Is 1 U M B £ R. 
295 
tions of our fyftem of numeration to very young begin¬ 
ners, who are commonly hurried injudicioufly. into the 
midft of complex operations, and which they learn to 
perform by mere routine. But we fhould not deilre. to 
fee it carried any farther. Th.e modern fancy of beguiling 
children into an acquifition of premature knowledge in 
the very handling of toys, we are little difpofed to ad¬ 
mire ; and we cannot help fufpefring, indeed, the ulti¬ 
mate utility of all thofe plans of education which are di¬ 
rected by a mechanical principle, and have an evident 
tendency to reduce the pupil to a fort of machine. 
When the calculations with counters became more in¬ 
volved, the table on which they were performed, being 
neceflarily of a very conliderable fize, was called the 
bench, or bank; and hence our term for an office where 
money-tranfaCHons are negotiated. The court of Exche¬ 
quer, introduced into England by the Norman conqueft, 
and intended for auditing the revenue of the crown, had 
its name from fcucearium, which, in modern Latin, figni- 
fies a chefs-board. The accounts were caft-up by the tel¬ 
lers, or computatores, on a large table covered with black 
cloth, chequered with white lines, on which were placed 
counters, or fmall foreign coins, to denote (ucceffively 
pence, fhillings, and pounds ; proceeding afterwards, on 
the feveral diftinCtures of the cloth, by units, tens, hun¬ 
dreds, &c. But of all the contrivances adopted with this 
view, the rudeJt undoubtedly is the method of regiltering 
by tallies. Thefe confift of ftraight well-feafoned flicks, 
of hazel or willow, fo called from the French verb tailler, 
to cut, becaufe they are fquared at each end. The fum 
of money was marked on the fide with notches, by the 
cutter of tallies, and likewife infcribed on both fides in 
Roman characters, by the writer of the tallies. The final left: 
notch fignified a penny, a larger one a (hilling, and one 
(till larger, a pound ; but other notches, increafmg fuc- 
ccffively in breadth, were made to denote ten, a hundred, 
and a thoufand. The flick was then cleft through the 
middle by the deputy-chamberlains, with a knife and a 
mallet; the one portion being called the tally, and the 
other portion named the counter-tally. After the union 
with Scotland had been concluded, in 1707, a (tore of hazel- 
rods for tallies was fent down to Edinburgh, being in¬ 
tended, no doubt, as a refinement on the Scottifli mode 
of keeping accounts. Their advantages, however, were 
not perceived or acknowledged; and they have fince been 
fuffered, vie believe, to lie as fo much ufelefs lumber. 
But the cafe is very different in England, where this very 
llrange practice has been handed down to our own times; 
a (triking inftance of the blind obftinacy with which an¬ 
cient ufages, however abfurd and ridiculous they may, 
through time, have become, are yet retained in our public 
offices. An aliufion to thefe abfurdities (by which we 
may be fure they are not extinCf) was made in the houfe 
of commons this day, June 8, 1819. Sir Henry Parnell, 
fpeaking upon the fubjeCI of examining the accounts of 
the revenue, faid, “ It appears from the Report of the 
Finance Committee, that the Exchequer forms are ufe- 
Jefs and inconvenient; accounts are kept in a character 
difficult to underftand, and by which the operation of 
fumming them is impoffible.” 
The Greeks, after having communicated to the founders 
of Rome the elements of the numeral characters, which 
are (till preferved, again exercifed their inventive genius 
in framing new fyftems of notation. Difcarding the Am¬ 
ple original ftrokes, they fought to draw materials of con- 
ftruCtion from their extended alphabet. They had no 
fewer than three different modes of proceeding. 
1. The letters of the alphabet, in their natural fuccef- 
fion, were employed to fignify the fmaller ordinal num¬ 
bers. In this way, for inftance, the books of Homer’s 
Iliad and Odyffey are ufually marked. But the practice 
could fcarcely be older than the time of Ariftotle, who, it 
is well known, firft collected and arranged thofe immortal 
poems, in the edition of the Vajket, for the ufe of his il- 
lultrious pupil Alexander the Great. 
