Let's first calculate the months from the Lantern Festival to the present. Multiply the combined and differential values of the new moon day (lunar calendar first day) by it separately. Subtract the differential from the combined when a full cycle is completed, and subtract 360 degrees when a full week (360 degrees) is completed. The remaining part that is less than a full week indicates the portion that enters the solar calendar; if it is full, subtract it, and the remaining is the part that enters the lunar calendar. For the remaining part, count one day for each complete lunar month of the week, and calculate these values in days according to the method; if the calculated month combined with the new moon day is less than one day, use the remaining days to represent it.
Add two days; the remaining days are 2580, and the differential is 914. Calculate these values in days according to the method, subtract 13 when it is full, and the remaining is the fractional day. This is how the lunar and solar calendars interrelate: the remaining parts before entering the calendar are in front, while the remaining parts after entering the calendar are behind. This indicates that the moon has reached the midpoint.
List the surplus and deficit sizes of the late or fast calendars separately. Multiply the reference number by the small part to get the differential, and adjust the remaining days of the lunar and solar calendars based on the surplus and deficit. If the surplus and deficit are insufficient, adjust the number of days to determine. Multiply the determined days by the profit and loss rate, counting one for every full month of the week, and use the total profit and loss to determine the additional time.
Multiply the difference rate by the small remainder of the new moon day, get one according to the method of differential, and use it to reduce the remaining days of entering the calendar. If it is insufficient, add one week of days, then subtract one day. Add the fractional day to its fraction, simplify the differential by the reference number to get the small part; this marks the moment when the new moon is recorded in the calendar at midnight.
To find the second day, add one day; the remaining days are 31, and the small part is 31. Subtract the small part from the remainder according to the reference number; subtract one week of days when the remainder reaches a full week, and add one more day. The calendar is calculated, and subtract the full fractional day from the remaining days; this is the beginning of entering the calendar. The remaining days that are not a full fractional day are retained; add the remaining 272, and the small part is 31; this is the time to enter the next calendar.
Multiply the common number by the surplus and remaining of the late and fast calendars at midnight; consider half a week as the small part when the remainder reaches a full week. Adjust the remaining days of the lunar and solar calendars with the surplus and deficit; if the surplus and deficit are insufficient, adjust the number of days using one week of days. Multiply the determined days by the profit and loss rate, counting one for every full month of the week, and use the total profit and loss to determine the midnight constant.
Multiply the profit and loss rate by the measured values from the recent solar terms at night; 1/200 is bright. Subtract it from the profit and loss rate to get dark; the profit and loss at midnight is the dark-bright constant.
The number of overtime hours or the fixed number of twilight (昏明定数) is divided by 12 to obtain the degree; one third of the remainder indicates weakness, while anything less than one indicates strength; two weak values together indicate weakness. The degree obtained is the degree to which the moon deviates from the ecliptic. The solar calendar uses the ecliptic corresponding to the day of the month to determine the extreme position, and the lunar calendar uses subtraction, which is the degree of the moon leaving the extreme. Strength is positive while weakness is negative; strong and weak values are added together, the same names are added, and different names are subtracted. When subtracting, subtract the same names, add the different names; if there is no corresponding match, they cancel each other out—two strong values add one weak and subtract one weak.
From the year Ji Chou in the First Yuan to the year Bing Xu in the eleventh year of Jian'an, a total of 7378 years have been accumulated.
Ji Chou, Wu Yin, Ding Mao, Bing Chen, Yi Si, Jia Wu, Gui Wei, Ren Shen, Xin You, Geng Xu, Ji Hai, Wu Zi, Ding Chou, Bing Yin—these are all years, and I will not explain further. Next are the Five Elements: Wood corresponds to Jupiter, Fire corresponds to Mars, Earth corresponds to Saturn, Metal corresponds to Venus, and Water corresponds to Mercury. Each star has its own degree of movement in the sky every day, and these degrees and cycles (weekly rate, daily rate) have fixed algorithms. Multiply the weekly rate by the year to obtain the monthly method; then multiply the monthly method by the number of days to get the month; divide the month by the monthly method to get the month. Then multiply the month by the common method to obtain the daily method. Finally, multiply the Dipper (斗分) by the weekly rate to calculate the Dipper value. It is noted that the daily method is obtained by multiplying the record method by the weekly rate, so here all calculations are done in minutes.
