This, then, is the azimuth of Aquila at the time mentioned, counted from north to east.

The polar star is used very advantageously in this way at the moment of its greatest digression, that is, at the moment when it is farthest from the meridian it is towards this time that its motion in azimuth is the least, and, indeed, perfectly insensible during the time occupied in observing a set of distances. It is necessary to calculate then the instant of greatest digression : let h be the hour angle at this instant, the complement of the latitude, the north polar distance of the star; at the instant of greatest digression we have a spherical triangle between the

From what has preceded, it will easily be seen how the deviation of the magnetic needle from the true meridian may be ascertained by an observer on land. In fact, he has only, by means of a properly constructed compass, to take the magnetic bearing of some signal, and then to determine the true azimuth of that signal by some one of the methods above explained. The true azimuth, compared with the magnetic azimuth, will give the deviation of the compass. But the observer at sea must obviously have recourse to other means. It is to be borne in mind that for the purposes of navigation, it is unnecessary to determine the magnetic deviation with mathematical accuracy: it is more important to employ methods that are

CHAPTER I.

Oriental Astronomy.-The Chinese. ASTRONOMY is in all probability the most ancient, as it is unquestionably the most perfect of the physical sciences. But the very antiquity of its origin, coæval it would seem with the earliest civilization of the East, throws an obscurity round it, which the present state of our knowledge does not enable us to dispel. Thus some have been induced to look to the Egyptians or Chaldæans, some to the Indians, and others to the Chinese, as the inventors of the science; but the truth is, that notwithstanding all the learning and acuteness that have been shewn in discussing these questions, the facts in our possession are too few and unconnected to guide us with any certainty to a conclusion. That in some of the nations mentioned, observations of the heavens, though perhaps rude and incomplete, have been made from the earliest times, appears unquestionable; but this is nearly all that can safely be affirmed. Whether any of these nations borrowed from the others, or all from a common source; or whether, on the other hand, there was no scientific communication between them, is a point upon which we may speculate with more or less probability, but which we can never hope to establish beyond controversy. In a fine climate and a level country, in the plains of Chaldæa, or the valley of the Nile, the spectacle of the heavens, everywhere so striking, must have forcibly arrested the attention of a people just beginning to emerge from barbarism. But it is principally to the superstitious ideas of the inhabitants of the East that we must look for the motives which induced them to follow with so much care the varying phenomena of the celestial sphere. The Chaldæans have been celebrated in all ages for their attachment to judicial astrology; the Chinese, from time immemorial, have considered solar eclipses and conjunctions of the planets as prognostics of importance to the empire, and the observation of them has been made a matter of state policy. Traces of a similar belief may be found in Egypt and India; and there can be little doubt that to a superstition vain and degrading in itself, we owe the early observations

made in China and Babylon, the zeal with which the Arabs embraced the science of Ptolemy, and the revival of astronomy in modern Europe.

In treating of the early Oriental, astronomy, we are induced to give the priority to the Chinese, without meaning to affirm that the science is of more ancient date 'among that people, than among the Babylonians and Egyptians. But it can scarcely be disputed that they possess the oldest authentic observations on record, and consequently have well-founded claims to our earliest notice. It is also to be remarked that the long residence of the Jesuit missionaries in China, and the peculiar opportunities they enjoyed of examining the records, afford great comparative facility in the investigation of this part of the subject. For a long time the office of president of the tribunal of mathematics was filled by members of this order: their assistance having become indispensable to the Chinese for the correction of their astronomical tables and methods of calculation. The Jesuits did not fail to profit by this opportunity of studying the history, antiquities, and scientific monuments of the country; and we owe to their researches a great mass of curious and interesting facts. Father Gaubil has written a treatise professedly on the history of Chinese Astronomy, which with another treatise on the same subject in the 26th volume of the Lettres Edifiantes comprise nearly all that is known on the subject. But after all it must be recollected that the learning and diligence of the missionaries have been able to collect nothing beyond detached observations, and fragments of science, which could convey no information except to those who were already versed in astronomical calculations. The reader will not expect a connected history of the origin and progress of astronomy in the east; this we can trace but imperfectly for Greece, a country with which we are so well acquainted: with regard to China and India we must be contented with establishing a few facts, which, at some future time, increased knowledge may perhaps enable us to connect.

