AS SHOWN IN THE NAMES OF NUMERALS. 427

more.

finger as it is used for enumeration. They begin 'with the little finger. This little finger, then, is one. Now six is five (that is, one whole hand) and one We can easily see, then, why their word for 'six comprehends the word for one. Again, seven is five (one whole hand) and two more-thus their 'word for seven comprehends the word for two. Again, when they have bent down the eighth finger, 'the most noticeable feature of the hand is that two fingers, that is, a finger and a thumb, remain extended. Now the Aht word for eight comprehends 'atlah, the word for two. The reason for this I 'imagine to be as follows:-Eight is ten (or the whole 'hands) wanting two. Again, when the ninth finger is down, only one finger is left extended. Their word for nine comprehends tsowwauk, the word for one. Nine is ten (or two whole hands) wanting

6

The Zamuca and Muysca Indians 2 have a cumbrous, but interesting, system of numeration. For five they say, 'hand finished.' For six, 'one of the other hand;' that is to say, take a finger of the other hand. For ten they say, 'two hands finished,' or sometimes more simply 'quicha,' that is 'foot.' Eleven is foot-one; twelve, foot-two; thirteen, foot-three, and so on: twenty is the feet finished; or in other cases 'Man,' because a man has ten fingers and ten toes, thus making twenty.

Among the Jaruroes the word for forty is 'noeni'pume;' i.e. two men, from noeni, two, and canipune,

men.

1 Scenes and Studies of Savage Life, pp. 121, 122.

2 Humboldt's Personal Researches, vol. ii. p. 117.

428 USE OF THE FINGERS IN ARITHMETIC,

Speaking of the Guiana natives, Mr. Brett observes 1 that another point in which the different nations agree ' is their method of numeration. The first four num'bers are represented by simple words, as in the table 'above given. Five is "my one hand," abar-dakabo in Arawak. Then comes a repetition, abar timen, biam timen, &c., up to nine. Biam-dakabo, "my two "hands," is ten. From ten to twenty they use the 'toes (kuti or okuti), as abar-kuti-bana, "eleven" biam"kuti bana, "twelve," &c. They call twenty abar-loko, one loko or man. They then proceed by men or scores; thus, forty-five is laboriously expressed by 'biam-loko-abar-dakabo tajeago, "two men and one "hand upon it." For higher numbers they have now recourse to our words hundred and thousand. So also among the Caribs, the word for 'ten,' Chonnoucabo raim, meant literally the fingers of both hands;' and that for twenty' was Chonnougouci raim, i.e. the fingers and toes.2

6

เ

The Coroados generally count only by the joints of the fingers, consequently only to three. Every greater number they express by the word 'mony.'

6

6

According to Dobritzhoffer the Guaranies, when questioned respecting a thing exceeding four, immediately reply ndipapahabi, ndipapahai, innumerable.'* So also the Abipones can only express three numbers in proper words: Iñitára, one, Iñoaka, two, Iñoaka yekaini, three. They make up for the other numbers

1 Brett's Indian Tribes of Guiana, Brazil, vol. ii. p. 255.

6

AS SHOWN IN THE NAMES OF NUMERALS. 429

by various arts; thus, geyenk ñatè, the fingers of an emu, which, as it has three in front and one turned back, are four, serves to express that number: nèen

halek, a beautiful skin spotted with five different 'colours, is used to signify the number five.' 'Hanámbegem, the fingers of one hand, means five; lanám rihegem, the fingers of both hands, ten; lanám rihegem 'cat gracherhaka anamichirihegem, the fingers of both 'hands and both feet, twenty.

Among the Malays and throughout Polynesia the word for five is ima, lima, or rima. In Bali, lima also means a hand; this is also the case in the Bugis, Mandhar, and Endé languages; in the Makasar dialect it is liman, in Sasak it is ima, in Bima it is rima, in Sembawa it is limang.1

In the Mpongwe language' tyani' or 'tani' is five, ntyame 'is 'hand.' The Koossa Kaffirs make little use of numerals. Lichtenstein could never discover that they had any word for eight, few could reckon beyond ten, and many did not know the names of any numerals. Yet if a single animal was missing out of a herd of several hundred, they observed it immediately.3 This, however, as Mr. Galton explains, is merely because they miss a face they know. Among the Zulu, 'tatitisupa' six, means literally take the thumb;' i.e., having used the finger of one hand, take the thumb of the next. 'The numbers,' says Lichtenstein, are 'commonly expressed among the Beetjuans by fingers 'held up, so that the word is rarely spoken; many are

1 Raffles's History of Java, Appendix F.

2 Grammar of the Mpongwe Lan

เ

guage. 1847.

3 Lichtenstein, vol. i. p. 280. See also App.

430

THE ORIGIN OF THE DECIMAL SYSTEM.

'even unacquainted with these numerals, and never employ anything but the sign. It therefore occasioned me no small trouble to learn the numerals, and I could by no means arrive at any denomination for the num'bers five and nine. Beyond ten even the most learned 'could not reckon, nor could I make out by what signs they ever designated these higher numbers.' 1

6

Even in our own language the word 'five' has a similar origin, since it is derived from the Greek TÉVTE, which again is evidently connected with the Persian pendji; now in Persian 'pentcha' means a hand, as Humboldt has already pointed out.2

Hence, no doubt, the prevalence of the decimal system in arithmetic; it has no particular advantage; indeed, either eight or twelve would, in some respects, have been more convenient; eight, because you can divide it by two, and then divide the result again by two; and twelve because it is divisible by six, four, three, and two. Ten, however, has naturally been selected, because we have ten fingers.

These examples, then, appear to me very instructive; we seem as it were to trace up the formation of the numerals; we perceive the true cause of the decimal system of notation; and we obtain interesting, if melancholy, evidence of the extent to which the faculty of thought lies dormant among the lower races of man.

1 Loc. cit. vol. ii. App.

2 Personal Researches, London, 1814, vol. ii. p. 116.

CHAPTER X.

LAWS.

THE

HE customs and laws of the lower races, so far as religious and family relations are concerned, have already been discussed. There are, however, some other points of view with reference to which it seems desirable to make some remarks. The progress and development of law is indeed one of the most interesting as well as important sections of human history. It is far less essential, as Goguet1 truly observes, 'de savoir 'le nombre des dynasties et les noms des souverains qui les composoient; mais il est essentiel de connoître 'les loix, les arts, les sciences et les usages d'une nation que toute l'antiquité a regardée comme un modèle de sagesse et de vertu. Voilà les objets que je me suis proposés, et que je vais traiter avec le plus d'exacti'tude qu'il me sera possible.' It is, however, impossible thoroughly to understand the laws of the most advanced nations, unless we take into consideration those customs of ruder communities from which they took their origin, by which they are so profoundly influenced.

It is, therefore, very much to be regretted that we are not more thoroughly acquainted with the laws and customs of savage races.

1 De l'Origine des Loix, des Arts, et des Sciences, vol. i. p. 45.