First, let's clarify the decay pattern used in calendar calculations. You see, multiplying the number of Sundays by the decay value is like using the weekly method to obtain a constant; however, this constant is not fixed; it changes over time. We must always pay attention to the change of this decay value. Whenever it reaches a cycle, subtract this value, and then start the decay calculation of the next cycle.
Next, we use the decay value to adjust the time of each day, that is, the adjustment from days to minutes. If there is a surplus or shortage, adjust the degree of the annual cycle. Then, multiply the total value by the fraction and remainder, add the fixed nighttime degree, and you will get the time of the next day. If the calculated cycle length is not equal to the number of Sundays, you need to subtract 1338, then multiply the total value by the resulting difference, add the remainder 837, then divide 899 by this difference, and finally add it to the decay value of the next cycle for continued calculation.
Then, we use the decay value to adjust the profit and loss rate, and then use this profit and loss rate to adjust the profit and loss at midnight. If there is a surplus or shortage after the end of the calendar cycle, reverse the adjustment, and the addition or subtraction values are the same as the previous steps.
To calculate the time of dusk and dawn, we multiply the monthly minute by the most recent solar term's nighttime measurement, then divide by 200 to get the Ming minute. Subtract the Ming minute from the monthly minute to get the dusk minute. These minute values are similar to the annual cycle and can be multiplied by the total value, added to the fixed degree at midnight, to get the fixed degree of dusk and dawn time. If the remainder exceeds half, round it; if it is less than half, discard it.
Next, let's look at the rules of the moon's movement. The four phases of the moon's movement traverse three channels, distributed in the sky. By dividing the speed of the moon's movement by the week, you can determine the number of days in the calendar. Multiply the number of weeks by the synodic number, then divide by the conjunction cycle to get the conjunction minute. Multiply the total value by the sum, then divide the remainder by the conjunction cycle to get the retreat minute. Based on the moon's movement cycle, we can calculate the daily progress and the difference rate within the conjunction cycle.
Yin and Yang calendar, decay, profit and loss rate, multiple:
The first day, subtract one, add seventeen; this is the initial value.
The second day, with a limit of 1290 and a differential of 457; this is the previous limit.
Subtract one, add sixteen; the total is seventeen.
The third day, subtract three, add fifteen; the total is thirty-three.
The fourth day, subtract four, add twelve; the total is forty-eight.
On the fifth day, subtract four and add eight, resulting in sixty.
On the sixth day, subtract three and add four, totaling sixty-eight.
On the seventh day, subtract three (if not enough, add one instead), totaling seventy-two.
On the eighth day, add four and subtract two, totaling seventy-three.
(If the loss exceeds the maximum, it indicates that the month has passed its halfway point, so it should be reduced.)
On the ninth day, add four and subtract six, totaling seventy-one.
On the tenth day, add three and subtract ten, totaling sixty-five.
On the eleventh day, add two and subtract thirteen, totaling fifty-five.
On the twelfth day, add one and subtract fifteen, totaling forty-two.
On the thirteenth day (the limit is three thousand nine hundred twelve, divided into one thousand seven hundred fifty-two parts.) This is the latter limit.
Add one (from the beginning, divide the day.) Subtract sixteen, totaling twenty-seven.
For the day divided (five thousand two hundred and three), after subtracting sixteen, it results in greater than eleven.
Less greater method, four hundred and seventy-three.
First, let's examine these numbers: the total for the historical week is one hundred seventy-five thousand six hundred sixty-five, the difference rate is eleven thousand nine hundred eighty-six, the conjunction is eighteen thousand three hundred twenty-eight, the micro-division is nine hundred fourteen, and the micro-division method is two thousand two hundred nine. What are these? It feels like professional terms in astronomical calculations.
Next, this sentence is a bit confusing: subtract the lunar month period (likely referring to a specific time cycle) from the accumulated month, and then multiply the remaining part by the conjunction and micro-division respectively. If the micro-division exceeds the micro-division method, deduct it from the conjunction; if the conjunction exceeds the week day (360 degrees), subtract the week day; the remainder that does not meet the historical week corresponds to the solar calendar; if it equals the historical week, subtract the historical week; the remainder corresponds to the lunar calendar. The remaining part, for every full month of the week day, add one day; except for this, the remainder of the month's conjunction into the historical week (probably referring to a certain date), if it is less than one day, it is expressed as a remainder.
This paragraph is about the calculation method: add two days, the day remainder is two thousand five hundred eighty, the micro-division is nine hundred fourteen. Calculate the number of days according to the method above; subtract thirteen if it reaches thirteen, and calculate the number of days according to the fraction. The lunar and solar calendars affect each other, and the sequence of entries into the calendar is determined by the calculation results. This is also the method used when the moon reaches the midpoint of its orbit.
Then, consider factors such as the pace of calendar entry, the size of profit and loss, and the number of occurrences in the fast and slow calendars: multiply the size of profit and loss by the number of occurrences to calculate the differential. Add or subtract the profit and loss from the yin and yang day residue; if the day residue is insufficient or exceeds, adjust based on the number of days in the month and week. Multiply the adjusted day residue by the profit and loss rate; if it equals the number of days in a month, use the comprehensive value of profit and loss to determine the overtime constant.
Continue calculating: multiply the difference rate by the remaining small remainder; if it equals the differential method, subtract it from the calendar's day residue. If it is not enough, add the month and week and then subtract one day. Add the remaining fraction to the fractional day, simplify the differential with the number of occurrences to get the small fraction, thus obtaining the time of entering the calendar at midnight.
Calculate the second day: add one day; the day residue is thirty-one, and the small fraction is also thirty-one. If the small fraction exceeds the number of occurrences, subtract the number of occurrences, then add one day. If the calendar calculation ends and the day residue exceeds the fractional day, subtract the fractional day, which is the starting time for the calendar entry. If it does not reach the fractional day, keep it, add the remainder of two thousand seven hundred and two, small fraction of thirty-one, which is the time of the next calendar entry.
This section outlines another calculation step: multiply the total number by the profit and loss and the remainder during midnight of the fast and slow calendars; if the remainder exceeds half of the weekly days, it is used as the small fraction. Add the profit number, subtract the loss number, adjust the yin and yang day residue; if the day residue is insufficient or exceeds, adjust based on the number of days in the month and week. Multiply the adjusted day residue by the profit and loss rate; if it equals the number of days in a month, use the comprehensive value of profit and loss to determine the midnight constant.
Finally, calculate the ecliptic degrees: multiply the profit and loss rate by the number of time intervals during the recent solar term night; one two-hundredth represents daytime, and subtracting this value from the profit and loss rate gives the nighttime, using the nighttime half as the twilight factor. Divide the overtime or twilight factor by twelve to get the degrees; one third of the remaining part is minor, less than one degree is strong, and two minors are weak. The result obtained is the degree of the moon's deviation from the ecliptic. For the solar calendar, use the ecliptic calendar corresponding to the added day to determine the extreme; for the lunar calendar, calculate the extreme by subtraction, which gives the degree to which the moon is away from the pole. A strong value is considered positive, while a weak value is negative; like terms are added, and unlike terms are subtracted. When subtracting, like terms cancel each other out, unlike terms are added, and those without correspondence cancel each other out; two strong add one minor and subtract one weak.
In summary, this text describes an extremely complex calendrical calculation method, filled with various technical terms and complicated calculation steps, making it difficult for even modern people to fully understand its specific meaning, let alone perform actual calculations. It requires profound knowledge of calendrical systems and mathematical skills to interpret.
From the year 178 AD to 211 AD, a total of 7378 years have passed. The intervening years, which correspond to the Chinese zodiac years, are 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, and Bing Yin.
The stars corresponding to the five elements are: Jupiter, Mars, Saturn, Venus, and Mercury. Each star has specific values for its orbital period (the time it takes for a planet to complete one orbit) and daily speed, which are used for calculations. The calculation method is very complex, involving cycles, daily rates, lunar years, lunar months, etc. Specifically, first calculate the star positions for each month, and then calculate the exact position of each star during each month. These calculations depend on several parameters, including "lunar year multiplied by cycles equals lunar law. Lunar month multiplied by days equals lunar fractions. Fractions as law equals lunar numbers. Total number multiplied by lunar law, daily degree law also. Dipper fractions multiplied by cycle rate equals Dipper fractions." These are all terms from ancient astronomical calculations, which are beyond the scope of this explanation.