Next, we calculate the New Moon and Old Moon phases for the Five Stars. Multiply the common method by the month, then divide by the daily method; the quotient is the old moon, and the remainder is the small moon. Then subtract 60 from the old moon. Calculate the entry and exit of the five stars in the month and the day. Multiply the common method by the month remainder, then multiply by the combined month method with the new moon, add these two results, simplify, and then divide by the daily method to obtain the result. Finally, calculate the degree and degree remainder of the five stars. Subtract the excess degrees; the remaining value is the degree remainder in minutes. Then multiply by the week and divide by the daily method; the quotient is the degree, and the remainder is the degree remainder. If the degree exceeds the weekly total, subtract both the weekly total and the Dipper value.
Key parameters include: Record Month: 7285, Leap Month: 7, Chapter Month: 235, Year Middle: 12, Common Method: 43026, Daily Method: 1457, Meeting Count: 47, Weekly Total: 215130, Dipper Value: 145.
Here are the specific data for Jupiter: the orbital period is 6722, the daily circumference is 7341, the total number of months is 13, the lunar excess is 64810, the total lunar cycle is 127718, the daily method is 3959258, the major lunar surplus is 23, the minor lunar surplus is 1370, the day the month begins is 15, the day surplus is 3484646, the lunar virtual part is 150, the lunar part is 974690, the degree is 33, and the degree surplus is 2509956.
Data for Mars: the orbital period is 3447, the daily circumference is 7271, the total number of months is 26, the lunar excess is 25627, the total lunar cycle is 64733, the daily method is 2006723, the major lunar surplus is 47, the minor lunar surplus is 1157, the day the month begins is 12, the day surplus is 973113, the lunar virtual part is 300, the lunar part is 494115, the degree is 48.
Wow, all these numbers are making my head spin! Is this some kind of astronomical calendar calculation? Let me translate it into plain language for you sentence by sentence.
First paragraph: The total is 1991760. Saturn: It makes 3529 orbits in a year. It makes 3653 orbits per day. A year is calculated as 12 months. There are 53843 extra orbits in a month. In total, that's 6751 orbits for the month. Calculated per day, it is a total of 278581 orbits. Major lunar surplus 54, minor lunar surplus 534. On the 24th of each month. There are 166272 extra orbits per day. Lunar virtual part 923. Lunar part 51175. Degree 12. The total is 1733148.
Second paragraph: Venus: It makes 9022 orbits in a year. It makes 7213 orbits per day. A year is calculated as 9 months. There are 152293 extra orbits in a month. In total, that's 171418 orbits for the month. Calculated per day, it is a total of 5313958 orbits. Major lunar surplus 25, minor lunar surplus 1129. On the 27th of each month. There are 56954 extra orbits per day. Lunar virtual part 328. Lunar part 1308190. Degree 292. The total is 56954.
Third paragraph: Mercury: It makes 11561 orbits in a year. It makes 1834 orbits per day. A year is calculated as 1 month. There are 211331 extra orbits in a month. In total, that's 219659 orbits for the month. Calculated per day, it is a total of 6809429 orbits. Major lunar surplus 29, minor lunar surplus 773. On the 28th of each month. There are 6419967 extra orbits per day. Lunar virtual part 684. Lunar part 1676345. Degree 57. The total is 6419967.
Last paragraph: Substitute the starting point of the year you want to calculate, multiply it by the orbital period; the portion that divides evenly by the daily circumference is called "integral sum," and the part that cannot be divided is called "total surplus." Divide the total surplus by the orbital period, and you will get an integer, representing which year of the past it is; if you cannot get an integer, then it is the current year. Subtract the orbital period from the total surplus to get the degree fraction. For Venus and Mercury, odd integral sums indicate morning, while even sums indicate evening.
