T’. H. McLeod on the Arabic Method of Notation. 49 
above figures; it is evidently made up of 1, and 0, but how from 
this circumstance does it get its significance? We conceive the 
way to be this: It is well known to land-surveyors and other 
lineal measurers, that the place where the measuring commences 
is but a point and has no lineal significance, and that the first unit 
of measure is at the distance of a unit from that point, and the 
second at two measures, and the third three, &c.; i. e. in measur- 
ing land the first pin is stuck at the distance of one chain, or 
measure, from the place of beginning, the second at the distance 
of two chains, the third at the distance of three chains, and so on. 
If then the place of beginning be represented by 0, and the sev- 
eral distances respectively by 1, 2, 3, 4, &c., the whole will be 
properly expressed. But when the pins are all exhausted and a 
tally is to be made, how is it to be done? Very naturally by 
placing down a 1, and a 0 (zero) (which has no lineal signifi- 
cance) to the right; the fact is thus recorded, and will read, one 
tally and no more; at the distance of one small measure (or one 
chain) from this point, a 1 tally and 1 chain will be marked down 
(11) and the expression will read one tally, and one chain more ; 
and so on to the second tally, which will be made and recorded 
by a 2 and a 0, to the right (20), which will read two tallys and 
no more. At the distance of one small measure or unit from this 
place there will be recorded 2 tallys and 1 chain more, or 21, 
which will read two tallys and one chain; at the distance of two 
small measures, the record will be 22, which will read two tallys 
and two chains, and so on. 
This we conceive to be the simple structure and probable ori- 
gin of the Indian method. In its structure it is strictly geomet- 
rical, using that term in its primitive signification. 
It will at once be perceived that the tally is not necessarily 
made at one small measure beyond 9, but that it may be made at 
any measure before or beyond that place; but in each case the 
point of repetition will always be expressed by 10, and this from 
the fact that it necessarily reads one principal or large measure 
and no more. This verifies the statement before made that r, in 
Barlow’s formula, will always be exy 10, and that its 
appearing as a power is accidental. 'The whole subject will be 
Ww 1 
clearly exhibited by the following Table : 
0: bv - Sriod See ee es fe 
0 Uw & Me eS Oe le 
20 21 2 83 UM SH 6 VW Bw DW BM ® 
30 31 32 33 34 3 6 37 3 39 36 
40 41 42 43 44 45 46 47 +48 «49 40 4p 
50 51 2 53 3 5 56 UT USB lf Ce 
60 61 62 63 64 6 66 67 68 69 65 6 
Wows 7 IS 78 AS 79 0 7 
80 81 82 8 8 8 86 87 88 89 86 8% 
9 91 92 93 94 9 9% 97 98 99 8 Ye 
0 61 62 68 04 6 6 67 98 89 66 % 
oO pl 92 93 a5 96 87 «698 89 88 Oe 
Szconp Sens, Vol. XIX, No. 55.—Jan,, 1855. 7 
