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But that the direct converse of all this was the case, will be proved; namely, that the epoch of the first sexagenary cycle, as stated in the Chinese annals, and the point in the ecliptic whence it originated, were the radices from whence the ancient Chinese astronomers computed, and regulated their calendars and almanacks; that the cycle itself is entirely astronomical, and determines its own epoch and the number of cycles elapsed, which number cannot be a cycle more or a cycle less than the number set down in the annals; and that it was consequently governed by, and entirely dependent on, the motions of the heavenly bodies. All of which is clearly demonstrable from the annals themselves, and conclusive with regard to their veracity, besides setting the recorded observations in a clear and unquestionable point of view, although these properties of the sexagenary cycle have, I believe, been entirely overlooked by the learned in Chinese antiquity.

The placing of the authority and antiquity of this cycle on their true bases, is the more important, as on it wholly depends the authority of the history of a nation which has seen all others rise and fall since the first beginning of kingdoms; a nation which existed before, not only the "fabulous," but the "" unknown ages of the Greek historians, and still continues in a flourishing state; and, finally, whose records connect the sacred account of the beginning of kingdoms with our own times by an unbroken series of years.

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It may be well to observe, in limine, that there is nothing absurd or extravagant in the periods assigned to the early parts of Chinese history. The times of the first two generations, Fohi and Xinnum, are agreed to be unknown. To the seven next before the commencement of the empire and dynasties (for the Chinese, like the Egyptians, the Phoenicians, and the Chaldeans, appropriated the history of the ante- and post-diluvian patriarchs to themselves), beginning from the setting out of the sexagenary cycle, 490 years are assigned, which is 70 years a-piece. The period of the first dynasty, consisting of 17 reigns, is 441 years, which gives a mean of 26 years to each prince; that of the 28 reigns of the second dynasty, 644 years, being the average of 23 years; that of the 35 reigns of the third, 873 years, or 25 years each; all which is perfectly consistent with history, and chronology, and the course of nature.

With the third dynasty the ancient line of emperors became extinct, and with it ends the history contained in the most ancient annals, called Xu Kim; the whole period being 2457 years, distributed among 85 successive generations and reigns.

The sexagenary cycle consists of a combination of two minor cycles, of 10, called kia and 12, called tse, or çu (the decaëteris

and dodecaeteris of the Chaldeans, which latter is still used by the Tartars and other Oriental nations), every year of either being designated by particular characters; so that 6 cycles of 10 and 5 of 12 being placed in parallel columns, the same years and characters of both can return only with the commencement of a new sexagenary cycle and hence the years of the cycle of 60 are marked by the corresponding characters of the cycles Kia and Tse for each year; so that all Chinese dates are fixed by their characters -a principle which not only applies to years but to the days of the year (as in the sossus of the Chaldeans). And as the sexagenary cycle of days will not divide into the number of days contained in the sexagenary cycle of years, it follows, that as the characters of each Chinese year determine the year of the cycle in which every recorded event occurred, so the character of the day determines the number of the current sexagenary cycle.

In like manner the twelve lunar months are designated by the characters of the cycle of 60, so that every five years the same characters for the months return (the intercalary months being named from the previous lunar months); a principle which seems to have some connection with the pentaeteris of the Egyptians, Greeks, Romans, and Hindoos.

The hours of the day and the signs of the Zodiac are named from the characters of the cycle Tse, or 12; and sometimes the lunar months are also named in this manner.

So far the sexagenary cycle is entirely of a civil nature.

