1
志二十八
Treatises 28
2
時憲九
Calendar 9
3
凌犯視差新法下
Lower section of the new occultation-parallax method
4
求均數時差
Finding the mean-motion time correction
5
以本日太陽引數宮度分，滿三十秒進一分用。 用後編日躔均數時差表，察其所對之數，得均數時差，記加減號。 引數有零分者，用中比例求之。
Use this day's solar argument in mansions, degrees, and minutes, rounding up whenever thirty seconds complete a minute. Consult the appended table of mean-motion time corrections for daily solar motion, read off the corresponding value, and note whether it is to be added or subtracted. If the argument includes fractional minutes, interpolate proportionally.
6
求升度時差
Finding the ascension time correction
7
以本日太陽黃道實行宮度分，滿三十秒進一分用。 用後編日躔升度時差表，察其所對之數，得升度時差，記加減號。 實行有零分者，用中比例求之。
Use this day's solar true ecliptic longitude in mansions, degrees, and minutes, rounding up whenever thirty seconds complete a minute. Consult the appended table of ascension time corrections for daily solar motion, read off the corresponding value, and note whether it is to be added or subtracted. If true longitude includes fractional minutes, interpolate proportionally.
8
求時差總
Finding the total time correction
9
以均數時差與升度時差相加減，得時差總。 兩時差同為加或同為減者，則相加得時差總，加亦為加，減亦為減。 兩時差一為加一為減者，則相減得時差總，加數大為加，減數大為減。
Combine the mean-motion and ascension time corrections by addition or subtraction to obtain the total time correction. When both corrections share the same sign, add them; the total keeps that sign. When the signs differ, subtract the smaller magnitude from the larger; the total takes the sign of whichever correction is greater.
10
求凌犯用時
Finding the apparent time of occultation
11
置凌犯時刻，加減時差總，得凌犯用時。
Take the mean occultation moment, apply the total time correction, and obtain the apparent time of occultation.
12
求本時太陽黃道經度
Finding the solar ecliptic longitude at the given instant
13
以周日一千四百四十分為一率，本次日兩太陽實行相減帶秒減，足三十秒進一分用，有度化分。 為二率，凌犯時刻化分為三率，求得四率與本日太陽實行相加，得本時太陽黃道經度。
Use 1,440 minutes per sidereal day as the first ratio. Take the difference between today's and tomorrow's solar true longitudes, including seconds, rounding up at thirty seconds per minute and converting degrees to minutes as needed. That difference is the second ratio; convert the occultation moment to minutes as the third. Solve for the fourth ratio, add it to today's solar true longitude, and obtain the solar ecliptic longitude at the instant in question.
14
求本時春分距午時分
Finding the equinox distance from noon at the given instant
15
以本時太陽黃道經度，滿三十分進一度用。 察黃平象限表內右邊所列春分距午時分與凌犯用時相加，內減十二時，不足減，加二十四時減之。 得本時春分距午時分。 滿二十四時去之。
Use the solar ecliptic longitude at the instant, rounding up whenever thirty minutes complete a degree. From the ecliptic horizon-quadrant table, read the equinox distance from noon on the right, add the apparent occultation time, and subtract twelve hours; if the result would be negative, add twenty-four hours first. This gives the equinox distance from noon at the given instant. Reduce by twenty-four hours whenever the total exceeds a full day.
16
求本時黃白大距
Finding the great ecliptic–lunar distance at the given instant
17
以周日一千四百四十分為一率，本次日兩黃白大距相減為二率，凌犯時刻化分為三率，求得四率。 加減本日黃白大距，本日黃白大距大相減，小相加。 得本時黃白大距。
Use 1,440 minutes per sidereal day as the first ratio, the day-to-day change in great ecliptic–lunar distance as the second, and the occultation moment in minutes as the third; solve for the fourth ratio. Apply the fourth ratio to today's great ecliptic–lunar distance, subtracting when today's value is larger and adding when it is smaller. This gives the great ecliptic–lunar distance at the given instant.
