The only numerals calling for any special note are those for 11 and 9. For 9 we should naturally expect a word corresponding in structure and meaning to the words for 7 and 8. But instead of the “four brought to and held up with the rest,” for which we naturally look, the Zuñi, to show that he has used all of his fingers but one, says “all but all are held up with the rest.” To express 11 he cannot use a similar form of composition, since he has already used it in constructing his word for 6, so he says “all the fingers and another over above held.”

The one remarkable point to be noted about the Zuñi scale is, after all, the formation of the words for 1 and 2. While the savage almost always counts on his fingers, it does not seem at all certain that these words would necessarily be of finger formation. The savage can always distinguish between one object and two objects, and it is hardly reasonable to believe that any external aid is needed to arrive at a distinct perception of this difference. The numerals for 1 and 2 would be the earliest to be formed in any language, and in most, if not all, cases they would be formed long before the need would be felt for terms to describe any higher number. If this theory be correct, we should expect to find finger names for numerals beginning not lower than 3, and oftener with 5 than with any other number. The highest authority has ventured the assertion that all numeral words have their origin in the names of the fingers;[69] substantially the same conclusion was reached by Professor Pott, of Halle, whose work on numeral nomenclature led him deeply into the study of the origin of these words. But we have abundant evidence at hand to show that, universal as finger counting has been, finger origin for numeral words has by no means been universal. That it is more frequently met with than any other origin is unquestionably true; but in many instances, which will be more fully considered in the following chapter, we find strictly non-digital derivations, especially in the case of the lowest members of the scale. But in nearly all languages the origin of the words for 1, 2, 3, and 4 are so entirely unknown that speculation respecting them is almost useless.

An excellent illustration of the ordinary method of formation which obtains among number scales is furnished by the Eskimos of Point Barrow,[70] who have pure numeral words up to 5, and then begin a systematic course of word formation from the names of their fingers. If the names of the first five numerals are of finger origin, they have so completely lost their original form, or else the names of the fingers themselves have so changed, that no resemblance is now to be detected between them. This scale is so interesting that it is given with considerable fulness, as follows:

1.atauzik.
2.madro.
3.pinasun.
4.sisaman.
5.tudlemut.
6.atautyimin akbinigin [tudlimu(t)]= 5 and 1 on the next.
7.madronin akbinigin= twice on the next.
8.pinasunin akbinigin= three times on the next.
9.kodlinotaila= that which has not its 10.
10.kodlin= the upper part—i.e. the fingers.
14.akimiaxotaityuna= I have not 15.
15.akimia. [This seems to be a real numeral word.]
20.inyuina= a man come to an end.
25.inyuina tudlimunin akbinidigin= a man come to an end and 5 on the next.
30.inyuina kodlinin akbinidigin= a man come to an end and 10 on the next.
35.inyuina akimiamin aipalin= a man come to an end accompanied by 1 fifteen times.
40.madro inyuina= 2 men come to an end.

In this scale we find the finger origin appearing so clearly and so repeatedly that one feels some degree of surprise at finding 5 expressed by a pure numeral instead of by some word meaning hand or fingers of one hand. In this respect the Eskimo dialects are somewhat exceptional among scales built up of digital words. The system of the Greenland Eskimos, though differing slightly from that of their Point Barrow cousins, shows the same peculiarity. The first ten numerals of this scale are:[71]

1.atausek.
2.mardluk.
3.pingasut.
4.sisamat.
5.tatdlimat.
6.arfinek-atausek= to the other hand 1.
7.arfinek-mardluk= to the other hand 2.
8.arfinek-pingasut= to the other hand 3.
9.arfinek-sisamat= to the other hand 4.
10.kulit.

The same process is now repeated, only the feet instead of the hands are used; and the completion of the second 10 is marked by the word innuk, man. It may be that the Eskimo word for 5 is, originally, a digital word, but if so, the fact has not yet been detected. From the analogy furnished by other languages we are justified in suspecting that this may be the case; for whenever a number system contains digital words, we expect them to begin with five, as, for example, in the Arawak scale,[72] which runs:

1.abba.
2.biama.
3.kabbuhin.
4.bibiti.
5.abbatekkábe= 1 hand.
6.abbatiman= 1 of the other.
7.biamattiman= 2 of the other.
8.kabbuhintiman= 3 of the other.
9.bibitiman= 4 of the other.
10.biamantekábbe= 2 hands.
11.abba kutihibena= 1 from the feet.
20.abba lukku= hands feet.

The four sets of numerals just given may be regarded as typifying one of the most common forms of primitive counting; and the words they contain serve as illustrations of the means which go to make up the number scales of savage races. Frequently the finger and toe origin of numerals is perfectly apparent, as in the Arawak system just given, which exhibits the simplest and clearest possible method of formation. Another even more interesting system is that of the Montagnais of northern Canada.[73] Here, as in the Zuñi scale, the words are digital from the outset.

1.inl'are= the end is bent.
2.nak'e= another is bent.
3.t'are= the middle is bent.
4.dinri= there are no more except this.
5.se-sunla-re= the row on the hand.
6.elkke-t'are= 3 from each side.
7.{t'a-ye-oyertan= there are still 3 of them.
inl'as dinri= on one side there are 4 of them.
8.elkke-dinri= 4 on each side.
9.inl'a-ye-oyert'an= there is still 1 more.
10.onernan= finished on each side.
11.onernan inl'are ttcharidhel= 1 complete and 1.
12.onernan nak'e ttcharidhel= 1 complete and 2, etc.