1
寶應元年六月望戊夜，月蝕三之一。 官曆加時在日出後，有交，不署蝕。 代宗以《至德曆》不與天合，詔司天臺官屬郭獻之等，復用《麟德》元紀，更立歲差，增損遲疾、交會及五星差數，以寫《大衍》舊術。 上元七曜，起赤道虛四度。 帝為制序，題曰《五紀曆》。
On the full-moon night of the sixth month in the first year of Baoying (day wu), the moon suffered a partial eclipse of one-third. According to the official calendar, the computed hour fell after sunrise; although a conjunction occurred, no eclipse was recorded. Because the Zhide Calendar did not match the heavens, Emperor Daizong ordered Guo Xianzhi and other officials of the Directorate of Astronomy to revive the Lindé era epoch, set precession anew, and adjust the parameters for lunar anomaly, syzygies, and the five planets, following the old Dayan procedures. At the high origin, the seven luminaries start at 4° of Xū on the celestial equator. The emperor wrote a preface and named the work the Wuji Calendar.
2
其與《大衍》小異者九事，曰：仲夏之朔，若月行極疾，合於亥正，朔不進，則朔之晨，月見東方矣。 依《大衍》，戌初進初朔，則朔之夕，月見西方矣。 當視定朔小餘不滿《五紀》通法，如晨初餘數減十刻已下者，進以明日為朔。 一也。 以三萬二千一百六十乘夜半定漏刻，六十七乘刻分從之，二千四百而一，為晨初餘數。 二也。 陽曆去交分，交前加一辰，交後減一辰，餘百八十三已下者，日亦蝕。 三也。 月蝕有差，以望日所入定數，視月道同名者，交前為加，交後為減； 異名者，交前為減，交後為加，各以加減去交分。 又交前減一辰，交後加一辰，餘如三百三十八已下者，既。 已上，以減望差，八十約之，得蝕分。 四也。 日蝕有差，以朔日所入定數，十五而一，以減百四，餘為定法。 以蝕差減去交分。 又交前減兩辰，餘為陰曆蝕。 其不足減者，反減蝕差。 在交後減兩辰，交前加三辰，餘為類同陽曆蝕。 又自小滿畢小暑，加時距午正八刻外者，皆減一辰； 三刻內者，皆加一辰。 自大寒畢立春，交前五辰外，自大暑畢立冬，交後五辰外，又減一辰。 不足減者，既。 加、減訖，各如定法而一，以減十五，餘為蝕分。 其陽曆蝕者，置去交分，以蝕差加之。 交前加一辰，交後減一辰。 所得，以減望差，餘如百四約之，得為蝕分。 五也。 所蝕分，日以十八乘之，月以二十乘之，皆十五而一，為泛用刻，不復因加。 六也。 日蝕定用刻在辰正前者，以十分之四為虧初刻，六為復末刻。 未正後者，六為虧初刻，四為復末刻。 不復相半。 七也。 五星乘數、除數，諸變皆通用之，不復變行異數。 入進退曆，皆用度中率。 八也。 以定合初日與前疾初日、後疾初日與合前伏初日先後定數，各同名者，相消為差； 異名者，相從為並。 皆四而一。 所得滿辰法，各為日。 乃以前日盈減、縮加其合後伏日變率，亦以後日盈加、縮減合前伏日變率。 太白、辰星夕變，則返加減留退。 二退度變率，若差於中率者，倍所差之數，曰伏差，以加減前疾日度變率。 熒惑均加減前疾兩變日度變率。 歲星、熒惑、鎮星前留日變率，若差於中率者，以所差之數為度，加減前遲日變率。 皆多於中率之數者，加之； 少於中率者，減之。 後留日變率，若差於中率者，以所差之數為日，以加減後遲日變率及加減二退度變率。 又以伏差加減後疾日度變率。 多於中率之數者，減之； 少於中率者，加之。 其熒惑均加減疾遲兩變日度變率。 歲星、鎮星無遲，即加減前後順行日度變率。 太白晨夕退行度變率，若差於中率者，亦倍所差之數為度，加減本疾度變率。 夕合前、後伏，雖亦退行，不取加、減。 二留日變率，若差於中率者，以所差之數為度，加減本遲度變率。 皆多於中率之數加之，少於中率減之。 其辰星二留日變率，若差於中率者，以所差之數為度，各加、減本遲度變率。 疾行度變率，若差於中率者，以所差之數為日，各加、減留日變率。 亦多於中率之數者，加之； 少於中率者，減之。 其留日變率，若少不足減者，侵減遲日變率。 加減訖，皆為日度定率。 九也。
Nine points on which it differs slightly from the Dayan: At the midsummer new moon, if the moon moves at its fastest and the conjunction falls exactly at the hai hour so that the new moon does not advance, the moon will be visible in the east on the morning of the new moon. Under the Dayan, if the first new moon is advanced to the start of the xu double-hour, the moon appears in the west on the evening of the new moon. When the fixed new moon's minor remainder falls short of the Wuji universal divisor, and the dawn-initial remainder would be reduced by ten quarter-hours or less, advance the new moon to the following day. This is the first point. Multiply the midnight fixed clepsydra quarters by 32,160, add 67 times the fractional quarters, divide by 2,400, and obtain the dawn-initial remainder. This is the second point. For solar-eclipse distance from conjunction: add one double-hour before conjunction and subtract one after; if the remainder is 183 or less, a solar eclipse also occurs. This is the third point. Lunar eclipses require correction: take the fixed entry for full moon; when the lunar path shares the same designation, add before conjunction and subtract after; when the designations differ, subtract before conjunction and add after, each time adjusting the distance from conjunction. Then subtract one double-hour before conjunction and add one after; if the remainder is 338 or less, the eclipse is total. If greater, subtract from the full-moon difference, divide by 80, and obtain the eclipse magnitude. This is the fourth point. Solar eclipses require correction: take the fixed entry for new moon, divide by fifteen, subtract from 104, and the remainder is the fixed divisor. Subtract the eclipse correction from the distance from conjunction. Then subtract two double-hours before conjunction; the remainder indicates a yin-half solar eclipse. If subtraction is insufficient, subtract the eclipse correction in reverse. After conjunction subtract two double-hours and before conjunction add three; the remainder is treated like a yang-half eclipse. From after Grain Full through Minor Heat, if the computed hour lies more than eight quarters from noon, subtract one double-hour; if within three quarters of noon, add one double-hour. From after Great Cold through Start of Spring, beyond five double-hours before conjunction, and from after Great Heat through Start of Winter, beyond five double-hours after conjunction, subtract another double-hour. If the remainder cannot be reduced further, the eclipse is total. After all adjustments, divide each by the fixed divisor, subtract from fifteen, and the remainder is the eclipse magnitude. For yang-half eclipses, set the distance from conjunction and add the eclipse correction. Add one double-hour before conjunction and subtract one after. Subtract the result from the full-moon difference, divide the remainder by 104, and obtain the eclipse magnitude. This is the fifth point. For the eclipse magnitude, multiply by 18 for solar eclipses and by 20 for lunar, divide each by 15 to get the provisional quarter-hours, with no further additive steps. This is the sixth point. If the fixed solar-eclipse quarters fall before the chen hour, assign four-tenths to initial obscuration and six-tenths to final restoration. If after the wei hour, assign six-tenths to initial obscuration and four-tenths to final restoration. The halves are no longer split evenly. This is the seventh point. Multipliers, divisors, and all planetary mutations use common values throughout, without separate numbers for each motion phase. On entering advance or retreat cycles, all phases use the mean-degree rate. This is the eighth point. Compare the fixed offsets of conjunction day with the start of prior fast motion, and of later fast motion with pre-conjunction hiding: where the designations match, cancel to obtain the difference; where they differ, combine as a sum. Divide each result by four. When the quotient fills the double-hour divisor, convert to days. Then subtract surplus and add deficit from the prior day to the post-conjunction hiding-day rate, and add surplus and subtract deficit from the later day to the pre-conjunction hiding-day rate. For Venus and Mercury in evening phase, reverse the additions and subtractions for station and retrograde. If the two retrograde-degree rates differ from the mean, double the difference—called hiding discrepancy—and apply it to the prior fast-motion daily degree rate. Mars applies the adjustment equally to both prior fast-motion daily degree rates. For Jupiter, Mars, and Saturn, if the prior station-day rate differs from the mean, use the difference in degrees to adjust the prior slow-motion daily rate. If the value exceeds the mean rate, add; if it is less, subtract. If the later station-day rate differs from the mean, use the difference in days to adjust the later slow-motion rate and both retrograde-degree rates. Also apply hiding discrepancy to the later fast-motion daily degree rate. If the value exceeds the mean rate, subtract; if it is less, add. Mars applies the same adjustment to both fast- and slow-motion daily degree rates. Jupiter and Saturn have no slow phase, so adjust the prior and later direct-motion daily degree rates instead. For Venus morning and evening retrograde-degree rates that differ from the mean, likewise double the difference in degrees and adjust the base fast-motion degree rate. For evening conjunction before and after hiding, even during retrograde, do not apply these adjustments. If either station-day rate differs from the mean, use the difference in degrees to adjust the base slow-motion degree rate. Add when above the mean rate and subtract when below. For Mercury's two station-day rates, if they differ from the mean, use the difference in degrees to adjust each base slow-motion degree rate. If a fast-motion degree rate differs from the mean, use the difference in days to adjust each station-day rate. Again, add when above the mean; subtract when below. If the station-day rate is too small to subtract from, reduce the slow-motion daily rate instead. After all adjustments, the results are the fixed daily-degree rates. This is the ninth point.
