Volume 30, Part 1 Treatises 20: Calendar 6, Part 1

1

憲宗即位，司天徐昂上新曆，名曰觀象。起元和二年用之，然無蔀章之數。至於察斂啟閉之候，循用舊法，測驗不合。至穆宗立，以為累世纘緒，必更曆紀，乃詔日官改撰曆術，名曰宣明。上元七曜，起赤道虛九度。其氣朔、發斂、日躔、月離，皆因大衍舊術；晷漏、交會，則稍增損之；更立新數，以步五星。其大略謂：

After Emperor Xianzong came to the throne, Xu Ang of the Astronomical Bureau submitted a new calendar called Observing Phenomena (Guanxiang). It was put into use from the second year of Yuanhe (807), but it lacked obscuration-cycle parameters. For fixing the seasons of gathering-in and opening-and-closing, the calendar still followed older methods, and observational tests failed to match. When Emperor Muzong acceded, holding that a dynasty continuing its line through successive reigns must renew its calendar era, he ordered the court astronomers to draft new calendrical methods, named Illuminating (Xuanming). At the high origin, the seven luminaries start at 9° of Xū on the celestial equator. Its procedures for central qi, new moons, solstitial timing, solar motion, and lunar motion all followed the old Dayan methods; while gnomon-clepsydra and syzygy parameters were adjusted slightly; and new constants were set to compute the five planets. Its general outline reads:

2

通法曰統法。策實曰章歲。揲法曰章月。掛限曰閏限。三元之策曰中節。四象之策曰合策。一象之策曰象準。策餘曰通餘。爻數曰紀法。通紀法為分，曰旬周。章歲乘年，曰通積分。地中之策曰候策。天中之策曰卦策。以貞悔之策減中節，曰辰數。以加季月之節，即土用事日。凡小餘滿辰法，為辰數；滿刻法，為刻。乾實曰象數。秒法三百。以乘統法，曰分統。

The universal divisor is termed the cycle constant. The divination solid is termed the chapter years. The stalking method is termed the chapter months. The hanging limit is termed the intercalation limit. The three-origin divination is termed the central node. The four-images divination is termed the combined divination. The one-image divination is termed the image standard. The divination remainder is termed the universal remainder. The line number is termed the cycle method. The universal cycle method taken as parts is called the ten-day cycle. Chapter years multiplied by the year-count yield the accumulated universal parts. The divination at the earth's center is termed the period divination. The divination at heaven's center is termed the hexagram divination. Subtract the central node from the true-and-false divination to obtain the chronogram number. Add this to the solar term of the last month of the season, and the result is the day on which Earth takes dominion. Whenever minor remainders fill the chronogram divisor, they form the chronogram number; when they fill the quarter-hour divisor, they form quarter-hours. The Qian solid is termed the image number. The second divisor is 300. Multiply the cycle constant by this to obtain the divided cycle.

3

凡步七曜入宿度，皆以刻法為度母。凡刻法乘盈縮分，如定氣而一，曰氣中率。與後氣中率相減，為合差。以定氣乘合差，併後定氣以除，為中差。加、減氣率，為初、末率。倍中差，百乘之，以定氣除，為日差。半之，以加、減初、末，各為定率。以日差累加、減之，為每日盈縮分。凡百乘氣下先後數，先減、後加常氣，為定氣限數。乘歲差千四百四十，為秒分。以加中節，因冬至黃道日度，累而裁之，得每定氣初日度。

In computing the seven luminaries' entry into lodge degrees, the quarter-hour divisor serves as the degree mother throughout. The quarter-hour divisor multiplied by the surplus-deficit parts, divided once per fixed qi, yields the central qi rate. Subtract this from the following qi's central rate to obtain the combined difference. Multiply the combined difference by the fixed qi, add the following fixed qi as divisor, and divide to obtain the central difference. Add or subtract the qi rate to obtain the initial and final rates. Double the central difference, multiply by 100, divide by the fixed qi, and obtain the daily difference. Halve this value, add or subtract it from the initial and final rates, and each becomes a fixed rate. Accumulate the daily difference by repeated addition and subtraction to obtain each day's surplus-deficit parts. Multiply the before-and-after qi descent count by 100, first subtract then add the regular qi, and obtain the fixed-qi limit number. Multiply the annual discrepancy by 1,440 to obtain second-parts. Add this to the central node; starting from the winter solstice yellow-path solar degree, accumulate and trim to obtain the initial solar degree for each fixed qi.

4

入轉曰曆。凡入曆，如曆中已下為進；已上，去之，為退。凡定朔小餘，秋分後，四分之三已上，進一日。春分後，昏明小餘差春分初日者，五而一，以減四分之三。定朔小餘如此數已上者，進一日。或有交，應見虧初，則否。定弦望小餘，不滿昏明小餘者，退一日。或有交，應見虧初者，亦如之。凡正交，以平交入曆朓朒定數，朓減、朒加平交入定氣餘，滿若不足，進退日算，為正交入定氣，不復以交率乘、交數除，及不加減平交入氣朓朒也。

Entry into rotation is termed the ephemeris. Whenever entering the ephemeris, if at or below the ephemeris midpoint it counts as advance; if above, subtract the excess, and that counts as retreat. For fixed new-moon minor remainders after the autumn equinox, if three-fourths or more, advance the date by one day. After the spring equinox, when twilight minor remainders differ from the spring equinox initial day, take one-fifth at a time to reduce the three-fourths threshold. If the fixed new-moon minor remainder reaches this number or higher, advance the date by one day. If a conjunction occurs and the initial phase of waning should be visible, then do not advance. If the fixed first- or full-moon minor remainder does not reach the twilight minor remainder, retreat the date by one day. If a conjunction occurs and the initial waning should be visible, the same rule applies. For the true crossing, take the waxing-and-waning fixed number of the mean crossing's entry into the ephemeris; waxing subtracts and waning adds from the mean crossing's entry into the fixed-qi remainder; if the result overflows or falls short, adjust the day count forward or back to obtain the true crossing's entry into fixed qi—without again multiplying by the crossing rate, dividing by the crossing number, or adding and subtracting the mean crossing's waxing-and-waning in qi.

5

凡推月度，以曆分乘夜半定全漏，如刻法而一，為晨分；以減曆分，為昏分。又以定朔、弦、望小餘乘曆分，統法除之，以減晨分，餘為前；不足，反相減，餘為後。乃前加、後減加時月度，為晨昏月度。以所入加時日度減後曆加時日度，餘加上弦之度及餘，以所入日前減、後加，又以後曆前加、後減，各為定程。乃累計距後曆每日曆度及分，以減定程，為盈；不足，反相減，為縮。以距後曆日數均其差，盈減、縮加每日曆分，為曆定分。累以加朔、弦、望晨昏月度，為每日晨昏月度，不復加減屈伸也。

To compute the lunar phase, multiply the ephemeris parts by the fixed full clepsydra at midnight, divide once by the quarter-hour divisor, and obtain the dawn parts; subtract this from the ephemeris parts to obtain the dusk parts. Multiply the fixed new-, first-, and full-moon minor remainders by the ephemeris parts, divide by the cycle constant, subtract from the dawn parts, and the remainder is the before portion; if insufficient, reverse the subtraction instead, and the remainder is the after portion. Add the before portion and subtract the after portion from the hour-addition lunar phase to obtain the dawn and dusk lunar phases. Subtract the following ephemeris's hour-addition solar degree from the current entry's hour-addition solar degree, add the remainder to the first-quarter degree and its remainder, subtract before the entry day and add after as required, and likewise add before and subtract after on the following ephemeris—each yielding a fixed course. Then accumulate the daily ephemeris degrees and parts from the distance to the following ephemeris and subtract from the fixed course; if positive, that is surplus; if insufficient, reverse the subtraction instead, and that is deficit. Spread the difference evenly over the days to the following ephemeris; subtract surplus and add deficit to each day's ephemeris parts to obtain the fixed ephemeris parts. Accumulate these to the new-, first-, and full-moon dawn and dusk lunar phases to obtain each day's dawn and dusk lunar phases, without further adding or subtracting waxing and waning.

6

爻統曰中統。象積曰刻法。消息曰屈伸。以屈伸準盈縮分，求每日所入，曰定衰。五乘之，二十四除之，曰漏差。屈加、伸減氣初夜半漏，得每日夜半定漏。刻法通為分，曰昏明小餘。二十一乘屈伸定數，二十五而一，為黃道屈伸差。乃屈減、伸加氣初去極度分，得每日去極度分。以萬二千三百八十六乘黃道屈伸差，萬六千二百七十七而一，為每日度差。屈減、伸加氣初距中度分，得每日距中度數。凡屈伸準消息於中晷，曰定數；於漏刻，曰漏差；於去極，曰屈伸差；於距中度，曰度差。

The line cycle is termed the central cycle. The image accumulation is termed the quarter-hour divisor. Increase-and-decrease is termed waxing-and-waning. Align surplus-deficit parts by waxing-and-waning, find each day's entry, and term it the fixed decline. Multiply by five, divide by twenty-four, and obtain the clepsydra difference. Add waning and subtract waxing from the initial qi midnight clepsydra to obtain each day's fixed midnight clepsydra. The quarter-hour divisor expressed as parts is termed the twilight minor remainder. Multiply the waxing-and-waning fixed number by 21 and divide by 25 to obtain the yellow-path waxing-and-waning difference. Subtract waning and add waxing from the initial qi's distance-from-pole parts to obtain each day's distance-from-pole parts. Multiply the yellow-path waxing-and-waning difference by 12,386 and divide by 16,277 to obtain the daily degree difference. Subtract waning and add waxing from the initial qi's mid-distance parts to obtain each day's mid-distance count. Waxing-and-waning aligned to increase-and-decrease at the midday gnomon shadow is termed the fixed number; for clepsydra quarter-hours, the clepsydra difference; for distance from the pole, the waxing-and-waning difference; for mid-distance, the degree difference.

7

交終曰終率。朔差曰交朔。望數曰交望。交限曰前準。望差曰後準。凡月行入四象陰陽度有分者，十乘之，七而一，為度分。不盡，十五乘之，七除，為大分。不盡又除，為小分。乃以一象之度九十除之，兼除度差分百一十三、大分七、小分一少，然後以次象除之。

Crossing completion is termed the completion rate. The new-moon difference is termed the crossing new moon. The full-moon number is termed the crossing full moon. The crossing limit is termed the forward standard. The full-moon difference is termed the rear standard. Whenever the moon's motion enters the four-images yin-yang degrees with fractional parts, multiply by 10, divide by 7, and obtain degree-parts. If a remainder remains, multiply by 15, divide by 7, and obtain major parts. If still not exhausted, divide again to obtain minor parts. Then divide by the 90° of one image, also dividing out degree-difference parts 113, major parts 7, and minor parts 1 slightly less, and then divide successively by each image.

8

凡日蝕，以定朔日出入辰刻距午正刻數，約百四十七，為時差。視定朔小餘如半法已下，以減半法，為初率；已上，減去半法，餘為末率。以乘時差，如刻法而一，初率以減，末率倍之，以加定朔小餘，為蝕定餘。月蝕，以定望小餘為蝕定餘。

For solar eclipses, take the fixed new-moon day's chronogram quarter-hours of sunrise and sunset relative to noon standard quarter-hours, reduce by approximately 147, and obtain the time difference. If the fixed new-moon minor remainder is at or below half the divisor, subtract it from the half divisor to obtain the initial rate; if above, subtract the half divisor; the remainder is the final rate. Multiply by the time difference and divide once by the quarter-hour divisor; subtract with the initial rate, double the final rate and add to the fixed new-moon minor remainder, and obtain the eclipse fixed remainder. For lunar eclipses, the fixed full-moon minor remainder serves as the eclipse fixed remainder.

9

凡日蝕，有氣差，有刻差，有加差。二至之初，氣差二千三百五十。距二至前後，每日損二十六，至二分而空。以日出沒辰刻距午正刻數，約其朔日氣差，以乘食甚距午正刻數。所得以減氣差，為定數。春分後，陰曆加之，陽曆減之；秋分後，陰曆減之，陽曆加之。

Solar eclipses involve qi difference, quarter-hour difference, and additive difference. At the start of the two solstices, the qi difference is 2,350. Moving away from the solstices before and after, decrease by 26 each day until the equinoxes, when it reaches zero. Take the chronogram quarter-hours of sunrise and sunset relative to noon, approximate the new-moon day's qi difference, and multiply by the greatest eclipse's distance from noon standard quarter-hours. Subtract the product from the qi difference to obtain the fixed number. After the spring equinox, add for yin months and subtract for yang months; after the autumn equinox, subtract for yin months and add for yang months.

10

二至初日，無刻差。自後每日益差分二、小分十。起立春至立夏，起立秋至立冬，皆以九十四分有半為刻差。自後日損差分二、小分十，至二至之初損盡。以朔日刻差乘食甚距午正刻數，為刻差定數。冬至後食甚在午正前，夏至後食甚在午正後，陰曆以減，陽曆以加；冬至後食甚在午正後，夏至後食甚在午正前，陰曆以加，陽曆以減。

On the first day of each solstice, there is no quarter-hour difference. Thereafter the difference increases each day by 2 parts and 10 minor parts. From Beginning of Spring to Beginning of Summer, and from Beginning of Autumn to Beginning of Winter, the quarter-hour difference is set at 94½ parts. Thereafter decrease the difference by 2 parts and 10 minor parts each day until it is exhausted at the next solstice. Multiply the new-moon day's quarter-hour difference by the greatest eclipse's distance from noon standard quarter-hours to obtain the fixed quarter-hour difference. After the winter solstice, if greatest eclipse falls before noon standard, and after the summer solstice if it falls after noon standard, subtract for yin months and add for yang months; After the winter solstice, if greatest eclipse falls after noon standard, and after the summer solstice if it falls before noon standard, add for yin months and subtract for yang months.

11

又立冬初日後，每氣增差十七。至冬至初日，得五十一。自後，每氣損十七，終于大寒，損盡。若蝕甚在午正後，則每刻累益其差，陰曆以減，陽曆以加。應加減差，同名相從，異名相銷，各為蝕差。以加減去交分，為定分。月在陰曆，不足減，反減蝕差。交前減之，餘為陽曆交後定分；交後減之，餘為陽曆交前定分：皆不蝕。陽曆不足減，亦反減蝕差。交前減之，餘為陰曆交後定分；交後減之，餘為陰曆交前定分：皆蝕。

After the first day of Start of Winter, increase the difference by 17 for each qi. By the first day of the winter solstice, it reaches 51. Thereafter decrease by 17 for each qi until Great Cold, when it is fully exhausted. If greatest eclipse falls after noon standard, cumulatively increase the difference for each quarter-hour; subtract for yin months and add for yang months. For the applicable add-subtract differences, combine matching signs and cancel opposite signs; each result is an eclipse correction. Add or subtract from the distance from conjunction to obtain the fixed fraction. When the moon is in a yin month, if subtraction is insufficient, subtract the eclipse correction in reverse. Subtract before conjunction; the remainder is the yang-month fixed fraction after conjunction; subtract after conjunction; the remainder is the yang-month fixed fraction before conjunction: in neither case is there an eclipse. When in a yang month subtraction is insufficient, likewise subtract the eclipse correction in reverse. Subtract before conjunction; the remainder is the yin-month fixed fraction after conjunction; subtract after conjunction; the remainder is the yin-month fixed fraction before conjunction: in both cases there is an eclipse.

12

凡去交定分，如陽曆蝕限已下，為陽曆蝕。以陽曆定法約，為蝕分。已上者，以陽曆蝕限減之，餘為陰曆蝕。以陰曆定法約之，以減十五，餘為蝕分。

In general, for the fixed distance from conjunction, if it is at or below the yang-month eclipse limit, the eclipse is a yang-month eclipse. Reduce by the yang-month fixed divisor to obtain the eclipse magnitude. If above, subtract the yang-month eclipse limit; the remainder is a yin-month eclipse. Reduce by the yin-month fixed divisor, subtract from 15, and the remainder is the eclipse magnitude.

13

凡月蝕去交分，二千一百四十七已下，皆既。已上者，以減後準，餘如定法五百六約，為蝕分。凡月蝕既，汎用刻二十。如去交分千四百三十五已下，因增半刻。七百一十二已下，又增半刻。凡日月帶蝕出沒，各以定法通蝕分，半定用刻約之，以乘見刻。多於半定用刻，出為進，沒為退。少於半定用刻，出為退，沒為進。各如定法而一，為見蝕之大分。朔晝、望夜皆為見刻。其九服蝕差，則不復考詳。

For lunar eclipses, when the distance from conjunction is 2,147 or less, the eclipse is total in every case. If above, subtract the posterior criterion; divide the remainder by fixed divisor 506 to obtain the eclipse magnitude. For total lunar eclipses, use 20 provisional quarter-hours throughout. If the distance from conjunction is 1,435 or less, add an additional half quarter-hour. If it is 712 or less, add another half quarter-hour. For solar and lunar grazing eclipses at rising and setting, convert each eclipse magnitude through the fixed divisor, divide by half the fixed applicable quarter-hours, and multiply by the visible quarter-hours. If the result exceeds half the fixed applicable quarter-hours, emergence counts as advance and setting as retreat. If it is less than half the fixed applicable quarter-hours, emergence counts as retreat and setting as advance. Divide each once by the fixed divisor to obtain the major fraction of visible eclipse. For new moons in daylight and full moons at night, both use visible quarter-hours. For eclipse corrections in the nine domains, no further detailed examination is made.

14

五星終率曰周率。因平合加中伏，得平見。金、水加夕，得晨；加晨，得夕。又以變差乘年，滿象數去之；不盡為變交。三百約為分，統法而一，以減平見。三十六乘平見秒，十二乘變交秒，同以三千六百為母。餘如交率已下，星在陽曆；已上，去之，為入陰曆。各以變策除，為變數，命初變算外；不盡為入其變度數及餘。自此百約餘分，母同刻法。以所入變下數，加減平見，為常見。金星晨見，先計自夕見，盡夕退，應加減先後差。同名相從，異名相銷。與晨常見加減差，異名相銷，同名相從。依加減晨平見為常見。

The five planets' terminal rate is termed the cycle rate. Add middle hiding to mean conjunction to obtain mean appearance. For Venus and Mercury, add evening visibility to obtain morning visibility; add morning visibility to obtain evening visibility. Also multiply the mutation difference by the year-count and cast out full image numbers; the remainder is the mutation crossing. Reduce to parts by 300, divide once by the cycle constant, and subtract from mean appearance. Multiply mean appearance seconds by 36 and mutation crossing seconds by 12, with 3,600 as the common denominator. If the remainder is at or below the crossing rate, the planet is in the yang half; if above, discard it; the remainder is entry into the yin half. Divide each by the mutation divination to obtain the mutation count, counting from outside the initial mutation tally; the remainder is entry into its mutation degree-count and remainder. From this point, reduce the remainder parts by 100; the denominator matches the quarter-hour divisor. Add or subtract from mean appearance by the number below for the mutation entered to obtain regular appearance. For Venus morning appearance, first compute from evening appearance through all evening retrograde, applying the prior-posterior differences to be added or subtracted. Where signs match, combine; where they differ, cancel. With the morning regular appearance add-subtract difference, cancel opposite signs and combine matching signs. Accordingly add or subtract from morning mean appearance to obtain regular appearance.

