se. In nearly all instances
we find such numerals singly, or at most in pairs; and in the structure of
any system as a whole, they are of no importance whatever. For example, in
the Pawnee, a pure decimal scale, we find the following odd sequence:[213]

6. shekshabish.
7. petkoshekshabish = 2-6, _i.e._ 2d 6.
8. touwetshabish = 3-6, _i.e._ 3d 6.
9. loksherewa = 10 - 1.

In the Uainuma scale the expressions for 7 and 8 are obviously referred to
6, though the meaning of 7 is not given, and it is impossible to guess what
it really does signify. The numerals in question are:[214]

6. aira-ettagapi.
7. aira-ettagapi-hairiwigani-apecapecapsi.
8. aira-ettagapi-matschahma = 6 + 2.

In the dialect of the Mille tribe a single trace of senary counting
appears, as the numerals given below show:[215]

6. dildjidji.
7. dildjidji me djuun = 6 + 1.

Finally, in the numerals used by the natives of the Marshall Islands, the
following curiously irregular sequence also contains a single senary
numeral:[216]

6. thil thino = 3 + 3.
7. thilthilim-thuon = 6 + 1.
8. rua-li-dok = 10 - 2.
9. ruathim-thuon = 10 - 2 + 1.

Many years ago a statement appeared which at once attracted attention and
awakened curiosity. It was to the effect that the Maoris, the aboriginal
inhabitants of New Zealand, used as the basis of their numeral system the
number 11; and that the system was quite extensively developed, having
simple words for 121 and 1331, _i.e._ for the square and cube of 11. No
apparent reason existed for this anomaly, and the Maori scale was for a
long time looked upon as something quite exceptional and outside all
ordinary rules of number-system formation. But a closer and more accurate
knowledge of the Maori language and customs served to correct the mistake,
and to show that this system was a simple decimal system, and that the
error arose from the following habit. Sometimes when counting a number of
objects the Maoris would put aside 1 to represent each 10, and then those
so set aside would afterward be counted to ascertain the number of tens in
the heap. Early observers among this people, seeing them count 10 and then
set aside 1, at the same time pronouncing the word _tekau_, imagined that
this word meant 11, and that the ignorant savage was making use of this
number as his base. This misconception found its way into the early New
Zealand dictionary, bu