3
《大衍》以四象考五星進退，或時弗葉。 獻之加減頗異，而偶與天合。 於是頒用，訖建中四年。
The Dayan judged the five planets' advance and retreat by the four images, but at times the results failed to match observation. Xianzhi's adjustments differed considerably, yet sometimes matched the heavens. It was then promulgated and remained in use until the fourth year of Jianzhong.
4
2.6.1歲星
2.6.1 Jupiter
5
2.6.2熒惑
2.6.2 Mars
6
2.6.3鎮星
2.6.3 Saturn
7
2.6.4太白
2.6.4 Venus
8
2.6.5辰星
2.6.5 Mercury
9
2.7.1歲星
2.7.1 Jupiter
10
2.7.2熒惑
2.7.2 Mars
11
2.7.3鎮星
2.7.3 Saturn
12
2.7.4太白
2.7.4 Venus
13
2.7.5辰星
2.7.5 Mercury
14
寶應五紀曆
Baoying Wuji Calendar
15
《寶應五紀曆》演紀上元甲子，距寶應元年壬寅，積二十六萬九千九百七十八算。
In computing the evolving era of the Baoying Wuji Calendar, the high origin falls in the year jiazi; reckoned back from the first year of Baoying (renyin), the accumulated count is 269,978.
16
《五紀》通法千三百四十。
Wuji universal divisor: 1,340.
17
策實四十八萬九千四百二十八。
Year-fraction constant: 489,428.
18
揲法三萬九千五百七十一。
New-moon constant: 39,571.
19
策餘七千二十八。
Stalk remainder: 7,028.
20
用差七千五百四十八。
Applied difference: 7,548.
21
掛限三萬八千三百五十七。
Intercalation threshold: 38,357.
22
三元之策十五，餘二百九十二，秒五； 秒母六。 以象統為母者，以四因之。
Three-origin interval: 15 stalks, remainder 292, 5 parts; part denominator 6. Where the image cycle is the denominator, multiply by four.
23
四象之策二十九，餘七百一十一。
Four-image interval: 29 stalks, remainder 711.
24
一象之策七，餘五百一十二太。
Single-image interval: 7 stalks, remainder 512 plus.
25
天中之策五，餘九十七，秒十五； 秒母十八。
Heaven-center interval: 5 stalks, remainder 97, 15 parts; part denominator 18.
26
地中之策六，餘百一十九，秒四； 秒母三十。
Earth-center interval: 6 stalks, remainder 119, 4 parts; part denominator 30.
27
貞悔之策三，餘五十八，秒十七。
Chaste-regret interval: 3 stalks, remainder 58, 17 parts.
28
辰法三百三十五。
Double-hour divisor: 335.
29
刻法百三十四。
Quarter-hour divisor: 134.
30
幹實四十八萬九千四百四十二，秒七十。
Cycle constant: 489,442, 70 parts.
31
周天度三百六十五，虛分三百四十二，秒七十。
Tropical year: 365°, remainder 342, 70 parts.
32
歲差十四，秒七十。
Precession: 14, 70 parts.
33
秒法百。
Part denominator: 100.
34
定氣所有日及餘，以辰計之，曰辰數，與《大衍》同。
The days and remainders for fixed qi, counted in double-hours as double-hour numbers, follow the Dayan method.
35
六虛之差七，秒七十。
Six-void correction: 7, 70 parts.
36
轉終分百三十六萬六千一百五十六。
Lunar revolution constant: 1,366,156.
37
轉終日二十七，餘七百四十三，秒五。
Synodic month: 27 days, remainder 743, 5 parts.
38
秒法三十七。
Part denominator: 37.
39
轉法六十七。 約轉分為度，曰逡程。 積逡程，曰轉積度。
Rotation divisor: 67. Reduce rotation parts to degrees, called the retrograde increment. The accumulated retrograde increment is called the rotation accumulated degrees.
40
七日初，千一百九十一。 末，百四十九。 十四日初，千四十二。 末，二百九十八。
Day 7, initial: 1,191. Final: 149. Day 14, initial: 1,042. Final: 298.
41
二十一日初，八百九十二。 末，四百四十八。 二十八日初，七百四十三。 末，五百九十七。
Day 21, initial: 892. Final: 448. Day 28, initial: 743. Final: 597.
42
半紀六百七十。
Half-cycle constant: 670.
43
象積四百八十。
Image-cycle constant: 480.
44
辰刻八刻，分百六十。
Double-hour quarters: 8 quarters, 160 parts.
45
昏明刻各二刻，分二百四十。
Twilight quarters: 2 quarters each, 240 parts.
46
交終三億六千四百六十四萬三千七百六十七。
Nodal revolution constant: 364,643,767.
47
交終日二十七，餘二百八十四，秒三千七百六十七。
Draconic month: 27 days, remainder 284, 3,767 parts.
48
交中日十三，餘八百一十二，秒千八百八十三半。
Half draconic month: 13 days, remainder 812, 1,883½ parts.
49
朔差日二，餘四百二十六，秒六千二百三十三。
New-moon interval: 2 days, remainder 426, 6,233 parts.
50
望差日一，餘二百一十三，秒三千一百一十六半。
Full-moon interval: 1 day, remainder 213, 3,116½ parts.
51
望數日十四，餘千二十五，秒五千。
Full-moon count: 14 days, remainder 1,025, 5,000 parts.
52
交限日十二，餘五百九十八，秒八千七百六十七。
Eclipse limit: 12 days, remainder 598, 8,767 parts.
53
交率六十一。
Nodal rate: 61.
54
交數七百七十七。 凡春分後陰曆交後，秋分後陽曆交後，為月道同名。 餘皆為異名。
Nodal number: 777. After the spring equinox in the yin half following conjunction, and after the autumn equinox in the yang half following conjunction, the lunar path is of the same designation. All other cases are of different designation.
55
辰分百一十三。
Double-hour fraction: 113.
56
秒法一萬。
Part denominator: 10,000.