15

凡常見計入定氣，求先後定數，各以差率乘之，差數而一，為定差。晨見先減、後加，夕見先加、後減常見，為定見。以常見與定見加減數，加減平見入變度數及餘秒，為定見初變所入。以所行度順加、退減之，即次變所入。各以所入變下差數加減日度變率。其水星常見與定見加減數，同名相從，異名相銷，反其加減。夕見差加疾行日率者，倍其差，加度率。又分其差，以加遲留日率。晨見亦分其差，以加遲留日率，以所差之數，加疾行日率，亦倍其差，加疾行度率。夕見差減疾行日率者，倍其差，減度率。又以其差減留日，不足減，侵減遲日。晨見差減留日，不足減者，侵減遲日，亦以其差減疾行日率，倍其差，以減度率。前變初日與後變末日先後數，同名相銷，異名相從，為先後定數。各以差率乘之，差數而一，為日差。金星用後變差率、差數。以先後定數減之，為度差。金星夕伏，以日差減先後定數，為度差。晨伏以先後定數加日差，為度差。水星夕伏，以先後定數為日差。倍之，為度差。乃以日度差，積盈者以減、積縮者以加末變日度率。金、水晨伏，反用其差。又倍退行差，差率乘之，差數而一，為日差。以退差減之，為度差。金星夕伏，以日差減退差，為度差。晨伏以退差加日差，為度差。以退行日度差應加者減末變日度率。晨伏反用其差。各加減變訖，為日度定率。

In general, set regular appearance against fixed qi, find the prior-posterior fixed numbers, multiply each by the difference rate and divide once by the difference number, and obtain the fixed difference. For morning appearance subtract first and add later; for evening appearance add first and subtract later from regular appearance to obtain fixed appearance. Use the add-subtract amounts of regular appearance and fixed appearance to adjust mean appearance's entered mutation degree-count and remainder seconds, obtaining the initial mutation entered at fixed appearance. Add for direct motion and subtract for retrograde by the degrees traveled; that is the next mutation entered. For each, add or subtract the difference number below the mutation entered to the daily-degree phase rate. For Mercury, the add-subtract amounts of regular appearance and fixed appearance combine matching signs, cancel opposite signs, and reverse the additions and subtractions. When evening appearance's difference adds to the swift-motion day rate, double the difference and add to the degree rate. Also divide the difference and add to the slow-and-stationary day rate. For morning appearance likewise divide the difference and add to the slow-and-stationary day rate; add the difference amount to the swift-motion day rate, double the difference, and add to the swift-motion degree rate. When evening appearance's difference subtracts from the swift-motion day rate, double the difference and subtract from the degree rate. Also subtract the difference from station days; if insufficient, encroach and subtract from slow days. When morning appearance's difference subtracts from station days, if insufficient encroach and subtract from slow days; also subtract the difference from the swift-motion day rate, double the difference, and subtract from the degree rate. The prior-posterior numbers of the first day of the prior mutation and the last day of the posterior mutation cancel matching signs and combine opposite signs to obtain the prior-posterior fixed number. Multiply each by the difference rate and divide once by the difference number to obtain the day difference. Venus uses the posterior mutation's difference rate and difference number. Subtract the prior-posterior fixed number to obtain the degree difference. For Venus evening hiding, subtract the day difference from the prior-posterior fixed number to obtain the degree difference. For morning hiding, add the day difference to the prior-posterior fixed number to obtain the degree difference. For Mercury evening hiding, take the prior-posterior fixed number as the day difference. Double it to obtain the degree difference. Then with the day-degree difference, subtract where surplus has accumulated and add where deficit has accumulated to the final mutation's daily-degree rate. For Venus and Mercury morning hiding, reverse the application of the difference. Also double the retrograde difference, multiply by the difference rate, divide once by the difference number, and obtain the day difference. Subtract the retrograde difference to obtain the degree difference. For Venus evening hiding, subtract the retrograde difference from the day difference to obtain the degree difference. For morning hiding, add the retrograde difference to the day difference to obtain the degree difference. Where the retrograde day-degree difference should add, subtract from the final mutation's daily-degree rate. For morning hiding, reverse the application of the difference. After all add-subtract adjustments to the phase rates, the result is the fixed daily-degree rate.

16

他亦皆準大衍曆法。其分秒不同，則各據本曆母法云。

All else likewise follows the Dayan Calendar methods. Where parts and seconds differ, each follows its own calendar's base divisors.

17

起長慶二年，用宣明曆。自敬宗至于僖宗，皆遵用之。雖朝廷多故，不暇討論，然大衍曆後，法制簡易，合望密近，無能出其右者。訖景福元年。

Beginning in the second year of Changqing, the Illuminating Calendar was used. From Emperor Jingzong through Emperor Xizong, all adhered to it. Though the court faced many troubles and lacked leisure for revision, among calendars after the Dayan it was the simplest in method and the closest in matching conjunctions and full moons, and none could surpass it. This continued until the first year of Jingfu.

18

觀象曆今有司無傳者。

The Observing Phenomena Calendar is no longer transmitted among the current officials.

19

長慶宣明曆演紀上元甲子，至長慶二年壬寅，積七百七萬一百三十八算外。

In computing the evolving era of the Changqing Illuminating Calendar, the high origin falls in the year jiazi; reckoned to the second year of Changqing (renyin), the accumulated count is 7,070,138 beyond the tally.

20

宣明統法八千四百。

Illuminating cycle constant: 8,400.

21

章歲三百六萬八千五十五。

Chapter years: 3,068,055.

22

章月二十四萬八千五十七。

Chapter months: 248,057.

23

通餘四萬四千五十五。

Universal remainder: 44,055.

24

章閏九萬一千三百七十一。

Intercalation chapter: 91,371.

25

閏限二十四萬四百四十三，秒六。

Intercalation limit: 240,443, 6 parts.

26

中節十五，餘千八百三十五，秒五。

Central node: 15, remainder 1,835, 5 parts.

27

合策二十九，餘四千四百五十七。

Combined divination: 29, remainder 4,457.

28

象準七，餘三千二百一十四少。

Image standard: 7, remainder 3,214 and slightly less.

29

中盈分三千六百七十一，秒二。

Central-qi surplus fraction: 3,671, 2 parts.

30

朔虛分三千九百四十三。

Synodic void fraction: 3,943.

31

旬周五十萬四千。

Ten-day cycle: 504,000.

32

紀法六十。

Cycle method: 60.

33

秒法八。

Second divisor: 8.

34

候數五，餘六百一十一，秒七。

Period number: 5, remainder 611, 7 parts.

35

卦位六，餘七百三十四，秒二。

Hexagram position: 6, remainder 734, 2 parts.

36

辰數十二，餘千四百六十八，秒四。

Chronogram count: 12, remainder 1,468, 4 parts.

37

刻法八十四。

Quarter-hour divisor: 84.

38

象數九億二千四十四萬六千一百九十九。

Image number: 920,446,199.

39

周天三百六十五度。

Circuit of heaven: 365 degrees.

40

虛分二千一百五十三，秒二百九十九。

Void fraction: 2,153, 299 parts.

41

歲差二萬九千六百九十九。

Annual discrepancy: 29,699.

42

分統二百五十二萬。

Divided cycle: 2,520,000.

43

秒母三百。

Second mother: 300.

44

氣節

Solar term

45

盈縮分

Surplus-deficit parts

46

先後數

Lead and lag counts

47

損益率

Rates of increase and decrease

48

朓朒數

Waxing-and-waning counts

49

冬至

Winter Solstice

50

盈六十

Surplus: 60

51

先初

Lead at initial

52

益四百四十九

Increase: 449

53

朒初

Waning initial

54

小寒

Lesser Cold

55

盈五十

Surplus: 50

56

先六十

Lead count: 60

57

益三百七十四

Increase: 374

58

朒四百四十九

Waning: 449

59

大寒

Greater Cold

60

盈四十

Surplus: 40

61

先百一十

Lead count: 110

62

益二百九十九

Increase: 299

63

朒八百二十三

Waning: 823

64

立春

Start of Spring

65

盈三十

Surplus: 30

66

先百五十

Lead count: 150

67

益二百二十四

Increase: 224

68

朒千一百二十二

Waning: 1,122

69

雨水

Rain Water

70

盈十八

Surplus: 18

71

先百八十

Lead count: 180

72

益百三十五

Increase: 135

73

朒千三百四十六

Waning: 1,346

74

驚蟄

Awakening of Insects

75

盈六

Surplus: 6

76

先百九十八

Lead count: 198

77

益四十五

Increase: 45

78

朒千四百八十一

Waning: 1,481

79

春分

Spring Equinox

80

縮六

Deficit: 6

81

先二百四

Lead count: 204

82

損四十五

Decrease: 45

83

朒千五百二十六

Waning: 1,526

84

清明

Clear and Bright

85

縮十八

Deficit: 18

86

先百九十八

Lead count: 198

87

損百三十五

Decrease: 135

88

朒千四百八十一

Waning: 1,481

89

穀雨

Grain Rain

90

縮三十

Deficit: 30

91

先百八十

Lead count: 180

92

損二百二十四

Decrease: 224

93

朒千三百四十六

Waning: 1,346

94

立夏

Start of Summer

95

縮四十

Deficit: 40

96

先百五十

Lead count: 150

97

損二百九十九

Decrease: 299

98

朒千一百二十二

Waning: 1,122

99

小滿

Lesser Fullness

100

縮五十

Deficit: 50

101

先百一十

Lead count: 110

102

損三百七十四

Decrease: 374

103

朒八百二十三

Waning: 823

104

芒種

Grain in Ear

105

縮六十

Deficit: 60

106

先六十

Lead count: 60

107

損四百四十九

Decrease: 449

108

朒四百四十九

Waning: 449

109

夏至

Summer Solstice

110

縮六十

Deficit: 60

111

後初

Lag at initial

112

益四百四十九

Increase: 449

113

朓初

Waxing initial

114

小暑

Lesser Heat

115

縮五十

Deficit: 50

116

後六十

Lag count: 60

117

益三百七十四

Increase: 374

118

朓四百四十九

Waxing: 449

119

大暑

Greater Heat

120

縮四十

Deficit: 40

121

後百一十

Lag count: 110

122

益二百九十九

Increase: 299

123

朓八百二十三

Waxing: 823

124

立秋

Start of Autumn

125

縮三十

Deficit: 30

126

後百五十

Lag count: 150

127

益二百二十四

Increase: 224

128

朓千一百二十二

Waxing: 1,122

129

處暑

End of Heat

130

縮十八

Deficit: 18

131

後百八十

Lag count: 180

132

益百三十五

Increase: 135

133

朓千三百四十六

Waxing: 1,346

134

白露

White Dew

135

縮六

Deficit: 6

136

後百九十八

Lag count: 198

137

益四十五

Increase: 45

138

朓千四百八十一

Waxing: 1,481

139

秋分

Autumn Equinox

140

盈六

Surplus: 6

141

後二百四

Lag count: 204

142

損四十五

Decrease: 45

143

朓千五百二十六

Waxing: 1,526

144

寒露

Cold Dew

145

盈十八

Surplus: 18

146

後百九十八

Lag count: 198

147

損百三十五

Decrease: 135

148

朓千四百八十一

Waxing: 1,481

149

霜降

Frost Descent

150

盈三十

Surplus: 30

151

後百八十

Lag count: 180

152

損二百二十四

Decrease: 224

153

朓千三百四十六

Waxing: 1,346

154

立冬

Start of Winter

155

盈四十

Surplus: 40

156

後百五十

Lag count: 150

157

損二百九十九

Decrease: 299

158

朓千一百二十二

Waxing: 1,122

159

小雪

Lesser Snow

160

盈五十

Surplus: 50

161

後百一十

Lag count: 110

162

損三百七十四

Decrease: 374

163

朓八百二十三

Waxing: 823

164

大雪

Greater Snow

165

盈六十

Surplus: 60

166

後六十

Lag count: 60

167

損四百四十九

Decrease: 449

168

朓四百四十九

Waxing: 449

169

二十四定氣皆百乘其氣盈縮分，盈減、縮加中節，為定氣所有日及餘、秒。

For all twenty-four fixed qi, multiply each term's surplus-deficit parts by 100; subtract surplus and add deficit from the central node to obtain each fixed qi's days, remainder, and parts.

170

六虛之差五十三，秒二百九十九。

Six-void correction: 53, 299 parts.

171

曆周二十三萬一千四百五十八，秒十九。

Ephemeris cycle: 231,458, 19 parts.

172

曆周日二十七，餘四千六百五十八，秒十九。

Ephemeris cycle length: 27 days, remainder 4,658, 19 parts.

173

曆中日十三，餘六千五百二十九，秒九半。

Ephemeris midpoint: 13 days, remainder 6,529, 9½ parts.

174

周差日一，餘八千一百九十八，秒八十一。

Circulation difference: 1 day, remainder 8,198, 81 parts.

175

秒母一百。

Second mother: 100.

176

七日：初數，七千四百六十五；末數，九百三十五。

Day 7: initial count 7,465; terminal count 935.

177

十四日：初數，六千五百二十九；末數，千八百七十一。

Day 14: initial count 6,529; terminal count 1,871.

178

上弦：九十一度，餘二千六百三十八，秒百四十九太。

First quarter: 91 degrees, remainder 2,638, 149 parts greater.

179

望：百八十二度，餘五千二百七十六，秒二百九十九半。

Full moon: 182 degrees, remainder 5,276, 299½ parts.

180

下弦：二百七十三度，餘七千九百一十五，秒百四十九半。

Last quarter: 273 degrees, remainder 7,915, 149½ parts.

181

曆日

Ephemeris day

182

曆分進退衰

Ephemeris parts and advance-retreat decrement

183

積度

Accumulated degrees

184

損益率

Rates of increase and decrease

185

朓朒積

Anomalistic accumulation

186

一日

Day 1

187

千一十二進十四

1,012, advance 14

188

初度

Initial degree

189

益八百三十

Increase rate: 830

190

朒初

Waning initial

191

二日

Day 2

192

千二十六進十六

1,026, advance 16

193

十二度四分

12° 4 parts

194

益七百二十六

Increase rate: 726

195

朒八百三十

Waning accumulation: 830

196

三日

Day 3

197

千四十二進十八

1,042, advance 18

198

二十四度二十二分

24° 22 parts

199

益六百六

Increase rate: 606

200

朒千五百五十六

Waning accumulation: 1,556

201

四日

Day 4

202

千六十進十八

1,060, advance 18

203

三十六度五十六分

36° 56 parts

204

益四百七十一

Increase rate: 471

205

朒二千一百六十二

Waning accumulation: 2,162

206

五日

Day 5

207

千七十八進十八

1,078, advance 18

208

四十九度二十四分

49° 24 parts

209

益三百三十七

Increase rate: 337

210

朒二千六百三十三

Waning accumulation: 2,633

211

六日

Day 6

212

千九十六進十九

1,096, advance 19

213

六十二度一十分

62° 10 parts

214

益二百二

Increase rate: 202

215

朒二千九百七十

Waning accumulation: 2,970

216

七日

Day 7

217

千一百一十五進十九

1,115, advance 19

218

七十五度十四分

75° 14 parts

219

初益五十三末損七

Initial increase rate: 53, terminal decrease rate: 7

220

朒三千一百七十二

Waning accumulation: 3,172

221

八日

Day 8

222

千一百三十四進十九

1,134, advance 19

223

八十八度三十七分

88° 37 parts

224

損八十二

Decrease rate: 82

225

朒三千二百一十八

Waning accumulation: 3,218

226

九日

Day 9

227

千一百五十三進十九

1,153, advance 19

228

百一度七十九分

101° 79 parts

229

損二百二十四

Decrease rate: 224

230

朒三千一百三十六

Waning accumulation: 3,136

231

十日

Ten days

232

千一百七十二進十九

1,172, advance 19

233

百一十五度五十六分

115° 56′

234

損三百六十六

Decrease rate: 366

235

朒二千九百一十二

Waning accumulation: 2,912

236

十一日

Day 11

237

千一百九十一進十八

1,191, advance 18

238

百二十九度五十二分

129° 52′

239

損五百九

Decrease rate: 509

240

朒二千五百四十六

Waning accumulation: 2,546

241

十二日

Day 12

242

千二百九進十四

1,209, advance 14

243

百四十三度六十七分

143° 67′

244

損六百四十三

Decrease rate: 643

245

朒二千三十七

Waning accumulation: 2,037

246

十三日

Day 13

247

千二百二十三進十一

1,223, advance 11

248

百五十八度十六分

158° 16′

249

損七百四十八

Decrease rate: 748

250

朒千三百九十四

Waning accumulation: 1,394

251

十四日

Day 14

252

千二百三十四進退空

1,234, advance-retreat: —

253

百七十二度六十三分

172° 63′

254

初損六百四十六

Initial decrease rate: 646

255

朒六百四十六

Waning accumulation: 646

256

一日

Day 1

257

千二百三十四退十四

1,234, retreat 14

258

百八十七度三十七分

187° 37′

259

益八百三十

Increase rate: 830

260

朓初

Waxing initial

261

二日

Day 2

262

千二百二十退十七

1,220, retreat 17

263

二百二度十一分

202° 11′

264

益七百二十六

Increase rate: 726

265

朓八百三十

Waxing accumulation: 830

266

三日

Day 3

267

千二百三退十八

1,203, retreat 18

268

二百一十六度五十五分

216° 55′

269

益五百九十八

Increase rate: 598

270

朓千五百五十六

Waxing accumulation: 1,556

271

四日

Day 4

272

千一百八十五退十八

1,185, retreat 18

273

二百三十度八十二分

230° 82′

274

益四百六十四

Increase rate: 464

275

朓二千一百五十四

Waxing accumulation: 2,154

276

五日

Day 5

277

千一百六十七退十八

1,167, retreat 18

278

二百四十五度七分

245° 7′

279

益三百二十九

Increase rate: 329

280

朓二千六百一十八

Waxing accumulation: 2,618

281

六日

Day 6

282

千一百四十九退十八

1,149, retreat 18

283

二百五十八度八十二分

258° 82′

284

益百九十五

Increase rate: 195

285

朓二千九百四十七

Waxing accumulation: 2,947

286

七日

Day 7

287

千一百三十一退十九

1,131, retreat 19

288

二百七十二度五十五分

272° 55′

289

初益五十三末損七

Initial increase rate: 53, terminal decrease rate: 7

290

朓三千一百四十二

Waxing accumulation: 3,142

291

八日

Day 8

292

千一百一十二退十九

1,112, retreat 19

293

二百八十六度十分

286° 10′

294

損八十二

Decrease rate: 82

295

朓三千一百八十八

Waxing accumulation: 3,188

296

九日

Day 9

297

千九十三退十九

1,093, retreat 19

298

二百九十九度三十分

299° 30′

299

損二百二十五

Decrease rate: 225

300

朓三千一百六

Waxing accumulation: 3,106

301

十日

Day 10

302

千七十四退十八

1,074, retreat 18

303

三百一十二度三十一分

312° 31′

304

損三百六十六

Decrease rate: 366

305

朓二千八百八十一

Waxing accumulation: 2,881

306

十一日

Day 11

307

千五十六退十七

1,056, retreat 17

308

三百二十五度十三分

325° 13′

309

損五百一

Decrease rate: 501

310

朓二千五百一十五

Waxing accumulation: 2,515

311

十二日

Day 12

312

千三十九退十五

1,039, retreat 15

313

三百三十七度六十一分

337° 61′

314

損六百二十八

Decrease rate: 628

315

朓二千一十四

Waxing accumulation: 2,014

316

十三日

Day 13

317

千二十四退十二

1,024, retreat 12

318

三百五十度八分

350° 8′

319

損七百四十

Decrease rate: 740

320

朓千三百八十六

Waxing accumulation: 1,386

321

十四日

Day 14

322

千一十二進退空

1,012, advance-retreat: —

323

三百六十二度二十四分

362° 24′

324

初損六百四十六

Initial decrease rate: 646

325

朓六百四十六

Waxing accumulation: 646

326

辰刻八刻，分二十八。

Double-hour quarters: 8 quarters, 28 parts.

