More rarely yet are instances met with of languages which make use of subtraction almost as freely as addition, in the composition of numerals. Within the past few years such an instance has been noticed in the case of the Bellacoola language of British Columbia. In their numeral scale 15, “one foot,” is followed by 16, “one man less 4”; 17, “one man less 3”; 18, “one man less 2”; 19, “one man less 1”; and 20, one man. Twenty-five is “one man and one hand”; 26, “one man and two hands less 4”; 36, “two men less 4”; and so on. This method of formation prevails throughout the entire numeral scale.[63]
One of the best known and most interesting examples of subtraction as a well-defined principle of formation is found in the Maya scale. Up to 40 no special peculiarity appears; but as the count progresses beyond that point we find a succession of numerals which one is almost tempted to call 60 − 19, 60 − 18, 60 − 17, etc. Literally translated the meanings seem to be 1 to 60, 2 to 60, 3 to 60, etc. The point of reference is 60, and the thought underlying the words may probably be expressed by the paraphrases, “1 on the third score, 2 on the third score, 3 on the third score,” etc. Similarly, 61 is 1 on the fourth score, 81 is one on the fifth score, 381 is 1 on the nineteenth score, and so on to 400. At 441 the same formation reappears; and it continues to characterize the system in a regular and consistent manner, no matter how far it is extended.[64]
The Yoruba language of Africa is another example of most lavish use of subtraction; but it here results in a system much less consistent and natural than that just considered. Here we find not only 5, 10, and 20 subtracted from the next higher unit, but also 40, and even 100. For example, 360 is 400 − 40; 460 is 500 − 40; 500 is 600 − 100; 1300 is 1400 − 100, etc. One of the Yoruba units is 200; and all the odd hundreds up to 2000, the next higher unit, are formed by subtracting 100 from the next higher multiple of 200. The system is quite complex, and very artificial; and seems to have been developed by intercourse with traders.[65]
It has already been stated that the primitive meanings of our own simple numerals have been lost. This is also true of the languages of nearly all other civilized peoples, and of numerous savage races as well. We are at liberty to suppose, and we do suppose, that in very many cases these words once expressed meanings closely connected with the names of the fingers, or with the fingers themselves, or both. Now and then a case is met with in which the numeral word frankly avows its meaning—as in the Botocudo language, where 1 is expressed by podzik, finger, and 2 by kripo, double finger;[66] and in the Eskimo dialect of Hudson's Bay, where eerkitkoka means both 10 and little finger.[67] Such cases are, however, somewhat exceptional.
In a few noteworthy instances, the words composing the numeral scale of a language have been carefully investigated and their original meanings accurately determined. The simple structure of many of the rude languages of the world should render this possible in a multitude of cases; but investigators are too often content with the mere numerals themselves, and make no inquiry respecting their meanings. But the following exposition of the Zuñi scale, given by Lieutenant Gushing[68] leaves nothing to be desired:
| 1. | töpinte | = taken to start with. |
| 2. | kwilli | = put down together with. |
| 3. | ha'ī | = the equally dividing finger. |
| 4. | awite | = all the fingers all but done with. |
| 5. | öpte | = the notched off. |
This finishes the list of original simple numerals, the Zuñi stopping, or “notching off,” when he finishes the fingers of one hand. Compounding now begins.
The process of formation indicated in 11 is used in the succeeding numerals up to 19.
| 20. | kwillik'yënästem'thlan | = two times all the fingers. |
| 100. | ässiästem'thlak'ya | = the fingers all the fingers. |
| 1000. | ässiästem'thlanak'yënästem'thla | = the fingers all the fingers times all the fingers. |