50 T. H. McLeod on the Arabic Method of Notation. 
It will here be seen that the repetitions do not necessarily begin 
at one measure beyond 9 but may begin at any measure before 
or after that point. It will also be seen how 10 obtains its sig- 
nificance. 
The Grecian Method, was also a method of large and small 
measures, but it had no 0 (zero), 1 (a unit) being the first figure 
in the sche eme, whence, it evidently had its origin in the consid- 
eration of sndividual objects and not in the measure of distances, 
i. e. it is arithmetical, using that term also in its primitive sense. 
It employs the letters of the Greek alphabet for its characters, the 
first letter representing a unit, the second letter two units, &c., to 
ten, which is expressed by 1 (iota), the tenth letter of the alpha- 
bet ; with this character the repetitions begin. A new character 
is introduced at each repetition, as at twenty, thirty, and so on to 
one hundred, to represent which a new character is added, when 
the whole is repeated; new characters are added for- each bun- 
dred afterwards, to one thousand, which is also represented b 
new character, as well as ten thousand, and one hundred thou- 
sand, &c. The scheme seems then to be simply this: one, ten and 
one,—twenty, twenty and one,—one hundred, one hundred and 
one,—one thousand, one thousand and one, &c. It is seen, con- 
trary to what has been stated, that any number could be expressed 
by this method, all that was necessary being to introduce a new 
character at the end of the roper repetition. If the Greeks did 
not express any number beyond 100,000,000, it was because they 
either did not understand the scheme of their notation, or because 
at this point it became unwieldy; the latter was probably the 
case. It will be also seen that the pag can commence and 
be carried on ~ any number what 
The R ethod, is rather a scutes of fives than of tens. 
It begins its asians with five, introducing a new character to 
express that number. It introduces new characters to express 
ten, fifty, one hundred, five hundred, one thousand, in each case 
making use of the previous figures in connection with the new 
ones to express the numbers beyon nd them. Thus: 
I, IT, Ill, IIT, ba 
VE Fn Vie Wn x 
Ki, Xi. “xen Ree ee 
AVE AVE, XV AVE, 2 
ENV, FEE XXXT EL cee 
which evidently reads, five, five and one, ten, or two fives—for 
five hundred and one, one thousand, one ben sand and one, &e. 
It is also - that it had its origin in contemplating and re- 
cording individual objects like the Grecian method, as like it, it 