In summary, this passage describes a complex method of calendar calculation, with a multitude of numbers used to calculate the orbits and times of the planets. Specific details require professional astronomical knowledge to fully understand. This is simply an ancient astronomical calculation program! Let's first calculate the conjunction date of the constellations. Multiply the number of months by the remainder of the month, add them together; if it exceeds the standard for a month, count it as one month; if not enough, note the remaining month remainder. Then subtract the total months from this month remainder; the remainder is the month of entry. Next, consider the impact of leap months; if the number of months is enough for a leap month, subtract it from the month of entry, and the remaining part is then deducted from the year. The remaining is the conjunction month outside the Tianzheng calculation. If a leap month transition occurs, adjust it using the new moon. Next, multiply the month remainder by the common method, then multiply the small remainder of the conjunction day, add these two results together, and then simplify the result. If the result is just enough for a daily method, that is the conjunction date of the constellations. If not enough, the remaining is the remainder of the day, recorded outside the Tianzheng calculation. Then, multiply the degrees and minutes by the day; if the result is enough for a daily method, record one degree; if not enough, record the remaining degrees and minutes, starting from the first five degrees before the Ox. The above outlines the method for calculating the conjunction date of the constellations. Next, calculate the conjunction cycle of the planets. Add the number of months; also add the remainder of the month; if it exceeds the standard for a month, record one month; if it does not exceed one year, record it in this year; if it exceeds one year, subtract it; if there is a leap month, consider it; the remaining is recorded in the next year; if it exceeds again, record it in the next two years. For Venus and Mercury, if added in the morning, it becomes evening; if added in the evening, it becomes morning. (This refers to the conversion between the morning star and the evening star of Venus and Mercury). Then, combine the large and small remainders of the new moon and the conjunction. If it exceeds a standard month, add the large and small remainders, adding 29 to the large remainder and 773 to the small remainder. If the small remainder exceeds the daily method, subtract it from the large remainder, using the same method as outlined earlier. Add the entry date of the month and the remainder of the day; if it exceeds the daily method, record one day. If the small remainder of the previous conjunction is just enough for its virtual division, subtract one day. If the small remainder exceeds 773, subtract 29 days; if not enough, subtract 30 days; the remainder is the entry date of the subsequent conjunction. Finally, add up the degrees; also add up the remainder of the degrees; if it exceeds the daily method, record one degree. The following are the operational data for Jupiter, Mars, Saturn, and Venus:
**Jupiter:** Retrograde for 32 days, 3,484,646 minutes; Direct for 366 days; Retrograde 5 degrees, 2,509,956 minutes; Direct 40 degrees. (Retrograde 12 degrees, actual movement 28 degrees.)
**Mars:** Retrograde for 143 days, 973,113 minutes; Direct for 636 days; Retrograde 110 degrees, 478,998 minutes; Direct 320 degrees. (Retrograde 17 degrees, actual movement 303 degrees.)
**Saturn:** Retrograde for 33 days, 166,272 minutes; Direct for 345 days; Retrograde 3 degrees, 1,733,148 minutes; Direct 15 degrees. (Retrograde 6 degrees, actual movement 9 degrees.)
**Venus:** Morning retrograde in the eastern sky for 82 days, 113,908 minutes; Direct in the west for 246 days. (Retrograde 6 degrees, actual movement 240 degrees.) Morning retrograde 100 degrees, 113,908 minutes; appearing in the east. (The number of days in the west is the same; retrograde for 10 days, retrograde 8 degrees.)
Mercury, in the morning it hides, having traveled a total of 6,122,555 minutes over 33 days. Then it appears in the west for a total of 32 days. (First, subtract one degree; ultimately, it is calculated as having moved 32 degrees.) It travels underground for a total of 65 degrees, also 6,122,555 minutes. After that, it appears in the east. The degrees it appears in the east are the same as those in the west, hiding for 18 days, retrograding 14 degrees.
