Three thousand.

Three thousand, one hundred and forty.

千

Six thousand.

IO Six thousand two hundred and three. 千

To denominate ten thousand they use an abbreviated form of the regu

lar numeral wan. It is this, which they thus apply,

Twenty thousand.

Thirty thousand.

Forty thousand.

Fifty thousand.

When other numbers are added to these, however, the figures denoting

the number of ten thousands are placed above this distinctive character as in the other cases: thus,

Thirty thousand.

Thirty-two thousand.

万

Beyond this character for ten thousand, the Chinese seldom use any distinctive character in this mode. Instead of using yih, chaò, king, and kai, the higher numeral characters, they prefer expressing the higher numbers by deeming them so many ten thousands :' thus they express a hundred thousand by placing the character for ten to the left of that for ten thousand; a million, by placing the character for a hundred to the left of that for ten thousand; and thus they express any greater number. is exemplified in the following numbers,

This

百十万

One million, nine hundred and twenty-three thousand.

8三1┻川二川

千十万

Fifty-three millions, one hundred and sixty-three thousand, two hundred and thirty.

Five hundred forty-three millions, four hundred seventy-five thousand, and thrce.

This last number, if written in the customary mode of numbering, would

The attentive reader will observe from these examples, that in this abbreviated mode, the Chinese express the omission of a place in notation by a small cypher, which they however term ling; and that they further insert a cypher for every place thus omitted, as may be seen in the last example given.

In this abbreviated mode, the chief advantage arises from the figures being placed from the left to the right, in the European manner. It is however still incommoded by the necessity of inserting characters underneath to denominate the various figures. This they do to denominate the figures above the tens of thousands; but below tens of thousands, they omit the denominative characters after writing the first; the rest being understood to follow in due course, unless interrupted by the insertion of cyphers, as in the hundreds and units' place of the last number.. This abbreviated mode, though said to be current throughout China, is still confined to accounts: nor have the characters for the figures as yet found their way into the various Chinese dictionaries.

THE SWAN PAN.

If the last mode of notation verges toward the regular decimal system, carried in Europe to so great a degree of perfection, the Swan pan, which according to Barrow, is in universal use, brings it fully into view. This instrument is an oblong frame of wood about eighteen inches long and eight inches wide, divided in the midst by a thin piece of wood, which runs length ways, and forms it into two compartments. These compartments have certain small pins of wood or brass, running across at right angles, on each of which are seven wooden balls about two thirds of an inch in diameter, perforated so as to admit of their being strung and easily moved on the pins, which are fastened into the sides of the frame. Of these seven

upper,

balls, five are in the lower compartment of the frame, and two in the and one in the upper is esteemed equal in value to the five in the lower compartments. Hence as the five in the lower are deemed five units, and the two in the upper two fives, or ten, each pin of wood is furnished with balls capable of expressing any number from one to fifteen.

These pins represent the various places in the Numeration table: the number of pins with their respective balls varies in different instruments, but some of them contain seventeen, which renders them capable of expressing any number as high as seventeen places, or, ten thousand billions. By this instrument, beginning to the left any where it will, a Chinese expresses any number with ease. For example; if he wishes to express thirty-two millions, one hundred and twenty-nine thousand, eight hundred and seven,' he begins to the left and expresses thirty millions by selecting and moving to the middle partition three of the lower balls, which by their relative position will denote thirty millions; he then from the five lower balls on the next pin to the right, selects two to express the two millions; afterwards one from the five on the next pin to the right to express a hundred thousand, and then two of the next five to the right to express the two tens of thousands: after which, to express the nine thousands, he selects of the balls on the next pin to the right, one from the upper two for five, and adds thereto four from the lower to complete the nine: to express the eight hundreds, he then places in view one from the upper two to denote five, and adds three from the lower five, thus forming the eight: lastly to

denote the absence of the tens, he passes by those on the next pin to the right, and to express the seven units, selects one from the upper two for five, and two from the lower five to complete the seven. Thus on eight of the pins, is expressed the sum required; which stands thus on the instrument itself,

This instrument, which is of Chinese origin, and the antiquity of which it is not easy to fathom, while it brings into full application the decimal system of arithmetic, admits of its being carried to any extent. Fractions, could be expressed thereon with perfect ease: the Chinese constantly express by it the various denominations of money, weights, and measures in use among them; which they easily distinguish by leaving one pin to the right as an interval between the whole numbers and the fractional parts of weights, measures, &c. and the same interval between each lower denomination. With this instrument, therefore, they contrive not only to express any number much more expeditiously than they could with the pen but proceed so far as to add, substract, and even multiply therewith.

* Common tradition ascribes the invention of this instrument to the great Tchyeu, the son of Wun-wang, and the brother of Woo-tang, the first emperor of the Tchyeu dynasty.