home *** CD-ROM | disk | FTP | other *** search
MacBinary | 1995-01-09 | 27.1 KB | [ ttro/ttxt]
open in: MacOS 8.1
extracted
|
Win98
extracted
|
DOS
extracted
view JSON data
|
view as text
This file was processed as: MacBinary
(archive/macBinary ).
You can browse this item here: Calendar System Facts Pt. 1
Confidence Program Detection Match Type Support
10%
dexvert
MacBinary (archive/macBinary)
fallback
Supported
1%
dexvert
Text File (text/txt)
fallback
Supported
100%
file
MacBinary II, Mon Jan 9 13:11:05 1995, modified Mon Jan 9 13:11:05 1995, creator SimpleText, type SimpleText read-only, 26220 bytes "Calendar System Facts Pt. 1" , at 0x66ec 1392 bytes resource
default (weak)
99%
file
data
default
74%
TrID
Mac SimpleText read-only (MacBinary)
default
25%
TrID
MacBinary 2
default (weak)
100%
siegfried
fmt/1762 MacBinary (II)
default
100%
lsar
MacBinary
default
id metadata key value macFileType [ ttro] macFileCreator [ ttxt]
hex view +--------+-------------------------+-------------------------+--------+--------+ |00000000| 00 1b 43 61 6c 65 6e 64 | 61 72 20 53 79 73 74 65 |..Calend|ar Syste| |00000010| 6d 20 46 61 63 74 73 20 | 50 74 2e 20 31 00 00 00 |m Facts |Pt. 1...| |00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........| |00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........| |00000040| 00 74 74 72 6f 74 74 78 | 74 00 00 00 00 00 00 00 |.ttrottx|t.......| |00000050| 00 00 00 00 00 66 6c 00 | 00 05 70 ab 37 2c b9 ab |.....fl.|..p.7,..| |00000060| 37 2c b9 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |7,......|........| |00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 de 31 00 00 |........|.....1..| |00000080| 42 61 73 69 63 20 41 73 | 74 72 6f 6e 6f 6d 69 63 |Basic As|tronomic| |00000090| 61 6c 20 44 61 74 61 0d | 0d 09 54 68 65 20 6c 65 |al Data.|..The le| |000000a0| 6e 67 74 68 20 6f 66 20 | 74 68 65 20 74 72 6f 70 |ngth of |the trop| |000000b0| 69 63 61 6c 20 79 65 61 | 72 20 3d 20 33 36 35 2e |ical yea|r = 365.| |000000c0| 32 34 32 31 39 39 20 64 | 61 79 73 20 69 6e 20 31 |242199 d|ays in 1| |000000d0| 39 30 30 2e 20 41 74 20 | 74 68 65 20 70 72 65 73 |900. At |the pres| |000000e0| 65 6e 74 20 74 69 6d 65 | 20 69 74 20 69 73 20 73 |ent time| it is s| |000000f0| 6c 6f 77 6c 79 20 67 65 | 74 74 69 6e 67 20 73 68 |lowly ge|tting sh| |00000100| 6f 72 74 65 72 2e 0d 0d | 09 54 68 65 20 6c 65 6e |orter...|.The len| |00000110| 67 74 68 20 6f 66 20 74 | 68 65 20 73 79 6e 6f 64 |gth of t|he synod| |00000120| 69 63 20 6d 6f 6e 74 68 | 20 3d 20 32 39 2e 35 33 |ic month| = 29.53| |00000130| 30 35 38 38 32 20 64 61 | 79 73 2e 20 41 74 20 74 |05882 da|ys. At t| |00000140| 68 65 20 70 72 65 73 65 | 6e 74 20 74 69 6d 65 20 |he prese|nt time | |00000150| 69 74 20 69 73 20 61 6c | 73 6f 20 67 65 74 74 69 |it is al|so getti| |00000160| 6e 67 20 73 68 6f 72 74 | 65 72 20 76 65 72 79 20 |ng short|er very | |00000170| 73 6c 6f 77 6c 79 2c 20 | 62 75 74 20 74 69 64 61 |slowly, |but tida| |00000180| 6c 20 65 66 66 65 63 74 | 73 20 77 69 6c 6c 20 63 |l effect|s will c| |00000190| 61 75 73 65 20 69 74 20 | 74 6f 20 67 72 6f 77 20 |ause it |to grow | |000001a0| 73 74 65 61 64 69 6c 79 | 20 6c 6f 6e 67 65 72 20 |steadily| longer | |000001b0| 69 6e 20 74 68 65 20 6c | 6f 6e 67 20 72 75 6e 2e |in the l|ong run.| |000001c0| 0d 0d 0d 4a 75 6c 69 61 | 6e 20 44 61 79 20 4e 75 |...Julia|n Day Nu| |000001d0| 6d 62 65 72 73 0d 0d 09 | 41 73 74 72 6f 6e 6f 6d |mbers...|Astronom| |000001e0| 65 72 73 20 6b 65 65 70 | 20 61 20 72 75 6e 6e 69 |ers keep| a runni| |000001f0| 6e 67 20 63 6f 75 6e 74 | 20 6f 66 20 64 61 79 73 |ng count| of days| |00000200| 20 77 68 69 63 68 20 62 | 65 67 61 6e 20 73 65 76 | which b|egan sev| |00000210| 65 72 61 6c 20 74 68 6f | 75 73 61 6e 64 20 79 65 |eral tho|usand ye| |00000220| 61 72 73 20 69 6e 20 74 | 68 65 20 70 61 73 74 2e |ars in t|he past.| |00000230| 20 54 68 69 73 20 72 75 | 6e 6e 69 6e 67 20 64 61 | This ru|nning da| |00000240| 79 20 63 6f 75 6e 74 20 | 69 73 20 69 6e 64 65 70 |y count |is indep| |00000250| 65 6e 64 65 6e 74 20 6f | 66 20 61 6c 6c 20 63 61 |endent o|f all ca| |00000260| 6c 65 6e 64 61 72 20 73 | 79 73 74 65 6d 73 2c 20 |lendar s|ystems, | |00000270| 61 6e 64 20 63 61 6e 20 | 74 68 65 72 65 66 6f 72 |and can |therefor| |00000280| 65 20 62 65 20 75 73 65 | 64 20 61 73 20 61 20 63 |e be use|d as a c| |00000290| 6f 6e 76 65 6e 69 65 6e | 74 20 77 61 79 20 74 6f |onvenien|t way to| |000002a0| 20 74 72 61 6e 73 66 6f | 72 6d 20 64 61 74 65 73 | transfo|rm dates| |000002b0| 20 66 72 6f 6d 20 6f 6e | 65 20 73 79 73 74 65 6d | from on|e system| |000002c0| 20 74 6f 20 61 6e 6f 74 | 68 65 72 2e 20 49 74 20 | to anot|her. It | |000002d0| 61 6c 73 6f 20 69 73 20 | 61 20 63 6f 6e 76 65 6e |also is |a conven| |000002e0| 69 65 6e 74 20 77 61 79 | 20 74 6f 20 64 65 66 69 |ient way| to defi| |000002f0| 6e 65 20 74 68 65 20 73 | 74 61 72 74 69 6e 67 20 |ne the s|tarting | |00000300| 70 6f 69 6e 74 73 20 28 | 66 69 72 73 74 20 64 61 |points (|first da| |00000310| 79 20 6f 66 20 74 68 65 | 20 66 69 72 73 74 20 6d |y of the| first m| |00000320| 6f 6e 74 68 20 6f 66 20 | 74 68 65 20 79 65 61 72 |onth of |the year| |00000330| 20 31 29 20 6f 66 20 63 | 61 6c 65 6e 64 61 72 20 | 1) of c|alendar | |00000340| 73 79 73 74 65 6d 73 2e | 20 42 79 20 63 6f 6e 76 |systems.| By conv| |00000350| 65 6e 74 69 6f 6e 2c 20 | 74 68 65 73 65 20 64 61 |ention, |these da| |00000360| 79 73 20 28 63 61 6c 6c | 65 64 20 4a 75 6c 69 61 |ys (call|ed Julia| |00000370| 6e 20 44 61 79 73 20 77 | 68 69 63 68 20 69 73 20 |n Days w|hich is | |00000380| 75 6e 66 6f 72 74 75 6e | 61 74 65 20 62 65 63 61 |unfortun|ate beca| |00000390| 75 73 65 20 74 68 65 79 | 20 6d 75 73 74 20 6e 6f |use they| must no| |000003a0| 74 20 62 65 20 63 6f 6e | 66 75 73 65 64 20 77 69 |t be con|fused wi| |000003b0| 74 68 20 74 68 65 20 4a | 75 6c 69 61 6e 20 43 61 |th the J|ulian Ca| |000003c0| 6c 65 6e 64 61 72 20 73 | 79 73 74 65 6d 29 20 62 |lendar s|ystem) b| |000003d0| 65 67 69 6e 20 61 74 20 | 6e 6f 6f 6e 2e 20 54 68 |egin at |noon. Th| |000003e0| 75 73 20 63 61 6c 65 6e | 64 61 72 20 64 61 79 73 |us calen|dar days| |000003f0| 2c 20 77 68 69 63 68 20 | 69 6e 20 74 68 65 20 47 |, which |in the G| |00000400| 72 65 67 6f 72 69 61 6e | 20 61 6e 64 20 72 65 6c |regorian| and rel| |00000410| 61 74 65 64 20 73 79 73 | 74 65 6d 73 20 62 65 67 |ated sys|tems beg| |00000420| 69 6e 20 61 74 20 6d 69 | 64 6e 69 67 68 74 2c 20 |in at mi|dnight, | |00000430| 75 73 75 61 6c 6c 79 20 | 68 61 76 65 20 74 68 65 |usually |have the| |00000440| 69 72 20 4a 75 6c 69 61 | 6e 20 44 61 79 20 6e 75 |ir Julia|n Day nu| |00000450| 6d 62 65 72 73 20 65 71 | 75 61 6c 20 74 6f 20 73 |mbers eq|ual to s| |00000460| 6f 6d 65 20 69 6e 74 65 | 67 65 72 20 70 6c 75 73 |ome inte|ger plus| |00000470| 20 30 2e 35 2e 20 47 69 | 76 65 6e 20 74 68 65 20 | 0.5. Gi|ven the | |00000480| 4a 75 6c 69 61 6e 20 44 | 61 79 20 6f 66 20 61 6e |Julian D|ay of an| |00000490| 79 20 63 61 6c 65 6e 64 | 61 72 20 64 61 74 65 2c |y calend|ar date,| |000004a0| 20 74 68 65 20 64 61 79 | 20 6f 66 20 74 68 65 20 | the day| of the | |000004b0| 77 65 65 6b 20 63 61 6e | 20 65 61 73 69 6c 79 20 |week can| easily | |000004c0| 62 65 20 63 6f 6d 70 75 | 74 65 64 20 73 69 6d 70 |be compu|ted simp| |000004d0| 6c 79 20 62 79 20 64 69 | 76 69 64 69 6e 67 20 62 |ly by di|viding b| |000004e0| 79 20 73 65 76 65 6e 20 | 61 6e 64 20 65 78 61 6d |y seven |and exam| |000004f0| 69 6e 69 6e 67 20 74 68 | 65 20 72 65 6d 61 69 6e |ining th|e remain| |00000500| 64 65 72 2e 0d 0d 09 54 | 68 65 20 7a 65 72 6f 20 |der....T|he zero | |00000510| 70 6f 69 6e 74 20 6f 66 | 20 74 68 65 20 4a 75 6c |point of| the Jul| |00000520| 69 61 6e 20 44 61 79 20 | 73 79 73 74 65 6d 20 6f |ian Day |system o| |00000530| 63 63 75 72 72 65 64 20 | 61 74 20 6e 6f 6f 6e 20 |ccurred |at noon | |00000540| 47 4d 54 20 6f 6e 20 4a | 61 6e 75 61 72 79 20 31 |GMT on J|anuary 1| |00000550| 2c 20 34 37 31 33 20 42 | 2e 43 2e 20 69 6e 20 74 |, 4713 B|.C. in t| |00000560| 68 65 20 4a 75 6c 69 61 | 6e 20 43 61 6c 65 6e 64 |he Julia|n Calend| |00000570| 61 72 2c 20 6f 72 20 4e | 6f 76 65 6d 62 65 72 20 |ar, or N|ovember | |00000580| 32 34 2c 20 34 37 31 34 | 20 42 2e 43 2e 20 69 6e |24, 4714| B.C. in| |00000590| 20 74 68 65 20 47 72 65 | 67 6f 72 69 61 6e 20 63 | the Gre|gorian c| |000005a0| 61 6c 65 6e 64 61 72 2e | 20 57 68 65 6e 20 61 73 |alendar.| When as| |000005b0| 74 72 6f 6e 6f 6d 65 72 | 73 20 75 73 65 20 74 68 |tronomer|s use th| |000005c0| 65 20 4a 75 6c 69 61 6e | 20 64 61 79 2c 20 74 68 |e Julian| day, th| |000005d0| 65 20 66 72 61 63 74 69 | 6f 6e 61 6c 20 70 61 72 |e fracti|onal par| |000005e0| 74 20 69 73 20 6d 65 61 | 6e 69 6e 67 66 75 6c 20 |t is mea|ningful | |000005f0| 61 6e 64 20 61 6c 6c 20 | 4a 75 6c 69 61 6e 20 44 |and all |Julian D| |00000600| 61 79 20 6e 75 6d 62 65 | 72 73 20 61 72 65 20 61 |ay numbe|rs are a| |00000610| 73 73 75 6d 65 64 20 74 | 6f 20 72 65 66 65 72 20 |ssumed t|o refer | |00000620| 74 6f 20 47 4d 54 20 28 | 6d 6f 72 65 20 74 65 63 |to GMT (|more tec| |00000630| 68 6e 69 63 61 6c 6c 79 | 2c 20 74 6f 20 61 20 71 |hnically|, to a q| |00000640| 75 61 6e 74 69 74 79 20 | 63 61 6c 6c 65 64 20 55 |uantity |called U| |00000650| 6e 69 76 65 72 73 61 6c | 20 54 69 6d 65 20 77 68 |niversal| Time wh| |00000660| 69 63 68 20 69 73 20 76 | 65 72 79 20 63 6c 6f 73 |ich is v|ery clos| |00000670| 65 20 74 6f 20 47 4d 54 | 29 2e 20 46 6f 72 20 63 |e to GMT|). For c| |00000680| 61 6c 65 6e 64 72 69 63 | 61 6c 20 70 75 72 70 6f |alendric|al purpo| |00000690| 73 65 73 2c 20 64 69 66 | 66 65 72 65 6e 63 65 73 |ses, dif|ferences| |000006a0| 20 6f 66 20 74 69 6d 65 | 20 7a 6f 6e 65 73 20 61 | of time| zones a| |000006b0| 72 65 20 67 65 6e 65 72 | 61 6c 6c 79 20 69 67 6e |re gener|ally ign| |000006c0| 6f 72 65 64 d1 74 68 61 | 74 20 69 73 2c 20 61 74 |ored.tha|t is, at| |000006d0| 20 65 61 63 68 20 6c 6f | 63 61 74 69 6f 6e 20 61 | each lo|cation a| |000006e0| 20 67 69 76 65 6e 20 64 | 61 74 65 20 73 74 61 72 | given d|ate star| |000006f0| 74 73 20 61 74 20 6d 69 | 64 6e 69 67 68 74 20 6c |ts at mi|dnight l| |00000700| 6f 63 61 6c 20 74 69 6d | 65 20 28 47 72 65 67 6f |ocal tim|e (Grego| |00000710| 72 69 61 6e 20 61 6e 64 | 20 69 74 73 20 72 65 6c |rian and| its rel| |00000720| 61 74 69 76 65 73 2c 20 | 45 6c 6c 69 6f 74 74 20 |atives, |Elliott | |00000730| 53 75 70 65 72 29 20 6f | 72 20 73 75 6e 73 65 74 |Super) o|r sunset| |00000740| 20 6c 6f 63 61 6c 20 74 | 69 6d 65 20 28 4a 65 77 | local t|ime (Jew| |00000750| 69 73 68 20 61 6e 64 20 | 49 73 6c 61 6d 69 63 29 |ish and |Islamic)| |00000760| 2e 0d 0d 0d 47 65 6e 65 | 72 61 6c 20 43 61 6c 65 |....Gene|ral Cale| |00000770| 6e 64 72 69 63 61 6c 20 | 52 75 6c 65 73 0d 0d 09 |ndrical |Rules...| |00000780| 31 29 09 54 68 65 20 69 | 6e 66 69 6e 69 74 65 20 |1).The i|nfinite | |00000790| 72 61 6e 67 65 20 6f 66 | 20 79 65 61 72 73 20 69 |range of| years i| |000007a0| 73 20 64 69 76 69 64 65 | 64 20 69 6e 74 6f 20 74 |s divide|d into t| |000007b0| 77 6f 20 65 72 61 73 2c | 20 65 61 63 68 20 6f 66 |wo eras,| each of| |000007c0| 20 77 68 69 63 68 20 69 | 73 20 73 6f 6d 65 74 69 | which i|s someti| |000007d0| 6d 65 73 20 67 69 76 65 | 6e 20 61 20 63 6f 6d 6d |mes give|n a comm| |000007e0| 6f 6e 20 61 62 62 72 65 | 76 69 61 74 69 6f 6e 20 |on abbre|viation | |000007f0| 28 65 2e 67 2e 2c 20 42 | 2e 43 2e 20 61 6e 64 20 |(e.g., B|.C. and | |00000800| 41 2e 44 2e 29 0d 0d 09 | 32 29 09 54 68 65 72 65 |A.D.)...|2).There| |00000810| 20 69 73 20 6e 65 76 65 | 72 20 61 20 79 65 61 72 | is neve|r a year| |00000820| 20 30 2e 20 50 6f 73 69 | 74 69 76 65 2d 6e 75 6d | 0. Posi|tive-num| |00000830| 62 65 72 65 64 20 79 65 | 61 72 73 20 61 72 65 20 |bered ye|ars are | |00000840| 69 6e 20 6f 6e 65 20 65 | 72 61 3b 20 6e 65 67 61 |in one e|ra; nega| |00000850| 74 69 76 65 2d 6e 75 6d | 62 65 72 65 64 20 79 65 |tive-num|bered ye| |00000860| 61 72 73 20 61 72 65 20 | 69 6e 20 74 68 65 20 6f |ars are |in the o| |00000870| 74 68 65 72 2e 20 54 68 | 65 20 61 62 62 72 65 76 |ther. Th|e abbrev| |00000880| 69 61 74 69 6f 6e 20 66 | 6f 72 20 74 68 65 20 65 |iation f|or the e| |00000890| 72 61 20 74 65 6c 6c 73 | 20 74 68 65 20 73 69 67 |ra tells| the sig| |000008a0| 6e 20 6f 66 20 74 68 65 | 20 79 65 61 72 2e 20 41 |n of the| year. A| |000008b0| 63 74 75 61 6c 20 70 6c | 75 73 20 61 6e 64 20 6d |ctual pl|us and m| |000008c0| 69 6e 75 73 20 73 69 67 | 6e 73 20 61 72 65 20 6e |inus sig|ns are n| |000008d0| 6f 72 6d 61 6c 6c 79 20 | 6e 6f 74 20 75 73 65 64 |ormally |not used| |000008e0| 2e 20 28 54 68 69 73 20 | 72 75 6c 65 20 69 73 20 |. (This |rule is | |000008f0| 64 75 65 20 74 6f 20 74 | 68 65 20 66 61 63 74 20 |due to t|he fact | |00000900| 74 68 61 74 20 6d 6f 64 | 65 72 6e 20 63 61 6c 65 |that mod|ern cale| |00000910| 6e 64 61 72 73 20 61 72 | 65 20 61 6c 6c 20 65 76 |ndars ar|e all ev| |00000920| 6f 6c 76 65 64 20 66 72 | 6f 6d 20 65 61 72 6c 69 |olved fr|om earli| |00000930| 65 72 20 6f 6e 65 73 20 | 77 68 69 63 68 20 77 65 |er ones |which we| |00000940| 72 65 20 64 65 76 65 6c | 6f 70 65 64 20 62 65 66 |re devel|oped bef| |00000950| 6f 72 65 20 74 68 65 20 | 63 6f 6e 63 65 70 74 73 |ore the |concepts| |00000960| 20 6f 66 20 7a 65 72 6f | 20 61 6e 64 20 6e 65 67 | of zero| and neg| |00000970| 61 74 69 76 65 20 69 6e | 74 65 67 65 72 73 20 77 |ative in|tegers w| |00000980| 65 72 65 20 77 65 6c 6c | 20 75 6e 64 65 72 73 74 |ere well| underst| |00000990| 6f 6f 64 2e 29 0d 0d 09 | 33 29 09 54 68 65 20 73 |ood.)...|3).The s| |000009a0| 65 71 75 65 6e 63 65 20 | 6f 66 20 77 65 65 6b 64 |equence |of weekd| |000009b0| 61 79 73 20 28 53 75 6e | 64 61 79 c9 53 61 74 75 |ays (Sun|day.Satu| |000009c0| 72 64 61 79 29 20 69 73 | 20 61 73 73 75 6d 65 64 |rday) is| assumed| |000009d0| 20 28 62 79 20 49 6e 74 | 65 72 43 61 6c 29 20 74 | (by Int|erCal) t| |000009e0| 6f 20 65 78 74 65 6e 64 | 20 69 6e 64 65 66 69 6e |o extend| indefin| |000009f0| 69 74 65 6c 79 20 69 6e | 74 6f 20 62 6f 74 68 20 |itely in|to both | |00000a00| 74 68 65 20 70 61 73 74 | 20 61 6e 64 20 66 75 74 |the past| and fut| |00000a10| 75 72 65 20 77 69 74 68 | 6f 75 74 20 69 6e 74 65 |ure with|out inte| |00000a20| 72 72 75 70 74 69 6f 6e | 2e 20 42 61 62 79 6c 6f |rruption|. Babylo| |00000a30| 6e 69 61 6e 73 20 64 65 | 76 65 6c 6f 70 65 64 20 |nians de|veloped | |00000a40| 74 68 65 20 73 65 76 65 | 6e 2d 64 61 79 20 77 65 |the seve|n-day we| |00000a50| 65 6b 2e 20 54 68 65 20 | 65 6d 70 65 72 6f 72 20 |ek. The |emperor | |00000a60| 43 6f 6e 73 74 61 6e 74 | 69 6e 65 20 6f 66 66 69 |Constant|ine offi| |00000a70| 63 69 61 6c 6c 79 20 61 | 64 6f 70 74 65 64 20 69 |cially a|dopted i| |00000a80| 74 20 66 6f 72 20 75 73 | 65 20 69 6e 20 74 68 65 |t for us|e in the| |00000a90| 20 52 6f 6d 61 6e 20 45 | 6d 70 69 72 65 20 69 6e | Roman E|mpire in| |00000aa0| 20 74 68 65 20 66 6f 75 | 72 74 68 20 63 65 6e 74 | the fou|rth cent| |00000ab0| 75 72 79 2c 20 61 6c 74 | 68 6f 75 67 68 20 69 74 |ury, alt|hough it| |00000ac0| 20 68 61 64 20 62 65 65 | 6e 20 69 6e 20 63 6f 6d | had bee|n in com| |00000ad0| 6d 6f 6e 20 75 73 65 20 | 66 6f 72 20 61 20 76 65 |mon use |for a ve| |00000ae0| 72 79 20 6c 6f 6e 67 20 | 74 69 6d 65 20 62 65 66 |ry long |time bef| |00000af0| 6f 72 65 20 74 68 61 74 | 2e 20 54 68 65 20 72 75 |ore that|. The ru| |00000b00| 6c 65 73 20 6f 66 20 6d | 6f 73 74 20 63 61 6c 65 |les of m|ost cale| |00000b10| 6e 64 61 72 73 20 61 72 | 65 20 63 6f 6d 70 6c 65 |ndars ar|e comple| |00000b20| 74 65 6c 79 20 69 6e 64 | 65 70 65 6e 64 65 6e 74 |tely ind|ependent| |00000b30| 20 6f 66 20 74 68 69 73 | 20 65 76 65 72 2d 72 65 | of this| ever-re| |00000b40| 70 65 61 74 69 6e 67 20 | 73 65 76 65 6e 2d 64 61 |peating |seven-da| |00000b50| 79 20 63 79 63 6c 65 2e | 20 54 68 65 20 4a 65 77 |y cycle.| The Jew| |00000b60| 69 73 68 20 63 61 6c 65 | 6e 64 61 72 20 69 73 20 |ish cale|ndar is | |00000b70| 61 6e 20 65 78 63 65 70 | 74 69 6f 6e 2e 20 49 74 |an excep|tion. It| |00000b80| 73 20 72 75 6c 65 73 20 | 70 72 65 76 65 6e 74 20 |s rules |prevent | |00000b90| 69 74 73 20 4e 65 77 20 | 59 65 61 72 d5 73 20 44 |its New |Year.s D| |00000ba0| 61 79 2c 20 52 6f 73 68 | 20 48 61 73 68 6f 6e 61 |ay, Rosh| Hashona| |00000bb0| 68 2c 20 66 72 6f 6d 20 | 6f 63 63 75 72 72 69 6e |h, from |occurrin| |00000bc0| 67 20 6f 6e 20 63 65 72 | 74 61 69 6e 20 64 61 79 |g on cer|tain day| |00000bd0| 73 20 6f 66 20 74 68 65 | 20 77 65 65 6b 2e 0d 0d |s of the| week...