An instrument employed by the ancients for facilitating calculations; similar to that now frequently employed for teaching children the rudiments of arithmetic, and which is commonly sold in our stationers' shops. It usually consists of twelve parallel wires, fixed in a light rectangular frame; each wire carrying 12 beads or balls. There are thus 12 times 12, answering to the common multiplication-table, all the results of which it demonstrates to the dullest capacity. All the operations of addition or subtraction are likewise performed by it, by merely moving the beads from one side to the other of the frame. By thus smoothing the difficulties of acquiring arithmetical knowledge at the very outset, and rendering it quite obvious and amusing at the same time, the apparatus becomes one of considerable importance in education.

Another kind of Abacus consists of a series of parallel wires fixed in a frame like the former. On each wire there are nine little balls; the lowest stand for units, the next above for tens, the next hundreds, and so on up to any number. The frame is divided into two compartments a and b, by a cross wire at c, which is sufficiently raised above the wires to allow the little balls to slide under it. Suppose the whole 63 balls to be placed in the compartment a, and it be proposed to note the sum of 4,346,072 : it is effected by sliding the balls shown in b from their previous situation in a.

A variety of machines for facilitating arithmetical computations, have been from time to time introduced and extensively used. Among the most celebrated of these are the inventions of Napier, Gunter, Lamb, Pascal, Stanhope and Babbage; some account of which we have introduced under the article,