Next, we need to calculate the large and small remainders for the five stars, as well as the days the five stars enter the month and the daily remainders. These calculation processes are also quite complex, requiring "using the total law to multiply each lunar number, and dividing each daily law for the large remainder; the remainder left over is the small remainder. Use sixty to reduce the large remainder." And other formulas. In summary, a series of complex calculations is required to determine the precise positions of the planets.
Finally, we need to calculate the degrees and remainders of the five planets, which also involves parameters like the zodiac and constellations. "Subtract more for the remainder, multiply by the zodiac, and approximate using the daily degree method; the result is the degree, with any excess as the remainder, disregarding values that exceed the zodiac and constellation divisions." These calculations will ultimately be used to predict the orbits of the planets.
Next are the specific numerical values: a total of 7285 months were calculated, including 7 intercalary months, totaling 235 months, with 12 months in a year, the general method is 43026, the daily method is 1457, the number of lunar days is 47, the circumference is 215130, and the constellation divisions are 145.
The following are the calculations for Jupiter: the circumference is 6722, the daily rate is 7341, the total lunar months are 13, the lunar remainder is 64810, the combined lunar method is 127718, the daily degree method is 3959258, the major lunar remainder is 23, the minor lunar remainder is 1370, the lunar entry day is 15, the daily remainder is 3484646, the virtual lunar division is 150, the constellation division is 974690, the degree is 33, and the remainder is 2509956.
The calculations for Mars: the circumference is 3447, the daily rate is 7271, the total lunar months are 26, the lunar remainder is 25627, the combined lunar method is 64733, the daily degree method is 2006723, the major lunar remainder is 47...
This text describes the process of ancient astronomical calculations, involving a large number of professional terms and complex calculation methods. Although we might struggle to fully understand their specific meanings now, we can sense the exploration of the universe and the rigorous calculation spirit of ancient astronomers.
At some time before Christ, I began recording astronomical data. The minor lunar remainder is 1157, the lunar entry day is 12, the daily remainder is 97313. The lunar virtual division is 300, the constellation division is 49415, the degree is 48, and the remainder is 1991706.
Saturn's circumference is 3529, the daily rate is 3653. The total lunar months are 12, the lunar remainder is 53843, the combined lunar method is 6751, the daily degree method is 278581. Here's another set of data: the major lunar remainder is 54, the minor lunar remainder is 534, the lunar entry day is 24, the daily remainder is 166272. The lunar virtual division is 923, the constellation division is 51175, the degree is 12, and the remainder is 1733148.
The orbital period of Venus is nine thousand twenty-two, and the period of the Sun is seven thousand two hundred thirteen. The combined lunar count is nine, with a remainder of one hundred fifty-two thousand, two hundred ninety-three; the combined lunar method is one hundred seventy-one thousand four hundred eighteen, and the daily method is five million three hundred thirteen thousand nine hundred fifty-eight. Then comes the next set: the large new moon remainder is twenty-five, the small new moon remainder is one thousand one hundred twenty-nine, the entry month day is twenty-seven, and the daily remainder is fifty-six thousand nine hundred fifty-four. The large new moon division is three hundred twenty-eight units, the Dipper division is one hundred thirty million eight hundred ninety, the degree count is two hundred ninety-two, and the degree remainder is fifty-six thousand nine hundred fifty-four.
The orbital period of Mercury is eleven thousand five hundred sixty-one, and the period of the Sun is one thousand eight hundred thirty-four. The combined lunar count is one, with a remainder of two hundred eleven thousand three hundred thirty-one; the combined lunar method is two hundred nineteen thousand six hundred fifty-nine, and the daily method is six million eight hundred thousand four hundred twenty-nine. Finally, here is this set of data: the large new moon remainder is twenty-nine, the small new moon remainder is seven hundred seventy-three, the entry month day is twenty-eight, and the daily remainder is six hundred forty-one million nine hundred sixty-seven; the large new moon division is six hundred eighty-four, the Dipper division is one hundred sixty-seven million six thousand three hundred forty-five, the degree count is fifty-seven, and the degree remainder is six hundred forty-one million nine hundred sixty-seven. These figures illustrate the complexities of planetary motion!