57
去交度乘數十一，除數千一百六十五。
Distance-from-node multiplier: 11; divisor: 1,165.
58
太陰損益差：冬至、夏至，益十九，積七十六； 小寒、小暑，益十六，積九十五； 大寒、大暑，益十四，積百一十一； 立春、立秋，益十二，積百二十五； 雨水、處暑，益十，積百三十七； 驚贄、白露，益七，積百四十七； 春分、秋分，損七，積百五十四。 清明、寒露，損十，積百四十七； 穀雨、霜降，損十二，積百三十七； 立夏、立秋，損十四，積百二十五； 小滿、小雪，損十七，積百一十一； 芒種、大雪，損十九，積九十五； 依定氣求朓朓術入之，得其望日所入定數。
Lunar correction table: at winter and summer solstice, add 19, cumulative 76; minor cold and minor heat, add 16, cumulative 95; major cold and major heat, add 14, cumulative 111; start of spring and start of autumn, add 12, cumulative 125; rain water and end of heat, add 10, cumulative 137; awakening of insects and white dew, add 7, cumulative 147; spring and autumn equinox, subtract 7, cumulative 154. Clear and bright and cold dew, subtract 10, cumulative 147; grain rain and frost descent, subtract 12, cumulative 137; start of summer and start of autumn, subtract 14, cumulative 125; minor fullness and minor snow, subtract 17, cumulative 111; bearded grain and major snow, subtract 19, cumulative 95; Using fixed qi, apply the waxing-waning method to obtain the fixed entry for full moon.
59
太陽每日蝕差：月在陰曆，自秋分後、春分前，皆以四百五十七為蝕差； 入春分後，日損五分； 入夏至初日，損不盡者七； 乃自後日益五分。 月在陽曆，自春分後、秋分前，亦以四百五十七為蝕差； 入秋分後，日損五分，入冬至初日，損不盡者七； 乃自後日益五分。 各得朔日所入定數。
Daily solar-eclipse correction: when the moon is in the yin half, from after autumn equinox until before spring equinox, use 457 as the eclipse correction; after spring equinox, decrease by five parts per day; on the first day of summer solstice, the remainder after decrease is seven; then increase by five parts per day thereafter. When the moon is in the yang half, from after spring equinox until before autumn equinox, likewise use 457; after autumn equinox, decrease five parts per day; on the first day of winter solstice, the remainder is seven; then increase five parts per day thereafter. Thus obtaining the fixed entry for each new moon.
60
終率五十三萬四千四百八十二，秒三十六。
Jupiter revolution constant: 534,482, 36 parts.
61
終日三百九十八，餘千一百六十二，秒三十六。
Jupiter synodic period: 398 days, remainder 1,162, 36 parts.
62
變差十四，秒八十八。
Anomaly correction: 14, 88 parts.
63
象算九十一，餘百五，秒十八。
Image computation: 91, remainder 105, 18 parts.
64
爻算十五，餘七十三，秒四十六，微分三十二。
Line computation: 15, remainder 73, 46 parts, 32 micro-parts.
65
乘數五。
Multiplier: 5.
66
除數四。
Divisor: 4.
67
終率百四萬五千八十八，秒八十三。
Mars revolution constant: 1,045,088, 83 parts.
68
終日七百七十九，餘千二百二十八，秒八十三。
Mars synodic period: 779 days, remainder 1,228, 83 parts.
69
變差三十二，秒五十七。
Anomaly correction: 32, 57 parts.
70
象算九十一，餘百六，秒二十八，微分五十四。
Image computation: 91, remainder 106, 28 parts, 54 micro-parts.
71
爻算十五，餘七十三，秒五十四，微分七十三。
Line computation: 15, remainder 73, 54 parts, 73 micro-parts.
72
乘數百二十七。
Multiplier: 127.
73
除數三十。
Divisor: 30.
74
終率五十萬六千六百二十三，秒二十九。
Saturn revolution constant: 506,623, 29 parts.
75
終日三百七十八，餘百三，秒二十九。
Saturn synodic period: 378 days, remainder 103, 29 parts.
76
變差九，秒八十七。
Anomaly correction: 9, 87 parts.
77
象算九十一，餘百四，秒八十六，微分六十六。
Image computation: 91, remainder 104, 86 parts, 66 micro-parts.
78
爻算十五，餘七十三，秒三十一，微分十一。
Line computation: 15, remainder 73, 31 parts, 11 micro-parts.
79
乘數十二。
Multiplier: 12.
80
除數十一。
Divisor: 11.
81
終率七十八萬二千四百四十九，秒九。
Venus revolution constant: 782,449, 9 parts.
82
終日五百八十三，餘千二百二十九，秒九。
Venus synodic period: 583 days, remainder 1,229, 9 parts.
83
中合二百九十二，餘千二百八十四，秒五十九，微分七十二。
Mid-conjunction: 292, remainder 1,284, 59 parts, 72 micro-parts.
84
變差四十九，秒七十二。
Anomaly correction: 49, 72 parts.
85
象算九十一，餘百七，秒三十五，微分七十二。
Image computation: 91, remainder 107, 35 parts, 72 micro-parts.
86
爻算十五，餘七十三，秒七十二，微分六十。
Line computation: 15, remainder 73, 72 parts, 60 micro-parts.
87
乘數十五。
Multiplier: 15.
88
除數二。
Divisor: 2.
89
終率十五萬五千二百七十八，秒六十六。
Mercury revolution constant: 155,278, 66 parts.
90
終日百一十五，餘千一百七十八，秒六十六。
Mercury synodic period: 115 days, remainder 1,178, 66 parts.
91
中合五十七，餘千二百五十九，秒三十三。
Mid-conjunction: 57, remainder 1,259, 33 parts.
92
變差五十，秒八十五。
Anomaly correction: 50, 85 parts.
93
象算九十一，餘百七，秒四十二，微分七十八。
Image computation: 91, remainder 107, 42 parts, 78 micro-parts.
94
爻算十五，餘七十三，秒七十三，微分七十七。
Line computation: 15, remainder 73, 73 parts, 77 micro-parts.
95
秒法百。
Part denominator: 100.
96
微分法九十六。
Micro-part denominator: 96.
97
德宗時，《五紀曆》氣朔加時稍後天，推測星度與《大衍》差率頗異。 詔司天徐承嗣與夏官正楊景風等，雜《麟德》、《大衍》之旨治新曆。 上元七曜，起赤道虛四度。 建中四年曆成，名曰《正元》。 其氣朔、發斂、日躔、月離、軌漏、交會，悉如《五紀》法。 惟發斂加時無辰法，皆以象統乘小餘，通法而一，為半辰數。 餘五因之，六刻法除之，得刻。 不盡，六而一，為刻分。 其軌漏夜半刻分以刻法准象積取其數用之，以刻法通夜半定漏刻，內分，二十而一，為晨初餘數。 月蝕去交分，如二百七十九已下者，既。 已上，以減望差，六十六約之，為蝕分。 日蝕差亦十五約之，以減八十五，餘為定法。 又加減去交分訖，以減望差，八十五約之，得蝕分。 日法不同也。 其五星寫《麟德曆》舊術，因冬至後夜半平合日算，加合後伏日及余，即平見日算。 金、水先得夕見； 其滿晨見伏日及餘秒去之，余為晨平見。 求入常氣，以取定見而推之。 《麟德曆》之啟蟄，《正元曆》之雨水； 《麟德曆》之雨水，《正元曆》之驚蟄也。 《麟德曆》熒惑前、後疾變度率，初行入氣差行，日益遲、疾一分，《正元曆》則二分，亦度母不同也。 詔起五年正月行新曆。 會硃泚之亂，改元興元。 自是頒用，訖元和元年。
Under Emperor Dezong, the Wuji Calendar's computed times for qi and new moons lagged slightly behind the heavens, and its planetary positions differed notably from the Dayan rates. The emperor ordered Xu Chengsi of the Astronomical Bureau and Yang Jingfeng, Director of the Summer Office, and others to combine the Lindé and Dayan methods in drafting a new calendar. At the high origin, the seven luminaries start at 4° of Xū on the celestial equator. The calendar was finished in the fourth year of Jianzhong (783) and given the title Zhengyuan Calendar. For central qi, new moons, solstitial procedures, solar and lunar motion, clepsydra tracks, and syzygies, it follows the Wuji Calendar throughout. Only for fixing the hour of issuing and gathering in there is no chronogram divisor; in every case multiply the minor remainder by the image cycle, divide by the universal divisor, and obtain the half-chronogram count. Multiply any remainder by five, divide by the six-quarter divisor, and obtain the quarter-hour quotient. The remainder, divided by six, gives the fractional quarters. For track-and-clepsydra midnight quarters, take the value scaled by the quarter-hour divisor against the image-cycle constant; convert the midnight fixed clepsydra quarters through the quarter-hour divisor, include fractional parts, divide by twenty, and obtain the dawn-initial remainder. For lunar eclipses, if the distance-from-node parts are 279 or less, the eclipse is total. If greater than that, subtract from the full-moon difference, divide by 66, and obtain the eclipse magnitude. For solar-eclipse correction, divide by 15, subtract from 85, and use the remainder as the fixed divisor. After all adjustments to the distance-from-node parts, subtract from the full-moon difference, divide by 85, and obtain the eclipse fraction. The solar divisor differs. The five planets follow the old Lindé Calendar procedures: from the mean-conjunction day count after winter-solstice midnight, add the post-conjunction hiding days and remainder to obtain the mean visibility day count. Venus and Mercury first reach evening visibility; Remove one full cycle of morning-visibility hiding days and remainders; what is left is the mean morning appearance. Determine entry into regular qi, obtain the fixed appearance, and compute accordingly. What the Lindé Calendar calls Awakening of Insects corresponds to Rain Water in the Zhengyuan Calendar; and Lindé Rain Water corresponds to Zhengyuan Awakening of Insects. In the Lindé Calendar, Mars's initial and final fast-phase degree rates increase or decrease by one part per day upon entering qi; the Zhengyuan Calendar uses two parts—the degree denominators also differ. An edict mandated use of the new calendar from the first month of the fifth year of the era. The Zhu Ci rebellion intervened, and the reign era was changed to Xingyuan. It was then promulgated and remained in use until the first year of Yuanhe (806).
98
建中正元曆
The Jianzhong Zhengyuan Calendar.
99
《建中正元曆》演紀上元甲子，距建中五年甲子，歲積四十萬二千九百算外。
In computing the evolving era of the Jianzhong Zhengyuan Calendar, the high origin is year jiazi; reckoned back from Jianzhong 5 (jiazi), the accumulated count is 402,900 beyond the tally.
100
《正元》通法千九十五。
Zhengyuan universal divisor: 1,905.
101
策實三十九萬九千九百四十三。
Year-fraction constant: 399,943.
102
揲法三萬三千三百三十六。
New-moon constant: 33,336.
103
章閏萬一千九百一十一。
Intercalation-cycle constant: 11,911.
104
策餘五千七百四十三。
Year-fraction remainder: 5,743.
105
用差六千一百六十八。
Correction difference: 6,168.
106
掛限三萬一千三百四十三。
Intercalation threshold: 31,343.
107
三元之策十五，餘二百三十九，秒七。
Three-origin interval: 15 stalks, remainder 239, 7 parts.
108
四象之策二十九，餘五百八十一。
Four-image interval: 29 stalks, remainder 581.
109
一象之策七，餘四百一十九。
Single-image interval: 7 stalks, remainder 419.
110
中盈分四百七十八，秒一十四。
Central-qi surplus fraction: 478, 14 parts.
111
朔虛分五百一十四。
Synodic void fraction: 514.
112
象統二十四。
Image-cycle denominator: 24.
113
象位六。
Image-cycle positions: 6.
114
天中之策五，餘七十九，秒五十五； 秒母七十二。
Heaven-center interval: 5 stalks, remainder 79, 55 parts; Part denominator: 72.
115
地中之策六，餘九十五，秒四十三； 秒母六十。
Earth-center interval: 6 stalks, remainder 95, 43 parts; Part denominator: 60.
116
貞悔之策三，餘四十七，秒五十一半。
Chaste-regret interval: 3 stalks, remainder 47, 51½ parts.
117
刻法二百一十九。 六刻法千三百一十四。
Quarter-hour divisor: 219. Six-quarter divisor: 1,314.
118
幹實三十九萬九千九百五十五，秒二。
Cycle constant: 399,955, 2 parts.
119
周天度三百六十五，虛分二百八十，秒二。
Tropical year: 365°, remainder 280, 2 parts.
120
歲差十二，秒二。
Precession: 12, 2 parts.
121
秒母百。
Part denominator: 100.
122
定氣辰數同《大衍》。
Fixed-qi chronogram counts follow the Dayan Calendar.
123
六虛之差六，秒二十。
Six-void correction: 6, 20 parts.
124
轉終分三億一百七十二萬一百三十二。
Lunar revolution constant: 317,201,032.
125
轉終日二十七，餘六百七，秒百三十二。
Synodic month: 27 days, remainder 607, 132 parts.
126
入轉秒法一萬。
Rotation-entry seconds divisor: 10,000.
127
轉法二百一十九。 約轉分為度，曰逡程。 積逡程，曰轉積度。
Rotation divisor: 219. Reduce rotation parts to degrees, called the retrograde increment. The accumulated retrograde increment is called the rotation accumulated degrees.
128
七日：初九百七十三，末百二十二。
Day 7: initial value 973, terminal value 122.
129
十四日：初八百五十一，末二百四十四。
Day 14: initial value 851, terminal value 244.
130
二十一日：初七百二十九，末三百六十六。
Day 21: initial value 729, terminal value 366.
131
二十八日：初六百七，末四百八十八。
Day 28: initial value 607, terminal value 488.
132
辰刻八刻，分七十三。
Double-hour quarters: 8 quarters, 73 parts.
133
刻法二百一十九。
Quarter-hour divisor: 219.
134
昏明刻各二刻，分百九半。
Twilight quarters: 2 quarters each, 109½ parts.
135
交終分二億九千七百九十七萬三千八百一十五。
Nodal revolution constant: 297,973,815.
136
交終日二十七，餘二百三十二，秒三千八百一十五。
Draconic month: 27 days, remainder 232, 3,815 parts.
137
交中日十三，餘六百六十三，秒六千九百七半。
Half draconic month: 13 days, remainder 663, 6,907½ parts.
138
朔差日二，餘三百四十八，秒六千一百八十五。
New-moon interval: 2 days, remainder 348, 6,185 parts.
139
望差日一，餘百七十四，秒三千九十二半。
Full-moon interval: 1 day, remainder 174, 3,092½ parts.
140
望數日十四，餘八百三十八。
Full-moon count: 14 days, remainder 838.
141
交限日十二，餘四百八十九，秒三千八百一十五。
Eclipse limit: 12 days, remainder 489, 3,815 parts.
142
交率六十一。
Nodal rate: 61.
143
交數七百七十七。
Nodal number: 777.
144
交辰法九十一少。
Nodal chronogram divisor: slightly under 91.
145
秒法一萬。
Seconds divisor: 10,000.
146
去交度乘數十一，除數九百四十五。
Distance-from-node multiplier: 11; divisor: 945.
