4G NU3IERAL SYSTEMS. S 



I 



The second object in this investigation is to ascertain the series a' 



of numbers upon which enumeration is based among different *t 



tribes. The most natural, and, among barbarous nations, most "flj 



common, is the quinary system, or that by fives, corresponding ^ 



with the fingers of one hand. In this the first five digits are \ 



simple, that is to say, are all different ; the second form compounds | 



or modifications of these first, as will be seen by referring back ''^, 



to the example given of the Mexican, 'In many cases, however, ? 



it has happened that, in the lapse of time, new words have been ; 



adopted for a portion, while the old have become obsolete, or 

 appear only occasionally in combination. In a number of voca- 

 bularies examined, it would appear that the numbers 7 and 8 most 

 frequently retain the compound form, and 10 has oftenest changed. 

 The t and 8 usually contain the elements of the words 2 and 3, 

 as representing the 2d and 3d fingers on the second hand. Nine 

 is frequently "one less than ten." 



Probably in almost all these languages the quinary system was 

 the oldest, and the decimal, where it now exists, has been of sub- 

 sequent introduction, or rather growth. In the Chinook, for 

 example, the names of the digits are all simple with the excep- 

 tion of that for seven. Thus makst two, sini-makd seven, sini 

 being, perhaps, an obsolete form of five. These obsolete forms 

 are sometimes revealed in the numeral ten and its compounds 

 and multiples. Thus the simple digit ten may have one name, 

 while in eleven=10-fl, or twenty=2xl0, the word will be 

 entirely different. In the Napa, of California,- /?,open signifies 

 two, and ma-ha-ish ten, but twenty is hopi-hol, the other multi- 

 ples retaining the syllable Jiol up to one hundred, which is ??ia- 

 ha-ish sol, the h being changed to s for euphony. 



Twenty is, in some languages, a translation of two tens, in 

 others a distinct word exists, and this is in many the name for 

 head, body, or person, as in the Opata, seis dosme (literally one 

 person), signifying, of course, all the fingers and toes of one 

 person. In the Nisqually the word for twenty, s'ha-lat-chi, means 

 literally the fingers and toes. As to the other multiples of ten, 

 they are usually expressed by the literal translation of 3x10, 

 4x10, &c. But in the Opata and kindred dialects this form 

 occurs, 20, seis dosme; 30, seis dosme macoi tarewa, i. e. ten 

 more than one person ; 40, wodun dosme, or two twenties ; 50, 



