In the Hawaiian and a few other languages of the islands of the central Pacific, where in general the number systems employed are decimal, we find a most interesting case of the development, within number scales already well established, of both binary and quaternary systems.  Their origin seems to have been perfectly natural, but the systems themselves must have been perfected very slowly.  In Tahitian, Rarotongan, Mangarevan, and other dialects found in the neighbouring islands of those southern latitudes, certain of the higher units, tekau, rau, mano, which originally signified 10, 100, 1000, have become doubled in value, and now stand for 20, 200, 2000.  In Hawaiian and other dialects they have again been doubled, and there they stand for 40, 400, 4000.[200] In the Marquesas group both forms are found, the former in the southern, the latter in the northern, part of the archipelago; and it seems probable that one or both of these methods of numeration are scattered somewhat widely throughout that region.  The origin of these methods is probably to be found in the fact that, after the migration from the west toward the east, nearly all the objects the natives would ever count in any great numbers were small,—­as yams, cocoanuts, fish, etc.,—­and would be most conveniently counted by pairs.  Hence the native, as he counted one pair, two pairs, etc., might readily say one, two, and so on, omitting the word “pair” altogether.  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,