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 compartment 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 assumed 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 0705/10000. [Illustration] 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_.