58G PRIMITIVE NUMBER SYSTEMS. 



we might expect to find the cases where counting stops with four more 

 numerals than those where three is the iiiuit, just as three is a much 

 more common limit than two. Such is not the case, however. Investi- 

 gation shows that if counting extends beyond three, it is almost sure to 

 reach five, the commonest limit among races whose number sense is very 

 weak. A few instances have been found where tribal numerals extend 

 to four without going beyond that point. The Tupis, of South America, 

 have only the four numerals "oyepe,"!; "mokoi," 2; ^'mosapira," o, and 

 "erundi," 4.* The Australians, of Lake Macquery, have no numeral 

 beyond ''woran," 4, except the indefinite expression "kanwol-kanwol," 

 which signifies " great-great. ''t The Tasmanians also have tour as their 

 proper number limit, but they have a compound expression, "pagan-a- 

 mara," 4 + 1, which they use for five,| A few other instances of the 

 same limit are given by various authors, but tliey must be received with 

 great caution. If a savage can count to four lie is practically certain 

 to extend his system one step further, and to make his scale contain 

 the number of steps which corresponds to the number of fingers on one 

 of his hands. 



This brings us again to the consideration of the relation existing 

 between the hand and its fingers, and primitive counting. Three com- 

 mon number limits are found among savage races, 5, 10, and 100. A 

 savage counts on his fingers until he reaches 5, and then he often 

 stops, saying merely "'many," for any greater number. With a slightly 

 higher degree of intelligence, or with an environment calling for more 

 extended use of the number sense, others go on from this point, 

 counting now on the fingers of the other hand. As a number limit 10 

 is used almost as commonly as 5; and it is no infrequent thing to find 

 the toes as well as the fingers made to do duty as counters, thus 

 bringing the total up to 20. The last named number is rarely the limit, 

 however. If a savage can count to 20 he is usually able to go on to 100, 

 and often to 1,000. 



The manner of counting just indicated has given rise to a peculiarity 

 in the names of certain numerals which must not pass unnoticed. 

 Counting as he does, the savage, on reaching 5 says, not unnaturally, 

 '' one hand." At 10 he says, following the same anology, "both hands." 

 At 20, having completed the tale of counters which ^Nature has placed 

 at his disposal, he says, "one man." Though by no means universal, 

 these names for 5, 10, and 20 are so common in all parts of the world 

 that specific examples of them need not be given. We also find 0, 7, 

 etc., often expressed by "hand one," ''hand two," or "one on the 

 other hand," " two on the other hand," etc.; and 11, 12, etc., by "one 

 on the foot," " two on the foot," etc. So frequently are these equiva- 



* Miille*, Grundriss der Spr., B. ii., 1 Abt., j). 389. 

 t Op. at., p. 14. 

 t Op. at., p. 89. 



