Any real numeral formation by the use of “little,” with the name of some higher unit, would, of course, be impossible.  The numeral scale must be complete before the nursery rhyme can be manufactured.

It is not to be supposed from the observations that have been made on the formation of savage numeral scales that all, or even the majority of tribes, proceed in the awkward and faltering manner indicated by many of the examples quoted.  Some of the North American Indian tribes have numeral scales which are, as far as they go, as regular and almost as simple as our own.  But where digital numeration is extensively resorted to, the expressions for higher numbers are likely to become complex, and to act as a real bar to the extension of the system.  The same thing is true, to an even greater degree, of tribes whose number sense is so defective that they begin almost from the outset to use combinations.  If a savage expresses the number 3 by the combination 2-1, it will at once be suspected that his numerals will, by the time he reaches 10 or 20, become so complex and confused that numbers as high as these will be expressed by finger pantomime rather than by words.  Such is often the case; and the comment is frequently made by explorers that the tribes they have visited have no words for numbers higher than 3, 4, 5, 10, or 20, but that counting is carried beyond that point by the aid of fingers or other objects.  So reluctant, in many cases, are savages to count by words, that limits have been assigned for spoken numerals, which subsequent investigation proved to fall far short of the real extent of the number systems to which they belonged.  One of the south-western Indian tribes of the United States, the Comanches, was for a time supposed to have no numeral words below 10, but to count solely by the use of fingers.  But the entire scale of this taciturn tribe was afterward discovered and published.

To illustrate the awkward and inconvenient forms of expression which abound in primitive numeral nomenclature, one has only to draw from such scales as those of the Zuni, or the Point Barrow Eskimos, given in the last chapter.  Terms such as are found there may readily be duplicated from almost any quarter of the globe.  The Soussous of Sierra Leone[126] call 99 tongo solo manani nun solo manani, i.e. to take (10 understood) 5 + 4 times and 5 + 4.  The Malagasy expression for 1832 is[127] roambistelo polo amby valonjato amby arivo, 2 + 30 + 800 + 1000.  The Aztec equivalent for 399 is[128] caxtolli onnauh poalli ipan caxtolli onnaui, (15 + 4) x 20 + 15 + 4; and the Sioux require for 29 the ponderous combination[129] wick a chimen ne nompah sam pah nep e chu wink a. These terms, long and awkward as they seem, are only the legitimate results which arise from combining the names of the higher and lower numbers, according to the peculiar genius of each language.  From some of the Australian tribes are derived expressions