gives the following theory,[10] which is well considered, and is based on the results of careful study and observation among the Zuni Indians of the Southwest:  “Primitive man when abroad never lightly quit hold of his weapons.  If he wanted to count, he did as the Zuni afield does to-day; he tucked his instrument under his left arm, thus constraining the latter, but leaving the right hand free, that he might check off with it the fingers of the rigidly elevated left hand.  From the nature of this position, however, the palm of the left hand was presented to the face of the counter, so that he had to begin his score on the little finger of it, and continue his counting from the right leftward.  An inheritance of this may be detected to-day in the confirmed habit the Zuni has of gesticulating from the right leftward, with the fingers of the right hand over those of the left, whether he be counting and summing up, or relating in any orderly manner.”  Here, then, is the reason for this otherwise unaccountable phenomenon.  If savage man is universally right-handed, he will almost inevitably use the index finger of his right hand to mark the fingers counted, and he will begin his count just where it is most convenient.  In his case it is with the little finger of the left hand.  In the case of the child trying to multiply 3 by 6, it was with the thumb of the same hand.  He had nothing to tuck under his arm; so, in raising his left hand to a position where both eye and counting finger could readily run over its fingers, he held the palm turned away from his face.  The same choice of starting-point then followed as with the savage—­the finger nearest his right hand; only in this case the finger was a thumb.  The deaf mute is sometimes taught in this manner, which is for him an entirely natural manner.  A left-handed child might be expected to count in a left-to-right manner, beginning, probably, with the thumb of his right hand.

To the law just given, that savages begin to count on the little finger of the left hand, there have been a few exceptions noted; and it has been observed that the method of progression on the second hand is by no means as invariable as on the first.  The Otomacs[11] of South America began their count with the thumb, and to express the number 3 would use the thumb, forefinger, and middle finger.  The Maipures,[12] oddly enough, seem to have begun, in some cases at least, with the forefinger; for they are reported as expressing 3 by means of the fore, middle, and ring fingers.  The Andamans[13] begin with the little finger of either hand, tapping the nose with each finger in succession.  If they have but one to express, they use the forefinger of either hand, pronouncing at the same time the proper word.  The Bahnars,[14] one of the native tribes of the interior of Cochin China, exhibit no particular order in the sequence of fingers used, though they employ their digits freely to assist them in counting.  Among certain of