among the ancients, was a kind of cupboard, or buffet. Livy, describing the luxury into which the Romans degenerated after the conquest of Asia, says, They had their *abaci*, beds, &c. plated over with gold. (Dec. IV. Lib. ix.)

**Abacus**, among the ancient mathematicians, signified a table covered with dust, on which they drew their diagrams; the word in this sense being derived from the Phoenician *abak*, dust.

**Abacus**, in architecture, signifies the superior part or member of the capital of a column, and serves as a kind of crowning to both. Vitruvius tells us the abacus was originally intended to represent a square tile laid over an urn, or rather over a basket.—An Athenian old woman happening to place a basket, thus covered, over the root of an acanthus; that plant shooting up the following spring, encompassed the basket all round, till meeting with the tile, it curled back in a kind of scroll. An ingenious sculptor passing by, took the hint, and immediately executed a capital on this plan; representing the brick by the abacus, the leaves by the volutes, and the basket by the vase, or body of the capital. Such was the rise of the first regular order.—The form of the abacus is not the same in all orders: in the Tuscan, Doric, and Ionic, it is generally square; but in the Corinthian and Composite, its four sides are arched inwards, and embellished in the middle with some ornament, as a rose or other flower. Scammozzi uses abacus for a concave moulding on the capital of the Tuscan pedestal; and Palladio calls the plinth above the echinus, or boul-

*See Pl. I. fig. 1.*

**Abacus** is also the name of an ancient instrument for facilitating operations in arithmetic. It is variously contrived. That chiefly used in Europe is made by drawing any number of parallel lines at the distance of two diameters of one of the counters used in the calculation. A counter placed on the lowest line, signifies 1; on the 2d, 10; on the 3d, 100; on the 4th, 1000, &c. In the intermediate spaces, the same counters are estimated at one half of the value of the line immediately superior, viz. between the 1st and 2d, 5; between the 2d and 3d, 50, &c. See Plate I. fig. 2. A B, where the same number, 1777 for example, is represented under both by different dispositions of the counters.

**Chinese Abacus.** See Chinese-Swanpan.

**Abacus Pythagoricus**, the common multiplication-table; so called from its being invented by Pythagoras.

**Abacus** is also used by modern writers for a table of numbers ready cast up, to expedite the operations of arithmetic. In this sense we have *Abaci* of addition, of multiplication, of division; an *Abacus logificus*; *Abacus* of squares, of cubes, &c.

**Abacus Logificus** is a rectangle triangle, whose sides, forming the right angle, contain the numbers from 1 to 60; and its area, the facts of each two of the numbers perpendicularly opposite. This is also called a *canon of sexagesimals*.

**Abacus & Palanx**, in the ancient music, denote the machinery, whereby the strings of polyplectra, or instruments of many strings, were struck with a plectrum made of quills.

**Abacus Harmonicus**, is used by Kircher for the structure and disposition of the keys of a musical instrument, whether to be touched with the hands or the feet.

**Abacus Major**, in metallurgic operations, the name of a trough used in the mines, wherein the ore is washed.