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 well.  The result is a complete decimal-quaternary system, such as is found nowhere else in the world except in this and a few of the neighbouring dialects of the Pacific.  This scale, which is almost identical with the Nukuhivan, is[203]

4 units  = 1 ha or tauna = 4.
10 tauna  = 1 tanaha      = 40.
10 tanaha = 1 lau         = 400.
10 lau    = 1 mano        = 4000.
10 mano   = 1 tini        = 40,000.
10 tini   = 1 lehu        = 400,000.

The quaternary element thus introduced has modified the entire structure of the Hawaiian number system.  Fifty is tanaha me ta umi, 40 + 10; 76 is 40 + 20 + 10 + 6; 100 is ua tanaha ma tekau, 2 x 40 + 10; 200 is lima tanaha, 5 x 40; and 864,895 is 2 x 400,000 + 40,000 + 6 x 4000 + 2 x 400 + 2 x 40 + 10 + 5.[204] Such examples show that this secondary influence, entering and incorporating itself as a part of a well-developed decimal system, has radically changed it by the establishment of 4 as the primary number base.  The role which 10 now plays is peculiar.  In the natural formation of a quaternary scale new units would be introduced at 16, 64, 256, etc.; that is, at the square, the cube, and each successive power of the base.  But, instead of this, the new units are introduced at 10 x 4, 100 x 4, 1000 x 4, etc.; that is, at the products of 4 by each successive power of the old base.  This leaves the scale a decimal scale still, even while it may justly be called quaternary; and produces one of the most singular and interesting instances of number-system formation that has ever been observed.  In this connection it is worth noting that these Pacific island number scales have been developed to very high limits—­in some cases into the millions.  The numerals for these large numbers do not seem in any way indefinite, but rather to convey to the mind of the native an idea as clear as can well be conveyed by numbers of such magnitude.  Beyond the limits given, the islanders have indefinite expressions, but as far as can be ascertained these are only used when the limits given above have actually been passed.  To quote one more example, the Hervey Islanders, who have a binary-decimal scale, count as follows: