( ,god1 & ref]r+ to ! appe>ance ( ! /> :i* ann\nc$ our ,savi\r's bir? to ! ,g5tiles1 & ! visit ( ! ,magi1 or wise ,m5 ( ! ,ea/ to ! infant ,jesus4 ,?is fe/ival is held on ! #f? ( ,janu>y inv>iably1 consequ5tly is n a movable fea/1 ?\gh ! l5g? ( ,epiphany-tide dep5ds ^u ! date ( ,ea/]4 ,z ,ea/] may happ5 z e>ly z ! #bb;d ( ,m>* or z late z ! #bf? ( ,april 7a v>iation ( ?irty-five days71 s ,epiphany-tide may consi/ ( no less ?an twelve days nor m ?an =ty-sev51 z ! season always ends ! day be=e ,septuagesima ,sunday4 7,see tables at ! close ( ?is *apt]47 ,septuagesima1 ,sexagesima1 ,qu9quagesima4 ,!re be+ exactly fifty days betwe5 ! ,sunday next be=e ,l5t & ,ea/] ,day1 inclusive1 t ,sunday 0 t]m$ ,qu9quagesima1 i4 e41 ! fiftie?2 & ! two imm$iately prec$+ ,sundays 7 call$ f ! next r\nd numb]s ,sexagesima1 ! sixtie?2 & ,septuagesima1 ! sev5tie?4 ,! ,pas*al ,season ext5ds f ,septuagesima ,sunday to ,l[ ,sunday1 a p]iod ( sev5ty days4 ,x takes its "n f ! ,pas*al fe/ival or ,ea/]1 ^: s]vices end ) ,l[ ,sunday1 ! octave1 or eigh? day1 ( ,ea/]4 ,x beg9s ) ,septuagesima ,sunday because ! *ur* s]vices !n beg9 to prep>e ! m9ds ( ! fai?ful = ! s]vices ( ,l5t1 :i* are !mselves ! prep>ation = ,ea/]4 ,may n ,septuagesima ,sunday be s call$ because !re are j sev5ty days 9 ! ,pas*al ,season8 ,%rove-tide lit]ally means confession-"t1 & is ! "n giv5 to ! days imm$iately prec$+ ,a% ,w$nesday4 ,^! days 7 s call$ because on !m1 & especially on ! la/ ( !m 7,%rove ,tuesday7 p 7 accu/om$ to confess _! s9s z a prep>ation = ,l5t4 ,9 mo/ ,roman ,ca?olic c\ntries x beg9s ) ,qu9quagesima ,sunday1 ! ,sunday be=e ,l5t4 ,a% ,w$nesday1 ! fir/ day ( ,l5t1 7,lat9 dies c9]um1 ! day ( ,a%es71 0 s call$ because x 0 cu/om>y on t day = p5it5ts to appe> 9 sackclo?1 ^u :i* occasion a%es 7 spr9kl$ ^u !m4 d--,l5t1 7,anglo-,saxon l5gt54 ,p]haps f l5egan1 to l5g!n1 because at ?is season ! days l5g!n7 ! =ty days fa/1 is ! prep>ation = ,ea/]1 & is obs]v$ 9 commemoration ( our ,"l's fa/ 9 ! wild]ness4 ,9 mo/ languages ! "n giv5 to ?is fa/ signifies ! numb] ( days--=ty2 b our ^w ,l5t signifies ! ,spr+ ,fa/1 = ,l5t5-tide 9 ! ,anglo-,saxon language 0 ! ,season ( ,spr+1 9 ,g]man1 ,l5z4 ,! six ,sundays 9 ! ,l5t5-tide ( =ty-six days are n c\nt$ 9 ! fa/1 z all ,sundays 9 ! ye> are reckon$ z fea/ days1 because our ,savi\r arose f ! dead on ! fir/ day ( ! week4 ,quadragesima ,sunday1 ! fir/ ,sunday 9 ,l5t1 is s call$ by analogy ) ! ?ree ,sundays :i* prec$e ,l5t1 & :i* 7z has already be5 /at$7 are call$ respectively ,septuagesima1 sev5tie?2 ,sexagesima1 sixtie?2 ,qu9quagesima1 fiftie?2 & !n ,quadragesima1 =tie?2 9 r\nd numb]s =ty days be=e ,ea/]4 ,holy ,week1 ! la/ week 9 ,l5t1 call$ also ,passion ,week1 because )9 x is commemorat$ our ,"l's suff]+s4 ,! days specially solemniz$ are ,palm ,sunday1 ,spy ,w$nesday1 ,holy1 or ,maundy ,?ursday1 & ,good ,friday4 ,palm ,sunday 7,lat9 ,dom9ica ,palm>ium1 or ,dom9ica 9 ,palmis7 is ! "n usually giv5 ! ,sunday be=e ,ea/]2 a day celebrat$ 9 commemoration ( ,*ri/'s triumphal entry into ,j]usalem1 s call$ because ! p :o _h come to ! fea/1 :5 !y he>d t ,jesus 0 com+1 took bran*es ( palm trees & w5t =? to meet him1 & cri$1 ,hosanna2 bless$ is ! ,k+ ( ,israel t come? 9 ! "n ( ! ,"l4 ,spy ,w$nesday1 s call$ 9 allusion to ! betrayal ( ,*ri/ by ,judas1 or ! day on :i* he made ! b>ga9 to deliv] him into ! h&s ( 8 enemies = ?irty pieces ( silv]4 ,maundy ,?ursday 7f ,dies m&ati1 m&ate ,?ursday71 s call$ ei!r f ! comm& giv5 8 disciples to love "o ano!r1 or to commemorate ! sacram5t ( ,8 supp]4 ,good ,friday1 s call$ 9 ackn[l$gm5t ( ! b5efit d]iv$ f ! dea? ( ,*ri/4 ,! clos+ sc5es 9 ! life ( ,*ri/1 ! ev5ts ( ,w$nesday1 ,?ursday & ,friday ( ,holy ,week1 are ev5ts ( mu* m importance ?an 7 ev] be=e cr[d$ into any "o week 9 ! hi/ory ( ! _w4 ,! betrayal on ,w$nesday1 ! in/itution ( ! sacram5t on ,?ursday night1 also ! words ( our ,savi\r z record$ 9 ,john's gospel1 f ! #ad? to ! #ag? *apt]s inclusive1 ! agony & ! bloody sweat 9 ! g>d51 ! arre/ & trial dur+ ,?ursday night & ,friday morn+1 ! crucifixion at ! ?ird h\r1 ! d>kness t 0 ov] all ! l& f ! six? to ! n9? h\r1 & ! la/ words ( ! bless$ ,jesus1 ,x is f9i%$1 7ta/$ dea? = e man72 ^! we say1 are ev5ts ( m importance to man ?an 7 ev] be=e cr[d$ into any "o week 9 ! _w's hi/ory4 ,! prophets :o prophesi$ ( ^! ?+s1 inquir$ & se>*$ dilig5tly1 se>*+ :at1 or :at mann] ( "t ! ,_s ( ,*ri/ :i* 0 9 !m did signify1 :5 x te/ifi$ be=eh& ! suff]+s ( ,*ri/ & ! glory t %\ld foll[4 ,& ab\t an h\r be=e ?is prophecy began to be fulfill$ our ,savi\r utt]$ ^! words3 ,v]ily1 v]ily1 ,i say unto y1 t ye %all weep & lam5t1 b ! _w %all rejoice2 & ye %all be sorr[ful1 b y\r sorr[ %all be turn$ into joy4 ,x 0 probably n m ?an an h\r f ! "t ^! words fell f ! ,savi\r's lips1 t he 0 arre/$ & l$ away to und]go a trial2 cruel mock+ & sc\rg+1 crucifixion & dea? ^u ! cross4 ,!n come? ,joseph ( ,arima!a1 br++ f9e l951 & ,nicodemus ) 8 hundr$ p\nds ( myrrh & aloes1 & !y two took ! body ( ! ,"l ,jesus & wrapp$ x 9 ! l95 ) ! spices1 & laid x 9 ,joseph's own new tomb1 :i* he _h hewn out 9 a rock1 :]e9 nev] man be=e 0 laid1 & roll$ a great /one aga9/ ! door ( ! sepul*] & dep>t$4 ,?us ende? ,passion ,week4 ,:ile ! body ( ,jesus is 9 ! sepul*] ! _w is rejoic+1 & ! disciples are weep+ & lam5t+1 accord+ to ! words ( ! ,savi\r1 ,ye %all weep & lam5t1 b ! _w %all rejoice4 ,he dies6 ! fri5d ( s9n]s dies6 ,lo6 ,salem's daught]s weep ar\nd2 ,a solemn d>kness veils ! skies1 ,a sudd5 trembl+ %akes ! gr\nd4 e--,ea/] 7,g]man1 ,o/]n1 ,old ,saxon ,o/]1 f o/51 signify+ ris+17 is a *ur* fe/ival 9 commemoration ( ! resurrection ( our ,"l f ! dead4 ,b ! app>5t victory :i* ! enemies ( ,*ri/ _h ga9$ 0 ( %ort duration1 ! rejoic+ ( ! _w did n long cont9ue1 ! rema9+ words ( our ,savi\r mu/ ne$s be fulfill$3 ,b y\r sorr[ %all be turn$ into joy4 ,n[1 ^u ! fir/ day ( ! week1 v e>ly 9 ! morn+1 7,ea/] morn+7 ! two ,m>ys came to ! sepul*] br++ ! sweet spices & o9tm5ts :i* !y _h prep>$ = ! purpose ( ano9t+ ! body ( ! ,"l ,jesus1 b 7 greatly a/oni%$ :5 !y saw t ! great /one1 :i* !y _h se5 roll$ aga9/ ! door ( ! sepul*] on ,friday aft]noon1 0 roll$ away1 & an angel sitt+ ^u x ^: c\nt5ance 0 l lightn+1 & = fe> ( :om ! keep]s did %ake & become z dead m54 ,b to ! wom5 he said1 ,fe> n ye2 = ,i "k t ye seek ,jesus :i* 0 crucifi$1 ,he is n "h1 = ,he is ris54 ,t y may "k = a c]ta9ty t ,he is ris51 come & see ! place :]e y saw ,him laid only a few h\rs ago4 ,n[ g quickly & tell ,8 disciples t ,he is ris5 f ! dead1 & behold ,he goe? be=e y into ,galilee1 !re %all ye see ,him4 ,& !y dep>t$ quickly f ! sepul*] ) fe> & great joy1 & did run to c>ry ! good news to ! disciples4 ,b h[ mu* great] _! joy soon aft] _! dep>ture :5 ,jesus himself met !m ) ! com=t+ words1 ,be n afraid1 b g tell my bre?r5 t !y g into ,galilee1 & !re %all !y see ,me4 ,! subject = conv]sation = ! pa/ two days _h be5 ,jesus & ! crucifixion1 b n[ ,jesus & ! resurrection4 ,"s believ$1 b "s d\bt$4 ,o!rs ran to ! sepul*] & f\nd x ev5 z ! wom5 _h said4 ,:ile ! *ief prie/s & eld]s hir$ ! soldi]s to say t ! disciples came by night & /ole him away :ile we slept4 ,b h[ %\ld !y "k :at _h become ( ,him if !y 7 sleep+8 ,! tru? 0 !y 7 s ov]come ) fe> by ! brightness ( ! angels' c\nt5ance t !y became z dead m51 n kn[+ :at 0 transpir+ ar\nd !m4 ,b x 0 truly good tid+s & great joy to ! disciples ( ,*ri/ on t ,ea/] morn+4 ,! ris+ ,god =sakes ! tomb2 ,9 va9 ! tomb =bids ,8 rise2 ,va9 ! /one1 ! wat*1 ! seal1 ,*ri/ has bur/ ! gates ( hell2 ,dea? 9 va9 =bids ,8 rise2 ,*ri/ ha? op5$ ,p>adise4 ,! _s ( ,*ri/ 9 ! prophets _h te/ifi$ be=eh& ! suff]+ ( ,*ri/ & ! glory t %\ld foll[4 ,t morn+ & t day 0 n only joyful to ! disciples ( ,*ri/1 b glori\s2 x 0 joy unspeakable & full ( glory4 ,al?\gh #ahfc ye>s h roll$ ar\nd s9ce t ,ea/] morn+1 yet we are z mu* int]e/$ 9 :at !n & !re transpir$ z 7 ! ,m>ys1 & ,pet]1 & ,john1 :o 7 ! fir/ at ! sepul*]1 & :o 7 p]mitt$ ! same day to see _! ris5 ,"l1 :om hav+ n se51 we love2 9 :om1 ?\gh n[ we see ,him n1 yet believ+1 we z well z !y rejoice ) joy unspeakable & full ( glory4 ,l[ ,sunday4 ,! fir/ ,sunday aft] ,ea/] is s call$ because x 0 cu/om>y to repeat on ?is day "s "p ( ! solemnity :i* 0 us$ on ,ea/] day1 :5ce x took ! "n ( ,l[ ,sunday1 be+ celebrat$ z a fea/1 b ( a l[] degree ?an ,ea/] day itself4 ,! next ,sunday aft] ,ea/] has be5 popul>ly1 s call$ 9 ,engl&1 p]haps by corruption = close1 7,pas*a ,clausum7 close ( ,ea/]4 ,dom9ica 9 ,albis1 7! ,sunday ( :ite g>m5ts7 a title anci5tly giv5 to ! fir/ ,sunday aft] ,ea/]1 because on ?is day ^? p]sons :o _h be5 baptiz$ at ,ea/] appe> = ! la/ "t 9 ! *rysomes1 or :ite robes :i* !y receiv$ at baptism4 ,^! 7 laid up 9 ! *ur* z evid5ces ( _! baptismal pr(ession4 ,rogation ,days1 7,lat9 rog>e1 to besee*17 are ! ,monday1 ,tuesday & ,w$nesday aft] ,rogation ,sunday & be=e ,asc5sion ,day1 7,holy ,?ursday47 ,ab\t ! middle ( ! fif? c5tury ,mam]tus1 bi%op ( ,vi5na1 ^u ! prospect ( a great fire t ?reat5$ 8 diocese1 appo9t$ t extraord9>y pray] & supplication %\ld be (f]$ up to ,god1 ) fa/+1 = av]t+ ! imp5d+ evils ^u ! above m5tion$ days2 f :i* supplications 7call$ by ! ,lat9s rogationes7 ^! days h ev] s9ce be5 call$ ,rogation ,days4 ,z reta9$ 9 our pres5t cal5d>1 !y are simply private fa/s4 f--,asc5sion ,day1 or ,holy ,?ursday1 "o ( ! great religi\s fe/ivals ( ! ,roman ,ca?olic & ,episcopal *ur*es1 is held on ! =tie? day aft] ,ea/]1 & t5 days be=e ,:itsun ,day1 to commemorate ! ,asc5sion ( our ,"l into heav54 ,asc5sion ,day has be5 obs]v$ at lea/ s9ce ! ye> ( our ,"l #fd1 & p]haps e>li]4 ,sa9t ,augu/9e believ$ x to h be5 in/itut$ ei!r by ! apo/les !mselves1 or ! bi%ops imm$iately succe$+ !m4 ,expectation ,week is ! :ole ( ! int]val betwe5 ,asc5sion ,day & ,:itsun ,day1 s call$ because at ?is "t ! apo/les1 accord+ to ! comm& ( our ,savi\r1 cont9u$ at ,j]usalem1 9 e>ne/ pray] & expectation ( ! ,holy ,com=t] :i* 0 to abide ) !m =ev]4 ,! ,sunday betwe5 ,asc5sion ,day & ,:itsun ,day is call$ ,expectation ,sunday4 ,p5teco/1 7,greek1 ,p5teco/os1 fiftie?71 a ,jewi% fe/ival2 s call$ because x 0 obs]v$ on ! fiftie? day aft] ! fea/ ( unleav5$ bread1 call$ also ! fea/ ( weeks1 be+ celebrat$ sev5 weeks f ! fea/ ( ! ,passov]4 ,x also commemorat$ ! giv+ ( ! law on ,m\nt ,s9ai ^u t day4 ,! orig9 ( ! ,anglo-,saxon "n ( ,:ite ,sunday1 :i* also occurs 9 ,icel&ic1 is some:at obscure1 = 9 ! ,roman *ur*es ! ,dom9ica 9 ,albis1 7,l[ ,sunday1 q4 v47 s call$ f ! :ite robes !n worn by ! p]sons baptiz$ at ,ea/]1 has always be5 ! ,sunday imm$iately foll[+ ,ea/]4 ,x h>dly seems probable t !re %\ld be ano!r ,sunday ( ,:ite ,g>m5ts )9 six weeks4 ,9 ,g]man x is kn[n by ! "n ,pf+/51 old ,g]man ,w+/51 old ,engli% ,:itsun1 h5ce1 probably1 our ^w ,:itsun ,day1 n ,:ite ,sunday4 g--,:itsun ,day1 or ,p5teco/1 is ! la/ ( ! f\r great fe/ivals 9 ! ecclesia/ical ye>1 held 9 commemoration ( ! outp\r+ ( ! ,holy ,_s on ! infant *ur* t5 days aft] ! ,asc5sion4 ,among ! la/ words ( our ,savi\r to ! apo/les on ! v day t ,he 0 tak5 up1 7 ,behold ,i s5d ! promise ( my ,fa!r ^u y1 b t>ry ye 9 ! city ( ,j]usalem until ye be end[$ ) p[] f on high4 ,aft] t5 days ( e>ne/1 believ+ pray]1 & expectation1 sudd5ly1 b n unexpect$ly1 !re came a s\nd f heav5 z a ru%+1 mighty w9d1 & x fill$ all ! h\se :]e !y 7 sitt+1 & !re appe>$ unto !m clov5 tongues l z ( fire1 & x sat ^u ea* ( !m2 & !y 7 all fill$ ) ! ,holy ,gho/1 & began to speak ) o!r tongues z ! ,_s gave !m utt]ance2 & ! multitude came toge!r1 & 7 amaz$1 say+ "o to ! o!r :at meane? ?is8 ,o!rs mock+ said1 ^! m5 are full ( new w9e4 ,b ,pet] lift$ up 8 voice & said1 ^! are n drunk5 z ye suppose1 see+ x is b ! ?ird h\r ( ! day1 7n9e o'clock 9 ! morn+17 m5 are n usually drunk s e>ly 9 ! morn+2 b ?is is t :i* ! prophet ,joel eight hundr$ ye>s ago said %\ld come to pass 9 ^! la/ days2 ! promise ( ! ,fa!r1 ! baptism ( ! ,holy ,gho/ = :i* !y _h be5 wait+ = ! pa/ t5 days2 some?+ ( t glory t %\ld foll[ ! crucifixion1 dea?1 resurrection & asc5sion ( ! ,"l ,jesus into ,heav51 ! glory ( ! ,*ri/ian *ur*1 ( ! ,*ri/ian disp5sation1 & :i* is de/9$ to fill ! :ole e>?4 ,waft1 ,waft1 ye w9ds 8 /ory1 ,& y1 ye wat]s1 roll1 ,till l a sea ( glory1 ,x spreads f pole to pole4 h--,tr9ity ,sunday1 ! octave1 or eigh? day ( ! fea/ ( ,p5teco/1 is a *ur* fe/ival held 9 commemoration ( ! doctr9e ( ! ,tr9ity4 ,! introduction ( ?is day into ! cal5d> is ( comp>atively rec5t date1 x be+ e/abli%$ by ,pope ,b5$ict ,,xi1 9 ! ye> ( our ,"l #acje4 ,x is probable t ! zeal ( _m ,*ri/ians aga9/ ! use ( images 9 ! eigh? & n9? c5turies may h be5 ! fir/ cause ( ! appo9tm5t ( a di/9ct day = m$itat+ ^u ! nature ( ! ,holy ,tr9ity 9 unity1 or ! "o true ,god z di/+ui%$ f idols4 ,! reason = its late introduction is t 9 ! cre$ ( ! *ur*1 & 9 its psalms1 hymns1 & doxologies1 great prom95ce 0 giv5 to ?is doctr9e1 & x 0 ?