20 hun = 1 kal = 20.
20 kal = 1 bak = 400.
20 bak = 1 pic = 8000.
20 pic = 1 calab = 160,000.
20 calab = 1 { kinchil } = 3,200,000.
{ tzotzceh }
20 kinchil = 1 alau = 64,000,000.

The original meaning of pic, given in the scale as “a sack,” was rather “a short petticoat, somtimes used as a sack.”  The word tzotzceh signified “deerskin.”  No reason can be given for the choice of this word as a numeral, though the appropriateness of the others is sufficiently manifest.  No evidence of digital numeration appears in the first 10 units, but, judging from the almost universal practice of the Indian tribes of both North and South America, such may readily have been the origin of Maya counting.  Whatever its origin, it certainly expanded and grew into a system whose perfection challenges our admiration.  It was worthy of the splendid civilization of this unfortunate race, and, through its simplicity and regularity, bears ample testimony to the intellectual capacity which originated it.

The only example of vigesimal reckoning which is comparable with that of the Mayas is the system employed by their northern neighbours, the Nahuatl, or, as they are more commonly designated, the Aztecs of Mexico.  This system is quite as pure and quite as simple as the Maya, but differs from it in some important particulars.  In its first 20 numerals it is quinary (see p. 141), and as a system must be regarded as quinary-vigesimal.  The Maya scale is decimal through its first 20 numerals, and, if it is to be regarded as a mixed scale, must be characterized as decimal-vigesimal.  But in both these instances the vigesimal element preponderates so strongly that these, in common with their kindred number systems of Mexico, Yucatan, and Central America, are always thought of and alluded to as vigesimal scales.  On account of its importance, the Nahuatl system[365] is given in fuller detail than most of the other systems I have made use of.

10. matlactli = 2 hands. 20. cempoalli = 1 counting. 21. cempoalli once = 20-1. 22. cempoalli omome = 20-2. 30. cempoalli ommatlactli = 20-10. 31. cempoalli ommatlactli once = 20-10-1. 40. ompoalli = 2 x 20. 50. ompoalli ommatlactli = 40-10. 60. eipoalli, or epoalli, = 3 x 20. 70. epoalli ommatlactli = 60-10. 80. nauhpoalli = 4 x 20. 90. nauhpoalli ommatlactli = 90-10. 100. macuilpoalli = 5 x 20. 120. chiquacempoalli = 6 x 20. 140. chicompoalli = 7 x 20. 160. chicuepoalli = 8 x 20. 180. chiconauhpoalli = 9 x 20. 200. matlacpoalli = 10 x 20. 220. matlactli oncempoalli = 11 x 20. 240. matlactli omompoalli = 12 x 20. 260. matlactli omeipoalli = 13 x 20. 280. matlactli onnauhpoalli = 14 x 20. 300. caxtolpoalli = 15 x 20. 320. caxtolli oncempoalli. 399. caxtolli onnauhpoalli ipan caxtolli onnaui = 19 x