ABACUS

ABACUS, or ABACISCUS, 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. See ARCHITECTURE, N^o 15.—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. Scamozzi uses abacus for a concave moulding on the capital of the Tuscan pedestal; and Palladio calls the plinth above the echinus, or boustin, in the Tuscan and Doric orders, by the same name.

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. 1. where the same number, 1802 for example, is represented under both divisions by different dispositions of the counters. A farther illustration of this mode of notation is given in fig. 2.

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. This instrument for computation is, under some variations, in use with most nations, as the Greeks, Romans, Germans, French, Chinese, &c.

Grecian Abacus, was an oblong frame, over which were stretched several brass wires, strung with little ivory balls, like the beads of a necklace; by the various arrangements of which all kinds of computations were easily made.

Roman Abacus was a little varied from the Gre-

cian, having pins sliding in grooves, instead of strings or wires and beads.

Chinese Abacus, or SHWANPAN, like the Grecian, consists of several series of beads strung on brass wires, stretched from the top to the bottom of the instrument, and divided in the middle by a cross piece from side to side. In the upper space every string has two beads, which are each counted for 5; and in the lower space every string has five beads, of different values, the first being counted as 1, the second as 10, the third as 100, and so on, as with us.

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

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

Abacus et Palmarum, 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.