The Number Concept: Its Origin and Development

esimal

at any geographical law of distribution has ever been observed which governs this, but merely that certain families of races have shown a preference for the one or the other method of counting. These families, disseminating their characteristics through their various branches, have produced certain groups of races which exhibit a well-marked tendency, here toward the decimal, and there toward the vigesimal form of numeration. As far as can be a

th fingers and toes used? If only the fingers are employed, the resulting scale must become decimal if sufficiently extended. If use is made of the toes in addition to the fingers

ess of evolution through which the decimal and the vigesimal scales come into being. After the completion of one count of the fingers the savage announces his result in some form which definitely states to his mind the fact that the end of a well-marked series has been reached. Beginning again, he now repeats his count of 10, either on his own fingers or on the fingers of another. With the completion of the second 10 the result is announced, not in a new unit, but by means of a duplication of the term already used. It is scarcely credible that the unit unconsciously adopted at the termination of the first count should now be dropped, and a new one substituted in its place. When the method here described is employed, 20 is not a natural unit to which higher numbers may be referred. It is wholly artificial; and it would be most surprising if it were adopted. But if the count of the second 10 is made on the toes in place of t

o be found in the ancient commercial intercourse which existed between the Britons and the Carthaginians and Ph?nicians, whose number systems showed traces of a vigesimal tendency. Considering the fact that the use of vigesimal counting was universal among Celtic races, this explanation is quite gratuitous. The reason why the Celts used this method is entirely unknown, and need not concern investigators in the least. But the fact tha

329 10

fi

iocad

ficid

ogad =

ficid

ctmoga

qe ficid

ocad

. c

0.

330 10.

fich

ar fichead

fhichea

head is dei

fichea

head is dei

ir fichea

ichead is dei

. c

0.

331 10

ug

r hugain

ugain

deugain

igain

thrigain

ar ugain

edwar ugain

. c

32 10.

fe

h as feed

aeed

as daeed

ee-feed

eed as jeih

re-feed

. k

sane, or j

.333 1

uegu

egond

ueguen

hand = ha

ueguen

tri ueguend

ueguend

piar ueguen

. c

h ueguen

h ueguen

ueguend

ueguend

u gand

ec ueguen

zec uegue

nd, or pemb

ar hand

0.

gher numerals in all these languages, and in Irish many of the lower also, are seen at a glance to be decimal. Among the scales here given the Breton, the legitimate descendant of the ancient Gallic, is especially interesting; but he

, 4-20-10. From 61 to 99 the French method of counting is wholly vigesimal, except for the presence of the one word soixante. In old French this element was still more pronounced. Soixante had not yet appeared; and 60 and 70 were treis vinz, 3-20, and treis vinz et dis, 3-20 and 10 respectively. Also, 120 was six vinz, 6-20, 140 was sept-vinz, etc.334 How far this method

Basque seems to become decimal above 100. It does not appear to be related to any other European system, but to be quite isola

ha

ho

eta hamar

rrogei

i eta hamar

urogei

i eta hamar

urogei

i eta hamar

. e

. mi

races of vigesimal counting, though the scales are, as a whole, decidedly decimal. T

edive

retyve

dstyve = half (

indstyve

sindstyve = h

sindstyv

indstyve = h

hun

er languages of this group have similar terms. Still, these are not pure numerals, but auxiliary words rather, which belong to the same category as pair, dozen, dizaine, etc., while the Danish words just given are the ordinary

pound rather than the remnant of a former vigesimal number system. With this single exception the Albani

dgiete

izet

edgiete

edgiete =

ongly developed in counting, and wherever their numeral scales have been taken down by explorers they have almost always been found to be decimal or quina

.338 10

de

pi

umgassih

ssigokang =

umgakro

ogokang = 2

umgade

degokang =

orrowed from

39 10

.

n-iri =

ato =

abuo =

anno =

u ise =

40 10

e = a perso

de ako tan

ra bande

bande = 5 per

.341 1

.

og

-dzi =

o-ta =

o-ri =

o-ru =

o-fa =

o-dze =

dzo = 20

42 10.

ed

ye-duup =

ba =

ta =

an = 2

. i

ethod of numeral building. It will be remembered that none of the European scales showed this persistency, but passed at that point into decimal numeration. This will often be fou

343 10

a kotu =

a gnorr

ba mui =

.344

oyongo mai = a

boyongo mahu

gboyongo = 2

gboyongo = 5

45 10.

es

gb

-ba =

ar

ta = 3

ad

ni = 4

be-guwo =

isun =

346 10.

tk

ka chkan

m ksde

de ka chkan

gachkir

a (from

0.

