in other words, a large number of repeated halves can be taken with 8 as a
starting-point, without producing a fractional result. With 8 as a base we
should obtain by successive halvings, 4, 2, 1. A similar process in our
decimal scale gives 5, 2-1/2, 1-1/4. All this is undeniably true, but,
granting the argument up to this point, one is then tempted to ask "What
of it?" A certain degree of simplicity would thereby be introduced into
the Theory of Numbers; but the only persons sufficiently interested in this
branch of mathematics to appreciate the benefit thus obtained are already
trained mathematicians, who are concerned rather with the pure science
involved, than with reckoning on any special base. A slightly increased
simplicity would appear in the work of stockbrokers, and others who reckon
extensively by quarters, eighths, and sixteenths. But such men experience
no difficulty whatever in performing their mental computations in the
decimal system; and they acquire through constant practice such quickness
and accuracy of calculation, that it is difficult to see how octonary
reckoning would materially assist them. Altogether, the reasons that have
in the past been adduced in favour of this form of arithmetic seem trivial.
There is no record of any tribe that ever counted by eights, nor is there
the slightest likelihood that such a system could ever meet with any
general favour. It is said that the ancient Saxons used the octonary
system,[220] but how, or for what purposes, is not stated. It is not to be
supposed that this was the common system of counting, for it is well known
that the decimal scale was in use as far back as the evidence of language
will take us. But the field of speculation into which one is led by the
octonary scale has proved most attractive to some, and the conclusion has
been soberly reached, that in the history of the Aryan race the octonary
was to be regarded as the predecessor of the decimal scale. In support of
this theory no direct evidence is brought forward, but certain verbal
resemblances. Those ignes fatuii of the philologist are made to perform
the duty of supporting an hypothesis which would never have existed but
for their own treacherous suggestions. Here is one of the most attractive
of them:

Between the Latin words _novus_, new, and _novem_, nine, there exists a
resemblance so close that it may well be more than accidental. Nine is,
then, the _new_ number; that is, the first number