es come into
being. After the completion of one count of the fingers the savage
announces his result in some form which definitely states to his mind the
fact that the end of a well-marked series has been reached. Beginning
again, he now repeats his count of 10, either on his own fingers or on the
fingers of another. With the completion of the second 10 the result is
announced, not in a new unit, but by means of a duplication of the term
already used. It is scarcely credible that the unit unconsciously adopted
at the termination of the first count should now be dropped, and a new one
substituted in its place. When the method here described is employed, 20 is
not a natural unit to which higher numbers may be referred. It is wholly
artificial; and it would be most surprising if it were adopted. But if the
count of the second 10 is made on the toes in place of the fingers, the
element of repetition which entered into the previous method is now
wanting. Instead of referring each new number to the 10 already completed,
the savage is still feeling his way along, designating his new terms by
such phrases as "1 on the foot," "2 on the other foot," etc. And now, when
20 is reached, a single series is finished instead of a double series as
before; and the result is expressed in one of the many methods already
noticed--"one man," "hands and feet," "the feet finished," "all the fingers
of hands and feet," or some equivalent formula. Ten is no longer the
natural base. The number from which the new start is made is 20, and the
resulting scale is inevitably vigesimal. If pebbles or sticks are used
instead of fingers, the system will probably be decimal. But back of the
stick and pebble counting the 10 natural counters always exist, and to them
we must always look for the origin of this scale.

In any collection of the principal vigesimal number systems of the world,
one would naturally begin with those possessed by the Celtic races of
Europe. These races, the earliest European peoples of whom we have any
exact knowledge, show a preference for counting by twenties, which is
almost as decided as that manifested by Teutonic races for counting by
tens. It has been conjectured by some writers that the explanation for this
was to be found in the ancient commercial intercourse which existed between
the Britons and the Carthaginians and Phoenicians, whose number systems
showed traces of a vigesimal tendency. Considering the fact that the use of