7 10. nu

tiki

re nujorquo

borsa =

rsa nujorqu

o.348 1

mu

nintang =

foola =

ola nintang

sabba =

bba nintang

u nani

ani nintan

. k

. Any one investigating African modes of counting with the material at present accessible, will find himself hampered by the fact that few explorers have collected any except the first ten numerals. This leaves the formation of higher terms entirely unknown, and shows nothing beyond the quinary or non-quinary character of

ure will add but little to our stock of knowledge on this point. New instances of counting by twenties may still be found in northern Siberia, where much ethnological work yet remains to be done, and where a

found, in which all but three or four contain v

.349 10.

ozpha =

hei zphaba

-gphozpha

gphozpha

-gphozpha

. s

10. an

qo

lebe

-qogo =

lda antshgo

-qogo =

lda antshgo

qogo =

. n

10. t

ch

i tshud =

jach

hurni tshu

chad =

nni tshud

-chad =

nni tshud

. w

10.

.

o-witsh

a-qo =

o-witsh =

b-qo =

qo-witsh

p-qo =

o-witsh =

. b

azar (P

hnia 1

.

ith =

z-tqa =

tqe ith =

z-tqa =

tqe ith =

ez-tqa

-tqe ith

. b

r (akin t

h 10.

.

-itt =

z-tq =

tqa-itt =

uz-tq =

-tqa-itt

wuz-tq

z-tqa-itt

hauz-tq

ha-tq =

iitsha-tq

-tqa itshatqa = 2

ia 10

ot

da athi

m-otsi

s da athi

-otsi =

s da athi

h-m-otsi

s da athi

. a

h-asi =

10.

.

do wit =

en ?ts

?ts do wit

en ?ts

?ts do wit

-an-?ts

0.

ia (akin

350 10.

ch

la antsgo

hogo =

da antsgo

chago

gelda antsg

chogo =

chogeld

. n

go (akin t

51 10.

.

kuno

no ku =

kuno zino

no ku =

kuno zino

o ku =

huno zino

bis

kuno zino

10. en

kobb

lowe

kawu =

ldanske

seci

ldansku = 3

kuku =

ansku = 4

. n

ergu (fro

sia 10

to-t

era-pschirr

'i-sch

-era-pschirr

-tsch =

-era-pschir

hitl =

-era-pschir

. s

tar) or schi-p

formed in the ordinary vigesimal manner. The reason for this anomaly is not obvious. I know of no other number system that presents the same peculiarity, and cannot give any hypothesis which will satisfacto

ounting to be more consistently vigesimal than in any scale we have thus far met with. The two following examples are exceedin

2 10. migitke

-kin = a

mingitkin par

h chlikki

n chlikki

likkin = 10 ×

hlikkin = 5 × 200, i.

53 10.

ch

i-doehoz =

choz =

i-richoz =

choz =

?] inichoz =

choz =

chikinichoz

ikinichoz

uwanochoz =

ano choz

ruwanochoz =

ano choz

bischano choz

chano choz

nebischano cho

ischano cho

hnewano choz

wano choz

gaschima chnewano cho

wano choz =

i gaschima toschnew

niwano choz

gaschima reschiniwa

iniwano cho

gaschima inischiniw

i schinewano c

inewano choz =

ord, and that number must be taken as the vigesimal unit corresponding to 100 in the decimal scale. But the Ainos have no simple numeral word for any number above 20, forming all higher numbers by combinations through one or more of the processes of addition, subtraction, and multiplication. The only number above 20 which is used as a unit is 200, which is expressed

mes to light in the following fragment of t

ka

fali =

nat =

fano =

sa kati = 2

gjo,

e following will suffice to illustrate the number systems of these dialects, which, as f

.355 10

mi h

si gelea

hisi =

hisi =

n hisi

e hisi =

s not seem in any way inferior to that of the Nicobar tribes, and one is at a loss to account for the superior development of the number sense in the case of the latter. The intercourse of the coast tribes with traders might furnish an explanation of the difficulty were it not for the fact that the numeration of the inland tribes is quite as well developed as that of the

