ABACUS, from the synonymous Greek word ag4, or from the Phenician word abek, dust, is the name of a smooth table covered with dust, on which the first ma thematicians made their calculations, and traced their diagrams. See Persius, Sat. 1. V. 131. Hence it be came the appellation of an instrument employed by the ancients for performing the operations of arithmetic.
The abacus generally used, is represented in the an nexed diagram, and consists of any number of parallel lines drawn at a distance from each other, equal to twice the diameter of a counter. A counter placed on the first or uppermost line signifies 10,000 ; and two counters. 2 x10,000 or 20,000. A counter on the second line, sig nifies 1000 ; a counter on the third line, 100 ; on the fourth line, 10 ; and, on the fifth, 1. When a counter is placed in any of the spaces between the parallel lines, it signifies one half of what it would signify if it were placed in the line immediately above it ; or five times what it would signify if it were placed on the line immediately below it. In the space between the second and third lines, for example, each counter signifies 500. In the annexed abacus, therefore, the counters on the first line will denote 40,000; those on the second, 3,000 ; those which lie between the second and third, 1,000 ; those on the third line, 300 ; that which lies between the third and fourth, 50; those on the fourth, 20 ; and those on the fifth. 4. The whole sum, consequently, which the counters in dicate, will be Instead of the parallel lines and counters, brass wires and ivory balls are frequently substituted. See Hist.
Inscript.tom. iii. p. S90. Wo!Ili Lexic. Alathemat. p. 171. Phil. Trans. No. 180.
An ingenious abacus, invented by the celebrated Par vault, is represented in Plate 1. fig. 1. It consists of two plates, PQRS, ABCD ; of which ABCD is the upper most, and is placed directly above PQRS. The plate PQRS is about an inch thick, and a foot long, and has a number of grooves, in which the slips of ivory, or copper, kg, If, lie, id, Ste. are moveable in either direction, like the sliding lid of a box. Each slip is divided into 26 equal parts, by horizontal lines cut pretty deep, and has a figure in every division, except the four middle ones, as appears from the plate. The uppermost plate, ABCD,
is pierced completely through by the two openings EF, GH, each being exactly opposite the line of ci phers, and also by the seven vertical openings, inn, op, &c. When the slips of ivory arc raised or depressed, the figures will appear in the openings EF, GI], but in such a manner, that the sum of the two figures on the same slip, which appear in the openings El", GH, will always amount to 10. This slip at N, contains units ; the slip at 1), tens ; the slip at C, hundreds, Ste. In order to move the slips, when the plate ABCD is placed upon the plate PQRS, a sharp point is introduced through the grooves mu, on, Sec. and placed in one of the cross strokes in the slips of ivory, so that, by a slight oblique pressure, the slip may be either raised or depressed. When any par ticular figure is wanted in the opening GH, we have on ly to place the sharp point in the cross stroke of the slip that appears through the grooves inn, 012, opposite to the figure required, and then move the slip downwards, till the sharp point is at n, or p, or the bottom of the groove, the required figure will appear in the opening GII. The reason of this may he readily understood by inspecting the figure.
The pieces of wood, between which the slips of ivory move, are interrupted in their length by a space equal to three of the spaces in the slips, as is represented by the shaded parts above g,f,r, Ste. and the middle of each interruption ought to be exactly opposite the opening GII. The lower surface of each slip of ivory, as T-T, is formed into teeth L, L, each tooth being opposite one of the 11 figures, and carries a catch M , with a spring N. By pressing against M, the catch may be made to lie within the slip T-T ; but when the pressure is removed, the spring N forces it out, as in the figure. Now, when the slip is moving in its groove the catch M will be kept within the slip by the pressure of one of the pieces of wood between which it moves, till the catch comes op posite to the interruption in the piece of wood, when the spring will force it out, so that it will enter into the teeth of the adjacent slip on the left hand, and carry it down one space.