THOMAS] MAZATEC NUMERALS 889

40 yi-cha=2x20.

41 yicha-ngu=40+l.

Soto45.

46 yicha-hu (yiclui-u-u<i;u)=40+5-f-l.

Soto49.

50 yichite (or ichite)=40+10.

51 ichite-iigu=40+]0-i-l.

So to55.

56 ichite-hu (iohite-u-ntru)=40+10+5+l.

Soto59.

60 ichite-ko-te=50+I0, orliterally40+10^10.

61 iohite-ko-te-ngu=50+10^1.

Soto65.

66 ichite-ko-te-hu ⁽ichite-kote-ngu)'=50+10+5+1.

Soto69.

70 ii-liite-kohu-ka=.50+20.

71 ichite-koho-ka-ugu=50+20+1.

Soto75.

76 ichite-koho-ka-hii (ichite-koho-k:i-u-iigu⁾

=50+20+5+

¹

.

Belniar doe.s not give any explanation of ^tlie Ttoho in the.se names;

however, itseem.s

—

^{Phough one} signification of ha ^is two

—

^{to play no}

other role here than hi in the

name

for ^»!(). etc.

80 ii-hite-koho-kate=504-20+10, literally 40+10+20+10.

90 iehite-k(>ho-yicha=50+40.

95 ichite-ko-ho-yicha-vi=50+40+5.

100 u-cha=5X20.

110 u-eha-te=5x20+10.

200 ho-ucha=2x5x20.

300 ha-uclia=3x5x20.

Soto 900.

1,000 te-uclia=10xlOO, literally 10x5x20.

2,000 ho-mi(ho-te-ucha)=2x 10X100.

Soto 9,000.

10,000 te-iiii ⁽ka-uoha⁾

=

V

There seems to he sonic mistake here in Belmar's parenthetical explanation: if hi ^is %) and ^lu-ha lOU,

M-uchu would

be 2,000. which, as

shown

above

from

his

own

list, is (ho-te-uclui).

As

//// isgiven as the equivalent of tr-iidia. 1.000. then lO.OOO, unless varjdng

from

the rule, should be te-te-ucha^ or /v?-(?-mcA«=20x5x100; the latter is

probably

what was

intended,as

we

judge

from

the followingnumbers:

20,000 ka-iui (ka-te-ucha)=20xl0xl00.

30,000 kate-mi (kAte-te-iicha)=30X10X100.

Soto90,000.

100,000 vu-ha-te-ucha=100xlOxlOO.

110,000 ucliate-te-ucha=110X10xlOO.

130,000 uclia-kate-te-ucha=(100+30)X10X100.

Although

this numeral system carries out thequinary count to an unusualextent,yetit isclearlj'quinar\'-vigesimal. Itisalittlestrange,

IIn this, as in the three following numbers (not given here), Belfiiar, whose list I follow, seems,probablyby a^slijiofthe pen.tohiive failedtogive thecompletename;it eertainly sliould beicliih'-kutf-ii-iufu.

hyU

Nl'MEKAI,

SYSTEMS

^fETH.ANN.19 however, that 10 should have what appears to he a simple integral name.

The name

for ^'20 is also simple, Imt that for 40 yt-chd

—

^i.s

composite, signifying^'2, times20.

The

intermediate

minor numbers

in this system are always added toth(> preceding l)ase and not. as in so

many

^{others, on that which follows, nor are they} su))ti'acted

from

a higher base or nuiiiber. as

we

iiave found to bethe; case in the related Zapot(>c.

Some

of ihfnuinlxTluuiitswliiciiap])ear to follow

somewhat

closeh' the quinary-vigesimal system having been presented, the next

method

of countingtowhich attention ^is called is that used by the

Maya. As

this system is the one in which

most

^interest centers because of it.'<

relation tothe numerals found in the codicesand inscriptions,

we

shall dwell

upon

^it

more

fully than

we

have

upon

the others. l)eginning with the numerals used by the

Maya

proper (Yucatecs).

