800 N U M 
to left, as pra&ifed by mod of the Oriental nations. In- 
(lead of the vertical lines ufed by the Romans, vve there¬ 
fore meet with horizontal ones, in the Chinefe notation. 
Thus, one is represented by a horizontal flroke, with a 
fort of barbed termination ; two by a pair of-fuch (trokes ; 
and three by as many parallel ftrokes; the mark for four 
has four (trokes, with a fort of flourifh ; three horizontal 
ftrokes, with two vertical ones, form the mark for five ; 
and the other fymbols exhibit the fucceflive (trokes abbre¬ 
viated, as far as nine. Ten is figured by a horizontal 
(troke, eroded with a vertical (core, to (how that the fil'd: 
rank of the denary fcale is completed; thus +. A 
hundred is dignified by two vertical Scores, connected by 
three (hort horizontal lines; a thoufand is reprefented by 
a fort of double crofs ; and the other ranks, afeending to 
a hundred millions, have the fame marks fuccefiively 
compounded. Thefe characters were engraved from a 
fet of numerals, printed with metallic types in 1814, at 
Serampore, in the “ Elements of Chinefe Grammar,” by 
the Rev. Dr. Marlhman, one of the Baptift mifiionaries, 
whofe zeal, talents, enterprife, and indefatigable a(Tidu- 
ity, in exploring the recondite dialefts of the Eaft, have 
reflected unfading lultre on his character. 
The numbers eleven, twelve, &c. are reprefented by 
putting the Several marks for one, two, See. the excelfes 
above ten, immediately below its Symbol. But, to denote 
twenty, thirty, &c. the marks of the multiples two, three, 
&c. are placed above the Symbol for ten : eleven, there¬ 
fore, is marked thus, ± ; twenty-one thus, This 
diftinCtion is purfued through all the other cafes. Thus, 
the marks for two, three, &c. placed over the fymbols 
of a hundred or of a thoufand, fignify So many hundreds 
or thoufands. The character for ten thoufand, called 
wan, appears to have been the higheft known, at an early 
period of the Chinefe hiltory; Since, in the.popular lan¬ 
guage at prefent, it is equivalent to all. But the Greeks 
them (elves had not advanced farther. In China, wan wan 
Signifies ten thoufand times ten thoufand, or a hundred 
millions ; though there is alfo a diftinCt character for this 
high number, as (liown on the plate. In the Eaftern drain 
of hyperbole, the phrafe wan wm, far outdoing “ a thou¬ 
sand years,” the meafure of Spanifli loyalty, is the ufual 
fliout with “Long live the emperor !” The Chinefe cha¬ 
racter chub for a million, though not of the greated anti¬ 
quity, is yet as old as the time of Confucius. The cha¬ 
racters for ten millions, and for a hundred millions, are 
not found in their olded books, but occur in the Impe¬ 
rial Dictionary. 
It is remarkable, that the Peruvian language was actu¬ 
ally richer in the names for numerals than the polifhed 
dialeCts of ancient Rome or Greece. The Romans, we 
have feen, went not farther than mille, a thoufand; and 
the Greeks made no didinCtive word beyond pveuz, 01- 
ten thoufand. But, the inhabitants of Peru, under the 
incas, had the term hue, to denote one; chunca, ten ; pa- 
cliac, a hundred ; huaranca, a thoufand ; and hunu, a 
million. Thefe words are either original, or have been 
formed, like our numerical terms, by the abbreviation 
of certain compound expredions. 
Philofophers, from Arillotle down to Locke, have too 
hadily given credit to the vague reports of travellers, 
concerning the very fcanty knowledge which Savages pof- 
fefs of the art of numeration. Even the cautious and 
discriminating, hidorian. Dr. Robertfon, thinks himfelf 
warranted to conclude, from authorities which he quotes, 
that certain tribes of native Americans could reckon no 
farther than ten, or perhaps twenty ; while others ad¬ 
vanced not beyond three. But it is utterly repugnant 
to congruity to luppofe, that any people (hould be iound 
fadeditute of mental faculties, as not to rife aboye thofe 
low numbers. It feems far more probable, that fuch 
numbers were merely the roots of the (ydemsof claflifica- 
tion adopted by the Several tribes, and midaken by un- 
philofophical travellers for the whole extent of their nu- 
B E R. 
meration. Every favage nation mud Surely be fuppofed 
capable of reckoning up the bands of warriors which 
they can bring into the field, amounting generally to hun¬ 
dreds, and often to thoufands. 
