reckoning
ceases, and arithmetic begins.

CHAPTER IV.

THE ORIGIN OF NUMBER WORDS.
(_CONTINUED_.)

By the slow, and often painful, process incident to the extension and
development of any mental conception in a mind wholly unused to
abstractions, the savage gropes his way onward in his counting from 1, or
more probably from 2, to the various higher numbers required to form his
scale. The perception of unity offers no difficulty to his mind, though he
is conscious at first of the object itself rather than of any idea of
number associated with it. The concept of duality, also, is grasped with
perfect readiness. This concept is, in its simplest form, presented to the
mind as soon as the individual distinguishes himself from another person,
though the idea is still essentially concrete. Perhaps the first glimmering
of any real number thought in connection with 2 comes when the savage
contrasts one single object with another--or, in other words, when he first
recognizes the _pair_. At first the individuals composing the pair are
simply "this one," and "that one," or "this and that"; and his number
system now halts for a time at the stage when he can, rudely enough it may
be, count 1, 2, many. There are certain cases where the forms of 1 and 2
are so similar than one may readily imagine that these numbers really were
"this" and "that" in the savage's original conception of them; and the same
likeness also occurs in the words for 3 and 4, which may readily enough
have been a second "this" and a second "that." In the Lushu tongue the
words for 1 and 2 are _tizi_ and _tazi_ respectively. In Koriak we find
_ngroka_, 3, and _ngraka_, 4; in Kolyma, _niyokh_, 3, and _niyakh_, 4; and
in Kamtschatkan, _tsuk_, 3, and _tsaak_, 4.[108] Sometimes, as in the case
of the Australian races, the entire extent of the count is carried through
by means of pairs. But the natural theory one would form is, that 2 is the
halting place for a very long time; that up to this point the fingers may
or may not have been used--probably not; and that when the next start is
made, and 3, 4, 5, and so on are counted, the fingers first come into
requisition. If the grammatical structure of the earlier languages of the
world's history is examined, the student is struck with the prevalence of
the dual number in them--something which tends to disappear as language
undergoes extended development. The dual number points unequivocally to the
time when 1