327

昏、明刻各二刻，分四十二。

Twilight quarters: 2 quarters each, 42 parts.

328

刻法八十四。度母同刻法。

Quarter-hour divisor: 84. Degree mother same as quarter-hour divisor.

329

距極度五十六，餘八十二分半。

Distance-from-pole: 56°, remainder 82½ parts.

330

北極出地三十四度，餘四十七分半。

North pole altitude: 34°, remainder 47½ parts.

331

定氣

Fixed qi

332

屈伸數

Waxing-and-waning number

333

黃道去極度

Ecliptic polar distance

334

陽城日晷

Yangcheng gnomon shadow

335

夜半定漏

Midnight fixed clepsydra

336

距中星度

Distance to culminating star

337

冬至

Winter Solstice

338

屈六十五

Waning: 65

339

百一十五度十七分

115° 17′

340

丈二尺七寸三十二分

shadow 1 zhang 2 chi 7 cun 32 parts

341

二十七刻四十分

27 quarter-hours 40 parts

342

八十二度二十二分

82° 22′

343

小寒

Lesser Cold

344

屈二百二十五

Waning: 225

345

百一十四度三十六分

114° 36′

346

丈二尺三寸九分十一

shadow 1 zhang 2 chi 3 cun 9 parts 11 parts

347

二十七刻二十九分

27 quarter-hours 29 parts

348

八十二度六十四分

82° 64′

349

大寒

Greater Cold

350

屈三百六十五

Waning: 365

351

百一十二度二十五分

112° 25′

352

丈一尺三寸八分三十

shadow 1 zhang 1 chi 3 cun 8 parts 30 parts

353

二十六刻七十四分

26 quarter-hours 74 parts

354

八十四度四十分

84° 40′

355

立春

Start of Spring

356

屈四百八十五

Waning: 485

357

百八度五十五分

108° 55′

358

九尺九寸四分七十八

shadow 9 chi 9 cun 4 parts 78 parts

359

二十六刻十分

26 quarter-hours 10 parts

360

八十七度二十一分

87° 21′

361

雨水

Rain Water

362

屈五百八十五

Waning: 585

363

百三度六十七分

103° 67′

364

八尺三寸七分八十一

shadow 8 chi 3 cun 7 parts 81 parts

365

二十五刻九分

25 quarter-hours 9 parts

366

九十度七十九分

90° 79′

367

驚蟄

Awakening of Insects

368

屈六百六十五

Waning: 665

369

九十七度八十分

97° 80′

370

六尺八寸八分七十四

shadow 6 chi 8 cun 8 parts 74 parts

371

二十三刻七十四分

23 quarter-hours 74 parts

372

九十五度三十三分

95° 33′

373

春分

Spring Equinox

374

屈六百六十五

Waning: 665

375

九十一度二十五分

91° 25′

376

五尺四寸四分七十

shadow 5 chi 4 cun 4 parts 70 parts

377

二十二刻四十二分

22 quarter-hours 42 parts

378

百度三十八分

100° 38′

379

清明

Clear and Bright

380

屈五百八十五

Waning: 585

381

八十四度五十五分

84° 55′

382

四尺一寸九分五十九

shadow 4 chi 1 cun 9 parts 59 parts

383

二十二刻十分

22 quarter-hours 10 parts

384

百五度四十三分

105° 43′

385

穀雨

Grain Rain

386

屈四百八十五

Waning: 485

387

七十八度六十七分

78° 67′

388

三尺二寸六十九

shadow 3 chi 2 cun 69 parts

389

十九刻七十五分

19 quarter-hours 75 parts

390

百九度八十一分

109° 81′

391

立夏

Start of Summer

392

屈三百六十五

Waning: 365

393

七十三度八十分

73° 80′

394

二尺四寸四分五十一

shadow 2 chi 4 cun 4 parts 51 parts

395

十八刻七十四分

18 quarter-hours 74 parts

396

百一十三度五十五分

113° 55′

397

小滿

Lesser Fullness

398

屈二百二十五

Waning: 225

399

七十度二十五分

70° 25′

400

尺八寸九分八十九

shadow 1 chi 8 cun 9 parts 89 parts

401

十八刻十分

18 quarter-hours 10 parts

402

百一十六度三十六分

116° 36′

403

芒種

Grain in Ear

404

屈六十五

Waning: 65

405

六十八度四分

68° 4′

406

尺五寸七分十四

shadow 1 chi 5 cun 7 parts 14 parts

407

十七刻五十五分

17 quarter-hours 55 parts

408

百一十八度十二分

118° 12′

409

夏至

Summer Solstice

410

伸六十五

Waxing: 65

411

六十七度三十四分

67° 34′

412

尺四寸七分八十

shadow 1 chi 4 cun 7 parts 80 parts

413

十七刻四十四分

17 quarter-hours 44 parts

414

百一十八度五十四分

118° 54′

415

小暑

Lesser Heat

416

伸二百二十五

Waxing: 225

417

六十八度四分

68° 4′

418

尺五寸七分十四

shadow 1 chi 5 cun 7 parts 14 parts

419

十七刻五十五分

17 quarter-hours 55 parts

420

百一十八度十二分

118° 12′

421

大暑

Greater Heat

422

伸三百六十五

Waxing: 365

423

七十度二十五分

70° 25′

424

尺八寸九分八十九

shadow 1 chi 8 cun 9 parts 89 parts

425

十八刻十分

18 quarter-hours 10 parts

426

百一十六度三十六分

116° 36′

427

立秋

Start of Autumn

428

伸四百八十五

Waxing: 485

429

七十三度八十分

73° 80′

430

二尺四寸四分五十一

shadow 2 chi 4 cun 4 parts 51 parts

431

十八刻七十四分

18 quarter-hours 74 parts

432

百一十三度五十五分

113° 55′

433

處暑

End of Heat

434

伸五百八十五

Waxing: 585

435

七十八度六十七分

78° 67′

436

三尺二寸六十九

Shadow: 3 chi, 2 cun, 69 parts

437

十九刻七十五分

19 quarter-hours 75 parts

438

百九度八十一分

109° 81′

439

白露

White Dew

440

伸六百六十五

Waxing: 665

441

八十四度五十五分

84° 55′

442

四尺一寸九分五十九

Shadow: 4 chi, 1 cun, 9 fen, 59 parts

443

二十一刻十分

21 quarter-hours 10 parts

444

百五度四十三分

105° 43′

445

秋分

Autumn Equinox

446

伸六百六十五

Waxing: 665

447

九十一度二十五分

91° 25′

448

五尺四寸五分七十

Shadow: 5 chi, 4 cun, 5 fen, 70 parts

449

二十二刻四十二分

22 quarter-hours 42 parts

450

百度三十八分

100° 38′

451

寒露

Cold Dew

452

伸五百八十五

Waxing: 585

453

九十七度八十分

97° 80′

454

六尺八寸八分七十四

Shadow: 6 chi, 8 cun, 8 fen, 74 parts

455

二十三刻七十四分

23 quarter-hours 74 parts

456

九十五度三十三分

95° 33′

457

霜降

Frost Descent

458

伸四百八十五

Waxing: 485

459

百三度六十七分

103° 67′

460

八尺三寸七分八十一

Shadow: 8 chi, 3 cun, 7 fen, 81 parts

461

二十五刻九分

25 quarter-hours 9 parts

462

九十度七十九分

90° 79′

463

立冬

Start of Winter

464

伸三百六十五

Waxing: 365

465

百八度五十五分

108° 55′

466

九尺九寸四分七十八

Shadow: 9 chi, 9 cun, 4 fen, 78 parts

467

二十六刻十分

26 quarter-hours 10 parts

468

八十七度二十一分

87° 21′

469

小雪

Lesser Snow

470

伸二百二十五

Waxing: 225

471

百一十二度二十五分

112° 25′

472

丈一尺三寸八分三十

Shadow: 1 zhang, 1 chi, 3 cun, 8 fen, 30 parts

473

二十六刻七十四分

26 quarter-hours 74 parts

474

八十四度四十分

84° 40′

475

大雪

Greater Snow

476

伸六十五

Waxing: 65

477

百一十四度四十六分

114° 46′

478

丈二尺三寸九分十一

Shadow: 1 zhang, 2 chi, 3 cun, 9 fen, 11 parts

479

二十七刻二十九分

27 quarter-hours 29 parts

480

八十二度六十四分

82° 64′

481

終率二十二萬八千五百八十二，秒六千五百一十二。

Completion rate: 228,582, seconds 6,512.

482

終日二十七，餘千七百八十二，秒六千五百一十二。

Synodic month: 27 days, remainder 1,782, seconds 6,512.

483

中日十三，餘五千九十一，秒三千二百五十六。

Median month: 13 days, remainder 5,091, seconds 3,256.

484

交朔日二，餘二千六百七十四，秒三千四百八十八。

Crossing new moon: 2 days, remainder 2,674, seconds 3,488.

485

交望日十四，餘六千四百二十八，秒五千。

Crossing full moon: 14 days, remainder 6,428, seconds 5,000.

486

前準日十二，餘三千七百五十四，秒千五百一十二。

Forward standard: 12 days, remainder 3,754, seconds 1,512.

487

後準日一，餘千三百三十七，秒千七百四十四。

Rear standard: 1 day, remainder 1,337, seconds 1,744.

488

陰曆蝕限六千六十。

Yin-month eclipse limit: 6,060.

489

陽曆蝕限二千六百四十。

Yang-month eclipse limit: 2,640.

490

陰曆定法四百四。

Yin-month fixed divisor: 404.

491

陽曆定法百七十六。

Yang-month fixed divisor: 176.

492

交率二百二。

Crossing rate: 202.

493

交數二千五百七十三。

Crossing number: 2,573.

494

秒法一萬。

Second divisor: 10,000.

495

去交度乘數十一，除數七千三百三。

Distance-from-conjunction multiplier: 11, divisor: 7,303.

496

歲星

Jupiter

497

周率三百三十五萬五百四十，秒八十三。

Cycle rate: 3,350,540, seconds 83.

498

周策三百九十八，餘七千三百四十，秒八十三。

Sidereal period: 398 days, remainder 7340, seconds 83.

499

中伏日十六，餘七千八百七十，秒四十一半。

Middle hiding: 16 days, remainder 7870, seconds 41½.

500

變差九十八，秒三十二。

Variation difference: 98, seconds 32.

501

交率百八十二，餘五十二，秒二十七。

Crossing rate: 182, remainder 52, seconds 27.

502

變策十五，餘十八，秒三十五。

Mutation divination: 15, remainder 18, seconds 35.

503

差率五。

Difference rate: 5.

504

差數四。

Difference number: 4.

505

熒惑

Mars

506

周率六百五十五萬一千三百九十五，秒二十六。

Cycle rate: 6,551,395, seconds 26.

507

周策七百七十九，餘七千七百九十五，秒二十六。

Sidereal period: 779 days, remainder 7795, seconds 26.

508

中伏日七十，餘八千九十七，秒六十三。

Middle hiding: 70 days, remainder 8097, seconds 63.

509

變差三千五，秒一。

Variation difference: 3,505, seconds 1.

510

交率百八十二，餘五十二，秒三十二。

Crossing rate: 182, remainder 52, seconds 32.

511

變策十五，餘十八，秒三十六。

Mutation divination: 15, remainder 18, seconds 36.

512

差率三十九。

Difference rate: 39.

513

差數十。

Difference number: 10.

514

鎮星

Saturn

515

周率三百一十七萬五千八百七十九，秒七十九。

Cycle rate: 3,175,879, seconds 79.

516

周策三百七十八，餘六百七十九，秒七十九。

Sidereal period: 378 days, remainder 679, seconds 79.

517

中伏日十八，餘四千五百三十九，秒八十九半。

Middle hiding: 18 days, remainder 4539, seconds 89½.

518

變差二百七十七，秒九十二。

Variation difference: 277, seconds 92.

519

交率百八十二，餘五十二，秒二十七。

Crossing rate: 182, remainder 52, seconds 27.

520

變策十五，餘十八，秒三十五。

Mutation divination: 15, remainder 18, seconds 35.

521

差率十。

Difference rate: 10.

522

差數九。

Difference number: 9.

523

太白

Venus

524

周率四百九十萬四千八百四十五，秒八十五。

Cycle rate: 4,904,845, seconds 85.

525

周策五百八十三，餘七千六百四十五，秒八十五。

Sidereal period: 583 days, remainder 7645, seconds 85.

526

夕見伏日二百五十六。

Evening appearance hiding: 256 days.

527

夕見伏行二百四十四度。

Evening appearance hiding motion: 244°.

528

晨見伏日三百二十七，餘七千六百四十五，秒八十五。

Morning appearance hiding: 327 days, remainder 7645, seconds 85.

529

晨見伏日三百四十九，餘七千六百四十五，秒八十五。

Morning appearance hiding: 349 days, remainder 7645, seconds 85.

530

中伏日四十一，餘八千二十二，秒九十二半。

Middle hiding: 41 days, remainder 8022, seconds 92½.

531

變差千二百三十六，秒十二。

Variation difference: 1236, seconds 12.

532

交率百八十二，餘五十二，秒二十九。

Crossing rate 182, remainder 52, seconds 29.

533

變策十五，餘十八，秒三十五。

Mutation divination 15, remainder 18, seconds 35.

