{"text_format":"3","workbook":"xlsx","n_sheets":14,"sheets":["Setup","NE","NS","SE","SS","NE_Cycles","NS_Cycles","SE_Cycles","SS_Cycles","NE_Data","NS_Data","SE_Data","SS_Data","SOLEX"],"not_rendered":{"charts":8,"macros":1,"defined_names":7},"unopened":[{"sheet":"NE","index":1,"reason":"not_a_worksheet"},{"sheet":"NS","index":2,"reason":"not_a_worksheet"},{"sheet":"SE","index":3,"reason":"not_a_worksheet"},{"sheet":"SS","index":4,"reason":"not_a_worksheet"}],"read":"whole","date_system":"1900"}

{"sheet":"Setup","index":0,"n_rows":36,"n_cols":8,"rows_kept":36}
["Solar Calendar Drift Calculator and Graphing Spreadsheet"]
["version 2.04(23), revised 2022 Jul 11"]
[]
["by Dr. Irv Bromberg, University of Toronto, Canada"]
["http://individual.utoronto.ca/kalendis/leap/"]
[]
["Shift Step Size: ",1000,"years (will be rounded to the nearest 100-year multiple, not less than 100)"]
["Delta T Multiplier: ",1,"1=normal, 0 to <1 = less Earth rotation slowing, >1 to 2 = more Earth rotation slowing"]
[]
["Reference (Epoch) Years",null,"(taken as the epoch of plotted leap cycles, rounded to the nearest 100-year multiple)"]
["Northward Equinox: ",0,{"$f":"\"mean equinox will be taken as zero drift at year \"&100*ROUND(NE_RefYear/100,0)","v":"mean equinox will be taken as zero drift at year 0"}]
["North Solstice: ",2000,{"$f":"\"mean solstice will be taken as zero drift at year \"&100*ROUND(NS_RefYear/100,0)","v":"mean solstice will be taken as zero drift at year 2000"}]
["Southward Equinox: ",1800,{"$f":"\"mean equinox will be taken as zero drift at year \"&100*ROUND(SE_RefYear/100,0)","v":"mean equinox will be taken as zero drift at year 1800"}]
["South Solstice: ",1000,{"$f":"\"mean solstice will be taken as zero drift at year \"&100*ROUND(SS_RefYear/100,0)","v":"mean solstice will be taken as zero drift at year 1000"}]
[]
[]
[]
["Worksheet ","Description",{"$nulls":4},"Worksheet ","Description"]
["Setup ","This worksheet, for setup and control.",{"$nulls":4},"SOLEX ","Precalculated equinox and solstice moments."]
["NE ","Calendar drift chart for the northward equinox.",{"$nulls":4},"SE ","Calendar drift chart for the southward equinox."]
["NS ","Calendar drift chart for the north solstice.",{"$nulls":4},"SS ","Calendar drift chart for the south solstice."]
["NE_Cycles ","Leap cycles evaluated for the northward equinox.",{"$nulls":4},"SE_Cycles ","Leap cycles evaluated for the southward equinox."]
["NE_Data ","Data generated for NE chart.",{"$nulls":4},"SE_Data ","Data generated for SE chart."]
["NS_Cycles ","Leap cycles evaluated for the north solstice.",{"$nulls":4},"SS_Cycles ","Leap cycles evaluated for the south solstice."]
["NS_Data ","Data generated for NS chart.",{"$nulls":4},"SS_Data ","Data generated for SS chart."]
[]
[null,"(Don't rename any sheets, the macros expect them to have the names as assigned.)"]
[]
["Negative drift implies equinoxes or solstices advancing to earlier mean dates in calendar year."]
["If a leap cycle is not wanted then delete its row from the list (don't leave a blank row), and delete its series from its chart."]
["If an additional leap cycle is wanted then insert it in the list (keep the list sorted descending by cycle mean year)"]
["and add a series for it to the appropriate chart, pointing to where the new column of data is (or will go)."]
["Linear Approximation leap rules (LANEY, LANSY, LASEY, LASSY) are not listed with the fixed arithmetic cycles, they are built-in."]
[]
["If desired, change the chart y-axes and x-axes to expand or contract the range displayed."]
["There is no point is making the x-axes wider than the limits of the mean astronomical polynomials."]

