of twine; thus, when two strings were tied about the stick, the ten dollars were seen to be an indisputable fact.”  This interesting method of computing the amount of her debt, 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 with the little finger and 149 with the thumb.  But the fact that nearly three-fourths of the children began with the thumb, and but one-fourth with the little finger, is really far less significant than would appear at first thought.  Children of this age, four to eight years, will count in either way, and sometimes seem at a loss themselves to know