838 PRIMITIVE NUMBERS (ETH. ANN, 19 
American number-systems—e. @., that of the Toba, whose ordinary 
numeration ends with six (the term meaning also ** many” or ** plenty”), 
though Barcena has traced it to ten. The terms are somewhat vari- 
able, and of such form as to imply actual or vestigial connotive char- 
acter; as recorded by Quevedo’ they are nathedac, cacayni or nivoca, 
cacaynilia, nalotapegat, nivoca cacainitia (2+-3), cacayni cacaynilia 
(23), nathedac cacayni cacaynilia (1+2% 8), nivoca nalotapegat (2X 4), 
nivoca nalotapegat nathedae (2X4-+-1), cacayni nivoca nalotapegat 
(2x4+-2). Now, it is noteworthy (1) that none of the terms connotes 
finger, hand, or man; (2) that there are alternative terms for two in 
both simple and composite uses; (3) that two is the most prominent 
factor in the composite part of the series; (4) that one of the terms 
for two and the term for three are closely similar, and distinguished 
only by inflection; (5) that the term for four apparently connotes 
equality (nalotath=equal) and declaration (na-pega=they say; sena- 
pega= I say, ete.); and (6) that the system is definitively not quinary or 
decimal. There are suggestions, both in the combinations and connota- 
tions of the terms, of two threes of ill-defined numeric character, 
corresponding respectively to the numeric two and three; and that 
four is an essentially mechanical square. There are also many indica- 
tions that the system is inchoate so far as the strictly numerical aspect 
is concerned. 
In the dearth of knowledge concerning the original or collateral 
meanings of the Australian and South American number-terms, it is 
dificult to formulate the fundamental concept or to give it graphic 
expression; but a suggestion of great inherent interest is found in the 
Shahaptian numeration, in which, according to Hewitt, the first two 
integer-terms are denotive or arbitrary merely, while the term for 
three means Middle or Middle onz—not middle finger or middle of 
the hand, but apparently a general (or semi-abstract) Middle like that 
of the Zuni ritual; and the suggestion is enforced by corresponding 
expressions in Serian, Iroquoian, and some other Amerindian tongues. 
The Zuni expression for the middle finger, as rendered by Cushing, is 
particularly suggestive, viz, ‘* Counter-equally-itself-which-does ”;* 
and the persistent tendency to double as well as to divide is illustrated 
by the Hai-it terms (incorporated by Dr Thomas, postea, p. 871) for 
two, four, and eight, viz, pen, tsoo'-7k, and pen'-tsoo-7h (2X 4), and still 
more clearly by the absence of the numeral nine—indeed this brief 
vocabulary displays a curious combination of the binary and quinary 
systems. 
In the light of these analogies the Australian thought-mode, with its 
numerical and social and fiducial expressions, and measurably also that 
1Arte de la Lengua Toba, por el Padre Alonso Barcena * * * con Vocabularios * * * por 
Samuel A. Lafone Queyedo, Biblioteca Lingiiistica del Museo de la Plata, vol. 11, 1898, p. 41. 
*Manual Concepts, Am. Anthropologist, yol. v, 1892, p. 293. 
