whether an invention of her own or a survival of the African life
of her parents, served the old negro woman's purpose perfectly; and it
illustrates, as well as a score of examples could, the methods of
numeration to which the children of barbarism resort when any number is to
be expressed which exceeds the number of counters with which nature has
provided them. The fingers are, however, often employed in counting numbers
far above the first decade. After giving the Il-Oigob numerals up to 60,
Mueller adds:[8] "Above 60 all numbers, indicated by the proper figure
pantomime, are expressed by means of the word _ipi_." We know, moreover,
that many of the American Indian tribes count one ten after another on
their fingers; so that, whatever number they are endeavouring to indicate,
we need feel no surprise if the savage continues to use his fingers
throughout the entire extent of his counts. In rare instances we find
tribes which, like the Mairassis of the interior of New Guinea, appear to
use nothing but finger pantomime.[9] This tribe, though by no means
destitute of the number sense, is said to have no numerals whatever, but to
use the single word _awari_ with each show of fingers, no matter how few or
how many are displayed.

In the methods of finger counting employed by savages a considerable degree
of uniformity has been observed. Not only does he use his fingers to assist
him in his tally, but he almost always begins with the little finger of his
left hand, thence proceeding towards the thumb, which is 5. From this point
onward the method varies. Sometimes the second 5 also is told off on the
left hand, the same order being observed as in the first 5; but oftener the
fingers of the right hand are used, with a reversal of the order previously
employed; _i.e._ the thumb denotes 6, the index finger 7, and so on to the
little finger, which completes the count to 10.

At first thought there would seem to be no good reason for any marked
uniformity of method in finger counting. Observation among children fails
to detect any such thing; the child beginning, with almost entire
indifference, on the thumb or on the little finger of the left hand. My own
observation leads to the conclusion that very young children have a slight,
though not decided preference for beginning with the thumb. Experiments in
five different primary rooms in the public schools of Worcester, Mass.,
showed that out of a total of 206 children, 57 began wi