First, calculate how many days are in a year by multiplying the weekly days by this number; if it is exactly an integer, it is called "accumulated harmony," and if it is not an integer, the remaining part is called "harmonic remainder." Dividing the weekly days by "accumulated harmony," if it divides evenly, that indicates how many years ago the celestial phenomenon occurred; if it does not divide evenly, look at the remainder: the remainder indicates how many years ago the celestial phenomenon occurred. If it cannot be evenly divided, use the remainder as the basis for further calculations. If the "accumulated harmony" of Venus and Mercury is an odd number, it appears in the morning; if it is an even number, it appears in the evening.
Next, calculate the months. Multiply the month count and the month remainder by "accumulated harmony"; if the result is an integer multiple of the month, use this integer to denote the month. If there is still a remainder, that is the month remainder. Then, subtract the effect of the leap month from this month remainder; the remaining part is the remaining months in the year, which need to be calculated separately and are called "combined months." If it is around the leap month, use the new moon day to adjust the calculation.
Then use some specific coefficients to multiply the month remainder and the new moon day remainder, then reduce by a common factor. If the result is an integer value in days, that is the day the celestial body appears; if it is not an integer, the leftover part represents the day remainder.
Then multiply the number of days per week by the degree calculated earlier. If the result is a multiple of the daily degree, it signifies a degree. If there is a remainder, continue the calculation from the five stars of the Ox constellation.
The above is the method of calculating celestial bodies.
Next, calculate the time when the celestial body will appear in the future. Add the number of months and the month remainder separately. If the sum is a multiple of months, it indicates how many months later it will be; if it is not a multiple, consider the remainder, which indicates how many years later. For Venus and Mercury, appearing in the morning adds one day to appear in the evening, and appearing in the evening adds one day to appear in the morning.
Next, add the new moon day remainder and the month remainder. If the result exceeds a certain threshold (like 29 or 773), subtract the corresponding value; if it is less than a certain value, keep the remainder. The final outcome indicates the day the celestial body will appear.
Finally, add the degree and the degree remainder. If the result is a multiple of the daily degree, it signifies a degree.
Jupiter:
In retrograde for 32 days and 3484646 minutes.
In direct motion for 366 days.
Retrograde 5 degrees, 2509956 minutes.
In direct motion for 40 degrees. (Retrograde 12 degrees, actual progress 28 degrees.)
Mars: In retrograde for 143 days and 973113 minutes.
In direct motion for 636 days.
Retrograde 110 degrees, 478998 minutes.
In direct motion for 320 degrees. (Retrograde 17 degrees, actual progress 303 degrees.)
Saturn: In retrograde for 33 days and 166272 minutes.
In direct motion for 345 days.
Retrograde 3 degrees, 1733148 minutes.
In direct motion for 15 degrees. (Retrograde 6 degrees, actual progress 9 degrees.)
Venus, appearing in the east during the morning, it stays for a total of 82 days, covering 113980 minutes. It then transitions to the west, remaining there for 246 days. (Subtracting 6 degrees retrograde, the final progress is 246 degrees.) When it appears in the morning, it moves 100 degrees, covering 113980 minutes. Then it moves back to the east. (It moves the same number of degrees as when in the west each day, stays for 10 days, and then moves back 8 degrees.)
Mercury, appearing in the morning, stays for 33 days, covering 612505 minutes. It then moves to the west and stays for 32 days. (Subtracting 1 degree retrograde, the final progress is 32 degrees.) It moves 65 degrees, covering 612505 minutes. Then it moves back to the east. (It moves the same number of degrees as when in the west each day, stays for 18 days, and then moves back 14 degrees.)
