elapsed from the epoch of any sexagenary cycle, by 21, the quotient will be the number of degrees which the origin of the Chinese year had receded through the ecliptic, from its place at the setting out of the given cycle-i. e. the point at the new moon nearest to which the current year of the cycle originated. In the same manner, by dividing the number of years elapsed from the epoch of any sexagenary cycle, by 18, the quotient will be the number of days which the origin of the Chinese year had receded through the Julian year, from its place at the setting out of the given cycle-i. e. the day answering to the degree of the ecliptic, at the new moon nearest to which the current year of the cycle originated.

In like manner, by dividing the number of years elapsed from the epoch of any sexagenary cycle, by 20, the quotient will be the number of days the origin of the year had receded through the Chinese tropical year, from its place at the setting out of the given cycle-i. e. the day answering to the degree of the ecliptic at the new moon nearest to which the current year of the cycle originated, as before.

In like manner, the day of the new moon is found, or very nearly, by reckoning backwards 3d. 7h. 52m. through the Julian year, for each cycle elapsed since the epact of the given cycle, and calculating the new moon of the current year in the usual way—i. e. dividing by the lunar cycle, 19, if the current number exceed it; multiplying the remainder by the epact 11; and dividing the product by 30, or subtracting 30 from it. The remainder will give the number of days the new moon had receded from the new moon at which the current cycle originated, sufficiently exact to demonstrate the Chinese system. But if the new moon found be distant more than half a lunation from the day answering to the degree at the new moon nearest to which the current year originates, then a lunation must be added, and the required new moon will fall 30 days later in the Julian year.

To demonstrate what we have advanced, let us compute from the epoch of the first sexagenary cycle, viz. the new moon nearest to the day answering to 15 deg. Aquarius, B. c. 2697. The 15 deg. Aquarius in that year coincided with Feb. 27 in the Julian year, and the nearest new moon was on the 11th March.

The first observation noted, as above, was the conjunction nearest to 5 deg. Aquarius, at which the year set out in the calendar of Chuen hio.

The first year of Chuenhio is placed an. 5, cycle 4, B. c. 2513, being the 185th year from the origin of the first cycle, which we will call the æra of Hoamti. But 184 complete years 218 for the anticipation of the place of the origin of the year in the ecliptic; and Aquarius 15° 81° Aquarius 6; and 184 18 10d. 5h. 20m. which the day answering

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to the required degree had receded; and Feb. 27 - 10 days = Feb. 16d. 18h. ferè, answering to Aquarius 6. The new moon of the current cycle had receded in 3 cycles, or 180 years, 3d.7h. 52m. x 3=9d. 23h. 36m.; and March 11-10 days=Mar. 1, the epoch of the fourth cycle. But for the fifth year, 4 x 11 44 days - 30 14 days, and Mar. 1 14 days = Feb. 15, for the new moon of the first year of Chuenhio.

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But it is not said in what year of Chuenhio his calendar was formed. His time is stated at 78 years, during which the place of the year's origin receded from the 7th to the 3d deg. of Aquarius. But after the lapse of a lunar cycle of 19, or in the 20th year of Chuenhio, the place of the year's origin had receded to Aquarius 5° 20′, the corresponding day being Feb. 15, which was also the day of the new moon, according to the same method of calculation.

There was therefore a conjunction in the 5th Aquarius, within the time assigned to Chuenhio; to which precise point the year had receded (reckoning from the assumed radix), agreeably to the Chinese annals, at the origin of the calendar for the twentieth year of his reign.

It should be remarked, that the ancient Chinese astronomers are said to have had no knowledge of equations, but computed the movements of the heavenly bodies by mean time and motion; and rectified the errors, which on this account crept into their calendars and cycles, by frequent observations of solstices and solar eclipses. The general rules I have mentioned cannot, therefore, give the exact place and time of the celestial phænomena at all seasons of the year, but with quite enough of exactness to explain their system.

At the commencement of the second dynasty, Xam, when Chim Tam began to reign, the calendar set out from the new moon nearest Capricornus 1°, or the winter solstice, as above.

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This dynasty began an. 32 cycle xvi., B. c. 1766, or in the 932d year of Hoamti. But 931 21 44° 20′ which the place of the year had receded in the ecliptic; and Aquarius 15° 44° 20′ = Capricornus 0° 40'; so 931 18 = 51 days from Feb. 27 Jan. 6, the actual day of the solstice, and therefore corresponding to Capricornus 1°.