| |00000be0| 09 34 29 09 43 61 6c 65 | 6e 64 61 72 73 20 61 72 |.4).Cale|ndars ar| |00000bf0| 65 20 6e 6f 74 68 69 6e | 67 20 6d 6f 72 65 20 74 |e nothin|g more t| |00000c00| 68 61 6e 20 64 61 79 2d | 63 6f 75 6e 74 69 6e 67 |han day-|counting| |00000c10| 20 73 79 73 74 65 6d 73 | 2e 20 4d 6f 6e 74 68 73 | systems|. Months| |00000c20| 20 61 6e 64 20 79 65 61 | 72 73 20 61 72 65 20 6d | and yea|rs are m| |00000c30| 65 72 65 6c 79 20 63 6f | 6e 76 65 6e 69 65 6e 74 |erely co|nvenient| |00000c40| 20 6c 61 72 67 65 72 20 | 67 72 6f 75 70 69 6e 67 | larger |grouping| |00000c50| 73 20 6f 66 20 64 61 79 | 73 2e 20 55 73 75 61 6c |s of day|s. Usual| |00000c60| 6c 79 2c 20 63 61 6c 65 | 6e 64 61 72 73 20 64 6f |ly, cale|ndars do| |00000c70| 20 6e 6f 74 20 64 65 70 | 65 6e 64 20 6f 6e 20 66 | not dep|end on f| |00000c80| 69 6e 65 72 20 64 69 76 | 69 73 69 6f 6e 73 20 6f |iner div|isions o| |00000c90| 66 20 74 69 6d 65 20 28 | 68 6f 75 72 73 2c 20 6d |f time (|hours, m| |00000ca0| 69 6e 75 74 65 73 2c 20 | 65 74 63 2e 29 20 69 6e |inutes, |etc.) in| |00000cb0| 20 74 68 65 69 72 20 72 | 75 6c 65 73 2e 20 4f 6e | their r|ules. On| |00000cc0| 63 65 20 61 67 61 69 6e | 2c 20 74 68 65 20 4a 65 |ce again|, the Je| |00000cd0| 77 69 73 68 20 63 61 6c | 65 6e 64 61 72 20 69 73 |wish cal|endar is| |00000ce0| 20 61 6e 20 65 78 63 65 | 70 74 69 6f 6e 2e 20 54 | an exce|ption. T| |00000cf0| 68 65 20 74 69 6d 65 20 | 6f 66 20 64 61 79 20 6f |he time |of day o| |00000d00| 66 20 6e 65 77 20 6d 6f | 6f 6e 20 6e 65 61 72 65 |f new mo|on neare| |00000d10| 73 74 20 74 68 65 20 73 | 74 61 72 74 20 6f 66 20 |st the s|tart of | |00000d20| 61 20 79 65 61 72 20 63 | 61 6e 20 61 66 66 65 63 |a year c|an affec| |00000d30| 74 20 74 68 65 20 64 61 | 74 65 20 6f 66 20 52 6f |t the da|te of Ro| |00000d40| 73 68 20 48 61 73 68 6f | 6e 61 68 2e 0d 0d 09 35 |sh Hasho|nah....5| |00000d50| 29 09 43 61 6c 65 6e 64 | 61 72 73 20 64 69 66 66 |).Calend|ars diff| |00000d60| 65 72 20 61 63 63 6f 72 | 64 69 6e 67 20 74 6f 20 |er accor|ding to | |00000d70| 74 68 65 20 73 69 67 6e | 69 66 69 63 61 6e 63 65 |the sign|ificance| |00000d80| 20 67 69 76 65 6e 20 74 | 6f 20 74 68 65 20 6c 61 | given t|o the la| |00000d90| 72 67 65 72 20 67 72 6f | 75 70 69 6e 67 73 20 28 |rger gro|upings (| |00000da0| 73 75 63 68 20 61 73 20 | 6d 6f 6e 74 68 73 20 6f |such as |months o| |00000db0| 72 20 79 65 61 72 73 29 | 2e 20 41 6c 74 68 6f 75 |r years)|. Althou| |00000dc0| 67 68 20 6e 6f 74 20 61 | 6c 6c 20 63 61 6c 65 6e |gh not a|ll calen| |00000dd0| 64 61 72 73 20 66 69 74 | 20 69 6e 74 6f 20 74 68 |dars fit| into th| |00000de0| 65 20 66 6f 6c 6c 6f 77 | 69 6e 67 20 67 72 6f 75 |e follow|ing grou| |00000df0| 70 73 2c 20 61 6c 6c 20 | 74 68 6f 73 65 20 69 6d |ps, all |those im| |00000e00| 70 6c 65 6d 65 6e 74 65 | 64 20 62 79 20 49 6e 74 |plemente|d by Int| |00000e10| 65 72 43 61 6c 20 64 6f | 2e 0d 0d 09 61 29 09 4c |erCal do|....a).L| |00000e20| 75 6e 61 72 20 63 61 6c | 65 6e 64 61 72 73 d1 69 |unar cal|endars.i| |00000e30| 6e 20 6c 75 6e 61 72 20 | 63 61 6c 65 6e 64 61 72 |n lunar |calendar| |00000e40| 73 20 74 68 65 20 67 6f | 61 6c 20 69 73 20 74 6f |s the go|al is to| |00000e50| 20 68 61 76 65 20 74 68 | 65 20 64 61 74 65 20 77 | have th|e date w| |00000e60| 69 74 68 69 6e 20 65 61 | 63 68 20 6d 6f 6e 74 68 |ithin ea|ch month| |00000e70| 20 62 65 20 61 20 67 6f | 6f 64 20 69 6e 64 69 63 | be a go|od indic| |00000e80| 61 74 6f 72 20 6f 66 20 | 74 68 65 20 70 68 61 73 |ator of |the phas| |00000e90| 65 20 6f 66 20 74 68 65 | 20 6d 6f 6f 6e 2e 20 4d |e of the| moon. M| |00000ea0| 6f 73 74 20 6c 75 6e 61 | 72 20 63 61 6c 65 6e 64 |ost luna|r calend| |00000eb0| 61 72 73 20 68 61 76 65 | 20 74 68 65 69 72 20 6d |ars have| their m| |00000ec0| 6f 6e 74 68 73 20 73 74 | 61 72 74 20 61 6e 64 20 |onths st|art and | |00000ed0| 65 6e 64 20 61 73 20 63 | 6c 6f 73 65 20 74 6f 20 |end as c|lose to | |00000ee0| 6e 65 77 20 6d 6f 6f 6e | 20 61 73 20 66 65 61 73 |new moon| as feas| |00000ef0| 69 62 6c 65 2e 20 49 6e | 20 73 75 63 68 20 63 61 |ible. In| such ca| |00000f00| 6c 65 6e 64 61 72 73 2c | 20 74 68 65 20 66 69 72 |lendars,| the fir| |00000f10| 73 74 20 69 73 20 6e 65 | 61 72 20 6e 65 77 20 6d |st is ne|ar new m| |00000f20| 6f 6f 6e 2c 20 74 68 65 | 20 65 69 67 68 74 68 20 |oon, the| eighth | |00000f30| 6e 65 61 72 20 66 69 72 | 73 74 20 71 75 61 72 74 |near fir|st quart| |00000f40| 65 72 2c 20 74 68 65 20 | 73 69 78 74 65 65 6e 74 |er, the |sixteent| |00000f50| 68 20 6e 65 61 72 20 66 | 75 6c 6c 20 6d 6f 6f 6e |h near f|ull moon| |00000f60| 2c 20 61 6e 64 20 74 68 | 65 20 74 77 65 6e 74 79 |, and th|e twenty| |00000f70| 2d 74 68 69 72 64 20 6e | 65 61 72 20 74 68 69 72 |-third n|ear thir| |00000f80| 64 20 71 75 61 72 74 65 | 72 2e 20 54 68 75 73 20 |d quarte|r. Thus | |00000f90| 69 74 20 69 73 20 64 65 | 73 69 72 61 62 6c 65 20 |it is de|sirable | |00000fa0| 74 6f 20 68 61 76 65 20 | 74 68 65 20 61 76 65 72 |to have |the aver| |00000fb0| 61 67 65 20 6c 65 6e 67 | 74 68 20 6f 66 20 61 20 |age leng|th of a | |00000fc0| 6d 6f 6e 74 68 20 62 65 | 20 32 39 2e 35 33 30 35 |month be| 29.5305| |00000fd0| 38 38 32 20 64 61 79 73 | 20 28 74 68 65 20 73 79 |882 days| (the sy| |00000fe0| 6e 6f 64 69 63 20 6d 6f | 6e 74 68 d1 74 68 65 20 |nodic mo|nth.the | |00000ff0| 61 76 65 72 61 67 65 20 | 74 69 6d 65 20 62 65 74 |average |time bet| |00001000| 77 65 65 6e 20 73 75 63 | 63 65 73 73 69 76 65 20 |ween suc|cessive | |00001010| 6e 65 77 20 6d 6f 6f 6e | 73 29 2e 20 59 65 61 72 |new moon|s). Year| |00001020| 73 20 61 72 65 20 6a 75 | 73 74 20 63 6f 6e 76 65 |s are ju|st conve| |00001030| 6e 69 65 6e 74 20 6c 61 | 72 67 65 72 20 67 72 6f |nient la|rger gro| |00001040| 75 70 69 6e 67 73 20 6f | 66 20 6d 6f 6e 74 68 73 |upings o|f months| |00001050| 2c 20 61 6e 64 20 62 65 | 61 72 20 6e 6f 20 70 61 |, and be|ar no pa| |00001060| 72 74 69 63 75 6c 61 72 | 20 72 65 6c 61 74 69 6f |rticular| relatio| |00001070| 6e 20 74 6f 20 74 68 65 | 20 6d 6f 74 69 6f 6e 20 |n to the| motion | |00001080| 6f 66 20 74 68 65 20 65 | 61 72 74 68 2d 6d 6f 6f |of the e|arth-moo| |00001090| 6e 20 73 79 73 74 65 6d | 20 61 72 6f 75 6e 64 20 |n system| around | |000010a0| 74 68 65 20 73 75 6e 2e | 0d 0d 09 62 29 09 53 6f |the sun.|...b).So| |000010b0| 6c 61 72 20 63 61 6c 65 | 6e 64 61 72 73 d1 69 6e |lar cale|ndars.in| |000010c0| 20 73 6f 6c 61 72 20 63 | 61 6c 65 6e 64 61 72 73 | solar c|alendars| |000010d0| 20 74 68 65 20 67 6f 61 | 6c 20 69 73 20 74 6f 20 | the goa|l is to | |000010e0| 68 61 76 65 20 74 68 65 | 20 64 61 74 65 20 28 6d |have the| date (m| |000010f0| 6f 6e 74 68 20 61 6e 64 | 20 64 61 79 29 20 62 65 |onth and| day) be| |00001100| 20 61 20 67 6f 6f 64 20 | 69 6e 64 69 63 61 74 6f | a good |indicato| |00001110| 72 20 6f 66 20 74 68 65 | 20 73 65 61 73 6f 6e 20 |r of the| season | |00001120| 6f 66 20 74 68 65 20 79 | 65 61 72 2e 20 54 68 75 |of the y|ear. Thu| |00001130| 73 20 69 74 20 69 73 20 | 64 65 73 69 72 61 62 6c |s it is |desirabl| |00001140| 65 20 66 6f 72 20 74 68 | 65 20 61 76 65 72 61 67 |e for th|e averag| |00001150| 65 20 6c 65 6e 67 74 68 | 20 6f 66 20 61 20 79 65 |e length| of a ye| |00001160| 61 72 20 74 6f 20 62 65 | 20 33 36 35 2e 32 34 32 |ar to be| 365.242| |00001170| 31 39 39 20 64 61 79 73 | 20 28 74 68 65 20 74 72 |199 days| (the tr| |00001180| 6f 70 69 63 61 6c 20 79 | 65 61 72 d1 74 68 65 20 |opical y|ear.the | |00001190| 6d 65 61 6e 20 74 69 6d | 65 20 62 65 74 77 65 65 |mean tim|e betwee| |000011a0| 6e 20 73 75 63 63 65 73 | 73 69 76 65 20 76 65 72 |n succes|sive ver| |000011b0| 6e 61 6c 20 65 71 75 69 | 6e 6f 78 65 73 29 2e 20 |nal equi|noxes). | |000011c0| 4d 6f 6e 74 68 73 20 62 | 65 61 72 20 6e 6f 20 66 |Months b|ear no f| |000011d0| 69 78 65 64 20 72 65 6c | 61 74 69 6f 6e 20 74 6f |ixed rel|ation to| |000011e0| 20 74 68 65 20 70 68 61 | 73 65 20 6f 66 20 74 68 | the pha|se of th| |000011f0| 65 20 6d 6f 6f 6e 2e 0d | 0d 09 63 29 09 4c 75 6e |e moon..|..c).Lun| |00001200| 69 2d 73 6f 6c 61 72 20 | 63 61 6c 65 6e 64 61 72 |i-solar |calendar| |00001210| 73 d1 69 6e 20 6c 75 6e | 69 2d 73 6f 6c 61 72 20 |s.in lun|i-solar | |00001220| 63 61 6c 65 6e 64 61 72 | 73 20 74 68 65 20 6f 62 |calendar|s the ob| |00001230| 6a 65 63 74 20 69 73 20 | 74 6f 20 62 65 20 62 6f |ject is |to be bo| |00001240| 74 68 20 61 20 6c 75 6e | 61 72 20 61 6e 64 20 61 |th a lun|ar and a| |00001250| 20 73 6f 6c 61 72 20 63 | 61 6c 65 6e 64 61 72 20 | solar c|alendar | |00001260| 61 74 20 74 68 65 20 73 | 61 6d 65 20 74 69 6d 65 |at the s|ame time| |00001270| 2e 20 4e 61 74 75 72 61 | 6c 6c 79 2c 20 74 68 69 |. Natura|lly, thi| |00001280| 73 20 6c 65 61 64 73 20 | 74 6f 20 6d 6f 72 65 20 |s leads |to more | |00001290| 63 6f 6d 70 6c 65 78 20 | 63 61 6c 65 6e 64 72 69 |complex |calendri| |000012a0| 63 61 6c 20 72 75 6c 65 | 73 2e 20 54 68 65 20 74 |cal rule|s. The t| |000012b0| 72 6f 70 69 63 61 6c 20 | 79 65 61 72 20 69 73 20 |ropical |year is | |000012c0| 6e 6f 77 68 65 72 65 20 | 63 6c 6f 73 65 20 74 6f |nowhere |close to| |000012d0| 20 61 6e 20 69 6e 74 65 | 67 65 72 20 6d 75 6c 74 | an inte|ger mult| |000012e0| 69 70 6c 65 20 6f 66 20 | 74 68 65 20 73 79 6e 6f |iple of |the syno| |000012f0| 64 69 63 20 6d 6f 6e 74 | 68 2e 20 54 68 65 20 66 |dic mont|h. The f| |00001300| 69 72 73 74 20 70 72 69 | 6f 72 69 74 79 20 69 6e |irst pri|ority in| |00001310| 20 6c 75 6e 69 2d 73 6f | 6c 61 72 20 63 61 6c 65 | luni-so|lar cale| |00001320| 6e 64 61 72 73 20 75 73 | 75 61 6c 6c 79 20 69 73 |ndars us|ually is| |00001330| 20 74 6f 20 6b 65 65 70 | 20 61 63 63 75 72 61 74 | to keep| accurat| |00001340| 65 20 77 69 74 68 20 72 | 65 73 70 65 63 74 20 74 |e with r|espect t| |00001350| 6f 20 74 68 65 20 6d 6f | 6f 6e 2e 20 45 78 74 72 |o the mo|on. Extr| |00001360| 61 20 6d 6f 6e 74 68 73 | 20 61 72 65 20 61 64 64 |a months| are add| |00001370| 65 64 20 6f 63 63 61 73 | 69 6f 6e 61 6c 6c 79 20 |ed occas|ionally | |00001380| 74 6f 20 61 63 68 69 65 | 76 65 20 72 65 61 73 6f |to achie|ve reaso| |00001390| 6e 61 62 6c 65 20 61 63 | 63 75 72 61 63 79 20 77 |nable ac|curacy w| |000013a0| 69 74 68 20 72 65 73 70 | 65 63 74 20 74 6f 20 74 |ith resp|ect to t| |000013b0| 68 65 20 73 75 6e 20 28 | 77 68 65 6e 20 61 76 65 |he sun (|when ave| |000013c0| 72 61 67 65 64 20 6f 76 | 65 72 20 73 65 76 65 72 |raged ov|er sever| |000013d0| 61 6c 20 79 65 61 72 73 | 29 2e 0d 0d 09 36 29 09 |al years|)....6).| |000013e0| 4c 75 6e 61 72 2c 20 53 | 6f 6c 61 72 2c 20 61 6e |Lunar, S|olar, an| |000013f0| 64 20 4c 75 6e 69 2d 53 | 6f 6c 61 72 20 63 61 6c |d Luni-S|olar cal| |00001400| 65 6e 64 61 72 73 20 64 | 69 66 66 65 72 20 61 63 |endars d|iffer ac| |00001410| 63 6f 72 64 69 6e 67 20 | 74 6f 20 77 68 65 74 68 |cording |to wheth| |00001420| 65 72 20 74 68 65 69 72 | 20 72 75 6c 65 73 20 61 |er their| rules a| |00001430| 72 65 20 64 65 66 69 6e | 65 64 20 69 6e 20 74 65 |re defin|ed in te| |00001440| 72 6d 73 20 6f 66 20 74 | 68 65 20 61 63 74 75 61 |rms of t|he actua| |00001450| 6c 20 73 75 6e 20 61 6e | 64 2f 6f 72 20 6d 6f 6f |l sun an|d/or moo| |00001460| 6e 2c 20 6f 72 20 64 65 | 66 69 6e 65 64 20 69 6e |n, or de|fined in| |00001470| 20 74 65 72 6d 73 20 6f | 66 20 6d 61 74 68 65 6d | terms o|f mathem| |00001480| 61 74 69 63 61 6c 20 66 | 6f 72 6d 75 6c 61 73 20 |atical f|ormulas | |00001490| 77 68 69 63 68 20 61 72 | 65 20 6d 65 61 6e 74 20 |which ar|e meant | |000014a0| 74 6f 20 61 70 70 72 6f | 78 69 6d 61 74 65 20 74 |to appro|ximate t| |000014b0| 68 65 20 73 75 6e 20 61 | 6e 64 20 6d 6f 6f 6e 2e |he sun a|nd moon.| |000014c0| 20 49 20 63 61 6c 6c 20 | 74 68 65 20 66 6f 72 6d | I call |the form| |000014d0| 65 72 20 74 79 70 65 20 | 70 68 79 73 69 63 61 6c |er type |physical| |000014e0| 20 61 6e 64 20 74 68 65 | 20 6c 61 74 74 65 72 20 | and the| latter | |000014f0| 74 79 70 65 20 6d 61 74 | 68 65 6d 61 74 69 63 61 |type mat|hematica| |00001500| 6c 2e 20 41 20 70 68 79 | 73 69 63 61 6c 20 63 61 |l. A phy|sical ca| |00001510| 6c 65 6e 64 61 72 20 63 | 61 6e 6e 6f 74 20 61 63 |lendar c|annot ac| |00001520| 74 75 61 6c 6c 79 20 62 | 65 20 69 6d 70 6c 65 6d |tually b|e implem| |00001530| 65 6e 74 65 64 20 77 69 | 74 68 20 61 20 66 69 6e |ented wi|th a fin| |00001540| 69 74 65 20 63 6f 6d 70 | 75 74 65 72 20 61 6c 67 |ite comp|uter alg| |00001550| 6f 72 69 74 68 6d 2e 20 | 4f 6e 65 20 6d 75 73 74 |orithm. |One must| |00001560| 20 6d 61 6b 65 20 61 70 | 70 72 6f 78 69 6d 61 74 | make ap|proximat| |00001570| 69 6f 6e 73 20 77 68 69 | 63 68 20 6d 65 61 6e 20 |ions whi|ch mean | |00001580| 74 68 61 74 20 74 68 65 | 20 65 72 72 6f 72 2c 20 |that the| error, | |00001590| 61 73 20 79 6f 75 20 67 | 6f 20 66 61 72 74 68 65 |as you g|o farthe| |000015a0| 72 20 69 6e 74 6f 20 74 | 68 65 20 70 61 73 74 20 |r into t|he past | |000015b0| 6f 72 20 66 75 74 75 72 | 65 2c 20 63 61 6e 6e 6f |or futur|e, canno| |000015c0| 74 20 62 65 20 71 75 61 | 6e 74 69 66 69 65 64 2e |t be qua|ntified.| |000015d0| 20 54 68 65 20 6d 6f 74 | 69 6f 6e 73 20 6f 66 20 | The mot|ions of | |000015e0| 74 68 65 20 73 75 6e 20 | 61 6e 64 20 6d 6f 6f 6e |the sun |and moon| |000015f0| 20 61 72 65 20 6e 6f 74 | 20 6b 6e 6f 77 6e 20 74 | are not| known t| |00001600| 6f 20 69 6e 66 69 6e 69 | 74 65 20 70 72 65 63 69 |o infini|te preci| |00001610| 73 69 6f 6e 2c 20 61 6e | 64 20 74 68 65 69 72 20 |sion, an|d their | |00001620| 6f 72 62 69 74 73 20 61 | 72 65 20 6e 6f 74 20 70 |orbits a|re not p| |00001630| 65 72 66 65 63 74 6c 79 | 20 73 74 61 62 6c 65 20 |erfectly| stable | |00001640| 6f 72 20 63 6f 6d 70 75 | 74 61 62 6c 65 20 6f 76 |or compu|table ov| |00001650| 65 72 20 76 65 72 79 20 | 6c 6f 6e 67 20 74 69 6d |er very |long tim| |00001660| 65 20 66 72 61 6d 65 73 | 2e 20 41 20 6d 61 74 68 |e frames|. A math| |00001670| 65 6d 61 74 69 63 61 6c | 20 63 61 6c 65 6e 64 61 |ematical| calenda| |00001680| 72 20 63 61 6e 20 62 65 | 20 69 6d 70 6c 65 6d 65 |r can be| impleme| |00001690| 6e 74 65 64 20 77 69 74 | 68 20 70 65 72 66 65 63 |nted wit|h perfec| |000016a0| 74 20 61 63 63 75 72 61 | 63 79 20 28 61 73 20 66 |t accura|cy (as f| |000016b0| 61 72 20 61 73 20 69 74 | 73 20 72 75 6c 65 73 20 |ar as it|s rules | |000016c0| 61 72 65 20 63 6f 6e 63 | 65 72 6e 65 64 29 20 6f |are conc|erned) o| |000016d0| 6e 20 61 20 63 6f 6d 70 | 75 74 65 72 2c 20 62 75 |n a comp|uter, bu| |000016e0| 74 20 6f 66 20 63 6f 75 | 72 73 65 20 6f 76 65 72 |t of cou|rse over| |000016f0| 20 76 65 72 79 20 6c 6f | 6e 67 20 74 69 6d 65 20 | very lo|ng time | |00001700| 73 70 61 6e 73 20 69 74 | 20 77 69 6c 6c 20 62 65 |spans it| will be| |00001710| 63 6f 6d 65 20 61 20 70 | 6f 6f 72 65 72 20 61 6e |come a p|oorer an| |00001720| 64 20 70 6f 6f 72 65 72 | 20 61 70 70 72 6f 78 69 |d poorer| approxi| |00001730| 6d 61 74 69 6f 6e 20 74 | 6f 20 74 68 65 20 73 75 |mation t|o the su| |00001740| 6e 20 61 6e 64 20 6d 6f | 6f 6e 20 77 68 69 63 68 |n and mo|on which| |00001750| 20 69 74 20 69 73 20 73 | 75 70 70 6f 73 65 64 20 | it is s|upposed | |00001760| 74 6f 20 74 72 61 63 6b | 2e 0d 0d 09 43 61 6c 65 |to track|....Cale| |00001770| 6e 64 61 72 20 73 79 73 | 74 65 6d 73 20 65 76 6f |ndar sys|tems evo| |00001780| 6c 76 65 20 6f 76 65 72 | 20 74 69 6d 65 2e 20 52 |lve over| time. R| |00001790| 75 6c 65 73 20 61 72 65 | 20 63 68 61 6e 67 65 64 |ules are| changed| |000017a0| 20 6f 72 20 73 74 61 6e | 64 61 72 64 69 7a 65 64 | or stan|dardized| |000017b0| 2c 20 61 6e 64 20 6f 63 | 63 61 73 69 6f 6e 61 6c |, and oc|casional| |000017c0| 6c 79 20 61 20 6e 65 77 | 20 73 79 73 74 65 6d 20 |ly a new| system | |000017d0| 72 65 70 6c 61 63 65 73 | 20 61 6e 20 6f 6c 64 65 |replaces| an olde| |000017e0| 72 20 73 79 73 74 65 6d | 2e 20 49 6e 74 65 72 43 |r system|. InterC| |000017f0| 61 6c 20 64 6f 65 73 20 | 6e 6f 74 20 61 74 74 65 |al does |not atte| |00001800| 6d 70 74 20 74 6f 20 66 | 6f 6c 6c 6f 77 20 74 68 |mpt to f|ollow th| |00001810| 65 20 76 61 72 69 6f 75 | 73 20 72 75 6c 65 73 20 |e variou|s rules | |00001820| 63 68 61 6e 67 65 73 20 | 69 6e 20 61 6e 79 20 6f |changes |in any o| |00001830| 66 20 69 74 73 20 69 6d | 70 6c 65 6d 65 6e 74 65 |f its im|plemente| |00001840| 64 20 63 61 6c 65 6e 64 | 61 72 73 2e 20 49 6e 20 |d calend|ars. In | |00001850| 66 61 63 74 2c 20 66 6f | 72 20 6d 6f 73 74 20 61 |fact, fo|r most a| |00001860| 6e 63 69 65 6e 74 20 63 | 61 6c 65 6e 64 61 72 73 |ncient c|alendars| |00001870| 20 74 68 65 72 65 20 77 | 65 72 65 20 66 65 77 20 | there w|ere few | |00001880| 66 69 78 65 64 20 72 75 | 6c 65 73 20 61 6e 64 20 |fixed ru|les and | |00001890| 74 68 6f 73 65 20 74 68 | 61 74 20 6d 61 79 20 68 |those th|at may h| |000018a0| 61 76 65 20 65 78 69 73 | 74 65 64 20 61 72 65 20 |ave exis|ted are | |000018b0| 6c 61 72 67 65 6c 79 20 | 75 6e 6b 6e 6f 77 6e 20 |largely |unknown | |000018c0| 74 6f 20 6d 6f 64 65 72 | 6e 20 73 63 68 6f 6c 61 |to moder|n schola| |000018d0| 72 73 2e 20 49 6e 74 65 | 72 43 61 6c 20 73 69 6d |rs. Inte|rCal sim| |000018e0| 70 6c 79 20 65 78 74 65 | 6e 64 73 20 74 68 65 20 |ply exte|nds the | |000018f0| 72 75 6c 65 73 20 6f 66 | 20 65 61 63 68 20 63 61 |rules of| each ca| |00001900| 6c 65 6e 64 61 72 20 69 | 6e 20 69 74 73 20 70 72 |lendar i|n its pr| |00001910| 65 73 65 6e 74 20 66 6f | 72 6d 20 69 6e 64 65 66 |esent fo|rm indef| |00001920| 69 6e 69 74 65 6c 79 20 | 69 6e 74 6f 20 62 6f 74 |initely |into bot| |00001930| 68 20 74 68 65 20 70 61 | 73 74 20 61 6e 64 20 74 |h the pa|st and t| |00001940| 68 65 20 66 75 74 75 72 | 65 2e 20 54 68 65 20 6f |he futur|e. The o| |00001950| 6e 6c 79 20 65 78 63 65 | 70 74 69 6f 6e 20 69 73 |nly exce|ption is| |00001960| 20 74 68 65 20 d2 57 65 | 73 74 65 72 6e 20 48 69 | the .We|stern Hi| |00001970| 73 74 6f 72 69 63 61 6c | 20 43 61 6c 65 6e 64 61 |storical| Calenda| |00001980| 72 d3 2c 20 77 68 69 63 | 68 20 69 73 20 6a 75 73 |r., whic|h is jus| |00001990| 74 20 61 20 67 72 61 66 | 74 20 6f 66 20 74 68 65 |t a graf|t of the| |000019a0| 20 47 72 65 67 6f 72 69 | 61 6e 20 43 61 6c 65 6e | Gregori|an Calen| |000019b0| 64 61 72 20 6f 6e 74 6f | 20 74 68 65 20 4a 75 6c |dar onto| the Jul| |000019c0| 69 61 6e 20 28 73 65 65 | 20 62 65 6c 6f 77 29 2e |ian (see| below).