Next is the calculation method: Calculate the daily journey and remaining degrees of the planet based on the established calculations, adding the remaining degrees of the star and the sun. If the remaining degrees complete a full cycle, begin the calculation anew, allowing you to determine the time and degrees of the planet's appearance. Multiply the denominator of the star's movement by the degrees of appearance. If the remaining degrees can be divided evenly by the sun's movement, you get an integer. If it cannot be evenly divided and exceeds half, count it as an integer. Then add this integer to the planet's movement degrees. If the degrees reach the denominator, add one degree. The methods for retrograde and direct motion are different. Multiply the current denominator by the original degrees to obtain the current degrees. Add the number of days stayed to the previous days, subtracting for retrograde. If the number of days stayed is insufficient to complete a degree, divide by the star's movement denominator; the degrees may increase or decrease, influencing one another. References like "such as reaching full" indicate precise division; "go and divide, take the full value" refers to taking the full value division.
As for Jupiter, it appears with the sun in the morning, then stops, moves forward for 16 days, covering 1,742,323 minutes, with the planet moving 2 degrees, covering 323,467 minutes. Then it appears in the east in the morning, behind the sun. During direct motion, Jupiter travels quickly, moving 11 degrees in 58 days, covering 58 minutes per day. Moving forward again at a slower speed, it covers 9 minutes per day, moving 9 degrees in 58 days. It stops for 25 days, then changes direction. Moving backward, it covers 7 minutes per day, retreating 12 degrees after 84 days. It stops again for 25 days, then moves forward, covering 58 minutes in 9 days, moving 9 degrees in 58 days. Moving forward, Jupiter travels quickly, covering 11 minutes per day, moving 11 degrees in 58 days, in front of the sun, stopping in the western sky at dusk. After 16 days, covering 1,742,323 minutes, with the planet moving 2 degrees, covering 323,467 minutes, it appears with the sun again. A complete cycle is 398 days, covering 3,484,646 minutes, with the planet moving 43 degrees, covering 2,509,956 minutes.
It is said that Mars, in the morning, appears with the sun and then disappears from view. Next, it moves forward for a total of 71 days, covering 1,489,868 minutes, which is equivalent to the planet moving 55 degrees and 242,860.5 minutes. In the morning during its forward movement, it can be seen in the east, behind the sun. During this phase, it covers 14/23 of a degree each day, totaling 112 degrees over 184 days. Then it slows down, covering 48 degrees over 92 days, at a rate of 12/23 of a degree per day. It then stops for 11 days without moving. It then begins retrograde motion, covering 17 degrees over 62 days, at a rate of 17/62 of a degree per day. It stops again for 11 days, then resumes forward motion, covering 48 degrees over 92 days, at a rate of 1/12 of a degree per day. Moving forward again, its speed increases, covering 112 degrees over 184 days, at a rate of 14/1 of a degree per day. At this point, it is in front of the sun, setting in the west at night. After 71 days, covering 1,489,868 minutes, the planet moves a total of 55 degrees and 242,860.5 minutes and then appears with the sun again. This completes one cycle, which lasts a total of 779 days and 973,113 minutes, with the planet moving a total of 414 degrees and 478,998 minutes.
Turning to Saturn, it also appears in the morning alongside the sun before disappearing from view. Next, it moves forward for a total of 16 days, covering 1,122,426.5 minutes, with the planet moving 1 degree and 1,995,864.5 minutes. In the morning during its forward movement, it can be seen in the east, behind the sun. During this phase, it covers 7.5 degrees over 87.5 days, at a rate of 3/35 of a degree per day. Then it stops for 34 days without moving. It then begins retrograde motion, covering 6 degrees over 102 days, at a rate of 1/17 of a degree per day. After another 34 days, it resumes forward motion, covering 7.5 degrees over 87 days, at a rate of 1/3 of a degree per day. At this point, it is in front of the sun, setting in the west at night. After 16 days, covering 1,122,426.5 minutes, the planet moves a total of 1 degree and 1,995,864.5 minutes and then appears with the sun again. This completes one cycle, which lasts a total of 378 days and 166,272 minutes, with the planet moving a total of 12 degrees and 1,733,148 minutes.
