532 POPULAR SCIENCE MONTHLY. 



their numeral systems which are not homogeneous with the 

 main characteristics of the system show great persistence. The 

 " score " of English is a remnant of old vigesimal counting, and 

 although it has lost its place in the ordinary number system, 

 it is still retained as a semi-poetical form. Still more marked 

 is the " quatre-vingts " of the French. In counting from 61 to 99 

 they use a purely vigesimal system. If these traces of vigesimal 

 counting still remain, it would seem probable that if the qui- 

 nary system had ever formed a part of the system it would also 

 somewhere have left its marks, fainter, it is true, on account of 

 its greater antiquity, but still discernible. Now the only indica- 

 tion from a philological source that such a system was ever 

 employed by the Aryan peoples seems to be the Homeric 7re/x7ra^e/ 

 (literally to five), meaning "to count." It is sometimes stated 

 also that the form of the Latin numerals I, II, III, IIII or IV, 

 V, VI, etc., implies the existence of an early form of quinary 

 counting. My own opinion is that evidence derived from written 

 numerals, between which and the formation of the numeral 

 system itself there can be no comparison as to dates, can be of 

 very little weight in deciding what was the scale upon which 

 the system was originally formed. If the Roman V for 5 and 

 VI for 6 were adopted because of a quinary element in the Roman 

 scale at the time these signs were first used, surely the spoken 

 language would have retained some marks of the same system. 

 The evidence all points, therefore, with the one exception quoted 

 above, to the nonexistence of a quinary element in Aryan counting. 

 The third natural scale, besides the quinary and decimal, is the 

 vigesimal. It is doubtful whether a pure vigesimal scale, un- 

 mixed with any quinary and decimal element, occurs in any part 

 of the world. In certain regions, or with certain races, a strong 

 tendency is found to make 20 the principal base of the nu- 

 meral system. This is so with the Celtic peoples, with some Asiatic 

 and a few African tribes, with some of the Eskimos, and with 

 the peoples who formerly occupied the Central American regions. 

 If a tribe counts up to 20, using their fingers and toes, and 

 then continue their counting beyond this point in a consistent 

 way, a vigesimal system will be the natural result ; but on account 

 of the practical difficulty of using the toes in any system of ges- 

 ture-counting, which, as we have seen, is the second stage in the 

 development of the number system, it seems plausible that most 

 tribes confined themselves to the fingers alone. This would ac- 

 count for the greater predominance of 10 and 5 as number bases. 

 It is true that in the case of many well-developed vigesimal scales 

 we have no positive evidence that they originated in the custom 

 of counting on the fingers and toes, but there is certainly great 

 probability that they did all begin in this way. There seems 



