In some of the early accounts of China, published in Europe, we find the description of certain instruments, said to have been discovered on a mountain near the city of Nankin, and afterwards placed by the Chinese partly in that capital and partly in Pekin. On a more accurate examination of those instruments it appeared, that they had all been constructed for some particular place lying under the 37th parallel of latitude; from whence it followed, that all the observations made with them at Pekin, which is in 39° 55'. north, as well as all those made at Nankin in 32° 4'. north, must have been entirely false: and the very act of placing them so distant from the parallel for which they were constructed, is in itself a sufficient proof of the ignorance of the Chinese in matters of this kind. Mr. Pauw has given the most probable conjecture respecting those instruments. He supposes them to have been made at Balk, in Bactriana, by some of those Greeks who obtained the government of that province under the successors of Alexander, and that they had passed into China during the period of the Mongul government.
The death of Kublai-Khan was speedily followed by the total expulsion of the Tartars from China; and most probably, at the same time, of all those learned men they had been the means of introducing into the country; for when the empire was again subdued by the Mantchoo Tartars, whose race now fills the throne, Sun-chee, the first Emperor of the present dynasty, observes in an edict published by him in 1650, that since the expulsion of the Monguls, the Chinese had not been able to make a correct almanack; and that error had been accumulating on error in their astronomical observations and chronology. At this time, some Mahomedans were again found to superintend the construction of the calendar; but the office devolving, at length, upon a Chinese, the unfortunate almanack-maker happened to insert a false intercalation, assigning thirteen months to the year 1670, when it should have contained no more than twelve. This mistake was an event too fortunate to be overlooked by some Catholic missionaries who, at that time, happened to be in the capital. They saw the advantages to be derived from convincing the Tartars of the ignorance of the Chinese in a matter of the last importance to the government, and they had little doubt of success, where prejudice was already operating in their favour. In short, the Europeans succeeded; the almanacks of that year were declared defective, were called in, a new edition printed off, and the poor almanack-maker is said to have been strangled.
Four German Jesuits were then appointed to fill the vacant places in the tribunal of mathematics; and, being men of learning, they proved of no small use at court. After these the Portuguese succeeded to the appointments of regulating the calendar, three of whom, as already observed, are now entrusted with this important office. Fortunately for these gentlemen, the Chinese have no means of detecting any little inaccuracies that may happen in their calculations. I saw, and conversed with, numbers of their learned men at the palace of Yuen-min-yuen, but I can safely say, that not a single Chinese, nor a Tartar, who shewed themselves there, were possessed of the slightest knowledge of astronomy, nor one who could explain any of the various phenomena of the heavenly bodies. Astronomy with them consists entirely in a certain jargon of judicial astrology; and they remain firmly attached to the belief of the doctrines of their great philosopher, delivered more than two thousand years ago, which teach them that "the heaven is round, the earth a square fixed in the middle; the other four elements placed at its four sides: water to the north; fire to the south; wood to the east; and metal to the west:" and they believe the stars to be stuck, like so many nails, at equal distances from the earth, in the blue vault of heaven.
As to the numerous eclipses taken notice of in the records of the country, they are mere registers, noted down whenever they happened, and not predictions or the result of calculations. It does not appear, indeed, that the Chinese were, at any time, able to predict an eclipse, notwithstanding all that has been said in their favour on this subject. The reputed Chinese tables, published by Father Couplet, have been detected to be those of Tycho Brahe; and Cassini found the chronology of their eclipses, published by Martinus, to be erroneous, and their returns impossible. It could not indeed be otherwise; the defectiveness of the calendar must necessarily falsify all their records as to time.
Had the missionaries been disposed to confer a real service on the Chinese, instead of misleading the world by their strange and wonderful accounts of this people; instead of bestowing so much time in translating into Chinese a set of logarithm tables for the use of Kaung-shee, the second Emperor of the present dynasty, of which they pretend he was so fond that he always carried them about with him suspended to his girdle, they should rather have taught them the use, and the convenience, of the Arabic numbers, of whose combinations and results their own language is not capable, and have instructed a few of their youth in the principles of arithmetic and the mathematics. For such an omission, however, human nature can readily find an excuse. It would be too great an instance of self-denial, to relinquish the advantages and the credit which their superior skill had gained them over a vast empire, by making the individuals of that empire participate in their knowledge.
When we reflect, for a moment, how many perplexities and difficulties were occasioned by the irregular coincidences of the solar and lunar periods, in the calendars of Europe, from the time of Julius Cæsar to the altering of the style by Pope Gregory, we may readily conceive how great must be the errors in the chronology of a country, where the inhabitants are entirely ignorant even of the first principles of astronomy, and where they depended on the adventitious aid of foreigners, to enable them to carry into execution one of the most important concerns of the government.
Every thing of their own invention and discovery carries with it such strong marks of originality, as cannot easily be mistaken. The language declares itself to be most unquestionably the production of the country; so does the mariner's compass; and they have a cycle, or period, to assist their chronology, of which I think none will dispute with them the invention. In their records it is carried back to the time of the Emperor Whang-tee, the third from Fo-shee. This cycle, consisting of sixty years, has no reference to the periods of the motions or coincidences of the sun and moon, as one of the same period among the Hindus, but is used merely as our century, to distinguish time into eras or ages. Instead of denominating any given year the first, second, or third year of such a cycle, they have assumed two sets of characters, one set consisting of ten, and the other of twelve; the first are called the ten roots, and the second the twelve branches. The combination of a root and a branch gives a name for the year; and the different permutations, of which they are capable, supply them with sixty distinct titles, making the complete cycle of sixty years. The nature of this period may be rendered familiar to such as are not conversant with the combination of numbers, by assuming the numerals from 1 to 10 for the ten roots, and the letters of the alphabet from a to m, for the twelve branches, and by placing them in a circle, in the following manner, where the cycle begins with the letter a.
Supposing these letters and figures to be Chinese characters, the first year of any cycle would be called 1a, the second 2b, the third 3c, and so on to 10k, the tenth year; the eleventh would be 1l, the twelfth 2m, the thirteenth 3a, and the sixtieth 10m, when the whole revolution would be completed. This cycle, though always used in the records of their history, never appears in the date of public acts. These only specify the time of the reign under which they are given, as the 1st. 2d. or 3d. day of the 1st. 2d. or 3d. moon, of the 1st. 2d. or 3d. year of the reign of such or such an Emperor.
Little progress as they appear to have made in the science of astronomy, their knowledge of geography, which supposes indeed an acquaintance with the former, is equally limited. Their own empire was considered to occupy the middle space of the square surface of the earth, the rest of which was made up of islands. When the Jesuits first entered China, they found the charts, even of their own country, rude and incorrect sketches, without any scale or proportion, wherein a ridge of mountains covered a whole province, and a river swept away half of another. At present they have neat and accurate maps of the country, copied after the original survey of the whole empire, undertaken and completed by the Jesuits, after several years of indefatigable labour.