\ght t !re 0 no ne$ to set ap>t a p>ticul> day = t :i* 0 done e day4 ,?is is ! la/ ( ! movable fea/s 9 ! ecclesia/ical ye>1 be+ held eight weeks aft] ,ea/]2 s x may happ5 z e>ly z ! #ag? ( ,may or z late z ! #bj? ( ,june4 ,! l5g? ( bo? ,epiphany & ,tr9ity-tide dep5d ^u ! date ( ,ea/]4 ,z ,epiphany-tide is %ort5$ by ! e>ly date ( ,ea/]1 s ,tr9ity-tide is l5g!n$ proportionately1 & z ,epiphany-tide is l5g!n$ by ! lat] date ( ,ea/] s ,tr9ity-tide is %ort5$ proportionately2 s ,tr9ity-tide may conta9 no m ?an #aif days nor less ?an #afa4 7,see tables at ! close ( ?is *apt]47 ,all ,sa9ts ,day1 or ,all hall[mass 7,anglo-,saxon all1 & halig1 holy7 a fe/ival celebrat$ by ! ,roman ,ca?olic & ,episcopal *ur*es on ! fir/ day ( ,novemb]1 9 honor ( all ,sa9ts & m>tyrs4 ,x 0 introduc$ into ! ,we/]n *ur* 9 ! beg9n+ ( ! sev5? c5tury by ,boniface4 ,! numb] ( sa9ts be+ exce$+ly multipli$1 x 0 f\nd too burd5some to d$icate a fea/ day to ea*1 !re be+1 inde$1 sc>cely h\rs en\gh 9 ! ye> to di/ribute among !m all4 ,x 0 !re=e resolv$ to commemorate on "o day all :o _h no p>ticul> day4 ,by ord] ( ,gregory ,,iv1 x 0 celebrat$ on ! fir/ ( ,novemb]1 #hcd2 =m]ly ! fir/ ( ,may 0 ! day appo9t$4 ,x 0 introduc$ into ,engl& ab\t #hgj1 & is /ill obs]v$ 9 ! ,engli% & ,lu!ran *ur*es1 z well z ! ,*ur* ( ,rome on ! fir/ ( ,novemb]4 ,all-,s\ls' ,day1 a fe/ival held by ,roman ,ca?olics on ! #b;d ( ,novemb]1 = special pray] 9 behalf ( all ! fai?ful dead4 ,x 0 fir/ introduc$ 9 #iih1 by ,odilon1 ,abbot ( ,clugni1 :o enjo9$ x on 8 own ord]4 ,x 0 soon aft] adopt$ by neighbor+ *ur*es4 ,x is ! day on :i*1 9 ! ,romi% *ur*1 extraord9>y masses are repeat$ = ! relief ( s\ls said to be 9 purgatory4 ,=m]ly on ?is day p]sons dress$ 9 black p]ambulat$ ! t[ns & cities1 ea* provid$ ) a bell ( dismal tone1 :i* 0 rung 9 public places by way ( exhortation to ! p to rememb] ! s\ls 9 purgatory4 ,9 "s p>ts ( ! we/ ( ,engl& x is /ill ! cu/om = ! village *ildr5 to g ar\nd to all _! neighbors s\l+1 z !y call x1 collect+ small contributions1 & s++ ! foll[+ v]ses1 tak5 d[n f two ( ! *ildr5 !mselves3 ,s\l6 ,s\l6 = a s\l-cake1 ,pray good mi/ress1 = a s\l-cake1 ,"o = ,pet]1 two = ,paul1 ,?ree = ,him t made u all4 ,s\l6 s\l6 = an apple or two2 ,if y've got no apples1 pe>s w d1 ,up ) y\r kettle1 & d[n ) y\r pan1 ,give me a good big "o & ,i'll be gone4 ,! s\l cake ref]r$ to 9 ! v]ses is a sort ( bun :i* ! p us$ to make1 & to give to "o ano!r on ! #b;d ( ,novemb]4 ,9 ! foll[+ tables !re is pres5t$ at "o view ! day ( ! mon? on :i* ! pr9cipal fea/s & fa/s fall 9 ! ecclesia/ical ye> #ahag-ah & #ahhe-hf4 ,9 ! =m] ,ea/] happ5s at its e>lie/ possible date1 9 ! latt] at its late/ date 9 ?is c5tury3 ---------------------------------------- ------------------------------ ,,ye> #ahag-ah4 ,days 9 ,sundays 9 ,ea* ,season4,ea* ,season4 ---------------------------------------- ------------------------------ a--,adv5t ,sunday1 ,novemb] #cj?2 ,adv5t-tide1 #be #d #a/ ,emb] ,week1 aft] ,decemb] #ac?2 ,emb] ,days1 ,w$nesday1 ,friday & ,saturday4 b--,*ri/mas1 ,decemb] #be?2 ,*ri/mas-tide1 #ab #b c--,epiphany1 ,janu>y #f?2 ,epiphany-tide1 #ab #a ,septuagesima ,sunday1 ,janu>y #ah?1 #g #a ,pas*al season f ,jan4 #ah? to ,m>* #bi?1 #gj days ,sexagesima ,sunday1 ,janu>y #be?1 #g #a ,qu9quagesima ,sunday1 ,febru>y #a/1 #c #a ,%rove-tide1 7confession "t7 ,%rove ,tues41 ,feb4 #c;d4 d--,a% ,w$nesday1 ,feb #d?1 ,l5t beg9s2 ,l5t5-tide1 #df #f ,fir/ ,sunday 9 ,l5t 7,quadragesima7 ,febru>y #h?4 #b;d ,emb] ,week aft] fir/ ,sunday 9 ,l5t2 ,emb] ,days1 ,w$nesday1 ,friday & ,saturday4 ,holy ,week1 ! week be=e ,ea/]2 ,special ,days1 ,palm ,sunday1 ,spy ,w$nesday1 ,maundy ,?ursday1 & ,good ,friday1 ,m>* #ae?1 #ah?1 #ai? & #bj?4 e--,ea/] ,sunday1 ,m>* #bb;d2 ,ea/]-tide1 #ci #f ,l[ ,sunday1 ,m>* #bi?2 ,pas*al ,season ends4 ,rogation ,sunday1 ,april #bf?2 ,rogation ,days1 ! ,monday1 ,tuesday & ,w$nesday aft] ,rogation ,sunday4 f--,asc5sion ,day 7,holy ,?ursday71 ,april #cj?2 ,asc5sion-tide1 #aj #a ,expectation ,sunday1 ,fir/ ,sunday aft] ,asc5sion1 ,may #c;d4 g--,:itsun ,day1 7,p5teco/7 ,may #aj?2 ,:itsun-tide1 #g #a #c;d ,emb] ,week1 aft] ,:itsun ,day2 ,emb] ,days1 ,w$nesday1 ,friday & ,saturday4 h--,tr9ity ,sunday1 ,may #ag?2 #aif #bh ,tr9ity-tide1 #d? ,emb] ,week1 aft] ,septemb] #ad?2 ,emb] ,days1 ,w$nesday1 ,friday & ,saturday4 ,all ,sa9ts' ,day1 ,novemb] #a/4 ,all ,s\ls' ,day1 ,novemb] #b;d4 ---------------------------- ,app5dix ,k4 #cfd #eb ---------------------------------------- ------------------------------ ---------------------------------------- ------------------------------ ,,ye> #ahhe-hf4 ,days 9 ,sundays 9 ,ea* ,season4,ea* ,season4 ---------------------------------------- ------------------------------ a--,adv5t ,sunday1 ,novemb] #bi?1 ,adv5t-tide1 #bf #d #a/ ,emb] ,week1 aft] ,decemb] #ac?2 ,emb] ,days1 ,w$nesday1 ,friday & ,saturday4 b--,*ri/mas1 ,decemb] #be?2 ,*ri/mas-tide1 #ab #b c--,epiphany1 ,janu>y #f?2 ,epiphany-tide1 #df #f ,septuagesima ,sunday1 ,febru>y #ba/1 #g #a ,pas*al season1 f ,feb4 #ba/ to ,may #b;d1 #gj days4 ,sexagesima ,sunday1 ,febru>y #bh?1 #g #a ,qu9quagesima ,sunday1 ,m>* #g?1 #c #a ,%rove-tide1 7confession "t7 ,%rove ,tues41 ,m>4 #i?4 d--,a% ,w$nesday1 ,m>* #aj?1 ,l5t beg9s2 ,l5t5-tide #df #f ,fir/ ,sunday 9 ,l5t 7,quadragesima7 ,m>* #ad?4 #b;d ,emb] ,week aft] fir/ ,sunday 9 ,l5t2 ,emb] ,days1 ,w$nesday1 ,friday & ,saturday4 ,holy ,week1 ! week be=e ,ea/]2 ,special ,days1 ,palm ,sunday1 ,spy ,w$nesday1 ,maundy ,?ursday & ,good ,friday1 ,april #ah?1 #ba/1 #bb;d & #bc;d4 e--,ea/] ,sunday1 ,april #be?2 ,ea/]-tide1 #ci #f ,l[ ,sunday1 ,may #b;d1 ,pas*al ,season ends4 ,rogation ,sunday1 ,may #cj?2 ,rogation ,days1 ! ,monday1 ,tuesday & ,w$nesday aft] ,rogation ,sunday4 f--,asc5sion ,day 7,holy ,?ursday71 ,june #c;d2 ,asc5sion-tide1 #aj #a ,expectation ,sunday1 fir/ ,sunday aft] ,asc5sion1 ,june #f?4 g--,:itsun ,day1 7,p5teco/7 ,june #ac?2 ,:itsun-tide1 #g #a #c;d ,emb] ,week1 aft] ,:itsun ,day2 ,emb] ,days1 ,w$nesday1 ,friday & ,saturday4 h--,tr9ity ,sunday1 ,june #bj?2 ,tr9ity-tide1 #afa #bc #d? ,emb] ,week1 aft] ,septemb] #ad?2 ,emb] ,days1 ,w$nesday1 ,friday & ,saturday4 ,all ,sa9ts' ,day1 ,novemb] #a/4 ,all ,s\ls' ,day1 ,novemb] #b;d ---------------------------- ,app5dix ,k4 #cfd #eb ---------------------------------------- ------------------------------ ,,*apt] ,,viii4 ,,hebrew ,,cal5d>4 ,to ! ,bible /ud5t a k ( ! ,hebrew cal5d> is indisp5sable1 if he w\ld "k h[ ! date ( ev5ts record$ 9 ! ,bible are made to correspond ) our pres5t ,engli% cal5d>4 ,f ! exodus 7#adia ,b4 ,c47 d[nw>d1 ! ,hebrew mon? 0 lun>1 & comm5c$ inv>iably ) ! new moon4 ,dr4 ,smi?1 au?or ( ,bible ,diction>y1 says t ! t]ms = mon? & moon h ! same close connection 9 ! ,hebrew language z 9 our own1 only ! ,hebrew ,code% 7t is new moon7 is1 p]haps1 m di/9ctive ?an ! correspond+ t]m 9 our language2 = x expresses n simply ! idea ( a lunation1 b ! recurr5ce ( a p]iod comm5c+ def9itely ) ! new moon4 ,?