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It will be seen, secondly, that two more of the eclipses are somehow given incorrectly. The 10th is recorded as happening in the 1st month of the 15th year of duke He, corresponding to -644. As proved by calculation, there was an eclipse in the 3d Chinese moon of that year, but it was not visible in Loo. This error, like the two former ones, must be left unexplained. The 15th eclipse appears as having occurred in the 17th year of duke Seuen, corresponding to -591, in the 6th month, on the cycle day Kwei-maou. But there was then no eclipse. Chinese astronomers discovered this error in the time of the eastern Tsin dynasty; but they have found no way of accounting for it. They have called attention, indeed, to the fact that an eclipse was possible on the 1st day of the fifth month; but that would be visible only in the southern hemisphere. It occurred to Mr. Chalmers, however, to try the 7th year of duke Seuen, and he found that that year, in the 6th month, on Kwei-maou, which was then the day of the new moon, there was an eclipse visible in Loo. No doubt, this was the eclipse intended in the text, inaccurately arranged under the 17th year instead of the 7th. This happy rectification of one error shows in what direction the rectification of the other errors is to be sought.

It will be seen, thirdly, that of the remaining 32 eclipses, the years, months, and cycle-days of 18, as determined by calculation, agree with those which are given in the text, while of the other 14 the years and cycle-days agree, and the months are different, generally by one month or two, and in two cases by three months. The difference of the months, however, gives confirmation to the truthfulness of the text, showing, indeed, that it is not absolutely correct, but proving, to my mind, that the historiographers entered the eclipses in the current months of the years when they were observed. In order to make those current months agree with the true months it would have been necessary that the process of intercalation should be regularly and scientifically observed. But it was not so observed in the time of the Ch'un Ts'ëw. In proof of this I need only refer the reader to what Mr. Chalmers has said on the subject in the prolegomena to vol. III. p. 99, and to his valuable table of the years and months of the Ch'un Ts'ëw, which concludes this section. There was not room for the same error with the cycle-days. No science was required in their application. Each successive day had its name determined by the successive terms of the cycle; and, when these were exhausted, the historiographers had only to begin again. Whether the months

were long or short, and whether the year contained an intercalary month or not, the cyclical names of the days were sure to be given correctly. All that was necessary was not to let any day go by unmarked. Those 14 eclipses,3 correct as to the years and cycledays of their occurrence, and incorrect, only in the months to which they are referred, from an assignable cause, are to be accepted with as little hesitation as the 18 in regard to the date of which the record and the calculation entirely agree. The errors in them are of such a character as to show that the text was not constructed subsequently, but was made by the historiographers of Loo, in the exercise of their duties, along the whole course of the period.

3. It is hardly necessary to point out how the long list of eclipses thus verified determines the chronology of the Ch'un Ts'ëw period. The first eclipse occurred in the 3d year of duke Yin, in The chronology is determined) -719, and therefore we know that the period by the eclipses ;—as in par. 1. commenced in -721. The last eclipse oc. curred in the last year of duke Ting, in -494, from which we have only to subtract 14 years of duke Gae's rule to get the last year of the period; and indeed in the supplementary text we have an eclipse occurring in Gae's 14th year, or in -480.

I have called attention in the preceding paragraph to the fact of the cycle-days being always given correctly for the eclipses. So they generally are for other events; but sometimes they are given wrong,—as will be seen by comparing the subjoined table with the text, the days which could not be verified being omitted in the table. The errors of this kind, which are on the whole wonderfully few, are for the most part pointed out in the notes, according to the calculations of Too Yu, who says that there must be an error of the month or of the day. In some cases there may be a corruption of the cyclical names through carelessness of transcribers, which would give an error of the day; more frequently, I believe, the month is wrongly given, through the same irregularity of intercalation which has made the months given for the eclipses differ from the true months as ascertained by calculation.

4. I take this opportunity to touch on another subject which has often perplexed students of ancient Chinese history,-the different commencements of the year in the three great ancient dynasties of The different commencements of the Hea, Shang, and Chow. According to year in the three ancient dynasties. the representations of the scholars of 3 Of the third and fourth of those eclipses the text does not give the cyclical days; but I have not thought it worth while to call attention to this in my text.

the Han and all subsequent dynasties, the beginning of the year was changed, to signalize the new dynasty, by an exercise of the royal prerogative. Indeed, the phrase 'san ching," occurring in the Shoo, III. ii. 3, has been interpreted as meaning the 'three commencements of the year;' in which case it would be necessary to suppose that even before the Hëa dynasty the year had begun at different dates and in different months. But if I were translating the Shoo-king afresh, I should feel compelled to cast about for another meaning for the phrase in that passage. In point of fact the Ch'un Ts'ëw seems to show that the new commencement arose from the necessity of error which there was not sufficient science to correct. The year of the Hea dynasty began originally with the first month of spring. By the end of that dynasty, through the neglect of the intercalation, it commenced, I suppose, a month earlier, and hence the sovereigns of Shang made that the beginning of their year. But during their tenure of the kingdom, the same process of error took place, and the year, I suppose again, had come to approximate to the time of the winter solstice when the kings of Chow superseded them. They adopted the retrogression, and made it their theory that the year should begin with the new moon preceding the winter solstice, i.e., between our November 22 and December 22. But their astronomers and historiographers had not knowledge enough to keep it there. An inspection of Mr. Chalmers' table following this paragraph shows a very marked tendency, increasing as time went on, to make the year begin in the month before the new moon preceding the winter solstice. Previous to the time of duke He, many of the years begin in the commencing month of the Shang dynasty; but subsequently, the 30th, 32d, and 33d years of duke He, the 18th year of Wăn, the 3d, 4th, and 6th of Seuen, the 1st, 4th, 7th, 10th and 12th of Ching, the 16th, 19th, 21st, and 27th of Seang, the 1st, 4th, 15th, 20th, and 28th of Ch'aou, and the 2d, 7th, and 10th of Ting, all began in the month before the proper commencement of the Chow year. This was, no doubt, the ordinary commencement of the year when the dynasty of Ts'in superseded that of Chow, and so its emperor declared that the year should then begin;-three months before the period of Hea, embracing a whole season, so that what was called its spring was actually the winter of the year, and the names of all the seasons were wrongly 三正

applied. Thus each of the four dynasties which ran out their course before our Christian era had its different commencement of the year. Chinese writers, however, generally speak only of 'three correct beginnings,' being unwilling to allow the dynasty of Ts'in to rank with those of Hea, Shang, and Chow.

As has been pointed out in the 'Astronomy of the ancient Chinese' by Mr. Chalmers, after the establishment of the Han dynasty, the Chinese endeavoured to open communications with the west; and from India they must have received great additions to their astronomical knowledge. Their scholars became able to make a reformation of the calendar; and adopting the maxim of Confucius, that the seasons of Hea should be followed, they determined and arranged that the year should thenceforth commence with the beginning of spring, as it has since, with more or less of correctness, done.

The above observations show that of the four 'correct beginnings of the year,' (including that of Ts'in), one only was correct, and the proper nomenclature regarding them would be 'one correct and three erroneous beginnings.' They should also end the partial and bigoted pretensions of Chinese writers, when they talk of the universal knowledge of their ancient worthies, and the more culpable partiality and bigotry of some Sinologues who try to bear out their assertions.

5. In the following table the intercalary months are indicated by a line. The principal guide in determining them has been the cycle-days given in connexion with many of the events referred to. According to the theory of the Chinese year, as explained in vol. III., p. 22, there ought to be 7 intercalary months in every 19 years. It will be seen that during the Ch'un Ts'ëw period these months were introduced very irregularly.

The small figures denote the cyclical numbers of the days mentioned in the text, so far as they can be verified. A small capital (E) indicates an eclipse. The most important thing to be observed in the table is the changing position of the first month, sometimes preceding, sometimes following, the winter solstice, without any apparent rule.

Cyclical Number of Shortest Day.

LUNAR MONTHS ACCORDING TO CONFUCIUS.

The small figures are the Cyclical numbers of days mentioned in the History.

YEARS.

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