The origin of the present Chinese year, as well as of that of all the adjacent nations, is from the new moon nearest to the day answering to the fifteenth degree of Aquarius; and it is agreed to by all, that this was the original epoch of the year and cycle; commencing from the first year of the patriarchial reign of Hoamti (B. C. 2697-2597), in whose time the sexagenary cycle is recorded to have been perfected, although discovered by Fohi, two generations earlier. This epoch is said to have been fixed by Chuenhio (B. c. 2513-2435), in the next generation but one after Hoamti. "This emperor decreed," says Martinius, "that the first day of the year and first month should set out from the conjunction of the sun and moon nearest to the 15° of Aquarius, which is still observed by the Chinese. The reason that the year originated at this time rather than any other, was because, when the sun is about the middle of Aquarius all things begin to vegetate. "I do not deny, however," continues Martinius, "that the beginning of the year among the Chinese was not always the same, but different, according to the will of different emperors." The origin of the year from the 15° Aquarius applies to the origin of the sexagenary cycle in the time of Hoamti, for it was from the new moon nearest 5 deg. Aquarius

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in the calender of Chuenhio. "The emperor Chuenhio," says Couplet, "fixed the origin of the year from the new moon nearest the beginning of spring, which answered in China to the 5 deg. Aquarius; which order of time was frequently changed and anticipated by a month or more; but at length, under the fifth dynasty of Han, and the fifth emperor Hia Vu (Vuti), it was recalled as it is now observed."

The apparent contradiction between Martinius and Couplet, about the origin of the calendar of Chuenhio from the 15° or 5° Aquarius, will be explained.

The calendar of the emperor Yu, the first of the first dynasty (B.c. 2207-1766), Hia, is recorded to have originated with the moon Yu and sign Aquarius; that of the emperor Chimtam, the first of the second dynasty (B. c. 1766-1123), of Xam, 441 years afterwards, one moon earlier, or the moon Tchew and sign Capricornus, answering to the Julian January, or from the new moon nearest the winter solstice. "The emperor Tangh (Chim Tam) decreed," says Martinius, " that the beginning of the lunar year should be the first conjunction nearest to the winter solstice." The calendar of the emperor Vuvam, the first of the third dynasty (B. c. 1123-250), Tcheu, 644 years afterwards, set out one moon earlier still, or from the moon Tse and sign Sagittarius, answering to the Julian December. This calendar was formed by the astronomer Tcheou Cong, the brother and first minister of the emperor. "In the city Teng Fong....in the province of Honan," says Duhalde, "there is still a tower to be seen, on the top of which it is said that Tcheou Cong, the most skilful mathematician that China ever had, who lived 1200 years before Ptolemy was born, made his observations." This calendar is named Tcheou, and the time of the year of all the eclipses recorded in the annals, from в. c. 776, the date of the first certain one, till the end of the third dynasty, B. c. 250, is reckoned from the first moon of this calendar-including the eclipses mentioned by Confucius, who was born in the year B. C. 551, and recorded in his book Tchun Tsiou, as observed from B. c. 709 to B. c. 481, according to the commentators who wrote under the third dynasty-and several other eclipses observed till the end of that dynasty."

Respecting those recorded in Tchun Tsiou, P. Souciet remarks, "that there is some doubt as to the months in which they happened," (in consequence of the variation of the Chinese year;) a difficulty which will be cleared up as we proceed, for the Tcheou calendar itself varied considerably before the end of the dynasties.

The calendar of Xi Hoamti, the second emperor of the fourth dynasty (B. c. 250-207), Tsi, 876 years after Vuvam, set out also from the new moon nearest 1 deg. Sagittarius. "The emperor

Xi," says Martinius, "decreed that the beginning of the year should be placed at the lunar conjunction in Sagittarius," at which he fixed his new epoch of the empire, after the destruction of the ancient annals.

In the calendar of the emperor Vuti, the fifth of the fifth dynasty (B. c. 207-A.D. 220), Han, about a century afterwards, the ancient beginning of the year was restored as above, namely, to the new moon nearest 15° Aquarius, and it has continued so ever since, as appears by a great number of eclipses recorded by the tribunal of mathematics, and verified by calculation.