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The 16th cycle set out at the new moon Jan 20; for 3d.7h. 52m. × 15 = 49d. 12h. O'. from Mar. 11; and the 32d year of the 16th cycle = 31 complete-1912 x 11 132÷÷30= 12 days from Jan. 20 Jan. 8, the new moon from which the first year of Chim Tam, whose reign was 13 years, set out; and this confirms the origin of the year, as we have stated it, in the reigns of Hoamti and Chuenhio.

This epoch, agreeing so perfectly with the movement of the cycle, proves that the calendar of Yu, the first Emperor of the first dynasty, Hia, originating one lunation and one sign after

that of the second dynasty, Xam, likewise corresponded with this

movement.

In the calendar of Tcheou Cong, in the reign of Vuvam, first emperor of the third dynasty, Tcheu, commencing an. 16 cycle 27, an. Hoamti 1576, B. c. 1123, the year set out one lunation and one sign before that of Chimtam, i. e. at the new moon nearest Sagittarius 1. But 157621 75 deg., which the year had receded in the ecliptic; and Aquarius 15°-75° 3′ = Scorpio 29° 57', differing but 3 min. from Ideg. Sagittarius; and 1576÷ 1887 days from February 27 December 1d. 13h. ferè the day answering to 1 deg. Sagittarius. But the 27th cycle set out from the new moon Dec. 14; for 3d. 7h. 52m. × 26= 86d. 12h. ferè from March 11. But the year of the cycle, 16 = 15 complete years 11 = 165305. 15 days, and Dec. 14 – 15 days = Nov. 29, the neomenia of the first of Vuvam. Previous to this time the origin of the cycle had receded from January to December in the Julian year, and therefore the cycles henceforward are to be antedated one year in Julian time, like the years of Nabonassar after the first year of Darius Hystaspes, B. C. 521. The time when this variation took place was soon after the commencement of the second dynasty, as will be seen by comparing the foregoing calculations.

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An eclipse of the sun is recorded to have been observed on the last day of the tenth moon in the second year of the thirty-third cycle, being the year of Hoamti 1922, B. c. 776. But 1921÷ 2191 deg. from Aquarius 15deg. Scorpio 13deg. 30m. ferè, and 1921÷ 18 = 106 days from Feb. 27 Nov. 12d. 16h. ferè the day answering to Scorpio 13° 30. But the thirty-third cycle set out from the new moon Nov. 25 в. c. 778; and the second year consequently from the new moon Nov. 14 B. C. 777; and the tenth moon ended September 5 B. c. 776, on which day there was an eclipse of the sun visible in China, according to the catalogue of M. Pingré, whose calculated eclipses ascend to B. c. 1000; and P. Gaubil also calculated and fixed upon this eclipse as that recorded in the Chinese annals.

Again, the same annals record an eclipse of the sun, and so do Confucius (in lib. Tchun Tsiou) and his commentators, on the last day of the eighth moon in the ninth year of the thirty-fourth cycle, being the year of Hoamti 1989, B. c. 709, which is the first eclipse of the Tchun Tsiou. But 1988÷21 = 94 2° from Aquarius 15° Scorpio 10 3°; and 1988 18110 d. from February 27 November 8 d., the day answering to the 11° Scorpio, to which the year had receded. But the thirty-fourth cycle set out at the new moon Nov. 21 B. c. 718 for 3d. 7h. 52m. x 33 cycles 109d. 19h. 36m. from March 11 November 21d. 12h. ferè; but the ninth year = 8 complete × 10d. 21h. 12m. 87d. lh. 36m. 3 lunations or 88d. 14h. 18m. Id. 13h.

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lunar excess + November 21d. 12h. = Nov. 23d. 1h. ferè, B. c. 719, the origin of the ninth year of the cycle. The end of the eighth moon therefore fell July 17, B. c. 709, on which day there was a solar eclipse visible in China, according to M. Pingré's catalogue, and this eclipse was also calculated and fixed upon by P. Souciet.

I may here remark, that the learned Mr. Bedford, who endeavours to confute the Chinese chronology by attempting to prove their recorded observations to be fictitious, calculated these two eclipses, assuming for a radix the new moons of February nearest Aquarius 15deg. for the origin of the year, as it is at present; according to which he finds the eclipse B. c. 776 should fall Dec. 3, being the last day of the tenth moon, as he reckons it, and the eclipse B. c. 709, about Oct. 14; but he finds by calculation that no eclipses could happen on either of these days, and therefore pronounces them false. This, compared with the above, is a powerful example of the truth of what is there advanced. Several other recorded eclipses may be examined, and verified in the same manner, down to the fourth dynasty, Tsin, whose second emperor, Xihoamti, caused the beginning of the calendar to be restored to its place in the original calendar of the Tcheou dynasty, from which it had receded about 48 days and 41 degrees in his reign.

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But it may be enough to examine the only eclipse recorded under the Tsin dynasty, which was on the last day of the fourth moon, in the 50th year of the 41st cycle, an. Hoamti 2450, B. C. 248, and 2 years before the reign of Xihoamti. 24502449 current 21 116 from 15° Aquarius = Libra 28°, the place of the origin of the year in the ecliptic; and 2449 ÷ 18=136 days from Feb. 27 Oct. 13, the day answering to Libra 29°. The 41st cycle began at the new moon, Oct. 30d. 8h. ferè; for 3d. 7h. 52m. × 40= 131d. 20h. 40m from March 11. But the 50th year of cycle 4149 complete 192 lunar cycles and 11 years 10d. 21h. 12m. the Chinese epact of the Julian year = 130d. 8h. 32m. - 118d. 3h. for 4 lunations 12d. 5h.; and Oct. 30d. 8h. 12d. 5h. Oct. 18d. 3h. the new which the 50th year set out B. C. 249 + 118d. 3h. for 4 moons = Feb. 13d. 6h. B. c. 248, the day of the eclipse at the end of the fourth moon.

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moon at

In conclusion, enough of evidence has, it is hoped, been brought forward, and practically applied, in these remarks, to determine the general principles of Chinese astronomical time, and to place the disputed portion of the history of this singular people on a footing of authority, at least equal to that of the early annals of the other primitive Oriental nations, with whose antiquities the general reader is more familiar. It is manifest, that, like the ancient Egyptians, the Chinese philosophers had

adopted into their records a system of revolving cycles, which connected, measured, and proved their different epochs and periods; in a manner analogous to the use of the revolving Sothoic period in the Hermaic Records, and the Canon of Ptolemy; the last-mentioned document being the admitted standard of chronological perfection, and the grand connecting link between the historical canons of the Old and New Testaments. For as in the case of the Ptolemaic Canon, by knowing the year of Nabonassar in which any king's reign began, and dividing it by 4, we deduct the quotient in days from Feb. 26, and thus ascertain the Thoth of his reign in the Julian year; and in like manner, by knowing the Thoth of his reign, and multiplying the difference between it and Feb. 26 by 4, we ascertain its date, in the expired quadrienniums of Nabonassar: so by dividing the year of Hoamti in which any Chinese reign commenced, by 21, we have the number of degrees which the Chou of the reign had receded from Aquarius 15°, and thus ascertain the degree answering to the Chou in the current year; and on the other hand, by knowing the current degree, and multiplying it by 21, &c. we ascertain the date in the expired periods of 21 years of the epoch of Hoamti. This so long as the cycle was permitted to revolve, after which we have the series of the annals written at the times of the history they relate. Thus the Thoth of the first year of Darius Hystaspes fell 31st Dec. in the Julian year, but Feb. 26 Dec. 31 = 57 days x 4 = 228, which shews that Darius began to reign in the 57th quadriennium, or a little before the 228th year of Nabonassar. So the Chou of Chimtam, the first emperor of the second Chinese dynasty, was at the winter solstice, Capricornus 0°; but Aquarius 15° Capricornus 0°-45°. Hence Chimtam began to reign in the 45th period of 21 years, or a little before the 945th of Hoamti: while the Nabonassarean Thoth, and the degree of the ecliptic in connection with the Chinese Chou, are obtained by the converse of these operations, as above.

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SUPPLEMENTARY NOTE.

In dismissing to the press these observations-which, although now first published, form part of the results of inquiries carried on many years since I would apprise the critical reader, that although it is hoped the principles developed, together with their practical results, will be found valid, and not unimportant towards the establishment of another pillar of chronological truth, the calculations, though right in principle, are generally more crude in practice than would have resulted from the present stage of my inquiries. It seems likewise necessary to state, for the satisfaction of those readers who, like myself, implicitly recognise the chronological integrity of the sacred Hebrew text, that although the general