48 T. H. McLeod on the Arabic Method of Notation. 
Its centesimal composition will then be: 
510 " H67 Azl160 Phi9 O 25-4 
It is easy to believe, that these regularly formed tables are small 
crystals. To remove doubts in this respect, we have had recourse 
to the kindness of M. Eas who examined our grains 
with a polarizing apparat This proved to him and to us, that 
the grains of ichthin are adit crystallized. 
Art. VIIl._— The Sah tac or Indian pies of Notation; by 
Tuomas H. McLro 
Tue subject of arithmetical notation in its relation particularly 
to the Arabic or Indian, the Roman, and Grecian systems, has ar- 
rested the attention of mathematicians from the earliest period of 
modern mathematical investigation ; but the mechanical structure, 
especially of the Indian, seems to have been overlooked, as well as 
the probable circumstances under which that structure originated. 
Barlow, in his Theory of Numbers, presents the following equation, 
N=ar" +br"-' + cr®-? + &e. ee” T 
where 7 may be any number whatever; ‘and a, b, c, &c. integers 
less than r, as expressing the scheme of the Indian method. It 
is undoubtedly a formula by which that method may be explained ; 
but that it exhibits its simple primitive mechanical structure, may 
be justly questioned. For in the first place it does not show the 
first position of 0 (zero) with any reliable certainty: the only pe 
we are left to refer it, from the explanations, is to 10, where it 
appears on the right cork which we apprehend is not its first 
place ; secondly, 7 appears ‘in the form of a power, which is nn- 
questionably true, but accidental; thirdly, it is asserted that r 
may be any number whatever, yet upon omens it will be 
found always to assume the form 10, whatever be its significance 
in the denary measure; and finally, it ean be in any manner 
supposed that the scheme had its origin in philosophy, as the ‘ 
formula would seem to indicate, bnt that it arose out of the cir- 
cumstances and necessities of the people from whom it sprung. 
aving finished these few restrictions, of which more might 
be made, concerning what mathematicians have said upon this 
ong we shall proceed to explain what we consider to be the 
simple primitive structure of the Indian method, and afterwards 
cara way of comparison to that of the Grecian and Roman 
ethor 
Sg a ern aoe 
The first peenlority . the Indian method is its 0 (zero), which 
stands as the origin of the scheme, as will be seen by writing it 
a 0,1,2,3,4,5, 6, 7, 8,9, 
where it evidently appears in its first place. * il next character- 
istic worthy of note, is the 10, wht deorn t appear among the 