| |000019d0| 20 54 68 75 73 2c 20 49 | 6e 74 65 72 43 61 6c 20 | Thus, I|nterCal | |000019e0| 64 6f 65 73 20 6e 6f 74 | 20 61 74 74 65 6d 70 74 |does not| attempt| |000019f0| 20 68 69 73 74 6f 72 69 | 63 61 6c 20 61 63 63 75 | histori|cal accu| |00001a00| 72 61 63 79 2c 20 6f 6e | 6c 79 20 6d 61 74 68 65 |racy, on|ly mathe| |00001a10| 6d 61 74 69 63 61 6c 20 | 61 63 63 75 72 61 63 79 |matical |accuracy| |00001a20| 2e 0d 0d 0d 4a 75 6c 69 | 61 6e 20 43 61 6c 65 6e |....Juli|an Calen| |00001a30| 64 61 72 0d 0d 09 55 73 | 69 6e 67 20 74 68 65 20 |dar...Us|ing the | |00001a40| 63 6c 61 73 73 69 66 69 | 63 61 74 69 6f 6e 20 73 |classifi|cation s| |00001a50| 63 68 65 6d 65 20 61 62 | 6f 76 65 2c 20 74 68 65 |cheme ab|ove, the| |00001a60| 20 4a 75 6c 69 61 6e 20 | 43 61 6c 65 6e 64 61 72 | Julian |Calendar| |00001a70| 20 69 73 20 61 20 6d 61 | 74 68 65 6d 61 74 69 63 | is a ma|thematic| |00001a80| 61 6c 20 73 6f 6c 61 72 | 20 63 61 6c 65 6e 64 61 |al solar| calenda| |00001a90| 72 2e 20 49 74 20 77 61 | 73 20 69 6e 73 74 69 74 |r. It wa|s instit| |00001aa0| 75 74 65 64 20 62 79 20 | 4a 75 6c 69 75 73 20 43 |uted by |Julius C| |00001ab0| 61 65 73 61 72 20 6f 6e | 20 4a 61 6e 75 61 72 79 |aesar on| January| |00001ac0| 20 31 20 28 4a 75 6c 69 | 61 6e 29 20 69 6e 20 74 | 1 (Juli|an) in t| |00001ad0| 68 65 20 79 65 61 72 20 | 77 68 69 63 68 20 69 73 |he year |which is| |00001ae0| 20 6e 6f 77 20 6b 6e 6f | 77 6e 20 61 73 20 34 35 | now kno|wn as 45| |00001af0| 20 42 2e 43 2e 20 49 74 | 20 77 61 73 20 61 20 6d | B.C. It| was a m| |00001b00| 6f 64 69 66 69 63 61 74 | 69 6f 6e 20 61 6e 64 20 |odificat|ion and | |00001b10| 69 6d 70 72 6f 76 65 6d | 65 6e 74 20 6f 76 65 72 |improvem|ent over| |00001b20| 20 61 6e 20 6f 6c 64 65 | 72 20 63 61 6c 65 6e 64 | an olde|r calend| |00001b30| 61 72 20 69 6e 20 75 73 | 65 20 69 6e 20 52 6f 6d |ar in us|e in Rom| |00001b40| 65 20 61 74 20 74 68 65 | 20 74 69 6d 65 2e 20 49 |e at the| time. I| |00001b50| 6e 20 6f 72 64 65 72 20 | 74 6f 20 67 65 74 20 74 |n order |to get t| |00001b60| 68 65 20 63 61 6c 65 6e | 64 61 72 20 62 61 63 6b |he calen|dar back| |00001b70| 20 69 6e 20 73 79 6e 63 | 68 72 6f 6e 69 73 6d 20 | in sync|hronism | |00001b80| 77 69 74 68 20 74 68 65 | 20 73 75 6e 2c 20 43 61 |with the| sun, Ca| |00001b90| 65 73 61 72 20 6c 65 6e | 67 74 68 65 6e 65 64 20 |esar len|gthened | |00001ba0| 74 68 65 20 79 65 61 72 | 20 34 36 20 42 2e 43 2e |the year| 46 B.C.| |00001bb0| 20 62 79 20 73 65 76 65 | 72 61 6c 20 6d 6f 6e 74 | by seve|ral mont| |00001bc0| 68 73 2e 20 49 6e 20 68 | 69 73 20 6e 65 77 20 73 |hs. In h|is new s| |00001bd0| 79 73 74 65 6d 2c 20 4a | 61 6e 75 61 72 79 2c 20 |ystem, J|anuary, | |00001be0| 4d 61 72 63 68 2c 20 4d | 61 79 2c 20 4a 75 6c 79 |March, M|ay, July| |00001bf0| 2c 20 53 65 70 74 65 6d | 62 65 72 2c 20 61 6e 64 |, Septem|ber, and| |00001c00| 20 4e 6f 76 65 6d 62 65 | 72 20 68 61 64 20 33 31 | Novembe|r had 31| |00001c10| 20 64 61 79 73 2e 20 41 | 70 72 69 6c 2c 20 4a 75 | days. A|pril, Ju| |00001c20| 6e 65 2c 20 41 75 67 75 | 73 74 2c 20 4f 63 74 6f |ne, Augu|st, Octo| |00001c30| 62 65 72 2c 20 61 6e 64 | 20 44 65 63 65 6d 62 65 |ber, and| Decembe| |00001c40| 72 20 68 61 64 20 33 30 | 20 64 61 79 73 2e 20 46 |r had 30| days. F| |00001c50| 65 62 72 75 61 72 79 20 | 6e 6f 72 6d 61 6c 6c 79 |ebruary |normally| |00001c60| 20 68 61 64 20 32 39 2c | 20 62 75 74 20 68 61 64 | had 29,| but had| |00001c70| 20 33 30 20 69 6e 20 6c | 65 61 70 20 79 65 61 72 | 30 in l|eap year| |00001c80| 73 2e 20 41 75 67 75 73 | 74 75 73 20 43 61 65 73 |s. Augus|tus Caes| |00001c90| 61 72 20 74 6f 6f 6b 20 | 61 20 64 61 79 20 66 72 |ar took |a day fr| |00001ca0| 6f 6d 20 46 65 62 72 75 | 61 72 79 20 61 6e 64 20 |om Febru|ary and | |00001cb0| 61 64 64 65 64 20 69 74 | 20 74 6f 20 41 75 67 75 |added it| to Augu| |00001cc0| 73 74 20 61 62 6f 75 74 | 20 33 30 20 42 2e 43 2e |st about| 30 B.C.| |00001cd0| 20 41 63 74 75 61 6c 6c | 79 2c 20 68 65 20 61 6c | Actuall|y, he al| |00001ce0| 73 6f 20 72 65 6e 61 6d | 65 64 20 74 68 65 20 6d |so renam|ed the m| |00001cf0| 6f 6e 74 68 2c 20 77 68 | 69 63 68 20 68 61 64 20 |onth, wh|ich had | |00001d00| 6e 6f 74 20 62 65 65 6e | 20 63 61 6c 6c 65 64 20 |not been| called | |00001d10| 41 75 67 75 73 74 20 62 | 65 66 6f 72 65 2e 20 41 |August b|efore. A| |00001d20| 64 64 69 74 69 6f 6e 61 | 6c 20 72 75 6c 65 20 63 |dditiona|l rule c| |00001d30| 68 61 6e 67 65 73 20 74 | 6f 6f 6b 20 70 6c 61 63 |hanges t|ook plac| |00001d40| 65 20 64 75 72 69 6e 67 | 20 74 68 65 20 6e 65 78 |e during| the nex| |00001d50| 74 20 66 65 77 20 64 65 | 63 61 64 65 73 2e 20 41 |t few de|cades. A| |00001d60| 6c 73 6f 2c 20 74 68 65 | 20 72 75 6c 65 73 20 77 |lso, the| rules w| |00001d70| 65 72 65 20 6e 6f 74 20 | 61 6c 77 61 79 73 20 63 |ere not |always c| |00001d80| 6f 72 72 65 63 74 6c 79 | 20 66 6f 6c 6c 6f 77 65 |orrectly| followe| |00001d90| 64 2e 20 54 68 65 20 63 | 61 6c 65 6e 64 61 72 20 |d. The c|alendar | |00001da0| 72 65 61 63 68 65 64 20 | 69 74 73 20 66 69 6e 61 |reached |its fina| |00001db0| 6c 20 66 6f 72 6d 2c 20 | 77 69 74 68 20 74 68 65 |l form, |with the| |00001dc0| 20 6d 6f 6e 74 68 20 6c | 65 6e 67 74 68 73 20 62 | month l|engths b| |00001dd0| 65 69 6e 67 20 77 68 61 | 74 20 77 65 20 61 72 65 |eing wha|t we are| |00001de0| 20 75 73 65 64 20 74 6f | 2c 20 69 6e 20 38 20 41 | used to|, in 8 A| |00001df0| 2e 44 2e 20 54 68 65 20 | 52 6f 6d 61 6e 20 79 65 |.D. The |Roman ye| |00001e00| 61 72 20 61 74 20 6f 6e | 65 20 74 69 6d 65 20 62 |ar at on|e time b| |00001e10| 65 67 61 6e 20 69 6e 20 | 4d 61 72 63 68 2c 20 6e |egan in |March, n| |00001e20| 6f 74 20 4a 61 6e 75 61 | 72 79 2e 20 54 68 65 20 |ot Janua|ry. The | |00001e30| 61 64 6f 70 74 69 6f 6e | 20 6f 66 20 4a 61 6e 75 |adoption| of Janu| |00001e40| 61 72 79 20 61 73 20 74 | 68 65 20 66 69 72 73 74 |ary as t|he first| |00001e50| 20 6d 6f 6e 74 68 20 6f | 63 63 75 72 72 65 64 20 | month o|ccurred | |00001e60| 61 72 6f 75 6e 64 20 31 | 35 33 20 42 2e 43 2e 20 |around 1|53 B.C. | |00001e70| 48 6f 77 65 76 65 72 2c | 20 45 6e 67 6c 61 6e 64 |However,| England| |00001e80| 20 77 61 73 20 72 65 63 | 6b 6f 6e 69 6e 67 20 74 | was rec|koning t| |00001e90| 68 65 20 73 74 61 72 74 | 20 6f 66 20 74 68 65 20 |he start| of the | |00001ea0| 79 65 61 72 20 61 74 20 | 4d 61 72 63 68 20 32 35 |year at |March 25| |00001eb0| 20 61 74 20 74 68 65 20 | 74 69 6d 65 20 69 74 20 | at the |time it | |00001ec0| 73 77 69 74 63 68 65 64 | 20 66 72 6f 6d 20 74 68 |switched| from th| |00001ed0| 65 20 4a 75 6c 69 61 6e | 20 63 61 6c 65 6e 64 61 |e Julian| calenda| |00001ee0| 72 20 74 6f 20 74 68 65 | 20 47 72 65 67 6f 72 69 |r to the| Gregori| |00001ef0| 61 6e 20 28 73 65 65 20 | 62 65 6c 6f 77 29 2e 20 |an (see |below). | |00001f00| 53 6f 20 69 74 20 69 73 | 20 6e 6f 74 20 71 75 69 |So it is| not qui| |00001f10| 74 65 20 63 6f 72 72 65 | 63 74 20 74 6f 20 73 61 |te corre|ct to sa| |00001f20| 79 20 74 68 61 74 20 74 | 68 65 20 4a 75 6c 69 61 |y that t|he Julia| |00001f30| 6e 20 63 61 6c 65 6e 64 | 61 72 20 77 61 73 20 66 |n calend|ar was f| |00001f40| 69 6e 61 6c 69 7a 65 64 | 20 69 6e 20 38 20 41 2e |inalized| in 8 A.| |00001f50| 44 2e 20 54 68 65 72 65 | 20 77 65 72 65 20 73 74 |D. There| were st| |00001f60| 69 6c 6c 20 61 20 66 65 | 77 20 72 75 6c 65 20 76 |ill a fe|w rule v| |00001f70| 61 72 69 61 74 69 6f 6e | 73 20 77 68 69 63 68 20 |ariation|s which | |00001f80| 76 61 72 69 65 64 20 66 | 72 6f 6d 20 74 69 6d 65 |varied f|rom time| |00001f90| 20 74 6f 20 74 69 6d 65 | 20 61 6e 64 20 70 6c 61 | to time| and pla| |00001fa0| 63 65 20 74 6f 20 70 6c | 61 63 65 2e 20 54 68 65 |ce to pl|ace. The| |00001fb0| 20 4a 75 6c 69 61 6e 20 | 63 61 6c 65 6e 64 61 72 | Julian |calendar| |00001fc0| 20 77 61 73 20 74 68 65 | 20 6f 66 66 69 63 69 61 | was the| officia| |00001fd0| 6c 20 63 61 6c 65 6e 64 | 61 72 20 6f 66 20 74 68 |l calend|ar of th| |00001fe0| 65 20 52 6f 6d 61 6e 20 | 45 6d 70 69 72 65 20 61 |e Roman |Empire a| |00001ff0| 6e 64 2c 20 6c 61 74 65 | 72 2c 20 74 68 65 20 65 |nd, late|r, the e| |00002000| 6e 74 69 72 65 20 43 68 | 72 69 73 74 69 61 6e 20 |ntire Ch|ristian | |00002010| 77 6f 72 6c 64 20 75 6e | 74 69 6c 20 69 74 73 20 |world un|til its | |00002020| 72 65 70 6c 61 63 65 6d | 65 6e 74 20 62 79 20 74 |replacem|ent by t| |00002030| 68 65 20 47 72 65 67 6f | 72 69 61 6e 20 63 61 6c |he Grego|rian cal| |00002040| 65 6e 64 61 72 2e 0d 0d | 09 54 68 65 72 65 20 68 |endar...|.There h| |00002050| 61 76 65 20 62 65 65 6e | 20 64 69 66 66 65 72 65 |ave been| differe| |00002060| 6e 74 20 6e 75 6d 62 65 | 72 69 6e 67 20 73 63 68 |nt numbe|ring sch| |00002070| 65 6d 65 73 20 66 6f 72 | 20 74 68 65 20 64 61 79 |emes for| the day| |00002080| 73 20 6f 66 20 46 65 62 | 72 75 61 72 79 20 69 6e |s of Feb|ruary in| |00002090| 20 6c 65 61 70 20 79 65 | 61 72 73 2e 20 4f 6e 65 | leap ye|ars. One| |000020a0| 20 63 6f 6d 6d 6f 6e 20 | 6d 65 74 68 6f 64 2c 20 | common |method, | |000020b0| 61 64 6f 70 74 65 64 20 | 62 79 20 74 68 65 20 49 |adopted |by the I| |000020c0| 6e 74 65 72 43 61 6c 20 | 70 72 6f 67 72 61 6d 2c |nterCal |program,| |000020d0| 20 77 61 73 20 74 6f 20 | 69 6e 73 65 72 74 20 61 | was to |insert a| |000020e0| 6e 20 75 6e 6e 75 6d 62 | 65 72 65 64 20 64 61 79 |n unnumb|ered day| |000020f0| 20 28 73 69 6d 70 6c 79 | 20 63 61 6c 6c 65 64 20 | (simply| called | |00002100| 74 68 65 20 62 69 73 65 | 78 74 69 6c 65 20 64 61 |the bise|xtile da| |00002110| 79 29 20 62 65 74 77 65 | 65 6e 20 46 65 62 72 75 |y) betwe|en Febru| |00002120| 61 72 79 20 32 34 20 61 | 6e 64 20 46 65 62 72 75 |ary 24 a|nd Febru| |00002130| 61 72 79 20 32 35 2e 0d | 0d 09 54 68 65 20 72 75 |ary 25..|..The ru| |00002140| 6c 65 73 20 6f 66 20 74 | 68 65 20 4a 75 6c 69 61 |les of t|he Julia| |00002150| 6e 20 63 61 6c 65 6e 64 | 61 72 20 61 73 20 69 6d |n calend|ar as im| |00002160| 70 6c 65 6d 65 6e 74 65 | 64 20 62 79 20 49 6e 74 |plemente|d by Int| |00002170| 65 72 43 61 6c 20 61 72 | 65 3a 0d 0d 09 31 29 09 |erCal ar|e:...1).| |00002180| 54 68 65 20 6e 65 67 61 | 74 69 76 65 20 79 65 61 |The nega|tive yea| |00002190| 72 20 65 72 61 20 69 73 | 20 6c 61 62 65 6c 65 64 |r era is| labeled| |000021a0| 20 42 2e 43 2e 20 28 42 | 65 66 6f 72 65 20 43 68 | B.C. (B|efore Ch| |000021b0| 72 69 73 74 29 2e 20 54 | 68 65 20 70 6f 73 69 74 |rist). T|he posit| |000021c0| 69 76 65 20 79 65 61 72 | 20 65 72 61 20 69 73 20 |ive year| era is | |000021d0| 6c 61 62 65 6c 65 64 20 | 41 2e 44 2e 20 28 41 6e |labeled |A.D. (An| |000021e0| 6e 6f 20 44 6f 6d 69 6e | 69 2c 20 4c 61 74 69 6e |no Domin|i, Latin| |000021f0| 20 66 6f 72 20 59 65 61 | 72 20 6f 66 20 74 68 65 | for Yea|r of the| |00002200| 20 4c 6f 72 64 29 2e 0d | 0d 09 32 29 09 4d 6f 6e | Lord)..|..2).Mon| |00002210| 74 68 73 20 61 72 65 20 | 6e 61 6d 65 64 20 28 69 |ths are |named (i| |00002220| 6e 20 6f 72 64 65 72 29 | 20 4a 61 6e 75 61 72 79 |n order)| January| |00002230| 2c 20 46 65 62 72 75 61 | 72 79 2c 20 4d 61 72 63 |, Februa|ry, Marc| |00002240| 68 2c 20 41 70 72 69 6c | 2c 20 4d 61 79 2c 20 4a |h, April|, May, J| |00002250| 75 6e 65 2c 20 4a 75 6c | 79 2c 20 41 75 67 75 73 |une, Jul|y, Augus| |00002260| 74 2c 20 53 65 70 74 65 | 6d 62 65 72 2c 20 4f 63 |t, Septe|mber, Oc| |00002270| 74 6f 62 65 72 2c 20 4e | 6f 76 65 6d 62 65 72 2c |tober, N|ovember,| |00002280| 20 44 65 63 65 6d 62 65 | 72 2e 20 59 65 61 72 73 | Decembe|r. Years| |00002290| 20 73 74 61 72 74 20 69 | 6e 20 4a 61 6e 75 61 72 | start i|n Januar| |000022a0| 79 2e 0d 0d 09 33 29 09 | 54 68 65 20 4a 75 6c 69 |y....3).|The Juli| |000022b0| 61 6e 20 44 61 79 20 6f | 66 20 6d 69 64 6e 69 67 |an Day o|f midnig| |000022c0| 68 74 20 61 74 20 74 68 | 65 20 73 74 61 72 74 20 |ht at th|e start | |000022d0| 6f 66 20 4a 61 6e 75 61 | 72 79 20 31 2c 20 31 20 |of Janua|ry 1, 1 | |000022e0| 41 2e 44 2e 20 4a 75 6c | 69 61 6e 20 28 61 20 53 |A.D. Jul|ian (a S| |000022f0| 61 74 75 72 64 61 79 29 | 20 69 73 20 31 37 32 31 |aturday)| is 1721| |00002300| 34 32 33 2e 35 2e 0d 0d | 09 34 29 09 4a 61 6e 75 |423.5...|.4).Janu| |00002310| 61 72 79 2c 20 4d 61 72 | 63 68 2c 20 4d 61 79 2c |ary, Mar|ch, May,| |00002320| 20 4a 75 6c 79 2c 20 41 | 75 67 75 73 74 2c 20 4f | July, A|ugust, O| |00002330| 63 74 6f 62 65 72 2c 20 | 61 6e 64 20 44 65 63 65 |ctober, |and Dece| |00002340| 6d 62 65 72 20 68 61 76 | 65 20 33 31 20 64 61 79 |mber hav|e 31 day| |00002350| 73 2e 0d 0d 09 35 29 09 | 41 70 72 69 6c 2c 20 4a |s....5).|April, J| |00002360| 75 6e 65 2c 20 53 65 70 | 74 65 6d 62 65 72 2c 20 |une, Sep|tember, | |00002370| 61 6e 64 20 4e 6f 76 65 | 6d 62 65 72 20 68 61 76 |and Nove|mber hav| |00002380| 65 20 33 30 20 64 61 79 | 73 2e 0d 0d 09 36 29 09 |e 30 day|s....6).| |00002390| 46 65 62 72 75 61 72 79 | 20 68 61 73 20 32 38 20 |February| has 28 | |000023a0| 64 61 79 73 20 69 6e 20 | 6e 6f 72 6d 61 6c 20 79 |days in |normal y| |000023b0| 65 61 72 73 20 61 6e 64 | 20 32 39 20 64 61 79 73 |ears and| 29 days| |000023c0| 20 69 6e 20 6c 65 61 70 | 20 79 65 61 72 73 2e 0d | in leap| years..| |000023d0| 0d 09 37 29 09 54 68 65 | 20 6c 65 61 70 20 79 65 |..7).The| leap ye| |000023e0| 61 72 20 63 79 63 6c 65 | 20 69 73 20 66 6f 75 72 |ar cycle| is four| |000023f0| 20 79 65 61 72 73 20 6c | 6f 6e 67 2e 20 4c 65 61 | years l|ong. Lea| |00002400| 70 20 79 65 61 72 73 20 | 6f 63 63 75 72 20 65 76 |p years |occur ev| |00002410| 65 72 79 20 66 6f 75 72 | 74 68 20 79 65 61 72 2c |ery four|th year,| |00002420| 20 61 73 20 66 6f 6c 6c | 6f 77 73 3a 0d 0d 09 09 | as foll|ows:....| |00002430| c9 39 20 42 2e 43 2e 2c | 20 35 20 42 2e 43 2e 2c |.9 B.C.,| 5 B.C.,| |00002440| 20 31 20 42 2e 43 2e 2c | 20 34 20 41 2e 44 2e 2c | 1 B.C.,| 4 A.D.,| |00002450| 20 38 20 41 2e 44 2c 20 | 31 32 20 41 2e 44 2e c9 | 8 A.D, |12 A.D..| |00002460| 20 20 28 4e 6f 74 65 20 | 74 68 61 74 20 49 20 64 | (Note |that I d| |00002470| 6f 20 6e 6f 74 20 73 69 | 6d 70 6c 79 20 73 61 79 |o not si|mply say| |00002480| 20 d2 79 65 61 72 73 20 | 65 76 65 6e 6c 79 20 64 | .years |evenly d| |00002490| 69 76 69 73 69 62 6c 65 | 20 62 79 20 34 d3 20 62 |ivisible| by 4. b| |000024a0| 65 63 61 75 73 65 20 74 | 68 61 74 20 73 69 6d 70 |ecause t|hat simp| |000024b0| 6c 69 66 69 63 61 74 69 | 6f 6e 20 6f 66 20 74 68 |lificati|on of th| |000024c0| 65 20 72 75 6c 65 20 6f | 6e 6c 79 20 77 6f 72 6b |e rule o|nly work| |000024d0| 73 20 66 6f 72 20 70 6f | 73 69 74 69 76 65 20 79 |s for po|sitive y| |000024e0| 65 61 72 73 2e 20 47 69 | 76 65 6e 20 61 6e 20 75 |ears. Gi|ven an u| |000024f0| 6e 61 6d 62 69 67 75 6f | 75 73 20 64 65 66 69 6e |nambiguo|us defin| |00002500| 69 74 69 6f 6e 20 6f 66 | 20 74 68 65 20 63 79 63 |ition of| the cyc| |00002510| 6c 65 73 2c 20 61 20 6d | 6f 72 65 20 70 72 65 63 |les, a m|ore prec| |00002520| 69 73 65 20 77 61 79 20 | 6f 66 20 73 74 61 74 69 |ise way |of stati| |00002530| 6e 67 20 74 68 65 20 72 | 75 6c 65 20 77 6f 75 6c |ng the r|ule woul| |00002540| 64 20 62 65 3a 20 d2 59 | 65 61 72 73 20 77 68 6f |d be: .Y|ears who| |00002550| 73 65 20 70 6f 73 69 74 | 69 6f 6e 20 69 6e 20 74 |se posit|ion in t| |00002560| 68 65 69 72 20 63 79 63 | 6c 65 20 69 73 20 64 69 |heir cyc|le is di| |00002570| 76 69 73 69 62 6c 65 20 | 62 79 20 34 20 61 72 65 |visible |by 4 are| |00002580| 20 6c 65 61 70 20 79 65 | 61 72 73 2e d3 29 0d 0d | leap ye|ars..)