SWANPAN, or Chinese ABACUS; a board or instrument for performing arithmetical operations, described by Du Halde in his History of China. The following construction is an improvement of that by Mr. G. Smethurk, published in the Gent. Mag. for 1748.
In the square frame of wood A B C D, are four Plate divisions formed by the bars E F and G H; of these CCLXX. divisions three are separated into two parts by the lesser bars a b. In each of the smaller divisions are placed wires, to be taken out at pleasure; and on each of the wires in the left-hand divisions is strung a small ivory ball, or large bead; and on the wires on the right-hand division are placed four such balls or beads.
The balls in the left-hand divisions, when brought up to the middle bar, stand each for five; and those in the right divisions, when brought to the bar, stand for units.
The balls in the two lower divisions represent integers, or the whole of any quantity; those on the uppermost wires stand for ten of such integers, the next for hundreds, and so on, as is expressed in the figure. The wires, in all the divisions, may be increased to any number you think proper.
The balls in the four upper divisions represent parts of integers; those in the two divisions next the left-hand stand for tens; and those in the two other divisions, for units of such parts.
Now if the sum you would set down be integers, begin with the balls in the two lower divisions: for example, on the third row from the top bring two balls, of the right-hand division, up to the middle bar (see the figure); then bring up two on the next row, and one on the same row in the left division; next, four on the top row, and one on the other side of the same row: then in the first row of units, from the bottom, and in the right-hand division, place two balls, on the second row one, and one also on the same line in the right-hand division of tens; lastly, on the third row of units place three balls. The balls being thus placed, if the integers be pounds sterling, they will express 279 l. 2s. 11 d. If the integers be hundred weights, the sum will be 279 cwt. 2 qrs. 11 lb. 3 oz.; or if they be years, they will denote 279 years, 2 months, 11 days, 3 hours.
A part of these balls may represent fractions, either vulgar or decimal: the balls in the first two divisions of parts may stand for the numerators, and those in the other two for denominators; or the numbers in either of these divisions may be added to those in the integers, as decimals. There may also be holes made in the bars where the dots are placed, in which pegs may be occasionally put, to show that those numbers stand for fractions.
By this instrument all the operations of arithmetic may be readily performed. Suppose, for example, you would multiply the sum set down in the division of integers, that is, 279, by 3. Begin with the lowest line, and say 3 times 2 is 6, therefore set that number up; then on the next row, say 3 times 7 is 21, therefore instead of 7 set up 1 on that line, and carry the
Swanpan the two tens to the line below, which will make the Sweden. number there 8. Then at the upper line say, 3 times 9 is 27, therefore set 7 on that line, and carry 2 to the next line below, which will make that number 3. So that the balls on the three lines will then express 837.
If you would divide 279 by 3, begin in like manner with the lowest line: but as 3 cannot be taken in 2, you add the next number to it, and say, the threes in 27 are 9; therefore set back the 2 on the lowest line, and place 9, instead of 7, on the next line above: then at the uppermost line say, the threes in 9 are 3; therefore instead of 9 place 3 on that line, and consequently the quotient will be 93. When there is a remainder, it may be placed with the divisor, as a fraction, in the upper divisions. Where there are many figures in the multiplicand and multiplier, the latter may be placed in the first two divisions of parts, and the former and products in the divisions of integers. In like manner, when there are several figures in the dividend and divisor, the former may be placed in the division of integers, the latter in the first two divisions of parts, and the figures of the quotient, as they rise, in the remaining two divisions.
It is well worth observing, that by means of this instrument a blind man may be taught to add, subtract, multiply, divide, and perform all the other operations of arithmetic, with as much certainty as another person can by figures.