the methods described above are found in all parts of the world, but
what I have called the direct is far more common than the other. In
general, where the smaller number precedes the larger it signifies
multiplication instead of addition. Thus, when we say "thirty," _i.e._
three-ten, we mean 3 x 10; just as "three hundred" means 3 x 100. When the
larger precedes the smaller, we must usually understand addition. But to
both these rules there are very many exceptions. Among higher numbers the
inverse order is very rarely used; though even here an occasional exception
is found. The Taensa Indians, for example, place the smaller numbers before
the larger, no matter how far their scale may extend. To say 1881 they make
a complete inversion of our own order, beginning with 1 and ending with
1000. Their full numeral for this is _yeha av wabki mar-u-wab mar-u-haki_,
which means, literally, 1 + 80 + 100 x 8 + 100 x 10.[54] Such exceptions
are, however, quite rare.

One other method of combination, that of subtraction, remains to be
considered. Every student of Latin will recall at once the _duodeviginti_,
2 from 20, and _undeviginti_, 1 from 20, which in that language are the
regular forms of expression for 18 and 19. At first they seem decidedly
odd; but familiarity soon accustoms one to them, and they cease entirely to
attract any special attention. This principle of subtraction, which, in the
formation of numeral words, is quite foreign to the genius of English, is
still of such common occurrence in other languages that the Latin examples
just given cease to be solitary instances.

The origin of numerals of this class is to be found in the idea of
reference, not necessarily to the last, but to the nearest, halting-point
in the scale. Many tribes seem to regard 9 as "almost 10," and to give it a
name which conveys this thought. In the Mississaga, one of the numerous
Algonquin languages, we have, for example, the word _cangaswi_, "incomplete
10," for 9.[55] In the Kwakiutl of British Columbia, 8 as well as 9 is
formed in this way; these two numbers being _matlguanatl_, 10 - 2, and
_nanema_, 10 - 1, respectively.[56] In many of the languages of British
Columbia we find a similar formation for 8 and 9, or for 9 alone. The same
formation occurs in Malay, resulting in the numerals _delapan_, 10 - 2, and
_sambilan_ 10 - 1.[57] In Green Island, one of the New Ireland group, these
become simply _andra-lua_, "less 2," and _andra-si_, "