We

^take

as our ^basisthe series asgiven

by

Beltranin hisArtedelIdioma

Maya.

l)lacing at the right the interpretations or ecjuivalents of the terms.

10 lahnn.

1 buluc.

12 lah-ca=ll-4-2.

18 ox-lahun=34-iO.

14 caii-lahun=44-10.

15 hn-lalinn=5

—

10.

10 uac-hihuii=0-' U).

17 uuc-laliiiii

= 7—

10.

IS naxaf-lahun=8

—

10.

lit b(jl(in-lahun=9T-10.

20 huii-kal=oiie20, or kal.

21 liiiii-tu-kal=1^20, or 1 to20.

22 (a-tu-kal=2-t-20.

23 ox-tu-kal=3-4-20.

24 (•an-tn-kal=4-20.

25 lio-t>i-kal=5-|-20.

26 uac-tu-kal=6-20.

27 imc-tu-kal=7+20.

28 uaxaf-tu-kaI=8+20.

29 bolon-tu-kal=9+20.

30 lahii-ca-kal

=

10+20.

31 buluc-tu-kal=lH-20.

.32 lahca-tu-kal

=

124-20, literally 10+2+20.

33 oxlalHi-lii-kaI= 13--20, liUMally 3^. 10-20.

34 i-anlabM-tu-kal

=

14+-20.

35 holiiu-(a-kal

=

15-r20.

36 uaclaluin-tii-kal

=

16+20.

37 uuclalni-tn-kal

=

17+20.

38 uaxailalui-tu-kal

=

^18+20.

39 l)o]onlalui-tu-kal=19-^20, literally9-^10+20.

40 ia-kal

=

2x20.

I'p to this point the forms arc (|iiitc regular, except that of 11, wliich has a

name

as yet uiiiiiterpreteil by the linguists.

With

this

THOMAS]

MAYA NUMERALS 891

exception, the

numbers from

10 to ^!!• ure

formed

1)v the addition of

1, 2, 3, etc., to 10, the decimal .sy.stem upplyiiiy here.

Twenty

has a distinct

name

—

hd. P^-om 21 to 30 the

numbers

are

formed

by tlie

addition to 20 of the

numbers from

1 to 10; and 40 istwice 20.

Before alluding to the change which occurs in the next step, atten- tion is called to lahun^ the

name

tor10.

Dr

Brinton'saysit isappar- ently a

compound

of hih and hun, and gives as the probable signitica- tion, '_{it finishes} one (man)."

As

to its derivation, I think he is cor- rect, as foA, as a substantive, signifies " end, limit, all, or the whole,"

and

A?m

"one."

The

signification of the term

would

therefore

seem

tobe

"

_onefinish," or ^'"ending," or "allof one count," but not " one

man."

Henderson, inhismanuscript Maya-EnglishDictionary,under lah, says, " whole hands," and this is doubtless the true rendering

when

used in this connection. /i«/, 20,as a verb signifies ^••to fasten, shut, close," as a substantive,

"a

fastening together, a closing or shutting up."

Calling20 a score, for the sake of simplicity, the count

from

21 to 39

may

be illustrated thus: hun-tu-Jcal, 1 on the score, or first score;

ca-tu-kal,2on thescore, etc.

Here

the additionistothe score already reached, but the additions to40

—

ca-kal

—

^{orsecondscore are counted}

difl'erently, for 41, insteadof l)einghun-tu-cakal, is him-tK-yoxkul, the latter

—

yoa'kalor o,i^al

—

^{being theterm for60, or thirdscore (3x20).}

As

^{it is} evident that this can notsignify 1 added to 60, there hasbeen a difference of opinion as to the true

meaning

of the expression and as to its correctness. Perez, as quoted by

Dr

Brinton. says, in an unpublished essay in the hitter's possession, that Beltran's

method

of expressing the

numbers

iserroneou.s; that41 should be Innt-tu-cakal

;

42, ca-tu-cakul; 83, ox-fx-caiikal, etc. Nevertheless, as

Dr

Brinton haspointedout, the numeralsabove40 are giveninPerez's Dictionary of the

Maya Language

according to Beltran's system, which appears

from

other evidence to be correct.