18
求本時月距正交
Finding the Moon's distance from the node at the given instant
19
以周日一千四百四十分為一率，本次日兩月距正交相減化秒為二率，凌犯時刻化分為三率，求得四率。 收作度分秒，與本日月距正交相加，得本時月距正交。
Use 1,440 minutes per sidereal day as the first ratio, the day-to-day change in lunar node distance (in seconds) as the second, and the occultation moment in minutes as the third; solve for the fourth ratio. Reduce the result to degrees, minutes, and seconds, add it to today's lunar node distance, and obtain the Moon's distance from the node at the instant in question.
20
求太陰實緯
Finding the Moon's true latitude
21
以半徑為一率，本時黃白大距正弦為二率，本時月距正交正弦為三率，如本時月距正交過三宮者，與六宮減，過六宮者減六宮； 過九宮者，與十二宮減，用其餘。 求得四率，為太陰實緯正弦，檢表得太陰實緯，記南北號。 本時月距正交初宮至五宮為北，六宮至十一宮為南。 如本時月距正交恰在初宮、六宮者，則無實緯。 恰在三宮、九宮者，則本時黃白大距即實緯度，三宮為北，九宮為南。
Use the radius as the first ratio, the sine of the great ecliptic–lunar distance at the instant as the second, and the sine of the lunar node distance as the third. If the node distance lies past the third mansion, subtract it from six mansions; if past the sixth, subtract six mansions; if past the ninth mansion, subtract from twelve mansions and use the remainder. Solve for the fourth ratio as the sine of lunar true latitude, look up the latitude in the table, and record whether it is north or south. At the instant in question, node distances in mansions one through five indicate north latitude; six through eleven indicate south. If the node distance stands exactly at the first or sixth mansion, the Moon has no true latitude. At the third or ninth mansion exactly, the great ecliptic–lunar distance at that instant equals the true latitude—north at the third mansion, south at the ninth.
22
求黃平象限及限距地高
Finding the ecliptic horizon quadrant and the quadrant's altitude above the horizon
23
以本時春分距午時分，察黃平象限表內，取其與時分相近者所對之數錄之，得黃平象限。 隨看左邊之限距地高錄之，得限距地高。
Using the equinox distance from noon at the instant, consult the ecliptic horizon-quadrant table, read the value nearest in time, and obtain the ecliptic horizon quadrant. Then read the quadrant's altitude above the horizon on the left and record it.
24
求星經度
Finding the star's ecliptic longitude
25
按所取之星，察儀象考成卷二十六表內所載本星之黃道經度，加入歲差，表以乾隆九年甲子為元，至道光十四年甲午，計九十年，應加歲差一度十六分三十秒，以後每年遞加歲差五十一秒。 得本年星經度。
For the selected star, read its ecliptic longitude from the table in fascicle 26 of the Yixiang Kaocheng and apply precession. The table uses Qianlong 9 (jiazi) as epoch; by Daoguang 14 (jiawu), ninety years have elapsed, requiring an addition of 1°16′30″, with 51″ added for each subsequent year. This gives the star's ecliptic longitude for the current year.
26
如求五星經度，則以周日一千四百四十分為一率，凌犯時刻化分為二率，一日星實行為三率，以本次日兩實行相減，得一日星實行。 求得四率，為距時星實行。 與本日星經度相加減，順行加，退行減。 得本時星經度。
For a planet's longitude, use 1,440 minutes per sidereal day as the first ratio, the occultation moment in minutes as the second, and the planet's daily true motion as the third—the last found by subtracting the two daily true motions. Solve for the fourth ratio as the planet's true motion over the elapsed interval. Apply it to today's stellar longitude, adding in direct motion and subtracting in retrograde. This gives the star's ecliptic longitude at the given instant.
27
求星緯度
Finding the star's ecliptic latitude
28
按所取之星，察儀象考成卷二十六表內所載本星之黃道緯度錄之，無歲差。 記南北號。
For the selected star, read its ecliptic latitude from the same table in fascicle 26 of the Yixiang Kaocheng; precession does not affect latitude. Record whether it is north or south.