Roger Williams, one of the earlied fettlers of New 
England, a man of fenfe and observation, though deeply 
tinCfured with the enthufiafm of the age, publifhed, in 
1643, a Small Key to the language and manners of the 
Indian nations who then furrounded that infant colony, 
in which he gives an ample lid of the numerals employee! 
by the native tribes. It hence appears, that thole people 
ufed the denary fcale of arrangement, and had a fet of 
didinft words toexprefs the numbers as high as a thoufand, 
and could even advance as far as a hundred thoufand, by 
help of combined terms. Thus, one they named nquit; 
ten, pinch; a hundred, pdwfunk; and a thoufand, mitta- 
nng. But thefe words are apparently compound, and 
would doubtlefs be found to throw much light on the 
fubjeCt of numeration, if we had any means ofanalyfing 
them. The fame author aflures us, that the Indians, era- 
ploying grains of corn for fymbols, were very expert in 
their computations. 
According to the teftimony of Leems, a refpedable 
Moravian miffionary, the Laplanders, in their computa¬ 
tions, join very fignificantly the cardinal to the ordinal 
numbers. Thus to exprefs eleven, and twelve, they fay 
auft nubbe lokkai, and gauft nubbe lokJiai; that is, “ one to 
the second ten,” and “ two to the second ten.” In 
like manner, to fignify twenty-one and twenty-two, thofe 
rude people ufed the expredions an ft gnoalmad lokkai, and 
gouftguoalmad lokkai, meaning, one added to the third 
ten, and “ two added to the third ten.” This procedure 
affords a curious and very happy iliuflration of the prin¬ 
ciple of numeral arrangement. 
Next to the decimal fcale itfelf, the fyftem of counting 
by progrelfive Jcores, or twenties, derived from the fame 
fource, appears to have been the molt prevalent. The 
favage who had reckoned the fingers on both hands, and 
then the toes on both feet, making twenty in all, might 
feem to have reached the utraoft limit of natural calcula¬ 
tion. The Guarinis, a very fimple and inoffenfive tribe, 
who live on the (hores of the Maranon, are accordingly 
faid to proceed no farther in their diredft numeration. 
When thefe people want to fignify a hundred, they Gnly 
place in a row five heaps of maize, each compofed of twen¬ 
ty grains. The Mexicans, however, being more ad¬ 
vanced in fociety, were accuflomed to employ the higher 
terms of the fame progreflion. In the ancient hierogly-^ 
phic paintings of that unfortunate race, units, as far as 
a fcore, are exhibited by J'mall balls; and twenty is de¬ 
noted by a figure, which forne authors, and particularly 
Clavigero, have miftaken fora club, but which was really 
a final/ Jiandard or flag. In the fame curious monuments, 
twenty (cores, or fourhundred, is fignified by afpreading 
open feather; probably, becaufe the grains of gold, lodged 
in the hollow of a quill, reprefented, in lome places, mo¬ 
ney, or the medium of exchange. This fymbol has, from 
the rudenefs af the drawing, been taken at times fora 
pine-apple, an ear of maize, or even the head of a fpear ; 
but its application to intimate the duplicate (cores is cer¬ 
tain and invariable. A (ack or bag was alfo painted by 
thofe ingenious people to reprefent twenty times twenty 
(cores, or eight thoufand. It was of the fame form as a 
purle called xiquipilli, and fuppofed to hold eight thou¬ 
land grains ot cacao. At fig. 4, we have exhibited the 
feries of Mexican hieroglyphic numerals, copied from 
Humboldt’s lplendid work entitled Vues des Cordilleres ; 
and, to illulfrate their application, we have reprefented 
the current year, 1819, byhelpof them. 
Traces of numeration by Jcores, or twenties, (till ex- 
ift on the old continent. The expreffion three fcore and 
ten, in our own language, is more venerable than Jeventy; 
and the compound ,J'oixanteet dix, and quatre-vingt dix, are 
the ordinary mode in French for iignifying Jeventy and 
ninety, feptantc and nonante being now never uied. The 
Arabians, 
