876 NUMERAL SYSTEMS [ETH. ANN. 19 
the Mexicans counted on the fingers.and hands, 4 was the first basis, 
the four fingers completing the first count, 5 being formed of 4+-1. 
He remarks as follows: **In the Hindu system the principal number 
of the system is 10, which is formed of 5+-5; to it the number 5 is 
essential; but in the Nahua system the essential number is 4, hence the 
20 is formed of 5 times 4, as 5 is formed of 4+1.” The same author 
says that among the manuscript notes of Ramirez he has found one 
that says, ‘‘the Nahoas formed the number 5 with the four fingers of 
the hand, completing the sum with the thumb, as 4++1.” However, 
it must be admitted that, in this dialect, in forming the numbers above 
5 until 20 is reached, 5 is the basis, and its name is derived from the 
term for hand. 
Charencey, ‘referring to the dialects of his so-called Chichimecan 
family, which corresponds substantially with Brinton’s Sonoran and 
Shoshonean branches of his Uto-Aztecan family, says that ‘*in almost 
all the idioms of this family, if not all, the name of the number 2 enters 
into composition in the word which signifies 4.” This is very apparent 
in the Shoshonean branch, as is seen in the following examples: 

Tribe 2 4 
— — = = ————— ~ | 
Cahuillo mewi | mewittsu 
Kauyuya | vuy vuitchiu 
Kechi (San Luis Rey) whii witcho 
Shoshone (Gatschet’s number 5) | wat watsuet | 
Southern Paiute | vay vatchue 
California Paiute | voahay yoatsagve | 
| Chemehuevi vay vatchue | 
Hopi lei nale | 
Tobikhar | vehe vatcha 
It is less apparent, however, in the Sonoran branch, as will be seen 
by reference to the lists given above. 
This fact seems to bear evidence in favor of Professor MeGee’s 
suggestion in regard to the primary steps in the development of num- 
ber systems—viz, that 2 and 4 were the first pausing points. An exam- 
ination of other systems outside the scope of the present paper will 
furnish many items of evidence in this direction. 
Hubert Bancroft* gives the following definitions of the Maya names 
of the first five numbers: Awn, paper; ca, calabash; ov, shelled corn; 
can, serpent, or count; and /o, entry; it is apparent, however, that 
the meanings given can have no reference to the use of the terms as 
number names. However, as the origin of the names of the primary 
1 Mélanges, p. 16. 2Native Races, yol. 11, p. 753. 