It appears that the Chinese, whose annals are in some particulars of more than doubtful veracity, carry up the

B

foundation of the Empire to a prince named Fou-hi, as early as nine and twenty centuries before Christ; and they refer to the same period the institution of their cycle of sixty years, and the composition of certain mysterious figures, of which we shall say more presently. Though the cycle just mentioned is purely civil, it is sufficiently ingenious to merit farther notice in this place. In order to give each year a name that shall indicate at once its place in the cycle, the Chinese have taken two series, the first composed of ten, the second of twelve monosyllables. In forming then the names of the respective years, they begin by combining the first word of the first series with the first of the second to make the name of the first year in the cycle; for the name of the second year they combine the second of the first with the second of the second series, and so on: after ten of these combinations, the first word of the first series answers to the eleventh of the second, the second of the first to the twelfth of the second, the third of the first to the first of the second, and so they proceed till the first word of the first series corresponds again to the first of the second*. This happens at the end of sixty years. There can be no question that this cycle is extremely ancient; it is quoted in the Chou-king; an historical work of which some parts are nearly as old as the time of the Emperor Yao; that is, about 2,300 B. C.; but there is some difficulty in fixing precisely its origin; the Chinese tribunal of mathematics places the first year of the first cycle at the eightyfirst year of the Emperor Yaof.

The first phenomenon recorded in the Chinese annals is a conjunction of five planets, in the reign of the Emperor Tehuen-hiu, which lasted from about 2514 to 2436 B.C. The conjunction is said to have taken place just beyond the constellation Che, which occupies about 170 of longitude, and the centre of which is in 6° Piscium; on the same year spring began before the first day of the first moons. According to the cal

The words of the first series are, Kia, Y, Ping, Ting, Vou, Ki, Keng Sin, Gin, Quey; of the second, Tse, Tcheou, Yn, Mao, Chin, Se, Ou, Oney, Chin, Yeou, Su, Hay. The first year of the cycle would be called Kia-Tse, the second Y-Tcheou, and so on; for example, the fifteenth would be Vou-Yn. V. Souciet, Recueil d'Observations faites à la Chine, p. 174. + Souciet, vol. iii. p. 14. Gaubil, in Souciet, vol. ii. p. 137.

The literal translation of the Chinese is, Hoc anno primæ lunæ primâ die præcesserat ver quinque planetæ convenere in cœlo transmissá constellatione Che.' De Mailla, Hist. de la Chine, vol. i. p. civ.

culations of Father De Mailla all these circumstances are verified in the year 2461.-In this year, the spring, which begins in China with the passage of the sun into 15° Aquarii, fell on the 4th of February, the new moon on the 6th, and on the 9th, the four planets Saturn, Jupiter, Mars, and Mercury, were, with the moon, comprised within an are of about 12°, from 15° to 27° Piscium.* But, in the first place, we must remark that these calculations cannot inspire a great confidence; they were made with the tables of Lahire, how quite antiquated; and even had they been founded on the best modern tables, for example, those of Delambre, Burckhardt, and Lindenau, they would be open to much doubt; as small errors in the elements will, in the course of forty centuries, produce deviations of considerable magnitude. Besides, a conjunction of five planets is recorded, whereas it appears, from De Mailla's own calculations, that only four were in conjunction; the Chinese text requiring, according to Gaubil, that the moon be not included among the five in questiont. According to the last mentioned astronomer, this con junction was supposed, in order to serve as an epoch for the tables. For it ap pears that for a long time the Chinese always took for epoch a fictitious general conjunction of the planets; the date of which they fixed by calculating backwards with the respective mean motions they supposed to belong to each planet, till they found the conjunction they sought. It is remarkable enough that the Indians fixed the epoch of their tables in a similar way; nor is this the only point of coincidence in the astronomy of the two nations. Both divided their zodiac nearly in a similar way, the latter into twenty-seven, the former into twenty-eight constellations; to which number they were probably led by ob serving the moon's revolution to take place in something between twenty-seven and twenty-eight days; subsequently both seem to have become acquainted with a division of the zodiac into twelve

On the 9th of February 2461 B.C., Gregorlat style, at half-past seven r.M., mean time on the meridian of Paris, the longitudes of the planets were as follows:

= 14.56.16 26.45.11

=23.18.21 17. 2.12 24.39.47

De Mailla, vol. i. pp. elv. vi. vii. viii.
Souciet, vol. ii. p. 149.

Souciet, vol. il. p. 16. Vide also Gaubil, Hist. de l'Astron. Chin. in the Lett. Edifiant. 1811. Tea louse, vol. xxvi, p. 212.

signs; but this division was purely mathematical, the constellations of the zodiac remaining unchanged.

The circumstance above-mentioned, that under the Emperor Tchuen-hiu, spring began with the passage of the sun into 15° Aquarii, appears to Bailly another proof of the connexion between the astronomy of India and China. The Indians who made use of a sidereal year, fixed the beginning of their year at the entry of the sun into the beginning oftheir zodiac, which, as we have just seen, was determined entirely by the fixed stars; now, in consequence of the phenomenon called the precession of the equinoxes, the beginning of this zodiac, which was marked by a certain fixed star, appeared to move, from year to year, at the rate of about 50" annually, (the Indians supposed 54"); and if, at some remote time, the beginning of the year coincided with the winter solstice, some centuries later it would coincide with the vernal equinox. Now, the Indians suppose, that, in the year 3102 B. C., the beginning of their zodiac was in 6° Aquarii: in the time of Tchuen-hiu, it would be pretty near 15° Aquarii, and the Indian year at that time would begin with the passage of the sun through that spot in the heavens. This, as we have just seen, was the moment at which Tchuenhiu fixed the beginning of the Chinese year. The explanation of Bailly is in genious and plausible; but it is difficult to admit the extreme antiquity which the reality of this determination by the Chinese necessarily implies.

Though Gaubil rejects the conjuncfion of Tchuenhiu, he seems to think that the beginning of civilization in China, and the earliest observations of the stars, are at least as old as this emperor, though later than the time at which Fou-hi is placed. For it would seem that the stars Tay-y and Tien-y of the Chinese catalogues have been successively observed in the pole. It is not easy to identify either of these stars with any contained in the modern European catalogues; but, according to Gaubil, the first was in the pole about the year 2259, the second about 2669 B. C. But about 2850, the star a Draconis was polar star; this, however, is not marked as having been such in the Chinese sphere, and hence Gaubil deduces that their observations are subsequent to this time. According to the opinion of the astronomer just mentioned, the authen

reign of the Emperor Yao, about threeand-twenty centuries before the Christian era, an antiquity still too great to be easily admitted. We have seen that the beginning of the cycle of sixty years, which the common tradition refers to Fo-hi, is fixed by the Tribunal of Mathematics more than eighty years after the Emperor Yao; and we may probably bring down to an age posterior to this prince, the date of the Kotou and the Koua, certain mysterious figures, supposed by the Chinese literati of all ages, to contain important astronomical truths. Unfortunately, these figures, if they have any meaning, have long ceased to be intelligible, and the commentary of Con-Fu-Tso on them is equally obscure*. The most eminent literati of the empire have in vain tortured their imagination to decipher these enigmatical records; and, even in Europe, they have exercised the ingenuity of a celebrated philosopher. Leibnitz imagined that he had found in the Koua, which are groups of straight lines, some continuous, others disjoined in the middle, (the straight and broken lines being combined in a variety of ways,) a system of binary arithmetic. This is a conjecture, perhaps rather specious, but difficult to establish by any solid reasons. After all, it is little better than a waste of time to employ it in speculating on the meaning of characters which have long been unintelligible to those who enjoyed the best opportunities for deciphering them. There are more interesting records of the time of Yao, to be found in the Chou-king, an extremely ancient work, one chapter of which, called the Yao-tien, is said by Gaubil to have been composed either in the time of this emperor, or very shortly afterwards. From a passage of this chapter, it very clearly appears that the solar year was fixed at the length of 3654 days, and a method of intercalation adopted to reconcile the motions of the sun and moon. Unfortunately, the intercalation used is not explained; but Gaubil thinks that it was the insertion of seven months in nineteen solar years, a period which, according to him, has been known in China from the most remote antiquity. In this he is confirmed by the Chinese annals, which attribute directly the intercalation in question to the Emperor Yao§. It is re

Souciet, vol. iii. p. 2, et seq.

+ Souciet, vol. iii. p. 6.

Lett. Edif. vol. xxvi. pp. 66 and 106.
In this period the months were alternately of