The only question as to the truth of the ancient observations, arises from the various beginnings of the year; but if it can be shewn that the origin of the ancient Chinese year varied, and receded through the ecliptic, according to a regular astronomical law, which fixes its origin for every year recited in the annals, and corresponds to the date of every recorded astronomical phenomenon, there can no longer be any doubt of the truth of these annals, or of the method to be used in verifying them.

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The Chinese astronomers have always computed the tropical year at nearly its true quantity, namely, 365d. 5h. 50m.; which they divide into 24 semimonths of 15d. 5h. 14m. 35 sec. each, named from the seasons. This year was therefore fixed, rather differed but about 1 min. per year from the true quantity, amounting to 1 hour in a sexagenary cycle, and 1 day in a cycle of 1440 years (the Chaldean and Persian embolismal period) or 24 cycles which variation was corrected by frequent observation of the solstices and equinoxes.

They estimated the lunation at 29d. 12h. 44m. and the lunar year at 354d. 8h. 48m., a quantity which differs not a minute from the truth; and was also corrected by frequent observations of solar eclipses, which were always referred to the last day of the month, which was reckoned from conjunction to conjunction.

The calendar has been always regulated by the lunar months, which were, and are still, reconciled to the solar tropical year by frequent intercalation. Martinius tells us that "The entire sexagenary cycle contains 22 embolismal years, the rest being either common, deficient, or abounding;" and, in another place, "The intercalary months recur 22 times in a sexagenary cycle." He moreover observes, "The emperor Hoamti invented the sexagenary cycle, which is a cycle of 60 years, in which space of time the same name of the year returns: but a conjunction of the sun and moon does not return at the same time, there being a difference of nearly 3 days;" and hence the variations in the Chinese calendar; " the year in that of Chuenhio being frequently anticipated by the space of a month or more,

till the emperor Vuti restored it," as Couplet tells us; and it is to be noted that all the variations mentioned are anticipatory.

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which the first year of each cycle anticipated that of the previous cycle in the tropical year and the ecliptic ;-a difference which in the space of 10 cycles, or 600 years, amounted to 29d. 2h. 40 m. being Od. 10h. 4m. only short of a lunation. So that by intercalating an additional lunation at the end of every lunar period of 600 years (the Patriarchal Lunar period, and the Nerus of the Chaldeans), the emperor Vuti and his successors rendered the Chinese year and cycle in some measure fixed, and prevented its varying more than a month from its place in the tropical year.

The anticipation of 2d. 21h. 52m. per cycle, would amount to the quantity of the tropical year in about 125 cycles and a half, or 7530 (7528 exact) years, which was therefore the annus magnus, or total revolution, of the sexagenary cycle.

This movement is at the rate of 2° 52′ 6′′ 41′′ 36′′, which each cycle receded through the ecliptic: for 360° ÷ 1251 cycles 2° 52′ 6′′ 41′′ 36′′ ferè.

The anticipation in time was at the rate of 3d. 7h. 52m. per cycle through the Julian year, which exceeds the Chinese tropical year 10m. annually, or 10 hours in a cycle; and 2d. 21h. 52m. the Chinese tropical epact + 10h. 3d. 7h. 52m. the Julian epact of the cycle, which amounts to the quantity of the Julian year in about 110 cycles or 6600 years (or 6593 exact).

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The Julian epact of the sexagenary cycle, I use in calculating the Chinese epacts, being the most convenient for chronological purposes.

It should be noted, that the true anticipation of the cycle, in time and motion, differs a little from the Chinese estimate, which is however sufficiently exact for our purpose.

The anticipation in motion is at the rate of 1 deg. in 21 years; for 7528y. 360 deg. 21 years ferè.

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The anticipation in time through the Chinese tropical year, is at the rate of 1 day in 20 years, or 3 days in 62 years; for 7528 years365d. 5h. 50m. = 203 years ferè.

The anticipation in time through the Julian year, is at the rate of 1 day in 18 years; for 6593 years365d. 6h. 0m. = 18 years ferè.

Hence it is evident, that by dividing the number of years

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