147
太陰損益差：冬至、夏至，益十六，積六十二。 小寒、小暑，益十三，積七十八。 大寒、大暑，益十一，積九十一。 立春、立秋，益十，積百二。 雨水、處暑，益八，積百一十二。 驚蟄、白露，益六，積百二十。 春分、秋分，損六，積百二十六。 清明、寒露，損八，積百二十。 穀雨、霜降，損十，積百一十二。 立夏、立冬，損十一，積百二。 小滿、小雪，損十三，積九十一。 芒種、大雪，損十六，積七十八。 以損益依入定氣求朓朒術入之，各得其望日所入定數。
Lunar correction table: at winter and summer solstice, add 16, cumulative 62; minor cold and minor heat, add 13, cumulative 78; major cold and major heat, add 11, cumulative 91; start of spring and start of autumn, add 10, cumulative 102; rain water and end of heat, add 8, cumulative 112; awakening of insects and white dew, add 6, cumulative 120; spring and autumn equinox, subtract 6, cumulative 126; clear and bright and cold dew, subtract 8, cumulative 120; grain rain and frost descent, subtract 10, cumulative 112; start of summer and start of winter, subtract 11, cumulative 102; minor fullness and minor snow, subtract 13, cumulative 91; bearded grain and major snow, subtract 16, cumulative 78. Apply the surplus-deficit values through fixed qi and the waxing-waning method to obtain the fixed entry for each full moon.
148
太陽每日蝕差：月在陰曆，自秋分後、春分前，皆以三百七十三為蝕差，入春分後，日損四分； 入夏至初日，損不盡者六； 乃自後日益四分。 月在陽曆，自春分後、秋分前，亦以三百七十三為蝕差； 入秋分後，日損四分； 入冬至初日，損不盡者六； 乃自後日益四分：各得朔日所入定數。
Daily solar-eclipse correction: when the moon is in the yin half, from after autumn equinox until before spring equinox, use 373 as the eclipse correction; after spring equinox, decrease by four parts per day; on the first day of summer solstice, the remainder after decrease is six; then increase by four parts per day thereafter. When the moon is in the yang half, from after spring equinox until before autumn equinox, likewise use 373; after autumn equinox, decrease by four parts per day; on the first day of winter solstice, the remainder after decrease is six; then increase by four parts per day thereafter, thus obtaining the fixed entry for each new moon.
149
終率四十三萬六千七百六十，秒四。
Jupiter revolution constant: 436,760, 4 parts.
150
終日三百九十八，餘九百五十，秒四。
Jupiter synodic period: 398 days, remainder 950, 4 parts.
151
合後伏日十七，餘千二十三。
Post-conjunction hiding: 17 days, remainder 1,023.
152
終率八十五萬四千七，秒七十九。
Mars revolution constant: 854,007, 79 parts.
153
終日七百七十九，餘千二，秒七十九。
Mars synodic period: 779 days, remainder 1,002, 79 parts.
154
合後伏日七十一，餘千四十九。
Post-conjunction hiding: 71 days, remainder 1,049.
155
終率四十一萬三千九百九十四，秒六十三。
Saturn revolution constant: 413,994, 63 parts.
156
終日三百七十八，餘八十四，秒六十三。
Saturn synodic period: 378 days, remainder 84, 63 parts.
157
合後伏日十八，餘五百九十。
Post-conjunction hiding: 18 days, remainder 590.
158
終率六十三萬九千三百八十九，秒二十八。
Venus revolution constant: 639,389, 28 parts.
159
終日五百八十三，餘四，秒二十八。
Venus synodic period: 583 days, remainder 4, 28 parts.
160
晨合後伏日四十一，餘九百一十五。
Morning post-conjunction hiding: 41 days, remainder 915.
161
夕見伏日二百五十六，餘五百二，秒一十四。
Evening visibility hiding: 256 days, remainder 502, 14 parts.
162
晨見伏日三百二十七，餘五百二，秒一十四。
Morning visibility hiding: 327 days, remainder 502, 14 parts.
163
終率十二萬六千八百八十八，秒四半。
Mercury revolution constant: 126,888, 4½ parts.
164
終日百一十五，餘九百六十三，秒四半。
Mercury synodic period: 115 days, remainder 963, 4½ parts.
165
晨合後伏日十六，餘千四十。
Morning post-conjunction hiding: 16 days, remainder 1,040.
166
夕見伏日五十二，餘四百八十一，秒五十二少。
Evening visibility hiding: 52 days, remainder 481, 52 parts less.
167
晨見伏日六十三，餘四百八十一，秒五十二少。
Morning visibility hiding: 63 days, remainder 481, 52 parts less.
168
秒法一百。
Part denominator: 100.
169
五星平見加減差
Five-planet mean visibility add-subtract corrections.
170
五星平見加減差
Five-planet mean visibility add-subtract corrections.
171
初見，去日十四度，見。 入冬至，畢小寒，均減六日。 自入大寒後，日損百九分半。 入春分初日，依平。 自後日加百四十五分半。 入立夏，畢小滿，均加六日。 自入芒種後，日損百四十五分。 入夏至，畢立秋，均加四日。 自入處暑後，日損二百九十一分半。 入白露初日，依平。 自後日減八十七分。 入小雪，畢大雪，均減六日。
Jupiter: at first appearance, when fourteen degrees from the sun, it is visible. From the Winter Solstice through Minor Cold, uniformly subtract six days. From Major Cold onward, subtract 109½ parts per day. At the Spring Equinox on the first day, follow the mean rate. From then on, add 145½ parts per day. From the Start of Summer through Minor Fullness, uniformly add six days. From Grain in Ear onward, subtract 145 parts per day. From the Summer Solstice through the Start of Autumn, uniformly add four days. From End of Heat onward, subtract 291½ parts per day. At White Dew on the first day, follow the mean rate. From then on, subtract 87 parts per day. From Minor Snow through Major Snow, uniformly subtract six days.
172
初見，去日十七度，見。 入冬至初日，減二十七日。 自後日損九百八十五分半。 入大寒初日，依平。 自後日加六百五十七分。 入驚蟄，畢穀雨，均加二十七日。 自入立夏後，日損三百二十三分。 入立秋，依平。 自入處暑後，日減三百二十三分。 入小雪，畢大雪，均減二十七日。
Mars: at first appearance, when seventeen degrees from the sun, it is visible. At the Winter Solstice on the first day, subtract 27 days. From then on, subtract 985½ parts per day. At Major Cold on the first day, follow the mean rate. From then on, add 657 parts per day. From Awakening of Insects through Grain Rain, uniformly add 27 days. From the Start of Summer onward, subtract 323 parts per day. At the Start of Autumn, follow the mean rate. From End of Heat onward, subtract 323 parts per day. From Minor Snow through Major Snow, uniformly subtract 27 days.
173
初見，去日十七度，見。 入冬至初日，減四日。 自後日益百四十五分半。 入大寒，畢春分，均減八日。 自入清明後，日損九十六分。 入小暑初日，依平。 自後日加百四十五分半。 入白露初日，加八日。 自後日損二百九十一分。 入秋分，均加四日。 自入寒露後，日損九十六分。 入小雪初日，依平。 自後日減百四十五分半。
Saturn: at first appearance, when seventeen degrees from the sun, it is visible. At the Winter Solstice on the first day, subtract four days. From then on, add 145½ parts per day. From Major Cold through the Spring Equinox, uniformly subtract eight days. From Clear Brightness onward, subtract 96 parts per day. At Minor Heat on the first day, follow the mean rate. From then on, add 145½ parts per day. At White Dew on the first day, add eight days. From then on, subtract 291 parts per day. At the Autumn Equinox, uniformly add four days. From Cold Dew onward, subtract 96 parts per day. At Minor Snow on the first day, follow the mean rate. From then on, subtract 145½ parts per day.