534

夕見差率三十一。

Evening appearance difference rate: 31

535

差數十。

Difference number: 10

536

晨見差率二。

Morning appearance difference rate: 2

537

差數三。

Difference number: 3

538

辰星

Mercury

539

周率九十七萬三千三百九十，秒二十五。

Cycle rate 973,390, seconds 25

540

周策百一十五，餘七千三百九十，秒二十五。

Cycle tally 115 days, remainder 7,390, seconds 25

541

夕見伏日五十二。

Evening appearance hiding days: 52

542

夕見伏行十八度。

Evening appearance hiding motion: 18°

543

晨見伏日六十三，餘七千三百九十，秒二十五。

Morning appearance hiding days 63, remainder 7,390, seconds 25

544

晨見伏行九十七度，餘七千三百九十，秒二十五。

Morning appearance hiding motion 97°, remainder 7,390, seconds 25

545

中伏日十八，餘七千八百九十五，秒十二半。

Middle hiding day 18, remainder 7,895, seconds 12½

546

變差三千二百一，餘十，秒六十七。

Variation difference 3,201, remainder 10, seconds 67

547

交率百八十二，餘五十二，秒三十二。

Crossing rate 182, remainder 52, seconds 32

548

變策十五，餘十八，秒三十六。

Mutation divination 15, remainder 18, seconds 36

549

差率、差數空。

Difference rate and difference number: —

550

秒法百。

Second divisor: 100

551

小分法三千六百。

Small-part divisor: 3,600

552

五星平見加減曆

Five planets mean appearance add-subtract calendar

553

變數

Mutation count

554

歲星

Jupiter

555

熒惑

Mars

556

鎮星

Saturn

557

太白夕太白晨

Venus evening; Venus morning

558

辰星夕辰星晨

Mercury evening; Mercury morning

559

陽初

Yang initial

560

減空

Subtract void

561

加空

Add void

562

五百八十

580

563

加空七十六

Add void: 76

564

加空二百七十七

Add void: 277

565

二

2

566

百二十六

126

567

九百七十

970

568

六百五

605

569

百二十六百三十九

759

570

百五十一三百七十八

528

571

三

3

572

二百二十九

229

573

千七百六十四

1,764

574

六百五

605

575

二百五十二百八十九

539

576

二百七十七四百五十四

724

577

四

4

578

三百四十

340

579

二千一百六十七

2,167

580

六百五

605

581

三百七十八二百二十七

597

582

三百七十八五百四

874

583

五

5

584

四百二十八

428

585

二千二百三十

2,230

586

五百八十

580

587

五百四二百五十二

752

588

四百五十四四百七十九

929

589

六

6

590

四百九十一

491

591

二千二百五十五

2,255

592

五百四

504

593

六百三十二百六十五

895

594

五百四四百五十四

954

595

七

7

596

五百一十七

517

597

二千二百六十八

2,268

598

三百七十八

378

599

七百五十六二百五十二

1,002

600

四百七十九四百三

873

601

八

8

602

四百九十一

491

603

二千一百九十二

2,192

604

二百二十七

227

605

六百三十二百二十七

857

606

四百五十四三百二十八

778

607

九

9

608

四百二十八

428

609

千九百六十六

1,966

610

七十六

76

611

五百四百八十九

989

612

四百三二百二十七

627

613

十

10

614

三百四十

340

615

千五百一十二

1,512

616

加七十六

Add: 76

617

三百七十八百三十九

1,209

618

三百二十八百二十六

1,146

619

十一

11

620

二百三十九

239

621

千二十一

1,021

622

百八十九

189

623

二百五十二七十六

326

624

二百二十七加空

227, add void

625

十二

12

626

百二十六

126

627

五百一十七

517

628

三百一十五

315

629

百二十六加空

126, add void

630

百二十六百五十一

771

631

陰初

Yin initial

632

加空

Add void

633

減空

Subtract void

634

四百五十四

454

635

減空七十六

Subtract void: 76

636

減空二百七十七

Subtract void: 277

637

二

2

638

百二十六

126

639

百二十六

126

640

六百五

605

641

百二十六百三十九

759

642

百五十一三百七十八

528

643

三

3

644

二百三十九

239

645

二百一十四

214

646

五百二十九

529

647

二百五十二百八十九

539

648

二百七十七四百五十四

724

649

四

4

650

三百四十

340

651

五百一十七

517

652

四百五十四

454

653

三百七十八二百二十七

597

654

三百七十八五百四

874

655

五

5

656

四百二十八

428

657

九百三十二

932

658

三百七十八

378

659

五百四二百五十二

752

660

四百五十四四百七十九

929

661

六

6

662

四百九十一

491

663

千四百二十四

1,424

664

三百二

302

665

六百三十二百六十六

896

666

五百四四百五十四

954

667

七

7

668

五百一十七

517

669

二千二百六十八

2,268

670

二百一十八

218

671

七百五十六二百五十二

1,002

672

四百七十九四百三

873

673

八

8

674

四百九十一

491

675

二千二百六十八

2,268

676

百一十三

113

677

六百三十二百三十七

867

678

四百五十四三百二十八

778

679

九

9

680

四百二十

420

681

二千二百五十五

2,255

682

減空

Subtract void

683

五百四百八十九

989

684

四百三二百二十七

627

685

十

10

686

三百四十

340

687

二千一百六十一

2,161

688

二百二十七

227

689

三百七十八百三十九

1,209

690

三百二十八百二十六

1,146

691

十一

11

692

二百三十九

239

693

二千七十九

2,079

694

四百三

403

695

二百五十二七十六

326

696

二百二十七減空

227, subtract void

697

十二

12

698

百二十六

126

699

千九十六

1,096

700

五百四

504

701

百二十六減空

126, subtract void

702

百二十六百五十一

771

703

歲星

Jupiter

704

前順百一十五日行十九度三十三分

Prior direct: 115 days, 19° 33′

705

前留二十五日

Prior station: 25 days

706

退行八十五日行十度八十二分

Retrograde: 85 days, 10° 82′

707

後留二十五日

Posterior station: 25 days

708

後順百一十五日行十九度三十三分

Posterior direct: 115 days, 19° 33′

709

初見去日十四度。

At first appearance, 14° from the Sun.

710

先疾，日益遲十三秒。

First fast; daily slowness increases 13 seconds.

711

益疾、益遲二十一秒。

Increase fast and increase slow: 21 seconds.

712

先遲，日益疾十三秒。

First slow; daily speed increases 13 seconds.

713

陽初

Yang initial

714

七十六

76

715

三十四

34

716

六十三

63

717

二

2

718

六十三

63

719

四十

40

720

七十六

76

721

三

3

722

五十

50

723

三十四

34

724

六十三

63

725

四

4

726

三十八

38

727

二十七

27

728

五十

50

729

五

5

730

二十五

25

731

二十

20

732

三十八

38

733

六

6

734

十三

13

735

十三

13

736

二十五

25

737

七

7

738

加空

Add void

739

七

7

740

十三

13

741

八

8

742

十三

13

743

減空

Subtract void

744

加空

Add void

745

九

9

746

二十五

25

747

七

7

748

十三

13

749

十

10

750

三十八

38

751

十三

13

752

二十五

25

753

十一

11

754

五十

50

755

二十

20

756

三十八

38

757

十二

12

758

六十三

63

759

二十七

27

760

五十

50

761

陰初

Yin initial

762

七十六

76

763

三十四

34

764

六十三

63

765

二

2

766

六十三

63

767

四十

40

768

七十六

76

769

三

3

770

五十

50

771

三十四

34

772

六十三

63

773

四

4

774

三十八

38

775

二十七

27

776

五十

50

777

五

5

778

二十五

25

779

二十

20

780

三十八

38

781

六

6

782

十三

13

783

十三

13

784

二十五

25

785

七

7

786

減空

Subtract void

787

七

7

788

十三

13

789

八

8

790

十三

13

791

加空

Add void

792

減空

Subtract void

793

九

9

794

二十五

25

795

七

7

796

十三

13

797

十

10

798

三十八

38

799

十三

13

800

二十五

25

801

十一

11

802

五十

50

803

二十

20

804

三十八

38

805

十二

12

806

六十三

63

807

二十七

27

808

五十

50

809

熒惑

Mars

810

前疾二百二十日行百四十度

Prior fast: 220 days, 140°

811

前遲六十日行二十五度

Prior slow: 60 days, 25°

812

前留

Prior station

813

退行六十三日行十七度

Retrograde: 63 days, 17°

814

後留

Posterior station

815

後遲六十日行二十五度

Posterior slow: 60 days, 25°

816

後疾二百七日行百三十四度

Posterior fast: 207 days, 134°

817

初見去日十七度。

At first appearance, 17° from the Sun.

818

先疾，日益遲五秒。

First fast; daily slowness increases 5 seconds.

819

先疾，日益遲四十二秒。

First fast; daily slowness increases 42 seconds.

820

十三日

Day 13

821

益疾、益遲九秒。

Increase fast and increase slow: 9 seconds.

822

十三日

Day 13

823

先遲，日益疾四十二秒。

First slow; daily speed increases 42 seconds.

824

先遲，日益疾五秒。

First slow; daily speed increases 5 seconds.

825

陽初

Yang initial

826

七百五十六

756

827

百一

101

828

五十

50

829

百一

101

830

二千五百二十

2,520

831

二

2

832

減空

Subtract void

833

百二十六

126

834

六十三

63

835

百二十六

126

836

千六百七十六

1,676

837

三

3

838

二百三十九

239

839

百五十一

151

840

七十六

76

841

百五十一

151

842

八百三十二

832

843

四

4

844

五百四

504

845

百二十六

126

846

百五十一

151

847

百二十六

126

848

減空

Subtract void

849

五

5

850

千八

1,008

851

百一

101

852

二百七十七

277

853

百一

101

854

六百三十

630

855

六

6

856

千八百三十八

1,838

857

七十六

76

858

二百五十二

252

859

七十六

76

860

七百六

706

861

七

7

862

二千五百二十

2,520

863

五十

50

864

二百二十七

227

865

五十

50

866

千六百七十六

1,676

867

八

8

868

三千二十四

3,024

869

二十五

25

870

百四十三

143

871

二十五

25

872

二千九百三十六

2,936

873

九

9

874

三千二百七十六

3,276

875

減空

Subtract void

876

三十八

38

877

加空

Add void

878

三千九百六

3,906

879

十

10

880

三千四百四十

3,440

881

二十五

25

882

加空

Add void

883

二十五

25

884

四千五百三十六

4,536

885

十一

11

886

三千六百一十六

3,616

887

五十

50

888

七十六

76

889

五十

50

890

四千四百六十

4,460

891

十二

12

892

三千四百四十

3,440

893

七十六

76

894

八十八

88

895

七十六

76

896

四千一百八

4,108

897

陰初

Yin initial

898

三千二百七十六

3,276

899

百一

101

900

百一十三

113

901

百一

101

902

三千六百九十六

3,696

903

二

2

904

二千五百二十

2,520

905

百二十六

126

906

百三十九

139

907

百二十六

126

908

三千二百八十

3,280

909

三

3

910

千三百三十八

1,338

911

百五十一

151

912

二百五十二

252

913

百五十一

151

914

二千二百六十八

2,268

915

四

4

916

加空

Add void

917

百二十六

126

918

二百七十七

277

919

百二十六

126

920

千八

1,008

921

五

5

922

千三百三十八

1,338

923

百一

101

924

百七十六

176

925

百一

101

926

加三百四十

Add: 340

927

六

6

928

二千六百九十六

2,696

929

七十六

76

930

百一

101

931

七十六

76

932

二千五百一十二

2,512

933

七

7

934

三千二百七十六

3,276

935

五十

50

936

七十六

76

937

五十

50

938

三千三百五十六

3,356

939

八

8

940

三千六百一十六

3,616

941

二十五

25

942

五十

50

943

二十五

25

944

四千三百三十二

4,332

945

九

9

946

三千五百三十一

3,531

947

加空

Add void

948

二十五

25

949

減空

Subtract void

950

四千三十二

4,032

951

十

10

952

二千九百三十八

2,938

953

二十五

25

954

減空

Subtract void

955

二十五

25

956

三千三百五十二

3,352

957

十一

11

958

二千二百六十八

2,268

959

五十

50

960

十三

13

961

五十

50

962

三千一百五十四

3,154

963

十二

12

964

千五百一十三

1,513

965

七十六

76

966

二十五

25

967

七十六

76

968

二千五百六十二

2,562

969

鎮星

Saturn

970

前順八十三日行七度三十六分

Prior direct: 83 days, 7° 36′

971

前留三十六日

Prior station: 36 days

972

退行百三日行六度

Retrograde: 103 days, 6°

973

後留三十六日

Posterior station: 36 days

974

後順八十三日行七度三十六分

Posterior direct: 83 days, 7° 36′

975

初見去日十七度。

At first appearance, 17° from the Sun.

976

先疾，日益遲八秒。

First fast; daily slowness increases 8 seconds.

977

益疾、益遲二秒。

Increase fast and increase slow: 2 seconds.

978

先遲，日益疾八秒。

First slow; daily speed increases 8 seconds.

979

陽初

Yang initial

980

二十六

26

981

二十

20

982

二十六

26

983

二

2

984

三十二

32

985

二十五

25

986

三十二

32

987

三

3

988

三十八

38

989

三十

30

990

三十八

38

991

四

4

992

三十二

32

993

二十五

25

994

三十二

32

995

五

5

996

二十六

26

997

二十

20

998

二十六

26

999

六

6

1000

二十

20

1001

十五

15

1002

二十

20

1003

七

7

1004

十三

13

1005

十

10

1006

十三

13

1007

八

8

1008

七

7

1009

五

5

1010

七

7

1011

九

9

1012

加空

Add void

1013

減空

Subtract void

1014

加空

Add void

1015

十

10

1016

七

7

1017

五

5

1018

七

7

1019

十一

11

1020

十三

13

1021

十

10

1022

十三

13

1023

十二

12

1024

二十

20

1025

十五

15

1026

二十

20

1027

陰初

Yin initial

1028

二十六

26

1029

二十

20

1030

二十六

26

1031

二

2

1032

三十二

32

1033

二十五

25

1034

三十二

32

1035

三

3

1036

三十八

38

1037

三十

30

1038

三十八

38

1039

四

4

1040

三十二

32

1041

二十五

25

1042

三十二

32

1043

五

5

1044

二十六

26

1045

二十

20

1046

二十六

26

1047

六

6

1048

二十

20

1049

十五

15

1050

二十

20

1051

七

7

1052

十三

13

1053

十

10

1054

十三

13

1055

八

8

1056

七

7

1057

五

5

1058

七

7

1059

九

9

1060

減空

Subtract void

1061

加空

Add void

1062

減空

Subtract void

1063

十

10

1064

七

7

1065

五

5

1066

七

7

1067

十一

11

1068

十三

13

1069

十

10

1070

十三

13

1071

十二

12

1072

二十

20

1073

十五

15

1074

二十

20

1075

太白

Venus

1076

夕疾百七十二日行二百六度

172, 206

1077

夕平十三日行十三度

13, 13

1078

夕遲四十二日行三十度

42, 30

1079

夕留

Evening station

1080

夕退十日行五度

10, 5

1081

晨見退行十日行五度

10, 5

1082

晨留

Morning station

1083

晨遲四十二日行三十度

42, 30

1084

晨平十三日行十三度

13, 13

1085

晨疾百七十二日行二百六度

172, 206

1086

初見去日十一度。

At first appearance, 11° from the Sun.

1087

先疾，日益遲八十四秒。

First fast; daily slowness increases 84 seconds.

1088

先疾，日益遲一分二十八秒

1, 28

1089

七日

Day 7

1090

先遲，日益疾八十四秒

First slow; daily speed increases 84 seconds.

1091

先疾，日益遲八十四秒

First fast; daily slowness increases 84 seconds.

1092

七日

Day 7

1093

先遲，日益疾一分二十八秒

1, 28

1094

先遲，日益疾十九秒。

First slow; daily speed increases 19 seconds.

1095

陽初

Yang initial

1096

二百二十七

227

1097

六

6

1098

減空

Subtract void

1099

四

4

1100

十三

13

1101

百六十四

164

1102

七十六

76

1103

四百五十四

454

1104

二

2

1105

百一十二

112

1106

十二

12

1107

十三

13

1108

空

—

1109

八

8

1110

百三十九

139

1111

八十八

88

1112

五百六十七

567

1113

三

3

1114

減空

Subtract void

1115

十八

18

1116

二十五

25

1117

減空

Subtract void

1118

四

4

1119

百一十三

113

1120

七十六

76

1121

六百八十

680

1122

四

4

1123

百一十三

113

1124

二十四

24

1125

三十八

38

1126

空

—

1127

空

—

1128

七十六

76

1129

六十三

63

1130

五百六十七

567

1131

五

5

1132

二百二十七

227

1133

三十一

31

1134

五十

50

1135

四

4

1136

空

—

1137

三十八

38

1138

五十

50

1139

四百五十四

454

1140

六

6

1141

三百四十

340

1142

三十八

38

1143

六十三

63

1144

八

8

1145

減空

Subtract void

1146

加空

Add void

1147

三十八

38

1148

三百四十

340

1149

七

7

1150

四百五十四

454

1151

三十一

31

1152

七十六

76

1153

十三

13

1154

空

—

1155

三十八

38

1156

加空

Add void

1157

二百二十七

227

1158

八

8

1159

五百六十七

567

1160

二十四

24

1161

六十三

63

1162

十三

13

1163

空

—

1164

七十六

76

1165

加空

Add void

1166

百一十三

113

1167

九

9

1168

六百八十

680

1169

十八

18

1170

五十

50

1171

十三

13

1172

四

4

1173

百一十三

113

1174

十八

18

1175

加空

Add void

1176

十

10

1177

五百六十七

567

1178

十二

12

1179

三十八

38

1180

十三

13

1181

八

8

1182

百三十九

139

1183

三十八

38

1184

百一十三

113

1185

十一

11

1186

四百五十四

454

1187

六

6

1188

二十五

25

1189

十三

13

1190

十三

13

1191

百六十四

164

1192

五十

50

1193

二百二十七

227

1194

十二

12

1195

三百四十

340

1196

加空

Add void

1197

十三

13

1198

八

8

1199

十三

13

1200

百七十六

176

1201

六十三

63

1202

三百四十

340

1203

陰初

Yin initial

1204

二百二十七

227

1205

六

6

1206

加空

Add void

1207

四

4

1208

十三

13

1209

百六十四

164

1210

七十六

76

1211

四百五十四

454

1212

二

2

1213

百一十三

113

1214

十二

12

1215

十三

13

1216

空

—

1217

八

8

1218

百三十九

139

1219

八十八

88

1220

五百六十七

567

1221

三

3

1222

加空

Add void

1223

十八

18

1224

二十五

25

1225

加空

Add void

1226

四

4

1227

百一十三

113

1228

七十六

76

1229

六百八十

680

1230

四

4

1231

百一十三

113

1232

二十四

24

1233

三十八

38

1234

空

—

1235

空

—

1236

七十六

76

1237

六十三

63

1238

五百六十七

567

1239

五

5

1240

二百二十七

227

1241

三十一

31

1242

五十

50

1243

四

4

1244

空

—

1245

三十八

38

1246

五十

50

1247

四百五十四

454

1248

六

6

1249

三百四十

340

1250

三十八

38

1251

六十三

63

1252

八

8

1253

加空

Add void

1254

減空

Subtract void

1255

三十八

38

1256

三百四十

340

1257

七

7

1258

四百五十四

454

1259

三十一

31

1260

七十六

76

1261

十三

13

1262

空

—

1263

三十八

38

1264

十九

19

1265

二百二十七

227

1266

八

8

1267

五百六十七

567

1268

二十四

24

1269

六十三

63

1270

十三

13

1271

空

—

1272

七十六

76

1273

減空

Subtract void

1274

百一十三

113

1275

九

9

1276

六百八十

680

1277

十八

18

1278

五十

50

1279

十三

13

1280

四

4

1281

百一十三

113

1282

十八

18

1283

減空

Subtract void

1284

十

10

1285

五百六十七

567

1286

十二

12

1287

三十八

38

1288

十三

13

1289

八

8

1290

百三十九

139

1291

三十八

38

1292

百一十三

113

1293

十一

11

1294

四百五十四

454

1295

六

6

1296

二十五

25

1297

十三

13

1298

十三

13

1299

百六十四

164

1300

五十

50

1301

二百二十七

227

1302

十二

12

1303

三百四十

340

1304

減空

Subtract void

1305

十三

13

1306

八

8

1307

十三

13

1308

百七十六

176

1309

六十三

63

1310

三百四十

340

1311

辰星

Mercury

1312

夕疾十二日行十七度

Evening fast: 12 days, 17°

1313

夕遲十一日行九度

Evening slow: 11 days, 9°

1314

夕留三日

Evening station: 3 days

1315

晨留三日

Morning station: 3 days

1316

晨遲十一日行九度

11, 9

1317

晨疾十二日行十七度

12, 17

1318

初見去日十七度。

At first appearance, 17° from the Sun.

1319

先疾，日益遲三分。

First fast; daily slowness increases 3 parts.

1320

先疾，日益遲六分。

First fast; daily slowness increases 6 parts.

1321

先遲，日益疾六分。

First slow; daily speed increases 6 parts.

1322

先遲，日益疾三分。

First slow; daily speed increases 3 parts.

