The Number Concept: Its Origin and Development Part 16

10. quinoi-da = 5 2.

11. cenai-ai-caibo = 1 + (the) hands.

12. dououni-ai-caibo = 2 + 10.

13. coum-ai-caibo = 3 + 10.

14. dekai-ai-caibo = 4 + 10.

15. quin-oibo = 5 3.

16. cenai-ai-quacoibo = 1 + 15.

17. dououni-ai-quacoibo = 2 + 15.

18. coum-ai-quacoibo = 3 + 15.

19. dekai-ai-quacoibo = 4 + 15.

20. quinoui-ai-quacoibo = 5 + 15.

The meanings a.s.signed to the numerals 6 to 9 are entirely conjectural. They obviously mean 1, 2, 3, 4, taken a second time, and as the meanings I have given are often found in primitive systems, they have, at a venture, been given here.

LIFU, LOYALTY ISLANDS.[244]

1. ca.

2. lue.

3. koeni.

4. eke.

5. tji pi.

6. ca ngemen = 1 above.

7. lue ngemen = 2 above.

8. koeni ngemen = 3 above.

9. eke ngemen = 4 above.

10. lue pi = 2 5.

11. ca ko.

12. lue ko.

13. koeni ko.

14. eke ko.

15. koeni pi = 3 5.

16. ca huai ano.

17. lua huai ano.

18. koeni huai ano.

19. eke huai ano.

20. ca atj = 1 man.

BONGO.[245]

1. kotu.

2. ngorr.

3. motta.

4. neheo.

5. mui.

6. dokotu = [5] + 1.

7. dongorr = [5] + 2.

8. domotta = [5] + 3.

9. doheo = [5] + 4.

10. kih.

11. ki dokpo kotu = 10 + 1.

12. ki dokpo ngorr = 10 + 2.

13. ki dokpo motta = 10 + 3.

14. ki dokpo neheo = 10 + 4.

15. ki dokpo mui = 10 + 5.

16. ki dokpo mui do mui okpo kotu = 10 + 5 more, to 5, 1 more.

17. ki dokpo mui do mui okpo ngorr = 10 + 5 more, to 5, 2 more.

18. ki dokpo mui do mui okpo motta = 10 + 5 more, to 5, 3 more.

19. ki dokpo mui do mui okpo nehea = 10 + 5 more, to 5, 4 more.

20. mbaba kotu.

Above 20, the Lufu and the Bongo systems are vigesimal, so that they are, as a whole, mixed systems.

The Welsh scale begins as though it were to present a pure decimal structure, and no hint of the quinary element appears until it has pa.s.sed 15. The Nahuatl, on the other hand, counts from 5 to 10 by the ordinary quinary method, and then appears to pa.s.s into the decimal form. But when 16 is reached, we find the quinary influence still persistent; and from this point to 20, the numeral words in both scales are such as to show that the notion of counting by fives is quite as prominent as the notion of referring to 10 as a base. Above 20 the systems become vigesimal, with a quinary or decimal structure appearing in all numerals except multiples of 20. Thus, in Welsh, 36 is _unarbymtheg ar ugain_, 1 + 5 + 10 + 20; and in Nahuatl the same number is _cempualli caxtolli oce_, 20 + 15 + 1. Hence these and similar number systems, though commonly alluded to as vigesimal, are really mixed scales, with 20 as their primary base. The Canaque scale differs from the Nahuatl only in forming a compound word for 15, instead of introducing a new and simple term.

In the examples which follow, it is not thought best to extend the lists of numerals beyond 10, except in special instances where the ill.u.s.tration of some particular point may demand it. The usual quinary scale will be found, with a few exceptions like those just instanced, to have the following structure or one similar to it in all essential details: 1, 2, 3, 4, 5, 5-1, 5-2, 5-3, 5-4, 10, 10-1, 10-2, 10-3, 10-4, 10-5, 10-5-1, 10-5-2, 10-5-3, 10-5-4, 20. From these forms the entire system can readily be constructed as soon as it is known whether its princ.i.p.al base is to be 10 or 20.

Turning first to the native African languages, I have selected the following quinary scales from the abundant material that has been collected by the various explorers of the "Dark Continent." In some cases the numerals of certain tribes, as given by one writer, are found to differ widely from the same numerals as reported by another. No attempt has been made at comparison of these varying forms of orthography, which are usually to be ascribed to difference of nationality on the part of the collectors.

FELOOPS.[246]

1. enory.

2. sickaba, or cookaba.

3. sisajee.

4. sibakeer.

5. footuck.

6. footuck-enory = 5-1.

7. footuck-cookaba = 5-2.

8. footuck-sisajee = 5-3.

9. footuck-sibakeer = 5-4.

10. sibankonyen.

KISSI.[247]

1. pili.

2. miu.

3. nga.

4. iol.

5. nguenu.

6. ngom-pum = 5-1.

7. ngom-miu = 5-2.

8. ngommag = 5-3.

9. nguenu-iol = 5-4.

10. to.

ASHANTEE.[248]