20. tkam.
30. tkam ka chkan = 20 + 10.
40. tkam ksde = 20 x 2.
50. tkam ksde ka chkan = 40 + 10.
60. tkam gachkir = 20 x 3.
100. mia (from Arabic).
1000. debu.

MUNDO.[347]

10. nujorquoi.
20. tiki bere.
30. tiki bire nujorquoi = 20 + 10.
40. tiki borsa = 20 x 2.
50. tike borsa nujorquoi = 40 + 10.

MANDINGO.[348]

10. tang.
20. mulu.
30. mulu nintang = 20 + 10.
40. mulu foola = 20 x 2.
50. mulu foola nintang = 40 + 10.
60. mulu sabba = 20 x 3.
70. mulu sabba nintang = 60 + 10.
80. mulu nani = 20 x 4.
90. mulu nani nintang = 80 + 10.
100. kemi.

This completes the scanty list of African vigesimal number systems that a
patient and somewhat extended search has yielded. It is remarkable that the
number is no greater. Quinary counting is not uncommon in the "Dark
Continent," and there is no apparent reason why vigesimal reckoning should
be any less common than quinary. Any one investigating African modes of
counting with the material at present accessible, will find himself
hampered by the fact that few explorers have collected any except the first
ten numerals. This leaves the formation of higher terms entirely unknown,
and shows nothing beyond the quinary or non-quinary character of the
system. Still, among those which Stanley, Schweinfurth, Salt, and others
have collected, by far the greatest number are decimal. As our knowledge of
African languages is extended, new examples of the vigesimal method may be
brought to light. But our present information leads us to believe that they
will be few in number.

In Asia the vigesimal system is to be found with greater frequency than in
Europe or Africa, but it is still the exception. As Asiatic languages are
much better known than African, it is probable that the future will add but
little to our stock of knowledge on this point. New instances of counting
by twenties may still be found in northern Siberia, where much ethnological
work yet remains to be done, and where a tendency toward this form of
numeration has been observed to exist. But the total number of Asiatic
vigesimal scales must always remain small--quite insignificant in
comparison with those of decimal formation.

In the Caucasus region a group of languages is found, in which all but
three or four contain vigesimal systems. These