29
如求五星緯度，則以周日一千四百四十分為一率，凌犯時刻化分為二率，一日星緯較為三率，本次日兩緯度同為南或同為北者，則相減得星緯較。 一為南一為北者，則相加得星緯較。 求得四率。 與本日星緯度相加減，本日緯度大相減，本日緯度小相加。 若相加為三率者，所得四率必與本日緯度相減，仍依本日南北號。 如所得四率大於本日星緯，則以所得四率轉減本日星緯，其南北號應與次日同。 得本時星緯度，記南北號。
For a planet's latitude, use 1,440 minutes per sidereal day as the first ratio, the occultation moment in minutes as the second, and the daily latitude change as the third—found by subtraction when both days' latitudes lie on the same side of the ecliptic. When one day is south and the other north, add the latitudes to obtain the daily latitude change. Solve for the fourth ratio. Apply it to today's stellar latitude, subtracting when today's latitude is larger and adding when it is smaller. When the daily latitude change was found by addition, subtract the fourth ratio from today's latitude while keeping today's north–south designation. If the fourth ratio exceeds today's stellar latitude, reverse the subtraction and assign the north–south sign of the following day. This gives the star's ecliptic latitude at the given instant; record whether it is north or south.
30
求月距限
Finding the Moon's distance from the quadrant
31
以星經度與黃平象限相減，得月距限，記東西號。 星經度大為限東，小為限西。 如星經度與黃平象限一在三宮內，一在九宮外，應將三宮內者加十二宮減之。 所得月距限太陰實緯南在六十度內，實緯北在八十度內者，不必求地平限度。 如緯南過六十度，緯北過八十度，則求地平限度。
Subtract the ecliptic horizon quadrant from the star's longitude to obtain the Moon's quadrant distance, noting whether it lies east or west. A greater stellar longitude places the Moon east of the quadrant; a lesser one places it west. If one value lies within the third mansion and the other beyond the ninth, add twelve mansions to the inner value before subtracting. When the resulting quadrant distance falls with lunar latitude south within 60° or north within 80°, the horizon limit need not be computed. If southern latitude exceeds 60° or northern latitude exceeds 80°, compute the horizon limit.
32
求距限差
Finding the quadrant-distance correction
33
以限距地高及太陰實緯度分，察距限差表內縱橫所對之數錄之，得距限差，記加減號。 太陰實緯南減北加。
Using the quadrant's altitude and the Moon's true latitude, read the intersecting value in the quadrant-distance correction table, and note whether to add or subtract. Subtract the correction for southern latitude; add it for northern latitude.
34
求地平限度
Finding the horizon limit
35
置九十度，加減距限差，得地平限度。
Start from 90° and apply the quadrant-distance correction to obtain the horizon limit.
36
以地平限度內減最小視經差八度五十五分一十七秒，得視地平限度，如月距限大於視地平限度者，為月在地平下，即不必算。 因太陰距地最近，其視行隨時不同，故取最小視經差以定視限。 乃按最小限距地高，月在黃道極南，求得最小黃經高弧交角二十六度六分二十四秒。 以最小太陰地半徑差及最速月實行，求得最小距分三十七分八秒。 變赤道度得九度一十七分，求其相當最小黃道度為八度三十一分三十四秒。 再加最小東西差二十三分四十三秒，得最小視經差八度五十五分一十七秒。 然月在最高時，地半徑差最小，而其月實行必遲，則距分轉大。 今俱取其最小者，恐有遺漏耳。
Subtract the minimum apparent longitude difference of 8°55′17″ from the horizon limit to obtain the apparent horizon limit. If the Moon's quadrant distance exceeds this value, the Moon is below the horizon and no further calculation is required. Because the Moon is nearest Earth and its apparent motion changes constantly, the minimum apparent longitude difference is used to set the apparent limit. Using the minimum quadrant altitude with the Moon at the southern ecliptic pole yields a minimum ecliptic-longitude and altitude-arc intersection angle of 26°6′24″. From the minimum lunar horizontal parallax and the fastest lunar true motion, the minimum separation distance of 37′8″ is found. Converting to equatorial measure gives 9°17′, which corresponds to a minimum ecliptic value of 8°31′34″. Adding the minimum east–west difference of 23′43″ yields the minimum apparent longitude difference of 8°55′17″. Yet at lunar culmination the horizontal parallax is smallest while true motion is slowest, which would make the separation distance larger. Taking every factor at its minimum may therefore risk missing some occultations.