Leon

de Rosny'^ suggests that hun-tn-yoA-nl should be explained thus: 60

—

^20-f1.

^However,

the correct rendering appears to be 1 on thethird score, or third 20. Itispossible thatanold and a

new

reck- oning prevailed

among

^the Mayas, as apparently

among

the Cakchi- quels. According toStolP the latter people had an old and a

more

recent

method

of enumerating, which

may

be represented as follows:

Olrt New

41 linn-r-iixc'al ca-viiiak-huii 42 oai-r-oxc'al ca-vinak-cai, etc

1MayaChronicles,p. 8S.

2Numeration desAnciens Mayas,in Conipte-Ruiidu("oiij;. Inivrnai. Anu'Ticranislos,p.^4-49; Nancy,

^Zur.Ethn. der Guatemala,p. 136.

is followed ^here.

41 li\ui-tn-yoxkal

=

l onortothe third20, or thirdscore.

42 (•a-tu-yoxkal=2onortothetliinl20, ortliirdscore.

4.3 ox-tu-yoxkal=8 onortotliethird20, ortlurdscore.

Soto49.

50 lahu-yoxkal^

=

10onthetliird 20, or third.score.

51 buhic-tu-yoxkal

= n

^onthe third20, or third score.

8oto59.

60 oxkal=3x20.

61 hun-tu-cankal

=

^l onthetonrtliscore, etc.

70 lahn-cankal

=

10on tliefourth score,etc.

71 hulnc-tn-cankal

=

^ll on the fonrthscore,etc.

80 <ankal=4x20.

90 lahu-yokal

=

10onthe^fiftliscore.

100 hokal=5x20.

101 lHin-tn-nackaI

=

^l on tliesixthscore.

110 lahu-ua<-kal

=

10onthe sixth^score.

119 liolonlahu-tu-uackal

=

19onthe sixth score.

120 uackal=6x20.

130 lahn.uuckal

=

10ontheseventhscore.

140 unckal=7x20.

150 lahn-uaxackal

=

10onthe eighth^score.

ItiO naxackal=8x20.

170 lahu-bolonkal

=

10onthe ninthscore.

180 l)olonkal=9X20.

190 lahn-tu-lahnnkal

=

10on thetenth^s<-ore.

200 lahunkal

=

10x20.

210 lahn-tu-liulnekal

=

10 ontheeleventhscore.

220 l)uhickal

=

llX20.

230 lahn-tn-lahcakal

=

10onthe twelfthscore.

240 lahcakal

=

12X20.

250 lahu-tu-yoxlahnnkal=10 on the thirteenthscore.

260 oxlaluikal=13x20.

270 lahn-tn-caniahukal

=

¹⁰on the fourteenth score.

280 (anlahunkal

=

14x20.

290 hihn-tu-holhukal

=

10 onthelifteenth score.

.300 holhukal=15x20.

310 lahu-tu-naclahnkal

=

10onthesixteenths<-ore.

320 iiaclahukai

=

li)X20

330 lahu-tu-uuclahuka

=10

onthe seventeenth^score.

340 uuclahukal

=

17x20.

•Op.clt.

STlicreasonforIhe omission"f'"inS" 71) iiiid'.«)isnot nppitrent.

JHuaiAs]

MAYA NUMERALS 893

350 lahu-tu-uaxaclahukal

=

10onthe eighteenthscore.

360 uaxaclahukal=18x20.

370 lahu-bol(iiihihukal

=

10on the nineteenthscore.

380 bolonlalin-kal

=

U)X-'0.