..| |00002590| 09 38 29 09 54 68 65 20 | 65 78 74 72 61 20 64 61 |.8).The |extra da| |000025a0| 79 20 69 6e 20 6c 65 61 | 70 20 79 65 61 72 73 20 |y in lea|p years | |000025b0| 69 73 20 61 64 64 65 64 | 20 62 65 74 77 65 65 6e |is added| between| |000025c0| 20 46 65 62 72 75 61 72 | 79 20 32 34 20 61 6e 64 | Februar|y 24 and| |000025d0| 20 46 65 62 72 75 61 72 | 79 20 32 35 2c 20 69 73 | Februar|y 25, is| |000025e0| 20 6e 6f 74 20 6e 75 6d | 62 65 72 65 64 2c 20 61 | not num|bered, a| |000025f0| 6e 64 20 69 73 20 72 65 | 66 65 72 72 65 64 20 74 |nd is re|ferred t| |00002600| 6f 20 61 73 20 d2 62 69 | 73 65 78 74 69 6c 65 20 |o as .bi|sextile | |00002610| 64 61 79 d3 2e 20 54 68 | 69 73 20 72 75 6c 65 20 |day.. Th|is rule | |00002620| 77 61 73 20 6e 6f 74 20 | 73 74 61 6e 64 61 72 64 |was not |standard| |00002630| 69 7a 65 64 d1 6f 74 68 | 65 72 20 70 6f 73 73 69 |ized.oth|er possi| |00002640| 62 69 6c 69 74 69 65 73 | 20 77 65 72 65 20 75 73 |bilities| were us| |00002650| 65 64 20 69 6e 20 76 61 | 72 69 6f 75 73 20 70 6c |ed in va|rious pl| |00002660| 61 63 65 73 20 61 6e 64 | 20 74 69 6d 65 73 2e 20 |aces and| times. | |00002670| 42 75 74 20 74 68 69 73 | 20 72 75 6c 65 20 77 61 |But this| rule wa| |00002680| 73 20 63 6f 6d 6d 6f 6e | 20 61 6e 64 20 69 73 20 |s common| and is | |00002690| 74 68 65 20 6f 6e 65 20 | 69 6d 70 6c 65 6d 65 6e |the one |implemen| |000026a0| 74 65 64 20 62 79 20 49 | 6e 74 65 72 43 61 6c 2e |ted by I|nterCal.| |000026b0| 0d 0d 09 57 69 74 68 20 | 61 20 6c 65 61 70 20 79 |...With |a leap y| |000026c0| 65 61 72 20 63 79 63 6c | 65 20 6f 66 20 66 6f 75 |ear cycl|e of fou| |000026d0| 72 20 79 65 61 72 73 20 | 63 6f 6e 74 61 69 6e 69 |r years |containi| |000026e0| 6e 67 20 34 28 33 36 35 | 29 20 2b 20 31 20 64 61 |ng 4(365|) + 1 da| |000026f0| 79 73 2c 20 74 68 65 20 | 61 76 65 72 61 67 65 20 |ys, the |average | |00002700| 79 65 61 72 20 69 73 20 | 33 36 35 2e 32 35 20 64 |year is |365.25 d| |00002710| 61 79 73 2c 20 66 6f 72 | 20 61 6e 20 65 72 72 6f |ays, for| an erro| |00002720| 72 20 6f 66 20 30 2e 30 | 30 37 38 20 64 61 79 73 |r of 0.0|078 days| |00002730| 20 70 65 72 20 79 65 61 | 72 2c 20 6f 72 20 61 62 | per yea|r, or ab| |00002740| 6f 75 74 20 6f 6e 65 20 | 64 61 79 20 65 76 65 72 |out one |day ever| |00002750| 79 20 31 32 38 20 79 65 | 61 72 73 2e 0d 0d 0d 47 |y 128 ye|ars....G| |00002760| 72 65 67 6f 72 69 61 6e | 20 43 61 6c 65 6e 64 61 |regorian| Calenda| |00002770| 72 0d 0d 09 54 68 65 20 | 47 72 65 67 6f 72 69 61 |r...The |Gregoria| |00002780| 6e 20 43 61 6c 65 6e 64 | 61 72 20 69 73 20 61 20 |n Calend|ar is a | |00002790| 73 6c 69 67 68 74 20 6d | 6f 64 69 66 69 63 61 74 |slight m|odificat| |000027a0| 69 6f 6e 20 6f 66 20 74 | 68 65 20 4a 75 6c 69 61 |ion of t|he Julia| |000027b0| 6e 2e 20 53 6f 20 69 74 | 20 69 73 20 61 6c 73 6f |n. So it| is also| |000027c0| 20 61 20 6d 61 74 68 65 | 6d 61 74 69 63 61 6c 20 | a mathe|matical | |000027d0| 73 6f 6c 61 72 20 63 61 | 6c 65 6e 64 61 72 2e 20 |solar ca|lendar. | |000027e0| 54 68 65 20 64 69 66 66 | 65 72 65 6e 63 65 73 20 |The diff|erences | |000027f0| 62 65 74 77 65 65 6e 20 | 74 68 65 20 47 72 65 67 |between |the Greg| |00002800| 6f 72 69 61 6e 20 61 6e | 64 20 4a 75 6c 69 61 6e |orian an|d Julian| |00002810| 20 63 61 6c 65 6e 64 61 | 72 73 20 69 6e 76 6f 6c | calenda|rs invol| |00002820| 76 65 20 74 68 65 20 6c | 65 61 70 20 79 65 61 72 |ve the l|eap year| |00002830| 20 72 75 6c 65 2c 20 74 | 68 65 20 7a 65 72 6f 20 | rule, t|he zero | |00002840| 70 6f 69 6e 74 2c 20 61 | 6e 64 20 74 68 65 20 6e |point, a|nd the n| |00002850| 75 6d 62 65 72 69 6e 67 | 20 73 79 73 74 65 6d 20 |umbering| system | |00002860| 6f 66 20 64 61 79 73 20 | 69 6e 20 46 65 62 72 75 |of days |in Febru| |00002870| 61 72 79 20 6f 66 20 6c | 65 61 70 20 79 65 61 72 |ary of l|eap year| |00002880| 73 2e 0d 0d 09 54 68 65 | 20 72 75 6c 65 20 64 69 |s....The| rule di| |00002890| 66 66 65 72 65 6e 63 65 | 73 20 62 65 74 77 65 65 |fference|s betwee| |000028a0| 6e 20 47 72 65 67 6f 72 | 69 61 6e 20 61 6e 64 20 |n Gregor|ian and | |000028b0| 4a 75 6c 69 61 6e 3a 0d | 0d 09 31 29 09 54 68 65 |Julian:.|..1).The| |000028c0| 20 4a 75 6c 69 61 6e 20 | 44 61 79 20 6f 66 20 6d | Julian |Day of m| |000028d0| 69 64 6e 69 67 68 74 20 | 61 74 20 74 68 65 20 73 |idnight |at the s| |000028e0| 74 61 72 74 20 6f 66 20 | 4a 61 6e 75 61 72 79 20 |tart of |January | |000028f0| 31 2c 20 31 20 41 2e 44 | 2e 20 47 72 65 67 6f 72 |1, 1 A.D|. Gregor| |00002900| 69 61 6e 20 28 20 61 20 | 4d 6f 6e 64 61 79 29 20 |ian ( a |Monday) | |00002910| 69 73 20 31 37 32 31 34 | 32 35 2e 35 2e 0d 0d 09 |is 17214|25.5....| |00002920| 32 29 09 54 68 65 20 65 | 78 74 72 61 20 64 61 79 |2).The e|xtra day| |00002930| 20 69 6e 20 46 65 62 72 | 75 61 72 79 20 6f 66 20 | in Febr|uary of | |00002940| 6c 65 61 70 20 79 65 61 | 72 73 20 69 73 20 73 69 |leap yea|rs is si| |00002950| 6d 70 6c 79 20 61 64 64 | 65 64 20 61 74 20 74 68 |mply add|ed at th| |00002960| 65 20 65 6e 64 2c 20 62 | 65 63 6f 6d 69 6e 67 20 |e end, b|ecoming | |00002970| 46 65 62 72 75 61 72 79 | 20 32 39 2e 0d 0d 09 33 |February| 29....3| |00002980| 29 09 4c 65 61 70 20 79 | 65 61 72 20 63 79 63 6c |).Leap y|ear cycl| |00002990| 65 73 20 61 72 65 20 34 | 30 30 20 79 65 61 72 73 |es are 4|00 years| |000029a0| 20 6c 6f 6e 67 2e 20 4f | 6e 65 20 63 79 63 6c 65 | long. O|ne cycle| |000029b0| 20 62 65 67 61 6e 20 69 | 6e 20 31 20 41 2e 44 2e | began i|n 1 A.D.| |000029c0| 20 61 6e 64 20 65 6e 64 | 65 64 20 69 6e 20 34 30 | and end|ed in 40| |000029d0| 30 20 41 2e 44 2e 20 54 | 68 65 20 63 79 63 6c 65 |0 A.D. T|he cycle| |000029e0| 20 70 72 65 63 65 64 69 | 6e 67 20 74 68 61 74 20 | precedi|ng that | |000029f0| 6f 6e 65 20 62 65 67 61 | 6e 20 69 6e 20 34 30 30 |one bega|n in 400| |00002a00| 20 42 2e 43 2e 20 61 6e | 64 20 65 6e 64 65 64 20 | B.C. an|d ended | |00002a10| 69 6e 20 31 20 42 2e 43 | 2e 20 57 69 74 68 69 6e |in 1 B.C|. Within| |00002a20| 20 61 6e 79 20 70 61 72 | 74 69 63 75 6c 61 72 20 | any par|ticular | |00002a30| 34 30 30 2d 79 65 61 72 | 20 63 79 63 6c 65 2c 20 |400-year| cycle, | |00002a40| 79 65 61 72 73 20 77 68 | 6f 73 65 20 70 6f 73 69 |years wh|ose posi| |00002a50| 74 69 6f 6e 20 69 6e 20 | 74 68 65 20 63 79 63 6c |tion in |the cycl| |00002a60| 65 20 69 73 20 64 69 76 | 69 73 69 62 6c 65 20 62 |e is div|isible b| |00002a70| 79 20 34 20 62 75 74 20 | 6e 6f 74 20 62 79 20 31 |y 4 but |not by 1| |00002a80| 30 30 20 41 4e 44 20 74 | 68 65 20 66 69 6e 61 6c |00 AND t|he final| |00002a90| 20 28 66 6f 75 72 2d 68 | 75 6e 64 72 65 64 74 68 | (four-h|undredth| |00002aa0| 29 20 79 65 61 72 20 61 | 72 65 20 6c 65 61 70 20 |) year a|re leap | |00002ab0| 79 65 61 72 73 2e 20 41 | 73 20 65 78 61 6d 70 6c |years. A|s exampl| |00002ac0| 65 73 2c 20 34 30 31 20 | 42 2e 43 2e 2c 20 31 20 |es, 401 |B.C., 1 | |00002ad0| 42 2e 43 2e 2c 20 61 6e | 64 20 32 30 30 30 20 41 |B.C., an|d 2000 A| |00002ae0| 2e 44 2e 20 61 72 65 20 | 6c 65 61 70 20 79 65 61 |.D. are |leap yea| |00002af0| 72 73 2c 20 62 75 74 20 | 35 30 31 20 42 2e 43 2e |rs, but |501 B.C.| |00002b00| 20 61 6e 64 20 31 39 30 | 30 20 41 2e 44 2e 20 61 | and 190|0 A.D. a| |00002b10| 72 65 20 6e 6f 74 2e 0d | 0d 09 54 68 65 20 47 72 |re not..|..The Gr| |00002b20| 65 67 6f 72 69 61 6e 20 | 63 61 6c 65 6e 64 61 72 |egorian |calendar| |00002b30| 20 77 61 73 20 69 6e 73 | 74 69 74 75 74 65 64 20 | was ins|tituted | |00002b40| 62 79 20 50 6f 70 65 20 | 47 72 65 67 6f 72 79 20 |by Pope |Gregory | |00002b50| 58 49 49 49 20 69 6e 20 | 31 35 38 32 20 41 2e 44 |XIII in |1582 A.D| |00002b60| 2e 20 49 74 20 68 61 64 | 20 62 65 65 6e 20 6e 6f |. It had| been no| |00002b70| 74 69 63 65 64 20 74 68 | 61 74 20 74 68 65 20 73 |ticed th|at the s| |00002b80| 65 61 73 6f 6e 73 20 77 | 65 72 65 20 6d 6f 76 69 |easons w|ere movi| |00002b90| 6e 67 20 65 61 72 6c 69 | 65 72 20 61 6e 64 20 65 |ng earli|er and e| |00002ba0| 61 72 6c 69 65 72 20 63 | 6f 6d 70 61 72 65 64 20 |arlier c|ompared | |00002bb0| 74 6f 20 67 69 76 65 6e | 20 63 61 6c 65 6e 64 61 |to given| calenda| |00002bc0| 72 20 64 61 74 65 73 2e | 20 45 71 75 69 76 61 6c |r dates.| Equival| |00002bd0| 65 6e 74 6c 79 2c 20 61 | 6e 79 20 66 69 78 65 64 |ently, a|ny fixed| |00002be0| 20 63 61 6c 65 6e 64 61 | 72 20 64 61 74 65 20 77 | calenda|r date w| |00002bf0| 61 73 20 6f 63 63 75 72 | 72 69 6e 67 20 6c 61 74 |as occur|ring lat| |00002c00| 65 72 20 61 6e 64 20 6c | 61 74 65 72 20 69 6e 20 |er and l|ater in | |00002c10| 74 68 65 20 79 65 61 72 | 20 61 73 20 64 65 66 69 |the year| as defi| |00002c20| 6e 65 64 20 62 79 20 74 | 68 65 20 73 65 61 73 6f |ned by t|he seaso| |00002c30| 6e 73 2e 20 49 74 20 77 | 61 73 20 63 6c 65 61 72 |ns. It w|as clear| |00002c40| 20 74 68 61 74 20 69 66 | 20 74 68 65 20 74 72 65 | that if| the tre| |00002c50| 6e 64 20 77 65 72 65 20 | 61 6c 6c 6f 77 65 64 20 |nd were |allowed | |00002c60| 74 6f 20 63 6f 6e 74 69 | 6e 75 65 2c 20 45 61 73 |to conti|nue, Eas| |00002c70| 74 65 72 20 28 77 68 69 | 63 68 20 69 73 20 73 75 |ter (whi|ch is su| |00002c80| 70 70 6f 73 65 64 20 74 | 6f 20 62 65 20 61 20 73 |pposed t|o be a s| |00002c90| 70 72 69 6e 67 20 74 69 | 6d 65 20 66 65 61 73 74 |pring ti|me feast| |00002ca0| 29 20 77 6f 75 6c 64 20 | 6d 6f 76 65 20 69 6e 74 |) would |move int| |00002cb0| 6f 20 73 75 6d 6d 65 72 | 2c 20 61 6e 64 20 74 68 |o summer|, and th| |00002cc0| 65 6e 20 61 75 74 75 6d | 6e 2c 20 65 74 63 2e 20 |en autum|n, etc. | |00002cd0| 54 68 65 20 50 6f 70 65 | 20 73 65 74 20 74 68 65 |The Pope| set the| |00002ce0| 20 7a 65 72 6f 20 70 6f | 69 6e 74 20 6f 66 20 74 | zero po|int of t| |00002cf0| 68 65 20 47 72 65 67 6f | 72 69 61 6e 20 63 61 6c |he Grego|rian cal| |00002d00| 65 6e 64 61 72 20 73 6f | 20 74 68 61 74 20 74 68 |endar so| that th| |00002d10| 65 20 76 65 72 6e 61 6c | 20 65 71 75 69 6e 6f 78 |e vernal| equinox| |00002d20| 20 77 6f 75 6c 64 20 6f | 63 63 75 72 20 63 6c 6f | would o|ccur clo| |00002d30| 73 65 20 74 6f 20 4d 61 | 72 63 68 20 32 31 2e 20 |se to Ma|rch 21. | |00002d40| 54 68 61 74 20 77 61 73 | 20 74 68 65 20 64 61 74 |That was| the dat| |00002d50| 65 20 69 74 20 68 61 64 | 20 69 6e 20 74 68 65 20 |e it had| in the | |00002d60| 66 6f 75 72 74 68 20 63 | 65 6e 74 75 72 79 20 41 |fourth c|entury A| |00002d70| 2e 44 2e 20 61 74 20 74 | 68 65 20 74 69 6d 65 20 |.D. at t|he time | |00002d80| 6f 66 20 74 68 65 20 43 | 6f 75 6e 63 69 6c 20 6f |of the C|ouncil o| |00002d90| 66 20 4e 69 63 61 65 61 | 2c 20 77 68 69 63 68 20 |f Nicaea|, which | |00002da0| 68 61 64 20 73 74 61 6e | 64 61 72 64 69 7a 65 64 |had stan|dardized| |00002db0| 20 74 68 65 20 72 75 6c | 65 20 75 73 65 64 20 74 | the rul|e used t| |00002dc0| 6f 20 63 6f 6d 70 75 74 | 65 20 74 68 65 20 64 61 |o comput|e the da| |00002dd0| 74 65 20 6f 66 20 45 61 | 73 74 65 72 2e 20 54 68 |te of Ea|ster. Th| |00002de0| 69 73 20 72 65 73 65 74 | 74 69 6e 67 20 6f 66 20 |is reset|ting of | |00002df0| 74 68 65 20 7a 65 72 6f | 20 70 6f 69 6e 74 20 72 |the zero| point r| |00002e00| 65 71 75 69 72 65 64 20 | 74 68 65 20 64 72 6f 70 |equired |the drop| |00002e10| 70 69 6e 67 20 6f 66 20 | 74 65 6e 20 64 61 79 73 |ping of |ten days| |00002e20| 20 66 72 6f 6d 20 74 68 | 65 20 63 61 6c 65 6e 64 | from th|e calend| |00002e30| 61 72 2e 20 42 79 20 64 | 65 63 72 65 65 20 6f 66 |ar. By d|ecree of| |00002e40| 20 74 68 65 20 50 6f 70 | 65 2c 20 4f 63 74 6f 62 | the Pop|e, Octob| |00002e50| 65 72 20 34 20 31 35 38 | 32 20 77 61 73 20 69 6d |er 4 158|2 was im| |00002e60| 6d 65 64 69 61 74 65 6c | 79 20 66 6f 6c 6c 6f 77 |mediatel|y follow| |00002e70| 65 64 20 62 79 20 4f 63 | 74 6f 62 65 72 20 31 35 |ed by Oc|tober 15| |00002e80| 20 31 35 38 32 2e 20 54 | 68 65 20 64 61 74 65 73 | 1582. T|he dates| |00002e90| 20 4f 63 74 6f 62 65 72 | 20 35 20 74 68 72 6f 75 | October| 5 throu| |00002ea0| 67 68 20 4f 63 74 6f 62 | 65 72 20 31 34 20 31 35 |gh Octob|er 14 15| |00002eb0| 38 32 20 77 65 72 65 20 | 73 69 6d 70 6c 79 20 64 |82 were |simply d| |00002ec0| 72 6f 70 70 65 64 2e 20 | 54 68 65 79 20 64 69 64 |ropped. |They did| |00002ed0| 20 6e 6f 74 20 65 78 69 | 73 74 2e 20 28 54 68 69 | not exi|st. (Thi| |00002ee0| 73 20 63 61 75 73 65 64 | 20 72 69 6f 74 69 6e 67 |s caused| rioting| |00002ef0| 20 69 6e 20 73 65 76 65 | 72 61 6c 20 63 69 74 69 | in seve|ral citi| |00002f00| 65 73 2e 20 50 65 6f 70 | 6c 65 20 74 68 6f 75 67 |es. Peop|le thoug| |00002f10| 68 74 20 74 68 65 69 72 | 20 6c 69 76 65 73 20 77 |ht their| lives w| |00002f20| 65 72 65 20 62 65 69 6e | 67 20 73 68 6f 72 74 65 |ere bein|g shorte| |00002f30| 6e 65 64 20 62 79 20 31 | 30 20 64 61 79 73 2e 29 |ned by 1|0 days.)| |00002f40| 20 54 68 65 20 72 75 6c | 65 20 66 6f 72 20 45 61 | The rul|e for Ea| |00002f50| 73 74 65 72 20 77 61 73 | 20 6d 6f 64 69 66 69 65 |ster was| modifie| |00002f60| 64 20 61 74 20 74 68 65 | 20 73 61 6d 65 20 74 69 |d at the| same ti| |00002f70| 6d 65 20 74 6f 20 6b 65 | 65 70 20 69 74 20 69 6e |me to ke|ep it in| |00002f80| 20 73 79 6e 63 68 72 6f | 6e 69 73 6d 20 77 69 74 | synchro|nism wit| |00002f90| 68 20 74 68 65 20 6e 65 | 77 20 6c 65 61 70 20 79 |h the ne|w leap y| |00002fa0| 65 61 72 20 72 75 6c 65 | 2e 0d 0d 09 4f 66 20 63 |ear rule|....Of c| |00002fb0| 6f 75 72 73 65 2c 20 74 | 68 65 20 50 6f 70 65 20 |ourse, t|he Pope | |00002fc0| 69 73 20 43 61 74 68 6f | 6c 69 63 2e 20 53 6f 20 |is Catho|lic. So | |00002fd0| 68 69 73 20 64 65 63 72 | 65 65 20 77 61 73 20 75 |his decr|ee was u| |00002fe0| 6e 69 76 65 72 73 61 6c | 6c 79 20 69 67 6e 6f 72 |niversal|ly ignor| |00002ff0| 65 64 20 65 78 63 65 70 | 74 20 69 6e 20 52 6f 6d |ed excep|t in Rom| |00003000| 61 6e 20 43 61 74 68 6f | 6c 69 63 20 63 6f 75 6e |an Catho|lic coun| |00003010| 74 72 69 65 73 20 61 6e | 64 20 74 68 65 69 72 20 |tries an|d their | |00003020| 63 6f 6c 6f 6e 69 65 73 | 2e 20 48 6f 77 65 76 65 |colonies|. Howeve| |00003030| 72 2c 20 72 65 6c 69 67 | 69 6f 75 73 20 62 65 6c |r, relig|ious bel| |00003040| 69 65 66 73 20 63 6f 75 | 6c 64 20 6e 6f 74 20 61 |iefs cou|ld not a| |00003050| 6c 74 65 72 20 74 68 65 | 20 66 61 63 74 20 74 68 |lter the| fact th| |00003060| 61 74 20 74 68 65 20 73 | 65 61 73 6f 6e 73 20 77 |at the s|easons w| |00003070| 65 72 65 20 6e 6f 74 69 | 63 65 61 62 6c 79 20 73 |ere noti|ceably s| |00003080| 6c 69 64 69 6e 67 2e 20 | 47 72 61 64 75 61 6c 6c |liding. |Graduall| |00003090| 79 2c 20 50 72 6f 74 65 | 73 74 61 6e 74 20 63 6f |y, Prote|stant co| |000030a0| 75 6e 74 72 69 65 73 20 | 61 64 6f 70 74 65 64 20 |untries |adopted | |000030b0| 74 68 65 20 47 72 65 67 | 6f 72 69 61 6e 20 63 61 |the Greg|orian ca| |000030c0| 6c 65 6e 64 61 72 2e 20 | 54 68 65 20 64 61 74 65 |lendar. |The date| |000030d0| 73 20 76 61 72 69 65 64 | 20 66 72 6f 6d 20 63 6f |s varied| from co| |000030e0| 75 6e 74 72 79 20 74 6f | 20 63 6f 75 6e 74 72 79 |untry to| country| |000030f0| 2e 20 54 68 65 20 6c 61 | 74 65 72 20 61 20 63 6f |. The la|ter a co| |00003100| 75 6e 74 72 79 20 6d 61 | 64 65 20 74 68 65 20 63 |untry ma|de the c| |00003110| 68 61 6e 67 65 2c 20 74 | 68 65 20 6d 6f 72 65 20 |hange, t|he more | |00003120| 64 61 79 73 20 68 61 64 | 20 74 6f 20 62 65 20 64 |days had| to be d| |00003130| 72 6f 70 70 65 64 2e 20 | 41 73 20 45 75 72 6f 70 |ropped. |As Europ| |00003140| 65 61 6e 20 69 6e 66 6c | 75 65 6e 63 65 20 73 70 |ean infl|uence sp| |00003150| 72 65 61 64 20 6f 76 65 | 72 20 74 68 65 20 67 6c |read ove|r the gl| |00003160| 6f 62 65 2c 20 6d 6f 73 | 74 20 6e 6f 6e 2d 43 68 |obe, mos|t non-Ch| |00003170| 72 69 73 74 69 61 6e 20 | 63 6f 75 6e 74 72 69 65 |ristian |countrie| |00003180| 73 20 61 64 6f 70 74 65 | 64 20 74 68 65 20 47 72 |s adopte|d the Gr| |00003190| 65 67 6f 72 69 61 6e 20 | 63 61 6c 65 6e 64 61 72 |egorian |calendar| |000031a0| 2c 20 61 74 20 6c 65 61 | 73 74 20 66 6f 72 20 63 |, at lea|st for c| |000031b0| 69 76 69 6c 20 75 73 65 | 2c 20 61 73 20 61 20 6d |ivil use|, as a m| |000031c0| 61 74 74 65 72 20 6f 66 | 20 65 63 6f 6e 6f 6d 69 |atter of| economi| |000031d0| 63 20 63 6f 6e 76 65 6e | 69 65 6e 63 65 2e 20 54 |c conven|ience. T| |000031e0| 68 65 20 6c 61 73 74 20 | 74 6f 20 6d 61 6b 65 20 |he last |to make | |000031f0| 74 68 65 20 63 68 61 6e | 67 65 20 77 65 72 65 2c |the chan|ge were,| |00003200| 20 69 6e 20 67 65 6e 65 | 72 61 6c 2c 20 45 61 73 | in gene|ral, Eas| |00003210| 74 65 72 6e 20 4f 72 74 | 68 6f 64 6f 78 20 43 68 |tern Ort|hodox Ch| |00003220| 72 69 73 74 69 61 6e 73 | 2e 20 54 6f 64 61 79 20 |ristians|. Today | |00003230| 74 68 69 73 20 63 61 6c | 65 6e 64 61 72 20 69 73 |this cal|endar is| |00003240| 20 74 68 65 20 63 69 76 | 69 6c 20 63 61 6c 65 6e | the civ|il calen| |00003250| 64 61 72 20 6e 65 61 72 | 6c 79 20 65 76 65 72 79 |dar near|ly every| |00003260| 77 68 65 72 65 20 28 62 | 75 74 20 65 78 63 65 70 |where (b|ut excep| |00003270| 74 69 6f 6e 73 2c 20 65 | 73 70 65 63 69 61 6c 6c |tions, e|speciall| |00003280| 79 20 69 6e 20 74 68 65 | 20 4d 69 64 64 6c 65 20 |y in the| Middle | |00003290| 45 61 73 74 2c 20 64 6f | 20 73 74 69 6c 6c 20 65 |East, do| still e| |000032a0| 78 69 73 74 29 2e 20 53 | 61 6d 70 6c 65 20 63 6f |xist). S|ample co| |000032b0| 6e 76 65 72 73 69 6f 6e | 20 64 61 74 65 73 3a 20 |nversion| dates: | |000032c0| 45 6e 67 6c 61 6e 64 d1 | 53 65 70 74 65 6d 62 65 |England.