\gh ! id5tification ( ! ,jewi% mon? ) our own _c be effect$ ) precision on acc\nt ( ! v>iations t mu/ necess>ily exi/ betwe5 ! lun> & ! sol> mon?1 ea* ( ! =m] rang+ ov] portions ( two ( ! latt]1 /ill x c be %[n h[ !y may be made to co9cide v ne>ly by a sy/ematic me?od ( int]calation4 ,n[ f new moon to new moon aga91 is ab\t #bi-a_/b days2 !re=e1 ! ,hebrew ye> consi/$ ( #ced days1 = #bi-a_/b x #ab #ced2 s t ! epact1 7:i* is ! excess ( ! sol> ye> beyond ! lun>7 is elev5 days4 ,h5ce1 _h !y no me?od ( int]calation1 ! comm5cem5t ( _! ye> w\ld g back elev5 days e ye>1 & consequ5tly make a revolution ( ! seasons e ?irty-?ree ye>s1 = #cfe _/ #aa #cc ne>ly4 ,to illu/rate1 let u suppose t ! new moon ( ,nisan1 :i* is ! fir/ mon? 9 ! ,sacr$ ye>1 %\ld on any giv5 ye> fall on ! #aj? ( ,april1 !n ! foll[+ ye> x w\ld fall on ! #cj? ( ,m>*1 :i* is elev5 days e>li]2 ! second ye> x w\ld fall on ! #ai? ( ,m>* or tw5ty-two days e>li]2 ! ?ird ye> ! new moon w\ld fall on ! #h? ( ,m>* or ?irty-?ree days e>li]1 b t w\ld n be ! new moon ( ,nisan1 :i* _c happ5 e>li] ?an ! #aa?1 s ! foll[+ moon :i* happ5s ?irty days lat] on ! #g? ( ,april is ! new moon ( ,nisan4 ,h5ce x may be se5 t by int]calat+ a full mon? e ?ree ye>s1 or :i* comes ne>] to accuracy sev5 times 9 n9ete5 ye>s1 re/ores ! co9cid5ce ( ! sol> & ! lun> ye>1 & consequ5tly ! moons to ! same day ( ! mon? on :i* !y fell n9ete5 ye>s be=e4 ,! me?od ( designat+ ! mon?s previ\s to ! exodus1 0 by _! num]ical ord]1 z ! anci5t ,hebrews _h no p>ticul> "n to express _! mon?4 ,!y said ! fir/1 second & ?ird mon?1 & s on4 ,no names ( mon?s appe> 9 ! ,bible until ab\t ! "t ( ! in/itution ( ! passov]1 :5 ! ,"l spake unto ,moses & ,a>on 9 ! l& ( ,egypt1 say+ ?is mon?1 7,abib1 :i* appe>s to h _h its orig9 9 ,egypt17 %all be unto y ! beg9n+ ( mon?s2 x %all be ! fir/ mon? ( ! ye> to y4 ,! names ( ! mon?s appe> to belong to two di/9ct p]iods4 ,9 ! fir/ place we h ^? peculi> to ! ,jews previ\s to ! captivity1 viz3 ,abib1 ! fir/ mon? 9 commemoration ( ! exodus2 ,zif1 ! second1 ,e?anim1 ! sev5?1 & ,bul1 ! eigh?4 ,^! names are ( ,hebrew orig91 & h ref]5ce to ! *>act]i/ics ( ! seasons1 a circum/ance :i* cle>ly %[s t ! mon?s1 by int]calation1 7 made to return at ! same p]iod ( ! ye>4 ,?us1 ,abib 0 ! mon? ( ! e>s ( corn1 t is ! mon? 9 :i* ! e>s ( corn became full1 or ripe on ! #af? day1 t is ! #b;d day ( ! fea/ ( unleav5$ bread4 ,zif1 ! mon? ( blossoms or ! bloom ( fl[]s4 ,e?anim1 ! mon? ( gifts1 t is ( fruits1 & ,bul1 ! mon? ( ra94 ,^! 7 sup]c$$ aft] ! captivity1 by ,nisan1 ,iy>1 ,tisri & ,hesvan1 or ,m>*esvan4 ,m>*esvan1 co9cid+ z x does ) ! ra9y season 9 ,pale/9e1 is consid]$ a pure ,hebrew t]m4 ,! mod]n ,jews consid] x a comp\nd ^w1 f m>1 drop1 & ,*esvan2 ! =m] betok5+ t x 0 wet1 & ! latt] be+ ! prop] "n ( ! mon?4 ,h5ce ! "n indicates ! wet mon?4 ,9 ! second place we h ! names ( six o!rs :i* appe> 9 ! ,bible subsequ5tly to ! ,babylonian captivity1 viz43 ,sivan1 ! ?ird2 ,elul1 ! six?2 ,kislev1 ! n9?2 ,tebet1 ! t5?2 ,sebat1 ! elev5?1 & ,ad>1 ! twelf?4 ,!re are two o!r mon?s ^: names d n appe> 9 ! ,bible1 viz43 ,tamuz1 ! f\r?1 & ,ab1 ! fif?4 ,! "n ( ! int]cal>y mon? is call$ ,ve-,ad>1 or #b;d ,ad> because plac$ 9 ! cal5d> aft] ,ad> & be=e ,nisan4 ,dr4 ,smi? says ^! names are probably borr[$ f ! ,syrians 9 ^: regul> cal5d> we f9d names answ]+ to mo/ ( !m4 ,he also says x 0 ! op9ion ( ! ,talmudi/s1 t ^! names 7 introduc$ by ! ,jews :o return$ f ! ,babyloni% captivity1 & also t !y are c]ta9ly us$ exclusively by writ]s ( ! po/-,babylonian p]iod4 ,inasmu* z ! ,hebrew mon?s co9cid$ ) ! seasons1 z we h already %[n1 x foll[s z a matt] ( c\rse1 t an additional mon? mu/ h be5 ins]t$ e ?ird ye>1 :i* w\ld br+ ! numb] up to ?irte54 ,no notice1 h[ev]1 is tak5 ( ?is mon? 9 ! ,bible1 nei!r h we reason to ?9k t x 0 ins]t$ accord+ to any exact rule1 b x 0 add$ :5ev] x 0 discov]$ t ! b>ley h>ve/ did n co9cide ) ! ord9>y return ( ! mon? ,abib4 ,x has already be5 %[n t 9 ! mod]n ,jewi% cal5d> ! int]cal>y mon? is introduc$ sev5 times 9 n9ete5 ye>s1 accord+ to ! ,metonic1 or lun> cycle :i* 0 adopt$ by ! ,jews ab\t #cfj ,a4 ,d4 ,! ,hebrew cal5d> is dat$ f ! creation1 :i* is suppos$ to h tak5 place #cgfa ye>s be=e ,*ri/4 ,h5ce1 to f9d ! numb] ( cycles elaps$ s9ce ! creation1 also ! numb] 9 ! cycle1 we h ! foll[+ rule3 ,add #cgfa to ! date1 divide ! sum by n9ete52 ! quoti5t is ! numb] ( cycles1 & ! rema9d] is ! numb] 9 ! cycle4 ,%\ld !re be no rema9d]1 ! propos$ ye> is1 ( c\rse1 ! la/ or n9ete5? ( ! cycle4 ,?us1 = ! ye> #ahhc1 we h #ahhc #cgfa _/ #ai #big1 rema9d] #a2 !re=e1 #big is ! numb] ( cycles1 & #a ! numb] 9 ! cycle4 ,aga91 = ! ye> #ahic1 we h #ahic #cgfa _/ #ai #big1 rema9d] #aa2 !re=e #big is ! numb] ( cycles1 & #aa ! numb] 9 ! cycle4 ,aga9 = ! ye> #aija1 we h #aija #cgfa _/ #ai #bih1 rema9d] #j2 !re=e #bih is ! numb] ( cycles1 & #ai ! la/ ( ! cycle4 ,h5ce x may be se5 t ! pres5t cycle comm5c$ ) #ahhc1 t #aa is ! numb] 9 ! cycle = ! pres5t ye> #ahic1 also t ! cycle ends ) #aija2 s t ! next cycle comm5ces ) #aijb4 ,if ! rema9d] aft] divid+ by n9ete5 be #c1 #f1 #h1 #aa1 #ad1 #ag or #ai 7#j71 ! ye> is int]cal>y or embolismic1 consi/+ ( #chd days2 if o!rwise x is ord9>y1 conta9+ only #ced days2 s t 9 a cycle ( n9ete5 ye>s1 we h twelve ord9>y ye>s ( #ced days ea*1 & sev5 embolismic ye>s ( #chd days ea*4 ,b1 9 ei!r case1 ! ye> is sometimes made a day m1 & sometimes a day less1 9 ord] t c]ta9 fe/ivals may fall on prop] days ( ! week = _! due obs]vance4 ,h5ce ! ord9>y ye> may consi/ ( #cec1 #ced or #cee days1 & ! embolismic ye> ( #chc1 #chd or #che days4 ,9 ! mod]n ,jewi% cal5d> ! ,new ,ye> comm5ces ) ! new moon ( ,tisri1 :i* may happ5 z e>ly z ! #e? ( ,septemb] or z late z ! #e? ( ,octob]4 ,! new moon ( ,nisan1 :i* is ! fir/ mon? 9 ! ,sacr$ ye>1 may happ5 z e>ly z ! #aa? ( ,m>* or z late z ! #aa? ( ,april4 ,x %\ld be borne 9 m9d t ! names ( ! mon?s ,abib1 ,zif1 ,e?anim & ,bul 7 sup]c$$ aft] ! captivity1 by ,nisan1 ,iy>1 ,tisri & ,hesvan or ,m>*esvan2 also ! "n ( ! ?ird mon? 9 ! civil ye>1 ,*isleu 9 ! ,bible1 ,kislev 9 ! mod]n ,jewi% cal5d>4 ,9 table ,no4 #a we h ! names ( ! mon?s 9 num]ical ord]1 also ! numb] ( days 9 ea* mon?4 ,?