Any real numeral formation by the use of “little,” with the name of some higher unit, would, of course, be impossible. The numeral scale must be complete before the nursery rhyme can be manufactured.

It is not to be supposed from the observations that have been made on the formation of savage numeral scales that all, or even the majority of tribes, proceed in the awkward and faltering manner indicated by many of the examples quoted. Some of the North American Indian tribes have numeral scales which are, as far as they go, as regular and almost as simple as our own. But where digital numeration is extensively resorted to, the expressions for higher numbers are likely to become complex, and to act as a real bar to the extension of the system. The same thing is true, to an even greater degree, of tribes whose number sense is so defective that they begin almost from the outset to use combinations. If a savage expresses the number 3 by the combination 2-1, it will at once be suspected that his numerals will, by the time he reaches 10 or 20, become so complex and confused that numbers as high as these will be expressed by finger pantomime rather than by words. Such is often the case; and the comment is frequently made by explorers that the tribes they have visited have no words for numbers higher than 3, 4, 5, 10, or 20, but that counting is carried beyond that point by the aid of fingers or other objects. So reluctant, in many cases, are savages to count by words, that limits have been assigned for spoken numerals, which subsequent investigation proved to fall far short of the real extent of the number systems to which they belonged. One of the south-western Indian tribes of the United States, the Comanches, was for a time supposed to have no numeral words below 10, but to count solely by the use of fingers. But the entire scale of this taciturn tribe was afterward discovered and published.

To illustrate the awkward and inconvenient forms of expression which abound in primitive numeral nomenclature, one has only to draw from such scales as those of the Zuñi, or the Point Barrow Eskimos, given in the last chapter. Terms such as are found there may readily be duplicated from almost any quarter of the globe. The Soussous of Sierra Leone[126] call 99 tongo solo manani nun solo manani, i.e. to take (10 understood) 5 + 4 times and 5 + 4. The Malagasy expression for 1832 is[127] roambistelo polo amby valonjato amby arivo, 2 + 30 + 800 + 1000. The Aztec equivalent for 399 is[128] caxtolli onnauh poalli ipan caxtolli onnaui, (15 + 4) × 20 + 15 + 4; and the Sioux require for 29 the ponderous combination[129] wick a chimen ne nompah sam pah nep e chu wink a. These terms, long and awkward as they seem, are only the legitimate results which arise from combining the names of the higher and lower numbers, according to the peculiar genius of each language. From some of the Australian tribes are derived expressions still more complex, as for 6, marh-jin-bang-ga-gudjir-gyn, half the hands and 1; and for 15, marh-jin-belli-belli-gudjir-jina-bang-ga, the hand on either side and half the feet.[130] The Maré tribe, one of the numerous island tribes of Melanesia,[131] required for a translation of the numeral 38, which occurs in John v. 5, “had an infirmity thirty and eight years,” the circumlocution, “one man and both sides five and three.” Such expressions, curious as they seem at first thought, are no more than the natural outgrowth of systems built up by the slow and tedious process which so often obtains among primitive races, where digit numerals are combined in an almost endless variety of ways, and where mere reduplication often serves in place of any independent names for higher units. To what extent this may be carried is shown by the language of the Cayubabi,[132] who have for 10 the word tunca, and for 100 and 1000 the compounds tunca tunca, and tunca tunca tunca respectively; or of the Sapibocones, who call 10 bururuche, hand hand, and 100 buruche buruche, hand hand hand hand.[133] More remarkable still is the Ojibwa language, which continues its numeral scale without limit, furnishing combinations which are really remarkable; as, e.g., that for 1,000,000,000, which is me das wac me das wac as he me das wac,[134] 1000 × 1000 × 1000. The Winnebago expression for the same number,[135] ho ke he hhuta hhu chen a ho ke he ka ra pa ne za is no less formidable, but it has every appearance of being an honest, native combination. All such primitive terms for larger numbers must, however, be received with caution. Savages are sometimes eager to display a knowledge they do not possess, and have been known to invent numeral words on the spot for the sake of carrying their scales to as high a limit as possible. The Choctaw words for million and billion are obvious attempts to incorporate the corresponding English terms into their own language.[136] For million they gave the vocabulary-hunter the phrase mil yan chuffa, and for billion, bil yan chuffa. The word chuffa signifies 1, hence these expressions are seen at a glance to be coined solely for the purpose of gratifying a little harmless Choctaw vanity. But this is innocence itself compared with the fraud perpetrated on Labillardière by the Tonga Islanders, who supplied the astonished and delighted investigator with a numeral vocabulary up to quadrillions. Their real limit was afterward found to be 100,000, and above that point they had palmed off as numerals a tolerably complete list of the obscene words of their language, together with a few nonsense terms. These were all accepted and printed in good faith, and the humiliating truth was not discovered until years afterward.[137]