Tribes

heng

i-tain = 20

inai =

n-inai =

a-inai =

in-inai = (1

hen

ribes 1

eang-

i-tanai = 20

inai =

ai-inai

m-inai =

anai-inai =

ang-mom

the scope of this work to enter into any discussion of that involved question. But either through contact or affinity, this form of numeration spread in prehistoric times over half or more than half of the western hemisphere. It was the method employed by the rude Eskimos of the north and their equally rude kinsmen of Paraguay and eastern Brazil; by the forest Indians of Oregon and British Columbia, and by their more southern kinsmen, the wild tribes of the Rio Grande and of the Orinoco. And, most striking and interesting of all, it was the method upon which were based the numeral systems of the highly civilized races of Mexico, Yucatan, and New Granada. Some of

kimos.357

enue

k kolinik

kepe ak

-kolmik che pah a

shu-kepe a

ma-kepe ak

ok ke pe ak

.358 10.

ti, or in

nik-tchikpalik

mallerok

as many times 10 as t

umipit

eronik arvenel

t?unik arvenel

amanik arvenel

tchang

ngner-park

with the Tchiglit language would justify one in giving definite meanings to these words, or in asserting that an error had been made in the numerals. But it is so rema

10. djinkat

e ka =

djinkat

n djinkat

n djinkat

rcu djinka

urcu djink

durcu djink

urcu djinka

ka = 5 men

nkat ka

djinkat k

n djinkat

stakable proof of decimal, numeration. The word ka, man, seems to mean either 10 or 20; a most unusual occurrence. The fact that a number system is partly decimal and partly vigesimal is found to be of

.360 1

tsak

ts ic haiu

lek =

stsek =

yek =

tc'ek =

p'ok =

lpok =

akutlek

wakutlek

iuk = 1

position. But the derivation of some of the terms used is detected with diff

n.361 10

edeel

ulewu

lgyitk, or t

toncwu

kce

. k

te kcenecal

kye

te kcenecal

gulal

itk te kcenec

alpqtal

gyitk te kcenec

. k'

ost careful and accurate of investigators, says in his comment on this system: "It will be seen at once that this system is quinary-vigesimal.... In 20 we fi

ndians.362

juyopamauj ajt

aco ajte

co juyopamauj ajte

uibo, Guiana 10

carena =

arena = 2

-carena =

10.

na

m'a-ratta

-te =

a-ratta = 2

u-te =

'a-ratta =

o-rate =

e-m'a ratta =

tta-te

hebe =

catan.36

= it is

e, or more correctly,

cakal =

kal =

yoxkal =

kal =

cankal =

nkal =

yokal =

okal =

uackal =

ckal =

uuckal =

ckal =

uncal =

hukal =

ak = 1 ty

hot

lah

lbak =

hotu

lahu

xbak =

apic (m

unpic =

ca pic (

alab = a f

000. k

,000.

ect regularity of the system, the following tabulation is made of the various Maya units, which will correspond to the "10 units make one ten, 10 tens make one hundred, 10 hund

= 1 k

= 1 bak

= 1 pic

1 calab =

b = 1{

ot

200,

= 1 alau =

fficiently manifest. No evidence of digital numeration appears in the first 10 units, but, judging from the almost universal practice of the Indian tribes of both North and South America, such may readily have been the origin of Maya counting. Whatever its origin, it c

particulars. In its first 20 numerals it is quinary (see p. 141), and as a system must be regarded as quinary-vigesimal. The Maya scale is decimal through its first 20 numerals, and, if it is to be regarded as a mixed scale, must be characterized as decimal-vigesimal. But in both these instances the vigesimal el

actli =

alli = 1

oalli on

alli omom

li ommatlac

ommatlactli

oalli =

i ommatlact

i, or epoal

i ommatlac

poalli =

li ommatlact

ilpoalli

acempoalli

ompoalli

uepoalli

nauhpoalli

acpoalli

li oncempoal

li omompoall

li omeipoall

li onnauhpoa

olpoalli

tolli on

oalli ipan caxtolli o

1 bunch of grass,

tzontli

tzontli

i onnauhtzont

uipilli, or

oalxiquipilli

tzonxiquipilli

altzonxiquipilli

li onnauhtzonxiquipilli ipan caxtolli onnauhpoalxiquipilli ipan caxtolli onnauhxiquipilli ipan caxtolli onnauhtzontli ipan caxtolli onnauhpoalli ipan caxtolli onnaui; i.e. 1,216,000,000 + 60,800,000 + 3,040,000 + 152,000 + 7600 + 380 + 19. To show the compounding which takes place in the higher numerals, the analysis may be made more literally, thus: (15 + 4) × 20 × 400 × 8000 + (15 + 4) × 400 × 8000 + (15 + 4) × 20 × 8000 + (15 + 4) × 8000 + (15 + 4) × 400 + (15 + 4) × 20 + 15 + 4. Of course this resolution suffers from the fact that it is given in digits arranged in accordance with decimal notation, while the Nahuatl numerals express values by a base twice as great. This gives

s of this region a

a.367 1

-inic =

nic-lahu

b-inic

nic-lahu =

-inic

ic-lahu =

-tnic =

-kal-laluh =

-inic =

bo-inic =

o-inic =

bo-inic =

bo-inic =

c-bo-inic

0.

axic-xi

of being simply lahuh-inic, 10 men, is tsa-bo-inic, 2 × 100, or more strictly, 2 times 5 men. Similarly, 300 is 3 × 100, 400 is 4 × 100, etc. The word for 1000 is simple instead of compound, and

o.368 1

pu

macauh =

uxam =

amacauh =

npuxam =

ziz puxum

puxam =

ton

nacopuxam =

tamen, the square of 20, is a simple word, and 1000 is, as it should be, 2 times 400, p

9 10. t

cei-

apoan tamoam

oa-tevi

ica-tevi

u-tevi =

evi-tevi

e those of the Quiches of Guatemala. The resemblance is so obvi

370 10.

uinac =

nac-lahuh

uinac =

ox-kal = ?1

-kal =

u-humuch

hu

-ho-kal =

. h

-tuc-ro

, a pure decimal system. As has already been stated, the native races of South America were, as a rule, exceedingly deficient in regard to the number sense. Their scales are rude, and show great poverty, both in formation of numeral words and in the actual extent to which counting was carried. If extended as far as 20, these scales are likely to become vigesimal, but many stop far short of

Muysca.371 1

ica = thus says th

eta =

saqui ubchih

-bosa =

-mica =

muyhica

-hisca =

a.372 1

di

?oguhanu

di?o =

oguhanu =

di?o =

oguhanu =

di?o =

oguhanu =

sudi?o =

mba = g

hadi?o =

oamba =

isudi?o =

i?oamba = 5

i?oamba = 1

For reasons already pointed out, no highly civilized race has ever used an exclusively quinary system; and all that can be said of the influence of this mode of counting is that it gives rise to the habit of collecting objects in groups of five, rather than of ten, when any attempt is being made to ascertain their sum. In the case of the subsidiary base 12, for

system of commerce; or as the Babylonians of old found that singularly curious system, the sexagesimal. Habituation, the laws which the habits and customs of every-day life impose upon us, are so powerful, that our instinctive readiness to make use of any concept depends, not on the intrinsic perfection or imperfection which pertains to it, but on the familiarity with which previous use has invested it. Hence, while one race may use a decimal, another a quinary-vigesimal, and another a sexagesimal scale, and while one system may actually be inherently superior to another, no user of one method of reckoning need ever think of any other method as possessing practical inconveniences, of which those employing it are ever conscious. And, to cite a single instan

al form is left, and until we can say of it now only that it is quartz, or that it is diorite, so too the numerals of many languages have suffered from the attrition of the ages, until all semblance of their origin has been lost, and we can say of them only that they are n

e

Of A

44, 159,

ng, R.

er, A.

n, J. J

, A.,

., 29, 47, 89,

w, H.

d, O., 45

y, E.

65, 87, 88, 136, 163

., 24, 27,

, 46, 52, 57, 61, 111

R. F.,

n, A. F.,

, P.

e, H.

16, 95, 96, 136,

, J., 89

24–27, 104,

, F. H.

court,

ncey,

mps, M

offer,

, J. O

P. B., 66, 6

y, A. M

A. A.,

R., 3

W., 8

J. E.,

l, R.

, 159, 166, 171,

on,

A. S., 5

, F.

. W., 1

, M.,

J. L.

r, G.

me, J.

A. C.,

, 114–116, 122, 130,

l, H.

té, J.

s, L.

, A. von

s, M.

J. W.,

, J.,

midt, S.

J. D

erg, J.

. G., 24,

G. W. von,

, H.

. C., 1

S. H

, Sir J

E. P

ald, J

zie, A

. H.,

, A.

