which carries us back to the time when the savage was groping his way onward in his attempt to give expression to some number greater than any he had ever used before; and now and then one of these fragments is such as to lead us to the border land of the might-have-been, and to cause us to speculate on the possibility of so great a numerical curiosity as a senary or a septenary scale.  The Bretons call 18 triouec’h, 3-6, but otherwise their language contains no hint of counting by sixes; and we are left at perfect liberty to theorize at will on the existence of so unusual a number word.  Pott remarks[208] that the Bolans, of western Africa, appear to make some use of 6 as their number base, but their system, taken as a whole, is really a quinary-decimal.  The language of the Sundas,[209] or mountaineers of Java, contains traces of senary counting.  The Akra words for 7 and 8, paggu and paniu, appear to mean 6-1 and 7-1, respectively; and the same is true of the corresponding Tambi words pagu and panjo.[210] The Watji tribe[211] call 6 andee, and 7 anderee, which probably means 6-1.  These words are to be regarded as accidental variations on the ordinary laws of formation, and are no more significant of a desire to count by sixes than is the Wallachian term deu-maw, which expresses 18 as 2-9, indicates the existence of a scale of which 9 is the base.  One remarkably interesting number system is that exhibited by the Mosquito tribe[212] of Central America, who possess an extensive quinary-vigesimal scale containing one binary and three senary compounds.  The first ten words of this singular scale, which has already been quoted, are: 

   1. kumi.
   2. wal.
   3. niupa.
   4. wal-wal = 2-2.
   5. mata-sip = fingers of one hand.
   6. matlalkabe.
   7. matlalkabe pura kumi = 6 + 1.
   8. matlalkabe pura wal = 6 + 2.
   9. matlalkabe pura niupa = 6 + 3.
  10. mata-wal-sip = fingers of the second hand.

In passing from 6 to 7, this tribe, also, has varied the almost universal law of progression, and has called 7 6-1.  Their 8 and 9 are formed in a similar manner; but at 10 the ordinary method is resumed, and is continued from that point onward.  Few number systems contain as many as three numerals which are associated with 6 as their base.  In nearly all instances we find such numerals singly, or at most in pairs; and in the structure of any system as a whole, they are of no importance whatever.  For example, in the Pawnee, a pure decimal scale, we find the following odd sequence:[213]

6. shekshabish. 7. petkoshekshabish = 2-6, i.e. 2d 6. 8. touwetshabish = 3-6, i.e. 3d 6. 9. loksherewa = 10 — 1.

In the Uainuma scale the expressions for 7 and 8 are obviously referred to 6, though the meaning of 7 is not given, and it is impossible to guess what it really does signify.  The numerals in question are:[214]