The essentially vigesimal character of this system changes in the formation of some of the higher numerals, and a suspicion of the decimal enters.  One hundred is boinic, 5 men; but 200, instead of being simply lahuh-inic, 10 men, is tsa-bo-inic, 2 x 100, or more strictly, 2 times 5 men.  Similarly, 300 is 3 x 100, 400 is 4 x 100, etc.  The word for 1000 is simple instead of compound, and the thousands appear to be formed wholly on the decimal base.  A comparison of this scale with that of the Nahuatl shows how much inferior it is to the latter, both in simplicity and consistency.

  TOTONACO.[368]

    10. cauh.
    20. puxam.
    30. puxamacauh = 20 + 10.
    40. tipuxam = 2 x 20.
    50. tipuxamacauh = 40 + 10.
    60. totonpuxam = 3 x 20.
   100. quitziz puxum = 5 x 20.
   200. copuxam = 10 x 20.
   400. tontaman.
  1000. titamanacopuxam = 2 x 400 + 200.

The essential character of the vigesimal element is shown by the last two numerals. Tontamen, the square of 20, is a simple word, and 1000 is, as it should be, 2 times 400, plus 200.  It is most unfortunate that the numeral for 8000, the cube of 20, is not given.

  CORA.[369]

    10. tamoamata.
    20. cei-tevi.
    30. ceitevi apoan tamoamata = 20 + 10.
    40. huapoa-tevi = 2 x 20.
    60. huaeica-tevi = 3 x 20.
   100. anxu-tevi = 5 x 20.
   400. ceitevi-tevi = 20 x 20.

Closely allied with the Maya numerals and method of counting are those of the Quiches of Guatemala.  The resemblance is so obvious that no detail in the Quiche scale calls for special mention.

  QUICHE.[370]

    10. lahuh.
    20. hu-uinac = 1 man.
    30. hu-uinac-lahuh = 20 + 10.
    40. ca-uinac = 2 men.
    50. lahu-r-ox-kal = -10 + 3 x 20.
    60. ox-kal = 3 x 20.
    70. lahu-u-humuch = -10 + 80.
    80. humuch.
    90. lahu-r-ho-kal = -10 + 100.
   100. hokal.
  1000. o-tuc-rox-o-kal.

Among South American vigesimal systems, the best known is that of the Chibchas or Muyscas of the Bogota region, which was obtained at an early date by the missionaries who laboured among them.  This system is much less extensive than that of some of the more northern races; but it is as extensive as almost any other South American system with the exception of the Peruvian, which was, however, a pure decimal system.  As has already been stated, the native races of South America were, as a rule, exceedingly deficient in regard to the number sense.  Their scales are rude, and show great poverty, both in formation of numeral words and in the actual extent to which counting was carried.  If extended as far as 20, these scales are likely to become vigesimal, but many stop far short of that limit, and no inconsiderable number of them fail to reach even 5.  In this respect we are reminded of the Australian scales, which were so rudimentary as really to preclude any proper use of the word “system” in connection with them.  Counting among the South American tribes was often equally limited, and even less regular.  Following are the significant numerals of the scale in question: