CHIBCHA, OR MUYSCA.[371]

    10. hubchibica.
    20. quihica ubchihica = thus says the foot, 10 = 10-10,
          or gueta = house.
    30. guetas asaqui ubchihica = 20 + 10.
    40. gue-bosa = 20 x 2.
    60. gue-mica = 20 x 3.
    80. gue-muyhica = 20 x 4.
   100. gue-hisca = 20 x 5.

  NAGRANDA.[372]

    10. guha.
    20. dino.
    30. ’badinoguhanu = 20 + 10.
    40. apudino = 2 x 20.
    50. apudinoguhanu = 2 x 20 + 10.
    60. asudino = 3 x 20.
    70. asudinoguhanu = 3 x 20 + 10.
    80. acudino = 4 x 20.
    90. acudinoguhanu = 4 x 20 + 10.
   100. huisudino = 5 x 20,
          or guhamba = great 10.
   200. guahadino = 10 x 20.
   400. dinoamba = great 20.
  1000. guhaisudino = 10 x 5 x 20.
  2000. hisudinoamba = 5 great 20’s.
  4000. guhadinoamba = 10 great 20’s.

In considering the influence on the manners and customs of any people which could properly be ascribed to the use among them of any other base than 10, it must not be forgotten that no races, save those using that base, have ever attained any great degree of civilization, with the exception of the ancient Aztecs and their immediate neighbours, north and south.  For reasons already pointed out, no highly civilized race has ever used an exclusively quinary system; and all that can be said of the influence of this mode of counting is that it gives rise to the habit of collecting objects in groups of five, rather than of ten, when any attempt is being made to ascertain their sum.  In the case of the subsidiary base 12, for which the Teutonic races have always shown such a fondness, the dozen and gross of commerce, the divisions of English money, and of our common weights and measures are probably an outgrowth of this preference; and the Babylonian base, 60, has fastened upon the world forever a sexagesimal method of dividing time, and of measuring the circumference of the circle.

The advanced civilization attained by the races of Mexico and Central America render it possible to see some of the effects of vigesimal counting, just as a single thought will show how our entire lives are influenced by our habit of counting by tens.  Among the Aztecs the universal unit was 20.  A load of cloaks, of dresses, or other articles of convenient size, was 20.  Time was divided into periods of 20 days each.  The armies were numbered by divisions of 8000;[373] and in countless other ways the vigesimal element of numbers entered into their lives, just as the decimal enters into ours; and it is to be supposed that they found it as useful and as convenient for all measuring purposes as we find our own system; as the tradesman of to-day finds the duodecimal system of commerce; or as the Babylonians of old found that singularly curious system, the sexagesimal.  Habituation, the laws which the habits and customs of every-day