{"sheet":"NE_Cycles","index":5,"n_rows":18,"n_cols":6,"rows_kept":18}
["Description","Leap Days Per Cycle","Years Per Cycle","Decimal Fraction","365 days +","Comments"]
["Julian",1,4,{"$f":"B2/C2","v":0.25},{"$f":"D2","v":"06:00:00"},"Way too long, but good for Sirius heliacal rising year."]
["Hebrew",24311,98496,{"$f":"B3/C3","v":0.24682220597790774},{"$f":"D3","v":"05:55:25.439"},"Exact fraction = molad interval x 235 months / 19 years - 365 days"]
["Gregorian",97,400,{"$f":"B4/C4","v":0.2425},"05:49:12"]
["Dee",8,33,0.24242424242424243,"05:49:05.455"]
["100 Saros",437,1803,0.24237382140876318,"05:49:01.098","4 x 25-Saros Lunar Cycle of 29+2958/5575 days"]
[null,127,524,0.24236641221374045,"05:49:00.458","http://individual.utoronto.ca/kalendis/symmetry.htm"]
[null,198,817,0.2423500611995104,"05:48:59.045"]
["Symmetry454",71,293,0.24232081911262798,"05:48:56.519","http://individual.utoronto.ca/kalendis/symmetry.htm"]
[null,228,941,0.24229543039319873,"05:48:54.325"]
[null,157,648,0.24228395061728394,"05:48:53.333"]
[null,86,355,0.24225352112676057,"05:48:50.704"]
[null,187,772,0.2422279792746114,"05:48:48.497"]
["Revised Julian",218,900,0.24222222222222223,"05:48:48","Greek and Sirian Orthodox Churches, reduces to 109/450"]
["Brij Vij",202,834,0.2422062350119904,"05:48:46.619","Reduces to 101/417"]
["Bonavian",{"$f":"7*31","v":217},{"$f":"7*128","v":896},0.2421875,"05:48:45","Reduces to 31/128"]
[null,206,851,0.24206815511163338,"05:48:34.689"]
["Josef Šuráň",15,62,0.24193548387096775,"05:48:23.226","Designed for \"Tropical Year\", but best for southward equinoctial year"]

{"sheet":"NS_Cycles","index":6,"n_rows":17,"n_cols":6,"rows_kept":17}
["Description","Leap Days Per Cycle","Years Per Cycle","Decimal Fraction","365 days +","Comments"]
[null,206,851,{"$f":"B2/C2","v":0.24206815511163338},{"$f":"D2","v":"05:48:34.689"}]
["Josef Šuráň",15,62,0.24193548387096775,"05:48:23.226","Designed for \"Tropical Year\", but best for southward equinoctial year"]
[null,22,91,0.24175824175824176,"05:48:07.912"]
[null,124,513,0.24171539961013644,"05:48:04.211"]
[null,109,451,0.24168514412416853,"05:48:01.596"]
[null,29,120,0.24166666666666667,"05:48:00"]
["Symmetry454",94,389,0.2416452442159383,"05:47:58.149","http://individual.utoronto.ca/kalendis/symmetry.htm"]
[null,173,716,0.24162011173184358,"05:47:55.978"]
[null,79,327,0.2415902140672783,"05:47:53.394"]
[null,222,919,0.24156692056583243,"05:47:51.382"]
[null,143,592,0.24155405405405406,"05:47:50.270"]
[null,207,857,0.24154025670945156,"05:47:49.078"]
[null,64,265,0.24150943396226415,"05:47:46.415"]
[null,241,998,0.24148296593186372,"05:47:44.128"]
[null,177,733,0.24147339699863574,"05:47:43.302"]
[null,113,468,0.24145299145299146,"05:47:41.538"]

{"sheet":"SE_Cycles","index":7,"n_rows":17,"n_cols":6,"rows_kept":17}
["Description","Leap Days Per Cycle","Years Per Cycle","Decimal Fraction","365 days +","Comments"]
["Revised Julian",218,900,{"$f":"B2/C2","v":0.24222222222222223},{"$f":"D2","v":"05:48:48"},"Greek and Sirian Orthodox Churches, reduces to 109/450"]