174
初見，去日十一度。 夕見：入冬至初日，依平。 自後日減百六十三分。 入雨水，畢春分，均減九日。 自入清明後，日減百六十三分。 入芒種，依平。 自入夏至，日加百六十三分。 入處暑，畢秋分，均加九日。 自入寒露後，日損百六十三分。 入大雪，依平。 晨見：入冬至，依平。 入小寒後，日加百九分半。 入立春，畢立夏，均加三日。 入小滿後，日損百九分半。 入夏至，依平。 入小暑後，日減百九分半。 入立秋，畢立冬，均減三日。 入小雪後，日損百九分半。
Venus: at first appearance it stands eleven degrees from the sun. Evening appearance: from the Winter Solstice, follow the mean rate on the first day. From then on, subtract 163 parts per day. From Rain Water through the Spring Equinox, uniformly subtract nine days. From Clear Brightness onward, subtract 163 parts per day. At Grain in Ear, follow the mean rate. From the Summer Solstice onward, add 163 parts per day. From End of Heat through the Autumn Equinox, uniformly add nine days. From Cold Dew onward, subtract 163 parts per day. At Major Snow, follow the mean rate. Morning appearance: from the Winter Solstice, follow the mean rate. From Minor Cold onward, add 109½ parts per day. From the Start of Spring through the Start of Summer, uniformly add three days. From Minor Fullness onward, subtract 109½ parts per day. At the Summer Solstice, follow the mean rate. From Minor Heat onward, subtract 109½ parts per day. From the Start of Autumn through the Start of Winter, uniformly subtract three days. From Minor Snow onward, subtract 109½ parts per day.
175
初見，去日十七度。 夕見：入冬至，畢清明，依平。 入穀雨，畢芒種，均減二日。 入夏至，畢大暑，依平。 入立秋，畢霜降，應見不見。 其在立秋及霜降二氣之內者，去日十八度外，三十六度內，有水、火、土、金一星已上者，見。 入立冬，畢大雪，依平。 晨見； 入冬至，均減四日。 入小寒，畢雨水，均減三日。 其在雨水氣內，去日度如前，晨無水、火、土、金一星已上者，不見。 入驚蟄，畢立夏，應見不見。 其在立夏氣內，去日度如前，晨有水、火、土、金一星已上者，亦見。 入小滿，畢寒露，依平。 入霜降，畢立冬，均加一日。 入小雪，畢大雪，依平。
Mercury: at first appearance it stands seventeen degrees from the sun. Evening appearance: from the Winter Solstice through Clear Brightness, follow the mean rate. From Grain Rain through Grain in Ear, uniformly subtract two days. From the Summer Solstice through Major Heat, follow the mean rate. From the Start of Autumn through Frost's Descent, it should appear but does not. If within the two qi of Start of Autumn and Frost's Descent, at more than eighteen but less than thirty-six degrees from the sun, and Mercury, Mars, Saturn, or Venus is also visible, it appears. From the Start of Winter through Major Snow, follow the mean rate. Morning appearance: From the Winter Solstice, uniformly subtract four days. From Minor Cold through Rain Water, uniformly subtract three days. If within the Rain Water qi, at the same solar distance as before, with no Mercury, Mars, Saturn, or Venus visible in the morning, it is not seen. From Awakening of Insects through the Start of Summer, it should appear but does not. If within the Start of Summer qi, at the same solar distance as before, with one or more of Mercury, Mars, Saturn, or Venus visible in the morning, it is seen as well. From Minor Fullness through Cold Dew, follow the mean rate. From Frost's Descent through the Start of Winter, uniformly add one day. From Minor Snow through Major Snow, follow the mean rate.
176
五星變行加減差日度率
Five-planet differential motion add-subtract daily degree rates.
177
五星變行加減差日度率
Five-planet differential motion add-subtract daily degree rates.
178
前順：差行。 百一十四日，行十八度九百七十一分。 先疾，二日益遲三分。
Prior direct motion: differential motion. 114 days, travels 18°971 parts. Fast at first; slowness increases by 3 parts every 2 days.
179
前留：二十六日。
Prior station: 26 days.
180
前退：差行。 四十二日，退六度。 先遲，日益疾二分。
Prior retrograde motion: differential motion. 42 days, retreats 6°. Slow at first; speed increases by 2 parts per day.
181
後退：差行。 四十二日，退六度。 先疾，日益遲二分。
Later retrograde motion: differential motion. 42 days, retreats 6°. Fast at first; slowness increases by 2 parts per day.
182
後留：二十五日。
Later station: 25 days.
183
後順：差行。 百一十四日，行十八度九百七十一分。 先遲，二日益疾三分。 日盡而夕伏。
Later direct motion: differential motion. 114 days, travels 18°971 parts. Slow at first; speed increases by 3 parts every 2 days. When its days are exhausted it disappears at evening.
184
前疾：入冬至初日，二百四十三日行百六十五度。 自後三日損日度各二。 小寒初日，二百三十三日行百五十五度。 自後二日損日度各一。 穀雨四日，依平。 畢小滿九日，百七十八日行百度。 自九日後，三日損日度各一。 夏至初日，依平。 畢六日，百七十一日行九十三度。 自六日後，每三日益日度各一。 立秋初日，百八十四日行百六度。 自後每日益日度各一。 白露初日，二百一十四日行百三十六度。 自後五日益日度各六。 秋分初日，二百三十二日行百五十四度。 自後每日益日度各一。 寒露初日，二百四十七日行百六十九度。 自後五日益日度各三。 霜降五日，依平。 畢立冬十三日，二百五十九日行百八十一度。 自入十三日後，二日損日度各一。
Prior fast motion: on the Winter Solstice first day, 243 days for 165°. From then on, subtract 2 each from the day-count and degree-count every 3 days. On the first day of Minor Cold, 233 days for 155°. From then on, subtract 1 each from the day-count and degree-count every 2 days. Four days into Grain Rain, follow the mean rate. Through nine days of Minor Fullness, 178 days for 100°. From after nine days, subtract 1 each from the day-count and degree-count every 3 days. On the Summer Solstice first day, follow the mean rate. Through six days, 171 days for 93°. From after six days, add 1 each to the day-count and degree-count every 3 days. On the first day of Start of Autumn, 184 days for 106°. From then on, add 1 each to the day-count and degree-count each day. On the first day of White Dew, 214 days for 136°. From then on, add 6 each to the day-count and degree-count every 5 days. On the first day of Autumn Equinox, 232 days for 154°. From then on, add 1 each to the day-count and degree-count each day. On the first day of Cold Dew, 247 days for 169°. From then on, add 3 each to the day-count and degree-count every 5 days. Five days into Frost's Descent, follow the mean rate. Through thirteen days of Start of Winter, 259 days for 181°. From after thirteen days entered, subtract 1 each from the day-count and degree-count every 2 days.
185
前遲：差行。 入冬至，六十日行二十五度； 先疾，日益遲三分。 自入小寒後，三日損日度各一。 大寒初日，五十五日行二十度。 自後三日益日度各一。 立春初日，畢清明，平，六十日行二十五度。 自入穀雨，每氣損度一。 立夏初日，畢小滿，平，六十日行二十三度。 自入芒種後，每氣益一度。 夏至初日，平。 畢處暑，六十日行二十五度。 自入白露後，三日損度一。 秋分初日，六十日行二十度。 自後每日益日一，三日益度二。 寒露初日，七十五日行三十度。 自後每日損日一，三日損度一。 霜降初日，六十日行二十五度。 自後二日損度一。 立冬一日，平。 畢氣末，六十日行十七度。 自小雪後，五日益度一。 大雪初日，六十日行二十度。 自後三日益度一。
Prior slow motion: differential motion. Entering Winter Solstice, 60 days for 25°; Fast at first; slowness increases by 3 parts per day. From Minor Cold onward, subtract 1 each from the day-count and degree-count every 3 days. On the first day of Major Cold, 55 days for 20°. From then on, add 1 each to the day-count and degree-count every 3 days. From the first day of Start of Spring through Clear Brightness, follow the mean rate: 60 days for 25°. From Grain Rain onward, subtract 1 degree per solar term. From the first day of Start of Summer through Minor Fullness, follow the mean rate: 60 days for 23°. From Grain in Ear onward, add 1 degree per solar term. On the Summer Solstice first day, follow the mean rate. Through End of Heat, 60 days for 25°. From White Dew onward, subtract 1 degree every 3 days. On the first day of Autumn Equinox, 60 days for 20°. From then on, add 1 to the day-count each day and 2 to the degree-count every 3 days. On the first day of Cold Dew, 75 days for 30°. From then on, subtract 1 from the day-count each day and 1 from the degree-count every 3 days. On the first day of Frost's Descent, 60 days for 25°. From then on, subtract 1 degree every 2 days. One day into Start of Winter, follow the mean rate. Through the end of the qi, 60 days for 17°. From Minor Snow onward, add 1 degree every 5 days. On the first day of Major Snow, 60 days for 20°. From then on, add 1 degree every 3 days.