Venus, when it meets the Sun in the morning, first "retrogrades," meaning it goes retrograde, moving backward four degrees over five days, and then it can be seen in the east in the morning, at which point it is behind the Sun. It continues to retrograde, moving three-forty-sixths of a degree each day, and after ten days, it has moved back six degrees. Then it "stays," remaining stationary for eight days. Next, it "turns," meaning it begins to move direct, at a slower speed, moving three-thirty-sixths of a degree each day, and after forty-six days, it has traveled thirty-three degrees, thus starting its direct motion. After that, the speed increases, moving one degree and fifteen minutes each day, and after ninety-one days, it has traveled one hundred six degrees. The speed continues to increase, moving one degree and twenty-two minutes each day, and after ninety-one days, it has traveled one hundred thirteen degrees, at which point it is behind the Sun and appears in the east in the morning. Finally, it moves direct, covering one fifty-six-thousand nine-hundred fifty-fourth of a circle in forty-one days, while the planet also moves fifty degrees of that same fraction, and then it meets the Sun again. One conjunction cycle lasts two hundred ninety-two days and one fifty-six-thousand nine-hundred fifty-fourth of a circle, and the planet's motion is the same.
When Venus meets the Sun in the evening, it first "retrogrades," this time moving retrograde, covering one fifty-six-thousand nine-hundred fifty-fourth of a circle in forty-one days, while the planet moves fifty degrees of that same fraction, and then it can be seen in the west in the evening, at which point it is in front of the Sun. It continues to move direct, with increasing speed, moving one degree and twenty-two minutes each day, and after ninety-one days, it has traveled one hundred thirteen degrees. The speed then starts to decrease, moving one degree and fifteen minutes each day, and after ninety-one days, it has traveled one hundred six degrees, and then, it starts moving direct again. The speed slows down, moving three-thirty-sixths of a degree each day, and after forty-six days, it has traveled thirty-three degrees. Then it "stays," remaining stationary for eight days. Next, it "turns," meaning it begins to retrograde, moving three-fifths of a degree each day, and after ten days, it has moved back six degrees, at which point it is in front of the Sun and appears in the west in the evening. It continues to retrograde, speeding up, moving back four degrees in five days, and then it meets the Sun again. Two conjunctions complete one cycle, totaling five hundred eighty-four days and one hundred thirteen thousand nine hundred eight-one parts of a circle, and the planet's motion is the same.
Mercury, when it meets the Sun in the morning, first "submerges," which refers to its retrograde motion, retracting seven degrees over the course of nine days. At this point, it is positioned behind the Sun and can be seen in the east in the morning. Continuing to move retrograde, it speeds up, retracting one degree per day. It then "pauses," remaining stationary for two days. After that, it "turns," meaning it begins its direct motion, traversing eight-ninths of a degree daily, moving eight degrees over nine days. By this time, it is again behind the Sun and becomes visible in the east at dawn. Afterward, it speeds up, moving one and a quarter degrees each day, covering twenty-five degrees in twenty days, at which point it is positioned behind the Sun and appears in the east in the morning. Finally, it moves direct, traversing one part in six hundred forty-one million nine thousand sixty-seven of a circle in sixteen days, and the planet moves thirty-two degrees and one part in six hundred forty-one million nine thousand sixty-seven of a circle, then it meets the Sun again. The period of one conjunction is fifty-seven days and one part in six hundred forty-one million nine thousand sixty-seven of a circle, and the planet's movement is the same.
Speaking of Mercury, it descends alongside the Sun, and then it appears to submerge, following a direct path. Specifically, it can cover thirty-two degrees and six hundred forty-one million nine hundred sixty-seven parts in one thousand of a degree every sixteen days. In the evening, you can spot it in the west, consistently positioned ahead of the Sun. When moving direct, it moves quite swiftly, covering one and a quarter degrees each day, allowing it to cover twenty-five degrees in twenty days. If it moves sluggishly, it typically covers about seven-eighths of a degree daily, taking nine days to cover eight degrees. If it becomes stationary, it stays inactive for two days.
It will also move in reverse, retracting one degree each day, and at this time it is still in front of the Sun, and you can observe it submerged in the west during the evening. When it goes retrograde, it also moves at a slow pace, taking nine days to move back seven degrees, and then it meets the Sun again. From one conjunction to the next, the complete cycle lasts 115 days and one part in six million two thousand five hundred fifty-five of a day, and this is how Mercury's movement repeats itself.