["Brij Vij",202,834,0.2422062350119904,"05:48:46.619","Reduces to 101/417"]
["Bonavian",{"$f":"7*31","v":217},{"$f":"7*128","v":896},0.2421875,"05:48:45","Reduces to 31/128"]
[null,206,851,0.24206815511163338,"05:48:34.689"]
[null,38,157,0.24203821656050956,"05:48:32.102"]
[null,129,533,0.24202626641651032,"05:48:31.069"]
[null,91,376,0.24202127659574468,"05:48:30.638"]
[null,53,219,0.2420091324200913,"05:48:29.589"]
[null,121,500,0.242,"05:48:28.800"]
[null,68,281,0.24199288256227758,"05:48:28.185"]
[null,83,343,0.24198250728862974,"05:48:27.289"]
[null,98,405,0.2419753086419753,"05:48:26.667"]
[null,113,467,0.24197002141327623,"05:48:26.210"]
[null,128,529,0.24196597353497165,"05:48:25.860"]
[null,173,715,0.24195804195804196,"05:48:25.175"]
["Josef Šuráň",15,62,0.24193548387096775,"05:48:23.226","Designed for \"Tropical Year\", but best for southward equinoctial year"]

{"sheet":"SS_Cycles","index":8,"n_rows":17,"n_cols":6,"rows_kept":17}
["Description","Leap Days Per Cycle","Years Per Cycle","Decimal Fraction","365 days +","Comments"]
[null,67,276,{"$f":"B2/C2","v":0.2427536231884058},{"$f":"D2","v":"05:49:33.913"}]
[null,242,997,0.242728184553661,"05:49:31.715"]
[null,25,103,0.24271844660194175,"05:49:30.874"]
[null,108,445,0.24269662921348314,"05:49:28.989"]
[null,149,614,0.24267100977198697,"05:49:26.775"]
[null,190,783,0.24265644955300128,"05:49:25.517"]
[null,33,136,0.2426470588235294,"05:49:24.706"]
[null,41,169,0.24260355029585798,"05:49:20.947"]
[null,138,569,0.24253075571177504,"05:49:14.657"]
["Gregorian",97,400,0.2425,"05:49:12","Well suited to the present era south solstitial year."]
["Dee",8,33,0.24242424242424243,"05:49:05.455"]
[null,157,648,0.24228395061728394,"05:48:53.333"]
[null,86,355,0.24225352112676057,"05:48:50.704"]
[null,187,772,0.2422279792746114,"05:48:48.497"]
[null,218,900,0.24222222222222223,"05:48:48"]
[null,202,834,{"$f":"B17/C17","v":0.2422062350119904},"05:48:46.619"]

{"sheet":"NE_Data","index":9,"n_rows":34,"n_cols":19,"rows_kept":34}
["Year","1/4 Julian","24311/98496 Hebrew","97/400 Gregorian","8/33 Dee","437/1803 100 Saros","127/524","198/817","71/293 Symmetry454","228/941","157/648","86/355","187/772","218/900 Revised Julian","202/834 Brij Vij","217/896 Bonavian","206/851","15/62 Josef Šuráň","LANEY"]
[-4000,31.0652670570416,18.3540909686726,1.06526705704164,0.762236754011383,0.560552692094461,0.530915912003366,{"v":0.465511855083378,"d":"4.66E-01"},{"v":0.348543507553586,"d":"3.49E-01"},{"v":0.246988629836551,"d":"2.47E-01"},{"v":0.201069526177434,"d":"2.01E-01"},{"v":0.079351564083936,"d":"7.94E-02"},{"v":-0.0228158445127065,"d":"-2.28E-02"},{"v":-0.0458440540694482,"d":"-4.58E-02"},{"v":-0.109792894996872,"d":"-1.10E-01"},{"v":-0.184732942958362,"d":"-1.85E-01"},-0.662112496424925,-1.19279745908739,{"v":0.348543507745489,"d":"3.49E-01"}]