(Saint Cric

er, A

n, 23, 79, 111, 1

on,

J. S

on, M.

, A.,

66, 69, 78, 80, 90, 108, 111, 121, 122, 130, 136,

J., 30,

n, J.

van, J

d, A.,

A. de

ot, J

M., 14

, W.

56, 84, 111, 118

E., 53,

, 145, 148, 149, 152, 157, 1

-Bey,

W. O.

, J.,

H., 45

y, W.

H. L

, H.

, A.

R., 66, 81, 83

der,

G., 143, 146,

n, R.

J. B.

ll, W.

G. E.,

38, 42, 64, 69

n, G.

B. A.

C. H.

G., 15

5, 18, 22, 63, 65, 78

s, J.

li, T

e, A.

R., jr.,

ll, W

sham,

r, C.

s, W. L

Of Sub

cus

kuta

ne, 7

asia

er,

, Life

ze,

, 19, 43

aide

ty Isla

deh,

33, 38, 42, 47, 64, 66, 69, 78, 80, 9

inu), 4

a,

ri,

a, 15

nia,

t Riv

ut,

lgonquin),

zon

ym,

10, 16, 19

15, 28, 31,

tum,

al,

pologi

o,

0, 136

age,

b,

, 52–5

tic

ara,

1, 5, 30,

76, 1

ntee

ic), 28, 11

boine,

pask

ntic

ra,

, 24–30, 57, 58, 71, 75, 76, 84, 103

ri,

ra,

, 83, 89, 93,

sess

onian

imma

ars,

iri,

ad,

nque

ares

ands, 16,

ea,

ing, 18

i,

re,

a,

e, 40

la, see

do Riv

, Bay

u?,

57, 112,

la, 4

y, ch

in,

nesti

aye

ta,

an,

ia, 2

, 143

zé,

oro

, 22, 31

ke,

Rive

, 7, 30,

eton), 120,

45, 46, 65, 86, 88

om,

ch,

t Rive

an, 2

ong

oe,

illo

ing mach

pa,

9, 53, 54

e, 142

aja

166, 16

von, 3

ier,

ginian

asus

(see Kir

(Cayubabi

, 169, 179

, Mo

29, 69, 79, 121,

lon

co,

on Bay

s XII.

