\r六十年交气日刻图\ps127a13.bmp\r
歌曰∶
欲知交气早晏时，漏下一刻甲子初。（六十日终期。）
八十七刻半二气，续此而起欤尽日。
七十五刻是三气，从兹又继诸六十二，
刻半之外四气始，五十刻后五气居。
毕于三十七刻半，六气承之廿五除。
自是转至戊辰首，复与漏下一刻如。
申子辰初相会合，巳酉丑初同刻昼。
寅午戌初气不异，亥卯未初当共储。
四岁一小周义三合，六甲交遍良弗虚。（十五小周为一大周。）
图自寅顺观，至子为甲子岁初气，子至戌为二气，自亥至酉为三气，酉至未为四气，自申至
午为五气，午至辰为六气，自巳至卯起乙丑岁初气。余岁继此推之，则气起同刻，三岁相合，义
自见矣。然昼夜百刻当分算于十二时，每一时该八刻零三分。
愚按∶六气每气主六十日八十七刻半，例申子辰年，初之气始于大寒寅初刻，至春分日子正
之中，是初之气才满六十日八十七刻半也。二之气即始于是日子时八十七刻六分，至小满日戌正
四刻，是二之气才满六十日
八十七刻半也。三气已后并仿此，按图推之。所谓八十七刻半者，十二时共有日刻，甲子年大寒
日寅初刻交初之气，至二月半子时五刻才满六十日八十七刻半，乃值子时之五刻也。百刻而除八
十七刻半，剩下十二刻半，算入二之气内，仍该找七十五刻，凑作八十七刻半。自前子时六刻交
二之气数起，至七十五刻乃值戌时四刻也。百刻而除七十五刻，剩下二十五刻，算入三之气内，
仍该找六十二刻半，凑作八十七刻半也。自前戌时五刻交三之气数起，至六十二刻半，乃值酉时
将五刻也。百刻而除六十二刻半，剩下三十七刻半算入四之气内，仍该找五十刻凑作八十七刻半
也。自前酉时六刻交四之气数起，至五十刻，乃值未之四刻也。百刻而除五十刻，剩下五十刻，
算入五之气内，仍该找三十七刻半，凑作八十七刻半。自前未之五刻交五之气数起，至三十七刻
半，乃值午时五刻。百刻而除三十七刻半，剩下六十二刻半，算入六之气内，仍该找二十五刻，
凑作八十七刻半也。自前午之六刻交六之气数起，至二十五刻，乃值辰之四刻也。百刻而除二十
五刻，剩下七十五刻，算入乙丑岁之初气内矣。
[Diagram of Daily and Ke Intervals for Qi Transmission over Sixty Years]
The verse states:
To know the early or late timing of Qi transmission, when the clepsydra (water clock) drips one *ke* (quarter-hour), it marks the beginning of the Jiazi cycle. (Sixty days constitute a period.)
Eighty-seven and a half *kes* mark the second Qi, continuing from this point until completion.
Seventy-five *kes* mark the third Qi; from here onward, after sixty-two and a half *kes*, the fourth Qi begins, and after fifty *kes*, the fifth Qi resides.
It concludes at thirty-seven and a half *kes*; the sixth Qi follows, leaving twenty-five *kes*.
From there, it transitions to the beginning of the Wuchen year, returning to the state where the clepsydra has dripped one *ke*.
In years of Shen, Zi, and Chen, the beginnings coincide; in years of Si, You, and Chou, the beginnings share the same *ke* during the day.
In years of Yin, Wu, and Xu, the Qi is identical; in years of Hai, Mao, and Wei, they are stored together.
Four years form a small cycle (Yi San He); six Jiazi cycles complete a full rotation without falsehood. (Fifteen small cycles constitute one great cycle.)
Observing the diagram clockwise from Yin to Zi represents the first Qi of the Jiazi year; from Zi to Xu is the second Qi; from Hai to You is the third Qi; from You to Wei is the fourth Qi; from Shen to Wu is the fifth Qi; from Wu to Chen is the sixth Qi; starting from Si to Mao begins the first Qi of the Yichou year. For subsequent years, deduce accordingly; the Qi starts at the same *ke*, coinciding every three years, revealing the principle naturally. However, the hundred *kes* of day and night should be divided among the twelve double-hours (*shi*), with each double-hour containing eight *kes* and three fen (minutes).
My commentary: Each of the Six Qi governs for sixty days and eighty-seven and a half *kes*. Taking the Shen, Zi, and Chen years as an example, the First Qi begins at the initial *ke* of Yin on the day of Major Cold (Dahan), ending at the midpoint of Zi hour on the day of Spring Equinox, exactly fulfilling sixty days and eighty-seven and a half *kes*. The Second Qi begins at eighty-seven *kes* and six fen of Zi hour on that day, ending at four *kes* of Xu hour on the day of Grain Full (Xiaoman), exactly fulfilling sixty days and eighty-seven and a half *kes*. The Third Qi and beyond follow this pattern, deduced via the diagram. Regarding the "eighty-seven and a half *kes": within the twelve double-hours, considering the daily *kes*, in the Jiazi year, the First Qi commences at the initial *ke* of Yin on Major Cold. By the fifth *ke* of Zi hour halfway through the second month, sixty days and eighty-seven and a half *kes* are completed, corresponding to the fifth *ke* of Zi hour. Subtracting eighty-seven and a half *kes* from one hundred leaves twelve and a half *kes*, which are added to the Second Qi, requiring a supplement of seventy-five *kes* to total eighty-seven and a half *kes*. Counting from the sixth *ke* of the previous Zi hour when the Second Qi began, reaching seventy-five *kes* corresponds to the fourth *ke* of Xu hour. Subtracting seventy-five *kes* from one hundred leaves twenty-five *kes*, added to the Third Qi, requiring a supplement of sixty-two and a half *kes* to total eighty-seven and a half *kes*. Counting from the fifth *ke* of the previous Xu hour when the Third Qi began, reaching sixty-two and a half *kes* corresponds to nearly five *kes* of You hour. Subtracting sixty-two and a half *kes* from one hundred leaves thirty-seven and a half *kes*, added to the Fourth Qi, requiring a supplement of fifty *kes* to total eighty-seven and a half *kes*. Counting from the sixth *ke* of the previous You hour when the Fourth Qi began, reaching fifty *kes* corresponds to the fourth *ke* of Wei hour. Subtracting fifty *kes* from one hundred leaves fifty *kes*, added to the Fifth Qi, requiring a supplement of thirty-seven and a half *kes* to total eighty-seven and a half *kes*. Counting from the fifth *ke* of the previous Wei hour when the Fifth Qi began, reaching thirty-seven and a half *kes* corresponds to the fifth *ke* of Wu hour. Subtracting thirty-seven and a half *kes* from one hundred leaves sixty-two and a half *kes*, added to the Sixth Qi, requiring a supplement of twenty-five *kes* to total eighty-seven and a half *kes*. Counting from the sixth *ke* of the previous Wu hour when the Sixth Qi began, reaching twenty-five *kes* corresponds to the fourth *ke* of Chen hour. Subtracting twenty-five *kes* from one hundred leaves seventy-five *kes*, which are then added to the First Qi of the Yichou year.