dition, subtraction, and multiplication. The
only number above 20 which is used as a unit is 200, which is expressed
merely as 10 twenties. Any even number of hundreds, or any number of
thousands, is then indicated as being so many times 10 twenties; and the
odd hundreds are so many times 10 twenties, plus 5 twenties more. This
scale is an excellent example of the cumbersome methods used by uncivilized
races in extending their number systems beyond the ordinary needs of daily
life.

In Central Asia a single vigesimal scale comes to light in the following
fragment of the Leptscha scale, of the Himalaya region:[354]

10. kati.
40. kafali = 4 x 10,
or kha nat = 2 x 20.
50. kafano = 5 x 10,
or kha nat sa kati = 2 x 20 + 10.
100. gjo, or kat.

Further to the south, among the Dravidian races, the vigesimal element is
also found. The following will suffice to illustrate the number systems of
these dialects, which, as far as the material at hand shows, are different
from each other only in minor particulars:

MUNDARI.[355]

10. gelea.
20. mi hisi.
30. mi hisi gelea = 20 + 10.
40. bar hisi = 2 x 20.
60. api hisi = 3 x 20.
80. upun hisi = 4 x 20.
100. mone hisi = 5 x 20.

In the Nicobar Islands of the Indian Ocean a well-developed example of
vigesimal numeration is found. The inhabitants of these islands are so low
in the scale of civilization that a definite numeral system of any kind is
a source of some surprise. Their neighbours, the Andaman Islanders, it will
be remembered, have but two numerals at their command; their intelligence
does not seem in any way inferior to that of the Nicobar tribes, and one is
at a loss to account for the superior development of the number sense in
the case of the latter. The intercourse of the coast tribes with traders
might furnish an explanation of the difficulty were it not for the fact
that the numeration of the inland tribes is quite as well developed as that
of the coast tribes; and as the former never come in contact with traders
and never engage in barter of any kind except in the most limited way, the
conclusion seems inevitable that this is merely one of the phenomena of
mental development among savage races for which we have at present no
adequate explanation. The principal numerals of the inland and of the coast
tribes are:[356]

INLAND TRIBES COAST TRIBES