186
前留：十三日前疾減一日率者，以其差分益此留及遲日率。 前疾加日率者，以其差分減此留及後遲日率。
Prior station: if the prior fast phase subtracted 1 from the day-rate, distribute the difference-parts to increase this station and slow day-rates. If the prior fast phase added to the day-rate, distribute the difference-parts to decrease this station and later slow day-rates.
187
退行：入冬至初日，六十三日行二十二度。 自後四日益度一。 小寒一日，六十三日行二十六度。 自入小寒一日後，三日半損度一。 立春三日，平。 畢雨水，六十三日退十七度。 自入驚蟄後，二日益日度各一，驚蟄八日，平。 畢氣末，六十七日退二十一度。 自入春分後，一日損日度各一。 春分四日，平。 畢芒種，六十三日退十七度。 自入夏至後，每六日損日度各一。 大暑初日，平。 畢氣末，五十八日退十二度。 立秋初日，平。 畢氣末，五十七日退十一度。 自入白露後，二日益日度各一。 白露十二日，平。 畢秋分，六十三日退十七度。 自入寒露後，三日益日度各一。 寒露九日，平。 畢氣末，六十六日退二十度。 自入霜降後，二日損日度各一。 霜降六日，平。 畢氣末，六十三日退十七度。 自入立冬後，三日益日度各一。 立冬十二日，平。 畢氣末，六十七日退二十一度。 自入小雪後，二日損日度各一。 小雪八日，平。 畢氣末，六十三日退十七度。 自入大雪後，三日益度一。
Retrograde motion: on the Winter Solstice first day, 63 days retreating 22°. From then on, add 1 degree every 4 days. One day into Minor Cold, 63 days retreating 26°. From after one day into Minor Cold, subtract 1 degree every 3.5 days. Three days into Start of Spring, follow the mean rate. Through Rain Water, 63 days retreating 17°. From Awakening of Insects onward, add 1 each to the day-count and degree-count every 2 days; eight days into Awakening of Insects, follow the mean rate. Through the end of the qi, 67 days retreating 21°. From Spring Equinox onward, subtract 1 each from the day-count and degree-count each day. Four days into Spring Equinox, follow the mean rate. Through Grain in Ear, 63 days retreating 17°. From the Summer Solstice onward, subtract 1 each from the day-count and degree-count every 6 days. On the first day of Major Heat, follow the mean rate. Through the end of the qi, 58 days retreating 12°. On the first day of Start of Autumn, follow the mean rate. Through the end of the qi, 57 days retreating 11°. From White Dew onward, add 1 each to the day-count and degree-count every 2 days. Twelve days into White Dew, follow the mean rate. Through Autumn Equinox, 63 days retreating 17°. From Cold Dew onward, add 1 each to the day-count and degree-count every 3 days. Nine days into Cold Dew, follow the mean rate. Through the end of the qi, 66 days retreating 20°. From Frost's Descent onward, subtract 1 each from the day-count and degree-count every 2 days. Six days into Frost's Descent, follow the mean rate. Through the end of the qi, 63 days retreating 17°. From Start of Winter onward, add 1 each to the day-count and degree-count every 3 days. Twelve days into Start of Winter, follow the mean rate. Through the end of the qi, 67 days retreating 21°. From Minor Snow onward, subtract 1 each from the day-count and degree-count every 2 days. Eight days into Minor Snow, follow the mean rate. Through the end of the qi, 63 days retreating 17°. From Major Snow onward, add 1 degree every 3 days.
188
後留：冬至初日，十三日。 大寒初日，平。 畢氣末，二十五日。 自入立春後，二日半損一日。 驚蟄初日，十三日。 自後三日益日一。 清明初日，三十三日。 自後每日損日一。 清明十日，平。 畢處暑，十三日。 自入白露後，二日損日一。 秋分十一日，無留。 自入秋分十一日後，日益日一。 霜降初日，十九日。 立冬畢大雪，十三日。
Later station: on the Winter Solstice first day, 13 days. On the first day of Major Cold, follow the mean rate. Through the end of the qi, 25 days. From Start of Spring onward, subtract 1 day every 2.5 days. On the first day of Awakening of Insects, 13 days. From then on, add 1 day every 3 days. On the first day of Clear Brightness, 33 days. From then on, subtract 1 day each day. Ten days into Clear Brightness, follow the mean rate. Through End of Heat, 13 days. From White Dew onward, subtract 1 day every 2 days. Eleven days into Autumn Equinox, no stationary period. From after eleven days into Autumn Equinox, add 1 day each day. On the first day of Frost's Descent, 19 days. From Start of Winter through Major Snow, 13 days.
189
後遲：差行。 六十日行二十五度。 先遲，日益疾三分，前疾加度者，此遲依數減之為定。 若不加度者，此遲入秋分至立冬減三度，入立冬到冬至減五度，後留定日十三日者，以所朒數加此遲日率。
Later slow motion: differential motion. 60 days for 25°. Slow at first; speed increases by 3 parts per day. If the prior fast phase added degrees, subtract that amount in this slow phase to obtain the fixed rate. If it added no degrees, subtract 3 degrees from this slow phase between the Autumn Equinox and the Start of Winter, and 5 degrees from the Start of Winter to the Winter Solstice; if the later stationary fixed days fall short by 13, add the shortfall in days to this slow day-rate.
190
後疾：冬至初日，二百一十日行百三十二度。 自後每日損日度各一。 大寒八日，百七十二日行九十四度。 自入大寒八日後，二日損日度各一。 雨水，平。 畢氣末，百六十一日行八十三度。 自入驚蟄後，三日益日度各一。 穀雨三日，百七十七日行九十九度。 自三日後，每日益日度各一。 芒種十四日，平。 畢夏至十日，二百三十三日行百五十五度。 自十日後，每日益日度各一。 小暑五日，二百五十三日行百七十五度。 自後每日益日度各一。 大暑初日，平。 畢處暑，二百六十三日行百八十五度。 自入白露後，二日損日度各一。 秋分一日，二百五十五日行百七十七度。 自一日後，每三日損日度各一。 大雪初日，二百五日行百二十七度。 自後三日益日度各一。
Later fast motion: on the Winter Solstice first day, 210 days for 132°. From then on, subtract 1 each from the day-count and degree-count each day. Eight days into Major Cold, 172 days for 94°. From after eight days into Major Cold, subtract 1 each from the day-count and degree-count every 2 days. At Rain Water, follow the mean rate. Through the end of the qi, 161 days for 83°. From Awakening of Insects onward, add 1 each to the day-count and degree-count every 3 days. Three days into Grain Rain, 177 days for 99°. From after three days, add 1 each to the day-count and degree-count each day. Fourteen days into Grain in Ear, follow the mean rate. Through ten days of Summer Solstice, 233 days for 155°. From after ten days, add 1 each to the day-count and degree-count each day. Five days into Minor Heat, 253 days for 175°. From then on, add 1 each to the day-count and degree-count each day. On the first day of Major Heat, follow the mean rate. Through End of Heat, 263 days for 185°. From White Dew onward, subtract 1 each from the day-count and degree-count every 2 days. One day into Autumn Equinox, 255 days for 177°. From after one day, subtract 1 each from the day-count and degree-count every 3 days. On the first day of Major Snow, 205 days for 127°. From then on, add 1 each to the day-count and degree-count every 3 days.