2. The firfl: letters of the words for numerals, were 
adopted as abbreviated fymbois. Thus, employing ca¬ 
pitals only, I being retained to denote one, the initial 
n of PENTE' marked five, the A of AEKA denoted ten, 
the H of HEKATON, exprelfed .an hundred, the X of XIAIA 
a thoufand, and the letter M of the word MYPIA repre- 
fented ten thoufand. A Ample and ingenious device was 
ufed for augmenting the powers of thofe fymbois : a large 
n placed over or round any letter, made it fignify five 
times more. Thus, |a| denoted fifty, |Hj five hundred, |X] 
five thoufand, and (Mj fifty thoufand. But Mr. Leflie fays 
the large n made the fum five thoufand times greater; 
and he writes the preceding numbers, 50,000, 500,000, See. 
3. But a mighty ftridewas afterwards made in numerical 
notation by the Greeks, when they diftributed the twenty - 
four letters of their alphabet into three dalles, corrdf- 
ponding to units, tens, and hundreds. To complete the 
fymbois to twenty-(even, for the nine digits, an additional 
chara&er was introduced in each clafs. The mark 
called episemon, was inferted among the units immedi¬ 
ately after s, the letter denoting five; and the lioppu and 
J'anpi, reprefented by 4 and 3 ), terminated reflectively the 
range of tens and of hundreds, or expreifed ninety and 
nine hundred. This arrangement of the fymbois, it is 
obvious, could extend only to- the expreffion of nine hun¬ 
dred and ninety-nine; but, by fubferibing an iota under 
any character, the value was augmented a thoufand-fold, 
or by writing the letter M, or the mark for a myriad, or 
ten thoufand, under it, the effect was increafed ten times 
more. This laft modification wasTometimes more limply 
accomplifhed by placing two dots over the character. 
Their Table of Notation, then, was as follows: 
a. 
1 
t 
10 
P 
100 
cc 
1000 
0 
2 
>6 
20 
(T 
200 
0 
2000 
V 
3 
* 
30 . 
T 
300 
/ 
o' 
4 
40 
U 
400 
y 
3000 
£ 
5 
V 
S° 
? 
500 
£ 
4000 
5 “ 
6 
| 
60 
600 
/ 
Z 
7 
0 
7 ° 
£ 
700 
£ 
1 
5000 
n 
8 
7r 
80 
U) 
800 
yj 
8000 
9 
9 
l 
90 
•D 
900 
'9 
9000 
a. 
M 
or a. 
0 
or 0 
A 
M 
£ 
M 
£ 
M 
0 
M 
or y 
or 
or ‘ 
or 9 
10,000 
20,000 
30,000 
40,000 
50.000 
90,000 
We fliall next fet do 
wn a few compound numbers: 
eblci reprefented 
- 
991 
“ ’ - 6420 
6 349 
- 
9999 
S'CC' 
/, 
4001 
- 
7382 
^ - 
370.000 
- 
8306 
S'rofi 
• M 
43 ? 72 o,ooo 
And fo on for other numbers ; whence it is evident, 
that neither the order nor the number of characters had 
any effect in fixing the value of any number intended to 
be exprefled; for 4001 is expreifed by two characters, 
6420 by three, and 7382 by four; alfo the value of each 
of thofe expreffions is the fame, in whatever order they 
are placed; thus, 03)49 is the fame as 3 ) 499 , or as 4093 ); 
and fo on for any other poffible combination ; but, as re¬ 
gularity tended, in a great meaf'ure, towards iimplicity, 
they always wrote the characters according to their value 
as in the examples above. 
This is the notation employed by Eutocius in his Com¬ 
mentaries on Archimedes, but it is evidently not very ap¬ 
plicable to calculations. Diophantus and Pappus repre- 
lented their myriads by the two letters Me. placed after 
the number, and hence, according to them, the above 
numbers would be written thus; 37o,ooo:=:a£.Mc, and 
43;7- 0 > 000 =9'To ( S.Me. Alfo 43,728,097 is exprefled by 
&'to( 3 .Mv.■/!%£, and 99,999,999 by 0 ^ 49 -Mv. 0 ^ 40 . This no- 
1 /1 1 
tation, in Come meafure, refembles that which we employ 
for complex numbers, fuch as feet and inches,, or pounds 
and 
