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 mid"dle; the other four elements placed at its four sides: water "to the north; fire to the south; wood to the east; and me"tal 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 æras 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 10 roots, and the letters of the alphabet from A to м, 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 2м, the thirteenth 3A, and the sixtieth 10, 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 first, second, or third day of the first, second, or third moon, of the first, second, or third 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 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.

Although the Chinese language be unfavourable for numerical combinations, it is admirably adapted for the concise operations of algebra, and the terse demonstrations of geometry, to neither of which, however, has it ever been made subservient; both the one and the other being totally unknown in the country. Their arithmetic is mechanical. To find the aggregate of numbers, a machine is in universal use, from the man of letters to the meanest shopman behind his counter. By this machine, which is called a Swan-pan, arithmetical operations are rendered palpable. It consists of a frame of wood, divided into two compartments by a bar running down the middle through this bar, at right angles, are inserted a number of parallel wires, and on each wire, in one compartment, are five moveable balls, and in the other two. These wires may be considered as the ascending and descending powers of a numeration table, proceeding in a tenfold proportion; so that if a ball upon any of the wires, in the larger compartment, be placed against the middle bar, and called unity, or one, a ball on the wire next above it will represent ten, and one on the next one hundred; so, also, a ball on the wire next below that expressing unity will be one tenth, the next lower one hundredth, and the third one thousandth, part of an unit; and the balls on the corresponding wires in the smaller com

partment will be five, fifty, five hundred, five tenths, five hundredths, five thousandths; the value or power of each of these, in the smaller division, being always five times as much as of those in the larger. In the following figure, suppose X be as-sumed as the line of units, the lines to the right will be integers decimally increasing, and those to the left fractional parts decimally decreasing; and the Swan-pan, in the present position of the balls, will represent the number 573916 000

0705

This is clearly a system of decimal arithmetic, which, for

the ease, simplicity, and convenience of its operations, it were to be wished was generally adopted in Europe, instead of the endless ways in which the integer is differently divided in different countries, and in the different provinces of the same country. The Swan-pan would be no bad instrument for teaching to a blind person the operations of arithmetic. Yet, paradoxical as it may seem, these operations, as performed by the Chinese, like their written characters, require more the exercise of the eye than of the mind. The simple addition or subtraction of the little balls, to or from the middle bar, shews at once, by their disposition on the board, the result of any required combination. The invention of it, I think, may fairly be attributed to the Chinese; though it has been compared, how justly I cannot pretend to say, to the Roman abacus.

It has been observed, and, perhaps, with a great deal of truth, that the arts which supply the luxuries, the conveni