390 lahu-hunl)ak

=

10on^] bak.

400 hiin-bak=one 400.

.500 ho-tu-liak [hukal-tn-bak?]

=

100+400?

600 lahu-tu-bak [lahuii-kal-tu-liak?]=200+400?

700 holhu-tu-bak [holhu-kal-tu-bak?]=300+400?

800 ca-bak=2x400.

900 ho-tu-yoxbak [hokal-tn-yoxliak]=100 onthe third liak,or third400.

1,000 lohu-yoxbak, orliunpic (modern).

2,000 capic (modern).

8,000 Imn-pic (formerand correctuseofthe term).

So

far I have followed Beltran's li.st, as it i.s that on which the nujnber.s asgivenl>v subsequentwritersand lexicographers are based, but ^{it I'arries} the luuueration only to S.OOO.

The names

for 500, 600, and TOO appear to be abl)re\'iated; I have therefore added in brackets the supposed complete terms. These, however, as will be seen by compai'ison. follow^{thi^} rule which prevails

from

-id to^Hit, that

is.theadditions are to the ^lastprecedingbasal number, andnottoward that which isto follow; the tir.st rule holds

good from

41 toH'.M, but thesecond is followedafter pa.ssing800orca-bak,as900laho-tn-ijo.i'hal', or,complete, hoh:tl-tiA-i/o:ch<d\ which ^is equivalent to 100on the third bak.

The

use ofImnp'ie for 1,000was adopted afterthearrivalof the Spaniards.

One

reason mentioned by Reltran for the change wa.sto preventconfusionand^tofacilitatethelumiberingofthecenturyingiv- ing dates.

The

proper native expression for 1,000

was

Jdhu-i/d.rhal^

or, complete, Jalmnh(ihtu-ij(>,i'hal\ e(iuivalent to 200 on the Hd bak.

Vap'u-

—

^2,000

—

^{isinaccordancewith}

^modern

^{usage; accordingtonative}

u.sage 2,000

would

))e Itnlxtl^ or .5x400. In counting the

minor

luun- bersabove^4t)(ithe particle catne."and,"

was

inserted,thus:4.50,Innihal' catuc lahui/o.i'hd.

However,

in coiuiting the added hundreds, tx, and notcafiic.was inserted, as ^isseen al)ove in 50t», <>00, and ^TtiO; hence,as Beltran indicates, thelatter wasonly protixed or preposed tothe

minor

munbers.

Bill- as a numeral ^is supposed to be derived

from

the verb hah^

hidiili, "to roll up,"

"to

tiearound,"and hence presiunably refers to aIjiuidleor package. Piesignifies'"cotton cloth," also a kind of petti- coat, which appears ^to have l)een the original meaning: as this article of dress

was

occasionally used as a sack the numeral

term

probably refers to it in this sense; and Henderson, in hismanuscript dictionary, givesasonesignification

"a

bag

made

out of a petticoat." This inter- pretation corresponds with the

Mexican

term for 8,000.

The

count

from

400. or one l)ak,

when

carried out regularly,

would

be 2 bak, o Ijak, and so on ^to 19 bak; 20 bak, or S.OOO,forminga

new

894 NUMERAL SVSTKMS

(t-tn.ANs.l9 basis to wliicli tlic naino ^{ji'k^}or Imn-pic. ono pic. was applied.

Above

this luiiiibor the count continued by nudtiplication. tiuis:

la-pic =2x«,000.

ox-pio =3X8,000.

(an-pic=4x8,000.

and so on tohdhuiliilnnt-jiic. or 11* pic.

For

:in pic. oi' Itio.doo. another sini])le term caJah

—

^is introdueed;

and ^foi- 20 calab. or3.i!<)<•.()()(».another simpleterm kinchil

—

^{is intro-}

duced: and for20 ^{kinohil. tiie} term (duu.

The

series of primarj' or

t)asal terms ai-e therefore as follows:

20units