But if this is so, the natural and inevitable question follows—­might not this have been the history of all numeral scales now purely decimal?  May not the changes of time have altered the compounds which were once a clear indication of quinary counting, until no trace remains by which they can be followed back to their true origin?  Perhaps so.  It is not in the least degree probable, but its possibility may, of course, be admitted.  But even then the universality of quinary counting for primitive peoples is by no means established.  In Chapter II, examples were given of races which had no number base.  Later on it was observed that in Australia and South America many tribes used 2 as their number base; in some cases counting on past 5 without showing any tendency to use that as a new unit.  Again, through the habit of counting upon the finger joints, instead of the fingers themselves, the use of 3 as a base is brought into prominence, and 6 and 9 become 2 threes and 3 threes, respectively, instead of 5 + 1 and 5 + 4.  The same may be noticed of 4.  Counting by means of his fingers, without including the thumbs, the savage begins by dividing into fours instead of fives.  Traces of this form of counting are somewhat numerous, especially among the North American aboriginal tribes.  Hence the quinary form of counting, however widespread its use may be shown to be, can in no way be claimed as the universal method of any stage of development in the history of mankind.

In the vast majority of cases, the passage from the base to the next succeeding number in any scale, is clearly defined.  But among races whose intelligence is of a low order, or—­if it be permissible to express it in this way—­among races whose number sense is feeble, progression from one number to the next is not always in accordance with any well-defined law.  After one or two distinct numerals the count may, as in the case of the Veddas and the Andamans, proceed by finger pantomime and by the repetition of the same word.  Occasionally the same word is used for two successive numbers, some gesture undoubtedly serving to distinguish the one from the other in the savage’s mind.  Examples of this are not infrequent among the forest tribes of South America.  In the Tariana dialect 9 and 10 are expressed by the same word, paihipawalianuda; in Cobeu, 8 and 9 by pepelicoloblicouilini; in Barre, 4, 5, and 9 by ualibucubi.[326] In other languages the change from one numeral to the next is so slight that one instinctively concludes that the savage is forming in his own mind another, to him new, numeral immediately from the last.  In such cases the entire number system is scanty, and the creeping hesitancy with which progress is made is visible in the forms which the numerals are made to take.  A single illustration or two of this must suffice; but the ones chosen are not isolated cases.  The scale of the Macunis,[327] one of the numerous tribes of Brazil, is