37
求距極分邊
Finding the polar-distance segment
38
以半徑為一率，月距限餘弦為二率，限距地高正切為三率，求得四率，為距極分邊正切，檢表得距極分邊。
Use the radius as the first ratio, the cosine of the Moon's quadrant distance as the second, and the tangent of the quadrant's altitude as the third. Solve for the fourth ratio as the tangent of the polar-distance segment and look up the segment in the table.
39
求月距黃極
Finding the Moon's distance from the ecliptic pole
40
置九十度，加減太陰實緯，南加北減。 得月距黃極。
Start from 90° and apply the Moon's true latitude, adding for south and subtracting for north. This gives the Moon's distance from the ecliptic pole.
41
求距月分邊
Finding the lunar-distance segment
42
以月距黃極內減距極分邊，得距月分邊。
Subtract the polar-distance segment from the Moon's ecliptic-pole distance to obtain the lunar-distance segment.
43
求黃經高弧交角
Finding the ecliptic-longitude and altitude-arc intersection angle
44
以距月分邊正弦為一率，距極分邊正弦為二率，月距限正切為三率，求得四率，為黃經高弧交角正切，檢表得黃經高弧交角。 若月距限為初度，是太陰正當黃平象限，則黃經與高弧合，無黃經高弧交角。
Use the sine of the lunar-distance segment as the first ratio, the sine of the polar-distance segment as the second, and the tangent of the Moon's quadrant distance as the third. Solve for the fourth ratio as the tangent of the intersection angle and look up the angle in the table. If the Moon's quadrant distance is zero—when the Moon lies exactly on the ecliptic horizon quadrant—ecliptic longitude and altitude coincide and no intersection angle arises.
45
求本次日月實引
Finding this day's and the next day's true lunar argument
46
以本日月引數加減本日初均，得本日月實引，以次日月引數加減次日初均，得次日月實引。
Apply each day's first equation to that day's lunar argument to obtain the true lunar argument for today and tomorrow respectively.
47
求本時月實引
Finding the true lunar argument at the given instant
48
以周日一千四百四十分為一率，凌犯時刻化分為二率，本次日兩實引相減帶秒減，足三十秒進一分用，度化分。 為三率，求得四率。 收為度分，與本日月實引相加，得本時月實引。
Use 1,440 minutes per sidereal day as the first ratio and the occultation moment in minutes as the second. Take the difference between today's and tomorrow's true arguments, including seconds, rounding at thirty seconds per minute and converting degrees to minutes. That difference is the third ratio; solve for the fourth. Reduce the result to degrees and minutes, add it to today's true lunar argument, and obtain the true lunar argument at the instant in question.
49
求本時本天心距地
Finding the geocentric distance of the lunar apogee at the given instant
50
以周日一千四百四十分為一率，凌犯時刻化分為二率，本次日兩本天心距地數相減為三率，求得四率。 與本日本天心距地數相加減，本日本天心距地數大相減，小相加。 得本時本天心距地。
Use 1,440 minutes per sidereal day as the first ratio, the occultation moment in minutes as the second, and the day-to-day change in the geocentric distance of the lunar apogee as the third; solve for the fourth ratio. Apply the fourth ratio to today's geocentric apogee distance, subtracting when today's value is larger and adding when it is smaller. This gives the geocentric distance of the lunar apogee at the given instant.
51
求距地較
Finding the geocentric-distance difference
52
以本時本天心距地內減距地小數，得距地較。
Subtract the tabulated geocentric-distance constant from the apogee's geocentric distance at the instant to obtain the geocentric-distance difference.
53
求月距天頂
Finding the Moon's distance from the zenith
54
以黃經高弧交角正弦為一率，限距地高正弦為二率，月距限正弦為三率，求得四率為月距天頂正弦，檢表得月距天頂。 若無黃經高弧交角，則以月距黃極內減限距地高即得。
Use the sine of the intersection angle as the first ratio, the sine of the quadrant's altitude as the second, and the sine of the Moon's quadrant distance as the third. Solve for the fourth ratio as the sine of the zenith distance and look up the Moon's distance from the zenith in the table. Without an intersection angle, subtract the quadrant's altitude from the Moon's ecliptic-pole distance.
55
求太陰地半徑差
Finding the lunar horizontal parallax
56
以本時月實引滿三十分，進一度用。 及本時本天心距地，察後編交食太陰地半徑差表內所對之數，即太陰地半徑差。 如本時本天心距地有遠近者，以距地較比例求之。
Use the true lunar argument at the instant, rounding up whenever thirty minutes complete a degree. Together with the apogee's geocentric distance at the instant, read the corresponding value in the appended eclipse lunar horizontal-parallax table. If the apogee distance at the instant differs from the tabulated value, interpolate using the geocentric-distance difference.
57
求本時高下差
Finding the altitude difference at the given instant
58
以半徑為一率，月距天頂正弦為二率，太陰地半徑差為三率，若推凌犯五星，除土、木二星無地半徑差外，火、金、水三星皆有地半徑差。 乃看星引數，自十宮十五度至一宮十五度，為最高限。 自一宮十五度至四宮十五度，自七宮十五度至十宮十五度，為中距限。 自四宮十五度至七宮十五度，為最卑限。 以星引數所當之限，察其本星最大地半徑差，與太陰地半徑差相減，得星月地平高下差，為三率。 求得四率，即本時高下差。
Use the radius as the first ratio, the sine of the Moon's zenith distance as the second, and the lunar horizontal parallax as the third. For planetary occultations, Mars, Venus, and Mercury all have horizontal parallax, unlike Saturn and Jupiter. Inspect the planet's argument: from 15° in the tenth mansion through 15° in the first mansion marks the highest limit. From 15° in the first through fourth mansions, and from 15° in the seventh through tenth mansions, marks the middle-distance limit. From 15° in the fourth through seventh mansions marks the lowest limit. For the limit matching the planet's argument, read its maximum horizontal parallax, subtract the lunar parallax, and use the planet–Moon horizon altitude difference as the third ratio. Solve for the fourth ratio to obtain the altitude difference at the given instant.
59
求東西差
Finding the east–west difference
60
以半徑為一率，黃經高弧交角正弦為二率，本時高下差為三率，求得四率，即東西差。 如無交角，則無東西差，高下差即南北差，凌犯用時即凌犯視時。
Use the radius as the first ratio, the sine of the intersection angle as the second, and the altitude difference at the instant as the third; the fourth ratio is the east–west difference. Without an intersection angle there is no east–west difference; the altitude difference serves as the north–south difference, and apparent occultation time equals apparent occultation moment.
61
求南北差
Finding the north–south difference
62
以半徑為一率，黃經高弧交角餘弦為二率，本時高下差為三率，求得四率，即南北差。
Use the radius as the first ratio, the cosine of the intersection angle as the second, and the altitude difference at the instant as the third; the fourth ratio is the north–south difference.
63
求太陰視緯
Finding the Moon's apparent latitude
64
以太陰實緯與南北差相加減，得太陰視緯，記南北號。 緯南相加仍為南，緯北相減仍為北，如南北差大，則反減變北為南。
Apply the north–south difference to the Moon's true latitude to obtain apparent latitude, noting whether it is north or south. Southern latitude remains south when added to; northern remains north when subtracted from. If the north–south difference is large enough, reverse the operation and flip the north–south designation.
65
求太陰距星
Finding the Moon's distance from the star
66
以太陰視緯與星緯相加減，得太陰距星，記月在上下號。 如兩緯度同為北或同為南者則相減； 月緯大，北為在上，南為在下； 月緯小，北為在下，南為在上。 兩緯度一為南一為北者則相加。 月緯北為在上，月緯南為在下。 若兩緯度相同，減盡無餘，為月掩星，凡相距在一度以內者用； 過一度外者，為緯大，不用，即不必算。
Combine the Moon's apparent latitude with the star's latitude to obtain the lunar–stellar separation, noting whether the Moon lies above or below the star. When both latitudes lie on the same side of the ecliptic, subtract; if lunar latitude is greater, north places the Moon above and south below; if lunar latitude is smaller, north places the Moon below and south above. When the latitudes lie on opposite sides of the ecliptic, add them. Northern lunar latitude places the Moon above the star; southern places it below. If the latitudes are equal and cancel completely, the Moon occults the star—used when the separation is within one degree; beyond one degree the latitude is too great and no further calculation is required.