Calculate the days and degrees that Mercury hides, then add the remaining degrees after it conjoins with the sun. If the remaining degrees are enough for a cycle, calculate it as previously done to determine the days and degrees Mercury is visible. Multiply the denominator of Mercury's movement by the degrees it appears; if the remaining degrees are enough for a cycle, count it as one cycle; if not enough but more than half, also count it as one cycle; then add the calculated degrees to its movement degrees; if the degrees are enough for a cycle, add one degree. The calculation methods for direct and retrograde are different; multiply the current running denominator by the remaining degrees; if the result equals the original denominator, that is its current running degrees. The remaining (referring to the remaining degrees) continues to use the previous result for calculation, and for retrograde, it needs to be subtracted. If the degrees it moves underground are not enough for a cycle, divide the remaining degrees using a 'dou' (a traditional Chinese measurement unit), using the running denominator as a ratio; the degrees will increase or decrease, and the increases and decreases must balance each other out. Any reference to "like fullness approaching fullness" refers to division seeking exact values; "go and divide it, take the complete value" refers to division for taking the complete value.
Jupiter, in the morning, appeared alongside the sun and then concealed itself. It was in direct motion, concealing itself for 16 days, traversing 1,742,323 minutes, and the planet moved 2 degrees and 3,234,467 minutes. Then it appeared in the eastern sky behind the sun. In direct motion, it moved quickly, covering 11 degrees in 58 days. Then it continued in direct motion, but at a slower speed, moving 9 degrees each day, covering 9 degrees in 58 days. After that, it stopped for 25 days before turning. In retrograde motion, it retreated 1/7 of a degree each day, moving back 12 degrees over 84 days. It stopped again and after 25 days resumed direct motion, moving 9/58 of a degree each day, covering 9 degrees in 58 days. In direct motion, it moved quickly, covering 11 degrees each day, traveling 11 degrees in 58 days, appearing in front of the sun and concealing itself in the western sky at night. It concealed itself for 16 days, traversed 1,742,323 minutes, and the planet moved 2 degrees and 3,234,467 minutes, then it reappeared alongside the sun. One cycle ended, totaling 398 days, traversing 3,484,646 minutes, and the planet moved 43 degrees and 2,509,956 minutes.
The sun: In the morning, it appeared with the sun and then concealed itself. Next was direct motion, lasting 71 days, traversing 1,489,868 minutes, meaning the planet moved 55 degrees and 242,860.5 minutes. Then it could be seen in the east in the morning, behind the sun. During direct motion, it moved 14/23 of a degree each day, covering 112 degrees in 184 days. Continuing in direct motion, but at a slower speed, it moved 12/23 of a degree each day, covering 48 degrees in 92 days. Then it stopped for 11 days. After that, it moved in retrograde, retreating 17/62 of a degree each day, moving back 17 degrees over 62 days. It stopped again for 11 days and then resumed direct motion, moving 12 degrees each day, covering 48 degrees in 92 days. It continued in direct motion, moving faster, covering 14 degrees each day, traveling 112 degrees in 184 days, at which point it was in front of the sun, concealing itself in the western sky at night. After 71 days, it traversed 1,489,868 minutes, and the planet moved 55 degrees and 242,860.5 minutes, then it reappeared alongside the sun. One cycle ended, totaling 779 days and 973,113 minutes, and the planet moved 414 degrees and 478,998 minutes.
Mars: It appears in the morning with the sun, then it disappears. Next is direct motion, lasting 16 days, traversing a distance equivalent to 1,122,426.5 minutes, which corresponds to 1 degree and 1,199,864.5 minutes of planetary motion. Then it can be seen in the eastern sky in the morning, just behind the sun. During direct motion, it travels 35 minutes of arc per day, covering 7.5 degrees in 87.5 days. After 34 days, it resumes direct motion. It then goes into retrograde, moving 17 minutes per day, retreating 6 degrees after 102 days. After another 34 days, it starts direct motion again, moving 3 minutes per day, covering 7.5 degrees in 87 days; at this point, it is in front of the sun and disappears in the western sky at night. After 16 days, having traversed 1,122,426.5 minutes of distance, the planet has moved 1 degree and 1,199,864.5 minutes, and then it appears with the sun again. One cycle is completed, totaling 378 days and 166,272 minutes, with the planet traveling 12 degrees and 1,733,148 minutes.
