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AB'ACUS (ἄβαξ). In its general signification, a rectangular slab of stone, marble, earthenware, &c.; whence it is applied in a more special sense to various other objects, which possess the characteristic form of a level tablet.

1. A tablet employed in making arithmetical calculations, on the plan of reckoning by decads; similar to that still in use amongst the Chinese (Davis, China, chap. 19.), and commonly called the Pythagorean multiplication table. The illustration (Image: Abacus/1.1) represents an original first published by Velser. (Histor. Augustan.) It is divided into compartments by parallel channels cut through it, into each of which is inserted a certain number of pins with a button at each end, in order that they might be moved up and down the channels without falling out. The numbers represented by the pins in each channel are marked on it; the longer ones at the bottom are for units; the shorter, at the top, for decimals.

A tray covered with sand was likewise employed for the same purpose, the lines being drawn out in a similar manner in the sand, and pebbles used, instead of pins, for making the calculations (Pers. Sat. i. 131.); this was still designated by the same name, as was also the tray of the same kind which geometricians used for describing their diagrams. Apul. Apol. p. 429. Varior.

2. A play-board, divided in like manner into compartments, for one of the ancient games of chance and skill; probably the one nearest allied to our "back-gammon," the ludus duodecim scriptorum, or the game of the twelve lines. Caryst. ap. Athen. x. 46.

The illustration (Image: Abacus/2.1) is copied from an original of marble belonging to the Christian era, which was excavated in a vineyard at Rome. It will be observed that it is divided, like our back-gammon boards, into four separate tables by the cross lines at each side; and each side into twelve compartments by the same number of lines, the duodecim scripta. The inequality of the lines upon which the pieces moved, and of the intervals between them, arose from the necessity of leaving room for a Greek inscription, which, in the original, runs down the centre, but has been omitted for convenience in the wood-cut; the meaning of it, according to the translation of Salmasius, is as follows: — "In playing thus at the throws of the dice, Jesus Christ gives victory and assistance to those who write his name and play with dice."

That the board here figured was actually used in a mixed game of chance and skill, such as our back-gammon, is proved by the lines upon its surface, forming the points upon which the counters moved, and the inscription which implies that the moves were first determined by a chance throw of the dice; and that the name abacus was most appropriately given to the board used at such a game, is testified by the nature of its surface divided into parallel lines, so closely resembling in appearance the counting-board, as well as the circumstance that it was, in fact, a table upon which numbers were reckoned, — the numbers cast up on the dice being added together to decide the move. See the Greek Epigram, quoted by Dr. Hyde, and Christie (Ancient Greek Games, p. 42.), in which a game of this description is described in detail.

3. Also the play-board used in another ancient game of skill, — the ludus latrunculorum, — having a closer resemblance to our chess and draught boards. (Macrob. Sat. i. 5.) Although games of this description were of very great antiquity, and are represented both by the Egyptian and Greek artists, yet the precise manner in which the surface of the board was divided has not been ascertained, because it is always expressed in profile, which only shows the men but not the face of the board. See LATRUNCULI, TABULA LATRUNCULARIA.

4. A "side-board" for setting out the plate, drinking vessels, and table utensils in the triclinium, or dining room. (Cic. Verr. iv. 16. Juv. iii. 204. Plin. H.N. xxxvii. 6.) The illustration (Image: Abacus/4.1), copied from a fictile lamp, shows one of these sideboards with the plate set out upon it. It consists of two slabs, the lower one supported upon two feet, and the upper by a bracket leg, which rests upon the one below. The simplest kinds were made of marble, the more costly of bronze; and the surface was sometimes perforated into holes, in order to receive such vessels as were made with sharp or narrow bottoms, and, consequently, not adapted to stand alone. This appears the most natural interpretation of the multiplices cavernæ (Sidon. Apoll. Carm. xvii. 7, 8.), for the term used to express the setting out of plate upon a side-board is exponere (Pet. Sat. lxxiii. 5.), which would be ill applied, if, according to the common acceptation, these cavernæ were partitions, like the pigeon holes in a cabinet, in which the plate would rather be hidden than displayed.

5. A slab of marble used for coating the walls of a room. (Plin. H.N. xxxv. 1.) Sometimes the whole surface of the wall was covered with these slabs, as in the example (Image: Abacus/5.1), which represents an apartment in Dido's palace from the Vatican Virgil; sometimes coffers or pannels only were inserted, as an ornament; and as extravagance is commonly accompanied by bad taste, the marble itself was occasionally painted upon (Plin. H.N. xxxiii. 56.); and sometimes the coating of stucco or hard white cement, which was capable of receiving a very high polish was sawed from the wall of an old house, and inserted as an abacus instead of marble. See Vitruv. vii. 3. 10., a passage which Becker, in his Gallus, p. 23. n. 11. Transl., is clearly mistaken in referring to sideboards.

6. A square tablet which the early builders placed upon the head of their wooden columns in order to provide a broad flat surface for the superincumbent beam which supported the roof, to lie upon, and thus constituted the first step in the formation of an architectural capital. Vitruv. iv. 1. 11.

It is credible that this simple tablet remained for a long period as the only capital; and in the Doric, the oldest and simplest of the Greek orders, it never lost its original character, but still continued with only the addition of one other and smaller member (the enchinus) as the most prominent and imposing portion of the capital. With the invention of the richer orders the size, form, and character of the abacus were materially altered, though the name was still retained, and applied to the crowning member of any capital. These varieties are fully explained and illustrated under the word CAPITULUM.

The illustration (Image: Abacus/6.1) represents one of the tombs sculptured in the rock at Beni-Hassan, which are supposed by Sir G. Wilkinson to be as old as 1740 B.C. It is highly curious for the early traces it affords of that style of building, which the labour, skill, and refinement of the Greeks gradually improved and embellished until it eventuated in the most perfect of all structures, the Greek Doric temple. There is no base, nor plinth; the columns are fluted; the capital consists of a mere abacus; a single beam or architrave forms the entablature, and supports a sort of sculptural cornice intended to imitate a thatching of reeds; and as there is no frieze (zophorus) between it and the architrave, we may infer that it is illustrative of a period when buildings were merely covered by an outer roof (tectum) without any soffit or ceiling cælum), for the beams which formed the ceiling or under roof were shown externally by the member subsequently termed a frieze. [ZOPHORUS.]

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