[-3500,27.2061469088076,16.0838678314847,0.956146908807568,{"v":0.690995393656067,"d":"6.91E-01"},{"v":0.514521839478675,"d":"5.15E-01"},{"v":0.48858965689908,"d":"4.89E-01"},{"v":0.431361107094062,"d":"4.31E-01"},{"v":0.329013803005523,"d":"3.29E-01"},{"v":0.240153285003089,"d":"2.40E-01"},{"v":0.199974069301334,"d":"2.00E-01"},{"v":0.0934708524695225,"d":"9.35E-02"},{"v":0.00407436994748878,"d":"4.07E-03"},{"v":-0.0160753134146034,"d":"-1.61E-02"},{"v":-0.0720305492260422,"d":"-7.20E-02"},{"v":-0.137603091192432,"d":"-1.38E-01"},{"v":-0.55531020047556,"d":"-5.55E-01"},-1.01965954280536,{"v":0.329013803042471,"d":"3.29E-01"}]
[-3000,23.3208353674272,13.7874533011504,0.820835367427208,0.59356264015446,0.442299593716712,0.420072008648503,{"v":0.371018965958456,"d":"3.71E-01"},{"v":0.283292705311169,"d":"2.83E-01"},{"v":0.207126547023449,"d":"2.07E-01"},{"v":0.172687219279055,"d":"1.73E-01"},{"v":0.0813987477089313,"d":"8.14E-02"},{"v":0.00477319126139264,"d":"4.77E-03"},{"v":-0.0124979659061637,"d":"-1.25E-02"},{"v":-0.0604595966016177,"d":"-6.05E-02"},{"v":-0.116664632572792,"d":"-1.17E-01"},-0.474699297672714,-0.872713019669504,{"v":0.283292705425993,"d":"2.83E-01"}]
[-2500,19.4372259586817,11.492740903451,0.687225958681665,{"v":0.497832019287785,"d":"4.98E-01"},{"v":0.371779480589566,"d":"3.72E-01"},{"v":0.353256493032745,"d":"3.53E-01"},{"v":0.312378957457668,"d":"3.12E-01"},{"v":0.239273740251633,"d":"2.39E-01"},{"v":0.175801941678515,"d":"1.76E-01"},{"v":0.147102501891482,"d":"1.47E-01"},{"v":0.071028775583045,"d":"7.10E-02"},{"v":0.00717414521011506,"d":"7.17E-03"},{"v":-0.00721848576279172,"d":"-7.22E-03"},{"v":-0.0471865113423746,"d":"-4.72E-02"},{"v":-0.0940240413183346,"d":"-9.40E-02"},{"v":-0.392386262234936,"d":"-3.92E-01"},-0.724064363898947,{"v":0.239273740211502,"d":"2.39E-01"}]
[-2000,15.5383960638428,9.1828080196583,0.538396063842811,0.386880912327683,0.286038881369223,0.271220491323675,0.238518462863681,{"v":0.180034289098785,"d":"1.80E-01"},{"v":0.129256850240267,"d":"1.29E-01"},{"v":0.106297298410709,"d":"1.06E-01"},{"v":0.0454383173639599,"d":"4.54E-02"},{"v":-0.00564538693436134,"d":"-5.65E-03"},{"v":-0.0171594917127322,"d":"-1.72E-02"},{"v":-0.049133912176444,"d":"-4.91E-02"},{"v":-0.0866039361571893,"d":"-8.66E-02"},{"v":-0.32529371289047,"d":"-3.25E-01"},-0.590636194221702,{"v":0.180034289136529,"d":"1.80E-01"}]
[-1500,11.6514115998289,6.88472056669048,0.401411599828862,{"v":0.287775236192488,"d":"2.88E-01"},{"v":0.212143712973671,"d":"2.12E-01"},{"v":0.20102992043951,"d":"2.01E-01"},{"v":0.176503399094486,"d":"1.77E-01"},{"v":0.132640268770842,"d":"1.33E-01"},{"v":0.0945571896269257,"d":"9.46E-02"},{"v":0.0773375257547286,"d":"7.73E-02"},{"v":0.0316932899696667,"d":"3.17E-02"},{"v":-0.00661948825404579,"d":"-6.62E-03"},{"v":-0.0152550668377671,"d":"-1.53E-02"},{"v":-0.0392358821854941,"d":"-3.92E-02"},{"v":-0.0673384001711383,"d":"-6.73E-02"},{"v":-0.246355732721099,"d":"-2.46E-01"},-0.445362593719551,{"v":0.132640268886462,"d":"1.33E-01"}]