Venus, when it meets with the sun in the morning, first disappears (goes into retrograde motion), then goes into retrograde, retreating 4 degrees in 5 days, after which it can be seen in the east in the morning, behind the sun. It continues to retrograde, moving 1.67 degrees per day, retreating 6 degrees in 10 days. Then it remains stationary for 8 days. It then turns (rotates), starting direct motion, moving slowly, 46/33 degrees per day, covering 33 degrees in 46 days. As it speeds up, it moves 6.07 degrees per day, covering 160 degrees in 91 days. Then it accelerates further during direct motion, moving 4.14 degrees per day, covering 113 degrees in 91 days; at this point, it is behind the sun and appears in the east in the morning. Continuing direct motion, it traverses 1/56 of a circle in 41 days, with the planet also covering 50 degrees in 41 days, then it meets with the sun again. One conjunction is completed, totaling 292 days and 1/56 of a circle, with the planet traveling the same distance.
When Venus conjoins with the Sun in the evening, it first conceals itself (伏) and then moves forward. In forty-one days, it travels one fifty-six-thousand nine hundred fifty-fourth of a complete circle, moving a total of fifty degrees and one fifty-six-thousand nine hundred fifty-fourth of a complete circle, and then can be seen in the western sky in front of the Sun at night. Continuing to move forward, it speeds up (顺，疾), traveling two twenty-second degrees each day, and in ninety-one days, it covers one hundred thirteen degrees. Then it slows down (更顺，减疾), traveling one-fifteenth of a degree each day, and in ninety-one days, it travels one hundred six degrees, then continues moving forward. The speed decreases (迟), covering three thirty-sixths of a degree each day, and in forty-six days, it travels thirty-three degrees. After that, it stops (留) for eight days, remaining stationary. Then it turns (旋) and begins its retrograde motion, moving backward three-fifths of a degree each day, and in ten days, it moves backward six degrees; at this point, it is in front of the Sun, appearing in the western sky at night. Continuing to move backward, it speeds up (逆，疾), moving backward four degrees in five days, and then it conjoins with the Sun again. Two conjunctions constitute one cycle, totaling five hundred eighty-four days and one hundred thirteen thousand nine hundred eight one-hundredth of a complete circle; the distance covered by the planet is the same.
As for Mercury, when it conjoins with the Sun in the morning, it first conceals itself (伏) and then moves backward, retreating seven degrees in nine days, after which it becomes visible in the eastern sky, positioned behind the Sun in the morning. Continuing to move backward, it speeds up (更逆，疾), moving backward one degree each day. Then it stops (留) for two days, remaining stationary. Next, it turns (旋) and begins to move forward, moving slowly (迟), covering eight-ninths of a degree each day, and in nine days, it covers eight degrees. The speed increases (疾), moving one and one-fourth degrees each day, and in twenty days, it travels twenty-five degrees; at this point, it is behind the Sun, appearing in the eastern sky in the morning. Continuing to move forward (顺), it travels one six hundred forty-one million nine hundred sixty-seven thousandth of a complete circle in sixteen days, and the planet also covers thirty-two degrees one six hundred forty-one million nine hundred sixty-seven thousandth of a complete circle, before conjoining with the Sun again. One conjunction totals fifty-seven days and six hundred forty-one million nine hundred sixty-seven thousandth of a complete circle; the distance covered by the planet is equivalent.
The sun has set, and it has encountered Mercury. The pattern of Mercury's movement is: when moving forward, it can cover 32 degrees and 641,960,667/1 of a degree in sixteen days; at this time, it can be seen in the evening to the west, positioned ahead of the sun. When moving forward quickly, it can cover 1.25 degrees in a day, and 25 degrees in twenty days. When moving forward slowly, it covers 8/7 degrees in a day, and 8 degrees in nine days. If Mercury stops, it remains stationary for two days. If Mercury moves backward, it will retreat one degree each day, and it can be seen in the west in the evening, positioned ahead of the sun. When moving backward slowly, it retreats seven degrees over nine days, and then it encounters the sun again. From one encounter to the next, it takes a total of 115 days and 601,255,005/1 of a day, and Mercury's movement is like this.
