ABACUS, an early device for tracing numerals on a dust covered board. There have been three standard types : a board covered with dust, whence the de rivation, or, at a later period, with wax, and serving the same purpose as a slate in the 19th century or as the modern pad of paper ; (2) a table marked with lines upon or between which were placed loose counters in the form of small discs of metal, bone, glass or other material, or (in China) in the form of rods; and (3) a table on which the coun ters were fastened by means of grooves, wires or rods as seen in the modern number frames often used in teaching children.
The early counter abacus was a table with lines to represent units, tens, hundreds, etc., or to represent different units of value, like pounds, shillings and pence. Addition on such an abacus was doubtless performed as represented in fig. 1, which shows the suc cessive steps in the addition of 64 and 239. Subtraction was simply the process of taking away counters; multiplication was considered as repeated addition, and division as repeated subtraction. This type of abacus was known in the Mediterranean countries, and Herodotus (c. 450 B.c.) is authority for the statement that the Egyptians wrote their figures and reckoned with pebbles "bringing the hand from right to left," while the Greeks proceeded in the opposite direction. There are several references to the abacus in Roman literature, and what is apparently a Greek computing table of some kind was found in the 19th century on the island of Salamis, being still preserved in the Epigraphical museum at Athens (fig. 2).
Latin writers tell of three types of abacus in use in Rome, namely : ( 1) the sand board or the wax tablet, (2) a marked table for counters, and (3) a table with grooves in which the counters were free to slide. Fig. 3 shows a late Roman abacus now in the British Museum, each upper button representing five units of the order in which the column stands, and each lower button representing one unit of the same order. Cicero (Phil. Frag., V., 59) speaks of the counters as aera (bronzes), but the common name was calculi (pebbles) or abaculi, the pieces being made of stone, ivory (Juvenal, xi., 131), metal or coloured glass (Pliny, Hist. Nat., xxxvi., 26, 67).
The earliest type of abacus in China seems to have been the "bamboo rods," that served instead of counters. These were known as early as the sixth century B.C. and they survived in Korea until the close of the 59th century (fig. 4). They found between this and the Roman abacus lies in the fact that it has one more bead in each section. In the 16th century this type, slightly changed and bearing the kindred name of soroban (fig. 7), found its way into Japan where it is still in use. An abacus differ ing considerably from the Roman or oriental types is found in the middle eastern countries. The Turks call it the coulba; the Armenians, the choreb; and the Russians, the s'choty (fig. 8). As in the case of the suan-pan and the soroban, this permits of rapid computation and serves a purpose similar to that of the modern calculating machines (q.v.).
There appeared in Europe in the middle ages the line abacus. This type of abacus somewhat resembled the Salamis table. It consisted of a table ruled with horizontal lines representing the successive powers of ten, each space representing half the value of the line immediately above it (fig. 9). This type was in use until well into the 18th century. A pupil who could compute on such a table was said to "know the lines," and the verb "to abacus" was used as the equivalent of the verb "to compute." The method employed may be inferred from a passage in Robert Recorde's Ground of Artes (about 1542) as shown in fig. so, while the general appearance of the table is seen in fig. I i (taken from the same book).
The discs that were used in computing were commonly known in Great Britain as "counters" (countures, cowntouris) ; in the Latin books as projectiles (pro, forward, + jacere, to throw), being thrown or cast upon the counting board, or as denarii sup putarii (computing pennies) ; and in France as jetons (with many their way into Japan about the year 600 and were known as sangi or sanchu. Until recent times they were used to represent alge braic coefficients, being placed on a board ruled as shown in fig. 5. Since the 12th century the suan-pan (computing tray; see fig. 6) has been generally used throughout China. The chief difference such variants as gects, jectoirs, gietons and jettons, from jacere, to throw). In Germany a counter was called a Rechenpfennig (translation from the Lat. denarius supputarius) or Zahlpfennig (number penny). Such later expressions as "cast an account," "borrow one," "carry two," and possibly "lay a wager" have their origin in this kind of computation. The Court of the Exchequer (Fr., chambre de rechiquier; Lat., scaccarium), the "counting house," the "counter" in the modern shop, billiard counters, poker "chips," and various games trace their origin to the counting board.