enne

cha,

hinese),

y, 62, 1

2, 6, 21,

, 65, 8

sag,

ssia,

eu,

n Chi

bian,

che,

ibo

's Cre

a,

xo,

, 64,

e,

r Isla

3, 4

, Robi

tu,

mey,

, 81,

30, 46,

y Isla

re, 91

ra,

é,

o,

, 136

il,

sion

ian, 1

numbe

uth

imal,

ch,

w,

n,

148,

ellad

ter Ba

, 68

1, 85, 89, 118, 123, 124,

a, 96,

, 48, 51, 52, 54, 61, 64,

uibo,

7, 39, 168, 169, 179

14,

Sand Pa

64,

l,

138,

hiva

op,

ndo P

i,

mime, 10, 23

goe

16,

r's Ri

s, 68

2, 15, 16, 54

ah,

finge

s Islan

1, 124, 129,

gan

ic,

bi,

169,

gia,

38–43, 1

re, 1

a,

o,

tation

h,

6, 129,

Isla

, 29, 52,

i, 23

ni, 5

mala,

to,

curu

ang

da,

13, 114,

d,

9, 25, 70

, 86,

k, 65,

ro,

Islan

sa, 8

End

laya

tot, 8

teca

s Bay,

, 1

Leig

, 1

dic, 1

nois

inger,

96, 1

6, 54, 55, 59, 62, 65, 66, 79, 80, 8

Ocean,

uropea

, 129

9, 80, 124

erong

nkas,

ff,

40, 86,

, 93

o, 61

fingers, 7

i,

ssin

i, 27, 1

atka, 7

i, 13

nkaw

en,

l Bay

assa,

55, 138,

si,

ahili

au,

th, 5

9, 19, 40

yma

enay

iak

dy,

, 1

butt

ma,

i,

e, 78

iutl

ardièr

ador

pperama

81, 86, 124, 128,

i,

nd, 10–

s Isla

scha

u,

r, 10–18, 48

ne,

on,

aliforn

i,

ami,

a,

ssar

Calculati

ie Rive

ni,

ascar

res,

assi

asy,

nta,

, 45, 90

colo,

adu

ingo

reva,

x,

21–23, 25

64, 9

howie

é,

ura,

s, 93, 1

Islands,

usetts,

, 2, 3, 35, 1

bani

tzinca

5, 46,

yi,

obi,

sha,

16, 22, 2

de,

, 195, 201

mi,

c, 90

inger, 1

le,

Yunga

si,

saga,

ssipp

bi,

gan,

can,

ko,

le,

roo,

olia

is, 53,

ee,

on Ba

Noula

o, 69,

, 95

vi,

ion, 19, 33

ari,

do,

lug,

River,

ca,

anda

1, 144, 177

va, 11

, 9, 15,

ne, 6

128

ledoni

ranad

inea,

brides

relan

ealan

rces,

imowr

iam, 6

ragu

ar, 7

ingal

a, 16

n Riv

28, 82, 171, 17

, 7,

l fram

149,

uall

a, 115

ry, ch

ssa

a, 84

aken

ha,

o,

n, 58

one,

, 54, 5

ch, 7

mac

, 165

wa,

r Bay

9, 113, 11

he hand),

Islan

136,

anag

aa,

55, 71,

na,

is,

91, 12

–9, 19, 4

no

vian), 2,

ppine

ilologist), 1

ian, 9

69, 7

ul, 57

Isle

arra

y, 25

30, 51, 64,

22, 28, 118

do,

m Bay

Darwi

ington,

Macka

acquar

Soun

, 22

a, 17

nary,

beyan

he,

hua,

id,

onga,

nd Riv

and, 10

ndedness

finge

rande

Napo

rte, 1

Russian)

ptin

ntoni

las,

, 40, 92

cone,

(Shast

atc

hian

d,

tic,

y, ch

e, 13

ral,

imal, 1

noe,

7, 19,

hwap

29, 30,

a Leo

langu

ux,

ng,

onic

Rive

ou, 8

rica, 4,

7–29, 54, 57, 72, 76, 78, 79, 1

h, 2,

int

k, 7

tlum

ky Ba

7, 9,

's Isl

tion, 1

da,

edish), 12

ona

nsa

ala

ti,

ata,

a,

ac, 5

bi,

na,

scan

ana,

24, 27, 79

gy,

chnia

it, 15

bu,

ne,

ry, c

aba,

, 41, 43, 17

as,

bet

54, 59, 61,

ch,

na,

kua,

, 136,

i,

a, 3

17, 96,

naco

ka,

's Bay

shi, 1

n, 86, 1

Rive

uma,

, 1

67,

ates, 29,

Yarr

rapar

rana

28, 31,

6, 147

oria

elo

atpu,

35, 46, 141,

chia,

o, 107

r Isla

sp

ndie,

ji,

okarr

era,

ebag

roi, 2

-Wirr

ke,

Mass., Scho

ua,

ro,

en,

tha,

3, 47, 64

n, 195

burra

55, 60,

ra,

, 16

48, 49, 53, 54

tno

f an Americanist, p. 406;

I received from Dr

ive Culture, V

Vol. XXXI

n Brazil, Tr. from German by

le de Madagascar, ch. xxviii. Quoted b

W., Atlantic Monthly

chwissenschaft, Bd.

de la Société d'Anthr.

," Am. Anthropolog

tive Culture,

it., lo

of Andaman Islands," Journ

vue d'Anthropolo

s," Journ. Anthr. Inst., 1889, p. 290. About a dozen tribes are

nesians, their Anthropolo

See Cushing's pa

rait," Journ. Anth. Inst., 1889, p. 305. For a similar

tive Culture,

G., Letter of

cobi, infra, is the same. See als

tive Culture,

it., lo

la Société d'Anthr.

Pérou et Bol

rding to the same authority, most of the tribes of the Uppe

., Vol. I

iensium. Bororos, p. 15; Gua

ists are, in order, from I. p. 294, III. p. 424, III. p. 114, III. p

ly Life and Origin of

parative Phil

lian Race, V

ustralian Langs.," Journ.

The next four lists are from II. p. 4, I. p.

cit., Vol.

., Vol. I

chwissenschaft

t., II.

, op. cit

. cit., Vo

'Anthropologie

l Inhabitants of the A

chwissenschaft

Tr. Eth. Soc.