[-1000,7.7584051474696,4.58061112537735,0.258405147469603,0.182647571711982,0.132226556232808,0.124817361210035,0.108466346979981,{"v":0.0792242600975896,"d":"7.92E-02"},{"v":0.0538355406683877,"d":"5.38E-02"},{"v":0.0423557647535517,"d":"4.24E-02"},{"v":0.0119262742301771,"d":"1.19E-02"},{"v":-0.0136155779190403,"d":"-1.36E-02"},{"v":-0.0193726303082258,"d":"-1.94E-02"},{"v":-0.035359840539968,"d":"-3.54E-02"},{"v":-0.0540948525303975,"d":"-5.41E-02"},-0.173439740897038,-0.306110981562597,{"v":0.079224260058254,"d":"7.92E-02"}]
[-500,3.87621955841314,2.28732254736701,0.12621955841314,{"v":0.0883407705343302,"d":"8.83E-02"},{"v":0.0631302627947434,"d":"6.31E-02"},{"v":0.0594256652833565,"d":"5.94E-02"},{"v":0.0512501581683296,"d":"5.13E-02"},{"v":0.036629114727134,"d":"3.66E-02"},{"v":0.0239347550125331,"d":"2.39E-02"},{"v":0.0181948670551151,"d":"1.82E-02"},{"v":0.00298012179342777,"d":"2.98E-03"},{"v":-0.00979080428118095,"d":"-9.79E-03"},{"v":-0.0126693304757737,"d":"-1.27E-02"},{"v":-0.0206629355916448,"d":"-2.07E-02"},{"v":-0.0300304415868595,"d":"-3.00E-02"},{"v":-0.0897028857701798,"d":"-8.97E-02"},-0.156038506102959,{"v":0.0366291147656739,"d":"3.66E-02"}]
[0,0,0,0,{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},{"v":0,"d":"0.00E+00"},0,0,{"v":0,"d":"0.00E+00"}]
[500,-3.85490381729323,-2.26600680624711,{"v":-0.104903817293234,"d":"-1.05E-01"},{"v":-0.0670250294144239,"d":"-6.70E-02"},{"v":-0.0418145216748371,"d":"-4.18E-02"},{"v":-0.0381099241634502,"d":"-3.81E-02"},{"v":-0.0299344170484233,"d":"-2.99E-02"},{"v":-0.0153133736072277,"d":"-1.53E-02"},{"v":-0.00261901389262675,"d":"-2.62E-03"},{"v":0.00312087406479122,"d":"3.12E-03"},{"v":0.0183356193264785,"d":"1.83E-02"},{"v":0.0311065454010873,"d":"3.11E-02"},{"v":0.03398507159568,"d":"3.40E-02"},{"v":0.0419786767115511,"d":"4.20E-02"},{"v":0.0513461827067658,"d":"5.13E-02"},{"v":0.111018626890086,"d":"1.11E-01"},0.177354247222866,{"v":-0.0153133735293522,"d":"-1.53E-02"}]
[1000,-7.69677812338341,-4.51898410129115,{"v":-0.19677812338341,"d":"-1.97E-01"},{"v":-0.121020547625847,"d":"-1.21E-01"},{"v":-0.0705995321465878,"d":"-7.06E-02"},{"v":-0.0631903371238423,"d":"-6.32E-02"},{"v":-0.0468393228938169,"d":"-4.68E-02"},{"v":-0.0175972360113974,"d":"-1.76E-02"},{"v":0.0077914834178614,"d":"7.79E-03"},{"v":0.0192712593326405,"d":"1.93E-02"},{"v":0.0497007498560151,"d":"4.97E-02"},{"v":0.0752426020052042,"d":"7.52E-02"},{"v":0.0809996543943612,"d":"8.10E-02"},{"v":0.0969868646261887,"d":"9.70E-02"},{"v":0.11572187661659,"d":"1.16E-01"},{"v":0.235066764983202,"d":"2.35E-01"},0.367738005648846,{"v":-0.0175972359720618,"d":"-1.76E-02"}]
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{"sheet":"SOLEX","index":13,"n_rows":168,"n_cols":5,"rows_kept":168}
["Numerically integrated equinox and solstice moments"]
["as computed by SOLEX version 9.1"]
["Each moment is in Terrestrial Time (TT), in days and fraction of a day,"]
["relative to zero = midnight TT on January 1, 2001 AD (start of 3rd millennium)."]
["Don't modify this page!"]
[]
["Year","NE","NS","SE","SS"]
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