67
求太陰實行
Finding the Moon's true motion
68
以本時月實引滿三十分，進一度用。 及本時本天心距地，察後編交食太陰實行表內所對之數，得太陰實行。 如本時本天心距地有遠近者，以距地較比例求之。
Use the true lunar argument at the instant, rounding up whenever thirty minutes complete a degree. Together with the apogee's geocentric distance at the instant, read the corresponding value in the appended eclipse lunar true-motion table. If the apogee distance at the instant differs from the tabulated value, interpolate using the geocentric-distance difference.
69
求距分
Finding the separation distance
70
以太陰實行為一率，東西差為二率，一小時化作三千六百秒為三率，求得四率，即距分，記加減號。 月距限東為減，月距限西為加。
Use lunar true motion as the first ratio, the east–west difference as the second, and 3,600 seconds per hour as the third; solve for the separation distance and note whether to add or subtract. Subtract when the Moon lies east of the quadrant; add when west.
71
求凌犯視時
Finding the apparent time of occultation
72
置凌犯用時，加減距分，得凌犯視時，如凌犯用時不足減距分，加二十四時減之，所得凌犯視時為在前一日； 如加滿二十四時去之，所得凌犯視時為在次日。 時刻在日出前日入後者用； 在日出後日入前者，即為在晝，不用。
Take the apparent occultation moment and apply the separation distance to obtain the apparent time of occultation. If subtraction would go negative, add twenty-four hours first—the result then falls on the previous day; if addition exceeds twenty-four hours, reduce by a full day—the result then falls on the following day. Use only times before sunrise or after sunset; between sunrise and sunset—that is, during daylight—the result is not used.
73
如月在緯南，月距限過六十度，及月在緯北，月距限過七十度者，須用下法求之。
When the Moon's southern latitude exceeds 60° of quadrant distance, or northern latitude exceeds 70°, apply the following procedure.
74
求視時春分距午時分
Finding the equinox distance from noon at apparent time
75
置本時春分距午，加減距分，得視時春分距午。 如本時春分距午不足減距分者，加二十四時減之； 若相加過二十四時者去之。
Take the equinox distance from noon at the given instant and apply the separation distance to obtain the value at apparent time. If subtraction would go negative, add twenty-four hours first; if the sum exceeds twenty-four hours, reduce by a full day.
76
求視時黃平象限
Finding the ecliptic horizon quadrant at apparent time
77
以視時春分距午時分，察黃平象限表內，取其與時分相近者，所對之數錄之，即得視時黃平象限。
Using the equinox distance from noon at apparent time, consult the ecliptic horizon-quadrant table and read the value nearest in time.
78
求視時月距限
Finding the Moon's quadrant distance at apparent time
79
置星經度，與視時黃平象限相減，得視時月距限，其度小於地平限度者用； 若大於地平限度者，為月在地平下，不用。
Take the star's longitude, subtract the ecliptic horizon quadrant at apparent time, and obtain the Moon's quadrant distance at apparent time—valid when the result is less than the horizon limit; if it exceeds the horizon limit, the Moon is below the horizon and the method is not used.
80
黃平象限表
Ecliptic horizon-quadrant table
81
黃平象限表，按京師北極高度三十九度五十五分，黃赤大距二十三度二十九分，依黃道經度，逐度推得春分距午時分、黃平象限宮度、限距地高度分，三段列之。 表名「春分距午」者，乃春分距午正赤道度所變之時分也。 「黃平象限」者，乃本時黃平象限之宮度也。 「限距地高」者，乃本時黃平象限距地平之高度也。 表自三宮初度列起者，因太陽黃道經度三宮初度為春分，即春分距午之初也。
The ecliptic horizon-quadrant table, computed for Beijing at polar altitude 39°55′ and obliquity 23°29′, lists three columns by ecliptic longitude: equinox distance from noon, ecliptic horizon quadrant, and quadrant altitude above the horizon. The column "Equinox distance from noon" gives the time equivalent of the true equatorial equinox distance from noon. "Ecliptic horizon quadrant" gives the mansion and degree of the quadrant at the instant in question. "Quadrant altitude above horizon" gives how high the ecliptic horizon quadrant stands above the horizon at that instant. The table begins at the third mansion's initial degree because solar ecliptic longitude there marks the spring equinox—the start of equinox distance from noon.
