bacus in its proper form will
again find in civilized countries a use as common as that of five centuries
ago.

In the elaborate calculating machines of the present, such as are used by
life insurance actuaries and others having difficult computations to make,
we have the extreme of development in the direction of artificial aid to
reckoning. But instead of appearing merely as an extraneous aid to a
defective intelligence, it now presents itself as a machine so complex that
a high degree of intellectual power is required for the mere grasp of its
construction and method of working.

CHAPTER II.

NUMBER SYSTEM LIMITS.

With respect to the limits to which the number systems of the various
uncivilized races of the earth extend, recent anthropological research has
developed many interesting facts. In the case of the Chiquitos and a few
other native races of Bolivia we found no distinct number sense at all, as
far as could be judged from the absence, in their language, of numerals in
the proper sense of the word. How they indicated any number greater than
_one_ is a point still requiring investigation. In all other known
instances we find actual number systems, or what may for the sake of
uniformity be dignified by that name. In many cases, however, the numerals
existing are so few, and the ability to count is so limited, that the term
_number system_ is really an entire misnomer.

Among the rudest tribes, those whose mode of living approaches most nearly
to utter savagery, we find a certain uniformity of method. The entire
number system may consist of but two words, _one_ and _many_; or of three
words, _one_, _two_, _many_. Or, the count may proceed to 3, 4, 5, 10, 20,
or 100; passing always, or almost always, from the distinct numeral limit
to the indefinite _many_ or several, which serves for the expression of any
number not readily grasped by the mind. As a matter of fact, most races
count as high as 10; but to this statement the exceptions are so numerous
that they deserve examination in some detail. In certain parts of the
world, notably among the native races of South America, Australia, and many
of the islands of Polynesia and Melanesia, a surprising paucity of numeral
words has been observed. The Encabellada of the Rio Napo have but two
distinct numerals; _tey_, 1, and _cayapa_, 2.[20] The Chaco languages[21]
of the Guaycuru stock are also notably poor in this respect. In the Mbocobi
dialect of this l