1323

校勘記0.85em|columns=2

Collation notes for this chapter.

1324

昭宗時，宣明曆施行已久，數亦漸差，詔太子少詹事邊岡與司天少監胡秀林、均州司馬王墀改治新曆，然術一出於岡。岡用算巧，能馳騁反覆于乘除間。由是簡捷、超徑、等接之術興，而經制、遠大、衰序之法廢矣。雖籌策便易，然皆冥於本原。其上元七曜，起赤道虛四度。景福元年，曆成，賜名崇玄。氣朔、發斂、盈縮、朓朒、定朔弦望、九道月度、交會、入蝕限去交前後，皆大衍之舊。餘雖不同，亦殊塗而至者。大略謂：

Under Emperor Zhaozong the Xuanming Calendar had been in force so long its figures had drifted; the throne ordered Bian Gang, Hu Xiulin, and Wang Chi to compile a new calendar, though the techniques all issued from Gang. Gang was deft with reckoning and moved freely through multiply-and-divide operations. Shortcut, super-direct, and equal-joining methods then arose, while canonical regulation, far magnitude, and ordered decline were set aside. Rod reckoning was easier, yet all lost sight of the root principle. Its upper origin for the seven luminaries starts at equatorial Xū 4°. In Jingfu year 1 the calendar was finished and named Chongxuan. Qi, new moons, issuing-and-gathering-in, surplus-deficit, waxing-and-waning, fixed syzygies, nine-path lunar position, conjunctions, and eclipse limits all follow Dayan. The rest differs, yet the same end is reached by another route. In broad outline:

1325

策實曰歲實。揲法曰朔實。三元之策曰氣策。四象之策曰平會。一象之策曰弦策。掛限曰閏限。爻數曰紀法。策餘曰歲餘。天中之策曰候策。地中之策曰卦策。貞悔之策曰土王策。辰法，半辰法也。乾實曰周天分。盈縮、朓朒，皆用常氣。盈縮分曰升降。先後曰盈縮。

Divination solid → year solid. Stalk method → new-moon solid. Three-origins divination → qi divination. Four-images divination → mean conjunction. One-image divination → quarter divination. The hanging limit is termed the intercalation limit. The line number is termed the cycle method. Divination remainder → year remainder. Heaven-center divination → hou divination. Earth-center divination → hexagram divination. True-and-changing divination → earth-kingship divination. The chen method is half the chen method. Qian solid → circuit-of-heaven parts. Surplus-deficit and waxing-and-waning all use regular qi. Surplus-deficit parts → ascent/descent. Prior and posterior → surplus-deficit.

1326

凡升降、損益，皆進一等，倍象統乘之，除法而一，為平行率。與後率相減，為差。半之，以加減平行率，為初、末率。倍差，進一等，以象統乘之，除法而一，為日差。以加減初、末為定。以日差累加減，為每日分。凡小餘，皆萬乘之，通法除，為約餘，則以萬為法。又以百約之，為大分，則以百為法。

For ascent-descent and decrease-increase, advance one rank, double the image tally, divide once—mean rate. Subtract from the posterior rate for the difference. Halve it; add or subtract to the mean rate for initial and final rates. Double the difference, advance one rank, multiply by the image tally, divide once for the daily difference. Add and subtract initial and final for the fixed value. Accumulate daily difference add/subtract for daily parts. For all minor remainders, multiply by 10,000; divide by the common divisor for reduced remainder, with 10,000 as divisor. Also reduce by 100 for major parts, with 100 as divisor.

1327

凡冬至赤道日度及約餘，以減其宿全度，乃累加次宿，皆為距後積度。滿限九十一度三十一分三十七小分，去之。餘半已下，為初；已上，以減限，為末。皆百四十四乘之，退一等，以減千三百一十五。所得以乘初、末度分，為差。又通初、末度分，與四千五百六十六先相減、後相乘，千六百九十除之，以減差，為定差，再退為分。至後以減、分後以加距後積度，為黃道積度。宿次相減，即其度也。

From winter-solstice equatorial degree and reduced remainder, subtract lodge full degrees and accumulate successive lodges for post-distance accumulation. When it fills the limit 91°31′37″, remove it. Remainder at or below half: initial; if above, subtract from the limit for final. All ×144, retreat one rank, subtract 1,315. Multiply initial and final degree-parts by the result for the difference. Convert initial and final degree-parts; subtract then multiply with 4,566, divide by 1,690 to subtract from the difference for fixed difference, retreat again for parts. After solstice subtract; after equinox add to post-distance accumulation for yellow-path accumulation. Subtract successive lodges for the degree.

1328

以冬至赤道日度及約餘，依前求定差以減之，為黃道日度。凡歲差，十一乘之，又以所求氣數乘之，三千八百八十八而一，以加前氣中積；又以盈縮分盈加、縮減之，命以冬至宿度，即其氣初加時宿度。

From winter-solstice equatorial degree and reduced remainder, subtract the fixed difference as before for yellow-path solar degree. Precession: ×11, also × the qi sought, ÷3,888, add to prior qi central accumulation; Add surplus and subtract deficit from surplus-deficit parts; count from winter-solstice lodge for qi initial added-time lodge degree.

1329

其定朔小餘，如日法四十分之二十九已上，以定朔小餘減日法，餘如晨初餘數已下，進一日。

If fixed-new-moon minor remainder ≥ 29/40 of the day divisor, subtract the day divisor; if remainder ≤ morning-initial remainder, advance one day.

1330

岡又作徑術求黃道月度。以蔀率去積年，為蔀周。不盡，為蔀餘。以歲餘乘蔀餘，副之。二因蔀周，三十七除之，以減副。百一十九約蔀餘，以加副。滿周天去之。餘，四因之為分，度母而一為度，即冬至加時平行月。

Gang also used a direct method to find yellow-path monthly degree. Remove obscuration rate from accumulated years for obscuration cycles. The remainder is obscuration remainder. Multiply obscuration remainder by year remainder and set aside. Double obscuration cycles, divide by 37, subtract from aside. Reduce obscuration remainder by 119 and add to the aside. Remove what fills the circuit of heaven. Remainder: ×4 for parts; ÷ degree mother once for degrees—winter-solstice added-time mean Moon.

1331

又以冬至約餘距午前後分，二百五十四乘之，萬約為分，度母為度；午前以加、午後以減加時月，為午中月。自此計日平行十三度十九分度之七。自冬至距定朔，累以平行減之，為定朔午中月。求次朔及弦望，各計日以平行加之。其分以度母除，為約分。

Winter-solstice reduced remainder noon distance ×254; ÷10,000 for parts; degree mother for degrees; Before noon add, after noon subtract from added-time Moon for noon-center Moon. From here count days: mean motion 13° 7′. From winter solstice to fixed new moon, accumulate subtracting mean motion for fixed-new-moon noon-center Moon. For next new moon and quarters, count days and add mean motion. Divide parts by the degree mother for reduced parts.

1332

又四十七除蔀餘，為率差。不盡，以乘七日三分半，副之。九因率差，退一等，為分，以減副。又百約冬至加時距午分，午前加之，午後減之，滿轉周去之，即冬至午中入轉。以冬至距朔日減之，即定朔午中入轉。求次朔及弦望，計日加之。

Also divide obscuration remainder by 47 for rate difference. Remainder × 7 days 3½ parts; set aside. 9 × rate difference, retreat one rank for parts, subtract from aside. Reduce winter-solstice added-time noon distance by 100; before noon add, after noon subtract; remove rotation cycle for winter-solstice noon-center entering rotation. Subtract winter-solstice-to-new-moon days for fixed-new-moon noon-center entering rotation. For next new moon and quarters, count days and add.

1333

各以所入日下損益率乘轉餘，百而一，以損益盈縮積，為定差。以盈加、縮減午中月，為定月。以月行定分乘其日晨昏距午分，萬約為分，滿百為度，以減午中定月，為晨月；加之，為昏月。

Each day: rotation remainder × that day's decrease-increase rate ÷100; adjust surplus-deficit accumulation for fixed difference. Add surplus and subtract deficit to noon-center Moon for fixed Moon. Fixed lunar motion × morning/evening noon distance ÷10,000; ÷100 for degrees; subtract from noon fixed Moon for morning Moon; Add for evening Moon.

1334

以朔昏月減上弦昏月，以上弦昏月減望昏月，以望晨月減下弦晨月，以下弦晨月減後朔晨月，各為定程。以相距日均，為平行度分。與次程相減，為差。以加、減平行，為初、末日定行。後少，加為初，減為末。後多，減為初，加為末。減相距日一，均差，為日差。累損、益初日，為每日定行。後多，累益之。後少，累減之。因朔弦望晨昏月，累加之，得每日晨昏月。

Differences between syzygy/quarter evening and morning Moons give each fixed interval. Average interval days for mean motion degree-parts. Subtract the next interval for the difference. Add and subtract to mean motion for initial- and final-day fixed motion. If the next is smaller, add initial and subtract final. If the next is larger, subtract initial and add final. Subtract one from interval days; average the difference for daily difference. Accumulate decrease and increase from day one for daily fixed motion. If the next is larger, accumulate increase. If the next is smaller, accumulate decrease. From syzygy/quarter morning and evening Moons, accumulate to daily morning and evening Moons.

1335

晷漏

Gnomon and clepsydra

1336

各計其日中入二至加時已來日數及餘。如初限已下，為後；已上，以減二至限，餘為前，副之。各以乘數乘之，用減初、末差。所得再乘其副，滿百萬為尺，不滿為寸、為分。夏至後，則退一等。皆命曰晷差。各至前後，以減冬至中晷；夏至前後，以加夏至中晷：為每日陽城中晷。與次日相減，後多曰息，後少曰消。以冬夏至午前、後約分乘之，萬而一，午前息減、消加，午後息加、消減中晷，為定數也。凡冬至初日，有減無加。夏至初日，有加無減。

For each, count days and remainder from solstice added time to that day's noon. At or below the initial limit: posterior; if above, subtract from solstice limit; remainder is anterior—set aside. Multiply each by its multiplier to subtract initial and final differences. Multiply again by the aside; one million fills a chi; remainder is cun and fen. After summer solstice, retreat one rank. All are named gnomon difference. Before and after each solstice, subtract from winter-solstice noon gnomon; before and after summer solstice, add to summer-solstice noon gnomon: daily Yang-city noon gnomon. Subtract the next day; larger next: breath-increase; smaller: breath-decrease. × solstice before/after-noon reduced parts ÷10,000; before/after noon rules on breath and gnomon for fixed number. Winter-solstice day one: subtract only, no add. Summer-solstice day one: add only, no subtract.

1337

又計二至加時已來至其日昏後夜半日數及餘。冬至後為息，夏至後為消。如一象已下，為初；已上，反減二至限，餘為末。令自相乘，進二位，以消息法除為分，副之。與五百分先相減，後相乘，千八百而一，以加副，為消息數。以象積乘之，百約為分，再退為度。春分後，以加六十七度四十分，秋分後，以減百一十五度二十分，即各其日黃道去極。與一象相減，則赤道內外也。以消息數，春分後加千七百五十二，秋分後以減二千七百四十八，即各其日晷漏母也。以減五千，為晨昏距午分。

Also count days and remainder from solstice added time to that day's after dusk and midnight. After winter solstice: breath-increase; after summer solstice: breath-decrease. At or below one image: initial; if above, inversely subtract from solstice limit; remainder is final. Self-multiply, advance two ranks, divide by breath-message method for parts, set aside. Subtract 500, multiply, ÷1800, add to aside for breath message number. Multiply by image accumulation; reduce by 100 for parts; retreat again for degrees. After spring equinox +67°40′; after autumn equinox −115°20′ for daily yellow-path polar distance. Subtract one image for inside or outside the equator. Breath message: after spring equinox +1752; after autumn equinox −2748 for daily gnomon-clepsydra mother. Subtract from 5,000 for morning and evening distance-from-noon parts.

1338

置晷漏母，千四百六十一乘，而再半之。百約，為距子度。以減半周天，餘為距中度。百三十五乘晷漏母，百約為分，得晨初餘數。凡晷漏，百為刻。不滿，以象積乘之，百約為分，得夜半定漏。

Set gnomon-clepsydra mother ×1461, halve again. Reduce by 100 for distance-from-zi degrees. Subtract from half the circuit of heaven; remainder is distance-from-center degrees. 135, 100 Gnomon-clepsydra: 100 per quarter-hour. 100, 0½

1339

九服中晷，各於其地立表候之。在陽城北，冬至前候晷景與陽城冬至同者，為差日之始；在陽城南，夏至前候晷景與陽城夏至同者，為差日之始。自差日之始，至二至日，為距差日數也。在至前者，計距前已來日數；至後者，計入至後已來日數。反減距差日，餘為距後日準。求初、末限晷差，各冬至前後以加、夏至前後以減冬夏至陽城中晷，得其地其日中晷。若不足減，減去夏至陽城中晷，即其日南倒中晷也。自餘之日，各計冬夏至後所求日數。減去距冬夏至差日，餘準初、末限入之。又九服所在，各於其地置水漏，以定二至夜刻，為漏率。以漏率乘每日晷漏母，各以陽城二至晷漏母除之，得其地每日晷漏母。

Nine-domain mid-gnomon: set up the gnomon and observe at each place. North of Yang-city, before winter solstice when the shadow matches Yang-city winter solstice: difference-day start; South of Yang-city, before summer solstice when the shadow matches Yang-city summer solstice: difference-day start. From difference-day start to solstice: days from difference. Before solstice: count days since prior distance; After solstice: count days since entering after solstice. Inversely subtract distance-difference days; remainder is post-distance day standard. Seek initial/final limit gnomon differences: add/subtract Yang-city solstice noon gnomons for local noon gnomon. If insufficient, subtract from summer-solstice Yang-city noon gnomon for south-inverted noon gnomon. Other days: count days after the solstice sought. Subtract distance-from-solstice difference days; remainder enters initial/final limits. At each nine-domain location, set a water clepsydra to fix solstice night quarter-hours as clepsydra rate. Daily gnomon-clepsydra mother × clepsydra rate ÷ Yang-city solstice mother for local daily mother.

1340

交會

Syzygies

1341

以四百一乘朔望加時入交常日及約餘，三十除，為度；不滿退除為分，得定朔望入交定積度分。以減周天，命起朔望加時黃道日躔，即交所在宿次。

Syzygy added-time entering-conjunction regular days and reduced remainder ×401, ÷30 for degrees; Remainder: retreat-divide for parts for fixed syzygy entering-conjunction accumulated degree-parts. Subtract from circuit of heaven; count from syzygy added-time solar pacing for conjunction lodge.

1342

凡入交定積度，如半交已上，為在陽曆；已上，減去半交，餘為入陰曆。以定朔望約餘乘轉分，萬約為分，滿百為度；以減入陰、陽曆積度，為定朔望夜半所入。

Entering-conjunction fixed accumulation at or above half-conjunction: yang half; if above, subtract half-conjunction; remainder enters yin half. 0, 100 Subtract from yin/yang accumulated degree for fixed syzygy midnight entry.

1343

如一象已下，為在少象；已上者，反減半交，餘為入老象。皆七十三乘之，退一等。用減千三百二十四，餘以乘老、少象度及餘，再退為分，副之。在少象三十度已下，老象六十一度已上，皆與九十一度先相減、後相乘，五十六除，為差。若少象三十度已上，反減九十一度，及老象六十度已下，皆自相乘，百五除，為差。皆以減副，百約為度，即朔望夜半月去黃道度分。

At or below one image: minor image; if above, inversely subtract half-conjunction; remainder: major image. 73, 1 Subtract 1,324; multiply major/minor image degrees by remainder; retreat twice for parts; set aside. 30, 61, 91, 56 30, 91, 60, 105 100, 0½

1344

凡定朔約餘距午前、後分，與五千先相減、後相乘，三萬除之；午前以減，午後倍之，以加約餘，為日蝕定餘。定望約餘，即為月蝕定餘。晨初餘數已下者，皆四百乘之，以晨初餘數除之，所得以加定望約餘，為或蝕小餘。各以象統乘之，萬約，為半辰之數。餘滿二千四百為刻。不盡退除，為刻分，即其辰刻日蝕有差。

For the fixed new moon's approximate remainder measured before and after noon, subtract from 5,000 first, then multiply, and divide by 30,000; Before noon subtract; after noon double and add to reduced remainder for solar eclipse fixed remainder. Fixed full-moon reduced remainder is lunar eclipse fixed remainder. At or below morning-initial remainder: ×400, ÷ morning-initial remainder, add to fixed full-moon reduced remainder for possible-eclipse minor remainder. 0, 0½ Remainder fills 2,400: quarter-hours. Remainder: retreat-divide for quarter-hour parts for eclipse hour offset.

1345

置其朔距天正中氣積度，以減三百六十五度半，餘以千乘，滿三百六十五度半除為分，曰限心。加二百五十分，為限首。減二百五十分，為限尾。滿若不足，加減一千，退蝕定餘一等。與限首、尾相近者，相減，餘為限內外分。其蝕定餘多於限首、少於限尾者，為外。少於限首、多於限尾者，為內。在限內者，令限內分自乘，百七十九而一，以減六百三十，餘為陰曆蝕差。限外者，置限外分與五百先相減、後相乘，四百四十六而一，為陰曆蝕差。又限內分亦與五百先相減，後相乘，三百一十三半而一，為陽曆蝕差。

365, 0½, 1,000, 365, 0½ Add: 250 Subtract 250 parts for limit tail. 1,000, 1 Near limit head and tail: subtract; remainder is inside-outside limit parts. Eclipse fixed remainder > limit head and < limit tail: outside. Less than limit head and greater than limit tail: inside. 179, 1, 630 500, 446, 1 500, 313½, 1

1346

在限內者，以陽曆蝕差加陰曆蝕差，為既前法。以減千四百八十，餘為既後法。在限外者，以六百一十分為既前法，八百八十分為既後法。其去交度分，在限外陰曆者，以陰曆差減之。不足減者，不蝕。又限外無陽曆。交在限內陰曆者，以陽曆蝕差加之。若在限內陽曆者，以去交度分反減陽曆蝕差。若不足反減者，不蝕。皆為去交定分。如既前法已下者，為既前分。已上者，以減千四百八十，餘為既後分。皆進一位。各以既前、後法除，為蝕分。在既後者，其虧復陰曆也。既前者，陽曆也。

Inside limit: yang-half + yin-half eclipse difference for pre-totality method. Subtract from 1,480; remainder is post-totality method. When outside the limit, take 610 as the pre-totality divisor and 880 as the post-totality divisor. Outside-limit yin half: subtract yin-half difference from distance-from-conjunction. If insufficient to subtract: no eclipse. Outside limit: no yang half. Inside limit yin half: add yang-half eclipse difference. Inside limit yang half: inversely subtract yang-half difference from distance-from-conjunction. If insufficient to inversely subtract: no eclipse. All become fixed distance-from-conjunction parts. At or below pre-totality method: pre-totality parts. If above, subtract from 1,480; remainder is post-totality parts. All advance one place. Divide by pre/post-totality methods for eclipse parts. Post-totality: waning and recovery is yin half. Pre-totality: yang half.

1347

凡朔望月行定分，日以九百乘，月以千乘，如千三百三十七而一，日以減千八百，月以減二千，餘為汎用刻分。凡月蝕汎用刻，在陽曆以三十四乘，在陰曆以四十一乘，百約，為月蝕既限。以減千四百八十，餘為月蝕定法。其去交度分，如既限已下者，既。已上者，以減千四百八十，餘進一位，以定法約，為蝕分。其蝕五分已下者，為或食；已上為的蝕。

900, 1,000, 1,337, 1, 1,800, 2,000 For lunar eclipses generally, multiply by 34 in a yang month and by 41 in a yin month, reduce by 100, and obtain the totality limit for a lunar eclipse. Subtract from 1,480; remainder is lunar eclipse fixed method. Distance-from-conjunction at or below totality limit: totality. If above that value, subtract from 1,480, carry the remainder one place, divide by the fixed divisor, and obtain the eclipse fraction. Eclipse parts ≤ five tenths: possible eclipse; above: definite eclipse.

1348

凡日月食分，汎用刻乘之，千而一，為定用刻。不盡，退除為刻分。既者，以汎為定。各以減蝕甚約餘，為虧初。加之，為復滿。凡蝕甚與晨昏分相近，如定用刻已下者，因相減，餘以乘蝕分，滿定用刻而一，所得以減蝕分，得帶蝕分。

1,000, 1 Remainder: retreat-divide for quarter-hour parts. Totality: take the general as fixed. Subtract from eclipse maximum reduced remainder for waning initial. Add: 0 When eclipse maximum nears morning/evening parts and ≤ fixed-use quarter-hours: adjust eclipse parts for carried eclipse parts.

1349

五星變差曰歲差。陰陽進退差曰盈縮。爻算曰畫度。畫有十二，亦爻數也。推冬至後加時平合日算，曰平合中積。副之，曰平合中星。歲差減中星，曰入曆。有餘者，皆約之。因平合以諸變常積日加中積，常積度加中星、入曆，各其變中積、中星、入曆也。

Five-planet mutation difference → year difference. Yin-yang advance-retreat difference → surplus-deficit. Line calculation → stroke degree. Strokes are twelve—also the line number. Push added-time mean conjunction after winter solstice: mean-conjunction central accumulation. Set aside: mean-conjunction central star. Year difference subtracts central star: entering the calendar. Remainders: all reduce. From mean conjunction add regular accumulated days/degrees to central accumulation, star, and entering calendar for each mutation.

1350

凡入曆盈限已下，為盈。已上，去之，為縮。各如畫度分而一，命畫數算外。不滿，以畫下損益乘之，畫度分除之，以損益盈縮積，為定差。盈加、縮減中積，為定積。準求所入氣及月日，加冬至大餘及約餘，為其變大小餘。以命日辰，則變行所在也。亦以盈加、縮減中星，應用躔差。視定積如半交已下，為在盈；已上，去之，為在縮。所得，令半交度先相減、後相乘，三千四百三十五除，為度。不盡退除為分者，亦盈加、縮減之。

Entering calendar at or below surplus limit: surplus. If above, remove for deficit. Each ÷ stroke degree-parts once; count outside stroke tally. Remainder: × decrease-increase below stroke, ÷ stroke degree-parts, adjust surplus-deficit accumulation for fixed difference. Surplus add, deficit subtract to central accumulation for fixed accumulation. Seek qi and month-day; add winter-solstice major and reduced remainders for mutation major/minor remainders. Count day and double-hour for mutation motion place. Also adjust central star with surplus/deficit, applying pacing difference. Fixed accumulation at or below half-conjunction: in surplus; if above, remove: in deficit. Take the result, let the half-crossing degree subtract first and then multiply, divide by 3,435, and obtain the degree value. Remainder retreat-divided for parts: also surplus add and deficit subtract.

1351

其變異術者，從其術，各為定星。命起冬至黃道日躔，得其變行加時所在宿度也。凡辰星依曆變置算，乃視晨見、晨順在冬至後，夕見、夕順在夏至後計中積去二至九十一日半已下，令自乘。已上，以減百八十二日半，亦自乘。五百而一，為日。以加晨夕見中積、中星，減晨夕順中積、中星，各為應見不見中積、中星也。凡盈縮定差，熒惑晨見變六十一乘之、五十四除之，乃為定差。太白、辰星再合，則半其差。其在夕見、晨疾二變，則盈減、縮加。凡歲、鎮、熒惑留退，皆用前遲入曆定差。又各視前遲定星，以變下減度減之。餘半交已下，為盈；已上，去之，為縮。又視之，七十三已下三因之，已上減半交，餘二因之，為差。歲、鎮二星，退一等。熒惑，全用之。在後退，又倍其差。後留，三之。皆滿百為度。以盈加、縮減中積，又以前遲定差盈加、縮減，乃為留退定積。其前後退中星，則以差縮加、盈減，又以前遲定差盈加、縮減，乃為退行定星。

Special mutation methods: follow each; fixed star. Count from winter-solstice yellow-path solar pacing for mutation added-time lodge degree. Mercury: set tally per calendar mutations; if morning/evening appearance and direct fall after the relevant solstice and central accumulation from solstice is ≤91½ days, self-multiply. 182, 0½ 500, 1 Add/subtract to evening/morning appearance vs direct central accumulation and star for visibility. Surplus-deficit fixed difference: Mars morning-appearance mutation ×61 ÷54 for fixed difference. Venus and Mercury at second conjunction: halve the difference. Evening appearance and morning fast mutations: surplus subtract, deficit add. Jupiter, Saturn, Mars station/retrograde: use prior slow entering-calendar fixed difference. Each view prior slow fixed star; subtract decrease-degree below mutation. Remainder at or below half-conjunction: surplus; if above, remove: deficit. 73, 3, 0½, 2 2, 1 Mars: use fully. Posterior retrograde: double the difference. Posterior station: triple it. All that fill 100 become degrees. Adjust central accumulation and prior slow fixed difference for station-retrograde fixed accumulation. Adjust prior/posterior retrograde central star with difference and prior slow fixed difference for retrograde fixed star.

1352

凡諸變定星迭相減，為日度率。熒惑遲日盈六十、度盈二十四者，所盈日度加疾變日度，為定率。太白退日率，百乘之，二百一十二除之、為留日。以減退日率，為定率。辰星退順日率一等，為留日。以減順日率，為定率。以日均度，為平行。又與後變平行相減，為差。半之，視後多少，以加減平行，為初、末日行分。以初日行分乘其變小餘，萬而一，順減、退加其變加時宿度，為夜半宿度。又減日率一，均差，為日差。視後多少，累損益初日，為每日行分。因夜半宿度，累加減之，得每日所至。

Successive fixed-star subtraction gives day-degree rate. Mars slow days surplus 60 and degrees surplus 24: add surplussed days and degrees to fast mutation day-degrees for fixed rate. 100, 212 Subtract from retrograde day rate for fixed rate. Mercury retrograde direct day rate one rank: station days. Subtract from direct day rate for fixed rate. Average daily degrees for mean motion. Subtract next mutation's mean motion for difference. Halve; add/subtract to mean motion for initial/final-day motion parts. First-day motion parts × mutation minor remainder ÷10,000; direct subtract and retrograde add to mutation added-time lodge degree for midnight lodge degree. Subtract one from day rate; average difference for daily difference. Accumulate decrease/increase from day one for daily motion parts. From midnight lodge degree, accumulate for each day's arrival.

1353

五星差行，衰殺不倫，皆以諸變類會消息署之。

Five-planet differential motion: key each mutation class to breath message.

1354

起二年頒用，至唐終。

Promulgated from year two until the Tang ended.

1355

景福崇玄曆演紀上元甲子，距景福元年壬子，歲積五千三百九十四萬七千三百八算外。

Chongxuan Jingfu upper origin jiazi; from Jingfu 1 renzi, year accumulation 5,394,7008 outside tally.

1356

崇玄通法萬三千五百。

Chongxuan common method: 13,500.

1357

歲實四百九十三萬八百一。

Year solid: 4,938,801.

1358

氣策十五，餘二千九百五十，秒一。

15, 2,950, 1

1359

朔實三十九萬八千六百六十三。

New-moon solid: 398,663.

1360

平會二十九，餘七千一百六十三。

29, 7,163

1361

望策十四，餘萬三百三十一半。

14, 331½

1362

弦策七，餘五千一百六十五太。

7, 5,165

1363

朔虛分六千三百三十七。

New-moon void parts: 6,337.

1364

中盈分五千九百，秒二。

5,900, 2

1365

歲餘七萬八百一。

Year remainder: 70,801.

1366

閏限三十八萬六千四百二十五，秒二十三。

386,425, 23

1367

象位六。

Image position: 6.

1368

象統二十四。

Image tally: 24.

1369

候策五，餘九百八十三，秒二十五；秒母七十二。

5, 983, 25 Second mother: 72.

1370

卦策六，餘千一百八十，秒一；秒母六十。

6, 1,180, 1 Second mother: 60.

1371

土王策三，餘五百九十，秒一；秒母百二十。

3, 590, 1 Second mother: 120.

1372

辰數五百六十二半。

Chen number: 562½.

1373

刻法百三十五。

Quarter-hour divisor: 135.

1374

周天分四百九十三萬九百六十一，秒二十四。

4,930,961, 24

1375

歲差百六十，秒二十四。

160, 24

1376

周天三百六十五度，虛分三千四百六十一，秒二十四。

365, 3,461, 24

1377

約虛分二千五百六十三，秒八十八。

2,563, 88

1378

除法七千三百五。

Divisor: 7,305.

1379

秒母一百。

Second mother: 100.

1380

二十四氣中積，自冬至，每氣以氣策及約餘累之。

24 qi central accumulations from winter solstice: accumulate qi divination and reduced remainder each qi.

1381

氣節

Solar term

1382

升降差

Ascent-descent difference

1383

盈縮分

Surplus-deficit parts

1384

損益數

Decrease-increase numbers

1385

朓朒積

Anomalistic accumulation

1386

冬至

Winter Solstice

1387

升七千七百四十

Ascent: 7,740

1388

盈初

Surplus initial

1389

益七百八十二

Increase: 782

1390

朒初

Waning initial

1391

小寒

Lesser Cold

1392

升六千六十九

Ascent: 6,069

1393

盈七千七百四十

Surplus: 7,740

1394

益六百一十三

Increase: 613

1395

朒七百八十二

Waning: 782

1396

大寒

Greater Cold

1397

升四千五百七十二

Ascent: 4,572

1398

盈萬三千八百九

Surplus: 3,809

1399

益四百六十二

Increase: 462

1400

朒千三百九十五

Waning: 1,395

1401

立春

Start of Spring

1402

升三千二百五十

Ascent: 3,250

1403

盈萬八千三百八十一

Surplus: 8,381

1404

益三百二十八

Increase: 328

1405

朒千八百五十七

Waning: 1,857

1406

雨水

Rain Water

1407

升千九百七十七

Ascent: 1,977

1408

盈二萬一千六百三十一

Surplus: 21,631

1409

益二百

Increase: 200

1410

朒二千一百八十五

Waning: 2,185

1411

驚蟄

Awakening of Insects

1412

升六百六十

Ascent: 660

1413

盈二萬三千六百八

Surplus: 23,608

1414

益六十七

Increase: 67

1415

朒二千三百八十五

Waning: 2,385

1416

春分

Spring Equinox

1417

降六百六十

Descent: 660

1418

盈二萬四千二百六十八

Surplus: 24,268

1419

損六十七

Decrease: 67

1420

朒二千四百五十二

Waning: 2,452

1421

清明

Clear and Bright

1422

降千九百七十七

Descent: 1,977

1423

盈二萬三千六百八

Surplus: 23,608

1424

損二百

Decrease: 200

1425

朒二千三百八十五

Waning: 2,385

1426

穀雨

Grain Rain

1427

降三千二百五十

Descent: 3,250

1428

盈二萬一千六百三十一

Surplus: 21,631

1429

損三百二十八

Decrease: 328

1430

朒二千一百八十五

Waning: 2,185

1431

立夏

Start of Summer

1432

降四千五百七十二

Descent: 4,572

1433

盈萬八千三百八十一

Surplus: 8,381

1434

損四百六十二

Decrease: 462

1435

朒千八百五十七

Waning: 1,857

1436

小滿

Lesser Fullness

1437

降六千六十九

Descent: 6,069

1438

盈萬三千八百九

Surplus: 3,809

1439

損六百一十三

Decrease: 613

1440

朒千三百九十五

Waning: 1,395

1441

芒種

Grain in Ear

1442

降七千七百四十

Descent: 7,740

1443

盈七千七百四十

Surplus: 7,740

1444

損七百八十二

Decrease: 782

1445

朒七百八十二

Waning: 782

1446

夏至

Summer Solstice

1447

降七千七百四十

Descent: 7,740

1448

縮初

Deficit initial

1449

益七百八十二

Increase: 782

1450

朓初

Waxing initial

1451

小暑

Lesser Heat

1452

降六千六十九

Descent: 6,069

1453

縮七千七百四十

Deficit: 7,740

1454

益六百一十三

Increase: 613

1455

朓七百八十二

Waxing: 782

1456

大暑

Greater Heat

1457

降四千五百七十二

Descent: 4,572

1458

縮萬三千八百九

Deficit: 3,809

1459

益四百六十二

Increase: 462

1460

朓千三百九十五

Waxing: 1,395

1461

立秋

Start of Autumn

1462

降三千二百五十

Descent: 3,250

1463

縮萬八千三百八十一

Deficit: 8,381

1464

益三百二十八

Increase: 328

1465

朓千八百五十七

Waxing: 1,857

1466

處暑

End of Heat

1467

降千九百七十七

Descent: 1,977

1468

縮二萬一千六百三十一

Deficit: 21,631

1469

益二百

Increase: 200

1470

朓二千一百八十五

Waxing: 2,185

1471

白露

White Dew

1472

降六百六十

Descent: 660

1473

縮二萬三千六百八

Deficit: 23,608

1474

益六十七

Increase: 67

1475

朓二千三百八十五

Waxing: 2,385

1476

秋分

Autumn Equinox

1477

升六百六十

Ascent: 660

1478

縮二萬四千二百六十八

Deficit: 24,268

1479

損六十七

Decrease: 67

1480

朓二千四百五十二

Waxing: 2,452

1481

寒露

Cold Dew

1482

升千九百七十七

Ascent: 1,977

1483

縮二萬三千六百八

Deficit: 23,608

1484

損二百

Decrease: 200

1485

朓二千三百八十五

Waxing: 2,385

1486

霜降

Frost Descent

1487

升三千二百五十

Ascent: 3,250

1488

縮二萬一千六百三十一

Deficit: 21,631

1489

損三百二十八

Decrease: 328

1490

朓二千一百八十五

Waxing: 2,185

1491

立冬

Start of Winter

1492

升四千五百七十二

Ascent: 4,572

1493

縮萬八千三百八十一

Deficit: 8,381

1494

損四百六十二

Decrease: 462

1495

朓千八百五十七

Waxing: 1,857

1496

小雪

Lesser Snow

1497

升六千六十九

Ascent: 6,069

1498

縮萬三千八百九

Deficit: 3,809

1499

損六百十三

Decrease: 613

1500

朓千三百九十五

Waxing: 1,395

1501

大雪

Greater Snow

1502

升七千七百四十

Ascent: 7,740

1503

縮七千七百四十

Deficit: 7,740

1504

損七百八十二

Decrease: 782

1505

朓七百八十二

Waxing: 782

1506

轉周分三十七萬一千九百八十六，秒九十七。

371,986, 97

1507

轉終日二十七，餘七千四百八十六，秒九十七。

27, 7,486, 97

1508

朔差日一，餘萬三千一百七十六，秒三。

1, 3,176, 3

1509

度母一百。每日累轉分為轉積度。

Degree mother: 100. Each day accumulate rotation parts for rotation accumulated degrees.

1510

秒母一百。

Second mother: 100.

