gether. Having
much more frequent occasion to employ this secondary than the primary
meaning of his numerals, the native would easily allow the original
significations to fall into disuse, and in the lapse of time to be entirely
forgotten. With a subsequent migration to the northward a second
duplication might take place, and so produce the singular effect of giving
to the same numeral word three different meanings in different parts of
Oceania. To illustrate the former or binary method of numeration, the
Tahuatan, one of the southern dialects of the Marquesas group, may be
employed.[201] Here the ordinary numerals are:

1. tahi,
10. onohuu.
20. takau.
200. au.
2,000. mano.
20,000. tini.
20,000. tufa.
2,000,000. pohi.

In counting fish, and all kinds of fruit, except breadfruit, the scale
begins with _tauna_, pair, and then, omitting _onohuu_, they employ the
same words again, but in a modified sense. _Takau_ becomes 10, _au_ 100,
etc.; but as the word "pair" is understood in each case, the value is the
same as before. The table formed on this basis would be:

2 (units) = 1 tauna = 2.
10 tauna = 1 takau = 20.
10 takau = 1 au = 200.
10 au = 1 mano = 2000.
10 mano = 1 tini = 20,000.
10 tini = 1 tufa = 200,000.
10 tufa = 1 pohi = 2,000,000.

For counting breadfruit they use _pona_, knot, as their unit, breadfruit
usually being tied up in knots of four. _Takau_ now takes its third
signification, 40, and becomes the base of their breadfruit system, so to
speak. For some unknown reason the next unit, 400, is expressed by _tauau_,
while _au_, which is the term that would regularly stand for that number,
has, by a second duplication, come to signify 800. The next unit, _mano_,
has in a similar manner been twisted out of its original sense, and in
counting breadfruit is made to serve for 8000. In the northern, or
Nukuhivan Islands, the decimal-quaternary system is more regular. It is in
the counting of breadfruit only,[202]

4 breadfruits = 1 pona = 4.
10 pona = 1 toha = 40.
10 toha = 1 au = 400.
10 au = 1 mano = 4000.
10 mano = 1 tini = 40,000.
10 tini = 1 tufa = 400,000.
10 tufa = 1 pohi = 4,000,000.

In the Hawaiian dialect this scale is, with slight modification, the
universal scale, used not only in counting breadfruit, but any other
objects as w