\gh ! mon?s consi/ ( #cj & #bi days alt]nately1 yet1 9 ! embolismic ye>1 ,ad>1 :i* 9 common ye>s has #bi days1 is giv5 #cj days1 & #b;d ,ad> #bi2 s t two mon?s ( #cj days come toge!r4 ,table ,no4 #b %[s ! e>lie/ & ! late/ possible date ( ! new moons ( ea* ( ! mon?s respectively4 ,,table #a4 ,,hebrew ,,mon?s4 ,sacr$ ,ye>4 ,civil ,ye>4 ,nisan #cj ,tisri #cj ,iy> #bi ,hesvan #bi ,sivan #cj ,kislev #cj ,tamuz #bi ,tebet #bi ,ab #cj ,sebat #cj ,elul #bi ,ad> #cj ,tisri #cj #b;d ,ad>1 ,embolismic #bi ,hesvan #bi ,nisan #cj ,kislev #cj ,iy> #bi ,tebet #bi ,sivan #cj ,sebat #cj ,tamuz #bi ,ad> #cj ,ab #cj #b;d ,ad>1 ,embolismic #bi ,elul #bi ,,table ,,ii4 ,,hebrew ,,mon?s4 ,nisan1 ,m>* #aa? or ,april #aa? ,iy>1 ,april #aa? ,may #aj? ,sivan1 ,may #aj? ,june #i? ,tamuz1 ,june #i? ,july #i? ,ab1 ,july #i? ,augu/ #g? ,elul1 ,augu/ #g? ,septemb] #e? ,tisri1 ,septemb] #e? ,octob] #e? ,hesvan1 ,octob] #f? ,novemb] #d? ,kislev1 ,novemb] #d? ,decemb] #c;d ,tebet1 ,decemb] #c;d ,janu>y #b;d ,sebat1 ,janu>y #c;d ,febru>y #aj? ,ad>1 ,febru>y #aj? ,m>* #ab? ,! *>ts on ! ?ree foll[+ pages are us$ to illu/rate ! correspond5ce ( ! ,hebrew mon?s ) our own4 ,ea* *>t repres5ts ! ecliptic1 :i* is ! app>5t pa? ( ! ,sun or real pa? ( ! ,e>?1 also ! names ( ! mon?s z !y occur 9 _! seasons4 ,! figures repres5t ! days ( ! mon? on :i* ! new moons ( ! ,hebrew cal5d> fall4 ,^! *>ts repres5t ! mon? & ! day ( ! mon? on :i* bo? ! ,sacr$ & ! ,civil ye> beg9s & ends = ?ree successive ye>s4 ,h5ce x may be se5 t by int]calat+ a mon? e ?ree ye>s ! new moons are re/or$1 v ne>ly1 to ! place !y occupi$ ?ree ye>s be=e4 ,,*>t ,i4 ,illu/ration3 ,?is *>t repres5ts ! day ( ! mon? on :i* all ! new moons fall 9 ! ye> #ahia-ib4 ,! sacr$ ye> comm5c$ ) ! new moon ( ,nisan on ! #i? ( ,april1 & ! civil ye> ) ! new moon ( ,tisri on ! #c;d ( ,octob]1 #ahia1 & end$ respectively ) ! #bh? ( ,m>* & ! #ba/ ( ,septemb]1 #ahib4 ,,*>t ,,ii4 ,illu/ration3 ,?is *>t repres5ts ! day ( ! mon? on :i* all ! new moons fall 9 ! ye> #ahib-ic4 ,x may be "h se5 t ! ye> beg9s & ends ab\t elev5 days e>li] ?an ! ye> prec$+1 also t all ! new moons fall elev5 days e>li] ?an !y did 9 ! prec$+ ye>4 ,,*>t ,,iii4 ,illu/ration3 ,?is *>t repres5ts ! ye> #ahic-id4 ,?\gh ! ye> beg9s ab\t elev5 days e>li] ?an ! prec$+1 viz43 ! #ag? ( ,m>*1 yet x be+ ! ye> 9 :i* a #b;d ,ad> is int]calat$1 in/ead ( fall+ back elev5 days1 ! beg9n+ ( ! foll[+ ye> is c>ri$ =w>d #bj days1 mak+ a ye> ( #chd days2 s t ! ye> #ahid-ie w comm5ce ) ,april #e4 ,9 #ahia we comm5c$ ) ,april #i4 ,x w be #ai ye>s be=e we comm5ce on ! #i? ( ,april aga94 ,,app5dix4 ,a4--,,page #ab4 ,au?ors diff] 9 reg>d to ! l5g? ( ! sol> ye>4 ,"o gives #cfe days1 #e h\rs1 #dg m9utes & #ea4e seconds2 ano!r1 #cfe days1 #e h\rs1 #dh m9utes & #df seconds2 & /ill ano!r1 #cfe days1 #e h\rs1 #dh m9utes & #di4fb seconds4 ,9 ?is "w ! la/ has be5 accept$ z ! true l5g? ( ! sol> ye>1 & all calculations h be5 made accord+ly4 ,b4--,,page #ai4 ,!re is an app>5t discrepancy among au?ors 9 reg>d to ! int]cal>y day4 ,:ile "o ass]ts t x 0 betwe5 ! #bd? & #be? ( ,febru>y1 ano!r equally reliable1 says t ! #be? 0 ! sexto cal5das & ! #bd? 0 ! bis-sexto cal5das ( ! ,julian cal5d>4 ,n[ x %\ld be borne 9 m9d t ! ,julian cal5d> is ! basis ( our own1 & is id5tical ) x 9 ! numb] ( mon?s 9 ! ye>1 & 9 ! numb] ( days 9 ! mon?4 ,also :5 ! me?od ( numb]+ ! days f ! beg9n+ ( ! mon? 0 adopt$1 ! int]calation 0 made to correspond ) ! int]cal>y day 9 ! ,julian cal5d>4 ,z 9 ! ,julian cal5d> !re 7 twice ! six? day1 s 9 ! re=m$ cal5d> !re 7 twice ! #bd? day1 :i* 0 equival5t to #bi days 9 ,febru>y4 ,:5 ! cal5d> 0 aga9 correct$1 mak+ ! #bi? ! int]cal>y day1 !n ! #bd? correspond$ ) ! bis-sexto cal5das ( ! ,julian cal5d>4 ,?is reconciles ! app>5t discrepancy4 ,:ile "o au?or ref]s to ! cal5d> 9 :i* ! ,julian rule ( int]calation is adopt$1 ano!r ref]s to ! cal5d> :5 s correct$ z to make ! #bi? ( ,febru>y ! int]cal>y day4 ,see foll[+ table3 ---------------------------------------- ------------------------------ ,,julian ,,me?od ,,mod]n ,,me?od ,,( ,,int]calation4 ,,( ,,int]calation4 ---------------------------------------- ------------------------------ #a ,cal4 ,cal5dae #a ,cal4 ,cal5dae #b #d ,qu>to ,nonas #b #d ,qu>to ,nonas #c #c ,t]tio ,nonas #c #c ,t]tio ,nonas #d #b ,pridie ,nonas #d #b ,pridie ,nonas #e ,nomes ,nonae #e ,nomes ,nonae #f #h ,octavo ,idus #f #h ,octavo ,idus #g #g ,septimo ,idus #g #g ,septimo ,ides #h #f ,sexto ,idus #h #f ,sexto ,idus #i #e ,qu9to ,idus #i #e ,qu9to ,idus #aj #d ,qu>to ,idus #aj #d ,qu>to ,idus #aa #c ,t]tio ,idus #aa #c ,t]tio ,idus #ab #b ,pridie ,idus #ab #b ,pridie ,idus #ac ,ides ,idus #ac ,ides ,idus #ad #af ,sextodecimo ,cal5das #ad #af ,sextodecimo ,cal5das #ae #ae ,qu9todecimo ,cal5das #ae #ae ,qu9todecimo ,cal5das #af #ad ,qu>todecimo ,cal5das #af #ad ,qu>todecimo ,cal5das #ag #ac ,t]tiodecimo ,cal5das #ag #ac ,t]tiodecimo ,cal5das #ah #ab ,duodecimo ,cal5das #ah #ab ,duodecimo ,cal5das #ai #aa ,undecimo ,cal5das #ai #aa ,undecimo ,cal5das #bj #aj ,decimo ,cal5das #bj #aj ,decimo ,cal5das #ba #i ,nono ,cal5das #ba #i ,nono ,cal5das #bb #h ,octavo ,cal5das #bb #h ,octavo ,cal5das #bc #g ,septimo ,cal5das #bc #g ,septimo ,cal5das #bd #f ,bis-,sexto ,cal5das #bd #f ,bis-sexto ,cal5das #bd #f ,sexto ,cal5das #be #f ,sexto ,cal5das #be #e ,qu9to ,cal5das #bf #e ,qu9to ,cal5das #bf #d ,qu>to ,cal5das #bg #d ,qu>to ,cal5das #bg #c ,t]tio ,cal5das #bh #c ,t]tio ,cal5das #bh #b ,pridie ,cal5das #bi #b ,pridie ,cal5das ---------------------------------------- -------------------------- ,c4--,,page #bj4 ,! city :]e ! great c\ncil 0 conv5$ 9 #cbe is n 9 ,france1 z "s h suppos$1 t be+ a m mod]n city ( ! same or?ography1 b pron\nc$ ,nees4 ,! city :i* is s frequ5tly ref]r$ to 9 ?is "w is 9 ,by?9ia1 "o ( ! prov9ces ( ,asia ,m9or1 situat$ ab\t #ed miles s\!a/ ( ,con/ant9ople1 ( ! same or?ography z ! =m]1 b pron\nc$ ,ni'ce1 & 0 s nam$ by ,lysima*us1 a ,greek g5]al1 ab\t #cjj ye>s be=e ,*ri/1 9 honor ( 8 wife ,nicea4 ,d4--,,page #bc4 ,betwe5 ! #bc;d & #bd? ( ,febru>y1 #df ye>s be=e ,*ri/1 !re 0 int]calat$ a mon? ( #bc days accord+ to an e/abli%$ me?od1 b /ill ! civil ye> 0 9 advance ( ! sol> ye> by #fg days2 s t :5 ! ,e>? 