., Native Races,

ong the Eskimos of Point Barro

Voyage,

arrative, Vo

. Anthr. Soc. of Lon

cted works, Edinburgh,

gns of Primeval Unity. See also Pe

In Darkest Afric

rough the Dark Conti

Grammaire et Vocabulaire

ang. of the Mississaga

ort on the Indians of

tin de la Soc. d'Anthr.

ourn. Anthr. In

cit.,

chwissenschaft

he Maya Chro

umerals in Am. I

received directly from Dr. Boas.

e Races, Vol. II. p. 753

Syst. of the Yoruba Nation," Journ

chwissenschaft

On Numerals in Am.

anual Concepts," Am.

der deutschen Spra

erican Anthropolo

rammatik der Gr?nland

Arawak Lang.

onnaire de la langue

ggio di Storia Am.

chwissenschaft

cit.,

chwissenschaft

ic," in Encyc. Metro

oya Dialects," Proc. Am. P

ian Languages and Traditions." J

" U. S. Geog. and Geol. Survey,

of Nov.

chwissenschaft

West. Am.," Tr. Am. Et

udies in So. Am. Nat

ogical Associati

tive Culture,

chwissenschaft

fra, Cha

we Speaking Peopl

tive Culture,

arkest Africa,

Proc. Brit. Ass. Adv.

hwestern Tribes of Canada," Proc.

orthwestern Am.," Tr. Am.

cit.,

hwissenschaft,

es of Aboriginal Know

, Tr. Eth. Soc., Lo

al, p. 247. The above are so unlike anything else in the world,

Z?hlmetho

, the Coast People of Texas. The meanings

In Darkest Africa

chwissenschaft,

ans. Am. Phil. As

314. In the illustration which follows, Burton gives

story of the Abipon

, Comparative P

ety of London ,

ourn. Anthr. Ins

Darkest Africa,

cit., l

itive Culture,

achwissenschaf

los. Ling. Br

itive Culture,

, Aborigines of

Tr. Am. Phil, So

f Api Gram.," Journ. An

Grammatik der Gr?nl

chwissenschaft,

ii. p. 18, and

., Nicaragua, V

rchives of Aboriginal Kn

itive Culture,

sous," Bull. de la Soc. d'An

tory of Madagasca

l. de la Soc. d'Anthr.

rchives of Aboriginal Kn

itive Culture,

t. Vol. I

cyc. Metropoli

cit., l

rchives of Aboriginal Kn

cit.,

cit.,

nga Lang., last part

éné Langs," Trans. Can.

thwestern Tribes of Canada," Proc. Bri

ep., 1890, pp.

cit.,

H., Native Races

al Soc. of London

Hebrew

ie Ph?nizische Spr

chwissenschaft,

s in Am. Indi

ples, etc., p. 253. The meanings

Z?hlmetho

, op. cit., Vo

bull, o

., Lang, of the Miss

st. Ind. Archip

, Vol. VII.; Wilkes, Expl. Ex

, op. cit.,

cit., l

H., Native Races

., Myth and S

H., The Melanesian

cit., l

H., The Melanesian

nese Art on Puget Sound,

, R. H., op.

itive Culture,

e by Chase, Proc. Amer. P

ii Opera, I

n de la Soc. d'Anthr.

he Australian Rac

bes of the Torres Straits," Jo

an Languages," Journ. Anthr. Inst., 1872, p. 88.

, Comparative Ph

this list differs slightly f

e Australian Race,

k, Tasman

D., Queens

k, Tasman

achwissenschaf

it., II.

it., II.

ialects of Queensland," Jour

he Australian Rac

t., Vol.

t., Vol.

t., Vol.

t., Vol.

t., Vol.

are taken from the same volume, pp. 282, 288, 340

The American

ossaria Ling.

cit.,

chwissenschaft,

etic," Encyc. Metro

es in So. Am. Nat

cit., l

, p. 67. The meanings of the numerals are fr

s. Soc. of Bengal,

e Australian Race,

H., Native Races

icle from which this is quoted, no evidence is given to substant

Exploring Expediti

cit.,

graphy and Phi

oc.

sian Researches,

s and Songs of the S

etic," Encyc. Metro

cyc. Metropoli

erschieden

of the Indian Archipe

Z?hlmetho

cit.,

chaft, II. i. p. 317. Se

Expedition, Vol.

ossaria Ling.

