204 The Decimal System. [July, 
itself and unity, whereas Io is only thus measured by 
2 and 5. 
It does not, however, seem at all probable that we shall 
change our present system of notation, at all events for some 
very considerable time to come. The use of another system, 
however, presents no very great, and certainly no insur- 
mountable, difficulties, as any one may easily convince himself. 
Let us take, for example, the duodecimal system. Here it 
will be necessary to introduce two new names, for we are 
now about to count by twelves instead of by tens. The first 
ten numbers can retain their old names, but the names of 
the other two, eleven and twelve, which belong essentially to 
the old system, must be changed. Instead of these let us 
take maun and bar respectively, and let us call the system 
of counting by twelves the ‘‘ bar” system.* In writing in 
figures we should have to introduce two new symbols, viz, 
one for ten and one for eleven, or maun as we will call it. 
Under the bar system, twelve or bar will be represented by 
Io in the same manner as ten under the decimal system. 
Let the symbol v represent ten and « stand for eleven. 
Our system would then be as follows :— 
One. . 27 Seven... 7 Bar-one. . mm Barseventeaa 
Two .2 Hight. 8 Bar-two. *12 Bar-eightieem 
Bar-three . 13 Bar-niney ing 
Three. 3° Nine . 9 
Four. 4 °'Ten. « v  Bar-four: ...14 (Bar-tenwygeare 
Five .5 Maun. «= SBar-five: ..15 ~-Bar-maunieee 
six. 6 Bar. . 20 .Bar-six .. 16° “lwo-banaeeeas 
and so on, two-bar-one 21, &c., up to three-bar 30, four-bar 
40, &c., ten-bar vo, maun-bar <o, and one “‘ gross” 100, or 
bar times bar. The word “ gross,” being convenient and 
already used in English to denote a dozen dozen, has been 
retained. 
Then one gross and one Iot, &c., one gross one-bar IIo, 
one gross two-bar 120, &c., one gross ten-bar Ivo, one gross 
maun-bar I<0, and so on, two gross 200, three gross 300, &c., 
up to bar gross 1000, which we will call ‘‘ one range.” A 
range of ranges might be called a bi-range, and so on a 
tri-range, &c. Anyone can frame a multiplication table, 
using the bar system in the same manner as is usually done 
in the decimal system, and anyone so doing will find that 
he will have no difficulty at all so long as he confines himself 
* The word “bar,” first suggested by the Hindoostanee word barah, meaning 
twelve, has been retained in consequence of its English signification, being 
used here in much the same sense as in the phrase ‘“‘a bar of music.” The 
word ‘‘ maun’’ was selected merely in order to have a short word, and one 
which should sound differently from the name of any other unit. 