82
用表之法，以本時太陽黃道經度之宮度，察其所對之春分距午時分，加凌犯用時，得數內減十二時，不足減者加二十四時減之，得本時春分距午時分。 依此時分，取其相近之春分距午時分所對之黃平象限宮度及限距地高度分，即得所求之黃平象限及限距地高也。 設本時太陽經度一宮十五度，凌犯用時十九時四十五分，求春分距午及黃平象限★限距地高，則察本表黃道經度一宮十五度所對之春分距午為二十一時九分五十四秒。 加凌犯用時十九時四十五分，內減十二時，餘過二十四時去之。 得四時五十四分五十四秒，為所求之春分距午時分。 乃以此時分察相近者，得四時五十四分五十一秒。 其所對之黃平象限為五宮十六度五十九分二十七秒，即所求之黃平象限宮度。 其所對之限距地高為七十二度四十九分五十八秒，即所求之限距地高也。 若黃道經度有零分者，滿三十分以上則進為一度，不用中比例，因逐度所差甚微故也。
To use the table: read the equinox distance from noon for the Sun's ecliptic mansion and degree, add the apparent occultation moment, subtract twelve hours, adding twenty-four hours first if needed. With that time, find the nearest tabulated equinox distance from noon and read off the corresponding ecliptic horizon quadrant and quadrant altitude. Suppose solar longitude is 15° in mansion 1 and the apparent occultation moment is 19:45. To find equinox distance from noon, ecliptic horizon quadrant, and quadrant altitude: at ecliptic longitude 15° in mansion 1 the table gives equinox distance from noon as 21:09:54. Add 19:45, subtract twelve hours, and reduce by twenty-four hours if the sum exceeds a full day. This yields 4:54:54 as the equinox distance from noon sought. The nearest tabulated time is 4:54:51. The corresponding ecliptic horizon quadrant is 16°59′27″ in mansion 5. The corresponding quadrant altitude is 72°49′58″. For fractional minutes in ecliptic longitude, round up at thirty minutes per degree without interpolation, since successive degrees differ only slightly.
83
表略
Table abbreviated
84
距限差表
Quadrant-distance correction table
85
距限差表，按限距地高度逐段列之，前列太陰實緯度分，中列黃道南北，自初度十分至五度十七分之距限差，緯南為減，緯北為加。
The quadrant-distance correction table is arranged by quadrant altitude, with lunar true latitude in the leading column, ecliptic north or south in the middle, and corrections from 0°10′ to 5°17′—subtracted for south latitude, added for north.
86
用表之法，以限距地高之度與太陰實緯度，察其縱橫相遇之數，即所求之距限差也。 設限距地高二十八度，太陰距黃道南四度二十分，求距限差，則察限距地高二十八度格內橫對太陰實緯四度二十分之距限差為八度十二分，即所求之距限差。 其緯在黃道南，是為減差也。 限距地高以逐度為率，若限距地高有三十分以上者，進作一度，不及三十分者去之。 太陰實緯以十分為率，若太陰實緯有零分者，五分以上進作十分，不足五分者去之。 俱不用中比例，因逐度分之數所差甚微故也。
To use the table: read the value at the intersection of quadrant altitude and lunar true latitude. Suppose quadrant altitude is 28° and the Moon lies 4°20′ south of the ecliptic. In the row for 28° altitude, the value opposite 4°20′ latitude is 8°12′. Because the latitude is south of the ecliptic, this is a subtractive correction. Quadrant altitude is read by whole degrees, rounding up at thirty minutes and discarding less. Lunar latitude is read to the nearest tenth of a degree, rounding at five minutes. Neither table uses interpolation, since successive entries differ only slightly.
87
表略
Table abbreviated