T’. H. McLeod on the Arabic Method of Notation. 51 
is destitute of 0, and consequently its origin* is a number and not 
@ point. 
In comparing these three methods, especially the last two with 
the first, it is manifest that they had an essentially different source. 
{t is equally certain that the Indian method could not have origin- 
ated with the Chaldeans, who numbered their flocks and herds 
and counted the stars, in which operation the unit would hold the 
first place in their notation; from which circumstance it is not 
improbable that the Grecian or Roman method came from them, 
or perhaps from the Phenicians, from whom came also their al- 
phabets. But it is certain that we must look to some different 
part of the globe to find the makers of the Indian method, to 
some Egyptian people, to some land measurers, like the dwellers 
on the Nile-—who indeed may have been the very ones, In an 
ethnological point of view, if in no other, these circumstances 
may be of importance, for numbers, like some word -of a lan- 
guage, may hold in their secret embrace some untold history of 
As a result of employing different measures, as circumstances 
require, in numerical expressions, it will be found that any vulgar 
fraction can be made to assume the integral, or decimal form, a 
circumstance which is often overlooked. Take for instance the 
problem of finding the one-third of ten, or the dividing ten by 
three. The well-known result is 3:33333333 é&c., without a 
complete expression being attained; but the difficulty will be 
obviated by using a measure of three, when ten will assume the 
form 101 and the three, 10.+ When the operation is performed 
With these expressions, thus, 101-10, the result will be as 
seen, 10-1, which is a complete expression: but it should be 
observed that this is not read ten and one-tenth, but three and 
one-third, just as the same expression in the denary measure is 
read ten and one-tenth, the advantage gained being that it is a 
ho 
+ When 3 asst 10, 9 will assume the form 100, a tly 10, 
being 1 saage thant 9, pe la ie form 101. Not that it should be considered 
to contain one hundred and one units, but that in the ternary measure it is the ex- 
Pression for 10. Barlow’s Rule for reducing numbers in the denary measure to any 
* measure is as fol ; : ; 
Divide the given number and several quotients as expressed in the denary meas- 
ure, by the posed measure, and note the remainders ; these remainders, read in 
an inverse order, will express the given number in the roposed measure. Thus 
change 1810 in the denary measure to the ternary measure: dividing 1810 by 8 
8!ves 603 and 1 remainder; so 603 by 3 gives 201 and 0 remainder; 201 by 8, 67 
and 0 remainder; and so on. Th T remainders afford for the result 2111001, 
for the ternary measure. 