One noteworthy and interesting fact relating to numeral nomenclature is the variation in form which words of this class undergo when applied to different classes of objects. To one accustomed as we are to absolute and unvarying forms for numerals, this seems at first a novel and almost unaccountable linguistic freak. But it is not uncommon among uncivilized races, and is extensively employed by so highly enlightened a people, even, as the Japanese. This variation in form is in no way analogous to that produced by inflectional changes, such as occur in Hebrew, Greek, Latin, etc. It is sufficient in many cases to produce almost an entire change in the form of the word; or to result in compounds which require close scrutiny for the detection of the original root. For example, in the Carrier, one of the Déné dialects of western Canada, the word tha means 3 things; thane, 3 persons; that, 3 times; thatoen, in 3 places; thauh, in 3 ways; thailtoh, all of the 3 things; thahoeltoh, all of the 3 persons; and thahultoh, all of the 3 times.[138] In the Tsimshian language of British Columbia we find seven distinct sets of numerals “which are used for various classes of objects that are counted. The first set is used in counting where there is no definite object referred to; the second class is used for counting flat objects and animals; the third for counting round objects and divisions of time; the fourth for counting men; the fifth for counting long objects, the numerals being composed with kan, tree; the sixth for counting canoes; and the seventh for measures. The last seem to be composed with anon, hand.”[139] The first ten numerals of each of these classes is given in the following table:

No.CountingFlat
Objects		Round
Objects		MenLong
Objects		CanoesMeasures
1gyakgakg'erelk'alk'awutskank'amaetk'al
2t'epqatt'epqatgoupelt'epqadalgaopskang'alpēeltkgulbel
3guantguantgutlegulalgaltskangaltskantkguleont
4tqalpqtqalpqtqalpqtqalpqdaltqaapskantqalpqsktqalpqalont
5kctōnckctōnckctōnckcenecalk'etoentskankctōonskkctonsilont
6k'altk'altk'altk'aldalk'aoltskank'altkk'aldelont
7t'epqaltt'epqaltt'epqaltt'epqaldalt'epqaltskant'epqaltkt'epqaldelont
8guandaltyuktaltyuktaltyuktleadalek'tlaedskanyuktaltkyuktaldelont
9kctemackctemackctemackctemacalkctemaestkankctemackkctemasilont
10gy'apgy'apkpēelkpalkpēetskangy'apskkpeont

Remarkable as this list may appear, it is by no means as extensive as that derived from many of the other British Columbian tribes. The numerals of the Shushwap, Stlatlumh, Okanaken, and other languages of this region exist in several different forms, and can also be modified by any of the innumerable suffixes of these tongues.[140] To illustrate the almost illimitable number of sets that may be formed, a table is given of “a few classes, taken from the Heiltsuk dialect.[141] It appears from these examples that the number of classes is unlimited.”

One.Two.Three.
Animate.menokmaalokyutuk
Round.menskammasemyutqsem
Long.ments'akmats'akyututs'ak
Flat.menaqsamatlqsayutqsa
Day.op'enequlsmatlp'enequlsyutqp'enequls
Fathom.op'enkhmatlp'enkhyutqp'enkh
Grouped together.——matloutlyutoutl
Groups of objects.nemtsmots'utlmatltsmots'utlyutqtsmots'utl
Filled cup.menqtlalamatl'aqtlalayutqtlala
Empty cup.menqtlamatl'aqtlayutqtla
Full box.menskamalamasemalayutqsemala
Empty box.menskammasemyutqsem
Loaded canoe.mentsakemats'akeyututs'ake
Canoe with crew.ments'akismats'aklayututs'akla
Together on beach.——maalis——
Together in house, etc.——maalitl——

Variation in numeral forms such as is exhibited in the above tables is not confined to any one quarter of the globe; but it is more universal among the British Columbian Indians than among any other race, and it is a more characteristic linguistic peculiarity of this than of any other region, either in the Old World or in the New. It was to some extent employed by the Aztecs,[142] and its use is current among the Japanese; in whose language Crawfurd finds fourteen different classes of numerals “without exhausting the list.”[143]

In examining the numerals of different languages it will be found that the tens of any ordinary decimal scale are formed in the same manner as in English. Twenty is simply 2 times 10; 30 is 3 times 10, and so on. The word “times” is, of course, not expressed, any more than in English; but the expressions briefly are, 2 tens, 3 tens, etc. But a singular exception to this method is presented by the Hebrew, and other of the Semitic languages. In Hebrew the word for 20 is the plural of the word for 10; and 30, 40, 50, etc. to 90 are plurals of 3, 4, 5, 6, 7, 8, 9. These numerals are as follows:[144]

10,eser,20,eserim,
3,shalosh,30,shaloshim,
4,arba,40,arbaim,
5,chamesh,50,chamishshim,
6,shesh,60,sheshshim,
7,sheba,70,shibim,
8,shemoneh,80,shemonim,
9,tesha,90,tishim.