ABACUS is also used by modern writers for a table of numbers readily 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 braids 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 Grecian, 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 braids 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 Logistica, is a rectangular triangle, whose sides, forming the right angle, contain the numbers from 1 to 60; and its area, the factors of each of the numbers perpendicularly opposite. This is also called a canon of sexagesimals.