9 h] annual revolutions %\ld arrive to t po9t ( ! ecliptic m>k$ ! #bb;d ( ,octob]1 x w\ld be ! #a/ day ( ,janu>y 9 ! ,roman ye>4 ,caes> & 8 a/ronom]s1 kn[+ ?is fact & fix+ on ! #a/ day ( ,janu>y1 #de ye>s be=e ,*ri/ & #gji f ! f\ndation ( ,rome1 = ! re=m$ cal5d> to take effect1 7 "u ! necessity ( int]calat+ two mon?s1 toge!r consi/+ ( #fg days4 ,n[1 z ! civil ye> w\ld end on ! #bb;d ( ,octob]1 true or sol> "t1 x w\ld be reckon$ 9 ! old cal5d> ! #a/ day ( ,janu>y2 s !y let ! old cal5d> come to a /& :ile ! ,e>? p]=ms #fg diurnal revolutions1 & !reby re/or$ ! concurr5ce ( ! sol> & ! civil ye>4 ,z an illu/ration1 let u suppose t 9 a c]ta9 %op :]e hangs a regulator are two clocks to be regulat$4 ,bo? are set ) ! regulator at #h a4 m4 to see h[ !y w run = t5 consecutive h\rs4 ,x 0 f\nd t :5 x 0 #f p4 m41 by ! fir/ clock1 x 0 #e3ej by ! regulator1 ! clock hav+ ga9$ "o m9ute e h\r4 ,to rectify ?is discrepancy we mu/ int]calate #aj m9utes by /opp+ ! clock until x is #f by ! regulator4 ,by ?is means ! co9cid5ce is re/or$1 & ! "t lo/ 9 ! prec$+ h\rs is n[ reckon$ 9 ?is la/ h\r1 mak+ x to consi/ ( #gj m9utes4 ,by ?is x may be se5 h[ ,caes> re=m$ ! ,roman cal5d>4 ,! ,roman ye> 0 too %ort1 by reason ( :i* ! cal5d> 0 ?r[n into confusion1 be+ #ij days 9 advance ( ! true "t1 s t ,decemb]1 ,janu>y & ,febru>y took ! place 9 ! seasons ( ,septemb]1 ,octob] & ,novemb]1 & ,septemb]1 ,octob] & ,novemb] ! place ( ,june1 ,july & ,augu/4 ,to make ! correction he mu/ /op ! old ,roman clock 7! cal5d>7 :ile ! ,e>? p]=ms #ij diurnal revolutions to re/ore ! concurr5ce ( ! sol> & ! civil ye>1 mak+ ! ye> #df ,b4 ,c4 to consi/ ( #dde days4 ,x 0 also f\nd t :5 x 0 #f p4 m41 by ! regulator1 x 0 only #e3ej by ! second clock1 x hav+ lo/ "o m9ute e h\r4 ,to rectify ?is discrepancy we mu/ suppress #aj m9utes1 call+ x #f p4 m41 turn+ ! h&s ( ! clock to co9cide ) ! regulator1 mak+ ! la/ h\r to consi/ ( only #ej m9utes1 too mu* "t hav+ be5 reckon$ 9 ! prec$+ h\rs4 ,x may be se5 by ?is illu/ration1 h[ ,gregory correct$ ! ,julian cal5d>1 ! ,julian ye> 0 too long1 consequ5tly beh9d true or sol> "t1 s t :5 ! correction 0 made 9 #aehb1 ! t5 days ga9$ _h to be suppress$ to re/ore ! co9cid5ce1 mak+ ! ye> to consi/ ( only #cee days4 ,z ! sol> ye> consi/s ( #cfe days & a fraction1 ,caes> int5d$ to reta9 ! concurr5ce ( ! sol> & ! civil ye> by int]calat+ a day e f\r ye>s2 b ?is made ! ye> a little too long1 by reason ( :i* x became necess>y1 9 #aehb1 to rectify ! error1 & by adopt+ ! ,gregorian rule1 ?ree int]calations are suppress$ e #djj ye>s2 s t by a s]ies ( int]calations & suppressions1 our cal5d> may be pres]v$ 9 its pres5t /ate ( p]fection4 ,e4--,,page #bc4 ,z ! day & ! civil ye> always comm5ce at ! same in/ance1 s !y mu/ end at ! same in/ance2 & z ! sol> ye> always ends ) a fraction1 n only ( a day1 b ( an h\r1 a m9ute & ev5 a second2 s !re is no rule ( int]calation by :i* ! sol> & ! civil ye> c be made to co9cide exactly4 ,b ! discrepancy is only a few h\rs 9 a hundr$ ye>s1 & t is s correct$ by ! ,gregorian rule ( int]calation t x w\ld am\nt to a little m ?an a day 9 #d1jjj ye>s2 & by ! improv$ me?od less ?an a day 9 #ajj1jjj ye>s4 ,f4--,,page #bf4 ,x has be5 /at$ t by adopt+ ! ,julian rule ( int]calation1 "t 0 ga9$2 x has also be5 /at$ t by ! same rule "t 0 lo/4 ,n[ bo? are true4 ,"t is ga9$ 9 t !re is too mu* "t 9 a giv5 ye>1 9 o!r words1 ! ye> is too long2 b :at is ga9$ 9 a giv5 ye> is lo/ to ! foll[+ ye>4 ,z an illu/ration let u take ! case ( ! suppos$ sol> ye> ( #cfe days1 & ! civil ye> ( #cff4 ,! civil ye> w\ld ga9 "o day e ye>1 or be too long by "o day2 b ! "o day ga9$ is lo/ to ! foll[+ ye>s1 & if cont9u$ #ca ye>s1 :5 ! ,e>? is 9 t "p ( its orbit m>k$ ! #a/ day ( ,janu>y #cb1 ! civil ye> w\ld reckon ! #a/ day ( ,decemb] #ca2 s t 9 ! ?irty-"o ye>s w\ld reckon ?irty-"o days too mu*1 & be=e ! civil ye> is complet$1 ! ,e>? w h pass$ on 9 its orbit to a po9t m>k$ ! #a/ day ( ,febru>y4 ,n[ to re=m su* a cal5d>1 we w\ld h to suppress or drop ! ?irty-"o days1 by call+ ! #a/ day ( ,decemb] ! #a/ day ( ,janu>y1 & ?us ! mon? ( ,decemb] w\ld disappe> f ! cal5d> 9 ! ye> #ca1 mak+ a ye> ( only elev5 mon?s1 consi/+ ( #ccd days4 ,if ?is me?od be cont9u$ #ib ye>s1 !re w\ld be ga9$ #ib days1 to ! loss ( #ib days 9 ! ye> #ib4 ,if ! cal5d> be n[ re=m$ by suppress+ #ib days1 call+ ! #a/ day ( ,octob]1 #ib1 ! #a/ day ( ,janu>y1 #ic1 !n ,octob]1 ,novemb] & ,decemb] w\ld disappe> f ! cal5d> 9 ! ye> #ib2 & if cont9u$ #cfe ye>s !re w\ld be cr[d$ into #cfd ye>s1 #cfd days too mu*2 ga9$ to ! #cfd ye>s to ! total loss ( ! ye> #cfe1 pass+ f #cfd to #cff2 #cfe disappe>+ f ! cal5d>4 ,g4--,,page #ej4 ,an era is a fix$ po9t ( "t f :i* a s]ies ( ye>s is reckon$4 ,among ! nations ( ! ,e>? !re are no less ?an tw5ty-five diff]5t eras2 b ! mo/ ( !m are n ( en\gh importance to be m5tion$ "h4 ,att5tion is p>ticul>ly call$ to ! ,roman era :i* comm5c$ ) ! build+ ( ! city ( ,rome #gec ye>s be=e ,*ri/4 ,also ! ,mahometan era1 or ! era ( ! ,hegira1 employ$ 9 ,turkey1 ,p]sia & ,arabia1 :i* is dat$ f ! flight ( ,mahomet f ,mecca to ,m$9a1 :i* 0 ,?ursday night1 ! #ae? ( ,july1 ,a4 ,d41 #fbb1 & x comm5c$ on ,friday1 ! day foll[+4 ,b !re is a po9t f :i* all computation orig9ally comm5c$1 namely1 ! creation ( man4 ,su* an era is call$ ! ,mundane era4 ,n[ !re are diff]5t ,mundane eras--! common ,mundane era #d1jjd ,b4 ,c41 ! ,grecian ,mundane era #e1eih ,b4 ,c41 & ! ,jewi% ,mundane era #c1gfa ,b4 ,c4 ,all ^! comm5ce computation f ! same po9t1 b diff] 9 reg>d to ! "t :i* has elaps$ s9ce _! computation comm5c$4 ,god's p us$ ! ,mundane era1 until ! ,great ,creator appe>$ among u1 z "o ( u1 9 ! p]son ( our ,"l ,jesus ,*ri/1 to accompli% ! great "w ( r$emption2 !n ,8 "n 0 introduc$ z ! turn+ po9t ( ! ages1 ! />t+ po9t ( computation4 ,?is 0 done by ,dionysius ,exiguus 9 ! ye> ( our ,"l ab\t #edj1 kn[n at t "t z ! ,dionysian1 z well z ! ,*ri/ian era1 & 0 fir/ us$ 9 hi/orical works by ! v5]able ,b$e e>ly 9 ! eigh? c5tury4 ,x 0 a great ?