|Septembe| |000032d0| 72 20 32 20 31 37 35 32 | 20 77 61 73 20 66 6f 6c |r 2 1752| was fol| |000032e0| 6c 6f 77 65 64 20 62 79 | 20 53 65 70 74 65 6d 62 |lowed by| Septemb| |000032f0| 65 72 20 31 34 20 31 37 | 35 32 3b 20 4a 61 70 61 |er 14 17|52; Japa| |00003300| 6e 20 69 6e 20 31 38 37 | 33 3b 20 54 75 72 6b 65 |n in 187|3; Turke| |00003310| 79 20 31 39 30 38 3b 20 | 47 72 65 65 63 65 20 63 |y 1908; |Greece c| |00003320| 6f 6e 76 65 72 74 65 64 | 20 69 6e 20 31 39 32 33 |onverted| in 1923| |00003330| 2e 20 57 68 65 6e 20 45 | 6e 67 6c 61 6e 64 20 73 |. When E|ngland s| |00003340| 77 69 74 63 68 65 64 2c | 20 69 74 20 61 6c 73 6f |witched,| it also| |00003350| 20 62 65 67 61 6e 20 72 | 65 63 6b 6f 6e 69 6e 67 | began r|eckoning| |00003360| 20 74 68 65 20 73 74 61 | 72 74 20 6f 66 20 61 20 | the sta|rt of a | |00003370| 79 65 61 72 20 61 73 20 | 4a 61 6e 75 61 72 79 20 |year as |January | |00003380| 31 2e 0d 0d 09 54 68 65 | 20 61 76 65 72 61 67 65 |1....The| average| |00003390| 20 6c 65 6e 67 74 68 20 | 6f 66 20 61 20 79 65 61 | length |of a yea| |000033a0| 72 20 69 6e 20 74 68 65 | 20 47 72 65 67 6f 72 69 |r in the| Gregori| |000033b0| 61 6e 20 63 61 6c 65 6e | 64 61 72 20 69 73 20 28 |an calen|dar is (| |000033c0| 34 30 30 28 33 36 35 29 | 2b 31 30 30 2d 33 29 2f |400(365)|+100-3)/| |000033d0| 34 30 30 20 3d 20 65 78 | 61 63 74 6c 79 20 33 36 |400 = ex|actly 36| |000033e0| 35 2e 32 34 32 35 20 64 | 61 79 73 2e 20 54 68 69 |5.2425 d|ays. Thi| |000033f0| 73 20 69 73 20 69 6e 20 | 65 72 72 6f 72 20 28 69 |s is in |error (i| |00003400| 6e 20 74 68 65 20 73 61 | 6d 65 20 64 69 72 65 63 |n the sa|me direc| |00003410| 74 69 6f 6e 20 61 73 20 | 74 68 65 20 65 72 72 6f |tion as |the erro| |00003420| 72 20 66 6f 72 20 74 68 | 65 20 4a 75 6c 69 61 6e |r for th|e Julian| |00003430| 20 43 61 6c 65 6e 64 61 | 72 29 20 62 79 20 61 62 | Calenda|r) by ab| |00003440| 6f 75 74 20 30 2e 30 30 | 30 33 20 64 61 79 73 20 |out 0.00|03 days | |00003450| 70 65 72 20 79 65 61 72 | 2c 20 6f 72 20 6f 6e 65 |per year|, or one| |00003460| 20 64 61 79 20 69 6e 20 | 33 33 32 32 20 79 65 61 | day in |3322 yea| |00003470| 72 73 2e 0d 0d 09 41 20 | 73 6c 69 67 68 74 20 63 |rs....A |slight c| |00003480| 68 61 6e 67 65 20 74 6f | 20 74 68 65 20 47 72 65 |hange to| the Gre| |00003490| 67 6f 72 69 61 6e 20 43 | 61 6c 65 6e 64 61 72 20 |gorian C|alendar | |000034a0| 68 61 73 20 62 65 65 6e | 20 70 72 6f 70 6f 73 65 |has been| propose| |000034b0| 64 20 77 68 69 63 68 20 | 77 6f 75 6c 64 20 69 6d |d which |would im| |000034c0| 70 72 6f 76 65 20 74 68 | 65 20 61 63 63 75 72 61 |prove th|e accura| |000034d0| 63 79 20 63 6f 6e 73 69 | 64 65 72 61 62 6c 79 2e |cy consi|derably.| |000034e0| 20 55 6e 64 65 72 20 74 | 68 65 20 6d 6f 64 69 66 | Under t|he modif| |000034f0| 69 65 64 20 72 75 6c 65 | 73 2c 20 74 68 65 20 6c |ied rule|s, the l| |00003500| 65 61 70 20 79 65 61 72 | 20 63 79 63 6c 65 20 77 |eap year| cycle w| |00003510| 6f 75 6c 64 20 62 65 20 | 34 30 30 30 20 79 65 61 |ould be |4000 yea| |00003520| 72 73 20 6c 6f 6e 67 2e | 20 59 65 61 72 73 20 77 |rs long.| Years w| |00003530| 68 6f 73 65 20 70 6f 73 | 69 74 69 6f 6e 20 69 6e |hose pos|ition in| |00003540| 20 74 68 65 20 63 79 63 | 6c 65 20 69 73 20 64 69 | the cyc|le is di| |00003550| 76 69 73 69 62 6c 65 20 | 62 79 20 34 20 62 75 74 |visible |by 4 but| |00003560| 20 6e 6f 74 20 62 79 20 | 31 30 30 20 41 4e 44 20 | not by |100 AND | |00003570| 79 65 61 72 73 20 77 68 | 6f 73 65 20 70 6f 73 69 |years wh|ose posi| |00003580| 74 69 6f 6e 20 69 6e 20 | 74 68 65 20 63 79 63 6c |tion in |the cycl| |00003590| 65 20 69 73 20 64 69 76 | 69 73 69 62 6c 65 20 62 |e is div|isible b| |000035a0| 79 20 34 30 30 20 62 75 | 74 20 6e 6f 74 20 62 79 |y 400 bu|t not by| |000035b0| 20 34 30 30 30 20 77 6f | 75 6c 64 20 62 65 20 6c | 4000 wo|uld be l| |000035c0| 65 61 70 20 79 65 61 72 | 73 2e 20 54 68 75 73 20 |eap year|s. Thus | |000035d0| 31 39 30 30 20 41 2e 44 | 2e 2c 20 32 31 30 30 20 |1900 A.D|., 2100 | |000035e0| 41 2e 44 2e 2c 20 61 6e | 64 20 31 30 31 20 42 2e |A.D., an|d 101 B.| |000035f0| 43 2e 20 77 6f 75 6c 64 | 20 6e 6f 74 20 62 65 20 |C. would| not be | |00003600| 6c 65 61 70 20 79 65 61 | 72 73 20 28 61 73 20 77 |leap yea|rs (as w| |00003610| 69 74 68 20 74 68 65 20 | 70 72 65 73 65 6e 74 20 |ith the |present | |00003620| 73 79 73 74 65 6d 29 2e | 20 34 30 31 20 42 2e 43 |system).| 401 B.C| |00003630| 2e 2c 20 32 30 30 30 20 | 41 2e 44 2e 2c 20 61 6e |., 2000 |A.D., an| |00003640| 64 20 33 32 30 30 20 41 | 2e 44 2e 20 77 6f 75 6c |d 3200 A|.D. woul| |00003650| 64 20 62 65 20 6c 65 61 | 70 20 79 65 61 72 73 20 |d be lea|p years | |00003660| 28 61 6c 73 6f 20 74 68 | 65 20 73 61 6d 65 20 61 |(also th|e same a| |00003670| 73 20 69 6e 20 74 68 65 | 20 70 72 65 73 65 6e 74 |s in the| present| |00003680| 20 73 79 73 74 65 6d 29 | 2c 20 62 75 74 20 31 20 | system)|, but 1 | |00003690| 42 2e 43 2e 20 61 6e 64 | 20 34 30 30 30 20 41 2e |B.C. and| 4000 A.| |000036a0| 44 2e 20 77 6f 75 6c 64 | 20 6e 6f 74 20 62 65 20 |D. would| not be | |000036b0| 6c 65 61 70 20 79 65 61 | 72 73 20 28 64 69 66 66 |leap yea|rs (diff| |000036c0| 65 72 65 6e 74 20 66 72 | 6f 6d 20 74 68 65 20 70 |erent fr|om the p| |000036d0| 72 65 73 65 6e 74 20 73 | 79 73 74 65 6d 29 2e 20 |resent s|ystem). | |000036e0| 54 6f 20 6d 79 20 6b 6e | 6f 77 6c 65 64 67 65 20 |To my kn|owledge | |000036f0| 6e 6f 20 63 6f 75 6e 74 | 72 79 20 68 61 73 20 62 |no count|ry has b| |00003700| 6f 74 68 65 72 65 64 20 | 74 6f 20 61 64 6f 70 74 |othered |to adopt| |00003710| 20 74 68 69 73 20 73 75 | 67 67 65 73 74 69 6f 6e | this su|ggestion| |00003720| 2e 20 4f 66 20 63 6f 75 | 72 73 65 20 69 74 20 77 |. Of cou|rse it w| |00003730| 69 6c 6c 20 6d 61 6b 65 | 20 6e 6f 20 70 72 61 63 |ill make| no prac| |00003740| 74 69 63 61 6c 20 64 69 | 66 66 65 72 65 6e 63 65 |tical di|fference| |00003750| 20 75 6e 74 69 6c 20 74 | 68 65 20 79 65 61 72 20 | until t|he year | |00003760| 34 30 30 30 20 41 2e 44 | 2e 20 54 68 69 73 20 63 |4000 A.D|. This c| |00003770| 68 61 6e 67 65 2c 20 69 | 66 20 61 64 6f 70 74 65 |hange, i|f adopte| |00003780| 64 2c 20 77 6f 75 6c 64 | 20 61 6c 73 6f 20 66 6f |d, would| also fo| |00003790| 72 63 65 20 61 20 6d 6f | 64 69 66 69 63 61 74 69 |rce a mo|dificati| |000037a0| 6f 6e 20 69 6e 20 74 68 | 65 20 72 75 6c 65 20 66 |on in th|e rule f| |000037b0| 6f 72 20 63 61 6c 63 75 | 6c 61 74 69 6e 67 20 74 |or calcu|lating t| |000037c0| 68 65 20 64 61 74 65 20 | 6f 66 20 45 61 73 74 65 |he date |of Easte| |000037d0| 72 2e 20 49 6e 74 65 72 | 43 61 6c 20 64 6f 65 73 |r. Inter|Cal does| |000037e0| 20 6e 6f 74 20 75 73 65 | 20 74 68 65 20 6d 6f 64 | not use| the mod| |000037f0| 69 66 69 65 64 20 72 75 | 6c 65 73 2c 20 62 75 74 |ified ru|les, but| |00003800| 20 73 74 69 63 6b 73 20 | 74 6f 20 74 68 65 20 74 | sticks |to the t| |00003810| 72 61 64 69 74 69 6f 6e | 61 6c 20 47 72 65 67 6f |radition|al Grego| |00003820| 72 69 61 6e 20 43 61 6c | 65 6e 64 61 72 20 72 75 |rian Cal|endar ru| |00003830| 6c 65 73 2e 0d 0d 0d 57 | 65 73 74 65 72 6e 20 48 |les....W|estern H| |00003840| 69 73 74 6f 72 69 63 61 | 6c 0d 0d 09 54 68 69 73 |istorica|l...This| |00003850| 20 d2 63 61 6c 65 6e 64 | 61 72 d3 20 69 73 20 6e | .calend|ar. is n| |00003860| 6f 74 20 61 20 74 72 75 | 65 20 63 61 6c 65 6e 64 |ot a tru|e calend| |00003870| 61 72 20 61 74 20 61 6c | 6c 2e 20 49 74 20 69 73 |ar at al|l. It is| |00003880| 20 6d 65 72 65 6c 79 20 | 61 20 63 6f 6e 63 61 74 | merely |a concat| |00003890| 65 6e 61 74 69 6f 6e 20 | 6f 66 20 74 68 65 20 4a |enation |of the J| |000038a0| 75 6c 69 61 6e 20 61 6e | 64 20 47 72 65 67 6f 72 |ulian an|d Gregor| |000038b0| 69 61 6e 20 63 61 6c 65 | 6e 64 61 72 73 2c 20 77 |ian cale|ndars, w| |000038c0| 69 74 68 20 74 68 65 20 | d2 73 74 69 74 63 68 d3 |ith the |.stitch.| |000038d0| 20 70 6f 69 6e 74 20 62 | 65 69 6e 67 20 4f 63 74 | point b|eing Oct| |000038e0| 6f 62 65 72 20 34 2c 20 | 31 35 38 32 20 28 4a 75 |ober 4, |1582 (Ju| |000038f0| 6c 69 61 6e 20 44 61 79 | 20 6e 75 6d 62 65 72 20 |lian Day| number | |00003900| 32 32 39 39 31 35 39 2e | 35 29 2e 20 55 70 20 74 |2299159.|5). Up t| |00003910| 6f 20 61 6e 64 20 69 6e | 63 6c 75 64 69 6e 67 20 |o and in|cluding | |00003920| 74 68 61 74 20 64 61 79 | 2c 20 74 68 65 20 4a 75 |that day|, the Ju| |00003930| 6c 69 61 6e 20 43 61 6c | 65 6e 64 61 72 20 72 75 |lian Cal|endar ru| |00003940| 6c 65 73 20 61 72 65 20 | 75 73 65 64 2e 20 41 66 |les are |used. Af| |00003950| 74 65 72 20 74 68 61 74 | 20 64 61 79 2c 20 74 68 |ter that| day, th| |00003960| 65 20 47 72 65 67 6f 72 | 69 61 6e 20 43 61 6c 65 |e Gregor|ian Cale| |00003970| 6e 64 61 72 20 72 75 6c | 65 73 20 61 72 65 20 75 |ndar rul|es are u| |00003980| 73 65 64 2e 20 54 68 75 | 73 20 74 68 69 73 20 63 |sed. Thu|s this c| |00003990| 61 6c 65 6e 64 61 72 20 | 61 63 63 75 72 61 74 65 |alendar |accurate| |000039a0| 6c 79 20 72 65 70 72 65 | 73 65 6e 74 73 20 68 69 |ly repre|sents hi| |000039b0| 73 74 6f 72 69 63 61 6c | 20 64 61 74 65 73 20 28 |storical| dates (| |000039c0| 69 6e 20 74 68 65 20 63 | 6f 75 6e 74 72 69 65 73 |in the c|ountries| |000039d0| 20 77 68 69 63 68 20 61 | 64 6f 70 74 65 64 20 74 | which a|dopted t| |000039e0| 68 65 20 47 72 65 67 6f | 72 69 61 6e 20 63 61 6c |he Grego|rian cal| |000039f0| 65 6e 64 61 72 20 61 73 | 20 73 6f 6f 6e 20 61 73 |endar as| soon as| |00003a00| 20 69 74 20 77 61 73 20 | 64 65 63 72 65 65 64 29 | it was |decreed)| |00003a10| 20 66 72 6f 6d 20 74 68 | 65 20 73 74 61 62 69 6c | from th|e stabil| |00003a20| 69 7a 61 74 69 6f 6e 20 | 6f 66 20 74 68 65 20 4a |ization |of the J| |00003a30| 75 6c 69 61 6e 20 63 61 | 6c 65 6e 64 61 72 20 66 |ulian ca|lendar f| |00003a40| 6f 72 77 61 72 64 2e 20 | 46 6f 72 20 43 68 72 69 |orward. |For Chri| |00003a50| 73 74 69 61 6e 20 63 6f | 75 6e 74 72 69 65 73 20 |stian co|untries | |00003a60| 77 68 69 63 68 20 77 61 | 69 74 65 64 20 74 6f 20 |which wa|ited to | |00003a70| 61 64 6f 70 74 20 74 68 | 65 20 47 72 65 67 6f 72 |adopt th|e Gregor| |00003a80| 69 61 6e 20 43 61 6c 65 | 6e 64 61 72 20 75 6e 74 |ian Cale|ndar unt| |00003a90| 69 6c 20 6c 61 74 65 72 | 2c 20 74 68 65 72 65 20 |il later|, there | |00003aa0| 69 73 20 61 20 70 65 72 | 69 6f 64 20 66 72 6f 6d |is a per|iod from| |00003ab0| 20 4f 63 74 6f 62 65 72 | 20 31 35 20 31 35 38 32 | October| 15 1582| |00003ac0| 20 75 6e 74 69 6c 20 74 | 68 65 69 72 20 64 61 74 | until t|heir dat| |00003ad0| 65 20 6f 66 20 73 77 69 | 74 63 68 69 6e 67 20 64 |e of swi|tching d| |00003ae0| 75 72 69 6e 67 20 77 68 | 69 63 68 20 74 68 65 20 |uring wh|ich the | |00003af0| 57 65 73 74 65 72 6e 20 | 48 69 73 74 6f 72 69 63 |Western |Historic| |00003b00| 61 6c 20 63 61 6c 65 6e | 64 61 72 20 69 73 20 6e |al calen|dar is n| |00003b10| 6f 74 20 68 69 73 74 6f | 72 69 63 61 6c 6c 79 20 |ot histo|rically | |00003b20| 61 63 63 75 72 61 74 65 | 2e 20 4f 66 20 63 6f 75 |accurate|. Of cou| |00003b30| 72 73 65 20 66 6f 72 20 | 6e 6f 6e 2d 43 68 72 69 |rse for |non-Chri| |00003b40| 73 74 69 61 6e 20 63 6f | 75 6e 74 72 69 65 73 2c |stian co|untries,| |00003b50| 20 74 68 65 20 4a 75 6c | 69 61 6e 20 43 61 6c 65 | the Jul|ian Cale| |00003b60| 6e 64 61 72 20 77 61 73 | 20 6e 65 76 65 72 20 75 |ndar was| never u| |00003b70| 73 65 64 20 73 6f 20 74 | 68 65 20 57 65 73 74 65 |sed so t|he Weste| |00003b80| 72 6e 20 48 69 73 74 6f | 72 69 63 61 6c 20 63 61 |rn Histo|rical ca| |00003b90| 6c 65 6e 64 61 72 20 6d | 61 6b 65 73 20 6c 65 73 |lendar m|akes les| |00003ba0| 73 20 73 65 6e 73 65 2e | 20 46 6f 72 20 66 75 6e |s sense.| For fun| |00003bb0| 2c 20 77 69 74 68 20 74 | 68 65 20 70 72 69 6d 61 |, with t|he prima| |00003bc0| 72 79 20 63 61 6c 65 6e | 64 61 72 20 73 79 73 74 |ry calen|dar syst| |00003bd0| 65 6d 20 73 65 74 20 74 | 6f 20 57 65 73 74 65 72 |em set t|o Wester| |00003be0| 6e 20 48 69 73 74 6f 72 | 69 63 61 6c 20 28 74 68 |n Histor|ical (th| |00003bf0| 65 20 64 65 66 61 75 6c | 74 29 2c 20 64 69 73 70 |e defaul|t), disp| |00003c00| 6c 61 79 20 4f 63 74 6f | 62 65 72 20 31 35 38 32 |lay Octo|ber 1582| |00003c10| 2e 0d 0d 0d 4a 65 77 69 | 73 68 20 43 61 6c 65 6e |....Jewi|sh Calen| |00003c20| 64 61 72 0d 0d 09 54 68 | 65 20 4a 65 77 69 73 68 |dar...Th|e Jewish| |00003c30| 20 63 61 6c 65 6e 64 61 | 72 20 69 73 20 61 20 6d | calenda|r is a m| |00003c40| 61 74 68 65 6d 61 74 69 | 63 61 6c 20 6c 75 6e 69 |athemati|cal luni| |00003c50| 2d 73 6f 6c 61 72 20 63 | 61 6c 65 6e 64 61 72 2e |-solar c|alendar.| |00003c60| 20 49 74 20 65 76 6f 6c | 76 65 64 20 73 6c 6f 77 | It evol|ved slow| |00003c70| 6c 79 20 6f 76 65 72 20 | 6d 61 6e 79 2c 20 6d 61 |ly over |many, ma| |00003c80| 6e 79 20 63 65 6e 74 75 | 72 69 65 73 2e 20 44 75 |ny centu|ries. Du| |00003c90| 72 69 6e 67 20 74 68 65 | 20 42 61 62 79 6c 6f 6e |ring the| Babylon| |00003ca0| 69 61 6e 20 63 61 70 74 | 69 76 69 74 79 20 74 68 |ian capt|ivity th| |00003cb0| 65 20 63 61 6c 65 6e 64 | 61 72 20 74 6f 6f 6b 20 |e calend|ar took | |00003cc0| 6f 6e 20 73 65 76 65 72 | 61 6c 20 66 65 61 74 75 |on sever|al featu| |00003cd0| 72 65 73 20 6f 66 20 74 | 68 65 20 42 61 62 79 6c |res of t|he Babyl| |00003ce0| 6f 6e 69 61 6e 20 63 61 | 6c 65 6e 64 61 72 2c 20 |onian ca|lendar, | |00003cf0| 69 6e 63 6c 75 64 69 6e | 67 20 74 68 65 20 63 68 |includin|g the ch| |00003d00| 61 6e 67 69 6e 67 20 6f | 66 20 6d 6f 73 74 20 6d |anging o|f most m| |00003d10| 6f 6e 74 68 20 6e 61 6d | 65 73 20 74 6f 20 74 68 |onth nam|es to th| |00003d20| 65 69 72 20 42 61 62 79 | 6c 6f 6e 69 61 6e 20 65 |eir Baby|lonian e| |00003d30| 71 75 69 76 61 6c 65 6e | 74 73 2e 20 42 75 74 20 |quivalen|ts. But | |00003d40| 6c 6f 6e 67 20 61 66 74 | 65 72 20 74 68 65 20 63 |long aft|er the c| |00003d50| 61 70 74 69 76 69 74 79 | 20 74 68 65 20 63 61 6c |aptivity| the cal| |00003d60| 65 6e 64 61 72 20 63 6f | 6e 74 69 6e 75 65 64 20 |endar co|ntinued | |00003d70| 74 6f 20 62 65 20 69 6d | 70 72 6f 76 65 64 2e 20 |to be im|proved. | |00003d80| 4d 61 6e 79 20 73 6f 75 | 72 63 65 73 20 28 6d 6f |Many sou|rces (mo| |00003d90| 73 74 20 72 65 63 65 6e | 74 6c 79 20 53 6b 79 20 |st recen|tly Sky | |00003da0| 61 6e 64 20 54 65 6c 65 | 73 63 6f 70 65 20 4d 61 |and Tele|scope Ma| |00003db0| 67 61 7a 69 6e 65 2c 20 | 53 65 70 74 65 6d 62 65 |gazine, |Septembe| |00003dc0| 72 20 31 39 39 34 20 69 | 73 73 75 65 2c 20 d2 48 |r 1994 i|ssue, .H| |00003dd0| 61 79 79 69 6d 20 53 65 | 6c 69 67 20 53 6c 6f 6e |ayyim Se|lig Slon| |00003de0| 69 6d 73 6b 69 d3 2c 20 | 70 61 67 65 73 20 39 33 |imski., |pages 93| |00003df0| d0 39 35 29 20 73 74 61 | 74 65 20 74 68 61 74 20 |.95) sta|te that | |00003e00| 69 74 20 72 65 61 63 68 | 65 64 20 69 74 73 20 70 |it reach|ed its p| |00003e10| 72 65 73 65 6e 74 20 66 | 6f 72 6d 20 69 6e 20 33 |resent f|orm in 3| |00003e20| 35 39 20 41 2e 44 2e 2c | 20 64 75 72 69 6e 67 20 |59 A.D.,| during | |00003e30| 74 68 65 20 74 69 6d 65 | 20 6f 66 20 50 61 74 72 |the time| of Patr| |00003e40| 69 61 72 63 68 20 48 69 | 6c 6c 65 6c 20 49 49 2e |iarch Hi|llel II.