AbacuS

ABACUS (Gr. abax, a slab Fr. abaque, tailloir), in

architecture, the upper member of the capital of a column.

Its chief function is to provide a larger supporting surface

for the architrave or arch it has to carry. In the Greek Doric

order the abacus is a plain square slab. In the Roman and

Renaissance Doric orders it is crowned by a moulding. In the

Archaic-Greek Ionic order, owing to the greater width of the

capital, the abacus is rectangular in plan, and consists of a

carved ovolo moulding. In later examples the abacus is square,

except where there are angle volutes, when it is slightly

curved over the same. In the Roman and Renaissance Ionic

capital, the abacus is square with a fillet On the top of an

ogee moulding, but curved over angle volutes. In the Greek

Corinthian order the abacus is moulded, its sides are concave

and its angles canted (except in one or two exceptional Greek

capitals, where it is brought to a sharp angle); and the same

shape is adopted in the Roman and Renaissance Corinthian and

Composite capitals, in some cases with the ovolo moulding

carved. In Romanesque architecture the abacus is square with

the lower edge splayed off and moulded or carved, and the

same was retained in France during the medieval period; but

in England,in Early English work, a circular deeply moulded

abacus was introduced, which in the 14th and 15th centuries

was transformed into an octagonal one. The diminutive of

Abacus, ABACISCUS, is applied in architecture to the chequers

or squares of a tessellated pavement . ``Abacus'' is also the

name of an instrument employed by the ancients for arithmetical

calculations; pebbles, hits of bone or coins being used as

counters. Fig. 1 shows a Roman abacus taken from an ancient

monument. It contains seven long and seven shorter rods

or bars, the former having four perforated beads running

on them and the latter one. The bar marked 1 indicates

units, X tens, and so on up to millions. The beads on the

shorter bars denote fives,--five units, five tens, &c. The

rod O and corresponding short rod are for marking ounces;

and the short quarter rods for fractions of an ounce.

The Swan-Pan of the Chinese (fig. 2) closely resembles

the Roman abacus in its construction and use. Computations

are made with it by means of balls of bone or ivory running

on slender bamboo rods, similar to the simpler board,

fitted up with beads strung on wires, which is employed in

teaching the rudiments of arithmetic in English schools.

FIG. 2.--Chinese Swan-Pan. The name of ``abacus'' is also

given, in logic, to an instrument, often called the ``logical

machine,'' analogous to the mathematical abacus. It is

constructed to show all the possible combinations of a set of

logical terms with their negatives, and, further, the way in which

these combinations are affected by the addition of attributes

or other limiting words, i.e. to simplify mechanically the

solution of logical problems. These instruments are all more

or less elaborate developments of the ``logical slate,'' on

which were written in vertical columns all the combinations

of symbols or letters which could be made logically out of a

definite number of terms. These were compared with any given

premises, and those which were incompatible were crossed

off. In the abacus the combinations are inscribed each on a

single slip of wood or similar substance, which is moved by a

key; incompatible combinations can thus be mechanically removed

at will, in accordance with any given series of premises.

The principal examples of such machines are those of W. S.

Jevons (Element. Lessons in Logic, C. xxiii.), John Venn

(see his Symbolic Logic, 2nd ed., 1894, p. 135), and Allan

Marquand (see American Academy of Arts and Sciences, 1885, pp.

303-7, and Johns Hopkins University Studies in Logic, 1883).

Source: An unnamed encyclopedia from a project that puts out-of-copyright texts into the public domain.

This is from a *very* old source, and reflects the thinking of the turn of the last century.