1511

轉終日

Rotation termination days

1512

轉分列差

Rotation column difference

1513

損益率

Rates of increase and decrease

1514

朓朒積

Anomalistic accumulation

1515

一日

Day 1

1516

千二百七進十六

1,207, 16

1517

益千三百一十九

Increase: 1,319

1518

朒初

Waning initial

1519

二日

Day 2

1520

千二百二十三進十七

1,223, 17

1521

益千一百五十

Increase: 1,150

1522

朒千三百一十九

Waning: 1,319

1523

三日

Day 3

1524

千二百四十進十八

1,240, 18

1525

益九百七十八

Increase: 978

1526

朒二千四百六十九

Waning: 2,469

1527

四日

Day 4

1528

千二百五十八進十八

1,258, 18

1529

益七百九十九

Increase: 799

1530

朒三千四百四十七

Waning: 3,447

1531

五日

Day 5

1532

千二百七十六進十九

1,276, 19

1533

益六百一十七

Increase: 617

1534

朒四千二百四十六

Waning: 4,246

1535

六日

Day 6

1536

千二百九十五進二十一

1,295, 21

1537

益四百三十一

Increase: 431

1538

朒四千八百六十三

Waning: 4,863

1539

七日

Day 7

1540

千三百一十六進二十三

1,316, 23

1541

初益二百一十三末損二十七

213, 27

1542

朒五千二百九十四

Waning: 5,294

1543

八日

Day 8

1544

千三百三十九進二十六

1,339, 26

1545

損二百八十五

Decrease: 285

1546

朒五千四百八十

Waning: 5,480

1547

九日

Day 9

1548

千三百六十五進十八

1,365, 18

1549

損四百七十一

Decrease: 471

1550

朒五千一百九十五

Waning: 5,195

1551

十日

Day 10

1552

千三百八十三進十八

1,383, 18

1553

損六百五十

Decrease: 650

1554

朒四千七百二十四

Waning: 4,724

1555

十一日

Day 11

1556

千四百一進十九

1,401, 19

1557

損八百四十

Decrease: 840

1558

朒四千七十四

Waning: 4,074

1559

十二日

Day 12

1560

千四百二十進十七

1,420, 17

1561

損千一十七

Decrease: 1,017

1562

朒三千二百三十四

Waning: 3,234

1563

十三日

Day 13

1564

千四百三十七進十六

1,437, 16

1565

損千一百八十五

Decrease: 1,185

1566

朒二千二百一十七

Waning: 2,217

1567

十四日

Day 14

1568

千四百五十三進十一

1,453, 11

1569

初損千三十二末益二百九十二

1,032, 292

1570

朒千三十二

Waning: 1,032

1571

十五日

Day 15

1572

千四百六十四退十七

1,464, 17

1573

益千二百八十四

Increase: 1,284

1574

朒二百九十三

Waning: 293

1575

十六日

Day 16

1576

千四百四十七退十八

1,447, 18

1577

益千一百一十

Increase: 1,110

1578

朓千五百七十七

Waxing: 1,577

1579

十七日

Day 17

1580

千四百二十九退十八

1,429, 18

1581

益九百四十一

Increase: 941

1582

朓二千六百八十七

Waxing: 2,687

1583

十八日

Day 18

1584

千四百一十一退十八

1,411, 18

1585

益七百五十七

Increase: 757

1586

朓三千六百二十八

Waxing: 3,628

1587

十九日

Day 19

1588

千三百九十三退十八

1,393, 18

1589

益五百七十八

Increase: 578

1590

朓四千三百八十五

Waxing: 4,385

1591

二十日

Day 20

1592

千三百七十五退二十二

1,375, 22

1593

益三百八十六

Increase: 386

1594

朓四千九百六十三

Waxing: 4,963

1595

二十一日

Day 21

1596

千三百五十三退二十五

1,353, 25

1597

初益百六十末損八十

160, 80

1598

朓五千三百四十九

Waxing: 5,349

1599

二十二日

Day 22

1600

千三百二十八退二十二

1,328, 22

1601

損三百二十四

Decrease: 324

1602

朓五千四百二十九

Waxing: 5,429

1603

二十三日

Day 23

1604

千三百六退十九

1,306, 19

1605

損五百一十六

Decrease: 516

1606

朓五千一百五

Waxing: 5,105

1607

二十四日

Day 24

1608

千二百八十七退十九

1,287, 19

1609

損六百九十七

Decrease: 697

1610

朓四千五百八十九

Waxing: 4,589

1611

二十五日

Day 25

1612

千二百六十八退十八

1,268, 18

1613

損八百七十九

Decrease: 879

1614

朓三千八百九十二

Waxing: 3,892

1615

二十六日

Day 26

1616

千二百五十退十七

1,250, 17

1617

損千五十三

Decrease: 1,053

1618

朓三千一十三

Waxing: 3,013

1619

二十七日

Day 27

1620

千二百三十三退十七

1,233, 17

1621

損千二百二十三

Decrease: 1,223

1622

朓千九百六十

Waxing: 1,960

1623

二十八日

Day 28

1624

千二百一十六退九

1,216, 9

1625

初損七百三十七末益入後

Initial decrease rate: 737, terminal increase rate enters thereafter

1626

朓七百三十七

Waxing: 737

1627

七日：初數萬一千九百九十六太，末數千五百三。

Day 7: initial count 11,996 greater, terminal count 1,503.

1628

十四日：初數萬四百九十三半，末數三千六半。

Day 14: initial count 10,493½, terminal count 3,006½.

1629

二十一日：初數八千九百九十少，末數四千五百九太。

Day 21: initial count 8,990 lesser, terminal count 4,509 greater.

1630

二十八日：初數七千四百八十七。

Day 28: initial count 7,487.

1631

蔀率九千三十六。

Obscuration rate: 9,036.

1632

歲餘六百三十九。

Year remainder: 639.

1633

周天分千七百三十五。

Circuit-of-heaven parts: 1,735.

1634

周天三百六十五度五分。

Circuit of heaven: 365° 5 parts.

1635

度母十九。

Degree mother: 19.

1636

月行定分同轉分。

Lunar motion fixed parts same as rotation parts.

1637

平行積度，日累十三度七分。

Mean-motion accumulated degrees; daily accumulation 13° 7 parts.

1638

入轉日

Entering rotation day

1639

損益數

Decrease-increase numbers

1640

盈縮積度

Surplus-deficit accumulated degrees

1641

一日

Day 1

1642

益百三十一

Increase rate: 131

1643

縮初空

Contraction initial empty

1644

二日

Day 2

1645

益百一十四

Increase rate: 114

1646

縮一度三十一分

Contraction: 1° 31 parts

1647

三日

Day 3

1648

益九十七

Increase rate: 97

1649

縮二度四十五分

Contraction: 2° 45 parts

1650

四日

Day 4

1651

益七十九

Increase rate: 79

1652

縮三度四十二分

Contraction: 3° 42 parts

1653

五日

Day 5

1654

益六十一

Increase rate: 61

1655

縮四度二十一分

Contraction: 4° 21 parts

1656

六日

Day 6

1657

益四十三

Increase rate: 43

1658

縮四度八十二分

Contraction: 4° 82 parts

1659

七日

Day 7

1660

初益二十一末損三

Initial increase rate: 21, terminal decrease rate: 3

1661

縮五度二十五分

Contraction: 5° 25 parts

1662

八日

Day 8

1663

損二十八

Decrease rate: 28

1664

縮五度四十三分

Contraction: 5° 43 parts

1665

九日

Day 9

1666

損四十七

Decrease rate: 47

1667

縮五度一十五分

Contraction: 5° 15 parts

1668

十日

Day 10

1669

損六十五

Decrease rate: 65

1670

縮四度六十八分

Contraction: 4° 68 parts

1671

十一日

Day 11

1672

損八十三

Decrease rate: 83

1673

縮四度三分

Contraction: 4° 3 parts

1674

十二日

Day 12

1675

損百一

Decrease rate: 101

1676

縮三度二十分

Contraction: 3° 20 parts

1677

十三日

Day 13

1678

損百一十七

Decrease rate: 117

1679

縮二度十九分

Contraction: 2° 19 parts

1680

十四日

Day 14

1681

初損百二末益二十九

102, 29

1682

縮一度二分

Contraction: 1° 2 parts

1683

十五日

Day 15

1684

益百二十七

Increase rate: 127

1685

盈二十九分

Surplus: 29 parts

1686

十六日

Day 16

1687

益百一十

Increase rate: 110

1688

盈一度五十六分

Surplus: 1° 56 parts

1689

十七日

Day 17

1690

益九十四

Increase rate: 94

1691

盈二度六十六分

Surplus: 2° 66 parts

1692

十八日

Day 18

1693

益七十五

Increase rate: 75

1694

盈三度六十分

Surplus: 3° 60 parts

1695

十九日

Day 19

1696

益五十七

Increase rate: 57

1697

盈四度三十五分

Surplus: 4° 35 parts

1698

二十日

Day 20

1699

益三十八

Increase rate: 38

1700

盈四度九十二分

Surplus: 4° 92 parts

1701

二十一日

Day 21

1702

初益十六末損八

16, 8

1703

盈五度三十分

Surplus: 5° 30 parts

1704

二十二日

Day 22

1705

損三十二

Decrease rate: 32

1706

盈五度三十八分

Surplus: 5° 38 parts

1707

二十三日

Day 23

1708

損五十一

Decrease rate: 51

1709

盈五度六分

Surplus: 5° 6 parts

1710

二十四日

Day 24

1711

損六十九

Decrease rate: 69

1712

盈四度五十五分

Surplus: 4° 55 parts

1713

二十五日

Day 25

1714

損八十七

Decrease rate: 87

1715

盈三度八十六分

Surplus: 3° 86 parts

1716

二十六日

Day 26

1717

損百四

Decrease rate: 104

1718

盈二度九十九分

Surplus: 2° 99 parts

1719

二十七日

Day 27

1720

損百二十一

Decrease rate: 121

1721

盈一度九十五分

Surplus: 1° 95 parts

1722

二十八日

Day 28

1723

初損七十四末益入後

Initial decrease rate: 74, terminal increase rate enters thereafter

1724

盈七十四分

Surplus: 74 parts

1725

轉周二十七日，五十五分半。

Rotation cycle: 27 days, 55½ parts.

1726

七日：初八十八分，小分八十七半；末十一分，小分十二半。

Day 7: initial 88 parts, 87½ minor parts; terminal 11 parts, 12½ minor parts.

1727

十四日：初七十七分太；末二十二分少。

Day 14: initial 77 parts greater; terminal 22 parts lesser.

1728

二十一日：初六十六分，小分六十二半；末三十三分，小分三十七半。

Day 21: initial 66 parts, 62½ minor parts; terminal 33 parts, 37½ minor parts.

1729

二十八日：初五十五分半。

Day 28: initial 55½ parts.

1730

入轉日母一百。

Entering rotation day mother: 100.

1731

二至限百八十二日，六十二分，小分二十二分半。

Two-solstice limit: 182 days, 62 parts, 22½ minor parts.

1732

消息法千六百六十七半。

Message method: 1,667½.

1733

一象九十一度三千一百三十一分。

One quadrant: 91° 3,131 parts.

1734

辰法八刻百六十分。

Chen method: 8 quarter-hours, 160 parts.

1735

昏、明二刻二百四十分。

Dusk and dawn: 2 quarter-hours, 240 parts.

1736

象積四百八十。

Image accumulation: 480.

1737

冬至前後限五十九日；差二千一百九十五分；乘數十五。

Winter-solstice before-and-after limit: 59 days; difference 2,195 parts; multiplier: 15.

1738

夏至前後限百二十三日六十二分，小分二十二半；差四千八百八十分；乘數四。

Summer-solstice before-and-after limit: 123 days 62 parts, 22½ minor parts; difference 4,880 parts; multiplier: 4.

1739

陽城冬至晷丈二尺七寸一分半。

Yangcheng winter-solstice gnomon: 1 zhang 2 chi 7 cun 1½ fen.

1740

夏至晷尺四寸七分，小分八十。

Summer-solstice gnomon: 4 chi 7 fen, 80 minor parts.

1741

交終分三十六萬七千三百六十四，秒九千六百七十三。

Crossing completion parts: 367,364, seconds 9,673.

1742

交終日二十七，餘二千八百六十四，秒九千六百七十三；約餘二千一百二十二。

Crossing completion day: 27, remainder 2,864, seconds 9,673; Reduced remainder: 2,122.

1743

交中日十三，餘八千一百八十二，秒四千八百三十六半；約餘六千六十一。

Crossing mid-day: 13, remainder 8,182, seconds 4,836½; Reduced remainder: 6,061.

1744

朔差日二，餘四千二百九十八，秒三百二十七；約餘三千一百八十四。

New-moon difference day: 2, remainder 4,298, seconds 327; Reduced remainder: 3,184.

1745

望策日十四，餘萬三百三十一，秒五千；約餘七千六百五十三。

Full-moon divination day: 14, remainder 10,331, seconds 5,000; Reduced remainder: 7,653.

1746

交限日十二，餘六千三十三，秒四千六百七十三；約餘四千四百六十九。

Crossing limit day: 12, remainder 6,033, seconds 4,673; Reduced remainder: 4,469.

1747

望差日一，餘二千一百四十九，秒百六十三半；約餘千五百九十二。

Full-moon difference day: 1, remainder 2,149, seconds 163½; Reduced remainder: 1,592.

1748

交率二百六十二。

Crossing rate: 262.

1749

交數三千三百五十。

Crossing number: 3,350.

1750

交終三百六十三度七十三分，小分六十四。

Crossing completion: 363° 73 parts, 64 minor parts.

1751

轉終三百七十四度二十八分。

Rotation completion: 374° 28 parts.

1752

半交百八十一度八十六分，小分八十二。

Half-crossing: 181° 86 parts, 82 minor parts.

1753

一象九十度，九十三分，小分四十一。

One quadrant: 90°, 93 parts, 41 minor parts.

1754

去交度乘數十一，除數八千六百三十二。

Distance-from-crossing degree multiplier: 11, divisor: 8,632.

1755

秒母一萬。

Second mother: 10,000.

1756

歲星

Jupiter

1757

終率五百三十八萬四千九百六十二，秒十一。

Completion rate: 5,384,962, seconds 11.

1758

平合日三百九十八，餘萬一千九百六十二，秒十一；約餘八千八百六十一。

Mean conjunction day: 398, remainder 11,962, seconds 11; Reduced remainder: 8,861.

1759

盈限二百五度。

Surplus limit: 205°.

1760

盈畫十七度八分，秒三十三。

Surplus daytime: 17° 8 parts, seconds 33.

1761

縮限百六十度二十五分，秒六十三太。

Contraction limit: 160° 25 parts, seconds 63 greater.

1762

縮畫十三度三十五分，秒四十七。

Contraction daytime: 13° 35 parts, seconds 47.

1763

歲差百三十三，秒九十二半。

Year difference: 133, seconds 92½.

1764

畫數

Daytime count

1765

損益

Increase-decrease

1766

盈差積

Surplus-difference accumulation

1767

損益

Increase-decrease

1768

縮差積

Contraction-difference accumulation

1769

初

Initial

1770

益百九十

Increase rate: 190

1771

盈初

Surplus initial

1772

益九十

Increase rate: 90

1773

縮初

Contraction initial

1774

二

2

1775

益百八十

Increase rate: 180

1776

盈一度九十

Surplus: 1° 90

1777

益百七十

Increase rate: 170

1778

縮九十

Contraction: 90

1779

三

3

1780

益百五十

Increase rate: 150

1781

盈三度七十

Surplus: 3° 70

1782

益二百一十

Increase rate: 210

1783

縮二度六十

Contraction: 2° 60

1784

四

4

1785

益百四十

Increase rate: 140

1786

盈五度二十

Surplus: 5° 20

1787

益百六十

Increase rate: 160

1788

縮四度七十

Contraction: 4° 70

1789

五

5

1790

益七十

Increase rate: 70

1791

盈六度六十

Surplus: 6° 60

1792

益八十

Increase rate: 80

1793

縮七度三十

Contraction: 7° 30

1794

六

6

1795

益四十五

Increase rate: 45

1796

盈七度三十

Surplus: 7° 30

1797

益四十

Increase rate: 40

1798

縮七度十

Contraction: 7° 10

1799

七

7

1800

損四十五

Decrease rate: 45

1801

盈七度七十五

Surplus: 7° 75

1802

益十五

Increase rate: 15

1803

縮七度五十

Contraction: 7° 50

1804

八

8

1805

損百四十五

Decrease rate: 145

1806

盈七度三十

Surplus: 7° 30

1807

益十

Increase rate: 10

1808

縮七度六十五

Contraction: 7° 65

1809

九

9

1810

損八十五

Decrease rate: 85

1811

盈五度八十五

Surplus: 5° 85

1812

損十

Decrease rate: 10

1813

縮七度七十五

Contraction: 7° 75

1814

十

10

1815

損二百

Decrease rate: 200

1816

盈五度

Surplus: 5°

1817

損二百六十五

Decrease rate: 265

1818

縮七度六十五

Contraction: 7° 65

1819

十一

11

1820

損百六十

Decrease rate: 160

1821

盈三度

Surplus: 3°

1822

損二百六十

Decrease rate: 260

1823

縮五度

Contraction: 5°

1824

十二

12

1825

損百四十

Decrease rate: 140

1826

盈一度四十

Surplus: 1° 40

1827

損二百四十

Decrease rate: 240

1828

縮二度四十

Contraction: 2° 40

1829

熒惑

Mars

1830

終率千五十二萬八千九百一十六，秒九十一。

Completion rate: 10,528,916, seconds 91.

1831

平合日七百七十九，餘萬二千四百一十六，秒九十一；約餘九千一百九十八。

Mean conjunction day: 779, remainder 12,416, seconds 91; Reduced remainder: 9,198.

1832

盈限百九十六度八十分。

Surplus limit: 196° 80 parts.

1833

盈畫十六度四十分。

Surplus daytime: 16° 40 parts.

1834

縮限百六十八度四十五分，秒六十三太。

Contraction limit: 168° 45 parts, seconds 63 greater.

1835

縮畫十四度三分，秒八十。

Contraction daytime: 14° 3 parts, seconds 80.

1836

歲差百三十三，秒四十六。

Year difference: 133, seconds 46.

1837

畫數

Daytime count

1838

損益

Increase-decrease

1839

盈差積

Surplus-difference accumulation

1840

損益

Increase-decrease

1841

縮差積

Contraction-difference accumulation

1842

初

Initial

1843

益千二百一十

Increase rate: 1,210

1844

盈初

Surplus initial

1845

益三百九十六

Increase rate: 396

1846

縮初

Contraction initial

1847

二

2

1848

益八百一十二

Increase rate: 812

1849

盈十二度十三

Surplus: 12° 13

1850

益四百四十一

Increase rate: 441

1851

縮三度九十六

Contraction: 3° 96

1852

三

3

1853

益四百七十三

Increase rate: 473

1854

盈二十度二十五

Surplus: 20° 25

1855

益四百五十七

Increase rate: 457

1856

縮八度三十七

Contraction: 8° 37

1857

四

4

1858

益二百二

Increase rate: 202

1859

盈二十四度九十八

Surplus: 24° 98

1860

益四百四十八

Increase rate: 448

1861

縮十二度九十四

Contraction: 12° 94

1862

五

5

1863

損十六

Decrease rate: 16

1864

盈二十七度

Surplus: 27°

1865

益四百五

Increase rate: 405

1866

縮十七度四十二

Contraction: 17° 42

1867

六

6

1868

損二百一十四

Decrease rate: 214

1869

盈二十六度八十四

Surplus: 26° 84

1870

益三百二十三

Increase rate: 323

1871

縮二十一度四十七

Contraction: 21° 47

1872

七

7

1873

損三百二十三

Decrease rate: 323

1874

盈二十四度七十

Surplus: 24° 70

1875

益二百一十四

Increase rate: 214

1876

縮二十四度七十

Contraction: 24° 70

1877

八

8

1878

損四百五

Decrease rate: 405

1879

盈二十一度四十七

Surplus: 21° 47

1880

益十六

Increase rate: 16

1881

縮二十六度八十四

Contraction: 26° 84

1882

九

9

1883

損四百四十八

Decrease rate: 448

1884

盈十七度四十二

Surplus: 17° 42

1885

損二百二

Decrease rate: 202

1886

縮二十七度

Contraction: 27°

1887

十

10

1888

損四百五十七

Decrease rate: 457

1889

盈十二度九十四

Surplus: 12° 94

1890

損四百七十三

Decrease rate: 473

1891

縮二十四度九十八

Contraction: 24° 98

1892

十一

11

1893

損四百四十一

Decrease rate: 441

1894

盈八度三十七

Surplus: 8° 37

1895

損八百一十二

Decrease rate: 812

1896

縮二十度二十五

Contraction: 20° 25

1897

十二

12

1898

損三百九十六

Decrease rate: 396

1899

盈三度九十六

Surplus: 3° 96

1900

損千二百一十三

Decrease rate: 1,213

1901

縮十二度十三

Contraction: 12° 13

1902

鎮星

Saturn

1903

終率五百一十萬四千八十四，秒五十四。

Completion rate: 5,104,084, seconds 54.