| |00003e50| 20 42 75 74 20 61 63 63 | 6f 72 64 69 6e 67 20 74 | But acc|ording t| |00003e60| 6f 20 74 68 65 20 45 6e | 63 79 63 6c 6f 70 65 64 |o the En|cycloped| |00003e70| 69 61 20 4a 75 64 61 69 | 63 61 20 69 74 20 64 69 |ia Judai|ca it di| |00003e80| 64 20 6e 6f 74 20 72 65 | 61 63 68 20 69 74 73 20 |d not re|ach its | |00003e90| 6d 6f 64 65 72 6e 20 66 | 6f 72 6d 20 75 6e 74 69 |modern f|orm unti| |00003ea0| 6c 20 74 68 65 20 74 65 | 6e 74 68 20 63 65 6e 74 |l the te|nth cent| |00003eb0| 75 72 79 20 41 2e 44 2e | 20 48 69 6c 6c 65 6c 20 |ury A.D.| Hillel | |00003ec0| 49 49 20 74 6f 6f 6b 20 | 61 20 76 65 72 79 20 69 |II took |a very i| |00003ed0| 6d 70 6f 72 74 61 6e 74 | 20 73 74 65 70 2c 20 68 |mportant| step, h| |00003ee0| 6f 77 65 76 65 72 2e 20 | 48 65 20 6d 61 64 65 20 |owever. |He made | |00003ef0| 70 75 62 6c 69 63 20 74 | 68 65 20 72 75 6c 65 73 |public t|he rules| |00003f00| 20 6f 66 20 74 68 65 20 | 4a 65 77 69 73 68 20 63 | of the |Jewish c| |00003f10| 61 6c 65 6e 64 61 72 2c | 20 77 68 69 63 68 20 75 |alendar,| which u| |00003f20| 6e 74 69 6c 20 74 68 65 | 6e 20 68 61 64 20 62 65 |ntil the|n had be| |00003f30| 65 6e 20 61 20 63 6c 6f | 73 65 6c 79 20 67 75 61 |en a clo|sely gua| |00003f40| 72 64 65 64 20 73 65 63 | 72 65 74 20 6b 6e 6f 77 |rded sec|ret know| |00003f50| 6e 20 6f 6e 6c 79 20 74 | 6f 20 61 20 66 65 77 20 |n only t|o a few | |00003f60| 4a 65 77 73 20 61 6e 64 | 20 6e 6f 20 47 65 6e 74 |Jews and| no Gent| |00003f70| 69 6c 65 73 2e 20 54 68 | 65 20 45 6e 63 79 63 6c |iles. Th|e Encycl| |00003f80| 6f 70 65 64 69 61 20 4a | 75 64 61 69 63 61 20 73 |opedia J|udaica s| |00003f90| 70 65 63 75 6c 61 74 65 | 73 20 74 68 61 74 20 48 |peculate|s that H| |00003fa0| 69 6c 6c 65 6c 20 49 49 | 20 73 74 61 6e 64 61 72 |illel II| standar| |00003fb0| 64 69 7a 65 64 20 74 68 | 65 20 6c 65 61 70 20 79 |dized th|e leap y| |00003fc0| 65 61 72 20 72 75 6c 65 | 20 28 52 75 6c 65 20 23 |ear rule| (Rule #| |00003fd0| 35 20 62 65 6c 6f 77 29 | 2e 20 54 68 65 20 6d 6f |5 below)|. The mo| |00003fe0| 72 65 20 73 75 62 74 6c | 65 20 66 65 61 74 75 72 |re subtl|e featur| |00003ff0| 65 73 20 65 6d 62 6f 64 | 69 65 64 20 69 6e 20 52 |es embod|ied in R| |00004000| 75 6c 65 20 37 66 20 62 | 65 6c 6f 77 20 61 70 70 |ule 7f b|elow app| |00004010| 61 72 65 6e 74 6c 79 20 | 74 6f 6f 6b 20 61 20 66 |arently |took a f| |00004020| 65 77 20 68 75 6e 64 72 | 65 64 20 6d 6f 72 65 20 |ew hundr|ed more | |00004030| 79 65 61 72 73 20 74 6f | 20 62 65 63 6f 6d 65 20 |years to| become | |00004040| 73 74 61 6e 64 61 72 64 | 69 7a 65 64 2e 0d 0d 09 |standard|ized....| |00004050| 54 68 65 20 73 74 61 72 | 74 69 6e 67 20 70 6f 69 |The star|ting poi| |00004060| 6e 74 20 6f 66 20 74 68 | 65 20 4a 65 77 69 73 68 |nt of th|e Jewish| |00004070| 20 63 61 6c 65 6e 64 61 | 72 20 77 61 73 20 69 6e | calenda|r was in| |00004080| 74 65 6e 64 65 64 20 62 | 79 20 69 74 73 20 64 65 |tended b|y its de| |00004090| 76 65 6c 6f 70 65 72 73 | 20 74 6f 20 63 6f 72 72 |velopers| to corr| |000040a0| 65 73 70 6f 6e 64 20 74 | 6f 20 74 68 65 20 63 72 |espond t|o the cr| |000040b0| 65 61 74 69 6f 6e 20 6f | 66 20 74 68 65 20 77 6f |eation o|f the wo| |000040c0| 72 6c 64 2e 20 54 68 65 | 72 65 66 6f 72 65 2c 20 |rld. The|refore, | |000040d0| 69 74 73 20 7a 65 72 6f | 20 70 6f 69 6e 74 20 69 |its zero| point i| |000040e0| 73 20 71 75 69 74 65 20 | 66 61 72 20 69 6e 20 74 |s quite |far in t| |000040f0| 68 65 20 70 61 73 74 20 | 61 6e 64 20 70 72 65 64 |he past |and pred| |00004100| 61 74 65 73 20 61 6e 79 | 20 77 72 69 74 74 65 6e |ates any| written| |00004110| 20 68 69 73 74 6f 72 79 | 2e 20 4e 6f 74 20 73 75 | history|. Not su| |00004120| 72 70 72 69 73 69 6e 67 | 6c 79 2c 20 6e 6f 20 65 |rprising|ly, no e| |00004130| 72 61 20 6c 61 62 65 6c | 20 66 6f 72 20 6e 65 67 |ra label| for neg| |00004140| 61 74 69 76 65 20 79 65 | 61 72 73 20 65 76 65 72 |ative ye|ars ever| |00004150| 20 64 65 76 65 6c 6f 70 | 65 64 2e 20 4e 65 67 61 | develop|ed. Nega| |00004160| 74 69 76 65 20 79 65 61 | 72 73 20 68 61 76 65 20 |tive yea|rs have | |00004170| 6e 6f 74 20 62 65 65 6e | 20 6e 65 65 64 65 64 2e |not been| needed.| |00004180| 20 41 6e 20 65 72 61 20 | 6c 61 62 65 6c 20 66 6f | An era |label fo| |00004190| 72 20 70 6f 73 69 74 69 | 76 65 20 79 65 61 72 73 |r positi|ve years| |000041a0| 20 65 78 69 73 74 73 2c | 20 61 74 20 6c 65 61 73 | exists,| at leas| |000041b0| 74 20 66 6f 72 20 75 73 | 65 20 62 79 20 73 63 68 |t for us|e by sch| |000041c0| 6f 6c 61 72 73 20 69 66 | 20 6e 6f 74 20 62 79 20 |olars if| not by | |000041d0| 74 68 65 20 6f 72 64 69 | 6e 61 72 79 20 66 6f 6c |the ordi|nary fol| |000041e0| 6b 73 2c 20 62 75 74 20 | 69 73 20 72 61 72 65 6c |ks, but |is rarel| |000041f0| 79 20 73 65 65 6e 2e 20 | 49 74 20 69 73 20 41 2e |y seen. |It is A.| |00004200| 4d 2e 20 28 41 6e 6e 6f | 20 4d 75 6e 64 69 2c 20 |M. (Anno| Mundi, | |00004210| 4c 61 74 69 6e 20 66 6f | 72 20 59 65 61 72 20 6f |Latin fo|r Year o| |00004220| 66 20 74 68 65 20 57 6f | 72 6c 64 29 2e 20 42 75 |f the Wo|rld). Bu| |00004230| 74 20 49 6e 74 65 72 43 | 61 6c 20 6e 65 65 64 73 |t InterC|al needs| |00004240| 20 65 72 61 20 6c 61 62 | 65 6c 73 20 73 69 6e 63 | era lab|els sinc| |00004250| 65 20 69 74 20 61 6c 6c | 6f 77 73 20 62 6f 74 68 |e it all|ows both| |00004260| 20 70 6f 73 69 74 69 76 | 65 20 61 6e 64 20 6e 65 | positiv|e and ne| |00004270| 67 61 74 69 76 65 20 79 | 65 61 72 73 2e 20 53 6f |gative y|ears. So| |00004280| 20 49 20 68 61 76 65 20 | 69 6e 76 65 6e 74 65 64 | I have |invented| |00004290| 20 28 77 69 74 68 6f 75 | 74 20 69 6e 74 65 6e 74 | (withou|t intent| |000042a0| 20 74 6f 20 6f 66 66 65 | 6e 64 29 20 74 68 65 20 | to offe|nd) the | |000042b0| 61 62 62 72 65 76 69 61 | 74 69 6f 6e 20 42 2e 57 |abbrevia|tion B.W| |000042c0| 2e 20 28 42 65 66 6f 72 | 65 20 74 68 65 20 57 6f |. (Befor|e the Wo| |000042d0| 72 6c 64 29 20 61 6e 64 | 20 75 73 65 20 41 2e 4d |rld) and| use A.M| |000042e0| 2e 20 65 76 65 6e 20 74 | 68 6f 75 67 68 20 69 74 |. even t|hough it| |000042f0| 20 69 73 20 6e 6f 74 20 | 63 6f 6d 6d 6f 6e 20 70 | is not |common p| |00004300| 72 61 63 74 69 63 65 2e | 0d 0d 09 54 68 65 20 4a |ractice.|...The J| |00004310| 65 77 69 73 68 20 63 61 | 6c 65 6e 64 61 72 20 6d |ewish ca|lendar m| |00004320| 6f 6e 74 68 20 6e 61 6d | 65 73 20 61 6e 64 20 6d |onth nam|es and m| |00004330| 6f 73 74 20 74 65 72 6d | 73 20 75 73 65 64 20 69 |ost term|s used i| |00004340| 6e 20 69 74 73 20 64 65 | 66 69 6e 69 74 69 6f 6e |n its de|finition| |00004350| 20 61 72 65 20 48 65 62 | 72 65 77 20 77 6f 72 64 | are Heb|rew word| |00004360| 73 2e 20 49 20 6b 6e 6f | 77 20 6f 66 20 6e 6f 20 |s. I kno|w of no | |00004370| 73 74 61 6e 64 61 72 64 | 20 74 72 61 6e 73 6c 69 |standard| transli| |00004380| 74 65 72 61 74 69 6f 6e | 20 73 63 68 65 6d 65 20 |teration| scheme | |00004390| 66 6f 72 20 63 6f 6e 76 | 65 72 74 69 6e 67 20 48 |for conv|erting H| |000043a0| 65 62 72 65 77 20 69 6e | 74 6f 20 45 6e 67 6c 69 |ebrew in|to Engli| |000043b0| 73 68 2e 20 54 68 65 72 | 65 66 6f 72 65 20 74 68 |sh. Ther|efore th| |000043c0| 65 20 45 6e 67 6c 69 73 | 68 20 73 70 65 6c 6c 69 |e Englis|h spelli| |000043d0| 6e 67 73 20 6f 66 20 4a | 65 77 69 73 68 20 6d 6f |ngs of J|ewish mo| |000043e0| 6e 74 68 73 2c 20 63 61 | 6c 65 6e 64 72 69 63 61 |nths, ca|lendrica| |000043f0| 6c 20 74 65 72 6d 73 2c | 20 61 6e 64 20 74 68 65 |l terms,| and the| |00004400| 20 6e 61 6d 65 73 20 6f | 66 20 72 65 6c 69 67 69 | names o|f religi| |00004410| 6f 75 73 20 68 6f 6c 69 | 64 61 79 73 20 28 73 75 |ous holi|days (su| |00004420| 63 68 20 61 73 20 52 6f | 73 68 20 48 61 73 68 6f |ch as Ro|sh Hasho| |00004430| 6e 61 68 29 20 61 72 65 | 20 73 6f 6d 65 77 68 61 |nah) are| somewha| |00004440| 74 20 61 72 62 69 74 72 | 61 72 79 2e 20 49 20 68 |t arbitr|ary. I h| |00004450| 61 76 65 20 75 73 65 64 | 20 74 68 65 20 73 70 65 |ave used| the spe| |00004460| 6c 6c 69 6e 67 73 20 66 | 6f 75 6e 64 20 69 6e 20 |llings f|ound in | |00004470| 74 68 65 20 4a 65 77 69 | 73 68 20 43 61 6c 65 6e |the Jewi|sh Calen| |00004480| 64 61 72 20 70 72 6f 67 | 72 61 6d 20 28 66 72 65 |dar prog|ram (fre| |00004490| 65 77 61 72 65 20 77 72 | 69 74 74 65 6e 20 62 79 |eware wr|itten by| |000044a0| 20 46 72 61 6e 6b 20 59 | 65 6c 6c 69 6e 20 6f 66 | Frank Y|ellin of| |000044b0| 20 52 65 64 77 6f 6f 64 | 20 43 69 74 79 20 43 61 | Redwood| City Ca| |000044c0| 6c 69 66 6f 72 6e 69 61 | 29 2e 20 49 20 77 69 73 |lifornia|). I wis| |000044d0| 68 20 74 6f 20 74 68 61 | 6e 6b 20 4d 72 2e 20 59 |h to tha|nk Mr. Y| |000044e0| 65 6c 6c 69 6e 20 66 6f | 72 20 6d 61 6b 69 6e 67 |ellin fo|r making| |000044f0| 20 68 69 73 20 73 6f 75 | 72 63 65 20 63 6f 64 65 | his sou|rce code| |00004500| 20 61 76 61 69 6c 61 62 | 6c 65 20 6f 6e 20 74 68 | availab|le on th| |00004510| 65 20 49 6e 74 65 72 6e | 65 74 2e 20 49 6e 20 73 |e Intern|et. In s| |00004520| 70 69 74 65 20 6f 66 20 | 72 65 61 64 69 6e 67 20 |pite of |reading | |00004530| 74 68 65 20 61 72 74 69 | 63 6c 65 20 6f 6e 20 74 |the arti|cle on t| |00004540| 68 65 20 4a 65 77 69 73 | 68 20 63 61 6c 65 6e 64 |he Jewis|h calend| |00004550| 61 72 20 69 6e 20 74 68 | 65 20 45 6e 63 79 63 6c |ar in th|e Encycl| |00004560| 6f 70 65 64 69 61 20 4a | 75 64 61 69 63 61 20 61 |opedia J|udaica a| |00004570| 6e 64 20 69 6e 20 73 70 | 69 74 65 20 6f 66 20 70 |nd in sp|ite of p| |00004580| 65 73 74 65 72 69 6e 67 | 20 73 65 76 65 72 61 6c |estering| several| |00004590| 20 4a 65 77 69 73 68 20 | 66 72 69 65 6e 64 73 2c | Jewish |friends,| |000045a0| 20 49 20 77 61 73 20 75 | 6e 61 62 6c 65 20 74 6f | I was u|nable to| |000045b0| 20 64 65 76 65 6c 6f 70 | 20 61 20 63 6f 6d 70 75 | develop| a compu| |000045c0| 74 65 72 20 61 6c 67 6f | 72 69 74 68 6d 20 66 6f |ter algo|rithm fo| |000045d0| 72 20 74 68 69 73 20 63 | 61 6c 65 6e 64 61 72 20 |r this c|alendar | |000045e0| 75 6e 74 69 6c 20 49 20 | 65 78 61 6d 69 6e 65 64 |until I |examined| |000045f0| 20 59 65 6c 6c 69 6e d5 | 73 20 73 6f 75 72 63 65 | Yellin.|s source| |00004600| 2e 20 54 68 65 20 d2 72 | 75 6c 65 73 d3 20 62 65 |. The .r|ules. be| |00004610| 6c 6f 77 20 61 72 65 20 | 6d 79 20 72 65 6e 64 65 |low are |my rende| |00004620| 72 69 6e 67 20 6f 66 20 | 72 75 6c 65 73 20 73 74 |ring of |rules st| |00004630| 61 74 65 64 20 69 6e 20 | 74 68 65 20 45 6e 63 79 |ated in |the Ency| |00004640| 63 6c 6f 70 65 64 69 61 | 20 4a 75 64 61 69 63 61 |clopedia| Judaica| |00004650| 20 61 73 20 69 6d 70 6c | 65 6d 65 6e 74 65 64 20 | as impl|emented | |00004660| 62 79 20 74 68 65 20 4a | 65 77 69 73 68 20 43 61 |by the J|ewish Ca| |00004670| 6c 65 6e 64 61 72 20 70 | 72 6f 67 72 61 6d 2e 20 |lendar p|rogram. | |00004680| 4d 79 20 63 6f 6e 74 72 | 69 62 75 74 69 6f 6e 73 |My contr|ibutions| |00004690| 20 69 6e 20 74 68 69 73 | 20 61 72 65 61 20 77 65 | in this| area we| |000046a0| 72 65 20 74 6f 20 70 72 | 6f 76 69 64 65 20 61 20 |re to pr|ovide a | |000046b0| 66 61 73 74 65 72 20 69 | 6d 70 6c 65 6d 65 6e 74 |faster i|mplement| |000046c0| 61 74 69 6f 6e 2c 20 72 | 65 6d 6f 76 65 20 59 65 |ation, r|emove Ye| |000046d0| 6c 6c 69 6e d5 73 20 6c | 69 6d 69 74 73 20 6f 66 |llin.s l|imits of| |000046e0| 20 64 61 74 65 73 20 63 | 6f 72 72 65 73 70 6f 6e | dates c|orrespon| |000046f0| 64 69 6e 67 20 74 6f 20 | 31 20 41 2e 44 2e 20 74 |ding to |1 A.D. t| |00004700| 68 72 6f 75 67 68 20 32 | 39 39 39 20 41 2e 44 2e |hrough 2|999 A.D.| |00004710| 2c 20 61 6e 64 20 65 78 | 74 65 6e 64 20 74 68 65 |, and ex|tend the| |00004720| 20 72 75 6c 65 73 20 69 | 6e 74 6f 20 6e 65 67 61 | rules i|nto nega| |00004730| 74 69 76 65 20 79 65 61 | 72 73 2e 20 49 20 68 65 |tive yea|rs. I he| |00004740| 61 72 74 69 6c 79 20 72 | 65 63 6f 6d 6d 65 6e 64 |artily r|ecommend| |00004750| 20 59 65 6c 6c 69 6e d5 | 73 20 70 72 6f 67 72 61 | Yellin.|s progra| |00004760| 6d 20 74 6f 20 61 6e 79 | 6f 6e 65 20 69 6e 74 65 |m to any|one inte| |00004770| 72 65 73 74 65 64 20 69 | 6e 20 74 68 65 20 4a 65 |rested i|n the Je| |00004780| 77 69 73 68 20 63 61 6c | 65 6e 64 61 72 2e 20 49 |wish cal|endar. I| |00004790| 74 20 68 61 73 20 6d 75 | 63 68 20 6d 6f 72 65 20 |t has mu|ch more | |000047a0| 65 78 74 65 6e 73 69 76 | 65 20 6c 61 62 65 6c 69 |extensiv|e labeli| |000047b0| 6e 67 20 6f 66 20 4a 65 | 77 69 73 68 20 72 65 6c |ng of Je|wish rel| |000047c0| 69 67 69 6f 75 73 20 66 | 65 73 74 69 76 61 6c 73 |igious f|estivals| |000047d0| 2c 20 68 6f 6c 79 64 61 | 79 73 2c 20 65 74 63 2e |, holyda|ys, etc.| |000047e0| 20 74 68 61 6e 20 49 6e | 74 65 72 43 61 6c 2e 0d | than In|terCal..| |000047f0| 0d 09 54 68 65 20 72 75 | 6c 65 73 20 6f 66 20 74 |..The ru|les of t| |00004800| 68 65 20 4a 65 77 69 73 | 68 20 63 61 6c 65 6e 64 |he Jewis|h calend| |00004810| 61 72 2c 20 77 68 65 6e | 20 73 74 61 74 65 64 20 |ar, when| stated | |00004820| 28 61 73 20 62 65 6c 6f | 77 29 20 69 6e 20 61 6c |(as belo|w) in al| |00004830| 67 6f 72 69 74 68 6d 69 | 63 20 66 6f 72 6d 20 66 |gorithmi|c form f| |00004840| 6f 72 20 75 73 65 20 69 | 6e 20 61 20 63 6f 6d 70 |or use i|n a comp| |00004850| 75 74 65 72 20 70 72 6f | 67 72 61 6d 2c 20 73 6f |uter pro|gram, so| |00004860| 75 6e 64 20 63 6f 6d 70 | 6c 69 63 61 74 65 64 20 |und comp|licated | |00004870| 61 6e 64 20 61 72 62 69 | 74 72 61 72 79 2e 20 54 |and arbi|trary. T| |00004880| 68 65 20 72 61 74 69 6f | 6e 61 6c 65 20 66 6f 72 |he ratio|nale for| |00004890| 20 74 68 65 20 72 75 6c | 65 73 20 69 73 20 65 78 | the rul|es is ex| |000048a0| 70 6c 61 69 6e 65 64 20 | 69 6e 20 74 68 65 20 45 |plained |in the E| |000048b0| 6e 63 79 63 6c 6f 70 65 | 64 69 61 20 4a 75 64 61 |ncyclope|dia Juda| |000048c0| 69 63 61 2e 20 54 6f 20 | 70 75 74 20 74 68 65 6d |ica. To |put them| |000048d0| 20 69 6e 20 74 68 65 20 | 73 69 6d 70 6c 65 73 74 | in the |simplest| |000048e0| 20 74 65 72 6d 73 d1 74 | 68 65 20 31 39 2d 79 65 | terms.t|he 19-ye| |000048f0| 61 72 20 6c 65 61 70 20 | 79 65 61 72 20 63 79 63 |ar leap |year cyc| |00004900| 6c 65 20 77 69 74 68 20 | 69 74 73 20 69 6d 70 6c |le with |its impl| |00004910| 69 65 64 20 63 79 63 6c | 65 20 6f 66 20 6d 6f 6e |ied cycl|e of mon| |00004920| 74 68 73 20 69 73 20 66 | 6f 6c 6c 6f 77 65 64 20 |ths is f|ollowed | |00004930| 65 78 61 63 74 6c 79 2c | 20 61 6e 64 20 6d 6f 6e |exactly,| and mon| |00004940| 74 68 73 20 73 74 61 72 | 74 20 6f 6e 20 6f 72 20 |ths star|t on or | |00004950| 6e 65 61 72 20 64 61 79 | 73 20 68 61 76 69 6e 67 |near day|s having| |00004960| 20 61 20 6e 65 77 20 6d | 6f 6f 6e 2e 20 4d 6f 73 | a new m|oon. Mos| |00004970| 74 20 6f 66 20 74 68 65 | 20 63 6f 6d 70 6c 65 78 |t of the| complex| |00004980| 69 74 79 20 69 73 20 69 | 6e 74 72 6f 64 75 63 65 |ity is i|ntroduce| |00004990| 64 20 62 65 63 61 75 73 | 65 20 69 74 20 69 73 20 |d becaus|e it is | |000049a0| 64 65 73 69 72 65 64 20 | 74 6f 20 70 72 65 76 65 |desired |to preve| |000049b0| 6e 74 20 63 65 72 74 61 | 69 6e 20 68 6f 6c 79 20 |nt certa|in holy | |000049c0| 64 61 79 73 20 28 65 73 | 70 65 63 69 61 6c 6c 79 |days (es|pecially| |000049d0| 20 59 6f 6d 20 4b 69 70 | 70 75 72 29 20 66 72 6f | Yom Kip|pur) fro| |000049e0| 6d 20 66 61 6c 6c 69 6e | 67 20 6f 6e 20 63 65 72 |m fallin|g on cer| |000049f0| 74 61 69 6e 20 64 61 79 | 73 20 6f 66 20 74 68 65 |tain day|s of the| |00004a00| 20 77 65 65 6b 2e 0d 0d | 09 4d 79 20 72 65 6e 64 | week...|.My rend| |00004a10| 65 72 69 6e 67 20 6f 66 | 20 74 68 65 20 72 75 6c |ering of| the rul| |00004a20| 65 73 20 6f 66 20 74 68 | 65 20 4a 65 77 69 73 68 |es of th|e Jewish| |00004a30| 20 43 61 6c 65 6e 64 61 | 72 3a 0d 0d 09 31 29 09 | Calenda|r:...1).| |00004a40| 54 68 65 20 6d 6f 6e 74 | 68 73 20 6f 66 20 61 20 |The mont|hs of a | |00004a50| 6e 6f 72 6d 61 6c 20 79 | 65 61 72 20 61 72 65 20 |normal y|ear are | |00004a60| 6e 61 6d 65 64 20 28 69 | 6e 20 6f 72 64 65 72 29 |named (i|n order)| |00004a70| 20 54 69 73 68 72 65 69 | 2c 20 43 68 65 73 68 76 | Tishrei|, Cheshv| |00004a80| 61 6e 2c 20 4b 69 73 6c | 65 76 2c 20 54 65 76 65 |an, Kisl|ev, Teve| |00004a90| 74 2c 20 53 68 76 61 74 | 2c 20 41 64 61 72 2c 20 |t, Shvat|, Adar, | |00004aa0| 4e 69 73 73 61 6e 2c 20 | 49 79 61 72 2c 20 53 69 |Nissan, |Iyar, Si| |00004ab0| 76 61 6e 2c 20 54 61 6d | 75 7a 2c 20 41 62 2c 20 |van, Tam|uz, Ab, | |00004ac0| 45 6c 75 6c 2e 20 54 68 | 65 72 65 20 61 72 65 20 |Elul. Th|ere are | |00004ad0| 31 32 20 6d 6f 6e 74 68 | 73 20 69 6e 20 6e 6f 72 |12 month|s in nor| |00004ae0| 6d 61 6c 20 79 65 61 72 | 73 2e 0d 0d 09 32 29 09 |mal year|s....2).