\ght ( ! little monk 7:e!r s call$ f 8 humility or littl5ess ( /ature is unkn[n71 to view ,*ri/ z ! turn+ po9t ( ! ages1 & to introduce ?is view into *ronology4 ,all honor to him :o introduc$ x1 & to ! nations :i* h approv$1 = ?us honor+ ! ,great ,r$eem]4 ,dionysius probably did n "k1 nei!r is x n[ kn[n = a c]ta9ty ! ye> ( ,*ri/'s bir?1 b x is evid5t1 h[ev]1 f ! be/ au?orities1 t ! era comm5c$ at lea/ five ye>s too late1 & probably m4 ,h4--,,page #eg4 ,x is record$ t1 9 ! "t ( ,numa1 ! v]nal equ9ox fell on ! #be? ( ,m>*1 & t ,julius ,caes> re/or$ x to ! #be?1 :5 he re=m$ ! anci5t ,roman cal5d> 9 ! ye> #df ,b4 ,c4 ,x is also record$ t 9 less ?an #djj ye>s f t "t1 at ! meet+ ( ! ,c\ncil ( ,nice 9 #cbe1 x _h fall5 back to ! #ba/--f\r days 9 less ?an #djj ye>s4 ,n[ !re is an error some:]e1 = x is f\nd by actual computation t ! discrepancy betwe5 ! sol> & ! ,julian ye> is ab\t ?ree days 9 #djj ye>s4 ,x c]ta9ly is true t ! v]nal equ9ox fell on ! #ba/ 9 #cbe1 & 0 re/or$ to t place by ,gregory 9 #aehb2 s9ce :i* "t x has be5 made to fall on ! #ba/ by ! ,gregorian rule ( int]calation4 ,aga9 x is /at$ by ! same au?or t ! discrepancies 9 "t f ,caes> to ,gregory is ?irte5 days1 f ! ,c\ncil ( ,nice to ,gregory t5 days2 n[ #aj #d #ad4 ,:ile our au?or /ates x is ?irte5 days1 he also /ates x is f\rte5 days2 a discrepancy ( "o day4 ,! mi/ake evid5tly is 9 mak+ ! #be? in/ead ( ! #bd?1 ! date ( ! v]nal equ9ox 9 ! "t ( ,caes>1 consequ5tly a diff]5ce ( f\r days in/ead ( ?ree f ,caes> to ! ,c\ncil ( ,nice4 ,i4--,,page #ei4 ,! concurr5ce ( ! sol> & ! civil ye> 0 re/or$ by ,gregory 9 #aehb1 or #afjj is ! same 9 computation2 b ! discrepancy betwe5 civil & sol> "t is #aa m9utes & #aj4ch seconds e ye>1 :i* 9 #ajj ye>s w am\nt to #ah h\rs1 & #cg4c m9utes2 reckon$ 9 r\nd numb]s #ah h\rs1 & is repres5t$ on ! *>t1 h\rs beh9d "t #ah4 ,! int]cal>y day or #bd h\rs be+ suppress$ 9 #agjj1 causes ! civil ye> to be #f h\rs 9 advance ( ! sol>1 & is repres5t$ on ! *>t #f h\rs 9 advance4 ,n[ ?is discrepancy ( #ah h\rs = ! next #ajj ye>s1 w cause ! civil ye> 9 #ahjj to be #ab h\rs beh9d2 aga9 suppress+ ! int]calation x w be #ab h\rs 9 advance4 ,9 #aijj x w be #f h\rs beh9d1 b ! correction makes #ah h\rs 9 advance4 ,! #ah h\rs ga9$ ! next #ajj ye>s re/ores ! co9cid5ce 9 ! ye> #bjjj & s on1 ! sol> & ! civil ye> be+ made to co9cide v ne>ly e #djj ye>s4 ,f close exam9ation x w become evid5t t ! sol> & ! civil ye> co9cide twice e #djj ye>s1 ?\gh no acc\nt is made ( x 9 computation4 ,f #f h\rs 9 advance 9 #agjj1 ! civil ye> falls back to #ab h\rs beh9d ! sol> 9 #ahjj1 consequ5tly !y mu/ co9cide 9 #agcc4 ,aga9 f #ab h\rs 9 advance 9 #ahjj1 x falls back to #f h\rs beh9d ! sol> 9 #aijj1 consequ5tly !y mu/ co9cide aga9 9 #ahfg4 ,discrepancy betwe5 ,julian & sol> "t 9--#a ye> is 7#cfe;d4 #f;h47 - 7#cfe;d4 #e;h4 #dhm4 #di4fbs47 7#aam4 #aj4chs47 #ajj ye>s is 7#aam4 #aj4chs47 x #ajj 7#ah;h4 #cg4c47 #djj 7#ah;h4 #cg4cm47 x #d 7#c;d4 #b;h4 #bi4bm47 #d1jjj 7#c;d4 #b;h4 #bi4bm47 x #aj 7#ca;d4 #j;h4 #ebm47 #ajj1jjj 7#ca;d4 #j;h4 #ebm47 x #be 7#ggc;d4 #ba;h4 #djm47 ,discrepancy betwe5 ,gregorian & sol> "t 9-- #a ye> is 4#cgcm4 #ajj ye>s is 4#cgcm4 x #ajj #cg4cm4 #djj ye>s #cg4cm4 x #d #b;h4 #bi4bm4 #d1jjj 7#b;h4 #bi4bm47 x #aj #a;d4 #j;h4 #ebm4 #ajj1jjj 7#a;d4 #j;h4 #ebm47 x #be #be;d4 #ba;h4 #djm4 ,discrepancy betwe5 correct$ ,gregorian & sol> "t 9-- #d1jjj ye>s is 7#a;d4 #j;h4 #ebm47 - #a day #ebm4 #ajj1jjj 7#ebm4 x #be7 #ba;h4 #djm4 ,j4--,,page #hi4 ,lilius1 au?or ( ! ,ext5d$ ,table ( ,epacts1 says1 :5 ! full moon falls on ! #aj? ( ,m>*1 ! foll[+ moon1 :i* happ5s #bi days lat]1 is ! pas*al moon1 mak+ ! #ah? ( ,april its late/ possible date4 ,=1 says he1 because ( ! d\ble epact t occurs on ! #d? & #e? ( ,april t lunation has only #bi days4 ,x may h be5 v conv5i5t = ,lilius1 9 8 peculi> me?od ( det]m9+ ! date ( ! pas*al moon1 to give to t lunation only #bi days2 b nev]!less1 :5 he did s1 x 0 at ! exp5se ( accuracy1 = he makes a diff]5ce ( #ab days 9 ! date ( ! pas*al moon ( t ye>1 & ! ye> prec$+1 & only #aj days diff]5ce betwe5 t ye> & ! succe$+ ye>2 :]eas ! diff]5ce is uni=mly #aa days f ye> to ye> ?r\gh ! :ole cycle ( #ai ye>s4 ,by ref]r+ to ! table on ! #ic;d page1 x w be se5 t1 9 fix+ ! date ( ! pas*al moon1 six times 9 a cycle ( #ai ye>s ! full moon falls be=e ! #ba/ ( ,m>*1 & 9 e in/ance except ?is "o ! foll[+ moon is reckon$ by ,lilius #cj days lat]4 ,by ?is uni=m me?od ( det]m9+ ! date ( ! pas*al moon1 we make ! #ai? ( ,april in/ead ( ! #ah?1 its late/ possible date2 s x %\ld be borne 9 m9d t :5ev] ! #ai? ( ,april is ! date ( ! pas*al moon1 z indicat$ 9 ! tables comm5c+ ) ! #ic;d page1 t ,lilius1 & probably mo/1 if n all o!r au?ors1 h ! #ah?4 ,n[ x is admitt$ t not)/&+ ! cumb]some app>atus employ$ by ,lilius 9 8 calculations1 ! conditions ( ! problem are n always satisfi$1 nor is x possible t !y c be always satisfi$ by any simil> me?od ( proce$+4 ,we admit t none ( ^! calculations are p]fectly exact1 b ! sum ( ! sol> & lun> inequalities is comp5sat$ 9 ! :ole p]iod1 or corrections made at ! end ( c]ta9 p]iods1 n by int]rupt+ ! ord] ( a uni=m me?od dur+ ! cycle ( #ai ye>s4 ,n[ ! table ( epacts 0 introduc$ by ,lilius himself1 mak+ ! excess ( ! sol> ye> beyond ! lun>1 9 r\nd numb]s #aa days4 ,!n :y int]rupt ?is ord] e #ai ye>s1 = a p]iod ( #aad ye>s2 t is f #aeif to #agaj1 by mak+ ! epact #ab days = "o ye>1 & ! foll[+ ye> only #aj8 ,aft] :i*1 f #agaj to #aijj1 a p]iod ( #aij ye>s1 accord+ to ,lilius' own calculations1 ! epact is uni=mly #aa days1 co9cid+ exactly ) ! calculations made 9 ?is "w4 ,!n aga9 aft] ! ye> #aijj1 he gives to t p>ticul> lunation1 9 e lun> cycle = a p]iod ( #cjd ye>s1 only #bi days2 & hav+ done s1 he is "u ! necessity ( giv+ only #bi days to ano!r lunation 9 ! same cycle1 & also to all ! cycles 9 ! p]iod to avoid ! absurdity ( mak+ ! pas*al moon fall twice on ! same day 9 ! c\rse ( a lun> cycle4 ,by ref]5ce to ! #aja/ page1 opposite ! ye> #aije1 x w be se5 t ! date ( ! pas*al moon is ! #ai? ( ,april4 ,lilius1 by giv+ to t lunation only #bi days1 makes its date ! #ah?2 & !n aga9 9 ! ye> #aiaf1 le/ he %\ld make ! pas*al moon fall twice on ! #ah? ( ,april 9 ! c\rse ( a lun> cycle1 7a ?