graphy and Phi

chwissenschaft,

e statements are based was obtained fr

Culture, Vo

Harper's Monthly

ry of Eng. under the Anglo-

ggested by a comparison found in the Bu

graphy and Phi

chwissenschaft,

ische Briefe, Vol. I. pp. 10

kind may be found in the last

Neumayer's Anleitung zu Wissenschaftliche

ediately following, except those for which the a

he Melanesian La

chwissenschaft,

the same, p. 83 and p. 210. The meaning gi

ized Nations," Tr. Am. E

nschaft, II. ii. p. 80

Brit. Ass'n. Adv. Sc

eschichte der Ma

os of Point Barrow," A

los. Ling. Br

, La République du

he Melanesian La

chwissenschaft,

W., Welsh G

Grammaire Nahuatl

is a purely digital scale, but unfortunately M. Moncelon doe

. Part of these numerals are fro

he Melanesian La

tische Ergebnisse einer Reis

in the Interior Distr

Z?hlmetho

cit.,

i. p. 101. The Kru scale, kindred w

n's Voyages and Trav

ravels, Vo

tische Ergebnisse einer Reis

ravels, Vo

Soussous," Bull. Soc. An

114. The Temne scale is from the same pag

t., I. ii

it., I.

., Central Af

chwissenschaft,

Z?hlmetho

op. cit., I

achwissenschaf

Z?hlmetho

p. cit., I.

Z?hlmetho

Linguistische E

schaft, I. ii. p. 261.

k Continent, Vol. II. p. 49

op. cit., I

entures in Equator

chwissenschaft,

entures in Equator

p. cit., III

6. In Balbi's text 7 and 8 are ansposed.

., p. 533. The next sc

Bull. Soc. Anth. de

Z?hlmetho

cit.,

teen Years in P

Islands of the West

cit.,

elanesian Langua

ol. 1. p. 385. Peacock doe

ds of the Western

Ago, p. 373. The next three scales

me page. Perhaps the meanings of the words for 6 to 9 are more properly "more 1,"

. 429. The meanings of 6 to 9 in this

chwissenschaft,

Dictionnaire Fran

Op. cit., I

chwissenschaft,

ohn W. Kelly, Bureau of Ed.

Z?hlmetho

Op. cit., I

bulaire Fran?ais

chwissenschaft,

i. p. 179, and Kleinschmidt

nt. des Am., 1877, p.

. 358. The next fourteen lists are, with the exception of the Micmac, fr

es of Aboriginal Knowl

ves of Aboriginal Kno

by a word signifying that the fingers, which have

ort B. A. A. S., 1

. Dr. Boas does not give the meanings assigned to 7 and

tions for 6 and 7 are obvious,

t, pp. 158, 160. The meanings assigned to the T

graphy and Phi

cit., l

graphy and Phi

chwissenschaft,

t., IV. i

t., II. i

eanings given for the words for 7

chwissenschaft,

Z?hlmetho

op. cit., I

ns of Mexico and Central America,"

ternationale des Americanis

can only guess at the meanings of 6 to 9. They

s transposed these two scales.

ur du Monde, 1866

. The meanings are

ory is to be found in Hervas' celebrated work,

Gallatin, Trumbull, and Boas, to wh

Indianier in Costa Rica," A

ive of Travels on the Amazon and Rio Negro, vocab. Simi

Glos. Bras

l des Americanistes, 1877, Vol. I

, Irish Gram

R. A., Gaelic

l, Welsh D

t Dict., pub. by

Grammaire Fran?ai

ss der Romanischen Phi

Z?hlmetho

Basque Gra

Z?hlmetho

cit.,

chwissenschaft,

cit.,

cit.,

cit., l

Reise nach Cent

achwissenschaf

it., IV.

t., I. ii

., Central Af

ncyc. Met., V

. p. 64. The next seven scales are fro

Z?hlmetho

3,-Akari, p. 84;

chwissenschaft,

Z?hlmetho

chwissenschaft,

t., III.

of the Nicobar Islands," Jou

Esk. and Esk. Eng. Vocab.," Bureau of Educatio

cabulaire Fran?ais

. Brit. Ass. Adv.

on the Northwestern Tr

ort on the Northwestern

Nations, p. 114. References

ic States, Vol. II. p. 763. The meanings are

Maya Chron

ionnaire de la langu

these numerals are taken, which makes the number in qu

ns of Mexico and Central America,"

tonacos were the first race Cortez

he Coras are of the M

emi-Civilized

Recherches, V

icaragua, Vo

emi-Civilized