| |00004af0| 54 68 65 20 6d 6f 6e 74 | 68 73 20 6f 66 20 61 20 |The mont|hs of a | |00004b00| 6c 65 61 70 20 79 65 61 | 72 20 61 72 65 20 6e 61 |leap yea|r are na| |00004b10| 6d 65 64 20 28 69 6e 20 | 6f 72 64 65 72 29 20 54 |med (in |order) T| |00004b20| 69 73 68 72 65 69 2c 20 | 43 68 65 73 68 76 61 6e |ishrei, |Cheshvan| |00004b30| 2c 20 4b 69 73 6c 65 76 | 2c 20 54 65 76 65 74 2c |, Kislev|, Tevet,| |00004b40| 20 53 68 76 61 74 2c 20 | 41 64 61 72 20 49 2c 20 | Shvat, |Adar I, | |00004b50| 41 64 61 72 20 49 49 2c | 20 4e 69 73 73 61 6e 2c |Adar II,| Nissan,| |00004b60| 20 49 79 61 72 2c 20 53 | 69 76 61 6e 2c 20 54 61 | Iyar, S|ivan, Ta| |00004b70| 6d 75 7a 2c 20 41 62 2c | 20 45 6c 75 6c 2e 20 54 |muz, Ab,| Elul. T| |00004b80| 68 65 72 65 20 61 72 65 | 20 31 33 20 6d 6f 6e 74 |here are| 13 mont| |00004b90| 68 73 20 69 6e 20 6c 65 | 61 70 20 79 65 61 72 73 |hs in le|ap years| |00004ba0| 2e 0d 0d 09 33 29 09 4d | 6f 6e 74 68 20 6c 65 6e |....3).M|onth len| |00004bb0| 67 74 68 73 20 61 72 65 | 20 61 73 20 66 6f 6c 6c |gths are| as foll| |00004bc0| 6f 77 73 3a 20 54 69 73 | 68 72 65 69 2c 20 53 68 |ows: Tis|hrei, Sh| |00004bd0| 76 61 74 2c 20 41 64 61 | 72 20 49 2c 20 4e 69 73 |vat, Ada|r I, Nis| |00004be0| 73 61 6e 2c 20 53 69 76 | 61 6e 2c 20 61 6e 64 20 |san, Siv|an, and | |00004bf0| 41 62 20 68 61 76 65 20 | 33 30 20 64 61 79 73 3b |Ab have |30 days;| |00004c00| 20 54 65 76 65 74 2c 20 | 41 64 61 72 2c 20 41 64 | Tevet, |Adar, Ad| |00004c10| 61 72 20 49 49 2c 20 49 | 79 61 72 2c 20 54 61 6d |ar II, I|yar, Tam| |00004c20| 75 7a 2c 20 61 6e 64 20 | 45 6c 75 6c 20 68 61 76 |uz, and |Elul hav| |00004c30| 65 20 32 39 20 64 61 79 | 73 3b 20 43 68 65 73 68 |e 29 day|s; Chesh| |00004c40| 76 61 6e 20 61 6e 64 20 | 4b 69 73 6c 65 76 20 63 |van and |Kislev c| |00004c50| 61 6e 20 65 61 63 68 20 | 68 61 76 65 20 65 69 74 |an each |have eit| |00004c60| 68 65 72 20 32 39 20 6f | 72 20 33 30 20 64 61 79 |her 29 o|r 30 day| |00004c70| 73 d1 74 68 65 69 72 20 | 76 61 72 69 61 62 6c 65 |s.their |variable| |00004c80| 20 6c 65 6e 67 74 68 73 | 20 61 72 65 20 72 65 6c | lengths| are rel| |00004c90| 61 74 65 64 20 74 6f 20 | 74 68 65 20 73 70 65 63 |ated to |the spec| |00004ca0| 69 61 6c 20 72 75 6c 65 | 73 20 66 6f 72 20 64 65 |ial rule|s for de| |00004cb0| 74 65 72 6d 69 6e 69 6e | 67 20 74 68 65 20 73 74 |terminin|g the st| |00004cc0| 61 72 74 20 6f 66 20 65 | 61 63 68 20 79 65 61 72 |art of e|ach year| |00004cd0| 20 28 31 20 54 69 73 68 | 72 65 69 20 3d 20 52 6f | (1 Tish|rei = Ro| |00004ce0| 73 68 20 48 61 73 68 6f | 6e 61 68 29 2e 20 54 68 |sh Hasho|nah). Th| |00004cf0| 65 20 70 72 65 63 69 73 | 65 20 72 75 6c 65 20 66 |e precis|e rule f| |00004d00| 6f 72 20 74 68 65 69 72 | 20 6c 65 6e 67 74 68 73 |or their| lengths| |00004d10| 20 63 61 6e 20 62 65 20 | 66 6f 75 6e 64 20 62 65 | can be |found be| |00004d20| 6c 6f 77 20 28 52 75 6c | 65 20 23 38 29 2e 0d 0d |low (Rul|e #8)...| |00004d30| 09 34 29 09 54 68 65 20 | 65 78 74 72 61 20 6d 6f |.4).The |extra mo| |00004d40| 6e 74 68 20 61 64 64 65 | 64 20 69 6e 20 6c 65 61 |nth adde|d in lea| |00004d50| 70 20 79 65 61 72 73 20 | 69 73 20 41 64 61 72 20 |p years |is Adar | |00004d60| 49 2e 20 41 64 61 72 20 | 61 6e 64 20 41 64 61 72 |I. Adar |and Adar| |00004d70| 20 49 49 20 61 72 65 20 | 61 63 74 75 61 6c 6c 79 | II are |actually| |00004d80| 20 74 68 65 20 73 61 6d | 65 20 6d 6f 6e 74 68 2e | the sam|e month.| |00004d90| 20 46 65 73 74 69 76 61 | 6c 73 20 77 68 69 63 68 | Festiva|ls which| |00004da0| 20 6f 63 63 75 72 20 69 | 6e 20 41 64 61 72 20 69 | occur i|n Adar i| |00004db0| 6e 20 6e 6f 72 6d 61 6c | 20 79 65 61 72 73 20 61 |n normal| years a| |00004dc0| 72 65 20 6f 62 73 65 72 | 76 65 64 20 69 6e 20 41 |re obser|ved in A| |00004dd0| 64 61 72 20 49 49 20 69 | 6e 20 6c 65 61 70 20 79 |dar II i|n leap y| |00004de0| 65 61 72 73 2e 0d 0d 09 | 35 29 09 54 68 65 20 6c |ears....|5).The l| |00004df0| 65 61 70 20 79 65 61 72 | 20 63 79 63 6c 65 20 69 |eap year| cycle i| |00004e00| 73 20 31 39 20 79 65 61 | 72 73 20 6c 6f 6e 67 2e |s 19 yea|rs long.| |00004e10| 20 4f 6e 65 20 63 79 63 | 6c 65 20 73 74 61 72 74 | One cyc|le start| |00004e20| 65 64 20 77 69 74 68 20 | 74 68 65 20 79 65 61 72 |ed with |the year| |00004e30| 20 31 20 41 2e 4d 2e 20 | 61 6e 64 20 65 6e 64 65 | 1 A.M. |and ende| |00004e40| 64 20 77 69 74 68 20 74 | 68 65 20 79 65 61 72 20 |d with t|he year | |00004e50| 31 39 20 41 2e 4d 2e 20 | 41 6e 6f 74 68 65 72 20 |19 A.M. |Another | |00004e60| 63 79 63 6c 65 20 73 74 | 61 72 74 65 64 20 77 69 |cycle st|arted wi| |00004e70| 74 68 20 74 68 65 20 79 | 65 61 72 20 31 39 20 42 |th the y|ear 19 B| |00004e80| 2e 57 2e 20 61 6e 64 20 | 65 6e 64 65 64 20 77 69 |.W. and |ended wi| |00004e90| 74 68 20 74 68 65 20 79 | 65 61 72 20 31 20 42 2e |th the y|ear 1 B.| |00004ea0| 57 2e 20 57 69 74 68 69 | 6e 20 61 6e 79 20 31 39 |W. Withi|n any 19| |00004eb0| 2d 79 65 61 72 20 63 79 | 63 6c 65 2c 20 6c 65 61 |-year cy|cle, lea| |00004ec0| 70 20 79 65 61 72 73 20 | 6f 63 63 75 72 20 69 6e |p years |occur in| |00004ed0| 20 74 68 65 20 74 68 69 | 72 64 2c 20 73 69 78 74 | the thi|rd, sixt| |00004ee0| 68 2c 20 65 69 67 68 74 | 68 2c 20 65 6c 65 76 65 |h, eight|h, eleve| |00004ef0| 6e 74 68 2c 20 66 6f 75 | 72 74 65 65 6e 74 68 2c |nth, fou|rteenth,| |00004f00| 20 73 65 76 65 6e 74 65 | 65 6e 74 68 2c 20 61 6e | sevente|enth, an| |00004f10| 64 20 6e 69 6e 65 74 65 | 65 6e 74 68 20 79 65 61 |d ninete|enth yea| |00004f20| 72 73 2e 20 41 6c 6c 20 | 6f 74 68 65 72 20 79 65 |rs. All |other ye| |00004f30| 61 72 73 20 69 6e 20 74 | 68 65 20 63 79 63 6c 65 |ars in t|he cycle| |00004f40| 20 61 72 65 20 6e 6f 72 | 6d 61 6c 20 79 65 61 72 | are nor|mal year| |00004f50| 73 2e 0d 0d 09 36 29 09 | 54 68 65 20 4a 65 77 69 |s....6).|The Jewi| |00004f60| 73 68 20 63 61 6c 65 6e | 64 61 72 20 64 61 79 20 |sh calen|dar day | |00004f70| 62 65 67 69 6e 73 20 61 | 74 20 73 75 6e 73 65 74 |begins a|t sunset| |00004f80| 2c 20 6e 6f 74 20 6d 69 | 64 6e 69 67 68 74 2e 20 |, not mi|dnight. | |00004f90| 49 6e 74 65 72 43 61 6c | 20 66 6f 6c 6c 6f 77 73 |InterCal| follows| |00004fa0| 20 74 68 65 20 6c 65 61 | 64 20 6f 66 20 74 68 65 | the lea|d of the| |00004fb0| 20 45 6e 63 79 63 6c 6f | 70 65 64 69 61 20 4a 75 | Encyclo|pedia Ju| |00004fc0| 64 61 69 63 61 20 61 6e | 64 20 6f 74 68 65 72 20 |daica an|d other | |00004fd0| 73 6f 75 72 63 65 73 20 | 69 6e 20 61 73 73 69 67 |sources |in assig| |00004fe0| 6e 69 6e 67 20 77 65 65 | 6b 64 61 79 73 20 74 6f |ning wee|kdays to| |00004ff0| 20 63 61 6c 65 6e 64 61 | 72 20 64 61 74 65 73 20 | calenda|r dates | |00005000| 61 73 20 66 6f 6c 6c 6f | 77 73 3a 20 49 66 20 61 |as follo|ws: If a| |00005010| 20 63 61 6c 65 6e 64 61 | 72 20 64 61 79 20 62 65 | calenda|r day be| |00005020| 67 69 6e 73 20 61 74 20 | 73 75 6e 73 65 74 20 6f |gins at |sunset o| |00005030| 6e 20 61 20 46 72 69 64 | 61 79 20 61 6e 64 20 65 |n a Frid|ay and e| |00005040| 6e 64 73 20 61 74 20 73 | 75 6e 73 65 74 20 6f 6e |nds at s|unset on| |00005050| 20 61 20 53 61 74 75 72 | 64 61 79 2c 20 74 68 61 | a Satur|day, tha| |00005060| 74 20 64 61 74 65 20 69 | 73 20 64 69 73 70 6c 61 |t date i|s displa| |00005070| 79 65 64 20 61 73 20 53 | 61 74 75 72 64 61 79 2c |yed as S|aturday,| |00005080| 20 61 6e 64 20 73 6f 20 | 66 6f 72 74 68 20 66 6f | and so |forth fo| |00005090| 72 20 6f 74 68 65 72 20 | 64 61 79 73 2e 20 42 75 |r other |days. Bu| |000050a0| 74 20 6e 6f 74 65 20 74 | 68 61 74 20 74 68 65 20 |t note t|hat the | |000050b0| 74 69 6d 65 73 20 6f 66 | 20 64 61 79 20 75 73 65 |times of| day use| |000050c0| 64 20 69 6e 20 52 75 6c | 65 20 23 37 20 62 65 6c |d in Rul|e #7 bel| |000050d0| 6f 77 20 61 72 65 20 6d | 65 61 73 75 72 65 64 20 |ow are m|easured | |000050e0| 66 72 6f 6d 20 36 3a 30 | 30 20 70 2e 6d 2e 0d 0d |from 6:0|0 p.m...| |000050f0| 09 37 29 09 54 68 65 20 | 4a 75 6c 69 61 6e 20 44 |.7).The |Julian D| |00005100| 61 79 20 6f 66 20 31 20 | 54 69 73 68 72 65 69 20 |ay of 1 |Tishrei | |00005110| 28 52 6f 73 68 20 48 61 | 73 68 6f 6e 61 68 29 20 |(Rosh Ha|shonah) | |00005120| 6f 66 20 61 6e 79 20 79 | 65 61 72 20 59 20 69 73 |of any y|ear Y is| |00005130| 20 64 65 74 65 72 6d 69 | 6e 65 64 20 61 73 20 66 | determi|ned as f| |00005140| 6f 6c 6c 6f 77 73 3a 0d | 0d 09 61 29 09 47 69 76 |ollows:.|..a).Giv| |00005150| 65 6e 20 61 6e 79 20 6e | 6f 6e 2d 7a 65 72 6f 20 |en any n|on-zero | |00005160| 69 6e 74 65 67 65 72 20 | 59 2c 20 63 6f 75 6e 74 |integer |Y, count| |00005170| 20 74 68 65 20 6d 6f 6e | 74 68 73 20 65 6c 61 70 | the mon|ths elap| |00005180| 73 65 64 20 66 72 6f 6d | 20 74 68 65 20 73 74 61 |sed from| the sta| |00005190| 72 74 20 6f 66 20 74 68 | 65 20 79 65 61 72 20 31 |rt of th|e year 1| |000051a0| 20 41 2e 4d 2e 20 74 6f | 20 74 68 65 20 73 74 61 | A.M. to| the sta| |000051b0| 72 74 20 6f 66 20 74 68 | 65 20 79 65 61 72 20 59 |rt of th|e year Y| |000051c0| 20 28 75 73 69 6e 67 20 | 72 75 6c 65 73 20 31 2c | (using |rules 1,| |000051d0| 20 32 2c 20 61 6e 64 20 | 35 20 61 62 6f 76 65 29 | 2, and |5 above)| |000051e0| 2e 20 53 69 6e 63 65 20 | 6e 65 67 61 74 69 76 65 |. Since |negative| |000051f0| 20 79 65 61 72 73 20 61 | 72 65 20 61 6c 6c 6f 77 | years a|re allow| |00005200| 65 64 2c 20 74 68 69 73 | 20 6e 75 6d 62 65 72 20 |ed, this| number | |00005210| 6f 66 20 6d 6f 6e 74 68 | 73 20 63 6f 75 6c 64 20 |of month|s could | |00005220| 62 65 20 6e 65 67 61 74 | 69 76 65 2e 0d 0d 09 62 |be negat|ive....b| |00005230| 29 09 4d 75 6c 74 69 70 | 6c 79 20 74 68 61 74 20 |).Multip|ly that | |00005240| 6e 75 6d 62 65 72 20 6f | 66 20 6d 6f 6e 74 68 73 |number o|f months| |00005250| 20 62 79 20 74 68 65 20 | 6e 75 6d 62 65 72 20 6f | by the |number o| |00005260| 66 20 d2 70 61 72 74 73 | d3 20 69 6e 20 61 20 73 |f .parts|. in a s| |00005270| 79 6e 6f 64 69 63 20 6d | 6f 6e 74 68 2e 20 d2 50 |ynodic m|onth. .P| |00005280| 61 72 74 73 d3 20 6f 66 | 20 61 20 64 61 79 20 61 |arts. of| a day a| |00005290| 72 65 20 65 71 75 61 6c | 20 74 6f 20 65 78 61 63 |re equal| to exac| |000052a0| 74 6c 79 20 33 20 31 2f | 33 20 73 65 63 6f 6e 64 |tly 3 1/|3 second| |000052b0| 73 2e 20 54 68 65 72 65 | 20 61 72 65 20 20 32 35 |s. There| are 25| |000052c0| 39 32 30 20 70 61 72 74 | 73 20 70 65 72 20 64 61 |920 part|s per da| |000052d0| 79 2e 20 42 79 20 64 65 | 66 69 6e 69 74 69 6f 6e |y. By de|finition| |000052e0| 20 28 74 68 69 73 20 69 | 73 20 77 68 61 74 20 65 | (this i|s what e| |000052f0| 6e 73 75 72 65 73 20 74 | 68 61 74 20 74 68 65 20 |nsures t|hat the | |00005300| 4a 65 77 69 73 68 20 63 | 61 6c 65 6e 64 61 72 20 |Jewish c|alendar | |00005310| 69 73 20 6d 61 74 68 65 | 6d 61 74 69 63 61 6c 2c |is mathe|matical,| |00005320| 20 6e 6f 74 20 70 68 79 | 73 69 63 61 6c 29 20 61 | not phy|sical) a| |00005330| 20 73 79 6e 6f 64 69 63 | 20 6d 6f 6e 74 68 20 69 | synodic| month i| |00005340| 6e 20 74 68 65 20 4a 65 | 77 69 73 68 20 63 61 6c |n the Je|wish cal| |00005350| 65 6e 64 61 72 20 63 6f | 6e 74 61 69 6e 73 20 65 |endar co|ntains e| |00005360| 78 61 63 74 6c 79 20 37 | 36 35 34 33 33 20 70 61 |xactly 7|65433 pa| |00005370| 72 74 73 2e 0d 0d 09 63 | 29 09 41 64 64 20 35 36 |rts....c|).Add 56| |00005380| 30 34 20 74 6f 20 74 68 | 65 20 72 65 73 75 6c 74 |04 to th|e result| |00005390| 20 6f 66 20 73 74 65 70 | 20 62 2e 20 28 54 68 69 | of step| b. (Thi| |000053a0| 73 20 69 73 20 74 68 65 | 20 74 69 6d 65 20 6f 66 |s is the| time of| |000053b0| 20 64 61 79 2c 20 69 6e | 20 70 61 72 74 73 2c 20 | day, in| parts, | |000053c0| 61 74 20 77 68 69 63 68 | 20 62 79 20 64 65 66 69 |at which| by defi| |000053d0| 6e 69 74 69 6f 6e 20 6e | 65 77 20 6d 6f 6f 6e 20 |nition n|ew moon | |000053e0| 6f 63 63 75 72 72 65 64 | 20 6f 6e 20 6f 72 20 6e |occurred| on or n| |000053f0| 65 61 72 20 31 20 54 69 | 73 68 72 65 69 20 6f 66 |ear 1 Ti|shrei of| |00005400| 20 74 68 65 20 79 65 61 | 72 20 31 20 41 2e 4d 2e | the yea|r 1 A.M.| |00005410| 29 0d 0d 09 64 29 09 44 | 65 74 65 72 6d 69 6e 65 |)...d).D|etermine| |00005420| 20 74 68 65 20 6e 75 6d | 62 65 72 20 6f 66 20 64 | the num|ber of d| |00005430| 61 79 73 20 65 6c 61 70 | 73 65 64 20 66 72 6f 6d |ays elap|sed from| |00005440| 20 74 68 65 20 6e 65 77 | 20 6d 6f 6f 6e 20 61 73 | the new| moon as| |00005450| 73 6f 63 69 61 74 65 64 | 20 77 69 74 68 20 31 20 |sociated| with 1 | |00005460| 54 69 73 68 72 65 69 20 | 31 20 41 2e 4d 2e 20 74 |Tishrei |1 A.M. t| |00005470| 6f 20 74 68 65 20 6e 65 | 77 20 6d 6f 6f 6e 20 61 |o the ne|w moon a| |00005480| 73 73 6f 63 69 61 74 65 | 64 20 77 69 74 68 20 31 |ssociate|d with 1| |00005490| 20 54 69 73 68 72 65 69 | 20 69 6e 20 74 68 65 20 | Tishrei| in the | |000054a0| 79 65 61 72 20 59 2e 20 | 54 68 61 74 20 69 73 2c |year Y. |That is,| |000054b0| 20 75 73 69 6e 67 20 69 | 6e 74 65 67 65 72 20 64 | using i|nteger d| |000054c0| 69 76 69 73 69 6f 6e 2c | 20 64 69 76 69 64 65 20 |ivision,| divide | |000054d0| 74 68 65 20 72 65 73 75 | 6c 74 20 66 72 6f 6d 20 |the resu|lt from | |000054e0| 73 74 65 70 20 63 20 62 | 79 20 32 35 39 32 30 2e |step c b|y 25920.| |000054f0| 20 4b 65 65 70 20 74 68 | 65 20 72 65 6d 61 69 6e | Keep th|e remain| |00005500| 64 65 72 20 68 61 6e 64 | 79 20 66 6f 72 20 75 73 |der hand|y for us| |00005510| 65 20 69 6e 20 6c 61 74 | 65 72 20 72 75 6c 65 73 |e in lat|er rules| |00005520| 2e 20 54 68 61 74 20 72 | 65 6d 61 69 6e 64 65 72 |. That r|emainder| |00005530| 20 69 73 20 74 68 65 20 | 74 69 6d 65 20 6f 66 20 | is the |time of | |00005540| 64 61 79 2c 20 69 6e 20 | 70 61 72 74 73 2c 20 6f |day, in |parts, o| |00005550| 66 20 74 68 65 20 6e 65 | 77 20 6d 6f 6f 6e 20 6e |f the ne|w moon n| |00005560| 65 61 72 65 73 74 20 74 | 68 65 20 73 74 61 72 74 |earest t|he start| |00005570| 20 6f 66 20 74 68 65 20 | 79 65 61 72 20 69 6e 20 | of the |year in | |00005580| 71 75 65 73 74 69 6f 6e | 2e 20 28 49 6e 74 65 67 |question|. (Integ| |00005590| 65 72 20 64 69 76 69 73 | 69 6f 6e 20 61 6e 64 20 |er divis|ion and | |000055a0| 6d 6f 64 75 6c 61 72 20 | 61 72 69 74 68 6d 65 74 |modular |arithmet| |000055b0| 69 63 20 77 69 74 68 20 | 6e 65 67 61 74 69 76 65 |ic with |negative| |000055c0| 20 6e 75 6d 62 65 72 73 | 20 72 65 71 75 69 72 65 | numbers| require| |000055d0| 20 63 61 72 65 2e 20 54 | 72 75 6e 63 61 74 69 6f | care. T|runcatio| |000055e0| 6e 20 6d 75 73 74 20 62 | 65 20 74 6f 77 61 72 64 |n must b|e toward| |000055f0| 73 20 6d 69 6e 75 73 20 | 69 6e 66 69 6e 69 74 79 |s minus |infinity| |00005600| 2c 20 61 6e 64 20 74 68 | 65 20 72 65 6d 61 69 6e |, and th|e remain| |00005610| 64 65 72 20 6d 75 73 74 | 20 61 6c 77 61 79 73 20 |der must| always | |00005620| 62 65 20 6e 6f 6e 2d 6e | 65 67 61 74 69 76 65 2e |be non-n|egative.| |00005630| 20 54 68 65 20 6c 61 63 | 6b 20 6f 66 20 61 20 79 | The lac|k of a y| |00005640| 65 61 72 20 30 20 6d 75 | 73 74 20 61 6c 73 6f 20 |ear 0 mu|st also | |00005650| 62 65 20 68 61 6e 64 6c | 65 64 2e 29 0d 0d 09 65 |be handl|ed.)...e| |00005660| 29 09 54 68 65 20 4a 75 | 6c 69 61 6e 20 44 61 79 |).The Ju|lian Day| |00005670| 20 61 74 20 6d 69 64 6e | 69 67 68 74 20 64 75 72 | at midn|ight dur| |00005680| 69 6e 67 20 31 20 54 69 | 73 68 72 65 69 20 31 20 |ing 1 Ti|shrei 1 | |00005690| 41 2e 4d 2e 20 28 61 20 | 4d 6f 6e 64 61 79 29 20 |A.M. (a |Monday) | |000056a0| 69 73 20 33 34 37 39 39 | 37 2e 35 2e 20 41 64 64 |is 34799|7.5. Add| |000056b0| 20 33 34 37 39 39 37 2e | 35 20 74 6f 20 74 68 65 | 347997.|5 to the| |000056c0| 20 69 6e 74 65 67 65 72 | 20 70 61 72 74 20 6f 66 | integer| part of| |000056d0| 20 74 68 65 20 72 65 73 | 75 6c 74 20 6f 66 20 73 | the res|ult of s| |000056e0| 74 65 70 20 64 2e 20 44 | 65 74 65 72 6d 69 6e 65 |tep d. D|etermine| |000056f0| 20 74 68 65 20 64 61 79 | 20 6f 66 20 74 68 65 20 | the day| of the | |00005700| 77 65 65 6b 20 6f 66 20 | 74 68 69 73 20 6e 65 77 |week of |this new| |00005710| 20 6d 6f 6f 6e 2e 0d 0d | 09 66 29 09 54 65 6e 74 | moon...|.f).Tent| |00005720| 61 74 69 76 65 6c 79 2c | 20 74 68 65 20 4a 75 6c |atively,| the Jul| |00005730| 69 61 6e 20 44 61 79 20 | 61 74 20 6d 69 64 6e 69 |ian Day |at midni| |00005740| 67 68 74 20 64 75 72 69 | 6e 67 20 31 20 54 69 73 |ght duri|ng 1 Tis| |00005750| 68 72 65 69 20 28 52 6f | 73 68 20 48 61 73 68 6f |hrei (Ro|sh Hasho| |00005760| 6e 61 68 29 20 6f 66 20 | 74 68 65 20 79 65 61 72 |nah) of |the year| |00005770| 20 69 6e 20 71 75 65 73 | 74 69 6f 6e 20 77 69 6c | in ques|tion wil| |00005780| 6c 20 62 65 20 74 68 65 | 20 6a 75 73 74 2d 63 61 |l be the| just-ca| |00005790| 6c 63 75 6c 61 74 65 64 | 20 61 6e 73 77 65 72 20 |lculated| answer | |000057a0| 74 6f 20 73 74 65 70 20 | 65 2e 20 49 74 20 72 65 |to step |e. It re| |000057b0| 70 72 65 73 65 6e 74 73 | 20 74 68 65 20 4a 75 6c |presents| the Jul| |000057c0| 69 61 6e 20 44 61 79 20 | 61 74 20 6d 69 64 6e 69 |ian Day |at midni| |000057d0| 67 68 74 20 6f 66 20 74 | 68 65 20 64 61 79 20 63 |ght of t|he day c| |000057e0| 6f 6e 74 61 69 6e 69 6e | 67 20 74 68 65 20 6e 65 |ontainin|g the ne| |000057f0| 77 20 6d 6f 6f 6e 20 6e | 65 61 72 65 73 74 20 74 |w moon n|earest t| |00005800| 68 65 20 73 74 61 72 74 | 20 6f 66 20 74 68 65 20 |he start| of the | |00005810| 79 65 61 72 20 59 2e 0d | 0d 09 09 49 66 20 6e 65 |year Y..|...If ne| |00005820| 63 65 73 73 61 72 79 2c | 20 61 64 6a 75 73 74 20 |cessary,| adjust | |00005830| 74 68 65 20 64 61 74 65 | 20 6f 66 20 52 6f 73 68 |the date| of Rosh| |00005840| 20 48 61 73 68 6f 6e 61 | 68 20 62 79 20 6f 6e 65 | Hashona|h by one| |00005850| 20 6f 72 20 74 77 6f 20 | 64 61 79 73 20 75 73 69 | or two |days usi| |00005860| 6e 67 20 74 68 65 20 66 | 6f 6c 6c 6f 77 69 6e 67 |ng the f|ollowing| |00005870| 20 72 75 6c 65 73 3a 0d | 0d 09 69 29 09 44 65 74 | rules:.|..i).Det| |00005880| 65 72 6d 69 6e 65 20 28 | 75 73 69 6e 67 20 72 75 |ermine (|using ru| |00005890| 6c 65 20 35 29 20 77 68 | 65 74 68 65 72 20 6f 72 |le 5) wh|ether or| |000058a0| 20 6e 6f 74 20 79 65 61 | 72 20 59 20 69 73 20 61 | not yea|r Y is a| |000058b0| 20 6c 65 61 70 20 79 65 | 61 72 2e 20 41 6c 73 6f | leap ye|ar. Also| |000058c0| 20 64 65 74 65 72 6d 69 | 6e 65 20 77 68 65 74 68 | determi|ne wheth| |000058d0| 65 72 20 6f 72 20 6e 6f | 74 20 74 68 65 20 79 65 |er or no|t the ye| |000058e0| 61 72 20 62 65 66 6f 72 | 65 20 74 68 65 20 79 65 |ar befor|e the ye| |000058f0| 61 72 20 59 20 77 61 73 | 20 61 20 6c 65 61 70 20 |ar Y was| a leap | |00005900| 79 65 61 72 2e 0d 0d 09 | 69 69 29 09 49 66 20 74 |year....|ii).If t| |00005910| 68 65 20 74 69 6d 65 20 | 6f 66 20 64 61 79 20 6f |he time |of day o| |00005920| 66 20 6e 65 77 20 6d 6f | 6f 6e 20 69 73 20 6e 6f |f new mo|on is no| |00005930| 6f 6e 20 6f 72 20 6c 61 | 74 65 72 20 28 74 68 65 |on or la|ter (the| |00005940| 20 72 65 6d 61 69 6e 64 | 65 72 20 69 6e 20 73 74 | remaind|er in st| |00005950| 65 70 20 64 20 65 71 75 | 61 6c 73 20 6f 72 20 65 |ep d equ|als or e| |00005960| 78 63 65 65 64 73 20 31 | 39 34 34 30 20 70 61 72 |xceeds 1|9440 par| |00005970| 74 73 29 20 4f 52 0d 0d | 09 69 69 69 29 09 49 66 |ts) OR..|.iii).If| |00005980| 20 74 68 65 20 79 65 61 | 72 20 59 20 69 73 20 6e | the yea|r Y is n| |00005990| 6f 74 20 61 20 6c 65 61 | 70 20 79 65 61 72 20 61 |ot a lea|p year a| |000059a0| 6e 64 20 69 66 20 74 68 | 65 20 6e 65 77 20 6d 6f |nd if th|e new mo| |000059b0| 6f 6e 20 69 73 20 6f 6e | 20 61 20 54 75 65 73 64 |on is on| a Tuesd| |000059c0| 61 79 20 61 6e 64 20 69 | 74 73 20 74 69 6d 65 20 |ay and i|ts time | |000059d0| 6f 66 20 64 61 79 20 28 | 72 65 6d 61 69 6e 64 65 |of day (|remainde| |000059e0| 72 20 69 6e 20 73 74 65 | 70 20 64 29 20 69 73 20 |r in ste|p d) is | |000059f0| 67 72 65 61 74 65 72 20 | 74 68 61 6e 20 6f 72 20 |greater |than or | |00005a00| 65 71 75 61 6c 20 74 6f | 20 39 39 32 34 20 70 61 |equal to| 9924 pa| |00005a10| 72 74 73 20 28 39 20 68 | 6f 75 72 73 20 70 6c 75 |rts (9 h|ours plu| |00005a20| 73 20 32 30 34 20 70 61 | 72 74 73 2c 20 6f 72 20 |s 204 pa|rts, or | |00005a30| 73 68 6f 72 74 6c 79 20 | 61 66 74 65 72 20 33 3a |shortly |after 3:| |00005a40| 30 30 20 61 2e 6d 2e 29 | 20 4f 52 0d 0d 09 69 76 |00 a.m.)| OR...iv| |00005a50| 29 09 49 66 20 74 68 65 | 20 70 72 65 63 65 64 69 |).If the| precedi| |00005a60| 6e 67 20 79 65 61 72 20 | 69 73 20 61 20 6c 65 61 |ng year |is a lea| |00005a70| 70 20 79 65 61 72 20 61 | 6e 64 20 74 68 65 20 6e |p year a|nd the n| |00005a80| 65 77 20 6d 6f 6f 6e 20 | 69 73 20 6f 6e 20 61 20 |ew moon |is on a | |00005a90| 4d 6f 6e 64 61 79 20 61 | 6e 64 20 69 74 73 20 74 |Monday a|nd its t| |00005aa0| 69 6d 65 20 6f 66 20 64 | 61 79 20 69 73 20 67 72 |ime of d|ay is gr| |00005ab0| 65 61 74 65 72 20 74 68 | 61 6e 20 6f 72 20 65 71 |eater th|an or eq| |00005ac0| 75 61 6c 20 74 6f 20 31 | 36 37 38 39 20 70 61 72 |ual to 1|6789 par| |00005ad0| 74 73 20 28 31 35 20 68 | 6f 75 72 73 20 70 6c 75 |ts (15 h|ours plu| |00005ae0| 73 20 35 38 39 20 70 61 | 72 74 73 2c 20 6f 72 20 |s 589 pa|rts, or | |00005af0| 61 20 66 65 77 20 6d 69 | 6e 75 74 65 73 20 61 66 |a few mi|nutes af| |00005b00| 74 65 72 20 39 3a 30 30 | 20 61 2e 6d 2e 29 20 54 |ter 9:00| a.m.) T| |00005b10| 48 45 4e 0d 0d 09 09 4d | 61 6b 65 20 74 68 65 20 |HEN....M|ake the | |00005b20| 74 65 6e 74 61 74 69 76 | 65 20 64 61 79 20 6f 66 |tentativ|e day of| |00005b30| 20 52 6f 73 68 20 48 61 | 73 68 6f 6e 61 68 20 62 | Rosh Ha|shonah b| |00005b40| 65 20 74 68 65 20 64 61 | 79 20 61 66 74 65 72 20 |e the da|y after | |00005b50| 74 68 65 20 64 61 79 20 | 6f 66 20 6e 65 77 20 6d |the day |of new m| |00005b60| 6f 6f 6e d1 74 68 61 74 | 20 69 73 2c 20 74 68 65 |oon.that| is, the| |00005b70| 20 6e 65 77 20 74 65 6e | 74 61 74 69 76 65 20 4a | new ten|tative J| |00005b80| 75 6c 69 61 6e 20 44 61 | 79 20 6f 66 20 52 6f 73 |ulian Da|y of Ros| |00005b90| 68 20 48 61 73 68 6f 6e | 61 68 20 65 71 75 61 6c |h Hashon|ah equal| |00005ba0| 73 20 74 68 65 20 61 6e | 73 77 65 72 20 74 6f 20 |s the an|swer to | |00005bb0| 73 74 65 70 20 65 20 70 | 6c 75 73 20 31 2e 0d 0d |step e p|lus 1...| |00005bc0| 09 76 29 09 53 65 74 20 | 74 68 65 20 61 63 74 75 |.v).Set |the actu| |00005bd0| 61 6c 20 52 6f 73 68 20 | 48 61 73 68 6f 6e 61 68 |al Rosh |Hashonah| |00005be0| 20 6f 66 20 74 68 65 20 | 79 65 61 72 20 69 6e 20 | of the |year in | |00005bf0| 71 75 65 73 74 69 6f 6e | 20 74 6f 20 74 68 65 20 |question| to the | |00005c00| 74 65 6e 74 61 74 69 76 | 65 20 64 61 79 20 28 61 |tentativ|e day (a| |00005c10| 66 74 65 72 20 70 6f 73 | 73 69 62 6c 65 20 61 64 |fter pos|sible ad| |00005c20| 6a 75 73 74 6d 65 6e 74 | 20 75 73 69 6e 67 20 72 |justment| using r| |00005c30| 75 6c 65 73 20 66 2e 69 | 69 20 74 68 72 6f 75 67 |ules f.i|i throug| |00005c40| 68 20 66 2e 69 76 29 20 | 75 6e 6c 65 73 73 20 69 |h f.iv) |unless i| |00005c50| 74 20 77 6f 75 6c 64 20 | 62 65 20 61 20 53 75 6e |t would |be a Sun| |00005c60| 64 61 79 2c 20 57 65 64 | 6e 65 73 64 61 79 2c 20 |day, Wed|nesday, | |00005c70| 6f 72 20 46 72 69 64 61 | 79 2e 20 49 6e 20 74 68 |or Frida|y. In th| |00005c80| 6f 73 65 20 63 61 73 65 | 73 2c 20 6d 61 6b 65 20 |ose case|s, make | |00005c90| 74 68 65 20 61 63 74 75 | 61 6c 20 52 6f 73 68 20 |the actu|al Rosh | |00005ca0| 48 61 73 68 6f 6e 61 68 | 20 6f 6e 65 20 64 61 79 |Hashonah| one day| |00005cb0| 20 61 66 74 65 72 20 74 | 68 65 20 74 65 6e 74 61 | after t|he tenta| |00005cc0| 74 69 76 65 20 64 61 79 | 2e 0d 0d 09 09 54 6f 20 |tive day|.....To | |00005cd0| 73 75 6d 6d 61 72 69 7a | 65 2c 20 74 68 65 20 4a |summariz|e, the J| |00005ce0| 75 6c 69 61 6e 20 44 61 | 79 20 61 74 20 6d 69 64 |ulian Da|y at mid| |00005cf0| 6e 69 67 68 74 20 64 75 | 72 69 6e 67 20 52 6f 73 |night du|ring Ros| |00005d00| 68 20 48 61 73 68 6f 6e | 61 68 20 69 73 20 74 68 |h Hashon|ah is th| |00005d10| 65 20 61 6e 73 77 65 72 | 20 74 6f 20 73 74 65 70 |e answer| to step| |00005d20| 20 37 65 20 70 6c 75 73 | 20 30 20 6f 72 20 31 20 | 7e plus| 0 or 1 | |00005d30| 6f 72 20 32 2c 20 64 65 | 70 65 6e 64 69 6e 67 20 |or 2, de|pending | |00005d40| 6f 6e 20 77 68 65 74 68 | 65 72 20 6f 72 20 6e 6f |on wheth|er or no| |00005d50| 74 20 61 6e 79 20 6f 66 | 20 74 68 65 20 63 6f 6e |t any of| the con| |00005d60| 64 69 74 69 6f 6e 73 20 | 69 6e 20 73 74 65 70 73 |ditions |in steps| |00005d70| 20 37 2e 66 2e 69 69 20 | 74 68 72 6f 75 67 68 20 | 7.f.ii |through | |00005d80| 37 2e 66 2e 69 76 20 61 | 72 65 20 74 72 75 65 20 |7.f.iv a|re true | |00005d90| 61 6e 64 20 77 68 65 74 | 68 65 72 20 6f 72 20 6e |and whet|her or n| |00005da0| 6f 74 20 74 68 65 20 63 | 6f 6e 64 69 74 69 6f 6e |ot the c|ondition| |00005db0| 20 69 6e 20 73 74 65 70 | 20 37 2e 66 2e 76 20 69 | in step| 7.f.v i| |00005dc0| 73 20 74 72 75 65 2e 0d | 0d 09 38 29 09 44 65 74 |s true..|..8).Det| |00005dd0| 65 72 6d 69 6e 65 20 74 | 68 65 20 6c 65 6e 67 74 |ermine t|he lengt| |00005de0| 68 73 20 6f 66 20 43 68 | 65 73 68 76 61 6e 20 61 |hs of Ch|eshvan a| |00005df0| 6e 64 20 4b 69 73 6c 65 | 76 20 61 73 20 66 6f 6c |nd Kisle|v as fol| |00005e00| 6c 6f 77 73 3a 0d 0d 09 | 61 29 09 53 75 62 74 72 |lows:...|a).Subtr| |00005e10| 61 63 74 20 74 68 65 20 | 4a 75 6c 69 61 6e 20 44 |act the |Julian D| |00005e20| 61 79 20 6f 66 20 52 6f | 73 68 20 48 61 73 68 6f |ay of Ro|sh Hasho| |00005e30| 6e 61 68 20 6f 66 20 74 | 68 65 20 79 65 61 72 20 |nah of t|he year | |00005e40| 59 20 66 72 6f 6d 20 74 | 68 65 20 4a 75 6c 69 61 |Y from t|he Julia| |00005e50| 6e 20 44 61 79 20 6f 66 | 20 52 6f 73 68 20 48 61 |n Day of| Rosh Ha| |00005e60| 73 68 6f 6e 61 68 20 6f | 66 20 74 68 65 20 79 65 |shonah o|f the ye| |00005e70| 61 72 20 66 6f 6c 6c 6f | 77 69 6e 67 20 74 68 65 |ar follo|wing the| |00005e80| 20 79 65 61 72 20 59 2e | 20 53 69 6d 70 6c 79 20 | year Y.| Simply | |00005e90| 72 65 61 70 70 6c 79 20 | 52 75 6c 65 20 23 37 20 |reapply |Rule #7 | |00005ea0| 69 6e 20 6f 72 64 65 72 | 20 74 6f 20 64 6f 20 74 |in order| to do t| |00005eb0| 68 69 73 2e 0d 0d 09 62 | 29 09 49 6e 20 73 70 69 |his....b|).In spi| |00005ec0| 74 65 20 6f 66 20 74 68 | 65 20 61 70 70 61 72 65 |te of th|e appare| |00005ed0| 6e 74 20 63 6f 6d 70 6c | 65 78 69 74 79 20 6f 66 |nt compl|exity of| |00005ee0| 20 74 68 65 20 72 75 6c | 65 73 2c 20 74 68 65 72 | the rul|es, ther| |00005ef0| 65 20 61 72 65 20 6f 6e | 6c 79 20 73 69 78 20 70 |e are on|ly six p| |00005f00| 6f 73 73 69 62 6c 65 20 | 61 6e 73 77 65 72 73 20 |ossible |answers | |00005f10| 74 6f 20 73 74 65 70 20 | 38 61 2e 20 28 41 63 74 |to step |8a. (Act| |00005f20| 75 61 6c 6c 79 2c 20 74 | 68 65 20 70 75 72 70 6f |ually, t|he purpo| |00005f30| 73 65 20 6f 66 20 72 75 | 6c 65 73 20 37 2e 66 2e |se of ru|les 7.f.| |00005f40| 69 69 20 74 68 72 6f 75 | 67 68 20 37 2e 66 2e 76 |ii throu|gh 7.f.v| |00005f50| 20 69 73 20 74 6f 20 66 | 6f 72 63 65 20 74 68 65 | is to f|orce the| |00005f60| 73 65 20 6c 65 6e 67 74 | 68 73 20 74 6f 20 62 65 |se lengt|hs to be| |00005f70| 20 74 68 65 20 6f 6e 6c | 79 20 6f 6e 65 73 20 70 | the onl|y ones p| |00005f80| 6f 73 73 69 62 6c 65 2e | 29 20 54 68 65 20 70 6f |ossible.|) The po| |00005f90| 73 73 69 62 6c 65 20 79 | 65 61 72 20 6c 65 6e 67 |ssible y|ear leng| |00005fa0| 74 68 73 20 61 72 65 3a | 20 33 35 33 2c 20 33 35 |ths are:| 353, 35| |00005fb0| 34 2c 20 33 35 35 2c 20 | 33 38 33 2c 20 33 38 34 |4, 355, |383, 384| |00005fc0| 2c 20 61 6e 64 20 33 38 | 35 2e 20 59 65 61 72 73 |, and 38|5. Years| |00005fd0| 20 6f 66 20 6c 65 6e 67 | 74 68 20 33 35 33 20 61 | of leng|th 353 a| |00005fe0| 6e 64 20 6c 65 6e 67 74 | 68 20 33 38 33 20 61 72 |nd lengt|h 383 ar| |00005ff0| 65 20 63 61 6c 6c 65 64 | 20 d2 64 65 66 65 63 74 |e called| .defect| |00006000| 69 76 65 d3 2e 20 59 65 | 61 72 73 20 6f 66 20 6c |ive.. Ye|ars of l| |00006010| 65 6e 67 74 68 20 33 35 | 34 20 61 6e 64 20 33 38 |ength 35|4 and 38| |00006020| 34 20 61 72 65 20 63 61 | 6c 6c 65 64 20 d2 72 65 |4 are ca|lled .re| |00006030| 67 75 6c 61 72 d3 2e 20 | 59 65 61 72 73 20 6f 66 |gular.. |Years of| |00006040| 20 6c 65 6e 67 74 68 20 | 33 35 35 20 61 6e 64 20 | length |355 and | |00006050| 33 38 35 20 61 72 65 20 | 63 61 6c 6c 65 64 20 d2 |385 are |called .| |00006060| 63 6f 6d 70 6c 65 74 65 | d3 2e 20 49 6e 20 64 65 |complete|.. In de| |00006070| 66 65 63 74 69 76 65 20 | 79 65 61 72 73 2c 20 62 |fective |years, b| |00006080| 6f 74 68 20 43 68 65 73 | 68 76 61 6e 20 61 6e 64 |oth Ches|hvan and| |00006090| 20 4b 69 73 6c 65 76 20 | 68 61 76 65 20 32 39 20 | Kislev |have 29 | |000060a0| 64 61 79 73 2e 20 49 6e | 20 72 65 67 75 6c 61 72 |days. In| regular| |000060b0| 20 79 65 61 72 73 2c 20 | 43 68 65 73 68 76 61 6e | years, |Cheshvan| |000060c0| 20 68 61 73 20 32 39 20 | 64 61 79 73 20 61 6e 64 | has 29 |days and| |000060d0| 20 4b 69 73 6c 65 76 20 | 68 61 73 20 33 30 2e 20 | Kislev |has 30. | |000060e0| 49 6e 20 63 6f 6d 70 6c | 65 74 65 20 79 65 61 72 |In compl|ete year| |000060f0| 73 2c 20 62 6f 74 68 20 | 43 68 65 73 68 76 61 6e |s, both |Cheshvan| |00006100| 20 61 6e 64 20 4b 69 73 | 6c 65 76 20 68 61 76 65 | and Kis|lev have| |00006110| 20 33 30 20 64 61 79 73 | 2e 0d 0d 09 54 68 65 20 | 30 days|....The | |00006120| 61 76 65 72 61 67 65 20 | 6c 65 6e 67 74 68 20 6f |average |length o| |00006130| 66 20 61 20 4a 65 77 69 | 73 68 20 6d 6f 6e 74 68 |f a Jewi|sh month| |00006140| 20 69 73 20 37 36 35 34 | 33 33 20 70 61 72 74 73 | is 7654|33 parts| |00006150| 2c 20 6f 72 20 32 39 2e | 35 33 30 35 39 34 31 c9 |, or 29.|5305941.| |00006160| 20 64 61 79 73 20 66 6f | 72 20 61 6e 20 65 72 72 | days fo|r an err| |00006170| 6f 72 20 6f 66 20 30 2e | 30 30 30 30 30 35 39 34 |or of 0.|00000594| |00006180| 20 64 61 79 73 20 70 65 | 72 20 6d 6f 6e 74 68 2e | days pe|r month.| |00006190| 20 49 6e 20 32 33 35 20 | 6d 6f 6e 74 68 73 20 28 | In 235 |months (| |000061a0| 74 68 65 20 6e 75 6d 62 | 65 72 20 6f 66 20 6d 6f |the numb|er of mo| |000061b0| 6e 74 68 73 20 69 6e 20 | 65 61 63 68 20 31 39 2d |nths in |each 19-| |000061c0| 79 65 61 72 20 63 79 63 | 6c 65 29 20 74 68 69 73 |year cyc|le) this| |000061d0| 20 65 72 72 6f 72 20 68 | 61 73 20 62 75 69 6c 74 | error h|as built| |000061e0| 20 75 70 20 74 6f 20 30 | 2e 30 30 31 34 30 20 64 | up to 0|.00140 d| |000061f0| 61 79 73 20 66 6f 72 20 | 61 6e 20 61 76 65 72 61 |ays for |an avera| |00006200| 67 65 20 65 72 72 6f 72 | 20 6f 66 20 30 2e 30 30 |ge error| of 0.00| |00006210| 30 30 37 33 35 20 64 61 | 79 73 20 70 65 72 20 79 |00735 da|ys per y| |00006220| 65 61 72 2e 20 54 68 75 | 73 20 74 68 65 20 4a 65 |ear. Thu|s the Je| |00006230| 77 69 73 68 20 63 61 6c | 65 6e 64 61 72 20 64 65 |wish cal|endar de| |00006240| 76 65 6c 6f 70 73 20 61 | 6e 20 65 72 72 6f 72 20 |velops a|n error | |00006250| 6f 66 20 6f 6e 65 20 64 | 61 79 20 77 69 74 68 20 |of one d|ay with | |00006260| 72 65 73 70 65 63 74 20 | 74 6f 20 74 68 65 20 6d |respect |to the m| |00006270| 6f 6f 6e 20 69 6e 20 61 | 70 70 72 6f 78 69 6d 61 |oon in a|pproxima| |00006280| 74 65 6c 79 20 31 33 36 | 30 30 20 79 65 61 72 73 |tely 136|00 years| |00006290| 20 28 66 6f 75 72 20 74 | 69 6d 65 73 20 61 73 20 | (four t|imes as | |000062a0| 61 63 63 75 72 61 74 65 | 20 77 69 74 68 20 72 65 |accurate| with re| |000062b0| 73 70 65 63 74 20 74 6f | 20 74 68 65 20 6d 6f 6f |spect to| the moo| |000062c0| 6e 20 61 73 20 74 68 65 | 20 47 72 65 67 6f 72 69 |n as the| Gregori| |000062d0| 61 6e 20 63 61 6c 65 6e | 64 61 72 20 69 73 20 77 |an calen|dar is w| |000062e0| 69 74 68 20 72 65 73 70 | 65 63 74 20 74 6f 20 74 |ith resp|ect to t| |000062f0| 68 65 20 73 75 6e 29 2e | 20 54 68 69 73 20 69 73 |he sun).| This is| |00006300| 20 69 6e 63 72 65 64 69 | 62 6c 79 20 61 63 63 75 | incredi|bly accu| |00006310| 72 61 74 65 20 66 6f 72 | 20 61 20 63 61 6c 65 6e |rate for| a calen| |00006320| 64 61 72 20 77 68 69 63 | 68 20 69 73 20 6f 76 65 |dar whic|h is ove| |00006330| 72 20 6f 6e 65 20 74 68 | 6f 75 73 61 6e 64 20 79 |r one th|ousand y| |00006340| 65 61 72 73 20 6f 6c 64 | 20 69 6e 20 69 74 73 20 |ears old| in its | |00006350| 70 72 65 73 65 6e 74 20 | 66 6f 72 6d 21 20 28 49 |present |form! (I| |00006360| 74 73 20 6d 6f 6e 74 68 | 20 69 73 20 73 6c 69 67 |ts month| is slig| |00006370| 68 74 6c 79 20 74 6f 6f | 20 6c 6f 6e 67 2c 20 73 |htly too| long, s| |00006380| 6f 20 6e 65 77 20 6d 6f | 6f 6e 73 20 77 69 6c 6c |o new mo|ons will| |00006390| 20 67 72 61 64 75 61 6c | 6c 79 20 73 6c 69 70 20 | gradual|ly slip | |000063a0| 62 61 63 6b 77 61 72 64 | 73 20 74 68 72 6f 75 67 |backward|s throug| |000063b0| 68 20 74 68 65 20 6d 6f | 6e 74 68 20 61 73 20 74 |h the mo|nth as t| |000063c0| 68 65 20 6d 69 6c 6c 65 | 6e 6e 69 61 20 67 6f 20 |he mille|nnia go | |000063d0| 62 79 2e 29 0d 0d 09 4f | 6e 20 61 76 65 72 61 67 |by.)...O|n averag| |000063e0| 65 2c 20 74 68 65 72 65 | 20 61 72 65 20 28 32 33 |e, there| are (23| |000063f0| 35 29 32 39 2e 35 33 30 | 35 39 34 31 20 64 61 79 |5)29.530|5941 day| +--------+-------------------------+-------------------------+--------+--------+ Only 25.0 KB of data is shown above.