in Malay, resulting in the numerals delapan, 10 — 2, and sambilan 10 — 1.[57] In Green Island, one of the New Ireland group, these become simply andra-lua, “less 2,” and andra-si, “less 1."[58] In the Admiralty Islands this formation is carried back one step further, and not only gives us shua-luea, “less 2,” and shu-ri, “less 1,” but also makes 7 appear as sua-tolu, “less 3."[59] Surprising as this numeral is, it is more than matched by the Ainu scale, which carries subtraction back still another step, and calls 6, 10 — 4.  The four numerals from 6 to 9 in this scale are respectively, iwa, 10 — 4, arawa, 10 — 3, tupe-san, 10 — 2, and sinepe-san, 10 — 1.[60] Numerous examples of this kind of formation will be found in later chapters of this work; but they will usually be found to occur in one or both of the numerals, 8 and 9.  Occasionally they appear among the higher numbers; as in the Maya languages, where, for example, 99 years is “one single year lacking from five score years,"[61] and in the Arikara dialects, where 98 and 99 are “5 men minus” and “5 men 1 not."[62] The Welsh, Danish, and other languages less easily accessible than these to the general student, also furnish interesting examples of a similar character.

More rarely yet are instances met with of languages which make use of subtraction almost as freely as addition, in the composition of numerals.  Within the past few years such an instance has been noticed in the case of the Bellacoola language of British Columbia.  In their numeral scale 15, “one foot,” is followed by 16, “one man less 4”; 17, “one man less 3”; 18, “one man less 2”; 19, “one man less 1”; and 20, one man.  Twenty-five is “one man and one hand”; 26, “one man and two hands less 4”; 36, “two men less 4”; and so on.  This method of formation prevails throughout the entire numeral scale.[63]

One of the best known and most interesting examples of subtraction as a well-defined principle of formation is found in the Maya scale.  Up to 40 no special peculiarity appears; but as the count progresses beyond that point we find a succession of numerals which one is almost tempted to call 60 — 19, 60 — 18, 60 — 17, etc.  Literally translated the meanings seem to be 1 to 60, 2 to 60, 3 to 60, etc.  The point of reference is 60, and the thought underlying the words may probably be expressed by the paraphrases, “1 on the third score, 2 on the third score, 3 on the third score,” etc.  Similarly, 61 is 1 on the fourth score, 81 is one on the fifth score, 381 is 1 on the nineteenth score, and so on to 400.  At 441 the same formation reappears; and it continues to characterize the system in a regular and consistent manner, no matter how far it is extended.[64]