PRACTICAL CALCULATION 
51 
ual parts, 
acts with 
sfactorily 
on of it is 
i, and the 
The size 
measure- 
show that 
,s; it may 
.ended for 
a banker’s 
3, or again 
)ring-table 
like tric- 
pinion has 
id between 
even been 
le was in- 
But there 
b was used 
lation and, 
i abacus, it 
Lve an idea 
like. The 
ith its in- 
seen. The 
ane except 
drachmae), 
e talent or 
a drachma, 
for jf-obol 
rpLTT] [XOpLOV, 
;ems to he 
five shorter 
ia; the first 
the 6 obols 
The longer 
lines would provide the spaces for the drachmae and higher 
denominations. On the assumption that the cross line indi 
cates the Roman method of having one pebble above it to 
represent 5, and four below it representing units, it is clear 
that,including denominations up to the talent (6000 drachmae), 
only five columns are necessary, namely one for the talent or 
6000 drachmae, and four for 1000, 100, 10 drachmae, and 1 
drachma respectively. But there are actually ten spaces pro 
vided by the eleven lines. On the theory of the game-board, 
five of the ten on one side (right or left) are supposed to 
belong to each of two players placed facing each other on the 
two longer sides of the table (but, if in playing they had to 
use the shorter columns for the fractions, it is not clear how 
they would make them suffice); the cross on the middle of the 
middle line might in that case serve to mark the separation 
between the lines belonging to the two players, or perhaps all 
the crosses may have the one object of helping the eye to dis 
tinguish all the columns from one another. On the assump 
tion that the table is an abacus, a possible explanation of the 
eleven lines is to suppose that they really supply five columns 
only, the odd lines marking the divisions between the columns, 
and the even lines, one in the middle of each column, 
marking where the pebbles should be placed in rows; in this 
case, if the crosses are intended to mark divisions between - the 
four pebbles representing units and the one pebble represent 
ing 5 in each column, the crosses are only required in the last 
three columns (for 100, 10, and 1), because, the highest de 
nomination being 6000 drachmae, there was no need for a 
division of the 1000-column, which only required five unit- 
pebbles altogether. Nagl, a thorough-going supporter of the 
abacus-theory to the exclusion of the other, goes further and 
shows how the Salaminian table could have been used for the 
special purpose of carrying out a long multiplication ; but this 
development seems far-fetched, and there is no evidence of 
such a use. 
The Greeks in fact had little need of the abacus for calcu 
lations. With their alphabetic numerals they could work out 
their additions, subtractions, multiplications, and divisions 
898-8, with 
without the help of any marked columns, in a form little less 
convenient than ours: examples of long multiplications, which 
E 2 
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