| | | | | | | | | | | | | | | | | | | | | | | | |O| |O| |O| |O| |O| |O| |O| |O| Ɔ |O| |O| |O| |O| |O| |O| |O| |O| |O| |O| |O| |O| |O| |O| |O| |O| |O| | | |O| |O| |O| |O| |O| |O| |O| |O| 2 |O| |O| |O| The lower groove marked I indicates units, X tens, and so on up to millions. The beads in the upper shorter grooves denote fives—five units, five tens, etc., essentially in a bi-quinary coded decimal place value system. Computations are made by means of beads which, we believe, would have been slid up and down the grooves to indicate the value of each column. The upper slots contained a single bead while the lower slots contained four beads, the only exceptions being the two rightmost columns, column 2 marked Ө and column 1 with three symbols down the side of a single slot or beside three separate slots with Ɛ, 3 or S or a symbol like the £ sign but without the horizontal bar beside the top slot, a backwards C beside the middle slot and a 2 symbol beside the bottom slot, depending on the example abacus and the source which could be Friedlein, Menninger or Ifrah. These latter two slots are for mixed-base math, a development unique to the Roman hand abacus described in following sections. The longer slot with five beads below the Ө position allowed for the counting of 1/12 of a whole unit called an uncia (from which the English words inch and ounce are derived), making the abacus useful for Roman measures and Roman currency. The first column was either a single slot with 4 beads or 3 slots with one, one and two beads respectively top to bottom. In either case, three symbols were included beside the single slot version or one symbol per slot for the three slot version. Many measures were aggregated by twelfths. Thus the Roman pound ('libra'), consisted of 12 ounces (unciae) (1 uncia = 28 grams). A measure of volume, congius, consisted of 12 heminae (1 hemina = 0.273 litres). The Roman foot (pes), was 12 inches (unciae) (1 uncia = 2.43 cm). The actus, the standard furrow length when plowing, was 120 pedes. There were however other measures in common use - for