1904

平合日三百七十八，餘千八十四，秒五十四；約餘八百三。

Mean conjunction day: 378, remainder 1,084, seconds 54; Reduced remainder: 803.

1905

盈限百八十二度六十二分，秒六十三太。

Surplus limit: 182° 62 parts, seconds 63 greater.

1906

盈畫十五度二十二分。

Surplus daytime: 15° 22 parts.

1907

縮限百八十二度六十三分。

Contraction limit: 182° 63 parts.

1908

縮畫十五度二十二分。

Contraction daytime: 15° 22 parts.

1909

歲差百三十二，秒九十四。

Year difference: 132, seconds 94.

1910

畫數

Daytime count

1911

損益

Increase-decrease

1912

盈差損

Surplus-difference decrease

1913

損益

Increase-decrease

1914

縮差積

Contraction-difference accumulation

1915

初

Initial

1916

益百

Increase rate: 100

1917

盈初

Surplus initial

1918

益三百

Increase rate: 300

1919

縮初

Contraction initial

1920

二

2

1921

益百三十

Increase rate: 130

1922

盈一度

Surplus: 1°

1923

益二百二十五

Increase rate: 225

1924

縮三度

Contraction: 3°

1925

三

3

1926

益百七十

Increase rate: 170

1927

盈二度三十

Surplus: 2° 30

1928

益二百

Increase rate: 200

1929

縮五度二十五

Contraction: 5° 25

1930

四

4

1931

益二百二十

Increase rate: 220

1932

盈四度

Surplus: 4°

1933

益五十

Increase rate: 50

1934

縮七度二十五

Contraction: 7° 25

1935

五

5

1936

益百二十

Increase rate: 120

1937

盈六度二十

Surplus: 6° 20

1938

損三十五

Decrease rate: 35

1939

縮七度七十五

Contraction: 7° 75

1940

六

6

1941

益三十五

Increase rate: 35

1942

盈七度四十

Surplus: 7° 40

1943

損二十

Decrease rate: 20

1944

縮七度四十

Contraction: 7° 40

1945

七

7

1946

損三十五

Decrease rate: 35

1947

盈七度七十五

Surplus: 7° 75

1948

損十五

Decrease rate: 15

1949

縮七度二十

Contraction: 7° 20

1950

八

8

1951

損百二十

Decrease rate: 120

1952

盈七度四十

Surplus: 7° 40

1953

損五

Decrease rate: 5

1954

縮七度五

Contraction: 7° 5

1955

九

9

1956

損二百二十

Decrease rate: 220

1957

盈六度二十

Surplus: 6° 20

1958

損百六十

Decrease rate: 160

1959

縮七度

Contraction: 7°

1960

十

10

1961

損百七十

Decrease rate: 170

1962

盈四度

Surplus: 4°

1963

損百七十

Decrease rate: 170

1964

縮五度四十

Contraction: 5° 40

1965

十一

11

1966

損百三十

Decrease rate: 130

1967

盈二度三十

Surplus: 2° 30

1968

損百八十

Decrease rate: 180

1969

縮三度七十

Contraction: 3° 70

1970

十二

12

1971

損百

Decrease rate: 100

1972

盈一度

Surplus: 1°

1973

損百九十

Decrease rate: 190

1974

縮一度九十

Contraction: 1° 90

1975

太白

Venus

1976

終率七百八十八萬二千六百四十八，秒七十六。

Completion rate: 7,882,648, seconds 76.

1977

平合日五百八十三，餘萬二千一百四十八，秒七十六；約餘八千九百九十九。

Mean conjunction day: 583, remainder 12,148, seconds 76; Reduced remainder: 8,999.

1978

再合日二百九十一，餘萬二千八百二十四，秒三十八；約餘九千五百。

Second conjunction day: 291, remainder 12,824, seconds 18; Reduced remainder: 9,500.

1979

盈限百九十七度十六分。

Surplus limit: 197° 16 parts.

1980

盈畫十六度四十三分。

Surplus daytime: 16° 43 parts.

1981

縮限百六十八度九分，秒六十三太。

Contraction limit: 168° 9 parts, seconds 63 greater.

1982

縮畫十四度，秒八十。

Contraction daytime: 14°, seconds 80.

1983

歲差百三十四，秒三十六。

Year difference: 134, seconds 36.

1984

畫數

Daytime count

1985

損益

Increase-decrease

1986

盈差積

Surplus-difference accumulation

1987

損益

Increase-decrease

1988

縮差積

Contraction-difference accumulation

1989

初

Initial

1990

益百八十三

Increase rate: 183

1991

盈初

Surplus initial

1992

益六十四

Increase rate: 64

1993

縮初

Contraction initial

1994

二

2

1995

益百五十

Increase rate: 150

1996

盈一度八十三

Surplus: 1° 83

1997

益百一十九

Increase rate: 119

1998

縮六十四

Contraction: 64

1999

三

3

2000

益百一十七

Increase rate: 117

2001

盈三度三十三

Surplus: 3° 33

2002

益百二

Increase rate: 102

2003

縮一度八十三

Contraction: 1° 83

2004

四

4

2005

益八十三

Increase rate: 83

2006

盈四度五十

Surplus: 4° 50

2007

益百

Increase rate: 100

2008

縮二度八十五

Contraction: 2° 85

2009

五

5

2010

益五十

Increase rate: 50

2011

盈五度三十三

Surplus: 5° 33

2012

益九十

Increase rate: 90

2013

縮三度八十五

Contraction: 3° 85

2014

六

6

2015

益七十

Increase rate: 70

2016

盈五度八十三

Surplus: 5° 83

2017

益七十三

Increase rate: 73

2018

縮四度七十五

Contraction: 4° 75

2019

七

7

2020

損十七

Decrease rate: 17

2021

盈六度

Surplus: 6°

2022

益四十五

Increase rate: 45

2023

縮五度四十八

Contraction: 5° 48

2024

八

8

2025

損五十

Decrease rate: 50

2026

盈五度八十三

Surplus: 5° 83

2027

益十五

Increase rate: 15

2028

縮五度九十三

Contraction: 5° 93

2029

九

9

2030

損八十三

Decrease rate: 83

2031

盈五度三十三

Surplus: 5° 33

2032

益五十一

Increase rate: 51

2033

縮六度八

Contraction: 6° 8

2034

十

10

2035

損百一十七

Decrease rate: 117

2036

盈四度五十

Surplus: 4° 50

2037

損百五

Decrease rate: 105

2038

縮五度五十七

Contraction: 5° 57

2039

十一

11

2040

損百五十

Decrease rate: 150

2041

盈三度三十三

Surplus: 3° 33

2042

損百八十

Decrease rate: 180

2043

縮四度五十二

Contraction: 4° 52

2044

十二

12

2045

損百八十三

Decrease rate: 183

2046

盈一度八十三

Surplus: 1° 83

2047

損二百七十二

Decrease rate: 272

2048

縮二度七十二

Contraction: 2° 72

2049

辰星

Mercury

2050

終率百五十六萬四千三百七十八，秒九十七。

Completion rate: 1,564,378, seconds 97.

2051

平合日百一十五，餘萬一千八百七十八，秒九十七；約餘八千八百。

Mean conjunction day: 115, remainder 11,878, seconds 97; Reduced remainder: 8,800.

2052

再合日五十七，餘萬二千六百八十九，秒四十八半；約餘九千四百。

Second conjunction day: 57, remainder 12,689, seconds 48½; Reduced remainder: 9,400.

2053

盈限百八十二度六十三分。

Surplus limit: 182° 63 parts.

2054

盈畫十五度二十二分。

Surplus daytime: 15° 22 parts.

2055

縮限百八十二度六十二分，秒六十三太。

Contraction limit: 182° 62 parts, seconds 63 greater.

2056

縮畫十五度二十一分，秒八十九。

Contraction daytime: 15° 21 parts, seconds 89.

2057

歲差百三十三，秒六十四。

Year difference: 133, seconds 64.

2058

畫數

Daytime count

2059

損益

Increase-decrease

2060

盈差積

Surplus-difference accumulation

2061

損益

Increase-decrease

2062

縮差損

Contraction-difference decrease

2063

初

Initial

2064

益九十二

Increase rate: 92

2065

盈初

Surplus initial

2066

益九十二

Increase rate: 92

2067

縮初

Contraction initial

2068

二

2

2069

益七十五

Increase rate: 75

2070

盈九十二

Surplus: 92

2071

益七十五

Increase rate: 75

2072

縮九十二

Contraction: 92

2073

三

3

2074

益五十八

Increase rate: 58

2075

盈一度六十七

Surplus: 1° 67

2076

益五十八

Increase rate: 58

2077

縮一度六十七

Contraction: 1° 67

2078

四

4

2079

益四十一

Increase rate: 41

2080

盈二度二十五

Surplus: 2° 25

2081

益四十一

Increase rate: 41

2082

縮二度二十五

Contraction: 2° 25

2083

五

5

2084

益二十五

Increase rate: 25

2085

盈二度六十六

Surplus: 2° 66

2086

益二十五

Increase rate: 25

2087

縮二度六十六

Contraction: 2° 66

2088

六

6

2089

益九

Increase rate: 9

2090

盈二度九十一

Surplus: 2° 91

2091

益九

Increase rate: 9

2092

縮二度九十一

Contraction: 2° 91

2093

七

7

2094

損九

Decrease rate: 9

2095

盈三度

Surplus: 3°

2096

損九

Decrease rate: 9

2097

縮三度

Contraction: 3°

2098

八

8

2099

損二十五

Decrease rate: 25

2100

盈二度九十一

Surplus: 2° 91

2101

損二十五

Decrease rate: 25

2102

縮二度九十一

Contraction: 2° 91

2103

九

9

2104

損四十一

Decrease rate: 41

2105

盈二度六十六

Surplus: 2° 66

2106

損四十一

Decrease rate: 41

2107

縮二度六十六

Contraction: 2° 66

2108

十

10

2109

損五十八

Decrease rate: 58

2110

盈二度二十五

Surplus: 2° 25

2111

損五十八

Decrease rate: 58

2112

縮二度二十五

Contraction: 2° 25

2113

十一

11

2114

損七十五

Decrease rate: 75

2115

盈一度六十七

Surplus: 1° 67

2116

損七十五

Decrease rate: 75

2117

縮一度六十七

Contraction: 1° 67

2118

十二

12

2119

損九十二

Decrease rate: 92

2120

盈九十二

Surplus: 92

2121

損九十二

Decrease rate: 92

2122

縮九十二

Contraction: 92

2123

五星入變曆

Five planets enter mutation calendar

2124

星名

Star name

2125

變目

Mutation item

2126

常積日

Regular accumulated days

2127

常積度

Regular accumulated degrees

2128

加減

Add-subtract

2129

歲星

Jupiter

2130

晨見

Morning appearance

2131

十七日五十分

17 days 50 parts

2132

三度五十分

3° 50 parts

2133

用日躔差

Use daily motion difference

2134

前疾

Prior fast

2135

九十八日

98 days

2136

十八度五十分

18° 50 parts

2137

前遲

Prior slow

2138

百三十一日五十分

131 days 50 parts

2139

二十二度五十分

22° 50 parts

2140

前留

Prior station

2141

百五十八日

158 days

2142

減六十五度

Subtract 65°

2143

前退

Prior retrograde

2144

百九十九日七十五分

199 days 75 parts

2145

十六度七十五分

16° 75 parts

2146

減七十一度

Subtract 71°

2147

後退

Posterior retrograde

2148

二百四十日

240 days

2149

十一度

11°

2150

減八十二度五十分

Subtract 82° 50 parts

2151

後留

Posterior station

2152

二百六十七日五十分

267 days 50 parts

2153

減八十七度

Subtract 87°

2154

後遲

Posterior slow

2155

三百一日

301 days

2156

十五度

15°

2157

後疾

Posterior fast

2158

三百八十一日三十八分

381 days 38 parts

2159

三十度十二分半

30° 12½ parts

2160

用日躔差

Use daily motion difference

2161

夕合

Evening conjunction

2162

三百九十八日八十七分

398 days 87 parts

2163

三十三度六十二分半

33° 62½ parts

2164

用日躔差

Use daily motion difference

2165

熒惑

Mars

2166

晨見

Morning appearance

2167

七十二日

72 days

2168

五十五度

55°

2169

用日躔差

Use daily motion difference

2170

前疾

Prior fast

2171

百九十三日

193 days

2172

百三十五度

135°

2173

前次疾

Prior secondary fast

2174

二百八十七日

287 days

2175

百九十二度五十分

192° 50 parts

2176

前遲

Prior slow

2177

三百四十七日

347 days

2178

二百一十六度七十五分

216° 75 parts

2179

前留

Prior station

2180

三百六十日

360 days

2181

減百二十度

Subtract 120°

2182

前退

Prior retrograde

2183

三百九十日

390 days

2184

二百七度二十五分

207° 25 parts

2185

減百二十五度五十分

Subtract 125° 50 parts

2186

後退

Posterior retrograde

2187

四百二十日

420 days

2188

百九十七度七十五分

197° 75 parts

2189

減百三十度

Subtract 130°

2190

後留

Posterior station

2191

四百三十三日

433 days

2192

減百三十五度

Subtract 135°

2193

後遲

Posterior slow

2194

四百九十三日

493 days

2195

二百二十二度

222°

2196

後次疾

Posterior secondary fast

2197

五百八十七日

587 days

2198

二百七十九度五十分

279° 50 parts

2199

後疾

Posterior fast

2200

七百七日九十二分

707 days 92 parts

2201

三百五十九度六十二分

359° 62 parts

2202

用日躔差

Use daily motion difference

2203

夕合

Evening conjunction

2204

七百七十九日九十二分

779 days 92 parts

2205

四百一十四度六十二分

414° 62 parts

2206

用日躔差

Use daily motion difference

2207

鎮星

Saturn

2208

晨見

Morning appearance

2209

十九日

19 days

2210

二度

2°

2211

用日躔差

Use daily motion difference

2212

前疾

Prior fast

2213

七十九日

79 days

2214

八度

8°

2215

前遲

Prior slow

2216

百三日

103 days

2217

九度六十分

9° 60 parts

2218

前留

Prior station

2219

百四十日

140 days

2220

減百七十二度

Subtract 172°

2221

前退

Prior retrograde

2222

百八十九日

189 days

2223

六度四十二分

6° 42 parts

2224

減百七十度

Subtract 170°

2225

後退

Posterior retrograde

2226

二百三十八日

238 days

2227

三度二十四分

3° 24 parts

2228

減百七十六度

Subtract 176°

2229

後留

Posterior station

2230

二百七十五日

275 days

2231

減百八十二度

Subtract 182°

2232

後遲

Posterior slow

2233

二百九十九日

299 days

2234

四度八十四分

4° 84 parts

2235

後疾

Posterior fast

2236

三百五十九日八分

359 days 8 parts

2237

十度八十三分

10° 83 parts

2238

用日躔差

Use daily motion difference

2239

夕合

Evening conjunction

2240

三百七十八日八分

378 days 8 parts

2241

十二度八十三分

12° 83 parts

2242

用日躔差

Use daily motion difference

2243

太白

Venus

2244

夕見

Evening appearance

2245

四十二日

42 days

2246

五十三度

53°

2247

用日躔差

Use daily motion difference

2248

夕疾

Evening fast

2249

百四十二日

142 days

2250

百八十度五十分

180° 50 parts

2251

夕次疾

Evening secondary fast

2252

二百一十九日

219 days

2253

二百六十五度

265°

2254

夕遲

Evening slow

2255

二百六十八日

268 days

2256

三百一度五十分

301° 50 parts

2257

夕留退

Evening station retrograde

2258

二百八十五日

285 days

2259

二百九十六度

296°

2260

用日躔差

Use daily motion difference

2261

再合

Second conjunction

2262

二百九十二日

292 days

2263

二百九十二度

292°

2264

用日躔差

Use daily motion difference

2265

晨見

Morning appearance

2266

二百九十九日

299 days

2267

二百八十八度

288°

2268

用日躔差

Use daily motion difference

2269

晨退留

Morning retrograde station

2270

三百一十六日

316 days

2271

二百八十二度五十分

282° 50 parts

2272

晨遲

Morning slow

2273

三百六十五日

365 days

2274

三百一十九度五十分

319° 50 parts

2275

晨次疾

Morning secondary fast

2276

四百四十二日

442 days

2277

四百三度五十分

403° 50 parts

2278

晨疾

Morning fast

2279

五百四十一百九十分

541 days 90 parts

2280

五百三十度九十分

530° 90 parts

2281

用日躔差

Use daily motion difference

2282

晨伏合

Morning hidden conjunction

2283

五百八十三日九十分

583 days 90 parts

2284

三百八十三度九十分

383° 90 parts

2285

用日躔差

Use daily motion difference

2286

辰星

Mercury

2287

夕見

Evening appearance

2288

十七日

17 days

2289

三十四度

34°

2290

用日躔差

Use daily motion difference

2291

夕順留

Evening direct station

2292

四十七日

47 days

2293

六十四度

64°

2294

用日躔差

Use daily motion difference

2295

再合

Second conjunction

2296

五十八日

58 days

2297

五十八度

58°

2298

用日躔差

Use daily motion difference

2299

晨見

Morning appearance

2300

六十九日

69 days

2301

五十二度

52°

2302

用日躔差

Use daily motion difference

2303

晨留順

Morning station direct

2304

九十八日八十八分

98 days 88 parts

2305

八十一度八十八分

81° 88 parts

2306

用日躔差

Use daily motion difference

2307

晨伏合

Morning hidden conjunction

2308

百一十五日八十八分

115 days 88 parts

2309

百一十五度八十八分

115° 88 parts

2310

用日躔差

Use daily motion difference

2311

校勘記0.85em|columns=2

Collation notes for this chapter.

Cite this Chapter