922 NUMERAL SYSTEMS (ETH. ANN. 19 
60-+-1, or ce-tapa quizahachaa-cayona, which is 4 from 60, ete. The 
Mazateca, Mixe, Zoque, and Trike appear to follow throughout the 
Nahuatl method of adding the minor numbers to the preceding base. 
The Othomian, Tarasean, and Totonacan systems are similar to 
the Huastecan—that is to say, are decimal-vigesimal—and form the 
higher numerals by adding the minor numbers to the preceding base. 
Extending our inquiry northward to the Sonoran and Shoshonean 
branches of the Nahuatlan family, we notice the gradual change to 
the decimal system. For example, in the Cahita count the quinary- 
vigesimal rule prevails; 6, 7, and 10 are based on 5; 8 on 4; 11 to 19 
on 10, or, rather, twice five. From 20 upward the count is vigesimal, 
10 when used retaining throughout its form of 2x5. The contact, 
however, in this region with the decimal system is clearly indicated 
by the following statement of the author of the Arte Lengua Cahita, 
given above: ‘‘Some nations say senutacaua or sesevchere for 20; others 
say for 10 sesavehere and follow up the count thus: 11, sesavahere aman 
senu,s 12, sesavehere aman uot, ete. For 20 they say wosavehere, which is 
two times 10. The Yaqui say for 5 sesavehere, and counting from 5 to 5 
say uosavehere. LO [=2 x Dil vahivehere, 15 [=3 x 4)] These also say for 
20 senu tacauda | LX 20] or nacquivehere [4x 5], and for 25 sesawehere (this 
particular count is of this nation only), and for 100 say mamnitacaua 
[5x20] or tacauvehere, which is 20 fives.” In the paragraph which 
follows he states in general terms that some of the tribes count by 
fives, others by tens, both using the same term, vedere, pretixing the 
‘*numeral abverbs” sesa, ‘Sone time,” wosa, *‘two times,” ete. The 
‘*nations” alluded to are probably the Cahita tribes, such as the Tehu- 
eco, Zuaque, Mayo, Yaqui, and other related or neighboring tribes. 
This change in the application of a given term in closely related dia- 
lects is not only interesting, but somewhat remarkable; and added to 
the fact that the closely related Tarahumari of the same section use the 
decimal system, indicates that the latter and the vigesimal system here 
came into contact. Do the data furnish evidence as to which was the 
spreading or aggressive and which the yielding one? Without entering 
into a discussion of the question the following facts are presented for 
the benefit of those desiring to look further into this subject. The 
similarity of the number names of the Cahita and Tarahumari to 
those of the Nahuatl is too apparent to pass unobserved even by the 
mere cursory glance. Include the allied Opata and take for example 
the numbers | to 5 and 10, as follow: 

] 2) 3 1 5 10 
——— — { 
| ee | . F 
Opata se go-de | vei-de nago marizi makoi 
| : . * . : . 
| Cahita se-nu | uoi vahi, or bei | naequi) mamni uo-mamni 
1. , : : | . 
farahumari | bire | oca bei-ca naguo|) marika makoe 
Nahuatl | ce ome yei navi macuilli matlactli 
