530 POPULAR SCIENCE MONTHLY. 



Before leaving this part of the subject the writer wishes 

 merely to add that the etymologies suggested above for six, 

 seven, and eight appear to be quite plausible ; for navan, or 

 nine, however, it appears to him that the association with the idea 

 of " last " is the more reasonable, and would fit in with the finger 

 interpretation of the others just as well as the one suggested. 



We return now to the general question of the development of 

 number systems, which we left at the point where men were sup- 

 posed to have learned to use their fingers and toes as a natural 

 abacus, and to have reached, therefore, the number 20. Be- 

 fore any further progress can be made a scale of notation must 

 be adopted. Of course, this is not done consciously. Within 

 certain limits it is probably entirely a matter of chance what 

 number will be selected as a base. I had better say what num- 

 ber will become the base ; for the use of the word " selected " 

 unconsciously implies that the savage exercises a choice, while 

 in fact, as already stated, he is simply led by circumstances. In 

 most cases he has adopted some kind of a base before he has 

 counted as far as 20. We have already seen that one of the 

 commonest forms for "6" is "hand-one" or five-one. When 

 the savage expresses 6 in this way he is committed to a quinary 

 scale. The chances are, however, overwhelmingly against his 

 carrying out this system consistently in all higher numbers, and 

 for very obvious reasons. A pure quinary system of numeration 

 is therefore extremely rare. Nevertheless, at least one such 

 exists, one that is purely quinary as far as it seems to be known ; 

 this is the scale of one of the Betoya dialects of South America. 

 In this scale 



Six = teyente tey = hand -f- 1. 



Eleven = caya ente-tey = 2 hands + 1. 



Sixteen = toazumba-entetey = 3 hands + 1. 



Twenty = caesea ente = 4 hands. 



(Conant, pages 57 and 140.) It would be interesting to know 

 whether this scale is carried on consistently that is, whether 

 25, the square of the base, is recognized as a new starting point, 

 or whether they call it simply " five hands," without any sign 

 to mark it off distinctly from other multiples of the base. 



What is generally found in these scales that introduce the 

 quinary element at 6 is that " 10 " is designated by some ex- 

 pression other than " two fives " ; and eleven then becomes 10 + 1 ; 

 twelve, 10 + 2, etc. that is, the quinary scale here merges into 

 the decimal ; and either we see no more of it, or it continues with 

 the other in a subsidiary place. The latter is the more usual. 

 Thus .sixteen is 10 + 5 + 1 ; seventeen, 10 + 5 + 2, etc. Thus is 

 formed a mixed decimal and quinary scale. 



It is a question over which there has been considerable dis- 