191
前順：差行。 八十三日，行七度四百七十四分。 先疾，三日益遲二分。
Prior direct motion: differential motion. 83 days, travels 7°474 parts. Fast at first; slowness increases by 2 parts every 3 days.
192
前留：三十七日。
Prior station: 37 days.
193
前退：差行。 五十一日，退三度。 先遲，二日益疾一分。
Prior retrograde motion: differential motion. 51 days, retreats 3°. Slow at first; speed increases by 1 part every 2 days.
194
後退：差行。 五十一日，退三度。 先疾，二日益遲一分。
Later retrograde motion: differential motion. 51 days, retreats 3°. Fast at first; slowness increases by 1 part every 2 days.
195
後留：三十六日。
Later station: 36 days.
196
後順：差行。 八十三日，行七度四百七十四分。 先遲，三日益疾二分。
Later direct motion: differential motion. 83 days, travels 7°474 parts. Slow at first; speed increases by 2 parts every 3 days.
197
夕見：入冬至，畢立夏，立秋畢大雪，百七十二日行二百六度。 自入小滿後，十日益度一，為定初。 入白露，畢春分，差行； 先疾，日益遲二分。 自余平行。 夏至畢小暑，百七十二日行二百九度。 自入大暑後，五日損一度，畢氣末。
Evening appearance: from the Winter Solstice through the Start of Summer, and from the Start of Autumn through Major Snow, 172 days for 206°. From Minor Fullness onward, add 1 degree every 10 days as the initial fixed rate. From White Dew through the Spring Equinox: differential motion; Fast at first; slowness increases by 2 parts per day. The remainder follows uniform motion. From the Summer Solstice through Minor Heat, 172 days for 209°. From Major Heat onward, subtract 1 degree every 5 days through the end of the qi.
198
夕平行：冬至及大暑、大雪各畢氣末，十三日行十三度。 自入冬至後，十日損一，畢立春。 入立秋，六日益一，畢秋分。 雨水畢芒種，七日行七度。 自入夏至後，五日益一，畢小暑。 寒露初日，二十三日行二十三度。 自後六日損一，畢小雪。
Evening uniform motion: at Winter Solstice, Major Heat, and Major Snow each through the end of the qi, 13 days for 13°. From the Winter Solstice onward, subtract 1 every 10 days through the Start of Spring. From the Start of Autumn, add 1 every 6 days through the Autumn Equinox. From Rain Water through Grain in Ear, 7 days for 7°. From the Summer Solstice onward, add 1 every 5 days through Minor Heat. On the first day of Cold Dew, 23 days for 23°. From then on, subtract 1 every 6 days through Minor Snow.
199
夕遲：差行。 四十二日行三十度。 先疾，日益遲十三分。 前加度過二百六度者，准數損此度。
Evening slow motion: differential motion. 42 days for 30°. Fast at first; slowness increases by 13 parts per day. If the prior phase added degrees beyond 206°, subtract that excess from this degree count.
200
夕留：七日。
Evening station: 7 days.
201
夕退：十日，退五度。 日盡而夕伏。
Evening retrograde: 10 days, retreats 5°. When its days are exhausted it disappears at evening.
202
晨退：十日，退五度。
Morning retrograde: 10 days, retreats 5°.
203
晨留：七日。
Morning station: 7 days.
204
晨遲：差行。 冬至畢立夏，大雪畢氣末，四十二日行三十度； 先遲，日益疾十三分。 自小滿後，率十日損一度，畢芒種。 夏至畢寒露，四十二日行二十七度； 差依前。 自入霜降後，每氣益一度，畢小雪。
Morning slow motion: differential motion. From the Winter Solstice through the Start of Summer, and from Major Snow through the end of the qi, 42 days for 30°; Slow at first; speed increases by 13 parts per day. From Minor Fullness onward, subtract 1 degree every 10 days through Grain in Ear. From the Summer Solstice through Cold Dew, 42 days for 27°; Apply the differential as before. From Frost's Descent onward, add 1 degree per solar term through Minor Snow.
205
晨平行：冬至畢氣末，立夏畢氣末，十三日行十三度。 自小寒後，六日益日度各一，畢雨水。 入小滿後，七日損日度各一，畢立秋。 驚蟄初日，二十三日行二十三度。 自後六日損日度各一，畢穀雨。 處暑畢寒露，無此平行。 自入霜降後，五日益日度各一，畢大雪。
Morning uniform motion: from the Winter Solstice through the end of the qi, and from the Start of Summer through the end of the qi, 13 days for 13°. From Minor Cold onward, add 1 each to the day-count and degree-count every 6 days through Rain Water. From Minor Fullness onward, subtract 1 each from the day-count and degree-count every 7 days through the Start of Autumn. On the first day of Awakening of Insects, 23 days for 23°. From then on, subtract 1 each from the day-count and degree-count every 6 days through Grain Rain. From End of Heat through Cold Dew: no such uniform motion. From Frost's Descent onward, add 1 each to the day-count and degree-count every 5 days through Major Snow.
206
晨疾：百七十二日，行二百六度。 前遲行損度不滿三十者，此疾依數益之。 處暑畢寒露，差行； 先遲，日益疾二分。 自余平行。 日盡而晨伏。
Morning fast motion: 172 days for 206°. If the prior slow phase diminished degrees by less than 30, add that amount in this fast phase. From End of Heat through Cold Dew: differential motion; Slow at first; speed increases by 2 parts per day. The remainder follows uniform motion. When its days are exhausted it disappears at morning.
207
夕見疾：十二日，行二十一度十分。 大暑畢處暑，十二日，行十七度十六分。
Evening appearance fast motion: 12 days for 21°10 parts. From Major Heat through End of Heat, 12 days for 17°16 parts.
208
夕平：七日，行七度。 自入大暑後，二日損度各一。 入立秋，無此平行。
Evening uniform motion: 7 days for 7°. From Major Heat onward, subtract 1 from the degree-count every 2 days. Entering the Start of Autumn, omit this uniform-motion phase.
209
夕遲：六日，行二度七分。 前疾行十七度者，無此遲行。
Evening slow motion: 6 days for 2°7 parts. If the prior fast phase traveled 17 degrees, omit this slow-motion phase.
210
夕伏留：五日。 日盡而夕伏。
Station at evening occultation: 5 days. When its days are exhausted it disappears at evening.
211
晨見留：五日。
Morning appearance station: 5 days.
212
晨遲：六日，行二度七分。 自入大寒，畢雨水，無此遲行。
Morning slow motion: 6 days for 2°7 parts. From Major Cold through Rain Water, omit this slow-motion phase.
213
晨平行：七日，行七度。 入大寒後，二日損日度各一。 入立春，無此平行。
Morning uniform motion: 7 days for 7°. From Major Cold onward, subtract 1 each from the day-count and degree-count every 2 days. Entering the Start of Spring, omit this uniform-motion phase.
214
晨疾； 十二日，行二十一度十分。 前無遲行者，十二日，行十七度十六分。 日盡而晨伏。
Morning fast motion; 12 days for 21°10 parts. If there was no prior slow phase, 12 days for 17°16 parts. When its days are exhausted it disappears at morning.