+ :i* _c really occur7 he = ! fir/ "t 9 m ?an #djj ye>s1 gives only #bi days to a second lunation 9 ! same cycle & ( c\rse to all ! cycles 9 ! p]iod ( #cjd ye>s4 ,n[ ! epacts = a lun> cycle ( #ai ye>s are repres5t$ ?us3 #bf -- #j1 #aa1 #bb1 #c1 #ad1 #be1 #f1 #ag1 #bh1 #i1 #bj #bg -- #a1 #ab1 #bc1 #d1 #ae1 #bf1 #g1 #ah ,! numb] #bf plac$ ov] ! #be %[s ,lilius' fir/ error 9 giv+ to t lunation only #bi days4 ,he !reby makes a diff]5ce ( #ab days betwe5 ! epact #ad & #bf1 & only #aj betwe5 #bf & #f4 ,he n[ has two epacts ( ! same numb] #bf4 ,9 ord] to get out ( ! dilemma he makes t #bg1 by giv+ to ano!r lunation only #bi days4 ,k4--,,page #abb-c4 ,x w probably be notic$ t accord+ to ! %[+ 9 ! tables ! ecclesia/ical ye> conta9s only #cfd days4 ,! reason = ?is is1 t ,adv5t ,sunday1 :i* is ! fir/ day ( ! ye>1 happ5s "o day e>li] e ye> until x occurs on ! #bg? ( ,novemb]1 its e>lie/ possible date2 !n ! fir/ ,sunday aft] ! #bf? ( ,novemb]1 :i* is ,adv5t ,sunday1 falls on ! #c;d ( ,decemb]1 its late/ possible date1 s t ! ye> beg9s six days lat]1 mak+ a ye> ( #cga days4 ,!n !re is ! loss ( a day e ye> until ,adv5t ,sunday aga9 falls on ! #bg? ( ,novemb] & s on4 ,h5ce1 did ! civil ye> always consi/ ( #cfe days1 !n ! ecclesia/ical ye> w\ld always conta9 ei!r #cfd or #cga days4 ,b z e f\r? ye> conta9s #cff days1 ?is ord] is s int]rupt$ t sometimes ! fir/ ,sunday falls on ! #b;d in/ead ( ! #c;d ( ,decemb]2 s t ! ye> beg9s only five days lat]1 mak+ a ye> ( only #cgj days4 ,h5ce ! ecclesia/ical ye> may consi/ ( ei!r #cfd1 #cgj or #cga days4 ,b five times out ( six x w conta9 only #cfd days4 ,l4--,,page #hc4 ,b :y did ! ,pope1 9 correct+ ! ,julian cal5d> 9 #aehb1 n correct ! :ole error ( ?irte5 days8 ,:y did he leave ! ?ree days uncorrect$8 ,?is "q has be5 ask$ an hundr$ times1 b a correct answ] has nev] yet be5 giv54 ,"s say t ! ,pope did accord+ to 8 be/ ability1 & w\ld make u believe t nei!r he nor 8 a/ronom]s knew :at ! error 04 ,?is is n true1 = hi/ory records ! fact ( ! error1 & j :at t error 04 ,he simply did n want to correct ! ?ree days1 & = good reasons1 :i* we %all endeavor to %[2 reasons :i* e *ur*man ought to "k4 ,:5 ,caes> =m$ 8 cal5d>1 #df ,b4 ,c41 ! v]nal equ9ox fell on ! #bd? ( ,m>*4 ,at ! meet+ ( ! ,c\ncil ( ,nice1 9 #cbe1 x _h fall5 back to ! #ba/1 ! error be+ ?ree days 9 ab\t #djj ye>s4 ,n[ x %\ld be borne 9 m9d t ! ,julian cal5d> 0 ! only "o 9 use at t "t1 & = ! next #abeg ye>s1 :5 9 #aehb1 x 0 correct$ by ,pope ,gregory ,,xiii4 ,ea/]1 & all ! movable fea/s1 _h be5 unsettl$ dur+ ! #abeg ye>s int]v5+1 f ! ,c\ncil ( ,nice to ,gregory1 on acc\nt ( ! errors ( ! ,julian cal5d>4 ,! ,ea/] "q _h be5 ! cause ( a good deal ( discussion betwe5 ! ,ea/]n & ,we/]n *ur*es dur+ ! second & ?ird c5turies1 z !y c\ld n agree on ! day ( ! week on :i* t ev5t %\ld be celebrat$4 ,! ,we/]n *ur*es obs]v$ ! ne>e/ ,sunday to ! full moon ( ,nisan4 ,! ,asiatics1 on ! o!r h&1 adopt$ ! #ad? ( ,nisan ^u :i* to commemorate ! crucifixion1 & obs]v$ ! fe/ival ( ,ea/] on ! ?ird day foll[+1 ^u :atev] day ( ! week t might fall4 ,f9ally1 ! ,c\ncil ( ,nice 0 conv5$1 & ! matt] came be=e t c\ncil1 & a reconciliation 0 accompli%$4 ,x 0 !n & !re agre$ by ! two p>ties t ,ea/] %\ld be celebrat$ on ! fir/ ,sunday aft] ! full moon t falls ^u or next foll[+ ! day ( ! v]nal equ9ox1 & t ! #ba/ ( ,m>* %\ld be acc\nt$ ! day ( ! v]nal equ9ox4 ,x has already be5 %[n t ! error 9 ! ,julian cal5d> is ?ree days 9 #djj ye>s2 s t 9 #djj ye>s f ! ,c\ncil ( ,nice ! v]nal equ9ox _h fall5 back to ! #ah? ( ,m>*2 9 #hjj ye>s x _h fall5 back to ! #ae?2 9 #abeg ye>s1 t is 9 #aehb1 x fell on ! #aa?4 ,/ill ! #ba/ ( ,m>*1 by ! only cal5d> 9 use at t "t1 0 acc\nt$ ! date ( ! v]nal equ9ox1 by :i* date ,ea/] 0 det]m9$1 s t1 9 #aehb1 :5 x 0 ! #ba/ by ! cal5d>1 ! correct date 0 ! #ca/4 ,h5ce1 ! error _h be5 increas+ at ! rate ( ?ree days e #djj ye>s until 9 #aehb x am\nt$ to t5 days4 ,aga9 x %\ld be borne 9 m9d t ! ,pope 0 a *ur*man & wi%$ to abide by ! decision ( t c\ncil 9 celebrat+ ! fe/ival ( ,ea/]1 s he drops ! t5 days & re/ores ! v]nal equ9ox to ! #ba/ ( ,m>*1 its date at ! meet+ ( ! ,c\ncil ( ,nice 9 #cbe1 ! date by :i* ,ea/] day 0 det]m9$4 ,he n only made ! correction1 b he s re=m$ ! cal5d> t ! sol> & ! civil ye> are n[ made to co9cide v ne>ly4 ,_h he dropp$ ! ?irte5 days1 ! v]nal equ9ox w\ld h be5 re/or$ to ! #bd? ( ,m>*1 its date 9 ! "t ( ,caes>1 & ! #bd? w\ld /ill be its date4 ,b ! ,c\ncil ( ,nice decid$ t ! #ba/ %\ld be ! date by :i* ,ea/] day %\ld be det]m9$4 ,h5ce ! reason = dropp+ ! t5 days in/ead ( ! ?irte5 is evid5t2 & x is also evid5t t ! ,pope act$ und]/&+ly :5 he made ! correction 9 #aehb4 ,,errata4 ,on #ea/ page1 n9? l9e f ! bottom ( ! page1 in/ead ( #adec _/ #dc #fc1 %\ld be #adec _/ #d #cfc4 ,on #gf? page1 twelf? l9e f ! top ( ! page1 #cef %\ld be #cfe4 ,,! ,,columbus ,,celebration4 ,,! ,,wellsboro ,,man ,,:o ,,br\ght ,,ab\t ,,! ,,*ange ,,9 ,,! ,,date4 ,/ate ,sup]9t5d5t ,d4 ,j4 ,wall]1 9 ! ,s*ool ,j\rnal4 ,:o br\ght ab\t ! *ange 9 ! date8 ,x 0 d[n 9 ! books z ,octob] #ab?4 ,! ,committee ( ! ,national ,educational ,association issu$ circul>s to ! c\ntry to obs]ve t day4 ,congress solemnly resolv$ t t day %\ld be celebrat$ ?r\gh\t ! l&4 ,! ,commission]s ( ! ,_w's ,fair fix$ ^u ,octob] #ab1 z d$ication-day1 & s5t out invitations to ! ex]cises4 ,sudd5ly !re 0 a *ange4 ,h]ald$ by no newspap] discussion1 prec$$ by no exhau/ive treatise1 )\t any au?oritative decree1 a *ange 0 made to ,octob] #ba4 ,! foll[+ facts are indisputable4 ,an ag$ retir$ m9i/] 9 ! ,me?odi/ ,episcopal ,*ur*1 liv+ 9 ,wellsboro1 ,tioga ,c\nty1 ,pa41 au?or ( a little book entitl$ ,our ,cal5d>1 ,rev4 ,george ,ni*ols ,pack]1 saw ! error4 ,he possess$ ! confid5ce ( ,judge ,h5ry ,w4 ,williams1 ( ! ,supreme ,c\rt ( ,p5nsylvania4 ,aft] lay+ ! facts be=e him1 he secur$ ?r\gh him ! approval by ! sev]al ,ju/ices compos+ t body1 ( an ef=t to *ange to ! prop] date1 ,octob] #ba/4 ,equipp$ ) ?is approval1 he secur$ ! endorsem5t ( 8 project by ,gov]nor ,pattison & "s ( ! heads ( ! ,executive dep>tm5ts at ,h>risburg4 ,he !n w5t to ,wa%+ton1 ga9$ an audi5ce ) ! ,presid5t1 laid ! subject be=e ! memb] ( ,congress f 8 di/rict1 & w5t be=e ! ,congressional ,committee4 ,! evid5ce 9 support ( ! proposition 0 s pres5t$ t x c\ld n be successfully disput$4 ,congressman ,w4 ,a4 ,/one skillfully enli/$ influ5tial collegiates 9 an ef=t to correct ! error already widely spread4 ,! correction by ! ,national ,legislature 0 9 "t to h its influ5ce ^u ,presid5t ,h>rison1 :o nam$ ,octob] #ba 9 8 proclamation1 z ! day to be obs]v$1 & ,bo/on & ,*icago fell into l9e4 ,all honor to ,rev4 ,george ,ni*ols ,pack]1 ( ,wellsboro1 ,tioga ,c\nty1 ,p5nsylvania4 ,transcrib]'s ,notes3 ,passages 9 italics are indicat$ by italics4 ,punctuation has be5 correct$ )\t note4 ,corrections not$ 9 ! ,errata section h be5 appli$ to ! text4 ,! foll[+ mispr9ts h be5 correct$3 aad correct$ to & 7page #h7 leap-ye> correct$ to leap-ye>s 7page #de7 miss+ ! add$ 7page #de7 #aiic correct$ to #agic 7page #fc7 co-incide /&>diz$ to co9cide 7page #ga7 ,caes> /&>diz$ to ,caes> 7page #ga7 conseq5tly correct$ to consequ5tly 7page #gd7 #agcf correct$ to #agcg 7page #if7 c\nt5ace correct$ to c\nt5ance 7page #aad7 ,o!r ?an ! corrections li/$ above1 inconsi/5cies 9 spell+ & hyph5ation h be5 reta9$ f ! orig9al4 ,on page #cg1 #c #djj is pres5t$ ) a space z 9 ! orig9al text4